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lfunc_lfunctions • Show schema
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{'Lhash': '1755889082518126070441253557059', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '5184.1', 'coefficient_field': '1.1.1.1', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1], [1, 1, 5], [1, -2, 7], [1, 2, 11], [1, 1, 13], [1, -3, 17], [1, 2, 19], [1, -6, 23], [1, 1, 29], [1, 8, 31], [1, 1, 37], [1, 2, 41], [1, 10, 43], [1, -4, 47], [1, -10, 53], [1, 4, 59], [1, 9, 61], [1, -14, 67], [1, -10, 71], [1, 9, 73], [1, -10, 79], [1, 12, 83], [1, -11, 89], [1, 2, 97], [1, -6, 101], [1, 12, 103], [1, 16, 107], [1, 5, 109], [1, 17, 113]], 'euler_factors_factorization': [[1], [1], [[[1, 1, 5], 1]], [[[1, -2, 7], 1]], [[[1, 2, 11], 1]], [[[1, 1, 13], 1]], [[[1, -3, 17], 1]], [[[1, 2, 19], 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0.7977671685473272, 0.39285188822815115, -0.021349720403894688, -0.42209655154541964, -0.7869939491253225, -1.0952260957986857], 'positive_zeros': ['1.38515225110294082706245571114271', '2.34932291764629378386923963816787', '3.36102040400281792770735695950600', '4.09193195998284307936737221915172', '5.12656573806582728748000894922458', '5.36986537425335647613270246538638', '6.51301414706917366998863156628730', '7.30754259073006344252649542525513', '7.83183883422768713644232091353740'], 'prelabel': '2-72e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 561615715028898241, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38515225110294082706245571114', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34932291764629378386923963817', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36102040400281792770735695951', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 2, 0, 0, 0, -2, 0, -1, 0, 0, 0, 3, 0, -2, 0, 0, 0, 6, 0, -4, 0, 0, 0, -1, 0, -8, 0, 0, 0, -2, 0, -1, 0, 0, 0, -2, 0, -10, 0, 0, 0, 4, 0, -3, 0, 0, 0, 10, 0, 2, 0, 0, 0, -4, 0, -9, 0, 0, 0, 1, 0, 14, 0, 0, 0, 10, 0, -9, 0, 0, 0, -4, 0, 10, 0, 0, 0, -12, 0, -3, 0, 0, 0, 11, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0], 'euler11': [1, 2, 11], 'euler13': [1, 1, 13], 'euler17': [1, -3, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, 1, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, 1, 37], 'euler41': [1, 2, 41], 'euler43': [1, 10, 43], 'euler47': [1, -4, 47], 'euler5': [1, 1, 5], 'euler53': [1, -10, 53], 'euler59': [1, 4, 59], 'euler61': [1, 9, 61], 'euler67': [1, -14, 67], 'euler7': [1, -2, 7], 'euler71': [1, -10, 71], 'euler73': [1, 9, 73], 'euler79': [1, -10, 79], 'euler83': [1, 12, 83], 'euler89': [1, -11, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 5], [1, -2, 7], [1, 2, 11], [1, 1, 13], [1, -3, 17], [1, 2, 19], [1, -6, 23], [1, 1, 29], [1, 8, 31], [1, 1, 37], [1, 2, 41], [1, 10, 43], [1, -4, 47], [1, -10, 53], [1, 4, 59], [1, 9, 61], [1, -14, 67], [1, -10, 71], [1, 9, 73], [1, -10, 79], [1, 12, 83], [1, -11, 89], [1, 2, 97]], 'index': 68, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5184/m', 'ModularForm/GL2/Q/holomorphic/5184/2/a/m/1/1', 'ModularForm/GL2/Q/holomorphic/5184/2/a/m'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-72e2-1.1-c1-0-68', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-72e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 561615715028898241, 'z1': {'__RealLiteral__': 0, 'data': '1.38515225110294082706245571114', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21548554
{'Lhash': '1755889082518126070441253557059', 'Lhash_array': ['1755889082518126070441253557059'], 'label': '2-72e2-1.1-c1-0-68', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/a/m'}
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id: 24569257
{'Lhash': '1755889082518126070441253557059', 'Lhash_array': ['1755889082518126070441253557059'], 'label': '2-72e2-1.1-c1-0-68', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/a/m/1/1'}
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id: 93401
{'Lhash': '561615715028898241', 'Lhash_array': ['561615715028898241'], 'label': '2-72e2-1.1-c1-0-68', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5184/m'}