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lfunc_lfunctions • Show schema
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{'Lhash': '1581240067854755328865683191137', 'a10': [-0.30987853221710426, 0.5367253619748938], 'a2': [0.23912327825655447, 0.0], 'a3': [-1.7031595602263268, 0.3150357319569717], 'a4': [-1.9428200577958383, 0.0], 'a5': [-1.295894462791016, 2.2445550508012158], 'a6': [-0.40726509743531086, 0.07533237699350426], 'a7': [0.0, 0.0], 'a8': [-0.9428200577958384, 0.0], 'a9': [2.80150497518067, -1.07311223739083], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7031595602263268, -0.3150357319569717]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.214', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '471820067638713371607050881582', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.23912327825655447, 0], [2.0, 0]], [[1.0, 0], [1.7031595602263268, -0.3150357319569717]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-21e2-63.25-c1-0-17', '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/441/2/h/g/214/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.460430011313353, 0.5685930118173316, 0.6578806221910366, 0.7266472979904565, 0.7700231725081348, 0.7803668567454246, 0.7480739700246888, 0.6626081498448265, 0.5136684833657216, 0.29244175381567994, -0.007108057797918511, -0.38697970182352837, -0.8439987495046914, -1.368925467094564, -1.9459396490222818, -2.5526325997005532, -3.1606139661220496, -3.7367982414500776, -4.245373924271506, -4.650381628870551, -4.918742790078195, -5.023497442516271, -4.946939200717154, -4.683290061985916, -4.240548196710943, -3.641177036498684, -2.9213878072928763, -2.1288982451925005, 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'9.753691305685788532744587156434021', '10.25518066981165553977525519739297', '11.47738900162174380659430182188038'], 'prelabel': '2-21e2-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.3987693025438973, 'root_number': '0.31269179296545496 + 0.9498546428859781*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.199384651272', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24737847129963641946849912318', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.72560182670650211030794877481', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.77306242370155286019633368997', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '63.25', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/h/g/214/3'], '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': '2-21e2-63.25-c1-0-17', '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': '2-21e2-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.19938465127194865, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24737847129963641946849912318', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1581240067854755328865683191137', 'Lhash_array': ['1581240067854755328865683191137'], 'label': '2-21e2-63.25-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/h/g/214/3'}