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lfunc_lfunctions • Show schema
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{'Lhash': '2408042958732254875890405907589', 'a10': 216, 'a2': -4, 'a3': 9, 'a4': 16, 'a5': -54, 'a6': -36, 'a7': 104, 'a8': -64, 'a9': 81, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.283755458679796, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 4]], [3, [1, -9]], [19, [1, -361]]], 'bad_primes': [2, 3, 19], 'central_character': '114.1', 'coefficient_field': '1.1.1.1', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[1, 4], [1, -9], [1, 54, 3125], [1, -104, 16807], [1, 330, 161051], [1, 46, 371293], [1, 618, 1419857], [1, -361], [1, 402, 6436343], [1, 2628, 20511149], [1, 2368, 28629151], [1, 12130, 69343957], [1, 18864, 115856201], [1, 10408, 147008443], [1, 4770, 229345007], [1, 19452, 418195493], [1, -30528, 714924299], [1, -11138, 844596301], [1, -49508, 1350125107], [1, -7572, 1804229351], [1, -2342, 2073071593], [1, -22424, 3077056399], [1, 46734, 3939040643], [1, 70104, 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15386239549], 1]], [[[1, 156792, 18424351793], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-114-1.1-c5-0-12', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/114/6/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [-6.927966227306349e-61, 0.1703022567769914, 0.33869963976681483, 0.5032988771061913, 0.6622301209337923, 0.8136591994614528, 0.9558004884778474, 1.086930561696908, 1.2054027403840033, 1.309662615642771, 1.3982645626975245, 1.469889206708455, 1.5233617355149414, 1.5576708877604242, 1.5719883767745997, 1.5656884431394635, 1.53836716388903, 1.489861085690256, 1.4202646950600744, 1.329946192631759, 1.2195610026087578, 1.0900624246894584, 0.9427088256628159, 0.7790667731633835, 0.6010095361352328, 0.41071041653145657, 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'9.949878674307051229738921057254069', '11.05478115143156214223463318380575', '11.87602005177780782341279750545197'], 'prelabel': '2-114-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.275950825100751, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 1362336043610711863, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89961094823661015590398451946', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.51700168806837292559859712960', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.05565544974233652585307204564', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.283755458679796, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'dirichlet_coefficients': [1, -4, 9, 16, -54, -36, 104, -64, 81, 216, -330, 144, -46, -416, -486, 256, -618, -324, 361, -864, 936, 1320, -402, -576, -209, 184, 729, 1664, -2628, 1944, -2368, -1024, -2970, 2472, -5616, 1296, -12130, -1444, -414, 3456, -18864, -3744, -10408, -5280, -4374, 1608, -4770, 2304, -5991, 836, -5562, -736, -19452, -2916, 17820, -6656, 3249, 10512, 30528, -7776, 11138, 9472, 8424, 4096, 2484, 11880, 49508, -9888, -3618, 22464, 7572, -5184, 2342, 48520, -1881, 5776, -34320, 1656, 22424, -13824, 6561, 75456, -46734, 14976, 33372, 41632, -23652, 21120, -70104, 17496, -4784, -6432, -21312, 19080, -19494, -9216, 105710, 23964, -26730, -3344], 'euler11': [1, 330, 161051], 'euler13': [1, 46, 371293], 'euler17': [1, 618, 1419857], 'euler19': [1, -361, 0], 'euler2': [1, 4, 0], 'euler23': [1, 402, 6436343], 'euler29': [1, 2628, 20511149], 'euler3': [1, -9, 0], 'euler31': [1, 2368, 28629151], 'euler37': [1, 12130, 69343957], 'euler41': [1, 18864, 115856201], 'euler43': [1, 10408, 147008443], 'euler47': [1, 4770, 229345007], 'euler5': [1, 54, 3125], 'euler53': [1, 19452, 418195493], 'euler59': [1, -30528, 714924299], 'euler61': [1, -11138, 844596301], 'euler67': [1, -49508, 1350125107], 'euler7': [1, -104, 16807], 'euler71': [1, -7572, 1804229351], 'euler73': [1, -2342, 2073071593], 'euler79': [1, -22424, 3077056399], 'euler83': [1, 46734, 3939040643], 'euler89': [1, 70104, 5584059449], 'euler97': [1, -105710, 8587340257], 'euler_factors': [[1, 4, 0], [1, -9, 0], [1, 54, 3125], [1, -104, 16807], [1, 330, 161051], [1, 46, 371293], [1, 618, 1419857], [1, -361, 0], [1, 402, 6436343], [1, 2628, 20511149], [1, 2368, 28629151], [1, 12130, 69343957], [1, 18864, 115856201], [1, 10408, 147008443], [1, 4770, 229345007], [1, 19452, 418195493], [1, -30528, 714924299], [1, -11138, 844596301], [1, -49508, 1350125107], [1, -7572, 1804229351], [1, -2342, 2073071593], [1, -22424, 3077056399], [1, 46734, 3939040643], [1, 70104, 5584059449], [1, -105710, 8587340257]], 'index': 12, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/6/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/114/6/a/a'], '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': '2-114-1.1-c5-0-12', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-114-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.275950825100751, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1362336043610711863, 'z1': {'__RealLiteral__': 0, 'data': '1.89961094823661015590398451946', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20616719
{'Lhash': '2408042958732254875890405907589', 'Lhash_array': ['2408042958732254875890405907589'], 'label': '2-114-1.1-c5-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/6/a/a'}
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id: 24556564
{'Lhash': '2408042958732254875890405907589', 'Lhash_array': ['2408042958732254875890405907589'], 'label': '2-114-1.1-c5-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/6/a/a/1/1'}