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lfunc_lfunctions • Show schema
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{'Lhash': '2449246230131620225201321031166', 'a10': [6.85356511318248, 1.7403003302212006], 'a2': [1.3660254037844386, 0.36602540378443865], 'a3': [2.9225977802197947, -0.6770688407055298], 'a4': [1.7320508075688772, 1.0], 'a5': [4.999569091086723, -0.06564223830947594], 'a6': [4.240167208633352, 0.14485179608982124], 'a7': [-2.7065203278478616, 6.45559816863986], 'a8': [2.0, 2.0], 'a9': [8.083155569891339, -3.9575997818039417], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.722085551566235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3660254037844386, -0.36602540378443865]]], [3, [[1.0, 0], [-2.9225977802197947, 0.6770688407055298]]], [5, [[1.0, 0], [-4.999569091086723, 0.06564223830947594]]], [7, [[1.0, 0], [2.7065203278478616, -6.45559816863986]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '210.17', 'coefficient_field': 'CDF', 'conductor': 210, 'conductor_radical': 210, 'conjugate': 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0.9519152793477959], 'positive_zeros': ['1.93211459821078053118787732574376', '3.14101382081667813740743621485979', '4.43686876699435431741992237869310', '5.64552101317315710336968301560096', '7.02524410757946639020979296124043', '7.982661642719391406251957478159045', '9.370388027753429953934991425900746', '10.38769253168940732250647624677168', '10.64386240528377221621370491718030', '12.70700868199878046820012750499052'], 'prelabel': '2-210-105.17-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': -0.08349693219669856, 'root_number': '0.9657926758254776 - 0.25931545908769893*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0417484660983', 'prec': 54}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93211459821078053118787732574', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.14101382081667813740743621486', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.43686876699435431741992237869', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.722085551566235, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.17', 'conductor': 210, 'conductor_radical': 210, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/210/3/w/b/17/15'], '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': '2-210-105.17-c2-0-22', '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': '2-210-105.17-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': -0.04174846609834928, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93211459821078053118787732574', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2449246230131620225201321031166', 'Lhash_array': ['2449246230131620225201321031166'], 'label': '2-210-105.17-c2-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/210/3/w/b/17/15'}