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lfunc_lfunctions • Show schema
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{'Lhash': '853733167024665985239038438503,1802029362042815356375879288829', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 6, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 477.2944672800165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, -8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, -2, -1, -10, 25], [1, -6, 23, -42, 49], [1, 0, 22, 0, 121], [1, 5, 12, 65, 169], [1, 4, -1, 68, 289], [1, -8, 19], [1, 6, 13, 138, 529], [1, 4, -13, 116, 841], [1, -14, 111, -434, 961], [1, 2, 75, 74, 1369], [1, 0, -41, 0, 1681], [1, -11, 78, -473, 1849], [1, 6, -11, 282, 2209], [1, 2, -49, 106, 2809], [1, 8, 5, 472, 3481], [1, 7, -12, 427, 3721], [1, -3, -58, -201, 4489], [1, 6, -35, 426, 5041], [1, 9, 8, 657, 5329], [1, -5, -54, -395, 6241], 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'4.03989490455344729230709226880720', '4.47351210385094920700078117889321', '4.88968745443964316322907829406029', '4.97222143434921049825181007593384', '5.36491778444830718988827758541796', '6.01513035474501692563058594376963', '6.20876152325514070858790975165890', '6.74792265808836219270128844739782', '7.29647068910001796852401970757914', '7.54427566591219358721419870725365', '8.034341938820332371636715427318504', '8.056498021957868892901208731155688', '8.511535382787352037929656385904340', '9.281968304190846881382656072116630'], 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 690715699342886256, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67347671895627927502237874484', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.42155051377593773348860172898', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.79780884082885014557631323343', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 477.2944672800165, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, -5, 0, 0, 0, -4, 0, 8, 0, 0, 0, -6, 0, 5, 0, 0, 0, -4, 0, 14, 0, 0, 0, 12, 0, -2, 0, 0, 0, 0, 0, 11, 0, 0, 0, -6, 0, 13, 0, 0, 0, -2, 0, 0, 0, 0, 0, -8, 0, -7, 0, 0, 0, -10, 0, 3, 0, 0, 0, -6, 0, -9, 0, 0, 0, 0, 0, 5, 0, 0, 0, 32, 0, -8, 0, 0, 0, 12, 0, -30, 0, 0, 0, 16, 0, 14, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 5, 12, 65, 169], 'euler17': [1, 4, -1, 68, 289], 'euler19': [1, -8, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 6, 13, 138, 529], 'euler29': [1, 4, -13, 116, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -14, 111, -434, 961], 'euler37': [1, 2, 75, 74, 1369], 'euler41': [1, 0, -41, 0, 1681], 'euler43': [1, -11, 78, -473, 1849], 'euler47': [1, 6, -11, 282, 2209], 'euler5': [1, -2, -1, -10, 25], 'euler53': [1, 2, -49, 106, 2809], 'euler59': [1, 8, 5, 472, 3481], 'euler61': [1, 7, -12, 427, 3721], 'euler67': [1, -3, -58, -201, 4489], 'euler7': [1, -6, 23, -42, 49], 'euler71': [1, 6, -35, 426, 5041], 'euler73': [1, 9, 8, 657, 5329], 'euler79': [1, -5, -54, -395, 6241], 'euler83': [1, -32, 422, -2656, 6889], 'euler89': [1, -12, 55, -1068, 7921], 'euler97': [1, -14, 99, -1358, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -2, -1, -10, 25], [1, -6, 23, -42, 49], [1, 0, 22, 0, 121], [1, 5, 12, 65, 169], [1, 4, -1, 68, 289], [1, -8, 19, 0, 0], [1, 6, 13, 138, 529], [1, 4, -13, 116, 841], [1, -14, 111, -434, 961], [1, 2, 75, 74, 1369], [1, 0, -41, 0, 1681], [1, -11, 78, -473, 1849], [1, 6, -11, 282, 2209], [1, 2, -49, 106, 2809], [1, 8, 5, 472, 3481], [1, 7, -12, 427, 3721], [1, -3, -58, -201, 4489], [1, 6, -35, 426, 5041], [1, 9, 8, 657, 5329], [1, -5, -54, -395, 6241], [1, -32, 422, -2656, 6889], [1, -12, 55, -1068, 7921], [1, -14, 99, -1358, 9409]], 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/s/p'], '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': '4-2736e2-1.1-c1e2-0-32', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 690715699342886256, 'z1': {'__RealLiteral__': 0, 'data': '0.67347671895627927502237874484', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '853733167024665985239038438503,1802029362042815356375879288829', 'Lhash_array': ['853733167024665985239038438503', '1802029362042815356375879288829'], 'label': '4-2736e2-1.1-c1e2-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/s/p'}