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lfunc_lfunctions • Show schema
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{'Lhash': '510397145626051975955807418090', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.5289611963132421, 2.5811388300841895], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 7.486832980505138], 'a8': [0, 0], 'a9': [-4.324555320336759, 7.8929222269921695], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.69763172323563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.5289611963132421, -2.5811388300841895]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.449', 'coefficient_field': 'CDF', 'conductor': 1200, 'conductor_radical': 30, 'conjugate': '2508688161571946726939099641824', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5289611963132421, -2.5811388300841895]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -7.486832980505138], [-49.0, 0]], [[1.0, 0], [0, -8.48528137423857], [-121.0, 0]], [[1.0, 0], [0, -10.0], [-169.0, 0]], [[1.0, 0], 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['0.40263235432078794796134316656304', '1.43216593897770524434621632810788', '2.85825799458431516945300067189486', '3.59017832702613495604378399737959', '4.81301818191082612966207515660782', '5.95871856531592153829835901948792', '6.84992628860909690069185661157552', '7.44131337113060767344391127926105', '8.251769709355844588178711875604562', '8.996864661309946187799060625283241'], 'prelabel': '2-1200-15.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.718184303013993, 'root_angle': 0.9773571300663519, 'root_number': '-0.997470995785390998055156279086312239791321235096345560067 + 0.07107469709327288997251406508745066896104312084139248440*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.48867856503317597', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40263235432078794796134316656', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.43216593897770524434621632811', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.85825799458431516945300067189', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.69763172323563, 'bad_primes': [2, 3, 5], 'central_character': '15.14', 'conductor': 1200, 'conductor_radical': 30, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/3/c/k/449/6'], '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': '2-1200-15.14-c2-0-12', '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': '2-1200-15.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.718184303013993, 'root_angle': 0.48867856503317597, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40263235432078794796134316656', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '510397145626051975955807418090', 'Lhash_array': ['510397145626051975955807418090'], 'label': '2-1200-15.14-c2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/3/c/k/449/6'}