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lfunc_lfunctions • Show schema
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{'Lhash': '470717829120750748380151845804,1987572389794727200964831660365', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 583.0660943780811, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 4, 7]]], 'bad_primes': [2, 3, 7], 'central_character': '3024.1', 'coefficient_field': '1.1.1.1', 'conductor': 9144576, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -7, 0, 25], [1, 4, 7], [1, 0, -10, 0, 121], [1, 0, -14, 0, 169], [1, 0, -7, 0, 289], [1, -4, 42, -76, 361], [1, 0, 2, 0, 529], [1, -12, 94, -348, 841], [1, -20, 162, -620, 961], [1, 22, 195, 814, 1369], [1, 0, -79, 0, 1681], [1, 0, -59, 0, 1849], [1, 18, 175, 846, 2209], [1, 24, 250, 1272, 2809], [1, 6, 127, 354, 3481], [1, 0, -110, 0, 3721], [1, 0, -122, 0, 4489], [1, 0, 50, 0, 5041], [1, 0, -98, 0, 5329], [1, 0, -11, 0, 6241], [1, 30, 391, 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'4.47954177623568957934762654333740', '4.53405262126083068144133957227450', '5.16103961017549742741081044620207', '5.23722392792882955840296559325769', '6.21591285797117636573162204165607', '6.34139643759429109096478155327536', '6.56413915701137997547852606465888', '6.90651622641196042568144878752540', '7.24724739595439216965252383462265', '7.948871936717258972109326072486233', '8.323066746112530379837904426300752', '8.366494203928348143144652794565551', '9.200042275059527863904609124796270'], 'prelabel': '4-3024e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.9139354463846185, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 948270359762628295, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37133089278386498690006053141', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.27100993785628968955229239785', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.56791815460575822623627054338', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 583.0660943780811, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 9144576, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 7, 0, 0, 0, 12, 0, 20, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, 9, 0, 0, 0, -24, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, 0, -14, 0, 169], 'euler17': [1, 0, -7, 0, 289], 'euler19': [1, -4, 42, -76, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 2, 0, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -20, 162, -620, 961], 'euler37': [1, 22, 195, 814, 1369], 'euler41': [1, 0, -79, 0, 1681], 'euler43': [1, 0, -59, 0, 1849], 'euler47': [1, 18, 175, 846, 2209], 'euler5': [1, 0, -7, 0, 25], 'euler53': [1, 24, 250, 1272, 2809], 'euler59': [1, 6, 127, 354, 3481], 'euler61': [1, 0, -110, 0, 3721], 'euler67': [1, 0, -122, 0, 4489], 'euler7': [1, 4, 7, 0, 0], 'euler71': [1, 0, 50, 0, 5041], 'euler73': [1, 0, -98, 0, 5329], 'euler79': [1, 0, -11, 0, 6241], 'euler83': [1, 30, 391, 2490, 6889], 'euler89': [1, 0, -130, 0, 7921], 'euler97': [1, 0, 106, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -7, 0, 25], [1, 4, 7, 0, 0], [1, 0, -10, 0, 121], [1, 0, -14, 0, 169], [1, 0, -7, 0, 289], [1, -4, 42, -76, 361], [1, 0, 2, 0, 529], [1, -12, 94, -348, 841], [1, -20, 162, -620, 961], [1, 22, 195, 814, 1369], [1, 0, -79, 0, 1681], [1, 0, -59, 0, 1849], [1, 18, 175, 846, 2209], [1, 24, 250, 1272, 2809], [1, 6, 127, 354, 3481], [1, 0, -110, 0, 3721], [1, 0, -122, 0, 4489], [1, 0, 50, 0, 5041], [1, 0, -98, 0, 5329], [1, 0, -11, 0, 6241], [1, 30, 391, 2490, 6889], [1, 0, -130, 0, 7921], [1, 0, 106, 0, 9409]], 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3024/2/b/e'], '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': '4-3024e2-1.1-c1e2-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-3024e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.9139354463846185, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 948270359762628295, 'z1': {'__RealLiteral__': 0, 'data': '0.37133089278386498690006053141', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '470717829120750748380151845804,1987572389794727200964831660365', 'Lhash_array': ['470717829120750748380151845804', '1987572389794727200964831660365'], 'factors': ['2-3024-28.27-c1-0-10', '2-3024-28.27-c1-0-54'], 'label': '4-3024e2-1.1-c1e2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3024/2/b/e'}