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lfunc_lfunctions • Show schema
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{'Lhash': '2196975587479936419006515160887', 'a10': [0.5, 0.8660254037844386], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.0, -1.0], 'a5': [-0.25881904510252074, 0.9659258262890683], 'a6': [0.25881904510252074, 0.9659258262890683], 'a7': [-1.224744871391589, -1.224744871391589], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [0.5, -0.8660254037844386]]], [5, [[1.0, 0], [0.25881904510252074, -0.9659258262890683]]], [13, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.467', 'coefficient_field': 'CDF', 'conductor': 1560, 'conductor_radical': 390, 'conjugate': '806367079774506637859380838154', 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1.4777572614960963, 0.8489592019685487, 0.2002288527439233, -0.43167497224972895], 'positive_zeros': ['1.73310815068788685387437250655783', '3.10273314721915476193497053928832', '4.04894625129553888989873840330575', '5.31717009219395415875327398768331', '5.84427966691479019290462172012883', '6.34062973198834430759545862384458', '7.33372601345514370876202692081225', '8.204202673094879301240036280316606', '8.776510363841565971432602227118548', '9.511396837612868670601114868503655'], 'prelabel': '2-1560-1560.467-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': 0.5737918088252166, 'root_number': '-0.22975292054736118352393736938184 + 0.97324898946773016378805774830813*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2868959044126083', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.73310815068788685387437250656', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10273314721915476193497053929', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04894625129553888989873840331', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.467', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/1/cs/c/467/4'], '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': '2-1560-1560.467-c0-0-11', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1560-1560.467-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': 0.2868959044126083, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73310815068788685387437250656', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2196975587479936419006515160887', 'Lhash_array': ['2196975587479936419006515160887'], 'label': '2-1560-1560.467-c0-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/1/cs/c/467/4'}