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lfunc_lfunctions • Show schema
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{'Lhash': '1275232741455080452166089431152', 'a10': [-1.4142135623730951, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.4142135623730951, 0.0], 'a6': [1.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.518823652533378, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '3822.1', 'coefficient_field': 'CDF', 'conductor': 3822, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.41421356237309503, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-5.242640687119285, 0], [17.0, 0]], [[1.0, 0], [-3.0, 0], [19.0, 0]], [[1.0, 0], [9.071067811865476, 0], [23.0, 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'group': 'GL2', 'index': 31, 'label': '2-3822-1.1-c1-0-31', 'leading_term': '3.61821150131249399979070449395', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3822/2/a/bs/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [3.618211501312494, 3.609915510207069, 3.5849152441123766, 3.5428832388678972, 3.483304480537825, 3.405520444900548, 3.3087868004237726, 3.1923413474410856, 3.055478417537868, 2.8976259110123945, 2.7184213459700994, 2.517783650952909, 2.295977876020919, 2.05367046198694, 1.791973152682994, 1.5124740408486677, 1.2172546019093735, 0.9088919003260135, 0.5904454645848404, 0.26542863425510166, -0.06223550157862729, -0.38827312250515716, -0.7081328467363726, -1.0170718765169122, -1.3102535586594453, -1.5828544129268203, -1.8301783036688113, 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'6.10927765434231720498422430719132', '7.15945700935716349767501988008935', '7.75434901552065513055240273509444', '8.255778077666497004749933639107470'], 'prelabel': '2-3822-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00598125479172727285268592316', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24084956120762708570795613312', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15891926873810763346200946546', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.518823652533378, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 3822, 'conductor_radical': 546, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3822/2/a/bs/1/1'], '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': '2-3822-1.1-c1-0-31', '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': '2-3822-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00598125479172727285268592316', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1275232741455080452166089431152', 'Lhash_array': ['1275232741455080452166089431152'], 'label': '2-3822-1.1-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3822/2/a/bs/1/1'}