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lfunc_lfunctions • Show schema
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{'Lhash': '3300375981068483329941692078228', 'a10': [1321.1092350094748, 1.4912693262153662e-58], 'a2': [4.898979485566356, 2.8284271247461903], 'a3': [-14.94083718496778, -22.489361578583864], 'a4': [16.0, 27.712812921102035], 'a5': [202.25272001573995, -116.77066234542148], 'a6': [-9.585334559252745, -152.43399017734592], 'a7': [95.57516899365294, -165.54104863898849], 'a8': [0.0, 181.01933598375618], 'a9': [-282.5427684245681, 672.019779478983], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.140973505157318, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-4.898979485566356, -2.8284271247461903]]], [3, [[1.0, 0], [14.94083718496778, 22.489361578583864]]]], 'bad_primes': [2, 3], 'central_character': '18.11', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '2091589865044225362010400339289', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.898979485566356, -2.8284271247461903]], 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'positive_zeros': ['2.60353758399536868074866720700419', '5.12952550875453119040663468064492', '6.34625458706468386567629492009404', '9.623049250838380313456543442972442', '10.47026477636543706282173826006145', '11.87379381084840535983161764828520', '13.70063761268388598062152130671762', '14.66190269839696483640443271229040', '15.99699330801760358346650753135227', '17.69116123045969451275203970485768'], 'prelabel': '2-18-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0349382067171766, 'root_angle': 0.1822430184708421, 'root_number': '0.840531210094048 + 0.5417631261518593*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0911215092354', 'prec': 50}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.60353758399536868074866720700', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.12952550875453119040663468064', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.34625458706468386567629492009', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.140973505157318, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/7/d/a/11/5'], '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': '2-18-9.2-c6-0-5', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-18-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0349382067171766, 'root_angle': 0.09112150923542105, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '2.60353758399536868074866720700', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3300375981068483329941692078228', 'Lhash_array': ['3300375981068483329941692078228'], 'label': '2-18-9.2-c6-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/7/d/a/11/5'}