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lfunc_lfunctions • Show schema
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{'Lhash': '2849741338565062801343240901342', 'a10': 0, 'a2': 4, 'a3': 26, 'a4': 16, 'a5': 0, 'a6': 104, 'a7': 22, 'a8': 64, 'a9': 433, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.019190990649033, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -4]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '50.1', 'coefficient_field': '1.1.1.1', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[1, -4], [1, -26, 243], [1], [1, -22, 16807], [1, 768, 161051], [1, -46, 371293], [1, 378, 1419857], [1, -1100, 2476099], [1, -1986, 6436343], [1, 5610, 20511149], [1, 3988, 28629151], [1, -142, 69343957], [1, -1542, 115856201], [1, -5026, 147008443], [1, 24738, 229345007], [1, -14166, 418195493], [1, -28380, 714924299], [1, -5522, 844596301], [1, -24742, 1350125107], [1, -42372, 1804229351], [1, -52126, 2073071593], [1, 39640, 3077056399], [1, -59826, 3939040643], [1, -57690, 5584059449], [1, -144382, 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[[[1, -28806, 18424351793], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-50-1.1-c5-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/50/6/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.859803435785714, 3.843326491938968, 3.7939879488957704, 3.7120755924080413, 3.598104726148616, 3.452869096849909, 3.2775071445241637, 3.073578732953923, 2.843146411372803, 2.588854356632888, 2.3139974878791087, 2.0225728766443085, 1.7193055412867584, 1.4096410651279419, 1.099698261166101, 0.7961763654780012, 0.506213005691758, 0.23719146766640092, -0.0035014505071222363, -0.20876251492567338, -0.3720960673236927, -0.4879632988353587, -0.5521414760605375, -0.5620744602165169, -0.5171930813299476, -0.41918202282277334, -0.272169139175997, 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'11.00687264443695052251940716716619', '12.90378539784589334649273375895219', '13.37909664764737732802977222766355', '14.52225701533708896050067772795767'], 'prelabel': '2-50-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.8318176125324586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 121163102903441517, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.24804953198617332104216478548', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.42340117537175849821087259903', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.14211270114479246595325699305', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.019190990649033, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'dirichlet_coefficients': [1, 4, 26, 16, 0, 104, 22, 64, 433, 0, -768, 416, 46, 88, 0, 256, -378, 1732, 1100, 0, 572, -3072, 1986, 1664, 0, 184, 4940, 352, -5610, 0, -3988, 1024, -19968, -1512, 0, 6928, 142, 4400, 1196, 0, 1542, 2288, 5026, -12288, 0, 7944, -24738, 6656, -16323, 0, -9828, 736, 14166, 19760, 0, 1408, 28600, -22440, 28380, 0, 5522, -15952, 9526, 4096, 0, -79872, 24742, -6048, 51636, 0, 42372, 27712, 52126, 568, 0, 17600, -16896, 4784, -39640, 0, 23221, 6168, 59826, 9152, 0, 20104, -145860, -49152, 57690, 0, 1012, 31776, -103688, -98952, 0, 26624, 144382, -65292, -332544, 0], 'euler11': [1, 768, 161051], 'euler13': [1, -46, 371293], 'euler17': [1, 378, 1419857], 'euler19': [1, -1100, 2476099], 'euler2': [1, -4, 0], 'euler23': [1, -1986, 6436343], 'euler29': [1, 5610, 20511149], 'euler3': [1, -26, 243], 'euler31': [1, 3988, 28629151], 'euler37': [1, -142, 69343957], 'euler41': [1, -1542, 115856201], 'euler43': [1, -5026, 147008443], 'euler47': [1, 24738, 229345007], 'euler5': [1, 0, 0], 'euler53': [1, -14166, 418195493], 'euler59': [1, -28380, 714924299], 'euler61': [1, -5522, 844596301], 'euler67': [1, -24742, 1350125107], 'euler7': [1, -22, 16807], 'euler71': [1, -42372, 1804229351], 'euler73': [1, -52126, 2073071593], 'euler79': [1, 39640, 3077056399], 'euler83': [1, -59826, 3939040643], 'euler89': [1, -57690, 5584059449], 'euler97': [1, -144382, 8587340257], 'euler_factors': [[1, -4, 0], [1, -26, 243], [1, 0, 0], [1, -22, 16807], [1, 768, 161051], [1, -46, 371293], [1, 378, 1419857], [1, -1100, 2476099], [1, -1986, 6436343], [1, 5610, 20511149], [1, 3988, 28629151], [1, -142, 69343957], [1, -1542, 115856201], [1, -5026, 147008443], [1, 24738, 229345007], [1, -14166, 418195493], [1, -28380, 714924299], [1, -5522, 844596301], [1, -24742, 1350125107], [1, -42372, 1804229351], [1, -52126, 2073071593], [1, 39640, 3077056399], [1, -59826, 3939040643], [1, -57690, 5584059449], [1, -144382, 8587340257]], 'index': 5, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/50/6/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/50/6/a/g'], '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': '2-50-1.1-c5-0-5', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-50-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.8318176125324586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 121163102903441517, 'z1': {'__RealLiteral__': 0, 'data': '2.24804953198617332104216478548', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10837924
{'Lhash': '2849741338565062801343240901342', 'Lhash_array': ['2849741338565062801343240901342'], 'label': '2-50-1.1-c5-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/6/a/g'}
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id: 24551381
{'Lhash': '2849741338565062801343240901342', 'Lhash_array': ['2849741338565062801343240901342'], 'label': '2-50-1.1-c5-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/6/a/g/1/1'}