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lfunc_lfunctions • Show schema
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{'Lhash': '218623368024611115849730030940,2029452061717381041029763276061', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 167.334019432485, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.1', 'coefficient_field': '1.1.1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1], [1, 1, 1], [1, -1, -6, -7, 49], [1, 6, 25, 66, 121], [1, -1, -12, -13, 169], [1, 0, 34, 0, 289], [1, 2, 39, 38, 361], [1, 6, 13, 138, 529], [1, 6, 7, 174, 841], [1, 8, 33, 248, 961], [1, 14, 123, 518, 1369], [1, -6, -5, -246, 1681], [1, -4, -27, -172, 1849], [1, 12, 97, 564, 2209], [1, 12, 142, 636, 2809], [1, 0, -59, 0, 3481], [1, 11, 60, 671, 3721], [1, -7, -18, -469, 4489], [1, 12, 178, 852, 5041], [1, -22, 267, -1606, 5329], [1, -1, -78, -79, 6241], 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'2.62541077174039872468217678731938', '3.13249868820268966518145681600620', '3.74908654342524861089860561508051', '4.04850110351683053181922841005740', '4.62823457667509550779019639423095', '5.19800022816892829605052492417292', '5.50128365907402003025237188559988', '5.70196077856203051079475351937324', '6.59004112898116291910758319678707', '6.63058003134488918092079384720992', '7.47101832687215880270867037410441', '7.66239061326064564193665794442017', '7.949043532999002027245448905818384', '8.243469341778876319583538226088491', '8.949883376218103070743808538598863', '8.961076822919021374393900967243200', '9.684165220106962423030180721426242'], 'prelabel': '4-1620e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.596632470443349, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1223256299254087203, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.17246342800236113239458994900', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.60095539050902192641329435932', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.91731612969935062924872538576', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 167.334019432485, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -6, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -6, 0, 0, 0, 0, 0, -6, 0, -8, 0, 0, 0, -1, 0, -14, 0, 0, 0, 6, 0, 4, 0, 0, 0, -12, 0, 7, 0, 0, 0, -12, 0, 6, 0, 0, 0, 0, 0, -11, 0, 0, 0, -1, 0, 7, 0, 0, 0, -12, 0, 22, 0, 0, 0, -6, 0, 1, 0, 0, 0, -6, 0, 0, 0, 0, 0, -24, 0, 1, 0, 0, 0, 2, 0, 13, 0, 0, 0], 'euler11': [1, 6, 25, 66, 121], 'euler13': [1, -1, -12, -13, 169], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, 2, 39, 38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 6, 13, 138, 529], 'euler29': [1, 6, 7, 174, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 33, 248, 961], 'euler37': [1, 14, 123, 518, 1369], 'euler41': [1, -6, -5, -246, 1681], 'euler43': [1, -4, -27, -172, 1849], 'euler47': [1, 12, 97, 564, 2209], 'euler5': [1, 1, 1, 0, 0], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, 11, 60, 671, 3721], 'euler67': [1, -7, -18, -469, 4489], 'euler7': [1, -1, -6, -7, 49], 'euler71': [1, 12, 178, 852, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, -1, -78, -79, 6241], 'euler83': [1, 6, -47, 498, 6889], 'euler89': [1, 24, 322, 2136, 7921], 'euler97': [1, -13, 72, -1261, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 1, 1, 0, 0], [1, -1, -6, -7, 49], [1, 6, 25, 66, 121], [1, -1, -12, -13, 169], [1, 0, 34, 0, 289], [1, 2, 39, 38, 361], [1, 6, 13, 138, 529], [1, 6, 7, 174, 841], [1, 8, 33, 248, 961], [1, 14, 123, 518, 1369], [1, -6, -5, -246, 1681], [1, -4, -27, -172, 1849], [1, 12, 97, 564, 2209], [1, 12, 142, 636, 2809], [1, 0, -59, 0, 3481], [1, 11, 60, 671, 3721], [1, -7, -18, -469, 4489], [1, 12, 178, 852, 5041], [1, -22, 267, -1606, 5329], [1, -1, -78, -79, 6241], [1, 6, -47, 498, 6889], [1, 24, 322, 2136, 7921], [1, -13, 72, -1261, 9409]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/2/i/d'], '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': '4-1620e2-1.1-c1e2-0-0', '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': '4-1620e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.596632470443349, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1223256299254087203, 'z1': {'__RealLiteral__': 0, 'data': '0.17246342800236113239458994900', 'prec': 103}}
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{'Lhash': '218623368024611115849730030940,2029452061717381041029763276061', 'Lhash_array': ['218623368024611115849730030940', '2029452061717381041029763276061'], 'label': '4-1620e2-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/2/i/d'}