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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': 0, 'A8': -3, 'A9': 0, 'Lhash': '1125703423818187903', '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': [0.0, 0], 'a8': [-1.0606601717798212, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 968.3857505130783, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1]], [11, [1, 1]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '121275.1', 'coefficient_field': '1.1.1.1', 'conductor': 121275, 'conductor_radical': 1155, 'degree': 2, 'euler_factors': [[1, -1, 2], [1], [1], [1], [1, 1], [1, -4, 13], [1, 4, 17], [1, 0, 19], [1, 4, 23], [1, -6, 29], [1, 10, 31], [1, -6, 37], [1, -4, 41], [1, 12, 43], [1, -10, 47], [1, 6, 53], [1, -2, 59], [1, 0, 61], [1, 8, 67], [1, -12, 71], [1, 8, 73], [1, -8, 79], [1, 0, 83], [1, 6, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 113, 'label': '2-121275-1.1-c1-0-113', 'leading_term': '7.33740712793', '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/121275/ew', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.598355942543779, 1.888297842517287, 0.2590163970276441, -2.367835307280217, -3.749661226025568, -2.289958791167855, 0.9317213120007604, 2.781886748322103, 1.410270416826799, -1.426386782853938, -2.350287460919235, -0.5753754858670475, 1.228057216014842, 0.7954459700261372, -0.6287451535882025, -0.5798849131877358, 0.5742476699983923, 0.4411856931186647, -1.014357580942588, -1.149441652656387, 0.6569642592352254, 1.536132712700674, 0.1131101760739341, -0.7672117089540009, 0.7340695585664508, 1.333654975942525, -1.71171128569511, -4.34796319511029, -1.435633809032347, 3.865390973922512, 4.159995339883061, -0.1699418397327711, -1.897914343321636, 0.454662899082323, 1.027361258348081, -1.455392854086002, -1.303316062999834, 2.207639764311624, 2.310553373328863, -2.203211053418082, -3.590570736690198, 0.7221622990497636, 3.214089558853592, 0.4149660809077725, -1.10052608750711, 1.886612549973455, 3.238852428900594, 0.09806728227469791, -1.787060912897959, 0.1379404450879663, 1.110934544141851, -0.3582812805816257, -0.4473568028462658, 0.7485389625720118, 0.09827657989432301, -0.6018864618368037, 1.112448472598583, 1.644075230830777, -0.96851434212575, -1.693938728230145, 0.7734426198645139, 0.6194374171184228, -1.991978887089414, -0.5981110625461136, 2.40685069436621, -0.475899671387842, -4.559006212196077, -0.7508471551603846, 5.356307967713488, 3.91579243948791, -0.3692628320905806, 0.07510171820158663, 0.9964869045628546, -0.2749232004006506, 2.6303320356547, 8.014675600035767, 5.926428300547813, -0.5280401849096279, -0.003340636110579582, 4.305959151767611, 2.862056934411997, -0.1050055737095053, 1.951655326839817, 3.232392591624395, -0.1027378801361677, -1.673248024249046, 0.01427506127583696, -0.01504347693732416, -0.276255957363503, 2.033512251319492, 2.471829263412032, -0.1613524730959907, -0.6779596143276564, 0.2837924502360423, -0.566422736123813, 0.21995249863907, 2.564440573750952, -0.2396607005208063, -4.810631303061587, -2.325567143672473, 1.516986876064025, -1.087052644845366, -1.97916579522334, 3.437727138996034, 4.596377000375326, 0.03984704219883755, -0.1637707398093875, 1.399265808326428, -2.23448116916518, -3.543105741711601, 1.080143641333397, 1.373248643340575, -2.379692077955713, -0.5174359536458029, 1.88530698533645, -1.973055150199274, -2.385041912067306, 4.174073250915564, 5.663968762662518, 0.9573879868996786], 'positive_zeros': ['0.7760465689535254', '1.678235857890743', '2.370826349460062', '3.061702135388496', '3.628734171267754', '4.122406940941044', '4.581909454051484', '5.168665293861473', '5.765871269974483', '6.154596299611079', '6.637886655643196', '7.313238704936703', '7.989911865793499', '8.456905023231455', '8.862365992733141', '9.348757244993429', '9.886578072053579', '10.46411343663098', '11.03034361747115', '11.36781944270972', '12.00669867685357', '12.48559990267212', '12.94187013152244', '13.33384447267675', '13.76736859505414', '14.11698354742728', '14.66723413481102', '15.17253829996155', '15.55725769811390', '16.03923334342609', '16.47779261578427', '17.02582073670859', '17.71476876510354', '17.99061948376467', '18.42225341453917', '18.58637571201078', '19.47122401449944', '19.75018942000643'], 'prelabel': '2-121275-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.118897000264617, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1125703423818187903, 'z1': {'__RealLiteral__': 0, 'data': '0.7760465689535254', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.678235857890743', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.370826349460062', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 968.3857505130783, 'bad_primes': [3, 5, 7, 11], 'central_character': '1.1', 'conductor': 121275, 'conductor_radical': 1155, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, 0, 0, 0, -3, 0, 0, -1, 0, 4, 0, 0, -1, -4, 0, 0, 0, 0, -1, -4, 0, 0, 4, 0, 0, 6, 0, -10, 5, 0, -4, 0, 0, 6, 0, 0, 0, 4, 0, -12, 1, 0, -4, 10, 0, 0, 0, 0, -4, -6, 0, 0, 0, 0, 6, 2, 0, 0, -10, 0, 7, 0, 0, -8, 4, 0, 0, 12, 0, -8, 6, 0, 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, -12, 0, 3, -6, 0, 0, 4, 0, 10, 0, 0, -10, 0, 0, 0], 'euler11': [1, 1, 0], 'euler13': [1, -4, 13], 'euler17': [1, 4, 17], 'euler19': [1, 0, 19], 'euler2': [1, -1, 2], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 10, 31], 'euler37': [1, -6, 37], 'euler41': [1, -4, 41], 'euler43': [1, 12, 43], 'euler47': [1, -10, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -2, 59], 'euler61': [1, 0, 61], 'euler67': [1, 8, 67], 'euler7': [1, 0, 0], 'euler71': [1, -12, 71], 'euler73': [1, 8, 73], 'euler79': [1, -8, 79], 'euler83': [1, 0, 83], 'euler89': [1, 6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, -1, 2], [1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -4, 13], [1, 4, 17], [1, 0, 19], [1, 4, 23], [1, -6, 29], [1, 10, 31], [1, -6, 37], [1, -4, 41], [1, 12, 43], [1, -10, 47], [1, 6, 53], [1, -2, 59], [1, 0, 61], [1, 8, 67], [1, -12, 71], [1, 8, 73], [1, -8, 79], [1, 0, 83], [1, 6, 89], [1, 10, 97]], 'index': 113, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/121275/ew'], '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': '2-121275-1.1-c1-0-113', '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': '2-121275-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.118897000264617, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1125703423818187903, 'z1': {'__RealLiteral__': 0, 'data': '0.7760465689535254', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1125703423818187903', 'Lhash_array': ['1125703423818187903'], 'factors': ['2-121275-1.1-c1-0-113'], 'label': '2-121275-1.1-c1-0-113', 'type': 'ECQ', 'url': 'EllipticCurve/Q/121275/ew'}