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lfunc_lfunctions • Show schema
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{'Lhash': '1232199756493929545084061337119,1851005524337111965331176216685', 'a10': 0, 'a2': 2, 'a3': 3, 'a4': 3, 'a5': 0, 'a6': 6, 'a7': 1, 'a8': 4, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 482.19155691135796, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [5, [1]], [11, [1, -2, 1]]], 'bad_primes': [2, 5, 11], 'central_character': '2750.1', 'coefficient_field': '1.1.1.1', 'conductor': 7562500, 'conductor_radical': 110, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, -3, 7, -9, 9], [1], [1, -1, 13, -7, 49], [1, -2, 1], [1, 2, 22, 26, 169], [1, -6, 38, -102, 289], [1, 0, 38, 0, 361], [1, -3, 47, -69, 529], [1, -5, 33, -145, 841], [1, -4, 66, -124, 961], [1, -6, 38, -222, 1369], [1, -9, 71, -369, 1681], [1, -13, 97, -559, 1849], [1, 9, 53, 423, 2209], [1, -8, 102, -424, 2809], [1, -10, 138, -590, 3481], [1, 11, 121, 671, 3721], [1, 4, 118, 268, 4489], [1, -24, 286, -1704, 5041], [1, 2, 102, 146, 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'root_analytic_conductor': 4.686028228238934, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1637477561360950426, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.972034215320911580751866605660', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.46018589349766774281830868782', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.28942256594814126408427138360', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 482.19155691135796, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 7562500, 'conductor_radical': 110, 'degree': 4, 'dirichlet_coefficients': [1, 2, 3, 3, 0, 6, 1, 4, 2, 0, 2, 9, -2, 2, 0, 5, 6, 4, 0, 0, 3, 4, 3, 12, 0, -4, -6, 3, 5, 0, 4, 6, 6, 12, 0, 6, 6, 0, -6, 0, 9, 6, 13, 6, 0, 6, -9, 15, -12, 0, 18, -6, 8, -12, 0, 4, 0, 10, 10, 0, -11, 8, 2, 7, 0, 12, -4, 18, 9, 0, 24, 8, -2, 12, 0, 0, 2, -12, -10, 0, -14, 18, -27, 9, 0, 26, 15, 8, -15, 0, -2, 9, 12, -18, 0, 18, 16, -24, 4, 0], 'euler11': [1, -2, 1, 0, 0], 'euler13': [1, 2, 22, 26, 169], 'euler17': [1, -6, 38, -102, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, -3, 47, -69, 529], 'euler29': [1, -5, 33, -145, 841], 'euler3': [1, -3, 7, -9, 9], 'euler31': [1, -4, 66, -124, 961], 'euler37': [1, -6, 38, -222, 1369], 'euler41': [1, -9, 71, -369, 1681], 'euler43': [1, -13, 97, -559, 1849], 'euler47': [1, 9, 53, 423, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -8, 102, -424, 2809], 'euler59': [1, -10, 138, -590, 3481], 'euler61': [1, 11, 121, 671, 3721], 'euler67': [1, 4, 118, 268, 4489], 'euler7': [1, -1, 13, -7, 49], 'euler71': [1, -24, 286, -1704, 5041], 'euler73': [1, 2, 102, 146, 5329], 'euler79': [1, 10, 138, 790, 6241], 'euler83': [1, 27, 347, 2241, 6889], 'euler89': [1, 15, 233, 1335, 7921], 'euler97': [1, -16, 178, -1552, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, -3, 7, -9, 9], [1, 0, 0, 0, 0], [1, -1, 13, -7, 49], [1, -2, 1, 0, 0], [1, 2, 22, 26, 169], [1, -6, 38, -102, 289], [1, 0, 38, 0, 361], [1, -3, 47, -69, 529], [1, -5, 33, -145, 841], [1, -4, 66, -124, 961], [1, -6, 38, -222, 1369], [1, -9, 71, -369, 1681], [1, -13, 97, -559, 1849], [1, 9, 53, 423, 2209], [1, -8, 102, -424, 2809], [1, -10, 138, -590, 3481], [1, 11, 121, 671, 3721], [1, 4, 118, 268, 4489], [1, -24, 286, -1704, 5041], [1, 2, 102, 146, 5329], [1, 10, 138, 790, 6241], [1, 27, 347, 2241, 6889], [1, 15, 233, 1335, 7921], [1, -16, 178, -1552, 9409]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2750/2/a/f'], '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': '4-2750e2-1.1-c1e2-0-0', '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': '4-2750e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.686028228238934, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1637477561360950426, 'z1': {'__RealLiteral__': 0, 'data': '0.972034215320911580751866605660', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1232199756493929545084061337119,1851005524337111965331176216685', 'Lhash_array': ['1232199756493929545084061337119', '1851005524337111965331176216685'], 'label': '4-2750e2-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2750/2/a/f'}