Lfunction data - 6-418e3-1.1-c1e3-0-1

Formats: - HTML - YAML - JSON - 2023-03-28T21:37:33.628673

• 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': '2244153403243899925604401226505,2843830357802767257902729835667,3332407741569710718060250687525', 'a10': 9, 'a2': -3, 'a3': 0, 'a4': 6, 'a5': -3, 'a6': 0, 'a7': -6, 'a8': -10, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.18434761548858, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 3, 3, 1]], [11, [1, 3, 3, 1]], [19, [1, 3, 3, 1]]], 'bad_primes': [2, 11, 19], 'central_character': '418.1', 'coefficient_field': '1.1.1.1', 'conductor': 73034632, 'conductor_radical': 418, 'degree': 6, 'euler_factors': [[1, 3, 3, 1], [1, 0, 3, -3, 9, 0, 27], [1, 3, 6, 12, 30, 75, 125], [1, 6, 15, 27, 105, 294, 343], [1, 3, 3, 1], [1, 0, 21, -29, 273, 0, 2197], [1, 9, 69, 302, 1173, 2601, 4913], [1, 3, 3, 1], [1, 15, 135, 766, 3105, 7935, 12167], [1, -6, 63, -201, 1827, -5046, 24389], [1, 3, 42, 52, 1302, 2883, 29791], [1, 6, 87, 348, 3219, 8214, 50653], [1, 9, 78, 616, 3198, 15129, 68921], [1, 21, 222, 1622, 9546, 38829, 79507], [1, 12, 81, 456, 3807, 26508, 103823], [1, 9, 69, 502, 3657, 25281, 148877], [1, 3, 153, 290, 9027, 10443, 205379], [1, -24, 339, -3120, 20679, -89304, 226981], [1, 0, 105, 123, 7035, 0, 300763], [1, -21, 216, -1676, 15336, -105861, 357911], [1, 3, 213, 426, 15549, 15987, 389017], [1, 6, 105, 4, 8295, 37446, 493039], [1, 33, 594, 6582, 49302, 227337, 571787], [1, -6, 231, -924, 20559, -47526, 704969], [1, -12, 195, -2072, 18915, -112908, 912673], [1, 0, 255, -56, 25755, 0, 1030301], [1, -3, 66, -470, 6798, -31827, 1092727], [1, 3, 285, 678, 30495, 34347, 1225043], [1, 3, 207, 106, 22563, 35643, 1295029], [1, 24, 531, 5936, 60003, 306456, 1442897]], 'euler_factors_factorization': [[[[1, 1], 3]], [[[1, 0, 3, -3, 9, 0, 27], 1]], [[[1, 3, 6, 12, 30, 75, 125], 1]], [[[1, 6, 15, 27, 105, 294, 343], 1]], [[[1, 1], 3]], [[[1, 0, 21, -29, 273, 0, 2197], 1]], [[[1, 9, 69, 302, 1173, 2601, 4913], 1]], [[[1, 1], 3]], [[[1, 15, 135, 766, 3105, 7935, 12167], 1]], [[[1, -6, 63, -201, 1827, -5046, 24389], 1]], [[[1, 3, 42, 52, 1302, 2883, 29791], 1]], [[[1, 6, 87, 348, 3219, 8214, 50653], 1]], [[[1, 9, 78, 616, 3198, 15129, 68921], 1]], [[[1, 21, 222, 1622, 9546, 38829, 79507], 1]], [[[1, 12, 81, 456, 3807, 26508, 103823], 1]], [[[1, 9, 69, 502, 3657, 25281, 148877], 1]], [[[1, 3, 153, 290, 9027, 10443, 205379], 1]], [[[1, -24, 339, -3120, 20679, -89304, 226981], 1]], [[[1, 0, 105, 123, 7035, 0, 300763], 1]], [[[1, -21, 216, -1676, 15336, -105861, 357911], 1]], [[[1, 3, 213, 426, 15549, 15987, 389017], 1]], [[[1, 6, 105, 4, 8295, 37446, 493039], 1]], [[[1, 33, 594, 6582, 49302, 227337, 571787], 1]], [[[1, -6, 231, -924, 20559, -47526, 704969], 1]], [[[1, -12, 195, -2072, 18915, -112908, 912673], 1]], [[[1, 0, 255, -56, 25755, 0, 1030301], 1]], [[[1, -3, 66, -470, 6798, -31827, 1092727], 1]], [[[1, 3, 285, 678, 30495, 34347, 1225043], 1]], [[[1, 3, 207, 106, 22563, 35643, 1295029], 1]], [[[1, 8, 113], 3]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '6-418e3-1.1-c1e3-0-1', '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}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'origin': 'ModularForm/GL2/Q/holomorphic/418/2/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0416666666667', 'prec': 50}, 'plot_values': [0.0, 0.0001698798590640423, 0.00136427664687199, 0.0046339938854667905, 0.011081704260198427, 0.0218807938235874, 0.038294205185991345, 0.06168894265820852, 0.09352164545282494, 0.13534358508237201, 0.1887910829430552, 0.25550584840385104, 0.3371250613745449, 0.4352362142238361, 0.5512080023808423, 0.68617224171207, 0.8409438716978008, 1.0157661775489848, 1.2103066310713466, 1.4235689014447224, 1.6536040762541442, 1.8975614408684658, 2.1516523318790175, 2.410934164660914, 2.669463340560911, 2.9203907225288153, 3.155958807802627, 3.367774173807667, 3.5470937917328995, 3.6851489699251965, 3.7734748134562905, 3.804367051435551, 3.7715335629516105, 3.670304734795005, 3.498116051281696, 3.255308418126944, 2.9449570176367605, 2.573127664276345, 2.1494855151712398, 1.6865123403943492, 1.1992902206216103, 0.7055634747593477, 0.22433309722796982, -0.22488742786157356, -0.6226839218743115, -0.951408335571389, -1.1961592399513457, -1.3457641583374447, -1.3939995468494797, -1.3401933451989194, -1.1898760699348803, -0.9548032568535733, -0.6525412007043898, -0.30606241890709934, 0.057718055089145945, 0.4095511296276198, 0.7194652434808201, 0.9591376353906458, 1.104044912516627, 1.1354399701774727, 1.0422747491553417, 0.8225451547034078, 0.4840177044098902, 0.044341049749627645, -0.4696712595627729, -1.023955038166114, -1.579133348033424, -2.093381158957941, -2.5268683724423715, -2.8441907200060546, -3.0177452348612115, -3.0325500677907207, -2.88643650621418, -2.5913110365890013, -2.175204101356394, -1.6782748995449348, -1.1502949598246328, -0.6481632064981697, -0.22867739733572, 0.056565678238669724, 0.16648529301411574, 0.07673988292424647, -0.21668830726774266, -0.6941887833753599, -1.312356211877761, -2.0062491447561523, -2.6926086953707173, -3.2774002458814357, -3.664471672598773, -3.7648942036158375, -3.507793687087761, -2.8501500169017073, -1.7852310180861999, -0.3482535844283566, 1.3810711680448062, 3.2806687093544316, 5.191519780683976, 6.927238723097853, 8.290957762258692, 9.088688013332384, 9.146630950268289, 8.33559715097343, 6.580035897628904, 3.8704568475001353, 0.2794211110199779, -4.046547916779464, -8.891219287425885, -13.974226137324106, -18.977685112599687, -23.56709424390119, -27.416530356587053, -30.239075256336147, -31.809487719895557, -31.99043596039046, -30.744817597878807, -28.140436158431434, -24.35527430525172, -19.660320227963282, -14.398216439835545, -8.961199690736738, -3.755337963785968, 0.8340275835467718, 4.4742707389869825, 6.913167144080123, 8.001393507352539, 7.705481208885985, 6.10695772220043, 3.395950384220879, -0.15122651265785308, -4.196778046182096, -8.369766410187129, -12.312609146702837, -15.702244876291271, -18.274956951926068, -19.86713235062615, -20.40672817440461, -19.9132614505633, -18.510492703205134, -16.387510800896525, -13.775985680820767, -10.938739250036498, -8.126398201579942, -5.554503735343337, -3.391674974168742, -1.740409221864731, -0.6345591606366044, -0.0455214396868687, 0.10764643981077561, -0.058475894529713766, -0.4114217375348441, -0.8217686467352018, -1.1795925668706044, -1.4080804809344067, -1.4681164305801764, -1.3586111069023403, -1.1124131546647138, -0.7840235475568088, -0.43776082195849514, -0.13494873734685597, 0.07816896540822911, 0.17759416702677092, 0.1657462848738921, 0.06901694580639697, -0.06843087909644559, -0.1934705920582694, -0.25583861347525616, -0.2184341493097141, -0.06593396423452737, 0.19055933657677865, 0.5136305418366927, 0.844026426984419, 1.1095218281832224, 1.2362528066562124, 1.161315370099669, 0.843690743527999, 0.2727305638763327, -0.5286975574006936, -1.504568798142311, -2.5708843218792614, -3.6302197755022254, -4.580188764460743, -5.325784143322771, -5.799777735604444, -5.963192339635978, -5.809330742203329, -5.372572088583172, -4.713218340280261, -3.9087915010081202, -3.049240496671391, -2.2179147326541733, -1.482043805121163, -0.8882212003664735, -0.4561624884063055, -0.18028151925191707, -0.03518979793172679, 0.017041334433050576, 0.0179466631558601, 0.004170357028394549, 0.001191074341926738, 0.020056092974871032, 0.05785958719871576, 0.10139387203569443, 0.1328805026743012, 0.13775123622614083, 0.11019312518931314, 0.05728182524673639, 0.0009348801492361879, -0.025768939010667864, 0.016175714833206706, 0.163476831080163, 0.44173323484698906, 0.8587158360066842, 1.3982655031146596, 2.020382532729101, 2.6653107215922445, 3.260484089268511, 3.731546345863708, 4.014306414650752, 4.066109386333773, 3.872742444623474, 3.4523577589982586, 2.8534875854948685, 2.147571336019775, 1.4190220487856502, 0.7490377448036442, 0.20537053869644253, -0.16727846771677518, -0.358639512196927, -0.3878267519380401, -0.29853529377915017, -0.15369281176696836, -0.01810925956012874, 0.053170883030690806, 0.024196191211838636, -0.1136753360296067, -0.3417797639658462, -0.6185794881966507, -0.8890131391178658, -1.0969346868389314, -1.1978735198450061, -1.1681139454038398, -1.0104157752949297, -0.7545362620158135, -0.4494392235639011, -0.1532798366053671, 0.08012404229381682, 0.21411502096377424, 0.2378888330479578, 0.17167561607996576, 0.06211055412900996, -0.027075981159378475, -0.028953390116450536, 0.10921814741996153, 0.4117990981778804, 0.8639870147182178, 1.4097986713415518, 1.958250636571923, 2.397587326986022, 2.6155786491214825, 2.52136621145278, 2.0661049553393913, 1.256528478795519, 0.15967390927339115, -1.1078367256014217, -2.392458833453339, -3.5265961292565735, -4.36900515014929, -4.816647836943134, -4.82217997757696, -4.4191400337596685, -3.697301641245784, -2.7872846562940765, -1.8483075981594494, -1.0238050701111274, -0.41783751230014043, -0.08115914967624499, 0.0007845290453067674, -0.10155983972498116, -0.28190759594132514, -0.426023512692529, -0.4427863954671834, -0.2903842852289377, 0.009395590466555803, 0.3701336389785314, 0.65838959702204, 0.7222952217735308, 0.4269007601428161, -0.30230341992853327, -1.4576465110120844, -2.936879430640874, -4.544822586628446, -6.029859789244566, -7.125206231380504, -7.604304444167615, -7.331791177556424, -6.296610325310614, -4.636498276465437, -2.6179268720029634, -0.5948150286290559, 1.0461695417679078, 1.9627007172764563, 1.9254618172332334, 0.8674107553965081, -1.0928317822662692, -3.6605631853317826, -6.423509031971769, -8.915834359818572, -10.700770310139415, -11.484258860414059, -11.146607621397564, -9.768807757040106, -7.651135191054975, -5.2154381133723415, -2.9202977708248294, -1.1725827384144851, -0.20315309636764733, -0.001484769469475457, -0.2898695645809304, -0.5484109254979203, -0.09977956859147305, 1.7654242355817846, 5.64012915229561, 11.859923306290035, 20.401703447082905, 30.825867543762296, 42.29036130117357, 53.68908911646537, 63.7586938589783, 71.25437343604604, 75.24718626083711, 75.17818607201163, 70.95437987550702, 63.10087207695488, 52.558054701784535, 40.55025074382178, 28.486417249560795, 17.64241440884387, 8.982327729511164, 3.0505603729547897, -0.13351062977610298, -1.0419518897940636, -0.5265774234890913, 0.3490361231167679, 0.5160478218269472, -0.8994151240441587, -4.416670501292475, -10.101527995063195, -17.57467918629853, -26.06880274310799, -34.55028624496313, -41.961998361636645, -47.34680131946371, -49.98909369575789, -49.61885831824171, -46.34957812084167, -40.6394270863556, -33.28163251713354, -25.185053851126963, -17.234185986725734, -10.19831325385628, -4.599012401576822, -0.6707927091350048, 1.6217998627306627, 2.5346064292248256, 2.46115218715396, 1.8354719479048685, 1.0486197893464317, 0.3888089991279446, 0.007786561989998995, -0.06844348948099492, 0.0876775382382142, 0.3516603843499857, 0.5957728675569973, 0.7231705276990823, 0.6962822972848869, 0.5325118926344177, 0.28867191341436665, 0.04196543541445878, -0.1408359195220643, -0.22223954509012006, -0.20143571123534412, -0.11019229360200737, 0.0016734686390294262, 0.08577432182157854, 0.11305109552017109, 0.08404935009118639, 0.029534612865918648, -0.0009413501101941698, 0.04367503319507454, 0.19652054599163155, 0.4578487982867887, 0.7891131563754887, 1.1205176571005064, 1.3674360383834676, 1.4521835958535596, 1.3321559302780583, 1.0133481240566906, 0.5543859786162981, 0.06126108167905389, -0.33821850631713035, -0.5243812180143024, -0.41548114486976967, 0.008091758935548202, 0.6930225450999191, 1.5247770202170283, 2.3462994486489293, 2.989490963946544, 3.327042265157071, 3.2885719343921362, 2.8773476763907624, 2.1878887840138947, 1.3670988671013593, 0.5837319206403436, -0.001014520272386985, -0.2813612718258246, -0.2277557115856877, 0.10840926888250287, 0.606427384066013, 1.1074594548525698, 1.4534381901587272, 1.5256190053288716, 1.2745896165949266, 0.7297057580389543, -0.006868537340995322, -0.7819501789297869, -1.440033650083718, -1.8505441025408562, -1.935899963917141, -1.7069126349595405, -1.2411692487774697, -0.6634671000434238, -0.12680146469327885, 0.2377979287194975, 0.34963773236713697, 0.1931900266197103, -0.17792595682554024, -0.6580539577694573, -1.1192580315116214, -1.4429282167180861, -1.5486828855941117, -1.4176337063333064, -1.0877836609711826, -0.6418580665296147, -0.18840704611486447, 0.1750605475530602, 0.38547018067107996, 0.4265492758427418, 0.3331510519095245, 0.1768605243970721, 0.04137246755884611, -0.002792099900389673, 0.07891667938455577, 0.2733048811973891, 0.5225089104979579, 0.738261254252959, 0.8285552333931243, 0.723611179602252, 0.3965561635242023, -0.1271485293639941, -0.7713385456388997, -1.4247236782360706, -1.9771204193024612, -2.334092234830829, -2.4373650826339963, -2.292977363790578, -1.9494874398086262, -1.4848737871822455, -0.9975274568462553, -0.5697858504552594, -0.2529722184603298, -0.06407699791737637, 0.01467425983029403, 0.022592692029069807, 0.00331150058967597, -0.010004337100571796, -0.003321987487890236, 0.018378034230575997, 0.03911921016726944, 0.04340156063522891, 0.027692295056098333, 0.0032161406078951523, -0.008940404276059553, 0.009242799666891337, 0.05549046646227655, 0.09552713890561826, 0.06151766658657238, -0.1313953545968871, -0.5539163161953323, -1.219940380061747, -2.0455897665845537, -2.8247231051887622, -3.238103465992525, -2.8875266810458404, -1.3687353456983498, 1.6063852166595523, 6.1345378165938165, 12.042069754909438, 18.82599569736178, 25.72377890600815, 31.802072787608655, 36.117660555994, 37.90743480361092, 36.74092955914007, 32.68495183359911, 26.304247224134524, 18.586762834564034, 10.822812232120581, 4.341691564795089, 0.25856652020381854, -0.7391494424765315, 1.46127312241084, 6.358271702827733, 12.954003728660421, 19.936745829853727, 25.924140348845086, 29.823814717851228, 30.96578520481467, 29.210692138005058, 25.05944277419402, 19.398875864301232, 13.294408747019817, 7.804552652360284, 3.6698612679795692, 1.1793281325783005, 0.15003929036438246, -0.005299051943008301, -0.08904185068088982, -0.8847277122933437, -2.9337880058106696, -6.373338325282513, -10.903154295922166, -15.839168168711014, -20.26489230840644, -23.3267172499618, -24.388682901116923, -23.18368528727189, -19.978465245017304, -15.413100978796102, -10.352571499811905, -5.73558138266733, -2.279582628057114, -0.3282497442870768, 0.20497402748944638, -0.19076845223948824, -0.7777210061116915, -0.7831496935581205, 0.3799325748312011, 2.936205702734801, 6.680919266906211, 11.00975574586842, 15.046058437094448, 17.90994760322293, 18.890132032958352, 17.613235959336127, 14.226000003173377, 9.28353927781004, 3.6311534528308647, -1.7365406737487012, -5.958239922894372, -8.47346049229551, -9.120434450886242, -8.149598099767845, -6.118637975070867, -3.728011127142234, -1.6340943064566424, -0.28390671877188245, 0.18063561173238563, -0.08523939085583672, -0.6985646525996941, -1.2066789419457844, -1.2285409323918834, -0.5657539449279254, 0.701253645753, 2.2745951162478604, 3.731625302451974, 4.642010546352738, 4.729219725869789, 3.9593494713699457, 2.570779407601658, 1.0164606291225895, -0.16020605083224243, -0.4787903764680797, 0.3293061376021055, 2.222096416567126, 4.839604331675792, 7.569392871104152, 9.676066162113797, 10.51852500690289, 9.677654606844012, 7.062736457023328, 2.9969263297628137, -1.897929752843691, -6.8256570594821415, -10.969892787877427, -13.69218325791388, -14.647470470396582, -13.852322395534797, -11.649664083062811, -8.605923442695264, -5.375893761671166, -2.5524998361150137, -0.5460265795850227, 0.48410305208404436, 0.6147550434868216, 0.10935095115159867, -0.6842344511401249, -1.4339538860300631, -1.8954227359103173, -1.9763177662518263, -1.7144557641580498, -1.2371448841521084, -0.7164679883793622, -0.29484855537424726, -0.045981525805093834, 0.03483787303409061, 0.017516521688162347, 0.0008569476026488377, 0.07052209080188486, 0.2665797767874543, 0.5684690370974087, 0.9073245783911827, 1.1896236073132542, 1.3279540907510092, 1.2811094309679705, 1.0586576909351264, 0.7164732703083145, 0.34585110324762974, 0.03471812814668341, -0.15797161122149572, -0.21618824184806235, -0.16937547605731826, -0.07636037242432468, -0.0006267259649156335, 0.014285585508966244, -0.03921496335809517, -0.1327925478218363, -0.2159047510395137, -0.23830629762235853, -0.17828887164558038, -0.053979312446373016, 0.07607597785256759, 0.1280301852494201, 0.024806908928635667, -0.2760043130414, -0.7567643163011819, -1.3363699699597134, -1.8884889443271005, -2.275823924096612, -2.3891347610458684, -2.1843829228423086, -1.7083245059127066, -1.0825708110001642, -0.47563646924138525, -0.059978721506329144, 0.0451519059606822, -0.19004227264606502, -0.6955298635667144, -1.315964175542924, -1.849535433289852, -2.1161495948223057, -2.0035992464539034, -1.498410127387632, -0.7069998710664769, 0.1812326733594019, 0.9460041685139123, 1.3920883772947932, 1.4033145284322028, 0.9757674575401495, 0.21639361083443606, -0.6911238556284728, -1.531615231514745, -2.1272149686221478, -2.372330534975617, -2.2510607029773118, -1.8481131516136755, -1.2993280878976534, -0.7490688317070681, -0.3168987314057368, -0.06073295485481719, 0.026937572367502386, 0.0018186797722801497, -0.06081438138657275, -0.09765784855967094, -0.07985509526718707, -0.017064249751118102, 0.05415949239542962, 0.09473570213635796, 0.08529150960317464, 0.038120779767067174, -0.005862318442229372, -0.0011215666353468817, 0.07325063168688843, 0.18652429366067122, 0.24727750690754377, 0.11786154092488527, -0.34579702687865005, -1.2399952575750703, -2.5642594325116916, -4.198575734357136, -5.901847147164011, -7.353364158070479, -8.261591813816533, -8.410054496302863, -7.721361683188478, -6.3416630543477055, -4.5559394887036015, -2.724525441479832, -1.2211184354640752, -0.2911620673154009, 0.0032046305409140653, -0.21211245083479005, -0.6649208719665275, -1.0394702262304725, -1.0960352168650669, -0.7603722916604867, -0.16566727635035344, 0.37208544595207266, 0.4717284005173644, -0.17584457402040266, -1.6757056672852806, -3.838452367684935, -6.1849784477166745, -8.072037264836764, -8.86585124776068, -8.146573741742557, -5.928018271283187, -2.708439933921757, 0.58251655488961, 2.754659628246116, 2.6633737311059833, -0.4799678089395817, -6.848542952514438, -15.875530467306556, -26.292912549014872, -36.44075816582776, -44.54299190860458, -49.07324213244541, -49.28999302775844, -45.21207921002385, -37.60576040579229, -27.982615706723042, -18.040756185227803, -9.305457320874135, -2.8847033809259615, 0.8129270145774902, 2.0630832786316264, 1.6434380918482445, 0.5493393580479814, -0.32460056592905584, -0.44090918248270633, 0.265725824057445, 1.425168279569843, 2.429276989673381, 2.673152364622104, 1.784966075094464, -0.19158390180836152, -2.8265943737803463, -5.419273975188369, -7.225004703772119, -7.7240521521255125, -6.771679775910092, -4.646879263514351, -1.962863018657808, 0.49376856146000164, 1.9707318602932198, 2.1300178587878107, 1.2707079545592812, 0.07790855698664091], 'positive_zeros': ['1.77032488513779722631352986231313', '2.24338659035128487223618747892452', '2.62880618758018956896955195938793', '3.28119770158828625991758593167251', '3.38906630830624826018373564927075', '3.88389667724099926371167586354224', '4.33624233421165427434713181342606', '5.03349903961452732989646293771647', '5.33168575139771341337615999556873', '6.08919808199730248833364214430723', '6.15727997045441429553088009993448', '6.60715229393566145156603212876881', '6.77147420273669735592495256262944', '6.97061081252628895073866007095140', '7.30710961509607260717210449096351', '8.104237365947781713185799950728250', '8.235074095051633705064262081961515', '8.237344083068515574965918741796989', '8.584188880922512527585273430603028', '8.658101307100522332694649716854954', '9.395386306719266426829043607877564', '9.632150176985009153552023325162979', '9.718630081459298121388729713651045', '10.19217144077825042623485694715495', '10.40084940776631647005763218700698', '10.47237483429772476526265485732630', '10.92210227927171637397655718039865'], 'prelabel': '6-418e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.826950137384576, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 1607218763882623315, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.77032488513779722631352986231', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24338659035128487223618747892', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.62880618758018956896955195939', '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': 37.18434761548858, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 73034632, 'conductor_radical': 418, 'degree': 6, 'dirichlet_coefficients': [1, -3, 0, 6, -3, 0, -6, -10, -3, 9, -3, 0, 0, 18, 0, 15, -9, 9, -3, -18, 0, 9, -15, 0, 3, 0, 3, -36, 6, 0, -3, -21, 0, 27, 18, -18, -6, 9, 0, 30, -9, 0, -21, -18, 9, 45, -12, 0, 21, -9, 0, 0, -9, -9, 9, 60, 0, -18, -3, 0, 24, 9, 18, 28, 0, 0, 0, -54, 0, -54, 21, 30, -3, 18, 0, -18, 18, 0, -6, -45, 0, 27, -33, 0, 27, 63, 0, 30, 6, -27, 0, -90, 0, 36, 9, 0, 12, -63, 9, 18], 'euler11': [1, 3, 3, 1, 0, 0, 0], 'euler13': [1, 0, 21, -29, 273, 0, 2197], 'euler17': [1, 9, 69, 302, 1173, 2601, 4913], 'euler19': [1, 3, 3, 1, 0, 0, 0], 'euler2': [1, 3, 3, 1, 0, 0, 0], 'euler23': [1, 15, 135, 766, 3105, 7935, 12167], 'euler29': [1, -6, 63, -201, 1827, -5046, 24389], 'euler3': [1, 0, 3, -3, 9, 0, 27], 'euler31': [1, 3, 42, 52, 1302, 2883, 29791], 'euler37': [1, 6, 87, 348, 3219, 8214, 50653], 'euler41': [1, 9, 78, 616, 3198, 15129, 68921], 'euler43': [1, 21, 222, 1622, 9546, 38829, 79507], 'euler47': [1, 12, 81, 456, 3807, 26508, 103823], 'euler5': [1, 3, 6, 12, 30, 75, 125], 'euler53': [1, 9, 69, 502, 3657, 25281, 148877], 'euler59': [1, 3, 153, 290, 9027, 10443, 205379], 'euler61': [1, -24, 339, -3120, 20679, -89304, 226981], 'euler67': [1, 0, 105, 123, 7035, 0, 300763], 'euler7': [1, 6, 15, 27, 105, 294, 343], 'euler71': [1, -21, 216, -1676, 15336, -105861, 357911], 'euler73': [1, 3, 213, 426, 15549, 15987, 389017], 'euler79': [1, 6, 105, 4, 8295, 37446, 493039], 'euler83': [1, 33, 594, 6582, 49302, 227337, 571787], 'euler89': [1, -6, 231, -924, 20559, -47526, 704969], 'euler97': [1, -12, 195, -2072, 18915, -112908, 912673], 'euler_factors': [[1, 3, 3, 1, 0, 0, 0], [1, 0, 3, -3, 9, 0, 27], [1, 3, 6, 12, 30, 75, 125], [1, 6, 15, 27, 105, 294, 343], [1, 3, 3, 1, 0, 0, 0], [1, 0, 21, -29, 273, 0, 2197], [1, 9, 69, 302, 1173, 2601, 4913], [1, 3, 3, 1, 0, 0, 0], [1, 15, 135, 766, 3105, 7935, 12167], [1, -6, 63, -201, 1827, -5046, 24389], [1, 3, 42, 52, 1302, 2883, 29791], [1, 6, 87, 348, 3219, 8214, 50653], [1, 9, 78, 616, 3198, 15129, 68921], [1, 21, 222, 1622, 9546, 38829, 79507], [1, 12, 81, 456, 3807, 26508, 103823], [1, 9, 69, 502, 3657, 25281, 148877], [1, 3, 153, 290, 9027, 10443, 205379], [1, -24, 339, -3120, 20679, -89304, 226981], [1, 0, 105, 123, 7035, 0, 300763], [1, -21, 216, -1676, 15336, -105861, 357911], [1, 3, 213, 426, 15549, 15987, 389017], [1, 6, 105, 4, 8295, 37446, 493039], [1, 33, 594, 6582, 49302, 227337, 571787], [1, -6, 231, -924, 20559, -47526, 704969], [1, -12, 195, -2072, 18915, -112908, 912673]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/418/2/a/g'], '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': '6-418e3-1.1-c1e3-0-1', '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}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-418e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.826950137384576, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1607218763882623315, 'z1': {'__RealLiteral__': 0, 'data': '1.77032488513779722631352986231', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '2244153403243899925604401226505,2843830357802767257902729835667,3332407741569710718060250687525', 'Lhash_array': ['2244153403243899925604401226505', '2843830357802767257902729835667', '3332407741569710718060250687525'], 'label': '6-418e3-1.1-c1e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/418/2/a/g'}