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lfunc_lfunctions • Show schema
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{'Lhash': '263175510706095451501744883367', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-2.0584219849035215, 1.1884304870898919], 'a6': [0, 0], 'a7': [4.0584219849035215, -7.02939307640743], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.084589681459306, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1728.1601', 'coefficient_field': 'CDF', 'conductor': 1728, 'conductor_radical': 6, 'conjugate': '1281923164796909733265489213758', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0584219849035215, -1.1884304870898919], [12.5, -21.650635094610966]], [[1.0, 0], [-4.0584219849035215, 7.02939307640743], [-24.5, -42.4352447854375]], [[1.0, 0], [17.616843969807043, 10.17108960823973], [60.5, 104.78907385791707]], [[1.0, 0], [-3.0584219849035215, 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'2-12e3-9.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': -0.5376591937831131, 'root_number': '-0.1180340381400065352405903641943530508278585206346650530 - 0.9930095497226416314434227450793695645660126527297937551*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.26882959689155655', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.20760887160761254164935793345', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.00147730258222819063180793169', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.59204200890360450930315458894', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.084589681459306, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/3/q/g/1601/1'], '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': '2-12e3-9.2-c2-0-4', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-12e3-9.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': -0.26882959689155655, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.20760887160761254164935793345', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '263175510706095451501744883367', 'Lhash_array': ['263175510706095451501744883367'], 'label': '2-12e3-9.2-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/3/q/g/1601/1'}