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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': 1, 'Lhash': '124366531833764831', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 323.8732305983134, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [13, [1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '40560.1', 'coefficient_field': '1.1.1.1', 'conductor': 40560, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, -4, 7], [1, 0, 11], [1], [1, 2, 17], [1, -4, 19], [1, -8, 23], [1, 6, 29], [1, 0, 31], [1, -6, 37], [1, 10, 41], [1, -4, 43], [1, -8, 47], [1, -10, 53], [1, 0, 59], [1, -6, 61], [1, 4, 67], [1, 0, 71], [1, -14, 73], [1, 16, 79], [1, -12, 83], [1, 2, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 27, 'label': '2-40560-1.1-c1-0-27', 'leading_term': '3.10261256301', '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/40560/bf', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.102612563005838, 2.623993134430386, 1.356745225997588, -0.1142807180160419, -0.8951455736718446, -0.4248595657264504, 0.8103461176461676, 1.425839138960993, 0.4269875764102749, -1.464362580246937, -2.106008144511958, -0.09599465656874204, 3.291086563533443, 4.897958908082172, 2.9363593096313, -0.8104967526336524, -2.743027885654707, -1.467132584966722, 0.770010603546631, 1.149335065915004, -0.1351978110310623, -0.654338451988056, 0.2803371112159648, 0.408029124988662, -1.834138193384794, -4.269120743874096, -3.694947957820571, -0.7750802687807975, 0.565547819995186, -1.045507912982313, -2.243435431318147, -0.2519448897870694, 2.372481373246504, 1.502388736685187, -1.814738081351096, -2.662242603938722, -0.06398985243010734, 1.319401924488009, -1.204553825541214, -3.756172666769439, -2.088482884258431, 1.543696261638806, 2.239885037305351, 0.2933285033203299, -0.2495905514572274, 0.955121120305463, 0.7070024708934114, -0.7748406031928439, 0.2153968893053692, 3.313296648086037, 3.451066075442924, -0.3290824319123621, -2.486600256334734, -0.3608781092853891, 1.2533353055611, -0.9901660905893623, -2.788414904475618, -0.3202275966815814, 2.456435368155545, 1.223268444591549, -0.6509443354812517, 0.966715255190232, 2.361172171701146, -1.156958170075037, -5.556536590403986, -4.524250403243091, -0.4564846413279141, 0.3920159244909339, -1.187625080702366, -0.7504173926262853, 0.5385137954554235, -0.542277099067465, -1.741210843499971, -0.4168612005512501, 0.04892246809415801, -2.27102099509627, -1.695029168564754, 4.477661004756653, 8.250227690344008, 3.750247459348737, -2.0264693010407, -1.437947203681528, 1.436344755220528, 0.7162667487542571, -0.3700477950313537, 1.70610703014629, 2.792779803380195, 0.5720358312201833, -0.07775119179265876, 2.050094296416461, 1.333781821217376, -2.407042140053926, -2.633892326691734, 0.5254777188046355, 0.4786996754461271, -2.280480208403541, -1.948564390333135, 0.05675189779582873, -0.8102435929059064, -1.552449592565345, 0.8729825136083021, 0.8614300583001872, -3.983483124819344, -5.186731641560189, 0.6971701992520682, 4.197191978062201, 0.6010846678098973, -2.223684065148982, -0.4768908721803815, 0.1494587683640868, -0.9954323868208609, 1.164088413913786, 4.254078256089465, 2.705441931884814, -0.09212512718735923, 0.3409644366290539, -0.1810560284582933, -3.655668532600889, -3.91109535262022, -0.3428838777248833, -0.03734826554888189], 'positive_zeros': ['0.7281305196615273', '1.341244879248390', '2.058160321039696', '2.757558142592397', '3.693414476446511', '4.401967151519942', '4.974692211503937', '5.435991778922042', '5.819429699641103', '6.830321776687621', '7.124238007476809', '7.769945027320821', '8.364111660854386', '9.005504933824223', '9.411608265776341', '10.13535543299975', '10.79510823463208', '11.06186423143917', '11.60849138523407', '11.97924871255123', '12.72998279115699', '13.28099269186838', '13.66981776452645', '14.27128105186120', '14.87114247186786', '15.15372509827763', '15.69336750062829', '16.54136556524280', '16.81553543637329', '17.36329450476040', '17.67542994222426', '18.31627447485787', '18.50879530649618', '19.08495770284415', '19.88807405593278'], 'prelabel': '2-40560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.996478283217343, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 124366531833764831, 'z1': {'__RealLiteral__': 0, 'data': '0.7281305196615273', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.341244879248390', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.058160321039696', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 323.8732305983134, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 40560, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 4, 0, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 4, 0, -4, 0, 8, 0, 1, 0, -1, 0, -6, 0, 0, 0, 0, 0, 4, 0, 6, 0, 0, 0, -10, 0, 4, 0, 1, 0, 8, 0, 9, 0, 2, 0, 10, 0, 0, 0, -4, 0, 0, 0, 6, 0, 4, 0, 0, 0, -4, 0, -8, 0, 0, 0, 14, 0, -1, 0, 0, 0, -16, 0, 1, 0, 12, 0, -2, 0, 6, 0, -2, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 0, 0], 'euler17': [1, 2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -6, 37], 'euler41': [1, 10, 41], 'euler43': [1, -4, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, -10, 53], 'euler59': [1, 0, 59], 'euler61': [1, -6, 61], 'euler67': [1, 4, 67], 'euler7': [1, -4, 7], 'euler71': [1, 0, 71], 'euler73': [1, -14, 73], 'euler79': [1, 16, 79], 'euler83': [1, -12, 83], 'euler89': [1, 2, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -4, 7], [1, 0, 11], [1, 0, 0], [1, 2, 17], [1, -4, 19], [1, -8, 23], [1, 6, 29], [1, 0, 31], [1, -6, 37], [1, 10, 41], [1, -4, 43], [1, -8, 47], [1, -10, 53], [1, 0, 59], [1, -6, 61], [1, 4, 67], [1, 0, 71], [1, -14, 73], [1, 16, 79], [1, -12, 83], [1, 2, 89], [1, 2, 97]], 'index': 27, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/40560/bf'], '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': '2-40560-1.1-c1-0-27', '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': '2-40560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.996478283217343, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 124366531833764831, 'z1': {'__RealLiteral__': 0, 'data': '0.7281305196615273', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '124366531833764831', 'Lhash_array': ['124366531833764831'], 'factors': ['2-40560-1.1-c1-0-27'], 'label': '2-40560-1.1-c1-0-27', 'type': 'ECQ', 'url': 'EllipticCurve/Q/40560/bf'}