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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': 1, 'Lhash': '2017175821740557628', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 685.1164493425861, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [11, [1, 1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '85800.1', 'coefficient_field': '1.1.1.1', 'conductor': 85800, 'conductor_radical': 4290, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, -4, 7], [1, 1], [1, 1], [1, -2, 17], [1, -4, 19], [1, -4, 23], [1, -6, 29], [1, 0, 31], [1, 10, 37], [1, 10, 41], [1, 4, 43], [1, 0, 47], [1, 10, 53], [1, 12, 59], [1, 2, 61], [1, 8, 67], [1, 8, 71], [1, -2, 73], [1, 16, 79], [1, -12, 83], [1, 10, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 74, 'label': '2-85800-1.1-c1-0-74', 'leading_term': '10.3416918955', '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/85800/cy', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.406375065411736, 3.776217373722605, 3.432538865600128, 1.717924237604838, 0.1033755089962917, -0.003499209854513507, 1.169080176252612, 1.773441725486286, 0.4546711965976891, -1.747743277186702, -2.435534759019448, -1.028088850776556, 0.1093526004270992, -1.291792988395372, -3.955564218946338, -4.390839149860564, -1.741880037755207, 0.825720759850771, 0.7402199809736894, -0.1361111028602161, 1.206037751278227, 3.322634177833961, 1.905863539716245, -2.941325019746893, -5.479482951335002, -2.361710600671763, 2.189160690741785, 2.647438267728809, 0.1481527124478516, -0.4949595385210087, 0.9718366118266255, 0.9054936437384665, -0.8335228587603345, -0.8744843286778462, 0.5153087032499738, -0.5480770995658252, -3.610409162943804, -3.534118402100886, 0.1852940854489019, 1.779739607820317, -0.5742393458898142, -1.480196116997783, 1.306115992436751, 2.425602740530113, -0.7036169494485158, -2.660440950069655, -0.4769849592219604, 0.6761261871516211, -1.823029889275255, -2.210831697617253, 2.266558286575084, 4.989803630349902, 1.852579344767104, -1.486637538116382, -0.6952052602529117, 0.2717192772156463, -1.090537489765523, -1.081062964665443, 0.8313177664277803, 0.3012982620989224, -1.803653299006158, -0.7444534371133585, 0.8509468301748206, -2.558391148017698, -6.518870165509529, -3.661729818189598, 1.471154508362972, 0.6879118521592587, -2.446636088855526, -1.199555378172965, 0.6415679467573977, -1.64345060513519, -3.134292871241527, -0.7415501834764356, -0.277266070579763, -2.974754370737039, -2.068674447454729, 2.072666048682052, 1.933273361694472, -1.42879711983146, -1.244353409377407, 0.714216386605414, -0.1540427446975447, -0.7296861109983488, 0.8026900310758595, -0.3359397244411587, -2.92428969681561, -0.4748439241836425, 2.834765114270145, -1.197798879829697, -6.342458699245027, -3.130999755986917, 2.167534429330173, 1.207546399095102, -0.4064537968097376, 2.071182296761832, 2.676812962281515, 0.1334357474175247, 0.207666894601595, 1.099186510519379, -1.333552767573245, -1.772183615955727, 2.305616494702866, 2.964911401097888, -1.071936449393554, -1.680385276608383, 0.6226372051293371, -0.2271048101132276, -1.151946752155733, 0.4643648449296508, -1.225885304849812, -4.852165655338244, -2.213341367137006, 2.059383855210573, -0.725900815050658, -3.385176696170348, 1.165527890872813, 3.705666155025983, -0.4614673663499463, -1.965354338982615], 'positive_zeros': ['1.278685302024058', '1.501163918793157', '2.301013889351919', '3.180817371101257', '3.318780480169980', '4.394131941480071', '4.918172162947348', '5.078829687536189', '5.856165850482684', '6.615845851882909', '7.267605792824229', '7.594252445483105', '8.129417464123340', '8.642689230155592', '8.944002144849675', '9.737604492303445', '10.19922601861682', '10.64977800503360', '11.20379682256527', '11.79495165046882', '12.09143292278254', '12.64061570614340', '13.35668498657162', '13.85340950778924', '14.07585458716458', '14.63569773357221', '15.03277342816299', '15.57292505905535', '15.85874416220937', '16.65766416169521', '17.04643245776037', '17.60839099938316', '17.86342289943134', '18.59615374205979', '18.70536827331684', '19.36962992618534', '19.88518979166107'], 'prelabel': '2-85800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.174729212402294, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2017175821740557628, 'z1': {'__RealLiteral__': 0, 'data': '1.278685302024058', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.501163918793157', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.301013889351919', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 685.1164493425861, 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '1.1', 'conductor': 85800, 'conductor_radical': 4290, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 4, 0, 1, 0, -1, 0, -1, 0, 0, 0, 2, 0, 4, 0, 4, 0, 4, 0, 0, 0, 1, 0, 6, 0, 0, 0, -1, 0, 0, 0, -10, 0, -1, 0, -10, 0, -4, 0, 0, 0, 0, 0, 9, 0, 2, 0, -10, 0, 0, 0, 4, 0, -12, 0, -2, 0, 4, 0, 0, 0, -8, 0, 4, 0, -8, 0, 2, 0, 0, 0, -4, 0, -16, 0, 1, 0, 12, 0, 0, 0, 6, 0, -10, 0, -4, 0, 0, 0, 0, 0, 14, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, 1, 0], 'euler17': [1, -2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 10, 37], 'euler41': [1, 10, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 10, 53], 'euler59': [1, 12, 59], 'euler61': [1, 2, 61], 'euler67': [1, 8, 67], 'euler7': [1, -4, 7], 'euler71': [1, 8, 71], 'euler73': [1, -2, 73], 'euler79': [1, 16, 79], 'euler83': [1, -12, 83], 'euler89': [1, 10, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, -4, 7], [1, 1, 0], [1, 1, 0], [1, -2, 17], [1, -4, 19], [1, -4, 23], [1, -6, 29], [1, 0, 31], [1, 10, 37], [1, 10, 41], [1, 4, 43], [1, 0, 47], [1, 10, 53], [1, 12, 59], [1, 2, 61], [1, 8, 67], [1, 8, 71], [1, -2, 73], [1, 16, 79], [1, -12, 83], [1, 10, 89], [1, -14, 97]], 'index': 74, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/85800/cy'], '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': '2-85800-1.1-c1-0-74', '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': '2-85800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.174729212402294, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2017175821740557628, 'z1': {'__RealLiteral__': 0, 'data': '1.278685302024058', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '2017175821740557628', 'Lhash_array': ['2017175821740557628'], 'label': '2-85800-1.1-c1-0-74', 'type': 'ECQ', 'url': 'EllipticCurve/Q/85800/cy'}