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lfunc_lfunctions • Show schema
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{'Lhash': '1694348987961919817354481504357', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.7015621187164243, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.28331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '7800.1', 'coefficient_field': 'CDF', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.7015621187164243, 0], [7.0, 0]], [[1.0, 0], [-0.7015621187164244, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.7015621187164244, 0], [17.0, 0]], [[1.0, 0], [2.0, 0], [19.0, 0]], [[1.0, 0], [6.701562118716424, 0], [23.0, 0]], [[1.0, 0], 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91, 'label': '2-7800-1.1-c1-0-91', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/7800/2/a/be/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-8.982047442069109e-61, 0.2212874711587274, 0.44121242143537104, 0.6583690735677102, 0.8712686046602774, 1.0783060376911358, 1.277736552362409, 1.4676633142068063, 1.6460381867710812, 1.810675933613737, 1.9592817944699716, 2.0894916755760806, 2.1989236510518926, 2.285239036926383, 2.346210966404496, 2.379798152329268, 2.384221356766067, 2.358039986168927, 2.3002261851710633, 2.2102338082463855, 2.088059705556569, 1.9342948691565338, 1.7501631517802656, 1.5375454963247603, 1.2989879027218934, 1.0376917112592698, 0.7574851963422015, 0.4627759381409658, 0.15848396446822122, -0.1500437785743194, -0.4571364742746365, 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'2-7800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33660567640394530148269003333', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38899228883228091557027120002', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09524265628747451708048227255', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.28331357659873, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'index': 91, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7800/2/a/be/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': '2-7800-1.1-c1-0-91', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-7800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33660567640394530148269003333', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1694348987961919817354481504357', 'Lhash_array': ['1694348987961919817354481504357'], 'label': '2-7800-1.1-c1-0-91', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/be/1/1'}