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lfunc_lfunctions • Show schema
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{'Lhash': '634173692777826308035121555466,2410124426104898652707956997132', 'a10': -3, 'a2': -1, 'a3': 0, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': -1, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 81.99366952191765, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 1]], [3, [1]], [7, [1, 1, 7]]], 'bad_primes': [2, 3, 7], 'central_character': '1134.1', 'coefficient_field': '1.1.1.1', 'conductor': 1285956, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, 1, 1], [1], [1, -3, 4, -15, 25], [1, 1, 7], [1, 3, -2, 33, 121], [1, 2, 27, 26, 169], [1, -3, -8, -51, 289], [1, -7, 30, -133, 361], [1, 9, 58, 207, 529], [1, 6, 67, 174, 841], [1, 8, 33, 248, 961], [1, -1, -36, -37, 1369], [1, 6, 91, 246, 1681], [1, 2, 87, 86, 1849], [1, 0, -47, 0, 2209], [1, -3, -44, -159, 2809], [1, 0, -59, 0, 3481], [1, 2, -57, 122, 3721], [1, -4, -51, -268, 4489], [1, 24, 286, 1704, 5041], [1, 11, 48, 803, 5329], [1, -16, 177, 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'6.03555339202875936953791011893068', '6.77387675113480571165664383008899', '7.33918464000050529623638159710419', '7.62872203459024012761075058413000', '7.80248977176881529367216742747610', '8.541776383106467103341770360382510', '8.858715184913233297577231728169612', '9.455967414600466782049884595481829', '9.556983611093547240577746528942339', '10.08193305818444774546168739272873'], 'prelabel': '4-1134e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1266939453246207303, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50027483335206789807484504301', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.68832937132653323321807153076', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.90125293647238192678882950015', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 81.99366952191765, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1285956, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 0, 3, 0, -1, 1, 0, -3, -3, 0, -2, 1, 0, -1, 3, 0, 7, 0, 0, 3, -9, 0, 5, 2, 0, 0, -6, 0, -8, 0, 0, -3, -3, 0, 1, -7, 0, 3, -6, 0, -2, 0, 0, 9, 0, 0, -6, -5, 0, 0, 3, 0, -9, -1, 0, 6, 0, 0, -2, 8, 0, 1, -6, 0, 4, 0, 0, 3, -24, 0, -11, -1, 0, 0, 3, 0, 16, -3, 0, 6, 18, 0, 9, 2, 0, -3, 3, 0, 2, 0, 0, 0, 21, 0, -2, 6, 0, 0], 'euler11': [1, 3, -2, 33, 121], 'euler13': [1, 2, 27, 26, 169], 'euler17': [1, -3, -8, -51, 289], 'euler19': [1, -7, 30, -133, 361], 'euler2': [1, 1, 1, 0, 0], 'euler23': [1, 9, 58, 207, 529], 'euler29': [1, 6, 67, 174, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 33, 248, 961], 'euler37': [1, -1, -36, -37, 1369], 'euler41': [1, 6, 91, 246, 1681], 'euler43': [1, 2, 87, 86, 1849], 'euler47': [1, 0, -47, 0, 2209], 'euler5': [1, -3, 4, -15, 25], 'euler53': [1, -3, -44, -159, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, 2, -57, 122, 3721], 'euler67': [1, -4, -51, -268, 4489], 'euler7': [1, 1, 7, 0, 0], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, 11, 48, 803, 5329], 'euler79': [1, -16, 177, -1264, 6241], 'euler83': [1, -18, 247, -1494, 6889], 'euler89': [1, -3, -80, -267, 7921], 'euler97': [1, 2, 195, 194, 9409], 'euler_factors': [[1, 1, 1, 0, 0], [1, 0, 0, 0, 0], [1, -3, 4, -15, 25], [1, 1, 7, 0, 0], [1, 3, -2, 33, 121], [1, 2, 27, 26, 169], [1, -3, -8, -51, 289], [1, -7, 30, -133, 361], [1, 9, 58, 207, 529], [1, 6, 67, 174, 841], [1, 8, 33, 248, 961], [1, -1, -36, -37, 1369], [1, 6, 91, 246, 1681], [1, 2, 87, 86, 1849], [1, 0, -47, 0, 2209], [1, -3, -44, -159, 2809], [1, 0, -59, 0, 3481], [1, 2, -57, 122, 3721], [1, -4, -51, -268, 4489], [1, 24, 286, 1704, 5041], [1, 11, 48, 803, 5329], [1, -16, 177, -1264, 6241], [1, -18, 247, -1494, 6889], [1, -3, -80, -267, 7921], [1, 2, 195, 194, 9409]], 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1134/2/g/c'], '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': '4-1134e2-1.1-c1e2-0-17', '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': '4-1134e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1266939453246207303, 'z1': {'__RealLiteral__': 0, 'data': '0.50027483335206789807484504301', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '634173692777826308035121555466,2410124426104898652707956997132', 'Lhash_array': ['634173692777826308035121555466', '2410124426104898652707956997132'], 'label': '4-1134e2-1.1-c1e2-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1134/2/g/c'}