-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2588348255174263938309941348081', 'a10': [5.604850330079272, 0.0], 'a2': [2.6860440244650348, 0.0], 'a3': [-4.331373934474082, 0.0], 'a4': [-0.7851674986356794, 0.0], 'a5': [2.086656167594111, 0.0], 'a6': [-11.634261074417717, 0.0], 'a7': [24.998475872457306, 0.0], 'a8': [-23.597346663634802, 0.0], 'a9': [-8.23919983975851, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.051551991659046, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [0, 0]]]], 'bad_primes': [17], 'central_character': '289.1', 'coefficient_field': 'CDF', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.6860440244650348, 0], [8.0, 0]], [[1.0, 0], [4.331373934474082, 0], [27.0, 0]], [[1.0, 0], [-2.086656167594111, 0], [125.0, 0]], [[1.0, 0], [-24.998475872457306, 0], [343.0, 0]], [[1.0, 0], [3.8215766387474797, 0], [1331.0, 0]], [[1.0, 0], [-17.67257891362284, 0], [2197.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [160.9145781261131, 0], [6859.0, 0]], [[1.0, 0], [99.96763407485304, 0], [12167.0, 0]], [[1.0, 0], [200.58346386614667, 0], [24389.0, 0]], [[1.0, 0], [-76.53819349782604, 0], [29791.0, 0]], [[1.0, 0], [244.75856341239603, 0], [50653.0, 0]], [[1.0, 0], [54.1131788075131, 0], [68921.0, 0]], [[1.0, 0], [-142.08723066888243, 0], [79507.0, 0]], [[1.0, 0], [468.4509791736005, 0], [103823.0, 0]], [[1.0, 0], [96.56731970128892, 0], [148877.0, 0]], [[1.0, 0], [-364.4841471830707, 0], [205379.0, 0]], [[1.0, 0], [-707.871560602128, 0], [226981.0, 0]], [[1.0, 0], [304.4544460064136, 0], [300763.0, 0]], [[1.0, 0], [470.00294602995933, 0], [357911.0, 0]], [[1.0, 0], [142.05627667450455, 0], [389017.0, 0]], [[1.0, 0], [-717.8649748909013, 0], [493039.0, 0]], [[1.0, 0], [367.639171910298, 0], [571787.0, 0]], [[1.0, 0], [-1042.2830483137445, 0], [704969.0, 0]], [[1.0, 0], [-903.5344165915218, 0], [912673.0, 0]], [[1.0, 0], [-443.2331945478897, 0], [1030301.0, 0]], [[1.0, 0], [1396.362571284407, 0], [1092727.0, 0]], [[1.0, 0], [-1843.8946554201261, 0], [1225043.0, 0]], [[1.0, 0], [-372.9602086410515, 0], [1295029.0, 0]], [[1.0, 0], [1779.1313079575827, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 46, 'label': '2-17e2-1.1-c3-0-46', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/289/4/a/g/1/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [-1.6760816539395536e-60, 0.24340006410889767, 0.48497576835966205, 0.7228875001649373, 0.9552664563934266, 1.180203285349924, 1.3957404757961154, 1.599869519606235, 1.7905336971972676, 1.9656371278210063, 2.123060497694737, 2.260683635098074, 2.3764148496945188, 2.4682266993952573, 2.5341975972734208, 2.5725584280018614, 2.5817431123785965, 2.560441844076079, 2.5076555294130123, 2.4227497937329847, 2.3055067823956725, 2.1561728863749035, 1.9755004681889896, 1.764781659510185, 1.5258723530866105, 1.261204623567167, 0.9737859882652563, 0.6671841620411499, 0.34549627053594106, 0.013301860815526787, -0.32440051668145103, -0.6622728937330119, -0.9947328470956606, -1.316062490291855, -1.620529576004372, -1.9025182264062397, -2.156666271019317, -2.3780056823876095, -2.562102181593979, -2.705189760951224, -2.8042956615443857, -2.8573512681662554, -2.8632844600242184, -2.822089194823809, -2.734868513883592, -2.603847738390907, -2.4323553767947272, -2.224770168604672, -1.9864337311341553, -1.7235294262655954, -1.4429292903887632, -1.1520121321773547, -0.8584571543784114, -0.5700186478366894, -0.2942883867481983, -0.038453271399854876, 0.19094353209300977, 0.3882292627496368, 0.5488072118083306, 0.6693327008973151, 0.7478512880089674, 0.7838919994996226, 0.778509640753055, 0.7342718231836229, 0.6551882227040662, 0.5465817006989772, 0.4149032041630226, 0.2674947350628076, 0.11230704750470585, -0.04241900532711452, -0.18849649836115617, -0.3181491186122572, -0.4243664587683153, -0.5012430433593607, -0.5442859543064965, -0.5506762944778804, -0.5194707585079336, -0.45173127347268677, -0.35057300265733243, -0.2211239176276245, -0.07039255063637156, 0.09295567444749038, 0.2589091105452352, 0.4164990343163718, 0.5542547563074529, 0.6607084759275764, 0.7249304392891345, 0.7370723934961045, 0.6888955879929648, 0.5742587881533465, 0.3895420397036901, 0.1339833140123511, -0.19009231520017622, -0.5771677046644712, -1.0185650234538228, -1.5026201778517, -2.0150008816732377, -2.5391624800730157, -3.0569290155337825, -3.5491805831063026, -3.996622072114559, -4.38060324444391, -4.683956047719576, -4.891812363653446, -4.992364257090591, -4.977529366788025, -4.843486437799496, -4.5910501283528715, -4.225860035059566, -3.758366185176641, -3.2036017753482007, -2.5807433487933635, -1.912468490012503, -1.2241310238455678, -0.5427831536840376, 0.10391752247731134, 0.6888710834752831, 1.1867181397355195, 1.5749890736855816, 1.8351656092969781, 1.953602579544251, 1.922262296823914, 1.739220974561182, 1.4089159619744107, 0.9421137748215791, 0.3555915547070079, -0.32846190574130246, -1.0833057192501812, -1.8787339481499985, -2.6823449667168147, -3.460937721660593, -4.181971641078393, -4.815022026341949, -5.333161120841945, -5.7141968883278995, -5.941706880470426, -6.005813272301858, -5.903656855192115, -5.639541986132336, -5.2247405324167255, -4.6769599324217195, -4.019497741426, -3.280121531589843, -2.4897278614716996, -1.6808463763611248, -0.8860642085832547, -0.1364511332082384, 0.5399329917267011, 1.1193702796479577, 1.5835857639840796, 1.9205582587788812, 2.12499721769632, 2.198459436159866, 2.1490989551086743, 1.9910637321323559, 1.7435724150227863, 1.4297227462463094, 1.075098666662476, 0.7062551202902873, 0.34916712156899016, 0.027732301358998884, -0.23758635775185546, -0.4308985089087666, -0.541738453646252, -0.5655809970138516, -0.5039906945440109, -0.364395865696216, -0.15950138791857482, 0.09362362085051928, 0.3747269356197574, 0.6617498723297596, 0.9323134359931984, 1.1652204058293794, 1.3418779805399523, 1.4475497540224955, 1.4723557563554905, 1.4119545625835563, 1.2678611796538823, 1.0473774029055238, 0.76313618288292, 0.43228670130006197, 0.07537070333275245, -0.2850384021961573, -0.6258455095167319, -0.9249935235068669, -1.162968667566392, -1.3241492415382927, -1.3979044976208717, -1.3793655205758548, -1.2698107540905632, -1.0766338538778666, -0.8128892967587805, -0.4964398365555575, -0.1487575648639545, 0.2065448852026635, 0.5453563121178815, 0.8447713977437644, 1.0847401589052685, 1.2495460293667988, 1.329005337369482, 1.3192976943882322, 1.2233602356370004, 1.0508073257098833, 0.8173694350505094, 0.5438782869417423, 0.2548578000560854, -0.023190462958178143, -0.2636948002348605, -0.44198462155068374, -0.5371881010245835, -0.5339200950415904, -0.42363493103980954, -0.20553848135395072, 0.11301830361461163, 0.516708220976002, 0.982964755154443, 1.4832533131066663, 1.9848045767823606, 2.4527033744569224, 2.852198521757853, 3.151079753664302, 3.3219587703877647, 3.344293490105693, 3.2060080173659946, 2.904584978828865, 2.44754035212977, 1.8522316214160166, 1.1449953625153766, 0.35965711788150745, -0.46449860250574315, -1.2851703999435897, -2.059734383204805, -2.748009629473075, -3.314904254541387, -3.732755704065181, -3.9831962752526944, -4.058404712882648, -3.961645184450637, -3.7070434029044765, -3.3186028610114247, -2.8285183687897377, -2.2748954707657445, -1.6990290912203403, -1.1424295196624088, -0.6438058475481041, -0.2362242963219818, 0.05534935267411378, 0.21593758488380874, 0.24172116176509298, 0.14039240960648056, -0.06934964193713491, -0.35914191669327183, -0.6930556973404071, -1.0303116392540073, -1.3284240374082363, -1.5465513848053687, -1.6488101594817544], 'positive_zeros': ['2.04184674760399630399440607845149', '3.87838291463079950847578081579960', '4.83204869234405139213720476123082', '5.65572591429008564824069379718539', '6.42928257209339339106637797026067', '8.074251617472804068893413282024242', '8.826694704173227030342047547955896', '10.27913562657937888979597741928667', '11.25663815305059234261978174745446'], 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.04184674760399630399440607845', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.87838291463079950847578081580', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.83204869234405139213720476123', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 17.051551991659046, 'bad_primes': [17], 'central_character': '1.1', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'index': 46, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/289/4/a/g/1/9'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-17e2-1.1-c3-0-46', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.04184674760399630399440607845', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2588348255174263938309941348081', 'Lhash_array': ['2588348255174263938309941348081'], 'label': '2-17e2-1.1-c3-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/289/4/a/g/1/9'}