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lfunc_lfunctions • Show schema
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{'Lhash': '1386045980176795223910736742300', 'a10': 0, 'a2': 0, 'a3': 30, 'a4': 0, 'a5': -32, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 657, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 125.74091473337684, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '784.1', 'coefficient_field': '1.1.1.1', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, -30, 243], [1, 32, 3125], [1], [1, -624, 161051], [1, -708, 371293], [1, 934, 1419857], [1, -1858, 2476099], [1, -1120, 6436343], [1, 1174, 20511149], [1, -2908, 28629151], [1, 12462, 69343957], [1, 2662, 115856201], [1, -7144, 147008443], [1, 7468, 229345007], [1, 27274, 418195493], [1, -2490, 714924299], [1, -11096, 844596301], [1, 39756, 1350125107], [1, -69888, 1804229351], [1, 16450, 2073071593], [1, 78376, 3077056399], [1, -109818, 3939040643], [1, -56966, 5584059449], [1, -115946, 8587340257], 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1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 62, 'label': '2-28e2-1.1-c5-0-62', 'leading_term': '5.61160538768716922577239469173000000000000000000000000000000000000000000000000000000000000', '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/784/6/a/n', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [5.611605387687169, 5.585535874424312, 5.5077379045852926, 5.379437064539424, 5.202655634636103, 4.980182213567669, 4.715529538241392, 4.412880859035142, 4.077025352153671, 3.713283184971716, 3.327420997429801, 2.9255587223230384, 2.514068838092597, 2.099469326675646, 1.688311792074458, 1.2870663774231343, 0.9020052933129759, 0.5390869310097909, 0.20384267337862927, -0.09873137409848745, -0.3642754378361186, -0.5891575950961981, -0.7705534619138186, 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'4.62113118220012519843899251095963', '6.37065069998397018754335660765453', '7.18950242076016733991085237186674', '7.978968531306661214106663257680192', '8.824195047513663950891143443373718', '9.163429126152729136039294504133588'], 'prelabel': '2-28e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.213425646669123, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'trace_hash': 1442693142796598882, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09339748660021126479644388013', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.93439585319624691971284313751', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33240806870580177835166028730', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 125.74091473337684, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, 30, 0, -32, 0, 0, 0, 657, 0, 624, 0, 708, 0, -960, 0, -934, 0, 1858, 0, 0, 0, 1120, 0, -2101, 0, 12420, 0, -1174, 0, 2908, 0, 18720, 0, 0, 0, -12462, 0, 21240, 0, -2662, 0, 7144, 0, -21024, 0, -7468, 0, 0, 0, -28020, 0, -27274, 0, -19968, 0, 55740, 0, 2490, 0, 11096, 0, 0, 0, -22656, 0, -39756, 0, 33600, 0, 69888, 0, -16450, 0, -63030, 0, 0, 0, -78376, 0, 212949, 0, 109818, 0, 29888, 0, -35220, 0, 56966, 0, 0, 0, 87240, 0, -59456, 0, 115946, 0, 409968, 0], 'euler11': [1, -624, 161051], 'euler13': [1, -708, 371293], 'euler17': [1, 934, 1419857], 'euler19': [1, -1858, 2476099], 'euler2': [1, 0, 0], 'euler23': [1, -1120, 6436343], 'euler29': [1, 1174, 20511149], 'euler3': [1, -30, 243], 'euler31': [1, -2908, 28629151], 'euler37': [1, 12462, 69343957], 'euler41': [1, 2662, 115856201], 'euler43': [1, -7144, 147008443], 'euler47': [1, 7468, 229345007], 'euler5': [1, 32, 3125], 'euler53': [1, 27274, 418195493], 'euler59': [1, -2490, 714924299], 'euler61': [1, -11096, 844596301], 'euler67': [1, 39756, 1350125107], 'euler7': [1, 0, 0], 'euler71': [1, -69888, 1804229351], 'euler73': [1, 16450, 2073071593], 'euler79': [1, 78376, 3077056399], 'euler83': [1, -109818, 3939040643], 'euler89': [1, -56966, 5584059449], 'euler97': [1, -115946, 8587340257], 'euler_factors': [[1, 0, 0], [1, -30, 243], [1, 32, 3125], [1, 0, 0], [1, -624, 161051], [1, -708, 371293], [1, 934, 1419857], [1, -1858, 2476099], [1, -1120, 6436343], [1, 1174, 20511149], [1, -2908, 28629151], [1, 12462, 69343957], [1, 2662, 115856201], [1, -7144, 147008443], [1, 7468, 229345007], [1, 27274, 418195493], [1, -2490, 714924299], [1, -11096, 844596301], [1, 39756, 1350125107], [1, -69888, 1804229351], [1, 16450, 2073071593], [1, 78376, 3077056399], [1, -109818, 3939040643], [1, -56966, 5584059449], [1, -115946, 8587340257]], 'index': 62, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/784/6/a/n/1/1', 'ModularForm/GL2/Q/holomorphic/784/6/a/n'], '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': '2-28e2-1.1-c5-0-62', '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': '2-28e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.213425646669123, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1442693142796598882, 'z1': {'__RealLiteral__': 0, 'data': '1.09339748660021126479644388013', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20798242
{'Lhash': '1386045980176795223910736742300', 'Lhash_array': ['1386045980176795223910736742300'], 'factors': ['2-28e2-1.1-c5-0-62'], 'label': '2-28e2-1.1-c5-0-62', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/784/6/a/n'}
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id: 24592977
{'Lhash': '1386045980176795223910736742300', 'Lhash_array': ['1386045980176795223910736742300'], 'factors': ['2-28e2-1.1-c5-0-62'], 'label': '2-28e2-1.1-c5-0-62', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/784/6/a/n/1/1'}