Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,3,Mod(3,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.3");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.h (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.871936845953\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 19.5 | ||
Character | \(\chi\) | \(=\) | 32.19 |
Dual form | 32.3.h.a.27.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.345994 | − | 1.96984i | 0.172997 | − | 0.984922i | ||||
\(3\) | −3.70255 | − | 1.53365i | −1.23418 | − | 0.511215i | −0.332291 | − | 0.943177i | \(-0.607822\pi\) |
−0.901892 | + | 0.431962i | \(0.857822\pi\) | |||||||
\(4\) | −3.76058 | − | 1.36311i | −0.940144 | − | 0.340777i | ||||
\(5\) | 7.20074 | − | 2.98264i | 1.44015 | − | 0.596529i | 0.480314 | − | 0.877097i | \(-0.340523\pi\) |
0.959834 | + | 0.280568i | \(0.0905227\pi\) | |||||||
\(6\) | −4.30210 | + | 6.76281i | −0.717017 | + | 1.12714i | ||||
\(7\) | 4.26150 | + | 4.26150i | 0.608786 | + | 0.608786i | 0.942629 | − | 0.333843i | \(-0.108346\pi\) |
−0.333843 | + | 0.942629i | \(0.608346\pi\) | |||||||
\(8\) | −3.98625 | + | 6.93612i | −0.498281 | + | 0.867015i | ||||
\(9\) | 4.99283 | + | 4.99283i | 0.554759 | + | 0.554759i | ||||
\(10\) | −3.38393 | − | 15.2163i | −0.338393 | − | 1.52163i | ||||
\(11\) | 6.19818 | − | 2.56737i | 0.563471 | − | 0.233397i | −0.0827202 | − | 0.996573i | \(-0.526361\pi\) |
0.646191 | + | 0.763175i | \(0.276361\pi\) | |||||||
\(12\) | 11.8332 | + | 10.8144i | 0.986099 | + | 0.901197i | ||||
\(13\) | −8.05345 | − | 3.33585i | −0.619496 | − | 0.256604i | 0.0507868 | − | 0.998710i | \(-0.483827\pi\) |
−0.670283 | + | 0.742106i | \(0.733827\pi\) | |||||||
\(14\) | 9.86895 | − | 6.92004i | 0.704925 | − | 0.494288i | ||||
\(15\) | −31.2354 | −2.08236 | ||||||||
\(16\) | 12.2839 | + | 10.2522i | 0.767742 | + | 0.640760i | ||||
\(17\) | 24.5802i | 1.44589i | 0.690904 | + | 0.722947i | \(0.257213\pi\) | ||||
−0.690904 | + | 0.722947i | \(0.742787\pi\) | |||||||
\(18\) | 11.5626 | − | 8.10762i | 0.642367 | − | 0.450423i | ||||
\(19\) | 4.96459 | − | 11.9856i | 0.261294 | − | 0.630820i | −0.737725 | − | 0.675101i | \(-0.764100\pi\) |
0.999019 | + | 0.0442815i | \(0.0140998\pi\) | |||||||
\(20\) | −31.1446 | + | 1.40106i | −1.55723 | + | 0.0700532i | ||||
\(21\) | −9.24278 | − | 22.3140i | −0.440132 | − | 1.06257i | ||||
\(22\) | −2.91279 | − | 13.0978i | −0.132399 | − | 0.595353i | ||||
\(23\) | −9.72199 | + | 9.72199i | −0.422695 | + | 0.422695i | −0.886131 | − | 0.463435i | \(-0.846617\pi\) |
0.463435 | + | 0.886131i | \(0.346617\pi\) | |||||||
\(24\) | 25.3968 | − | 19.5678i | 1.05820 | − | 0.815326i | ||||
\(25\) | 25.2768 | − | 25.2768i | 1.01107 | − | 1.01107i | ||||
\(26\) | −9.35754 | + | 14.7099i | −0.359906 | + | 0.565764i | ||||
\(27\) | 2.97384 | + | 7.17949i | 0.110142 | + | 0.265907i | ||||
\(28\) | −10.2168 | − | 21.8346i | −0.364886 | − | 0.779807i | ||||
\(29\) | −5.86371 | + | 14.1563i | −0.202197 | + | 0.488147i | −0.992155 | − | 0.125014i | \(-0.960102\pi\) |
0.789958 | + | 0.613161i | \(0.210102\pi\) | |||||||
\(30\) | −10.8073 | + | 61.5289i | −0.360242 | + | 2.05096i | ||||
\(31\) | − | 17.5320i | − | 0.565550i | −0.959186 | − | 0.282775i | \(-0.908745\pi\) | ||
0.959186 | − | 0.282775i | \(-0.0912549\pi\) | |||||||
\(32\) | 24.4453 | − | 20.6501i | 0.763915 | − | 0.645316i | ||||
\(33\) | −26.8865 | −0.814743 | ||||||||
\(34\) | 48.4192 | + | 8.50460i | 1.42409 | + | 0.250135i | ||||
\(35\) | 43.3965 | + | 17.9754i | 1.23990 | + | 0.513583i | ||||
\(36\) | −11.9702 | − | 25.5817i | −0.332504 | − | 0.710603i | ||||
\(37\) | −36.0346 | + | 14.9260i | −0.973909 | + | 0.403406i | −0.812166 | − | 0.583427i | \(-0.801712\pi\) |
−0.161743 | + | 0.986833i | \(0.551712\pi\) | |||||||
\(38\) | −21.8920 | − | 13.9264i | −0.576106 | − | 0.366485i | ||||
\(39\) | 24.7023 | + | 24.7023i | 0.633391 | + | 0.633391i | ||||
\(40\) | −8.01597 | + | 61.8348i | −0.200399 | + | 1.54587i | ||||
\(41\) | 10.9784 | + | 10.9784i | 0.267765 | + | 0.267765i | 0.828199 | − | 0.560434i | \(-0.189366\pi\) |
−0.560434 | + | 0.828199i | \(0.689366\pi\) | |||||||
\(42\) | −47.1531 | + | 10.4863i | −1.12269 | + | 0.249674i | ||||
\(43\) | −22.4024 | + | 9.27937i | −0.520985 | + | 0.215799i | −0.627650 | − | 0.778496i | \(-0.715983\pi\) |
0.106664 | + | 0.994295i | \(0.465983\pi\) | |||||||
\(44\) | −26.8084 | + | 1.20599i | −0.609281 | + | 0.0274090i | ||||
\(45\) | 50.8439 | + | 21.0603i | 1.12987 | + | 0.468006i | ||||
\(46\) | 15.7871 | + | 22.5146i | 0.343197 | + | 0.489447i | ||||
\(47\) | 27.0104 | 0.574690 | 0.287345 | − | 0.957827i | \(-0.407227\pi\) | ||||
0.287345 | + | 0.957827i | \(0.407227\pi\) | |||||||
\(48\) | −29.7584 | − | 56.7982i | −0.619967 | − | 1.18330i | ||||
\(49\) | − | 12.6792i | − | 0.258760i | ||||||
\(50\) | −41.0458 | − | 58.5371i | −0.820916 | − | 1.17074i | ||||
\(51\) | 37.6973 | − | 91.0093i | 0.739163 | − | 1.78450i | ||||
\(52\) | 25.7385 | + | 23.5224i | 0.494971 | + | 0.452354i | ||||
\(53\) | −34.0172 | − | 82.1247i | −0.641833 | − | 1.54952i | −0.824204 | − | 0.566293i | \(-0.808377\pi\) |
0.182371 | − | 0.983230i | \(-0.441623\pi\) | |||||||
\(54\) | 15.1714 | − | 3.37395i | 0.280952 | − | 0.0624805i | ||||
\(55\) | 36.9740 | − | 36.9740i | 0.672254 | − | 0.672254i | ||||
\(56\) | −46.5457 | + | 12.5709i | −0.831173 | + | 0.224480i | ||||
\(57\) | −36.7633 | + | 36.7633i | −0.644970 | + | 0.644970i | ||||
\(58\) | 25.8568 | + | 16.4486i | 0.445807 | + | 0.283596i | ||||
\(59\) | 27.8391 | + | 67.2095i | 0.471849 | + | 1.13914i | 0.963345 | + | 0.268264i | \(0.0864499\pi\) |
−0.491497 | + | 0.870879i | \(0.663550\pi\) | |||||||
\(60\) | 117.463 | + | 42.5773i | 1.95772 | + | 0.709621i | ||||
\(61\) | −6.37082 | + | 15.3805i | −0.104440 | + | 0.252140i | −0.967457 | − | 0.253034i | \(-0.918572\pi\) |
0.863018 | + | 0.505174i | \(0.168572\pi\) | |||||||
\(62\) | −34.5354 | − | 6.06598i | −0.557022 | − | 0.0978384i | ||||
\(63\) | 42.5539i | 0.675459i | ||||||||
\(64\) | −32.2196 | − | 55.2983i | −0.503431 | − | 0.864035i | ||||
\(65\) | −67.9404 | −1.04524 | ||||||||
\(66\) | −9.30258 | + | 52.9623i | −0.140948 | + | 0.802458i | ||||
\(67\) | −99.2165 | − | 41.0968i | −1.48084 | − | 0.613386i | −0.511542 | − | 0.859258i | \(-0.670925\pi\) |
−0.969302 | + | 0.245873i | \(0.920925\pi\) | |||||||
\(68\) | 33.5055 | − | 92.4357i | 0.492728 | − | 1.35935i | ||||
\(69\) | 50.9062 | − | 21.0860i | 0.737771 | − | 0.305595i | ||||
\(70\) | 50.4237 | − | 79.2650i | 0.720339 | − | 1.13236i | ||||
\(71\) | −2.55754 | − | 2.55754i | −0.0360217 | − | 0.0360217i | 0.688867 | − | 0.724888i | \(-0.258109\pi\) |
−0.724888 | + | 0.688867i | \(0.758109\pi\) | |||||||
\(72\) | −54.5336 | + | 14.7282i | −0.757411 | + | 0.204559i | ||||
\(73\) | 30.7498 | + | 30.7498i | 0.421230 | + | 0.421230i | 0.885627 | − | 0.464397i | \(-0.153729\pi\) |
−0.464397 | + | 0.885627i | \(0.653729\pi\) | |||||||
\(74\) | 16.9342 | + | 76.1469i | 0.228840 | + | 1.02901i | ||||
\(75\) | −132.354 | + | 54.8230i | −1.76473 | + | 0.730973i | ||||
\(76\) | −35.0074 | + | 38.3054i | −0.460623 | + | 0.504019i | ||||
\(77\) | 37.3544 | + | 15.4727i | 0.485122 | + | 0.200944i | ||||
\(78\) | 57.2065 | − | 40.1128i | 0.733416 | − | 0.514267i | ||||
\(79\) | −90.6600 | −1.14759 | −0.573797 | − | 0.818997i | \(-0.694530\pi\) | ||||
−0.573797 | + | 0.818997i | \(0.694530\pi\) | |||||||
\(80\) | 119.031 | + | 37.1847i | 1.48789 | + | 0.464809i | ||||
\(81\) | − | 94.6916i | − | 1.16903i | ||||||
\(82\) | 25.4241 | − | 17.8272i | 0.310051 | − | 0.217405i | ||||
\(83\) | −39.3191 | + | 94.9247i | −0.473724 | + | 1.14367i | 0.488781 | + | 0.872407i | \(0.337442\pi\) |
−0.962505 | + | 0.271264i | \(0.912558\pi\) | |||||||
\(84\) | 4.34169 | + | 96.5126i | 0.0516868 | + | 1.14896i | ||||
\(85\) | 73.3140 | + | 176.996i | 0.862517 | + | 2.08230i | ||||
\(86\) | 10.5278 | + | 47.3398i | 0.122417 | + | 0.550463i | ||||
\(87\) | 43.4214 | − | 43.4214i | 0.499096 | − | 0.499096i | ||||
\(88\) | −6.89991 | + | 53.2256i | −0.0784081 | + | 0.604836i | ||||
\(89\) | 109.290 | − | 109.290i | 1.22798 | − | 1.22798i | 0.263248 | − | 0.964728i | \(-0.415206\pi\) |
0.964728 | − | 0.263248i | \(-0.0847937\pi\) | |||||||
\(90\) | 59.0771 | − | 92.8680i | 0.656413 | − | 1.03187i | ||||
\(91\) | −20.1040 | − | 48.5355i | −0.220924 | − | 0.533357i | ||||
\(92\) | 49.8124 | − | 23.3081i | 0.541439 | − | 0.253349i | ||||
\(93\) | −26.8879 | + | 64.9132i | −0.289118 | + | 0.697992i | ||||
\(94\) | 9.34545 | − | 53.2063i | 0.0994196 | − | 0.566025i | ||||
\(95\) | − | 101.113i | − | 1.06434i | ||||||
\(96\) | −122.180 | + | 38.9677i | −1.27271 | + | 0.405913i | ||||
\(97\) | 63.7161 | 0.656867 | 0.328433 | − | 0.944527i | \(-0.393479\pi\) | ||||
0.328433 | + | 0.944527i | \(0.393479\pi\) | |||||||
\(98\) | −24.9761 | − | 4.38694i | −0.254859 | − | 0.0447647i | ||||
\(99\) | 43.7650 | + | 18.1280i | 0.442070 | + | 0.183112i | ||||
\(100\) | −129.511 | + | 60.6004i | −1.29511 | + | 0.606004i | ||||
\(101\) | −14.4312 | + | 5.97761i | −0.142883 | + | 0.0591842i | −0.452979 | − | 0.891521i | \(-0.649639\pi\) |
0.310096 | + | 0.950705i | \(0.399639\pi\) | |||||||
\(102\) | −166.231 | − | 105.747i | −1.62972 | − | 1.03673i | ||||
\(103\) | −9.69681 | − | 9.69681i | −0.0941438 | − | 0.0941438i | 0.658466 | − | 0.752610i | \(-0.271205\pi\) |
−0.752610 | + | 0.658466i | \(0.771205\pi\) | |||||||
\(104\) | 55.2409 | − | 42.5622i | 0.531163 | − | 0.409252i | ||||
\(105\) | −133.110 | − | 133.110i | −1.26771 | − | 1.26771i | ||||
\(106\) | −173.543 | + | 38.5939i | −1.63719 | + | 0.364093i | ||||
\(107\) | 138.127 | − | 57.2140i | 1.29091 | − | 0.534710i | 0.371650 | − | 0.928373i | \(-0.378792\pi\) |
0.919255 | + | 0.393662i | \(0.128792\pi\) | |||||||
\(108\) | −1.39693 | − | 31.0527i | −0.0129345 | − | 0.287525i | ||||
\(109\) | −32.0941 | − | 13.2938i | −0.294442 | − | 0.121962i | 0.230573 | − | 0.973055i | \(-0.425940\pi\) |
−0.525014 | + | 0.851093i | \(0.675940\pi\) | |||||||
\(110\) | −60.0402 | − | 85.6257i | −0.545820 | − | 0.778416i | ||||
\(111\) | 156.311 | 1.40821 | ||||||||
\(112\) | 8.65814 | + | 96.0372i | 0.0773048 | + | 0.857475i | ||||
\(113\) | 125.923i | 1.11436i | 0.830392 | + | 0.557180i | \(0.188117\pi\) | ||||
−0.830392 | + | 0.557180i | \(0.811883\pi\) | |||||||
\(114\) | 59.6981 | + | 85.1378i | 0.523667 | + | 0.746823i | ||||
\(115\) | −41.0083 | + | 99.0028i | −0.356594 | + | 0.860894i | ||||
\(116\) | 41.3475 | − | 45.2428i | 0.356444 | − | 0.390024i | ||||
\(117\) | −23.5542 | − | 56.8648i | −0.201318 | − | 0.486024i | ||||
\(118\) | 142.024 | − | 31.5846i | 1.20360 | − | 0.267666i | ||||
\(119\) | −104.748 | + | 104.748i | −0.880239 | + | 0.880239i | ||||
\(120\) | 124.512 | − | 216.653i | 1.03760 | − | 1.80544i | ||||
\(121\) | −53.7338 | + | 53.7338i | −0.444081 | + | 0.444081i | ||||
\(122\) | 28.0930 | + | 17.8711i | 0.230270 | + | 0.146484i | ||||
\(123\) | −23.8110 | − | 57.4849i | −0.193586 | − | 0.467357i | ||||
\(124\) | −23.8981 | + | 65.9306i | −0.192727 | + | 0.531698i | ||||
\(125\) | 32.0540 | − | 77.3852i | 0.256432 | − | 0.619081i | ||||
\(126\) | 83.8246 | + | 14.7234i | 0.665275 | + | 0.116852i | ||||
\(127\) | − | 79.4160i | − | 0.625322i | −0.949865 | − | 0.312661i | \(-0.898780\pi\) | ||
0.949865 | − | 0.312661i | \(-0.101220\pi\) | |||||||
\(128\) | −120.077 | + | 44.3347i | −0.938100 | + | 0.346365i | ||||
\(129\) | 97.1771 | 0.753311 | ||||||||
\(130\) | −23.5070 | + | 133.832i | −0.180823 | + | 1.02948i | ||||
\(131\) | 53.2656 | + | 22.0633i | 0.406608 | + | 0.168422i | 0.576607 | − | 0.817022i | \(-0.304376\pi\) |
−0.169999 | + | 0.985444i | \(0.554376\pi\) | |||||||
\(132\) | 101.109 | + | 36.6493i | 0.765976 | + | 0.277646i | ||||
\(133\) | 72.2331 | − | 29.9199i | 0.543106 | − | 0.224962i | ||||
\(134\) | −115.283 | + | 181.222i | −0.860319 | + | 1.35240i | ||||
\(135\) | 42.8277 | + | 42.8277i | 0.317242 | + | 0.317242i | ||||
\(136\) | −170.491 | − | 97.9828i | −1.25361 | − | 0.720462i | ||||
\(137\) | 50.7359 | + | 50.7359i | 0.370335 | + | 0.370335i | 0.867599 | − | 0.497264i | \(-0.165662\pi\) |
−0.497264 | + | 0.867599i | \(0.665662\pi\) | |||||||
\(138\) | −23.9230 | − | 107.573i | −0.173355 | − | 0.779515i | ||||
\(139\) | 133.213 | − | 55.1786i | 0.958366 | − | 0.396968i | 0.151997 | − | 0.988381i | \(-0.451430\pi\) |
0.806369 | + | 0.591413i | \(0.201430\pi\) | |||||||
\(140\) | −138.693 | − | 126.752i | −0.990667 | − | 0.905372i | ||||
\(141\) | −100.007 | − | 41.4244i | −0.709272 | − | 0.293790i | ||||
\(142\) | −5.92286 | + | 4.15307i | −0.0417102 | + | 0.0292469i | ||||
\(143\) | −58.4811 | −0.408959 | ||||||||
\(144\) | 10.1440 | + | 112.519i | 0.0704444 | + | 0.781379i | ||||
\(145\) | 119.425i | 0.823620i | ||||||||
\(146\) | 71.2116 | − | 49.9331i | 0.487751 | − | 0.342007i | ||||
\(147\) | −19.4455 | + | 46.9455i | −0.132282 | + | 0.319357i | ||||
\(148\) | 155.857 | − | 7.01134i | 1.05309 | − | 0.0473739i | ||||
\(149\) | 5.00779 | + | 12.0899i | 0.0336093 | + | 0.0811401i | 0.939793 | − | 0.341744i | \(-0.111018\pi\) |
−0.906184 | + | 0.422884i | \(0.861018\pi\) | |||||||
\(150\) | 62.1989 | + | 279.686i | 0.414659 | + | 1.86457i | ||||
\(151\) | −17.6867 | + | 17.6867i | −0.117130 | + | 0.117130i | −0.763243 | − | 0.646112i | \(-0.776394\pi\) |
0.646112 | + | 0.763243i | \(0.276394\pi\) | |||||||
\(152\) | 63.3434 | + | 82.2125i | 0.416733 | + | 0.540872i | ||||
\(153\) | −122.725 | + | 122.725i | −0.802123 | + | 0.802123i | ||||
\(154\) | 43.4032 | − | 68.2289i | 0.281839 | − | 0.443045i | ||||
\(155\) | −52.2918 | − | 126.244i | −0.337367 | − | 0.814475i | ||||
\(156\) | −59.2229 | − | 126.567i | −0.379634 | − | 0.811325i | ||||
\(157\) | 73.8536 | − | 178.298i | 0.470405 | − | 1.13566i | −0.493580 | − | 0.869701i | \(-0.664312\pi\) |
0.963985 | − | 0.265958i | \(-0.0856882\pi\) | |||||||
\(158\) | −31.3678 | + | 178.586i | −0.198531 | + | 1.13029i | ||||
\(159\) | 356.241i | 2.24051i | ||||||||
\(160\) | 114.432 | − | 221.608i | 0.715202 | − | 1.38505i | ||||
\(161\) | −82.8605 | −0.514662 | ||||||||
\(162\) | −186.528 | − | 32.7627i | −1.15141 | − | 0.202239i | ||||
\(163\) | −132.246 | − | 54.7779i | −0.811322 | − | 0.336061i | −0.0618408 | − | 0.998086i | \(-0.519697\pi\) |
−0.749481 | + | 0.662025i | \(0.769697\pi\) | |||||||
\(164\) | −26.3203 | − | 56.2497i | −0.160490 | − | 0.342986i | ||||
\(165\) | −193.603 | + | 80.1929i | −1.17335 | + | 0.486018i | ||||
\(166\) | 173.383 | + | 110.296i | 1.04447 | + | 0.664433i | ||||
\(167\) | −109.750 | − | 109.750i | −0.657187 | − | 0.657187i | 0.297526 | − | 0.954714i | \(-0.403838\pi\) |
−0.954714 | + | 0.297526i | \(0.903838\pi\) | |||||||
\(168\) | 191.617 | + | 24.8403i | 1.14058 | + | 0.147859i | ||||
\(169\) | −65.7709 | − | 65.7709i | −0.389177 | − | 0.389177i | ||||
\(170\) | 374.020 | − | 83.1777i | 2.20012 | − | 0.489281i | ||||
\(171\) | 84.6294 | − | 35.0546i | 0.494909 | − | 0.204998i | ||||
\(172\) | 96.8946 | − | 4.35888i | 0.563341 | − | 0.0253423i | ||||
\(173\) | −287.188 | − | 118.957i | −1.66005 | − | 0.687613i | −0.661964 | − | 0.749535i | \(-0.730277\pi\) |
−0.998081 | + | 0.0619221i | \(0.980277\pi\) | |||||||
\(174\) | −70.5098 | − | 100.557i | −0.405229 | − | 0.577913i | ||||
\(175\) | 215.434 | 1.23105 | ||||||||
\(176\) | 102.459 | + | 32.0075i | 0.582152 | + | 0.181861i | ||||
\(177\) | − | 291.542i | − | 1.64713i | ||||||
\(178\) | −177.470 | − | 253.098i | −0.997025 | − | 1.42190i | ||||
\(179\) | 48.9443 | − | 118.162i | 0.273432 | − | 0.660122i | −0.726194 | − | 0.687490i | \(-0.758712\pi\) |
0.999625 | + | 0.0273677i | \(0.00871248\pi\) | |||||||
\(180\) | −162.495 | − | 148.505i | −0.902751 | − | 0.825025i | ||||
\(181\) | 38.9220 | + | 93.9660i | 0.215039 | + | 0.519149i | 0.994184 | − | 0.107694i | \(-0.0343466\pi\) |
−0.779145 | + | 0.626843i | \(0.784347\pi\) | |||||||
\(182\) | −102.563 | + | 22.8089i | −0.563534 | + | 0.125323i | ||||
\(183\) | 47.1765 | − | 47.1765i | 0.257795 | − | 0.257795i | ||||
\(184\) | −28.6786 | − | 106.187i | −0.155862 | − | 0.577104i | ||||
\(185\) | −214.957 | + | 214.957i | −1.16193 | + | 1.16193i | ||||
\(186\) | 118.566 | + | 75.4247i | 0.637451 | + | 0.405509i | ||||
\(187\) | 63.1065 | + | 152.353i | 0.337468 | + | 0.814719i | ||||
\(188\) | −101.575 | − | 36.8182i | −0.540291 | − | 0.195841i | ||||
\(189\) | −17.9224 | + | 43.2684i | −0.0948273 | + | 0.228933i | ||||
\(190\) | −199.176 | − | 34.9844i | −1.04830 | − | 0.184128i | ||||
\(191\) | − | 66.5635i | − | 0.348500i | −0.984701 | − | 0.174250i | \(-0.944250\pi\) | ||
0.984701 | − | 0.174250i | \(-0.0557500\pi\) | |||||||
\(192\) | 34.4867 | + | 254.158i | 0.179618 | + | 1.32374i | ||||
\(193\) | 275.880 | 1.42943 | 0.714714 | − | 0.699417i | \(-0.246557\pi\) | ||||
0.714714 | + | 0.699417i | \(0.246557\pi\) | |||||||
\(194\) | 22.0454 | − | 125.511i | 0.113636 | − | 0.646962i | ||||
\(195\) | 251.553 | + | 104.197i | 1.29001 | + | 0.534341i | ||||
\(196\) | −17.2832 | + | 47.6813i | −0.0881796 | + | 0.243272i | ||||
\(197\) | 167.300 | − | 69.2980i | 0.849240 | − | 0.351767i | 0.0847497 | − | 0.996402i | \(-0.472991\pi\) |
0.764490 | + | 0.644636i | \(0.222991\pi\) | |||||||
\(198\) | 50.8518 | − | 79.9380i | 0.256827 | − | 0.403727i | ||||
\(199\) | −233.526 | − | 233.526i | −1.17350 | − | 1.17350i | −0.981370 | − | 0.192125i | \(-0.938462\pi\) |
−0.192125 | − | 0.981370i | \(-0.561538\pi\) | |||||||
\(200\) | 74.5634 | + | 276.083i | 0.372817 | + | 1.38041i | ||||
\(201\) | 304.326 | + | 304.326i | 1.51406 | + | 1.51406i | ||||
\(202\) | 6.78184 | + | 30.4955i | 0.0335735 | + | 0.150968i | ||||
\(203\) | −85.3151 | + | 35.3387i | −0.420271 | + | 0.174082i | ||||
\(204\) | −265.819 | + | 290.862i | −1.30304 | + | 1.42579i | ||||
\(205\) | 111.797 | + | 46.3078i | 0.545351 | + | 0.225892i | ||||
\(206\) | −22.4562 | + | 15.7462i | −0.109011 | + | 0.0764377i | ||||
\(207\) | −97.0806 | −0.468988 | ||||||||
\(208\) | −64.7278 | − | 123.542i | −0.311192 | − | 0.593953i | ||||
\(209\) | − | 87.0348i | − | 0.416434i | ||||||
\(210\) | −308.261 | + | 216.150i | −1.46791 | + | 1.02929i | ||||
\(211\) | 32.7097 | − | 78.9682i | 0.155022 | − | 0.374257i | −0.827219 | − | 0.561880i | \(-0.810078\pi\) |
0.982241 | + | 0.187623i | \(0.0600783\pi\) | |||||||
\(212\) | 15.9792 | + | 355.205i | 0.0753735 | + | 1.67550i | ||||
\(213\) | 5.54706 | + | 13.3918i | 0.0260425 | + | 0.0628722i | ||||
\(214\) | −64.9117 | − | 291.884i | −0.303325 | − | 1.36394i | ||||
\(215\) | −133.637 | + | 133.637i | −0.621566 | + | 0.621566i | ||||
\(216\) | −61.6523 | − | 7.99232i | −0.285427 | − | 0.0370015i | ||||
\(217\) | 74.7128 | − | 74.7128i | 0.344298 | − | 0.344298i | ||||
\(218\) | −37.2912 | + | 58.6209i | −0.171060 | + | 0.268903i | ||||
\(219\) | −66.6933 | − | 161.012i | −0.304536 | − | 0.735214i | ||||
\(220\) | −189.443 | + | 88.6438i | −0.861104 | + | 0.402927i | ||||
\(221\) | 81.9957 | − | 197.955i | 0.371021 | − | 0.895725i | ||||
\(222\) | 54.0828 | − | 307.909i | 0.243616 | − | 1.38698i | ||||
\(223\) | 373.446i | 1.67465i | 0.546708 | + | 0.837323i | \(0.315881\pi\) | ||||
−0.546708 | + | 0.837323i | \(0.684119\pi\) | |||||||
\(224\) | 192.174 | + | 16.1731i | 0.857920 | + | 0.0722015i | ||||
\(225\) | 252.406 | 1.12180 | ||||||||
\(226\) | 248.048 | + | 43.5685i | 1.09756 | + | 0.192781i | ||||
\(227\) | 7.71962 | + | 3.19757i | 0.0340071 | + | 0.0140862i | 0.399622 | − | 0.916680i | \(-0.369141\pi\) |
−0.365615 | + | 0.930766i | \(0.619141\pi\) | |||||||
\(228\) | 188.363 | − | 88.1387i | 0.826155 | − | 0.386573i | ||||
\(229\) | −165.203 | + | 68.4293i | −0.721410 | + | 0.298818i | −0.713017 | − | 0.701147i | \(-0.752672\pi\) |
−0.00839310 | + | 0.999965i | \(0.502672\pi\) | |||||||
\(230\) | 180.831 | + | 115.034i | 0.786224 | + | 0.500149i | ||||
\(231\) | −114.577 | − | 114.577i | −0.496004 | − | 0.496004i | ||||
\(232\) | −74.8153 | − | 97.1018i | −0.322480 | − | 0.418542i | ||||
\(233\) | 14.0197 | + | 14.0197i | 0.0601703 | + | 0.0601703i | 0.736552 | − | 0.676381i | \(-0.236453\pi\) |
−0.676381 | + | 0.736552i | \(0.736453\pi\) | |||||||
\(234\) | −120.165 | + | 26.7232i | −0.513524 | + | 0.114202i | ||||
\(235\) | 194.495 | − | 80.5625i | 0.827638 | − | 0.342819i | ||||
\(236\) | −13.0771 | − | 290.694i | −0.0554114 | − | 1.23175i | ||||
\(237\) | 335.673 | + | 139.040i | 1.41634 | + | 0.586668i | ||||
\(238\) | 170.096 | + | 242.581i | 0.714688 | + | 1.01925i | ||||
\(239\) | −230.951 | −0.966321 | −0.483161 | − | 0.875532i | \(-0.660511\pi\) | ||||
−0.483161 | + | 0.875532i | \(0.660511\pi\) | |||||||
\(240\) | −383.692 | − | 320.230i | −1.59871 | − | 1.33429i | ||||
\(241\) | 111.407i | 0.462269i | 0.972922 | + | 0.231135i | \(0.0742438\pi\) | ||||
−0.972922 | + | 0.231135i | \(0.925756\pi\) | |||||||
\(242\) | 87.2557 | + | 124.439i | 0.360561 | + | 0.514210i | ||||
\(243\) | −118.459 | + | 285.985i | −0.487485 | + | 1.17689i | ||||
\(244\) | 44.9233 | − | 49.1555i | 0.184112 | − | 0.201457i | ||||
\(245\) | −37.8177 | − | 91.3000i | −0.154358 | − | 0.372653i | ||||
\(246\) | −121.475 | + | 27.0146i | −0.493800 | + | 0.109815i | ||||
\(247\) | −79.9641 | + | 79.9641i | −0.323741 | + | 0.323741i | ||||
\(248\) | 121.604 | + | 69.8871i | 0.490340 | + | 0.281803i | ||||
\(249\) | 291.162 | − | 291.162i | 1.16932 | − | 1.16932i | ||||
\(250\) | −141.346 | − | 89.9162i | −0.565385 | − | 0.359665i | ||||
\(251\) | 93.4234 | + | 225.544i | 0.372205 | + | 0.898581i | 0.993376 | + | 0.114907i | \(0.0366570\pi\) |
−0.621172 | + | 0.783675i | \(0.713343\pi\) | |||||||
\(252\) | 58.0056 | − | 160.027i | 0.230181 | − | 0.635029i | ||||
\(253\) | −35.2987 | + | 85.2186i | −0.139521 | + | 0.336833i | ||||
\(254\) | −156.437 | − | 27.4775i | −0.615894 | − | 0.108179i | ||||
\(255\) | − | 767.772i | − | 3.01087i | ||||||
\(256\) | 45.7867 | + | 251.872i | 0.178854 | + | 0.983876i | ||||
\(257\) | −278.684 | −1.08437 | −0.542187 | − | 0.840258i | \(-0.682403\pi\) | ||||
−0.542187 | + | 0.840258i | \(0.682403\pi\) | |||||||
\(258\) | 33.6227 | − | 191.424i | 0.130321 | − | 0.741953i | ||||
\(259\) | −217.169 | − | 89.9543i | −0.838490 | − | 0.347314i | ||||
\(260\) | 255.495 | + | 92.6102i | 0.982674 | + | 0.356193i | ||||
\(261\) | −99.9564 | + | 41.4033i | −0.382975 | + | 0.158633i | ||||
\(262\) | 61.8909 | − | 97.2912i | 0.236225 | − | 0.371340i | ||||
\(263\) | 271.210 | + | 271.210i | 1.03122 | + | 1.03122i | 0.999497 | + | 0.0317197i | \(0.0100984\pi\) |
0.0317197 | + | 0.999497i | \(0.489902\pi\) | |||||||
\(264\) | 107.176 | − | 186.488i | 0.405971 | − | 0.706395i | ||||
\(265\) | −489.898 | − | 489.898i | −1.84867 | − | 1.84867i | ||||
\(266\) | −33.9454 | − | 152.640i | −0.127614 | − | 0.573835i | ||||
\(267\) | −572.263 | + | 237.039i | −2.14331 | + | 0.887787i | ||||
\(268\) | 317.092 | + | 289.791i | 1.18318 | + | 1.08131i | ||||
\(269\) | 54.9518 | + | 22.7618i | 0.204282 | + | 0.0846163i | 0.482478 | − | 0.875908i | \(-0.339737\pi\) |
−0.278197 | + | 0.960524i | \(0.589737\pi\) | |||||||
\(270\) | 99.1821 | − | 69.5458i | 0.367341 | − | 0.257577i | ||||
\(271\) | 443.976 | 1.63829 | 0.819143 | − | 0.573589i | \(-0.194449\pi\) | ||||
0.819143 | + | 0.573589i | \(0.194449\pi\) | |||||||
\(272\) | −252.000 | + | 301.940i | −0.926470 | + | 1.11007i | ||||
\(273\) | 210.537i | 0.771199i | ||||||||
\(274\) | 117.496 | − | 82.3875i | 0.428818 | − | 0.300684i | ||||
\(275\) | 91.7754 | − | 221.565i | 0.333729 | − | 0.805693i | ||||
\(276\) | −220.179 | + | 9.90494i | −0.797751 | + | 0.0358875i | ||||
\(277\) | 23.1329 | + | 55.8478i | 0.0835124 | + | 0.201617i | 0.960119 | − | 0.279590i | \(-0.0901986\pi\) |
−0.876607 | + | 0.481207i | \(0.840199\pi\) | |||||||
\(278\) | −62.6023 | − | 281.500i | −0.225188 | − | 1.01259i | ||||
\(279\) | 87.5345 | − | 87.5345i | 0.313744 | − | 0.313744i | ||||
\(280\) | −297.669 | + | 229.349i | −1.06310 | + | 0.819103i | ||||
\(281\) | −159.772 | + | 159.772i | −0.568582 | + | 0.568582i | −0.931731 | − | 0.363149i | \(-0.881702\pi\) |
0.363149 | + | 0.931731i | \(0.381702\pi\) | |||||||
\(282\) | −116.202 | + | 182.666i | −0.412062 | + | 0.647753i | ||||
\(283\) | −185.468 | − | 447.761i | −0.655366 | − | 1.58219i | −0.804883 | − | 0.593434i | \(-0.797772\pi\) |
0.149517 | − | 0.988759i | \(-0.452228\pi\) | |||||||
\(284\) | 6.13162 | + | 13.1040i | 0.0215902 | + | 0.0461410i | ||||
\(285\) | −155.071 | + | 374.375i | −0.544109 | + | 1.31359i | ||||
\(286\) | −20.2341 | + | 115.199i | −0.0707487 | + | 0.402793i | ||||
\(287\) | 93.5687i | 0.326023i | ||||||||
\(288\) | 225.154 | + | 18.9487i | 0.781784 | + | 0.0657940i | ||||
\(289\) | −315.186 | −1.09061 | ||||||||
\(290\) | 235.249 | + | 41.3203i | 0.811202 | + | 0.142484i | ||||
\(291\) | −235.912 | − | 97.7178i | −0.810693 | − | 0.335800i | ||||
\(292\) | −73.7216 | − | 157.552i | −0.252471 | − | 0.539563i | ||||
\(293\) | 476.574 | − | 197.403i | 1.62653 | − | 0.673732i | 0.631696 | − | 0.775216i | \(-0.282359\pi\) |
0.994837 | + | 0.101485i | \(0.0323592\pi\) | |||||||
\(294\) | 85.7474 | + | 54.5474i | 0.291658 | + | 0.185535i | ||||
\(295\) | 400.924 | + | 400.924i | 1.35906 | + | 1.35906i | ||||
\(296\) | 40.1143 | − | 309.439i | 0.135521 | − | 1.04540i | ||||
\(297\) | 36.8648 | + | 36.8648i | 0.124124 | + | 0.124124i | ||||
\(298\) | 25.5479 | − | 5.68155i | 0.0857310 | − | 0.0190656i | ||||
\(299\) | 110.727 | − | 45.8645i | 0.370323 | − | 0.153393i | ||||
\(300\) | 572.458 | − | 25.7525i | 1.90819 | − | 0.0858416i | ||||
\(301\) | −135.012 | − | 55.9237i | −0.448544 | − | 0.185793i | ||||
\(302\) | 28.7206 | + | 40.9595i | 0.0951012 | + | 0.135628i | ||||
\(303\) | 62.5998 | 0.206600 | ||||||||
\(304\) | 183.862 | − | 96.3315i | 0.604810 | − | 0.316880i | ||||
\(305\) | 129.753i | 0.425420i | ||||||||
\(306\) | 199.287 | + | 284.211i | 0.651264 | + | 0.928794i | ||||
\(307\) | −196.212 | + | 473.698i | −0.639127 | + | 1.54299i | 0.188716 | + | 0.982032i | \(0.439567\pi\) |
−0.827844 | + | 0.560959i | \(0.810433\pi\) | |||||||
\(308\) | −119.383 | − | 109.104i | −0.387608 | − | 0.354235i | ||||
\(309\) | 21.0314 | + | 50.7744i | 0.0680629 | + | 0.164318i | ||||
\(310\) | −266.773 | + | 59.3272i | −0.860558 | + | 0.191378i | ||||
\(311\) | 386.346 | − | 386.346i | 1.24227 | − | 1.24227i | 0.283215 | − | 0.959057i | \(-0.408599\pi\) |
0.959057 | − | 0.283215i | \(-0.0914008\pi\) | |||||||
\(312\) | −269.807 | + | 72.8685i | −0.864767 | + | 0.233553i | ||||
\(313\) | 127.090 | − | 127.090i | 0.406038 | − | 0.406038i | −0.474316 | − | 0.880354i | \(-0.657305\pi\) |
0.880354 | + | 0.474316i | \(0.157305\pi\) | |||||||
\(314\) | −325.667 | − | 207.170i | −1.03716 | − | 0.659778i | ||||
\(315\) | 126.923 | + | 306.420i | 0.402931 | + | 0.972761i | ||||
\(316\) | 340.934 | + | 123.579i | 1.07890 | + | 0.391074i | ||||
\(317\) | −24.4377 | + | 58.9979i | −0.0770906 | + | 0.186113i | −0.957726 | − | 0.287681i | \(-0.907116\pi\) |
0.880636 | + | 0.473794i | \(0.157116\pi\) | |||||||
\(318\) | 701.739 | + | 123.257i | 2.20673 | + | 0.387602i | ||||
\(319\) | 102.797i | 0.322249i | ||||||||
\(320\) | −396.940 | − | 302.089i | −1.24044 | − | 0.944027i | ||||
\(321\) | −599.167 | −1.86657 | ||||||||
\(322\) | −28.6693 | + | 163.222i | −0.0890349 | + | 0.506902i | ||||
\(323\) | 294.608 | + | 122.031i | 0.912099 | + | 0.377804i | ||||
\(324\) | −129.075 | + | 356.095i | −0.398380 | + | 1.09906i | ||||
\(325\) | −287.885 | + | 119.246i | −0.885801 | + | 0.366911i | ||||
\(326\) | −153.660 | + | 241.550i | −0.471350 | + | 0.740952i | ||||
\(327\) | 98.4421 | + | 98.4421i | 0.301046 | + | 0.301046i | ||||
\(328\) | −119.910 | + | 32.3848i | −0.365579 | + | 0.0987341i | ||||
\(329\) | 115.105 | + | 115.105i | 0.349863 | + | 0.349863i | ||||
\(330\) | 90.9821 | + | 409.114i | 0.275703 | + | 1.23974i | ||||
\(331\) | 53.7512 | − | 22.2645i | 0.162390 | − | 0.0672643i | −0.300007 | − | 0.953937i | \(-0.596989\pi\) |
0.462398 | + | 0.886673i | \(0.346989\pi\) | |||||||
\(332\) | 277.255 | − | 303.375i | 0.835106 | − | 0.913781i | ||||
\(333\) | −254.438 | − | 105.392i | −0.764078 | − | 0.316492i | ||||
\(334\) | −254.164 | + | 178.218i | −0.760970 | + | 0.533587i | ||||
\(335\) | −837.010 | −2.49854 | ||||||||
\(336\) | 115.230 | − | 368.861i | 0.342946 | − | 1.09780i | ||||
\(337\) | − | 368.803i | − | 1.09437i | −0.837012 | − | 0.547185i | \(-0.815700\pi\) | ||
0.837012 | − | 0.547185i | \(-0.184300\pi\) | |||||||
\(338\) | −152.315 | + | 106.802i | −0.450636 | + | 0.315983i | ||||
\(339\) | 193.121 | − | 466.235i | 0.569678 | − | 1.37532i | ||||
\(340\) | −34.4384 | − | 765.540i | −0.101289 | − | 2.25159i | ||||
\(341\) | −45.0113 | − | 108.667i | −0.131998 | − | 0.318671i | ||||
\(342\) | −39.7709 | − | 178.835i | −0.116289 | − | 0.522911i | ||||
\(343\) | 262.846 | − | 262.846i | 0.766315 | − | 0.766315i | ||||
\(344\) | 24.9387 | − | 192.376i | 0.0724961 | − | 0.559231i | ||||
\(345\) | 303.670 | − | 303.670i | 0.880204 | − | 0.880204i | ||||
\(346\) | −333.692 | + | 524.557i | −0.964429 | + | 1.51606i | ||||
\(347\) | 166.265 | + | 401.400i | 0.479151 | + | 1.15677i | 0.960008 | + | 0.279973i | \(0.0903255\pi\) |
−0.480857 | + | 0.876799i | \(0.659675\pi\) | |||||||
\(348\) | −222.477 | + | 104.101i | −0.639303 | + | 0.299142i | ||||
\(349\) | −24.6685 | + | 59.5550i | −0.0706833 | + | 0.170645i | −0.955273 | − | 0.295726i | \(-0.904439\pi\) |
0.884590 | + | 0.466370i | \(0.154439\pi\) | |||||||
\(350\) | 74.5390 | − | 424.372i | 0.212969 | − | 1.21249i | ||||
\(351\) | − | 67.7399i | − | 0.192991i | ||||||
\(352\) | 98.4999 | − | 190.753i | 0.279829 | − | 0.541913i | ||||
\(353\) | 245.534 | 0.695563 | 0.347782 | − | 0.937576i | \(-0.386935\pi\) | ||||
0.347782 | + | 0.937576i | \(0.386935\pi\) | |||||||
\(354\) | −574.292 | − | 100.872i | −1.62229 | − | 0.284948i | ||||
\(355\) | −26.0444 | − | 10.7880i | −0.0733646 | − | 0.0303886i | ||||
\(356\) | −559.967 | + | 262.019i | −1.57294 | + | 0.736008i | ||||
\(357\) | 548.483 | − | 227.189i | 1.53637 | − | 0.636384i | ||||
\(358\) | −215.826 | − | 137.296i | −0.602866 | − | 0.383508i | ||||
\(359\) | 61.7019 | + | 61.7019i | 0.171872 | + | 0.171872i | 0.787801 | − | 0.615930i | \(-0.211219\pi\) |
−0.615930 | + | 0.787801i | \(0.711219\pi\) | |||||||
\(360\) | −348.753 | + | 268.708i | −0.968759 | + | 0.746412i | ||||
\(361\) | 136.259 | + | 136.259i | 0.377448 | + | 0.377448i | ||||
\(362\) | 198.565 | − | 44.1586i | 0.548523 | − | 0.121985i | ||||
\(363\) | 281.361 | − | 116.543i | 0.775099 | − | 0.321056i | ||||
\(364\) | 9.44365 | + | 209.925i | 0.0259441 | + | 0.576718i | ||||
\(365\) | 313.137 | + | 129.706i | 0.857910 | + | 0.355358i | ||||
\(366\) | −76.6076 | − | 109.253i | −0.209310 | − | 0.298506i | ||||
\(367\) | 123.349 | 0.336102 | 0.168051 | − | 0.985778i | \(-0.446253\pi\) | ||||
0.168051 | + | 0.985778i | \(0.446253\pi\) | |||||||
\(368\) | −219.095 | + | 19.7523i | −0.595367 | + | 0.0536747i | ||||
\(369\) | 109.626i | 0.297090i | ||||||||
\(370\) | 349.058 | + | 497.806i | 0.943400 | + | 1.34542i | ||||
\(371\) | 205.010 | − | 494.939i | 0.552588 | − | 1.33407i | ||||
\(372\) | 189.598 | − | 207.460i | 0.509672 | − | 0.557688i | ||||
\(373\) | −11.5942 | − | 27.9909i | −0.0310836 | − | 0.0750425i | 0.907575 | − | 0.419889i | \(-0.137931\pi\) |
−0.938659 | + | 0.344846i | \(0.887931\pi\) | |||||||
\(374\) | 321.945 | − | 71.5969i | 0.860816 | − | 0.191436i | ||||
\(375\) | −237.363 | + | 237.363i | −0.632968 | + | 0.632968i | ||||
\(376\) | −107.670 | + | 187.348i | −0.286357 | + | 0.498265i | ||||
\(377\) | 94.4462 | − | 94.4462i | 0.250520 | − | 0.250520i | ||||
\(378\) | 79.0310 | + | 50.2749i | 0.209077 | + | 0.133002i | ||||
\(379\) | 205.083 | + | 495.114i | 0.541115 | + | 1.30637i | 0.923937 | + | 0.382546i | \(0.124953\pi\) |
−0.382821 | + | 0.923823i | \(0.625047\pi\) | |||||||
\(380\) | −137.828 | + | 380.242i | −0.362704 | + | 1.00064i | ||||
\(381\) | −121.796 | + | 294.041i | −0.319674 | + | 0.771762i | ||||
\(382\) | −131.120 | − | 23.0306i | −0.343245 | − | 0.0602894i | ||||
\(383\) | − | 605.809i | − | 1.58175i | −0.611979 | − | 0.790874i | \(-0.709626\pi\) | ||
0.611979 | − | 0.790874i | \(-0.290374\pi\) | |||||||
\(384\) | 512.584 | + | 20.0037i | 1.33485 | + | 0.0520930i | ||||
\(385\) | 315.129 | 0.818517 | ||||||||
\(386\) | 95.4528 | − | 543.440i | 0.247287 | − | 1.40788i | ||||
\(387\) | −158.182 | − | 65.5210i | −0.408738 | − | 0.169305i | ||||
\(388\) | −239.609 | − | 86.8519i | −0.617549 | − | 0.223845i | ||||
\(389\) | −426.567 | + | 176.690i | −1.09657 | + | 0.454215i | −0.856294 | − | 0.516489i | \(-0.827239\pi\) |
−0.240279 | + | 0.970704i | \(0.577239\pi\) | |||||||
\(390\) | 292.287 | − | 459.468i | 0.749453 | − | 1.17812i | ||||
\(391\) | −238.968 | − | 238.968i | −0.611172 | − | 0.611172i | ||||
\(392\) | 87.9448 | + | 50.5427i | 0.224349 | + | 0.128935i | ||||
\(393\) | −163.381 | − | 163.381i | −0.415728 | − | 0.415728i | ||||
\(394\) | −78.6214 | − | 353.532i | −0.199547 | − | 0.897290i | ||||
\(395\) | −652.819 | + | 270.407i | −1.65271 | + | 0.684573i | ||||
\(396\) | −139.871 | − | 127.828i | −0.353209 | − | 0.322799i | ||||
\(397\) | 294.458 | + | 121.969i | 0.741708 | + | 0.307226i | 0.721353 | − | 0.692567i | \(-0.243520\pi\) |
0.0203548 | + | 0.999793i | \(0.493520\pi\) | |||||||
\(398\) | −540.808 | + | 379.211i | −1.35881 | + | 0.952791i | ||||
\(399\) | −313.333 | −0.785296 | ||||||||
\(400\) | 569.639 | − | 51.3552i | 1.42410 | − | 0.128388i | ||||
\(401\) | − | 48.4544i | − | 0.120834i | −0.998173 | − | 0.0604169i | \(-0.980757\pi\) | ||
0.998173 | − | 0.0604169i | \(-0.0192430\pi\) | |||||||
\(402\) | 704.770 | − | 494.180i | 1.75316 | − | 1.22930i | ||||
\(403\) | −58.4842 | + | 141.193i | −0.145122 | + | 0.350356i | ||||
\(404\) | 62.4178 | − | 2.80791i | 0.154500 | − | 0.00695028i | ||||
\(405\) | −282.431 | − | 681.850i | −0.697362 | − | 1.68358i | ||||
\(406\) | 40.0932 | + | 180.284i | 0.0987516 | + | 0.444050i | ||||
\(407\) | −185.029 | + | 185.029i | −0.454616 | + | 0.454616i | ||||
\(408\) | 480.981 | + | 624.259i | 1.17888 | + | 1.53005i | ||||
\(409\) | −242.037 | + | 242.037i | −0.591778 | + | 0.591778i | −0.938111 | − | 0.346334i | \(-0.887427\pi\) |
0.346334 | + | 0.938111i | \(0.387427\pi\) | |||||||
\(410\) | 129.900 | − | 204.201i | 0.316830 | − | 0.498050i | ||||
\(411\) | −110.041 | − | 265.663i | −0.267740 | − | 0.646382i | ||||
\(412\) | 23.2478 | + | 49.6834i | 0.0564266 | + | 0.120591i | ||||
\(413\) | −167.777 | + | 405.049i | −0.406239 | + | 0.980749i | ||||
\(414\) | −33.5893 | + | 191.234i | −0.0811336 | + | 0.461917i | ||||
\(415\) | 800.803i | 1.92965i | ||||||||
\(416\) | −265.755 | + | 84.7589i | −0.638833 | + | 0.203747i | ||||
\(417\) | −577.851 | −1.38573 | ||||||||
\(418\) | −171.445 | − | 30.1135i | −0.410155 | − | 0.0720419i | ||||
\(419\) | 163.261 | + | 67.6248i | 0.389644 | + | 0.161396i | 0.568900 | − | 0.822407i | \(-0.307369\pi\) |
−0.179256 | + | 0.983802i | \(0.557369\pi\) | |||||||
\(420\) | 319.126 | + | 682.012i | 0.759824 | + | 1.62384i | ||||
\(421\) | −624.400 | + | 258.635i | −1.48314 | + | 0.614335i | −0.969810 | − | 0.243860i | \(-0.921586\pi\) |
−0.513325 | + | 0.858195i | \(0.671586\pi\) | |||||||
\(422\) | −144.238 | − | 91.7555i | −0.341795 | − | 0.217430i | ||||
\(423\) | 134.859 | + | 134.859i | 0.318814 | + | 0.318814i | ||||
\(424\) | 705.228 | + | 91.4225i | 1.66327 | + | 0.215619i | ||||
\(425\) | 621.309 | + | 621.309i | 1.46190 | + | 1.46190i | ||||
\(426\) | 28.2990 | − | 6.29337i | 0.0664296 | − | 0.0147732i | ||||
\(427\) | −92.6933 | + | 38.3948i | −0.217080 | + | 0.0899176i | ||||
\(428\) | −597.426 | + | 26.8757i | −1.39585 | + | 0.0627936i | ||||
\(429\) | 216.529 | + | 89.6893i | 0.504730 | + | 0.209066i | ||||
\(430\) | 217.006 | + | 309.481i | 0.504665 | + | 0.719723i | ||||
\(431\) | 606.510 | 1.40722 | 0.703608 | − | 0.710588i | \(-0.251571\pi\) | ||||
0.703608 | + | 0.710588i | \(0.251571\pi\) | |||||||
\(432\) | −37.0750 | + | 118.680i | −0.0858217 | + | 0.274723i | ||||
\(433\) | − | 3.82972i | − | 0.00884462i | −0.999990 | − | 0.00442231i | \(-0.998592\pi\) | ||
0.999990 | − | 0.00442231i | \(-0.00140767\pi\) | |||||||
\(434\) | −121.322 | − | 173.023i | −0.279545 | − | 0.398670i | ||||
\(435\) | 183.156 | − | 442.177i | 0.421047 | − | 1.01650i | ||||
\(436\) | 102.572 | + | 93.7403i | 0.235256 | + | 0.215001i | ||||
\(437\) | 68.2580 | + | 164.789i | 0.156197 | + | 0.377092i | ||||
\(438\) | −340.244 | + | 75.6663i | −0.776813 | + | 0.172754i | ||||
\(439\) | −36.3389 | + | 36.3389i | −0.0827765 | + | 0.0827765i | −0.747283 | − | 0.664506i | \(-0.768642\pi\) |
0.664506 | + | 0.747283i | \(0.268642\pi\) | |||||||
\(440\) | 109.068 | + | 403.843i | 0.247883 | + | 0.917826i | ||||
\(441\) | 63.3054 | − | 63.3054i | 0.143550 | − | 0.143550i | ||||
\(442\) | −361.571 | − | 230.010i | −0.818034 | − | 0.520385i | ||||
\(443\) | −208.435 | − | 503.207i | −0.470508 | − | 1.13591i | −0.963939 | − | 0.266122i | \(-0.914258\pi\) |
0.493431 | − | 0.869785i | \(-0.335742\pi\) | |||||||
\(444\) | −587.820 | − | 213.069i | −1.32392 | − | 0.479886i | ||||
\(445\) | 460.995 | − | 1112.94i | 1.03594 | − | 2.50099i | ||||
\(446\) | 735.631 | + | 129.210i | 1.64940 | + | 0.289709i | ||||
\(447\) | − | 52.4435i | − | 0.117323i | ||||||
\(448\) | 98.3497 | − | 372.957i | 0.219530 | − | 0.832494i | ||||
\(449\) | 431.670 | 0.961402 | 0.480701 | − | 0.876884i | \(-0.340382\pi\) | ||||
0.480701 | + | 0.876884i | \(0.340382\pi\) | |||||||
\(450\) | 87.3310 | − | 497.201i | 0.194069 | − | 1.10489i | ||||
\(451\) | 96.2316 | + | 39.8604i | 0.213374 | + | 0.0883823i | ||||
\(452\) | 171.646 | − | 473.542i | 0.379749 | − | 1.04766i | ||||
\(453\) | 92.6110 | − | 38.3607i | 0.204439 | − | 0.0846815i | ||||
\(454\) | 8.96966 | − | 14.1001i | 0.0197570 | − | 0.0310575i | ||||
\(455\) | −289.528 | − | 289.528i | −0.636325 | − | 0.636325i | ||||
\(456\) | −108.447 | − | 401.542i | −0.237822 | − | 0.880575i | ||||
\(457\) | −187.054 | − | 187.054i | −0.409309 | − | 0.409309i | 0.472189 | − | 0.881497i | \(-0.343464\pi\) |
−0.881497 | + | 0.472189i | \(0.843464\pi\) | |||||||
\(458\) | 77.6358 | + | 349.100i | 0.169510 | + | 0.762227i | ||||
\(459\) | −176.473 | + | 73.0976i | −0.384473 | + | 0.159254i | ||||
\(460\) | 289.166 | − | 316.409i | 0.628623 | − | 0.687845i | ||||
\(461\) | 253.784 | + | 105.121i | 0.550508 | + | 0.228028i | 0.640558 | − | 0.767909i | \(-0.278703\pi\) |
−0.0900508 | + | 0.995937i | \(0.528703\pi\) | |||||||
\(462\) | −265.342 | + | 186.056i | −0.574332 | + | 0.402718i | ||||
\(463\) | −765.246 | −1.65280 | −0.826400 | − | 0.563084i | \(-0.809615\pi\) | ||||
−0.826400 | + | 0.563084i | \(0.809615\pi\) | |||||||
\(464\) | −217.161 | + | 113.778i | −0.468020 | + | 0.245211i | ||||
\(465\) | 547.620i | 1.17768i | ||||||||
\(466\) | 32.4673 | − | 22.7659i | 0.0696723 | − | 0.0488538i | ||||
\(467\) | −110.687 | + | 267.223i | −0.237018 | + | 0.572211i | −0.996972 | − | 0.0777657i | \(-0.975221\pi\) |
0.759954 | + | 0.649977i | \(0.225221\pi\) | |||||||
\(468\) | 11.0643 | + | 245.951i | 0.0236417 | + | 0.525537i | ||||
\(469\) | −247.677 | − | 597.945i | −0.528096 | − | 1.27494i | ||||
\(470\) | −91.4014 | − | 410.999i | −0.194471 | − | 0.874466i | ||||
\(471\) | −546.893 | + | 546.893i | −1.16113 | + | 1.16113i | ||||
\(472\) | −577.147 | − | 74.8186i | −1.22277 | − | 0.158514i | ||||
\(473\) | −115.030 | + | 115.030i | −0.243193 | + | 0.243193i | ||||
\(474\) | 390.029 | − | 613.117i | 0.822845 | − | 1.29349i | ||||
\(475\) | −177.468 | − | 428.447i | −0.373618 | − | 0.901993i | ||||
\(476\) | 536.698 | − | 251.131i | 1.12752 | − | 0.527586i | ||||
\(477\) | 240.193 | − | 579.877i | 0.503549 | − | 1.21568i | ||||
\(478\) | −79.9076 | + | 454.937i | −0.167171 | + | 0.951751i | ||||
\(479\) | 158.059i | 0.329977i | 0.986296 | + | 0.164988i | \(0.0527586\pi\) | ||||
−0.986296 | + | 0.164988i | \(0.947241\pi\) | |||||||
\(480\) | −763.559 | + | 645.015i | −1.59075 | + | 1.34378i | ||||
\(481\) | 339.994 | 0.706848 | ||||||||
\(482\) | 219.454 | + | 38.5461i | 0.455299 | + | 0.0799712i | ||||
\(483\) | 306.795 | + | 127.079i | 0.635186 | + | 0.263103i | ||||
\(484\) | 275.315 | − | 128.825i | 0.568833 | − | 0.266168i | ||||
\(485\) | 458.803 | − | 190.042i | 0.945985 | − | 0.391840i | ||||
\(486\) | 522.360 | + | 332.295i | 1.07481 | + | 0.683734i | ||||
\(487\) | −675.116 | − | 675.116i | −1.38628 | − | 1.38628i | −0.832996 | − | 0.553280i | \(-0.813376\pi\) |
−0.553280 | − | 0.832996i | \(-0.686624\pi\) | |||||||
\(488\) | −81.2855 | − | 105.499i | −0.166569 | − | 0.216187i | ||||
\(489\) | 405.636 | + | 405.636i | 0.829521 | + | 0.829521i | ||||
\(490\) | −192.931 | + | 42.9057i | −0.393738 | + | 0.0875627i | ||||
\(491\) | 87.1226 | − | 36.0874i | 0.177439 | − | 0.0734977i | −0.292195 | − | 0.956359i | \(-0.594386\pi\) |
0.469634 | + | 0.882861i | \(0.344386\pi\) | |||||||
\(492\) | 11.1850 | + | 248.633i | 0.0227337 | + | 0.505352i | ||||
\(493\) | −347.963 | − | 144.131i | −0.705808 | − | 0.292355i | ||||
\(494\) | 129.850 | + | 185.184i | 0.262854 | + | 0.374866i | ||||
\(495\) | 369.210 | 0.745878 | ||||||||
\(496\) | 179.741 | − | 215.361i | 0.362381 | − | 0.434196i | ||||
\(497\) | − | 21.7979i | − | 0.0438590i | ||||||
\(498\) | −472.803 | − | 674.283i | −0.949404 | − | 1.35398i | ||||
\(499\) | 164.812 | − | 397.892i | 0.330285 | − | 0.797378i | −0.668284 | − | 0.743906i | \(-0.732971\pi\) |
0.998569 | − | 0.0534724i | \(-0.0170289\pi\) | |||||||
\(500\) | −226.026 | + | 247.320i | −0.452052 | + | 0.494640i | ||||
\(501\) | 238.038 | + | 574.674i | 0.475125 | + | 1.14705i | ||||
\(502\) | 476.610 | − | 105.993i | 0.949423 | − | 0.211141i | ||||
\(503\) | −270.905 | + | 270.905i | −0.538578 | + | 0.538578i | −0.923111 | − | 0.384533i | \(-0.874362\pi\) |
0.384533 | + | 0.923111i | \(0.374362\pi\) | |||||||
\(504\) | −295.159 | − | 169.631i | −0.585633 | − | 0.336569i | ||||
\(505\) | −86.0864 | + | 86.0864i | −0.170468 | + | 0.170468i | ||||
\(506\) | 155.654 | + | 99.0181i | 0.307617 | + | 0.195688i | ||||
\(507\) | 142.651 | + | 344.389i | 0.281362 | + | 0.679269i | ||||
\(508\) | −108.253 | + | 298.650i | −0.213096 | + | 0.587893i | ||||
\(509\) | −194.137 | + | 468.689i | −0.381409 | + | 0.920803i | 0.610285 | + | 0.792182i | \(0.291055\pi\) |
−0.991694 | + | 0.128621i | \(0.958945\pi\) | |||||||
\(510\) | −1512.39 | − | 265.645i | −2.96547 | − | 0.520872i | ||||
\(511\) | 262.081i | 0.512878i | ||||||||
\(512\) | 511.991 | − | 3.04640i | 0.999982 | − | 0.00595000i | ||||
\(513\) | 100.814 | 0.196519 | ||||||||
\(514\) | −96.4230 | + | 548.964i | −0.187593 | + | 1.06802i | ||||
\(515\) | −98.7463 | − | 40.9021i | −0.191740 | − | 0.0794215i | ||||
\(516\) | −365.442 | − | 132.463i | −0.708221 | − | 0.256711i | ||||
\(517\) | 167.416 | − | 69.3458i | 0.323821 | − | 0.134131i | ||||
\(518\) | −252.335 | + | 396.665i | −0.487133 | + | 0.765763i | ||||
\(519\) | 880.889 | + | 880.889i | 1.69728 | + | 1.69728i | ||||
\(520\) | 270.828 | − | 471.243i | 0.520822 | − | 0.906237i | ||||
\(521\) | −240.434 | − | 240.434i | −0.461486 | − | 0.461486i | 0.437656 | − | 0.899142i | \(-0.355809\pi\) |
−0.899142 | + | 0.437656i | \(0.855809\pi\) | |||||||
\(522\) | 46.9737 | + | 211.224i | 0.0899880 | + | 0.404643i | ||||
\(523\) | 846.467 | − | 350.618i | 1.61848 | − | 0.670398i | 0.624611 | − | 0.780936i | \(-0.285257\pi\) |
0.993872 | + | 0.110538i | \(0.0352574\pi\) | |||||||
\(524\) | −170.235 | − | 155.578i | −0.324875 | − | 0.296904i | ||||
\(525\) | −797.656 | − | 330.400i | −1.51935 | − | 0.629333i | ||||
\(526\) | 628.078 | − | 440.404i | 1.19407 | − | 0.837271i | ||||
\(527\) | 430.941 | 0.817725 | ||||||||
\(528\) | −330.270 | − | 275.645i | −0.625512 | − | 0.522054i | ||||
\(529\) | 339.966i | 0.642657i | ||||||||
\(530\) | −1134.52 | + | 795.521i | −2.14061 | + | 1.50098i | ||||
\(531\) | −196.570 | + | 474.561i | −0.370188 | + | 0.893713i | ||||
\(532\) | −312.422 | + | 14.0546i | −0.587260 | + | 0.0264183i | ||||
\(533\) | −51.7916 | − | 125.036i | −0.0971699 | − | 0.234589i | ||||
\(534\) | 268.931 | + | 1209.28i | 0.503615 | + | 2.26458i | ||||
\(535\) | 823.967 | − | 823.967i | 1.54012 | − | 1.54012i | ||||
\(536\) | 680.555 | − | 524.356i | 1.26969 | − | 0.978276i | ||||
\(537\) | −362.437 | + | 362.437i | −0.674929 | + | 0.674929i | ||||
\(538\) | 63.8502 | − | 100.371i | 0.118681 | − | 0.186563i | ||||
\(539\) | −32.5523 | − | 78.5883i | −0.0603939 | − | 0.145804i | ||||
\(540\) | −102.678 | − | 219.436i | −0.190145 | − | 0.406363i | ||||
\(541\) | −6.87337 | + | 16.5938i | −0.0127049 | + | 0.0306724i | −0.930105 | − | 0.367294i | \(-0.880284\pi\) |
0.917400 | + | 0.397967i | \(0.130284\pi\) | |||||||
\(542\) | 153.613 | − | 874.563i | 0.283419 | − | 1.61358i | ||||
\(543\) | − | 407.606i | − | 0.750656i | ||||||
\(544\) | 507.584 | + | 600.870i | 0.933059 | + | 1.10454i | ||||
\(545\) | −270.752 | −0.496793 | ||||||||
\(546\) | 414.726 | + | 72.8447i | 0.759571 | + | 0.133415i | ||||
\(547\) | 354.417 | + | 146.804i | 0.647929 | + | 0.268381i | 0.682349 | − | 0.731026i | \(-0.260958\pi\) |
−0.0344200 | + | 0.999407i | \(0.510958\pi\) | |||||||
\(548\) | −121.638 | − | 259.955i | −0.221967 | − | 0.474370i | ||||
\(549\) | −108.601 | + | 44.9839i | −0.197816 | + | 0.0819379i | ||||
\(550\) | −404.696 | − | 257.444i | −0.735811 | − | 0.468079i | ||||
\(551\) | 140.560 | + | 140.560i | 0.255100 | + | 0.255100i | ||||
\(552\) | −56.6696 | + | 437.146i | −0.102662 | + | 0.791931i | ||||
\(553\) | −386.348 | − | 386.348i | −0.698639 | − | 0.698639i | ||||
\(554\) | 118.015 | − | 26.2452i | 0.213024 | − | 0.0473741i | ||||
\(555\) | 1125.56 | − | 466.221i | 2.02803 | − | 0.840037i | ||||
\(556\) | −576.171 | + | 25.9195i | −1.03628 | + | 0.0466178i | ||||
\(557\) | −549.588 | − | 227.647i | −0.986692 | − | 0.408701i | −0.169792 | − | 0.985480i | \(-0.554310\pi\) |
−0.816900 | + | 0.576779i | \(0.804310\pi\) | |||||||
\(558\) | −142.143 | − | 202.716i | −0.254737 | − | 0.363290i | ||||
\(559\) | 211.371 | 0.378123 | ||||||||
\(560\) | 348.790 | + | 665.715i | 0.622839 | + | 1.18878i | ||||
\(561\) | − | 660.876i | − | 1.17803i | ||||||
\(562\) | 259.445 | + | 370.005i | 0.461646 | + | 0.658372i | ||||
\(563\) | −150.445 | + | 363.205i | −0.267219 | + | 0.645125i | −0.999350 | − | 0.0360391i | \(-0.988526\pi\) |
0.732131 | + | 0.681164i | \(0.238526\pi\) | |||||||
\(564\) | 319.619 | + | 292.101i | 0.566701 | + | 0.517909i | ||||
\(565\) | 375.583 | + | 906.737i | 0.664748 | + | 1.60484i | ||||
\(566\) | −946.190 | + | 210.422i | −1.67171 | + | 0.371770i | ||||
\(567\) | 403.528 | − | 403.528i | 0.711690 | − | 0.711690i | ||||
\(568\) | 27.9344 | − | 7.54442i | 0.0491803 | − | 0.0132824i | ||||
\(569\) | 510.987 | − | 510.987i | 0.898045 | − | 0.898045i | −0.0972186 | − | 0.995263i | \(-0.530995\pi\) |
0.995263 | + | 0.0972186i | \(0.0309946\pi\) | |||||||
\(570\) | 683.806 | + | 434.997i | 1.19966 | + | 0.763153i | ||||
\(571\) | 328.247 | + | 792.459i | 0.574864 | + | 1.38784i | 0.897371 | + | 0.441277i | \(0.145474\pi\) |
−0.322507 | + | 0.946567i | \(0.604526\pi\) | |||||||
\(572\) | 219.923 | + | 79.7161i | 0.384480 | + | 0.139364i | ||||
\(573\) | −102.085 | + | 246.454i | −0.178158 | + | 0.430112i | ||||
\(574\) | 184.316 | + | 32.3742i | 0.321108 | + | 0.0564011i | ||||
\(575\) | 491.482i | 0.854752i | ||||||||
\(576\) | 115.228 | − | 436.962i | 0.200048 | − | 0.758615i | ||||
\(577\) | 305.039 | 0.528663 | 0.264332 | − | 0.964432i | \(-0.414849\pi\) | ||||
0.264332 | + | 0.964432i | \(0.414849\pi\) | |||||||
\(578\) | −109.052 | + | 620.867i | −0.188672 | + | 1.07416i | ||||
\(579\) | −1021.46 | − | 423.102i | −1.76418 | − | 0.730746i | ||||
\(580\) | 162.789 | − | 449.106i | 0.280671 | − | 0.774322i | ||||
\(581\) | −572.080 | + | 236.963i | −0.984647 | + | 0.407854i | ||||
\(582\) | −274.113 | + | 430.900i | −0.470985 | + | 0.740378i | ||||
\(583\) | −421.689 | − | 421.689i | −0.723309 | − | 0.723309i | ||||
\(584\) | −335.861 | + | 90.7080i | −0.575104 | + | 0.155322i | ||||
\(585\) | −339.215 | − | 339.215i | −0.579855 | − | 0.579855i | ||||
\(586\) | −223.962 | − | 1007.08i | −0.382188 | − | 1.71856i | ||||
\(587\) | −388.900 | + | 161.088i | −0.662521 | + | 0.274425i | −0.688499 | − | 0.725237i | \(-0.741730\pi\) |
0.0259780 | + | 0.999663i | \(0.491730\pi\) | |||||||
\(588\) | 137.118 | − | 150.036i | 0.233194 | − | 0.255163i | ||||
\(589\) | −210.132 | − | 87.0394i | −0.356760 | − | 0.147775i | ||||
\(590\) | 928.475 | − | 651.040i | 1.57369 | − | 1.10346i | ||||
\(591\) | −725.716 | −1.22795 | ||||||||
\(592\) | −595.668 | − | 186.083i | −1.00620 | − | 0.314330i | ||||
\(593\) | − | 1039.64i | − | 1.75319i | −0.481228 | − | 0.876595i | \(-0.659809\pi\) | ||
0.481228 | − | 0.876595i | \(-0.340191\pi\) | |||||||
\(594\) | 85.3730 | − | 59.8630i | 0.143726 | − | 0.100779i | ||||
\(595\) | −441.839 | + | 1066.69i | −0.742587 | + | 1.79276i | ||||
\(596\) | −2.35235 | − | 52.2911i | −0.00394690 | − | 0.0877367i | ||||
\(597\) | 506.494 | + | 1222.79i | 0.848399 | + | 2.04822i | ||||
\(598\) | −52.0351 | − | 233.983i | −0.0870152 | − | 0.391276i | ||||
\(599\) | 22.4929 | − | 22.4929i | 0.0375507 | − | 0.0375507i | −0.688082 | − | 0.725633i | \(-0.741547\pi\) |
0.725633 | + | 0.688082i | \(0.241547\pi\) | |||||||
\(600\) | 147.339 | − | 1136.56i | 0.245565 | − | 1.89427i | ||||
\(601\) | −640.653 | + | 640.653i | −1.06598 | + | 1.06598i | −0.0683147 | + | 0.997664i | \(0.521762\pi\) |
−0.997664 | + | 0.0683147i | \(0.978238\pi\) | |||||||
\(602\) | −156.874 | + | 246.603i | −0.260588 | + | 0.409639i | ||||
\(603\) | −290.182 | − | 700.561i | −0.481230 | − | 1.16179i | ||||
\(604\) | 90.6211 | − | 42.4033i | 0.150035 | − | 0.0702041i | ||||
\(605\) | −226.654 | + | 547.192i | −0.374636 | + | 0.904450i | ||||
\(606\) | 21.6592 | − | 123.312i | 0.0357412 | − | 0.203485i | ||||
\(607\) | − | 860.149i | − | 1.41705i | −0.705686 | − | 0.708524i | \(-0.749361\pi\) | ||
0.705686 | − | 0.708524i | \(-0.250639\pi\) | |||||||
\(608\) | −126.143 | − | 395.510i | −0.207472 | − | 0.650511i | ||||
\(609\) | 370.080 | 0.607685 | ||||||||
\(610\) | 255.593 | + | 44.8938i | 0.419005 | + | 0.0735964i | ||||
\(611\) | −217.527 | − | 90.1026i | −0.356018 | − | 0.147467i | ||||
\(612\) | 628.803 | − | 294.229i | 1.02746 | − | 0.480766i | ||||
\(613\) | 724.830 | − | 300.235i | 1.18243 | − | 0.489779i | 0.297148 | − | 0.954831i | \(-0.403965\pi\) |
0.885283 | + | 0.465052i | \(0.153965\pi\) | |||||||
\(614\) | 865.223 | + | 550.404i | 1.40916 | + | 0.896424i | ||||
\(615\) | −342.914 | − | 342.914i | −0.557584 | − | 0.557584i | ||||
\(616\) | −256.225 | + | 197.417i | −0.415949 | + | 0.320482i | ||||
\(617\) | −704.685 | − | 704.685i | −1.14212 | − | 1.14212i | −0.988063 | − | 0.154052i | \(-0.950768\pi\) |
−0.154052 | − | 0.988063i | \(-0.549232\pi\) | |||||||
\(618\) | 107.294 | − | 23.8610i | 0.173615 | − | 0.0386101i | ||||
\(619\) | −33.0442 | + | 13.6874i | −0.0533832 | + | 0.0221121i | −0.409215 | − | 0.912438i | \(-0.634198\pi\) |
0.355832 | + | 0.934550i | \(0.384198\pi\) | |||||||
\(620\) | 24.5635 | + | 546.028i | 0.0396186 | + | 0.880691i | ||||
\(621\) | −98.7106 | − | 40.8873i | −0.158954 | − | 0.0658410i | ||||
\(622\) | −627.369 | − | 894.716i | −1.00863 | − | 1.43845i | ||||
\(623\) | 931.477 | 1.49515 | ||||||||
\(624\) | 50.1879 | + | 556.691i | 0.0804293 | + | 0.892133i | ||||
\(625\) | 240.835i | 0.385335i | ||||||||
\(626\) | −206.375 | − | 294.320i | −0.329673 | − | 0.470159i | ||||
\(627\) | −133.481 | + | 322.250i | −0.212888 | + | 0.513956i | ||||
\(628\) | −520.772 | + | 569.834i | −0.829255 | + | 0.907379i | ||||
\(629\) | −366.885 | − | 885.738i | −0.583282 | − | 1.40817i | ||||
\(630\) | 647.514 | − | 144.000i | 1.02780 | − | 0.228571i | ||||
\(631\) | −718.112 | + | 718.112i | −1.13805 | + | 1.13805i | −0.149255 | + | 0.988799i | \(0.547688\pi\) |
−0.988799 | + | 0.149255i | \(0.952312\pi\) | |||||||
\(632\) | 361.393 | − | 628.829i | 0.571825 | − | 0.994982i | ||||
\(633\) | −242.218 | + | 242.218i | −0.382651 | + | 0.382651i | ||||
\(634\) | 107.761 | + | 68.5514i | 0.169971 | + | 0.108125i | ||||
\(635\) | −236.870 | − | 571.854i | −0.373023 | − | 0.900557i | ||||
\(636\) | 485.595 | − | 1339.67i | 0.763515 | − | 2.10640i | ||||
\(637\) | −42.2960 | + | 102.112i | −0.0663988 | + | 0.160301i | ||||
\(638\) | 202.495 | + | 35.5673i | 0.317390 | + | 0.0557481i | ||||
\(639\) | − | 25.5388i | − | 0.0399668i | ||||||
\(640\) | −732.407 | + | 677.389i | −1.14439 | + | 1.05842i | ||||
\(641\) | −338.159 | −0.527549 | −0.263774 | − | 0.964584i | \(-0.584967\pi\) | ||||
−0.263774 | + | 0.964584i | \(0.584967\pi\) | |||||||
\(642\) | −207.308 | + | 1180.27i | −0.322910 | + | 1.83842i | ||||
\(643\) | 332.477 | + | 137.716i | 0.517071 | + | 0.214178i | 0.625930 | − | 0.779879i | \(-0.284720\pi\) |
−0.108859 | + | 0.994057i | \(0.534720\pi\) | |||||||
\(644\) | 311.603 | + | 112.948i | 0.483856 | + | 0.175385i | ||||
\(645\) | 699.747 | − | 289.845i | 1.08488 | − | 0.449372i | ||||
\(646\) | 342.314 | − | 538.110i | 0.529898 | − | 0.832987i | ||||
\(647\) | −31.2745 | − | 31.2745i | −0.0483377 | − | 0.0483377i | 0.682525 | − | 0.730862i | \(-0.260882\pi\) |
−0.730862 | + | 0.682525i | \(0.760882\pi\) | |||||||
\(648\) | 656.793 | + | 377.465i | 1.01357 | + | 0.582507i | ||||
\(649\) | 345.103 | + | 345.103i | 0.531746 | + | 0.531746i | ||||
\(650\) | 135.289 | + | 608.348i | 0.208138 | + | 0.935919i | ||||
\(651\) | −391.211 | + | 162.045i | −0.600938 | + | 0.248917i | ||||
\(652\) | 422.651 | + | 386.262i | 0.648238 | + | 0.592426i | ||||
\(653\) | 355.409 | + | 147.215i | 0.544271 | + | 0.225445i | 0.637841 | − | 0.770168i | \(-0.279828\pi\) |
−0.0935696 | + | 0.995613i | \(0.529828\pi\) | |||||||
\(654\) | 227.976 | − | 159.855i | 0.348587 | − | 0.244427i | ||||
\(655\) | 449.359 | 0.686044 | ||||||||
\(656\) | 22.3049 | + | 247.409i | 0.0340014 | + | 0.377148i | ||||
\(657\) | 307.057i | 0.467363i | ||||||||
\(658\) | 266.564 | − | 186.913i | 0.405113 | − | 0.284062i | ||||
\(659\) | −116.271 | + | 280.702i | −0.176435 | + | 0.425952i | −0.987214 | − | 0.159401i | \(-0.949044\pi\) |
0.810779 | + | 0.585352i | \(0.199044\pi\) | |||||||
\(660\) | 837.370 | − | 37.6697i | 1.26874 | − | 0.0570753i | ||||
\(661\) | 179.920 | + | 434.366i | 0.272194 | + | 0.657134i | 0.999577 | − | 0.0290979i | \(-0.00926347\pi\) |
−0.727383 | + | 0.686232i | \(0.759263\pi\) | |||||||
\(662\) | −25.2600 | − | 113.585i | −0.0381571 | − | 0.171579i | ||||
\(663\) | −607.186 | + | 607.186i | −0.915817 | + | 0.915817i | ||||
\(664\) | −501.673 | − | 651.116i | −0.755532 | − | 0.980596i | ||||
\(665\) | 430.892 | − | 430.892i | 0.647957 | − | 0.647957i | ||||
\(666\) | −295.639 | + | 464.739i | −0.443903 | + | 0.697806i | ||||
\(667\) | −80.6200 | − | 194.634i | −0.120870 | − | 0.291805i | ||||
\(668\) | 263.123 | + | 562.326i | 0.393896 | + | 0.841805i | ||||
\(669\) | 572.734 | − | 1382.70i | 0.856105 | − | 2.06682i | ||||
\(670\) | −289.600 | + | 1648.78i | −0.432240 | + | 2.46086i | ||||
\(671\) | 111.688i | 0.166449i | ||||||||
\(672\) | −686.730 | − | 354.609i | −1.02192 | − | 0.527692i | ||||
\(673\) | 1168.06 | 1.73561 | 0.867803 | − | 0.496908i | \(-0.165531\pi\) | ||||
0.867803 | + | 0.496908i | \(0.165531\pi\) | |||||||
\(674\) | −726.484 | − | 127.604i | −1.07787 | − | 0.189323i | ||||
\(675\) | 256.644 | + | 106.305i | 0.380213 | + | 0.157490i | ||||
\(676\) | 157.684 | + | 336.990i | 0.233260 | + | 0.498505i | ||||
\(677\) | −604.882 | + | 250.550i | −0.893474 | + | 0.370089i | −0.781707 | − | 0.623645i | \(-0.785651\pi\) |
−0.111767 | + | 0.993734i | \(0.535651\pi\) | |||||||
\(678\) | −851.591 | − | 541.732i | −1.25603 | − | 0.799015i | ||||
\(679\) | 271.526 | + | 271.526i | 0.399891 | + | 0.399891i | ||||
\(680\) | −1519.91 | − | 197.034i | −2.23516 | − | 0.289756i | ||||
\(681\) | −23.6783 | − | 23.6783i | −0.0347699 | − | 0.0347699i | ||||
\(682\) | −229.630 | + | 51.0671i | −0.336701 | + | 0.0748785i | ||||
\(683\) | −369.863 | + | 153.202i | −0.541527 | + | 0.224308i | −0.636644 | − | 0.771158i | \(-0.719678\pi\) |
0.0951163 | + | 0.995466i | \(0.469678\pi\) | |||||||
\(684\) | −366.039 | + | 16.4665i | −0.535144 | + | 0.0240739i | ||||
\(685\) | 516.663 | + | 214.009i | 0.754253 | + | 0.312422i | ||||
\(686\) | −426.823 | − | 608.709i | −0.622191 | − | 0.887331i | ||||
\(687\) | 716.618 | 1.04311 | ||||||||
\(688\) | −370.321 | − | 115.686i | −0.538258 | − | 0.168148i | ||||
\(689\) | 774.863i | 1.12462i | ||||||||
\(690\) | −493.115 | − | 703.252i | −0.714660 | − | 1.01921i | ||||
\(691\) | 74.8080 | − | 180.602i | 0.108260 | − | 0.261364i | −0.860460 | − | 0.509518i | \(-0.829824\pi\) |
0.968721 | + | 0.248154i | \(0.0798239\pi\) | |||||||
\(692\) | 917.840 | + | 838.816i | 1.32636 | + | 1.21216i | ||||
\(693\) | 109.252 | + | 263.757i | 0.157650 | + | 0.380602i | ||||
\(694\) | 848.222 | − | 188.635i | 1.22222 | − | 0.271808i | ||||
\(695\) | 794.653 | − | 794.653i | 1.14339 | − | 1.14339i | ||||
\(696\) | 128.087 | + | 474.264i | 0.184034 | + | 0.681414i | ||||
\(697\) | −269.851 | + | 269.851i | −0.387160 | + | 0.387160i | ||||
\(698\) | 108.779 | + | 69.1987i | 0.155844 | + | 0.0991386i | ||||
\(699\) | −30.4073 | − | 73.4097i | −0.0435011 | − | 0.105021i | ||||
\(700\) | −810.157 | − | 293.661i | −1.15737 | − | 0.419515i | ||||
\(701\) | 250.206 | − | 604.050i | 0.356927 | − | 0.861698i | −0.638802 | − | 0.769371i | \(-0.720570\pi\) |
0.995729 | − | 0.0923265i | \(-0.0294303\pi\) | |||||||
\(702\) | −133.437 | − | 23.4376i | −0.190081 | − | 0.0333869i | ||||
\(703\) | 505.998i | 0.719769i | ||||||||
\(704\) | −341.674 | − | 260.029i | −0.485333 | − | 0.369359i | ||||
\(705\) | −843.681 | −1.19671 | ||||||||
\(706\) | 84.9533 | − | 483.663i | 0.120330 | − | 0.685076i | ||||
\(707\) | −86.9722 | − | 36.0251i | −0.123016 | − | 0.0509548i | ||||
\(708\) | −397.403 | + | 1096.36i | −0.561304 | + | 1.54854i | ||||
\(709\) | −771.157 | + | 319.424i | −1.08767 | + | 0.450527i | −0.853193 | − | 0.521595i | \(-0.825337\pi\) |
−0.234476 | + | 0.972122i | \(0.575337\pi\) | |||||||
\(710\) | −30.2618 | + | 47.5709i | −0.0426223 | + | 0.0670013i | ||||
\(711\) | −452.650 | − | 452.650i | −0.636639 | − | 0.636639i | ||||
\(712\) | 322.391 | + | 1193.70i | 0.452796 | + | 1.67655i | ||||
\(713\) | 170.446 | + | 170.446i | 0.239055 | + | 0.239055i | ||||
\(714\) | −257.755 | − | 1159.03i | −0.361002 | − | 1.62330i | ||||
\(715\) | −421.107 | + | 174.428i | −0.588961 | + | 0.243956i | ||||
\(716\) | −345.126 | + | 377.640i | −0.482020 | + | 0.527431i | ||||
\(717\) | 855.106 | + | 354.197i | 1.19262 | + | 0.493998i | ||||
\(718\) | 142.892 | − | 100.195i | 0.199013 | − | 0.139547i | ||||
\(719\) | 263.077 | 0.365893 | 0.182947 | − | 0.983123i | \(-0.441436\pi\) | ||||
0.182947 | + | 0.983123i | \(0.441436\pi\) | |||||||
\(720\) | 408.647 | + | 779.961i | 0.567566 | + | 1.08328i | ||||
\(721\) | − | 82.6459i | − | 0.114627i | ||||||
\(722\) | 315.553 | − | 221.264i | 0.437054 | − | 0.306459i | ||||
\(723\) | 170.859 | − | 412.489i | 0.236319 | − | 0.570525i | ||||
\(724\) | −18.2832 | − | 406.421i | −0.0252530 | − | 0.561355i | ||||
\(725\) | 209.609 | + | 506.041i | 0.289116 | + | 0.697988i | ||||
\(726\) | −132.223 | − | 594.560i | −0.182126 | − | 0.818954i | ||||
\(727\) | 320.334 | − | 320.334i | 0.440625 | − | 0.440625i | −0.451597 | − | 0.892222i | \(-0.649146\pi\) |
0.892222 | + | 0.451597i | \(0.149146\pi\) | |||||||
\(728\) | 416.788 | + | 54.0304i | 0.572511 | + | 0.0742176i | ||||
\(729\) | 274.585 | − | 274.585i | 0.376660 | − | 0.376660i | ||||
\(730\) | 363.844 | − | 571.954i | 0.498416 | − | 0.783499i | ||||
\(731\) | −228.089 | − | 550.655i | −0.312023 | − | 0.753289i | ||||
\(732\) | −241.718 | + | 113.104i | −0.330215 | + | 0.154514i | ||||
\(733\) | 119.193 | − | 287.758i | 0.162610 | − | 0.392575i | −0.821482 | − | 0.570234i | \(-0.806852\pi\) |
0.984092 | + | 0.177659i | \(0.0568524\pi\) | |||||||
\(734\) | 42.6782 | − | 242.979i | 0.0581446 | − | 0.331034i | ||||
\(735\) | 396.041i | 0.538832i | ||||||||
\(736\) | −36.8966 | + | 438.417i | −0.0501313 | + | 0.595676i | ||||
\(737\) | −720.473 | −0.977576 | ||||||||
\(738\) | 215.947 | + | 37.9301i | 0.292611 | + | 0.0513958i | ||||
\(739\) | −760.509 | − | 315.013i | −1.02911 | − | 0.426269i | −0.196716 | − | 0.980461i | \(-0.563028\pi\) |
−0.832389 | + | 0.554191i | \(0.813028\pi\) | |||||||
\(740\) | 1101.37 | − | 515.352i | 1.48834 | − | 0.696422i | ||||
\(741\) | 418.708 | − | 173.434i | 0.565058 | − | 0.234054i | ||||
\(742\) | −904.020 | − | 575.084i | −1.21836 | − | 0.775046i | ||||
\(743\) | 89.2306 | + | 89.2306i | 0.120095 | + | 0.120095i | 0.764600 | − | 0.644505i | \(-0.222937\pi\) |
−0.644505 | + | 0.764600i | \(0.722937\pi\) | |||||||
\(744\) | −343.064 | − | 445.258i | −0.461108 | − | 0.598466i | ||||
\(745\) | 72.1196 | + | 72.1196i | 0.0968049 | + | 0.0968049i | ||||
\(746\) | −59.1492 | + | 13.1541i | −0.0792885 | + | 0.0176328i | ||||
\(747\) | −670.257 | + | 277.629i | −0.897265 | + | 0.371659i | ||||
\(748\) | −29.6436 | − | 658.954i | −0.0396304 | − | 0.880955i | ||||
\(749\) | 832.445 | + | 344.810i | 1.11141 | + | 0.460361i | ||||
\(750\) | 385.442 | + | 549.694i | 0.513922 | + | 0.732926i | ||||
\(751\) | −418.271 | −0.556953 | −0.278476 | − | 0.960443i | \(-0.589829\pi\) | ||||
−0.278476 | + | 0.960443i | \(0.589829\pi\) | |||||||
\(752\) | 331.792 | + | 276.915i | 0.441213 | + | 0.368238i | ||||
\(753\) | − | 978.366i | − | 1.29929i | ||||||
\(754\) | −153.367 | − | 218.722i | −0.203404 | − | 0.290082i | ||||
\(755\) | −74.6042 | + | 180.110i | −0.0988135 | + | 0.238557i | ||||
\(756\) | 126.378 | − | 138.284i | 0.167167 | − | 0.182915i | ||||
\(757\) | −212.675 | − | 513.443i | −0.280944 | − | 0.678260i | 0.718914 | − | 0.695099i | \(-0.244640\pi\) |
−0.999858 | + | 0.0168395i | \(0.994640\pi\) | |||||||
\(758\) | 1046.25 | − | 232.675i | 1.38028 | − | 0.306959i | ||||
\(759\) | 261.390 | − | 261.390i | 0.344388 | − | 0.344388i | ||||
\(760\) | 701.330 | + | 403.060i | 0.922802 | + | 0.530343i | ||||
\(761\) | 60.9342 | − | 60.9342i | 0.0800712 | − | 0.0800712i | −0.665937 | − | 0.746008i | \(-0.731968\pi\) |
0.746008 | + | 0.665937i | \(0.231968\pi\) | |||||||
\(762\) | 537.075 | + | 341.656i | 0.704823 | + | 0.448367i | ||||
\(763\) | −80.1175 | − | 193.421i | −0.105003 | − | 0.253500i | ||||
\(764\) | −90.7333 | + | 250.317i | −0.118761 | + | 0.327640i | ||||
\(765\) | −517.665 | + | 1249.75i | −0.676686 | + | 1.63367i | ||||
\(766\) | −1193.35 | − | 209.607i | −1.55790 | − | 0.273638i | ||||
\(767\) | − | 634.135i | − | 0.826773i | ||||||
\(768\) | 216.755 | − | 1002.79i | 0.282233 | − | 1.30572i | ||||
\(769\) | 387.688 | 0.504146 | 0.252073 | − | 0.967708i | \(-0.418888\pi\) | ||||
0.252073 | + | 0.967708i | \(0.418888\pi\) | |||||||
\(770\) | 109.033 | − | 620.755i | 0.141601 | − | 0.806176i | ||||
\(771\) | 1031.84 | + | 427.402i | 1.33831 | + | 0.554348i | ||||
\(772\) | −1037.47 | − | 376.054i | −1.34387 | − | 0.487117i | ||||
\(773\) | 19.2892 | − | 7.98984i | 0.0249537 | − | 0.0103361i | −0.370172 | − | 0.928963i | \(-0.620701\pi\) |
0.395125 | + | 0.918627i | \(0.370701\pi\) | |||||||
\(774\) | −183.796 | + | 288.923i | −0.237463 | + | 0.373286i | ||||
\(775\) | −443.154 | − | 443.154i | −0.571812 | − | 0.571812i | ||||
\(776\) | −253.988 | + | 441.942i | −0.327304 | + | 0.569513i | ||||
\(777\) | 666.120 | + | 666.120i | 0.857297 | + | 0.857297i | ||||
\(778\) | 200.462 | + | 901.404i | 0.257663 | + | 1.15862i | ||||
\(779\) | 186.085 | − | 77.0791i | 0.238877 | − | 0.0989462i | ||||
\(780\) | −803.952 | − | 734.733i | −1.03071 | − | 0.941965i | ||||
\(781\) | −22.4183 | − | 9.28595i | −0.0287046 | − | 0.0118898i | ||||
\(782\) | −553.412 | + | 388.049i | −0.707688 | + | 0.496226i | ||||
\(783\) | −119.072 | −0.152072 | ||||||||
\(784\) | 129.990 | − | 155.750i | 0.165803 | − | 0.198661i | ||||
\(785\) | − | 1504.16i | − | 1.91613i | ||||||
\(786\) | −378.364 | + | 265.307i | −0.481380 | + | 0.337540i | ||||
\(787\) | 521.707 | − | 1259.51i | 0.662906 | − | 1.60040i | −0.130321 | − | 0.991472i | \(-0.541601\pi\) |
0.793228 | − | 0.608925i | \(-0.208399\pi\) | |||||||
\(788\) | −723.606 | + | 32.5520i | −0.918282 | + | 0.0413096i | ||||
\(789\) | −588.228 | − | 1420.11i | −0.745536 | − | 1.79988i | ||||
\(790\) | 306.787 | + | 1379.51i | 0.388338 | + | 1.74622i | ||||
\(791\) | −536.619 | + | 536.619i | −0.678406 | + | 0.678406i | ||||
\(792\) | −300.196 | + | 231.296i | −0.379036 | + | 0.292041i | ||||
\(793\) | 102.614 | − | 102.614i | 0.129400 | − | 0.129400i | ||||
\(794\) | 342.140 | − | 537.836i | 0.430907 | − | 0.677376i | ||||
\(795\) | 1062.54 | + | 2565.20i | 1.33653 | + | 3.22667i | ||||
\(796\) | 559.870 | + | 1196.51i | 0.703354 | + | 1.50316i | ||||
\(797\) | −397.554 | + | 959.781i | −0.498813 | + | 1.20424i | 0.451310 | + | 0.892367i | \(0.350957\pi\) |
−0.950123 | + | 0.311875i | \(0.899043\pi\) | |||||||
\(798\) | −108.411 | + | 617.218i | −0.135854 | + | 0.773456i | ||||
\(799\) | 663.921i | 0.830940i | ||||||||
\(800\) | 95.9300 | − | 1139.87i | 0.119912 | − | 1.42484i | ||||
\(801\) | 1091.33 | 1.36246 | ||||||||
\(802\) | −95.4475 | − | 16.7649i | −0.119012 | − | 0.0209039i | ||||
\(803\) | 269.539 | + | 111.647i | 0.335665 | + | 0.139037i | ||||
\(804\) | −729.612 | − | 1559.27i | −0.907477 | − | 1.93939i | ||||
\(805\) | −596.657 | + | 247.143i | −0.741189 | + | 0.307010i | ||||
\(806\) | 257.894 | + | 164.057i | 0.319967 | + | 0.203544i | ||||
\(807\) | −168.553 | − | 168.553i | −0.208864 | − | 0.208864i | ||||
\(808\) | 16.0650 | − | 123.925i | 0.0198825 | − | 0.153372i | ||||
\(809\) | −349.674 | − | 349.674i | −0.432230 | − | 0.432230i | 0.457157 | − | 0.889386i | \(-0.348868\pi\) |
−0.889386 | + | 0.457157i | \(0.848868\pi\) | |||||||
\(810\) | −1440.86 | + | 320.430i | −1.77884 | + | 0.395593i | ||||
\(811\) | 179.312 | − | 74.2736i | 0.221100 | − | 0.0915827i | −0.269384 | − | 0.963033i | \(-0.586820\pi\) |
0.490484 | + | 0.871450i | \(0.336820\pi\) | |||||||
\(812\) | 369.004 | − | 16.5999i | 0.454439 | − | 0.0204433i | ||||
\(813\) | −1643.84 | − | 680.901i | −2.02194 | − | 0.837517i | ||||
\(814\) | 300.459 | + | 428.496i | 0.369114 | + | 0.526408i | ||||
\(815\) | −1115.65 | −1.36889 | ||||||||
\(816\) | 1396.11 | − | 731.468i | 1.71092 | − | 0.896407i | ||||
\(817\) | 314.574i | 0.385035i | ||||||||
\(818\) | 393.032 | + | 560.519i | 0.480479 | + | 0.685231i | ||||
\(819\) | 141.953 | − | 342.706i | 0.173325 | − | 0.418444i | ||||
\(820\) | −357.299 | − | 326.536i | −0.435730 | − | 0.398214i | ||||
\(821\) | −41.2552 | − | 99.5988i | −0.0502499 | − | 0.121314i | 0.896761 | − | 0.442515i | \(-0.145914\pi\) |
−0.947011 | + | 0.321201i | \(0.895914\pi\) | |||||||
\(822\) | −561.389 | + | 124.846i | −0.682955 | + | 0.151881i | ||||
\(823\) | −818.928 | + | 818.928i | −0.995053 | + | 0.995053i | −0.999988 | − | 0.00493500i | \(-0.998429\pi\) |
0.00493500 | + | 0.999988i | \(0.498429\pi\) | |||||||
\(824\) | 105.912 | − | 28.6043i | 0.128534 | − | 0.0347140i | ||||
\(825\) | −679.606 | + | 679.606i | −0.823765 | + | 0.823765i | ||||
\(826\) | 739.834 | + | 470.639i | 0.895683 | + | 0.569781i | ||||
\(827\) | 30.9529 | + | 74.7270i | 0.0374280 | + | 0.0903591i | 0.941488 | − | 0.337046i | \(-0.109428\pi\) |
−0.904060 | + | 0.427405i | \(0.859428\pi\) | |||||||
\(828\) | 365.079 | + | 132.331i | 0.440916 | + | 0.159821i | ||||
\(829\) | 87.1070 | − | 210.295i | 0.105075 | − | 0.253673i | −0.862594 | − | 0.505896i | \(-0.831162\pi\) |
0.967669 | + | 0.252223i | \(0.0811618\pi\) | |||||||
\(830\) | 1577.46 | + | 277.073i | 1.90055 | + | 0.333823i | ||||
\(831\) | − | 242.257i | − | 0.291525i | ||||||
\(832\) | 75.0123 | + | 552.821i | 0.0901591 | + | 0.664449i | ||||
\(833\) | 311.658 | 0.374140 | ||||||||
\(834\) | −199.933 | + | 1138.28i | −0.239728 | + | 1.36484i | ||||
\(835\) | −1117.63 | − | 462.937i | −1.33848 | − | 0.554416i | ||||
\(836\) | −118.638 | + | 327.301i | −0.141911 | + | 0.391508i | ||||
\(837\) | 125.871 | − | 52.1375i | 0.150384 | − | 0.0622909i | ||||
\(838\) | 189.698 | − | 298.201i | 0.226370 | − | 0.355848i | ||||
\(839\) | 500.637 | + | 500.637i | 0.596707 | + | 0.596707i | 0.939435 | − | 0.342728i | \(-0.111351\pi\) |
−0.342728 | + | 0.939435i | \(0.611351\pi\) | |||||||
\(840\) | 1453.87 | − | 392.657i | 1.73080 | − | 0.467448i | ||||
\(841\) | 428.660 | + | 428.660i | 0.509703 | + | 0.509703i | ||||
\(842\) | 293.432 | + | 1319.46i | 0.348494 | + | 1.56705i | ||||
\(843\) | 836.595 | − | 346.529i | 0.992402 | − | 0.411067i | ||||
\(844\) | −230.650 | + | 252.379i | −0.273281 | + | 0.299027i | ||||
\(845\) | −669.771 | − | 277.428i | −0.792628 | − | 0.328317i | ||||
\(846\) | 312.311 | − | 218.990i | 0.369161 | − | 0.258853i | ||||
\(847\) | −457.973 | −0.540701 | ||||||||
\(848\) | 424.093 | − | 1357.56i | 0.500109 | − | 1.60089i | ||||
\(849\) | 1942.30i | 2.28775i | ||||||||
\(850\) | 1438.85 | − | 1008.91i | 1.69277 | − | 1.18696i | ||||
\(851\) | 205.218 | − | 495.439i | 0.241149 | − | 0.582184i | ||||
\(852\) | −2.60567 | − | 57.9221i | −0.00305830 | − | 0.0679837i | ||||
\(853\) | 222.935 | + | 538.212i | 0.261354 | + | 0.630964i | 0.999023 | − | 0.0441988i | \(-0.0140735\pi\) |
−0.737669 | + | 0.675162i | \(0.764074\pi\) | |||||||
\(854\) | 43.5605 | + | 195.876i | 0.0510076 | + | 0.229363i | ||||
\(855\) | 504.839 | − | 504.839i | 0.590455 | − | 0.590455i | ||||
\(856\) | −153.765 | + | 1186.13i | −0.179632 | + | 1.38567i | ||||
\(857\) | −172.645 | + | 172.645i | −0.201453 | + | 0.201453i | −0.800622 | − | 0.599169i | \(-0.795498\pi\) |
0.599169 | + | 0.800622i | \(0.295498\pi\) | |||||||
\(858\) | 251.592 | − | 395.497i | 0.293230 | − | 0.460952i | ||||
\(859\) | 66.9122 | + | 161.540i | 0.0778954 | + | 0.188056i | 0.958030 | − | 0.286668i | \(-0.0925477\pi\) |
−0.880135 | + | 0.474724i | \(0.842548\pi\) | |||||||
\(860\) | 684.712 | − | 320.389i | 0.796177 | − | 0.372546i | ||||
\(861\) | 143.501 | − | 346.443i | 0.166668 | − | 0.402372i | ||||
\(862\) | 209.849 | − | 1194.73i | 0.243444 | − | 1.38600i | ||||
\(863\) | 325.900i | 0.377636i | 0.982012 | + | 0.188818i | \(0.0604656\pi\) | ||||
−0.982012 | + | 0.188818i | \(0.939534\pi\) | |||||||
\(864\) | 220.954 | + | 114.095i | 0.255734 | + | 0.132054i | ||||
\(865\) | −2422.77 | −2.80089 | ||||||||
\(866\) | −7.54396 | − | 1.32506i | −0.00871127 | − | 0.00153009i | ||||
\(867\) | 1166.99 | + | 483.383i | 1.34601 | + | 0.557535i | ||||
\(868\) | −382.805 | + | 179.121i | −0.441019 | + | 0.206361i | ||||
\(869\) | −561.927 | + | 232.758i | −0.646637 | + | 0.267846i | ||||
\(870\) | −807.648 | − | 513.778i | −0.928331 | − | 0.590550i | ||||
\(871\) | 661.942 | + | 661.942i | 0.759980 | + | 0.759980i | ||||
\(872\) | 220.143 | − | 169.616i | 0.252457 | − | 0.194514i | ||||
\(873\) | 318.124 | + | 318.124i | 0.364403 | + | 0.364403i | ||||
\(874\) | 348.226 | − | 77.4415i | 0.398428 | − | 0.0886058i | ||||
\(875\) | 466.375 | − | 193.179i | 0.533000 | − | 0.220776i | ||||
\(876\) | 31.3285 | + | 696.408i | 0.0357631 | + | 0.794986i | ||||
\(877\) | 93.3817 | + | 38.6800i | 0.106479 | + | 0.0441049i | 0.435287 | − | 0.900292i | \(-0.356647\pi\) |
−0.328808 | + | 0.944397i | \(0.606647\pi\) | |||||||
\(878\) | 59.0089 | + | 84.1550i | 0.0672083 | + | 0.0958485i | ||||
\(879\) | −2067.29 | −2.35186 | ||||||||
\(880\) | 833.246 | − | 75.1204i | 0.946870 | − | 0.0853641i | ||||
\(881\) | 129.296i | 0.146760i | 0.997304 | + | 0.0733801i | \(0.0233786\pi\) | ||||
−0.997304 | + | 0.0733801i | \(0.976621\pi\) | |||||||
\(882\) | −102.798 | − | 146.605i | −0.116552 | − | 0.166219i | ||||
\(883\) | 28.1493 | − | 67.9584i | 0.0318792 | − | 0.0769631i | −0.907138 | − | 0.420833i | \(-0.861738\pi\) |
0.939017 | + | 0.343870i | \(0.111738\pi\) | |||||||
\(884\) | −578.186 | + | 632.657i | −0.654056 | + | 0.715675i | ||||
\(885\) | −869.565 | − | 2099.31i | −0.982559 | − | 2.37211i | ||||
\(886\) | −1063.36 | + | 236.478i | −1.20018 | + | 0.266905i | ||||
\(887\) | 338.588 | − | 338.588i | 0.381723 | − | 0.381723i | −0.490000 | − | 0.871723i | \(-0.663003\pi\) |
0.871723 | + | 0.490000i | \(0.163003\pi\) | |||||||
\(888\) | −623.096 | + | 1084.19i | −0.701684 | + | 1.22094i | ||||
\(889\) | 338.431 | − | 338.431i | 0.380687 | − | 0.380687i | ||||
\(890\) | −2032.82 | − | 1293.16i | −2.28407 | − | 1.45299i | ||||
\(891\) | −243.109 | − | 586.916i | −0.272849 | − | 0.658716i | ||||
\(892\) | 509.048 | − | 1404.37i | 0.570682 | − | 1.57441i | ||||
\(893\) | 134.096 | − | 323.736i | 0.150163 | − | 0.362526i | ||||
\(894\) | −103.306 | − | 18.1452i | −0.115554 | − | 0.0202966i | ||||
\(895\) | − | 996.837i | − | 1.11378i | ||||||
\(896\) | −700.640 | − | 322.775i | −0.781964 | − | 0.360240i | ||||
\(897\) | −480.310 | −0.535463 | ||||||||
\(898\) | 149.355 | − | 850.322i | 0.166320 | − | 0.946907i | ||||
\(899\) | 248.188 | + | 102.803i | 0.276071 | + | 0.114352i | ||||
\(900\) | −949.192 | − | 344.057i | −1.05466 | − | 0.382286i | ||||
\(901\) | 2018.64 | − | 836.148i | 2.24045 | − | 0.928023i | ||||
\(902\) | 111.814 | − | 175.770i | 0.123963 | − | 0.194867i | ||||
\(903\) | 414.120 | + | 414.120i | 0.458605 | + | 0.458605i | ||||
\(904\) | −873.415 | − | 501.959i | −0.966167 | − | 0.555265i | ||||
\(905\) | 560.535 | + | 560.535i | 0.619375 | + | 0.619375i | ||||
\(906\) | −43.5218 | − | 195.702i | −0.0480373 | − | 0.216006i | ||||
\(907\) | 1031.84 | − | 427.401i | 1.13764 | − | 0.471225i | 0.267268 | − | 0.963622i | \(-0.413879\pi\) |
0.870371 | + | 0.492397i | \(0.163879\pi\) | |||||||
\(908\) | −24.6716 | − | 22.5474i | −0.0271713 | − | 0.0248319i | ||||
\(909\) | −101.898 | − | 42.2075i | −0.112099 | − | 0.0464329i | ||||
\(910\) | −670.500 | + | 470.150i | −0.736814 | + | 0.516649i | ||||
\(911\) | 857.136 | 0.940873 | 0.470437 | − | 0.882434i | \(-0.344096\pi\) | ||||
0.470437 | + | 0.882434i | \(0.344096\pi\) | |||||||
\(912\) | −828.498 | + | 74.6924i | −0.908440 | + | 0.0818995i | ||||
\(913\) | 689.307i | 0.754992i | ||||||||
\(914\) | −433.187 | + | 303.748i | −0.473947 | + | 0.332328i | ||||
\(915\) | 198.995 | − | 480.417i | 0.217481 | − | 0.525046i | ||||
\(916\) | 714.534 | − | 32.1439i | 0.780059 | − | 0.0350916i | ||||
\(917\) | 132.968 | + | 321.014i | 0.145004 | + | 0.350070i | ||||
\(918\) | 82.9322 | + | 372.916i | 0.0903401 | + | 0.406227i | ||||
\(919\) | 447.382 | − | 447.382i | 0.486814 | − | 0.486814i | −0.420486 | − | 0.907299i | \(-0.638140\pi\) |
0.907299 | + | 0.420486i | \(0.138140\pi\) | |||||||
\(920\) | −523.226 | − | 679.088i | −0.568724 | − | 0.738140i | ||||
\(921\) | 1452.97 | − | 1452.97i | 1.57760 | − | 1.57760i | ||||
\(922\) | 294.879 | − | 463.544i | 0.319826 | − | 0.502759i | ||||
\(923\) | 12.0655 | + | 29.1286i | 0.0130720 | + | 0.0315586i | ||||
\(924\) | 274.694 | + | 587.056i | 0.297288 | + | 0.635342i | ||||
\(925\) | −533.558 | + | 1288.12i | −0.576820 | + | 1.39257i | ||||
\(926\) | −264.771 | + | 1507.42i | −0.285929 | + | 1.62788i | ||||
\(927\) | − | 96.8291i | − | 0.104454i | ||||||
\(928\) | 148.988 | + | 467.140i | 0.160548 | + | 0.503384i | ||||
\(929\) | −357.338 | −0.384648 | −0.192324 | − | 0.981332i | \(-0.561602\pi\) | ||||
−0.192324 | + | 0.981332i | \(0.561602\pi\) | |||||||
\(930\) | 1078.73 | + | 189.473i | 1.15992 | + | 0.203735i | ||||
\(931\) | −151.968 | − | 62.9473i | −0.163231 | − | 0.0676125i | ||||
\(932\) | −33.6117 | − | 71.8324i | −0.0360641 | − | 0.0770734i | ||||
\(933\) | −2022.98 | + | 837.947i | −2.16826 | + | 0.898122i | ||||
\(934\) | 488.090 | + | 310.494i | 0.522580 | + | 0.332435i | ||||
\(935\) | 908.827 | + | 908.827i | 0.972007 | + | 0.972007i | ||||
\(936\) | 488.314 | + | 63.3028i | 0.521703 | + | 0.0676312i | ||||
\(937\) | −504.116 | − | 504.116i | −0.538011 | − | 0.538011i | 0.384934 | − | 0.922944i | \(-0.374224\pi\) |
−0.922944 | + | 0.384934i | \(0.874224\pi\) | |||||||
\(938\) | −1263.55 | + | 281.000i | −1.34707 | + | 0.299573i | ||||
\(939\) | −665.468 | + | 275.646i | −0.708698 | + | 0.293552i | ||||
\(940\) | −841.229 | + | 37.8433i | −0.894924 | + | 0.0402589i | ||||
\(941\) | −503.223 | − | 208.442i | −0.534775 | − | 0.221511i | 0.0989183 | − | 0.995096i | \(-0.468462\pi\) |
−0.633693 | + | 0.773585i | \(0.718462\pi\) | |||||||
\(942\) | 888.073 | + | 1266.52i | 0.942752 | + | 1.34450i | ||||
\(943\) | −213.463 | −0.226366 | ||||||||
\(944\) | −347.070 | + | 1111.00i | −0.367659 | + | 1.17691i | ||||
\(945\) | 365.021i | 0.386265i | ||||||||
\(946\) | 186.792 | + | 266.392i | 0.197455 | + | 0.281598i | ||||
\(947\) | −137.566 | + | 332.113i | −0.145265 | + | 0.350700i | −0.979719 | − | 0.200378i | \(-0.935783\pi\) |
0.834454 | + | 0.551077i | \(0.185783\pi\) | |||||||
\(948\) | −1072.80 | − | 980.431i | −1.13164 | − | 1.03421i | ||||
\(949\) | −145.065 | − | 350.219i | −0.152861 | − | 0.369040i | ||||
\(950\) | −905.376 | + | 201.345i | −0.953028 | + | 0.211942i | ||||
\(951\) | 180.964 | − | 180.964i | 0.190288 | − | 0.190288i | ||||
\(952\) | −308.995 | − | 1144.10i | −0.324574 | − | 1.20179i | ||||
\(953\) | 129.115 | − | 129.115i | 0.135483 | − | 0.135483i | −0.636113 | − | 0.771596i | \(-0.719459\pi\) |
0.771596 | + | 0.636113i | \(0.219459\pi\) | |||||||
\(954\) | −1059.16 | − | 673.777i | −1.11023 | − | 0.706265i | ||||
\(955\) | −198.535 | − | 479.306i | −0.207890 | − | 0.501891i | ||||
\(956\) | 868.508 | + | 314.811i | 0.908481 | + | 0.329300i | ||||
\(957\) | 157.655 | − | 380.612i | 0.164739 | − | 0.397714i | ||||
\(958\) | 311.351 | + | 54.6874i | 0.325001 | + | 0.0570850i | ||||
\(959\) | 432.422i | 0.450909i | ||||||||
\(960\) | 1006.39 | + | 1727.26i | 1.04833 | + | 1.79923i | ||||
\(961\) | 653.628 | 0.680154 | ||||||||
\(962\) | 117.636 | − | 669.735i | 0.122283 | − | 0.696190i | ||||
\(963\) | 975.304 | + | 403.984i | 1.01278 | + | 0.419506i | ||||
\(964\) | 151.860 | − | 418.954i | 0.157531 | − | 0.434600i | ||||
\(965\) | 1986.54 | − | 822.851i | 2.05859 | − | 0.852695i | ||||
\(966\) | 356.475 | − | 560.370i | 0.369021 | − | 0.580093i | ||||
\(967\) | 657.007 | + | 657.007i | 0.679428 | + | 0.679428i | 0.959871 | − | 0.280443i | \(-0.0904813\pi\) |
−0.280443 | + | 0.959871i | \(0.590481\pi\) | |||||||
\(968\) | −158.508 | − | 586.901i | −0.163748 | − | 0.606303i | ||||
\(969\) | −903.648 | − | 903.648i | −0.932557 | − | 0.932557i | ||||
\(970\) | −215.611 | − | 969.524i | −0.222279 | − | 0.999509i | ||||
\(971\) | −654.912 | + | 271.274i | −0.674472 | + | 0.279376i | −0.693514 | − | 0.720443i | \(-0.743938\pi\) |
0.0190418 | + | 0.999819i | \(0.493938\pi\) | |||||||
\(972\) | 835.302 | − | 913.996i | 0.859364 | − | 0.940325i | ||||
\(973\) | 802.830 | + | 332.543i | 0.825108 | + | 0.341771i | ||||
\(974\) | −1563.46 | + | 1096.29i | −1.60519 | + | 1.12555i | ||||
\(975\) | 1248.79 | 1.28081 | ||||||||
\(976\) | −235.942 | + | 123.618i | −0.241744 | + | 0.126657i | ||||
\(977\) | 1493.20i | 1.52835i | 0.645010 | + | 0.764174i | \(0.276853\pi\) | ||||
−0.645010 | + | 0.764174i | \(0.723147\pi\) | |||||||
\(978\) | 939.387 | − | 658.692i | 0.960518 | − | 0.673509i | ||||
\(979\) | 396.811 | − | 957.986i | 0.405323 | − | 0.978536i | ||||
\(980\) | 17.7644 | + | 394.890i | 0.0181270 | + | 0.402949i | ||||
\(981\) | −93.8668 | − | 226.615i | −0.0956848 | − | 0.231004i | ||||
\(982\) | −40.9426 | − | 184.104i | −0.0416931 | − | 0.187479i | ||||
\(983\) | −856.189 | + | 856.189i | −0.870996 | + | 0.870996i | −0.992581 | − | 0.121585i | \(-0.961202\pi\) |
0.121585 | + | 0.992581i | \(0.461202\pi\) | |||||||
\(984\) | 493.639 | + | 63.9930i | 0.501666 | + | 0.0650336i | ||||
\(985\) | 997.994 | − | 997.994i | 1.01319 | − | 1.01319i | ||||
\(986\) | −404.309 | + | 635.565i | −0.410050 | + | 0.644590i | ||||
\(987\) | −249.651 | − | 602.711i | −0.252939 | − | 0.610650i | ||||
\(988\) | 409.711 | − | 191.711i | 0.414687 | − | 0.194040i | ||||
\(989\) | 127.582 | − | 308.010i | 0.129001 | − | 0.311435i | ||||
\(990\) | 127.744 | − | 727.286i | 0.129035 | − | 0.734632i | ||||
\(991\) | − | 1223.32i | − | 1.23443i | −0.786793 | − | 0.617217i | \(-0.788260\pi\) | ||
0.786793 | − | 0.617217i | \(-0.211740\pi\) | |||||||
\(992\) | −362.039 | − | 428.576i | −0.364958 | − | 0.432032i | ||||
\(993\) | −233.162 | −0.234806 | ||||||||
\(994\) | −42.9385 | − | 7.54196i | −0.0431977 | − | 0.00758748i | ||||
\(995\) | −2378.08 | − | 985.034i | −2.39003 | − | 0.989984i | ||||
\(996\) | −1491.82 | + | 698.050i | −1.49781 | + | 0.700854i | ||||
\(997\) | 604.001 | − | 250.185i | 0.605819 | − | 0.250938i | −0.0586209 | − | 0.998280i | \(-0.518670\pi\) |
0.664440 | + | 0.747342i | \(0.268670\pi\) | |||||||
\(998\) | −726.761 | − | 462.323i | −0.728217 | − | 0.463249i | ||||
\(999\) | −214.323 | − | 214.323i | −0.214537 | − | 0.214537i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 32.3.h.a.19.5 | ✓ | 28 | |
3.2 | odd | 2 | 288.3.u.a.19.3 | 28 | |||
4.3 | odd | 2 | 128.3.h.a.111.6 | 28 | |||
8.3 | odd | 2 | 256.3.h.a.223.2 | 28 | |||
8.5 | even | 2 | 256.3.h.b.223.6 | 28 | |||
32.5 | even | 8 | 128.3.h.a.15.6 | 28 | |||
32.11 | odd | 8 | 256.3.h.b.31.6 | 28 | |||
32.21 | even | 8 | 256.3.h.a.31.2 | 28 | |||
32.27 | odd | 8 | inner | 32.3.h.a.27.5 | yes | 28 | |
96.59 | even | 8 | 288.3.u.a.91.3 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.19.5 | ✓ | 28 | 1.1 | even | 1 | trivial | |
32.3.h.a.27.5 | yes | 28 | 32.27 | odd | 8 | inner | |
128.3.h.a.15.6 | 28 | 32.5 | even | 8 | |||
128.3.h.a.111.6 | 28 | 4.3 | odd | 2 | |||
256.3.h.a.31.2 | 28 | 32.21 | even | 8 | |||
256.3.h.a.223.2 | 28 | 8.3 | odd | 2 | |||
256.3.h.b.31.6 | 28 | 32.11 | odd | 8 | |||
256.3.h.b.223.6 | 28 | 8.5 | even | 2 | |||
288.3.u.a.19.3 | 28 | 3.2 | odd | 2 | |||
288.3.u.a.91.3 | 28 | 96.59 | even | 8 |