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lfunc_lfunctions • Show schema
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{'Lhash': '1133865165963175653525616768034', 'a10': [-495.91925886602104, 858.9573528078508], 'a2': [-4.0, -6.928203230275509], 'a3': [36.53195132298983, 63.27519579105146], 'a4': [-32.0, 55.42562584220407], 'a5': [-61.98990735825263, -107.36966910098135], 'a6': [292.25561058391867, -506.2015663284117], 'a7': [1245.2628366012514, 0.0], 'a8': [512.0, 0.0], 'a9': [-1575.6669349305973, 2729.135187106119], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.870630968396632, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.0, 6.928203230275509]]], [19, [[1.0, 0], [3524.866071145814, -29689.174090575256]]]], 'bad_primes': [2, 19], 'central_character': '38.7', 'coefficient_field': 'CDF', 'conductor': 38, 'conductor_radical': 38, 'conjugate': '2439228988253376631584594993907', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.0, 6.928203230275509]], [[1.0, 0], [-36.53195132298983, -63.27519579105146], [-1093.5, 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-2.2976882327569466], 'positive_zeros': ['0.894461901220283530137175177038374', '2.59300211696128584354588851797831', '5.30036570198713179025210865304815', '7.38602166237008394375415758955305', '7.62350407612314522853860552005597', '8.978265489521348169340089203529813', '10.88105394605650817409936298100538', '12.34197979888206959319927138731465', '13.63486431969032951477512740400566', '14.54890807171450445079767120724296'], 'prelabel': '2-38-19.7-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.445378203970739, 'root_angle': -0.3946312485512337, 'root_number': '0.32501320911540454 - 0.9457094764781129*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.197315624276', 'prec': 50}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.894461901220283530137175177038', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.59300211696128584354588851798', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.30036570198713179025210865305', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.870630968396632, 'bad_primes': [2, 19], 'central_character': '19.7', 'conductor': 38, 'conductor_radical': 38, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/38/8/c/a/7/6'], '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': '2-38-19.7-c7-0-5', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-38-19.7-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.445378203970739, 'root_angle': -0.19731562427561686, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.894461901220283530137175177038', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1133865165963175653525616768034', 'Lhash_array': ['1133865165963175653525616768034'], 'label': '2-38-19.7-c7-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/38/8/c/a/7/6'}