Newspace parameters
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.t (of order \(2\), degree \(1\), not minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
Defining polynomial: |
\( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.2 | ||
Root | \(1.45161 + 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.1009 |
Dual form | 1680.2.t.i.1009.5 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.311108 | + | 2.21432i | −0.139132 | + | 0.990274i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.80642 | 1.14768 | 0.573840 | − | 0.818967i | \(-0.305453\pi\) | ||||
0.573840 | + | 0.818967i | \(0.305453\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.622216i | 0.172572i | 0.996270 | + | 0.0862858i | \(0.0274998\pi\) | ||||
−0.996270 | + | 0.0862858i | \(0.972500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.21432 | + | 0.311108i | 0.571735 | + | 0.0803277i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.42864i | 1.07410i | 0.843550 | + | 0.537051i | \(0.180462\pi\) | ||||
−0.843550 | + | 0.537051i | \(0.819538\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.622216 | 0.142746 | 0.0713730 | − | 0.997450i | \(-0.477262\pi\) | ||||
0.0713730 | + | 0.997450i | \(0.477262\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.62222i | − | 0.546770i | −0.961905 | − | 0.273385i | \(-0.911857\pi\) | ||
0.961905 | − | 0.273385i | \(-0.0881433\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.80642 | − | 1.37778i | −0.961285 | − | 0.275557i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.61285 | −1.78506 | −0.892531 | − | 0.450987i | \(-0.851072\pi\) | ||||
−0.892531 | + | 0.450987i | \(0.851072\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.622216 | 0.111753 | 0.0558766 | − | 0.998438i | \(-0.482205\pi\) | ||||
0.0558766 | + | 0.998438i | \(0.482205\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.80642i | − | 0.662613i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.21432 | − | 0.311108i | −0.374288 | − | 0.0525868i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.24443i | 0.204583i | 0.994754 | + | 0.102292i | \(0.0326175\pi\) | ||||
−0.994754 | + | 0.102292i | \(0.967383\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.622216 | 0.0996342 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.62222 | 0.721869 | 0.360934 | − | 0.932591i | \(-0.382458\pi\) | ||||
0.360934 | + | 0.932591i | \(0.382458\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.85728i | 0.740728i | 0.928887 | + | 0.370364i | \(0.120767\pi\) | ||||
−0.928887 | + | 0.370364i | \(0.879233\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.311108 | − | 2.21432i | 0.0463772 | − | 0.330091i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.6128i | 1.69391i | 0.531666 | + | 0.846954i | \(0.321566\pi\) | ||||
−0.531666 | + | 0.846954i | \(0.678434\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.42864 | 0.620134 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.4795i | 1.85155i | 0.378074 | + | 0.925775i | \(0.376587\pi\) | ||||
−0.378074 | + | 0.925775i | \(0.623413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.18421 | + | 8.42864i | −0.159679 | + | 1.13652i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.622216i | − | 0.0824145i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.6128 | 1.51186 | 0.755932 | − | 0.654650i | \(-0.227184\pi\) | ||||
0.755932 | + | 0.654650i | \(0.227184\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.10171 | −1.03732 | −0.518659 | − | 0.854981i | \(-0.673569\pi\) | ||||
−0.518659 | + | 0.854981i | \(0.673569\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.37778 | − | 0.193576i | −0.170893 | − | 0.0240102i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.62222 | −0.315678 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.56199 | −0.304053 | −0.152026 | − | 0.988376i | \(-0.548580\pi\) | ||||
−0.152026 | + | 0.988376i | \(0.548580\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.9906i | 1.28636i | 0.765717 | + | 0.643178i | \(0.222385\pi\) | ||||
−0.765717 | + | 0.643178i | \(0.777615\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.37778 | + | 4.80642i | −0.159093 | + | 0.554998i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.80642i | 0.433782i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.75557 | −0.760061 | −0.380030 | − | 0.924974i | \(-0.624086\pi\) | ||||
−0.380030 | + | 0.924974i | \(0.624086\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 11.6128i | − | 1.27468i | −0.770585 | − | 0.637338i | \(-0.780036\pi\) | ||
0.770585 | − | 0.637338i | \(-0.219964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.80642 | − | 1.37778i | −1.06366 | − | 0.149442i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.61285i | 1.03061i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.23506 | 0.872915 | 0.436457 | − | 0.899725i | \(-0.356233\pi\) | ||||
0.436457 | + | 0.899725i | \(0.356233\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.622216 | −0.0652259 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 0.622216i | − | 0.0645208i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.193576 | + | 1.37778i | −0.0198605 | + | 0.141358i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.23506i | − | 0.430006i | −0.976613 | − | 0.215003i | \(-0.931024\pi\) | ||
0.976613 | − | 0.215003i | \(-0.0689761\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.80642 | −0.382560 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.7239 | 1.86310 | 0.931550 | − | 0.363613i | \(-0.118457\pi\) | ||||
0.931550 | + | 0.363613i | \(0.118457\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.857279i | 0.0844702i | 0.999108 | + | 0.0422351i | \(0.0134479\pi\) | ||||
−0.999108 | + | 0.0422351i | \(0.986552\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.311108 | + | 2.21432i | −0.0303610 | + | 0.216095i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11.0923i | − | 1.07234i | −0.844111 | − | 0.536169i | \(-0.819871\pi\) | ||
0.844111 | − | 0.536169i | \(-0.180129\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.61285 | −0.537613 | −0.268807 | − | 0.963194i | \(-0.586629\pi\) | ||||
−0.268807 | + | 0.963194i | \(0.586629\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.24443 | 0.118116 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.2351i | 1.52727i | 0.645650 | + | 0.763633i | \(0.276586\pi\) | ||||
−0.645650 | + | 0.763633i | \(0.723414\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.80642 | + | 0.815792i | 0.541452 | + | 0.0760730i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.622216i | − | 0.0575239i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.42864 | −0.405973 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.48886 | 0.317169 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 4.62222i | − | 0.416771i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.54617 | − | 10.2143i | 0.406622 | − | 0.913597i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3461i | 1.36175i | 0.732400 | + | 0.680875i | \(0.238400\pi\) | ||||
−0.732400 | + | 0.680875i | \(0.761600\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.85728 | 0.427660 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.622216i | 0.0539529i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.21432 | − | 0.311108i | −0.190578 | − | 0.0267759i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.0923i | 1.46030i | 0.683288 | + | 0.730149i | \(0.260549\pi\) | ||||
−0.683288 | + | 0.730149i | \(0.739451\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.4795 | −1.14332 | −0.571658 | − | 0.820492i | \(-0.693700\pi\) | ||||
−0.571658 | + | 0.820492i | \(0.693700\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.6128 | 0.977978 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.36842i | 0.198057i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.99063 | − | 21.2859i | 0.248358 | − | 1.76770i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.34614 | 0.765666 | 0.382833 | − | 0.923818i | \(-0.374949\pi\) | ||||
0.382833 | + | 0.923818i | \(0.374949\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.14272 | 0.581266 | 0.290633 | − | 0.956835i | \(-0.406134\pi\) | ||||
0.290633 | + | 0.956835i | \(0.406134\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.42864i | − | 0.358034i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.193576 | + | 1.37778i | −0.0155484 | + | 0.110666i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.99063i | 0.557913i | 0.960304 | + | 0.278957i | \(0.0899886\pi\) | ||||
−0.960304 | + | 0.278957i | \(0.910011\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.4795 | 1.06899 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.62222 | 0.206660 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.6128i | − | 1.22289i | −0.791286 | − | 0.611446i | \(-0.790588\pi\) | ||
0.791286 | − | 0.611446i | \(-0.209412\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.42864 | + | 1.18421i | 0.656169 | + | 0.0921905i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.51114i | − | 0.116935i | −0.998289 | − | 0.0584677i | \(-0.981379\pi\) | ||
0.998289 | − | 0.0584677i | \(-0.0186215\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6128 | 0.970219 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.622216 | −0.0475820 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.53035i | − | 0.496493i | −0.968697 | − | 0.248247i | \(-0.920146\pi\) | ||
0.968697 | − | 0.248247i | \(-0.0798543\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.37778 | − | 4.80642i | 0.104151 | − | 0.363331i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 11.6128i | − | 0.872875i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.29529 | −0.470532 | −0.235266 | − | 0.971931i | \(-0.575596\pi\) | ||||
−0.235266 | + | 0.971931i | \(0.575596\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.85728 | −0.509698 | −0.254849 | − | 0.966981i | \(-0.582026\pi\) | ||||
−0.254849 | + | 0.966981i | \(0.582026\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.10171i | 0.598896i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.75557 | − | 0.387152i | −0.202593 | − | 0.0284640i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.8573i | 1.23273i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5620 | 0.764239 | 0.382119 | − | 0.924113i | \(-0.375194\pi\) | ||||
0.382119 | + | 0.924113i | \(0.375194\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.24443i | 0.377502i | 0.982025 | + | 0.188751i | \(0.0604440\pi\) | ||||
−0.982025 | + | 0.188751i | \(0.939556\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.193576 | + | 1.37778i | −0.0138623 | + | 0.0986652i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.7462i | − | 1.26436i | −0.774820 | − | 0.632182i | \(-0.782159\pi\) | ||
0.774820 | − | 0.632182i | \(-0.217841\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.2351 | −1.43443 | −0.717213 | − | 0.696854i | \(-0.754582\pi\) | ||||
−0.717213 | + | 0.696854i | \(0.754582\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 9.61285i | − | 0.674690i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.43801 | + | 10.2351i | −0.100435 | + | 0.714848i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.62222i | 0.182257i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.36842 | 0.163827 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.3274 | −1.46824 | −0.734120 | − | 0.679020i | \(-0.762405\pi\) | ||||
−0.734120 | + | 0.679020i | \(0.762405\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.56199i | 0.175545i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.7556 | − | 1.51114i | −0.733524 | − | 0.103059i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.622216i | 0.0422387i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.9906 | 0.742678 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.75557 | −0.185360 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.71456i | 0.650535i | 0.945622 | + | 0.325267i | \(0.105454\pi\) | ||||
−0.945622 | + | 0.325267i | \(0.894546\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.80642 | + | 1.37778i | 0.320428 | + | 0.0918523i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 11.3461i | − | 0.753070i | −0.926402 | − | 0.376535i | \(-0.877115\pi\) | ||
0.926402 | − | 0.376535i | \(-0.122885\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.34614 | −0.0889555 | −0.0444778 | − | 0.999010i | \(-0.514162\pi\) | ||||
−0.0444778 | + | 0.999010i | \(0.514162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.80642 | 0.250444 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.3778i | 1.00743i | 0.863869 | + | 0.503716i | \(0.168034\pi\) | ||||
−0.863869 | + | 0.503716i | \(0.831966\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.7146 | − | 3.61285i | −1.67743 | − | 0.235676i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.75557i | 0.438821i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.53972 | 0.487704 | 0.243852 | − | 0.969812i | \(-0.421589\pi\) | ||||
0.243852 | + | 0.969812i | \(0.421589\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.9813 | 1.54477 | 0.772385 | − | 0.635155i | \(-0.219064\pi\) | ||||
0.772385 | + | 0.635155i | \(0.219064\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.311108 | − | 2.21432i | 0.0198759 | − | 0.141468i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.387152i | 0.0246339i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.6128 | −0.735934 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.1017 | −0.890092 | −0.445046 | − | 0.895508i | \(-0.646813\pi\) | ||||
−0.445046 | + | 0.895508i | \(0.646813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 9.98126i | − | 0.627517i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.37778 | + | 9.80642i | −0.0862802 | + | 0.614102i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 17.0192i | − | 1.06163i | −0.847488 | − | 0.530815i | \(-0.821886\pi\) | ||
0.847488 | − | 0.530815i | \(-0.178114\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.24443 | −0.0773252 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.61285 | 0.595020 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 12.6035i | − | 0.777164i | −0.921414 | − | 0.388582i | \(-0.872965\pi\) | ||
0.921414 | − | 0.388582i | \(-0.127035\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.8479 | − | 4.19358i | −1.83354 | − | 0.257609i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 8.23506i | − | 0.503978i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.76494 | −0.229552 | −0.114776 | − | 0.993391i | \(-0.536615\pi\) | ||||
−0.114776 | + | 0.993391i | \(0.536615\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.8666 | 1.08532 | 0.542661 | − | 0.839952i | \(-0.317417\pi\) | ||||
0.542661 | + | 0.839952i | \(0.317417\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.622216i | 0.0376582i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.2953 | − | 5.24443i | −1.10325 | − | 0.316251i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.24443i | 0.0747706i | 0.999301 | + | 0.0373853i | \(0.0119029\pi\) | ||||
−0.999301 | + | 0.0373853i | \(0.988097\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.622216 | −0.0372511 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.95899 | −0.534448 | −0.267224 | − | 0.963634i | \(-0.586106\pi\) | ||||
−0.267224 | + | 0.963634i | \(0.586106\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 30.5718i | − | 1.81731i | −0.417551 | − | 0.908654i | \(-0.637111\pi\) | ||
0.417551 | − | 0.908654i | \(-0.362889\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.37778 | + | 0.193576i | 0.0816129 | + | 0.0114665i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.62222i | 0.272841i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.61285 | −0.153697 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.23506 | −0.248264 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 5.67307i | − | 0.331424i | −0.986174 | − | 0.165712i | \(-0.947008\pi\) | ||
0.986174 | − | 0.165712i | \(-0.0529923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.61285 | + | 25.7146i | −0.210348 | + | 1.49716i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.80642i | 0.220871i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.63158 | 0.0943569 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.85728 | −0.279969 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 18.7239i | − | 1.07566i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.52051 | − | 17.9398i | 0.144324 | − | 1.02723i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.85728i | − | 0.277220i | −0.990347 | − | 0.138610i | \(-0.955737\pi\) | ||
0.990347 | − | 0.138610i | \(-0.0442634\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.857279 | 0.0487689 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.5718 | 1.96039 | 0.980195 | − | 0.198037i | \(-0.0634567\pi\) | ||||
0.980195 | + | 0.198037i | \(0.0634567\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.33677i | − | 0.358176i | −0.983833 | − | 0.179088i | \(-0.942685\pi\) | ||
0.983833 | − | 0.179088i | \(-0.0573146\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.21432 | + | 0.311108i | 0.124763 | + | 0.0175289i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 15.9684i | − | 0.896872i | −0.893815 | − | 0.448436i | \(-0.851981\pi\) | ||
0.893815 | − | 0.448436i | \(-0.148019\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −36.5906 | −2.04868 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.0923 | −0.619114 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.75557i | 0.153324i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.857279 | − | 2.99063i | 0.0475533 | − | 0.165890i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.61285i | 0.310391i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.6128 | −0.640237 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.6128 | 1.51774 | 0.758870 | − | 0.651243i | \(-0.225752\pi\) | ||||
0.758870 | + | 0.651243i | \(0.225752\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.24443i | − | 0.0681944i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.0000i | − | 0.871576i | −0.900049 | − | 0.435788i | \(-0.856470\pi\) | ||
0.900049 | − | 0.435788i | \(-0.143530\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.2351 | 0.881768 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.36842 | 0.128257 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.815792 | − | 5.80642i | 0.0439208 | − | 0.312607i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 11.8666i | − | 0.637035i | −0.947917 | − | 0.318517i | \(-0.896815\pi\) | ||
0.947917 | − | 0.318517i | \(-0.103185\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.8163 | −1.16780 | −0.583899 | − | 0.811826i | \(-0.698474\pi\) | ||||
−0.583899 | + | 0.811826i | \(0.698474\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.622216 | −0.0332114 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.79706i | − | 0.148872i | −0.997226 | − | 0.0744361i | \(-0.976284\pi\) | ||
0.997226 | − | 0.0744361i | \(-0.0237157\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.797056 | − | 5.67307i | 0.0423033 | − | 0.301095i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.42864i | 0.234388i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.0509 | −0.688798 | −0.344399 | − | 0.938823i | \(-0.611917\pi\) | ||||
−0.344399 | + | 0.938823i | \(0.611917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6128 | −0.979624 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.48886i | − | 0.183118i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −24.3368 | − | 3.41927i | −1.27384 | − | 0.178973i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 10.4889i | − | 0.547514i | −0.961799 | − | 0.273757i | \(-0.911734\pi\) | ||
0.961799 | − | 0.273757i | \(-0.0882664\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.62222 | −0.240623 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.4795 | −0.699820 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.1847i | 1.56290i | 0.623966 | + | 0.781452i | \(0.285521\pi\) | ||||
−0.623966 | + | 0.781452i | \(0.714479\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.2143 | − | 4.54617i | −0.527465 | − | 0.234763i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.98126i | − | 0.308051i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.8573 | −0.660434 | −0.330217 | − | 0.943905i | \(-0.607122\pi\) | ||||
−0.330217 | + | 0.943905i | \(0.607122\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.3461 | 0.786207 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.4701i | 1.25037i | 0.780479 | + | 0.625183i | \(0.214975\pi\) | ||||
−0.780479 | + | 0.625183i | \(0.785025\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.42864 | − | 1.18421i | −0.429563 | − | 0.0603528i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 4.85728i | − | 0.246909i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.61285 | 0.0817746 | 0.0408873 | − | 0.999164i | \(-0.486982\pi\) | ||||
0.0408873 | + | 0.999164i | \(0.486982\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.6128 | 0.587287 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.00000i | − | 0.201773i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.10171 | − | 14.9590i | 0.105749 | − | 0.752668i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 22.2163i | − | 1.11501i | −0.830175 | − | 0.557503i | \(-0.811760\pi\) | ||
0.830175 | − | 0.557503i | \(-0.188240\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.622216 | 0.0311497 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.9813 | 0.997817 | 0.498908 | − | 0.866655i | \(-0.333734\pi\) | ||||
0.498908 | + | 0.866655i | \(0.333734\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.387152i | 0.0192854i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.311108 | + | 2.21432i | −0.0154591 | + | 0.110030i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.73683i | 0.234796i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.73329 | 0.283493 | 0.141747 | − | 0.989903i | \(-0.454728\pi\) | ||||
0.141747 | + | 0.989903i | \(0.454728\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.0923 | 0.843103 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.6128i | 0.571431i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.7146 | + | 3.61285i | 1.26228 | + | 0.177348i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.4795i | 0.660094i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.3684 | 1.28818 | 0.644091 | − | 0.764949i | \(-0.277236\pi\) | ||||
0.644091 | + | 0.764949i | \(0.277236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.3274 | −0.941960 | −0.470980 | − | 0.882144i | \(-0.656100\pi\) | ||||
−0.470980 | + | 0.882144i | \(0.656100\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 11.6128i | − | 0.564636i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.10171 | − | 21.2859i | 0.295976 | − | 1.03252i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.10171i | − | 0.392069i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.36842 | 0.114348 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.9491 | 1.29809 | 0.649047 | − | 0.760748i | \(-0.275168\pi\) | ||||
0.649047 | + | 0.760748i | \(0.275168\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.13335i | − | 0.102522i | −0.998685 | − | 0.0512612i | \(-0.983676\pi\) | ||
0.998685 | − | 0.0512612i | \(-0.0163241\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.2859 | − | 2.99063i | −1.02058 | − | 0.143390i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.63158i | − | 0.0780492i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.5205 | −0.502116 | −0.251058 | − | 0.967972i | \(-0.580779\pi\) | ||||
−0.251058 | + | 0.967972i | \(0.580779\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.88892i | 0.327303i | 0.986518 | + | 0.163651i | \(0.0523272\pi\) | ||||
−0.986518 | + | 0.163651i | \(0.947673\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.56199 | + | 18.2351i | −0.121450 | + | 0.864425i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 9.34614i | − | 0.442057i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −39.9180 | −1.88385 | −0.941923 | − | 0.335829i | \(-0.890984\pi\) | ||||
−0.941923 | + | 0.335829i | \(0.890984\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.5941 | 0.828474 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 7.14272i | − | 0.335594i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.193576 | − | 1.37778i | 0.00907499 | − | 0.0645915i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.47013i | 0.396216i | 0.980180 | + | 0.198108i | \(0.0634796\pi\) | ||||
−0.980180 | + | 0.198108i | \(0.936520\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.42864 | −0.206711 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.1146 | 1.86832 | 0.934162 | − | 0.356849i | \(-0.116149\pi\) | ||||
0.934162 | + | 0.356849i | \(0.116149\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 33.5941i | − | 1.56125i | −0.624999 | − | 0.780625i | \(-0.714901\pi\) | ||
0.624999 | − | 0.780625i | \(-0.285099\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.37778 | + | 0.193576i | 0.0638932 | + | 0.00897688i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.3461i | 0.525037i | 0.964927 | + | 0.262518i | \(0.0845530\pi\) | ||||
−0.964927 | + | 0.262518i | \(0.915447\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.99063 | 0.322111 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.4889i | 0.850119i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.99063 | − | 0.857279i | −0.137220 | − | 0.0393347i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 13.4795i | − | 0.617184i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.2864 | 1.65797 | 0.828984 | − | 0.559273i | \(-0.188919\pi\) | ||||
0.828984 | + | 0.559273i | \(0.188919\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.774305 | −0.0353053 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 2.62222i | − | 0.119315i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.37778 | + | 1.31756i | 0.425823 | + | 0.0598274i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 38.8385i | − | 1.75994i | −0.475027 | − | 0.879971i | \(-0.657562\pi\) | ||
0.475027 | − | 0.879971i | \(-0.342438\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.6128 | −0.706037 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.7467 | 1.29732 | 0.648660 | − | 0.761079i | \(-0.275330\pi\) | ||||
0.648660 | + | 0.761079i | \(0.275330\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 42.5718i | − | 1.91734i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.18421 | − | 8.42864i | 0.0532262 | − | 0.378839i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 2.56199i | − | 0.114921i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.63158 | −0.252104 | −0.126052 | − | 0.992024i | \(-0.540231\pi\) | ||||
−0.126052 | + | 0.992024i | \(0.540231\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.51114 | −0.0675126 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.9590i | 1.55874i | 0.626561 | + | 0.779372i | \(0.284462\pi\) | ||||
−0.626561 | + | 0.779372i | \(0.715538\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.82516 | + | 41.4608i | −0.259216 | + | 1.84498i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 12.6128i | − | 0.560156i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.9906 | 0.487151 | 0.243576 | − | 0.969882i | \(-0.421680\pi\) | ||||
0.243576 | + | 0.969882i | \(0.421680\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.9906 | −0.486197 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.622216i | 0.0274715i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.89829 | − | 0.266706i | −0.0836486 | − | 0.0117525i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.2034i | 1.94406i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.53035 | −0.286651 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.90766 | 0.302630 | 0.151315 | − | 0.988486i | \(-0.451649\pi\) | ||||
0.151315 | + | 0.988486i | \(0.451649\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 37.7146i | − | 1.64914i | −0.565758 | − | 0.824571i | \(-0.691416\pi\) | ||
0.565758 | − | 0.824571i | \(-0.308584\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.80642 | − | 1.37778i | −0.209770 | − | 0.0601314i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.75557i | 0.120034i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.1240 | 0.701043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.6128 | −0.503955 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.87601i | 0.124574i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.5620 | + | 3.45091i | 1.06191 | + | 0.149196i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.29529i | 0.271662i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.80642 | −0.163954 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.12399 | −0.134311 | −0.0671553 | − | 0.997743i | \(-0.521392\pi\) | ||||
−0.0671553 | + | 0.997743i | \(0.521392\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.85728i | 0.294274i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.74620 | − | 12.4286i | 0.0747990 | − | 0.532384i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5.51114i | − | 0.235639i | −0.993035 | − | 0.117820i | \(-0.962410\pi\) | ||
0.993035 | − | 0.117820i | \(-0.0375905\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.10171 | 0.345773 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.98126 | −0.254810 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.75557i | − | 0.287276i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.387152 | + | 2.75557i | −0.0164337 | + | 0.116967i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 36.7052i | − | 1.55525i | −0.628729 | − | 0.777624i | \(-0.716425\pi\) | ||
0.628729 | − | 0.777624i | \(-0.283575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.02227 | −0.127829 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.8573 | 0.711715 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.4924i | 1.15867i | 0.815091 | + | 0.579333i | \(0.196687\pi\) | ||||
−0.815091 | + | 0.579333i | \(0.803313\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −35.9496 | − | 5.05086i | −1.51241 | − | 0.212491i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.2444 | −0.974457 | −0.487229 | − | 0.873274i | \(-0.661992\pi\) | ||||
−0.487229 | + | 0.873274i | \(0.661992\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.5111 | 1.06761 | 0.533804 | − | 0.845608i | \(-0.320762\pi\) | ||||
0.533804 | + | 0.845608i | \(0.320762\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 10.5620i | − | 0.441234i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.61285 | + | 12.6035i | −0.150666 | + | 0.525601i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 26.0701i | − | 1.08531i | −0.839955 | − | 0.542656i | \(-0.817419\pi\) | ||
0.839955 | − | 0.542656i | \(-0.182581\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.24443 | 0.217951 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.6128 | 0.481782 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 51.3087i | 2.12499i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.37778 | + | 0.193576i | 0.0569644 | + | 0.00800339i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 12.2667i | − | 0.506301i | −0.967427 | − | 0.253151i | \(-0.918533\pi\) | ||
0.967427 | − | 0.253151i | \(-0.0814668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.387152 | 0.0159523 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.7462 | −0.729981 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14.9175i | − | 0.612588i | −0.951937 | − | 0.306294i | \(-0.900911\pi\) | ||
0.951937 | − | 0.306294i | \(-0.0990891\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.37778 | − | 9.80642i | 0.0564837 | − | 0.402024i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.2351i | 0.828166i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.5620 | −1.08529 | −0.542647 | − | 0.839961i | \(-0.682578\pi\) | ||||
−0.542647 | + | 0.839961i | \(0.682578\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.7146 | 1.61999 | 0.809995 | − | 0.586436i | \(-0.199470\pi\) | ||||
0.809995 | + | 0.586436i | \(0.199470\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.08541 | + | 7.72546i | −0.0441283 | + | 0.314084i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.28544i | 0.255118i | 0.991831 | + | 0.127559i | \(0.0407143\pi\) | ||||
−0.991831 | + | 0.127559i | \(0.959286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.61285 | −0.389532 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.22570 | −0.292320 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 45.7146i | − | 1.84639i | −0.384328 | − | 0.923197i | \(-0.625567\pi\) | ||
0.384328 | − | 0.923197i | \(-0.374433\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.2351 | + | 1.43801i | 0.412718 | + | 0.0579861i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 4.88892i | − | 0.196821i | −0.995146 | − | 0.0984103i | \(-0.968624\pi\) | ||
0.995146 | − | 0.0984103i | \(-0.0313758\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.2351 | 0.491769 | 0.245884 | − | 0.969299i | \(-0.420922\pi\) | ||||
0.245884 | + | 0.969299i | \(0.420922\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.62222 | 0.105226 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.23506i | 0.329931i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2034 | + | 13.2444i | 0.848137 | + | 0.529777i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 2.36842i | − | 0.0945854i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.51114 | −0.219743 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.24443 | −0.0495400 | −0.0247700 | − | 0.999693i | \(-0.507885\pi\) | ||||
−0.0247700 | + | 0.999693i | \(0.507885\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.3274i | 0.847688i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33.9813 | − | 4.77430i | −1.34851 | − | 0.189462i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.622216i | − | 0.0246531i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.56199 | 0.101351 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −48.1847 | −1.90318 | −0.951590 | − | 0.307369i | \(-0.900551\pi\) | ||||
−0.951590 | + | 0.307369i | \(0.900551\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 4.85728i | − | 0.191552i | −0.995403 | − | 0.0957762i | \(-0.969467\pi\) | ||
0.995403 | − | 0.0957762i | \(-0.0305333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.51114 | + | 10.7556i | −0.0595010 | + | 0.423500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.203420i | 0.00799728i | 0.999992 | + | 0.00399864i | \(0.00127281\pi\) | ||||
−0.999992 | + | 0.00399864i | \(0.998727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 44.2034 | 1.73514 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.622216 | 0.0243866 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 27.3145i | − | 1.06890i | −0.845200 | − | 0.534449i | \(-0.820519\pi\) | ||
0.845200 | − | 0.534449i | \(-0.179481\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.24443 | + | 8.85728i | −0.0486240 | + | 0.346083i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 10.9906i | − | 0.428785i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.3176 | 1.29787 | 0.648934 | − | 0.760845i | \(-0.275215\pi\) | ||||
0.648934 | + | 0.760845i | \(0.275215\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.5906 | 0.567508 | 0.283754 | − | 0.958897i | \(-0.408420\pi\) | ||||
0.283754 | + | 0.958897i | \(0.408420\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.75557i | 0.107017i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.37778 | − | 0.193576i | −0.0534282 | − | 0.00750656i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.2070i | 0.976017i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.71456 | 0.375587 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.8385 | −1.19051 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.53341i | 0.174750i | 0.996175 | + | 0.0873751i | \(0.0278479\pi\) | ||||
−0.996175 | + | 0.0873751i | \(0.972152\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.37778 | − | 4.80642i | 0.0530309 | − | 0.184999i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.2672i | 1.04796i | 0.851730 | + | 0.523981i | \(0.175554\pi\) | ||||
−0.851730 | + | 0.523981i | \(0.824446\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.23506 | 0.162527 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.3461 | −0.434785 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.5812i | 1.13189i | 0.824442 | + | 0.565947i | \(0.191489\pi\) | ||||
−0.824442 | + | 0.565947i | \(0.808511\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.8479 | − | 5.31756i | −1.44609 | − | 0.203174i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.34614i | 0.0513585i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.38715 | −0.319525 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.99063 | −0.113769 | −0.0568845 | − | 0.998381i | \(-0.518117\pi\) | ||||
−0.0568845 | + | 0.998381i | \(0.518117\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 3.80642i | − | 0.144594i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.19358 | − | 29.8479i | 0.159071 | − | 1.13220i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.4701i | 0.775361i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.3778 | 0.581641 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.0420 | −1.55013 | −0.775067 | − | 0.631879i | \(-0.782284\pi\) | ||||
−0.775067 | + | 0.631879i | \(0.782284\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.774305i | 0.0292035i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.61285 | + | 25.7146i | −0.136068 | + | 0.968466i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.7239i | 0.704186i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.4291 | 1.55590 | 0.777952 | − | 0.628324i | \(-0.216259\pi\) | ||||
0.777952 | + | 0.628324i | \(0.216259\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.75557 | 0.253354 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.63158i | − | 0.0611033i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.24443 | − | 0.736833i | −0.196131 | − | 0.0275560i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 7.53972i | − | 0.281576i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.9590 | −0.707051 | −0.353525 | − | 0.935425i | \(-0.615017\pi\) | ||||
−0.353525 | + | 0.935425i | \(0.615017\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.857279 | −0.0319267 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 23.9813i | − | 0.891873i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 46.2034 | + | 13.2444i | 1.71595 | + | 0.491886i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.7975i | 1.55018i | 0.631848 | + | 0.775092i | \(0.282297\pi\) | ||||
−0.631848 | + | 0.775092i | \(0.717703\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.5111 | −0.795618 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.3145i | 0.565654i | 0.959171 | + | 0.282827i | \(0.0912722\pi\) | ||||
−0.959171 | + | 0.282827i | \(0.908728\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.21432 | − | 0.311108i | −0.0816764 | − | 0.0114754i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.7368 | −1.20424 | −0.602122 | − | 0.798404i | \(-0.705678\pi\) | ||||
−0.602122 | + | 0.798404i | \(0.705678\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.387152 | 0.0142224 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.3778i | 1.37126i | 0.727951 | + | 0.685629i | \(0.240473\pi\) | ||||
−0.727951 | + | 0.685629i | \(0.759527\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.90766 | + | 20.6953i | −0.106528 | + | 0.758219i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.6128i | 0.424892i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.0923 | 0.405305 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.3497 | −0.742570 | −0.371285 | − | 0.928519i | \(-0.621083\pi\) | ||||
−0.371285 | + | 0.928519i | \(0.621083\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.1017i | 0.513895i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.22216 | + | 15.8163i | −0.0808725 | + | 0.575613i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.95899i | 0.252929i | 0.991971 | + | 0.126464i | \(0.0403629\pi\) | ||||
−0.991971 | + | 0.126464i | \(0.959637\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.98126 | −0.362297 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.6419 | 1.76327 | 0.881634 | − | 0.471934i | \(-0.156444\pi\) | ||||
0.881634 | + | 0.471934i | \(0.156444\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 5.61285i | − | 0.203199i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.80642 | + | 1.37778i | 0.354552 | + | 0.0498139i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.22570i | 0.260905i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.6923 | 0.890426 | 0.445213 | − | 0.895425i | \(-0.353128\pi\) | ||||
0.445213 | + | 0.895425i | \(0.353128\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.0192 | −0.612932 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.0415i | 1.29632i | 0.761503 | + | 0.648161i | \(0.224462\pi\) | ||||
−0.761503 | + | 0.648161i | \(0.775538\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.99063 | − | 0.857279i | −0.107427 | − | 0.0307944i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.24443i | 0.0446437i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.87601 | 0.103044 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.75203 | −0.348955 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 9.61285i | − | 0.343535i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.4795 | − | 2.17484i | −0.552487 | − | 0.0776234i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 32.2034i | − | 1.14793i | −0.818881 | − | 0.573964i | \(-0.805405\pi\) | ||
0.818881 | − | 0.573964i | \(-0.194595\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.6035 | −0.448696 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.2351 | −0.577252 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5.04101i | − | 0.179012i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.19358 | + | 29.8479i | −0.148731 | + | 1.05860i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.5526i | 0.621746i | 0.950451 | + | 0.310873i | \(0.100621\pi\) | ||||
−0.950451 | + | 0.310873i | \(0.899379\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51.4291 | −1.81943 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.23506 | −0.290972 |