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lfunc_lfunctions • Show schema
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{'Lhash': '566993141754059746488967604117', 'a10': [-2.1631201090664947, 6.732080762569041], 'a2': [0, 1.4142135623730951], 'a3': [0, -1.7320508075688772], 'a4': [-2.0, 0], 'a5': [4.760299958708073, 1.5295568976419025], 'a6': [2.449489742783178, 0], 'a7': [-5.009865789591656, 0], 'a8': [0, -2.8284271247461903], 'a9': [-3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.80113824086049, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.4142135623730951]]], [3, [[1.0, 0], [0, 1.7320508075688772]]], [5, [[1.0, 0], [-4.760299958708073, -1.5295568976419025]]], [23, [[1.0, 0], [-19.008557385706307, -12.948928377063105]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '690.229', 'coefficient_field': 'CDF', 'conductor': 690, 'conductor_radical': 690, 'conjugate': '1909391650826210586708719821718', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.4142135623730951]], [[1.0, 0], [0, 1.7320508075688772]], 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{'__RealLiteral__': 0, 'data': '-0.35534358366264895', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44727872305821303695449044013', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17643510937532580081758905230', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.12024716400771596178435444368', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.80113824086049, 'bad_primes': [2, 3, 5, 23], 'central_character': '115.114', 'conductor': 690, 'conductor_radical': 690, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/690/3/f/a/229/28'], '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': '2-690-115.114-c2-0-12', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-690-115.114-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.336027933588585, 'root_angle': -0.35534358366264895, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44727872305821303695449044013', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '566993141754059746488967604117', 'Lhash_array': ['566993141754059746488967604117'], 'label': '2-690-115.114-c2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/690/3/f/a/229/28'}