Lfunction data - 12-1680e6-1.1-c1e6-0-3

Formats: - HTML - YAML - JSON - 2024-04-25T19:30:59.930005

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': '507726076796327780207933175909,609597239521663371665535180270,1310356884999610493187723318518,1416727778634120766837053650959,1705670239806742336018546496584,2314037611345437190072435818899', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5827983.7536337515, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3, 6, -7, 6, -3, 1]], [5, [1, -3, 6, -7, 6, -3, 1]], [7, [1, 0, -6, 4, -42, 0, 343]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1680.1', 'coefficient_field': '1.1.1.1', 'conductor': 22483074023424000000, 'conductor_radical': 210, 'degree': 12, 'euler_factors': [[1], [1, -3, 6, -7, 6, -3, 1], [1, -3, 6, -7, 6, -3, 1], [1, 0, -6, 4, -42, 0, 343], [1, 3, 12, 111, 222, 741, 5074, 8151, 26862, 147741, 175692, 483153, 1771561], [1, 6, 57, 306, 1686, 6774, 28973, 88062, 284934, 672282, 1627977, 2227758, 4826809], [1, 6, 39, 214, 756, 2694, 12725, 45798, 218484, 1051382, 3257319, 8519142, 24137569], [1, -3, -51, 50, 2115, -1143, -44706, -21717, 763515, 342950, -6646371, -7428297, 47045881], [1, 3, -36, -97, 642, 597, -13546, 13731, 339618, -1180199, -10074276, 19309029, 148035889], [1, -12, 198, -1572, 14859, -86880, 579868, -2519520, 12496419, -38339508, 140041638, -246133788, 594823321], [1, -12, 78, -204, -1218, 18168, -127402, 563208, -1170498, -6077364, 72034638, -343549812, 887503681], [1, 3, -15, 390, 165, -5037, 92954, -186369, 225885, 19754670, -28112415, 208031871, 2565726409], [1, 18, 327, 3574, 37455, 288312, 2113142, 11820792, 62961855, 246323654, 924023847, 2085411618, 4750104241], [1, 0, 180, -176, 15840, -15840, 863358, -681120, 29288160, -13993232, 615384180, 0, 6321363049], [1, -3, -60, 637, 252, -16287, 142082, -765489, 556668, 66135251, -292780860, -688035021, 10779215329], [1, -15, 6, 7, 11664, -54399, -166888, -2883147, 32764176, 1042139, 47342886, -6272932395, 22164361129], [1, -30, 441, -5010, 52200, -489990, 4032079, -28909410, 181708200, -1028948790, 5343756201, -21447728970, 42180533641], [1, 0, -183, 0, 22326, 0, -1588867, 0, 83075046, 0, -2533788903, 0, 51520374361], [1, 0, -162, -176, 15390, 14256, -1149078, 955152, 69085710, -52934288, -3264481602, 0, 90458382169], [1, -24, 198, 144, -4941, -145608, 2427964, -10338168, -24907581, 51539184, 5031512838, -43301504424, 128100283921], [1, 18, 24, 28, 19752, 113322, -303966, 8272506, 105258408, 10892476, 681557784, 37315288674, 151334226289], [1, -6, -114, 932, 5154, -32646, -177042, -2579034, 32166114, 459512348, -4440309234, -18462338394, 243087455521], [1, 12, 522, 4812, 110763, 785424, 12340420, 65190192, 763046307, 2751439044, 24773243562, 47268487716, 326940373369], [1, 0, -177, 584, 15576, -51684, -1293079, -4599876, 123377496, 411701896, -11105376657, 0, 496981290961], [1, -48, 1542, -33520, 575055, -7692768, 84630804, -746198496, 5410692495, -30592798960, 136512151302, -412192332336, 832972004929], [1, 18, -21, -1094, 18444, 189138, 71057, 19102938, 188147244, -1127149294, -2185268421, 189181809018, 1061520150601], [1, -12, -18, 1400, -10506, 2292, 750210, 236076, -111458154, 1529817800, -2025915858, -139112888916, 1194052296529], [1, 0, -87, 2456, -1740, -106836, 3148187, -11431452, -19921260, 3008705608, -11403925287, 0, 1500730351849], [1, 12, -132, -940, 20580, 7332, -2904114, 799188, 244510980, -1217327260, -18632877252, 184634874588, 1677100110841], [1, -36, 738, -12372, 178191, -2320200, 26895580, -262182600, 2275320879, -17851521684, 120328952418, -663276664548, 2081951752609]], 'euler_factors_factorization': [[1], [[[1, -1, 1], 3]], [[[1, -1, 1], 3]], [[[1, 0, -6, 4, -42, 0, 343], 1]], [[[1, 3, 12, 111, 222, 741, 5074, 8151, 26862, 147741, 175692, 483153, 1771561], 1]], [[[1, 3, 24, 81, 312, 507, 2197], 2]], [[[1, 6, 39, 214, 756, 2694, 12725, 45798, 218484, 1051382, 3257319, 8519142, 24137569], 1]], [[[1, -8, 19], 3], [[1, 7, 19], 3]], [[[1, 3, -36, -97, 642, 597, -13546, 13731, 339618, -1180199, -10074276, 19309029, 148035889], 1]], [[[1, -6, 81, -300, 2349, -5046, 24389], 2]], [[[1, -12, 78, -204, -1218, 18168, -127402, 563208, -1170498, -6077364, 72034638, -343549812, 887503681], 1]], [[[1, 3, -15, 390, 165, -5037, 92954, -186369, 225885, 19754670, -28112415, 208031871, 2565726409], 1]], [[[1, 9, 123, 680, 5043, 15129, 68921], 2]], [[[1, 0, 90, -88, 3870, 0, 79507], 2]], [[[1, -3, -60, 637, 252, -16287, 142082, -765489, 556668, 66135251, -292780860, -688035021, 10779215329], 1]], [[[1, -15, 6, 7, 11664, -54399, -166888, -2883147, 32764176, 1042139, 47342886, -6272932395, 22164361129], 1]], [[[1, -30, 441, -5010, 52200, -489990, 4032079, -28909410, 181708200, -1028948790, 5343756201, -21447728970, 42180533641], 1]], [[[1, 0, -61, 0, 3721], 3]], [[[1, 0, -162, -176, 15390, 14256, -1149078, 955152, 69085710, -52934288, -3264481602, 0, 90458382169], 1]], [[[1, -12, 27, 396, 1917, -60492, 357911], 2]], [[[1, -3, -36, 887, -2628, -15987, 389017], 1], [[1, 21, 123, 266, 8979, 111909, 389017], 1]], [[[1, -6, -114, 932, 5154, -32646, -177042, -2579034, 32166114, 459512348, -4440309234, -18462338394, 243087455521], 1]], [[[1, 6, 243, 948, 20169, 41334, 571787], 2]], [[[1, 0, -177, 584, 15576, -51684, -1293079, -4599876, 123377496, 411701896, -11105376657, 0, 496981290961], 1]], [[[1, -8, 97], 6]], [[[1, 18, -21, -1094, 18444, 189138, 71057, 19102938, 188147244, -1127149294, -2185268421, 189181809018, 1061520150601], 1]], [[[1, -12, -18, 1400, -10506, 2292, 750210, 236076, -111458154, 1529817800, -2025915858, -139112888916, 1194052296529], 1]], [[[1, 0, -87, 2456, -1740, -106836, 3148187, -11431452, -19921260, 3008705608, -11403925287, 0, 1500730351849], 1]], [[[1, 12, -132, -940, 20580, 7332, -2904114, 799188, 244510980, -1217327260, -18632877252, 184634874588, 1677100110841], 1]], [[[1, -18, 207, -2460, 23391, -229842, 1442897], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 3, 'label': '12-1680e6-1.1-c1e6-0-3', 'leading_term': '11.2320254717685820624926220553574141517770239189280516702299753462519286475435487316984552', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1680/2/bg/v', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.009765625', 'prec': 37}, 'plot_values': [11.232025471768578, 11.207150673196992, 11.16444613211227, 11.101887154445974, 11.01753080178189, 10.909543366178363, 10.776277852728477, 10.616948606149299, 10.432442590356887, 10.224089883746533, 9.993306421858987, 9.74157679746824, 9.470364411391662, 9.181035689145217, 8.874683132489903, 8.552409309995433, 8.215414403061558, 7.865011457713942, 7.502628305591459, 7.129796081532852, 6.748181141689856, 6.35952738403344, 5.965632200242102, 5.568337384285904, 5.1695247798492066, 4.7711045579033575, 4.374996894992158, 3.983142207339464, 3.597500902921653, 3.2200383643450206, 2.852713028384592, 2.497466262774981, 2.156213374768971, 1.8308335083996048, 1.5231540910664456, 1.234936725662429, 0.9678650757773221, 0.7235332365491257, 0.5034370240687461, 0.30895848664496156, 0.14135038925201016, 0.0017244075052502245, -0.10896009401246687, -0.1899054696018466, -0.24048838455025442, -0.26027311761476085, -0.24902019691804542, -0.20669380441547924, -0.13346780794886576, -0.029732723793356966, 0.10389480722880667, 0.26657142948748475, 0.4572276792841388, 0.6745690434665335, 0.9170770359992431, 1.1830125444564406, 1.4704182398673233, 1.7771321444350345, 2.1008002994680193, 2.4388867654689057, 2.7886899620876386, 3.1473604950380487, 3.5119178936287736, 3.879276954405391, 4.2462686080430405, 4.6096653901786935, 4.966211250488414, 5.312649948880485, 5.645756409047952, 5.962365156118449, 6.259399671190626, 6.533907737233973, 6.783092581010789, 7.00434574281239, 7.1952839620182205, 7.353770509647585, 7.477944775612054, 7.5662478814406, 7.617445231630251, 7.630650336795555, 7.605355433929029, 7.541436617578805, 7.43915977832694, 7.2991860018115355, 7.122572459363435, 6.910773836264115, 6.665658208457639, 6.389476136100109, 6.084835979321357, 5.754681242861743, 5.402262328878416, 5.0311132325367565, 4.645037021206723, 4.2480419871995485, 3.8442897888918894, 3.438047516017683, 3.0336378025574344, 2.63539290757644, 2.2476143059131273, 1.8744955727611583, 1.5200602121210562, 1.1881064119608116, 0.8821533056932601, 0.6053918236909971, 0.36064014370342123, 0.15028327008851305, -0.023771928758825122, -0.16013288671816558, -0.25795180010684526, -0.31694968136036294, -0.3374359571716887, -0.3203231473339807, -0.26712865419083603, -0.1799675955436995, -0.06153750771556544, 0.08490407522106833, 0.2555676440219376, 0.4461747669612532, 0.6520085711171557, 0.8679706041352322, 1.0886443437644937, 1.3083646921651293, 1.5212940078195003, 1.7215055796774497, 1.9030683588939967, 2.0601332337593723, 2.1870206293782064, 2.278310187942265, 2.3289347505397062, 2.334261740448488, 2.290170886656431, 2.193128253899883, 2.040254117175053, 1.8293857487933503, 1.5591423969382736, 1.228955799439312, 0.839095613101494, 0.3906873862639682, -0.11428247192036842, -0.672968747335981, -1.28167335205366, -1.9358921482071607, -2.6303657383367383, -3.3591372626845577, -4.115619712747269, -4.892671922744586, -5.682684551687702, -6.477689781085961, -7.269469429753804, -8.049660991553726, -8.809868895800435, -9.541781644611945, -10.237305284779044, -10.888678371750663, -11.488572854487149, -12.030195960084828, -12.507386099131137, -12.914712534300765, -13.247593739038365, -13.50233417498173, -13.676164871302642, -13.767281668067191, -13.774871291480089, -13.699144029006131, -13.541359035158992, -13.303761079975391, -12.98953136092289, -12.602737685359493, -12.14828025519667, -11.631823760537522, -11.059730580879902, -10.438925309424217, -9.776778985814554, -9.081005032204722, -8.35954571939629, -7.620452929146685, -6.871779685427512, -6.121441770749389, -5.377105636201267, -4.646087564364706, -3.935252442547148, -3.2509250422360325, -2.598801739937528, -1.983888356584178, -1.4104549394728205, -0.8819984587376658, -0.4012221814089815, 0.02997907210174414, 0.4105391365445476, 0.7401766352833979, 1.0193514556864895, 1.2492168058543327, 1.431561384554389, 1.5687539413100615, 1.663700963115288, 1.7197303472511378, 1.7404940605722463, 1.7298815774520344, 1.6919339229078338, 1.6307700618456835, 1.5505288871840632, 1.4552559040666082, 1.3488239290017303, 1.234872532575794, 1.1167571180044809, 0.997513193670398, 0.8798349657794935, 0.7660286712598418, 0.6579965127803045, 0.5572378537726814, 0.46486000067090594, 0.3815990866331668, 0.30785055378117154, 0.24369051882161197, 0.1889134329202312, 0.14307675203877487, 0.10554748932071799, 0.07555011999662968, 0.052213749441517035, 0.0346133408247201, 0.021811509053749865, 0.01289654068767146, 0.007014698720605329, 0.0033961978660195487, 0.0013742527416381151, 0.000396822873519563, 3.185710829719816e-05, -3.441281147082712e-05, -5.747286138420201e-06, 9.996265046416366e-06, -1.8165400680377386e-05, -6.724449830445516e-05, -8.589983127193807e-05, -2.1491328295048466e-05, 0.00015276584425353624, 0.0004118749325418252, 0.0006556443509392613, 0.0006890085233263261, 0.00020713449701175262, -0.001213804571513837, -0.004119515173094736, -0.009173711975862028, -0.017147232794020917, -0.02890031084764869, -0.04535834947775926, -0.0674817986834077, -0.09623134404511124, -0.13252928987464263, -0.17721839125826638, -0.23101945497192428, -0.29448928873995944, -0.36798170940607894, -0.45161244361135455, -0.545228277257364, -0.6483862442124171, -0.7603368064878336, -0.8800179800407211, -1.0060615711821104, -1.136803957540794, -1.270311522055899, -1.4044246140829793, -1.5367979105531366, -1.6649570999543413, -1.78635378056167, -1.8984281439713797, -1.998682962272722, -2.0847744782198387, -2.154579927135769, -2.2062546159795797, -2.238288514782699, -2.2495605444972626, -2.2393922758693336, -2.2076158124036724, -2.1545702664428235, -2.0810911490919564, -1.9885009999391468, -1.8785860554394904, -1.7535732660677565, -1.6160968671726927, -1.4690949253319905, -1.3157220377161103, -1.1592615898677876, -1.0030356535208966, -0.8503137585624228, -0.7042113898262962, -0.5675717216377559, -0.4428691613281677, -0.33212828590585103, -0.23685510266297233, -0.15797590320420452, -0.09579829777940044, -0.0499837481654674, -0.01954822708639479, -0.002885585862002024, 0.0021897423461076774, -0.0016226618932898486, -0.011193875163258036, -0.023067665201666972, -0.03357799053549867, -0.03897895449083482, -0.03558334061893312, -0.019903555914201666, 0.011211124470495744, 0.06044054489067596, 0.1298689215294386, 0.22087551885405649, 0.33404456959212464, 0.46910086429959263, 0.624881466370536, 0.7993194723052574, 0.9894608818298956, 1.191512996671921, 1.4009220678213512, 1.6124877487290679, 1.8205283776285706, 2.0190239738880518, 2.2017836096717054, 2.3626326688393102, 2.4956078038846665, 2.5951686108771037, 2.6564461431039694, 2.6753860042805675, 2.6488946706714596, 2.57497745378173, 2.4528483628582847, 2.283025886625576, 2.0674227133575784, 1.809285544610684, 1.5131305128576498, 1.1846568502164136, 0.8306219035762015, 0.4586892366787434, 0.0772490641527211, -0.3048569251964506, -0.678595186904824, -1.0350006667127545, -1.3654414543807616, -1.6618842605191728, -1.91717194862915, -2.1252666628528027, -2.2814493767694084, -2.3824800485820203, -2.42671566750253, -2.4141952379881517, -2.3467071113898355, -2.227720707564245, -2.062272658379779, -1.8568122858062157, -1.6189989774084106, -1.3574688695286337, -1.0815858836496683, -0.801069530058615, -0.5256343122614117, -0.2646369324295555, -0.02672620177603287, 0.18048669977795775, 0.35072889079283015, 0.4793748237852764, 0.5636796520700499, 0.6029458253028647, 0.5986248186630251, 0.5543465430275639, 0.47587255404606577, 0.37098076679882075, 0.2492649927849765, 0.12186063824938224, 0.0011045401489426334, -0.09986435771332819, -0.1675536732067998, -0.18859211092846978, -0.15022450450929692, -0.04081150301648719, 0.14968441858926176, 0.4292419252961227, 0.8033758439010193, 1.274799987682351, 1.8431604476612329, 2.5048536331534903, 3.2529356621931917, 4.0771475881533865, 4.964099449905845, 5.897495979614869, 6.858464097900053, 7.825971388050687, 8.77733203963667, 9.68882946595429, 10.536523226059074, 11.29685441317368, 11.94727986953337, 12.466948671274343, 12.837357914731731, 13.043042515818376, 13.072365490609744, 12.917758895519782, 12.575985613633458, 12.048362200693536, 11.340864562720835, 10.464189897794235, 9.433761850670978, 8.269160765457428, 6.993606251301985, 5.633406004299669, 4.217314421399062, 2.7758293904636138, 1.3404466183617818, -0.0573720853976871, -1.387092442441236, -2.61993867798644, -3.729689636283874, -4.693413955872029, -5.4921790678205396, -6.111621206912595, -6.542333247210972, -6.780114077330081, -6.826056424652294, -6.686523175650084, -6.373051494718704, -5.90189300268138, -5.293461723843739, -4.571683310096421, -3.763249262680758, -2.8968247451538245, -2.0022369661989043, -1.1094387473481, -0.24755879116911922, 0.5559782451223306, 1.2762698177375498, 1.8916616918065994, 2.384374888630352, 2.7410567130009102, 2.9531338027007155, 3.0169962972630526, 2.934022390749987, 2.71043892075245, 2.3570402984197028, 1.8887396909064618, 1.323983251012264, 0.6840613385295683, -0.007678970030376516, -0.7266864544208449, -1.4480566079455592, -2.1474098507174104, -2.8017245883607247, -3.3901206596487454, -3.8945795885800902, -4.300488555250792, -4.597125936481941, -4.777941993096674, -4.84069830058348, -4.787489267211307, -4.624536483513609, -4.361865988387637, -4.012895808936362, -3.5938313393828665, -3.123008093371246, -2.6201394746413773, -2.1055268066132533, -1.5992801122244507, -1.120543343348705, -0.6867763693317166, -0.31310852406775597, -0.011791165104269584, 0.2082219173652729, 0.34157300298625737, 0.38666999148738945, 0.3456456918348895, 0.2241890795832122, 0.03125106669778053, -0.22137253250544756, -0.5195696481277612, -0.8475622550315782, -1.188613976248888, -1.5257411408812565, -1.842426391084217, -2.123312331780285, -2.3548802363189627, -2.526092507764533, -2.628802180933368, -2.6580668148980418, -2.612353460380471, -2.4936188661437315, -2.3072557778694156, -2.0619210551857856, -1.7690862702206922, -1.4425365175787381, -1.0978064601286506, -0.7515362811529426, -0.4207776171924653, -0.12226058654929949, 0.12836355180539538, 0.31718863783097334, 0.432645801822304, 0.46600205441762804, 0.41176744630881734, 0.2680326329956801, 0.036550525750179974, -0.2773224558959006, -0.6648156499451743, -1.1140639163757209, -1.6105256990083483, -2.137477818000033, -2.6767508980961354, -3.209463248327013, -3.7167510480190735, -4.180497113570946, -4.584026081637118, -4.912771577788158, -5.154885553182195, -5.3016823451332495, -5.34795291815862, -5.292140657721327, -5.136390720245562, -4.886476775142264, -4.551504447241306, -4.14349452820494, -3.6768631207133615, -3.167811296468952, -2.63365871665665, -2.0921487781910284, -1.5606826971700218, -1.0556073580281016, -0.5915688538383292, -0.180951589802756, 0.16656867461990882, 0.44436870485645275, 0.6490764375347684, 0.7806071435477879, 0.8420312200684548, 0.8393144549396835, 0.7809478204490576, 0.6774666757122079, 0.5408387101158916, 0.38375876550227406, 0.21896527398990814, 0.058596913343351244, -0.08644709207769817, -0.20709782904148524, -0.2966636950776006, -0.351202616568373, -0.3696774233047667, -0.35402409434851373, -0.3090789055868769, -0.2423823606177232, -0.16378326423311002, -0.08484473068361408, -0.018215374308528005, 0.02306362895845052, 0.02630106322025028, -0.020040085455863887, -0.1255762400359076, -0.2973507896852042, -0.539286542340113, -0.8517538445397689, -1.23119817772672, -1.6700673698511201, -2.1569742399799128, -2.677014790019909, -3.212259244121819, -3.7423033175455602, -4.245117253838181, -4.698095136271126, -5.079098216317211, -5.367526035856382, -5.5453029439092285, -5.5978981946174855, -5.515358744352718, -5.293051024250757, -4.932240665314925, -4.440425112351327, -3.831443938955041, -3.125416172726711, -2.348294791164529, -1.5310748830654004, -0.7089172759064873, 0.07996117762191654, 0.795591620960148, 1.3977351449993682, 1.8474853928005033, 2.1088994592615955, 2.150384814183546, 1.9461022772999508, 1.4772618272195355, 0.733213283404963, -0.2877652757056754, -1.578207608578942, -3.121319456493097, -4.891107557356123, -6.852864530085106, -8.963976256189252, -11.175212183885694, -13.432849423555693, -15.679996826060025, -17.858189932210102, -19.909231613376217, -21.777053634102703, -23.4098685074707, -24.763009567773597, -25.799638895223392, -26.49167204351457, -26.820720059185582, -26.778714963220356, -26.368576773190703, -25.60513653167273, -24.51350569680778, -23.127830579445178, -21.490109077559442, -19.648756404751545, -17.65720614358258, -15.572665689673924, -13.453194897701051, -11.355504109063403, -9.333105806510103, -7.43461294194522, -5.702339906149327, -4.17119501714717, -2.867224954426682, -1.8069425650755002, -0.9971521000524393, -0.43514041006719545, -0.109219786541427, 0.00045039917604251686, -0.07920908935671372, -0.315643053773796, -0.6722999153733176, -1.110369266315483, -1.5905423494359567, -2.0747299230488454, -2.5277394020368575, -2.9187586842535524, -3.2225900670304446, -3.4205985103342775, -3.5013461324160517, -3.4608858986781246, -3.302708581537847, -3.0373394297792315, -2.681617010712483, -2.2576954929942996, -1.7918013510157194, -1.312805581375256, -0.8507280375006797, -0.4351965055065791, -0.09393102908202419, 0.14867729963189463, 0.2728239063981745, 0.26428693395790204, 0.11513155318342326, -0.17584028406519675, -0.6029445010070984, -1.1537856326149254, -1.80979092444738, -2.547223242021227, -3.338157020461201, -4.151653018600456, -4.955099899996996, -5.715634879844225, -6.401720098983192, -6.984995782206147, -7.441234498388341, -7.751259052675666, -7.901760693399626, -7.885876329625628, -7.703659702060584, -7.362567731441631, -6.876574785427044, -6.265351497991463, -5.553393936547506, -4.768958749739197, -3.942973961170181, -3.107976182862874, -2.2961900632588095, -1.5380358952451236, -0.8608801958247696, -0.2879339453277927, 0.16261231437519522, 0.4782050734205788, 0.6526100347268198, 0.6860676592358501, 0.5850964778294137, 0.3620295430162965, 0.0342899110439861, -0.37655404136511367, -0.8458331261148445, -1.3470122320820006, -1.8529975145275117, -2.337432906667123, -2.775943411398526, -3.1473009843827797, -3.434333055753427, -3.6246382722889856, -3.71106382931969, -3.6919131917815053, -3.5709053824418344, -3.3569033994692927, -3.063271630535185, -2.707059805116766, -2.308036534221943, -1.8876036556270088, -1.4676501296767588, -1.069391720769598, -0.7122196069611199, -0.41269694607446633, -0.18371682145399615, -0.03385496983879007, 0.03305283991238927, 0.01807831304403774, -0.07291120234203202, -0.22960300840019082, -0.4378139006847387, -0.6802654593440703, -0.9375420803174705, -1.1891884572511011, -1.4148076185740388, -1.5951544757332656, -1.713181839666143, -1.7549927166642996, -1.710634429189292, -1.5747172087976755, -1.3466963797551412, -1.0309452041003246, -0.636603214963904, -0.17717055877004712, 0.33012804673047935, 0.8652079962555691, 1.4061352161317058, 1.9302037426411567, 2.415066032467907, 2.8398331169719335, 3.186148110296749, 3.4392386660907657, 3.5885914153115848, 3.628466052331454, 3.5581679710448153, 3.382086614609502, 3.1095282647030853, 2.7543538538029675, 2.3341636208961978, 1.8693579808709853, 1.3821092952065641, 0.8952555874778708, 0.43116249563027076, 0.010579900145584702, -0.3484794578013502, -0.6316536601829368, -0.8289462363330111, -0.9352267733194966, -0.9505031571049128, -0.8799408978783294, -0.7335482646153694, -0.5256299306062144, -0.27403260810902397, 0.000790476669392347, 0.27687220017487646, 0.5319681379524097, 0.7447479082532197, 0.8959320588533157, 0.9693421190517405, 0.9528080648524602, 0.8389007463738218, 0.6254783456491374, 0.31578455601423505, -0.08167087753877725, -0.5534704395608809, -1.0819034597632915, -1.6458016350293887, -2.2216122218177414, -2.784629852879802, -3.310246224967664, -3.775193580209717, -4.158721806325738, -4.443716608527555, -4.6177715036571785, -4.673766213818325, -4.610217802791941, -4.431370123393525, -4.147009401277851, -3.77205188356874, -3.3259361923939874, -2.831425246831059, -2.3133479193825104, -1.7972855102858005, -1.3081987667664714, -0.869071189221561, -0.4996010676447886, -0.21491794482847942, -0.024615462079998825, 0.06793499850308023, 0.06598301926037455, -0.02051145561502403, -0.17511991074493716, -0.375557993884841, -0.5946062025611466, -0.8012858180724136, -0.9622502014710173, -1.043337876098504, -1.0112977054166798, -0.8354419271206783, -0.4892061290666135, 0.04842649315985181, 0.7917307392310542, 1.7472613351878004, 2.913042857528515, 4.2784045300588245, 5.824153208396841, 7.5231002016458435, 9.340868629450078, 11.236976551624375, 13.16614576999841, 15.08007379515216, 16.929339418958183, 18.665151901285082, 20.24110280231693, 21.614866671705084, 22.74982014316174, 23.616493729169235, 24.193485249908996, 24.46805954319695, 24.43648360837831, 24.104057732718964, 23.48496637030771, 22.601407094754535, 21.482446975039224, 20.16280195107161, 18.681449897492463, 17.080202016511326, 15.402084773050229, 13.689623571821423, 11.983401633292758, 10.32078068220417, 8.734836300372896, 7.25346218079923, 5.8985719265819245, 4.685870266677302, 3.624860298554746, 2.719070271576213, 1.9665015489308626, 1.3602094462017835, 0.8890438334903665, 0.5387076812135432, 0.2927615242423098, 0.13358866730856603, 0.043313160190015264, 0.004637224878292058, 0.0015859164216491665, 0.020133367291731027, 0.04860314312630458, 0.07788963995760262, 0.10151559454637579, 0.11554671358128579, 0.11839221266214384, 0.11043286755111231, 0.09357937006057959, 0.07079848956314208, 0.04563251429590424, 0.02174612378412179, 0.0025251383298162708, -0.00928424288869723, -0.011823793373983848, -0.004264038778918346, 0.013156811762211647, 0.03919293277634539, 0.07174403807003531, 0.10806757433141065, 0.1450426398641084, 0.1794591369841228, 0.20830633445026153, 0.2290436202499959, 0.2398424309775482, 0.23973052028830022, 0.2286684084920917, 0.207552013775566, 0.1781343464383153, 0.14288298655016185, 0.10478032966239906, 0.06704249102428851, 0.03283099916374254, 0.004966741669841588, -0.014331220128397435, -0.023663124351155265, -0.022620403591735925, -0.011875588129989269, 0.006821370943116851, 0.030737454291046042, 0.056333777073049346, 0.079511231804381, 0.09591557543285748, 0.10130183867583062, 0.09190969550414828, 0.06481649979970293, 0.01825360622194717, -0.048135830891725684, -0.1331144047657794, -0.2337833157533598, -0.34563463863633664, -0.46271444108987836, -0.577898505611798, -0.6832697726179132, -0.7705907185167962, -0.8318347526034913, -0.8597284224483296, -0.8482967854413076, -0.7933738183711889, -0.6930497393288388, -0.547971295952348, -0.3615126404870161, -0.1398197512011359, 0.10830399579074186, 0.37167780902245473, 0.6372282153217708, 0.8906663990581578, 1.117142162963334, 1.301985222663167, 1.4315177604146188, 1.4939223419764733, 1.480010728395586, 1.3839293901500638, 1.2035526754800228, 0.940781852413634, 0.6017655945197745, 0.19679013754432925, -0.26006231511104033, -0.7514942275632812, -1.2577861664142518, -1.7576010734782341, -2.2289821865607387, -2.6504620058449007, -3.0021776347825506, -3.267085450395635, -3.4317729713603815, -3.4871599243480618, -3.42908540152936, -3.258620925387683, -2.9821874506939294, -2.6115036396990674, -2.162890979167566, -1.6564650979438769, -1.1151662341991273, -0.5636280375617867, -0.02696226033479133, 0.4705059225055258, 0.9066691666320361, 1.2628640849310726, 1.5249060696117764, 1.6839156257882941, 1.7368983888605432, 1.6870505424516349, 1.543723207574877, 1.3220423994731185, 1.0422269225236127, 0.7286357708921347, 0.4085724276573213, 0.11088906411580375, -0.13550154559552732, -0.30313642991972684, -0.36747304904087724, -0.3082447118798751, -0.1106359968442918, 0.23378743321714746, 0.7265184233371111, 1.3618489149914281, 2.126951269352775, 3.0022941676259407, 3.9624167319762273, 4.977137563398202, 6.012826521271779, 7.033870311989721, 8.004211989218842, 8.888918935592065, 9.655819060295919, 10.277275970541472, 10.731204248163264, 11.00186676333318, 11.080469298559949, 10.965472415341928, 10.66269831140392, 10.185349949031234, 9.552901210892392, 8.789957986306254, 7.925091838855698, 6.989533046544777, 6.015865033523566, 5.036690103502825, 4.08293044648325, 3.182538944223825, 2.3594706191414305, 1.6328826586125358, 1.0165752833017994, 0.5186667327571791, 0.14157068861043187, -0.11769401145975948, -0.2669537006830412, -0.3181402398432043, -0.28639548638809215, -0.1890495821763751, -0.04453634495940855, 0.12863955173439956, 0.31285599394835867, 0.49221024016634657, 0.6532157848573863, 0.785365660617648, 0.8813730391858083, 0.937224702741666, 0.9520555149832873, 0.9278467618724855, 0.86900781056518, 0.7818738603219354, 0.6740106735591069, 0.5535566814108396, 0.4286061807766378, 0.30666140801011804, 0.19418131169824712, 0.09623779673799966, 0.016273482475385136, -0.04396973322940068, -0.08438185046868904, -0.10630169388391572, -0.11224392083210882, -0.10556400225991205, -0.09007016645269683, -0.06963460937454323, -0.04783744149882469, -0.02766768737672523, -0.011301545119214938, 2.974227943473535e-05, 0.006070676055096258, 0.007471845960427321, 0.005633503190377227, 0.002479779582574202, 0.00018575208300926734, 0.0008829743379169214, 0.006373189248011781, 0.017880236630955504, 0.035862193518972484, 0.05990222528760104, 0.0886917057986144, 0.12011828587083336, 0.15144000379755973, 0.1795348060600444, 0.20120786955679307, 0.21352699929066796, 0.21416578898785565, 0.201730636602448, 0.17598028242290317, 0.1379572253434343, 0.09000628601554415, 0.0356665718713136, -0.020566034797303148, -0.07361091683971405, -0.11830809054472403, -0.14998167446162716, -0.16503418523558178, -0.16153438318513308, -0.13975860492427314, -0.10264530641732836, -0.05604801214254173, -0.008795321744055054, 0.02746305706532547, 0.038645956042004624, 0.008867930608681964, -0.07869537528598444, -0.24073771921291945, -0.4926387698977258, -0.8472127719194367, -1.3134625423271606, -1.8954307744802414, -2.591224156330528, -3.3923070395120605, -4.283109354427894, -5.241017727219063, -6.236832639479067, -7.235644650601582, -8.198290376075043, -9.08293574542277, -9.846990810231784, -10.44938539405748, -10.85283968667499, -11.02621821498226, -10.947024991320959, -10.602888128667617, -9.992923088861264, -9.128585200932495, -8.033842322196513, -6.744861642620997, -5.309062409599043, -3.78286856034813, -2.229150817623807, -0.714193528227006, 0.6956365346390718, 1.9374670443147464, 2.9557572410464, 3.7058629968095875, 4.157029536423837, 4.294782736324585, 4.12258962517889, 3.662756127884584, 2.956513580348852, 2.062384761160449, 1.0536787857679484, 0.015150426198495241, -0.9611516194598959, -1.780704070425738, -2.351950569019957, -2.5920089132284416, -2.4320282441668954, -1.8220879604369724, -0.7354053241062809, 0.8283418769654329, 2.8406255295305365, 5.24369508465149, 7.951625211096186, 10.852835803911812, 13.814098050919737, 16.68575715605747, 19.308292746705778, 21.52007167137491, 23.16549755204477, 24.103311103057777, 24.214359942412322, 23.40900810777716, 21.63410543983212, 18.877794371169735, 15.172675585180022, 10.59683352137158, 5.272957189866206, -0.6343802850903906, -6.923061894352202, -13.360917716968151, -19.694637591662545, -25.659672435144937, -30.991034264021383, -35.434425943573345, -38.75704338598678, -40.75836505176172, -41.27953410362868, -40.211326734152536, -37.50034844777067, -33.15279447339766, -27.233814468659325, -19.866533165655596, -11.228929939935718, -1.548195430287058, 8.906946998098967, 19.837215522331384, 30.928556188447892, 41.86128737730396, 52.32057054642237, 62.007846948970595, 70.65206720840607, 78.02110147241467, 83.93567135683757, 88.26964078072777, 90.9513672666134, 91.965305686966, 91.3505979307777, 89.19935616961675, 85.65626902120977, 80.90479941039013, 75.15691891031243, 68.64359905653659, 61.60479834348271, 54.28099871540601, 46.90645889420527, 39.69617540657018, 32.837800808325014, 26.486387239546865, 20.761032433455327, 15.743693522965655, 11.479855463314774, 7.978445374434782, 5.215191470429862, 3.1376864579070496, 1.671312922760283, 0.7257192080674187, 0.2014093943875312, -0.003991776333972027, 0.010368367913334998, 0.15390214495054955, 0.3488500667963233, 0.5333573679314569, 0.6632081666800005, 0.712303192101652, 0.6719187597850416, 0.5488672168938521, 0.3627664664752903, 0.14260580824585742, -0.07704848428412718, -0.2599220159972422, -0.37174939622942677, -0.38360311050745305, -0.27460449020253097, -0.03381726356494746, 0.33879229336110306, 0.8322298797745351, 1.4252071703991886, 2.0877214273385234, 2.783241081923264, 3.4714051786037055, 4.111161774638209, 4.663627208993882, 5.09495499810746, 5.378650197741263, 5.497368374566662, 5.444179136495859, 5.2232534044290135, 4.849451330466001, 4.347006285003051, 3.7476544068600663, 3.088365121586182, 2.40876393681562, 1.748493424082264, 1.144137953509071, 0.6264986879235537, 0.21847364927470686, -0.06649934985902373, -0.22530808132719862, -0.2653925022807403, -0.204205484368302, -0.06784242392357225, 0.11095217185962648, 0.29526225619745966, 0.4468055665980194, 0.5289275620035415, 0.5094842253941565, 0.3634507305860444, 0.07508877548430028, -0.3604659631150754, -0.9363456878830337, -1.6340869112735747, -2.4244550989797737, -3.2689761689581305, -4.122121873993971, -4.934057954362113, -5.653921043798141, -6.233634688332441, -6.630892155805779, -6.811943196148348, -6.754051518099305, -6.447343237763692, -5.896022101470659, -5.118906676268037, -4.148163275373449, -3.0275147177048334, -1.8098507810980846, -0.5542222558429137, 0.6776197348781886, 1.8251015242043733, 2.832783253253982, 3.6538245224115387, 4.252937861133978, 4.608681796868443, 4.715035120678532, 4.58222759883019, 4.2359364183838055, 3.7156137217685203, 3.072006567187098, 2.363911929798345, 1.654375951723705, 1.0064778390208666, 0.47872129861932666, 0.12081390529907522, -0.030062534127687272, 0.04768035003752367, 0.3578388127270734, 0.8852977039522733, 1.596128757008397, 2.4388634814284607, 3.3468904766724705, 4.241874566925698, 5.038099411618266, 5.647736961431671, 5.986039449339007, 5.976588301194105, 5.556355039207442, 4.6801819934069115, 3.324596221859362, 1.4907322850615965, -0.7947212451515107, -3.479673076005522, -6.488017253697041, -9.72227809776065, -13.067515549911056, -16.396666185546533, -19.576413021986397, -22.47325801711117, -24.95972596697141, -26.920439083131317, -28.25799849850924, -28.898729109461872, -28.795708643555493, -27.930848137549084, -26.3159849002124, -23.99263924985473, -21.03056020970655, -17.524659028178124, -13.590032117387914, -9.356812727626295, -4.96458824232091, -0.5564952151743685, 3.7271450159564754, 7.755990749436279, 11.41429554049627, 14.604815002593877, 17.252037625382258, 19.30442408909935, 20.735958224761248, 21.547544531321268, 21.76380544581774, 21.42996914389694, 20.608589814057233, 19.37563248236696, 17.816588120085452, 16.02290064018436, 14.085884356520497, 12.0923272715395, 10.121001149799904, 8.23982510119483, 6.503993909382951, 4.9549381012126705, 3.619211551129657, 2.5090100364972643, 1.6236337873617785, 0.9513297262380945, 0.4715142359078342, 0.15721256165829417, -0.0225132346879081, -0.10008696369001692, -0.10698961611395845, -0.07171863705578115, -0.018179930927967856, 0.035490144971736116, 0.07699834501919955, 0.09953201469451388, 0.10114075271750492], 'positive_zeros': ['0.40052525254586409025884160255851', '0.48088743018928932095811419481992', '1.03368931846337799919101645160138', '1.11760115790506573613924689158901', '1.34553656938248704343014882161439', '1.82545380480142947965529767327278', '2.20921371405296256982263906229543', '2.22837775637324665941174664900094', '2.24151866656048863547949085955032', '2.27703082264184881162816148601704', '2.32629750348473789017423777144623', '2.86462696011883405096737668017574', '2.87841661121519747938145832927066', '2.94626401559529630655921305361772', '3.24415618197963131238473012084792', '3.45820767401382408886681173336486', '3.57431420486419470027456187147779', '3.62555406049829866538716136269419', '3.95466969700081031597230570869953', '4.14354541173826357530056680892639', '4.27723784882652851560720159748425', '4.50239579310215658796897273663372', '4.56187965960075036909377890283011', '4.77012183717626622800290617638556', '4.83526525511328457342839742248844', '5.10250577106568618688785991672764', '5.21862865101679570379876551102927', '5.32573002439548885970873465308742', '5.34858174752300007548716110144654', '5.60444389359879539015809639281138', '5.69085651456778617351526719645683', '6.05435457397004477267599158097760', '6.05605893332825445760503105206444', '6.26305880474052168960002893989407', '6.30327416597551178453032598553137', '6.56840406499210408603676721731670', '6.63174723141037190265293991216298', '6.85900452145187793161710611782875', '6.87772087981611025332090785295294', '7.03474728243169743182416633824068', '7.22682618721496326036817573795356', '7.32419109979615794902820295801129', '7.42002174491530076948101789092709', '7.65806693687548170788200712235660', '7.68384557883349899071171747636609', '7.78245435005371334664504612275687', '8.216749119502124400726540825991458', '8.220608010166144566599136092002425', '8.341464584916436401001756747212042', '8.372091488934302871446924749902135', '8.547035312774767588991175996912114', '8.590569581515778709164756727173343', '8.674866205027888530587687611136628', '8.833728010642536359035704746346238', '8.969167696820773299126704832534899', '9.150897404033547221547116195181627', '9.281425776148190646011415804204074', '9.329801522681314760372346914986721', '9.643463510221116917161323955380121', '9.699891815025189627702847350461182'], 'prelabel': '12-1680e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.662631231720593, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e6-0', 'trace_hash': 1214803332656147482, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40052525254586409025884160256', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.48088743018928932095811419482', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.03368931846337799919101645160', 'prec': 103}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 5827983.7536337515, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 22483074023424000000, 'conductor_radical': 210, 'degree': 12, 'dirichlet_coefficients': [1, 0, 3, 0, 3, 0, 0, 0, 3, 0, -3, 0, -6, 0, 9, 0, -6, 0, 3, 0, 0, 0, -3, 0, 3, 0, -2, 0, 12, 0, 12, 0, -9, 0, 0, 0, -3, 0, -18, 0, -18, 0, 0, 0, 9, 0, 3, 0, 6, 0, -18, 0, 15, 0, -9, 0, 9, 0, 30, 0, 0, 0, 0, 0, -18, 0, 0, 0, -9, 0, 24, 0, -18, 0, 9, 0, 0, 0, 6, 0, -9, 0, -12, 0, -18, 0, 36, 0, 0, 0, 0, 0, 36, 0, 9, 0, 48, 0, -9, 0], 'euler11': [1, 3, 12, 111, 222, 741, 5074, 8151, 26862, 147741, 175692, 483153, 1771561], 'euler13': [1, 6, 57, 306, 1686, 6774, 28973, 88062, 284934, 672282, 1627977, 2227758, 4826809], 'euler17': [1, 6, 39, 214, 756, 2694, 12725, 45798, 218484, 1051382, 3257319, 8519142, 24137569], 'euler19': [1, -3, -51, 50, 2115, -1143, -44706, -21717, 763515, 342950, -6646371, -7428297, 47045881], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 3, -36, -97, 642, 597, -13546, 13731, 339618, -1180199, -10074276, 19309029, 148035889], 'euler29': [1, -12, 198, -1572, 14859, -86880, 579868, -2519520, 12496419, -38339508, 140041638, -246133788, 594823321], 'euler3': [1, -3, 6, -7, 6, -3, 1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -12, 78, -204, -1218, 18168, -127402, 563208, -1170498, -6077364, 72034638, -343549812, 887503681], 'euler37': [1, 3, -15, 390, 165, -5037, 92954, -186369, 225885, 19754670, -28112415, 208031871, 2565726409], 'euler41': [1, 18, 327, 3574, 37455, 288312, 2113142, 11820792, 62961855, 246323654, 924023847, 2085411618, 4750104241], 'euler43': [1, 0, 180, -176, 15840, -15840, 863358, -681120, 29288160, -13993232, 615384180, 0, 6321363049], 'euler47': [1, -3, -60, 637, 252, -16287, 142082, -765489, 556668, 66135251, -292780860, -688035021, 10779215329], 'euler5': [1, -3, 6, -7, 6, -3, 1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -15, 6, 7, 11664, -54399, -166888, -2883147, 32764176, 1042139, 47342886, -6272932395, 22164361129], 'euler59': [1, -30, 441, -5010, 52200, -489990, 4032079, -28909410, 181708200, -1028948790, 5343756201, -21447728970, 42180533641], 'euler61': [1, 0, -183, 0, 22326, 0, -1588867, 0, 83075046, 0, -2533788903, 0, 51520374361], 'euler67': [1, 0, -162, -176, 15390, 14256, -1149078, 955152, 69085710, -52934288, -3264481602, 0, 90458382169], 'euler7': [1, 0, -6, 4, -42, 0, 343, 0, 0, 0, 0, 0, 0], 'euler71': [1, -24, 198, 144, -4941, -145608, 2427964, -10338168, -24907581, 51539184, 5031512838, -43301504424, 128100283921], 'euler73': [1, 18, 24, 28, 19752, 113322, -303966, 8272506, 105258408, 10892476, 681557784, 37315288674, 151334226289], 'euler79': [1, -6, -114, 932, 5154, -32646, -177042, -2579034, 32166114, 459512348, -4440309234, -18462338394, 243087455521], 'euler83': [1, 12, 522, 4812, 110763, 785424, 12340420, 65190192, 763046307, 2751439044, 24773243562, 47268487716, 326940373369], 'euler89': [1, 0, -177, 584, 15576, -51684, -1293079, -4599876, 123377496, 411701896, -11105376657, 0, 496981290961], 'euler97': [1, -48, 1542, -33520, 575055, -7692768, 84630804, -746198496, 5410692495, -30592798960, 136512151302, -412192332336, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -3, 6, -7, 6, -3, 1, 0, 0, 0, 0, 0, 0], [1, -3, 6, -7, 6, -3, 1, 0, 0, 0, 0, 0, 0], [1, 0, -6, 4, -42, 0, 343, 0, 0, 0, 0, 0, 0], [1, 3, 12, 111, 222, 741, 5074, 8151, 26862, 147741, 175692, 483153, 1771561], [1, 6, 57, 306, 1686, 6774, 28973, 88062, 284934, 672282, 1627977, 2227758, 4826809], [1, 6, 39, 214, 756, 2694, 12725, 45798, 218484, 1051382, 3257319, 8519142, 24137569], [1, -3, -51, 50, 2115, -1143, -44706, -21717, 763515, 342950, -6646371, -7428297, 47045881], [1, 3, -36, -97, 642, 597, -13546, 13731, 339618, -1180199, -10074276, 19309029, 148035889], [1, -12, 198, -1572, 14859, -86880, 579868, -2519520, 12496419, -38339508, 140041638, -246133788, 594823321], [1, -12, 78, -204, -1218, 18168, -127402, 563208, -1170498, -6077364, 72034638, -343549812, 887503681], [1, 3, -15, 390, 165, -5037, 92954, -186369, 225885, 19754670, -28112415, 208031871, 2565726409], [1, 18, 327, 3574, 37455, 288312, 2113142, 11820792, 62961855, 246323654, 924023847, 2085411618, 4750104241], [1, 0, 180, -176, 15840, -15840, 863358, -681120, 29288160, -13993232, 615384180, 0, 6321363049], [1, -3, -60, 637, 252, -16287, 142082, -765489, 556668, 66135251, -292780860, -688035021, 10779215329], [1, -15, 6, 7, 11664, -54399, -166888, -2883147, 32764176, 1042139, 47342886, -6272932395, 22164361129], [1, -30, 441, -5010, 52200, -489990, 4032079, -28909410, 181708200, -1028948790, 5343756201, -21447728970, 42180533641], [1, 0, -183, 0, 22326, 0, -1588867, 0, 83075046, 0, -2533788903, 0, 51520374361], [1, 0, -162, -176, 15390, 14256, -1149078, 955152, 69085710, -52934288, -3264481602, 0, 90458382169], [1, -24, 198, 144, -4941, -145608, 2427964, -10338168, -24907581, 51539184, 5031512838, -43301504424, 128100283921], [1, 18, 24, 28, 19752, 113322, -303966, 8272506, 105258408, 10892476, 681557784, 37315288674, 151334226289], [1, -6, -114, 932, 5154, -32646, -177042, -2579034, 32166114, 459512348, -4440309234, -18462338394, 243087455521], [1, 12, 522, 4812, 110763, 785424, 12340420, 65190192, 763046307, 2751439044, 24773243562, 47268487716, 326940373369], [1, 0, -177, 584, 15576, -51684, -1293079, -4599876, 123377496, 411701896, -11105376657, 0, 496981290961], [1, -48, 1542, -33520, 575055, -7692768, 84630804, -746198496, 5410692495, -30592798960, 136512151302, -412192332336, 832972004929]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1680/2/bg/v'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '12-1680e6-1.1-c1e6-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-1680e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.662631231720593, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 1214803332656147482, 'z1': {'__RealLiteral__': 0, 'data': '0.40052525254586409025884160256', 'prec': 103}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': '507726076796327780207933175909,609597239521663371665535180270,1310356884999610493187723318518,1416727778634120766837053650959,1705670239806742336018546496584,2314037611345437190072435818899', 'Lhash_array': ['507726076796327780207933175909', '609597239521663371665535180270', '1310356884999610493187723318518', '1416727778634120766837053650959', '1705670239806742336018546496584', '2314037611345437190072435818899'], 'label': '12-1680e6-1.1-c1e6-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1680/2/bg/v'}