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lfunc_lfunctions • Show schema
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{'Lhash': '1511131625061389228494009839013,1781233425856096735671882050824', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.911575573494213, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '450.1', 'coefficient_field': '1.1.1.1', 'conductor': 202500, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 0, 1], [1], [1], [1, 0, -10, 0, 49], [1, -12, 58, -132, 121], [1, 0, -10, 0, 169], [1, 0, 2, 0, 289], [1, -8, 54, -152, 361], [1, 0, -46, 0, 529], [1, -12, 94, -348, 841], [1, 8, 78, 248, 961], [1, 0, -10, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, -22, 0, 1849], [1, 0, -94, 0, 2209], [1, 0, -70, 0, 2809], [1, 12, 154, 708, 3481], [1, -4, 126, -244, 3721], [1, 0, -118, 0, 4489], [1, 24, 286, 1704, 5041], [1, 0, -46, 0, 5329], [1, -8, 174, -632, 6241], [1, 0, -22, 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'4.30730624874092149814131848952818', '5.08681591364366779099800787329180', '5.67061075796970096100998333241462', '6.35378265604245827247284872399800', '6.52060427724931337192128274937189', '7.27066054679861735713409817003785', '7.42803712387726107542782245602750', '8.327062825083179742073637693112798', '8.822788090344997879108240222198686', '9.172244035568603665863444619636325', '9.261949268368779885007966893659903', '10.00527370541858331902712317373118', '10.16572437153849807630074510988527', '11.04238032527484228369273696026842', '11.41259106026623354709253200328012'], 'prelabel': '4-450e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8955917521865353, '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': 534751053105437122, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19207266165402611601661331382', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.40514541273076448597784095033', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.82189013550091374750763219830', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.911575573494213, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 202500, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 1, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 4, 0, 0, -1, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, -12, 58, -132, 121], 'euler13': [1, 0, -10, 0, 169], 'euler17': [1, 0, 2, 0, 289], 'euler19': [1, -8, 54, -152, 361], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, 0, -46, 0, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 0, -22, 0, 1849], 'euler47': [1, 0, -94, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -70, 0, 2809], 'euler59': [1, 12, 154, 708, 3481], 'euler61': [1, -4, 126, -244, 3721], 'euler67': [1, 0, -118, 0, 4489], 'euler7': [1, 0, -10, 0, 49], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, 0, -46, 0, 5329], 'euler79': [1, -8, 174, -632, 6241], 'euler83': [1, 0, -22, 0, 6889], 'euler89': [1, 24, 322, 2136, 7921], 'euler97': [1, 0, -190, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -10, 0, 49], [1, -12, 58, -132, 121], [1, 0, -10, 0, 169], [1, 0, 2, 0, 289], [1, -8, 54, -152, 361], [1, 0, -46, 0, 529], [1, -12, 94, -348, 841], [1, 8, 78, 248, 961], [1, 0, -10, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, -22, 0, 1849], [1, 0, -94, 0, 2209], [1, 0, -70, 0, 2809], [1, 12, 154, 708, 3481], [1, -4, 126, -244, 3721], [1, 0, -118, 0, 4489], [1, 24, 286, 1704, 5041], [1, 0, -46, 0, 5329], [1, -8, 174, -632, 6241], [1, 0, -22, 0, 6889], [1, 24, 322, 2136, 7921], [1, 0, -190, 0, 9409]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/2/c/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': '4-450e2-1.1-c1e2-0-8', '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': '4-450e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8955917521865353, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 534751053105437122, 'z1': {'__RealLiteral__': 0, 'data': '1.19207266165402611601661331382', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1511131625061389228494009839013,1781233425856096735671882050824', 'Lhash_array': ['1511131625061389228494009839013', '1781233425856096735671882050824'], 'factors': ['2-450-5.4-c1-0-3', '2-450-5.4-c1-0-4'], 'label': '4-450e2-1.1-c1e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/2/c/d'}