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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': 0, 'A8': 0, 'A9': 1, 'Lhash': '1594482452989049437', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1878.0814555405154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '235200.1', 'coefficient_field': '1.1.1.1', 'conductor': 235200, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1], [1, 3, 11], [1, -4, 13], [1, 0, 17], [1, -4, 19], [1, 8, 23], [1, -3, 29], [1, 5, 31], [1, -8, 37], [1, -8, 41], [1, -6, 43], [1, 10, 47], [1, -9, 53], [1, -5, 59], [1, -10, 61], [1, -6, 67], [1, -10, 71], [1, 2, 73], [1, -11, 79], [1, -7, 83], [1, 18, 89], [1, -17, 97]], 'gamma_factors': [[], [0]], 'index': 269, 'label': '2-235200-1.1-c1-0-269', 'leading_term': '3.88495132822', '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/235200/rr', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.884951328224406, 2.921507302055201, 0.6956923401957895, -1.025062418216929, -0.5950637042813322, 1.631344801077619, 3.179413076606644, 2.194332658403493, -0.01705086899175008, -0.5391927009435449, 0.9879056410293728, 1.680461786532323, -0.1375484289716245, -2.030064069772329, -1.286125778282424, 0.3546679117060951, -0.4682599844705295, -2.447010645967805, -1.226254631376594, 2.677395653595319, 3.692068275747285, 0.4702182843659648, -1.442685120546031, 0.7252494106819612, 2.035303483193632, -0.7324760340998472, -2.513729997089929, 0.7793013745114928, 4.205228382280504, 2.584183925512734, -0.3861028207894132, 0.1090382617943418, 1.277268478662499, -0.02728549749820797, -0.3191095391908832, 2.240085898871425, 2.644653754125337, -0.6974545492801782, -2.003872497191649, -0.02211041197256246, -0.480700798987187, -3.083055234299536, -1.532589842251274, 2.357121038375336, 1.688030646929415, -0.5524766064552332, 2.26220657262343, 5.259309801522246, 1.729103007154342, -2.150145364124564, 0.2803924847887524, 2.994913019190946, 1.059908603290232, 0.06578578359256966, 1.904548302442779, 1.038067092276899, -1.441817693022569, -0.5173204016911725, 0.08448014499070713, -3.114996717595581, -3.654451480490283, 0.5944223843041706, 1.942034582432484, -0.3033580429575963, -0.008199791812310986, 0.434452183675321, -1.766847439383331, 1.110824177785346, 9.557202768405554, 10.52269722703957, 2.556499084243407, -1.511639762374368, -0.1089556438421931, -0.5687424977430615, -0.3020102392659919, 3.000510402770217, 2.031808627859207, -2.640676846299946, -2.277020573718126, 0.4819194405285959, -0.7268412355514552, -1.103164578028766, 1.379449639553227, 0.5558115310116345, -1.455544418136379, 0.02066775809781214, -0.9257700962848768, -4.912259500388213, -2.961265017516453, 1.257638487272818, -1.349184495248001, -3.24265239937145, 1.672081669398726, 3.152485783344271, -0.733025907175065, -0.5659032803598877, 0.6196672550270409, -2.618715163195345, -2.707740924361972, 0.9962202617984705, -0.4765716027688149, -3.369147024838012, -1.023182136765448, 0.3376357436463425, -1.136202181480114, -0.1764050895373791, -0.4525571752691328, -2.984800754427617, 0.03346072313497481, 4.15735418248536, 0.9433469881177554, -1.244252927095894, 1.862178445946744, 0.6789868310270015, -1.962835930826496, 1.739015428637539, 3.046093127323531, -0.903165876862245, 0.4871205773362545, 3.307708893085891, -0.8416255043626553], 'positive_zeros': ['0.5788378519830668', '1.078412726170906', '1.997597647678537', '2.358346739541912', '2.986257395916083', '3.672297479120298', '3.937898467892491', '4.582027555515558', '5.283202604638216', '5.687974699339317', '6.198886676317642', '6.708200131033864', '7.448440191214174', '7.734436469504895', '8.245967240921573', '8.543260892265012', '9.201257860743890', '9.753402646414710', '9.943941446143974', '10.58826388311087', '11.14375110881592', '11.35522988018363', '12.07955004369125', '12.48342105385104', '13.13706295934085', '13.23330896846883', '13.83793255892621', '14.31893304365660', '14.51177845009615', '15.21548526085666', '15.70897521808644', '16.00133142377357', '16.30811930420961', '16.70788253793750', '17.59642339746776', '18.02987024934779', '18.12547242378175', '18.52776183260956', '19.10279797527061', '19.67750996952030', '19.91519732810268'], 'prelabel': '2-235200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.336837165862896, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1594482452989049437, 'z1': {'__RealLiteral__': 0, 'data': '0.5788378519830668', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.078412726170906', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.997597647678537', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1878.0814555405154, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 235200, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -3, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, 1, 0, 3, 0, -5, 0, -3, 0, 0, 0, 8, 0, 4, 0, 8, 0, 6, 0, 0, 0, -10, 0, 0, 0, 0, 0, 9, 0, 0, 0, 4, 0, 5, 0, 10, 0, 0, 0, 0, 0, 6, 0, -8, 0, 10, 0, -2, 0, 0, 0, 0, 0, 11, 0, 1, 0, 7, 0, 0, 0, 3, 0, -18, 0, 0, 0, -5, 0, 0, 0, 17, 0, -3, 0], 'euler11': [1, 3, 11], 'euler13': [1, -4, 13], 'euler17': [1, 0, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -3, 29], 'euler3': [1, -1, 0], 'euler31': [1, 5, 31], 'euler37': [1, -8, 37], 'euler41': [1, -8, 41], 'euler43': [1, -6, 43], 'euler47': [1, 10, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, -5, 59], 'euler61': [1, -10, 61], 'euler67': [1, -6, 67], 'euler7': [1, 0, 0], 'euler71': [1, -10, 71], 'euler73': [1, 2, 73], 'euler79': [1, -11, 79], 'euler83': [1, -7, 83], 'euler89': [1, 18, 89], 'euler97': [1, -17, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 0, 0], [1, 3, 11], [1, -4, 13], [1, 0, 17], [1, -4, 19], [1, 8, 23], [1, -3, 29], [1, 5, 31], [1, -8, 37], [1, -8, 41], [1, -6, 43], [1, 10, 47], [1, -9, 53], [1, -5, 59], [1, -10, 61], [1, -6, 67], [1, -10, 71], [1, 2, 73], [1, -11, 79], [1, -7, 83], [1, 18, 89], [1, -17, 97]], 'index': 269, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/235200/rr'], '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': '2-235200-1.1-c1-0-269', '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': '2-235200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.336837165862896, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1594482452989049437, 'z1': {'__RealLiteral__': 0, 'data': '0.5788378519830668', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1594482452989049437', 'Lhash_array': ['1594482452989049437'], 'label': '2-235200-1.1-c1-0-269', 'type': 'ECQ', 'url': 'EllipticCurve/Q/235200/rr'}