Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8005,2,Mod(1,8005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8005 = 5 \cdot 1601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8005.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: | \(63.9202468180\) |
Analytic rank: | \(1\) |
Dimension: | \(126\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.76854 | −1.95765 | −0.978827 | − | 0.204690i | \(-0.934382\pi\) | ||||
−0.978827 | + | 0.204690i | \(0.934382\pi\) | |||||||
\(3\) | −3.01214 | −1.73906 | −0.869530 | − | 0.493881i | \(-0.835578\pi\) | ||||
−0.869530 | + | 0.493881i | \(0.835578\pi\) | |||||||
\(4\) | 5.66482 | 2.83241 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 8.33923 | 3.40448 | ||||||||
\(7\) | −2.50261 | −0.945899 | −0.472949 | − | 0.881090i | \(-0.656811\pi\) | ||||
−0.472949 | + | 0.881090i | \(0.656811\pi\) | |||||||
\(8\) | −10.1462 | −3.58722 | ||||||||
\(9\) | 6.07298 | 2.02433 | ||||||||
\(10\) | −2.76854 | −0.875489 | ||||||||
\(11\) | −2.69707 | −0.813196 | −0.406598 | − | 0.913607i | \(-0.633285\pi\) | ||||
−0.406598 | + | 0.913607i | \(0.633285\pi\) | |||||||
\(12\) | −17.0632 | −4.92573 | ||||||||
\(13\) | 4.24001 | 1.17597 | 0.587983 | − | 0.808873i | \(-0.299922\pi\) | ||||
0.587983 | + | 0.808873i | \(0.299922\pi\) | |||||||
\(14\) | 6.92858 | 1.85174 | ||||||||
\(15\) | −3.01214 | −0.777731 | ||||||||
\(16\) | 16.7605 | 4.19013 | ||||||||
\(17\) | 0.690069 | 0.167366 | 0.0836831 | − | 0.996492i | \(-0.473332\pi\) | ||||
0.0836831 | + | 0.996492i | \(0.473332\pi\) | |||||||
\(18\) | −16.8133 | −3.96293 | ||||||||
\(19\) | 2.42673 | 0.556731 | 0.278366 | − | 0.960475i | \(-0.410207\pi\) | ||||
0.278366 | + | 0.960475i | \(0.410207\pi\) | |||||||
\(20\) | 5.66482 | 1.26669 | ||||||||
\(21\) | 7.53822 | 1.64497 | ||||||||
\(22\) | 7.46694 | 1.59196 | ||||||||
\(23\) | −5.69511 | −1.18751 | −0.593757 | − | 0.804645i | \(-0.702356\pi\) | ||||
−0.593757 | + | 0.804645i | \(0.702356\pi\) | |||||||
\(24\) | 30.5618 | 6.23839 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −11.7386 | −2.30214 | ||||||||
\(27\) | −9.25626 | −1.78137 | ||||||||
\(28\) | −14.1768 | −2.67917 | ||||||||
\(29\) | 1.64674 | 0.305791 | 0.152896 | − | 0.988242i | \(-0.451140\pi\) | ||||
0.152896 | + | 0.988242i | \(0.451140\pi\) | |||||||
\(30\) | 8.33923 | 1.52253 | ||||||||
\(31\) | −1.66321 | −0.298721 | −0.149361 | − | 0.988783i | \(-0.547722\pi\) | ||||
−0.149361 | + | 0.988783i | \(0.547722\pi\) | |||||||
\(32\) | −26.1098 | −4.61560 | ||||||||
\(33\) | 8.12394 | 1.41420 | ||||||||
\(34\) | −1.91048 | −0.327645 | ||||||||
\(35\) | −2.50261 | −0.423019 | ||||||||
\(36\) | 34.4023 | 5.73372 | ||||||||
\(37\) | 8.15047 | 1.33993 | 0.669965 | − | 0.742393i | \(-0.266309\pi\) | ||||
0.669965 | + | 0.742393i | \(0.266309\pi\) | |||||||
\(38\) | −6.71851 | −1.08989 | ||||||||
\(39\) | −12.7715 | −2.04508 | ||||||||
\(40\) | −10.1462 | −1.60425 | ||||||||
\(41\) | 3.71560 | 0.580280 | 0.290140 | − | 0.956984i | \(-0.406298\pi\) | ||||
0.290140 | + | 0.956984i | \(0.406298\pi\) | |||||||
\(42\) | −20.8699 | −3.22029 | ||||||||
\(43\) | −2.04638 | −0.312070 | −0.156035 | − | 0.987752i | \(-0.549871\pi\) | ||||
−0.156035 | + | 0.987752i | \(0.549871\pi\) | |||||||
\(44\) | −15.2784 | −2.30330 | ||||||||
\(45\) | 6.07298 | 0.905307 | ||||||||
\(46\) | 15.7672 | 2.32474 | ||||||||
\(47\) | −11.1338 | −1.62403 | −0.812015 | − | 0.583637i | \(-0.801629\pi\) | ||||
−0.812015 | + | 0.583637i | \(0.801629\pi\) | |||||||
\(48\) | −50.4850 | −7.28689 | ||||||||
\(49\) | −0.736930 | −0.105276 | ||||||||
\(50\) | −2.76854 | −0.391531 | ||||||||
\(51\) | −2.07858 | −0.291060 | ||||||||
\(52\) | 24.0189 | 3.33082 | ||||||||
\(53\) | 2.13498 | 0.293263 | 0.146631 | − | 0.989191i | \(-0.453157\pi\) | ||||
0.146631 | + | 0.989191i | \(0.453157\pi\) | |||||||
\(54\) | 25.6263 | 3.48730 | ||||||||
\(55\) | −2.69707 | −0.363672 | ||||||||
\(56\) | 25.3920 | 3.39315 | ||||||||
\(57\) | −7.30966 | −0.968189 | ||||||||
\(58\) | −4.55905 | −0.598633 | ||||||||
\(59\) | 2.86001 | 0.372342 | 0.186171 | − | 0.982517i | \(-0.440392\pi\) | ||||
0.186171 | + | 0.982517i | \(0.440392\pi\) | |||||||
\(60\) | −17.0632 | −2.20285 | ||||||||
\(61\) | −5.76997 | −0.738769 | −0.369384 | − | 0.929277i | \(-0.620431\pi\) | ||||
−0.369384 | + | 0.929277i | \(0.620431\pi\) | |||||||
\(62\) | 4.60466 | 0.584793 | ||||||||
\(63\) | −15.1983 | −1.91481 | ||||||||
\(64\) | 38.7650 | 4.84562 | ||||||||
\(65\) | 4.24001 | 0.525908 | ||||||||
\(66\) | −22.4915 | −2.76851 | ||||||||
\(67\) | −0.413507 | −0.0505179 | −0.0252589 | − | 0.999681i | \(-0.508041\pi\) | ||||
−0.0252589 | + | 0.999681i | \(0.508041\pi\) | |||||||
\(68\) | 3.90911 | 0.474049 | ||||||||
\(69\) | 17.1545 | 2.06516 | ||||||||
\(70\) | 6.92858 | 0.828124 | ||||||||
\(71\) | −6.95110 | −0.824943 | −0.412472 | − | 0.910970i | \(-0.635334\pi\) | ||||
−0.412472 | + | 0.910970i | \(0.635334\pi\) | |||||||
\(72\) | −61.6177 | −7.26171 | ||||||||
\(73\) | 6.74409 | 0.789337 | 0.394668 | − | 0.918824i | \(-0.370860\pi\) | ||||
0.394668 | + | 0.918824i | \(0.370860\pi\) | |||||||
\(74\) | −22.5649 | −2.62312 | ||||||||
\(75\) | −3.01214 | −0.347812 | ||||||||
\(76\) | 13.7470 | 1.57689 | ||||||||
\(77\) | 6.74971 | 0.769201 | ||||||||
\(78\) | 35.3584 | 4.00355 | ||||||||
\(79\) | 12.6083 | 1.41854 | 0.709270 | − | 0.704937i | \(-0.249025\pi\) | ||||
0.709270 | + | 0.704937i | \(0.249025\pi\) | |||||||
\(80\) | 16.7605 | 1.87388 | ||||||||
\(81\) | 9.66219 | 1.07358 | ||||||||
\(82\) | −10.2868 | −1.13599 | ||||||||
\(83\) | 0.741885 | 0.0814324 | 0.0407162 | − | 0.999171i | \(-0.487036\pi\) | ||||
0.0407162 | + | 0.999171i | \(0.487036\pi\) | |||||||
\(84\) | 42.7026 | 4.65924 | ||||||||
\(85\) | 0.690069 | 0.0748484 | ||||||||
\(86\) | 5.66548 | 0.610925 | ||||||||
\(87\) | −4.96020 | −0.531789 | ||||||||
\(88\) | 27.3650 | 2.91711 | ||||||||
\(89\) | 6.94176 | 0.735825 | 0.367912 | − | 0.929860i | \(-0.380073\pi\) | ||||
0.367912 | + | 0.929860i | \(0.380073\pi\) | |||||||
\(90\) | −16.8133 | −1.77228 | ||||||||
\(91\) | −10.6111 | −1.11235 | ||||||||
\(92\) | −32.2618 | −3.36352 | ||||||||
\(93\) | 5.00982 | 0.519494 | ||||||||
\(94\) | 30.8243 | 3.17929 | ||||||||
\(95\) | 2.42673 | 0.248978 | ||||||||
\(96\) | 78.6463 | 8.02681 | ||||||||
\(97\) | 17.8179 | 1.80914 | 0.904568 | − | 0.426329i | \(-0.140193\pi\) | ||||
0.904568 | + | 0.426329i | \(0.140193\pi\) | |||||||
\(98\) | 2.04022 | 0.206093 | ||||||||
\(99\) | −16.3792 | −1.64618 | ||||||||
\(100\) | 5.66482 | 0.566482 | ||||||||
\(101\) | −5.89006 | −0.586083 | −0.293041 | − | 0.956100i | \(-0.594667\pi\) | ||||
−0.293041 | + | 0.956100i | \(0.594667\pi\) | |||||||
\(102\) | 5.75464 | 0.569794 | ||||||||
\(103\) | −6.20848 | −0.611740 | −0.305870 | − | 0.952073i | \(-0.598947\pi\) | ||||
−0.305870 | + | 0.952073i | \(0.598947\pi\) | |||||||
\(104\) | −43.0200 | −4.21845 | ||||||||
\(105\) | 7.53822 | 0.735655 | ||||||||
\(106\) | −5.91079 | −0.574107 | ||||||||
\(107\) | 10.4002 | 1.00542 | 0.502712 | − | 0.864454i | \(-0.332336\pi\) | ||||
0.502712 | + | 0.864454i | \(0.332336\pi\) | |||||||
\(108\) | −52.4350 | −5.04556 | ||||||||
\(109\) | −17.1238 | −1.64017 | −0.820083 | − | 0.572244i | \(-0.806073\pi\) | ||||
−0.820083 | + | 0.572244i | \(0.806073\pi\) | |||||||
\(110\) | 7.46694 | 0.711944 | ||||||||
\(111\) | −24.5504 | −2.33022 | ||||||||
\(112\) | −41.9451 | −3.96344 | ||||||||
\(113\) | −14.1289 | −1.32914 | −0.664568 | − | 0.747228i | \(-0.731384\pi\) | ||||
−0.664568 | + | 0.747228i | \(0.731384\pi\) | |||||||
\(114\) | 20.2371 | 1.89538 | ||||||||
\(115\) | −5.69511 | −0.531072 | ||||||||
\(116\) | 9.32845 | 0.866125 | ||||||||
\(117\) | 25.7495 | 2.38054 | ||||||||
\(118\) | −7.91806 | −0.728917 | ||||||||
\(119\) | −1.72697 | −0.158311 | ||||||||
\(120\) | 30.5618 | 2.78989 | ||||||||
\(121\) | −3.72584 | −0.338712 | ||||||||
\(122\) | 15.9744 | 1.44625 | ||||||||
\(123\) | −11.1919 | −1.00914 | ||||||||
\(124\) | −9.42178 | −0.846101 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 42.0772 | 3.74853 | ||||||||
\(127\) | −12.4650 | −1.10609 | −0.553046 | − | 0.833151i | \(-0.686535\pi\) | ||||
−0.553046 | + | 0.833151i | \(0.686535\pi\) | |||||||
\(128\) | −55.1028 | −4.87045 | ||||||||
\(129\) | 6.16398 | 0.542708 | ||||||||
\(130\) | −11.7386 | −1.02955 | ||||||||
\(131\) | 13.1798 | 1.15153 | 0.575763 | − | 0.817617i | \(-0.304705\pi\) | ||||
0.575763 | + | 0.817617i | \(0.304705\pi\) | |||||||
\(132\) | 46.0206 | 4.00558 | ||||||||
\(133\) | −6.07318 | −0.526611 | ||||||||
\(134\) | 1.14481 | 0.0988965 | ||||||||
\(135\) | −9.25626 | −0.796652 | ||||||||
\(136\) | −7.00157 | −0.600380 | ||||||||
\(137\) | −10.1907 | −0.870654 | −0.435327 | − | 0.900272i | \(-0.643367\pi\) | ||||
−0.435327 | + | 0.900272i | \(0.643367\pi\) | |||||||
\(138\) | −47.4929 | −4.04286 | ||||||||
\(139\) | −4.48278 | −0.380225 | −0.190112 | − | 0.981762i | \(-0.560885\pi\) | ||||
−0.190112 | + | 0.981762i | \(0.560885\pi\) | |||||||
\(140\) | −14.1768 | −1.19816 | ||||||||
\(141\) | 33.5365 | 2.82428 | ||||||||
\(142\) | 19.2444 | 1.61495 | ||||||||
\(143\) | −11.4356 | −0.956291 | ||||||||
\(144\) | 101.786 | 8.48220 | ||||||||
\(145\) | 1.64674 | 0.136754 | ||||||||
\(146\) | −18.6713 | −1.54525 | ||||||||
\(147\) | 2.21974 | 0.183081 | ||||||||
\(148\) | 46.1709 | 3.79523 | ||||||||
\(149\) | −18.6283 | −1.52609 | −0.763045 | − | 0.646345i | \(-0.776297\pi\) | ||||
−0.763045 | + | 0.646345i | \(0.776297\pi\) | |||||||
\(150\) | 8.33923 | 0.680895 | ||||||||
\(151\) | −11.5208 | −0.937548 | −0.468774 | − | 0.883318i | \(-0.655304\pi\) | ||||
−0.468774 | + | 0.883318i | \(0.655304\pi\) | |||||||
\(152\) | −24.6221 | −1.99712 | ||||||||
\(153\) | 4.19078 | 0.338804 | ||||||||
\(154\) | −18.6868 | −1.50583 | ||||||||
\(155\) | −1.66321 | −0.133592 | ||||||||
\(156\) | −72.3482 | −5.79249 | ||||||||
\(157\) | 19.0766 | 1.52247 | 0.761237 | − | 0.648473i | \(-0.224592\pi\) | ||||
0.761237 | + | 0.648473i | \(0.224592\pi\) | |||||||
\(158\) | −34.9065 | −2.77701 | ||||||||
\(159\) | −6.43087 | −0.510001 | ||||||||
\(160\) | −26.1098 | −2.06416 | ||||||||
\(161\) | 14.2527 | 1.12327 | ||||||||
\(162\) | −26.7502 | −2.10169 | ||||||||
\(163\) | 1.32430 | 0.103727 | 0.0518636 | − | 0.998654i | \(-0.483484\pi\) | ||||
0.0518636 | + | 0.998654i | \(0.483484\pi\) | |||||||
\(164\) | 21.0482 | 1.64359 | ||||||||
\(165\) | 8.12394 | 0.632448 | ||||||||
\(166\) | −2.05394 | −0.159417 | ||||||||
\(167\) | −11.5501 | −0.893771 | −0.446885 | − | 0.894591i | \(-0.647467\pi\) | ||||
−0.446885 | + | 0.894591i | \(0.647467\pi\) | |||||||
\(168\) | −76.4842 | −5.90089 | ||||||||
\(169\) | 4.97767 | 0.382898 | ||||||||
\(170\) | −1.91048 | −0.146527 | ||||||||
\(171\) | 14.7375 | 1.12701 | ||||||||
\(172\) | −11.5924 | −0.883909 | ||||||||
\(173\) | −9.89021 | −0.751939 | −0.375970 | − | 0.926632i | \(-0.622690\pi\) | ||||
−0.375970 | + | 0.926632i | \(0.622690\pi\) | |||||||
\(174\) | 13.7325 | 1.04106 | ||||||||
\(175\) | −2.50261 | −0.189180 | ||||||||
\(176\) | −45.2042 | −3.40740 | ||||||||
\(177\) | −8.61476 | −0.647525 | ||||||||
\(178\) | −19.2185 | −1.44049 | ||||||||
\(179\) | 4.20597 | 0.314369 | 0.157185 | − | 0.987569i | \(-0.449758\pi\) | ||||
0.157185 | + | 0.987569i | \(0.449758\pi\) | |||||||
\(180\) | 34.4023 | 2.56420 | ||||||||
\(181\) | −16.0787 | −1.19512 | −0.597560 | − | 0.801824i | \(-0.703863\pi\) | ||||
−0.597560 | + | 0.801824i | \(0.703863\pi\) | |||||||
\(182\) | 29.3773 | 2.17759 | ||||||||
\(183\) | 17.3799 | 1.28476 | ||||||||
\(184\) | 57.7837 | 4.25987 | ||||||||
\(185\) | 8.15047 | 0.599235 | ||||||||
\(186\) | −13.8699 | −1.01699 | ||||||||
\(187\) | −1.86116 | −0.136102 | ||||||||
\(188\) | −63.0708 | −4.59991 | ||||||||
\(189\) | 23.1648 | 1.68499 | ||||||||
\(190\) | −6.71851 | −0.487412 | ||||||||
\(191\) | 22.9853 | 1.66316 | 0.831579 | − | 0.555407i | \(-0.187437\pi\) | ||||
0.831579 | + | 0.555407i | \(0.187437\pi\) | |||||||
\(192\) | −116.766 | −8.42683 | ||||||||
\(193\) | −2.07766 | −0.149553 | −0.0747765 | − | 0.997200i | \(-0.523824\pi\) | ||||
−0.0747765 | + | 0.997200i | \(0.523824\pi\) | |||||||
\(194\) | −49.3297 | −3.54166 | ||||||||
\(195\) | −12.7715 | −0.914586 | ||||||||
\(196\) | −4.17458 | −0.298184 | ||||||||
\(197\) | 19.2123 | 1.36882 | 0.684408 | − | 0.729099i | \(-0.260061\pi\) | ||||
0.684408 | + | 0.729099i | \(0.260061\pi\) | |||||||
\(198\) | 45.3466 | 3.22264 | ||||||||
\(199\) | 2.98337 | 0.211485 | 0.105743 | − | 0.994394i | \(-0.466278\pi\) | ||||
0.105743 | + | 0.994394i | \(0.466278\pi\) | |||||||
\(200\) | −10.1462 | −0.717444 | ||||||||
\(201\) | 1.24554 | 0.0878536 | ||||||||
\(202\) | 16.3069 | 1.14735 | ||||||||
\(203\) | −4.12114 | −0.289247 | ||||||||
\(204\) | −11.7748 | −0.824400 | ||||||||
\(205\) | 3.71560 | 0.259509 | ||||||||
\(206\) | 17.1884 | 1.19757 | ||||||||
\(207\) | −34.5863 | −2.40392 | ||||||||
\(208\) | 71.0647 | 4.92745 | ||||||||
\(209\) | −6.54506 | −0.452731 | ||||||||
\(210\) | −20.8699 | −1.44016 | ||||||||
\(211\) | −10.4886 | −0.722064 | −0.361032 | − | 0.932554i | \(-0.617575\pi\) | ||||
−0.361032 | + | 0.932554i | \(0.617575\pi\) | |||||||
\(212\) | 12.0943 | 0.830640 | ||||||||
\(213\) | 20.9377 | 1.43463 | ||||||||
\(214\) | −28.7933 | −1.96827 | ||||||||
\(215\) | −2.04638 | −0.139562 | ||||||||
\(216\) | 93.9158 | 6.39016 | ||||||||
\(217\) | 4.16237 | 0.282560 | ||||||||
\(218\) | 47.4080 | 3.21088 | ||||||||
\(219\) | −20.3142 | −1.37270 | ||||||||
\(220\) | −15.2784 | −1.03007 | ||||||||
\(221\) | 2.92590 | 0.196817 | ||||||||
\(222\) | 67.9687 | 4.56176 | ||||||||
\(223\) | 12.1410 | 0.813024 | 0.406512 | − | 0.913645i | \(-0.366745\pi\) | ||||
0.406512 | + | 0.913645i | \(0.366745\pi\) | |||||||
\(224\) | 65.3427 | 4.36589 | ||||||||
\(225\) | 6.07298 | 0.404866 | ||||||||
\(226\) | 39.1165 | 2.60199 | ||||||||
\(227\) | 18.6424 | 1.23734 | 0.618669 | − | 0.785652i | \(-0.287672\pi\) | ||||
0.618669 | + | 0.785652i | \(0.287672\pi\) | |||||||
\(228\) | −41.4079 | −2.74231 | ||||||||
\(229\) | 16.3824 | 1.08258 | 0.541288 | − | 0.840837i | \(-0.317937\pi\) | ||||
0.541288 | + | 0.840837i | \(0.317937\pi\) | |||||||
\(230\) | 15.7672 | 1.03966 | ||||||||
\(231\) | −20.3311 | −1.33769 | ||||||||
\(232\) | −16.7081 | −1.09694 | ||||||||
\(233\) | 7.54060 | 0.494001 | 0.247000 | − | 0.969015i | \(-0.420555\pi\) | ||||
0.247000 | + | 0.969015i | \(0.420555\pi\) | |||||||
\(234\) | −71.2885 | −4.66028 | ||||||||
\(235\) | −11.1338 | −0.726288 | ||||||||
\(236\) | 16.2015 | 1.05462 | ||||||||
\(237\) | −37.9778 | −2.46693 | ||||||||
\(238\) | 4.78120 | 0.309919 | ||||||||
\(239\) | 7.05731 | 0.456500 | 0.228250 | − | 0.973603i | \(-0.426700\pi\) | ||||
0.228250 | + | 0.973603i | \(0.426700\pi\) | |||||||
\(240\) | −50.4850 | −3.25879 | ||||||||
\(241\) | −15.9314 | −1.02623 | −0.513115 | − | 0.858320i | \(-0.671508\pi\) | ||||
−0.513115 | + | 0.858320i | \(0.671508\pi\) | |||||||
\(242\) | 10.3151 | 0.663082 | ||||||||
\(243\) | −1.33508 | −0.0856454 | ||||||||
\(244\) | −32.6858 | −2.09249 | ||||||||
\(245\) | −0.736930 | −0.0470807 | ||||||||
\(246\) | 30.9853 | 1.97555 | ||||||||
\(247\) | 10.2894 | 0.654697 | ||||||||
\(248\) | 16.8753 | 1.07158 | ||||||||
\(249\) | −2.23466 | −0.141616 | ||||||||
\(250\) | −2.76854 | −0.175098 | ||||||||
\(251\) | −13.3903 | −0.845189 | −0.422595 | − | 0.906319i | \(-0.638881\pi\) | ||||
−0.422595 | + | 0.906319i | \(0.638881\pi\) | |||||||
\(252\) | −86.0957 | −5.42352 | ||||||||
\(253\) | 15.3601 | 0.965681 | ||||||||
\(254\) | 34.5099 | 2.16534 | ||||||||
\(255\) | −2.07858 | −0.130166 | ||||||||
\(256\) | 75.0245 | 4.68903 | ||||||||
\(257\) | −28.4061 | −1.77193 | −0.885963 | − | 0.463757i | \(-0.846501\pi\) | ||||
−0.885963 | + | 0.463757i | \(0.846501\pi\) | |||||||
\(258\) | −17.0652 | −1.06243 | ||||||||
\(259\) | −20.3975 | −1.26744 | ||||||||
\(260\) | 24.0189 | 1.48959 | ||||||||
\(261\) | 10.0006 | 0.619021 | ||||||||
\(262\) | −36.4888 | −2.25429 | ||||||||
\(263\) | 12.4424 | 0.767229 | 0.383615 | − | 0.923493i | \(-0.374679\pi\) | ||||
0.383615 | + | 0.923493i | \(0.374679\pi\) | |||||||
\(264\) | −82.4271 | −5.07304 | ||||||||
\(265\) | 2.13498 | 0.131151 | ||||||||
\(266\) | 16.8138 | 1.03092 | ||||||||
\(267\) | −20.9095 | −1.27964 | ||||||||
\(268\) | −2.34244 | −0.143087 | ||||||||
\(269\) | 18.6614 | 1.13781 | 0.568904 | − | 0.822404i | \(-0.307368\pi\) | ||||
0.568904 | + | 0.822404i | \(0.307368\pi\) | |||||||
\(270\) | 25.6263 | 1.55957 | ||||||||
\(271\) | 12.6900 | 0.770865 | 0.385432 | − | 0.922736i | \(-0.374052\pi\) | ||||
0.385432 | + | 0.922736i | \(0.374052\pi\) | |||||||
\(272\) | 11.5659 | 0.701286 | ||||||||
\(273\) | 31.9621 | 1.93443 | ||||||||
\(274\) | 28.2135 | 1.70444 | ||||||||
\(275\) | −2.69707 | −0.162639 | ||||||||
\(276\) | 97.1770 | 5.84937 | ||||||||
\(277\) | 17.4769 | 1.05009 | 0.525044 | − | 0.851075i | \(-0.324049\pi\) | ||||
0.525044 | + | 0.851075i | \(0.324049\pi\) | |||||||
\(278\) | 12.4108 | 0.744349 | ||||||||
\(279\) | −10.1006 | −0.604710 | ||||||||
\(280\) | 25.3920 | 1.51746 | ||||||||
\(281\) | 14.7127 | 0.877686 | 0.438843 | − | 0.898564i | \(-0.355388\pi\) | ||||
0.438843 | + | 0.898564i | \(0.355388\pi\) | |||||||
\(282\) | −92.8472 | −5.52897 | ||||||||
\(283\) | −7.74277 | −0.460260 | −0.230130 | − | 0.973160i | \(-0.573915\pi\) | ||||
−0.230130 | + | 0.973160i | \(0.573915\pi\) | |||||||
\(284\) | −39.3767 | −2.33658 | ||||||||
\(285\) | −7.30966 | −0.432987 | ||||||||
\(286\) | 31.6599 | 1.87209 | ||||||||
\(287\) | −9.29872 | −0.548886 | ||||||||
\(288\) | −158.564 | −9.34349 | ||||||||
\(289\) | −16.5238 | −0.971989 | ||||||||
\(290\) | −4.55905 | −0.267717 | ||||||||
\(291\) | −53.6701 | −3.14620 | ||||||||
\(292\) | 38.2041 | 2.23572 | ||||||||
\(293\) | −26.0317 | −1.52079 | −0.760394 | − | 0.649463i | \(-0.774994\pi\) | ||||
−0.760394 | + | 0.649463i | \(0.774994\pi\) | |||||||
\(294\) | −6.14543 | −0.358409 | ||||||||
\(295\) | 2.86001 | 0.166516 | ||||||||
\(296\) | −82.6963 | −4.80662 | ||||||||
\(297\) | 24.9647 | 1.44860 | ||||||||
\(298\) | 51.5732 | 2.98756 | ||||||||
\(299\) | −24.1473 | −1.39648 | ||||||||
\(300\) | −17.0632 | −0.985145 | ||||||||
\(301\) | 5.12129 | 0.295186 | ||||||||
\(302\) | 31.8958 | 1.83539 | ||||||||
\(303\) | 17.7417 | 1.01923 | ||||||||
\(304\) | 40.6733 | 2.33278 | ||||||||
\(305\) | −5.76997 | −0.330387 | ||||||||
\(306\) | −11.6023 | −0.663261 | ||||||||
\(307\) | 25.4141 | 1.45046 | 0.725230 | − | 0.688506i | \(-0.241733\pi\) | ||||
0.725230 | + | 0.688506i | \(0.241733\pi\) | |||||||
\(308\) | 38.2359 | 2.17869 | ||||||||
\(309\) | 18.7008 | 1.06385 | ||||||||
\(310\) | 4.60466 | 0.261527 | ||||||||
\(311\) | 0.941557 | 0.0533908 | 0.0266954 | − | 0.999644i | \(-0.491502\pi\) | ||||
0.0266954 | + | 0.999644i | \(0.491502\pi\) | |||||||
\(312\) | 129.582 | 7.33614 | ||||||||
\(313\) | 11.7140 | 0.662116 | 0.331058 | − | 0.943610i | \(-0.392594\pi\) | ||||
0.331058 | + | 0.943610i | \(0.392594\pi\) | |||||||
\(314\) | −52.8142 | −2.98048 | ||||||||
\(315\) | −15.1983 | −0.856329 | ||||||||
\(316\) | 71.4235 | 4.01789 | ||||||||
\(317\) | 3.87286 | 0.217521 | 0.108761 | − | 0.994068i | \(-0.465312\pi\) | ||||
0.108761 | + | 0.994068i | \(0.465312\pi\) | |||||||
\(318\) | 17.8041 | 0.998406 | ||||||||
\(319\) | −4.44135 | −0.248668 | ||||||||
\(320\) | 38.7650 | 2.16703 | ||||||||
\(321\) | −31.3268 | −1.74849 | ||||||||
\(322\) | −39.4591 | −2.19897 | ||||||||
\(323\) | 1.67461 | 0.0931780 | ||||||||
\(324\) | 54.7345 | 3.04081 | ||||||||
\(325\) | 4.24001 | 0.235193 | ||||||||
\(326\) | −3.66638 | −0.203062 | ||||||||
\(327\) | 51.5794 | 2.85235 | ||||||||
\(328\) | −37.6992 | −2.08159 | ||||||||
\(329\) | 27.8635 | 1.53617 | ||||||||
\(330\) | −22.4915 | −1.23811 | ||||||||
\(331\) | 25.7940 | 1.41777 | 0.708884 | − | 0.705325i | \(-0.249199\pi\) | ||||
0.708884 | + | 0.705325i | \(0.249199\pi\) | |||||||
\(332\) | 4.20264 | 0.230650 | ||||||||
\(333\) | 49.4977 | 2.71246 | ||||||||
\(334\) | 31.9768 | 1.74969 | ||||||||
\(335\) | −0.413507 | −0.0225923 | ||||||||
\(336\) | 126.344 | 6.89266 | ||||||||
\(337\) | −9.77008 | −0.532210 | −0.266105 | − | 0.963944i | \(-0.585737\pi\) | ||||
−0.266105 | + | 0.963944i | \(0.585737\pi\) | |||||||
\(338\) | −13.7809 | −0.749581 | ||||||||
\(339\) | 42.5582 | 2.31145 | ||||||||
\(340\) | 3.90911 | 0.212001 | ||||||||
\(341\) | 4.48579 | 0.242919 | ||||||||
\(342\) | −40.8014 | −2.20629 | ||||||||
\(343\) | 19.3625 | 1.04548 | ||||||||
\(344\) | 20.7630 | 1.11946 | ||||||||
\(345\) | 17.1545 | 0.923566 | ||||||||
\(346\) | 27.3815 | 1.47204 | ||||||||
\(347\) | 3.58853 | 0.192642 | 0.0963212 | − | 0.995350i | \(-0.469292\pi\) | ||||
0.0963212 | + | 0.995350i | \(0.469292\pi\) | |||||||
\(348\) | −28.0986 | −1.50624 | ||||||||
\(349\) | −18.8296 | −1.00792 | −0.503962 | − | 0.863726i | \(-0.668125\pi\) | ||||
−0.503962 | + | 0.863726i | \(0.668125\pi\) | |||||||
\(350\) | 6.92858 | 0.370348 | ||||||||
\(351\) | −39.2466 | −2.09483 | ||||||||
\(352\) | 70.4198 | 3.75339 | ||||||||
\(353\) | −5.48246 | −0.291802 | −0.145901 | − | 0.989299i | \(-0.546608\pi\) | ||||
−0.145901 | + | 0.989299i | \(0.546608\pi\) | |||||||
\(354\) | 23.8503 | 1.26763 | ||||||||
\(355\) | −6.95110 | −0.368926 | ||||||||
\(356\) | 39.3238 | 2.08416 | ||||||||
\(357\) | 5.20189 | 0.275313 | ||||||||
\(358\) | −11.6444 | −0.615426 | ||||||||
\(359\) | 18.5829 | 0.980767 | 0.490383 | − | 0.871507i | \(-0.336857\pi\) | ||||
0.490383 | + | 0.871507i | \(0.336857\pi\) | |||||||
\(360\) | −61.6177 | −3.24754 | ||||||||
\(361\) | −13.1110 | −0.690050 | ||||||||
\(362\) | 44.5145 | 2.33963 | ||||||||
\(363\) | 11.2227 | 0.589041 | ||||||||
\(364\) | −60.1099 | −3.15062 | ||||||||
\(365\) | 6.74409 | 0.353002 | ||||||||
\(366\) | −48.1171 | −2.51512 | ||||||||
\(367\) | 33.2531 | 1.73580 | 0.867899 | − | 0.496740i | \(-0.165470\pi\) | ||||
0.867899 | + | 0.496740i | \(0.165470\pi\) | |||||||
\(368\) | −95.4531 | −4.97584 | ||||||||
\(369\) | 22.5648 | 1.17468 | ||||||||
\(370\) | −22.5649 | −1.17309 | ||||||||
\(371\) | −5.34304 | −0.277397 | ||||||||
\(372\) | 28.3797 | 1.47142 | ||||||||
\(373\) | −15.6300 | −0.809289 | −0.404645 | − | 0.914474i | \(-0.632605\pi\) | ||||
−0.404645 | + | 0.914474i | \(0.632605\pi\) | |||||||
\(374\) | 5.15270 | 0.266440 | ||||||||
\(375\) | −3.01214 | −0.155546 | ||||||||
\(376\) | 112.966 | 5.82575 | ||||||||
\(377\) | 6.98217 | 0.359600 | ||||||||
\(378\) | −64.1328 | −3.29863 | ||||||||
\(379\) | 9.42724 | 0.484245 | 0.242122 | − | 0.970246i | \(-0.422156\pi\) | ||||
0.242122 | + | 0.970246i | \(0.422156\pi\) | |||||||
\(380\) | 13.7470 | 0.705207 | ||||||||
\(381\) | 37.5464 | 1.92356 | ||||||||
\(382\) | −63.6357 | −3.25589 | ||||||||
\(383\) | −32.2772 | −1.64929 | −0.824643 | − | 0.565653i | \(-0.808624\pi\) | ||||
−0.824643 | + | 0.565653i | \(0.808624\pi\) | |||||||
\(384\) | 165.977 | 8.47000 | ||||||||
\(385\) | 6.74971 | 0.343997 | ||||||||
\(386\) | 5.75208 | 0.292773 | ||||||||
\(387\) | −12.4276 | −0.631732 | ||||||||
\(388\) | 100.935 | 5.12421 | ||||||||
\(389\) | 37.5651 | 1.90463 | 0.952313 | − | 0.305124i | \(-0.0986979\pi\) | ||||
0.952313 | + | 0.305124i | \(0.0986979\pi\) | |||||||
\(390\) | 35.3584 | 1.79044 | ||||||||
\(391\) | −3.93002 | −0.198750 | ||||||||
\(392\) | 7.47704 | 0.377647 | ||||||||
\(393\) | −39.6994 | −2.00257 | ||||||||
\(394\) | −53.1899 | −2.67967 | ||||||||
\(395\) | 12.6083 | 0.634390 | ||||||||
\(396\) | −92.7854 | −4.66264 | ||||||||
\(397\) | 14.5819 | 0.731844 | 0.365922 | − | 0.930645i | \(-0.380754\pi\) | ||||
0.365922 | + | 0.930645i | \(0.380754\pi\) | |||||||
\(398\) | −8.25957 | −0.414015 | ||||||||
\(399\) | 18.2933 | 0.915808 | ||||||||
\(400\) | 16.7605 | 0.838026 | ||||||||
\(401\) | 17.5640 | 0.877106 | 0.438553 | − | 0.898705i | \(-0.355491\pi\) | ||||
0.438553 | + | 0.898705i | \(0.355491\pi\) | |||||||
\(402\) | −3.44833 | −0.171987 | ||||||||
\(403\) | −7.05202 | −0.351286 | ||||||||
\(404\) | −33.3661 | −1.66003 | ||||||||
\(405\) | 9.66219 | 0.480118 | ||||||||
\(406\) | 11.4095 | 0.566246 | ||||||||
\(407\) | −21.9824 | −1.08963 | ||||||||
\(408\) | 21.0897 | 1.04410 | ||||||||
\(409\) | 23.8667 | 1.18013 | 0.590067 | − | 0.807354i | \(-0.299101\pi\) | ||||
0.590067 | + | 0.807354i | \(0.299101\pi\) | |||||||
\(410\) | −10.2868 | −0.508029 | ||||||||
\(411\) | 30.6959 | 1.51412 | ||||||||
\(412\) | −35.1699 | −1.73270 | ||||||||
\(413\) | −7.15751 | −0.352198 | ||||||||
\(414\) | 95.7537 | 4.70604 | ||||||||
\(415\) | 0.741885 | 0.0364177 | ||||||||
\(416\) | −110.706 | −5.42779 | ||||||||
\(417\) | 13.5028 | 0.661234 | ||||||||
\(418\) | 18.1203 | 0.886292 | ||||||||
\(419\) | 12.5347 | 0.612359 | 0.306180 | − | 0.951974i | \(-0.400949\pi\) | ||||
0.306180 | + | 0.951974i | \(0.400949\pi\) | |||||||
\(420\) | 42.7026 | 2.08367 | ||||||||
\(421\) | −12.1373 | −0.591537 | −0.295768 | − | 0.955260i | \(-0.595576\pi\) | ||||
−0.295768 | + | 0.955260i | \(0.595576\pi\) | |||||||
\(422\) | 29.0381 | 1.41355 | ||||||||
\(423\) | −67.6153 | −3.28757 | ||||||||
\(424\) | −21.6620 | −1.05200 | ||||||||
\(425\) | 0.690069 | 0.0334732 | ||||||||
\(426\) | −57.9668 | −2.80850 | ||||||||
\(427\) | 14.4400 | 0.698800 | ||||||||
\(428\) | 58.9151 | 2.84777 | ||||||||
\(429\) | 34.4456 | 1.66305 | ||||||||
\(430\) | 5.66548 | 0.273214 | ||||||||
\(431\) | −11.9966 | −0.577858 | −0.288929 | − | 0.957351i | \(-0.593299\pi\) | ||||
−0.288929 | + | 0.957351i | \(0.593299\pi\) | |||||||
\(432\) | −155.140 | −7.46416 | ||||||||
\(433\) | −10.9161 | −0.524592 | −0.262296 | − | 0.964987i | \(-0.584480\pi\) | ||||
−0.262296 | + | 0.964987i | \(0.584480\pi\) | |||||||
\(434\) | −11.5237 | −0.553155 | ||||||||
\(435\) | −4.96020 | −0.237823 | ||||||||
\(436\) | −97.0034 | −4.64562 | ||||||||
\(437\) | −13.8205 | −0.661126 | ||||||||
\(438\) | 56.2406 | 2.68728 | ||||||||
\(439\) | 16.2590 | 0.776002 | 0.388001 | − | 0.921659i | \(-0.373166\pi\) | ||||
0.388001 | + | 0.921659i | \(0.373166\pi\) | |||||||
\(440\) | 27.3650 | 1.30457 | ||||||||
\(441\) | −4.47537 | −0.213113 | ||||||||
\(442\) | −8.10046 | −0.385300 | ||||||||
\(443\) | 34.1307 | 1.62160 | 0.810800 | − | 0.585324i | \(-0.199033\pi\) | ||||
0.810800 | + | 0.585324i | \(0.199033\pi\) | |||||||
\(444\) | −139.073 | −6.60013 | ||||||||
\(445\) | 6.94176 | 0.329071 | ||||||||
\(446\) | −33.6130 | −1.59162 | ||||||||
\(447\) | 56.1111 | 2.65396 | ||||||||
\(448\) | −97.0137 | −4.58347 | ||||||||
\(449\) | 9.14809 | 0.431725 | 0.215863 | − | 0.976424i | \(-0.430744\pi\) | ||||
0.215863 | + | 0.976424i | \(0.430744\pi\) | |||||||
\(450\) | −16.8133 | −0.792587 | ||||||||
\(451\) | −10.0212 | −0.471881 | ||||||||
\(452\) | −80.0377 | −3.76466 | ||||||||
\(453\) | 34.7022 | 1.63045 | ||||||||
\(454\) | −51.6122 | −2.42228 | ||||||||
\(455\) | −10.6111 | −0.497456 | ||||||||
\(456\) | 74.1653 | 3.47311 | ||||||||
\(457\) | −29.7851 | −1.39329 | −0.696644 | − | 0.717417i | \(-0.745324\pi\) | ||||
−0.696644 | + | 0.717417i | \(0.745324\pi\) | |||||||
\(458\) | −45.3552 | −2.11931 | ||||||||
\(459\) | −6.38745 | −0.298141 | ||||||||
\(460\) | −32.2618 | −1.50421 | ||||||||
\(461\) | 6.17372 | 0.287539 | 0.143769 | − | 0.989611i | \(-0.454078\pi\) | ||||
0.143769 | + | 0.989611i | \(0.454078\pi\) | |||||||
\(462\) | 56.2874 | 2.61873 | ||||||||
\(463\) | 11.9037 | 0.553212 | 0.276606 | − | 0.960983i | \(-0.410790\pi\) | ||||
0.276606 | + | 0.960983i | \(0.410790\pi\) | |||||||
\(464\) | 27.6001 | 1.28130 | ||||||||
\(465\) | 5.00982 | 0.232325 | ||||||||
\(466\) | −20.8765 | −0.967083 | ||||||||
\(467\) | −12.6322 | −0.584549 | −0.292275 | − | 0.956334i | \(-0.594412\pi\) | ||||
−0.292275 | + | 0.956334i | \(0.594412\pi\) | |||||||
\(468\) | 145.866 | 6.74267 | ||||||||
\(469\) | 1.03485 | 0.0477848 | ||||||||
\(470\) | 30.8243 | 1.42182 | ||||||||
\(471\) | −57.4612 | −2.64767 | ||||||||
\(472\) | −29.0183 | −1.33567 | ||||||||
\(473\) | 5.51922 | 0.253774 | ||||||||
\(474\) | 105.143 | 4.82939 | ||||||||
\(475\) | 2.42673 | 0.111346 | ||||||||
\(476\) | −9.78299 | −0.448403 | ||||||||
\(477\) | 12.9657 | 0.593660 | ||||||||
\(478\) | −19.5385 | −0.893668 | ||||||||
\(479\) | −10.8534 | −0.495904 | −0.247952 | − | 0.968772i | \(-0.579758\pi\) | ||||
−0.247952 | + | 0.968772i | \(0.579758\pi\) | |||||||
\(480\) | 78.6463 | 3.58970 | ||||||||
\(481\) | 34.5581 | 1.57571 | ||||||||
\(482\) | 44.1066 | 2.00900 | ||||||||
\(483\) | −42.9310 | −1.95343 | ||||||||
\(484\) | −21.1062 | −0.959372 | ||||||||
\(485\) | 17.8179 | 0.809071 | ||||||||
\(486\) | 3.69622 | 0.167664 | ||||||||
\(487\) | 17.1432 | 0.776834 | 0.388417 | − | 0.921484i | \(-0.373022\pi\) | ||||
0.388417 | + | 0.921484i | \(0.373022\pi\) | |||||||
\(488\) | 58.5432 | 2.65013 | ||||||||
\(489\) | −3.98897 | −0.180388 | ||||||||
\(490\) | 2.04022 | 0.0921678 | ||||||||
\(491\) | −33.7075 | −1.52120 | −0.760600 | − | 0.649221i | \(-0.775095\pi\) | ||||
−0.760600 | + | 0.649221i | \(0.775095\pi\) | |||||||
\(492\) | −63.4002 | −2.85830 | ||||||||
\(493\) | 1.13636 | 0.0511791 | ||||||||
\(494\) | −28.4866 | −1.28167 | ||||||||
\(495\) | −16.3792 | −0.736192 | ||||||||
\(496\) | −27.8763 | −1.25168 | ||||||||
\(497\) | 17.3959 | 0.780313 | ||||||||
\(498\) | 6.18675 | 0.277235 | ||||||||
\(499\) | 0.547428 | 0.0245062 | 0.0122531 | − | 0.999925i | \(-0.496100\pi\) | ||||
0.0122531 | + | 0.999925i | \(0.496100\pi\) | |||||||
\(500\) | 5.66482 | 0.253338 | ||||||||
\(501\) | 34.7904 | 1.55432 | ||||||||
\(502\) | 37.0716 | 1.65459 | ||||||||
\(503\) | −10.7403 | −0.478888 | −0.239444 | − | 0.970910i | \(-0.576965\pi\) | ||||
−0.239444 | + | 0.970910i | \(0.576965\pi\) | |||||||
\(504\) | 154.205 | 6.86885 | ||||||||
\(505\) | −5.89006 | −0.262104 | ||||||||
\(506\) | −42.5251 | −1.89047 | ||||||||
\(507\) | −14.9934 | −0.665882 | ||||||||
\(508\) | −70.6120 | −3.13290 | ||||||||
\(509\) | −17.6672 | −0.783084 | −0.391542 | − | 0.920160i | \(-0.628058\pi\) | ||||
−0.391542 | + | 0.920160i | \(0.628058\pi\) | |||||||
\(510\) | 5.75464 | 0.254820 | ||||||||
\(511\) | −16.8779 | −0.746632 | ||||||||
\(512\) | −97.5027 | −4.30905 | ||||||||
\(513\) | −22.4625 | −0.991743 | ||||||||
\(514\) | 78.6435 | 3.46882 | ||||||||
\(515\) | −6.20848 | −0.273578 | ||||||||
\(516\) | 34.9178 | 1.53717 | ||||||||
\(517\) | 30.0285 | 1.32065 | ||||||||
\(518\) | 56.4712 | 2.48120 | ||||||||
\(519\) | 29.7907 | 1.30767 | ||||||||
\(520\) | −43.0200 | −1.88655 | ||||||||
\(521\) | −34.6464 | −1.51789 | −0.758944 | − | 0.651156i | \(-0.774284\pi\) | ||||
−0.758944 | + | 0.651156i | \(0.774284\pi\) | |||||||
\(522\) | −27.6871 | −1.21183 | ||||||||
\(523\) | 45.2173 | 1.97721 | 0.988607 | − | 0.150517i | \(-0.0480938\pi\) | ||||
0.988607 | + | 0.150517i | \(0.0480938\pi\) | |||||||
\(524\) | 74.6612 | 3.26159 | ||||||||
\(525\) | 7.53822 | 0.328995 | ||||||||
\(526\) | −34.4472 | −1.50197 | ||||||||
\(527\) | −1.14773 | −0.0499958 | ||||||||
\(528\) | 136.161 | 5.92567 | ||||||||
\(529\) | 9.43433 | 0.410188 | ||||||||
\(530\) | −5.91079 | −0.256748 | ||||||||
\(531\) | 17.3688 | 0.753743 | ||||||||
\(532\) | −34.4034 | −1.49158 | ||||||||
\(533\) | 15.7542 | 0.682390 | ||||||||
\(534\) | 57.8889 | 2.50510 | ||||||||
\(535\) | 10.4002 | 0.449639 | ||||||||
\(536\) | 4.19552 | 0.181219 | ||||||||
\(537\) | −12.6690 | −0.546707 | ||||||||
\(538\) | −51.6649 | −2.22743 | ||||||||
\(539\) | 1.98755 | 0.0856098 | ||||||||
\(540\) | −52.4350 | −2.25644 | ||||||||
\(541\) | 10.4143 | 0.447747 | 0.223873 | − | 0.974618i | \(-0.428130\pi\) | ||||
0.223873 | + | 0.974618i | \(0.428130\pi\) | |||||||
\(542\) | −35.1329 | −1.50909 | ||||||||
\(543\) | 48.4313 | 2.07839 | ||||||||
\(544\) | −18.0175 | −0.772496 | ||||||||
\(545\) | −17.1238 | −0.733505 | ||||||||
\(546\) | −88.4884 | −3.78695 | ||||||||
\(547\) | −39.9530 | −1.70827 | −0.854133 | − | 0.520055i | \(-0.825912\pi\) | ||||
−0.854133 | + | 0.520055i | \(0.825912\pi\) | |||||||
\(548\) | −57.7287 | −2.46605 | ||||||||
\(549\) | −35.0409 | −1.49551 | ||||||||
\(550\) | 7.46694 | 0.318391 | ||||||||
\(551\) | 3.99619 | 0.170243 | ||||||||
\(552\) | −174.053 | −7.40818 | ||||||||
\(553\) | −31.5536 | −1.34180 | ||||||||
\(554\) | −48.3856 | −2.05571 | ||||||||
\(555\) | −24.5504 | −1.04210 | ||||||||
\(556\) | −25.3942 | −1.07695 | ||||||||
\(557\) | 11.9982 | 0.508378 | 0.254189 | − | 0.967155i | \(-0.418191\pi\) | ||||
0.254189 | + | 0.967155i | \(0.418191\pi\) | |||||||
\(558\) | 27.9641 | 1.18381 | ||||||||
\(559\) | −8.67666 | −0.366984 | ||||||||
\(560\) | −41.9451 | −1.77250 | ||||||||
\(561\) | 5.60607 | 0.236689 | ||||||||
\(562\) | −40.7327 | −1.71821 | ||||||||
\(563\) | 38.4643 | 1.62108 | 0.810538 | − | 0.585686i | \(-0.199175\pi\) | ||||
0.810538 | + | 0.585686i | \(0.199175\pi\) | |||||||
\(564\) | 189.978 | 7.99952 | ||||||||
\(565\) | −14.1289 | −0.594408 | ||||||||
\(566\) | 21.4362 | 0.901029 | ||||||||
\(567\) | −24.1807 | −1.01549 | ||||||||
\(568\) | 70.5272 | 2.95925 | ||||||||
\(569\) | −19.8237 | −0.831054 | −0.415527 | − | 0.909581i | \(-0.636403\pi\) | ||||
−0.415527 | + | 0.909581i | \(0.636403\pi\) | |||||||
\(570\) | 20.2371 | 0.847639 | ||||||||
\(571\) | 46.3466 | 1.93955 | 0.969773 | − | 0.244008i | \(-0.0784622\pi\) | ||||
0.969773 | + | 0.244008i | \(0.0784622\pi\) | |||||||
\(572\) | −64.7805 | −2.70861 | ||||||||
\(573\) | −69.2349 | −2.89233 | ||||||||
\(574\) | 25.7439 | 1.07453 | ||||||||
\(575\) | −5.69511 | −0.237503 | ||||||||
\(576\) | 235.419 | 9.80913 | ||||||||
\(577\) | −13.8951 | −0.578459 | −0.289230 | − | 0.957260i | \(-0.593399\pi\) | ||||
−0.289230 | + | 0.957260i | \(0.593399\pi\) | |||||||
\(578\) | 45.7468 | 1.90282 | ||||||||
\(579\) | 6.25819 | 0.260082 | ||||||||
\(580\) | 9.32845 | 0.387343 | ||||||||
\(581\) | −1.85665 | −0.0770268 | ||||||||
\(582\) | 148.588 | 6.15916 | ||||||||
\(583\) | −5.75819 | −0.238480 | ||||||||
\(584\) | −68.4269 | −2.83153 | ||||||||
\(585\) | 25.7495 | 1.06461 | ||||||||
\(586\) | 72.0698 | 2.97717 | ||||||||
\(587\) | 30.7790 | 1.27038 | 0.635192 | − | 0.772354i | \(-0.280921\pi\) | ||||
0.635192 | + | 0.772354i | \(0.280921\pi\) | |||||||
\(588\) | 12.5744 | 0.518560 | ||||||||
\(589\) | −4.03617 | −0.166307 | ||||||||
\(590\) | −7.91806 | −0.325982 | ||||||||
\(591\) | −57.8700 | −2.38045 | ||||||||
\(592\) | 136.606 | 5.61448 | ||||||||
\(593\) | 17.7468 | 0.728774 | 0.364387 | − | 0.931248i | \(-0.381279\pi\) | ||||
0.364387 | + | 0.931248i | \(0.381279\pi\) | |||||||
\(594\) | −69.1159 | −2.83586 | ||||||||
\(595\) | −1.72697 | −0.0707990 | ||||||||
\(596\) | −105.526 | −4.32251 | ||||||||
\(597\) | −8.98632 | −0.367785 | ||||||||
\(598\) | 66.8529 | 2.73382 | ||||||||
\(599\) | −1.43162 | −0.0584944 | −0.0292472 | − | 0.999572i | \(-0.509311\pi\) | ||||
−0.0292472 | + | 0.999572i | \(0.509311\pi\) | |||||||
\(600\) | 30.5618 | 1.24768 | ||||||||
\(601\) | −14.7309 | −0.600887 | −0.300443 | − | 0.953800i | \(-0.597135\pi\) | ||||
−0.300443 | + | 0.953800i | \(0.597135\pi\) | |||||||
\(602\) | −14.1785 | −0.577873 | ||||||||
\(603\) | −2.51122 | −0.102265 | ||||||||
\(604\) | −65.2631 | −2.65552 | ||||||||
\(605\) | −3.72584 | −0.151477 | ||||||||
\(606\) | −49.1186 | −1.99531 | ||||||||
\(607\) | −15.2816 | −0.620261 | −0.310130 | − | 0.950694i | \(-0.600373\pi\) | ||||
−0.310130 | + | 0.950694i | \(0.600373\pi\) | |||||||
\(608\) | −63.3615 | −2.56965 | ||||||||
\(609\) | 12.4134 | 0.503018 | ||||||||
\(610\) | 15.9744 | 0.646784 | ||||||||
\(611\) | −47.2073 | −1.90980 | ||||||||
\(612\) | 23.7400 | 0.959632 | ||||||||
\(613\) | −26.6706 | −1.07722 | −0.538608 | − | 0.842557i | \(-0.681049\pi\) | ||||
−0.538608 | + | 0.842557i | \(0.681049\pi\) | |||||||
\(614\) | −70.3600 | −2.83950 | ||||||||
\(615\) | −11.1919 | −0.451302 | ||||||||
\(616\) | −68.4839 | −2.75929 | ||||||||
\(617\) | −35.1352 | −1.41449 | −0.707246 | − | 0.706968i | \(-0.750062\pi\) | ||||
−0.707246 | + | 0.706968i | \(0.750062\pi\) | |||||||
\(618\) | −51.7740 | −2.08265 | ||||||||
\(619\) | −17.7790 | −0.714600 | −0.357300 | − | 0.933990i | \(-0.616303\pi\) | ||||
−0.357300 | + | 0.933990i | \(0.616303\pi\) | |||||||
\(620\) | −9.42178 | −0.378388 | ||||||||
\(621\) | 52.7154 | 2.11540 | ||||||||
\(622\) | −2.60674 | −0.104521 | ||||||||
\(623\) | −17.3725 | −0.696016 | ||||||||
\(624\) | −214.057 | −8.56913 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −32.4308 | −1.29619 | ||||||||
\(627\) | 19.7146 | 0.787327 | ||||||||
\(628\) | 108.065 | 4.31227 | ||||||||
\(629\) | 5.62439 | 0.224259 | ||||||||
\(630\) | 42.0772 | 1.67640 | ||||||||
\(631\) | 8.10402 | 0.322616 | 0.161308 | − | 0.986904i | \(-0.448429\pi\) | ||||
0.161308 | + | 0.986904i | \(0.448429\pi\) | |||||||
\(632\) | −127.926 | −5.08862 | ||||||||
\(633\) | 31.5931 | 1.25571 | ||||||||
\(634\) | −10.7222 | −0.425831 | ||||||||
\(635\) | −12.4650 | −0.494659 | ||||||||
\(636\) | −36.4297 | −1.44453 | ||||||||
\(637\) | −3.12459 | −0.123801 | ||||||||
\(638\) | 12.2961 | 0.486806 | ||||||||
\(639\) | −42.2139 | −1.66996 | ||||||||
\(640\) | −55.1028 | −2.17813 | ||||||||
\(641\) | −41.2787 | −1.63041 | −0.815205 | − | 0.579172i | \(-0.803376\pi\) | ||||
−0.815205 | + | 0.579172i | \(0.803376\pi\) | |||||||
\(642\) | 86.7295 | 3.42294 | ||||||||
\(643\) | −5.15876 | −0.203441 | −0.101721 | − | 0.994813i | \(-0.532435\pi\) | ||||
−0.101721 | + | 0.994813i | \(0.532435\pi\) | |||||||
\(644\) | 80.7387 | 3.18155 | ||||||||
\(645\) | 6.16398 | 0.242706 | ||||||||
\(646\) | −4.63623 | −0.182410 | ||||||||
\(647\) | −44.9058 | −1.76543 | −0.882715 | − | 0.469909i | \(-0.844287\pi\) | ||||
−0.882715 | + | 0.469909i | \(0.844287\pi\) | |||||||
\(648\) | −98.0344 | −3.85116 | ||||||||
\(649\) | −7.71364 | −0.302787 | ||||||||
\(650\) | −11.7386 | −0.460427 | ||||||||
\(651\) | −12.5376 | −0.491389 | ||||||||
\(652\) | 7.50191 | 0.293798 | ||||||||
\(653\) | −4.51806 | −0.176805 | −0.0884026 | − | 0.996085i | \(-0.528176\pi\) | ||||
−0.0884026 | + | 0.996085i | \(0.528176\pi\) | |||||||
\(654\) | −142.800 | −5.58391 | ||||||||
\(655\) | 13.1798 | 0.514978 | ||||||||
\(656\) | 62.2754 | 2.43145 | ||||||||
\(657\) | 40.9568 | 1.59788 | ||||||||
\(658\) | −77.1414 | −3.00728 | ||||||||
\(659\) | −48.8745 | −1.90388 | −0.951939 | − | 0.306287i | \(-0.900913\pi\) | ||||
−0.951939 | + | 0.306287i | \(0.900913\pi\) | |||||||
\(660\) | 46.0206 | 1.79135 | ||||||||
\(661\) | 24.1138 | 0.937920 | 0.468960 | − | 0.883220i | \(-0.344629\pi\) | ||||
0.468960 | + | 0.883220i | \(0.344629\pi\) | |||||||
\(662\) | −71.4118 | −2.77550 | ||||||||
\(663\) | −8.81321 | −0.342277 | ||||||||
\(664\) | −7.52731 | −0.292116 | ||||||||
\(665\) | −6.07318 | −0.235508 | ||||||||
\(666\) | −137.036 | −5.31005 | ||||||||
\(667\) | −9.37835 | −0.363131 | ||||||||
\(668\) | −65.4290 | −2.53152 | ||||||||
\(669\) | −36.5705 | −1.41390 | ||||||||
\(670\) | 1.14481 | 0.0442279 | ||||||||
\(671\) | 15.5620 | 0.600764 | ||||||||
\(672\) | −196.821 | −7.59255 | ||||||||
\(673\) | −18.8466 | −0.726482 | −0.363241 | − | 0.931695i | \(-0.618330\pi\) | ||||
−0.363241 | + | 0.931695i | \(0.618330\pi\) | |||||||
\(674\) | 27.0489 | 1.04188 | ||||||||
\(675\) | −9.25626 | −0.356274 | ||||||||
\(676\) | 28.1976 | 1.08452 | ||||||||
\(677\) | 44.6115 | 1.71456 | 0.857280 | − | 0.514850i | \(-0.172152\pi\) | ||||
0.857280 | + | 0.514850i | \(0.172152\pi\) | |||||||
\(678\) | −117.824 | −4.52501 | ||||||||
\(679\) | −44.5914 | −1.71126 | ||||||||
\(680\) | −7.00157 | −0.268498 | ||||||||
\(681\) | −56.1534 | −2.15180 | ||||||||
\(682\) | −12.4191 | −0.475551 | ||||||||
\(683\) | −42.6610 | −1.63238 | −0.816189 | − | 0.577785i | \(-0.803917\pi\) | ||||
−0.816189 | + | 0.577785i | \(0.803917\pi\) | |||||||
\(684\) | 83.4854 | 3.19214 | ||||||||
\(685\) | −10.1907 | −0.389368 | ||||||||
\(686\) | −53.6060 | −2.04669 | ||||||||
\(687\) | −49.3460 | −1.88267 | ||||||||
\(688\) | −34.2984 | −1.30761 | ||||||||
\(689\) | 9.05235 | 0.344867 | ||||||||
\(690\) | −47.4929 | −1.80802 | ||||||||
\(691\) | −4.83168 | −0.183806 | −0.0919029 | − | 0.995768i | \(-0.529295\pi\) | ||||
−0.0919029 | + | 0.995768i | \(0.529295\pi\) | |||||||
\(692\) | −56.0263 | −2.12980 | ||||||||
\(693\) | 40.9909 | 1.55712 | ||||||||
\(694\) | −9.93500 | −0.377127 | ||||||||
\(695\) | −4.48278 | −0.170042 | ||||||||
\(696\) | 50.3271 | 1.90764 | ||||||||
\(697\) | 2.56402 | 0.0971192 | ||||||||
\(698\) | 52.1305 | 1.97317 | ||||||||
\(699\) | −22.7133 | −0.859097 | ||||||||
\(700\) | −14.1768 | −0.535834 | ||||||||
\(701\) | −45.4664 | −1.71724 | −0.858621 | − | 0.512611i | \(-0.828678\pi\) | ||||
−0.858621 | + | 0.512611i | \(0.828678\pi\) | |||||||
\(702\) | 108.656 | 4.10095 | ||||||||
\(703\) | 19.7790 | 0.745981 | ||||||||
\(704\) | −104.552 | −3.94044 | ||||||||
\(705\) | 33.5365 | 1.26306 | ||||||||
\(706\) | 15.1784 | 0.571247 | ||||||||
\(707\) | 14.7405 | 0.554375 | ||||||||
\(708\) | −48.8010 | −1.83406 | ||||||||
\(709\) | 14.5335 | 0.545818 | 0.272909 | − | 0.962040i | \(-0.412014\pi\) | ||||
0.272909 | + | 0.962040i | \(0.412014\pi\) | |||||||
\(710\) | 19.2444 | 0.722229 | ||||||||
\(711\) | 76.5698 | 2.87159 | ||||||||
\(712\) | −70.4324 | −2.63957 | ||||||||
\(713\) | 9.47217 | 0.354736 | ||||||||
\(714\) | −14.4016 | −0.538968 | ||||||||
\(715\) | −11.4356 | −0.427666 | ||||||||
\(716\) | 23.8261 | 0.890422 | ||||||||
\(717\) | −21.2576 | −0.793880 | ||||||||
\(718\) | −51.4475 | −1.92000 | ||||||||
\(719\) | 39.5220 | 1.47392 | 0.736961 | − | 0.675935i | \(-0.236260\pi\) | ||||
0.736961 | + | 0.675935i | \(0.236260\pi\) | |||||||
\(720\) | 101.786 | 3.79335 | ||||||||
\(721\) | 15.5374 | 0.578644 | ||||||||
\(722\) | 36.2982 | 1.35088 | ||||||||
\(723\) | 47.9875 | 1.78467 | ||||||||
\(724\) | −91.0829 | −3.38507 | ||||||||
\(725\) | 1.64674 | 0.0611582 | ||||||||
\(726\) | −31.0706 | −1.15314 | ||||||||
\(727\) | 22.7282 | 0.842944 | 0.421472 | − | 0.906842i | \(-0.361514\pi\) | ||||
0.421472 | + | 0.906842i | \(0.361514\pi\) | |||||||
\(728\) | 107.662 | 3.99023 | ||||||||
\(729\) | −24.9651 | −0.924634 | ||||||||
\(730\) | −18.6713 | −0.691056 | ||||||||
\(731\) | −1.41214 | −0.0522300 | ||||||||
\(732\) | 98.4542 | 3.63897 | ||||||||
\(733\) | 4.40089 | 0.162551 | 0.0812753 | − | 0.996692i | \(-0.474101\pi\) | ||||
0.0812753 | + | 0.996692i | \(0.474101\pi\) | |||||||
\(734\) | −92.0626 | −3.39809 | ||||||||
\(735\) | 2.21974 | 0.0818762 | ||||||||
\(736\) | 148.698 | 5.48109 | ||||||||
\(737\) | 1.11525 | 0.0410809 | ||||||||
\(738\) | −62.4716 | −2.29961 | ||||||||
\(739\) | −7.93698 | −0.291966 | −0.145983 | − | 0.989287i | \(-0.546635\pi\) | ||||
−0.145983 | + | 0.989287i | \(0.546635\pi\) | |||||||
\(740\) | 46.1709 | 1.69728 | ||||||||
\(741\) | −30.9930 | −1.13856 | ||||||||
\(742\) | 14.7924 | 0.543047 | ||||||||
\(743\) | 16.7652 | 0.615057 | 0.307528 | − | 0.951539i | \(-0.400498\pi\) | ||||
0.307528 | + | 0.951539i | \(0.400498\pi\) | |||||||
\(744\) | −50.8306 | −1.86354 | ||||||||
\(745\) | −18.6283 | −0.682489 | ||||||||
\(746\) | 43.2722 | 1.58431 | ||||||||
\(747\) | 4.50545 | 0.164846 | ||||||||
\(748\) | −10.5431 | −0.385495 | ||||||||
\(749\) | −26.0276 | −0.951028 | ||||||||
\(750\) | 8.33923 | 0.304506 | ||||||||
\(751\) | −11.9219 | −0.435035 | −0.217517 | − | 0.976056i | \(-0.569796\pi\) | ||||
−0.217517 | + | 0.976056i | \(0.569796\pi\) | |||||||
\(752\) | −186.608 | −6.80489 | ||||||||
\(753\) | 40.3335 | 1.46983 | ||||||||
\(754\) | −19.3304 | −0.703972 | ||||||||
\(755\) | −11.5208 | −0.419284 | ||||||||
\(756\) | 131.225 | 4.77259 | ||||||||
\(757\) | 29.2836 | 1.06433 | 0.532165 | − | 0.846641i | \(-0.321379\pi\) | ||||
0.532165 | + | 0.846641i | \(0.321379\pi\) | |||||||
\(758\) | −26.0997 | −0.947984 | ||||||||
\(759\) | −46.2668 | −1.67938 | ||||||||
\(760\) | −24.6221 | −0.893138 | ||||||||
\(761\) | 31.0015 | 1.12380 | 0.561902 | − | 0.827204i | \(-0.310070\pi\) | ||||
0.561902 | + | 0.827204i | \(0.310070\pi\) | |||||||
\(762\) | −103.949 | −3.76566 | ||||||||
\(763\) | 42.8543 | 1.55143 | ||||||||
\(764\) | 130.207 | 4.71074 | ||||||||
\(765\) | 4.19078 | 0.151518 | ||||||||
\(766\) | 89.3607 | 3.22873 | ||||||||
\(767\) | 12.1265 | 0.437862 | ||||||||
\(768\) | −225.984 | −8.15450 | ||||||||
\(769\) | −44.3196 | −1.59821 | −0.799103 | − | 0.601194i | \(-0.794692\pi\) | ||||
−0.799103 | + | 0.601194i | \(0.794692\pi\) | |||||||
\(770\) | −18.6868 | −0.673427 | ||||||||
\(771\) | 85.5632 | 3.08148 | ||||||||
\(772\) | −11.7696 | −0.423595 | ||||||||
\(773\) | 11.6248 | 0.418113 | 0.209057 | − | 0.977904i | \(-0.432961\pi\) | ||||
0.209057 | + | 0.977904i | \(0.432961\pi\) | |||||||
\(774\) | 34.4064 | 1.23671 | ||||||||
\(775\) | −1.66321 | −0.0597443 | ||||||||
\(776\) | −180.784 | −6.48978 | ||||||||
\(777\) | 61.4400 | 2.20415 | ||||||||
\(778\) | −104.000 | −3.72860 | ||||||||
\(779\) | 9.01678 | 0.323060 | ||||||||
\(780\) | −72.3482 | −2.59048 | ||||||||
\(781\) | 18.7476 | 0.670840 | ||||||||
\(782\) | 10.8804 | 0.389083 | ||||||||
\(783\) | −15.2426 | −0.544726 | ||||||||
\(784\) | −12.3513 | −0.441119 | ||||||||
\(785\) | 19.0766 | 0.680871 | ||||||||
\(786\) | 109.909 | 3.92034 | ||||||||
\(787\) | −19.6425 | −0.700180 | −0.350090 | − | 0.936716i | \(-0.613849\pi\) | ||||
−0.350090 | + | 0.936716i | \(0.613849\pi\) | |||||||
\(788\) | 108.834 | 3.87705 | ||||||||
\(789\) | −37.4782 | −1.33426 | ||||||||
\(790\) | −34.9065 | −1.24192 | ||||||||
\(791\) | 35.3592 | 1.25723 | ||||||||
\(792\) | 166.187 | 5.90520 | ||||||||
\(793\) | −24.4647 | −0.868767 | ||||||||
\(794\) | −40.3706 | −1.43270 | ||||||||
\(795\) | −6.43087 | −0.228080 | ||||||||
\(796\) | 16.9002 | 0.599013 | ||||||||
\(797\) | −24.5901 | −0.871027 | −0.435514 | − | 0.900182i | \(-0.643433\pi\) | ||||
−0.435514 | + | 0.900182i | \(0.643433\pi\) | |||||||
\(798\) | −50.6456 | −1.79284 | ||||||||
\(799\) | −7.68307 | −0.271808 | ||||||||
\(800\) | −26.1098 | −0.923121 | ||||||||
\(801\) | 42.1572 | 1.48955 | ||||||||
\(802\) | −48.6268 | −1.71707 | ||||||||
\(803\) | −18.1893 | −0.641885 | ||||||||
\(804\) | 7.05575 | 0.248837 | ||||||||
\(805\) | 14.2527 | 0.502340 | ||||||||
\(806\) | 19.5238 | 0.687697 | ||||||||
\(807\) | −56.2109 | −1.97872 | ||||||||
\(808\) | 59.7617 | 2.10241 | ||||||||
\(809\) | 25.5573 | 0.898548 | 0.449274 | − | 0.893394i | \(-0.351683\pi\) | ||||
0.449274 | + | 0.893394i | \(0.351683\pi\) | |||||||
\(810\) | −26.7502 | −0.939905 | ||||||||
\(811\) | 32.0207 | 1.12440 | 0.562199 | − | 0.827002i | \(-0.309955\pi\) | ||||
0.562199 | + | 0.827002i | \(0.309955\pi\) | |||||||
\(812\) | −23.3455 | −0.819267 | ||||||||
\(813\) | −38.2242 | −1.34058 | ||||||||
\(814\) | 60.8591 | 2.13311 | ||||||||
\(815\) | 1.32430 | 0.0463882 | ||||||||
\(816\) | −34.8381 | −1.21958 | ||||||||
\(817\) | −4.96602 | −0.173739 | ||||||||
\(818\) | −66.0761 | −2.31030 | ||||||||
\(819\) | −64.4410 | −2.25175 | ||||||||
\(820\) | 21.0482 | 0.735036 | ||||||||
\(821\) | −10.3653 | −0.361751 | −0.180876 | − | 0.983506i | \(-0.557893\pi\) | ||||
−0.180876 | + | 0.983506i | \(0.557893\pi\) | |||||||
\(822\) | −84.9830 | −2.96412 | ||||||||
\(823\) | −39.1992 | −1.36640 | −0.683200 | − | 0.730232i | \(-0.739412\pi\) | ||||
−0.683200 | + | 0.730232i | \(0.739412\pi\) | |||||||
\(824\) | 62.9925 | 2.19445 | ||||||||
\(825\) | 8.12394 | 0.282839 | ||||||||
\(826\) | 19.8158 | 0.689482 | ||||||||
\(827\) | 23.7597 | 0.826206 | 0.413103 | − | 0.910684i | \(-0.364445\pi\) | ||||
0.413103 | + | 0.910684i | \(0.364445\pi\) | |||||||
\(828\) | −195.925 | −6.80888 | ||||||||
\(829\) | −7.07428 | −0.245700 | −0.122850 | − | 0.992425i | \(-0.539203\pi\) | ||||
−0.122850 | + | 0.992425i | \(0.539203\pi\) | |||||||
\(830\) | −2.05394 | −0.0712932 | ||||||||
\(831\) | −52.6430 | −1.82616 | ||||||||
\(832\) | 164.364 | 5.69829 | ||||||||
\(833\) | −0.508532 | −0.0176196 | ||||||||
\(834\) | −37.3830 | −1.29447 | ||||||||
\(835\) | −11.5501 | −0.399706 | ||||||||
\(836\) | −37.0766 | −1.28232 | ||||||||
\(837\) | 15.3951 | 0.532132 | ||||||||
\(838\) | −34.7028 | −1.19879 | ||||||||
\(839\) | −25.1614 | −0.868669 | −0.434335 | − | 0.900752i | \(-0.643016\pi\) | ||||
−0.434335 | + | 0.900752i | \(0.643016\pi\) | |||||||
\(840\) | −76.4842 | −2.63896 | ||||||||
\(841\) | −26.2883 | −0.906492 | ||||||||
\(842\) | 33.6027 | 1.15802 | ||||||||
\(843\) | −44.3167 | −1.52635 | ||||||||
\(844\) | −59.4159 | −2.04518 | ||||||||
\(845\) | 4.97767 | 0.171237 | ||||||||
\(846\) | 187.196 | 6.43592 | ||||||||
\(847\) | 9.32433 | 0.320388 | ||||||||
\(848\) | 35.7835 | 1.22881 | ||||||||
\(849\) | 23.3223 | 0.800419 | ||||||||
\(850\) | −1.91048 | −0.0655290 | ||||||||
\(851\) | −46.4179 | −1.59118 | ||||||||
\(852\) | 118.608 | 4.06345 | ||||||||
\(853\) | 46.3115 | 1.58568 | 0.792838 | − | 0.609432i | \(-0.208603\pi\) | ||||
0.792838 | + | 0.609432i | \(0.208603\pi\) | |||||||
\(854\) | −39.9777 | −1.36801 | ||||||||
\(855\) | 14.7375 | 0.504013 | ||||||||
\(856\) | −105.522 | −3.60668 | ||||||||
\(857\) | −41.9166 | −1.43184 | −0.715922 | − | 0.698180i | \(-0.753993\pi\) | ||||
−0.715922 | + | 0.698180i | \(0.753993\pi\) | |||||||
\(858\) | −95.3639 | −3.25567 | ||||||||
\(859\) | −46.7191 | −1.59404 | −0.797018 | − | 0.603956i | \(-0.793590\pi\) | ||||
−0.797018 | + | 0.603956i | \(0.793590\pi\) | |||||||
\(860\) | −11.5924 | −0.395296 | ||||||||
\(861\) | 28.0090 | 0.954545 | ||||||||
\(862\) | 33.2132 | 1.13125 | ||||||||
\(863\) | 46.8241 | 1.59391 | 0.796956 | − | 0.604037i | \(-0.206442\pi\) | ||||
0.796956 | + | 0.604037i | \(0.206442\pi\) | |||||||
\(864\) | 241.679 | 8.22209 | ||||||||
\(865\) | −9.89021 | −0.336277 | ||||||||
\(866\) | 30.2215 | 1.02697 | ||||||||
\(867\) | 49.7720 | 1.69035 | ||||||||
\(868\) | 23.5791 | 0.800326 | ||||||||
\(869\) | −34.0053 | −1.15355 | ||||||||
\(870\) | 13.7325 | 0.465576 | ||||||||
\(871\) | −1.75327 | −0.0594073 | ||||||||
\(872\) | 173.742 | 5.88364 | ||||||||
\(873\) | 108.208 | 3.66229 | ||||||||
\(874\) | 38.2627 | 1.29426 | ||||||||
\(875\) | −2.50261 | −0.0846037 | ||||||||
\(876\) | −115.076 | −3.88806 | ||||||||
\(877\) | −31.7358 | −1.07164 | −0.535821 | − | 0.844331i | \(-0.679998\pi\) | ||||
−0.535821 | + | 0.844331i | \(0.679998\pi\) | |||||||
\(878\) | −45.0138 | −1.51914 | ||||||||
\(879\) | 78.4111 | 2.64474 | ||||||||
\(880\) | −45.2042 | −1.52383 | ||||||||
\(881\) | 24.1310 | 0.812995 | 0.406498 | − | 0.913652i | \(-0.366750\pi\) | ||||
0.406498 | + | 0.913652i | \(0.366750\pi\) | |||||||
\(882\) | 12.3902 | 0.417201 | ||||||||
\(883\) | 49.9052 | 1.67944 | 0.839721 | − | 0.543018i | \(-0.182718\pi\) | ||||
0.839721 | + | 0.543018i | \(0.182718\pi\) | |||||||
\(884\) | 16.5747 | 0.557466 | ||||||||
\(885\) | −8.61476 | −0.289582 | ||||||||
\(886\) | −94.4923 | −3.17453 | ||||||||
\(887\) | 0.380344 | 0.0127707 | 0.00638535 | − | 0.999980i | \(-0.497967\pi\) | ||||
0.00638535 | + | 0.999980i | \(0.497967\pi\) | |||||||
\(888\) | 249.093 | 8.35901 | ||||||||
\(889\) | 31.1951 | 1.04625 | ||||||||
\(890\) | −19.2185 | −0.644207 | ||||||||
\(891\) | −26.0596 | −0.873028 | ||||||||
\(892\) | 68.7768 | 2.30282 | ||||||||
\(893\) | −27.0187 | −0.904148 | ||||||||
\(894\) | −155.346 | −5.19554 | ||||||||
\(895\) | 4.20597 | 0.140590 | ||||||||
\(896\) | 137.901 | 4.60695 | ||||||||
\(897\) | 72.7351 | 2.42856 | ||||||||
\(898\) | −25.3269 | −0.845169 | ||||||||
\(899\) | −2.73887 | −0.0913463 | ||||||||
\(900\) | 34.4023 | 1.14674 | ||||||||
\(901\) | 1.47329 | 0.0490823 | ||||||||
\(902\) | 27.7442 | 0.923780 | ||||||||
\(903\) | −15.4261 | −0.513347 | ||||||||
\(904\) | 143.355 | 4.76791 | ||||||||
\(905\) | −16.0787 | −0.534474 | ||||||||
\(906\) | −96.0745 | −3.19186 | ||||||||
\(907\) | −39.9864 | −1.32773 | −0.663863 | − | 0.747854i | \(-0.731084\pi\) | ||||
−0.663863 | + | 0.747854i | \(0.731084\pi\) | |||||||
\(908\) | 105.606 | 3.50465 | ||||||||
\(909\) | −35.7702 | −1.18642 | ||||||||
\(910\) | 29.3773 | 0.973847 | ||||||||
\(911\) | 17.5380 | 0.581061 | 0.290530 | − | 0.956866i | \(-0.406168\pi\) | ||||
0.290530 | + | 0.956866i | \(0.406168\pi\) | |||||||
\(912\) | −122.514 | −4.05684 | ||||||||
\(913\) | −2.00091 | −0.0662205 | ||||||||
\(914\) | 82.4613 | 2.72758 | ||||||||
\(915\) | 17.3799 | 0.574563 | ||||||||
\(916\) | 92.8031 | 3.06630 | ||||||||
\(917\) | −32.9840 | −1.08923 | ||||||||
\(918\) | 17.6839 | 0.583656 | ||||||||
\(919\) | −25.3706 | −0.836900 | −0.418450 | − | 0.908240i | \(-0.637427\pi\) | ||||
−0.418450 | + | 0.908240i | \(0.637427\pi\) | |||||||
\(920\) | 57.7837 | 1.90507 | ||||||||
\(921\) | −76.5509 | −2.52244 | ||||||||
\(922\) | −17.0922 | −0.562901 | ||||||||
\(923\) | −29.4727 | −0.970106 | ||||||||
\(924\) | −115.172 | −3.78887 | ||||||||
\(925\) | 8.15047 | 0.267986 | ||||||||
\(926\) | −32.9559 | −1.08300 | ||||||||
\(927\) | −37.7040 | −1.23836 | ||||||||
\(928\) | −42.9959 | −1.41141 | ||||||||
\(929\) | −2.64760 | −0.0868649 | −0.0434324 | − | 0.999056i | \(-0.513829\pi\) | ||||
−0.0434324 | + | 0.999056i | \(0.513829\pi\) | |||||||
\(930\) | −13.8699 | −0.454812 | ||||||||
\(931\) | −1.78833 | −0.0586103 | ||||||||
\(932\) | 42.7161 | 1.39921 | ||||||||
\(933\) | −2.83610 | −0.0928498 | ||||||||
\(934\) | 34.9728 | 1.14434 | ||||||||
\(935\) | −1.86116 | −0.0608664 | ||||||||
\(936\) | −261.259 | −8.53953 | ||||||||
\(937\) | 37.2446 | 1.21673 | 0.608364 | − | 0.793658i | \(-0.291826\pi\) | ||||
0.608364 | + | 0.793658i | \(0.291826\pi\) | |||||||
\(938\) | −2.86501 | −0.0935461 | ||||||||
\(939\) | −35.2843 | −1.15146 | ||||||||
\(940\) | −63.0708 | −2.05714 | ||||||||
\(941\) | −2.98457 | −0.0972943 | −0.0486472 | − | 0.998816i | \(-0.515491\pi\) | ||||
−0.0486472 | + | 0.998816i | \(0.515491\pi\) | |||||||
\(942\) | 159.084 | 5.18323 | ||||||||
\(943\) | −21.1608 | −0.689090 | ||||||||
\(944\) | 47.9353 | 1.56016 | ||||||||
\(945\) | 23.1648 | 0.753552 | ||||||||
\(946\) | −15.2802 | −0.496802 | ||||||||
\(947\) | −58.0874 | −1.88759 | −0.943793 | − | 0.330537i | \(-0.892770\pi\) | ||||
−0.943793 | + | 0.330537i | \(0.892770\pi\) | |||||||
\(948\) | −215.138 | −6.98734 | ||||||||
\(949\) | 28.5950 | 0.928234 | ||||||||
\(950\) | −6.71851 | −0.217977 | ||||||||
\(951\) | −11.6656 | −0.378283 | ||||||||
\(952\) | 17.5222 | 0.567898 | ||||||||
\(953\) | 20.0137 | 0.648307 | 0.324153 | − | 0.946005i | \(-0.394921\pi\) | ||||
0.324153 | + | 0.946005i | \(0.394921\pi\) | |||||||
\(954\) | −35.8961 | −1.16218 | ||||||||
\(955\) | 22.9853 | 0.743787 | ||||||||
\(956\) | 39.9784 | 1.29299 | ||||||||
\(957\) | 13.3780 | 0.432448 | ||||||||
\(958\) | 30.0481 | 0.970809 | ||||||||
\(959\) | 25.5035 | 0.823551 | ||||||||
\(960\) | −116.766 | −3.76859 | ||||||||
\(961\) | −28.2337 | −0.910766 | ||||||||
\(962\) | −95.6754 | −3.08470 | ||||||||
\(963\) | 63.1601 | 2.03531 | ||||||||
\(964\) | −90.2483 | −2.90670 | ||||||||
\(965\) | −2.07766 | −0.0668822 | ||||||||
\(966\) | 118.856 | 3.82414 | ||||||||
\(967\) | 36.8362 | 1.18457 | 0.592286 | − | 0.805728i | \(-0.298226\pi\) | ||||
0.592286 | + | 0.805728i | \(0.298226\pi\) | |||||||
\(968\) | 37.8031 | 1.21504 | ||||||||
\(969\) | −5.04417 | −0.162042 | ||||||||
\(970\) | −49.3297 | −1.58388 | ||||||||
\(971\) | −51.7636 | −1.66117 | −0.830586 | − | 0.556891i | \(-0.811994\pi\) | ||||
−0.830586 | + | 0.556891i | \(0.811994\pi\) | |||||||
\(972\) | −7.56298 | −0.242583 | ||||||||
\(973\) | 11.2187 | 0.359654 | ||||||||
\(974\) | −47.4617 | −1.52077 | ||||||||
\(975\) | −12.7715 | −0.409015 | ||||||||
\(976\) | −96.7076 | −3.09554 | ||||||||
\(977\) | −42.8538 | −1.37101 | −0.685507 | − | 0.728066i | \(-0.740419\pi\) | ||||
−0.685507 | + | 0.728066i | \(0.740419\pi\) | |||||||
\(978\) | 11.0436 | 0.353136 | ||||||||
\(979\) | −18.7224 | −0.598370 | ||||||||
\(980\) | −4.17458 | −0.133352 | ||||||||
\(981\) | −103.993 | −3.32023 | ||||||||
\(982\) | 93.3207 | 2.97798 | ||||||||
\(983\) | −28.9764 | −0.924204 | −0.462102 | − | 0.886827i | \(-0.652905\pi\) | ||||
−0.462102 | + | 0.886827i | \(0.652905\pi\) | |||||||
\(984\) | 113.555 | 3.62001 | ||||||||
\(985\) | 19.2123 | 0.612153 | ||||||||
\(986\) | −3.14606 | −0.100191 | ||||||||
\(987\) | −83.9289 | −2.67149 | ||||||||
\(988\) | 58.2874 | 1.85437 | ||||||||
\(989\) | 11.6544 | 0.370587 | ||||||||
\(990\) | 45.3466 | 1.44121 | ||||||||
\(991\) | 18.7791 | 0.596539 | 0.298270 | − | 0.954482i | \(-0.403591\pi\) | ||||
0.298270 | + | 0.954482i | \(0.403591\pi\) | |||||||
\(992\) | 43.4261 | 1.37878 | ||||||||
\(993\) | −77.6952 | −2.46558 | ||||||||
\(994\) | −48.1613 | −1.52758 | ||||||||
\(995\) | 2.98337 | 0.0945791 | ||||||||
\(996\) | −12.6589 | −0.401114 | ||||||||
\(997\) | −53.8370 | −1.70504 | −0.852518 | − | 0.522699i | \(-0.824925\pi\) | ||||
−0.852518 | + | 0.522699i | \(0.824925\pi\) | |||||||
\(998\) | −1.51558 | −0.0479747 | ||||||||
\(999\) | −75.4429 | −2.38691 |
(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 | 8005.2.a.e.1.2 | ✓ | 126 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8005.2.a.e.1.2 | ✓ | 126 | 1.1 | even | 1 | trivial |