Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,3,Mod(209,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.209");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.c (of order \(2\), degree \(1\), 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: | \(30.5177896084\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.10 | ||
Character | \(\chi\) | \(=\) | 1120.209 |
Dual form | 1120.3.c.g.209.9 |
$q$-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 \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.23212i | 1.07737i | 0.842506 | + | 0.538686i | \(0.181079\pi\) | ||||
−0.842506 | + | 0.538686i | \(0.818921\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.82711 | + | 3.21764i | 0.765423 | + | 0.643528i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.97525 | + | 0.588096i | 0.996465 | + | 0.0840137i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.44659 | −0.160732 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 13.5631i | − | 1.23301i | −0.787352 | − | 0.616504i | \(-0.788548\pi\) | ||
0.787352 | − | 0.616504i | \(-0.211452\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.1906i | 1.63004i | 0.579430 | + | 0.815022i | \(0.303275\pi\) | ||||
−0.579430 | + | 0.815022i | \(0.696725\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.3998 | + | 12.3697i | −0.693319 | + | 0.824646i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.174717 | −0.0102775 | −0.00513874 | − | 0.999987i | \(-0.501636\pi\) | ||||
−0.00513874 | + | 0.999987i | \(0.501636\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.7233 | 1.09070 | 0.545351 | − | 0.838208i | \(-0.316396\pi\) | ||||
0.545351 | + | 0.838208i | \(0.316396\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.90080 | + | 22.5448i | −0.0905141 | + | 1.07356i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 27.0982i | − | 1.17818i | −0.808067 | − | 0.589091i | \(-0.799486\pi\) | ||
0.808067 | − | 0.589091i | \(-0.200514\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.29361 | + | 24.6285i | 0.171744 | + | 0.985142i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 24.4135i | 0.904204i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 18.8246i | 0.649124i | 0.945864 | + | 0.324562i | \(0.105217\pi\) | ||||
−0.945864 | + | 0.324562i | \(0.894783\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.48886i | 0.241576i | 0.992678 | + | 0.120788i | \(0.0385421\pi\) | ||||
−0.992678 | + | 0.120788i | \(0.961458\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 43.8375 | 1.32841 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 24.8028 | + | 24.6945i | 0.708652 | + | 0.705558i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 66.6203 | 1.80055 | 0.900274 | − | 0.435324i | \(-0.143366\pi\) | ||||
0.900274 | + | 0.435324i | \(0.143366\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −68.4904 | −1.75617 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 40.1326i | − | 0.978844i | −0.872047 | − | 0.489422i | \(-0.837208\pi\) | ||
0.872047 | − | 0.489422i | \(-0.162792\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −27.6721 | −0.643536 | −0.321768 | − | 0.946818i | \(-0.604277\pi\) | ||||
−0.321768 | + | 0.946818i | \(0.604277\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.53627 | − | 4.65461i | −0.123028 | − | 0.103436i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.05114 | 0.192577 | 0.0962887 | − | 0.995353i | \(-0.469303\pi\) | ||||
0.0962887 | + | 0.995353i | \(0.469303\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.3083 | + | 8.20423i | 0.985883 | + | 0.167433i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 0.564706i | − | 0.0110727i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −60.9906 | −1.15077 | −0.575383 | − | 0.817884i | \(-0.695147\pi\) | ||||
−0.575383 | + | 0.817884i | \(0.695147\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 43.6411 | − | 51.9075i | 0.793475 | − | 0.943773i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 66.9803i | 1.17509i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.5469 | 0.246557 | 0.123279 | − | 0.992372i | \(-0.460659\pi\) | ||||
0.123279 | + | 0.992372i | \(0.460659\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35.7308 | 0.585751 | 0.292875 | − | 0.956151i | \(-0.405388\pi\) | ||||
0.292875 | + | 0.956151i | \(0.405388\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.0903 | − | 0.850734i | −0.160164 | − | 0.0135037i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −68.1836 | + | 81.0987i | −1.04898 | + | 1.24767i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 92.9010 | 1.38658 | 0.693291 | − | 0.720658i | \(-0.256160\pi\) | ||||
0.693291 | + | 0.720658i | \(0.256160\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 87.5845 | 1.26934 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −66.0567 | −0.930376 | −0.465188 | − | 0.885212i | \(-0.654013\pi\) | ||||
−0.465188 | + | 0.885212i | \(0.654013\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −51.4978 | −0.705450 | −0.352725 | − | 0.935727i | \(-0.614745\pi\) | ||||
−0.352725 | + | 0.935727i | \(0.614745\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −79.6024 | + | 13.8775i | −1.06136 | + | 0.185033i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.97640 | − | 94.6060i | 0.103590 | − | 1.22865i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −77.1971 | −0.977179 | −0.488589 | − | 0.872514i | \(-0.662488\pi\) | ||||
−0.488589 | + | 0.872514i | \(0.662488\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −91.9267 | −1.13490 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 94.6032i | − | 1.13980i | −0.821715 | − | 0.569899i | \(-0.806982\pi\) | ||
0.821715 | − | 0.569899i | \(-0.193018\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.668662 | − | 0.562176i | −0.00786661 | − | 0.00661384i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −60.8433 | −0.699348 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 59.6907i | 0.670682i | 0.942097 | + | 0.335341i | \(0.108851\pi\) | ||||
−0.942097 | + | 0.335341i | \(0.891149\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.4621 | + | 147.810i | −0.136946 | + | 1.62428i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −24.2049 | −0.260267 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 79.3106 | + | 66.6802i | 0.834848 | + | 0.701897i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 28.6155 | 0.295006 | 0.147503 | − | 0.989062i | \(-0.452876\pi\) | ||||
0.147503 | + | 0.989062i | \(0.452876\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.6202i | 0.198184i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −193.520 | −1.91604 | −0.958021 | − | 0.286697i | \(-0.907443\pi\) | ||||
−0.958021 | + | 0.286697i | \(0.907443\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −164.516 | −1.59725 | −0.798624 | − | 0.601831i | \(-0.794438\pi\) | ||||
−0.798624 | + | 0.601831i | \(0.794438\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −79.8157 | + | 80.1656i | −0.760150 | + | 0.763482i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 79.2388 | 0.740550 | 0.370275 | − | 0.928922i | \(-0.379263\pi\) | ||||
0.370275 | + | 0.928922i | \(0.379263\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 135.174i | 1.24013i | 0.784551 | + | 0.620065i | \(0.212894\pi\) | ||||
−0.784551 | + | 0.620065i | \(0.787106\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 215.325i | 1.93986i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 40.6363i | 0.359613i | 0.983702 | + | 0.179807i | \(0.0575472\pi\) | ||||
−0.983702 | + | 0.179807i | \(0.942453\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 87.1921 | − | 103.708i | 0.758192 | − | 0.901807i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 30.6541i | − | 0.262001i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.21870 | − | 0.102750i | −0.0102411 | − | 0.000863449i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −62.9573 | −0.520309 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 129.713 | 1.05458 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −62.8136 | + | 108.072i | −0.502509 | + | 0.864572i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 102.631i | 0.808118i | 0.914733 | + | 0.404059i | \(0.132401\pi\) | ||||
−0.914733 | + | 0.404059i | \(0.867599\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 89.4394i | − | 0.693329i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 73.4099 | 0.560381 | 0.280191 | − | 0.959944i | \(-0.409602\pi\) | ||||
0.280191 | + | 0.959944i | \(0.409602\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 144.550 | + | 12.1873i | 1.08685 | + | 0.0916339i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −78.5539 | + | 93.4333i | −0.581880 | + | 0.692099i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 34.6820i | − | 0.253153i | −0.991957 | − | 0.126577i | \(-0.959601\pi\) | ||
0.991957 | − | 0.126577i | \(-0.0403990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −41.2578 | −0.296819 | −0.148409 | − | 0.988926i | \(-0.547415\pi\) | ||||
−0.148409 | + | 0.988926i | \(0.547415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29.2544i | 0.207478i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 287.410 | 2.00986 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −60.5707 | + | 72.0438i | −0.417729 | + | 0.496854i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −26.5171 | + | 156.138i | −0.180388 | + | 1.06216i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 197.409i | − | 1.32489i | −0.749110 | − | 0.662446i | \(-0.769518\pi\) | ||
0.749110 | − | 0.662446i | \(-0.230482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 77.3543 | 0.512280 | 0.256140 | − | 0.966640i | \(-0.417549\pi\) | ||||
0.256140 | + | 0.966640i | \(0.417549\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.252744 | 0.00165192 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.0964 | + | 28.6607i | −0.155461 | + | 0.184908i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 111.633i | − | 0.711038i | −0.934669 | − | 0.355519i | \(-0.884304\pi\) | ||
0.934669 | − | 0.355519i | \(-0.115696\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 197.129i | − | 1.23980i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.9363 | − | 189.017i | 0.0989834 | − | 1.17402i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −311.331 | −1.91001 | −0.955004 | − | 0.296592i | \(-0.904150\pi\) | ||||
−0.955004 | + | 0.296592i | \(0.904150\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 167.771 | + | 141.053i | 1.01679 | + | 0.854868i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.1911 | −0.102941 | −0.0514704 | − | 0.998675i | \(-0.516391\pi\) | ||||
−0.0514704 | + | 0.998675i | \(0.516391\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −280.040 | −1.65704 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −29.9782 | −0.175311 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 192.100i | 1.11040i | 0.831716 | + | 0.555201i | \(0.187359\pi\) | ||||
−0.831716 | + | 0.555201i | \(0.812641\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.4651 | + | 174.315i | 0.0883719 | + | 0.996088i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 47.0172i | 0.265634i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 116.518i | 0.650936i | 0.945553 | + | 0.325468i | \(0.105522\pi\) | ||||
−0.945553 | + | 0.325468i | \(0.894478\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 116.427 | 0.643241 | 0.321620 | − | 0.946869i | \(-0.395773\pi\) | ||||
0.321620 | + | 0.946869i | \(0.395773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 115.486i | 0.631072i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 254.963 | + | 214.360i | 1.37818 | + | 1.15870i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.36970i | 0.0126722i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.3575 | + | 170.290i | −0.0759655 | + | 0.901008i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −126.956 | −0.664692 | −0.332346 | − | 0.943157i | \(-0.607840\pi\) | ||||
−0.332346 | + | 0.943157i | \(0.607840\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 231.635i | − | 1.20018i | −0.799932 | − | 0.600090i | \(-0.795131\pi\) | ||
0.799932 | − | 0.600090i | \(-0.204869\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −262.121 | − | 220.377i | −1.34421 | − | 1.13014i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −77.9924 | −0.395900 | −0.197950 | − | 0.980212i | \(-0.563428\pi\) | ||||
−0.197950 | + | 0.980212i | \(0.563428\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 227.874i | − | 1.14509i | −0.819872 | − | 0.572547i | \(-0.805956\pi\) | ||
0.819872 | − | 0.572547i | \(-0.194044\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 300.267i | 1.49387i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.0707 | + | 131.306i | −0.0545353 | + | 0.646829i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 129.132 | − | 153.592i | 0.629913 | − | 0.749229i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 39.2000i | 0.189372i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 281.072i | − | 1.34484i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 214.499i | − | 1.01658i | −0.861185 | − | 0.508291i | \(-0.830277\pi\) | ||
0.861185 | − | 0.508291i | \(-0.169723\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 213.503i | − | 1.00236i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −105.904 | − | 89.0387i | −0.492578 | − | 0.414133i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.40417 | + | 52.2367i | −0.0202957 | + | 0.240722i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 166.447i | − | 0.760032i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.70235i | − | 0.0167527i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.8367 | −0.0485949 | −0.0242975 | − | 0.999705i | \(-0.507735\pi\) | ||||
−0.0242975 | + | 0.999705i | \(0.507735\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.21110 | − | 35.6274i | −0.0276049 | − | 0.158344i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 297.246i | 1.30945i | 0.755865 | + | 0.654727i | \(0.227216\pi\) | ||||
−0.755865 | + | 0.654727i | \(0.772784\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 39.4044 | 0.172072 | 0.0860358 | − | 0.996292i | \(-0.472580\pi\) | ||||
0.0860358 | + | 0.996292i | \(0.472580\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 305.778 | + | 25.7807i | 1.32371 | + | 0.111605i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 316.557i | − | 1.35861i | −0.733855 | − | 0.679306i | \(-0.762281\pi\) | ||
0.733855 | − | 0.679306i | \(-0.237719\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 34.6398 | + | 29.1233i | 0.147403 | + | 0.123929i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 249.510i | − | 1.05279i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 181.500 | 0.759416 | 0.379708 | − | 0.925106i | \(-0.376024\pi\) | ||||
0.379708 | + | 0.925106i | \(0.376024\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 203.756i | − | 0.845460i | −0.906256 | − | 0.422730i | \(-0.861072\pi\) | ||
0.906256 | − | 0.422730i | \(-0.138928\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 77.3963i | − | 0.318503i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 158.483 | + | 186.837i | 0.646870 | + | 0.762600i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 439.139i | 1.77789i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 305.769 | 1.22799 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −120.326 | −0.479388 | −0.239694 | − | 0.970848i | \(-0.577047\pi\) | ||||
−0.239694 | + | 0.970848i | \(0.577047\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −367.535 | −1.45271 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.81702 | − | 2.16120i | 0.00712557 | − | 0.00847528i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 214.282 | 0.833783 | 0.416892 | − | 0.908956i | \(-0.363119\pi\) | ||||
0.416892 | + | 0.908956i | \(0.363119\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 464.693 | + | 39.1791i | 1.79418 | + | 0.151271i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 27.2315i | − | 0.104335i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 388.319i | − | 1.47650i | −0.674529 | − | 0.738248i | \(-0.735653\pi\) | ||
0.674529 | − | 0.738248i | \(-0.264347\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −233.418 | − | 196.246i | −0.880822 | − | 0.740549i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −192.927 | −0.722574 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 442.119 | 1.64357 | 0.821783 | − | 0.569800i | \(-0.192980\pi\) | ||||
0.821783 | + | 0.569800i | \(0.192980\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 277.087i | 1.02246i | 0.859444 | + | 0.511231i | \(0.170810\pi\) | ||||
−0.859444 | + | 0.511231i | \(0.829190\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −477.738 | − | 40.2789i | −1.74996 | − | 0.147542i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 334.039 | − | 58.2346i | 1.21469 | − | 0.211762i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 287.260 | 1.03704 | 0.518520 | − | 0.855065i | \(-0.326483\pi\) | ||||
0.518520 | + | 0.855065i | \(0.326483\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 10.8333i | − | 0.0388291i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 234.412 | 0.834206 | 0.417103 | − | 0.908859i | \(-0.363045\pi\) | ||||
0.417103 | + | 0.908859i | \(0.363045\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 76.8321i | − | 0.271491i | −0.990744 | − | 0.135746i | \(-0.956657\pi\) | ||
0.990744 | − | 0.135746i | \(-0.0433430\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −215.518 | + | 256.341i | −0.756204 | + | 0.899443i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.6018 | − | 279.935i | 0.0822363 | − | 0.975383i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −288.969 | −0.999894 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 92.4889i | 0.317831i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 248.602i | 0.848472i | 0.905552 | + | 0.424236i | \(0.139457\pi\) | ||||
−0.905552 | + | 0.424236i | \(0.860543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 55.6725 | + | 46.8066i | 0.188720 | + | 0.158666i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 331.123 | 1.11489 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 574.226 | 1.92049 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −193.020 | − | 16.2738i | −0.641261 | − | 0.0540659i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 625.481i | − | 2.06429i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 136.746 | + | 114.969i | 0.448347 | + | 0.376947i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 244.931i | 0.797822i | 0.916990 | + | 0.398911i | \(0.130612\pi\) | ||||
−0.916990 | + | 0.398911i | \(0.869388\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 531.737i | − | 1.72083i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 556.903i | − | 1.79069i | −0.445378 | − | 0.895343i | \(-0.646931\pi\) | ||
0.445378 | − | 0.895343i | \(-0.353069\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 64.7781 | 0.206959 | 0.103479 | − | 0.994632i | \(-0.467002\pi\) | ||||
0.103479 | + | 0.994632i | \(0.467002\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −35.8795 | − | 35.7229i | −0.113903 | − | 0.113406i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −562.104 | −1.77320 | −0.886599 | − | 0.462539i | \(-0.846938\pi\) | ||||
−0.886599 | + | 0.462539i | \(0.846938\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 255.319 | 0.800375 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 256.109i | 0.797848i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.62072 | −0.0112097 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −521.893 | + | 90.9841i | −1.60582 | + | 0.279951i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −436.899 | −1.33608 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 63.1340 | + | 5.32294i | 0.191897 | + | 0.0161791i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 115.044i | − | 0.347566i | −0.984784 | − | 0.173783i | \(-0.944401\pi\) | ||
0.984784 | − | 0.173783i | \(-0.0555991\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −96.3722 | −0.289406 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 355.543 | + | 298.922i | 1.06132 | + | 0.892304i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 93.7824i | 0.278286i | 0.990272 | + | 0.139143i | \(0.0444348\pi\) | ||||
−0.990272 | + | 0.139143i | \(0.955565\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −131.341 | −0.387437 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 101.572 | 0.297865 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 332.138 | + | 85.6365i | 0.968331 | + | 0.249669i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 335.196 | + | 281.815i | 0.971582 | + | 0.816856i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −306.423 | −0.883063 | −0.441531 | − | 0.897246i | \(-0.645565\pi\) | ||||
−0.441531 | + | 0.897246i | \(0.645565\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 386.434 | 1.10726 | 0.553631 | − | 0.832762i | \(-0.313242\pi\) | ||||
0.553631 | + | 0.832762i | \(0.313242\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −517.336 | −1.47389 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 140.883 | 0.399103 | 0.199551 | − | 0.979887i | \(-0.436052\pi\) | ||||
0.199551 | + | 0.979887i | \(0.436052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −252.807 | − | 212.547i | −0.712131 | − | 0.598723i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.332101 | − | 3.93897i | 0.000930256 | − | 0.0110335i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 331.195 | 0.922549 | 0.461274 | − | 0.887258i | \(-0.347392\pi\) | ||||
0.461274 | + | 0.887258i | \(0.347392\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 68.4565 | 0.189630 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 203.486i | − | 0.560566i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −197.088 | − | 165.701i | −0.539967 | − | 0.453976i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.40380 | 0.00654988 | 0.00327494 | − | 0.999995i | \(-0.498958\pi\) | ||||
0.00327494 | + | 0.999995i | \(0.498958\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 58.0554i | 0.157332i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −425.424 | − | 35.8683i | −1.14670 | − | 0.0966800i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −91.6748 | −0.245777 | −0.122889 | − | 0.992420i | \(-0.539216\pi\) | ||||
−0.122889 | + | 0.992420i | \(0.539216\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −349.300 | − | 203.021i | −0.931467 | − | 0.541389i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −398.904 | −1.05810 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 217.188i | − | 0.573055i | −0.958072 | − | 0.286527i | \(-0.907499\pi\) | ||
0.958072 | − | 0.286527i | \(-0.0925009\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −331.715 | −0.870644 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −425.682 | −1.11144 | −0.555721 | − | 0.831369i | \(-0.687558\pi\) | ||||
−0.555721 | + | 0.831369i | \(0.687558\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 334.934 | − | 336.403i | 0.869959 | − | 0.873773i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 40.0302 | 0.103437 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 678.005i | − | 1.74294i | −0.490446 | − | 0.871471i | \(-0.663166\pi\) | ||
0.490446 | − | 0.871471i | \(-0.336834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.73451i | 0.0121087i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 237.270i | 0.603739i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −295.442 | − | 248.392i | −0.747955 | − | 0.628841i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 8.36325i | − | 0.0210661i | −0.999945 | − | 0.0105331i | \(-0.996647\pi\) | ||
0.999945 | − | 0.0105331i | \(-0.00335284\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −39.3908 | + | 467.204i | −0.0987239 | + | 1.17094i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 579.986 | 1.44635 | 0.723174 | − | 0.690665i | \(-0.242682\pi\) | ||||
0.723174 | + | 0.690665i | \(0.242682\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −158.693 | −0.393780 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −351.814 | − | 295.787i | −0.868677 | − | 0.730338i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 903.576i | − | 2.22009i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 374.870i | − | 0.916551i | −0.888810 | − | 0.458276i | \(-0.848467\pi\) | ||
0.888810 | − | 0.458276i | \(-0.151533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 112.096 | 0.272740 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 101.468 | + | 8.55495i | 0.245685 | + | 0.0207142i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 304.399 | − | 362.057i | 0.733491 | − | 0.872427i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 133.350i | − | 0.319784i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 142.070 | 0.339068 | 0.169534 | − | 0.985524i | \(-0.445774\pi\) | ||||
0.169534 | + | 0.985524i | \(0.445774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 92.9811i | − | 0.220858i | −0.993884 | − | 0.110429i | \(-0.964778\pi\) | ||
0.993884 | − | 0.110429i | \(-0.0352224\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.0933 | −0.0309534 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.750167 | − | 4.30303i | −0.00176510 | − | 0.0101248i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 249.231 | + | 21.0131i | 0.583680 | + | 0.0492111i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 928.942i | 2.16537i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 432.813 | 1.00421 | 0.502103 | − | 0.864808i | \(-0.332560\pi\) | ||||
0.502103 | + | 0.864808i | \(0.332560\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 681.677 | 1.57431 | 0.787156 | − | 0.616755i | \(-0.211553\pi\) | ||||
0.787156 | + | 0.616755i | \(0.211553\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −232.854 | − | 195.772i | −0.535297 | − | 0.450050i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 561.564i | − | 1.28504i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 676.687i | − | 1.54143i | −0.637181 | − | 0.770714i | \(-0.719899\pi\) | ||
0.637181 | − | 0.770714i | \(-0.280101\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −69.8823 | − | 11.8682i | −0.158463 | − | 0.0269120i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −57.8517 | −0.130591 | −0.0652954 | − | 0.997866i | \(-0.520799\pi\) | ||||
−0.0652954 | + | 0.997866i | \(0.520799\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −192.063 | + | 228.443i | −0.431602 | + | 0.513355i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 638.049 | 1.42740 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 509.913 | 1.13566 | 0.567832 | − | 0.823145i | \(-0.307782\pi\) | ||||
0.567832 | + | 0.823145i | \(0.307782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −544.322 | −1.20692 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 250.018i | 0.551916i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −523.292 | + | 525.586i | −1.15009 | + | 1.15513i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 470.149i | − | 1.02877i | −0.857559 | − | 0.514386i | \(-0.828020\pi\) | ||
0.857559 | − | 0.514386i | \(-0.171980\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 4.26546i | − | 0.00929294i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −210.628 | −0.456893 | −0.228447 | − | 0.973556i | \(-0.573365\pi\) | ||||
−0.228447 | + | 0.973556i | \(0.573365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 708.908i | 1.53112i | 0.643365 | + | 0.765559i | \(0.277538\pi\) | ||||
−0.643365 | + | 0.765559i | \(0.722462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −92.6348 | − | 77.8825i | −0.199215 | − | 0.167489i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 630.872i | 1.35090i | 0.737404 | + | 0.675452i | \(0.236051\pi\) | ||||
−0.737404 | + | 0.675452i | \(0.763949\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 648.008 | + | 54.6347i | 1.38168 | + | 0.116492i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 360.811 | 0.766053 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 375.319i | 0.793486i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 88.9779 | + | 510.385i | 0.187322 | + | 1.07450i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 88.2284 | 0.184965 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 235.461i | − | 0.491569i | −0.969325 | − | 0.245784i | \(-0.920954\pi\) | ||
0.969325 | − | 0.245784i | \(-0.0790455\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1411.72i | 2.93497i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 610.924 | + | 51.5081i | 1.26485 | + | 0.106642i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 109.515 | + | 92.0745i | 0.225804 | + | 0.189844i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 11.0384i | − | 0.0226661i | −0.999936 | − | 0.0113331i | \(-0.996392\pi\) | ||
0.999936 | − | 0.0113331i | \(-0.00360750\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1006.26i | − | 2.05779i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 423.608i | − | 0.862745i | −0.902174 | − | 0.431373i | \(-0.858029\pi\) | ||
0.902174 | − | 0.431373i | \(-0.141971\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.28898i | − | 0.00667135i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −63.1308 | + | 75.0889i | −0.127537 | + | 0.151695i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −460.762 | − | 38.8477i | −0.927087 | − | 0.0781644i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.3655i | 0.0327966i | 0.999866 | + | 0.0163983i | \(0.00521997\pi\) | ||||
−0.999866 | + | 0.0163983i | \(0.994780\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 55.5637i | − | 0.110906i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −399.152 | −0.793542 | −0.396771 | − | 0.917918i | \(-0.629869\pi\) | ||||
−0.396771 | + | 0.917918i | \(0.629869\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −740.624 | − | 622.678i | −1.46658 | − | 1.23303i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 905.123i | − | 1.78525i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.2063 | 0.0632737 | 0.0316369 | − | 0.999499i | \(-0.489928\pi\) | ||||
0.0316369 | + | 0.999499i | \(0.489928\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −359.210 | − | 30.2857i | −0.702956 | − | 0.0592674i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 505.929i | 0.986217i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −629.623 | − | 529.354i | −1.22257 | − | 1.02787i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 122.761i | − | 0.237450i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −620.888 | −1.19632 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 180.110i | 0.345701i | 0.984948 | + | 0.172850i | \(0.0552977\pi\) | ||||
−0.984948 | + | 0.172850i | \(0.944702\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 92.5194i | 0.176901i | 0.996081 | + | 0.0884507i | \(0.0281916\pi\) | ||||
−0.996081 | + | 0.0884507i | \(0.971808\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −563.408 | + | 49.9850i | −1.07316 | + | 0.0952095i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.30843i | − | 0.00248279i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −205.311 | −0.388111 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.0434 | −0.0396297 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 850.432 | 1.59556 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 303.256 | + | 254.962i | 0.566834 | + | 0.476564i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −376.599 | −0.701301 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 111.275 | − | 655.210i | 0.206447 | − | 1.21560i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 99.4342i | 0.183797i | 0.995768 | + | 0.0918986i | \(0.0292936\pi\) | ||||
−0.995768 | + | 0.0918986i | \(0.970706\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 376.304i | 0.693010i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −434.941 | + | 517.327i | −0.798057 | + | 0.949223i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −103.740 | −0.189652 | −0.0948262 | − | 0.995494i | \(-0.530230\pi\) | ||||
−0.0948262 | + | 0.995494i | \(0.530230\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −51.6879 | −0.0941491 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 390.108i | 0.708000i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −538.469 | − | 45.3993i | −0.973724 | − | 0.0820964i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −692.836 | + | 824.072i | −1.24835 | + | 1.48481i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −547.554 | −0.983041 | −0.491520 | − | 0.870866i | \(-0.663559\pi\) | ||||
−0.491520 | + | 0.870866i | \(0.663559\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 586.387i | − | 1.04899i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.65916 | −0.0136527 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 801.866i | − | 1.42427i | −0.702041 | − | 0.712137i | \(-0.747728\pi\) | ||
0.702041 | − | 0.712137i | \(-0.252272\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −130.753 | + | 155.520i | −0.231421 | + | 0.275256i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −641.212 | − | 54.0617i | −1.13089 | − | 0.0953469i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 429.252 | 0.754398 | 0.377199 | − | 0.926132i | \(-0.376887\pi\) | ||||
0.377199 | + | 0.926132i | \(0.376887\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 705.248i | 1.23511i | 0.786527 | + | 0.617556i | \(0.211877\pi\) | ||||
−0.786527 | + | 0.617556i | \(0.788123\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 410.338i | − | 0.716122i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 667.388 | − | 116.349i | 1.16068 | − | 0.202346i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 856.994 | 1.48526 | 0.742629 | − | 0.669702i | \(-0.233578\pi\) | ||||
0.742629 | + | 0.669702i | \(0.233578\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 748.671 | 1.29304 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 55.6358 | − | 659.881i | 0.0957586 | − | 1.13577i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 827.220i | 1.41890i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 98.6338 | − | 117.317i | 0.168605 | − | 0.200541i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 87.0152i | − | 0.148237i | −0.997249 | − | 0.0741186i | \(-0.976386\pi\) | ||
0.997249 | − | 0.0741186i | \(-0.0236143\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 155.194i | 0.263487i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 252.081i | − | 0.426532i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −330.416 | −0.557193 | −0.278597 | − | 0.960408i | \(-0.589869\pi\) | ||||
−0.278597 | + | 0.960408i | \(0.589869\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.33347 | − | 4.31456i | −0.00728315 | − | 0.00725136i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 736.514 | 1.23369 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −734.397 | −1.22604 | −0.613019 | − | 0.790068i | \(-0.710045\pi\) | ||||
−0.613019 | + | 0.790068i | \(0.710045\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 806.504i | − | 1.34194i | −0.741486 | − | 0.670969i | \(-0.765879\pi\) | ||
0.741486 | − | 0.670969i | \(-0.234121\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −134.390 | −0.222869 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −240.945 | − | 202.574i | −0.398256 | − | 0.334833i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −771.044 | −1.27025 | −0.635127 | − | 0.772408i | \(-0.719052\pi\) | ||||
−0.635127 | + | 0.772408i | \(0.719052\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −424.397 | − | 35.7817i | −0.696876 | − | 0.0587548i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 191.799i | 0.313910i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 933.654 | 1.52309 | 0.761545 | − | 0.648112i | \(-0.224441\pi\) | ||||
0.761545 | + | 0.648112i | \(0.224441\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 496.428 | + | 417.370i | 0.807199 | + | 0.678651i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 256.389i | − | 0.415542i | −0.978178 | − | 0.207771i | \(-0.933379\pi\) | ||
0.978178 | − | 0.207771i | \(-0.0666208\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 298.064 | 0.481524 | 0.240762 | − | 0.970584i | \(-0.422603\pi\) | ||||
0.240762 | + | 0.970584i | \(0.422603\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 661.562 | 1.06532 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −35.1038 | + | 416.358i | −0.0563465 | + | 0.668311i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −588.130 | + | 211.491i | −0.941008 | + | 0.338385i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 908.459 | 1.44890 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.6397 | −0.0185051 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 526.570 | 0.834501 | 0.417250 | − | 0.908792i | \(-0.362994\pi\) | ||||
0.417250 | + | 0.908792i | \(0.362994\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 693.286 | 1.09524 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −330.229 | + | 392.780i | −0.520046 | + | 0.618552i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −173.852 | + | 1023.68i | −0.272924 | + | 1.60703i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 95.5571 | 0.149542 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −204.664 | −0.319289 | −0.159644 | − | 0.987175i | \(-0.551035\pi\) | ||||
−0.159644 | + | 0.987175i | \(0.551035\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 580.457i | 0.902733i | 0.892339 | + | 0.451367i | \(0.149063\pi\) | ||||
−0.892339 | + | 0.451367i | \(0.850937\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 287.784 | − | 342.295i | 0.446176 | − | 0.530690i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1027.02 | 1.58735 | 0.793676 | − | 0.608341i | \(-0.208165\pi\) | ||||
0.793676 | + | 0.608341i | \(0.208165\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 197.300i | − | 0.304007i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −168.835 | − | 14.2348i | −0.259347 | − | 0.0218660i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −540.051 | −0.827030 | −0.413515 | − | 0.910497i | \(-0.635699\pi\) | ||||
−0.413515 | + | 0.910497i | \(0.635699\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 280.948 | + | 236.207i | 0.428929 | + | 0.360621i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 74.4963 | 0.113389 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 648.051i | 0.983386i | 0.870769 | + | 0.491693i | \(0.163622\pi\) | ||||
−0.870769 | + | 0.491693i | \(0.836378\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 63.5996 | 0.0962172 | 0.0481086 | − | 0.998842i | \(-0.484681\pi\) | ||||
0.0481086 | + | 0.998842i | \(0.484681\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.9664 | 0.0180489 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 513.997 | + | 511.753i | 0.772928 | + | 0.769554i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 510.112 | 0.764785 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 35.0254i | − | 0.0523549i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 484.620i | − | 0.722235i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 499.088i | 0.741587i | 0.928715 | + | 0.370793i | \(0.120914\pi\) | ||||
−0.928715 | + | 0.370793i | \(0.879086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −601.269 | + | 104.822i | −0.890769 | + | 0.155292i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 528.808i | 0.781105i | 0.920581 | + | 0.390553i | \(0.127716\pi\) | ||||
−0.920581 | + | 0.390553i | \(0.872284\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 199.601 | + | 16.8287i | 0.293963 | + | 0.0247845i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −960.735 | −1.41077 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 300.950 | 0.440629 | 0.220315 | − | 0.975429i | \(-0.429292\pi\) | ||||
0.220315 | + | 0.975429i | \(0.429292\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 111.594 | − | 132.732i | 0.162911 | − | 0.193769i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 127.360i | 0.185385i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1292.42i | − | 1.87580i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 761.277 | 1.10170 | 0.550852 | − | 0.834603i | \(-0.314303\pi\) | ||||
0.550852 | + | 0.834603i | \(0.314303\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11.5386 | + | 136.856i | −0.0166502 | + | 0.197484i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −157.898 | − | 132.753i | −0.227192 | − | 0.191011i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.01185i | 0.0100600i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1023.15 | 1.46373 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1086.65i | 1.55015i | 0.631870 | + | 0.775074i | \(0.282288\pi\) | ||||
−0.631870 | + | 0.775074i | \(0.717712\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1380.59 | 1.96386 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −94.1299 | + | 111.960i | −0.133518 | + | 0.158808i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1349.85 | − | 113.808i | −1.90927 | − | 0.160974i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 353.798i | − | 0.499010i | −0.968374 | − | 0.249505i | \(-0.919732\pi\) | ||
0.968374 | − | 0.249505i | \(-0.0802679\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 111.673 | 0.157064 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 202.934 | 0.284620 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1099.95 | + | 924.780i | 1.53839 | + | 1.29340i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 586.631i | 0.818174i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 63.4719i | 0.0882781i | 0.999025 | + | 0.0441390i | \(0.0140545\pi\) | ||||
−0.999025 | + | 0.0441390i | \(0.985946\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1147.54 | − | 96.7515i | −1.59160 | − | 0.134191i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 658.563 | 0.910876 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −463.622 | + | 80.8255i | −0.639479 | + | 0.111483i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 888.016 | 1.22148 | 0.610740 | − | 0.791831i | \(-0.290872\pi\) | ||||
0.610740 | + | 0.791831i | \(0.290872\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −577.186 | −0.791750 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.83478 | 0.00661393 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 54.1893i | − | 0.0739281i | −0.999317 | − | 0.0369640i | \(-0.988231\pi\) | ||
0.999317 | − | 0.0369640i | \(-0.0117687\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −603.880 | + | 512.236i | −0.821605 | + | 0.696920i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1260.02i | − | 1.70967i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1414.92i | 1.91464i | 0.289034 | + | 0.957319i | \(0.406666\pi\) | ||||
−0.289034 | + | 0.957319i | \(0.593334\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1419.35 | −1.91545 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 51.9266i | − | 0.0698877i | −0.999389 | − | 0.0349439i | \(-0.988875\pi\) | ||
0.999389 | − | 0.0349439i | \(-0.0111252\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 635.190 | − | 755.506i | 0.852605 | − | 1.01410i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 136.852i | 0.183202i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 552.711 | + | 46.6000i | 0.737932 | + | 0.0622163i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −926.269 | −1.23338 | −0.616690 | − | 0.787206i | \(-0.711527\pi\) | ||||
−0.616690 | + | 0.787206i | \(0.711527\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 388.909i | − | 0.516480i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 296.044 | + | 248.898i | 0.392111 | + | 0.329666i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 899.385 | 1.18809 | 0.594046 | − | 0.804431i | \(-0.297530\pi\) | ||||
0.594046 | + | 0.804431i | \(0.297530\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1187.92i | − | 1.56511i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 673.539i | 0.885071i | 0.896751 | + | 0.442536i | \(0.145921\pi\) | ||||
−0.896751 | + | 0.442536i | \(0.854079\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −79.4953 | + | 942.873i | −0.104188 | + | 1.23575i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.967281 | + | 0.813239i | 0.00126442 | + | 0.00106306i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 308.256i | 0.401899i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1344.86i | 1.74884i | 0.485172 | + | 0.874419i | \(0.338757\pi\) | ||||
−0.485172 | + | 0.874419i | \(0.661243\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 692.586i | 0.898295i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 163.160i | − | 0.211074i | −0.994415 | − | 0.105537i | \(-0.966344\pi\) | ||
0.994415 | − | 0.105537i | \(-0.0336561\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −184.440 | + | 32.1542i | −0.237987 | + | 0.0414894i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −126.631 | + | 1501.94i | −0.162975 | + | 1.93300i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 831.681i | − | 1.06763i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 895.933i | 1.14716i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −459.574 | −0.586940 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 359.195 | − | 427.232i | 0.457573 | − | 0.544245i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1155.66i | − | 1.46844i | −0.678912 | − | 0.734220i | \(-0.737548\pi\) | ||
0.678912 | − | 0.734220i | \(-0.262452\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1255.09 | 1.59074 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.8980 | + | 283.448i | −0.0302124 | + | 0.358342i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 757.156i | 0.954800i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 634.289 | − | 754.434i | 0.797848 | − | 0.948974i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 46.6189i | − | 0.0584930i | −0.999572 | − | 0.0292465i | \(-0.990689\pi\) | ||
0.999572 | − | 0.0292465i | \(-0.00931077\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.58139 | −0.00197921 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 86.3480i | − | 0.107800i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 698.469i | 0.869825i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 669.177 | − | 672.111i | 0.831276 | − | 0.834920i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1428.98i | 1.77073i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −254.107 | −0.314100 | −0.157050 | − | 0.987591i | \(-0.550198\pi\) | ||||
−0.157050 | + | 0.987591i | \(0.550198\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1418.08 | −1.74855 | −0.874276 | − | 0.485429i | \(-0.838663\pi\) | ||||
−0.874276 | + | 0.485429i | \(0.838663\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −895.578 | −1.10157 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1191.50 | − | 1001.75i | −1.46196 | − | 1.22914i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −573.457 | −0.701906 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.0275 | − | 213.820i | 0.0220117 | − | 0.261074i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 435.911i | − | 0.530951i | −0.964118 | − | 0.265475i | \(-0.914471\pi\) | ||
0.964118 | − | 0.265475i | \(-0.0855289\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 454.623i | 0.552397i | 0.961101 | + | 0.276199i | \(0.0890747\pi\) | ||||
−0.961101 | + | 0.276199i | \(0.910925\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 188.221 | + | 1079.65i | 0.228147 | + | 1.30867i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 616.875 | 0.745919 | 0.372959 | − | 0.927848i | \(-0.378343\pi\) | ||||
0.372959 | + | 0.927848i | \(0.378343\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −167.324 | −0.201838 | −0.100919 | − | 0.994895i | \(-0.532178\pi\) | ||||
−0.100919 | + | 0.994895i | \(0.532178\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 928.459i | 1.11728i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.44028 | − | 1.43342i | −0.0101324 | − | 0.00172079i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −65.7923 | − | 55.3148i | −0.0787932 | − | 0.0662452i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −182.829 | −0.218434 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 713.072i | 0.849907i | 0.905215 | + | 0.424954i | \(0.139710\pi\) | ||||
−0.905215 | + | 0.424954i | \(0.860290\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 486.635 | 0.578639 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 757.647i | 0.898751i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1071.75 | − | 901.068i | −1.26834 | − | 1.06635i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −439.143 | − | 37.0249i | −0.518469 | − | 0.0437130i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 248.330 | 0.292497 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1805.29i | − | 2.12137i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 942.438i | − | 1.10485i | −0.833562 | − | 0.552426i | \(-0.813702\pi\) | ||
0.833562 | − | 0.552426i | \(-0.186298\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −114.730 | − | 96.4589i | −0.134187 | − | 0.112817i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 334.940 | 0.390828 | 0.195414 | − | 0.980721i | \(-0.437395\pi\) | ||||
0.195414 | + | 0.980721i | \(0.437395\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1345.43 | −1.56628 | −0.783138 | − | 0.621848i | \(-0.786382\pi\) | ||||
−0.783138 | + | 0.621848i | \(0.786382\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 904.783 | + | 76.2838i | 1.05085 | + | 0.0885991i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 513.792i | − | 0.595355i | −0.954666 | − | 0.297678i | \(-0.903788\pi\) | ||
0.954666 | − | 0.297678i | \(-0.0962121\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −618.107 | + | 735.187i | −0.714574 | + | 0.849927i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 933.984i | − | 1.07726i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1047.03i | 1.20487i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1968.63i | 2.26019i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −41.3950 | −0.0474169 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −501.697 | + | 716.886i | −0.573368 | + | 0.819298i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −311.483 | −0.355169 | −0.177585 | − | 0.984106i | \(-0.556828\pi\) | ||||
−0.177585 | + | 0.984106i | \(0.556828\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −803.512 | −0.914121 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1360.45i | − | 1.54421i | −0.635495 | − | 0.772105i | \(-0.719204\pi\) | ||
0.635495 | − | 0.772105i | \(-0.280796\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 493.662 | 0.559073 | 0.279537 | − | 0.960135i | \(-0.409819\pi\) | ||||
0.279537 | + | 0.960135i | \(0.409819\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −151.284 | + | 179.940i | −0.170943 | + | 0.203322i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 293.223 | 0.330579 | 0.165289 | − | 0.986245i | \(-0.447144\pi\) | ||||
0.165289 | + | 0.986245i | \(0.447144\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −60.3569 | + | 715.877i | −0.0678930 | + | 0.805261i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1246.81i | 1.39934i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 187.570 | 0.210045 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −374.911 | + | 445.926i | −0.418895 | + | 0.498241i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1855.97i | 2.06908i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −140.975 | −0.156813 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.6561 | 0.0118270 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 52.5989 | − | 623.862i | 0.0582491 | − | 0.690878i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 445.578 | + | 374.619i | 0.492351 | + | 0.413943i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1322.64 | −1.45825 | −0.729127 | − | 0.684378i | \(-0.760074\pi\) | ||||
−0.729127 | + | 0.684378i | \(0.760074\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 279.945 | 0.307970 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.6878 | −0.0545420 | −0.0272710 | − | 0.999628i | \(-0.508682\pi\) | ||||
−0.0272710 | + | 0.999628i | \(0.508682\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1283.11 | −1.40538 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −371.593 | + | 441.979i | −0.406112 | + | 0.483037i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 512.053 | + | 43.1721i | 0.558400 | + | 0.0470797i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −927.263 | −1.00899 | −0.504496 | − | 0.863414i | \(-0.668322\pi\) | ||||
−0.504496 | + | 0.863414i | \(0.668322\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −791.647 | −0.859552 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1399.78i | − | 1.51655i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 286.041 | + | 1640.76i | 0.309234 | + | 1.77379i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 237.988 | 0.256729 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 406.847i | − | 0.437940i | −0.975732 | − | 0.218970i | \(-0.929730\pi\) | ||
0.975732 | − | 0.218970i | \(-0.0702698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1001.11 | + | 170.019i | 1.07530 | + | 0.182620i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1799.98 | 1.92924 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.62485 | + | 9.06912i | −0.00815492 | + | 0.00969960i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −648.308 | −0.691897 | −0.345949 | − | 0.938253i | \(-0.612443\pi\) | ||||
−0.345949 | + | 0.938253i | \(0.612443\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 209.370i | 0.222972i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −543.789 | −0.577884 | −0.288942 | − | 0.957347i | \(-0.593304\pi\) | ||||
−0.288942 | + | 0.957347i | \(0.593304\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1087.52 | −1.15326 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −602.881 | + | 605.524i | −0.637969 | + | 0.640766i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −609.736 | −0.643861 | −0.321930 | − | 0.946763i | \(-0.604332\pi\) | ||||
−0.321930 | + | 0.946763i | \(0.604332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1091.27i | − | 1.14991i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1816.79i | − | 1.91039i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1454.58i | − | 1.52632i | −0.646210 | − | 0.763159i | \(-0.723647\pi\) | ||
0.646210 | − | 0.763159i | \(-0.276353\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −485.876 | − | 408.499i | −0.508771 | − | 0.427748i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 825.223i | 0.862302i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.3963 | − | 241.916i | 0.0212683 | − | 0.252258i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 904.917 | 0.941641 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −114.626 | −0.119030 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 745.317 | − | 886.493i | 0.772349 | − | 0.918646i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1095.53i | − | 1.13292i | −0.824089 | − | 0.566460i | \(-0.808313\pi\) | ||
0.824089 | − | 0.566460i | \(-0.191687\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 11.7026i | − | 0.0120770i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1248.77 | 1.28607 | 0.643035 | − | 0.765836i | \(-0.277675\pi\) | ||||
0.643035 | + | 0.765836i | \(0.277675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −287.784 | − | 24.2635i | −0.295769 | − | 0.0249368i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −294.071 | − | 1686.82i | −0.301612 | − | 1.73007i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 17.6376i | − | 0.0180529i | −0.999959 | − | 0.00902643i | \(-0.997127\pi\) | ||
0.999959 | − | 0.00902643i | \(-0.00287324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 809.590 | 0.826956 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 195.542i | − | 0.199329i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 639.985 | 0.651053 | 0.325527 | − | 0.945533i | \(-0.394458\pi\) | ||||
0.325527 | + | 0.945533i | \(0.394458\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −298.486 | − | 250.951i | −0.303031 | − | 0.254773i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.2044 | + | 204.057i | −0.0174310 | + | 0.206744i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 749.862i | 0.758203i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −978.203 | −0.987086 | −0.493543 | − | 0.869721i | \(-0.664299\pi\) | ||||
−0.493543 | + | 0.869721i | \(0.664299\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 371.837 | 0.374458 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 733.215 | − | 872.098i | 0.736899 | − | 0.876481i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 14.7356i | − | 0.0147799i | −0.999973 | − | 0.00738996i | \(-0.997648\pi\) | ||
0.999973 | − | 0.00738996i | \(-0.00235232\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1626.43i | 1.62806i |
(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 | 1120.3.c.g.209.10 | 80 | ||
4.3 | odd | 2 | 280.3.c.g.69.17 | ✓ | 80 | ||
5.4 | even | 2 | inner | 1120.3.c.g.209.35 | 80 | ||
7.6 | odd | 2 | inner | 1120.3.c.g.209.37 | 80 | ||
8.3 | odd | 2 | 280.3.c.g.69.62 | yes | 80 | ||
8.5 | even | 2 | inner | 1120.3.c.g.209.7 | 80 | ||
20.19 | odd | 2 | 280.3.c.g.69.64 | yes | 80 | ||
28.27 | even | 2 | 280.3.c.g.69.18 | yes | 80 | ||
35.34 | odd | 2 | inner | 1120.3.c.g.209.8 | 80 | ||
40.19 | odd | 2 | 280.3.c.g.69.19 | yes | 80 | ||
40.29 | even | 2 | inner | 1120.3.c.g.209.38 | 80 | ||
56.13 | odd | 2 | inner | 1120.3.c.g.209.36 | 80 | ||
56.27 | even | 2 | 280.3.c.g.69.61 | yes | 80 | ||
140.139 | even | 2 | 280.3.c.g.69.63 | yes | 80 | ||
280.69 | odd | 2 | inner | 1120.3.c.g.209.9 | 80 | ||
280.139 | even | 2 | 280.3.c.g.69.20 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.3.c.g.69.17 | ✓ | 80 | 4.3 | odd | 2 | ||
280.3.c.g.69.18 | yes | 80 | 28.27 | even | 2 | ||
280.3.c.g.69.19 | yes | 80 | 40.19 | odd | 2 | ||
280.3.c.g.69.20 | yes | 80 | 280.139 | even | 2 | ||
280.3.c.g.69.61 | yes | 80 | 56.27 | even | 2 | ||
280.3.c.g.69.62 | yes | 80 | 8.3 | odd | 2 | ||
280.3.c.g.69.63 | yes | 80 | 140.139 | even | 2 | ||
280.3.c.g.69.64 | yes | 80 | 20.19 | odd | 2 | ||
1120.3.c.g.209.7 | 80 | 8.5 | even | 2 | inner | ||
1120.3.c.g.209.8 | 80 | 35.34 | odd | 2 | inner | ||
1120.3.c.g.209.9 | 80 | 280.69 | odd | 2 | inner | ||
1120.3.c.g.209.10 | 80 | 1.1 | even | 1 | trivial | ||
1120.3.c.g.209.35 | 80 | 5.4 | even | 2 | inner | ||
1120.3.c.g.209.36 | 80 | 56.13 | odd | 2 | inner | ||
1120.3.c.g.209.37 | 80 | 7.6 | odd | 2 | inner | ||
1120.3.c.g.209.38 | 80 | 40.29 | even | 2 | inner |