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lfunc_lfunctions • Show schema
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{'Lhash': '1210926178394354946617682437211', 'a10': [-3779.6182881346786, -6546.490908265767], 'a2': [-8.0, 13.856406460551018], 'a3': [0, 0], 'a4': [-128.0, -221.70250336881628], 'a5': [-236.2261430084174, 409.1556817666104], 'a6': [0, 0], 'a7': [-844.6470480868478, 6296.044660273478], 'a8': [4096.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.89451535664803, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [8.0, -13.856406460551018]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [844.6470480868478, -6296.044660273478]]]], 'bad_primes': [2, 3, 7], 'central_character': '126.37', 'coefficient_field': 'CDF', 'conductor': 126, 'conductor_radical': 42, 'conjugate': '159161720153170580315254459491', 'degree': 2, 'euler_factors': [[[1.0, 0], [8.0, -13.856406460551018]], [[1.0, 0], [0, 0]], [[1.0, 0], [236.2261430084174, -409.1556817666104], [-976562.5, -1691455.8667664817]], [[1.0, 0], 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2.3903137814860123, 2.51195771901541, 2.526965635034675], 'positive_zeros': ['0.955252321243991270987312943077203', '2.34681204870527995328068234945616', '3.82855066749489549003060882137442', '4.75851657023038262284010513438494', '6.55825677890249707797629738105001', '7.68441229377767775243515645676465', '8.735720665455917620937790595118801', '9.870858120483074591027749722177195', '10.73568089066266948848652164515895', '11.63243751902703957454846187193201'], 'prelabel': '2-126-7.2-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.055713212164894, 'root_angle': 0.355609850320305, 'root_number': '0.4382178312839733152892985952177464150467859909037125425 + 0.8988688070818628081154152794155908992109156940489613790*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1778049251601525', 'prec': 60}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.955252321243991270987312943077', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.34681204870527995328068234946', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82855066749489549003060882137', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.89451535664803, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 126, 'conductor_radical': 42, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/126/10/g/d/37/2'], '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': '2-126-7.2-c9-0-20', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-126-7.2-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.055713212164894, 'root_angle': 0.1778049251601525, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.955252321243991270987312943077', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1210926178394354946617682437211', 'Lhash_array': ['1210926178394354946617682437211'], 'label': '2-126-7.2-c9-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/126/10/g/d/37/2'}