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lfunc_lfunctions • Show schema
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{'Lhash': '2280372889854199825958177238884', 'a10': -1120, 'a2': 8, 'a3': -27, 'a4': 64, 'a5': -140, 'a6': -216, 'a7': -60, 'a8': 512, 'a9': 729, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 35.6118929051899, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -8]], [3, [1, 27]], [19, [1, 6859]]], 'bad_primes': [2, 3, 19], 'central_character': '114.1', 'coefficient_field': '1.1.1.1', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[1, -8], [1, 27], [1, 140, 78125], [1, 60, 823543], [1, -3976, 19487171], [1, -1592, 62748517], [1, 23682, 410338673], [1, 6859], [1, 70370, 3404825447], [1, -97502, 17249876309], [1, 234890, 27512614111], [1, -146968, 94931877133], [1, 232282, 194754273881], [1, 409028, 271818611107], [1, 891710, 506623120463], [1, -30862, 1174711139837], [1, 374820, 2488651484819], [1, 1548106, 3142742836021], [1, -3944928, 6060711605323], [1, -477232, 9095120158391], [1, -514206, 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-2.8087842315993514], 'positive_zeros': ['1.79889702213183872215484773743157', '3.65533615208293891543198853030638', '4.61154946252590856745432307775151', '6.04054158131555224612591823387377', '6.90707608457718981682770998428961', '8.280774078054575963366629692465445', '9.729081305622310368702145217749039', '11.06040326366247908053777874662033', '11.70478069424092871045758471960962'], 'prelabel': '2-114-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.967570100567726, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c7-0', 'trace_hash': 2133782847835744269, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79889702213183872215484773743', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65533615208293891543198853031', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.61154946252590856745432307775', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 35.6118929051899, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'dirichlet_coefficients': [1, 8, -27, 64, -140, -216, -60, 512, 729, -1120, 3976, -1728, 1592, -480, 3780, 4096, -23682, 5832, -6859, -8960, 1620, 31808, -70370, -13824, -58525, 12736, -19683, -3840, 97502, 30240, -234890, 32768, -107352, -189456, 8400, 46656, 146968, -54872, -42984, -71680, -232282, 12960, -409028, 254464, -102060, -562960, -891710, -110592, -819943, -468200, 639414, 101888, 30862, -157464, -556640, -30720, 185193, 780016, -374820, 241920, -1548106, -1879120, -43740, 262144, -222880, -858816, 3944928, -1515648, 1899990, 67200, 477232, 373248, 514206, 1175744, 1580175, -438976, -238560, -343872, -4866382, -573440, 531441, -1858256, 2043204, 103680, 3315480, -3272224, -2632554, 2035712, -7822422, -816480, -95520, -4503680, 6342030, -7133680, 960260, -884736, -2747090, -6559544, 2898504, -3745600], 'euler11': [1, -3976, 19487171], 'euler13': [1, -1592, 62748517], 'euler17': [1, 23682, 410338673], 'euler19': [1, 6859, 0], 'euler2': [1, -8, 0], 'euler23': [1, 70370, 3404825447], 'euler29': [1, -97502, 17249876309], 'euler3': [1, 27, 0], 'euler31': [1, 234890, 27512614111], 'euler37': [1, -146968, 94931877133], 'euler41': [1, 232282, 194754273881], 'euler43': [1, 409028, 271818611107], 'euler47': [1, 891710, 506623120463], 'euler5': [1, 140, 78125], 'euler53': [1, -30862, 1174711139837], 'euler59': [1, 374820, 2488651484819], 'euler61': [1, 1548106, 3142742836021], 'euler67': [1, -3944928, 6060711605323], 'euler7': [1, 60, 823543], 'euler71': [1, -477232, 9095120158391], 'euler73': [1, -514206, 11047398519097], 'euler79': [1, 4866382, 19203908986159], 'euler83': [1, -2043204, 27136050989627], 'euler89': [1, 7822422, 44231334895529], 'euler97': [1, 2747090, 80798284478113], 'euler_factors': [[1, -8, 0], [1, 27, 0], [1, 140, 78125], [1, 60, 823543], [1, -3976, 19487171], [1, -1592, 62748517], [1, 23682, 410338673], [1, 6859, 0], [1, 70370, 3404825447], [1, -97502, 17249876309], [1, 234890, 27512614111], [1, -146968, 94931877133], [1, 232282, 194754273881], [1, 409028, 271818611107], [1, 891710, 506623120463], [1, -30862, 1174711139837], [1, 374820, 2488651484819], [1, 1548106, 3142742836021], [1, -3944928, 6060711605323], [1, -477232, 9095120158391], [1, -514206, 11047398519097], [1, 4866382, 19203908986159], [1, -2043204, 27136050989627], [1, 7822422, 44231334895529], [1, 2747090, 80798284478113]], 'index': 16, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/8/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/114/8/a/c'], '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': '2-114-1.1-c7-0-16', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-114-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.967570100567726, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 2133782847835744269, 'z1': {'__RealLiteral__': 0, 'data': '1.79889702213183872215484773743', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20590305
{'Lhash': '2280372889854199825958177238884', 'Lhash_array': ['2280372889854199825958177238884'], 'label': '2-114-1.1-c7-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/8/a/c'}
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id: 24566045
{'Lhash': '2280372889854199825958177238884', 'Lhash_array': ['2280372889854199825958177238884'], 'label': '2-114-1.1-c7-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/8/a/c/1/1'}