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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': -3, 'A9': 0, 'Lhash': '199378819290586651', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-1.0606601717798212, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2125.4180758014318, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1, 1]], [13, [1]]], 'bad_primes': [3, 5, 7, 13], 'central_character': '266175.1', 'coefficient_field': '1.1.1.1', 'conductor': 266175, 'conductor_radical': 1365, 'degree': 2, 'euler_factors': [[1, -1, 2], [1], [1], [1, 1], [1, -6, 11], [1], [1, 2, 17], [1, 0, 19], [1, 0, 23], [1, -2, 29], [1, 8, 31], [1, -2, 37], [1, 4, 41], [1, -4, 43], [1, -12, 47], [1, 0, 53], [1, -4, 59], [1, 14, 61], [1, 4, 67], [1, 2, 71], [1, 6, 73], [1, -16, 79], [1, -4, 83], [1, 0, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 89, 'label': '2-266175-1.1-c1-0-89', 'leading_term': '9.27557024032', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/266175/dm', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.99712738141437, 2.29210292662432, 0.4330099037025326, -1.865789271333604, -1.893010422666414, 0.8985571877623187, 3.490639636917427, 2.52678312409589, -1.164296847472251, -3.183261905684094, -1.341616347494636, 1.405593988596146, 1.469339551619525, -0.238720940230361, -0.5970753301319893, 0.2466983302780361, -0.1477903954347445, -1.234079302318652, -0.2998747620583554, 1.759016055174116, 1.303516366518709, -1.137905333405779, -1.361421674339441, 0.5758948773869351, 0.5291263580869744, -0.9988346804007593, 0.5171890668584775, 3.464868395169748, 1.673921312199991, -2.686854875427704, -0.8836151085185354, 6.124889055362144, 7.941195149029466, 2.822373879946404, -0.5007258626471043, 0.2441526576609638, -0.5762679584021979, -2.032899616993506, 0.811575485003738, 3.155326299771199, -1.688867186540567, -6.998141533510189, -4.154889385820043, 0.4825384939125006, -1.605591233201976, -4.90193638315884, -2.703289056556349, 0.113138217186606, -0.3063922885760883, 0.4546348494469384, 2.685273585798197, 1.607287226584167, -0.7233751575812355, 0.08561563041772, 0.9397937249845965, -0.393864627940326, 0.02482034788019701, 1.680446351848114, 0.5931999053532134, -0.001599649709623773, 2.155317241361754, 0.5206271909334894, -4.60352285028584, -3.26553619086157, 2.518331844789794, 1.92393594392868, -1.299579201975803, 1.32299675670911, 3.255468137522751, -0.2106760851306754, -0.2987170777129633, 2.997845848914471, 0.06208023353822057, -4.340838311313918, -1.451362117681883, 0.7811979732472141, -2.845182184180503, -2.636778519350957, 1.657670152062399, 0.6764122153746336, -0.9417040758647053, 3.216733894709172, 3.95369169819813, -1.849452763726664, -3.179773005885623, 0.5331023162786644, 0.8867074679421513, -0.3320477709212531, 0.1364503606513803, -0.68716226847062, -0.9090513160426217, 1.306567941750957, 0.6895164653857373, -1.475443265263275, 0.2753400765241905, 0.8526672583739229, -2.085978085525187, -0.8416006268632547, 1.926960492310498, -0.8382704960794662, -1.556717476561671, 2.121142913663483, -0.6381595911830131, -5.009080128466099, 0.5128293572308278, 5.460452712010475, 1.259140144298007, -1.023018993963597, 0.07989904899488785, -2.565107976535983, -2.310077988399736, 1.626089494444599, -1.430366490848803, -4.484462659677262, 2.136308573969945, 5.473305976835276, 0.3891594050431603, 0.2297157929174382, 3.48349448883441, 1.198945570341815], 'positive_zeros': ['0.7921438649146732', '1.433293330327803', '2.173957887020701', '2.857052232561470', '3.460913949349963', '3.916490766941329', '4.217236910568485', '4.784456818753317', '5.380838346983880', '5.921523307724670', '6.326294970953983', '6.708018228562738', '7.336218792047464', '7.785225894290878', '8.665727810519230', '8.937997311600507', '9.173698976757465', '9.701921566985259', '10.18957404989268', '10.95001122688731', '11.14750312112172', '11.97512787102036', '12.16098049461135', '12.44294495996020', '13.14426794718797', '13.48799048699809', '13.92902214415763', '14.24663354076221', '14.83969663952945', '15.00029900986607', '15.52585915868764', '16.12992075408055', '16.61513577536806', '16.92063747222612', '17.48497378941658', '17.77182010925880', '18.25262042951335', '18.83333280632540', '19.07537060116686', '19.64034556032170'], 'prelabel': '2-266175-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.102256732197304, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 199378819290586651, 'z1': {'__RealLiteral__': 0, 'data': '0.7921438649146732', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.433293330327803', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.173957887020701', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2125.4180758014318, 'bad_primes': [3, 5, 7, 13], 'central_character': '1.1', 'conductor': 266175, 'conductor_radical': 1365, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, 0, 0, -1, -3, 0, 0, 6, 0, 0, -1, 0, -1, -2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 2, 0, -8, 5, 0, -2, 0, 0, 2, 0, 0, 0, -4, 0, 4, -6, 0, 0, 12, 0, 1, 0, 0, 0, 0, 0, 0, 3, 0, 2, 4, 0, -14, -8, 0, 7, 0, 0, -4, 2, 0, 0, -2, 0, -6, 2, 0, 0, -6, 0, 16, 0, 0, -4, 4, 0, 0, 4, 0, -18, 0, 0, 0, 0, 0, 12, 0, 0, 10, 1, 0, 0], 'euler11': [1, -6, 11], 'euler13': [1, 0, 0], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, -1, 2], 'euler23': [1, 0, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, -2, 37], 'euler41': [1, 4, 41], 'euler43': [1, -4, 43], 'euler47': [1, -12, 47], 'euler5': [1, 0, 0], 'euler53': [1, 0, 53], 'euler59': [1, -4, 59], 'euler61': [1, 14, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 2, 71], 'euler73': [1, 6, 73], 'euler79': [1, -16, 79], 'euler83': [1, -4, 83], 'euler89': [1, 0, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, -1, 2], [1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -6, 11], [1, 0, 0], [1, 2, 17], [1, 0, 19], [1, 0, 23], [1, -2, 29], [1, 8, 31], [1, -2, 37], [1, 4, 41], [1, -4, 43], [1, -12, 47], [1, 0, 53], [1, -4, 59], [1, 14, 61], [1, 4, 67], [1, 2, 71], [1, 6, 73], [1, -16, 79], [1, -4, 83], [1, 0, 89], [1, -10, 97]], 'index': 89, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/266175/dm'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, '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': '2-266175-1.1-c1-0-89', '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': '2-266175-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.102256732197304, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 199378819290586651, 'z1': {'__RealLiteral__': 0, 'data': '0.7921438649146732', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '199378819290586651', 'Lhash_array': ['199378819290586651'], 'factors': ['2-266175-1.1-c1-0-89'], 'label': '2-266175-1.1-c1-0-89', 'type': 'ECQ', 'url': 'EllipticCurve/Q/266175/dm'}