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lfunc_lfunctions • Show schema
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{'Lhash': '1784686128423576534523582969756', 'a10': [0, 0], 'a2': [-0.25881904510252074, -0.9659258262890683], 'a3': [0.9659258262890683, 0.25881904510252074], 'a4': [-0.8660254037844386, 0.5], 'a5': [0, 0], 'a6': [0, -1.0], 'a7': [-2.463125514079171, 0.9659258262890683], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.384292212234444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.25881904510252074, 0.9659258262890683]]], [3, [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.463125514079171, -0.9659258262890683]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.943', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '821343213937427412710643597162', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.25881904510252074, 0.9659258262890683]], 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'2.98128891579702322603457716987372', '3.95183956782990973698701087478329', '5.00027244179180863368611502687406', '6.16086015428611985016112868657367', '6.89258890315629592549659637446737', '7.57642697400233613687425286781577', '8.434006471687055552689373823896026', '9.298744478630267524000372964015957', '9.915893560775941492312450444121460'], 'prelabel': '2-1050-35.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955642303762565, 'root_angle': 0.5655466911214377, 'root_number': '-0.2044687918316735807952540067793247824182796373216333100 + 0.9788730832783664478835906273927667314953484933825436263*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.28277334556071887', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40786911480360551169720011895', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.98128891579702322603457716987', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95183956782990973698701087478', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.384292212234444, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.33', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/2/bc/f/943/1'], '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': '2-1050-35.33-c1-0-21', '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': '2-1050-35.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955642303762565, 'root_angle': 0.28277334556071887, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40786911480360551169720011895', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1784686128423576534523582969756', 'Lhash_array': ['1784686128423576534523582969756'], 'label': '2-1050-35.33-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/2/bc/f/943/1'}