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lfunc_lfunctions • Show schema
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{'Lhash': '3226446674305720863944604834602', 'a10': [-4.810983402419703, 0.0], 'a2': [1.8323703376532245, 0.0], 'a3': [-0.8537572728867462, 0.0], 'a4': [1.3575810543113922, 0.0], 'a5': [-2.6255518895712333, 0.0], 'a6': [-1.5643995023933834, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.1771494204262627, 0.0], 'a9': [-2.271098518992986, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '3226446674305720863944604834602', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8323703376532245, 0], [2.0, 0]], [[1.0, 0], [0.8537572728867462, 0], [3.0, 0]], [[1.0, 0], [2.6255518895712333, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.2646886218009743, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 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'5.48217746204445058971135128653395', '6.32342859475185033882178366916527', '7.13768332964509585083016667950844', '8.449741418327615560594390767121940', '9.066871999657878669626046464859954', '10.59190352532471801106003334473057'], 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.54521764414013401196169758983', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.93380645730471702769847673701', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27325350001535669933167167696', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/a/m/1/5'], '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': '2-637-1.1-c1-0-38', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.54521764414013401196169758983', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3226446674305720863944604834602', 'Lhash_array': ['3226446674305720863944604834602'], 'label': '2-637-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/a/m/1/5'}