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lfunc_lfunctions • Show schema
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{'Lhash': '271988098083283951742873776203', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -10.0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 7.0], 'a8': [0, 0], 'a9': [-73.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.30133700401845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -7.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '700.449', 'coefficient_field': 'CDF', 'conductor': 700, 'conductor_radical': 70, 'conjugate': '1334770699608794148815536447352', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 10.0], [-27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -7.0]], [[1.0, 0], [40.0, 0], [1331.0, 0]], [[1.0, 0], [0, 12.0], [-2197.0, 0]], [[1.0, 0], [0, -58.0], [-4913.0, 0]], [[1.0, 0], [26.0, 0], [6859.0, 0]], [[1.0, 0], [0, 64.0], [-12167.0, 0]], [[1.0, 0], [-62.0, 0], [24389.0, 0]], [[1.0, 0], [-252.0, 0], [29791.0, 0]], 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'10.17303113598695881277814355868991'], 'prelabel': '2-700-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.426611626978749, 'root_angle': -0.14758361765043326, 'root_number': '0.89442719099991587856366946749251049417624734384461028971 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07379180882521663', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.21456077726332072415174863030', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59870392667337996769121661753', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51519055349033545532931939871', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.30133700401845, 'bad_primes': [2, 5, 7], 'central_character': '5.4', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/700/4/e/a/449/1'], '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': '2-700-5.4-c3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-700-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.426611626978749, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.21456077726332072415174863030', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '271988098083283951742873776203', 'Lhash_array': ['271988098083283951742873776203'], 'label': '2-700-5.4-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/4/e/a/449/1'}