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lfunc_lfunctions • Show schema
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{'Lhash': '1763934506680890081171007107023,1897857741507336815641528618453', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3879.2111500809283, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -2, 1]], [5, [1]], [13, [1, 2, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '7800.1', 'coefficient_field': '1.1.1.1', 'conductor': 60840000, 'conductor_radical': 390, 'degree': 4, 'euler_factors': [[1], [1, -2, 1], [1], [1, 0, 11, 0, 49], [1, 0, 19, 0, 121], [1, 2, 1], [1, 2, 23, 34, 289], [1, 0, 26, 0, 361], [1, 4, 50, 92, 529], [1, 6, 19, 174, 841], [1, 8, 51, 248, 961], [1, -8, 78, -296, 1369], [1, 12, 106, 492, 1681], [1, 4, 42, 172, 1849], [1, 4, 23, 188, 2209], [1, -10, 83, -530, 2809], [1, 0, 115, 0, 3481], [1, 18, 191, 1098, 3721], [1, 12, 167, 804, 4489], [1, 8, 50, 568, 5041], [1, 0, 134, 0, 5329], [1, -28, 354, -2212, 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'1.49714577594618275039195659692576', '2.21420271529053899329789591262011', '2.29206969083974955684692140418309', '3.06265860163795337941528915294181', '3.18157302446985698821435014933151', '3.79553154389294020237737901573845', '3.90137553403901883946351988471101', '4.53942545429798153325837382976994', '4.70976069931090867610643054847281', '5.25818093304295091329302169153656', '5.47009164199701246073051548576757', '6.16917976653034522961243962018869', '6.21290191906727633118859970872331', '6.87778309291198541974304450250177', '6.93076419460991232522066732014201', '7.48961279535085172827033369350685', '7.81931526795431775030148457717499'], 'prelabel': '4-7800e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 840197678649842600, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39149897169086584558767442574', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.49714577594618275039195659693', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.21420271529053899329789591262', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3879.2111500809283, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 60840000, 'conductor_radical': 390, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, -6, 0, -8, 0, 0, 0, 0, 0, 8, 0, -4, 0, -12, 0, -4, 0, 0, 0, -4, 0, -11, 0, -4, 0, 10, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, -12, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 28, 0, 5, 0, -24, 0, 0, 0, -12, 0, 8, 0, 0, 0, -16, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, 0, 19, 0, 121], 'euler13': [1, 2, 1, 0, 0], 'euler17': [1, 2, 23, 34, 289], 'euler19': [1, 0, 26, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 4, 50, 92, 529], 'euler29': [1, 6, 19, 174, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 8, 51, 248, 961], 'euler37': [1, -8, 78, -296, 1369], 'euler41': [1, 12, 106, 492, 1681], 'euler43': [1, 4, 42, 172, 1849], 'euler47': [1, 4, 23, 188, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -10, 83, -530, 2809], 'euler59': [1, 0, 115, 0, 3481], 'euler61': [1, 18, 191, 1098, 3721], 'euler67': [1, 12, 167, 804, 4489], 'euler7': [1, 0, 11, 0, 49], 'euler71': [1, 8, 50, 568, 5041], 'euler73': [1, 0, 134, 0, 5329], 'euler79': [1, -28, 354, -2212, 6241], 'euler83': [1, 24, 307, 1992, 6889], 'euler89': [1, -8, 146, -712, 7921], 'euler97': [1, -4, 150, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 11, 0, 49], [1, 0, 19, 0, 121], [1, 2, 1, 0, 0], [1, 2, 23, 34, 289], [1, 0, 26, 0, 361], [1, 4, 50, 92, 529], [1, 6, 19, 174, 841], [1, 8, 51, 248, 961], [1, -8, 78, -296, 1369], [1, 12, 106, 492, 1681], [1, 4, 42, 172, 1849], [1, 4, 23, 188, 2209], [1, -10, 83, -530, 2809], [1, 0, 115, 0, 3481], [1, 18, 191, 1098, 3721], [1, 12, 167, 804, 4489], [1, 8, 50, 568, 5041], [1, 0, 134, 0, 5329], [1, -28, 354, -2212, 6241], [1, 24, 307, 1992, 6889], [1, -8, 146, -712, 7921], [1, -4, 150, -388, 9409]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7800/2/a/bc'], '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': '4-7800e2-1.1-c1e2-0-6', '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': 2, 'prelabel': '4-7800e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 840197678649842600, 'z1': {'__RealLiteral__': 0, 'data': '1.39149897169086584558767442574', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1763934506680890081171007107023,1897857741507336815641528618453', 'Lhash_array': ['1763934506680890081171007107023', '1897857741507336815641528618453'], 'label': '4-7800e2-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/bc'}