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lfunc_lfunctions • Show schema
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{'Lhash': '233276226087347597426489019577', 'a10': [-947.9106275667606, 2.978498620476156e-59], 'a2': [-7.576916667339795, -13.123604632547977], 'a3': [12.805017409622462, -22.17894074527012], 'a4': [-50.819332367623154, 88.02166566745287], 'a5': [31.276265438312052, -54.17208081016695], 'a6': [-388.0901993461787, 1.0863583722153477e-59], 'a7': [-403.4247574735037, 698.7521769752606], 'a8': [-399.4752810816891, 0.0], 'a9': [765.5630582785313, 1325.9941133362297], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.55824594291251, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[37, [[1.0, 0], [156052.6663582857, 265667.91762550024]]]], 'bad_primes': [37], 'central_character': '37.26', 'coefficient_field': 'CDF', 'conductor': 37, 'conductor_radical': 37, 'conjugate': '2247388881726177004341819991005', 'degree': 2, 'euler_factors': [[[1.0, 0], [7.576916667339795, 13.123604632547977], [-64.0, 110.85125168440814]], [[1.0, 0], 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['0.18402249487780643464263506500724', '3.32020950306768127449603443402723', '5.47657466536788308336857647128675', '7.06204564077146371249381023507227', '7.999787862886932370853521833574355', '9.584024468245896266935268294236974', '10.32798995828663682221349909729902', '12.40014822442029498551642090218725', '13.90234567604277573192404217833685', '15.06447390202409641120847403663058'], 'prelabel': '2-37-37.26-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3997420406425705, 'root_angle': -0.2888974275319686, 'root_number': '0.6156403367642518 - 0.7880272684043356*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.144448713766', 'prec': 50}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.18402249487780643464263506501', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.32020950306768127449603443403', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.47657466536788308336857647129', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.55824594291251, 'bad_primes': [37], 'central_character': '37.26', 'conductor': 37, 'conductor_radical': 37, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/37/8/c/a/26/5'], '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': '2-37-37.26-c7-0-1', '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': '2-37-37.26-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3997420406425705, 'root_angle': -0.1444487137659843, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.18402249487780643464263506501', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '233276226087347597426489019577', 'Lhash_array': ['233276226087347597426489019577'], 'label': '2-37-37.26-c7-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/37/8/c/a/26/5'}