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lfunc_lfunctions • Show schema
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{'Lhash': '141507635010924345774028612462', 'a10': [1.6184407500101492, 2.8032216080574583], 'a2': [-0.8660254037844386, -0.5], 'a3': [1.6002062903825311, -0.9238795325112867], 'a4': [0.5, 0.8660254037844386], 'a5': [-2.8032216080574583, -1.6184407500101492], 'a6': [-1.8477590650225735, 0], 'a7': [0, 0], 'a8': [0, -1.0], 'a9': [0.20710678118654752, -0.3587194676071504], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.2360395200945005, 3.077694966166166]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.901', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '1866641421288792696721306599526', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-1.6002062903825311, 0.9238795325112867], [1.5, 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'label': '2-1078-77.54-c1-0-1', 'leading_term': '0.233823047374926087292192133712286779510076944170690243', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1078/2/i/d/901/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.2338230473749261, 0.11429655070805272, -0.012327356880107157, -0.1465047534035279, -0.2886831935943192, -0.4392444113972547, -0.5984483153177766, -0.7663809326653049, -0.9429083841331972, -1.1276383639895962, -1.3198900647971132, -1.5186730759957623, -1.7226755152366588, -1.9302614993936926, -2.1394779906580124, -2.3480710203211, -2.553511262485684, -2.7530288754497207, -2.943657433819616, -3.122286632704118, -3.285723257032125, -3.4307596797523954, -3.5542488915790025, -3.653184783509726, -3.7247861144555516, -3.766582313681832, 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'7.41454685043958849068237030971484', '7.80114171590168104197720096386867', '8.941768682602161208789985664140576', '9.614979018083477531092365500878383'], 'prelabel': '2-1078-77.54-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.5152620747581143, 'root_number': '-0.0479288527837311824821238391303064559404372814660699172 - 0.9988507521501074705389478290300542713186696885197763509*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2576310373790571', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11162984105040232218714145664', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54537402275618926927450631933', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09454248253222668059828095815', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '77.54', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/i/d/901/4'], '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': '2-1078-77.54-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1078-77.54-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.2576310373790571, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.11162984105040232218714145664', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '141507635010924345774028612462', 'Lhash_array': ['141507635010924345774028612462'], 'label': '2-1078-77.54-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/i/d/901/4'}