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lfunc_lfunctions • Show schema
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{'Lhash': '1760381594425786162989519722519', 'a10': [0.0, 0.0], 'a2': [2.53767343619882, 0.0], 'a3': [-1.0, 0.0], 'a4': [4.439786468789127, 0.0], 'a5': [0.0, 0.0], 'a6': [-2.53767343619882, 0.0], 'a7': [1.0405354972461556, 0.0], 'a8': [6.19138131184349, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.53767343619882, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0405354972461556, 0], [7.0, 0]], [[1.0, 0], [-2.971006864778638, 0], [11.0, 0]], [[1.0, 0], [-5.669221072623267, 0], [13.0, 0]], [[1.0, 0], [5.0836132293107035, 0], [17.0, 0]], [[1.0, 0], [5.371560612260395, 0], [19.0, 0]], [[1.0, 0], 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[[1.0, 0], [3.8728085439873503, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 49, 'label': '2-1875-1.1-c1-0-49', 'leading_term': '4.96319454093922786194279666960', '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/1875/2/a/p/1/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [4.963194540939228, 4.958275533754574, 4.943252863605826, 4.917346529272172, 4.87931162182808, 4.82751634166303, 4.760042763543325, 4.674803497440701, 4.569667235488569, 4.442586710338795, 4.291723543842206, 4.1155655614713424, 3.913033174764963, 3.6835722693633204, 3.427231643118975, 3.1447234420913, 2.83746530044463, 2.50760307210046, 2.1580132107651226, 1.7922840603901422, 1.4146755936469375, 1.0300574993115448, 0.6438259746523789, 0.2618001190342078, 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'6.00916313858621882675854258872508', '6.48908366108361147448701299741730', '7.09727066814418356724825728384273', '8.398950665637307366353301471004991', '9.118462917690198840513046517792756'], 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38869621811313374227001036047', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50003513441518027904301912754', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82685654000343620602718516805', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 49, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/p/1/8'], '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': '2-1875-1.1-c1-0-49', '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': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38869621811313374227001036047', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1760381594425786162989519722519', 'Lhash_array': ['1760381594425786162989519722519'], 'label': '2-1875-1.1-c1-0-49', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/p/1/8'}