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lfunc_lfunctions • Show schema
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{'Lhash': '2180252295841643786146796702774', 'a10': [0.0, 0.0], 'a2': [2.706362161738162, 0.0], 'a3': [1.0, 0.0], 'a4': [5.324396150488057, 0.0], 'a5': [0.0, 0.0], 'a6': [2.706362161738162, 0.0], 'a7': [0.4702941842383722, 0.0], 'a8': [8.99701995230888, 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], [-2.706362161738162, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.4702941842383722, 0], [7.0, 0]], [[1.0, 0], [3.18147816442886, 0], [11.0, 0]], [[1.0, 0], [-0.5634441756789654, 0], [13.0, 0]], [[1.0, 0], [1.706362161738162, 0], [17.0, 0]], [[1.0, 0], [-3.7401005216554997, 0], [19.0, 0]], [[1.0, 0], 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[[1.0, 0], [-11.775843332580445, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 68, 'label': '2-1875-1.1-c1-0-68', 'leading_term': '7.14020195074092164843744955290', '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/h/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [7.140201950740922, 7.1376332541379615, 7.129587624201808, 7.11506588126095, 7.092465885569987, 7.059671817855478, 7.014169212454911, 6.953177738488072, 6.873793622857524, 6.77313433888017, 6.648479408033056, 6.497402540397859, 6.317891611805088, 6.108453994115055, 5.86820547572095, 5.596941463519576, 5.295189417287309, 4.964241616704232, 4.606167477417012, 4.223804776216746, 3.820729357824914, 3.4012031996028966, 2.9701011126621952, 2.5328168527680304, 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'4.31306932818624656674694980169458', '5.03729246103247927089008975375048', '5.81740036152896033280465309952308', '6.61105896077978953567954110260962', '7.61333265618931646549851847363369', '7.947921582124019923367039444049318', '9.307416444362207140165137116652007'], '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': '1.71991579970782834998441634687', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67251453519567784684462333184', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39093853213543805150769537653', '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': 68, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/h/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': '2-1875-1.1-c1-0-68', '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': '1.71991579970782834998441634687', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2180252295841643786146796702774', 'Lhash_array': ['2180252295841643786146796702774'], 'label': '2-1875-1.1-c1-0-68', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/h/1/4'}