  ***   Warning: new maximum stack size = 2000000000 (1907.349 Mbytes).
================================================================
  MTFT PAPER 32: EXTENDED ANALYSIS
================================================================

================================================================
  1. CUSP EQUIVALENCE CLASSES OF Gamma_0(143)
================================================================

  N = 143 = 11 x 13 (squarefree)
  Divisors of 143: 1, 11, 13, 143
  Number of cusp classes: 4
  Representatives: inf (d=1), 1/11 (d=11), 1/13 (d=13), 0 (d=143)

  Cusp class assignments for tested fractions:
  (d = gcd(denominator, 143) determines the class)

  1/7  gcd(7, 143) = 1  -> cusp class d=1 (inf-class)
  2/7  gcd(7, 143) = 1  -> cusp class d=1 (inf-class)
  3/7  gcd(7, 143) = 1  -> cusp class d=1 (inf-class)
  1/11  gcd(11, 143) = 11  -> cusp class d=11 (1/11-class)
  2/11  gcd(11, 143) = 11  -> cusp class d=11 (1/11-class)
  3/11  gcd(11, 143) = 11  -> cusp class d=11 (1/11-class)
  5/11  gcd(11, 143) = 11  -> cusp class d=11 (1/11-class)
  7/11  gcd(11, 143) = 11  -> cusp class d=11 (1/11-class)
  1/13  gcd(13, 143) = 13  -> cusp class d=13 (1/13-class)
  2/13  gcd(13, 143) = 13  -> cusp class d=13 (1/13-class)
  3/13  gcd(13, 143) = 13  -> cusp class d=13 (1/13-class)
  5/13  gcd(13, 143) = 13  -> cusp class d=13 (1/13-class)
  1/77  gcd(77, 143) = 11  -> cusp class d=11 (1/11-class)
  2/77  gcd(77, 143) = 11  -> cusp class d=11 (1/11-class)
  3/77  gcd(77, 143) = 11  -> cusp class d=11 (1/11-class)
  4/77  gcd(77, 143) = 11  -> cusp class d=11 (1/11-class)
  5/77  gcd(77, 143) = 11  -> cusp class d=11 (1/11-class)
  6/77  gcd(77, 143) = 11  -> cusp class d=11 (1/11-class)
  1/143  gcd(143, 143) = 143  -> cusp class d=143 (0-class)
  2/143  gcd(143, 143) = 143  -> cusp class d=143 (0-class)
  3/143  gcd(143, 143) = 143  -> cusp class d=143 (0-class)
  4/143  gcd(143, 143) = 143  -> cusp class d=143 (0-class)
  5/143  gcd(143, 143) = 143  -> cusp class d=143 (0-class)
  6/143  gcd(143, 143) = 143  -> cusp class d=143 (0-class)
  7/143  gcd(143, 143) = 143  -> cusp class d=143 (0-class)
  8/143  gcd(143, 143) = 143  -> cusp class d=143 (0-class)
  9/143  gcd(143, 143) = 143  -> cusp class d=143 (0-class)
  10/143  gcd(143, 143) = 143  -> cusp class d=143 (0-class)

  Cusp widths:
  inf (d=1):  width = 143/(1 * gcd(1, 143)) = 143/1 = 143
  1/11 (d=11): width = 143/(11 * gcd(11, 13)) = 143/11 = 13
  1/13 (d=13): width = 143/(13 * gcd(13, 11)) = 143/13 = 11
  0 (d=143):  width = 143/(143 * gcd(143,1)) = 1
  ***   variable name expected: psi=143*(1+1/11)*(1+1/13);
  ***                           ^--------------------------
  Sum of widths: 143 + 13 + 11 + 1 = 168 = psi(143) = |PSL(2,7)| CHECK: psi

================================================================
  2. HECKE POLYNOMIAL FACTORIZATION (ALGEBRAIC Q2/Q4)
================================================================

  f3 coefficient field minimal polynomial:
  P(y) = y^6 - 10*y^4 - 2*y^3 + 24*y^2 + 7*y - 12

  a2(f3) = -y, so T2 eigenvalues are roots of P(y)
  If Q2/Q4 split exists, P should factor over Q as deg 2 x deg 4

  Factorization of P over Q:
  Mat([y^6 - 10*y^4 - 2*y^3 + 24*y^2 + 7*y - 12, 1])
  Number of irreducible factors: 1
  Factor 1: y^6 - 10*y^4 - 2*y^3 + 24*y^2 + 7*y - 12  degree = 6  multiplicity = 1

  Interpretation:
  P is IRREDUCIBLE over Q -> no algebraic Q2/Q4 split

  T2 Hecke polynomial H3(x) = P(-x):
  H3(x) = x^6 - 10*x^4 + 2*x^3 + 24*x^2 - 7*x - 12

  Factorization of H3 over Q:
  Mat([x^6 - 10*x^4 + 2*x^3 + 24*x^2 - 7*x - 12, 1])
  Factor 1: x^6 - 10*x^4 + 2*x^3 + 24*x^2 - 7*x - 12  degree = 6

  Roots of H3 (T2 eigenvalues on f3):
  lambda_1 = -2.7089899587502103351009201938996518184408574402973 + 0.E-57*I  |.| = 2.7089899587502103351009201938996518184408574402973
  lambda_2 = -1.7012607013273055722120888441189194566181597421685 + 0.E-57*I  |.| = 1.7012607013273055722120888441189194566181597421685
  lambda_3 = -0.63303622567224008934548519173751180230631945660995 + 0.E-57*I  |.| = 0.63303622567224008934548519173751180230631945660995
  lambda_4 = 1.2312713859754463100412194596285719741740495501492 + 0.E-57*I  |.| = 1.2312713859754463100412194596285719741740495501492
  lambda_5 = 1.3653644962925056583543996489859418930306818439900 + 0.E-57*I  |.| = 1.3653644962925056583543996489859418930306818439900
  lambda_6 = 2.4466510034818040282628751211415692101606052449367 + 0.E-57*I  |.| = 2.4466510034818040282628751211415692101606052449367

  --- f2 coefficient field ---
  f2 minpoly: y^4 - 4*y^2 - y + 1
  Factorization: Mat([y^4 - 4*y^2 - y + 1, 1])
  (Expected: irreducible of degree 4)

  --- Trace verification ---
  Tr(a2(f1)) = 0 (from q-expansion)
  Tr(a2(f2)) = Tr(y^3 - 3y) mod f2_minpoly
    Tr(y) mod (y^4 - 4y^2 - y + 1) = 0 (coeff of y^3 is 0)
  Tr(a2(f3)) = Tr(-y) = 0 (coeff of y^5 is 0) CHECK

================================================================
  3. BROAD RESONANCE SCAN (c <= 50)
================================================================
  Computing modular symbols...
  *** mfsymbol: Warning: increasing stack size to 16000000.
  *** mfsymbol: Warning: increasing stack size to 32000000.
  *** mfsymbol: Warning: increasing stack size to 64000000.
  *** mfsymbol: Warning: increasing stack size to 128000000.
  *** mfsymbol: Warning: increasing stack size to 256000000.
  f1 done.
  *** mfsymbol: Warning: increasing stack size to 16000000.
  *** mfsymbol: Warning: increasing stack size to 32000000.
  *** mfsymbol: Warning: increasing stack size to 64000000.
  *** mfsymbol: Warning: increasing stack size to 128000000.
  *** mfsymbol: Warning: increasing stack size to 256000000.
  *** mfsymbol: Warning: increasing stack size to 512000000.
  *** mfsymbol: Warning: increasing stack size to 1024000000.
  *** mfsymbol: Warning: increasing stack size to 2000000000.
  f2 done.
  *** mfsymbol: Warning: increasing stack size to 16000000.
  *** mfsymbol: Warning: increasing stack size to 32000000.
  *** mfsymbol: Warning: increasing stack size to 64000000.
  *** mfsymbol: Warning: increasing stack size to 128000000.
  *** mfsymbol: Warning: increasing stack size to 256000000.
  *** mfsymbol: Warning: increasing stack size to 512000000.
  *** mfsymbol: Warning: increasing stack size to 1024000000.
  *** mfsymbol: Warning: increasing stack size to 2000000000.
  f3 done.

  Scanning all coprime a/c with c <= 50...

  a/c		|Om1|		|Tr(Om2)|	|Tr(Om3)|	d3/d2		delta		cusp_class
  4/23	0.31352300915287423503215575582714111095417953831197	0.84597573470494071886981642182776213689072058630174	1.4168982036448657005668418891225855655701066262936	1.5195702273324869745565218854817001342266843029682	0.0098016690896469707096464471766538342218220781317876	d=1
  8/23	0.31352300915287423503215575582714111095417953831197	0.84597573470494071886981642182776213689072058630174	1.4168982036448657005668418891225855655701066262936	1.5195702273324869745565218854817001342266843029682	0.0098016690896469707096464471766538342218220781317876	d=1
  15/23	0.31352300915287423503215575582714111095417953831197	0.84597573470494071886981642182776213689072058630174	1.4168982036448657005668418891225855655701066262936	1.5195702273324869745565218854817001342266843029682	0.0098016690896469707096464471766538342218220781317876	d=1
  19/23	0.31352300915287423503215575582714111095417953831197	0.84597573470494071886981642182776213689072058630174	1.4168982036448657005668418891225855655701066262936	1.5195702273324869745565218854817001342266843029682	0.0098016690896469707096464471766538342218220781317876	d=1
  1/38	0.35707103607581022597288631471025379701624954889098	0.90430009877318463987368266075390467145512229343146	1.5301808894346309989931783372600833288670443985801	1.5660406215454115675657776628690745116832321913145	0.036668725123277622299609330210720543234725810214519	d=1
  17/38	0.35707103607581022597288631471025379701624954889098	0.90430009877318463987368266075390467145512229343146	1.5301808894346309989931783372600833288670443985801	1.5660406215454115675657776628690745116832321913145	0.036668725123277622299609330210720543234725810214519	d=1
  21/38	0.35707103607581022597288631471025379701624954889098	0.90430009877318463987368266075390467145512229343146	1.5301808894346309989931783372600833288670443985801	1.5660406215454115675657776628690745116832321913145	0.036668725123277622299609330210720543234725810214519	d=1
  37/38	0.35707103607581022597288631471025379701624954889098	0.90430009877318463987368266075390467145512229343146	1.5301808894346309989931783372600833288670443985801	1.5660406215454115675657776628690745116832321913145	0.036668725123277622299609330210720543234725810214519	d=1
  9/43	0.35707103607581022597288631471025379701624954889098	0.92284650410115141152274660763860322716594329278686	1.4611082431941015651542037781709913363206746609377	1.4839114720059930406569921146016353600108885049438	0.045460424416140904609176218056718608437617876156141	d=1
  11/43	0.31352300915287423503215575582714111095417953831197	1.0767275398261890563211925498932277926183999797307	2.2868436988493767622230554731523432015236335203753	1.6105047354951459074217336328047548309895113269999	0.081132839073011962155565300146400862541004945899891	d=1
  12/43	0.31352300915287423503215575582714111095417953831197	1.0767275398261890563211925498932277926183999797307	2.2868436988493767622230554731523432015236335203753	1.6105047354951459074217336328047548309895113269999	0.081132839073011962155565300146400862541004945899891	d=1
  14/43	0.35707103607581022597288631471025379701624954889098	0.92284650410115141152274660763860322716594329278686	1.4611082431941015651542037781709913363206746609377	1.4839114720059930406569921146016353600108885049438	0.045460424416140904609176218056718608437617876156141	d=1
  29/43	0.35707103607581022597288631471025379701624954889098	0.92284650410115141152274660763860322716594329278686	1.4611082431941015651542037781709913363206746609377	1.4839114720059930406569921146016353600108885049438	0.045460424416140904609176218056718608437617876156141	d=1
  31/43	0.31352300915287423503215575582714111095417953831197	1.0767275398261890563211925498932277926183999797307	2.2868436988493767622230554731523432015236335203753	1.6105047354951459074217336328047548309895113269999	0.081132839073011962155565300146400862541004945899891	d=1
  32/43	0.31352300915287423503215575582714111095417953831197	1.0767275398261890563211925498932277926183999797307	2.2868436988493767622230554731523432015236335203753	1.6105047354951459074217336328047548309895113269999	0.081132839073011962155565300146400862541004945899891	d=1
  34/43	0.35707103607581022597288631471025379701624954889098	0.92284650410115141152274660763860322716594329278686	1.4611082431941015651542037781709913363206746609377	1.4839114720059930406569921146016353600108885049438	0.045460424416140904609176218056718608437617876156141	d=1
  3/44	0.35707103607581022597288631471025379701624954889098	0.83158696638747955539632388391163997617962264760872	1.3640199046205393778506512699815622249703625778763	1.5853499890054022747956956072937959120904786089487	0.055978092583268329529527274635441943641972227848692	d=11
  9/44	0.35707103607581022597288631471025379701624954889098	0.83158696638747955539632388391163997617962264760872	1.3640199046205393778506512699815622249703625778763	1.5853499890054022747956956072937959120904786089487	0.055978092583268329529527274635441943641972227848692	d=11
  35/44	0.35707103607581022597288631471025379701624954889098	0.83158696638747955539632388391163997617962264760872	1.3640199046205393778506512699815622249703625778763	1.5853499890054022747956956072937959120904786089487	0.055978092583268329529527274635441943641972227848692	d=11
  41/44	0.35707103607581022597288631471025379701624954889098	0.83158696638747955539632388391163997617962264760872	1.3640199046205393778506512699815622249703625778763	1.5853499890054022747956956072937959120904786089487	0.055978092583268329529527274635441943641972227848692	d=11
  4/45	0.35707103607581022597288631471025379701624954889098	1.1882062141325948057371564211534784706663941098742	2.2194009486421396096524153573653964715644972365550	1.5196794065907192402820569817552882661589020111055	0.0096924898314147049841113509030657022896043699944691	d=1
  7/45	0.35707103607581022597288631471025379701624954889098	1.1882062141325948057371564211534784706663941098742	2.2194009486421396096524153573653964715644972365550	1.5196794065907192402820569817552882661589020111055	0.0096924898314147049841113509030657022896043699944691	d=1
  38/45	0.35707103607581022597288631471025379701624954889098	1.1882062141325948057371564211534784706663941098742	2.2194009486421396096524153573653964715644972365550	1.5196794065907192402820569817552882661589020111055	0.0096924898314147049841113509030657022896043699944691	d=1
  41/45	0.35707103607581022597288631471025379701624954889098	1.1882062141325948057371564211534784706663941098742	2.2194009486421396096524153573653964715644972365550	1.5196794065907192402820569817552882661589020111055	0.0096924898314147049841113509030657022896043699944691	d=1
  5/46	0.31352300915287423503215575582714111095417953831197	1.1001496769047650870813996203866261562613592381134	2.1119146862991794338159363418112486238216039082869	1.5195043295711435454417303701103496714065227376830	0.0098675668509903998244379625480042970419836434170023	d=1
  11/46	0.31352300915287423503215575582714111095417953831197	1.1001496769047650870813996203866261562613592381134	2.1119146862991794338159363418112486238216039082869	1.5195043295711435454417303701103496714065227376830	0.0098675668509903998244379625480042970419836434170023	d=1
  35/46	0.31352300915287423503215575582714111095417953831197	1.1001496769047650870813996203866261562613592381134	2.1119146862991794338159363418112486238216039082869	1.5195043295711435454417303701103496714065227376830	0.0098675668509903998244379625480042970419836434170023	d=1
  41/46	0.31352300915287423503215575582714111095417953831197	1.1001496769047650870813996203866261562613592381134	2.1119146862991794338159363418112486238216039082869	1.5195043295711435454417303701103496714065227376830	0.0098675668509903998244379625480042970419836434170023	d=1

  --- BEST RESULT ---
  Best mass cycle: {inf, 38/45}
  d3/d2 = 1.5196794065907192402820569817552882661589020111055
  delta = 0.0096924898314147049841113509030657022896043699944691
  cusp class d = 1

  --- TOP 10 CLOSEST (by |delta|) ---
  Total non-trivial cycles tested: 544
  #1: 38/45  d3/d2=1.5196794065907192402820569817552882661589020111055  delta=0.0096924898314147049841113509030657022896043699944691  |Om1|=0.35707103607581022597288631471025379701624954889098  cusp d=1
  #2: 4/45  d3/d2=1.5196794065907192402820569817552882661589020111055  delta=0.0096924898314147049841113509030657022896043699944691  |Om1|=0.35707103607581022597288631471025379701624954889098  cusp d=1
  #3: 7/45  d3/d2=1.5196794065907192402820569817552882661589020111055  delta=0.0096924898314147049841113509030657022896043699944691  |Om1|=0.35707103607581022597288631471025379701624954889098  cusp d=1
  #4: 41/45  d3/d2=1.5196794065907192402820569817552882661589020111055  delta=0.0096924898314147049841113509030657022896043699944691  |Om1|=0.35707103607581022597288631471025379701624954889098  cusp d=1
  #5: 4/23  d3/d2=1.5195702273324869745565218854817001342266843029682  delta=0.0098016690896469707096464471766538342218220781317876  |Om1|=0.31352300915287423503215575582714111095417953831197  cusp d=1
  #6: 19/23  d3/d2=1.5195702273324869745565218854817001342266843029682  delta=0.0098016690896469707096464471766538342218220781317876  |Om1|=0.31352300915287423503215575582714111095417953831197  cusp d=1
  #7: 8/23  d3/d2=1.5195702273324869745565218854817001342266843029682  delta=0.0098016690896469707096464471766538342218220781317876  |Om1|=0.31352300915287423503215575582714111095417953831197  cusp d=1
  #8: 15/23  d3/d2=1.5195702273324869745565218854817001342266843029682  delta=0.0098016690896469707096464471766538342218220781317876  |Om1|=0.31352300915287423503215575582714111095417953831197  cusp d=1
  #9: 41/46  d3/d2=1.5195043295711435454417303701103496714065227376830  delta=0.0098675668509903998244379625480042970419836434170023  |Om1|=0.31352300915287423503215575582714111095417953831197  cusp d=1
  #10: 35/46  d3/d2=1.5195043295711435454417303701103496714065227376830  delta=0.0098675668509903998244379625480042970419836434170023  |Om1|=0.31352300915287423503215575582714111095417953831197  cusp d=1

================================================================
  4. j-INVARIANT OF 143.a1
================================================================
  Elliptic curve: [0, -1, 1, -1, -2]
  Conductor: 143
  ***   at top-level: j=ellj(E)
  ***                   ^-------
  *** ellj: incorrect type in ellj (t_VEC).
  j-invariant: j

  Known CM j-invariants (class number 1):
    D=-3: j=0
    D=-4: j=1728
    D=-7: j=-3375
    D=-8: j=8000
    D=-11: j=-32768
    D=-19: j=-884736
    D=-43: j=-884736000
    D=-67: j=-147197952000
    D=-163: j=-262537412640768000

  Global data: [143, [1, 0, 0, 0], 2, [11, 1; 13, 1], [[1, 5, 0, 1], [1, 6, 0, 2]]]
  Minimal discriminant: -1859

  Has CM? j = j
  Checking class number 2 CM j-invariants...
  (These are algebraic integers of degree 2, not rational)
  Since j is rational and not in the class-1 list: NOT CM

  Mordell-Weil rank: [1, 1, 0, [[4, 6]]]
  Torsion subgroup: [1, [], []]
  L(E, 1) = 0.94569641120026263299701827350746638680451561313760

================================================================
  ANALYSIS COMPLETE
================================================================
(23:07) gp > \l
   log = 0 (off)
