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lfunc_lfunctions • Show schema
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{'Lhash': '3104048491344077956041017642686', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.3027756377319947, 0.0], 'a4': [0.0, 0.0], 'a5': [1.3027756377319946, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.60555127546399, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.908326913195984, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.727143799659801, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 37], 'central_character': '592.1', 'coefficient_field': 'CDF', 'conductor': 592, 'conductor_radical': 74, 'conjugate': '3104048491344077956041017642686', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.3027756377319947, 0], [3.0, 0]], [[1.0, 0], [-1.3027756377319946, 0], [5.0, 0]], [[1.0, 0], [4.60555127546399, 0], [7.0, 0]], [[1.0, 0], [1.3027756377319946, 0], [11.0, 0]], [[1.0, 0], [2.302775637731995, 0], [13.0, 0]], [[1.0, 0], [6.0, 0], [17.0, 0]], [[1.0, 0], 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'9.205567592866676475011363485538569', '10.21046196995803390636417901993571'], 'prelabel': '2-592-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1741995767775784, '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': '2.44866250273160536395057437176', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.14944936528460844957574778014', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.62172140576878930420954882071', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.727143799659801, 'bad_primes': [2, 37], 'central_character': '1.1', 'conductor': 592, 'conductor_radical': 74, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/592/2/a/f/1/2'], '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': '2-592-1.1-c1-0-16', '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': '2-592-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1741995767775784, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.44866250273160536395057437176', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3104048491344077956041017642686', 'Lhash_array': ['3104048491344077956041017642686'], 'label': '2-592-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/592/2/a/f/1/2'}