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lfunc_lfunctions • Show schema
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{'Lhash': '2593594615173424613844477658434', 'a10': [-0.34780995234739975, 4.224253754694952], 'a2': [0.116048589965386, -1.4094441190650469], 'a3': [0, 0], 'a4': [-1.9730654495340914, -0.32712800530500863], 'a5': [-2.9971062332695433, 0], 'a6': [0, 0], 'a7': [0, -1.0], 'a8': [-0.6900401065864756, 2.7429627506224223], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.0733807856176, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.116048589965386, 1.4094441190650469]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1512.323', 'coefficient_field': 'CDF', 'conductor': 1512, 'conductor_radical': 42, 'conjugate': '73883232328317433218360059882', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.116048589965386, 1.4094441190650469]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.9971062332695433, 0], [5.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 5.362905721113769], 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1.0460369743958586], 'positive_zeros': ['2.04598539590204950123224612665224', '3.81610135791905604237418749523600', '4.19907043414613103657883348790047', '5.09413301846709715690564755349565', '6.16675843078660471289051065736177', '7.17324306745427214461980905865049', '7.46811886248516428617186059749513', '8.314063536697571966856088365350544', '9.223328281211721270062338266094568', '9.692509494510790862511202302441991'], 'prelabel': '2-1512-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.474677076451508, 'root_angle': -0.42155146151525685, 'root_number': '0.2439660193289924596937656800185479999859555530652075695 - 0.9697837807536098804306791795569097841439729718366248298*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.21077573075762843', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.04598539590204950123224612665', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.81610135791905604237418749524', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19907043414613103657883348790', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.0733807856176, 'bad_primes': [2, 3, 7], 'central_character': '24.11', 'conductor': 1512, 'conductor_radical': 42, 'degree': 2, 'index': 93, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1512/2/j/d/323/27'], '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': '2-1512-24.11-c1-0-93', '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': '2-1512-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.474677076451508, 'root_angle': -0.21077573075762843, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.04598539590204950123224612665', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2593594615173424613844477658434', 'Lhash_array': ['2593594615173424613844477658434'], 'label': '2-1512-24.11-c1-0-93', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1512/2/j/d/323/27'}