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lfunc_lfunctions • Show schema
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{'Lhash': '976996838159603006181822094942', 'a10': [-3.1288871819733695, -2.010813693816471], 'a2': [0.14231483827328514, 0.9898214418809327], 'a3': [0.5272079434038438, -1.154424367236368], 'a4': [-0.9594929736144974, 0.28173255684142967], 'a5': [-2.435633583045239, 2.8108709963104506], 'a6': [1.2177035049222946, 0.35755000958909056], 'a7': [0.8412535328311812, -0.5406408174555976], 'a8': [-0.41541501300188644, -0.9096319953545183], 'a9': [0.9098347977548766, 1.050005330130836], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.5711829450852295, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.14231483827328514, -0.9898214418809327]]], [7, [[1.0, 0], [-0.8412535328311812, 0.5406408174555976]]], [23, [[1.0, 0], [-3.485338527767149, -3.2943004336067956]]]], 'bad_primes': [2, 7, 23], 'central_character': '322.141', 'coefficient_field': 'CDF', 'conductor': 322, 'conductor_radical': 322, 'conjugate': 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[32.817786027149026, 71.86092763300695]], [[1.0, 0], [4.702932954915017, 5.4274739569140245], [-11.812131576682667, 82.15517967611741]], [[1.0, 0], [0.5390383953702895, -1.180329443585005], [-58.28260532113037, -67.26171211752899]], [[1.0, 0], [3.9437275519417914, -4.551304215161867], [-13.804539312508659, -96.01267986245047]], [[1.0, 0], [-8.23234264733648, -9.500629873133878], [-14.373798665601798, 99.9719656299742]], [[1.0, 0], [-0.7809167720305331, 5.4313954515125555], [-98.82777628229323, -29.01845335466726]], [[1.0, 0], [-1.327697295150467, -2.9072515484870833], [-70.07009853214551, 80.86520445590564]], [[1.0, 0], [-10.934702303440634, -3.2107182886843537], [91.69663507859875, 58.929849102660135]], [[1.0, 0], [-2.344527137426441, -16.306544418369636], [-108.4227060184382, 31.835778923081556]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-322-23.3-c1-0-4', '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/322/2/i/e/141/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0995642945823254, 0.9483435615905008, 0.7953785495463073, 0.6338601609029814, 0.45718503759971907, 0.2600006015512883, 0.03901053563625692, -0.20646935490184073, -0.4741706382558623, -0.7587196969554572, -1.0516721284175656, -1.341754742326653, -1.6153428176762035, -1.8571921340504027, -2.0514248969219477, -2.1827397525168495, -2.2377824904972443, -2.206579849585579, -2.083908511560612, -1.8704495888495967, -1.573570291414775, -1.2075829887086584, -0.7933602778453979, -0.3572337076509508, 0.07082823654491237, 0.4596849937757512, 0.7799645887250861, 1.0072270180047969, 1.1250260563542038, 1.127500875816937, 1.0211224849958682, 0.825259605775941, 0.5713176568053099, 0.3003403980343214, 0.05913701379823932, -0.10480840624769228, 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'rational': False, 'root_analytic_conductor': 1.6034908621770283, 'root_angle': -0.6563516571929421, 'root_number': '-0.47167836799851465 - 0.8817706715253449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.328175828596', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77071461014865079698051701731', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.97875830720643996068797338945', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.28733929712051931114911765946', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.5711829450852295, 'bad_primes': [2, 7, 23], 'central_character': '23.3', 'conductor': 322, 'conductor_radical': 322, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/322/2/i/e/141/3'], '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': '2-322-23.3-c1-0-4', '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': '2-322-23.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6034908621770283, 'root_angle': -0.32817582859647104, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77071461014865079698051701731', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '976996838159603006181822094942', 'Lhash_array': ['976996838159603006181822094942'], 'label': '2-322-23.3-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/322/2/i/e/141/3'}