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lfunc_lfunctions • Show schema
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{'Lhash': '534908398198594778181432443340,1976019931833124200206833667309', 'a10': 1, 'a2': -1, 'a3': 1, 'a4': 0, 'a5': -1, 'a6': -1, 'a7': 0, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 137.78085756426492, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 1]], [3, [1, -1, 1]], [5, [1, 1, 1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1470.1', 'coefficient_field': '1.1.1.1', 'conductor': 2160900, 'conductor_radical': 210, 'degree': 4, 'euler_factors': [[1, 1, 1], [1, -1, 1], [1, 1, 1], [1], [1, 2, -7, 22, 121], [1, -4, 30, -52, 169], [1, -4, -1, -68, 289], [1, 0, -19, 0, 361], [1, 8, 41, 184, 529], [1, 0, 58, 0, 841], [1, -2, -27, -62, 961], [1, 8, 27, 296, 1369], [1, 4, 86, 164, 1681], [1, 4, 90, 172, 1849], [1, 10, 53, 470, 2209], [1, -2, -49, -106, 2809], [1, 4, -43, 236, 3481], [1, -10, 39, -610, 3721], [1, 2, -63, 134, 4489], [1, 24, 286, 1704, 5041], [1, 10, 27, 730, 5329], 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'1.55880487216064039821656358375858', '1.75750546362769892564625976572306', '2.74482973394057912047619159578907', '3.14303702469919046431421656438542', '3.82438806796431671286478404337282', '3.86508951889876980065559246619477', '4.75081773305131912254256728444221', '5.02622196228000690420719415981202', '5.82316499118906002741641061236179', '5.88863237856568533960982210817073', '6.60670607145177418835476222483968', '6.94431194689249343162199815074526', '7.64648976897921049246507904540259', '7.77615168113390262045509967384784', '8.145483186668815280605286638129697', '8.479973754203268523874327020103877', '8.976216198043642749658718548144219', '9.005603816107176656862476784201674', '9.859470346948589495423058948290417'], 'prelabel': '4-1470e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4260778007990744, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 72744388271818481, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42196832321326491726024629919', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.55880487216064039821656358376', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.75750546362769892564625976572', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 137.78085756426492, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 2160900, 'conductor_radical': 210, 'degree': 4, 'dirichlet_coefficients': [1, -1, 1, 0, -1, -1, 0, 1, 0, 1, -2, 0, 4, 0, -1, -1, 4, 0, 0, 0, 0, 2, -8, 1, 0, -4, -1, 0, 0, 1, 2, 0, -2, -4, 0, 0, -8, 0, 4, -1, -4, 0, -4, 0, 0, 8, -10, -1, 0, 0, 4, 0, 2, 1, 2, 0, 0, 0, -4, 0, 10, -2, 0, 1, -4, 2, -2, 0, -8, 0, -24, 0, -10, 8, 0, 0, 0, -4, -16, 1, -1, 4, 32, 0, -4, 4, 0, -2, -14, 0, 0, 0, 2, 10, 0, 0, 12, 0, 0, 0], 'euler11': [1, 2, -7, 22, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, -4, -1, -68, 289], 'euler19': [1, 0, -19, 0, 361], 'euler2': [1, 1, 1, 0, 0], 'euler23': [1, 8, 41, 184, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, -1, 1, 0, 0], 'euler31': [1, -2, -27, -62, 961], 'euler37': [1, 8, 27, 296, 1369], 'euler41': [1, 4, 86, 164, 1681], 'euler43': [1, 4, 90, 172, 1849], 'euler47': [1, 10, 53, 470, 2209], 'euler5': [1, 1, 1, 0, 0], 'euler53': [1, -2, -49, -106, 2809], 'euler59': [1, 4, -43, 236, 3481], 'euler61': [1, -10, 39, -610, 3721], 'euler67': [1, 2, -63, 134, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, 10, 27, 730, 5329], 'euler79': [1, 16, 177, 1264, 6241], 'euler83': [1, -32, 422, -2656, 6889], 'euler89': [1, 14, 107, 1246, 7921], 'euler97': [1, -12, 230, -1164, 9409], 'euler_factors': [[1, 1, 1, 0, 0], [1, -1, 1, 0, 0], [1, 1, 1, 0, 0], [1, 0, 0, 0, 0], [1, 2, -7, 22, 121], [1, -4, 30, -52, 169], [1, -4, -1, -68, 289], [1, 0, -19, 0, 361], [1, 8, 41, 184, 529], [1, 0, 58, 0, 841], [1, -2, -27, -62, 961], [1, 8, 27, 296, 1369], [1, 4, 86, 164, 1681], [1, 4, 90, 172, 1849], [1, 10, 53, 470, 2209], [1, -2, -49, -106, 2809], [1, 4, -43, 236, 3481], [1, -10, 39, -610, 3721], [1, 2, -63, 134, 4489], [1, 24, 286, 1704, 5041], [1, 10, 27, 730, 5329], [1, 16, 177, 1264, 6241], [1, -32, 422, -2656, 6889], [1, 14, 107, 1246, 7921], [1, -12, 230, -1164, 9409]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1470/2/i/g'], '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': '4-1470e2-1.1-c1e2-0-9', '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': '4-1470e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4260778007990744, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 72744388271818481, 'z1': {'__RealLiteral__': 0, 'data': '0.42196832321326491726024629919', 'prec': 103}}
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lfunc_instances • Show schema
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