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lfunc_lfunctions • Show schema
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{'Lhash': '871220001310592874985110924029,900144226458455789470855034179', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2879.3387376695364, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [5, [1, -2, 1]], [7, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '6720.1', 'coefficient_field': '1.1.1.1', 'conductor': 45158400, 'conductor_radical': 210, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, -2, 1], [1, -2, 1], [1, 2, 6, 22, 121], [1, 2, 10, 26, 169], [1, -4, 38, -68, 289], [1, 6, 30, 114, 361], [1, 0, 46, 0, 529], [1, -4, 62, -116, 841], [1, -2, 46, -62, 961], [1, -4, 78, -148, 1369], [1, -4, 86, -164, 1681], [1, 4, 22, 172, 1849], [1, 0, 94, 0, 2209], [1, 2, -46, 106, 2809], [1, -8, 134, -472, 3481], [1, 0, 54, 0, 3721], [1, 12, 102, 804, 4489], [1, 2, 126, 142, 5041], [1, -22, 250, -1606, 5329], [1, 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122, -1582, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 7, 'label': '4-6720e2-1.1-c1e2-0-7', 'leading_term': '2.93292572599766703865190383203231305680216990087345330689958800000000000000000000000000000', 'load_key': 'CMFs-workshop', '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, 'origin': 'ModularForm/GL2/Q/holomorphic/6720/2/a/ct', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.025390625', 'prec': 37}, 'plot_values': [2.9329257259976673, 2.9221148807018245, 2.9006109425316766, 2.8607658969995837, 2.8040006958267782, 2.7326514740826084, 2.646936971446262, 2.5471607727186103, 2.434318504966908, 2.309540913141197, 2.1739870832133703, 2.028979150422557, 1.876024816865967, 1.7167807492383191, 1.5530474756735562, 1.386763435662507, 1.2199985990461522, 1.0549288412611892, 0.8938247549313123, 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'prelabel': '4-6720e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.325262463441187, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1596008065641551658, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68727139888052538684776912316', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.71008858931348487960499533584', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.73919828323421313220491907440', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2879.3387376695364, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 45158400, 'conductor_radical': 210, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 2, 0, 2, 0, 3, 0, -2, 0, -2, 0, -4, 0, 4, 0, -6, 0, -4, 0, 0, 0, 3, 0, -4, 0, 4, 0, 2, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, -4, 0, 6, 0, 0, 0, 3, 0, -8, 0, -2, 0, -4, 0, 12, 0, 8, 0, 0, 0, 6, 0, -4, 0, -12, 0, 0, 0, -2, 0, 22, 0, -6, 0, -4, 0, 12, 0, 5, 0, 8, 0, 8, 0, -8, 0, 16, 0, -4, 0, -4, 0, -12, 0, 18, 0, -6, 0], 'euler11': [1, 2, 6, 22, 121], 'euler13': [1, 2, 10, 26, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, 6, 30, 114, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, -4, 62, -116, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -2, 46, -62, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 4, 22, 172, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, 2, -46, 106, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, 0, 54, 0, 3721], 'euler67': [1, 12, 102, 804, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, 2, 126, 142, 5041], 'euler73': [1, -22, 250, -1606, 5329], 'euler79': [1, -12, 126, -948, 6241], 'euler83': [1, -8, 182, -664, 6889], 'euler89': [1, -16, 174, -1424, 7921], 'euler97': [1, -18, 258, -1746, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, -2, 1, 0, 0], [1, -2, 1, 0, 0], [1, 2, 6, 22, 121], [1, 2, 10, 26, 169], [1, -4, 38, -68, 289], [1, 6, 30, 114, 361], [1, 0, 46, 0, 529], [1, -4, 62, -116, 841], [1, -2, 46, -62, 961], [1, -4, 78, -148, 1369], [1, -4, 86, -164, 1681], [1, 4, 22, 172, 1849], [1, 0, 94, 0, 2209], [1, 2, -46, 106, 2809], [1, -8, 134, -472, 3481], [1, 0, 54, 0, 3721], [1, 12, 102, 804, 4489], [1, 2, 126, 142, 5041], [1, -22, 250, -1606, 5329], [1, -12, 126, -948, 6241], [1, -8, 182, -664, 6889], [1, -16, 174, -1424, 7921], [1, -18, 258, -1746, 9409]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6720/2/a/ct'], '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': '4-6720e2-1.1-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': '4-6720e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.325262463441187, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1596008065641551658, 'z1': {'__RealLiteral__': 0, 'data': '0.68727139888052538684776912316', 'prec': 103}}
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