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lfunc_lfunctions • Show schema
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{'Lhash': '1246667612342251552491060932923', 'a10': [-1.3027756377319946, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [1.3027756377319946, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.116186243894532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '2394.1', 'coefficient_field': 'CDF', 'conductor': 2394, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.3027756377319946, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.302775637731995, 0], [11.0, 0]], [[1.0, 0], [0.6055512754639893, 0], [13.0, 0]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.605551275463989, 0], [23.0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-2394-1.1-c1-0-12', 'leading_term': '1.682800972963273220695208556449', '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/2394/2/a/q/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.6828009729632731, 1.6786009921948923, 1.6659502418558367, 1.644701069032091, 1.6146229834982442, 1.5754250191738493, 1.5267850892443864, 1.4683846384074892, 1.3999467162273498, 1.3212755622019794, 1.2322958761574734, 1.1330901083899114, 1.0239323047098117, 0.9053172518406607, 0.7779838687814549, 0.6429319707247694, 0.5014316934949726, 0.3550250134903857, 0.20551893883761804, 0.05497009042882472, -0.09433945588803444, -0.2399350271264905, -0.3791906867442571, -0.509378616165176, -0.6277258966469925, 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'6.41419493288544355415798987996496', '7.59892525676571574826897773990178', '8.278492448305657074646989458852049', '8.974173038857062072842449375046380'], 'prelabel': '2-2394-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372206107206582, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.983447341182025989187843292750', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.92281314483725312982576680740', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97692665940707432912947827403', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.116186243894532, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 2394, 'conductor_radical': 798, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2394/2/a/q/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': '2-2394-1.1-c1-0-12', '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': '2-2394-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372206107206582, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.983447341182025989187843292750', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1246667612342251552491060932923', 'Lhash_array': ['1246667612342251552491060932923'], 'factors': ['2-2394-1.1-c1-0-12'], 'label': '2-2394-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/2/a/q/1/2'}