Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(17,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.g (of order \(8\), degree \(4\), not 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: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 49.8 | ||
Character | \(\chi\) | \(=\) | 128.49 |
Dual form | 128.4.g.a.81.8 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 2.66269 | − | 1.10292i | 0.512435 | − | 0.212258i | −0.111455 | − | 0.993769i | \(-0.535551\pi\) |
0.623890 | + | 0.781512i | \(0.285551\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.50788 | + | 13.2972i | −0.492640 | + | 1.18934i | 0.460732 | + | 0.887539i | \(0.347587\pi\) |
−0.953372 | + | 0.301798i | \(0.902413\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.48055 | + | 6.48055i | 0.349917 | + | 0.349917i | 0.860079 | − | 0.510162i | \(-0.170414\pi\) |
−0.510162 | + | 0.860079i | \(0.670414\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −13.2184 | + | 13.2184i | −0.489570 | + | 0.489570i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −49.3605 | − | 20.4458i | −1.35298 | − | 0.560422i | −0.415858 | − | 0.909430i | \(-0.636519\pi\) |
−0.937120 | + | 0.349008i | \(0.886519\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.4409 | + | 51.7628i | 0.457433 | + | 1.10434i | 0.969433 | + | 0.245355i | \(0.0789045\pi\) |
−0.512001 | + | 0.858985i | \(0.671096\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 41.4811i | 0.714025i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.73808i | 0.0533305i | 0.999644 | + | 0.0266653i | \(0.00848882\pi\) | ||||
−0.999644 | + | 0.0266653i | \(0.991511\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 36.7064 | + | 88.6171i | 0.443212 | + | 1.07001i | 0.974815 | + | 0.223015i | \(0.0715899\pi\) |
−0.531603 | + | 0.846994i | \(0.678410\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 24.4033 | + | 10.1082i | 0.253582 | + | 0.105037i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 45.4559 | − | 45.4559i | 0.412097 | − | 0.412097i | −0.470372 | − | 0.882468i | \(-0.655880\pi\) |
0.882468 | + | 0.470372i | \(0.155880\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −58.0905 | − | 58.0905i | −0.464724 | − | 0.464724i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −50.3966 | + | 121.668i | −0.359216 | + | 0.867223i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 51.9617 | − | 21.5233i | 0.332726 | − | 0.137820i | −0.210065 | − | 0.977687i | \(-0.567368\pi\) |
0.542791 | + | 0.839868i | \(0.317368\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 73.5204 | 0.425957 | 0.212978 | − | 0.977057i | \(-0.431684\pi\) | ||||
0.212978 | + | 0.977057i | \(0.431684\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −153.982 | −0.812267 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −121.867 | + | 50.4791i | −0.588552 | + | 0.243786i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −165.530 | + | 399.624i | −0.735485 | + | 1.77562i | −0.112109 | + | 0.993696i | \(0.535760\pi\) |
−0.623376 | + | 0.781922i | \(0.714240\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 114.181 | + | 114.181i | 0.468809 | + | 0.468809i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 334.781 | − | 334.781i | 1.27522 | − | 1.27522i | 0.331906 | − | 0.943312i | \(-0.392308\pi\) |
0.943312 | − | 0.331906i | \(-0.107692\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −328.962 | − | 136.261i | −1.16666 | − | 0.483245i | −0.286570 | − | 0.958059i | \(-0.592515\pi\) |
−0.880086 | + | 0.474814i | \(0.842515\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −102.962 | − | 248.573i | −0.341083 | − | 0.823446i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 185.755i | − | 0.576492i | −0.957556 | − | 0.288246i | \(-0.906928\pi\) | ||
0.957556 | − | 0.288246i | \(-0.0930721\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 259.005i | − | 0.755116i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.12282 | + | 9.95337i | 0.0113198 | + | 0.0273284i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 412.832 | + | 171.001i | 1.06994 | + | 0.443184i | 0.846970 | − | 0.531641i | \(-0.178424\pi\) |
0.222971 | + | 0.974825i | \(0.428424\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 543.744 | − | 543.744i | 1.33306 | − | 1.33306i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 195.476 | + | 195.476i | 0.454235 | + | 0.454235i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 214.856 | − | 518.709i | 0.474100 | − | 1.14458i | −0.488235 | − | 0.872712i | \(-0.662359\pi\) |
0.962335 | − | 0.271867i | \(-0.0876410\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 85.1187 | − | 35.2573i | 0.178661 | − | 0.0740038i | −0.291560 | − | 0.956553i | \(-0.594174\pi\) |
0.470221 | + | 0.882549i | \(0.344174\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −171.325 | −0.342618 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −806.394 | −1.53878 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 252.042 | − | 104.399i | 0.459579 | − | 0.190364i | −0.140868 | − | 0.990028i | \(-0.544989\pi\) |
0.600447 | + | 0.799665i | \(0.294989\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 70.9008 | − | 171.170i | 0.123702 | − | 0.298643i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −430.147 | − | 430.147i | −0.719001 | − | 0.719001i | 0.249400 | − | 0.968401i | \(-0.419767\pi\) |
−0.968401 | + | 0.249400i | \(0.919767\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 41.8371 | − | 41.8371i | 0.0670775 | − | 0.0670775i | −0.672772 | − | 0.739850i | \(-0.734897\pi\) |
0.739850 | + | 0.672772i | \(0.234897\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −218.746 | − | 90.6077i | −0.336782 | − | 0.139500i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −187.383 | − | 452.383i | −0.277329 | − | 0.669531i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1211.19i | 1.72493i | 0.506119 | + | 0.862464i | \(0.331080\pi\) | ||||
−0.506119 | + | 0.862464i | \(0.668920\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 125.180i | − | 0.171715i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 290.920 | + | 702.342i | 0.384730 | + | 0.928820i | 0.991037 | + | 0.133589i | \(0.0426504\pi\) |
−0.606307 | + | 0.795231i | \(0.707350\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −49.7061 | − | 20.5889i | −0.0634280 | − | 0.0262727i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 114.620 | − | 114.620i | 0.141247 | − | 0.141247i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 365.332 | + | 365.332i | 0.435113 | + | 0.435113i | 0.890363 | − | 0.455250i | \(-0.150450\pi\) |
−0.455250 | + | 0.890363i | \(0.650450\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −196.503 | + | 474.400i | −0.226364 | + | 0.546491i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 195.762 | − | 81.0874i | 0.218275 | − | 0.0904126i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1380.53 | −1.49095 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 508.891 | 0.532681 | 0.266340 | − | 0.963879i | \(-0.414185\pi\) | ||||
0.266340 | + | 0.963879i | \(0.414185\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 922.727 | − | 382.206i | 0.936743 | − | 0.388012i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −184.802 | + | 446.152i | −0.182065 | + | 0.439543i | −0.988392 | − | 0.151927i | \(-0.951452\pi\) |
0.806327 | + | 0.591470i | \(0.201452\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 610.875 | + | 610.875i | 0.584382 | + | 0.584382i | 0.936104 | − | 0.351722i | \(-0.114404\pi\) |
−0.351722 | + | 0.936104i | \(0.614404\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −268.821 | + | 268.821i | −0.249849 | + | 0.249849i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −603.347 | − | 249.914i | −0.545119 | − | 0.225796i | 0.0930915 | − | 0.995658i | \(-0.470325\pi\) |
−0.638211 | + | 0.769862i | \(0.720325\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −271.916 | − | 656.462i | −0.238943 | − | 0.576860i | 0.758231 | − | 0.651986i | \(-0.226064\pi\) |
−0.997174 | + | 0.0751265i | \(0.976064\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1246.64i | 1.06600i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1651.29i | 1.37469i | 0.726329 | + | 0.687347i | \(0.241225\pi\) | ||||
−0.726329 | + | 0.687347i | \(0.758775\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 354.071 | + | 854.803i | 0.287107 | + | 0.693137i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −967.635 | − | 400.807i | −0.764597 | − | 0.316707i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.2248 | + | 24.2248i | −0.0186612 | + | 0.0186612i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1077.27 | + | 1077.27i | 0.809369 | + | 0.809369i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 522.180 | − | 1260.66i | 0.382792 | − | 0.924142i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −569.754 | + | 236.000i | −0.407683 | + | 0.168868i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −313.499 | −0.219044 | −0.109522 | − | 0.993984i | \(-0.534932\pi\) | ||||
−0.109522 | + | 0.993984i | \(0.534932\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1026.21 | −0.700408 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −516.522 | + | 213.951i | −0.344494 | + | 0.142694i | −0.548221 | − | 0.836334i | \(-0.684695\pi\) |
0.203726 | + | 0.979028i | \(0.434695\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −336.410 | + | 812.166i | −0.219327 | + | 0.529501i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1340.27 | − | 1340.27i | −0.854458 | − | 0.854458i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 544.876 | − | 544.876i | 0.339795 | − | 0.339795i | −0.516495 | − | 0.856290i | \(-0.672764\pi\) |
0.856290 | + | 0.516495i | \(0.172764\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2149.49 | + | 890.348i | 1.31164 | + | 0.543297i | 0.925361 | − | 0.379086i | \(-0.123762\pi\) |
0.386275 | + | 0.922384i | \(0.373762\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −204.873 | − | 494.608i | −0.122365 | − | 0.295415i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2993.41i | − | 1.75050i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 809.493i | 0.463619i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −285.662 | − | 689.650i | −0.160279 | − | 0.386948i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1483.83 | + | 614.624i | 0.815841 | + | 0.337932i | 0.751282 | − | 0.659982i | \(-0.229436\pi\) |
0.0645591 | + | 0.997914i | \(0.479436\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2047.66 | + | 2047.66i | −1.10355 | + | 1.10355i | −0.109572 | + | 0.993979i | \(0.534948\pi\) |
−0.993979 | + | 0.109572i | \(0.965052\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −49.4115 | − | 49.4115i | −0.0261090 | − | 0.0261090i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −404.942 | + | 977.616i | −0.209843 | + | 0.506606i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1545.54 | − | 640.184i | 0.785653 | − | 0.325428i | 0.0464585 | − | 0.998920i | \(-0.485206\pi\) |
0.739194 | + | 0.673492i | \(0.235206\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1287.85 | 0.642345 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 589.159 | 0.288399 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1275.93 | − | 528.509i | 0.613121 | − | 0.253963i | −0.0544412 | − | 0.998517i | \(-0.517338\pi\) |
0.667562 | + | 0.744554i | \(0.267338\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 848.114 | − | 2047.53i | 0.400155 | − | 0.966060i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1744.38 | + | 1744.38i | 0.808287 | + | 0.808287i | 0.984375 | − | 0.176088i | \(-0.0563442\pi\) |
−0.176088 | + | 0.984375i | \(0.556344\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −666.164 | + | 666.164i | −0.303215 | + | 0.303215i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1656.58 | − | 686.176i | −0.740828 | − | 0.306861i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −286.418 | − | 691.473i | −0.125872 | − | 0.303883i | 0.848364 | − | 0.529414i | \(-0.177588\pi\) |
−0.974236 | + | 0.225531i | \(0.927588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 752.916i | − | 0.325229i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1618.13i | − | 0.687154i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −944.647 | − | 2280.58i | −0.394448 | − | 0.952282i | −0.988958 | − | 0.148194i | \(-0.952654\pi\) |
0.594510 | − | 0.804088i | \(-0.297346\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1523.13 | − | 630.902i | −0.625489 | − | 0.259086i | 0.0473461 | − | 0.998879i | \(-0.484924\pi\) |
−0.672835 | + | 0.739793i | \(0.734924\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 187.759 | − | 187.759i | 0.0758444 | − | 0.0758444i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4402.17 | − | 4402.17i | −1.74948 | − | 1.74948i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 76.4281 | − | 184.514i | 0.0298876 | − | 0.0721550i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1115.07 | + | 461.879i | −0.429152 | + | 0.177760i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1792.15 | 0.678931 | 0.339465 | − | 0.940619i | \(-0.389754\pi\) | ||||
0.339465 | + | 0.940619i | \(0.389754\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3221.65 | 1.20155 | 0.600776 | − | 0.799417i | \(-0.294858\pi\) | ||||
0.600776 | + | 0.799417i | \(0.294858\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2147.18 | + | 889.391i | −0.788527 | + | 0.326618i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 365.826 | − | 883.183i | 0.132305 | − | 0.319412i | −0.843819 | − | 0.536628i | \(-0.819698\pi\) |
0.976123 | + | 0.217216i | \(0.0696977\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −198.562 | − | 198.562i | −0.0707321 | − | 0.0707321i | 0.670856 | − | 0.741588i | \(-0.265927\pi\) |
−0.741588 | + | 0.670856i | \(0.765927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 555.965 | − | 555.965i | 0.195098 | − | 0.195098i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 476.223 | + | 197.258i | 0.164652 | + | 0.0682010i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2607.71 | + | 6295.58i | 0.888442 | + | 2.14489i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1201.71i | 0.403500i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 5124.68i | − | 1.69608i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −87.1014 | − | 210.281i | −0.0284185 | − | 0.0686084i | 0.909033 | − | 0.416724i | \(-0.136822\pi\) |
−0.937452 | + | 0.348115i | \(0.886822\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1619.77 | − | 670.930i | −0.521055 | − | 0.215828i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3623.77 | − | 3623.77i | 1.14948 | − | 1.14948i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 476.453 | + | 476.453i | 0.149049 | + | 0.149049i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 65.2562 | − | 157.542i | 0.0201352 | − | 0.0486106i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −193.494 | + | 80.1477i | −0.0588950 | + | 0.0243951i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2508.49 | 0.753278 | 0.376639 | − | 0.926360i | \(-0.377080\pi\) | ||||
0.376639 | + | 0.926360i | \(0.377080\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1535.73 | 0.455030 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2537.71 | + | 1051.15i | −0.741998 | + | 0.307345i | −0.721472 | − | 0.692444i | \(-0.756534\pi\) |
−0.0205258 | + | 0.999789i | \(0.506534\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 697.363 | − | 1683.58i | 0.201236 | − | 0.485826i | −0.790755 | − | 0.612132i | \(-0.790312\pi\) |
0.991991 | + | 0.126306i | \(0.0403120\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −997.888 | − | 997.888i | −0.284226 | − | 0.284226i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2051.84 | + | 2051.84i | −0.576911 | + | 0.576911i | −0.934051 | − | 0.357140i | \(-0.883752\pi\) |
0.357140 | + | 0.934051i | \(0.383752\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2470.02 | + | 1023.12i | 0.685644 | + | 0.284003i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1335.85 | + | 3225.02i | 0.366129 | + | 0.883914i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2551.88i | − | 0.690659i | −0.938482 | − | 0.345329i | \(-0.887767\pi\) | ||
0.938482 | − | 0.345329i | \(-0.112233\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2268.42i | 0.606314i | 0.952941 | + | 0.303157i | \(0.0980407\pi\) | ||||
−0.952941 | + | 0.303157i | \(0.901959\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1498.77 | − | 3618.35i | −0.395663 | − | 0.955216i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3444.04 | + | 1426.57i | 0.898088 | + | 0.372000i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3800.05 | + | 3800.05i | −0.978914 | + | 0.978914i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1549.26 | + | 1549.26i | 0.394298 | + | 0.394298i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2808.05 | + | 6779.23i | −0.706145 | + | 1.70479i | 0.00326968 | + | 0.999995i | \(0.498959\pi\) |
−0.709415 | + | 0.704791i | \(0.751041\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3173.11 | + | 1314.35i | −0.788505 | + | 0.326610i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −155.060 | −0.0380793 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2117.45 | −0.513942 | −0.256971 | − | 0.966419i | \(-0.582724\pi\) | ||||
−0.256971 | + | 0.966419i | \(0.582724\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3662.51 | + | 1517.06i | −0.878677 | + | 0.363960i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −402.348 | + | 971.354i | −0.0954203 | + | 0.230365i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −632.092 | − | 632.092i | −0.148200 | − | 0.148200i | 0.629114 | − | 0.777313i | \(-0.283418\pi\) |
−0.777313 | + | 0.629114i | \(0.783418\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4547.66 | + | 4547.66i | −1.05419 | + | 1.05419i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1375.70 | + | 569.833i | 0.315323 | + | 0.130611i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 835.101 | + | 2016.11i | 0.189283 | + | 0.456968i | 0.989822 | − | 0.142312i | \(-0.0454535\pi\) |
−0.800539 | + | 0.599280i | \(0.795454\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2528.01i | − | 0.566663i | −0.959022 | − | 0.283331i | \(-0.908560\pi\) | ||
0.959022 | − | 0.283331i | \(-0.0914396\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1479.91i | 0.328088i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1679.67 | + | 4055.08i | 0.368320 | + | 0.889202i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1743.13 | − | 722.029i | −0.378103 | − | 0.156616i | 0.185534 | − | 0.982638i | \(-0.440598\pi\) |
−0.563637 | + | 0.826022i | \(0.690598\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −971.822 | + | 971.822i | −0.208536 | + | 0.208536i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3983.45 | − | 3983.45i | −0.845667 | − | 0.845667i | 0.143922 | − | 0.989589i | \(-0.454029\pi\) |
−0.989589 | + | 0.143922i | \(0.954029\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 580.183 | − | 1400.69i | 0.121867 | − | 0.294213i | −0.851159 | − | 0.524907i | \(-0.824100\pi\) |
0.973026 | + | 0.230695i | \(0.0740999\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3675.94 | + | 1522.62i | −0.764013 | + | 0.316465i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4339.13 | 0.892441 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4899.03 | 0.997156 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1355.02 | − | 561.267i | 0.272964 | − | 0.113066i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −797.079 | + | 1924.32i | −0.158928 | + | 0.383686i | −0.983206 | − | 0.182499i | \(-0.941581\pi\) |
0.824278 | + | 0.566185i | \(0.191581\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5713.98 | + | 5713.98i | 1.12773 | + | 1.12773i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4975.20 | − | 4975.20i | 0.972021 | − | 0.972021i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3327.54 | + | 1378.31i | 0.643601 | + | 0.266588i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1248.81 | − | 3014.90i | −0.239137 | − | 0.577328i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1391.79i | 0.263882i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1326.03i | 0.248946i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2999.31 | − | 7240.97i | −0.557588 | − | 1.34614i | −0.911670 | − | 0.410923i | \(-0.865206\pi\) |
0.354082 | − | 0.935215i | \(-0.384794\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2300.32 | + | 952.824i | 0.423498 | + | 0.175418i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5951.01 | + | 5951.01i | −1.08505 | + | 1.08505i | −0.0890208 | + | 0.996030i | \(0.528374\pi\) |
−0.996030 | + | 0.0890208i | \(0.971626\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2649.88 | + | 2649.88i | 0.478531 | + | 0.478531i | 0.904661 | − | 0.426131i | \(-0.140124\pi\) |
−0.426131 | + | 0.904661i | \(0.640124\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 943.638 | − | 2278.14i | 0.168787 | − | 0.407488i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5107.96 | − | 2115.79i | 0.905021 | − | 0.374872i | 0.118873 | − | 0.992910i | \(-0.462072\pi\) |
0.786149 | + | 0.618038i | \(0.212072\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3004.92 | −0.527408 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1882.16 | −0.327265 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −331.258 | + | 137.212i | −0.0570641 | + | 0.0236367i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1761.42 | − | 4252.43i | 0.300633 | − | 0.725793i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1448.05 | − | 1448.05i | −0.244886 | − | 0.244886i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1203.79 | − | 1203.79i | 0.201724 | − | 0.201724i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2534.49 | − | 1049.82i | −0.420870 | − | 0.174330i | 0.162189 | − | 0.986760i | \(-0.448145\pi\) |
−0.583059 | + | 0.812430i | \(0.698145\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3094.35 | − | 7470.43i | −0.509218 | − | 1.22936i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3926.47i | 0.640376i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3412.65i | − | 0.551629i | −0.961211 | − | 0.275814i | \(-0.911053\pi\) | ||
0.961211 | − | 0.275814i | \(-0.0889475\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1821.25 | + | 4396.88i | 0.291789 | + | 0.704442i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3629.01 | − | 1503.18i | −0.576310 | − | 0.238715i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3901.32 | − | 3901.32i | 0.614145 | − | 0.614145i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1885.56 | + | 1885.56i | 0.294247 | + | 0.294247i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1608.37 | − | 3882.95i | 0.248824 | − | 0.600714i | −0.749281 | − | 0.662252i | \(-0.769601\pi\) |
0.998105 | + | 0.0615384i | \(0.0196007\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5617.33 | − | 2326.78i | 0.861573 | − | 0.356875i | 0.0922505 | − | 0.995736i | \(-0.470594\pi\) |
0.769323 | + | 0.638861i | \(0.220594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7378.43 | −1.12203 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8007.64 | −1.20738 | −0.603688 | − | 0.797221i | \(-0.706303\pi\) | ||||
−0.603688 | + | 0.797221i | \(0.706303\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8088.95 | − | 3350.55i | 1.20934 | − | 0.500927i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −37.7852 | + | 91.2214i | −0.00560169 | + | 0.0135237i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7420.49 | − | 7420.49i | −1.09092 | − | 1.09092i | −0.995431 | − | 0.0954845i | \(-0.969560\pi\) |
−0.0954845 | − | 0.995431i | \(-0.530440\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1655.59 | + | 1655.59i | −0.241375 | + | 0.241375i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4056.58 | + | 1680.29i | 0.586544 | + | 0.242954i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 325.882 | + | 786.750i | 0.0467328 | + | 0.112823i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4739.58i | − | 0.674126i | −0.941482 | − | 0.337063i | \(-0.890566\pi\) | ||
0.941482 | − | 0.337063i | \(-0.109434\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8850.53i | 1.24862i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1567.20 | + | 3783.56i | 0.219313 | + | 0.529468i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6348.63 | − | 2629.69i | −0.881285 | − | 0.365040i | −0.104290 | − | 0.994547i | \(-0.533257\pi\) |
−0.776995 | + | 0.629507i | \(0.783257\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1256.79 | + | 1256.79i | −0.173068 | + | 0.173068i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2228.21 | + | 2228.21i | 0.304399 | + | 0.304399i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2437.33 | − | 5884.23i | 0.330335 | − | 0.797500i | −0.668230 | − | 0.743955i | \(-0.732948\pi\) |
0.998565 | − | 0.0535452i | \(-0.0170521\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −834.752 | + | 345.765i | −0.112246 | + | 0.0464937i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −205.714 | −0.0274451 | −0.0137226 | − | 0.999906i | \(-0.504368\pi\) | ||||
−0.0137226 | + | 0.999906i | \(0.504368\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7047.52 | 0.932921 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6149.49 | − | 2547.20i | 0.807743 | − | 0.334578i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 736.006 | − | 1776.88i | 0.0959305 | − | 0.231597i | −0.868629 | − | 0.495464i | \(-0.834998\pi\) |
0.964559 | + | 0.263867i | \(0.0849981\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 169.918 | + | 169.918i | 0.0219773 | + | 0.0219773i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1139.37 | + | 1139.37i | −0.146243 | + | 0.146243i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16105.4 | − | 6671.08i | −2.05152 | − | 0.849768i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1882.80 | − | 4545.49i | −0.238023 | − | 0.574638i | 0.759055 | − | 0.651026i | \(-0.225661\pi\) |
−0.997078 | + | 0.0763880i | \(0.975661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2533.58i | 0.317889i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6670.63i | 0.830712i | 0.909659 | + | 0.415356i | \(0.136343\pi\) | ||||
−0.909659 | + | 0.415356i | \(0.863657\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1576.34 | + | 3805.62i | 0.194846 | + | 0.470401i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1664.54 | + | 689.476i | 0.204227 | + | 0.0845935i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16341.3 | − | 16341.3i | 1.99019 | − | 1.99019i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2441.40 | − | 2441.40i | −0.295158 | − | 0.295158i | 0.543956 | − | 0.839114i | \(-0.316926\pi\) |
−0.839114 | + | 0.543956i | \(0.816926\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 849.880 | − | 2051.79i | 0.101999 | − | 0.246247i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4753.91 | − | 1969.13i | 0.566403 | − | 0.234612i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10941.5 | −1.29421 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6705.42 | 0.787448 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15396.0 | − | 6377.25i | 1.79510 | − | 0.743554i | 0.806838 | − | 0.590772i | \(-0.201177\pi\) |
0.988260 | − | 0.152782i | \(-0.0488231\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1566.59 | + | 3782.09i | −0.181356 | + | 0.437833i | −0.988247 | − | 0.152868i | \(-0.951149\pi\) |
0.806890 | + | 0.590702i | \(0.201149\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2455.38 | + | 2455.38i | 0.282233 | + | 0.282233i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 217.147 | − | 217.147i | 0.0247840 | − | 0.0247840i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 780.103 | + | 323.129i | 0.0884117 | + | 0.0366213i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3301.50 | − | 7970.54i | −0.371557 | − | 0.897019i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8391.23i | 0.937799i | 0.883252 | + | 0.468899i | \(0.155349\pi\) | ||||
−0.883252 | + | 0.468899i | \(0.844651\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 14275.6i | − | 1.58439i | −0.610270 | − | 0.792193i | \(-0.708939\pi\) | ||
0.610270 | − | 0.792193i | \(-0.291061\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 892.809 | + | 2155.43i | 0.0984067 | + | 0.237575i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5696.70 | + | 2359.65i | 0.623593 | + | 0.258301i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11181.1 | + | 11181.1i | −1.21559 | + | 1.21559i | −0.246429 | + | 0.969161i | \(0.579257\pi\) |
−0.969161 | + | 0.246429i | \(0.920743\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3423.63 | + | 3423.63i | 0.369682 | + | 0.369682i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4372.54 | + | 10556.2i | −0.468952 | + | 1.13215i | 0.495670 | + | 0.868511i | \(0.334923\pi\) |
−0.964622 | + | 0.263639i | \(0.915077\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6870.09 | + | 2845.68i | −0.731850 | + | 0.303142i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4628.87 | 0.489794 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9965.25 | −1.04741 | −0.523707 | − | 0.851898i | \(-0.675451\pi\) | ||||
−0.523707 | + | 0.851898i | \(0.675451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23369.8 | + | 9680.09i | −2.44000 | + | 1.01068i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3193.88 | + | 7710.70i | −0.331261 | + | 0.799736i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5225.88 | − | 5225.88i | −0.538446 | − | 0.538446i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11250.2 | − | 11250.2i | 1.15155 | − | 1.15155i | 0.165312 | − | 0.986241i | \(-0.447137\pi\) |
0.986241 | − | 0.165312i | \(-0.0528632\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −454.805 | − | 188.387i | −0.0462495 | − | 0.0191572i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 567.298 | + | 1369.58i | 0.0573139 | + | 0.138368i | 0.949942 | − | 0.312425i | \(-0.101141\pi\) |
−0.892629 | + | 0.450793i | \(0.851141\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1601.42i | 0.160744i | 0.996765 | + | 0.0803720i | \(0.0256108\pi\) | ||||
−0.996765 | + | 0.0803720i | \(0.974389\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3049.71i | 0.304144i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4458.09 | + | 10762.8i | 0.441747 | + | 1.06647i | 0.975335 | + | 0.220728i | \(0.0708433\pi\) |
−0.533588 | + | 0.845744i | \(0.679157\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2309.93 | + | 956.805i | 0.227426 | + | 0.0942029i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3409.22 | − | 3409.22i | 0.333522 | − | 0.333522i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13451.8 | + | 13451.8i | 1.30764 | + | 1.30764i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3015.52 | − | 7280.10i | 0.291287 | − | 0.703229i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7717.33 | + | 3196.62i | −0.740781 | + | 0.306841i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3203.43 | 0.305571 | 0.152785 | − | 0.988259i | \(-0.451176\pi\) | ||||
0.152785 | + | 0.988259i | \(0.451176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24234.8 | −2.29732 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1568.75 | − | 649.797i | 0.147786 | − | 0.0612149i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2802.91 | + | 6766.82i | −0.262420 | + | 0.633537i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12622.9 | + | 12622.9i | 1.17454 | + | 1.17454i | 0.981116 | + | 0.193422i | \(0.0619586\pi\) |
0.193422 | + | 0.981116i | \(0.438041\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2814.51 | − | 2814.51i | 0.260279 | − | 0.260279i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2183.75 | − | 904.539i | −0.200716 | − | 0.0831391i | 0.280061 | − | 0.959982i | \(-0.409645\pi\) |
−0.480777 | + | 0.876843i | \(0.659645\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 80.4558 | + | 194.237i | 0.00734999 | + | 0.0177444i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14374.8i | 1.30525i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5575.18i | − | 0.503181i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3796.86 | − | 9166.43i | −0.340623 | − | 0.822336i | −0.997653 | − | 0.0684718i | \(-0.978188\pi\) |
0.657030 | − | 0.753864i | \(-0.271812\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6568.65 | + | 2720.82i | 0.585760 | + | 0.242630i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5777.19 | − | 5777.19i | 0.512112 | − | 0.512112i | −0.403061 | − | 0.915173i | \(-0.632054\pi\) |
0.915173 | + | 0.403061i | \(0.132054\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4914.71 | − | 4914.71i | −0.433073 | − | 0.433073i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1039.06 | + | 2508.52i | −0.0910184 | + | 0.219738i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10526.2 | − | 4360.11i | 0.916636 | − | 0.379683i | 0.126043 | − | 0.992025i | \(-0.459772\pi\) |
0.790593 | + | 0.612342i | \(0.209772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 542.255 | 0.0469431 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12631.8 | −1.08715 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11487.6 | + | 4758.30i | −0.982917 | + | 0.407138i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3797.90 | + | 9168.95i | −0.323079 | + | 0.779981i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1525.28 | − | 1525.28i | −0.129003 | − | 0.129003i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3790.76 | + | 3790.76i | −0.318764 | + | 0.318764i | −0.848292 | − | 0.529528i | \(-0.822369\pi\) |
0.529528 | + | 0.848292i | \(0.322369\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10160.9 | + | 4208.78i | 0.849531 | + | 0.351887i | 0.764604 | − | 0.644500i | \(-0.222934\pi\) |
0.0849264 | + | 0.996387i | \(0.472934\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −830.409 | − | 2004.78i | −0.0690324 | − | 0.166659i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 274.826i | 0.0227165i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8034.51i | 0.660353i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4016.45 | + | 9696.56i | 0.328247 | + | 0.792457i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24507.2 | + | 10151.2i | 1.99160 | + | 0.824948i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6646.33 | − | 6646.33i | 0.537095 | − | 0.537095i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5030.61 | − | 5030.61i | −0.404258 | − | 0.404258i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5295.56 | + | 12784.6i | −0.423184 | + | 1.02166i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 870.092 | − | 360.404i | 0.0691463 | − | 0.0286413i | −0.347842 | − | 0.937553i | \(-0.613086\pi\) |
0.416989 | + | 0.908912i | \(0.363086\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4751.47 | −0.375516 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10226.8 | 0.803794 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1669.92 | + | 691.704i | −0.130531 | + | 0.0540679i | −0.446993 | − | 0.894537i | \(-0.647505\pi\) |
0.316462 | + | 0.948605i | \(0.397505\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −659.087 | + | 1591.18i | −0.0512371 | + | 0.123697i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3814.66 | + | 3814.66i | 0.294936 | + | 0.294936i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7849.17 | + | 7849.17i | −0.603581 | + | 0.603581i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16576.9 | − | 6866.36i | −1.26784 | − | 0.525155i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4440.93 | + | 10721.4i | 0.337825 | + | 0.815581i | 0.997924 | + | 0.0644026i | \(0.0205142\pi\) |
−0.660099 | + | 0.751178i | \(0.729486\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 19949.5i | − | 1.50944i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 575.598i | − | 0.0433186i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4527.75 | − | 10931.0i | −0.338938 | − | 0.818268i | −0.997818 | − | 0.0660203i | \(-0.978970\pi\) |
0.658881 | − | 0.752247i | \(-0.271030\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21957.5 | − | 9095.11i | −1.63498 | − | 0.677229i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 811.235 | − | 811.235i | 0.0600859 | − | 0.0600859i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10557.5 | − | 10557.5i | −0.777844 | − | 0.777844i | 0.201620 | − | 0.979464i | \(-0.435379\pi\) |
−0.979464 | + | 0.201620i | \(0.935379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4454.66 | − | 10754.5i | 0.326483 | − | 0.788199i | −0.672366 | − | 0.740219i | \(-0.734722\pi\) |
0.998848 | − | 0.0479798i | \(-0.0152783\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4771.96 | − | 1976.61i | 0.347908 | − | 0.144108i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5281.11 | −0.383022 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17387.0 | 1.25447 | 0.627234 | − | 0.778831i | \(-0.284187\pi\) | ||||
0.627234 | + | 0.778831i | \(0.284187\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8578.27 | − | 3553.24i | 0.615718 | − | 0.255039i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2666.25 | + | 6436.89i | −0.190386 | + | 0.459633i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16881.4 | − | 16881.4i | −1.19924 | − | 1.19924i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10659.2 | − | 10659.2i | 0.753342 | − | 0.753342i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7009.84 | − | 2903.57i | −0.492891 | − | 0.204162i | 0.122372 | − | 0.992484i | \(-0.460950\pi\) |
−0.615263 | + | 0.788322i | \(0.710950\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2698.67 | + | 6515.17i | 0.188789 | + | 0.455777i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 2755.12i | − | 0.191761i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 10833.0i | − | 0.750181i | −0.926988 | − | 0.375091i | \(-0.877612\pi\) | ||
0.926988 | − | 0.375091i | \(-0.122388\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −188.695 | − | 455.550i | −0.0130013 | − | 0.0313878i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −747.708 | − | 309.711i | −0.0512590 | − | 0.0212322i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3185.59 | − | 3185.59i | 0.217295 | − | 0.217295i | −0.590063 | − | 0.807358i | \(-0.700897\pi\) |
0.807358 | + | 0.590063i | \(0.200897\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2409.29 | + | 2409.29i | 0.163522 | + | 0.163522i | 0.784125 | − | 0.620603i | \(-0.213112\pi\) |
−0.620603 | + | 0.784125i | \(0.713112\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1951.60 | + | 4711.57i | −0.131800 | + | 0.318193i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20258.2 | + | 8391.20i | −1.36134 | + | 0.563886i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28227.6 | 1.88752 | 0.943759 | − | 0.330636i | \(-0.107263\pi\) | ||||
0.943759 | + | 0.330636i | \(0.107263\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1485.60 | 0.0988496 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9615.19 | − | 3982.74i | 0.636643 | − | 0.263706i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9916.41 | − | 23940.3i | 0.653377 | − | 1.57739i | −0.154470 | − | 0.987998i | \(-0.549367\pi\) |
0.807846 | − | 0.589393i | \(-0.200633\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13887.1 | + | 13887.1i | 0.910538 | + | 0.910538i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10610.2 | − | 10610.2i | 0.692304 | − | 0.692304i | −0.270435 | − | 0.962738i | \(-0.587167\pi\) |
0.962738 | + | 0.270435i | \(0.0871674\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2228.33 | + | 923.005i | 0.144692 | + | 0.0599333i | 0.453854 | − | 0.891076i | \(-0.350049\pi\) |
−0.309162 | + | 0.951009i | \(0.600049\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3239.71 | + | 7821.36i | 0.209348 | + | 0.505411i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4735.10i | 0.304507i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 19145.0i | − | 1.22528i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5652.13 | − | 13645.4i | −0.360007 | − | 0.869133i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1493.83 | − | 618.765i | −0.0946946 | − | 0.0392238i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4628.63 | + | 4628.63i | −0.292017 | + | 0.292017i | −0.837877 | − | 0.545860i | \(-0.816203\pi\) |
0.545860 | + | 0.837877i | \(0.316203\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −463.848 | − | 463.848i | −0.0291253 | − | 0.0291253i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1726.72 | − | 4168.66i | 0.107910 | − | 0.260517i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13406.8 | − | 5553.29i | 0.833905 | − | 0.345415i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11371.7 | 0.704003 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6544.85 | 0.403286 | 0.201643 | − | 0.979459i | \(-0.435372\pi\) | ||||
0.201643 | + | 0.979459i | \(0.435372\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12954.9 | + | 5366.09i | −0.794543 | + | 0.329110i | −0.742768 | − | 0.669548i | \(-0.766488\pi\) |
−0.0517744 | + | 0.998659i | \(0.516488\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5652.24 | − | 13645.7i | 0.345049 | − | 0.833022i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6054.03 | − | 6054.03i | −0.367865 | − | 0.367865i | 0.498833 | − | 0.866698i | \(-0.333762\pi\) |
−0.866698 | + | 0.498833i | \(0.833762\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21210.8 | + | 21210.8i | −1.28289 | + | 1.28289i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1794.14 | + | 743.156i | 0.108015 | + | 0.0447413i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5840.08 | − | 14099.2i | −0.349985 | − | 0.844937i | −0.996621 | − | 0.0821390i | \(-0.973825\pi\) |
0.646636 | − | 0.762798i | \(-0.276175\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 8046.71i | − | 0.480017i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1106.04i | 0.0656783i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7839.56 | + | 18926.4i | 0.463408 | + | 1.11877i | 0.966989 | + | 0.254818i | \(0.0820157\pi\) |
−0.503581 | + | 0.863948i | \(0.667984\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29468.7 | − | 12206.3i | −1.73404 | − | 0.718262i | −0.999199 | − | 0.0400217i | \(-0.987257\pi\) |
−0.734840 | − | 0.678241i | \(-0.762743\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −426.817 | + | 426.817i | −0.0250018 | + | 0.0250018i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8946.62 | − | 8946.62i | −0.521707 | − | 0.521707i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1383.61 | − | 3340.33i | 0.0803202 | − | 0.193910i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6679.34 | − | 2766.67i | 0.386006 | − | 0.159889i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4922.36 | −0.283198 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17972.6 | 1.02941 | 0.514704 | − | 0.857368i | \(-0.327902\pi\) | ||||
0.514704 | + | 0.857368i | \(0.327902\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9995.31 | − | 4140.19i | 0.569955 | − | 0.236083i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1779.19 | + | 4295.35i | −0.101004 | + | 0.243846i | −0.966301 | − | 0.257414i | \(-0.917130\pi\) |
0.865297 | + | 0.501259i | \(0.167130\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3297.89 | + | 3297.89i | 0.186394 | + | 0.186394i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5597.79 | + | 5597.79i | −0.314989 | + | 0.314989i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7660.17 | + | 3172.95i | 0.429149 | + | 0.177759i | 0.586793 | − | 0.809737i | \(-0.300390\pi\) |
−0.157645 | + | 0.987496i | \(0.550390\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4244.21 | + | 10246.4i | 0.236734 | + | 0.571527i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 5252.00i | − | 0.291668i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25035.8i | 1.38431i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3344.80 | − | 8075.06i | −0.184142 | − | 0.444558i | 0.804670 | − | 0.593722i | \(-0.202342\pi\) |
−0.988813 | + | 0.149163i | \(0.952342\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8456.69 | + | 3502.87i | 0.463554 | + | 0.192010i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23678.3 | + | 23678.3i | −1.29233 | + | 1.29233i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1251.44 | + | 1251.44i | 0.0680080 | + | 0.0680080i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3200.39 | + | 7726.43i | −0.173176 | + | 0.418084i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11050.1 | + | 4577.09i | −0.595371 | + | 0.246611i | −0.659960 | − | 0.751301i | \(-0.729427\pi\) |
0.0645882 | + | 0.997912i | \(0.479427\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41489.6 | −2.22590 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7705.32 | 0.411630 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4088.94 | + | 1693.69i | −0.217511 | + | 0.0900960i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10279.5 | − | 24817.0i | 0.544508 | − | 1.31456i | −0.377005 | − | 0.926211i | \(-0.623046\pi\) |
0.921513 | − | 0.388347i | \(-0.126954\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16010.0 | − | 16010.0i | −0.844473 | − | 0.844473i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3341.94 | − | 3341.94i | 0.175535 | − | 0.175535i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 39804.0 | + | 16487.4i | 2.08194 | + | 0.862367i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2814.53 | − | 6794.87i | −0.146598 | − | 0.353918i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 8782.64i | − | 0.455546i | −0.973714 | − | 0.227773i | \(-0.926856\pi\) | ||
0.973714 | − | 0.227773i | \(-0.0731444\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7917.62i | 0.408970i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2501.89 | + | 6040.10i | 0.128695 | + | 0.310697i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4268.78 | − | 1768.19i | −0.218674 | − | 0.0905776i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19402.1 | + | 19402.1i | −0.989798 | + | 0.989798i | −0.999948 | − | 0.0101501i | \(-0.996769\pi\) |
0.0101501 | + | 0.999948i | \(0.496769\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5591.61 | − | 5591.61i | −0.284083 | − | 0.284083i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 509.353 | − | 1229.69i | 0.0257717 | − | 0.0622184i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12567.1 | − | 5205.47i | 0.633256 | − | 0.262303i | −0.0428799 | − | 0.999080i | \(-0.513653\pi\) |
0.676136 | + | 0.736777i | \(0.263653\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10743.8 | 0.539172 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14575.4 | −0.728484 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9220.93 | − | 3819.43i | 0.458995 | − | 0.190122i | −0.141191 | − | 0.989982i | \(-0.545093\pi\) |
0.600186 | + | 0.799860i | \(0.295093\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5927.21 | + | 14309.5i | −0.293848 | + | 0.709412i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22825.1 | + | 22825.1i | 1.12702 | + | 1.12702i | 0.990660 | + | 0.136355i | \(0.0435389\pi\) |
0.136355 | + | 0.990660i | \(0.456461\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16345.5 | + | 16345.5i | −0.803831 | + | 0.803831i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13129.3 | − | 5438.35i | −0.643075 | − | 0.266370i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2290.44 | − | 5529.60i | −0.111737 | − | 0.269756i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 16863.5i | − | 0.819384i | −0.912224 | − | 0.409692i | \(-0.865636\pi\) | ||
0.912224 | − | 0.409692i | \(-0.134364\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21148.1i | 1.02348i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15949.9 | − | 38506.4i | −0.768842 | − | 1.85615i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13042.4 | + | 5402.33i | 0.626200 | + | 0.259381i | 0.673138 | − | 0.739517i | \(-0.264946\pi\) |
−0.0469375 | + | 0.998898i | \(0.514946\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6999.40 | + | 6999.40i | −0.334733 | + | 0.334733i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14227.7 | + | 14227.7i | 0.677732 | + | 0.677732i | 0.959487 | − | 0.281754i | \(-0.0909163\pi\) |
−0.281754 | + | 0.959487i | \(0.590916\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2492.07 | − | 6016.40i | 0.118243 | − | 0.285463i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 929.187 | − | 384.882i | 0.0439148 | − | 0.0181901i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31456.5 | 1.48087 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22350.4 | 1.04808 | 0.524041 | − | 0.851693i | \(-0.324424\pi\) | ||||
0.524041 | + | 0.851693i | \(0.324424\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5638.12 | + | 2335.39i | −0.263362 | + | 0.109088i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4110.34 | − | 9923.25i | 0.191253 | − | 0.461726i | −0.798943 | − | 0.601406i | \(-0.794607\pi\) |
0.990197 | + | 0.139680i | \(0.0446074\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4270.84 | − | 4270.84i | −0.197952 | − | 0.197952i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8078.94 | + | 8078.94i | −0.373012 | + | 0.373012i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 41955.9 | + | 17378.7i | 1.92969 | + | 0.799302i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12437.6 | + | 30027.0i | 0.569849 | + | 1.37574i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7406.78i | 0.338055i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24077.4i | 1.09473i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8016.15 | − | 19352.7i | −0.363081 | − | 0.876555i | −0.994846 | − | 0.101395i | \(-0.967669\pi\) |
0.631765 | − | 0.775160i | \(-0.282331\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2380.22 | − | 985.918i | −0.107399 | − | 0.0444862i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10701.3 | + | 10701.3i | −0.481029 | + | 0.481029i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3650.03 | + | 3650.03i | 0.163451 | + | 0.163451i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7093.30 | + | 17124.7i | −0.316445 | + | 0.763965i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29414.5 | + | 12183.9i | −1.30730 | + | 0.541500i | −0.924095 | − | 0.382164i | \(-0.875179\pi\) |
−0.383203 | + | 0.923664i | \(0.625179\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 694.367 | 0.0307446 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9658.19 | −0.426037 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2920.49 | + | 1209.71i | −0.128346 | + | 0.0531627i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3245.02 | + | 7834.17i | −0.142077 | + | 0.343004i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4447.23 | + | 4447.23i | 0.193990 | + | 0.193990i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12484.4 | − | 12484.4i | 0.542558 | − | 0.542558i | −0.381720 | − | 0.924278i | \(-0.624668\pi\) |
0.924278 | + | 0.381720i | \(0.124668\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9708.35 | + | 4021.33i | 0.420353 | + | 0.174116i | 0.582826 | − | 0.812597i | \(-0.301947\pi\) |
−0.162473 | + | 0.986713i | \(0.551947\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2788.20 | − | 6731.31i | −0.120279 | − | 0.290378i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19877.3i | 0.854321i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 34153.3i | − | 1.46251i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3673.35 | − | 8868.26i | −0.156725 | − | 0.378366i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11520.4 | − | 4771.89i | −0.489724 | − | 0.202850i | 0.124136 | − | 0.992265i | \(-0.460384\pi\) |
−0.613860 | + | 0.789415i | \(0.710384\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6083.57 | + | 6083.57i | −0.257667 | + | 0.257667i | −0.824105 | − | 0.566438i | \(-0.808321\pi\) |
0.566438 | + | 0.824105i | \(0.308321\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8944.88 | + | 8944.88i | 0.377480 | + | 0.377480i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12142.2 | − | 29314.0i | 0.510553 | − | 1.23258i | −0.433010 | − | 0.901389i | \(-0.642549\pi\) |
0.943563 | − | 0.331194i | \(-0.107451\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27644.8 | + | 11450.9i | −1.15820 | + | 0.479740i | −0.877274 | − | 0.479990i | \(-0.840640\pi\) |
−0.280922 | + | 0.959731i | \(0.590640\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5437.77 | −0.226996 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 968.182 | 0.0402707 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32803.1 | + | 13587.5i | −1.35952 | + | 0.563132i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3705.18 | + | 8945.09i | −0.153010 | + | 0.369400i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23430.1 | − | 23430.1i | −0.964119 | − | 0.964119i | 0.0352588 | − | 0.999378i | \(-0.488774\pi\) |
−0.999378 | + | 0.0352588i | \(0.988774\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15008.9 | + | 15008.9i | −0.615394 | + | 0.615394i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15000.1 | − | 6213.26i | −0.612849 | − | 0.253850i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5188.96 | − | 12527.3i | −0.211249 | − | 0.510001i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13962.6i | 0.566424i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 4369.49i | − | 0.176632i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10641.0 | + | 25689.6i | 0.428635 | + | 1.03482i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14855.1 | − | 6153.17i | −0.596281 | − | 0.246988i | 0.0640694 | − | 0.997945i | \(-0.479592\pi\) |
−0.660350 | + | 0.750958i | \(0.729592\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18248.4 | − | 18248.4i | 0.729922 | − | 0.729922i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7730.96 | − | 7730.96i | −0.308150 | − | 0.308150i | 0.536042 | − | 0.844192i | \(-0.319919\pi\) |
−0.844192 | + | 0.536042i | \(0.819919\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13473.0 | + | 32526.7i | −0.535149 | + | 1.29196i | 0.392925 | + | 0.919570i | \(0.371463\pi\) |
−0.928075 | + | 0.372394i | \(0.878537\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11553.8 | − | 4785.72i | 0.457318 | − | 0.189427i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35318.4 | −1.39311 | −0.696555 | − | 0.717504i | \(-0.745285\pi\) | ||||
−0.696555 | + | 0.717504i | \(0.745285\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10772.2 | 0.423429 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13044.6 | − | 5403.25i | 0.510978 | − | 0.211654i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24763.7 | − | 59784.8i | 0.966687 | − | 2.33379i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10808.0 | + | 10808.0i | 0.420453 | + | 0.420453i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6726.72 | + | 6726.72i | −0.260785 | + | 0.260785i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5221.73 | − | 2162.91i | −0.201745 | − | 0.0835654i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15599.5 | + | 37660.6i | 0.600637 | + | 1.45007i | 0.872927 | + | 0.487850i | \(0.162219\pi\) |
−0.272290 | + | 0.962215i | \(0.587781\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6002.98i | 0.230348i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 4797.82i | − | 0.183476i | −0.995783 | − | 0.0917382i | \(-0.970758\pi\) | ||
0.995783 | − | 0.0917382i | \(-0.0292423\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17629.3 | + | 42560.9i | 0.671884 | + | 1.62207i | 0.778406 | + | 0.627761i | \(0.216029\pi\) |
−0.106522 | + | 0.994310i | \(0.533971\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21516.6 | + | 8912.48i | 0.817259 | + | 0.338520i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15374.2 | − | 15374.2i | 0.581978 | − | 0.581978i | −0.353469 | − | 0.935446i | \(-0.614998\pi\) |
0.935446 | + | 0.353469i | \(0.114998\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2031.65 | − | 2031.65i | −0.0766471 | − | 0.0766471i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2559.40 | + | 6178.95i | −0.0962326 | + | 0.232326i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16461.1 | − | 6818.39i | 0.616851 | − | 0.255508i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35528.3 | 1.32691 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10380.4 | 0.386389 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3820.25 | − | 1582.40i | 0.141727 | − | 0.0587052i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −639.215 | + | 1543.20i | −0.0236352 | + | 0.0570605i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6650.40 | − | 6650.40i | −0.245085 | − | 0.245085i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16778.5 | − | 16778.5i | 0.616282 | − | 0.616282i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39565.2 | − | 16388.4i | −1.44844 | − | 0.599965i | −0.486616 | − | 0.873616i | \(-0.661769\pi\) |
−0.961829 | + | 0.273651i | \(0.911769\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3454.63 | − | 8340.21i | −0.126054 | − | 0.304320i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 16563.3i | − | 0.602379i | −0.953564 | − | 0.301189i | \(-0.902616\pi\) | ||
0.953564 | − | 0.301189i | \(-0.0973837\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 40616.1i | − | 1.47228i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1462.51 | + | 3530.82i | 0.0528406 | + | 0.127569i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4733.87 | − | 1960.83i | −0.170476 | − | 0.0706133i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21215.7 | − | 21215.7i | 0.761526 | − | 0.761526i | −0.215072 | − | 0.976598i | \(-0.568999\pi\) |
0.976598 | + | 0.215072i | \(0.0689986\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15972.5 | − | 15972.5i | −0.571456 | − | 0.571456i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13042.9 | − | 31488.3i | 0.465127 | − | 1.12292i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32830.1 | − | 13598.7i | 1.16697 | − | 0.483374i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16149.6 | −0.572192 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2955.93 | −0.104393 | −0.0521963 | − | 0.998637i | \(-0.516622\pi\) | ||||
−0.0521963 | + | 0.998637i | \(0.516622\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22952.3 | − | 9507.14i | 0.807981 | − | 0.334677i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9282.20 | + | 22409.2i | −0.325708 | + | 0.786328i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2032.56 | + | 2032.56i | 0.0710928 | + | 0.0710928i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8962.97 | − | 8962.97i | 0.312495 | − | 0.312495i | −0.533381 | − | 0.845875i | \(-0.679079\pi\) |
0.845875 | + | 0.533381i | \(0.179079\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9978.43 | + | 4133.20i | 0.346788 | + | 0.143644i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19192.4 | − | 46334.5i | −0.664882 | − | 1.60517i | −0.790058 | − | 0.613033i | \(-0.789949\pi\) |
0.125176 | − | 0.992135i | \(-0.460051\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 30435.5i | − | 1.05103i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 17371.3i | − | 0.597978i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6058.72 | − | 14627.0i | −0.207901 | − | 0.501916i | 0.785192 | − | 0.619253i | \(-0.212564\pi\) |
−0.993092 | + | 0.117336i | \(0.962564\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3062.63 | + | 1268.58i | 0.104760 | + | 0.0433929i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11267.4 | − | 11267.4i | 0.384195 | − | 0.384195i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10134.7 | − | 10134.7i | −0.344487 | − | 0.344487i | 0.513564 | − | 0.858051i | \(-0.328325\pi\) |
−0.858051 | + | 0.513564i | \(0.828325\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9870.97 | + | 23830.6i | −0.334468 | + | 0.807478i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8001.17 | + | 3314.19i | −0.270262 | + | 0.111946i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7062.19 | 0.237800 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24385.7 | −0.818561 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11278.7 | − | 4671.81i | 0.377417 | − | 0.156331i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17744.5 | + | 42839.0i | −0.591933 | + | 1.42905i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28442.7 | + | 28442.7i | 0.945869 | + | 0.945869i | 0.998608 | − | 0.0527388i | \(-0.0167951\pi\) |
−0.0527388 | + | 0.998608i | \(0.516795\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −730.705 | + | 730.705i | −0.0242246 | + | 0.0242246i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43067.2 | − | 17839.0i | −1.42337 | − | 0.589579i | −0.467664 | − | 0.883906i | \(-0.654904\pi\) |
−0.955705 | + | 0.294328i | \(0.904904\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8159.94 | + | 19699.8i | 0.268855 | + | 0.649072i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 13265.6i | − | 0.435733i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 4088.33i | − | 0.133877i | −0.997757 | − | 0.0669383i | \(-0.978677\pi\) | ||
0.997757 | − | 0.0669383i | \(-0.0213231\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10563.5 | − | 25502.4i | −0.344851 | − | 0.832545i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12271.7 | + | 5083.09i | 0.399393 | + | 0.165434i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19001.7 | − | 19001.7i | 0.616541 | − | 0.616541i | −0.328101 | − | 0.944643i | \(-0.606409\pi\) |
0.944643 | + | 0.328101i | \(0.106409\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9728.93 | + | 9728.93i | 0.314710 | + | 0.314710i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1877.64 | − | 4533.02i | 0.0605531 | − | 0.146188i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21147.1 | + | 8759.43i | −0.679919 | + | 0.281632i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31837.0 | 1.02052 | 0.510261 | − | 0.860020i | \(-0.329549\pi\) | ||||
0.510261 | + | 0.860020i | \(0.329549\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7906.43 | −0.252672 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3733.97 | − | 1546.66i | 0.118970 | − | 0.0492789i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12897.2 | + | 31136.5i | −0.409686 | + | 0.989070i | 0.575534 | + | 0.817778i | \(0.304794\pi\) |
−0.985220 | + | 0.171292i | \(0.945206\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −40279.4 | − | 40279.4i | −1.27566 | − | 1.27566i |
(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 | 128.4.g.a.49.8 | 44 | ||
4.3 | odd | 2 | 32.4.g.a.21.6 | ✓ | 44 | ||
8.3 | odd | 2 | 256.4.g.b.97.8 | 44 | |||
8.5 | even | 2 | 256.4.g.a.97.4 | 44 | |||
32.3 | odd | 8 | 32.4.g.a.29.6 | yes | 44 | ||
32.13 | even | 8 | 256.4.g.a.161.4 | 44 | |||
32.19 | odd | 8 | 256.4.g.b.161.8 | 44 | |||
32.29 | even | 8 | inner | 128.4.g.a.81.8 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.21.6 | ✓ | 44 | 4.3 | odd | 2 | ||
32.4.g.a.29.6 | yes | 44 | 32.3 | odd | 8 | ||
128.4.g.a.49.8 | 44 | 1.1 | even | 1 | trivial | ||
128.4.g.a.81.8 | 44 | 32.29 | even | 8 | inner | ||
256.4.g.a.97.4 | 44 | 8.5 | even | 2 | |||
256.4.g.a.161.4 | 44 | 32.13 | even | 8 | |||
256.4.g.b.97.8 | 44 | 8.3 | odd | 2 | |||
256.4.g.b.161.8 | 44 | 32.19 | odd | 8 |