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lfunc_lfunctions • Show schema
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{'Lhash': '1434244718728668343779772638795,2121863182239797431943375055488', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': 25, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12199.550537224195, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1, 26, 169]]], 'bad_primes': [2, 3, 13], 'central_character': '1872.1', 'coefficient_field': '1.1.1.1', 'conductor': 3504384, 'conductor_radical': 78, 'degree': 4, 'euler_factors': [[1], [1], [1, -3, 88, -375, 15625], [1, -25, 824, -8575, 117649], [1, 56, 3154, 74536, 1771561], [1, 26, 169], [1, -13, 3280, -63869, 24137569], [1, -124, 16394, -850516, 47045881], [1, 172, 29102, 2092724, 148035889], [1, 196, 53710, 4780244, 594823321], [1, -78, 40006, -2323698, 887503681], [1, -161, 35352, -8155133, 2565726409], [1, 234, 40498, 16127514, 4750104241], [1, 135, 12442, 10733445, 6321363049], [1, 237, 221232, 24606051, 10779215329], [1, 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'4.63057170273788552177578929989244', '5.17570063661038346643307938354677', '5.23525270373015295894163574208479', '5.89098509069072670520825994336555', '6.07819600951342864751100577777377', '6.76002197705200091642272714306565', '7.27464702160173075250566866599976', '7.80396932831637635643053594073285', '7.81400889849141200233362729283835', '8.087206963869121225972023405634895', '8.476366516958382200284847045201492'], 'prelabel': '4-1872e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.509594451297657, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 2156640724853796625, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13141958712475277380742238075', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.67385491069682334192302001204', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.05741504857799731794972447230', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 12199.550537224195, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 3504384, 'conductor_radical': 78, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 3, 0, 25, 0, 0, 0, -56, 0, -26, 0, 0, 0, 13, 0, 124, 0, 0, 0, -172, 0, -79, 0, 0, 0, -196, 0, 78, 0, 0, 0, 75, 0, 161, 0, 0, 0, -234, 0, -135, 0, 0, 0, -237, 0, -199, 0, 0, 0, -666, 0, -168, 0, 0, 0, 136, 0, -146, 0, 0, 0, -78, 0, 4, 0, 0, 0, -563, 0, -1480, 0, 0, 0, -1400, 0, 896, 0, 0, 0, 1902, 0, 39, 0, 0, 0, 272, 0, -650, 0, 0, 0, 372, 0, -2160, 0, 0, 0], 'euler11': [1, 56, 3154, 74536, 1771561], 'euler13': [1, 26, 169, 0, 0], 'euler17': [1, -13, 3280, -63869, 24137569], 'euler19': [1, -124, 16394, -850516, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 172, 29102, 2092724, 148035889], 'euler29': [1, 196, 53710, 4780244, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -78, 40006, -2323698, 887503681], 'euler37': [1, -161, 35352, -8155133, 2565726409], 'euler41': [1, 234, 40498, 16127514, 4750104241], 'euler43': [1, 135, 12442, 10733445, 6321363049], 'euler47': [1, 237, 221232, 24606051, 10779215329], 'euler5': [1, -3, 88, -375, 15625], 'euler53': [1, 666, 406818, 99152082, 22164361129], 'euler59': [1, -136, 57682, -27931544, 42180533641], 'euler61': [1, 146, 457466, 33139226, 51520374361], 'euler67': [1, -4, 526778, -1203052, 90458382169], 'euler7': [1, -25, 824, -8575, 117649], 'euler71': [1, 563, 787016, 201503893, 128100283921], 'euler73': [1, 1480, 1311326, 575745160, 151334226289], 'euler79': [1, -896, 1176270, -441762944, 243087455521], 'euler83': [1, -1902, 2047318, -1087538874, 326940373369], 'euler89': [1, -272, 341902, -191751568, 496981290961], 'euler97': [1, 2160, 2346718, 1971373680, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -3, 88, -375, 15625], [1, -25, 824, -8575, 117649], [1, 56, 3154, 74536, 1771561], [1, 26, 169, 0, 0], [1, -13, 3280, -63869, 24137569], [1, -124, 16394, -850516, 47045881], [1, 172, 29102, 2092724, 148035889], [1, 196, 53710, 4780244, 594823321], [1, -78, 40006, -2323698, 887503681], [1, -161, 35352, -8155133, 2565726409], [1, 234, 40498, 16127514, 4750104241], [1, 135, 12442, 10733445, 6321363049], [1, 237, 221232, 24606051, 10779215329], [1, 666, 406818, 99152082, 22164361129], [1, -136, 57682, -27931544, 42180533641], [1, 146, 457466, 33139226, 51520374361], [1, -4, 526778, -1203052, 90458382169], [1, 563, 787016, 201503893, 128100283921], [1, 1480, 1311326, 575745160, 151334226289], [1, -896, 1176270, -441762944, 243087455521], [1, -1902, 2047318, -1087538874, 326940373369], [1, -272, 341902, -191751568, 496981290961], [1, 2160, 2346718, 1971373680, 832972004929]], 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1872/4/a/bc'], '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': '4-1872e2-1.1-c3e2-0-12', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 2, 'prelabel': '4-1872e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.509594451297657, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 2156640724853796625, 'z1': {'__RealLiteral__': 0, 'data': '1.13141958712475277380742238075', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1434244718728668343779772638795,2121863182239797431943375055488', 'Lhash_array': ['1434244718728668343779772638795', '2121863182239797431943375055488'], 'factors': ['2-1872-1.1-c3-0-57', '2-1872-1.1-c3-0-88'], 'label': '4-1872e2-1.1-c3e2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1872/4/a/bc'}