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lfunc_lfunctions • Show schema
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{'Lhash': '1111516536837003046931102520183,1846337592761721411777488187960', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 6, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 880.4929104244396, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '1089.1', 'coefficient_field': '1.1.1.1', 'conductor': 1185921, 'conductor_radical': 33, 'degree': 4, 'euler_factors': [[1, 0, -6, 0, 16], [1], [1, 0, -18, 0, 625], [1, -2, 99, -98, 2401], [1], [1, -32, 594, -5408, 28561], [1, 0, -450, 0, 83521], [1, -66, 1811, -23826, 130321], [1, 0, -480, 0, 279841], [1, 0, -1520, 0, 707281], [1, -62, 2883, -59582, 923521], [1, 114, 5987, 156066, 1874161], [1, 0, -3120, 0, 2825761], [1, 0, 3698, 0, 3418801], [1, 0, -720, 0, 4879681], [1, 0, 2320, 0, 7890481], [1, 0, -2160, 0, 12117361], [1, -210, 18467, -781410, 13845841], [1, 206, 19587, 924734, 20151121], [1, 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'5.15019612548564688930750614089565', '5.84360145878746044250049397617397', '5.96069484627692619948180969143793', '6.79778640389330186747262637348915', '6.81893965854202978867851421303267', '7.22142900092143141849208689779115', '7.957585860392948710862648915010321', '8.072269743828641353320962854261528', '8.603718318026404854878091153008375', '8.989557462170483258618647923452345', '9.495727103434120399017220993914988', '10.07420051806461618699947572836707'], 'prelabel': '4-33e4-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.447302156924686, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2e2-0', 'trace_hash': 2081904685488120783, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.876831941417362337641165149912', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.45650354476959540702847990280', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.60111092638966518630347977692', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 880.4929104244396, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 1185921, 'conductor_radical': 33, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 6, 0, 0, 2, 0, 0, 0, 0, 0, 32, 0, 0, 20, 0, 0, 66, 0, 0, 0, 0, 0, 18, 0, 0, 12, 0, 0, 62, 0, 0, 0, 0, 0, -114, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -95, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 210, 0, 0, 24, 0, 0, -206, 0, 0, 0, 0, 0, -94, 0, 0, 396, 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, -50, 0, 0, 108], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, -32, 594, -5408, 28561], 'euler17': [1, 0, -450, 0, 83521], 'euler19': [1, -66, 1811, -23826, 130321], 'euler2': [1, 0, -6, 0, 16], 'euler23': [1, 0, -480, 0, 279841], 'euler29': [1, 0, -1520, 0, 707281], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -62, 2883, -59582, 923521], 'euler37': [1, 114, 5987, 156066, 1874161], 'euler41': [1, 0, -3120, 0, 2825761], 'euler43': [1, 0, 3698, 0, 3418801], 'euler47': [1, 0, -720, 0, 4879681], 'euler5': [1, 0, -18, 0, 625], 'euler53': [1, 0, 2320, 0, 7890481], 'euler59': [1, 0, -2160, 0, 12117361], 'euler61': [1, -210, 18467, -781410, 13845841], 'euler67': [1, 206, 19587, 924734, 20151121], 'euler7': [1, -2, 99, -98, 2401], 'euler71': [1, 0, 4030, 0, 25411681], 'euler73': [1, 94, 12867, 500926, 28398241], 'euler79': [1, -46, 13011, -287086, 38950081], 'euler83': [1, 0, -2528, 0, 47458321], 'euler89': [1, 0, -13250, 0, 62742241], 'euler97': [1, 50, 19443, 470450, 88529281], 'euler_factors': [[1, 0, -6, 0, 16], [1, 0, 0, 0, 0], [1, 0, -18, 0, 625], [1, -2, 99, -98, 2401], [1, 0, 0, 0, 0], [1, -32, 594, -5408, 28561], [1, 0, -450, 0, 83521], [1, -66, 1811, -23826, 130321], [1, 0, -480, 0, 279841], [1, 0, -1520, 0, 707281], [1, -62, 2883, -59582, 923521], [1, 114, 5987, 156066, 1874161], [1, 0, -3120, 0, 2825761], [1, 0, 3698, 0, 3418801], [1, 0, -720, 0, 4879681], [1, 0, 2320, 0, 7890481], [1, 0, -2160, 0, 12117361], [1, -210, 18467, -781410, 13845841], [1, 206, 19587, 924734, 20151121], [1, 0, 4030, 0, 25411681], [1, 94, 12867, 500926, 28398241], [1, -46, 13011, -287086, 38950081], [1, 0, -2528, 0, 47458321], [1, 0, -13250, 0, 62742241], [1, 50, 19443, 470450, 88529281]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/3/b/b'], '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': '4-33e4-1.1-c2e2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-33e4-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.447302156924686, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 2081904685488120783, 'z1': {'__RealLiteral__': 0, 'data': '0.876831941417362337641165149912', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1111516536837003046931102520183,1846337592761721411777488187960', 'Lhash_array': ['1111516536837003046931102520183', '1846337592761721411777488187960'], 'label': '4-33e4-1.1-c2e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/3/b/b'}