Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(13,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.13");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.i (of order \(9\), degree \(6\), 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: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 13.7 | ||
Character | \(\chi\) | \(=\) | 108.13 |
Dual form | 108.4.i.a.25.7 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 2.66172 | + | 4.46265i | 0.512248 | + | 0.858838i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −12.8040 | − | 10.7439i | −1.14523 | − | 0.960961i | −0.145631 | − | 0.989339i | \(-0.546521\pi\) |
−0.999597 | + | 0.0283783i | \(0.990966\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −20.8033 | − | 7.57178i | −1.12327 | − | 0.408838i | −0.287427 | − | 0.957803i | \(-0.592800\pi\) |
−0.835845 | + | 0.548965i | \(0.815022\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −12.8305 | + | 23.7566i | −0.475204 | + | 0.879875i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −41.5462 | + | 34.8614i | −1.13879 | + | 0.955554i | −0.999398 | − | 0.0346836i | \(-0.988958\pi\) |
−0.139387 | + | 0.990238i | \(0.544513\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.2534 | − | 69.4923i | 0.261421 | − | 1.48259i | −0.517615 | − | 0.855613i | \(-0.673180\pi\) |
0.779036 | − | 0.626979i | \(-0.215709\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13.8654 | − | 85.7371i | 0.238669 | − | 1.47582i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.7250 | − | 30.7006i | 0.252879 | − | 0.437999i | −0.711439 | − | 0.702748i | \(-0.751956\pi\) |
0.964317 | + | 0.264750i | \(0.0852893\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 37.9595 | + | 65.7479i | 0.458343 | + | 0.793873i | 0.998874 | − | 0.0474510i | \(-0.0151098\pi\) |
−0.540531 | + | 0.841324i | \(0.681776\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.5823 | − | 112.992i | −0.224269 | − | 1.17413i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −161.185 | + | 58.6666i | −1.46128 | + | 0.531862i | −0.945717 | − | 0.324991i | \(-0.894639\pi\) |
−0.515562 | + | 0.856853i | \(0.672417\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 26.8068 | + | 152.029i | 0.214454 | + | 1.21623i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −140.169 | + | 5.97534i | −0.999093 | + | 0.0425909i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −25.1440 | − | 142.599i | −0.161004 | − | 0.913100i | −0.953089 | − | 0.302689i | \(-0.902116\pi\) |
0.792085 | − | 0.610411i | \(-0.208996\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 160.113 | − | 58.2764i | 0.927650 | − | 0.337637i | 0.166372 | − | 0.986063i | \(-0.446795\pi\) |
0.761278 | + | 0.648426i | \(0.224572\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −266.158 | − | 92.6149i | −1.40401 | − | 0.488551i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 185.016 | + | 320.457i | 0.893526 | + | 1.54763i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −180.731 | + | 313.036i | −0.803029 | + | 1.39089i | 0.114585 | + | 0.993413i | \(0.463446\pi\) |
−0.917614 | + | 0.397473i | \(0.869887\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 342.735 | − | 130.286i | 1.40722 | − | 0.534936i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −24.4277 | + | 138.536i | −0.0930479 | + | 0.527701i | 0.902280 | + | 0.431150i | \(0.141892\pi\) |
−0.995328 | + | 0.0965508i | \(0.969219\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 269.808 | − | 226.396i | 0.956870 | − | 0.802909i | −0.0235712 | − | 0.999722i | \(-0.507504\pi\) |
0.980441 | + | 0.196813i | \(0.0630592\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 419.521 | − | 166.332i | 1.38974 | − | 0.551006i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −74.2539 | − | 27.0262i | −0.230448 | − | 0.0838761i | 0.224215 | − | 0.974540i | \(-0.428018\pi\) |
−0.454663 | + | 0.890663i | \(0.650240\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 112.692 | + | 94.5596i | 0.328547 | + | 0.275684i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 184.185 | − | 2.61583i | 0.505706 | − | 0.00718216i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −195.786 | −0.507420 | −0.253710 | − | 0.967280i | \(-0.581651\pi\) | ||||
−0.253710 | + | 0.967280i | \(0.581651\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 906.505 | 2.22242 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −192.372 | + | 344.402i | −0.447023 | + | 0.800302i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −199.404 | − | 167.320i | −0.440003 | − | 0.369207i | 0.395707 | − | 0.918377i | \(-0.370499\pi\) |
−0.835711 | + | 0.549170i | \(0.814944\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 347.480 | + | 126.472i | 0.729348 | + | 0.265461i | 0.679889 | − | 0.733315i | \(-0.262028\pi\) |
0.0494591 | + | 0.998776i | \(0.484250\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 446.797 | − | 397.066i | 0.893510 | − | 0.794058i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −903.509 | + | 758.134i | −1.72410 | + | 1.44669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.6574 | + | 77.4549i | −0.0249032 | + | 0.141233i | −0.994724 | − | 0.102585i | \(-0.967289\pi\) |
0.969821 | + | 0.243818i | \(0.0783999\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −690.838 | − | 563.159i | −1.20532 | − | 0.982556i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −365.521 | + | 633.100i | −0.610976 | + | 1.05824i | 0.380100 | + | 0.924945i | \(0.375890\pi\) |
−0.991076 | + | 0.133297i | \(0.957444\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −361.799 | − | 626.655i | −0.580074 | − | 1.00472i | −0.995470 | − | 0.0950773i | \(-0.969690\pi\) |
0.415396 | − | 0.909641i | \(-0.363643\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −607.100 | + | 524.287i | −0.934691 | + | 0.807193i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1128.26 | − | 410.653i | 1.66983 | − | 0.607769i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 52.6510 | + | 298.599i | 0.0749836 | + | 0.425253i | 0.999072 | + | 0.0430739i | \(0.0137151\pi\) |
−0.924088 | + | 0.382179i | \(0.875174\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −399.756 | − | 609.620i | −0.548362 | − | 0.836241i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.20364 | + | 46.5252i | 0.0108490 | + | 0.0615277i | 0.989752 | − | 0.142800i | \(-0.0456104\pi\) |
−0.978903 | + | 0.204327i | \(0.934499\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −556.794 | + | 202.656i | −0.710503 | + | 0.258602i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 569.442 | − | 491.766i | 0.701730 | − | 0.606010i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −340.199 | − | 589.241i | −0.405180 | − | 0.701792i | 0.589163 | − | 0.808014i | \(-0.299458\pi\) |
−0.994342 | + | 0.106223i | \(0.966124\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −781.091 | + | 1352.89i | −0.899786 | + | 1.55848i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 686.243 | + | 559.413i | 0.765162 | + | 0.623747i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 220.351 | − | 1249.67i | 0.237974 | − | 1.34962i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 426.854 | − | 358.173i | 0.446809 | − | 0.374917i | −0.391441 | − | 0.920203i | \(-0.628023\pi\) |
0.838250 | + | 0.545286i | \(0.183579\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −295.130 | − | 1434.29i | −0.299613 | − | 1.45607i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 42.5638 | + | 15.4920i | 0.0419332 | + | 0.0152624i | 0.362902 | − | 0.931827i | \(-0.381786\pi\) |
−0.320968 | + | 0.947090i | \(0.604008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1512.45 | − | 1269.10i | −1.44686 | − | 1.21406i | −0.934833 | − | 0.355087i | \(-0.884451\pi\) |
−0.512025 | − | 0.858971i | \(-0.671104\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −937.628 | + | 1678.63i | −0.871458 | + | 1.56017i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1552.11 | 1.40232 | 0.701160 | − | 0.713004i | \(-0.252666\pi\) | ||||
0.701160 | + | 0.713004i | \(0.252666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1881.98 | −1.65377 | −0.826887 | − | 0.562368i | \(-0.809891\pi\) | ||||
−0.826887 | + | 0.562368i | \(0.809891\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1878.03 | + | 26.6722i | −1.60590 | + | 0.0228073i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −801.214 | − | 672.299i | −0.667008 | − | 0.559686i | 0.245170 | − | 0.969480i | \(-0.421156\pi\) |
−0.912178 | + | 0.409794i | \(0.865601\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2694.13 | + | 980.582i | 2.18460 | + | 0.795128i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1493.69 | + | 1182.72i | 1.18027 | + | 0.934552i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −601.195 | + | 504.463i | −0.463122 | + | 0.388605i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 279.643 | − | 1585.93i | 0.210100 | − | 1.19153i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −683.259 | + | 259.732i | −0.500873 | + | 0.190401i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 245.487 | − | 425.196i | 0.175656 | − | 0.304246i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −445.810 | − | 772.165i | −0.311490 | − | 0.539517i | 0.667195 | − | 0.744883i | \(-0.267495\pi\) |
−0.978685 | + | 0.205366i | \(0.934161\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1728.48 | + | 601.458i | 1.17972 | + | 0.410507i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 395.806 | − | 144.062i | 0.263983 | − | 0.0960819i | −0.206638 | − | 0.978417i | \(-0.566252\pi\) |
0.470621 | + | 0.882336i | \(0.344030\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −291.855 | − | 1655.19i | −0.190279 | − | 1.07912i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1858.93 | + | 1429.45i | 1.18512 | + | 0.911312i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 29.8041 | + | 169.027i | 0.0185864 | + | 0.105409i | 0.992690 | − | 0.120695i | \(-0.0385123\pi\) |
−0.974103 | + | 0.226104i | \(0.927401\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 354.692 | − | 129.097i | 0.216436 | − | 0.0787761i | −0.231527 | − | 0.972829i | \(-0.574372\pi\) |
0.447962 | + | 0.894052i | \(0.352150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −77.0344 | − | 403.305i | −0.0460104 | − | 0.240883i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1913.52 | + | 3314.31i | 1.11900 | + | 1.93816i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1210.12 | + | 2095.98i | −0.693066 | + | 1.20043i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −122.033 | + | 754.595i | −0.0684701 | + | 0.423387i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 177.014 | − | 1003.90i | 0.0973257 | − | 0.551962i | −0.896684 | − | 0.442671i | \(-0.854031\pi\) |
0.994010 | − | 0.109291i | \(-0.0348579\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −810.985 | + | 680.498i | −0.437067 | + | 0.366742i | −0.834610 | − | 0.550841i | \(-0.814307\pi\) |
0.397544 | + | 0.917583i | \(0.369863\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 501.921 | + | 814.990i | 0.265215 | + | 0.430641i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2676.21 | − | 974.060i | −1.38683 | − | 0.504764i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −682.838 | − | 572.969i | −0.347111 | − | 0.291261i | 0.452518 | − | 0.891755i | \(-0.350526\pi\) |
−0.799629 | + | 0.600495i | \(0.794970\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −521.127 | − | 873.725i | −0.259925 | − | 0.435792i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3797.39 | 1.85886 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1261.47 | 0.606173 | 0.303086 | − | 0.952963i | \(-0.401983\pi\) | ||||
0.303086 | + | 0.952963i | \(0.401983\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2412.86 | + | 4045.41i | 1.13843 | + | 1.90870i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1362.74 | − | 1143.48i | −0.631450 | − | 0.529850i | 0.269929 | − | 0.962880i | \(-0.413000\pi\) |
−0.901379 | + | 0.433030i | \(0.857444\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2614.53 | − | 951.612i | −1.19005 | − | 0.433141i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2048.99 | + | 58.2122i | −0.916316 | + | 0.0260327i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2778.70 | − | 2331.60i | 1.22116 | − | 1.02467i | 0.222395 | − | 0.974957i | \(-0.428613\pi\) |
0.998763 | − | 0.0497167i | \(-0.0158319\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 593.459 | − | 3365.68i | 0.256350 | − | 1.45384i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 215.933 | − | 1335.23i | 0.0916978 | − | 0.567017i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 975.147 | − | 1689.00i | 0.407184 | − | 0.705263i | −0.587389 | − | 0.809305i | \(-0.699844\pi\) |
0.994573 | + | 0.104042i | \(0.0331775\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1929.16 | + | 3341.40i | 0.792226 | + | 1.37218i | 0.924585 | + | 0.380975i | \(0.124411\pi\) |
−0.132359 | + | 0.991202i | \(0.542255\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 360.491 | + | 1887.31i | 0.145619 | + | 0.762373i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5677.31 | − | 2066.37i | 2.25624 | − | 0.821204i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 333.859 | + | 1893.41i | 0.130557 | + | 0.740426i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2961.22 | + | 937.020i | 1.13967 | + | 0.360625i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 236.098 | + | 1338.98i | 0.0894421 | + | 0.507251i | 0.996309 | + | 0.0858348i | \(0.0273557\pi\) |
−0.906867 | + | 0.421416i | \(0.861533\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1975.24 | + | 718.930i | −0.736690 | + | 0.268133i | −0.682994 | − | 0.730424i | \(-0.739322\pi\) |
−0.0536961 | + | 0.998557i | \(0.517100\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5788.17 | − | 2014.11i | −2.12564 | − | 0.739657i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 744.973 | + | 1290.33i | 0.269427 | + | 0.466661i | 0.968714 | − | 0.248180i | \(-0.0798323\pi\) |
−0.699287 | + | 0.714841i | \(0.746499\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −537.438 | + | 930.870i | −0.191447 | + | 0.331596i | −0.945730 | − | 0.324953i | \(-0.894651\pi\) |
0.754283 | + | 0.656549i | \(0.227985\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −382.006 | + | 145.215i | −0.134053 | + | 0.0509586i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −556.647 | + | 3156.90i | −0.192458 | + | 1.09148i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1801.19 | − | 1511.38i | 0.613661 | − | 0.514923i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 674.367 | − | 4581.94i | 0.226434 | − | 1.53849i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3869.13 | − | 1408.25i | −1.28054 | − | 0.466080i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2250.23 | − | 1888.17i | −0.734180 | − | 0.616051i | 0.197087 | − | 0.980386i | \(-0.436852\pi\) |
−0.931268 | + | 0.364335i | \(0.881296\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3798.22 | + | 53.9432i | −1.22183 | + | 0.0173527i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5887.01 | −1.86740 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3772.13 | −1.18004 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1833.54 | − | 3282.56i | 0.565748 | − | 1.01285i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1916.26 | − | 1607.93i | −0.583266 | − | 0.489418i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.0168 | + | 9.46936i | 0.00781263 | + | 0.00284357i | 0.345924 | − | 0.938263i | \(-0.387566\pi\) |
−0.338111 | + | 0.941106i | \(0.609788\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3955.64 | − | 1313.77i | −1.17204 | − | 0.389265i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2720.48 | + | 2282.76i | −0.795440 | + | 0.667453i | −0.947085 | − | 0.320982i | \(-0.895987\pi\) |
0.151646 | + | 0.988435i | \(0.451543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −449.344 | + | 2548.36i | −0.129666 | + | 0.735372i | 0.848761 | + | 0.528777i | \(0.177349\pi\) |
−0.978427 | + | 0.206595i | \(0.933762\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4835.71 | + | 3941.99i | 1.37734 | + | 1.12279i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2151.96 | + | 3727.31i | −0.605064 | + | 1.04800i | 0.386978 | + | 0.922089i | \(0.373519\pi\) |
−0.992041 | + | 0.125912i | \(0.959814\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 660.384 | + | 1143.82i | 0.183314 | + | 0.317509i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1192.40 | + | 1029.75i | −0.326813 | + | 0.282234i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1776.21 | + | 646.488i | −0.480726 | + | 0.174970i | −0.571005 | − | 0.820947i | \(-0.693446\pi\) |
0.0902790 | + | 0.995917i | \(0.471224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 294.365 | + | 1669.43i | 0.0786793 | + | 0.446212i | 0.998542 | + | 0.0539728i | \(0.0171884\pi\) |
−0.919863 | + | 0.392239i | \(0.871700\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1656.48 | − | 3406.61i | 0.437298 | − | 0.899316i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −426.974 | − | 2421.49i | −0.111340 | − | 0.631442i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5034.10 | − | 1832.26i | 1.29681 | − | 0.472001i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −185.790 | + | 160.447i | −0.0472850 | + | 0.0408350i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −81.6710 | − | 141.458i | −0.0205380 | − | 0.0355728i | 0.855574 | − | 0.517681i | \(-0.173205\pi\) |
−0.876112 | + | 0.482108i | \(0.839871\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4651.42 | − | 8056.50i | 1.15586 | − | 2.00201i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2386.41 | − | 1945.36i | −0.586051 | − | 0.477739i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −312.000 | + | 1769.44i | −0.0757277 | + | 0.429473i | 0.923247 | + | 0.384206i | \(0.125525\pi\) |
−0.998975 | + | 0.0452667i | \(0.985586\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6130.05 | − | 5143.72i | 1.47067 | − | 1.23404i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3710.27 | + | 1232.28i | 0.879924 | + | 0.292245i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3362.81 | + | 1223.96i | 0.788440 | + | 0.286969i | 0.704687 | − | 0.709518i | \(-0.251087\pi\) |
0.0837527 | + | 0.996487i | \(0.473309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2506.85 | + | 2103.50i | 0.581112 | + | 0.487611i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1724.07 | − | 3086.58i | 0.395173 | − | 0.707475i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1080.51 | 0.244908 | 0.122454 | − | 0.992474i | \(-0.460924\pi\) | ||||
0.122454 | + | 0.992474i | \(0.460924\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7858.41 | −1.76149 | −0.880746 | − | 0.473590i | \(-0.842958\pi\) | ||||
−0.880746 | + | 0.473590i | \(0.842958\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8116.51 | + | 115.273i | −1.79939 | + | 0.0255554i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6413.65 | − | 5381.70i | −1.40639 | − | 1.18010i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5715.93 | + | 2080.43i | 1.23984 | + | 0.451267i | 0.876958 | − | 0.480567i | \(-0.159569\pi\) |
0.362887 | + | 0.931833i | \(0.381791\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −669.882 | + | 4551.46i | −0.143745 | + | 0.976663i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4250.20 | + | 3566.34i | −0.902297 | + | 0.757117i | −0.970638 | − | 0.240545i | \(-0.922674\pi\) |
0.0683411 | + | 0.997662i | \(0.478229\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −975.267 | + | 5531.01i | −0.204854 | + | 1.16178i | 0.692816 | + | 0.721114i | \(0.256370\pi\) |
−0.897670 | + | 0.440669i | \(0.854741\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6163.36 | − | 2342.92i | 1.28100 | − | 0.486957i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1557.14 | − | 2697.05i | 0.320262 | − | 0.554710i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1828.15 | + | 3166.45i | 0.372105 | + | 0.644504i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2734.57 | + | 951.546i | 0.550870 | + | 0.191686i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5648.62 | − | 2055.93i | 1.12626 | − | 0.409927i | 0.289330 | − | 0.957229i | \(-0.406567\pi\) |
0.836935 | + | 0.547302i | \(0.184345\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 755.515 | + | 4284.74i | 0.149111 | + | 0.845652i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5615.17 | − | 5134.73i | 1.09705 | − | 1.00319i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2101.82 | + | 11920.0i | 0.406525 | + | 2.30552i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7327.12 | + | 2666.86i | −1.40308 | + | 0.510681i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 44.1576 | + | 231.183i | 0.00837224 | + | 0.0438320i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3090.34 | − | 5352.63i | −0.580172 | − | 1.00489i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 959.723 | − | 1662.29i | 0.178418 | − | 0.309029i | −0.762921 | − | 0.646492i | \(-0.776235\pi\) |
0.941339 | + | 0.337463i | \(0.109569\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1637.82 | − | 10127.5i | 0.301529 | − | 1.86451i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1333.89 | + | 7564.89i | −0.243210 | + | 1.37931i | 0.581404 | + | 0.813615i | \(0.302504\pi\) |
−0.824614 | + | 0.565696i | \(0.808608\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6883.88 | + | 5776.26i | −1.24313 | + | 1.04311i | −0.245858 | + | 0.969306i | \(0.579070\pi\) |
−0.997273 | + | 0.0738052i | \(0.976486\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9986.83 | + | 283.728i | −1.78633 | + | 0.0507500i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3964.88 | + | 1443.10i | 0.702491 | + | 0.255686i | 0.668474 | − | 0.743735i | \(-0.266948\pi\) |
0.0340172 | + | 0.999421i | \(0.489170\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6015.82 | + | 5047.87i | 1.05587 | + | 0.885976i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4131.28 | + | 6926.53i | 0.718335 | + | 1.20436i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2691.33 | 0.463621 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10893.3 | 1.85924 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5009.31 | − | 8398.64i | −0.847142 | − | 1.42032i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1340.09 | + | 1124.47i | 0.224564 | + | 0.188431i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4463.91 | + | 1624.73i | 0.741265 | + | 0.269798i | 0.684925 | − | 0.728613i | \(-0.259835\pi\) |
0.0563398 | + | 0.998412i | \(0.482057\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5117.80 | − | 8309.98i | −0.842204 | − | 1.36752i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1007.04 | − | 845.003i | 0.164239 | − | 0.137813i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1170.70 | − | 6639.39i | 0.189235 | − | 1.07321i | −0.731156 | − | 0.682210i | \(-0.761019\pi\) |
0.920392 | − | 0.390997i | \(-0.127870\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 867.628 | − | 5365.01i | 0.139006 | − | 0.859550i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4620.49 | + | 8002.92i | −0.733764 | + | 1.27092i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2168.36 | + | 3755.71i | 0.341343 | + | 0.591223i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2795.01 | + | 14633.0i | 0.436169 | + | 2.28352i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5429.26 | − | 1976.09i | 0.839936 | − | 0.305712i | 0.114006 | − | 0.993480i | \(-0.463632\pi\) |
0.725930 | + | 0.687768i | \(0.241409\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −980.754 | − | 5562.13i | −0.150426 | − | 0.853106i | −0.962849 | − | 0.270039i | \(-0.912963\pi\) |
0.812424 | − | 0.583067i | \(-0.198148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1302.30 | + | 9813.87i | −0.198039 | + | 1.49238i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1941.90 | − | 11013.0i | −0.292795 | − | 1.66052i | −0.676030 | − | 0.736874i | \(-0.736301\pi\) |
0.383235 | − | 0.923651i | \(-0.374810\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11482.1 | − | 4179.14i | 1.71664 | − | 0.624805i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3851.45 | − | 1340.19i | −0.570982 | − | 0.198684i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4436.64 | − | 7684.48i | −0.652247 | − | 1.12973i | −0.982576 | − | 0.185860i | \(-0.940493\pi\) |
0.330329 | − | 0.943866i | \(-0.392840\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 547.646 | − | 948.551i | 0.0798434 | − | 0.138293i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7821.80 | − | 2973.36i | 1.13096 | − | 0.429920i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2100.20 | + | 11910.8i | −0.301177 | + | 1.70806i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4478.44 | + | 3757.85i | −0.636982 | + | 0.534491i | −0.903090 | − | 0.429452i | \(-0.858707\pi\) |
0.266108 | + | 0.963943i | \(0.414262\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2977.74 | − | 2357.81i | −0.420094 | − | 0.332636i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4072.99 | + | 1482.45i | 0.569971 | + | 0.207452i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 663.209 | + | 556.499i | 0.0920635 | + | 0.0772504i | 0.687658 | − | 0.726035i | \(-0.258639\pi\) |
−0.595594 | + | 0.803285i | \(0.703083\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2550.92 | − | 36.2288i | 0.351277 | − | 0.00498892i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10217.6 | −1.39584 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1536.47 | −0.208240 | −0.104120 | − | 0.994565i | \(-0.533203\pi\) | ||||
−0.104120 | + | 0.994565i | \(0.533203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2259.28 | − | 4044.78i | 0.303797 | − | 0.543886i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −999.899 | − | 839.015i | −0.133401 | − | 0.111936i | 0.573646 | − | 0.819103i | \(-0.305528\pi\) |
−0.707047 | + | 0.707167i | \(0.749973\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18858.3 | − | 6863.85i | −2.49638 | − | 0.908609i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1916.63 | + | 9314.52i | 0.251751 | + | 1.22347i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8814.64 | − | 7396.36i | 1.14889 | − | 0.964037i | 0.149201 | − | 0.988807i | \(-0.452330\pi\) |
0.999693 | + | 0.0247702i | \(0.00788542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1055.90 | + | 5988.33i | −0.136571 | + | 0.774535i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1696.42 | + | 1382.89i | 0.217744 | + | 0.177501i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2533.96 | − | 4388.95i | 0.322778 | − | 0.559068i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7192.58 | − | 12457.9i | −0.909283 | − | 1.57492i | −0.815062 | − | 0.579373i | \(-0.803297\pi\) |
−0.0942206 | − | 0.995551i | \(-0.530036\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6609.71 | − | 5708.10i | 0.829322 | − | 0.716197i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11581.1 | + | 4215.16i | −1.44222 | + | 0.524926i | −0.940407 | − | 0.340050i | \(-0.889556\pi\) |
−0.501814 | + | 0.864976i | \(0.667334\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2087.84 | − | 11840.7i | −0.258071 | − | 1.46359i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1431.19 | + | 12100.5i | −0.175596 | + | 1.48464i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3404.17 | − | 19306.0i | −0.414590 | − | 2.35126i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8895.19 | + | 3237.58i | −1.07540 | + | 0.391414i | −0.818194 | − | 0.574943i | \(-0.805024\pi\) |
−0.257207 | + | 0.966356i | \(0.582802\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −674.980 | + | 582.908i | −0.0810080 | + | 0.0699580i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2881.35 | + | 4990.65i | 0.343298 | + | 0.594609i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 394.820 | − | 683.849i | 0.0467011 | − | 0.0808888i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1520.20 | + | 1239.24i | 0.178525 | + | 0.145530i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2393.77 | + | 13575.7i | −0.279101 | + | 1.58286i | 0.446526 | + | 0.894771i | \(0.352661\pi\) |
−0.725627 | + | 0.688089i | \(0.758450\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6924.37 | + | 5810.23i | −0.801598 | + | 0.672621i | −0.948587 | − | 0.316517i | \(-0.897486\pi\) |
0.146988 | + | 0.989138i | \(0.453042\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1594.77 | − | 1417.26i | 0.183310 | − | 0.162907i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5142.52 | + | 1871.72i | 0.586939 | + | 0.213628i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6271.10 | − | 5262.08i | −0.710726 | − | 0.596370i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9697.36 | + | 17361.1i | −1.09136 | + | 1.95385i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7656.71 | 0.855709 | 0.427855 | − | 0.903848i | \(-0.359269\pi\) | ||||
0.427855 | + | 0.903848i | \(0.359269\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15823.7 | 1.75620 | 0.878102 | − | 0.478473i | \(-0.158810\pi\) | ||||
0.878102 | + | 0.478473i | \(0.158810\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12574.6 | + | 178.588i | −1.38599 | + | 0.0196842i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9975.71 | − | 8370.62i | −1.09200 | − | 0.916295i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8402.95 | − | 3058.42i | −0.913556 | − | 0.332507i | −0.157884 | − | 0.987458i | \(-0.550467\pi\) |
−0.755672 | + | 0.654951i | \(0.772689\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3692.31 | + | 1463.93i | −0.398695 | + | 0.158074i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.8250 | + | 21.6698i | −0.00276972 | + | 0.00232407i | −0.644171 | − | 0.764881i | \(-0.722798\pi\) |
0.641402 | + | 0.767205i | \(0.278353\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1974.81 | + | 11199.7i | −0.210371 | + | 1.19307i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4951.20 | − | 1882.13i | 0.523900 | − | 0.199154i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6809.18 | − | 11793.8i | 0.715691 | − | 1.23961i | −0.247002 | − | 0.969015i | \(-0.579445\pi\) |
0.962693 | − | 0.270597i | \(-0.0872212\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3814.69 | − | 6607.24i | −0.398285 | − | 0.689851i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5195.44 | − | 1807.85i | −0.538859 | − | 0.187506i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24536.4 | − | 8930.51i | 2.52809 | − | 0.920151i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1345.77 | − | 7632.27i | −0.137752 | − | 0.781230i | −0.972904 | − | 0.231211i | \(-0.925731\pi\) |
0.835152 | − | 0.550020i | \(-0.185380\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2301.04 | + | 4409.17i | −0.233994 | + | 0.448372i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −612.250 | − | 3472.24i | −0.0618553 | − | 0.350799i | −0.999990 | − | 0.00452774i | \(-0.998559\pi\) |
0.938134 | − | 0.346271i | \(-0.112552\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 430.400 | − | 156.653i | 0.0432017 | − | 0.0157241i | −0.320329 | − | 0.947306i | \(-0.603793\pi\) |
0.363531 | + | 0.931582i | \(0.381571\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2776.42 | − | 14535.7i | −0.276889 | − | 1.44962i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2690.34 | + | 4659.80i | 0.266582 | + | 0.461734i | 0.967977 | − | 0.251039i | \(-0.0807722\pi\) |
−0.701395 | + | 0.712773i | \(0.747439\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 870.590 | − | 1507.91i | 0.0857145 | − | 0.148462i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 739.440 | − | 4572.35i | 0.0723388 | − | 0.447310i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3317.03 | + | 18811.8i | −0.322446 | + | 1.82868i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8978.00 | + | 7533.44i | −0.867240 | + | 0.727701i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2512.04 | − | 4651.22i | 0.241128 | − | 0.446467i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8832.30 | + | 3214.70i | 0.842502 | + | 0.306646i | 0.726979 | − | 0.686659i | \(-0.240924\pi\) |
0.115522 | + | 0.993305i | \(0.463146\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19539.0 | + | 16395.2i | 1.85219 | + | 1.55417i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10107.6 | + | 16946.4i | 0.952196 | + | 1.59646i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9313.63 | −0.871979 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8531.94 | −0.793879 | −0.396939 | − | 0.917845i | \(-0.629928\pi\) | ||||
−0.396939 | + | 0.917845i | \(0.629928\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3357.68 | + | 5629.51i | 0.310511 | + | 0.520604i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13067.3 | − | 10964.8i | −1.20106 | − | 1.00781i | −0.999599 | − | 0.0283132i | \(-0.990986\pi\) |
−0.201462 | − | 0.979496i | \(-0.564569\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4823.53 | − | 1755.62i | −0.440651 | − | 0.160384i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11630.9 | + | 21535.5i | −1.05610 | + | 1.95545i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12397.7 | − | 10402.9i | 1.11894 | − | 0.938904i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 678.059 | − | 3845.46i | 0.0608299 | − | 0.344983i | −0.939169 | − | 0.343455i | \(-0.888403\pi\) |
0.999999 | − | 0.00152782i | \(-0.000486322\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1475.70 | − | 9125.06i | 0.131596 | − | 0.813728i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8186.51 | − | 14179.5i | 0.725683 | − | 1.25692i | −0.233010 | − | 0.972474i | \(-0.574857\pi\) |
0.958692 | − | 0.284445i | \(-0.0918093\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −378.545 | − | 655.660i | −0.0333565 | − | 0.0577752i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2712.43 | − | 14200.7i | −0.237600 | − | 1.24393i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13457.6 | − | 4898.15i | 1.17190 | − | 0.426536i | 0.318564 | − | 0.947901i | \(-0.396799\pi\) |
0.853333 | + | 0.521366i | \(0.174577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2781.73 | + | 15776.0i | 0.240815 | + | 1.36573i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5713.61 | − | 8988.98i | −0.491739 | − | 0.773632i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5730.48 | + | 32499.2i | 0.490321 | + | 2.78075i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4027.14 | − | 1465.76i | 0.342579 | − | 0.124688i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17801.2 | + | 6194.28i | 1.50556 | + | 0.523890i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6002.38 | − | 10396.4i | −0.504739 | − | 0.874234i | −0.999985 | − | 0.00548128i | \(-0.998255\pi\) |
0.495246 | − | 0.868753i | \(-0.335078\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1823.72 | + | 3158.77i | −0.152477 | + | 0.264099i | −0.932138 | − | 0.362104i | \(-0.882058\pi\) |
0.779660 | + | 0.626203i | \(0.215392\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16599.5 | − | 6310.08i | 1.37992 | − | 0.524561i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1048.88 | − | 5948.51i | 0.0866983 | − | 0.491691i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13218.4 | − | 11091.6i | 1.08641 | − | 0.911610i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6533.41 | − | 2590.37i | 0.533947 | − | 0.211700i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9327.89 | + | 3395.07i | 0.758041 | + | 0.275904i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19873.3 | − | 16675.7i | −1.60598 | − | 1.34757i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10133.0 | − | 143.911i | 0.814286 | − | 0.0115647i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7978.38 | −0.637576 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7624.55 | 0.605924 | 0.302962 | − | 0.953003i | \(-0.402024\pi\) | ||||
0.302962 | + | 0.953003i | \(0.402024\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9776.61 | + | 17503.0i | −0.772661 | + | 1.38329i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24097.0 | + | 20219.8i | 1.89395 | + | 1.58921i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3960.55 | + | 1441.52i | 0.309582 | + | 0.112678i | 0.492139 | − | 0.870517i | \(-0.336215\pi\) |
−0.182557 | + | 0.983195i | \(0.558437\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7462.90 | + | 6632.25i | −0.580162 | + | 0.515587i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8421.10 | − | 7066.14i | 0.651090 | − | 0.546330i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1165.61 | − | 6610.50i | 0.0896324 | − | 0.508331i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24332.9 | + | 19835.8i | 1.86103 | + | 1.51708i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8126.05 | + | 14074.7i | −0.618154 | + | 1.07067i | 0.371669 | + | 0.928365i | \(0.378786\pi\) |
−0.989822 | + | 0.142308i | \(0.954548\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12426.7 | − | 21523.7i | −0.940241 | − | 1.62855i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7560.98 | + | 6529.61i | −0.569028 | + | 0.491409i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13643.5 | + | 4965.82i | −1.02132 | + | 0.371731i | −0.797770 | − | 0.602962i | \(-0.793987\pi\) |
−0.223551 | + | 0.974692i | \(0.571765\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3035.70 | + | 17216.3i | 0.226040 | + | 1.28194i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3700.33 | + | 15709.0i | 0.274073 | + | 1.16352i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 669.121 | + | 3794.77i | 0.0492988 | + | 0.279587i | 0.999485 | − | 0.0320961i | \(-0.0102183\pi\) |
−0.950186 | + | 0.311683i | \(0.899107\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9021.71 | + | 3283.63i | −0.661203 | + | 0.240658i | −0.650756 | − | 0.759287i | \(-0.725548\pi\) |
−0.0104473 | + | 0.999945i | \(0.503326\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5346.96 | + | 4617.60i | −0.389830 | + | 0.336654i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13239.9 | − | 22932.1i | −0.960245 | − | 1.66319i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2519.05 | + | 4363.13i | −0.181750 | + | 0.314800i | −0.942476 | − | 0.334273i | \(-0.891509\pi\) |
0.760727 | + | 0.649072i | \(0.224843\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8465.88 | − | 6901.24i | −0.607651 | − | 0.495346i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 181.615 | − | 1029.99i | 0.0129685 | − | 0.0735478i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8134.16 | − | 6825.37i | 0.577843 | − | 0.484868i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6418.23 | − | 31191.6i | −0.453609 | − | 2.20447i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26587.6 | − | 9677.08i | −1.86948 | − | 0.680436i | −0.969806 | − | 0.243878i | \(-0.921580\pi\) |
−0.899676 | − | 0.436558i | \(-0.856197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9909.36 | + | 8314.94i | 0.693223 | + | 0.581683i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3775.39 | + | 6759.05i | −0.262773 | + | 0.470440i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6418.01 | −0.444446 | −0.222223 | − | 0.974996i | \(-0.571331\pi\) | ||||
−0.222223 | + | 0.974996i | \(0.571331\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13117.6 | 0.903815 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5584.65 | + | 79.3146i | −0.382855 | + | 0.00543740i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19148.7 | − | 16067.6i | −1.30616 | − | 1.09600i | −0.989045 | − | 0.147617i | \(-0.952840\pi\) |
−0.317120 | − | 0.948385i | \(-0.602716\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4731.73 | + | 1722.21i | 0.321150 | + | 0.116889i | 0.497565 | − | 0.867427i | \(-0.334228\pi\) |
−0.176415 | + | 0.984316i | \(0.556450\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1664.84 | − | 1318.24i | −0.112434 | − | 0.0890264i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20619.6 | + | 17301.9i | −1.38563 | + | 1.16268i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2916.95 | + | 16542.9i | −0.195050 | + | 1.10618i | 0.717297 | + | 0.696768i | \(0.245379\pi\) |
−0.912347 | + | 0.409417i | \(0.865732\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15569.8 | + | 5918.66i | −1.03599 | + | 0.393820i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2787.97 | + | 4828.91i | −0.184598 | + | 0.319733i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6512.11 | − | 11279.3i | −0.429073 | − | 0.743176i | 0.567718 | − | 0.823223i | \(-0.307826\pi\) |
−0.996791 | + | 0.0800468i | \(0.974493\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11539.0 | + | 4015.22i | 0.756582 | + | 0.263267i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19391.5 | − | 7057.92i | 1.26527 | − | 0.460520i | 0.379735 | − | 0.925095i | \(-0.376015\pi\) |
0.885534 | + | 0.464575i | \(0.153793\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −905.701 | − | 5136.48i | −0.0588097 | − | 0.333526i | 0.941181 | − | 0.337904i | \(-0.109718\pi\) |
−0.999990 | + | 0.00437732i | \(0.998607\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22242.6 | − | 9186.36i | 1.43730 | − | 0.593617i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2615.65 | + | 14834.1i | 0.168208 | + | 0.953956i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10421.6 | − | 3793.13i | 0.666979 | − | 0.242761i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4014.02 | − | 21015.0i | −0.255669 | − | 1.33853i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6406.92 | + | 11097.1i | 0.406138 | + | 0.703451i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2190.76 | + | 3794.50i | −0.138213 | + | 0.239393i | −0.926820 | − | 0.375505i | \(-0.877469\pi\) |
0.788607 | + | 0.614898i | \(0.210803\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2436.75 | − | 15067.7i | 0.153005 | − | 0.946112i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2587.87 | + | 14676.6i | −0.161727 | + | 0.917199i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7952.02 | − | 6672.53i | 0.494616 | − | 0.415032i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10350.5 | − | 16806.5i | −0.640783 | − | 1.04046i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4363.85 | − | 1588.31i | −0.268895 | − | 0.0978697i | 0.204054 | − | 0.978960i | \(-0.434588\pi\) |
−0.472949 | + | 0.881090i | \(0.656810\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7650.57 | + | 6419.59i | 0.469221 | + | 0.393723i | 0.846510 | − | 0.532372i | \(-0.178699\pi\) |
−0.377289 | + | 0.926095i | \(0.623144\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15669.6 | − | 26271.7i | −0.956571 | − | 1.60379i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27979.8 | 1.70016 | 0.850078 | − | 0.526658i | \(-0.176555\pi\) | ||||
0.850078 | + | 0.526658i | \(0.176555\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14117.5 | 0.853866 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10040.4 | − | 16833.7i | −0.604474 | − | 1.01346i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17499.4 | − | 14683.7i | −1.04871 | − | 0.879968i | −0.0557484 | − | 0.998445i | \(-0.517754\pi\) |
−0.992957 | + | 0.118477i | \(0.962199\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6615.70 | − | 2407.92i | −0.394652 | − | 0.143641i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19529.3 | − | 554.831i | 1.15968 | − | 0.0329468i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21442.2 | − | 17992.2i | 1.26748 | − | 1.06354i | 0.272638 | − | 0.962117i | \(-0.412104\pi\) |
0.994843 | − | 0.101427i | \(-0.0323407\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5005.68 | + | 28388.6i | −0.294551 | + | 1.67048i | 0.374469 | + | 0.927239i | \(0.377825\pi\) |
−0.669021 | + | 0.743244i | \(0.733286\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2075.10 | − | 12831.5i | 0.121554 | − | 0.751634i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14046.2 | + | 24328.8i | −0.819083 | + | 1.41869i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12418.6 | + | 21509.7i | 0.720915 | + | 1.24866i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.9911 | + | 141.309i | 0.00155984 | + | 0.00816639i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18845.4 | + | 6859.18i | −1.08423 | + | 0.394629i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3476.92 | − | 19718.6i | −0.199146 | − | 1.12941i | −0.906390 | − | 0.422443i | \(-0.861173\pi\) |
0.707244 | − | 0.706970i | \(-0.249938\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4665.90 | − | 21149.5i | −0.266060 | − | 1.20599i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4675.19 | − | 26514.3i | −0.265409 | − | 1.50521i | −0.767867 | − | 0.640609i | \(-0.778682\pi\) |
0.502458 | − | 0.864602i | \(-0.332429\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11592.0 | + | 4219.14i | −0.655169 | + | 0.238462i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17428.3 | − | 6064.51i | −0.980696 | − | 0.341252i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10823.6 | + | 18747.1i | 0.606376 | + | 1.05027i | 0.991832 | + | 0.127548i | \(0.0407108\pi\) |
−0.385456 | + | 0.922726i | \(0.625956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1434.39 | − | 2484.44i | 0.0800079 | − | 0.138578i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12568.5 | + | 4777.74i | −0.697987 | + | 0.265331i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2399.04 | + | 13605.6i | −0.132650 | + | 0.752297i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10158.7 | + | 8524.19i | −0.559271 | + | 0.469284i | −0.878066 | − | 0.478539i | \(-0.841166\pi\) |
0.318795 | + | 0.947824i | \(0.396722\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4720.42 | + | 32072.5i | −0.258750 | + | 1.75806i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5928.49 | − | 2157.79i | −0.323569 | − | 0.117769i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3820.16 | + | 3205.50i | 0.207603 | + | 0.174199i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22361.6 | + | 317.585i | −1.21001 | + | 0.0171848i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20645.6 | −1.11237 | −0.556187 | − | 0.831057i | \(-0.687736\pi\) | ||||
−0.556187 | + | 0.831057i | \(0.687736\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27441.9 | −1.47225 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3346.71 | + | 5991.59i | −0.178786 | + | 0.320080i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −768.165 | − | 644.567i | −0.0408626 | − | 0.0342878i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7122.25 | + | 2592.29i | 0.377266 | + | 0.137314i | 0.523691 | − | 0.851908i | \(-0.324555\pi\) |
−0.146425 | + | 0.989222i | \(0.546777\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7769.24 | − | 2580.36i | −0.409802 | − | 0.136106i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22389.0 | + | 18786.6i | −1.17598 | + | 0.986763i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11107.7 | − | 62995.1i | 0.580987 | − | 3.29494i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7612.82 | − | 6205.84i | −0.396522 | − | 0.323238i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −947.326 | + | 1640.82i | −0.0491367 | + | 0.0851073i | −0.889548 | − | 0.456842i | \(-0.848980\pi\) |
0.840411 | + | 0.541950i | \(0.182314\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21854.7 | + | 37853.4i | 1.12886 | + | 1.95525i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6666.55 | + | 5757.19i | −0.342921 | + | 0.296144i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21005.1 | − | 7645.22i | 1.07601 | − | 0.391636i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3900.92 | + | 22123.2i | 0.199006 | + | 1.12862i | 0.906598 | + | 0.421996i | \(0.138670\pi\) |
−0.707592 | + | 0.706621i | \(0.750219\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19611.6 | − | 1675.11i | 0.996372 | − | 0.0851046i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2168.14 | − | 12296.1i | −0.109701 | − | 0.622146i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4541.24 | − | 1652.88i | 0.228833 | − | 0.0832883i | −0.225059 | − | 0.974345i | \(-0.572257\pi\) |
0.453892 | + | 0.891057i | \(0.350035\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9669.78 | − | 8350.76i | 0.485272 | − | 0.419078i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2132.77 | − | 3694.07i | −0.106597 | − | 0.184631i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3014.98 | + | 5222.09i | −0.150078 | + | 0.259943i | −0.931256 | − | 0.364366i | \(-0.881286\pi\) |
0.781178 | + | 0.624309i | \(0.214619\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21576.1 | + | 17588.5i | 1.06966 | + | 0.871969i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2481.91 | − | 14075.6i | 0.122547 | − | 0.694999i | −0.860187 | − | 0.509978i | \(-0.829654\pi\) |
0.982735 | − | 0.185021i | \(-0.0592354\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13052.2 | + | 10952.1i | −0.641874 | + | 0.538596i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1210.54 | − | 402.051i | −0.0592922 | − | 0.0196925i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −32289.0 | − | 11752.2i | −1.57519 | − | 0.573321i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 125.354 | + | 105.185i | 0.00609088 | + | 0.00511085i | 0.645828 | − | 0.763483i | \(-0.276512\pi\) |
−0.639737 | + | 0.768594i | \(0.720957\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 413.894 | − | 740.991i | 0.0200307 | − | 0.0358608i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17695.1 | 0.852966 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1044.73 | 0.0501604 | 0.0250802 | − | 0.999685i | \(-0.492016\pi\) | ||||
0.0250802 | + | 0.999685i | \(0.492016\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 48334.1 | − | 686.453i | 2.31149 | − | 0.0328283i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10258.8 | + | 8608.15i | 0.488674 | + | 0.410046i | 0.853551 | − | 0.521009i | \(-0.174444\pi\) |
−0.364877 | + | 0.931056i | \(0.618889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39151.5 | + | 14250.0i | 1.85764 | + | 0.676125i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2329.52 | − | 15827.7i | 0.110097 | − | 0.748043i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14070.8 | + | 11806.8i | −0.662409 | + | 0.555827i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1313.03 | − | 7446.58i | 0.0615724 | − | 0.349194i | −0.938421 | − | 0.345495i | \(-0.887711\pi\) |
0.999993 | − | 0.00369990i | \(-0.00117772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8726.84 | + | 3317.40i | −0.407639 | + | 0.154959i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9922.23 | − | 17185.8i | 0.461679 | − | 0.799652i | −0.537366 | − | 0.843349i | \(-0.680581\pi\) |
0.999045 | + | 0.0436977i | \(0.0139138\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13151.8 | + | 22779.6i | 0.609583 | + | 1.05583i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 39271.1 | + | 13665.1i | 1.81318 | + | 0.630931i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10035.7 | + | 3652.71i | −0.461576 | + | 0.168000i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6884.76 | − | 39045.4i | −0.315437 | − | 1.78893i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4376.48 | + | 19837.6i | 0.199748 | + | 0.905414i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2587.18 | + | 14672.6i | 0.117631 | + | 0.667120i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32270.1 | − | 11745.3i | 1.46163 | − | 0.531990i | 0.515817 | − | 0.856699i | \(-0.327489\pi\) |
0.945814 | + | 0.324709i | \(0.105266\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3488.73 | + | 18264.9i | 0.157417 | + | 0.824141i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11577.4 | + | 20052.6i | 0.520411 | + | 0.901378i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13046.6 | − | 22597.5i | 0.584237 | − | 1.01193i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2714.65 | + | 16786.1i | −0.121105 | + | 0.748859i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3574.73 | + | 20273.3i | −0.158875 | + | 0.901024i | 0.796282 | + | 0.604925i | \(0.206797\pi\) |
−0.955157 | + | 0.296099i | \(0.904314\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2145.87 | + | 1800.60i | −0.0950130 | + | 0.0797253i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18363.3 | − | 521.705i | 0.810032 | − | 0.0230132i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36877.4 | + | 13422.3i | 1.62064 | + | 0.589866i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −48621.9 | − | 40798.7i | −2.12882 | − | 1.78629i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2876.02 | + | 4821.96i | 0.125453 | + | 0.210336i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13618.5 | 0.591845 | 0.295922 | − | 0.955212i | \(-0.404373\pi\) | ||||
0.295922 | + | 0.955212i | \(0.404373\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23405.4 | −1.01341 | −0.506704 | − | 0.862120i | \(-0.669136\pi\) | ||||
−0.506704 | + | 0.862120i | \(0.669136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20916.9 | − | 35069.3i | −0.902320 | − | 1.51284i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16151.9 | − | 13553.1i | −0.694206 | − | 0.582508i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25126.9 | + | 9145.43i | 1.07598 | + | 0.391626i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22118.3 | − | 35914.3i | −0.943682 | − | 1.53229i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16317.5 | + | 13692.0i | −0.693647 | + | 0.582039i | −0.919958 | − | 0.392016i | \(-0.871778\pi\) |
0.226311 | + | 0.974055i | \(0.427333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5338.93 | − | 30278.6i | 0.226128 | − | 1.28244i | −0.634389 | − | 0.773014i | \(-0.718748\pi\) |
0.860517 | − | 0.509422i | \(-0.170141\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6945.29 | − | 42946.5i | 0.293096 | − | 1.81237i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9905.43 | + | 17156.7i | −0.416500 | + | 0.721399i | −0.995585 | − | 0.0938682i | \(-0.970077\pi\) |
0.579085 | + | 0.815267i | \(0.303410\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17037.8 | + | 29510.4i | 0.713811 | + | 1.23636i | 0.963416 | + | 0.268009i | \(0.0863656\pi\) |
−0.249606 | + | 0.968348i | \(0.580301\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5929.97 | + | 31045.7i | 0.247543 | + | 1.29599i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4900.49 | − | 1783.63i | 0.203832 | − | 0.0741887i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5163.25 | + | 29282.3i | 0.213990 | + | 1.21360i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22094.6 | + | 9125.26i | −0.912428 | + | 0.376840i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1352.26 | − | 7669.05i | −0.0556439 | − | 0.315572i | 0.944263 | − | 0.329191i | \(-0.106776\pi\) |
−0.999907 | + | 0.0136189i | \(0.995665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3216.03 | − | 1170.54i | 0.131864 | − | 0.0479945i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −27228.1 | − | 9474.56i | −1.11244 | − | 0.387095i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23252.6 | + | 40274.7i | 0.946643 | + | 1.63963i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17825.8 | + | 30875.2i | −0.723143 | + | 1.25252i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27278.9 | + | 10369.7i | −1.10272 | + | 0.419185i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10766.5 | − | 61059.6i | 0.433689 | − | 2.45957i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28259.9 | − | 23712.9i | 1.13435 | − | 0.951834i | 0.135112 | − | 0.990830i | \(-0.456861\pi\) |
0.999239 | + | 0.0389967i | \(0.0124162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 26860.8 | + | 21268.7i | 1.07441 | + | 0.850730i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3050.77 | + | 1110.39i | 0.121601 | + | 0.0442592i | 0.402104 | − | 0.915594i | \(-0.368279\pi\) |
−0.280503 | + | 0.959853i | \(0.590501\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3091.57 | + | 2594.14i | 0.122798 | + | 0.103039i | 0.702118 | − | 0.712060i | \(-0.252238\pi\) |
−0.579321 | + | 0.815100i | \(0.696682\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16180.7 | − | 229.802i | 0.640460 | − | 0.00909596i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24524.1 | 0.967334 | 0.483667 | − | 0.875252i | \(-0.339305\pi\) | ||||
0.483667 | + | 0.875252i | \(0.339305\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −60629.0 | −2.38318 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9264.74 | + | 16586.6i | −0.362915 | + | 0.649724i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12597.0 | − | 10570.1i | −0.491742 | − | 0.412621i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5215.17 | + | 1898.17i | 0.202881 | + | 0.0738426i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3032.23 | + | 14736.2i | 0.117555 | + | 0.571299i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8326.43 | + | 6986.71i | −0.321697 | + | 0.269936i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6912.31 | + | 39201.6i | −0.266148 | + | 1.50940i | 0.499597 | + | 0.866258i | \(0.333481\pi\) |
−0.765746 | + | 0.643144i | \(0.777630\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24209.9 | + | 19735.5i | 0.928987 | + | 0.757295i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24739.8 | − | 42850.6i | 0.946090 | − | 1.63868i | 0.192536 | − | 0.981290i | \(-0.438329\pi\) |
0.753554 | − | 0.657386i | \(-0.228338\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13884.6 | − | 24048.9i | −0.529167 | − | 0.916544i | −0.999421 | − | 0.0340133i | \(-0.989171\pi\) |
0.470254 | − | 0.882531i | \(-0.344162\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17110.3 | + | 14776.4i | −0.649896 | + | 0.561246i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4131.95 | − | 1503.91i | 0.156412 | − | 0.0569292i | −0.262628 | − | 0.964897i | \(-0.584589\pi\) |
0.419039 | + | 0.907968i | \(0.362367\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3427.65 | + | 19439.2i | 0.129313 | + | 0.733373i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37860.5 | + | 11391.3i | 1.42354 | + | 0.428310i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1041.73 | − | 5907.94i | −0.0390371 | − | 0.221390i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30632.3 | + | 11149.2i | −1.14405 | + | 0.416400i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −47600.3 | + | 41107.3i | −1.77183 | + | 1.53014i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12336.0 | − | 21366.6i | −0.457652 | − | 0.792676i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3470.30 | + | 6010.74i | −0.128316 | + | 0.222249i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −31404.0 | − | 25600.0i | −1.15732 | − | 0.943427i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11198.5 | − | 63510.0i | 0.411327 | − | 2.33275i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9794.91 | − | 8218.90i | 0.358583 | − | 0.300887i | −0.445643 | − | 0.895211i | \(-0.647025\pi\) |
0.804226 | + | 0.594324i | \(0.202580\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −914.152 | + | 812.403i | −0.0333559 | + | 0.0296432i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22355.4 | − | 8136.70i | −0.813027 | − | 0.295918i | −0.0981533 | − | 0.995171i | \(-0.531294\pi\) |
−0.714874 | + | 0.699254i | \(0.753516\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1962.76 | − | 1646.95i | −0.0711478 | − | 0.0597001i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15661.3 | − | 28038.3i | 0.565844 | − | 1.01303i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9324.88 | −0.335807 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15288.8 | −0.548782 | −0.274391 | − | 0.961618i | \(-0.588476\pi\) | ||||
−0.274391 | + | 0.961618i | \(0.588476\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9972.72 | − | 141.635i | 0.356800 | − | 0.00506735i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39516.7 | + | 33158.5i | 1.40922 | + | 1.18248i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −52435.3 | − | 19084.9i | −1.86385 | − | 0.678387i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 49555.1 | − | 19647.6i | 1.75577 | − | 0.696129i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5701.58 | − | 4784.19i | 0.201359 | − | 0.168961i | −0.536532 | − | 0.843880i | \(-0.680266\pi\) |
0.737892 | + | 0.674919i | \(0.235822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1939.36 | + | 10998.7i | −0.0682707 | + | 0.387183i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −37309.9 | + | 14182.9i | −1.30919 | + | 0.497671i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16067.8 | − | 27830.2i | 0.562002 | − | 0.973417i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25673.1 | − | 44467.1i | −0.895095 | − | 1.55035i | −0.833687 | − | 0.552237i | \(-0.813774\pi\) |
−0.0614078 | − | 0.998113i | \(-0.519559\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −44100.4 | − | 15345.6i | −1.53265 | − | 0.533317i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18838.6 | − | 6856.68i | 0.652625 | − | 0.237536i | 0.00557575 | − | 0.999984i | \(-0.498225\pi\) |
0.647049 | + | 0.762449i | \(0.276003\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4190.07 | − | 23763.1i | −0.144695 | − | 0.820607i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −27848.3 | − | 43812.6i | −0.958630 | − | 1.50817i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5554.84 | + | 31503.0i | 0.190610 | + | 1.08100i | 0.918533 | + | 0.395345i | \(0.129375\pi\) |
−0.727922 | + | 0.685660i | \(0.759514\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47981.0 | + | 17463.6i | −1.64123 | + | 0.597359i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4113.35 | + | 21535.0i | 0.140257 | + | 0.734301i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13941.4 | + | 24147.2i | 0.473878 | + | 0.820780i | 0.999553 | − | 0.0299051i | \(-0.00952051\pi\) |
−0.525675 | + | 0.850686i | \(0.676187\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11362.8 | − | 19680.9i | 0.385017 | − | 0.666869i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6514.48 | + | 40282.5i | −0.220045 | + | 1.36066i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 659.814 | − | 3741.99i | 0.0222174 | − | 0.126001i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −581.184 | + | 487.672i | −0.0195087 | + | 0.0163698i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19914.4 | + | 36872.9i | −0.666388 | + | 1.23387i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33015.2 | + | 12016.5i | 1.10134 | + | 0.400856i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25894.2 | − | 21727.8i | −0.861119 | − | 0.722565i | 0.101090 | − | 0.994877i | \(-0.467767\pi\) |
−0.962209 | + | 0.272312i | \(0.912212\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7163.55 | + | 12010.5i | 0.237489 | + | 0.398175i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10379.3 | −0.343036 | −0.171518 | − | 0.985181i | \(-0.554867\pi\) | ||||
−0.171518 | + | 0.985181i | \(0.554867\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8356.25 | −0.275323 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 28994.9 | + | 48613.1i | 0.952390 | + | 1.59678i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10729.8 | − | 9003.36i | −0.351358 | − | 0.294824i | 0.449977 | − | 0.893040i | \(-0.351432\pi\) |
−0.801335 | + | 0.598216i | \(0.795876\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34675.7 | + | 12620.9i | 1.13201 | + | 0.412019i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24146.8 | − | 44709.6i | 0.785881 | − | 1.45512i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24025.0 | + | 20159.4i | −0.779532 | + | 0.654105i | −0.943131 | − | 0.332422i | \(-0.892134\pi\) |
0.163599 | + | 0.986527i | \(0.447690\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4324.48 | − | 24525.3i | 0.139888 | − | 0.793343i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1451.17 | + | 8973.37i | −0.0467997 | + | 0.289387i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30207.2 | + | 52320.4i | −0.971217 | + | 1.68220i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13380.0 | − | 23174.8i | −0.428889 | − | 0.742858i | 0.567885 | − | 0.823108i | \(-0.307762\pi\) |
−0.996775 | + | 0.0802493i | \(0.974428\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4631.06 | + | 24245.5i | 0.147998 | + | 0.774830i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16882.5 | − | 6144.73i | 0.537901 | − | 0.195780i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2457.75 | + | 13938.6i | 0.0780718 | + | 0.442767i | 0.998638 | + | 0.0521799i | \(0.0166169\pi\) |
−0.920566 | + | 0.390587i | \(0.872272\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23462.4 | − | 44957.8i | 0.743061 | − | 1.42383i |
(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 | 108.4.i.a.13.7 | ✓ | 54 | |
3.2 | odd | 2 | 324.4.i.a.253.8 | 54 | |||
27.2 | odd | 18 | 324.4.i.a.73.8 | 54 | |||
27.25 | even | 9 | inner | 108.4.i.a.25.7 | yes | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.i.a.13.7 | ✓ | 54 | 1.1 | even | 1 | trivial | |
108.4.i.a.25.7 | yes | 54 | 27.25 | even | 9 | inner | |
324.4.i.a.73.8 | 54 | 27.2 | odd | 18 | |||
324.4.i.a.253.8 | 54 | 3.2 | odd | 2 |