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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': '1316399584937204650', '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, 4, 11], [1, -2, 13], [1, -2, 17], [1, -4, 19], [1, 0, 23], [1, -10, 29], [1, 0, 31], [1, -6, 37], [1, -6, 41], [1, -4, 43], [1, -8, 47], [1, -6, 53], [1, -4, 59], [1, 10, 61], [1, 4, 67], [1, -16, 71], [1, 14, 73], [1, 8, 79], [1, 4, 83], [1, 10, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 640, 'label': '2-235200-1.1-c1-0-640', 'leading_term': '7.04441458806', '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/235200/cj', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.538463145267329, 1.918704406335884, 0.9263249827627325, -0.1099827767451157, 0.6434639992882132, 3.126403427512583, 4.668744622500432, 2.946423870277568, -0.5779125365859629, -2.007266035349676, -0.3614239748270546, 0.692293562529684, -1.744145340756703, -4.905053032934056, -4.229299878635581, -0.6526942432488823, 0.6213734631176873, -1.554533154543755, -2.706316169439074, -0.7038620169580136, 0.8035015559077553, -0.4672870712913462, -1.282550699128256, 0.2480253260590406, 0.3954389800786659, -2.653015432194858, -4.093040815178888, -1.1717099635613, 1.120260363156673, -0.5385493955933819, -1.399925467124149, 1.329442069989636, 2.154116109602866, -1.35392073297233, -2.341549366296052, 2.120463476754139, 4.385262999845976, 0.634957820301786, -2.091380607624239, -0.1399110187365385, 0.7420454689489853, -1.298911978798084, -1.123304249869959, 0.8318109695845154, -0.4966539752144908, -2.606409208386343, -0.5148443023958713, 1.801301820456644, 0.1369512429681409, -0.5195811799574875, 2.100423927622185, 1.704347171964364, -1.870287832101088, -1.474634969630793, 0.9689164551704587, -1.191722398239056, -2.882549560252605, 2.077476414094581, 5.545780081140278, 1.151754186886128, -2.410789552996841, -0.007705245997770361, 1.230996991281104, -0.2590767448001445, 0.6750097461738342, 1.052699174385416, -2.542109563754547, -3.329924488788316, 0.7299592046424448, 1.629348499215896, -0.7449803974497823, -0.01021394508809778, 0.9568936775738277, -0.9621745309681412, -0.0889123886194303, 2.22061233578514, -1.719942396860241, -6.019916819786432, -2.242362989499394, 1.100937944440417, -2.240193578895835, -2.639147214564067, 1.897179572829257, 2.022793023966479, -0.3900149659835558, 0.5804152696732164, -0.6747298351551655, -4.95442559224233, -3.603112826780166, 0.6156775238229552, -0.26793041517499, -1.590687161068069, 0.02424325780228121, -0.7772136643209724, -1.642659099735913, 1.233336126284866, 0.905857541613142, -2.34979543901528, 0.6177924076483172, 4.451014800882885, 0.9226995503803921, -1.038327349114557, 2.176958893757209, 0.4660851678783223, -3.404827367754634, -0.8257231321853433, 0.8804366023574859, -1.973641943997591, -0.5785804752359069, 2.231226240093261, -0.7661042018184664, -2.104373495839881, 1.216456924901365, 1.170539085347238, -0.4366064446657678, 0.3102579194969959, -1.509728314889612, -2.69036451824194, 1.947350453245243, 3.088741747957895], 'positive_zeros': ['0.9503263975924160', '1.132445768982925', '2.205610434166515', '2.793606022893126', '3.112160573899546', '4.056975857104346', '4.347286584935887', '5.073294599849481', '5.435909214475125', '5.964794679056341', '6.296079443477884', '7.083889251453529', '7.444756977444472', '7.896127917206401', '8.414840423030314', '8.897821290306772', '9.534421991097415', '10.01387480578487', '10.35238770432469', '10.87376291741419', '11.20486098829895', '11.78694648032189', '12.26466879448908', '12.56210511780713', '13.11486946260899', '13.62007928802885', '13.91600620164033', '14.41873973328560', '15.04965943866949', '15.50060536656513', '15.94153191082128', '16.15477488711204', '16.59130642757375', '17.20507271220835', '17.65831581135410', '18.00122890811079', '18.38424232767617', '18.75720018164159', '19.17902142065215', '19.85541962954869'], 'prelabel': '2-235200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.336837165862896, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1316399584937204650, 'z1': {'__RealLiteral__': 0, 'data': '0.9503263975924160', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.132445768982925', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.205610434166515', '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, -4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, -1, 0, 10, 0, 0, 0, 4, 0, 0, 0, 6, 0, -2, 0, 6, 0, 4, 0, 0, 0, 8, 0, 0, 0, -2, 0, 6, 0, 0, 0, -4, 0, 4, 0, -10, 0, 0, 0, 0, 0, -4, 0, 0, 0, 16, 0, -14, 0, 0, 0, 0, 0, -8, 0, 1, 0, -4, 0, 0, 0, -10, 0, -10, 0, 0, 0, 0, 0, 0, 0, 10, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, -2, 13], 'euler17': [1, -2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -10, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -6, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 10, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -16, 71], 'euler73': [1, 14, 73], 'euler79': [1, 8, 79], 'euler83': [1, 4, 83], 'euler89': [1, 10, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 0, 0], [1, 4, 11], [1, -2, 13], [1, -2, 17], [1, -4, 19], [1, 0, 23], [1, -10, 29], [1, 0, 31], [1, -6, 37], [1, -6, 41], [1, -4, 43], [1, -8, 47], [1, -6, 53], [1, -4, 59], [1, 10, 61], [1, 4, 67], [1, -16, 71], [1, 14, 73], [1, 8, 79], [1, 4, 83], [1, 10, 89], [1, -10, 97]], 'index': 640, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/235200/cj'], '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-c1-0-640', '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': '2-235200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.336837165862896, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1316399584937204650, 'z1': {'__RealLiteral__': 0, 'data': '0.9503263975924160', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1316399584937204650', 'Lhash_array': ['1316399584937204650'], 'label': '2-235200-1.1-c1-0-640', 'type': 'ECQ', 'url': 'EllipticCurve/Q/235200/cj'}