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lfunc_lfunctions • Show schema
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{'Lhash': '2219724438888791257189309328428', 'a10': [7.38199752152804, 0.0], 'a2': [2.329423498720254, 0.0], 'a3': [0.0, 0.0], 'a4': [3.426213836390108, 0.0], 'a5': [3.1690233766352858, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [3.322256024687081, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.551978056479133, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 17], 'central_character': '1071.1', 'coefficient_field': 'CDF', 'conductor': 1071, 'conductor_radical': 357, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.329423498720254, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.1690233766352858, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.40621856749175117, 0], [11.0, 0]], [[1.0, 0], [-3.079400512998604, 0], [13.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.5794464844419036, 0], [19.0, 0]], 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[109.0, 0]], [[1.0, 0], [4.838092724713871, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 31, 'label': '2-1071-1.1-c1-0-31', 'leading_term': '4.8686955742801667954810037873200', '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/1071/2/a/m/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [4.868695574280167, 4.868229137185911, 4.866531796119414, 4.862726266816445, 4.855404830430703, 4.842705713000754, 4.82241058940399, 4.7920559419564395, 4.749051250320324, 4.690798006935043, 4.614804932638419, 4.518796143298866, 4.400810145408623, 4.2592883112358795, 4.093151908531112, 3.901866909276429, 3.6854957758288274, 3.444735317777305, 3.1809396081848886, 2.8961269006360797, 2.592969534516658, 2.2747659735407066, 1.9453943965594163, 1.6092476450113058, 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'5.56445135232467930104627945509877', '6.34236019401565509210068832055894', '6.69042861127185264420172008973573', '8.166561169304786587105265140755875', '9.232780643362219863575807214365922', '10.01617372088883412442866584374586'], 'prelabel': '2-1071-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9243765244029594, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75105383020301437125779422172', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73885673412750403632093243225', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.70338840549253129316472031337', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.551978056479133, 'bad_primes': [3, 7, 17], 'central_character': '1.1', 'conductor': 1071, 'conductor_radical': 357, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1071/2/a/m/1/5'], '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': '2-1071-1.1-c1-0-31', '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': '2-1071-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9243765244029594, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75105383020301437125779422172', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2219724438888791257189309328428', 'Lhash_array': ['2219724438888791257189309328428'], 'factors': ['2-1071-1.1-c1-0-31'], 'label': '2-1071-1.1-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1071/2/a/m/1/5'}