Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.a (trivial) |
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: | yes |
Analytic conductor: | \(60.8699614608\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 19x^{8} - x^{7} + 124x^{6} + 6x^{5} - 316x^{4} + 17x^{3} + 253x^{2} - 70x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(2.79866\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.79866 | 1.97895 | 0.989476 | − | 0.144700i | \(-0.0462218\pi\) | ||||
0.989476 | + | 0.144700i | \(0.0462218\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.83249 | 2.91625 | ||||||||
\(5\) | 1.67767 | 0.750278 | 0.375139 | − | 0.926969i | \(-0.377595\pi\) | ||||
0.375139 | + | 0.926969i | \(0.377595\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 10.7258 | 3.79216 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.69523 | 1.48476 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.87113 | −1.62836 | −0.814180 | − | 0.580613i | \(-0.802813\pi\) | ||||
−0.814180 | + | 0.580613i | \(0.802813\pi\) | |||||||
\(14\) | 2.79866 | 0.747973 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 18.3530 | 4.58825 | ||||||||
\(17\) | −0.304169 | −0.0737717 | −0.0368859 | − | 0.999319i | \(-0.511744\pi\) | ||||
−0.0368859 | + | 0.999319i | \(0.511744\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.62860 | 1.06187 | 0.530937 | − | 0.847411i | \(-0.321840\pi\) | ||||
0.530937 | + | 0.847411i | \(0.321840\pi\) | |||||||
\(20\) | 9.78502 | 2.18800 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.38164 | 0.288092 | 0.144046 | − | 0.989571i | \(-0.453989\pi\) | ||||
0.144046 | + | 0.989571i | \(0.453989\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.18541 | −0.437083 | ||||||||
\(26\) | −16.4313 | −3.22244 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.83249 | 1.10224 | ||||||||
\(29\) | 3.96868 | 0.736965 | 0.368483 | − | 0.929635i | \(-0.379877\pi\) | ||||
0.368483 | + | 0.929635i | \(0.379877\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.764099 | 0.137236 | 0.0686181 | − | 0.997643i | \(-0.478141\pi\) | ||||
0.0686181 | + | 0.997643i | \(0.478141\pi\) | |||||||
\(32\) | 29.9121 | 5.28776 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.851264 | −0.145991 | ||||||||
\(35\) | 1.67767 | 0.283578 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.21023 | 0.527759 | 0.263879 | − | 0.964556i | \(-0.414998\pi\) | ||||
0.263879 | + | 0.964556i | \(0.414998\pi\) | |||||||
\(38\) | 12.9539 | 2.10140 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 17.9945 | 2.84517 | ||||||||
\(41\) | −8.31274 | −1.29823 | −0.649116 | − | 0.760690i | \(-0.724861\pi\) | ||||
−0.649116 | + | 0.760690i | \(0.724861\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.01069 | 0.154129 | 0.0770647 | − | 0.997026i | \(-0.475445\pi\) | ||||
0.0770647 | + | 0.997026i | \(0.475445\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.86674 | 0.570119 | ||||||||
\(47\) | 2.58688 | 0.377335 | 0.188668 | − | 0.982041i | \(-0.439583\pi\) | ||||
0.188668 | + | 0.982041i | \(0.439583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.11623 | −0.864966 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −34.2434 | −4.74870 | ||||||||
\(53\) | 1.45374 | 0.199686 | 0.0998430 | − | 0.995003i | \(-0.468166\pi\) | ||||
0.0998430 | + | 0.995003i | \(0.468166\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.7258 | 1.43330 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.1070 | 1.45842 | ||||||||
\(59\) | 2.49444 | 0.324749 | 0.162374 | − | 0.986729i | \(-0.448085\pi\) | ||||
0.162374 | + | 0.986729i | \(0.448085\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.39295 | −0.434423 | −0.217211 | − | 0.976125i | \(-0.569696\pi\) | ||||
−0.217211 | + | 0.976125i | \(0.569696\pi\) | |||||||
\(62\) | 2.13845 | 0.271584 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 47.0078 | 5.87598 | ||||||||
\(65\) | −9.84984 | −1.22172 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.16878 | 0.753636 | 0.376818 | − | 0.926287i | \(-0.377018\pi\) | ||||
0.376818 | + | 0.926287i | \(0.377018\pi\) | |||||||
\(68\) | −1.77406 | −0.215137 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.69523 | 0.561188 | ||||||||
\(71\) | −7.59943 | −0.901886 | −0.450943 | − | 0.892553i | \(-0.648912\pi\) | ||||
−0.450943 | + | 0.892553i | \(0.648912\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.7455 | 1.49175 | 0.745877 | − | 0.666084i | \(-0.232031\pi\) | ||||
0.745877 | + | 0.666084i | \(0.232031\pi\) | |||||||
\(74\) | 8.98434 | 1.04441 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 26.9963 | 3.09669 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.15519 | 0.692512 | 0.346256 | − | 0.938140i | \(-0.387453\pi\) | ||||
0.346256 | + | 0.938140i | \(0.387453\pi\) | |||||||
\(80\) | 30.7903 | 3.44246 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −23.2645 | −2.56914 | ||||||||
\(83\) | −2.01266 | −0.220918 | −0.110459 | − | 0.993881i | \(-0.535232\pi\) | ||||
−0.110459 | + | 0.993881i | \(0.535232\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.510295 | −0.0553493 | ||||||||
\(86\) | 2.82859 | 0.305014 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.0843908 | −0.00894541 | −0.00447270 | − | 0.999990i | \(-0.501424\pi\) | ||||
−0.00447270 | + | 0.999990i | \(0.501424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.87113 | −0.615462 | ||||||||
\(92\) | 8.05840 | 0.840146 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.23980 | 0.746728 | ||||||||
\(95\) | 7.76527 | 0.796700 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.03775 | 0.105367 | 0.0526837 | − | 0.998611i | \(-0.483223\pi\) | ||||
0.0526837 | + | 0.998611i | \(0.483223\pi\) | |||||||
\(98\) | 2.79866 | 0.282707 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −12.7464 | −1.27464 | ||||||||
\(101\) | −19.6972 | −1.95994 | −0.979971 | − | 0.199139i | \(-0.936185\pi\) | ||||
−0.979971 | + | 0.199139i | \(0.936185\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.41267 | −0.237727 | −0.118864 | − | 0.992911i | \(-0.537925\pi\) | ||||
−0.118864 | + | 0.992911i | \(0.537925\pi\) | |||||||
\(104\) | −62.9729 | −6.17500 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.06851 | 0.395169 | ||||||||
\(107\) | −9.26256 | −0.895445 | −0.447723 | − | 0.894172i | \(-0.647765\pi\) | ||||
−0.447723 | + | 0.894172i | \(0.647765\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.30530 | 0.795503 | 0.397752 | − | 0.917493i | \(-0.369791\pi\) | ||||
0.397752 | + | 0.917493i | \(0.369791\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 18.3530 | 1.73420 | ||||||||
\(113\) | −5.47962 | −0.515479 | −0.257740 | − | 0.966214i | \(-0.582978\pi\) | ||||
−0.257740 | + | 0.966214i | \(0.582978\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.31794 | 0.216149 | ||||||||
\(116\) | 23.1473 | 2.14917 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.98110 | 0.642662 | ||||||||
\(119\) | −0.304169 | −0.0278831 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −9.49572 | −0.859702 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.45660 | 0.400215 | ||||||||
\(125\) | −12.0548 | −1.07821 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.0576 | −1.77983 | −0.889913 | − | 0.456130i | \(-0.849235\pi\) | ||||
−0.889913 | + | 0.456130i | \(0.849235\pi\) | |||||||
\(128\) | 71.7346 | 6.34050 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −27.5664 | −2.41773 | ||||||||
\(131\) | 4.22096 | 0.368787 | 0.184394 | − | 0.982852i | \(-0.440968\pi\) | ||||
0.184394 | + | 0.982852i | \(0.440968\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.62860 | 0.401350 | ||||||||
\(134\) | 17.2643 | 1.49141 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.26247 | −0.279754 | ||||||||
\(137\) | 14.5361 | 1.24191 | 0.620953 | − | 0.783848i | \(-0.286746\pi\) | ||||
0.620953 | + | 0.783848i | \(0.286746\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.94615 | −0.589165 | −0.294583 | − | 0.955626i | \(-0.595181\pi\) | ||||
−0.294583 | + | 0.955626i | \(0.595181\pi\) | |||||||
\(140\) | 9.78502 | 0.826985 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −21.2682 | −1.78479 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.65814 | 0.552929 | ||||||||
\(146\) | 35.6704 | 2.95211 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18.7236 | 1.53907 | ||||||||
\(149\) | −13.9640 | −1.14398 | −0.571989 | − | 0.820262i | \(-0.693828\pi\) | ||||
−0.571989 | + | 0.820262i | \(0.693828\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.37080 | 0.111554 | 0.0557771 | − | 0.998443i | \(-0.482236\pi\) | ||||
0.0557771 | + | 0.998443i | \(0.482236\pi\) | |||||||
\(152\) | 49.6456 | 4.02679 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.28191 | 0.102965 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8997 | −1.26894 | −0.634469 | − | 0.772949i | \(-0.718781\pi\) | ||||
−0.634469 | + | 0.772949i | \(0.718781\pi\) | |||||||
\(158\) | 17.2263 | 1.37045 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 50.1827 | 3.96729 | ||||||||
\(161\) | 1.38164 | 0.108888 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4685 | 0.819957 | 0.409978 | − | 0.912095i | \(-0.365536\pi\) | ||||
0.409978 | + | 0.912095i | \(0.365536\pi\) | |||||||
\(164\) | −48.4840 | −3.78596 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.63275 | −0.437186 | ||||||||
\(167\) | 8.57355 | 0.663442 | 0.331721 | − | 0.943378i | \(-0.392371\pi\) | ||||
0.331721 | + | 0.943378i | \(0.392371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.4702 | 1.65156 | ||||||||
\(170\) | −1.42814 | −0.109534 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.89486 | 0.449479 | ||||||||
\(173\) | −13.7471 | −1.04517 | −0.522586 | − | 0.852587i | \(-0.675033\pi\) | ||||
−0.522586 | + | 0.852587i | \(0.675033\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.18541 | −0.165202 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.236181 | −0.0177025 | ||||||||
\(179\) | 3.85014 | 0.287773 | 0.143887 | − | 0.989594i | \(-0.454040\pi\) | ||||
0.143887 | + | 0.989594i | \(0.454040\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.5568 | −1.45365 | −0.726823 | − | 0.686825i | \(-0.759004\pi\) | ||||
−0.726823 | + | 0.686825i | \(0.759004\pi\) | |||||||
\(182\) | −16.4313 | −1.21797 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 14.8192 | 1.09249 | ||||||||
\(185\) | 5.38571 | 0.395966 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 15.0880 | 1.10040 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 21.7324 | 1.57663 | ||||||||
\(191\) | 2.54502 | 0.184151 | 0.0920755 | − | 0.995752i | \(-0.470650\pi\) | ||||
0.0920755 | + | 0.995752i | \(0.470650\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.6282 | −1.55683 | −0.778415 | − | 0.627750i | \(-0.783976\pi\) | ||||
−0.778415 | + | 0.627750i | \(0.783976\pi\) | |||||||
\(194\) | 2.90430 | 0.208517 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.83249 | 0.416607 | ||||||||
\(197\) | −22.0693 | −1.57237 | −0.786187 | − | 0.617989i | \(-0.787948\pi\) | ||||
−0.786187 | + | 0.617989i | \(0.787948\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.8315 | −0.909598 | −0.454799 | − | 0.890594i | \(-0.650289\pi\) | ||||
−0.454799 | + | 0.890594i | \(0.650289\pi\) | |||||||
\(200\) | −23.4404 | −1.65749 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −55.1257 | −3.87863 | ||||||||
\(203\) | 3.96868 | 0.278547 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.9461 | −0.974035 | ||||||||
\(206\) | −6.75224 | −0.470451 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −107.753 | −7.47132 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.7406 | 1.22131 | 0.610655 | − | 0.791897i | \(-0.290906\pi\) | ||||
0.610655 | + | 0.791897i | \(0.290906\pi\) | |||||||
\(212\) | 8.47891 | 0.582334 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −25.9227 | −1.77204 | ||||||||
\(215\) | 1.69561 | 0.115640 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.764099 | 0.0518704 | ||||||||
\(218\) | 23.2437 | 1.57426 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.78581 | 0.120127 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.1174 | 1.14627 | 0.573133 | − | 0.819462i | \(-0.305728\pi\) | ||||
0.573133 | + | 0.819462i | \(0.305728\pi\) | |||||||
\(224\) | 29.9121 | 1.99859 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.3356 | −1.02011 | ||||||||
\(227\) | −20.4871 | −1.35978 | −0.679888 | − | 0.733316i | \(-0.737971\pi\) | ||||
−0.679888 | + | 0.733316i | \(0.737971\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.4342 | 1.61466 | 0.807328 | − | 0.590103i | \(-0.200913\pi\) | ||||
0.807328 | + | 0.590103i | \(0.200913\pi\) | |||||||
\(230\) | 6.48712 | 0.427748 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 42.5674 | 2.79469 | ||||||||
\(233\) | −23.7053 | −1.55298 | −0.776491 | − | 0.630128i | \(-0.783002\pi\) | ||||
−0.776491 | + | 0.630128i | \(0.783002\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.33994 | 0.283106 | ||||||||
\(236\) | 14.5488 | 0.947048 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.851264 | −0.0551793 | ||||||||
\(239\) | −1.57997 | −0.102200 | −0.0510998 | − | 0.998694i | \(-0.516273\pi\) | ||||
−0.0510998 | + | 0.998694i | \(0.516273\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2382 | 0.788333 | 0.394167 | − | 0.919039i | \(-0.371033\pi\) | ||||
0.394167 | + | 0.919039i | \(0.371033\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −19.7894 | −1.26688 | ||||||||
\(245\) | 1.67767 | 0.107183 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −27.1751 | −1.72911 | ||||||||
\(248\) | 8.19561 | 0.520422 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −33.7372 | −2.13373 | ||||||||
\(251\) | −19.4107 | −1.22520 | −0.612598 | − | 0.790395i | \(-0.709875\pi\) | ||||
−0.612598 | + | 0.790395i | \(0.709875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −56.1345 | −3.52219 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 106.745 | 6.67157 | ||||||||
\(257\) | 0.270104 | 0.0168486 | 0.00842431 | − | 0.999965i | \(-0.497318\pi\) | ||||
0.00842431 | + | 0.999965i | \(0.497318\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.21023 | 0.199474 | ||||||||
\(260\) | −57.4491 | −3.56284 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.8130 | 0.729812 | ||||||||
\(263\) | 27.9927 | 1.72611 | 0.863053 | − | 0.505113i | \(-0.168549\pi\) | ||||
0.863053 | + | 0.505113i | \(0.168549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.43889 | 0.149820 | ||||||||
\(266\) | 12.9539 | 0.794253 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 35.9794 | 2.19779 | ||||||||
\(269\) | −1.11686 | −0.0680960 | −0.0340480 | − | 0.999420i | \(-0.510840\pi\) | ||||
−0.0340480 | + | 0.999420i | \(0.510840\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.8310 | −1.50837 | −0.754187 | − | 0.656660i | \(-0.771969\pi\) | ||||
−0.754187 | + | 0.656660i | \(0.771969\pi\) | |||||||
\(272\) | −5.58241 | −0.338483 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 40.6817 | 2.45767 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.4335 | 0.747057 | 0.373528 | − | 0.927619i | \(-0.378148\pi\) | ||||
0.373528 | + | 0.927619i | \(0.378148\pi\) | |||||||
\(278\) | −19.4399 | −1.16593 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 17.9945 | 1.07537 | ||||||||
\(281\) | −6.73560 | −0.401812 | −0.200906 | − | 0.979611i | \(-0.564389\pi\) | ||||
−0.200906 | + | 0.979611i | \(0.564389\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.1606 | 0.663430 | 0.331715 | − | 0.943380i | \(-0.392373\pi\) | ||||
0.331715 | + | 0.943380i | \(0.392373\pi\) | |||||||
\(284\) | −44.3236 | −2.63012 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.31274 | −0.490685 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9075 | −0.994558 | ||||||||
\(290\) | 18.6339 | 1.09422 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 74.3383 | 4.35032 | ||||||||
\(293\) | −16.9009 | −0.987363 | −0.493682 | − | 0.869643i | \(-0.664349\pi\) | ||||
−0.493682 | + | 0.869643i | \(0.664349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.18486 | 0.243652 | ||||||||
\(296\) | 34.4324 | 2.00134 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −39.0805 | −2.26388 | ||||||||
\(299\) | −8.11179 | −0.469117 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.01069 | 0.0582554 | ||||||||
\(302\) | 3.83640 | 0.220760 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 84.9487 | 4.87214 | ||||||||
\(305\) | −5.69226 | −0.325938 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.3453 | 0.647511 | 0.323755 | − | 0.946141i | \(-0.395054\pi\) | ||||
0.323755 | + | 0.946141i | \(0.395054\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.58762 | 0.203763 | ||||||||
\(311\) | −23.8487 | −1.35234 | −0.676169 | − | 0.736747i | \(-0.736361\pi\) | ||||
−0.676169 | + | 0.736747i | \(0.736361\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.9666 | 1.75034 | 0.875169 | − | 0.483818i | \(-0.160750\pi\) | ||||
0.875169 | + | 0.483818i | \(0.160750\pi\) | |||||||
\(314\) | −44.4980 | −2.51116 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 35.9001 | 2.01954 | ||||||||
\(317\) | −3.20875 | −0.180221 | −0.0901106 | − | 0.995932i | \(-0.528722\pi\) | ||||
−0.0901106 | + | 0.995932i | \(0.528722\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 78.8637 | 4.40862 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.86674 | 0.215485 | ||||||||
\(323\) | −1.40787 | −0.0783362 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.8309 | 0.711728 | ||||||||
\(326\) | 29.2978 | 1.62265 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −89.1612 | −4.92310 | ||||||||
\(329\) | 2.58688 | 0.142619 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.98424 | −0.218994 | −0.109497 | − | 0.993987i | \(-0.534924\pi\) | ||||
−0.109497 | + | 0.993987i | \(0.534924\pi\) | |||||||
\(332\) | −11.7388 | −0.644252 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.9945 | 1.31292 | ||||||||
\(335\) | 10.3492 | 0.565437 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.3006 | 0.615582 | 0.307791 | − | 0.951454i | \(-0.400410\pi\) | ||||
0.307791 | + | 0.951454i | \(0.400410\pi\) | |||||||
\(338\) | 60.0878 | 3.26835 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.97629 | −0.161412 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 10.8405 | 0.584483 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −38.4734 | −2.06834 | ||||||||
\(347\) | 6.58840 | 0.353684 | 0.176842 | − | 0.984239i | \(-0.443412\pi\) | ||||
0.176842 | + | 0.984239i | \(0.443412\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.4343 | −1.09382 | −0.546912 | − | 0.837190i | \(-0.684197\pi\) | ||||
−0.546912 | + | 0.837190i | \(0.684197\pi\) | |||||||
\(350\) | −6.11623 | −0.326926 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.5457 | −1.94513 | −0.972565 | − | 0.232630i | \(-0.925267\pi\) | ||||
−0.972565 | + | 0.232630i | \(0.925267\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.7494 | −0.676665 | ||||||||
\(356\) | −0.492209 | −0.0260870 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.7752 | 0.569489 | ||||||||
\(359\) | 0.314474 | 0.0165973 | 0.00829864 | − | 0.999966i | \(-0.497358\pi\) | ||||
0.00829864 | + | 0.999966i | \(0.497358\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.42393 | 0.127575 | ||||||||
\(362\) | −54.7328 | −2.87669 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −34.2434 | −1.79484 | ||||||||
\(365\) | 21.3829 | 1.11923 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.6952 | 1.18468 | 0.592340 | − | 0.805688i | \(-0.298204\pi\) | ||||
0.592340 | + | 0.805688i | \(0.298204\pi\) | |||||||
\(368\) | 25.3572 | 1.32184 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 15.0728 | 0.783597 | ||||||||
\(371\) | 1.45374 | 0.0754742 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.8020 | −1.69843 | −0.849213 | − | 0.528051i | \(-0.822923\pi\) | ||||
−0.849213 | + | 0.528051i | \(0.822923\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 27.7465 | 1.43092 | ||||||||
\(377\) | −23.3006 | −1.20004 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.4514 | 1.30735 | 0.653675 | − | 0.756776i | \(-0.273227\pi\) | ||||
0.653675 | + | 0.756776i | \(0.273227\pi\) | |||||||
\(380\) | 45.2909 | 2.32338 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.12264 | 0.364426 | ||||||||
\(383\) | 13.9526 | 0.712944 | 0.356472 | − | 0.934306i | \(-0.383979\pi\) | ||||
0.356472 | + | 0.934306i | \(0.383979\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −60.5299 | −3.08089 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.05266 | 0.307277 | ||||||||
\(389\) | 9.06975 | 0.459855 | 0.229927 | − | 0.973208i | \(-0.426151\pi\) | ||||
0.229927 | + | 0.973208i | \(0.426151\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.420251 | −0.0212530 | ||||||||
\(392\) | 10.7258 | 0.541737 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −61.7645 | −3.11165 | ||||||||
\(395\) | 10.3264 | 0.519577 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.1849 | 1.21381 | 0.606904 | − | 0.794775i | \(-0.292411\pi\) | ||||
0.606904 | + | 0.794775i | \(0.292411\pi\) | |||||||
\(398\) | −35.9109 | −1.80005 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −40.1089 | −2.00545 | ||||||||
\(401\) | −3.86368 | −0.192943 | −0.0964715 | − | 0.995336i | \(-0.530756\pi\) | ||||
−0.0964715 | + | 0.995336i | \(0.530756\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.48613 | −0.223470 | ||||||||
\(404\) | −114.884 | −5.71568 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.1070 | 0.551230 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.0985 | −0.993806 | −0.496903 | − | 0.867806i | \(-0.665530\pi\) | ||||
−0.496903 | + | 0.867806i | \(0.665530\pi\) | |||||||
\(410\) | −39.0303 | −1.92757 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.0719 | −0.693272 | ||||||||
\(413\) | 2.49444 | 0.122744 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.37659 | −0.165750 | ||||||||
\(416\) | −175.618 | −8.61038 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.12825 | 0.103972 | 0.0519859 | − | 0.998648i | \(-0.483445\pi\) | ||||
0.0519859 | + | 0.998648i | \(0.483445\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.84998 | −0.187636 | −0.0938182 | − | 0.995589i | \(-0.529907\pi\) | ||||
−0.0938182 | + | 0.995589i | \(0.529907\pi\) | |||||||
\(422\) | 49.6498 | 2.41691 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 15.5926 | 0.757242 | ||||||||
\(425\) | 0.664734 | 0.0322443 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.39295 | −0.164196 | ||||||||
\(428\) | −54.0238 | −2.61134 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.74544 | 0.228846 | ||||||||
\(431\) | −16.7030 | −0.804555 | −0.402278 | − | 0.915518i | \(-0.631781\pi\) | ||||
−0.402278 | + | 0.915518i | \(0.631781\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.9215 | 0.813196 | 0.406598 | − | 0.913607i | \(-0.366715\pi\) | ||||
0.406598 | + | 0.913607i | \(0.366715\pi\) | |||||||
\(434\) | 2.13845 | 0.102649 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 48.4406 | 2.31988 | ||||||||
\(437\) | 6.39505 | 0.305917 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.7946 | 1.27883 | 0.639417 | − | 0.768860i | \(-0.279176\pi\) | ||||
0.639417 | + | 0.768860i | \(0.279176\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.99789 | 0.237725 | ||||||||
\(443\) | 3.92408 | 0.186439 | 0.0932194 | − | 0.995646i | \(-0.470284\pi\) | ||||
0.0932194 | + | 0.995646i | \(0.470284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.141580 | −0.00671154 | ||||||||
\(446\) | 47.9058 | 2.26841 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 47.0078 | 2.22091 | ||||||||
\(449\) | −19.6785 | −0.928686 | −0.464343 | − | 0.885655i | \(-0.653709\pi\) | ||||
−0.464343 | + | 0.885655i | \(0.653709\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −31.9598 | −1.50326 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −57.3364 | −2.69093 | ||||||||
\(455\) | −9.84984 | −0.461768 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.7725 | −0.924921 | −0.462460 | − | 0.886640i | \(-0.653033\pi\) | ||||
−0.462460 | + | 0.886640i | \(0.653033\pi\) | |||||||
\(458\) | 68.3830 | 3.19533 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13.5194 | 0.630343 | ||||||||
\(461\) | 9.69184 | 0.451394 | 0.225697 | − | 0.974198i | \(-0.427534\pi\) | ||||
0.225697 | + | 0.974198i | \(0.427534\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.21162 | 0.335152 | 0.167576 | − | 0.985859i | \(-0.446406\pi\) | ||||
0.167576 | + | 0.985859i | \(0.446406\pi\) | |||||||
\(464\) | 72.8372 | 3.38138 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −66.3429 | −3.07328 | ||||||||
\(467\) | −36.5718 | −1.69234 | −0.846171 | − | 0.532912i | \(-0.821098\pi\) | ||||
−0.846171 | + | 0.532912i | \(0.821098\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.16878 | 0.284848 | ||||||||
\(470\) | 12.1460 | 0.560253 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 26.7550 | 1.23150 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.1154 | −0.464127 | ||||||||
\(476\) | −1.77406 | −0.0813140 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.42179 | −0.202248 | ||||||||
\(479\) | 38.9699 | 1.78058 | 0.890290 | − | 0.455394i | \(-0.150502\pi\) | ||||
0.890290 | + | 0.455394i | \(0.150502\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.8477 | −0.859381 | ||||||||
\(482\) | 34.2506 | 1.56007 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.74100 | 0.0790548 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.9835 | −1.08679 | −0.543397 | − | 0.839476i | \(-0.682862\pi\) | ||||
−0.543397 | + | 0.839476i | \(0.682862\pi\) | |||||||
\(488\) | −36.3923 | −1.64740 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.69523 | 0.212109 | ||||||||
\(491\) | 3.19310 | 0.144103 | 0.0720513 | − | 0.997401i | \(-0.477045\pi\) | ||||
0.0720513 | + | 0.997401i | \(0.477045\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.20715 | −0.0543672 | ||||||||
\(494\) | −76.0539 | −3.42183 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.0235 | 0.629674 | ||||||||
\(497\) | −7.59943 | −0.340881 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.5331 | 1.23255 | 0.616275 | − | 0.787531i | \(-0.288641\pi\) | ||||
0.616275 | + | 0.787531i | \(0.288641\pi\) | |||||||
\(500\) | −70.3094 | −3.14433 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −54.3241 | −2.42460 | ||||||||
\(503\) | −33.1568 | −1.47839 | −0.739195 | − | 0.673492i | \(-0.764794\pi\) | ||||
−0.739195 | + | 0.673492i | \(0.764794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.0454 | −1.47050 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −116.986 | −5.19042 | ||||||||
\(509\) | 7.69479 | 0.341066 | 0.170533 | − | 0.985352i | \(-0.445451\pi\) | ||||
0.170533 | + | 0.985352i | \(0.445451\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.7455 | 0.563830 | ||||||||
\(512\) | 155.274 | 6.86221 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.755929 | 0.0333426 | ||||||||
\(515\) | −4.04767 | −0.178362 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 8.98434 | 0.394749 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −105.648 | −4.63297 | ||||||||
\(521\) | 8.09827 | 0.354792 | 0.177396 | − | 0.984140i | \(-0.443233\pi\) | ||||
0.177396 | + | 0.984140i | \(0.443233\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.3528 | −0.846241 | −0.423120 | − | 0.906073i | \(-0.639065\pi\) | ||||
−0.423120 | + | 0.906073i | \(0.639065\pi\) | |||||||
\(524\) | 24.6187 | 1.07547 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 78.3422 | 3.41588 | ||||||||
\(527\) | −0.232415 | −0.0101241 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0911 | −0.917003 | ||||||||
\(530\) | 6.82563 | 0.296487 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 26.9963 | 1.17044 | ||||||||
\(533\) | 48.8052 | 2.11399 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.5395 | −0.671833 | ||||||||
\(536\) | 66.1654 | 2.85791 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.12571 | −0.134759 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.5883 | 1.22911 | 0.614554 | − | 0.788875i | \(-0.289336\pi\) | ||||
0.614554 | + | 0.788875i | \(0.289336\pi\) | |||||||
\(542\) | −69.4934 | −2.98500 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.09832 | −0.390087 | ||||||||
\(545\) | 13.9336 | 0.596849 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.3917 | −1.00016 | −0.500078 | − | 0.865980i | \(-0.666695\pi\) | ||||
−0.500078 | + | 0.865980i | \(0.666695\pi\) | |||||||
\(548\) | 84.7820 | 3.62171 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.3694 | 0.782564 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.15519 | 0.261745 | ||||||||
\(554\) | 34.7971 | 1.47839 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −40.5134 | −1.71815 | ||||||||
\(557\) | 25.4361 | 1.07776 | 0.538881 | − | 0.842382i | \(-0.318847\pi\) | ||||
0.538881 | + | 0.842382i | \(0.318847\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.93392 | −0.250978 | ||||||||
\(560\) | 30.7903 | 1.30113 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.8506 | −0.795167 | ||||||||
\(563\) | 39.8791 | 1.68070 | 0.840352 | − | 0.542041i | \(-0.182348\pi\) | ||||
0.840352 | + | 0.542041i | \(0.182348\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.19301 | −0.386753 | ||||||||
\(566\) | 31.2348 | 1.31290 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −81.5103 | −3.42010 | ||||||||
\(569\) | 32.2487 | 1.35194 | 0.675968 | − | 0.736931i | \(-0.263726\pi\) | ||||
0.675968 | + | 0.736931i | \(0.263726\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.6844 | 0.865615 | 0.432807 | − | 0.901486i | \(-0.357523\pi\) | ||||
0.432807 | + | 0.901486i | \(0.357523\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −23.2645 | −0.971043 | ||||||||
\(575\) | −3.01945 | −0.125920 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.7198 | 0.654424 | 0.327212 | − | 0.944951i | \(-0.393891\pi\) | ||||
0.327212 | + | 0.944951i | \(0.393891\pi\) | |||||||
\(578\) | −47.3183 | −1.96818 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 38.8336 | 1.61248 | ||||||||
\(581\) | −2.01266 | −0.0834993 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 136.707 | 5.65697 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −47.3000 | −1.95394 | ||||||||
\(587\) | −20.5683 | −0.848946 | −0.424473 | − | 0.905441i | \(-0.639541\pi\) | ||||
−0.424473 | + | 0.905441i | \(0.639541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.53671 | 0.145727 | ||||||||
\(590\) | 11.7120 | 0.482175 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 58.9174 | 2.42149 | ||||||||
\(593\) | 21.1496 | 0.868511 | 0.434255 | − | 0.900790i | \(-0.357012\pi\) | ||||
0.434255 | + | 0.900790i | \(0.357012\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.510295 | −0.0209201 | ||||||||
\(596\) | −81.4451 | −3.33612 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.7021 | −0.928359 | ||||||||
\(599\) | 33.6993 | 1.37691 | 0.688457 | − | 0.725277i | \(-0.258288\pi\) | ||||
0.688457 | + | 0.725277i | \(0.258288\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.7888 | 1.50065 | 0.750324 | − | 0.661070i | \(-0.229897\pi\) | ||||
0.750324 | + | 0.661070i | \(0.229897\pi\) | |||||||
\(602\) | 2.82859 | 0.115285 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.99519 | 0.325320 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.0614 | −0.489558 | −0.244779 | − | 0.969579i | \(-0.578715\pi\) | ||||
−0.244779 | + | 0.969579i | \(0.578715\pi\) | |||||||
\(608\) | 138.451 | 5.61494 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.9307 | −0.645015 | ||||||||
\(611\) | −15.1879 | −0.614437 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.57642 | −0.346398 | −0.173199 | − | 0.984887i | \(-0.555410\pi\) | ||||
−0.173199 | + | 0.984887i | \(0.555410\pi\) | |||||||
\(614\) | 31.7517 | 1.28139 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.0309560 | 0.00124624 | 0.000623121 | − | 1.00000i | \(-0.499802\pi\) | ||||
0.000623121 | 1.00000i | \(0.499802\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.2938 | −0.855869 | −0.427934 | − | 0.903810i | \(-0.640759\pi\) | ||||
−0.427934 | + | 0.903810i | \(0.640759\pi\) | |||||||
\(620\) | 7.47672 | 0.300272 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −66.7445 | −2.67621 | ||||||||
\(623\) | −0.0843908 | −0.00338105 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.29689 | −0.371876 | ||||||||
\(626\) | 86.6650 | 3.46383 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −92.7351 | −3.70053 | ||||||||
\(629\) | −0.976451 | −0.0389336 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.7895 | 0.867426 | 0.433713 | − | 0.901051i | \(-0.357203\pi\) | ||||
0.433713 | + | 0.901051i | \(0.357203\pi\) | |||||||
\(632\) | 66.0196 | 2.62612 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.98019 | −0.356649 | ||||||||
\(635\) | −33.6501 | −1.33536 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.87113 | −0.232623 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 120.347 | 4.75714 | ||||||||
\(641\) | 39.8969 | 1.57583 | 0.787916 | − | 0.615783i | \(-0.211160\pi\) | ||||
0.787916 | + | 0.615783i | \(0.211160\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.15604 | 0.282207 | 0.141103 | − | 0.989995i | \(-0.454935\pi\) | ||||
0.141103 | + | 0.989995i | \(0.454935\pi\) | |||||||
\(644\) | 8.05840 | 0.317546 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.94016 | −0.155024 | ||||||||
\(647\) | 4.74897 | 0.186701 | 0.0933506 | − | 0.995633i | \(-0.470242\pi\) | ||||
0.0933506 | + | 0.995633i | \(0.470242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 35.9092 | 1.40848 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 61.0575 | 2.39120 | ||||||||
\(653\) | 5.03380 | 0.196988 | 0.0984938 | − | 0.995138i | \(-0.468598\pi\) | ||||
0.0984938 | + | 0.995138i | \(0.468598\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.08139 | 0.276693 | ||||||||
\(656\) | −152.564 | −5.95661 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.23980 | 0.282237 | ||||||||
\(659\) | 6.55136 | 0.255205 | 0.127602 | − | 0.991825i | \(-0.459272\pi\) | ||||
0.127602 | + | 0.991825i | \(0.459272\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.4255 | 1.41679 | 0.708394 | − | 0.705818i | \(-0.249420\pi\) | ||||
0.708394 | + | 0.705818i | \(0.249420\pi\) | |||||||
\(662\) | −11.1505 | −0.433378 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.5875 | −0.837757 | ||||||||
\(665\) | 7.76527 | 0.301124 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.48328 | 0.212313 | ||||||||
\(668\) | 50.0052 | 1.93476 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 28.9639 | 1.11897 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.9908 | −1.23315 | −0.616577 | − | 0.787295i | \(-0.711481\pi\) | ||||
−0.616577 | + | 0.787295i | \(0.711481\pi\) | |||||||
\(674\) | 31.6265 | 1.21821 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 125.225 | 4.81634 | ||||||||
\(677\) | −21.6417 | −0.831760 | −0.415880 | − | 0.909420i | \(-0.636526\pi\) | ||||
−0.415880 | + | 0.909420i | \(0.636526\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.03775 | 0.0398251 | ||||||||
\(680\) | −5.47335 | −0.209893 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.1587 | 0.886144 | 0.443072 | − | 0.896486i | \(-0.353889\pi\) | ||||
0.443072 | + | 0.896486i | \(0.353889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.3869 | 0.931775 | ||||||||
\(686\) | 2.79866 | 0.106853 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18.5493 | 0.707184 | ||||||||
\(689\) | −8.53508 | −0.325161 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.69598 | 0.102560 | 0.0512800 | − | 0.998684i | \(-0.483670\pi\) | ||||
0.0512800 | + | 0.998684i | \(0.483670\pi\) | |||||||
\(692\) | −80.1798 | −3.04798 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.4387 | 0.699923 | ||||||||
\(695\) | −11.6534 | −0.442038 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.52847 | 0.0957728 | ||||||||
\(698\) | −57.1887 | −2.16463 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.7464 | −0.481769 | ||||||||
\(701\) | 0.447285 | 0.0168937 | 0.00844686 | − | 0.999964i | \(-0.497311\pi\) | ||||
0.00844686 | + | 0.999964i | \(0.497311\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.8589 | 0.560413 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −102.279 | −3.84932 | ||||||||
\(707\) | −19.6972 | −0.740789 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.2291 | 0.421718 | 0.210859 | − | 0.977517i | \(-0.432374\pi\) | ||||
0.210859 | + | 0.977517i | \(0.432374\pi\) | |||||||
\(710\) | −35.6811 | −1.33909 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.905163 | −0.0339224 | ||||||||
\(713\) | 1.05571 | 0.0395366 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.4559 | 0.839218 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.880105 | 0.0328452 | ||||||||
\(719\) | −9.04358 | −0.337268 | −0.168634 | − | 0.985679i | \(-0.553936\pi\) | ||||
−0.168634 | + | 0.985679i | \(0.553936\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.41267 | −0.0898525 | ||||||||
\(722\) | 6.78375 | 0.252465 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −114.065 | −4.23919 | ||||||||
\(725\) | −8.67321 | −0.322115 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.1368 | −1.63694 | −0.818471 | − | 0.574548i | \(-0.805178\pi\) | ||||
−0.818471 | + | 0.574548i | \(0.805178\pi\) | |||||||
\(728\) | −62.9729 | −2.33393 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 59.8433 | 2.21490 | ||||||||
\(731\) | −0.307421 | −0.0113704 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.0438 | 1.03582 | 0.517911 | − | 0.855435i | \(-0.326710\pi\) | ||||
0.517911 | + | 0.855435i | \(0.326710\pi\) | |||||||
\(734\) | 63.5161 | 2.34442 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 41.3277 | 1.52336 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.7065 | 1.60777 | 0.803886 | − | 0.594784i | \(-0.202762\pi\) | ||||
0.803886 | + | 0.594784i | \(0.202762\pi\) | |||||||
\(740\) | 31.4122 | 1.15473 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.06851 | 0.149360 | ||||||||
\(743\) | −21.3676 | −0.783901 | −0.391950 | − | 0.919986i | \(-0.628199\pi\) | ||||
−0.391950 | + | 0.919986i | \(0.628199\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.4271 | −0.858301 | ||||||||
\(746\) | −91.8017 | −3.36110 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.26256 | −0.338446 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.23940 | 0.0817169 | 0.0408585 | − | 0.999165i | \(-0.486991\pi\) | ||||
0.0408585 | + | 0.999165i | \(0.486991\pi\) | |||||||
\(752\) | 47.4770 | 1.73131 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −65.2106 | −2.37483 | ||||||||
\(755\) | 2.29976 | 0.0836967 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.7090 | 1.73401 | 0.867007 | − | 0.498296i | \(-0.166041\pi\) | ||||
0.867007 | + | 0.498296i | \(0.166041\pi\) | |||||||
\(758\) | 71.2297 | 2.58718 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 83.2891 | 3.02121 | ||||||||
\(761\) | −35.6430 | −1.29206 | −0.646029 | − | 0.763313i | \(-0.723572\pi\) | ||||
−0.646029 | + | 0.763313i | \(0.723572\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.30530 | 0.300672 | ||||||||
\(764\) | 14.8438 | 0.537030 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 39.0486 | 1.41088 | ||||||||
\(767\) | −14.6452 | −0.528808 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0645 | −0.795665 | −0.397832 | − | 0.917458i | \(-0.630237\pi\) | ||||
−0.397832 | + | 0.917458i | \(0.630237\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −126.146 | −4.54010 | ||||||||
\(773\) | 18.9064 | 0.680016 | 0.340008 | − | 0.940423i | \(-0.389570\pi\) | ||||
0.340008 | + | 0.940423i | \(0.389570\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.66987 | −0.0599836 | ||||||||
\(776\) | 11.1307 | 0.399570 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.3832 | 0.910030 | ||||||||
\(779\) | −38.4763 | −1.37856 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.17614 | −0.0420587 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 18.3530 | 0.655464 | ||||||||
\(785\) | −26.6746 | −0.952056 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.64396 | −0.236832 | −0.118416 | − | 0.992964i | \(-0.537782\pi\) | ||||
−0.118416 | + | 0.992964i | \(0.537782\pi\) | |||||||
\(788\) | −128.719 | −4.58543 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 28.9000 | 1.02822 | ||||||||
\(791\) | −5.47962 | −0.194833 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.9205 | 0.707397 | ||||||||
\(794\) | 67.6854 | 2.40207 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −74.8394 | −2.65261 | ||||||||
\(797\) | 15.3017 | 0.542014 | 0.271007 | − | 0.962577i | \(-0.412643\pi\) | ||||
0.271007 | + | 0.962577i | \(0.412643\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.786847 | −0.0278367 | ||||||||
\(800\) | −65.3704 | −2.31119 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.8131 | −0.381825 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.31794 | 0.0816966 | ||||||||
\(806\) | −12.5551 | −0.442236 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −211.269 | −7.43241 | ||||||||
\(809\) | 24.7092 | 0.868728 | 0.434364 | − | 0.900737i | \(-0.356973\pi\) | ||||
0.434364 | + | 0.900737i | \(0.356973\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.7880 | −0.905539 | −0.452770 | − | 0.891628i | \(-0.649564\pi\) | ||||
−0.452770 | + | 0.891628i | \(0.649564\pi\) | |||||||
\(812\) | 23.1473 | 0.812311 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.5627 | 0.615195 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.67810 | 0.163666 | ||||||||
\(818\) | −56.2488 | −1.96669 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −81.3403 | −2.84053 | ||||||||
\(821\) | −18.3066 | −0.638905 | −0.319452 | − | 0.947602i | \(-0.603499\pi\) | ||||
−0.319452 | + | 0.947602i | \(0.603499\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.84388 | −0.168847 | −0.0844235 | − | 0.996430i | \(-0.526905\pi\) | ||||
−0.0844235 | + | 0.996430i | \(0.526905\pi\) | |||||||
\(824\) | −25.8779 | −0.901500 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.98110 | 0.242903 | ||||||||
\(827\) | 25.8818 | 0.900000 | 0.450000 | − | 0.893029i | \(-0.351424\pi\) | ||||
0.450000 | + | 0.893029i | \(0.351424\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 54.1465 | 1.88058 | 0.940292 | − | 0.340368i | \(-0.110552\pi\) | ||||
0.940292 | + | 0.340368i | \(0.110552\pi\) | |||||||
\(830\) | −9.44992 | −0.328011 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −275.989 | −9.56820 | ||||||||
\(833\) | −0.304169 | −0.0105388 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.3836 | 0.497766 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.95625 | 0.205755 | ||||||||
\(839\) | −32.3629 | −1.11729 | −0.558645 | − | 0.829407i | \(-0.688679\pi\) | ||||
−0.558645 | + | 0.829407i | \(0.688679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2496 | −0.456882 | ||||||||
\(842\) | −10.7748 | −0.371323 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 103.472 | 3.56164 | ||||||||
\(845\) | 36.0200 | 1.23913 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 26.6804 | 0.916210 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.86036 | 0.0638100 | ||||||||
\(851\) | 4.43538 | 0.152043 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.12615 | −0.209755 | −0.104878 | − | 0.994485i | \(-0.533445\pi\) | ||||
−0.104878 | + | 0.994485i | \(0.533445\pi\) | |||||||
\(854\) | −9.49572 | −0.324937 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −99.3488 | −3.39567 | ||||||||
\(857\) | −22.6396 | −0.773354 | −0.386677 | − | 0.922215i | \(-0.626377\pi\) | ||||
−0.386677 | + | 0.922215i | \(0.626377\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.7204 | −0.468134 | −0.234067 | − | 0.972220i | \(-0.575204\pi\) | ||||
−0.234067 | + | 0.972220i | \(0.575204\pi\) | |||||||
\(860\) | 9.88965 | 0.337234 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −46.7460 | −1.59218 | ||||||||
\(863\) | −43.6306 | −1.48520 | −0.742601 | − | 0.669734i | \(-0.766408\pi\) | ||||
−0.742601 | + | 0.669734i | \(0.766408\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.0631 | −0.784170 | ||||||||
\(866\) | 47.3575 | 1.60927 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.45660 | 0.151267 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.2177 | −1.22719 | ||||||||
\(872\) | 89.0813 | 3.01667 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 17.8976 | 0.605394 | ||||||||
\(875\) | −12.0548 | −0.407526 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.9122 | −1.14513 | −0.572567 | − | 0.819858i | \(-0.694052\pi\) | ||||
−0.572567 | + | 0.819858i | \(0.694052\pi\) | |||||||
\(878\) | 74.9889 | 2.53075 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.7514 | −0.429605 | −0.214803 | − | 0.976657i | \(-0.568911\pi\) | ||||
−0.214803 | + | 0.976657i | \(0.568911\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.882229 | 0.0296894 | 0.0148447 | − | 0.999890i | \(-0.495275\pi\) | ||||
0.0148447 | + | 0.999890i | \(0.495275\pi\) | |||||||
\(884\) | 10.4158 | 0.350320 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.9822 | 0.368953 | ||||||||
\(887\) | 34.4245 | 1.15586 | 0.577931 | − | 0.816086i | \(-0.303860\pi\) | ||||
0.577931 | + | 0.816086i | \(0.303860\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.0576 | −0.672711 | ||||||||
\(890\) | −0.396235 | −0.0132818 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 99.8372 | 3.34280 | ||||||||
\(893\) | 11.9736 | 0.400682 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.45928 | 0.215910 | ||||||||
\(896\) | 71.7346 | 2.39649 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −55.0734 | −1.83782 | ||||||||
\(899\) | 3.03246 | 0.101138 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.442181 | −0.0147312 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −58.7736 | −1.95478 | ||||||||
\(905\) | −32.8099 | −1.09064 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.1339 | 1.23301 | 0.616505 | − | 0.787351i | \(-0.288548\pi\) | ||||
0.616505 | + | 0.787351i | \(0.288548\pi\) | |||||||
\(908\) | −119.491 | −3.96544 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −27.5664 | −0.913816 | ||||||||
\(911\) | 38.9275 | 1.28973 | 0.644864 | − | 0.764298i | \(-0.276914\pi\) | ||||
0.644864 | + | 0.764298i | \(0.276914\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −55.3366 | −1.83037 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 142.512 | 4.70874 | ||||||||
\(917\) | 4.22096 | 0.139388 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.1897 | 0.962881 | 0.481440 | − | 0.876479i | \(-0.340114\pi\) | ||||
0.481440 | + | 0.876479i | \(0.340114\pi\) | |||||||
\(920\) | 24.8618 | 0.819671 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27.1242 | 0.893287 | ||||||||
\(923\) | 44.6173 | 1.46860 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.01568 | −0.230674 | ||||||||
\(926\) | 20.1829 | 0.663250 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 118.712 | 3.89690 | ||||||||
\(929\) | −18.9850 | −0.622879 | −0.311440 | − | 0.950266i | \(-0.600811\pi\) | ||||
−0.311440 | + | 0.950266i | \(0.600811\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.62860 | 0.151696 | ||||||||
\(932\) | −138.261 | −4.52888 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −102.352 | −3.34906 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.8921 | 0.649847 | 0.324924 | − | 0.945740i | \(-0.394661\pi\) | ||||
0.324924 | + | 0.945740i | \(0.394661\pi\) | |||||||
\(938\) | 17.2643 | 0.563700 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 25.3127 | 0.825608 | ||||||||
\(941\) | −10.9695 | −0.357595 | −0.178797 | − | 0.983886i | \(-0.557221\pi\) | ||||
−0.178797 | + | 0.983886i | \(0.557221\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.4852 | −0.374010 | ||||||||
\(944\) | 45.7805 | 1.49003 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.5321 | 1.31712 | 0.658558 | − | 0.752530i | \(-0.271167\pi\) | ||||
0.658558 | + | 0.752530i | \(0.271167\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −74.8308 | −2.42911 | ||||||||
\(950\) | −28.3096 | −0.918484 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.26247 | −0.105737 | ||||||||
\(953\) | −46.6243 | −1.51031 | −0.755154 | − | 0.655547i | \(-0.772438\pi\) | ||||
−0.755154 | + | 0.655547i | \(0.772438\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.26971 | 0.138164 | ||||||||
\(956\) | −9.21516 | −0.298039 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 109.063 | 3.52368 | ||||||||
\(959\) | 14.5361 | 0.469396 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4162 | −0.981166 | ||||||||
\(962\) | −52.7483 | −1.70067 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 71.3794 | 2.29897 | ||||||||
\(965\) | −36.2850 | −1.16806 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.2512 | −0.876338 | −0.438169 | − | 0.898893i | \(-0.644373\pi\) | ||||
−0.438169 | + | 0.898893i | \(0.644373\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.87247 | 0.156446 | ||||||||
\(971\) | −23.2361 | −0.745683 | −0.372842 | − | 0.927895i | \(-0.621617\pi\) | ||||
−0.372842 | + | 0.927895i | \(0.621617\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.94615 | −0.222684 | ||||||||
\(974\) | −67.1215 | −2.15071 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −62.2709 | −1.99324 | ||||||||
\(977\) | 28.7747 | 0.920583 | 0.460292 | − | 0.887768i | \(-0.347745\pi\) | ||||
0.460292 | + | 0.887768i | \(0.347745\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 9.78502 | 0.312571 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.93640 | 0.285172 | ||||||||
\(983\) | 28.1922 | 0.899192 | 0.449596 | − | 0.893232i | \(-0.351568\pi\) | ||||
0.449596 | + | 0.893232i | \(0.351568\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37.0251 | −1.17972 | ||||||||
\(986\) | −3.37839 | −0.107590 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −158.499 | −5.04252 | ||||||||
\(989\) | 1.39641 | 0.0444034 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.6676 | −1.51421 | −0.757106 | − | 0.653293i | \(-0.773387\pi\) | ||||
−0.757106 | + | 0.653293i | \(0.773387\pi\) | |||||||
\(992\) | 22.8558 | 0.725673 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −21.2682 | −0.674587 | ||||||||
\(995\) | −21.5270 | −0.682451 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.6624 | 0.591046 | 0.295523 | − | 0.955336i | \(-0.404506\pi\) | ||||
0.295523 | + | 0.955336i | \(0.404506\pi\) | |||||||
\(998\) | 77.0557 | 2.43916 | ||||||||
\(999\) | 0 | 0 |
(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 | 7623.2.a.cy.1.10 | 10 | ||
3.2 | odd | 2 | 2541.2.a.br.1.1 | 10 | |||
11.7 | odd | 10 | 693.2.m.j.379.1 | 20 | |||
11.8 | odd | 10 | 693.2.m.j.64.1 | 20 | |||
11.10 | odd | 2 | 7623.2.a.cx.1.1 | 10 | |||
33.8 | even | 10 | 231.2.j.g.64.5 | ✓ | 20 | ||
33.29 | even | 10 | 231.2.j.g.148.5 | yes | 20 | ||
33.32 | even | 2 | 2541.2.a.bq.1.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.g.64.5 | ✓ | 20 | 33.8 | even | 10 | ||
231.2.j.g.148.5 | yes | 20 | 33.29 | even | 10 | ||
693.2.m.j.64.1 | 20 | 11.8 | odd | 10 | |||
693.2.m.j.379.1 | 20 | 11.7 | odd | 10 | |||
2541.2.a.bq.1.10 | 10 | 33.32 | even | 2 | |||
2541.2.a.br.1.1 | 10 | 3.2 | odd | 2 | |||
7623.2.a.cx.1.1 | 10 | 11.10 | odd | 2 | |||
7623.2.a.cy.1.10 | 10 | 1.1 | even | 1 | trivial |