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lfunc_lfunctions • Show schema
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{'Lhash': '1538927322586762617090109480733', 'a10': [0.892385482931524, 0.0], 'a2': [0.6561839248038946, 0.0], 'a3': [-0.20475333253931335, 0.0], 'a4': [-1.5694226568289567, 0.0], 'a5': [1.359962426995175, 0.0], 'a6': [-0.13435584536232362, 0.0], 'a7': [0.0, 0.0], 'a8': [-2.34219776824197, 0.0], 'a9': [-2.958076072814045, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.12411791382232, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 13], 'central_character': '8281.1', 'coefficient_field': 'CDF', 'conductor': 8281, 'conductor_radical': 91, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6561839248038946, 0], [2.0, 0]], [[1.0, 0], [0.20475333253931335, 0], [3.0, 0]], [[1.0, 0], [-1.359962426995175, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.9055126498212016, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.566334066488624, 0], [17.0, 0]], [[1.0, 0], 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[[1.0, 0], [10.57622461947003, 0], [109.0, 0]], [[1.0, 0], [2.3466534895795355, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 364, 'label': '2-91e2-1.1-c1-0-364', '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/8281/2/a/cd/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-9.091436382500262e-61, 0.21019514836684638, 0.41876866146119884, 0.62405643467871, 0.8243130930666172, 1.0176802591738234, 1.2021647880919553, 1.375629190725253, 1.535795687335188, 1.6802645264753175, 1.8065464323501972, 1.9121083512840993, 1.994431080519756, 2.051076887777533, 2.079764863220492, 2.0784514751615504, 2.0454136135724763, 1.9793312893865014, 1.879367104463486, 1.7452396127647145, 1.5772877573010484, 1.376523691967081, 1.144671486033641, 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'5.19065346780208609813190192518552', '6.08317807152053092865562182045645', '6.40692748606181296530646447718052', '7.47471045594710939824721421469460'], 'prelabel': '2-91e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131673746149824, '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': '1.21399960076514160510021024523', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33577796029993186202790757595', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33537730490894149019626877718', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 66.12411791382232, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 8281, 'conductor_radical': 91, 'degree': 2, 'index': 364, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8281/2/a/cd/1/4'], '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': '2-91e2-1.1-c1-0-364', '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': '2-91e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131673746149824, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21399960076514160510021024523', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1538927322586762617090109480733', 'Lhash_array': ['1538927322586762617090109480733'], 'label': '2-91e2-1.1-c1-0-364', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8281/2/a/cd/1/4'}