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lfunc_lfunctions • Show schema
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{'Lhash': '1636541895949842803123591463815', 'a10': [-0.3174560369632379, 3.1463028564643287], 'a2': [1.195029935193084, 0.7562429860781609], 'a3': [-0.356193092015173, 1.695029935193084], 'a4': [0.856193092015173, 1.807466013286418], 'a5': [1.0, 2.0], 'a6': [-1.7075159073494057, 1.756242986078161], 'a7': [1.0, 0.0], 'a8': [-0.34370711985885116, 2.807466013286418], 'a9': [-2.746252962401341, -1.2075159073494057], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3537168848937777, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.195029935193084, -0.7562429860781609]]], [3, [[1.0, 0], [0.356193092015173, -1.695029935193084]]], [5, [[1.0, 0], [-1.0, -2.0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '420.239', 'coefficient_field': 'CDF', 'conductor': 420, 'conductor_radical': 210, 'conjugate': '3575632844931189425922455065571', 'degree': 2, 'euler_factors': [[[1.0, 0], 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-0.1739300557830629, 0.36577406345271163, 0.8190853639913516, 0.9147925874890419], 'positive_zeros': ['1.29100392147110390733562118322458', '2.20769190707857523623744196602953', '3.94751327307647830301103170862137', '5.18173113297807740402360381589630', '5.84910047408575402630550357540578', '6.92360441214418520343453436205106', '7.994134064617705568239967389256268', '9.195291664267133955317753124459823', '10.03507637367814503021529961043756', '11.43117207438538891404704708852042'], 'prelabel': '2-420-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8313156158602968, 'root_angle': -0.7224690472043988, 'root_number': '-0.6433814252809124 - 0.7655457802140261*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.361234523602', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29100392147110390733562118322', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20769190707857523623744196603', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94751327307647830301103170862', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3537168848937777, 'bad_primes': [2, 3, 5, 7], 'central_character': '60.59', 'conductor': 420, 'conductor_radical': 210, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/420/2/l/f/239/8'], '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': '2-420-60.59-c1-0-26', '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': '2-420-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8313156158602968, 'root_angle': -0.3612345236021994, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29100392147110390733562118322', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1636541895949842803123591463815', 'Lhash_array': ['1636541895949842803123591463815'], 'label': '2-420-60.59-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/420/2/l/f/239/8'}