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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': -1, 'A3': 1, 'A4': -1, 'A5': 2, 'A6': -1, 'A7': 0, 'A8': 3, 'A9': 1, 'Lhash': '1380467224825648488', 'a10': [-0.6324555320336759, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [-0.5, 0], 'a5': [0.8944271909999159, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [1.0606601717798212, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 259.4100010465337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [7, [1]], [13, [1, 1]], [17, [1, 1]]], 'bad_primes': [3, 7, 13, 17], 'central_character': '32487.1', 'coefficient_field': '1.1.1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, -1], [1, -2, 5], [1], [1, -4, 11], [1, 1], [1, 1], [1, -4, 19], [1, 0, 23], [1, 2, 29], [1, -8, 31], [1, 2, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, 10, 53], [1, 4, 59], [1, 14, 61], [1, 4, 67], [1, 0, 71], [1, -14, 73], [1, 8, 79], [1, -4, 83], [1, -6, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 17, 'label': '2-32487-1.1-c1-0-17', 'leading_term': '5.45670074521', '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/32487/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.282250526434013, 2.074529067970844, 1.992472872841351, 1.092591731058365, 0.08451100793081863, -0.0829029754288844, 0.8540783649742641, 1.929666818945706, 1.645935348457398, -0.4179216827820961, -2.733175461214142, -3.047620987060414, -0.8627526617093357, 1.588353704223012, 1.49909020794965, -1.226081036648167, -3.54584446362568, -2.799599769562718, -0.1957305865973187, 0.3978464372901428, -2.588860168413043, -5.982077131289398, -5.606448554882473, -1.751336790590166, 0.9994089205254664, -0.2801313694183658, -3.069425938584909, -3.05202909568401, -0.09335080903384237, 1.909644718461723, 0.8285606724679396, -0.9352112696318372, -0.5270491875189851, 1.130745982175826, 1.38570461887653, 0.2686357256572384, -0.1031284013838642, 0.4583288541067734, 0.2462613561123812, -0.428542771248116, 0.7110378569900601, 3.004017031686174, 2.300116428676297, -2.252075848188213, -5.053123900876752, -1.788787065457248, 3.125920408098402, 2.450678584228784, -2.712863468430827, -4.474181141875569, -0.4067156928771035, 3.248036469217792, 2.082722968173924, -0.3429763914522596, -0.134522228046836, 0.4161474606026957, -1.168723858724661, -1.654570669026881, 1.494232980416615, 3.589110784722329, 0.07897497821620708, -4.39240827471746, -2.70239890780222, 2.781498276819296, 4.050631251315829, 0.4989481917253791, -1.436236980201694, 0.1002099422682919, 0.8549021604272135, -0.29126429692793, -0.07980460364648995, 1.422396229643767, 0.8918655172607837, -0.8606674170679676, -0.1813326331524921, 1.752719222856179, 1.121437478945174, -0.5935450675211692, 0.2600405367442013, 1.399982829181231, -0.807591688823482, -2.641113140149885, 0.6588114939993597, 4.677186514320073, 3.139946929214694, -0.2664023198634429, 0.7593852335196843, 2.820632939338441, 0.4338125645167274, -2.15551220827772, -0.1798074830560479, -0.01333987096075394, -7.190222861844903, -12.92178996959272, -7.833596812446064, 1.170939119594679, 2.854359660486979, -0.2557893394733783, -0.07535353927519654, 1.861732743174207, 0.8081375340099738, -0.5870853791577273, 0.6928780473350101, 1.221942582831009, -0.6713304887191189, -1.172767707846322, 0.1373318233007139, -0.4170297731475376, -1.623317845254075, 0.01205839883775487, 1.508956163370733, -0.5566963449344465, -1.774064935542859, 0.9376468642421821, 2.063937513573246, -0.5944206837557822, -0.4112140877965616, 3.689211283355656, 4.012423289415726, 0.4600506720338111], 'positive_zeros': ['1.281931186044459', '1.538706369946090', '2.458935197952399', '3.325573810103288', '3.902334102268935', '4.773111017113988', '5.055460654250835', '6.119738642247438', '6.474444399202381', '7.257348821742786', '7.848461449020156', '8.328695316978420', '9.077268392204329', '9.307172869672124', '9.822040785289717', '10.15632217817647', '10.88832180043411', '11.57921797018903', '12.12316405733530', '12.76973394407322', '13.44616209216974', '13.77948737220147', '14.09530035650785', '14.65282980466102', '15.25360273982723', '15.87055225398957', '16.53450399611319', '16.98695071799489', '17.43676996873906', '17.76403346391461', '18.36266722127672', '18.77165416835970', '19.38757032107241', '19.71466609738199'], 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1380467224825648488, 'z1': {'__RealLiteral__': 0, 'data': '1.281931186044459', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.538706369946090', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.458935197952399', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 259.4100010465337, 'bad_primes': [3, 7, 13, 17], 'central_character': '1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, -1, 2, -1, 0, 3, 1, -2, 4, -1, -1, 0, 2, -1, -1, -1, 4, -2, 0, -4, 0, 3, -1, 1, 1, 0, -2, -2, 8, -5, 4, 1, 0, -1, -2, -4, -1, 6, -2, 0, -4, -4, 2, 0, -8, -1, 0, 1, -1, 1, -10, -1, 8, 0, 4, 2, -4, -2, -14, -8, 0, 7, -2, -4, -4, 1, 0, 0, 0, 3, 14, 2, -1, -4, 0, 1, -8, -2, 1, 2, 4, 0, -2, 4, -2, 12, 6, -2, 0, 0, 8, 8, 8, -5, 6, 0, 4, 1], 'euler11': [1, -4, 11], 'euler13': [1, 1, 0], 'euler17': [1, 1, 0], 'euler19': [1, -4, 19], 'euler2': [1, 1, 2], 'euler23': [1, 0, 23], 'euler29': [1, 2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 2, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, 10, 53], 'euler59': [1, 4, 59], 'euler61': [1, 14, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, -14, 73], 'euler79': [1, 8, 79], 'euler83': [1, -4, 83], 'euler89': [1, -6, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 1, 2], [1, -1, 0], [1, -2, 5], [1, 0, 0], [1, -4, 11], [1, 1, 0], [1, 1, 0], [1, -4, 19], [1, 0, 23], [1, 2, 29], [1, -8, 31], [1, 2, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, 10, 53], [1, 4, 59], [1, 14, 61], [1, 4, 67], [1, 0, 71], [1, -14, 73], [1, 8, 79], [1, -4, 83], [1, -6, 89], [1, -6, 97]], 'index': 17, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/f'], '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': '2-32487-1.1-c1-0-17', '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': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1380467224825648488, 'z1': {'__RealLiteral__': 0, 'data': '1.281931186044459', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1380467224825648488', 'Lhash_array': ['1380467224825648488'], 'label': '2-32487-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/f'}