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lfunc_lfunctions • Show schema
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{'Lhash': '1235582171797921082080930570164', 'a10': [-984.0, 0], 'a2': [4.898979485566356, 2.8284271247461903], 'a3': [0, 0], 'a4': [16.0, 27.712812921102035], 'a5': [-150.64361918116546, 86.97413408594535], 'a6': [0, 0], 'a7': [242.0, -419.1562954316683], 'a8': [0, 181.01933598375618], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.26876154641587, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-4.898979485566356, -2.8284271247461903]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.107', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '1086833655431227487810629826171', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.898979485566356, -2.8284271247461903]], [[1.0, 0], [0, 0]], [[1.0, 0], [150.64361918116546, -86.97413408594535], [7812.5, -13531.646934131853]], [[1.0, 0], [-242.0, 419.1562954316683], [-58824.5, -101887.02272983543]], 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'8.683619810380128394899485499930861', '9.503173716956654058995307638188280', '11.33150400763226096692522321342414', '11.86495595429433786855972211988536'], 'prelabel': '2-162-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.104814620151529, 'root_angle': -0.1111111111111111, 'root_number': '0.9396926207859083840541092773247314699362081342644646331 - 0.342020143325668733044099614682259580763083367514160629*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.05555555555555555', 'prec': 67}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.974702470519451748452545281303', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.47834121020123300726526553451', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07260889787333175308090272135', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.26876154641587, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/7/d/d/107/2'], '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': '2-162-9.2-c6-0-14', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-162-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.104814620151529, 'root_angle': -0.05555555555555555, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.974702470519451748452545281303', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1235582171797921082080930570164', 'Lhash_array': ['1235582171797921082080930570164'], 'label': '2-162-9.2-c6-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/7/d/d/107/2'}