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lfunc_lfunctions • Show schema
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{'A10': -1, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': -1, 'A9': 0, 'Lhash': '851171895702920844', 'a10': [-0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 290.76725392029056, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [7, [1, -1]], [17, [1]]], 'bad_primes': [2, 3, 7, 17], 'central_character': '36414.1', 'coefficient_field': '1.1.1.1', 'conductor': 36414, 'conductor_radical': 714, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -1, 5], [1, -1], [1, 3, 11], [1, 0, 13], [1], [1, 0, 19], [1, -4, 23], [1, 3, 29], [1, -5, 31], [1, 4, 37], [1, 0, 41], [1, -6, 43], [1, 12, 47], [1, -7, 53], [1, 7, 59], [1, -6, 61], [1, -6, 67], [1, 12, 71], [1, 3, 73], [1, -5, 79], [1, -8, 83], [1, -16, 89], [1, -7, 97]], 'gamma_factors': [[], [0]], 'index': 50, 'label': '2-36414-1.1-c1-0-50', 'leading_term': '4.46376595411', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/36414/bc', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.025781973484322, 1.521712167366005, 1.107616164954779, -0.0908978069336796, -1.264158344242995, -1.416710100989679, -0.3445670761614613, 0.8972724759389522, 0.8639697793484853, -0.6211975183565392, -1.855208157715311, -0.884372443475231, 1.975647450827358, 3.768897625812959, 1.856050084580965, -2.717381393567647, -5.715656589018916, -4.254781850830041, -0.2635089489565923, 1.705817280056839, 0.01337877057098084, -2.202388653019634, -1.441068194407291, 1.326181048390151, 2.129106599820669, -0.2325378915744016, -2.42659252074934, -1.45838594284957, 1.035993741793817, 1.492312935458446, -0.1380132519524781, -0.6866900042538367, 0.8517330648947888, 1.708388277441913, 0.1381493523435805, -1.476167488224627, -0.6034056906390537, 1.076790610359069, 0.5501283070045982, -1.278459127578785, -1.253033641134351, 0.2386654879548965, -0.111621795861731, -2.205952234283406, -2.180271557950522, 0.4446923012007298, 0.9940139762657152, -2.265363069750258, -4.059327681097359, -0.5466451464468576, 3.587833790729022, 2.549925413949313, -0.7168693011531663, 0.2146061886932631, 3.648817091792043, 2.578738977865362, -2.644213157429078, -4.473977544047306, -1.152681633603047, 0.6779053584750278, -1.917228203153943, -3.568294984401832, -1.214970529698692, 0.4655762330640146, -1.530337548114878, -2.863515526752416, -0.444537036775451, 1.827278229581775, 0.8514264787826835, -0.2837657977901426, 0.6546665532835984, 0.7440862491884797, -1.112639395581773, -1.27267770629982, 0.9051979624675865, 1.234508498714263, -0.470645593152321, 0.5636267161376246, 3.951281864369884, 3.772299606505085, 0.02273485696336375, -1.082645449988753, 0.8992395899104105, 0.722217386711879, -0.8918387557567496, 0.7400725164897686, 2.314629764603757, -2.380142004206016, -8.236652876979461, -5.938012180298929, 0.536391901730653, 0.6881586441864126, -3.239991561760074, -1.753013334105312, 3.10398903189228, 2.679266389868487, -1.139671432849624, -1.084845118112708, 0.7435983444933426, -1.010939639193433, -3.027844434429297, -1.016616563561517, 0.9838982716289598, -0.2921408219442145, -0.7966004711343165, 0.8581913196211699, 0.2022173078546164, -2.317406697348423, -1.551660068945732, 1.028389894676379, 0.4899638807934425, -0.7131182080018837, 1.33313639071987, 2.740655147867471, 0.4785789198709723, -0.7299162758905005, 0.7987966825452885, 0.3284744240385498, -0.9581543601566787, 2.470867096249233], 'positive_zeros': ['0.9833536244631855', '1.810354375356201', '2.410748021275531', '3.086241504956990', '3.857599455244869', '4.768399145845441', '5.251226163344540', '5.880410313975523', '6.480841690470668', '7.139041534456677', '7.729335044077277', '8.133250435083169', '8.765535357849614', '9.326678409124175', '9.822730601120129', '10.45136470769689', '10.73311909395726', '11.45774939209453', '11.84731538238784', '12.52637096200448', '13.17762055294939', '13.48333025351543', '14.12684182778217', '14.83601959075487', '15.09831387955213', '15.86443850064189', '16.09804040278058', '16.78388306027704', '17.38076462445058', '17.61654934062159', '18.10979345772794', '18.64974065660343', '19.17019024970371', '19.44784742864355'], 'prelabel': '2-36414-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.05189883620855, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 851171895702920844, 'z1': {'__RealLiteral__': 0, 'data': '0.9833536244631855', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.810354375356201', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.410748021275531', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 290.76725392029056, 'bad_primes': [2, 3, 7, 17], 'central_character': '1.1', 'conductor': 36414, 'conductor_radical': 714, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 1, 0, 1, -1, 0, -1, -3, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 3, 4, 0, -4, 0, 0, 1, -3, 0, 5, -1, 0, 0, 1, 0, -4, 0, 0, -1, 0, 0, 6, -3, 0, -4, -12, 0, 1, 4, 0, 0, 7, 0, -3, -1, 0, 3, -7, 0, 6, -5, 0, 1, 0, 0, 6, 0, 0, -1, -12, 0, -3, 4, 0, 0, -3, 0, 5, 1, 0, 0, 8, 0, 0, -6, 0, 3, 16, 0, 0, 4, 0, 12, 0, 0, 7, -1, 0, -4], 'euler11': [1, 3, 11], 'euler13': [1, 0, 13], 'euler17': [1, 0, 0], 'euler19': [1, 0, 19], 'euler2': [1, 1, 0], 'euler23': [1, -4, 23], 'euler29': [1, 3, 29], 'euler3': [1, 0, 0], 'euler31': [1, -5, 31], 'euler37': [1, 4, 37], 'euler41': [1, 0, 41], 'euler43': [1, -6, 43], 'euler47': [1, 12, 47], 'euler5': [1, -1, 5], 'euler53': [1, -7, 53], 'euler59': [1, 7, 59], 'euler61': [1, -6, 61], 'euler67': [1, -6, 67], 'euler7': [1, -1, 0], 'euler71': [1, 12, 71], 'euler73': [1, 3, 73], 'euler79': [1, -5, 79], 'euler83': [1, -8, 83], 'euler89': [1, -16, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -1, 5], [1, -1, 0], [1, 3, 11], [1, 0, 13], [1, 0, 0], [1, 0, 19], [1, -4, 23], [1, 3, 29], [1, -5, 31], [1, 4, 37], [1, 0, 41], [1, -6, 43], [1, 12, 47], [1, -7, 53], [1, 7, 59], [1, -6, 61], [1, -6, 67], [1, 12, 71], [1, 3, 73], [1, -5, 79], [1, -8, 83], [1, -16, 89], [1, -7, 97]], 'index': 50, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/36414/bc'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-36414-1.1-c1-0-50', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-36414-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.05189883620855, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 851171895702920844, 'z1': {'__RealLiteral__': 0, 'data': '0.9833536244631855', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '851171895702920844', 'Lhash_array': ['851171895702920844'], 'label': '2-36414-1.1-c1-0-50', 'type': 'ECQ', 'url': 'EllipticCurve/Q/36414/bc'}