Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,3,Mod(209,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.209");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.l (of order \(4\), degree \(2\), 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: | \(12.2071158433\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 433.19 | ||
Character | \(\chi\) | \(=\) | 448.433 |
Dual form | 448.3.l.b.209.19 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.75534 | + | 1.75534i | 0.585114 | + | 0.585114i | 0.936304 | − | 0.351190i | \(-0.114223\pi\) |
−0.351190 | + | 0.936304i | \(0.614223\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.25602 | − | 3.25602i | 0.651203 | − | 0.651203i | −0.302079 | − | 0.953283i | \(-0.597681\pi\) |
0.953283 | + | 0.302079i | \(0.0976808\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.90539 | − | 4.99371i | 0.700770 | − | 0.713388i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.83754i | − | 0.315283i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.01178 | + | 2.01178i | 0.182889 | + | 0.182889i | 0.792613 | − | 0.609725i | \(-0.208720\pi\) |
−0.609725 | + | 0.792613i | \(0.708720\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.07310 | + | 6.07310i | 0.467162 | + | 0.467162i | 0.900994 | − | 0.433832i | \(-0.142839\pi\) |
−0.433832 | + | 0.900994i | \(0.642839\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.4309 | 0.762057 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 9.55815i | − | 0.562244i | −0.959672 | − | 0.281122i | \(-0.909293\pi\) | ||
0.959672 | − | 0.281122i | \(-0.0907065\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −25.2086 | − | 25.2086i | −1.32677 | − | 1.32677i | −0.908173 | − | 0.418595i | \(-0.862523\pi\) |
−0.418595 | − | 0.908173i | \(-0.637477\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17.3763 | − | 0.155043i | 0.827444 | − | 0.00738300i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 14.0394i | − | 0.610408i | −0.952287 | − | 0.305204i | \(-0.901275\pi\) | ||
0.952287 | − | 0.305204i | \(-0.0987247\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.79671i | 0.151869i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 20.7789 | − | 20.7789i | 0.769591 | − | 0.769591i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −11.2161 | + | 11.2161i | −0.386764 | + | 0.386764i | −0.873531 | − | 0.486768i | \(-0.838176\pi\) |
0.486768 | + | 0.873531i | \(0.338176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 16.5180i | − | 0.532837i | −0.963857 | − | 0.266419i | \(-0.914160\pi\) | ||
0.963857 | − | 0.266419i | \(-0.0858404\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.06271i | 0.214022i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.287592 | − | 32.2316i | −0.00821691 | − | 0.920904i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 27.6654 | + | 27.6654i | 0.747714 | + | 0.747714i | 0.974049 | − | 0.226335i | \(-0.0726746\pi\) |
−0.226335 | + | 0.974049i | \(0.572675\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 21.3208i | 0.546686i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.9650 | 0.316219 | 0.158110 | − | 0.987422i | \(-0.449460\pi\) | ||||
0.158110 | + | 0.987422i | \(0.449460\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 50.9760 | + | 50.9760i | 1.18549 | + | 1.18549i | 0.978301 | + | 0.207187i | \(0.0664309\pi\) |
0.207187 | + | 0.978301i | \(0.433569\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.23909 | − | 9.23909i | −0.205313 | − | 0.205313i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 66.5020i | 1.41494i | 0.706745 | + | 0.707468i | \(0.250163\pi\) | ||||
−0.706745 | + | 0.707468i | \(0.749837\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.874351 | − | 48.9922i | −0.0178439 | − | 0.999841i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.7778 | − | 16.7778i | 0.328977 | − | 0.328977i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 39.3660 | + | 39.3660i | 0.742755 | + | 0.742755i | 0.973107 | − | 0.230353i | \(-0.0739880\pi\) |
−0.230353 | + | 0.973107i | \(0.573988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.1008 | 0.238196 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 88.4994i | − | 1.55262i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 30.4313 | − | 30.4313i | 0.515785 | − | 0.515785i | −0.400508 | − | 0.916293i | \(-0.631166\pi\) |
0.916293 | + | 0.400508i | \(0.131166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.9950 | + | 11.9950i | 0.196639 | + | 0.196639i | 0.798558 | − | 0.601918i | \(-0.205597\pi\) |
−0.601918 | + | 0.798558i | \(0.705597\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −14.1699 | − | 13.9192i | −0.224919 | − | 0.220940i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 39.5482 | 0.608434 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 19.5294 | − | 19.5294i | 0.291483 | − | 0.291483i | −0.546183 | − | 0.837666i | \(-0.683920\pi\) |
0.837666 | + | 0.546183i | \(0.183920\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 24.6440 | − | 24.6440i | 0.357159 | − | 0.357159i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 69.7628i | 0.982574i | 0.870998 | + | 0.491287i | \(0.163473\pi\) | ||||
−0.870998 | + | 0.491287i | \(0.836527\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −143.326 | −1.96337 | −0.981686 | − | 0.190507i | \(-0.938987\pi\) | ||||
−0.981686 | + | 0.190507i | \(0.938987\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.66453 | + | 6.66453i | −0.0888604 | + | 0.0888604i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19.9148 | − | 0.177693i | 0.258633 | − | 0.00230770i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −66.7548 | −0.844998 | −0.422499 | − | 0.906363i | \(-0.638847\pi\) | ||||
−0.422499 | + | 0.906363i | \(0.638847\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 47.4105 | 0.585314 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 60.7490 | + | 60.7490i | 0.731916 | + | 0.731916i | 0.970999 | − | 0.239083i | \(-0.0768468\pi\) |
−0.239083 | + | 0.970999i | \(0.576847\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −31.1215 | − | 31.1215i | −0.366135 | − | 0.366135i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −39.3763 | −0.452602 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −78.9394 | −0.886960 | −0.443480 | − | 0.896284i | \(-0.646256\pi\) | ||||
−0.443480 | + | 0.896284i | \(0.646256\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 60.1182 | − | 0.536415i | 0.660640 | − | 0.00589467i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 28.9947 | − | 28.9947i | 0.311771 | − | 0.311771i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −164.159 | −1.72799 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 35.4878i | 0.365854i | 0.983126 | + | 0.182927i | \(0.0585572\pi\) | ||||
−0.983126 | + | 0.182927i | \(0.941443\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.70850 | − | 5.70850i | 0.0576616 | − | 0.0576616i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 135.312 | − | 135.312i | 1.33972 | − | 1.33972i | 0.443400 | − | 0.896324i | \(-0.353772\pi\) |
0.896324 | − | 0.443400i | \(-0.146228\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 76.3602 | 0.741361 | 0.370680 | − | 0.928760i | \(-0.379125\pi\) | ||||
0.370680 | + | 0.928760i | \(0.379125\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 56.0727 | − | 57.0824i | 0.534026 | − | 0.543642i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −61.8636 | − | 61.8636i | −0.578164 | − | 0.578164i | 0.356233 | − | 0.934397i | \(-0.384061\pi\) |
−0.934397 | + | 0.356233i | \(0.884061\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −95.4954 | + | 95.4954i | −0.876105 | + | 0.876105i | −0.993129 | − | 0.117024i | \(-0.962664\pi\) |
0.117024 | + | 0.993129i | \(0.462664\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 97.1246i | 0.874996i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −141.353 | −1.25091 | −0.625456 | − | 0.780260i | \(-0.715087\pi\) | ||||
−0.625456 | + | 0.780260i | \(0.715087\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −45.7125 | − | 45.7125i | −0.397500 | − | 0.397500i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.2327 | − | 17.2327i | 0.147288 | − | 0.147288i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −47.7306 | − | 46.8864i | −0.401098 | − | 0.394003i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 112.906i | − | 0.933103i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 22.7580 | + | 22.7580i | 0.185024 | + | 0.185024i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 93.7626 | + | 93.7626i | 0.750101 | + | 0.750101i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 80.1444 | 0.631058 | 0.315529 | − | 0.948916i | \(-0.397818\pi\) | ||||
0.315529 | + | 0.948916i | \(0.397818\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 178.961i | 1.38729i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −90.0359 | − | 90.0359i | −0.687297 | − | 0.687297i | 0.274337 | − | 0.961634i | \(-0.411542\pi\) |
−0.961634 | + | 0.274337i | \(0.911542\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −249.542 | + | 2.22658i | −1.87626 | + | 0.0167412i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 135.313i | − | 1.00232i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 253.079i | 1.84729i | 0.383247 | + | 0.923646i | \(0.374806\pi\) | ||||
−0.383247 | + | 0.923646i | \(0.625194\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −49.2592 | + | 49.2592i | −0.354382 | + | 0.354382i | −0.861737 | − | 0.507355i | \(-0.830623\pi\) |
0.507355 | + | 0.861737i | \(0.330623\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −116.734 | + | 116.734i | −0.827899 | + | 0.827899i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.4354i | 0.170877i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 73.0399i | 0.503723i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 84.4633 | − | 87.5329i | 0.574580 | − | 0.595462i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 40.4528 | + | 40.4528i | 0.271495 | + | 0.271495i | 0.829702 | − | 0.558207i | \(-0.188510\pi\) |
−0.558207 | + | 0.829702i | \(0.688510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 34.5523i | 0.228823i | 0.993433 | + | 0.114412i | \(0.0364983\pi\) | ||||
−0.993433 | + | 0.114412i | \(0.963502\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −27.1217 | −0.177266 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −53.7828 | − | 53.7828i | −0.346986 | − | 0.346986i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.2009 | + | 17.2009i | 0.109560 | + | 0.109560i | 0.759762 | − | 0.650202i | \(-0.225316\pi\) |
−0.650202 | + | 0.759762i | \(0.725316\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 138.202i | 0.869193i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −70.1087 | − | 68.8687i | −0.435458 | − | 0.427756i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 38.9774 | − | 38.9774i | 0.239125 | − | 0.239125i | −0.577363 | − | 0.816488i | \(-0.695918\pi\) |
0.816488 | + | 0.577363i | \(0.195918\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 22.9963 | + | 22.9963i | 0.139372 | + | 0.139372i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −137.053 | −0.820679 | −0.410339 | − | 0.911933i | \(-0.634590\pi\) | ||||
−0.410339 | + | 0.911933i | \(0.634590\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 95.2349i | − | 0.563520i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −71.5305 | + | 71.5305i | −0.418307 | + | 0.418307i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 59.0992 | + | 59.0992i | 0.341614 | + | 0.341614i | 0.856974 | − | 0.515360i | \(-0.172342\pi\) |
−0.515360 | + | 0.856974i | \(0.672342\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.9597 | + | 18.6243i | 0.108341 | + | 0.106425i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 106.835 | 0.603586 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −150.604 | + | 150.604i | −0.841364 | + | 0.841364i | −0.989036 | − | 0.147673i | \(-0.952822\pi\) |
0.147673 | + | 0.989036i | \(0.452822\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −195.403 | + | 195.403i | −1.07958 | + | 1.07958i | −0.0830294 | + | 0.996547i | \(0.526460\pi\) |
−0.996547 | + | 0.0830294i | \(0.973540\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 42.1106i | 0.230113i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 180.158 | 0.973828 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.2288 | − | 19.2288i | 0.102828 | − | 0.102828i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.83533 | − | 205.693i | −0.00971073 | − | 1.08832i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −59.1682 | −0.309781 | −0.154891 | − | 0.987932i | \(-0.549503\pi\) | ||||
−0.154891 | + | 0.987932i | \(0.549503\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −190.929 | −0.989269 | −0.494634 | − | 0.869101i | \(-0.664698\pi\) | ||||
−0.494634 | + | 0.869101i | \(0.664698\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 69.4207 | + | 69.4207i | 0.356004 | + | 0.356004i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 142.902 | + | 142.902i | 0.725390 | + | 0.725390i | 0.969698 | − | 0.244308i | \(-0.0785608\pi\) |
−0.244308 | + | 0.969698i | \(0.578561\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −138.990 | −0.698440 | −0.349220 | − | 0.937041i | \(-0.613553\pi\) | ||||
−0.349220 | + | 0.937041i | \(0.613553\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 68.5614 | 0.341102 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.990681 | + | 111.030i | 0.00488020 | + | 0.546944i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 42.2142 | − | 42.2142i | 0.205923 | − | 0.205923i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −39.8374 | −0.192451 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 101.428i | − | 0.485302i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −212.666 | + | 212.666i | −1.00789 | + | 1.00789i | −0.00792508 | + | 0.999969i | \(0.502523\pi\) |
−0.999969 | + | 0.00792508i | \(0.997477\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −122.458 | + | 122.458i | −0.574918 | + | 0.574918i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 331.957 | 1.54399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −82.4860 | − | 81.0270i | −0.380120 | − | 0.373396i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −251.586 | − | 251.586i | −1.14880 | − | 1.14880i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 58.0476 | − | 58.0476i | 0.262659 | − | 0.262659i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 346.003i | − | 1.55158i | −0.630988 | − | 0.775792i | \(-0.717350\pi\) | ||
0.630988 | − | 0.775792i | \(-0.282650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.7733 | 0.0478815 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 189.005 | + | 189.005i | 0.832622 | + | 0.832622i | 0.987875 | − | 0.155252i | \(-0.0496191\pi\) |
−0.155252 | + | 0.987875i | \(0.549619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 151.137 | − | 151.137i | 0.659987 | − | 0.659987i | −0.295390 | − | 0.955377i | \(-0.595450\pi\) |
0.955377 | + | 0.295390i | \(0.0954496\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 35.2692 | + | 34.6453i | 0.152680 | + | 0.149980i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.5086i | 0.0451015i | 0.999746 | + | 0.0225507i | \(0.00717873\pi\) | ||||
−0.999746 | + | 0.0225507i | \(0.992821\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 216.532 | + | 216.532i | 0.921411 | + | 0.921411i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −117.178 | − | 117.178i | −0.494420 | − | 0.494420i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 362.334 | 1.51604 | 0.758021 | − | 0.652230i | \(-0.226166\pi\) | ||||
0.758021 | + | 0.652230i | \(0.226166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 363.356i | − | 1.50770i | −0.657046 | − | 0.753851i | \(-0.728194\pi\) | ||
0.657046 | − | 0.753851i | \(-0.271806\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −103.789 | − | 103.789i | −0.427115 | − | 0.427115i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −162.366 | − | 156.673i | −0.662720 | − | 0.639480i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 306.189i | − | 1.23963i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 213.271i | 0.856509i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −54.1542 | + | 54.1542i | −0.215754 | + | 0.215754i | −0.806706 | − | 0.590952i | \(-0.798752\pi\) |
0.590952 | + | 0.806706i | \(0.298752\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.2441 | − | 28.2441i | 0.111637 | − | 0.111637i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 109.258i | − | 0.428462i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 45.3701i | 0.176537i | 0.996097 | + | 0.0882687i | \(0.0281334\pi\) | ||||
−0.996097 | + | 0.0882687i | \(0.971867\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 273.863 | − | 2.44358i | 1.05739 | − | 0.00943469i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 31.8263 | + | 31.8263i | 0.121940 | + | 0.121940i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 502.464i | 1.91051i | 0.295787 | + | 0.955254i | \(0.404418\pi\) | ||||
−0.295787 | + | 0.955254i | \(0.595582\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 256.353 | 0.967368 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −138.566 | − | 138.566i | −0.518973 | − | 0.518973i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −81.3588 | − | 81.3588i | −0.302449 | − | 0.302449i | 0.539522 | − | 0.841971i | \(-0.318605\pi\) |
−0.841971 | + | 0.539522i | \(0.818605\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 192.959i | − | 0.712026i | −0.934481 | − | 0.356013i | \(-0.884136\pi\) | ||
0.934481 | − | 0.356013i | \(-0.115864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 106.470 | + | 104.587i | 0.389999 | + | 0.383101i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.63814 | + | 7.63814i | −0.0277750 | + | 0.0277750i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −211.837 | − | 211.837i | −0.764756 | − | 0.764756i | 0.212422 | − | 0.977178i | \(-0.431865\pi\) |
−0.977178 | + | 0.212422i | \(0.931865\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −46.8704 | −0.167994 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 85.3556i | 0.303756i | 0.988399 | + | 0.151878i | \(0.0485322\pi\) | ||||
−0.988399 | + | 0.151878i | \(0.951468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 87.4756 | − | 87.4756i | 0.309101 | − | 0.309101i | −0.535460 | − | 0.844561i | \(-0.679862\pi\) |
0.844561 | + | 0.535460i | \(0.179862\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −288.156 | − | 288.156i | −1.01107 | − | 1.01107i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 63.5983 | − | 64.7435i | 0.221597 | − | 0.225587i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 197.642 | 0.683882 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −62.2933 | + | 62.2933i | −0.214066 | + | 0.214066i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.7055 | − | 30.7055i | 0.104797 | − | 0.104797i | −0.652764 | − | 0.757561i | \(-0.726391\pi\) |
0.757561 | + | 0.652764i | \(0.226391\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 198.170i | − | 0.671762i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 83.6052 | 0.281499 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 85.2627 | − | 85.2627i | 0.285159 | − | 0.285159i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 504.617 | − | 4.50252i | 1.67647 | − | 0.0149585i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 475.038 | 1.56778 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 78.1117 | 0.256104 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.6433 | − | 31.6433i | −0.103073 | − | 0.103073i | 0.653690 | − | 0.756763i | \(-0.273220\pi\) |
−0.756763 | + | 0.653690i | \(0.773220\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 134.038 | + | 134.038i | 0.433781 | + | 0.433781i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 499.800 | 1.60708 | 0.803538 | − | 0.595254i | \(-0.202948\pi\) | ||||
0.803538 | + | 0.595254i | \(0.202948\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −52.7521 | −0.168537 | −0.0842685 | − | 0.996443i | \(-0.526855\pi\) | ||||
−0.0842685 | + | 0.996443i | \(0.526855\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −91.4587 | + | 0.816055i | −0.290345 | + | 0.00259065i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 218.091 | − | 218.091i | 0.687983 | − | 0.687983i | −0.273803 | − | 0.961786i | \(-0.588282\pi\) |
0.961786 | + | 0.273803i | \(0.0882816\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45.1287 | −0.141469 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 217.184i | − | 0.676584i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −240.947 | + | 240.947i | −0.745967 | + | 0.745967i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.0578 | + | 23.0578i | −0.0709471 | + | 0.0709471i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −335.254 | −1.02524 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 332.092 | + | 326.218i | 1.00940 | + | 0.991544i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.4515 | + | 20.4515i | 0.0617871 | + | 0.0617871i | 0.737325 | − | 0.675538i | \(-0.236089\pi\) |
−0.675538 | + | 0.737325i | \(0.736089\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 78.5018 | − | 78.5018i | 0.235741 | − | 0.235741i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 127.176i | − | 0.379629i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 451.093 | 1.33855 | 0.669277 | − | 0.743013i | \(-0.266604\pi\) | ||||
0.669277 | + | 0.743013i | \(0.266604\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −248.123 | − | 248.123i | −0.731926 | − | 0.731926i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.2304 | − | 33.2304i | 0.0974500 | − | 0.0974500i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −248.942 | − | 235.959i | −0.725779 | − | 0.687928i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 160.482i | − | 0.465166i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 313.926 | + | 313.926i | 0.904687 | + | 0.904687i | 0.995837 | − | 0.0911505i | \(-0.0290544\pi\) |
−0.0911505 | + | 0.995837i | \(0.529054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −400.540 | − | 400.540i | −1.14768 | − | 1.14768i | −0.987008 | − | 0.160670i | \(-0.948634\pi\) |
−0.160670 | − | 0.987008i | \(-0.551366\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 252.385 | 0.719046 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 464.090i | 1.31470i | 0.753584 | + | 0.657352i | \(0.228323\pi\) | ||||
−0.753584 | + | 0.657352i | \(0.771677\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 227.149 | + | 227.149i | 0.639855 | + | 0.639855i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.48192 | − | 166.085i | −0.00415105 | − | 0.465225i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 126.355i | 0.351963i | 0.984393 | + | 0.175982i | \(0.0563099\pi\) | ||||
−0.984393 | + | 0.175982i | \(0.943690\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 909.946i | 2.52063i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 198.188 | − | 198.188i | 0.545972 | − | 0.545972i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −466.672 | + | 466.672i | −1.27855 | + | 1.27855i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 90.0661i | 0.245412i | 0.992443 | + | 0.122706i | \(0.0391572\pi\) | ||||
−0.992443 | + | 0.122706i | \(0.960843\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 36.7887i | − | 0.0996985i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 389.688 | − | 3.47705i | 1.05037 | − | 0.00937211i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −363.710 | − | 363.710i | −0.975094 | − | 0.975094i | 0.0246037 | − | 0.999697i | \(-0.492168\pi\) |
−0.999697 | + | 0.0246037i | \(0.992168\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 329.171i | 0.877789i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −136.234 | −0.361362 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −290.869 | − | 290.869i | −0.767465 | − | 0.767465i | 0.210194 | − | 0.977660i | \(-0.432590\pi\) |
−0.977660 | + | 0.210194i | \(0.932590\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 140.681 | + | 140.681i | 0.369241 | + | 0.369241i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 234.051i | − | 0.611099i | −0.952176 | − | 0.305550i | \(-0.901160\pi\) | ||
0.952176 | − | 0.305550i | \(-0.0988402\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 64.2643 | − | 65.4214i | 0.166920 | − | 0.169926i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 144.647 | − | 144.647i | 0.373764 | − | 0.373764i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 83.4977 | + | 83.4977i | 0.214647 | + | 0.214647i | 0.806238 | − | 0.591591i | \(-0.201500\pi\) |
−0.591591 | + | 0.806238i | \(0.701500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −134.191 | −0.343198 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 316.088i | − | 0.804295i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −217.355 | + | 217.355i | −0.550265 | + | 0.550265i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 174.436 | + | 174.436i | 0.439386 | + | 0.439386i | 0.891805 | − | 0.452419i | \(-0.149439\pi\) |
−0.452419 | + | 0.891805i | \(0.649439\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −441.941 | − | 434.124i | −1.10762 | − | 1.08803i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −187.735 | −0.468168 | −0.234084 | − | 0.972216i | \(-0.575209\pi\) | ||||
−0.234084 | + | 0.972216i | \(0.575209\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 100.315 | − | 100.315i | 0.248921 | − | 0.248921i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 154.369 | − | 154.369i | 0.381159 | − | 0.381159i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 111.313i | 0.273497i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −144.940 | −0.354377 | −0.177188 | − | 0.984177i | \(-0.556700\pi\) | ||||
−0.177188 | + | 0.984177i | \(0.556700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −444.240 | + | 444.240i | −1.08088 | + | 1.08088i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.68789 | − | 301.243i | −0.00650820 | − | 0.729401i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 395.600 | 0.953253 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −172.933 | −0.414708 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −177.168 | − | 177.168i | −0.422835 | − | 0.422835i | 0.463344 | − | 0.886179i | \(-0.346650\pi\) |
−0.886179 | + | 0.463344i | \(0.846650\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 468.234 | + | 468.234i | 1.11220 | + | 1.11220i | 0.992853 | + | 0.119342i | \(0.0380784\pi\) |
0.119342 | + | 0.992853i | \(0.461922\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 188.702 | 0.446105 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 36.2895 | 0.0853871 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 118.740 | − | 1.05947i | 0.278079 | − | 0.00248120i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −42.8926 | + | 42.8926i | −0.0999827 | + | 0.0999827i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −497.233 | −1.15367 | −0.576836 | − | 0.816860i | \(-0.695713\pi\) | ||||
−0.576836 | + | 0.816860i | \(0.695713\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 210.739i | − | 0.486696i | −0.969939 | − | 0.243348i | \(-0.921754\pi\) | ||
0.969939 | − | 0.243348i | \(-0.0782457\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −128.210 | + | 128.210i | −0.294736 | + | 0.294736i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −353.913 | + | 353.913i | −0.809870 | + | 0.809870i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −762.892 | −1.73779 | −0.868897 | − | 0.494993i | \(-0.835171\pi\) | ||||
−0.868897 | + | 0.494993i | \(0.835171\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −139.017 | + | 2.48101i | −0.315232 | + | 0.00562587i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 140.252 | + | 140.252i | 0.316596 | + | 0.316596i | 0.847458 | − | 0.530862i | \(-0.178132\pi\) |
−0.530862 | + | 0.847458i | \(0.678132\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −257.028 | + | 257.028i | −0.577591 | + | 0.577591i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 142.017i | 0.317711i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −599.904 | −1.33609 | −0.668044 | − | 0.744122i | \(-0.732868\pi\) | ||||
−0.668044 | + | 0.744122i | \(0.732868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.0827 | + | 26.0827i | 0.0578330 | + | 0.0578330i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −60.6512 | + | 60.6512i | −0.133888 | + | 0.133888i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 193.999 | − | 197.493i | 0.426372 | − | 0.434050i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 557.580i | − | 1.22009i | −0.792368 | − | 0.610044i | \(-0.791152\pi\) | ||
0.792368 | − | 0.610044i | \(-0.208848\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −198.608 | − | 198.608i | −0.432698 | − | 0.432698i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 482.593 | + | 482.593i | 1.04684 | + | 1.04684i | 0.998848 | + | 0.0479917i | \(0.0152821\pi\) |
0.0479917 | + | 0.998848i | \(0.484718\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 326.635 | 0.705475 | 0.352737 | − | 0.935722i | \(-0.385251\pi\) | ||||
0.352737 | + | 0.935722i | \(0.385251\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 188.814i | − | 0.406052i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 213.948 | + | 213.948i | 0.458132 | + | 0.458132i | 0.898042 | − | 0.439910i | \(-0.144990\pi\) |
−0.439910 | + | 0.898042i | \(0.644990\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.72496 | − | 193.323i | −0.00367794 | − | 0.412203i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 60.3870i | 0.128210i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 205.105i | 0.433625i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 95.7098 | − | 95.7098i | 0.201494 | − | 0.201494i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 111.703 | − | 111.703i | 0.234178 | − | 0.234178i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 437.605i | 0.913581i | 0.889574 | + | 0.456790i | \(0.151001\pi\) | ||||
−0.889574 | + | 0.456790i | \(0.848999\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 336.030i | 0.698607i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.17671 | − | 243.953i | −0.00450665 | − | 0.505079i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 115.549 | + | 115.549i | 0.238245 | + | 0.238245i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 681.542i | − | 1.39947i | −0.714402 | − | 0.699735i | \(-0.753301\pi\) | ||
0.714402 | − | 0.699735i | \(-0.246699\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 136.837 | 0.279831 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −324.611 | − | 324.611i | −0.661122 | − | 0.661122i | 0.294523 | − | 0.955644i | \(-0.404839\pi\) |
−0.955644 | + | 0.294523i | \(0.904839\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 107.206 | + | 107.206i | 0.217455 | + | 0.217455i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 37.1740i | − | 0.0750989i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 348.375 | + | 342.213i | 0.700956 | + | 0.688558i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.3782 | + | 23.3782i | −0.0468501 | + | 0.0468501i | −0.730144 | − | 0.683294i | \(-0.760547\pi\) |
0.683294 | + | 0.730144i | \(0.260547\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −240.576 | − | 240.576i | −0.480191 | − | 0.480191i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 693.554 | 1.37884 | 0.689418 | − | 0.724364i | \(-0.257867\pi\) | ||||
0.689418 | + | 0.724364i | \(0.257867\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 881.157i | − | 1.74487i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 167.170 | − | 167.170i | 0.329724 | − | 0.329724i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 175.357 | + | 175.357i | 0.344512 | + | 0.344512i | 0.858061 | − | 0.513548i | \(-0.171669\pi\) |
−0.513548 | + | 0.858061i | \(0.671669\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −703.070 | + | 715.730i | −1.37587 | + | 1.40065i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1047.62 | −2.04214 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 248.630 | − | 248.630i | 0.482777 | − | 0.482777i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −133.787 | + | 133.787i | −0.258776 | + | 0.258776i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 207.479i | 0.399766i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 602.394 | 1.15623 | 0.578113 | − | 0.815957i | \(-0.303789\pi\) | ||||
0.578113 | + | 0.815957i | \(0.303789\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 296.480 | − | 296.480i | 0.566883 | − | 0.566883i | −0.364371 | − | 0.931254i | \(-0.618716\pi\) |
0.931254 | + | 0.364371i | \(0.118716\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.588654 | + | 65.9729i | 0.00112125 | + | 0.125663i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −157.881 | −0.299585 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 331.895 | 0.627401 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −86.3502 | − | 86.3502i | −0.162618 | − | 0.162618i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 78.7377 | + | 78.7377i | 0.147726 | + | 0.147726i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −402.858 | −0.753005 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −528.724 | −0.984588 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 96.8023 | − | 100.320i | 0.179596 | − | 0.186123i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −221.579 | + | 221.579i | −0.409573 | + | 0.409573i | −0.881590 | − | 0.472017i | \(-0.843526\pi\) |
0.472017 | + | 0.881590i | \(0.343526\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −686.000 | −1.26335 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 621.869i | 1.14104i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −545.973 | + | 545.973i | −0.998123 | + | 0.998123i | −0.999998 | − | 0.00187545i | \(-0.999403\pi\) |
0.00187545 | + | 0.999998i | \(0.499403\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 34.0363 | − | 34.0363i | 0.0619969 | − | 0.0619969i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 565.486 | 1.02629 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −327.458 | + | 333.355i | −0.592149 | + | 0.602811i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 316.239 | + | 316.239i | 0.569800 | + | 0.569800i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 87.7052 | − | 87.7052i | 0.157460 | − | 0.157460i | −0.623980 | − | 0.781440i | \(-0.714485\pi\) |
0.781440 | + | 0.623980i | \(0.214485\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 619.165i | 1.10763i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 67.5064 | 0.120332 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −125.548 | − | 125.548i | −0.222997 | − | 0.222997i | 0.586762 | − | 0.809759i | \(-0.300402\pi\) |
−0.809759 | + | 0.586762i | \(0.800402\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −460.248 | + | 460.248i | −0.814598 | + | 0.814598i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 232.567 | − | 236.754i | 0.410170 | − | 0.417556i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 963.505i | − | 1.69333i | −0.532126 | − | 0.846665i | \(-0.678607\pi\) | ||
0.532126 | − | 0.846665i | \(-0.321393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 254.297 | + | 254.297i | 0.445355 | + | 0.445355i | 0.893807 | − | 0.448452i | \(-0.148025\pi\) |
−0.448452 | + | 0.893807i | \(0.648025\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −103.860 | − | 103.860i | −0.181257 | − | 0.181257i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 53.3036 | 0.0927018 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 792.088i | − | 1.37277i | −0.727239 | − | 0.686384i | \(-0.759197\pi\) | ||
0.727239 | − | 0.686384i | \(-0.240803\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −335.146 | − | 335.146i | −0.578835 | − | 0.578835i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 601.361 | − | 5.36574i | 1.03504 | − | 0.00923535i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 158.391i | 0.271683i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 112.220i | − | 0.191829i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −436.848 | + | 436.848i | −0.744204 | + | 0.744204i | −0.973384 | − | 0.229180i | \(-0.926396\pi\) |
0.229180 | + | 0.973384i | \(0.426396\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −416.394 | + | 416.394i | −0.706952 | + | 0.706952i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 501.683i | 0.848872i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 668.916i | − | 1.12802i | −0.825768 | − | 0.564010i | \(-0.809258\pi\) | ||
0.825768 | − | 0.564010i | \(-0.190742\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −308.075 | + | 2.74885i | −0.517773 | + | 0.00461991i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −243.974 | − | 243.974i | −0.408667 | − | 0.408667i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 411.756i | 0.687405i | 0.939079 | + | 0.343703i | \(0.111681\pi\) | ||||
−0.939079 | + | 0.343703i | \(0.888319\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −688.982 | −1.14639 | −0.573196 | − | 0.819418i | \(-0.694297\pi\) | ||||
−0.573196 | + | 0.819418i | \(0.694297\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −55.4154 | − | 55.4154i | −0.0918995 | − | 0.0918995i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −367.622 | − | 367.622i | −0.607640 | − | 0.607640i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 768.094i | 1.26539i | 0.774400 | + | 0.632697i | \(0.218052\pi\) | ||||
−0.774400 | + | 0.632697i | \(0.781948\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −193.156 | + | 196.634i | −0.317170 | + | 0.322880i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −403.873 | + | 403.873i | −0.661004 | + | 0.661004i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −163.362 | − | 163.362i | −0.266495 | − | 0.266495i | 0.561191 | − | 0.827686i | \(-0.310343\pi\) |
−0.827686 | + | 0.561191i | \(0.810343\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 148.201 | 0.240977 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 652.431i | − | 1.05742i | −0.848801 | − | 0.528712i | \(-0.822675\pi\) | ||
0.848801 | − | 0.528712i | \(-0.177325\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −78.1751 | + | 78.1751i | −0.126293 | + | 0.126293i | −0.767428 | − | 0.641135i | \(-0.778464\pi\) |
0.641135 | + | 0.767428i | \(0.278464\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −291.724 | − | 291.724i | −0.469765 | − | 0.469765i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −387.228 | + | 394.201i | −0.621554 | + | 0.632746i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 515.667 | 0.825067 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 178.041 | − | 178.041i | 0.283957 | − | 0.283957i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 264.430 | − | 264.430i | 0.420398 | − | 0.420398i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 219.948i | − | 0.348570i | −0.984695 | − | 0.174285i | \(-0.944239\pi\) | ||
0.984695 | − | 0.174285i | \(-0.0557614\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −746.602 | −1.17947 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 260.951 | − | 260.951i | 0.410947 | − | 0.410947i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 292.225 | − | 302.845i | 0.458751 | − | 0.475423i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 197.955 | 0.309789 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −186.577 | −0.291072 | −0.145536 | − | 0.989353i | \(-0.546491\pi\) | ||||
−0.145536 | + | 0.989353i | \(0.546491\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −215.904 | − | 215.904i | −0.335776 | − | 0.335776i | 0.518999 | − | 0.854775i | \(-0.326305\pi\) |
−0.854775 | + | 0.518999i | \(0.826305\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 582.699 | + | 582.699i | 0.903409 | + | 0.903409i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −663.677 | −1.02578 | −0.512888 | − | 0.858456i | \(-0.671424\pi\) | ||||
−0.512888 | + | 0.858456i | \(0.671424\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 122.442 | 0.188663 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.56099 | − | 287.021i | −0.00393394 | − | 0.440893i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −411.703 | + | 411.703i | −0.630479 | + | 0.630479i | −0.948188 | − | 0.317709i | \(-0.897086\pi\) |
0.317709 | + | 0.948188i | \(0.397086\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −586.317 | −0.895140 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 406.694i | 0.619017i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 149.906 | − | 149.906i | 0.227475 | − | 0.227475i | −0.584162 | − | 0.811637i | \(-0.698577\pi\) |
0.811637 | + | 0.584162i | \(0.198577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 166.233 | − | 166.233i | 0.251487 | − | 0.251487i | −0.570093 | − | 0.821580i | \(-0.693093\pi\) |
0.821580 | + | 0.570093i | \(0.193093\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 203.787 | 0.307371 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −805.264 | + | 819.764i | −1.21092 | + | 1.23273i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 157.468 | + | 157.468i | 0.236084 | + | 0.236084i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 607.355 | − | 607.355i | 0.907854 | − | 0.907854i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 48.2625i | 0.0719262i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 315.076 | 0.468167 | 0.234083 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234083 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 78.8917 | + | 78.8917i | 0.116877 | + | 0.116877i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 496.264 | − | 496.264i | 0.733034 | − | 0.733034i | −0.238186 | − | 0.971220i | \(-0.576553\pi\) |
0.971220 | + | 0.238186i | \(0.0765528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 177.216 | + | 174.082i | 0.260996 | + | 0.256379i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 663.538i | 0.974359i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 387.884 | + | 387.884i | 0.567913 | + | 0.567913i | 0.931543 | − | 0.363631i | \(-0.118463\pi\) |
−0.363631 | + | 0.931543i | \(0.618463\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 824.029 | + | 824.029i | 1.20296 | + | 1.20296i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 530.594 | 0.772335 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 478.147i | 0.693973i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 776.671 | + | 776.671i | 1.12398 | + | 1.12398i | 0.991137 | + | 0.132844i | \(0.0424108\pi\) |
0.132844 | + | 0.991137i | \(0.457589\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.504211 | − | 56.5090i | −0.000727577 | − | 0.0815426i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 320.777i | 0.461550i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 123.921i | − | 0.177792i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.4463 | + | 18.4463i | −0.0263895 | + | 0.0263895i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −504.506 | + | 504.506i | −0.719695 | + | 0.719695i | −0.968543 | − | 0.248848i | \(-0.919948\pi\) |
0.248848 | + | 0.968543i | \(0.419948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1394.81i | − | 1.98409i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 760.174i | 1.07826i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.9516 | − | 1339.47i | −0.0169047 | − | 1.89458i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 329.265 | + | 329.265i | 0.464408 | + | 0.464408i | 0.900097 | − | 0.435689i | \(-0.143495\pi\) |
−0.435689 | + | 0.900097i | \(0.643495\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 189.420i | 0.266413i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −231.902 | −0.325249 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 79.5622 | + | 79.5622i | 0.111276 | + | 0.111276i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 636.021 | + | 636.021i | 0.887058 | + | 0.887058i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 612.721i | − | 0.852185i | −0.904680 | − | 0.426093i | \(-0.859890\pi\) | ||
0.904680 | − | 0.426093i | \(-0.140110\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 374.576 | − | 381.321i | 0.519523 | − | 0.528878i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 637.814 | − | 637.814i | 0.882177 | − | 0.882177i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −42.5845 | − | 42.5845i | −0.0587372 | − | 0.0587372i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −884.961 | −1.21728 | −0.608639 | − | 0.793447i | \(-0.708284\pi\) | ||||
−0.608639 | + | 0.793447i | \(0.708284\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 791.064i | − | 1.08514i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 487.236 | − | 487.236i | 0.666534 | − | 0.666534i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 630.619 | + | 630.619i | 0.860327 | + | 0.860327i | 0.991376 | − | 0.131049i | \(-0.0418346\pi\) |
−0.131049 | + | 0.991376i | \(0.541835\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.99458 | − | 560.022i | −0.0135981 | − | 0.761935i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 78.5774 | 0.106618 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 885.422 | − | 885.422i | 1.19813 | − | 1.19813i | 0.223410 | − | 0.974725i | \(-0.428281\pi\) |
0.974725 | − | 0.223410i | \(-0.0717189\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 537.466 | − | 537.466i | 0.725325 | − | 0.725325i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 454.580i | − | 0.611817i | −0.952061 | − | 0.305909i | \(-0.901040\pi\) | ||
0.952061 | − | 0.305909i | \(-0.0989602\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 263.430 | 0.353597 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 172.378 | − | 172.378i | 0.230760 | − | 0.230760i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −612.394 | + | 5.46418i | −0.817615 | + | 0.00729530i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −220.761 | −0.293956 | −0.146978 | − | 0.989140i | \(-0.546955\pi\) | ||||
−0.146978 | + | 0.989140i | \(0.546955\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −190.119 | −0.252481 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 112.503 | + | 112.503i | 0.149011 | + | 0.149011i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 195.831 | + | 195.831i | 0.258693 | + | 0.258693i | 0.824522 | − | 0.565829i | \(-0.191444\pi\) |
−0.565829 | + | 0.824522i | \(0.691444\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 99.1562 | 0.130641 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1450.33 | 1.90583 | 0.952913 | − | 0.303244i | \(-0.0980698\pi\) | ||||
0.952913 | + | 0.303244i | \(0.0980698\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.43476 | + | 945.319i | 0.0110547 | + | 1.23895i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −88.3086 | + | 88.3086i | −0.115436 | + | 0.115436i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 369.625 | 0.481910 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 95.3790i | 0.124030i | 0.998075 | + | 0.0620150i | \(0.0197527\pi\) | ||||
−0.998075 | + | 0.0620150i | \(0.980247\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −79.6401 | + | 79.6401i | −0.103295 | + | 0.103295i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 811.244 | − | 811.244i | 1.04948 | − | 1.04948i | 0.0507646 | − | 0.998711i | \(-0.483834\pi\) |
0.998711 | − | 0.0507646i | \(-0.0161658\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 62.7140 | 0.0809212 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 485.012 | + | 476.434i | 0.624211 | + | 0.613171i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −326.829 | − | 326.829i | −0.419550 | − | 0.419550i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −140.347 | + | 140.347i | −0.179702 | + | 0.179702i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 466.119i | 0.595299i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 112.013 | 0.142692 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −96.6979 | − | 96.6979i | −0.122869 | − | 0.122869i | 0.642998 | − | 0.765867i | \(-0.277690\pi\) |
−0.765867 | + | 0.642998i | \(0.777690\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −881.996 | + | 881.996i | −1.11787 | + | 1.11787i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −693.391 | + | 705.876i | −0.876601 | + | 0.892385i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 145.694i | 0.183725i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 449.987 | + | 449.987i | 0.566021 | + | 0.566021i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −581.633 | − | 581.633i | −0.729778 | − | 0.729778i | 0.240798 | − | 0.970575i | \(-0.422591\pi\) |
−0.970575 | + | 0.240798i | \(0.922591\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 635.636 | 0.795539 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 223.994i | 0.279643i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −288.340 | − | 288.340i | −0.359079 | − | 0.359079i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −452.513 | + | 4.03762i | −0.562128 | + | 0.00501567i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 285.625i | − | 0.353935i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 296.533i | − | 0.366543i | −0.983062 | − | 0.183272i | \(-0.941331\pi\) | ||
0.983062 | − | 0.183272i | \(-0.0586688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 605.219 | − | 605.219i | 0.746262 | − | 0.746262i | −0.227513 | − | 0.973775i | \(-0.573059\pi\) |
0.973775 | + | 0.227513i | \(0.0730594\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 338.709 | − | 338.709i | 0.416617 | − | 0.416617i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 253.822i | − | 0.311438i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2570.07i | − | 3.14574i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.52210 | − | 170.588i | −0.00185849 | − | 0.208288i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 460.505 | + | 460.505i | 0.560907 | + | 0.560907i | 0.929565 | − | 0.368658i | \(-0.120183\pi\) |
−0.368658 | + | 0.929565i | \(0.620183\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1126.18i | − | 1.36839i | −0.729300 | − | 0.684194i | \(-0.760154\pi\) | ||
0.729300 | − | 0.684194i | \(-0.239846\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −26.8151 | −0.0325031 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −686.896 | − | 686.896i | −0.830587 | − | 0.830587i | 0.157010 | − | 0.987597i | \(-0.449815\pi\) |
−0.987597 | + | 0.157010i | \(0.949815\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −732.088 | − | 732.088i | −0.883098 | − | 0.883098i | 0.110750 | − | 0.993848i | \(-0.464675\pi\) |
−0.993848 | + | 0.110750i | \(0.964675\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 743.694i | − | 0.894939i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −468.275 | + | 8.35718i | −0.562154 | + | 0.0100326i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −446.248 | + | 446.248i | −0.534429 | + | 0.534429i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −343.226 | − | 343.226i | −0.410067 | − | 0.410067i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 903.003 | 1.07628 | 0.538142 | − | 0.842854i | \(-0.319126\pi\) | ||||
0.538142 | + | 0.842854i | \(0.319126\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 589.396i | 0.700828i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −149.828 | + | 149.828i | −0.177732 | + | 0.177732i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −310.086 | − | 310.086i | −0.366966 | − | 0.366966i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −563.818 | − | 553.845i | −0.665664 | − | 0.653891i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 307.099 | 0.361719 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 388.406 | − | 388.406i | 0.456411 | − | 0.456411i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.7225 | − | 38.7225i | 0.0453957 | − | 0.0453957i | −0.684045 | − | 0.729440i | \(-0.739781\pi\) |
0.729440 | + | 0.684045i | \(0.239781\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 465.809i | 0.544806i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −653.919 | −0.763032 | −0.381516 | − | 0.924362i | \(-0.624598\pi\) | ||||
−0.381516 | + | 0.924362i | \(0.624598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 340.187 | − | 340.187i | 0.396026 | − | 0.396026i | −0.480802 | − | 0.876829i | \(-0.659655\pi\) |
0.876829 | + | 0.480802i | \(0.159655\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 225.284 | − | 2.01013i | 0.261654 | − | 0.00233465i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 106.239 | 0.123104 | 0.0615519 | − | 0.998104i | \(-0.480395\pi\) | ||||
0.0615519 | + | 0.998104i | \(0.480395\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 384.856 | 0.444920 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 346.929 | + | 346.929i | 0.400149 | + | 0.400149i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −134.296 | − | 134.296i | −0.154541 | − | 0.154541i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 237.207 | 0.272339 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 100.698 | 0.115347 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 928.165 | − | 8.28170i | 1.06076 | − | 0.00946480i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −535.021 | + | 535.021i | −0.610059 | + | 0.610059i | −0.942961 | − | 0.332903i | \(-0.891972\pi\) |
0.332903 | + | 0.942961i | \(0.391972\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 107.797 | 0.122636 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 370.517i | 0.420564i | 0.977641 | + | 0.210282i | \(0.0674382\pi\) | ||||
−0.977641 | + | 0.210282i | \(0.932562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −109.056 | + | 109.056i | −0.123507 | + | 0.123507i | −0.766158 | − | 0.642652i | \(-0.777834\pi\) |
0.642652 | + | 0.766158i | \(0.277834\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 347.856 | − | 347.856i | 0.393057 | − | 0.393057i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1435.92 | −1.61884 | −0.809422 | − | 0.587227i | \(-0.800220\pi\) | ||||
−0.809422 | + | 0.587227i | \(0.800220\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 393.139 | − | 400.218i | 0.442226 | − | 0.450189i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 95.3792 | + | 95.3792i | 0.107047 | + | 0.107047i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1676.42 | − | 1676.42i | 1.87729 | − | 1.87729i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 980.739i | 1.09580i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 299.330 | 0.333702 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 185.268 | + | 185.268i | 0.206082 | + | 0.206082i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 376.266 | − | 376.266i | 0.417609 | − | 0.417609i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 893.679 | + | 877.872i | 0.989677 | + | 0.972172i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1272.47i | 1.40605i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −726.879 | − | 726.879i | −0.801410 | − | 0.801410i | 0.181906 | − | 0.983316i | \(-0.441773\pi\) |
−0.983316 | + | 0.181906i | \(0.941773\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −383.954 | − | 383.954i | −0.422392 | − | 0.422392i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 474.695 | 0.521070 | 0.260535 | − | 0.965464i | \(-0.416101\pi\) | ||||
0.260535 | + | 0.965464i | \(0.416101\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 244.427i | 0.267718i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 137.113 | + | 137.113i | 0.149850 | + | 0.149850i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −891.275 | + | 7.95254i | −0.971946 | + | 0.00867235i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 947.682i | 1.03121i | 0.856827 | + | 0.515605i | \(0.172433\pi\) | ||||
−0.856827 | + | 0.515605i | \(0.827567\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 111.090i | − | 0.120619i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −423.676 | + | 423.676i | −0.459021 | + | 0.459021i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −105.038 | + | 105.038i | −0.113554 | + | 0.113554i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 216.675i | − | 0.233738i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 448.957i | 0.483269i | 0.970367 | + | 0.241634i | \(0.0776834\pi\) | ||||
−0.970367 | + | 0.241634i | \(0.922317\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1212.98 | + | 1257.07i | −1.30288 | + | 1.35023i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 877.321 | + | 877.321i | 0.940323 | + | 0.940323i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 125.219i | − | 0.133924i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 857.680 | 0.915347 | 0.457674 | − | 0.889120i | \(-0.348683\pi\) | ||||
0.457674 | + | 0.889120i | \(0.348683\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −92.5980 | − | 92.5980i | −0.0986134 | − | 0.0986134i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −151.657 | − | 151.657i | −0.161166 | − | 0.161166i | 0.621917 | − | 0.783083i | \(-0.286354\pi\) |
−0.783083 | + | 0.621917i | \(0.786354\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 182.021i | − | 0.193023i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −675.715 | − | 663.764i | −0.715043 | − | 0.702395i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −908.719 | + | 908.719i | −0.959577 | + | 0.959577i | −0.999214 | − | 0.0396372i | \(-0.987380\pi\) |
0.0396372 | + | 0.999214i | \(0.487380\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −870.434 | − | 870.434i | −0.917212 | − | 0.917212i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 765.648 | 0.805097 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 844.182i | − | 0.885815i | −0.896567 | − | 0.442908i | \(-0.853947\pi\) | ||
0.896567 | − | 0.442908i | \(-0.146053\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −192.653 | + | 192.653i | −0.201731 | + | 0.201731i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −79.2164 | − | 79.2164i | −0.0827758 | − | 0.0827758i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1263.80 | + | 1241.45i | 1.31784 | + | 1.29453i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 688.157 | 0.716084 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −175.541 | + | 175.541i | −0.182285 | + | 0.182285i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −621.668 | + | 621.668i | −0.644215 | + | 0.644215i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1481.66i | − | 1.53223i | −0.642705 | − | 0.766114i | \(-0.722188\pi\) | ||
0.642705 | − | 0.766114i | \(-0.277812\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −845.890 | −0.872952 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −736.360 | + | 736.360i | −0.758352 | + | 0.758352i | −0.976022 | − | 0.217671i | \(-0.930154\pi\) |
0.217671 | + | 0.976022i | \(0.430154\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.35088 | + | 487.621i | 0.00447161 | + | 0.501152i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −80.9488 | −0.0830244 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 736.267 | 0.753600 | 0.376800 | − | 0.926295i | \(-0.377024\pi\) | ||||
0.376800 | + | 0.926295i | \(0.377024\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −158.808 | − | 158.808i | −0.162215 | − | 0.162215i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 270.972 | + | 270.972i | 0.276221 | + | 0.276221i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 564.432 | 0.574194 | 0.287097 | − | 0.957902i | \(-0.407310\pi\) | ||||
0.287097 | + | 0.957902i | \(0.407310\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 930.581 | 0.944752 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.3107 | + | 1155.56i | 0.0104465 | + | 1.17078i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 715.672 | − | 715.672i | 0.723632 | − | 0.723632i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 715.833 | 0.722334 | 0.361167 | − | 0.932501i | \(-0.382378\pi\) | ||||
0.361167 | + | 0.932501i | \(0.382378\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 71.7989i | 0.0723051i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −452.552 | + | 452.552i | −0.454826 | + | 0.454826i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −892.876 | + | 892.876i | −0.895562 | + | 0.895562i | −0.995040 | − | 0.0994775i | \(-0.968283\pi\) |
0.0994775 | + | 0.995040i | \(0.468283\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1149.72 | 1.15087 |
(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 | 448.3.l.b.433.19 | 56 | ||
4.3 | odd | 2 | 112.3.l.b.69.25 | yes | 56 | ||
7.6 | odd | 2 | inner | 448.3.l.b.433.10 | 56 | ||
16.3 | odd | 4 | 112.3.l.b.13.26 | yes | 56 | ||
16.13 | even | 4 | inner | 448.3.l.b.209.10 | 56 | ||
28.27 | even | 2 | 112.3.l.b.69.26 | yes | 56 | ||
112.13 | odd | 4 | inner | 448.3.l.b.209.19 | 56 | ||
112.83 | even | 4 | 112.3.l.b.13.25 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.3.l.b.13.25 | ✓ | 56 | 112.83 | even | 4 | ||
112.3.l.b.13.26 | yes | 56 | 16.3 | odd | 4 | ||
112.3.l.b.69.25 | yes | 56 | 4.3 | odd | 2 | ||
112.3.l.b.69.26 | yes | 56 | 28.27 | even | 2 | ||
448.3.l.b.209.10 | 56 | 16.13 | even | 4 | inner | ||
448.3.l.b.209.19 | 56 | 112.13 | odd | 4 | inner | ||
448.3.l.b.433.10 | 56 | 7.6 | odd | 2 | inner | ||
448.3.l.b.433.19 | 56 | 1.1 | even | 1 | trivial |