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lfunc_lfunctions • Show schema
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{'Lhash': '1802227048602973266981169465495,1911756433107511672204223836047', 'a10': 0, 'a2': 0, 'a3': 6, 'a4': 0, 'a5': 6, 'a6': 0, 'a7': 10, 'a8': 0, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15528.159000700882, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -6, 9]], [11, [1, 22, 121]]], 'bad_primes': [2, 3, 11], 'central_character': '2112.1', 'coefficient_field': '1.1.1.1', 'conductor': 4460544, 'conductor_radical': 66, 'degree': 4, 'euler_factors': [[1], [1, -6, 9], [1, -6, 242, -750, 15625], [1, -10, 694, -3430, 117649], [1, 22, 121], [1, -2, -518, -4394, 4826809], [1, 104, 7022, 510952, 24137569], [1, 4, -1578, 27436, 47045881], [1, 102, 24062, 1241034, 148035889], [1, -392, 75702, -9560488, 594823321], [1, 64, 33406, 1906624, 887503681], [1, -164, -770, -8307092, 2565726409], [1, 732, 264998, 50450172, 4750104241], [1, 168, 87462, 13357176, 6321363049], [1, 314, 197870, 32600422, 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'data': '1.42170646097473393085516616965', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.50810991038328436082166500723', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.30335863360138121773310135049', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 15528.159000700882, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 4460544, 'conductor_radical': 66, 'degree': 4, 'dirichlet_coefficients': [1, 0, 6, 0, 6, 0, 10, 0, 27, 0, -22, 0, 2, 0, 36, 0, -104, 0, -4, 0, 60, 0, -102, 0, -206, 0, 108, 0, 392, 0, -64, 0, -132, 0, 60, 0, 164, 0, 12, 0, -732, 0, -168, 0, 162, 0, -314, 0, -594, 0, -624, 0, 382, 0, -132, 0, -24, 0, -508, 0, 6, 0, 270, 0, 12, 0, -216, 0, -612, 0, -878, 0, 260, 0, -1236, 0, -220, 0, 118, 0, 405, 0, -496, 0, -624, 0, 2352, 0, -1756, 0, 20, 0, -384, 0, -24, 0, 1968, 0, -594, 0], 'euler11': [1, 22, 121, 0, 0], 'euler13': [1, -2, -518, -4394, 4826809], 'euler17': [1, 104, 7022, 510952, 24137569], 'euler19': [1, 4, -1578, 27436, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 102, 24062, 1241034, 148035889], 'euler29': [1, -392, 75702, -9560488, 594823321], 'euler3': [1, -6, 9, 0, 0], 'euler31': [1, 64, 33406, 1906624, 887503681], 'euler37': [1, -164, -770, -8307092, 2565726409], 'euler41': [1, 732, 264998, 50450172, 4750104241], 'euler43': [1, 168, 87462, 13357176, 6321363049], 'euler47': [1, 314, 197870, 32600422, 10779215329], 'euler5': [1, -6, 242, -750, 15625], 'euler53': [1, -382, 310962, -56871014, 22164361129], 'euler59': [1, 508, 418086, 104332532, 42180533641], 'euler61': [1, -6, 66354, -1361886, 51520374361], 'euler67': [1, 216, 298758, 64964808, 90458382169], 'euler7': [1, -10, 694, -3430, 117649], 'euler71': [1, 878, 841070, 314245858, 128100283921], 'euler73': [1, -260, -58058, -101144420, 151334226289], 'euler79': [1, -118, 829606, -58178602, 243087455521], 'euler83': [1, 496, 441030, 283606352, 326940373369], 'euler89': [1, 1756, 1701014, 1237925564, 496981290961], 'euler97': [1, -1968, 2769054, -1796140464, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, -6, 9, 0, 0], [1, -6, 242, -750, 15625], [1, -10, 694, -3430, 117649], [1, 22, 121, 0, 0], [1, -2, -518, -4394, 4826809], [1, 104, 7022, 510952, 24137569], [1, 4, -1578, 27436, 47045881], [1, 102, 24062, 1241034, 148035889], [1, -392, 75702, -9560488, 594823321], [1, 64, 33406, 1906624, 887503681], [1, -164, -770, -8307092, 2565726409], [1, 732, 264998, 50450172, 4750104241], [1, 168, 87462, 13357176, 6321363049], [1, 314, 197870, 32600422, 10779215329], [1, -382, 310962, -56871014, 22164361129], [1, 508, 418086, 104332532, 42180533641], [1, -6, 66354, -1361886, 51520374361], [1, 216, 298758, 64964808, 90458382169], [1, 878, 841070, 314245858, 128100283921], [1, -260, -58058, -101144420, 151334226289], [1, -118, 829606, -58178602, 243087455521], [1, 496, 441030, 283606352, 326940373369], [1, 1756, 1701014, 1237925564, 496981290961], [1, -1968, 2769054, -1796140464, 832972004929]], 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2112/4/a/bl'], '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': '4-2112e2-1.1-c3e2-0-13', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 2, 'prelabel': '4-2112e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.162976033841703, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1355832914015890377, 'z1': {'__RealLiteral__': 0, 'data': '1.42170646097473393085516616965', 'prec': 103}}
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{'Lhash': '1802227048602973266981169465495,1911756433107511672204223836047', 'Lhash_array': ['1802227048602973266981169465495', '1911756433107511672204223836047'], 'factors': ['2-2112-1.1-c3-0-103', '2-2112-1.1-c3-0-110'], 'label': '4-2112e2-1.1-c3e2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2112/4/a/bl'}