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lfunc_lfunctions • Show schema
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{'Lhash': '2432394390187963049826486428754,2737966558701466886220871147654', 'a10': 3, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': 4, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.67334019432485, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '162.1', 'coefficient_field': '1.1.1.1', 'conductor': 26244, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1, -1, 1], [1], [1, -3, 4, -15, 25], [1, -4, 9, -28, 49], [1, 0, -11, 0, 121], [1, -1, -12, -13, 169], [1, 6, 43, 102, 289], [1, 8, 54, 152, 361], [1, 0, -23, 0, 529], [1, 9, 52, 261, 841], [1, -4, -15, -124, 961], [1, 2, 75, 74, 1369], [1, 6, -5, 246, 1681], [1, 8, 21, 344, 1849], [1, -12, 97, -564, 2209], [1, 12, 142, 636, 2809], [1, 0, -59, 0, 3481], [1, -1, -60, -61, 3721], [1, -4, -51, -268, 4489], [1, 24, 286, 1704, 5041], [1, -22, 267, -1606, 5329], [1, -16, 177, -1264, 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'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 14387151734701852, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91882084049818752724148443255', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.15987477796209772498727713910', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53881614318847338394124695872', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.67334019432485, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 26244, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 0, 3, 0, 4, -1, 0, 3, 0, 0, 1, 4, 0, -1, -6, 0, -8, 0, 0, 0, 0, 0, 5, 1, 0, 0, -9, 0, 4, 0, 0, -6, 12, 0, -2, -8, 0, -3, -6, 0, -8, 0, 0, 0, 12, 0, 7, 5, 0, 0, -12, 0, 0, -4, 0, -9, 0, 0, 1, 4, 0, 1, 3, 0, 4, 0, 0, 12, -24, 0, 22, -2, 0, 0, 0, 0, 16, -3, 0, -6, 12, 0, -18, -8, 0, 0, -6, 0, 4, 0, 0, 12, -24, 0, -2, 7, 0, 0], 'euler11': [1, 0, -11, 0, 121], 'euler13': [1, -1, -12, -13, 169], 'euler17': [1, 6, 43, 102, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 0, -23, 0, 529], 'euler29': [1, 9, 52, 261, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4, -15, -124, 961], 'euler37': [1, 2, 75, 74, 1369], 'euler41': [1, 6, -5, 246, 1681], 'euler43': [1, 8, 21, 344, 1849], 'euler47': [1, -12, 97, -564, 2209], 'euler5': [1, -3, 4, -15, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, -1, -60, -61, 3721], 'euler67': [1, -4, -51, -268, 4489], 'euler7': [1, -4, 9, -28, 49], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, -16, 177, -1264, 6241], 'euler83': [1, -12, 61, -996, 6889], 'euler89': [1, 6, 187, 534, 7921], 'euler97': [1, 2, -93, 194, 9409], 'euler_factors': [[1, -1, 1, 0, 0], [1, 0, 0, 0, 0], [1, -3, 4, -15, 25], [1, -4, 9, -28, 49], [1, 0, -11, 0, 121], [1, -1, -12, -13, 169], [1, 6, 43, 102, 289], [1, 8, 54, 152, 361], [1, 0, -23, 0, 529], [1, 9, 52, 261, 841], [1, -4, -15, -124, 961], [1, 2, 75, 74, 1369], [1, 6, -5, 246, 1681], [1, 8, 21, 344, 1849], [1, -12, 97, -564, 2209], [1, 12, 142, 636, 2809], [1, 0, -59, 0, 3481], [1, -1, -60, -61, 3721], [1, -4, -51, -268, 4489], [1, 24, 286, 1704, 5041], [1, -22, 267, -1606, 5329], [1, -16, 177, -1264, 6241], [1, -12, 61, -996, 6889], [1, 6, 187, 534, 7921], [1, 2, -93, 194, 9409]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/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': '4-162e2-1.1-c1e2-0-7', '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': '4-162e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 14387151734701852, 'z1': {'__RealLiteral__': 0, 'data': '1.91882084049818752724148443255', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2432394390187963049826486428754,2737966558701466886220871147654', 'Lhash_array': ['2432394390187963049826486428754', '2737966558701466886220871147654'], 'label': '4-162e2-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/c/d'}