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lfunc_lfunctions • Show schema
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{'Lhash': '429970952321087598990978605221,867151166288395972316851427020,1066763048274944696800944998069,1103591291880733745720098048339,1256047658713182981526692547218', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1263389371.5139055, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -5, 10, -10, 5, -1]], [23, [1, -5, 10, -10, 5, -1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '8280.1', 'coefficient_field': '1.1.1.1', 'conductor': 38918104863436800000, 'conductor_radical': 690, 'degree': 10, 'euler_factors': [[1], [1], [1, -5, 10, -10, 5, -1], [1, 2, 7, -1, 30, 46, 210, -49, 2401, 4802, 16807], [1, -1, 20, -16, 227, -174, 2497, -1936, 26620, -14641, 161051], [1, -4, 19, -133, 496, -1606, 6448, -22477, 41743, -114244, 371293], [1, 4, 39, 115, 406, 1566, 6902, 33235, 191607, 334084, 1419857], [1, -7, 54, -352, 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'6.42986413431045574438234186874319', '6.62860657479361185724672934578950', '6.88524400381432345104979220302913', '6.88604838299135277703639506661873', '6.99810823511478750310205297496884', '7.12701054666033135049347327987034', '7.35566462744005159835792049976811', '7.64102370581321334639074817791086', '7.74151651941721753376528805423613', '7.75439918450227469210137170157134', '7.88452945363152081708365430270905', '8.025934477765864123626538632131179'], 'prelabel': '10-8280e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e5-0', 'trace_hash': 57835080045177114, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33918727466675367037138430248', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.68406165400172018254651081345', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.841527663918498789589108559110', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1263389371.5139055, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 38918104863436800000, 'conductor_radical': 690, 'degree': 10, 'dirichlet_coefficients': [1, 0, 0, 0, 5, 0, -2, 0, 0, 0, 1, 0, 4, 0, 0, 0, -4, 0, 7, 0, 0, 0, 5, 0, 15, 0, 0, 0, -4, 0, 19, 0, 0, 0, -10, 0, 15, 0, 0, 0, -25, 0, 0, 0, 0, 0, 11, 0, -3, 0, 0, 0, -3, 0, 5, 0, 0, 0, 1, 0, -5, 0, 0, 0, 20, 0, 9, 0, 0, 0, -1, 0, -1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 45, 0, -20, 0, 0, 0, -6, 0, -8, 0, 0, 0, 35, 0, 25, 0, 0, 0], 'euler11': [1, -1, 20, -16, 227, -174, 2497, -1936, 26620, -14641, 161051], 'euler13': [1, -4, 19, -133, 496, -1606, 6448, -22477, 41743, -114244, 371293], 'euler17': [1, 4, 39, 115, 406, 1566, 6902, 33235, 191607, 334084, 1419857], 'euler19': [1, -7, 54, -352, 1949, -7810, 37031, -127072, 370386, -912247, 2476099], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], 'euler29': [1, 4, 104, 500, 4907, 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1419857], [1, -7, 54, -352, 1949, -7810, 37031, -127072, 370386, -912247, 2476099], [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], [1, 4, 104, 500, 4907, 22264, 142303, 420500, 2536456, 2829124, 20511149], [1, -19, 227, -2173, 16253, -98336, 503843, -2088253, 6762557, -17546899, 28629151], [1, -15, 249, -2256, 20618, -125810, 762866, -3088464, 12612597, -28112415, 69343957], [1, 25, 417, 4753, 42913, 303514, 1759433, 7989793, 28740057, 70644025, 115856201], [1, 0, 215, 0, 18490, 0, 795070, 0, 17094005, 0, 147008443], [1, -11, 125, -952, 5780, -41402, 271660, -2102968, 12977875, -53676491, 229345007], [1, 3, 105, 196, 8458, 24194, 448274, 550564, 15632085, 23671443, 418195493], [1, -1, 153, 0, 14236, -6606, 839924, 0, 31422987, -12117361, 714924299], [1, 5, 190, 652, 18257, 49998, 1113677, 2426092, 43126390, 69229205, 844596301], [1, -9, 209, -1980, 24396, -176326, 1634532, -8888220, 62859467, -181360089, 1350125107], [1, 1, 141, -123, 12967, -23580, 920657, -620043, 50465451, 25411681, 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[{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '10-8280e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e5-0', 'trace_hash': 57835080045177114, 'z1': {'__RealLiteral__': 0, 'data': '0.33918727466675367037138430248', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '429970952321087598990978605221,867151166288395972316851427020,1066763048274944696800944998069,1103591291880733745720098048339,1256047658713182981526692547218', 'Lhash_array': ['429970952321087598990978605221', '867151166288395972316851427020', '1066763048274944696800944998069', '1103591291880733745720098048339', '1256047658713182981526692547218'], 'label': '10-8280e5-1.1-c1e5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/a/bs'}