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lfunc_lfunctions • Show schema
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{'Lhash': '3221029903260871569474655459340', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, -0.8660254037844386], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5, -0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.74', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2147733096335648342089129626793', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 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['2.54094456523031923158939771246347', '3.75847791594342867408926511147107', '5.50466788895028055692504694322166', '5.96142704152549843878073701497144', '7.26895720981183049590510254049067', '8.494182551239677130502888253345433', '9.759334153033061636597031405849836', '10.29239079010745481225468279533710', '11.38895877606578105374239008949566', '12.06213236697114044589849094033052'], 'prelabel': '2-273-273.74-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': 0.27221390444651283, 'root_number': '0.65607875013015079962236484958458 + 0.75469243644524432992285552131217*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.13610695222325642', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.54094456523031923158939771246', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.75847791594342867408926511147', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.50466788895028055692504694322', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'bad_primes': [3, 7, 13], 'central_character': '273.74', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 1, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/1/s/a/74/1', 'ArtinRepresentation/2.273.6t5.d.b'], 'is_instance_Artin': True, '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': '2-273-273.74-c0-0-1', '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': '2-273-273.74-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': 0.13610695222325642, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.54094456523031923158939771246', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24596551
{'Lhash': '3221029903260871569474655459340', 'Lhash_array': ['3221029903260871569474655459340'], 'label': '2-273-273.74-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.273.6t5.d.b'}
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id: 19808146
{'Lhash': '3221029903260871569474655459340', 'Lhash_array': ['3221029903260871569474655459340'], 'label': '2-273-273.74-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/1/s/a/74/1'}