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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 5, 'A8': 0, 'A9': 0, 'Lhash': '2217295285886823454', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [1.889822365046136, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 258.71530254894856, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '32400.1', 'coefficient_field': '1.1.1.1', 'conductor': 32400, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, -5, 7], [1, 0, 11], [1, -1, 13], [1, 6, 17], [1, 5, 19], [1, 9, 23], [1, 0, 29], [1, -4, 31], [1, -10, 37], [1, 3, 41], [1, -8, 43], [1, 3, 47], [1, 3, 53], [1, 9, 59], [1, -8, 61], [1, 4, 67], [1, 6, 71], [1, 2, 73], [1, 2, 79], [1, -6, 83], [1, -6, 89], [1, -16, 97]], 'gamma_factors': [[], [0]], 'index': 20, 'label': '2-180e2-1.1-c1-0-20', 'leading_term': '2.48092676479', '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/32400/df', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.48092676478763, 1.973122795448723, 0.5920506602167055, -1.131387428576169, -2.298349843315301, -2.176108600626559, -0.9306081936375074, 0.2731926901971419, 0.242036093152735, -0.9115435562739714, -1.538770985049304, 0.006688704860226103, 3.371263448390435, 6.053630978049409, 5.754811343379664, 2.89407911962626, 0.2523419772723301, -0.1764106519988185, 0.5738726542920918, 0.06991379668454548, -1.968510181134814, -3.02889647340793, -1.297097776620549, 1.409179691578938, 1.758288830332243, -0.4024491651066131, -1.490327037011865, 0.8926845660808429, 4.328536201133259, 4.738181630672412, 2.041278701944204, 0.02180287133645541, 0.6108063189042278, 1.397938006827174, 0.1884667423765908, -0.9537794163774866, 0.8115419746965992, 3.551979036301217, 2.638862887678465, -1.957188132457798, -4.883495067945649, -3.109397973083902, -0.1597478044877446, -0.1670425725413013, -1.641894781793925, -1.068198635843216, 0.5157540746997211, -0.2164923709561762, -1.987678717297897, -0.4762368258187783, 3.609141428859224, 4.571876330341387, 0.9841438072867507, -1.650627332634545, 0.05797063973091184, 2.117751877864569, 0.6469289480946192, -1.549274857384977, -0.8848114007637359, 0.2044073469588696, -1.560622841276693, -3.395551245526046, -1.703335531426825, 0.2736581520809238, -2.096792277442519, -5.600947195058643, -4.039493080064893, 0.780360574894789, 2.074507288054606, -0.3800037173376383, -1.245775300897941, -0.02218897482342707, -0.4849279005582092, -1.603787444277743, 0.5319845216458655, 3.327623808534028, 1.080217362750149, -3.713946824007173, -3.634218273804913, 0.617321613080528, 1.968184974042904, -0.001528297834493243, 0.2411249118311608, 2.431625300336433, 1.694279078316352, -0.7675164438664038, -0.2656252286742231, 1.18648478172861, -0.69459950972195, -2.248523787637957, 1.5462721338391, 5.784899745717309, 3.540685433775587, -1.343748100390409, -1.682887223444856, 0.3806950598219399, -0.1623984374937607, -0.9527883903945391, 0.6488963598029741, 0.4908579807116457, -2.806154217827429, -3.012169040856081, 1.103355933610308, 1.860765162998255, -2.483345577554552, -4.060848142254802, -0.8614304047088029, 0.2678090359612271, -1.741779390540031, -1.130850074929884, 1.439169821012386, 0.8361947315698617, -0.7893403162048195, 0.4885121116058795, 0.2867321679300496, -4.415154395382729, -6.320770488753341, -1.426383669630694, 2.143639400385483, -0.4300639786304216, -2.447973091253077], 'positive_zeros': ['0.5856060584573518', '1.674448938359543', '2.065975597797337', '2.749388311334862', '4.044958212009499', '4.312444527209488', '4.761195618254557', '5.610656199769833', '6.208219406016186', '6.685364847387752', '7.759700819746638', '7.846757969169000', '8.525977708076715', '8.926968918120101', '9.651480369399073', '10.52544260044876', '10.71833914926088', '11.39730952552731', '11.72128191416915', '12.28170160915583', '13.06121087915139', '13.49504376481548', '14.05842188242099', '14.64244192365455', '14.81950884212750', '15.66980823238938', '15.83307894374917', '16.70445073106102', '17.21298058147092', '17.75689305216777', '17.90072898314528', '18.46162449756644', '19.05327736118202', '19.71169843640777'], 'prelabel': '2-180e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.084629387988663, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2217295285886823454, 'z1': {'__RealLiteral__': 0, 'data': '0.5856060584573518', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.674448938359543', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.065975597797337', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 258.71530254894856, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 32400, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 1, 0, 0, 0, -6, 0, -5, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 10, 0, 0, 0, -3, 0, 8, 0, 0, 0, -3, 0, 18, 0, 0, 0, -3, 0, 0, 0, 0, 0, -9, 0, 8, 0, 0, 0, 0, 0, -4, 0, 0, 0, -6, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 5, 0, 0, 0, 0, 0, 16, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -1, 13], 'euler17': [1, 6, 17], 'euler19': [1, 5, 19], 'euler2': [1, 0, 0], 'euler23': [1, 9, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -10, 37], 'euler41': [1, 3, 41], 'euler43': [1, -8, 43], 'euler47': [1, 3, 47], 'euler5': [1, 0, 0], 'euler53': [1, 3, 53], 'euler59': [1, 9, 59], 'euler61': [1, -8, 61], 'euler67': [1, 4, 67], 'euler7': [1, -5, 7], 'euler71': [1, 6, 71], 'euler73': [1, 2, 73], 'euler79': [1, 2, 79], 'euler83': [1, -6, 83], 'euler89': [1, -6, 89], 'euler97': [1, -16, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, -5, 7], [1, 0, 11], [1, -1, 13], [1, 6, 17], [1, 5, 19], [1, 9, 23], [1, 0, 29], [1, -4, 31], [1, -10, 37], [1, 3, 41], [1, -8, 43], [1, 3, 47], [1, 3, 53], [1, 9, 59], [1, -8, 61], [1, 4, 67], [1, 6, 71], [1, 2, 73], [1, 2, 79], [1, -6, 83], [1, -6, 89], [1, -16, 97]], 'index': 20, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32400/df'], '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': '2-180e2-1.1-c1-0-20', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-180e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.084629387988663, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2217295285886823454, 'z1': {'__RealLiteral__': 0, 'data': '0.5856060584573518', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2217295285886823454', 'Lhash_array': ['2217295285886823454'], 'factors': ['2-180e2-1.1-c1-0-20'], 'label': '2-180e2-1.1-c1-0-20', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32400/df'}