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lfunc_lfunctions • Show schema
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{'Lhash': '425811624379238763953679826447,1408441236397656189990173554614', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 517.8976424479346, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [3, [1, 0, 1]], [5, [1]], [19, [1, 2, 1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '2850.1', 'coefficient_field': '1.1.1.1', 'conductor': 8122500, 'conductor_radical': 570, 'degree': 4, 'euler_factors': [[1, 0, 1], [1, 0, 1], [1], [1, 0, -10, 0, 49], [1, 4, 26, 44, 121], [1, 0, -26, 0, 169], [1, 0, -30, 0, 289], [1, 2, 1], [1, 0, 18, 0, 529], [1, 0, 58, 0, 841], [1, 0, 62, 0, 961], [1, 0, -58, 0, 1369], [1, 16, 146, 656, 1681], [1, 0, -50, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, -6, 0, 2809], [1, -16, 182, -944, 3481], [1, -4, 126, -244, 3721], [1, 0, -134, 0, 4489], [1, -16, 206, -1136, 5041], [1, 0, -142, 0, 5329], [1, -16, 222, 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'5.51328388472852407928465851005654', '5.67031966948073120559224563016656', '6.45105118184684078240211004390329', '6.69225628771676496979331775382166', '7.02853815781715657927744891689713', '7.54983137185411787538601788227610', '7.999880118589760327918723378290735', '8.259742304248469417798217552968563', '8.466966762762631626376120802926507', '9.109135943420475501148330172575990'], 'prelabel': '4-2850e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.770467961957707, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 140485977921149524, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33590614346143575041293761890', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.11106422869525614238707343327', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.93527283066148369654845880233', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 517.8976424479346, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 8122500, 'conductor_radical': 570, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, 0, 0, -1, 0, -4, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -16, 0, 0, 4, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 4, 0, 0, -1, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 2, 0, 0, 16, 0, 1, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, 0, -26, 0, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, 2, 1, 0, 0], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, 0, 18, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 0, -58, 0, 1369], 'euler41': [1, 16, 146, 656, 1681], 'euler43': [1, 0, -50, 0, 1849], 'euler47': [1, 0, -30, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -6, 0, 2809], 'euler59': [1, -16, 182, -944, 3481], 'euler61': [1, -4, 126, -244, 3721], 'euler67': [1, 0, -134, 0, 4489], 'euler7': [1, 0, -10, 0, 49], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, 0, -142, 0, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 0, 90, 0, 6889], 'euler89': [1, 32, 434, 2848, 7921], 'euler97': [1, 0, -130, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 0], [1, 0, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, -10, 0, 49], [1, 4, 26, 44, 121], [1, 0, -26, 0, 169], [1, 0, -30, 0, 289], [1, 2, 1, 0, 0], [1, 0, 18, 0, 529], [1, 0, 58, 0, 841], [1, 0, 62, 0, 961], [1, 0, -58, 0, 1369], [1, 16, 146, 656, 1681], [1, 0, -50, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, -6, 0, 2809], [1, -16, 182, -944, 3481], [1, -4, 126, -244, 3721], [1, 0, -134, 0, 4489], [1, -16, 206, -1136, 5041], [1, 0, -142, 0, 5329], [1, -16, 222, -1264, 6241], [1, 0, 90, 0, 6889], [1, 32, 434, 2848, 7921], [1, 0, -130, 0, 9409]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2850/2/d/n'], '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': '4-2850e2-1.1-c1e2-0-5', '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': '4-2850e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.770467961957707, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 140485977921149524, 'z1': {'__RealLiteral__': 0, 'data': '0.33590614346143575041293761890', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '425811624379238763953679826447,1408441236397656189990173554614', 'Lhash_array': ['425811624379238763953679826447', '1408441236397656189990173554614'], 'label': '4-2850e2-1.1-c1e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2850/2/d/n'}