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lfunc_lfunctions • Show schema
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{'Lhash': '1415356219803050212996203142479', 'a10': [-0.7890633810588171, 0], 'a2': [0.9114041708083149, 1.578598330070185], 'a3': [0, 0], 'a4': [-0.6613151251335843, 1.1454313965451377], 'a5': [-0.21644167492645028, 0.3748879778479186], 'a6': [0, 0], 'a7': [0.34552881921330164, 0.5984734703567197], 'a8': [1.234715230171774, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.270631674670657, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [43, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [3, 43], 'central_character': '1161.388', 'coefficient_field': 'CDF', 'conductor': 1161, 'conductor_radical': 129, 'conjugate': '1821548420671848258930852450444', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9114041708083149, -1.578598330070185], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.21644167492645028, -0.3748879778479186], [-2.5, -4.330127018922194]], [[1.0, 0], 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'2.618690120287519370318909663175765292229517210754713125', '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/1161/2/f/d/388/17', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.6186901202875195, 2.5336554547802703, 2.4444893670768484, 2.350863605776556, 2.2522623789271625, 2.148052555222507, 2.037557755478809, 1.9201320536073272, 1.7952295717712883, 1.6624670577485987, 1.5216773943651845, 1.3729527706794247, 1.2166768620446335, 1.0535457994923976, 0.8845779791273758, 0.7111129133753612, 0.5347994077703451, 0.3575734038247219, 0.18162589373594587, 0.00936140732653529, -0.15665229428342456, -0.31374250902161327, -0.4591968488645878, -0.5903342043674564, -0.7045799146949407, -0.7995433912144952, -0.8730962106246404, -0.9234484921990072, -0.9492212173741634, 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'8.102185700455135598508365816328254', '8.896118405329336237245710217509704', '9.698608076592187532019328535212036'], 'prelabel': '2-1161-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.044771202351772, 'root_angle': -0.5371016774559731, 'root_number': '-0.1162946124824920456596946947481412095915541889126921820 - 0.99321476182522931996579390256138641879849726541276250950*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2685508387279866', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11651918876402354622401903036', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20739736242977617560300470939', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37770852428936416065557194070', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.270631674670657, 'bad_primes': [3, 43], 'central_character': '9.4', 'conductor': 1161, 'conductor_radical': 129, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1161/2/f/d/388/17'], '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': '2-1161-9.4-c1-0-18', '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': '2-1161-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.044771202351772, 'root_angle': -0.2685508387279866, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11651918876402354622401903036', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1415356219803050212996203142479', 'Lhash_array': ['1415356219803050212996203142479'], 'label': '2-1161-9.4-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1161/2/f/d/388/17'}