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lfunc_lfunctions • Show schema
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{'Lhash': '1424401351132986720372816649821', '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], [2.414213562373095, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.242640687119285, 0], [17.0, 0]], [[1.0, 0], [-3.0, 0], [19.0, 0]], [[1.0, 0], [-5.0710678118654755, 0], [23.0, 0]], 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'GL2', 'index': 38, 'label': '2-3822-1.1-c1-0-38', 'leading_term': '4.36000358537151050259407325933', '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/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [4.36000358537151, 4.352221940583876, 4.328748574538312, 4.289207977460378, 4.233006267678994, 4.159376947626773, 4.06744083340705, 3.956276586239505, 3.8249979218790187, 3.672833541275502, 3.4992060468571697, 3.30380649895157, 3.086661742606494, 2.848192129341916, 2.5892577271931208, 2.3111915348734255, 2.015818589559389, 1.7054601923384398, 1.382922786242004, 1.051471325315825, 0.714787283073086, 0.3769117741832583, 0.04217460842052506, -0.284889540352673, -0.5996362907395658, -0.8974160964237822, -1.1736858643757824, -1.4241249907662785, 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'6.95637270481319983302452012979892', '7.72689131307410011798144234982194', '8.400251344616668488071078817233872'], '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': '1.12365453925280019383108899458', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37753522456644293595311079088', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81721772140154688142432070458', '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': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3822/2/a/bs/1/2'], '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-c1-0-38', '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': '1.12365453925280019383108899458', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1424401351132986720372816649821', 'Lhash_array': ['1424401351132986720372816649821'], 'label': '2-3822-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3822/2/a/bs/1/2'}