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lfunc_lfunctions • Show schema
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{'Lhash': '1350385177536550211588001259888,1396536776307013462636763192156', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': 0, '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, 1]]], '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, 0, -5, 0, 25], [1, 1, 1], [1, 0, -11, 0, 121], [1, -4, 3, -52, 169], [1, -12, 70, -204, 289], [1, -4, 42, -76, 361], [1, 0, -23, 0, 529], [1, -6, 7, -174, 841], [1, -4, -15, -124, 961], [1, -4, 78, -148, 1369], [1, 6, -5, 246, 1681], [1, 8, 21, 344, 1849], [1, -12, 97, -564, 2209], [1, -12, 142, -636, 2809], [1, -6, -23, -354, 3481], [1, 8, 3, 488, 3721], [1, -4, -51, -268, 4489], [1, 0, 142, 0, 5041], [1, -4, 150, -292, 5329], [1, 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3.00915861815445, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1454305293775596897, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06526607354851973657984272848', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.10167326553198431223830906085', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.43237795903141877385950354742', '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, 0, 0, -1, -1, 0, 0, 0, 0, 4, -1, 0, -1, 12, 0, 4, 0, 0, 0, 0, 0, 5, 4, 0, 0, 6, 0, 4, 0, 0, 12, 0, 0, 4, 4, 0, 0, -6, 0, -8, 0, 0, 0, 12, 0, 0, 5, 0, 0, 12, 0, 0, 1, 0, 6, 6, 0, -8, 4, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, -8, 0, 0, -6, 6, 0, 0, -8, 0, 0, -12, 0, -4, 0, 0, 12, 0, 0, 10, 0, 0, 0], 'euler11': [1, 0, -11, 0, 121], 'euler13': [1, -4, 3, -52, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, -4, 42, -76, 361], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 0, -23, 0, 529], 'euler29': [1, -6, 7, -174, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4, -15, -124, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 6, -5, 246, 1681], 'euler43': [1, 8, 21, 344, 1849], 'euler47': [1, -12, 97, -564, 2209], 'euler5': [1, 0, -5, 0, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, -6, -23, -354, 3481], 'euler61': [1, 8, 3, 488, 3721], 'euler67': [1, -4, -51, -268, 4489], 'euler7': [1, 1, 1, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 8, -15, 632, 6241], 'euler83': [1, -6, -47, -498, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, -10, 3, -970, 9409], 'euler_factors': [[1, -1, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, -5, 0, 25], [1, 1, 1, 0, 0], [1, 0, -11, 0, 121], [1, -4, 3, -52, 169], [1, -12, 70, -204, 289], [1, -4, 42, -76, 361], [1, 0, -23, 0, 529], [1, -6, 7, -174, 841], [1, -4, -15, -124, 961], [1, -4, 78, -148, 1369], [1, 6, -5, 246, 1681], [1, 8, 21, 344, 1849], [1, -12, 97, -564, 2209], [1, -12, 142, -636, 2809], [1, -6, -23, -354, 3481], [1, 8, 3, 488, 3721], [1, -4, -51, -268, 4489], [1, 0, 142, 0, 5041], [1, -4, 150, -292, 5329], [1, 8, -15, 632, 6241], [1, -6, -47, -498, 6889], [1, 12, 214, 1068, 7921], [1, -10, 3, -970, 9409]], 'index': 59, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1134/2/f/l'], '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-c1e2-0-59', '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': 1454305293775596897, 'z1': {'__RealLiteral__': 0, 'data': '1.06526607354851973657984272848', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1350385177536550211588001259888,1396536776307013462636763192156', 'Lhash_array': ['1350385177536550211588001259888', '1396536776307013462636763192156'], 'factors': ['2-1134-9.7-c1-0-12', '2-1134-9.4-c1-0-13'], 'label': '4-1134e2-1.1-c1e2-0-59', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1134/2/f/l'}