Newspace parameters
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.w (of order \(8\), degree \(4\), not minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 431.5 | ||
Character | \(\chi\) | \(=\) | 1152.431 |
Dual form | 1152.2.w.a.719.5 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.0913223 | − | 0.0378270i | 0.0408406 | − | 0.0169167i | −0.362170 | − | 0.932112i | \(-0.617964\pi\) |
0.403010 | + | 0.915195i | \(0.367964\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.05457 | + | 3.05457i | 1.15452 | + | 1.15452i | 0.985636 | + | 0.168884i | \(0.0540163\pi\) |
0.168884 | + | 0.985636i | \(0.445984\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.25649 | + | 2.17731i | −1.58489 | + | 0.656483i | −0.989179 | − | 0.146715i | \(-0.953130\pi\) |
−0.595712 | + | 0.803198i | \(0.703130\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.57202 | + | 3.79519i | −0.436000 | + | 1.05260i | 0.541317 | + | 0.840818i | \(0.317926\pi\) |
−0.977318 | + | 0.211779i | \(0.932074\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.56471 | 0.622034 | 0.311017 | − | 0.950404i | \(-0.399330\pi\) | ||||
0.311017 | + | 0.950404i | \(0.399330\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.64058 | − | 1.09376i | −0.605791 | − | 0.250927i | 0.0586367 | − | 0.998279i | \(-0.481325\pi\) |
−0.664428 | + | 0.747353i | \(0.731325\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.03079 | − | 4.03079i | −0.840477 | − | 0.840477i | 0.148443 | − | 0.988921i | \(-0.452574\pi\) |
−0.988921 | + | 0.148443i | \(0.952574\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.52863 | + | 3.52863i | −0.705725 | + | 0.705725i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.06984 | + | 4.99704i | −0.384360 | + | 0.927927i | 0.606752 | + | 0.794892i | \(0.292472\pi\) |
−0.991111 | + | 0.133035i | \(0.957528\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.44203i | − | 0.258996i | −0.991580 | − | 0.129498i | \(-0.958663\pi\) | ||
0.991580 | − | 0.129498i | \(-0.0413366\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.394496 | + | 0.163406i | 0.0666820 | + | 0.0276206i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.07758 | − | 5.01573i | −0.341552 | − | 0.824581i | −0.997559 | − | 0.0698256i | \(-0.977756\pi\) |
0.656007 | − | 0.754755i | \(-0.272244\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.296726 | + | 0.296726i | −0.0463409 | + | 0.0463409i | −0.729897 | − | 0.683557i | \(-0.760432\pi\) |
0.683557 | + | 0.729897i | \(0.260432\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.72382 | + | 6.57588i | 0.415378 | + | 1.00281i | 0.983669 | + | 0.179984i | \(0.0576047\pi\) |
−0.568291 | + | 0.822828i | \(0.692395\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.42367i | − | 1.08285i | −0.840748 | − | 0.541427i | \(-0.817884\pi\) | ||
0.840748 | − | 0.541427i | \(-0.182116\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.6608i | 1.66583i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.53235 | − | 3.69941i | −0.210484 | − | 0.508153i | 0.783014 | − | 0.622004i | \(-0.213681\pi\) |
−0.993498 | + | 0.113851i | \(0.963681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.397674 | + | 0.397674i | −0.0536223 | + | 0.0536223i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.988255 | + | 2.38586i | 0.128660 | + | 0.310612i | 0.975062 | − | 0.221931i | \(-0.0712361\pi\) |
−0.846402 | + | 0.532544i | \(0.821236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4346 | + | 4.32215i | 1.33601 | + | 0.553395i | 0.932365 | − | 0.361519i | \(-0.117742\pi\) |
0.403649 | + | 0.914914i | \(0.367742\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.406051i | 0.0503644i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.690522 | − | 1.66707i | 0.0843606 | − | 0.203665i | −0.876070 | − | 0.482184i | \(-0.839844\pi\) |
0.960431 | + | 0.278519i | \(0.0898437\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.97957 | + | 2.97957i | −0.353610 | + | 0.353610i | −0.861451 | − | 0.507841i | \(-0.830444\pi\) |
0.507841 | + | 0.861451i | \(0.330444\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.22401 | + | 9.22401i | 1.07959 | + | 1.07959i | 0.996546 | + | 0.0830429i | \(0.0264638\pi\) |
0.0830429 | + | 0.996546i | \(0.473536\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −22.7071 | − | 9.40558i | −2.58771 | − | 1.07187i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.12181 | 0.126213 | 0.0631065 | − | 0.998007i | \(-0.479899\pi\) | ||||
0.0631065 | + | 0.998007i | \(0.479899\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.13529 | + | 9.98348i | −0.453907 | + | 1.09583i | 0.516916 | + | 0.856036i | \(0.327080\pi\) |
−0.970824 | + | 0.239794i | \(0.922920\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.234216 | − | 0.0970152i | 0.0254042 | − | 0.0105228i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0590 | + | 12.0590i | 1.27825 | + | 1.27825i | 0.941644 | + | 0.336609i | \(0.109280\pi\) |
0.336609 | + | 0.941644i | \(0.390720\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.3945 | + | 6.79084i | −1.71862 | + | 0.711874i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.282518 | −0.0289857 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.5545 | −1.88393 | −0.941963 | − | 0.335717i | \(-0.891022\pi\) | ||||
−0.941963 | + | 0.335717i | \(0.891022\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.24603 | + | 2.17298i | −0.521999 | + | 0.216219i | −0.628095 | − | 0.778137i | \(-0.716165\pi\) |
0.106096 | + | 0.994356i | \(0.466165\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0095 | + | 11.0095i | 1.08479 | + | 1.08479i | 0.996055 | + | 0.0887398i | \(0.0282839\pi\) |
0.0887398 | + | 0.996055i | \(0.471716\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.182628 | − | 0.0756468i | 0.0176553 | − | 0.00731305i | −0.373838 | − | 0.927494i | \(-0.621959\pi\) |
0.391494 | + | 0.920181i | \(0.371959\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.10265 | − | 5.07626i | 0.201398 | − | 0.486217i | −0.790621 | − | 0.612305i | \(-0.790242\pi\) |
0.992019 | + | 0.126088i | \(0.0402423\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.91777 | −0.556697 | −0.278348 | − | 0.960480i | \(-0.589787\pi\) | ||||
−0.278348 | + | 0.960480i | \(0.589787\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.520573 | − | 0.215629i | −0.0485437 | − | 0.0201075i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.83410 | + | 7.83410i | 0.718151 | + | 0.718151i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.1118 | − | 15.1118i | 1.37380 | − | 1.37380i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.377900 | + | 0.912331i | −0.0338004 | + | 0.0816014i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.70061i | 0.860790i | 0.902641 | + | 0.430395i | \(0.141626\pi\) | ||||
−0.902641 | + | 0.430395i | \(0.858374\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.7327 | + | 5.27407i | 1.11246 | + | 0.460798i | 0.861786 | − | 0.507273i | \(-0.169346\pi\) |
0.250678 | + | 0.968070i | \(0.419346\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.72486 | − | 11.4068i | −0.409698 | − | 0.989098i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.62861 | − | 5.62861i | 0.480884 | − | 0.480884i | −0.424530 | − | 0.905414i | \(-0.639561\pi\) |
0.905414 | + | 0.424530i | \(0.139561\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.202389 | − | 0.488610i | −0.0171664 | − | 0.0414434i | 0.915064 | − | 0.403309i | \(-0.132140\pi\) |
−0.932230 | + | 0.361865i | \(0.882140\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 23.3722i | − | 1.95448i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.534637i | 0.0443992i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.35052 | − | 3.26046i | −0.110639 | − | 0.267107i | 0.858856 | − | 0.512217i | \(-0.171176\pi\) |
−0.969495 | + | 0.245110i | \(0.921176\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.6492 | − | 13.6492i | 1.11076 | − | 1.11076i | 0.117709 | − | 0.993048i | \(-0.462445\pi\) |
0.993048 | − | 0.117709i | \(-0.0375552\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.0545476 | − | 0.131690i | −0.00438137 | − | 0.0105776i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.4587 | − | 6.40321i | −1.23374 | − | 0.511032i | −0.331987 | − | 0.943284i | \(-0.607719\pi\) |
−0.901753 | + | 0.432252i | \(0.857719\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 24.6247i | − | 1.94070i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.04288 | − | 14.5888i | 0.473315 | − | 1.14268i | −0.489374 | − | 0.872074i | \(-0.662775\pi\) |
0.962689 | − | 0.270609i | \(-0.0872252\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.58872 | − | 6.58872i | 0.509850 | − | 0.509850i | −0.404630 | − | 0.914480i | \(-0.632600\pi\) |
0.914480 | + | 0.404630i | \(0.132600\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.73986 | − | 2.73986i | −0.210759 | − | 0.210759i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.8204 | + | 7.38143i | 1.35486 | + | 0.561200i | 0.937640 | − | 0.347608i | \(-0.113006\pi\) |
0.417216 | + | 0.908807i | \(0.363006\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.5569 | −1.62955 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.07369 | + | 9.83475i | −0.304482 | + | 0.735084i | 0.695383 | + | 0.718639i | \(0.255235\pi\) |
−0.999865 | + | 0.0164446i | \(0.994765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.06280 | − | 3.33972i | 0.599303 | − | 0.248239i | −0.0623442 | − | 0.998055i | \(-0.519858\pi\) |
0.661647 | + | 0.749815i | \(0.269858\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.379459 | − | 0.379459i | −0.0278984 | − | 0.0278984i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.4814 | + | 5.58417i | −0.985856 | + | 0.408355i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.0520 | 0.944411 | 0.472205 | − | 0.881489i | \(-0.343458\pi\) | ||||
0.472205 | + | 0.881489i | \(0.343458\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.05926 | −0.220210 | −0.110105 | − | 0.993920i | \(-0.535119\pi\) | ||||
−0.110105 | + | 0.993920i | \(0.535119\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.46774 | − | 2.26481i | 0.389560 | − | 0.161361i | −0.179302 | − | 0.983794i | \(-0.557384\pi\) |
0.568862 | + | 0.822433i | \(0.307384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.48835 | + | 4.48835i | 0.318170 | + | 0.318170i | 0.848064 | − | 0.529894i | \(-0.177768\pi\) |
−0.529894 | + | 0.848064i | \(0.677768\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −21.5863 | + | 8.94133i | −1.51506 | + | 0.627559i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0158735 | + | 0.0383220i | −0.00110865 | + | 0.00267652i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.2617 | 1.12484 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.322439 | − | 0.133558i | −0.0221976 | − | 0.00919454i | 0.371557 | − | 0.928410i | \(-0.378824\pi\) |
−0.393755 | + | 0.919216i | \(0.628824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.497491 | + | 0.497491i | 0.0339286 | + | 0.0339286i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.40478 | − | 4.40478i | 0.299016 | − | 0.299016i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.03178 | + | 9.73358i | −0.271207 | + | 0.654752i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 19.1612i | − | 1.28313i | −0.767068 | − | 0.641566i | \(-0.778285\pi\) | ||
0.767068 | − | 0.641566i | \(-0.221715\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.4451 | + | 8.05441i | 1.29061 | + | 0.534590i | 0.919169 | − | 0.393864i | \(-0.128862\pi\) |
0.371446 | + | 0.928455i | \(0.378862\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.97193 | − | 16.8317i | −0.460718 | − | 1.11227i | −0.968103 | − | 0.250552i | \(-0.919388\pi\) |
0.507385 | − | 0.861719i | \(-0.330612\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.7768 | + | 16.7768i | −1.09909 | + | 1.09909i | −0.104569 | + | 0.994518i | \(0.533346\pi\) |
−0.994518 | + | 0.104569i | \(0.966654\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.280815 | − | 0.677947i | −0.0183183 | − | 0.0442244i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.10976i | 0.589261i | 0.955611 | + | 0.294631i | \(0.0951966\pi\) | ||||
−0.955611 | + | 0.294631i | \(0.904803\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.39995i | 0.476673i | 0.971183 | + | 0.238336i | \(0.0766020\pi\) | ||||
−0.971183 | + | 0.238336i | \(0.923398\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.441093 | + | 1.06489i | 0.0281804 | + | 0.0680336i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.30210 | − | 8.30210i | 0.528250 | − | 0.528250i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.84250 | − | 11.6908i | −0.305656 | − | 0.737919i | −0.999836 | − | 0.0181174i | \(-0.994233\pi\) |
0.694180 | − | 0.719802i | \(-0.255767\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.9641 | + | 12.4115i | 1.88382 | + | 0.780306i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.02571i | 0.375873i | 0.982181 | + | 0.187937i | \(0.0601800\pi\) | ||||
−0.982181 | + | 0.187937i | \(0.939820\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.97478 | − | 21.6670i | 0.557666 | − | 1.34632i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.79218 | + | 6.79218i | −0.418824 | + | 0.418824i | −0.884798 | − | 0.465974i | \(-0.845704\pi\) |
0.465974 | + | 0.884798i | \(0.345704\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.279875 | − | 0.279875i | −0.0171926 | − | 0.0171926i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.8548 | − | 5.73883i | −0.844740 | − | 0.349903i | −0.0820193 | − | 0.996631i | \(-0.526137\pi\) |
−0.762721 | + | 0.646728i | \(0.776137\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.62497 | −0.341692 | −0.170846 | − | 0.985298i | \(-0.554650\pi\) | ||||
−0.170846 | + | 0.985298i | \(0.554650\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.8653 | − | 26.2311i | 0.655201 | − | 1.58179i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00843 | + | 0.417706i | −0.0605908 | + | 0.0250975i | −0.412773 | − | 0.910834i | \(-0.635440\pi\) |
0.352182 | + | 0.935931i | \(0.385440\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.7589 | + | 21.7589i | 1.29803 | + | 1.29803i | 0.929693 | + | 0.368335i | \(0.120072\pi\) |
0.368335 | + | 0.929693i | \(0.379928\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.3614 | − | 9.26239i | 1.32925 | − | 0.550592i | 0.398807 | − | 0.917035i | \(-0.369424\pi\) |
0.930441 | + | 0.366443i | \(0.119424\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.81274 | −0.107003 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4223 | −0.613074 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.2423 | − | 12.1126i | 1.70835 | − | 0.707623i | 0.708355 | − | 0.705856i | \(-0.249438\pi\) |
0.999998 | − | 0.00176683i | \(-0.000562400\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.180500 | + | 0.180500i | 0.0105091 | + | 0.0105091i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.6341 | − | 8.96114i | 1.25113 | − | 0.518236i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.7664 | + | 28.4066i | −0.678204 | + | 1.63733i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.11641 | 0.0639252 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.7854 | − | 5.71009i | −0.786773 | − | 0.325892i | −0.0471275 | − | 0.998889i | \(-0.515007\pi\) |
−0.739645 | + | 0.672997i | \(0.765007\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.4220 | − | 11.4220i | −0.647684 | − | 0.647684i | 0.304749 | − | 0.952433i | \(-0.401427\pi\) |
−0.952433 | + | 0.304749i | \(0.901427\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.24707 | − | 2.24707i | 0.127012 | − | 0.127012i | −0.640743 | − | 0.767755i | \(-0.721374\pi\) |
0.767755 | + | 0.640743i | \(0.221374\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.05906 | − | 2.55679i | 0.0594826 | − | 0.143604i | −0.891344 | − | 0.453328i | \(-0.850237\pi\) |
0.950826 | + | 0.309724i | \(0.100237\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 30.7736i | − | 1.72299i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.77233 | − | 2.80519i | −0.376823 | − | 0.156085i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.84475 | − | 18.9389i | −0.435148 | − | 1.05054i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.6761 | − | 22.6761i | 1.25018 | − | 1.25018i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.123439 | + | 0.298008i | 0.00678481 | + | 0.0163800i | 0.927236 | − | 0.374478i | \(-0.122178\pi\) |
−0.920451 | + | 0.390858i | \(0.872178\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 0.178361i | − | 0.00974489i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.5067i | − | 0.899179i | −0.893235 | − | 0.449590i | \(-0.851570\pi\) | ||
0.893235 | − | 0.449590i | \(-0.148430\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.13974 | + | 7.58001i | 0.170027 | + | 0.410481i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2368 | + | 14.2368i | −0.768716 | + | 0.768716i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.96248 | − | 14.3947i | −0.320083 | − | 0.772748i | −0.999248 | − | 0.0387633i | \(-0.987658\pi\) |
0.679166 | − | 0.733985i | \(-0.262342\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.57618 | + | 0.652873i | 0.0843707 | + | 0.0349475i | 0.424470 | − | 0.905442i | \(-0.360461\pi\) |
−0.340099 | + | 0.940390i | \(0.610461\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.7091i | 0.995786i | 0.867239 | + | 0.497893i | \(0.165893\pi\) | ||||
−0.867239 | + | 0.497893i | \(0.834107\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.159393 | + | 0.384810i | −0.00845972 | + | 0.0204236i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.5065 | + | 23.5065i | −1.24062 | + | 1.24062i | −0.280882 | + | 0.959742i | \(0.590627\pi\) |
−0.959742 | + | 0.280882i | \(0.909373\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.65868 | − | 7.65868i | −0.403088 | − | 0.403088i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.19127 | + | 0.493442i | 0.0623542 | + | 0.0258279i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.95190 | 0.154088 | 0.0770440 | − | 0.997028i | \(-0.475452\pi\) | ||||
0.0770440 | + | 0.997028i | \(0.475452\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.61945 | − | 15.9808i | 0.343665 | − | 0.829680i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.7552 | + | 8.18287i | −1.02289 | + | 0.423693i | −0.830140 | − | 0.557556i | \(-0.811739\pi\) |
−0.192746 | + | 0.981249i | \(0.561739\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.7109 | − | 15.7109i | −0.809152 | − | 0.809152i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.26476 | + | 1.76652i | −0.219066 | + | 0.0907402i | −0.489518 | − | 0.871993i | \(-0.662827\pi\) |
0.270451 | + | 0.962734i | \(0.412827\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.45328 | 0.483040 | 0.241520 | − | 0.970396i | \(-0.422354\pi\) | ||||
0.241520 | + | 0.970396i | \(0.422354\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.42945 | −0.123816 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.8554 | − | 8.63860i | 1.05741 | − | 0.437994i | 0.214880 | − | 0.976640i | \(-0.431064\pi\) |
0.842532 | + | 0.538646i | \(0.181064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.3378 | − | 10.3378i | −0.522806 | − | 0.522806i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.102446 | − | 0.0424345i | 0.00515461 | − | 0.00213511i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.29268 | − | 7.94922i | 0.165255 | − | 0.398960i | −0.819460 | − | 0.573137i | \(-0.805726\pi\) |
0.984714 | + | 0.174177i | \(0.0557264\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.5903 | −1.62748 | −0.813740 | − | 0.581229i | \(-0.802572\pi\) | ||||
−0.813740 | + | 0.581229i | \(0.802572\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.47278 | + | 2.26690i | 0.272619 | + | 0.112922i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.8416 | + | 21.8416i | 1.08265 | + | 1.08265i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.41708 | − | 5.41708i | 0.267858 | − | 0.267858i | −0.560379 | − | 0.828236i | \(-0.689344\pi\) |
0.828236 | + | 0.560379i | \(0.189344\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.26908 | + | 10.3065i | −0.210068 | + | 0.507149i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.06814i | 0.0524329i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.0298 | − | 9.12504i | −1.07623 | − | 0.445787i | −0.227042 | − | 0.973885i | \(-0.572906\pi\) |
−0.849184 | + | 0.528097i | \(0.822906\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.82553 | + | 6.82144i | 0.137708 | + | 0.332457i | 0.977656 | − | 0.210210i | \(-0.0674147\pi\) |
−0.839948 | + | 0.542667i | \(0.817415\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.04991 | + | 9.04991i | −0.438985 | + | 0.438985i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.6709 | + | 45.0756i | 0.903549 | + | 2.18136i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.73112i | 0.324226i | 0.986772 | + | 0.162113i | \(0.0518310\pi\) | ||||
−0.986772 | + | 0.162113i | \(0.948169\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.1160i | − | 0.582257i | −0.956684 | − | 0.291129i | \(-0.905969\pi\) | ||
0.956684 | − | 0.291129i | \(-0.0940308\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.23489 | + | 15.0524i | 0.298255 | + | 0.720052i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.0767 | + | 14.0767i | −0.671843 | + | 0.671843i | −0.958141 | − | 0.286298i | \(-0.907575\pi\) |
0.286298 | + | 0.958141i | \(0.407575\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.5313 | + | 35.0817i | 0.690404 | + | 1.66678i | 0.743965 | + | 0.668218i | \(0.232943\pi\) |
−0.0535615 | + | 0.998565i | \(0.517057\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.55741 | + | 0.645102i | 0.0738285 | + | 0.0305808i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 25.9809i | − | 1.22611i | −0.790039 | − | 0.613056i | \(-0.789940\pi\) | ||
0.790039 | − | 0.613056i | \(-0.210060\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.913674 | − | 2.20580i | 0.0430232 | − | 0.103867i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.24031 | + | 1.24031i | −0.0581467 | + | 0.0581467i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.23785 | + | 6.23785i | 0.291794 | + | 0.291794i | 0.837789 | − | 0.545994i | \(-0.183848\pi\) |
−0.545994 | + | 0.837789i | \(0.683848\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.3278 | + | 9.66269i | 1.08648 | + | 0.450036i | 0.852779 | − | 0.522271i | \(-0.174915\pi\) |
0.233704 | + | 0.972308i | \(0.424915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.99595 | −0.185707 | −0.0928537 | − | 0.995680i | \(-0.529599\pi\) | ||||
−0.0928537 | + | 0.995680i | \(0.529599\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.26272 | + | 17.5338i | −0.336079 | + | 0.811366i | 0.662006 | + | 0.749499i | \(0.269706\pi\) |
−0.998084 | + | 0.0618671i | \(0.980294\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.20142 | − | 2.98293i | 0.332531 | − | 0.137739i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.6354 | − | 28.6354i | −1.31666 | − | 1.31666i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.1771 | − | 5.45814i | 0.604607 | − | 0.250437i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.7665 | −0.994537 | −0.497268 | − | 0.867597i | \(-0.665664\pi\) | ||||
−0.497268 | + | 0.867597i | \(0.665664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.3017 | 1.01687 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.69444 | + | 0.701861i | −0.0769407 | + | 0.0318699i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.10128 | + | 9.10128i | 0.412419 | + | 0.412419i | 0.882580 | − | 0.470162i | \(-0.155804\pi\) |
−0.470162 | + | 0.882580i | \(0.655804\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.2645 | + | 6.32276i | −0.688876 | + | 0.285342i | −0.699532 | − | 0.714601i | \(-0.746608\pi\) |
0.0106556 | + | 0.999943i | \(0.496608\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.30855 | + | 12.8160i | −0.239085 | + | 0.577202i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.2026 | −0.816500 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.2595 | + | 13.3623i | 1.44413 | + | 0.598180i | 0.960796 | − | 0.277255i | \(-0.0894246\pi\) |
0.483337 | + | 0.875434i | \(0.339425\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.34111 | + | 7.34111i | 0.327324 | + | 0.327324i | 0.851568 | − | 0.524244i | \(-0.175652\pi\) |
−0.524244 | + | 0.851568i | \(0.675652\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.396882 | + | 0.396882i | −0.0176610 | + | 0.0176610i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.55299 | − | 18.2345i | 0.334780 | − | 0.808231i | −0.663419 | − | 0.748248i | \(-0.730895\pi\) |
0.998199 | − | 0.0599832i | \(-0.0191047\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 56.3508i | 2.49281i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.42186 | + | 0.588955i | 0.0626548 | + | 0.0259525i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.1636 | + | 39.0225i | 0.710876 | + | 1.71621i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.3209 | + | 26.3209i | −1.15314 | + | 1.15314i | −0.167218 | + | 0.985920i | \(0.553478\pi\) |
−0.985920 | + | 0.167218i | \(0.946522\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.50275 | − | 13.2848i | −0.240619 | − | 0.580905i | 0.756726 | − | 0.653732i | \(-0.226798\pi\) |
−0.997345 | + | 0.0728276i | \(0.976798\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 3.69839i | − | 0.161104i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.49450i | 0.412805i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.659674 | − | 1.59259i | −0.0285737 | − | 0.0689829i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0138165 | − | 0.0138165i | 0.000597339 | − | 0.000597339i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.3892 | − | 61.2950i | −1.09359 | − | 2.64016i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.34772 | + | 0.558245i | 0.0579431 | + | 0.0240008i | 0.411467 | − | 0.911425i | \(-0.365017\pi\) |
−0.353524 | + | 0.935426i | \(0.615017\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 0.543113i | − | 0.0232644i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.11417 | + | 7.51828i | −0.133152 | + | 0.321458i | −0.976367 | − | 0.216119i | \(-0.930660\pi\) |
0.843215 | + | 0.537577i | \(0.180660\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.9312 | − | 10.9312i | 0.465683 | − | 0.465683i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.42664 | + | 3.42664i | 0.145715 | + | 0.145715i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.3810 | − | 4.29993i | −0.439855 | − | 0.182194i | 0.151755 | − | 0.988418i | \(-0.451508\pi\) |
−0.591610 | + | 0.806224i | \(0.701508\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.2386 | −1.23666 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.95005 | − | 4.70784i | 0.0821848 | − | 0.198412i | −0.877445 | − | 0.479677i | \(-0.840754\pi\) |
0.959630 | + | 0.281265i | \(0.0907540\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.540424 | + | 0.223851i | −0.0227358 | + | 0.00941749i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.12423 | − | 3.12423i | −0.130974 | − | 0.130974i | 0.638581 | − | 0.769555i | \(-0.279522\pi\) |
−0.769555 | + | 0.638581i | \(0.779522\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.4029 | + | 13.8360i | −1.39787 | + | 0.579017i | −0.949198 | − | 0.314680i | \(-0.898103\pi\) |
−0.448672 | + | 0.893697i | \(0.648103\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.4463 | 1.18629 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.0315 | −0.584141 | −0.292070 | − | 0.956397i | \(-0.594344\pi\) | ||||
−0.292070 | + | 0.956397i | \(0.594344\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −43.1268 | + | 17.8637i | −1.78920 | + | 0.741112i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.1095 | + | 16.1095i | 0.667188 | + | 0.667188i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0165 | − | 4.97740i | 0.495975 | − | 0.205439i | −0.120652 | − | 0.992695i | \(-0.538499\pi\) |
0.616627 | + | 0.787255i | \(0.288499\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.57724 | + | 3.80780i | −0.0649891 | + | 0.156898i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.6528 | −0.724914 | −0.362457 | − | 0.932000i | \(-0.618062\pi\) | ||||
−0.362457 | + | 0.932000i | \(0.618062\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.01177 | + | 0.419088i | 0.0414785 | + | 0.0171809i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.25995 | − | 5.25995i | −0.214916 | − | 0.214916i | 0.591436 | − | 0.806352i | \(-0.298561\pi\) |
−0.806352 | + | 0.591436i | \(0.798561\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.54574 | − | 6.54574i | 0.267006 | − | 0.267006i | −0.560886 | − | 0.827893i | \(-0.689540\pi\) |
0.827893 | + | 0.560886i | \(0.189540\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.808413 | − | 1.95168i | 0.0328667 | − | 0.0793472i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.72276i | 0.0699248i | 0.999389 | + | 0.0349624i | \(0.0111311\pi\) | ||||
−0.999389 | + | 0.0349624i | \(0.988869\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.1743 | + | 11.6702i | 1.13981 | + | 0.472125i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.6267 | + | 40.1405i | 0.671547 | + | 1.62126i | 0.778982 | + | 0.627046i | \(0.215736\pi\) |
−0.107435 | + | 0.994212i | \(0.534264\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.78933 | + | 7.78933i | −0.313587 | + | 0.313587i | −0.846297 | − | 0.532711i | \(-0.821173\pi\) |
0.532711 | + | 0.846297i | \(0.321173\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.0171 | − | 26.5976i | −0.442814 | − | 1.06905i | −0.974957 | − | 0.222394i | \(-0.928613\pi\) |
0.532143 | − | 0.846655i | \(-0.321387\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 73.6703i | 2.95154i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 24.8535i | − | 0.994141i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.32840 | − | 12.8639i | −0.212457 | − | 0.512917i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.0548 | − | 21.0548i | 0.838177 | − | 0.838177i | −0.150442 | − | 0.988619i | \(-0.548070\pi\) |
0.988619 | + | 0.150442i | \(0.0480696\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.366944 | + | 0.885882i | 0.0145617 | + | 0.0351552i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −44.2551 | − | 18.3311i | −1.75345 | − | 0.726303i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 5.65123i | − | 0.223210i | −0.993753 | − | 0.111605i | \(-0.964401\pi\) | ||
0.993753 | − | 0.111605i | \(-0.0355992\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.0022 | + | 41.0470i | −0.670502 | + | 1.61874i | 0.110256 | + | 0.993903i | \(0.464833\pi\) |
−0.780759 | + | 0.624833i | \(0.785167\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.0151270 | − | 0.0151270i | 0.000594703 | − | 0.000594703i | −0.706809 | − | 0.707404i | \(-0.749866\pi\) |
0.707404 | + | 0.706809i | \(0.249866\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.3895 | − | 10.3895i | −0.407824 | − | 0.407824i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.8575 | + | 11.9531i | 1.12928 | + | 0.467763i | 0.867536 | − | 0.497375i | \(-0.165703\pi\) |
0.261744 | + | 0.965137i | \(0.415703\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.36228 | 0.0532289 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.25678 | − | 17.5194i | 0.282684 | − | 0.682459i | −0.717212 | − | 0.696855i | \(-0.754582\pi\) |
0.999896 | + | 0.0143952i | \(0.00458229\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.6310 | + | 6.47456i | −0.607974 | + | 0.251831i | −0.665362 | − | 0.746521i | \(-0.731723\pi\) |
0.0573877 | + | 0.998352i | \(0.481723\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.862971 | − | 0.862971i | −0.0334646 | − | 0.0334646i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.4851 | − | 11.7989i | 1.10295 | − | 0.456856i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −64.2600 | −2.48073 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.5987 | 1.02530 | 0.512652 | − | 0.858596i | \(-0.328663\pi\) | ||||
0.512652 | + | 0.858596i | \(0.328663\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.3000 | + | 10.8938i | −1.01079 | + | 0.418683i | −0.825743 | − | 0.564047i | \(-0.809244\pi\) |
−0.185047 | + | 0.982730i | \(0.559244\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −56.6761 | − | 56.6761i | −2.17503 | − | 2.17503i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.9528 | − | 12.4069i | 1.14611 | − | 0.474735i | 0.272884 | − | 0.962047i | \(-0.412022\pi\) |
0.873228 | + | 0.487312i | \(0.162022\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.301105 | − | 0.726931i | 0.0115046 | − | 0.0277746i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.4489 | 0.626652 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.94272 | + | 4.11841i | 0.378239 | + | 0.156672i | 0.563699 | − | 0.825980i | \(-0.309378\pi\) |
−0.185460 | + | 0.982652i | \(0.559378\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.0369653 | − | 0.0369653i | −0.00140217 | − | 0.00140217i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.761018 | + | 0.761018i | −0.0288256 | + | 0.0288256i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.59430 | − | 13.5058i | 0.211294 | − | 0.510108i | −0.782329 | − | 0.622866i | \(-0.785968\pi\) |
0.993623 | + | 0.112757i | \(0.0359683\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.5168i | 0.585228i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.6619 | − | 9.38686i | −0.852288 | − | 0.353029i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.92207 | + | 11.8829i | 0.184852 | + | 0.446273i | 0.988955 | − | 0.148218i | \(-0.0473537\pi\) |
−0.804102 | + | 0.594491i | \(0.797354\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.81252 | + | 5.81252i | −0.217680 | + | 0.217680i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.884098 | − | 2.13440i | −0.0330634 | − | 0.0798221i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 16.1029i | − | 0.600537i | −0.953855 | − | 0.300268i | \(-0.902924\pi\) | ||
0.953855 | − | 0.300268i | \(-0.0970762\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 67.2584i | 2.50483i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.3290 | − | 24.9364i | −0.383609 | − | 0.926113i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.0560 | + | 21.0560i | −0.780923 | + | 0.780923i | −0.979987 | − | 0.199064i | \(-0.936210\pi\) |
0.199064 | + | 0.979987i | \(0.436210\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.98581 | + | 16.8652i | 0.258379 | + | 0.623783i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.2426 | + | 17.0832i | 1.52333 | + | 0.630984i | 0.978255 | − | 0.207404i | \(-0.0665015\pi\) |
0.545074 | + | 0.838388i | \(0.316501\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.2664i | 0.378168i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.2262 | + | 27.1024i | −0.412962 | + | 0.996977i | 0.571377 | + | 0.820688i | \(0.306409\pi\) |
−0.984338 | + | 0.176290i | \(0.943591\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.8059 | + | 15.8059i | −0.579863 | + | 0.579863i | −0.934865 | − | 0.355003i | \(-0.884480\pi\) |
0.355003 | + | 0.934865i | \(0.384480\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.246666 | − | 0.246666i | −0.00903715 | − | 0.00903715i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.788918 | + | 0.326780i | 0.0288264 | + | 0.0119403i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.4955 | 0.455969 | 0.227984 | − | 0.973665i | \(-0.426787\pi\) | ||||
0.227984 | + | 0.973665i | \(0.426787\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.730170 | − | 1.76279i | 0.0265736 | − | 0.0641544i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.0398 | − | 12.4429i | 1.09182 | − | 0.452245i | 0.237176 | − | 0.971467i | \(-0.423778\pi\) |
0.854639 | + | 0.519222i | \(0.173778\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.5032 | + | 15.5032i | 0.561992 | + | 0.561992i | 0.929873 | − | 0.367881i | \(-0.119917\pi\) |
−0.367881 | + | 0.929873i | \(0.619917\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.9285 | − | 9.08308i | 0.793865 | − | 0.328830i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.6084 | −0.383046 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.08253 | −0.255403 | −0.127701 | − | 0.991813i | \(-0.540760\pi\) | ||||
−0.127701 | + | 0.991813i | \(0.540760\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.3534 | − | 12.5728i | 1.09173 | − | 0.452211i | 0.237123 | − | 0.971480i | \(-0.423796\pi\) |
0.854611 | + | 0.519268i | \(0.173796\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.08838 | + | 5.08838i | 0.182780 | + | 0.182780i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.10808 | − | 0.458981i | 0.0397011 | − | 0.0164447i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.17464 | − | 22.1495i | 0.328294 | − | 0.792573i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.65394 | −0.0590316 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.1276 | + | 15.3788i | 1.32346 | + | 0.548194i | 0.928782 | − | 0.370627i | \(-0.120857\pi\) |
0.394675 | + | 0.918821i | \(0.370857\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.0763 | − | 18.0763i | −0.642718 | − | 0.642718i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.8068 | + | 32.8068i | −1.16500 | + | 1.16500i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.87919 | − | 4.53677i | 0.0665644 | − | 0.160701i | −0.887097 | − | 0.461584i | \(-0.847281\pi\) |
0.953661 | + | 0.300883i | \(0.0972814\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 19.0396i | − | 0.673572i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −68.5694 | − | 28.4024i | −2.41976 | − | 1.00230i | ||||
\(804\) | 0 | 0 |