Table lfunc_lfunctions
L-functions
{'Lhash': '2730609802400218642278264302986', 'a10': [0.6180339887498949, 0.0], 'a2': [-1.618033988749895, 0.0], 'a3': [1.0, 0.0], 'a4': [0.6180339887498949, 0.0], 'a5': [-0.38196601125010515, 0.0], 'a6': [-1.618033988749895, 0.0], 'a7': [-3.0, 0.0], 'a8': [2.23606797749979, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8985695933724793, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '363.1', 'coefficient_field': 'CDF', 'conductor': 363, 'conductor_radical': 33, 'conjugate': '2730609802400218642278264302986', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.618033988749895, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.38196601125010515, 0], [5.0, 0]], [[1.0, 0], [3.0, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [6.23606797749979, 0], [13.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [17.0, 0]], [[1.0, 0], [-0.8541019662496846, 0], [19.0, 0]], [[1.0, 0], [5.47213595499958, 0], [23.0, 0]], [[1.0, 0], [-4.47213595499958, 0], [29.0, 0]], [[1.0, 0], [3.8541019662496847, 0], [31.0, 0]], [[1.0, 0], [4.23606797749979, 0], [37.0, 0]], [[1.0, 0], [5.944271909999159, 0], [41.0, 0]], [[1.0, 0], [1.7639320225002102, 0], [43.0, 0]], [[1.0, 0], [0.6180339887498949, 0], [47.0, 0]], [[1.0, 0], [7.381966011250105, 0], [53.0, 0]], [[1.0, 0], [5.326237921249264, 0], [59.0, 0]], [[1.0, 0], [1.1458980337503155, 0], [61.0, 0]], [[1.0, 0], [-10.562305898749054, 0], [67.0, 0]], [[1.0, 0], [-14.562305898749054, 0], [71.0, 0]], [[1.0, 0], [1.2360679774997898, 0], [73.0, 0]], [[1.0, 0], [0.5278640450004206, 0], [79.0, 0]], [[1.0, 0], [-12.70820393249937, 0], [83.0, 0]], [[1.0, 0], [-9.47213595499958, 0], [89.0, 0]], [[1.0, 0], [-15.034441853748634, 0], [97.0, 0]], [[1.0, 0], [-3.0, 0], [101.0, 0]], [[1.0, 0], [6.0, 0], [103.0, 0]], [[1.0, 0], [0.2360679774997897, 0], [107.0, 0]], [[1.0, 0], [0, 0], [109.0, 0]], [[1.0, 0], [12.70820393249937, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 10050297, 'index': 14, 'label': '2-363-1.1-c1-0-14', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/363/2/a/e/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [-1.5294754221464548e-120, 0.14515427589180996, 0.2937580629225941, 0.4482308797442064, 0.6091260213778399, 0.7745968657798328, 0.9401755578024036, 1.0988230990846237, 1.2412114851414433, 1.3562215282454517, 1.4316565234462557, 1.4551710565754081, 1.4153970366052093, 1.3032208362870912, 1.1131321330430155, 0.8445321371377095, 0.5028615580892852, 0.10039188486331789, -0.3434780489111626, -0.8025609193554603, -1.2449573715387892, -1.6349124441142058, -1.9354157977204904, -2.111418009084459, -2.133439206478203, -1.981257093163245, -1.6472916685376422, -1.1392666100444686, -0.48173363519487156, 0.28389596101094017, 1.1010565042214082, 1.901552135321502, 2.6107826375604093, 3.1543350541592248, 3.465393094264473, 3.4922392739153776, 3.2050117761700254, 2.6008542066594424, 1.706678643533882, 0.578955495010895, -0.6997621703876878, -2.027502488260599, -3.2922442799318326, -4.383119463098277, -5.20225634122545, -5.6758760827528985, -5.763224829672433, -5.4620830411443295, -4.809940312291281, -3.8804285584605442, -2.775212709237879, -1.6121678683187095, -0.5112350728485628, 0.42024533163969024, 1.1007480158356096, 1.4844521423689545, 1.566321047191446, 1.3815235381831836, 0.9991535438774161, 0.5110649260419561, 0.01741993605143518, -0.38887871831826654, -0.6364489280932368, -0.6860885935100666, -0.5360530776068707, -0.22100928363478659, 0.1952341491180063, 0.632045325112766, 1.00723682998202, 1.2525842506073679, 1.3267516152053584, 1.2231441920675603, 0.9710500275107309, 0.6296255005612753, 0.2756279735336177, -0.012943158580809869, -0.1742127127178022, -0.1773323275492554, -0.03171252187425943, 0.21171030608059555, 0.46803404291420864, 0.633928389625482, 0.6086237707054053, 0.31651955865675996, -0.27306727146167137, -1.1332969159393396, -2.1775615092404466, -3.269017905669896, -4.241085712499319, -4.925845283682523, -5.18544496182369, -4.940628396178417, -4.190587155909242, -3.0195980451821254, -1.5881566517066734, -0.10919255642285744, 1.1870834876023812, 2.0936832710449926, 2.4652409965078768, 2.2468061594756725, 1.4869693037113791, 0.33199965773053336, -0.9987643995780936, -2.2523189638274532, -3.189122591970395, -3.6290261502218297, -3.486939877385828, -2.7908594182830493, -1.6781320713038723, -0.3700801830990652, 0.8705211403119503, 1.7909931859957142, 2.1991341921917766, 2.002200158011242, 1.2263447583671487, 0.01222850883666335, -1.4126359421337593, -2.7793743876121764, -3.831823010386979, -4.377986915507831, -4.328105951755813, -3.7112891255874922, -2.6672017879008822, -1.4146424132327502, -0.2038649105472492, 0.7369315147148676, 1.2492312318442162, 1.2755461104815895, 0.8677264194412346, 0.17069407706730297, -0.6143651810491723, -1.2786361321638395, -1.6547408364377418, -1.6548106025345959, -1.288784790652555, -0.6588893111575738, 0.06804601915364168, 0.7034512013128477, 1.0844357344046813, 1.1140743398003725, 0.7846719687348496, 0.17837765801493774, -0.5548049855803006, -1.2358683656824787, -1.7024957714228737, -1.8498345617688152, -1.655842177314777, -1.184692736443101, -0.5674691554899554, 0.034619122577258056, 0.47453645501233677, 0.6591450442313066, 0.573334586062126, 0.2816320329026829, -0.09353495338546602, -0.4112266082637253, -0.5581549618520054, -0.4883725829422519, -0.24444464396816523, 0.04730924394698074, 0.20797126421082973, 0.05657177960356172, -0.5329624446669025, -1.584204074562326, -2.994299480460818, -4.542608256148241, -5.9325464913495765, -6.858288015668442, -7.080640518699047, -6.49279991648963, -5.15799168794865, -3.307176482759384, -1.2946702366064524, 0.47966097639040256, 1.663819332517734, 2.0399000981721134, 1.5810001075982867, 0.4631426622949741, -0.9726476854761839, -2.300475541261858, -3.113237081817153, -3.124525027787563, -2.243158941068352, -0.6009722807416855, 1.474118690300179, 3.5340267774396756, 5.11713074562591, 5.859341010674597, 5.581911155002702, 4.334041075325895, 2.3797504324804657, 0.1326956216817642, -1.9441500355073673, -3.4482255534689044, -4.128752783553812, -3.9372291264029635, -3.025624733036181, -1.6948004776637347, -0.3086486734513067, 0.8020085609497228, 1.4199066889114742, 1.4856298421600862, 1.0959008831671553, 0.4592271641006433, -0.17595176389410885, -0.5983711314965129, -0.6935885868464985, -0.46960851277650784, -0.04275348188093918, 0.4097211671383676, 0.7138317912217, 0.758757182745286, 0.5331993076517821, 0.12687697302750706, -0.3028154846189995, -0.5876463807556237, -0.6098524267188203, -0.3472605369208199, 0.11339798824601499, 0.6004298633223375, 0.9116622605764083, 0.8824469853314919, 0.44508738836385003, -0.34048163589460145, -1.2963800399299885, -2.175795368755495, -2.7374219244888827, -2.8224836018216193, -2.409501849950567, -1.6278632930328063, -0.7234972054442202, 0.015020200862859396, 0.34850167937781446, 0.16891716699275156, -0.4558447908652666, -1.290757554562206, -1.996572893044491, -2.2305148960067362, -1.7556837547041881, -0.5257997461891638, 1.2822529633134172, 3.3010156713397856, 5.063860305631156, 6.13074195474567, 6.212406510243154, 5.256228515771148, 3.4670779181740845, 1.2552454583827937, -0.8749330048721502, -2.464038307857252, -3.2234844052656775, -3.1109630883973627, -2.3326308352679797, -1.2711025347354683, -0.3608326749683287, 0.051252398939348146, -0.18292178801385708], 'positive_zeros': ['2.15407132052680465264893855069665', '3.58014662113298503108212757707159', '4.93286077599260726790850476019411', '6.56497603865813640787210971212724', '7.50470918349601455325913291569239', '8.193649732012210798534917023753214', '9.368161890918320204769588635154530', '9.768570950460357282081378252607651', '10.44962004892279487113516353833279'], 'prelabel': '2-363-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7025186029446138, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15407132052680465264893855070', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.58014662113298503108212757707', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.93286077599260726790850476019', 'prec': 100}}