Formats: - HTML - YAML - JSON - 2026-03-06T04:42:23.840719
Query: /api/lfunc_lfunctions/?_offset=0
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{'A10': 1, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': -1, 'A6': 1, 'A7': -4, 'A8': -1, 'A9': 1, 'Lhash': '2059988367962920134', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.4082482904638631, 0], 'a7': [-1.5118578920369088, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 234.5206307365006, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1, 1]], [11, [1, -1]], [89, [1, 1]]], 'bad_primes': [2, 3, 5, 11, 89], 'central_character': '29370.1', 'coefficient_field': '1.1.1.1', 'conductor': 29370, 'conductor_radical': 29370, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, 1], [1, 4, 7], [1, -1], [1, -1, 13], [1, -2, 17], [1, -3, 19], [1, 3, 23], [1, -1, 29], [1, -3, 31], [1, 4, 37], [1, -4, 41], [1, 10, 43], [1, 0, 47], [1, 4, 53], [1, -1, 59], [1, -14, 61], [1, -2, 67], [1, 1, 71], [1, -2, 73], [1, 1, 79], [1, -9, 83], [1, 1], [1, 0, 97]], 'gamma_factors': [[], [0]], 'id': 7777979, 'index': 1, 'label': '2-29370-1.1-c1-0-1', 'leading_term': '0.6794879273', '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': 0, 'origin': 'EllipticCurve/Q/29370/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.6794879273003696, 0.4166449575206518, -0.2267860682372615, -0.7885651908334468, -0.6241985809222232, 0.5812740473583174, 2.25605266642379, 3.03887300681214, 1.824475810448094, -0.9842818353070651, -3.394130657031121, -3.468787327376031, -1.368084753542383, 0.5184192428660437, 0.01274002702117099, -2.195579378232886, -2.935201193777958, -0.14390272447607, 4.260124971338676, 6.017233551500903, 3.307103346982744, -0.969850824551185, -2.500481176475941, -0.5734520055807485, 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'2.168907252278017', '3.153809264249860', '3.501801090301917', '4.258399830647281', '5.186254815179859', '5.803592449983000', '6.429651135594236', '6.817167802825430', '7.370058894907609', '8.116563787916997', '8.590480915747357', '9.410341192936197', '9.772820327754042', '10.17694690504646', '10.80971433413006', '11.44164526986648', '11.98307385133568', '12.29518059456552', '12.94113965011596', '13.46390072145191', '14.09293623047518', '14.78789164415145', '15.44112533267769', '15.93801231999401', '16.20240935324371', '16.60391687147158', '17.23108888407774', '17.69556482085027', '18.32694762430887', '18.73413130553493', '19.30110250809993', '19.50209183522083'], 'prelabel': '2-29370-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.314066433723625, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2059988367962920134, 'z1': {'__RealLiteral__': 0, 'data': '0.4195678506100672', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.152376636200120', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.168907252278017', 'prec': 57}}