Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.82194 | −1.62925 | −0.814623 | − | 0.579990i | \(-0.803056\pi\) | ||||
−0.814623 | + | 0.579990i | \(0.803056\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.46398 | −0.654710 | −0.327355 | − | 0.944901i | \(-0.606157\pi\) | ||||
−0.327355 | + | 0.944901i | \(0.606157\pi\) | |||||||
\(6\) | 2.82194 | 1.15205 | ||||||||
\(7\) | 3.02991 | 1.14520 | 0.572600 | − | 0.819835i | \(-0.305935\pi\) | ||||
0.572600 | + | 0.819835i | \(0.305935\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.96334 | 1.65445 | ||||||||
\(10\) | 1.46398 | 0.462950 | ||||||||
\(11\) | −6.50685 | −1.96189 | −0.980945 | − | 0.194285i | \(-0.937761\pi\) | ||||
−0.980945 | + | 0.194285i | \(0.937761\pi\) | |||||||
\(12\) | −2.82194 | −0.814623 | ||||||||
\(13\) | −4.43326 | −1.22957 | −0.614783 | − | 0.788696i | \(-0.710756\pi\) | ||||
−0.614783 | + | 0.788696i | \(0.710756\pi\) | |||||||
\(14\) | −3.02991 | −0.809778 | ||||||||
\(15\) | 4.13125 | 1.06668 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.53706 | −1.58547 | −0.792735 | − | 0.609567i | \(-0.791343\pi\) | ||||
−0.792735 | + | 0.609567i | \(0.791343\pi\) | |||||||
\(18\) | −4.96334 | −1.16987 | ||||||||
\(19\) | −1.63213 | −0.374437 | −0.187218 | − | 0.982318i | \(-0.559947\pi\) | ||||
−0.187218 | + | 0.982318i | \(0.559947\pi\) | |||||||
\(20\) | −1.46398 | −0.327355 | ||||||||
\(21\) | −8.55023 | −1.86581 | ||||||||
\(22\) | 6.50685 | 1.38727 | ||||||||
\(23\) | −2.19016 | −0.456680 | −0.228340 | − | 0.973581i | \(-0.573330\pi\) | ||||
−0.228340 | + | 0.973581i | \(0.573330\pi\) | |||||||
\(24\) | 2.82194 | 0.576026 | ||||||||
\(25\) | −2.85677 | −0.571354 | ||||||||
\(26\) | 4.43326 | 0.869435 | ||||||||
\(27\) | −5.54041 | −1.06625 | ||||||||
\(28\) | 3.02991 | 0.572600 | ||||||||
\(29\) | −1.73018 | −0.321287 | −0.160643 | − | 0.987013i | \(-0.551357\pi\) | ||||
−0.160643 | + | 0.987013i | \(0.551357\pi\) | |||||||
\(30\) | −4.13125 | −0.754260 | ||||||||
\(31\) | −5.54987 | −0.996786 | −0.498393 | − | 0.866951i | \(-0.666076\pi\) | ||||
−0.498393 | + | 0.866951i | \(0.666076\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 18.3619 | 3.19640 | ||||||||
\(34\) | 6.53706 | 1.12110 | ||||||||
\(35\) | −4.43572 | −0.749774 | ||||||||
\(36\) | 4.96334 | 0.827223 | ||||||||
\(37\) | 4.87651 | 0.801693 | 0.400847 | − | 0.916145i | \(-0.368716\pi\) | ||||
0.400847 | + | 0.916145i | \(0.368716\pi\) | |||||||
\(38\) | 1.63213 | 0.264767 | ||||||||
\(39\) | 12.5104 | 2.00327 | ||||||||
\(40\) | 1.46398 | 0.231475 | ||||||||
\(41\) | −6.60449 | −1.03145 | −0.515724 | − | 0.856755i | \(-0.672477\pi\) | ||||
−0.515724 | + | 0.856755i | \(0.672477\pi\) | |||||||
\(42\) | 8.55023 | 1.31933 | ||||||||
\(43\) | −1.91376 | −0.291845 | −0.145923 | − | 0.989296i | \(-0.546615\pi\) | ||||
−0.145923 | + | 0.989296i | \(0.546615\pi\) | |||||||
\(44\) | −6.50685 | −0.980945 | ||||||||
\(45\) | −7.26621 | −1.08318 | ||||||||
\(46\) | 2.19016 | 0.322922 | ||||||||
\(47\) | 7.13736 | 1.04109 | 0.520545 | − | 0.853834i | \(-0.325729\pi\) | ||||
0.520545 | + | 0.853834i | \(0.325729\pi\) | |||||||
\(48\) | −2.82194 | −0.407312 | ||||||||
\(49\) | 2.18037 | 0.311482 | ||||||||
\(50\) | 2.85677 | 0.404009 | ||||||||
\(51\) | 18.4472 | 2.58312 | ||||||||
\(52\) | −4.43326 | −0.614783 | ||||||||
\(53\) | 1.62511 | 0.223226 | 0.111613 | − | 0.993752i | \(-0.464398\pi\) | ||||
0.111613 | + | 0.993752i | \(0.464398\pi\) | |||||||
\(54\) | 5.54041 | 0.753955 | ||||||||
\(55\) | 9.52588 | 1.28447 | ||||||||
\(56\) | −3.02991 | −0.404889 | ||||||||
\(57\) | 4.60577 | 0.610050 | ||||||||
\(58\) | 1.73018 | 0.227184 | ||||||||
\(59\) | −10.9135 | −1.42082 | −0.710409 | − | 0.703789i | \(-0.751490\pi\) | ||||
−0.710409 | + | 0.703789i | \(0.751490\pi\) | |||||||
\(60\) | 4.13125 | 0.533342 | ||||||||
\(61\) | 3.73230 | 0.477872 | 0.238936 | − | 0.971035i | \(-0.423201\pi\) | ||||
0.238936 | + | 0.971035i | \(0.423201\pi\) | |||||||
\(62\) | 5.54987 | 0.704834 | ||||||||
\(63\) | 15.0385 | 1.89467 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.49020 | 0.805010 | ||||||||
\(66\) | −18.3619 | −2.26020 | ||||||||
\(67\) | −14.0409 | −1.71537 | −0.857684 | − | 0.514177i | \(-0.828098\pi\) | ||||
−0.857684 | + | 0.514177i | \(0.828098\pi\) | |||||||
\(68\) | −6.53706 | −0.792735 | ||||||||
\(69\) | 6.18050 | 0.744045 | ||||||||
\(70\) | 4.43572 | 0.530170 | ||||||||
\(71\) | −7.17329 | −0.851312 | −0.425656 | − | 0.904885i | \(-0.639957\pi\) | ||||
−0.425656 | + | 0.904885i | \(0.639957\pi\) | |||||||
\(72\) | −4.96334 | −0.584935 | ||||||||
\(73\) | −14.9201 | −1.74626 | −0.873131 | − | 0.487486i | \(-0.837914\pi\) | ||||
−0.873131 | + | 0.487486i | \(0.837914\pi\) | |||||||
\(74\) | −4.87651 | −0.566883 | ||||||||
\(75\) | 8.06163 | 0.930877 | ||||||||
\(76\) | −1.63213 | −0.187218 | ||||||||
\(77\) | −19.7152 | −2.24676 | ||||||||
\(78\) | −12.5104 | −1.41652 | ||||||||
\(79\) | 1.93882 | 0.218135 | 0.109067 | − | 0.994034i | \(-0.465214\pi\) | ||||
0.109067 | + | 0.994034i | \(0.465214\pi\) | |||||||
\(80\) | −1.46398 | −0.163678 | ||||||||
\(81\) | 0.744700 | 0.0827444 | ||||||||
\(82\) | 6.60449 | 0.729344 | ||||||||
\(83\) | −3.85911 | −0.423592 | −0.211796 | − | 0.977314i | \(-0.567931\pi\) | ||||
−0.211796 | + | 0.977314i | \(0.567931\pi\) | |||||||
\(84\) | −8.55023 | −0.932906 | ||||||||
\(85\) | 9.57010 | 1.03802 | ||||||||
\(86\) | 1.91376 | 0.206366 | ||||||||
\(87\) | 4.88247 | 0.523455 | ||||||||
\(88\) | 6.50685 | 0.693633 | ||||||||
\(89\) | 17.6573 | 1.87167 | 0.935836 | − | 0.352436i | \(-0.114647\pi\) | ||||
0.935836 | + | 0.352436i | \(0.114647\pi\) | |||||||
\(90\) | 7.26621 | 0.765926 | ||||||||
\(91\) | −13.4324 | −1.40810 | ||||||||
\(92\) | −2.19016 | −0.228340 | ||||||||
\(93\) | 15.6614 | 1.62401 | ||||||||
\(94\) | −7.13736 | −0.736162 | ||||||||
\(95\) | 2.38940 | 0.245148 | ||||||||
\(96\) | 2.82194 | 0.288013 | ||||||||
\(97\) | 14.0099 | 1.42249 | 0.711246 | − | 0.702943i | \(-0.248131\pi\) | ||||
0.711246 | + | 0.702943i | \(0.248131\pi\) | |||||||
\(98\) | −2.18037 | −0.220251 | ||||||||
\(99\) | −32.2957 | −3.24584 | ||||||||
\(100\) | −2.85677 | −0.285677 | ||||||||
\(101\) | −17.4527 | −1.73661 | −0.868303 | − | 0.496034i | \(-0.834789\pi\) | ||||
−0.868303 | + | 0.496034i | \(0.834789\pi\) | |||||||
\(102\) | −18.4472 | −1.82654 | ||||||||
\(103\) | 8.61001 | 0.848369 | 0.424185 | − | 0.905576i | \(-0.360561\pi\) | ||||
0.424185 | + | 0.905576i | \(0.360561\pi\) | |||||||
\(104\) | 4.43326 | 0.434717 | ||||||||
\(105\) | 12.5173 | 1.22157 | ||||||||
\(106\) | −1.62511 | −0.157845 | ||||||||
\(107\) | −18.7433 | −1.81198 | −0.905990 | − | 0.423300i | \(-0.860872\pi\) | ||||
−0.905990 | + | 0.423300i | \(0.860872\pi\) | |||||||
\(108\) | −5.54041 | −0.533127 | ||||||||
\(109\) | −13.3799 | −1.28156 | −0.640780 | − | 0.767724i | \(-0.721389\pi\) | ||||
−0.640780 | + | 0.767724i | \(0.721389\pi\) | |||||||
\(110\) | −9.52588 | −0.908257 | ||||||||
\(111\) | −13.7612 | −1.30616 | ||||||||
\(112\) | 3.02991 | 0.286300 | ||||||||
\(113\) | −9.12519 | −0.858425 | −0.429213 | − | 0.903203i | \(-0.641209\pi\) | ||||
−0.429213 | + | 0.903203i | \(0.641209\pi\) | |||||||
\(114\) | −4.60577 | −0.431370 | ||||||||
\(115\) | 3.20635 | 0.298993 | ||||||||
\(116\) | −1.73018 | −0.160643 | ||||||||
\(117\) | −22.0038 | −2.03425 | ||||||||
\(118\) | 10.9135 | 1.00467 | ||||||||
\(119\) | −19.8067 | −1.81568 | ||||||||
\(120\) | −4.13125 | −0.377130 | ||||||||
\(121\) | 31.3391 | 2.84901 | ||||||||
\(122\) | −3.73230 | −0.337907 | ||||||||
\(123\) | 18.6375 | 1.68048 | ||||||||
\(124\) | −5.54987 | −0.498393 | ||||||||
\(125\) | 11.5021 | 1.02878 | ||||||||
\(126\) | −15.0385 | −1.33973 | ||||||||
\(127\) | −19.6183 | −1.74084 | −0.870420 | − | 0.492310i | \(-0.836153\pi\) | ||||
−0.870420 | + | 0.492310i | \(0.836153\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.40050 | 0.475488 | ||||||||
\(130\) | −6.49020 | −0.569228 | ||||||||
\(131\) | 14.9845 | 1.30920 | 0.654601 | − | 0.755974i | \(-0.272837\pi\) | ||||
0.654601 | + | 0.755974i | \(0.272837\pi\) | |||||||
\(132\) | 18.3619 | 1.59820 | ||||||||
\(133\) | −4.94522 | −0.428805 | ||||||||
\(134\) | 14.0409 | 1.21295 | ||||||||
\(135\) | 8.11104 | 0.698087 | ||||||||
\(136\) | 6.53706 | 0.560548 | ||||||||
\(137\) | −19.9718 | −1.70630 | −0.853152 | − | 0.521662i | \(-0.825312\pi\) | ||||
−0.853152 | + | 0.521662i | \(0.825312\pi\) | |||||||
\(138\) | −6.18050 | −0.526119 | ||||||||
\(139\) | 21.5488 | 1.82775 | 0.913873 | − | 0.406000i | \(-0.133077\pi\) | ||||
0.913873 | + | 0.406000i | \(0.133077\pi\) | |||||||
\(140\) | −4.43572 | −0.374887 | ||||||||
\(141\) | −20.1412 | −1.69619 | ||||||||
\(142\) | 7.17329 | 0.601969 | ||||||||
\(143\) | 28.8466 | 2.41227 | ||||||||
\(144\) | 4.96334 | 0.413611 | ||||||||
\(145\) | 2.53295 | 0.210350 | ||||||||
\(146\) | 14.9201 | 1.23479 | ||||||||
\(147\) | −6.15288 | −0.507481 | ||||||||
\(148\) | 4.87651 | 0.400847 | ||||||||
\(149\) | −23.6769 | −1.93968 | −0.969842 | − | 0.243736i | \(-0.921627\pi\) | ||||
−0.969842 | + | 0.243736i | \(0.921627\pi\) | |||||||
\(150\) | −8.06163 | −0.658230 | ||||||||
\(151\) | 9.82987 | 0.799944 | 0.399972 | − | 0.916527i | \(-0.369020\pi\) | ||||
0.399972 | + | 0.916527i | \(0.369020\pi\) | |||||||
\(152\) | 1.63213 | 0.132383 | ||||||||
\(153\) | −32.4456 | −2.62307 | ||||||||
\(154\) | 19.7152 | 1.58870 | ||||||||
\(155\) | 8.12488 | 0.652606 | ||||||||
\(156\) | 12.5104 | 1.00163 | ||||||||
\(157\) | −9.91111 | −0.790993 | −0.395496 | − | 0.918468i | \(-0.629427\pi\) | ||||
−0.395496 | + | 0.918468i | \(0.629427\pi\) | |||||||
\(158\) | −1.93882 | −0.154245 | ||||||||
\(159\) | −4.58596 | −0.363690 | ||||||||
\(160\) | 1.46398 | 0.115738 | ||||||||
\(161\) | −6.63600 | −0.522990 | ||||||||
\(162\) | −0.744700 | −0.0585091 | ||||||||
\(163\) | −11.5771 | −0.906787 | −0.453393 | − | 0.891311i | \(-0.649787\pi\) | ||||
−0.453393 | + | 0.891311i | \(0.649787\pi\) | |||||||
\(164\) | −6.60449 | −0.515724 | ||||||||
\(165\) | −26.8815 | −2.09272 | ||||||||
\(166\) | 3.85911 | 0.299525 | ||||||||
\(167\) | −0.324636 | −0.0251211 | −0.0125606 | − | 0.999921i | \(-0.503998\pi\) | ||||
−0.0125606 | + | 0.999921i | \(0.503998\pi\) | |||||||
\(168\) | 8.55023 | 0.659664 | ||||||||
\(169\) | 6.65383 | 0.511833 | ||||||||
\(170\) | −9.57010 | −0.733993 | ||||||||
\(171\) | −8.10082 | −0.619485 | ||||||||
\(172\) | −1.91376 | −0.145923 | ||||||||
\(173\) | −5.38821 | −0.409658 | −0.204829 | − | 0.978798i | \(-0.565664\pi\) | ||||
−0.204829 | + | 0.978798i | \(0.565664\pi\) | |||||||
\(174\) | −4.88247 | −0.370139 | ||||||||
\(175\) | −8.65577 | −0.654315 | ||||||||
\(176\) | −6.50685 | −0.490473 | ||||||||
\(177\) | 30.7973 | 2.31486 | ||||||||
\(178\) | −17.6573 | −1.32347 | ||||||||
\(179\) | 14.8329 | 1.10866 | 0.554331 | − | 0.832296i | \(-0.312974\pi\) | ||||
0.554331 | + | 0.832296i | \(0.312974\pi\) | |||||||
\(180\) | −7.26621 | −0.541591 | ||||||||
\(181\) | −8.95412 | −0.665555 | −0.332777 | − | 0.943005i | \(-0.607986\pi\) | ||||
−0.332777 | + | 0.943005i | \(0.607986\pi\) | |||||||
\(182\) | 13.4324 | 0.995676 | ||||||||
\(183\) | −10.5323 | −0.778572 | ||||||||
\(184\) | 2.19016 | 0.161461 | ||||||||
\(185\) | −7.13910 | −0.524877 | ||||||||
\(186\) | −15.6614 | −1.14835 | ||||||||
\(187\) | 42.5357 | 3.11052 | ||||||||
\(188\) | 7.13736 | 0.520545 | ||||||||
\(189\) | −16.7870 | −1.22107 | ||||||||
\(190\) | −2.38940 | −0.173345 | ||||||||
\(191\) | 19.7490 | 1.42899 | 0.714494 | − | 0.699641i | \(-0.246657\pi\) | ||||
0.714494 | + | 0.699641i | \(0.246657\pi\) | |||||||
\(192\) | −2.82194 | −0.203656 | ||||||||
\(193\) | 5.61538 | 0.404204 | 0.202102 | − | 0.979365i | \(-0.435223\pi\) | ||||
0.202102 | + | 0.979365i | \(0.435223\pi\) | |||||||
\(194\) | −14.0099 | −1.00585 | ||||||||
\(195\) | −18.3149 | −1.31156 | ||||||||
\(196\) | 2.18037 | 0.155741 | ||||||||
\(197\) | −15.3217 | −1.09162 | −0.545811 | − | 0.837908i | \(-0.683778\pi\) | ||||
−0.545811 | + | 0.837908i | \(0.683778\pi\) | |||||||
\(198\) | 32.2957 | 2.29516 | ||||||||
\(199\) | 2.13728 | 0.151508 | 0.0757540 | − | 0.997127i | \(-0.475864\pi\) | ||||
0.0757540 | + | 0.997127i | \(0.475864\pi\) | |||||||
\(200\) | 2.85677 | 0.202004 | ||||||||
\(201\) | 39.6225 | 2.79476 | ||||||||
\(202\) | 17.4527 | 1.22797 | ||||||||
\(203\) | −5.24230 | −0.367937 | ||||||||
\(204\) | 18.4472 | 1.29156 | ||||||||
\(205\) | 9.66883 | 0.675300 | ||||||||
\(206\) | −8.61001 | −0.599888 | ||||||||
\(207\) | −10.8705 | −0.755553 | ||||||||
\(208\) | −4.43326 | −0.307392 | ||||||||
\(209\) | 10.6200 | 0.734604 | ||||||||
\(210\) | −12.5173 | −0.863778 | ||||||||
\(211\) | 9.11310 | 0.627372 | 0.313686 | − | 0.949527i | \(-0.398436\pi\) | ||||
0.313686 | + | 0.949527i | \(0.398436\pi\) | |||||||
\(212\) | 1.62511 | 0.111613 | ||||||||
\(213\) | 20.2426 | 1.38700 | ||||||||
\(214\) | 18.7433 | 1.28126 | ||||||||
\(215\) | 2.80169 | 0.191074 | ||||||||
\(216\) | 5.54041 | 0.376977 | ||||||||
\(217\) | −16.8156 | −1.14152 | ||||||||
\(218\) | 13.3799 | 0.906200 | ||||||||
\(219\) | 42.1035 | 2.84509 | ||||||||
\(220\) | 9.52588 | 0.642235 | ||||||||
\(221\) | 28.9805 | 1.94944 | ||||||||
\(222\) | 13.7612 | 0.923592 | ||||||||
\(223\) | 2.83838 | 0.190072 | 0.0950359 | − | 0.995474i | \(-0.469703\pi\) | ||||
0.0950359 | + | 0.995474i | \(0.469703\pi\) | |||||||
\(224\) | −3.02991 | −0.202445 | ||||||||
\(225\) | −14.1791 | −0.945275 | ||||||||
\(226\) | 9.12519 | 0.606998 | ||||||||
\(227\) | −12.8931 | −0.855743 | −0.427872 | − | 0.903839i | \(-0.640736\pi\) | ||||
−0.427872 | + | 0.903839i | \(0.640736\pi\) | |||||||
\(228\) | 4.60577 | 0.305025 | ||||||||
\(229\) | −4.75894 | −0.314480 | −0.157240 | − | 0.987560i | \(-0.550260\pi\) | ||||
−0.157240 | + | 0.987560i | \(0.550260\pi\) | |||||||
\(230\) | −3.20635 | −0.211420 | ||||||||
\(231\) | 55.6351 | 3.66052 | ||||||||
\(232\) | 1.73018 | 0.113592 | ||||||||
\(233\) | −24.6821 | −1.61698 | −0.808490 | − | 0.588509i | \(-0.799715\pi\) | ||||
−0.808490 | + | 0.588509i | \(0.799715\pi\) | |||||||
\(234\) | 22.0038 | 1.43843 | ||||||||
\(235\) | −10.4489 | −0.681613 | ||||||||
\(236\) | −10.9135 | −0.710409 | ||||||||
\(237\) | −5.47124 | −0.355395 | ||||||||
\(238\) | 19.8067 | 1.28388 | ||||||||
\(239\) | 4.15919 | 0.269036 | 0.134518 | − | 0.990911i | \(-0.457051\pi\) | ||||
0.134518 | + | 0.990911i | \(0.457051\pi\) | |||||||
\(240\) | 4.13125 | 0.266671 | ||||||||
\(241\) | 21.2315 | 1.36764 | 0.683820 | − | 0.729651i | \(-0.260318\pi\) | ||||
0.683820 | + | 0.729651i | \(0.260318\pi\) | |||||||
\(242\) | −31.3391 | −2.01456 | ||||||||
\(243\) | 14.5197 | 0.931442 | ||||||||
\(244\) | 3.73230 | 0.238936 | ||||||||
\(245\) | −3.19202 | −0.203931 | ||||||||
\(246\) | −18.6375 | −1.18828 | ||||||||
\(247\) | 7.23567 | 0.460395 | ||||||||
\(248\) | 5.54987 | 0.352417 | ||||||||
\(249\) | 10.8902 | 0.690136 | ||||||||
\(250\) | −11.5021 | −0.727459 | ||||||||
\(251\) | −14.0693 | −0.888047 | −0.444024 | − | 0.896015i | \(-0.646449\pi\) | ||||
−0.444024 | + | 0.896015i | \(0.646449\pi\) | |||||||
\(252\) | 15.0385 | 0.947335 | ||||||||
\(253\) | 14.2511 | 0.895957 | ||||||||
\(254\) | 19.6183 | 1.23096 | ||||||||
\(255\) | −27.0062 | −1.69120 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.5882 | −1.09712 | −0.548562 | − | 0.836110i | \(-0.684824\pi\) | ||||
−0.548562 | + | 0.836110i | \(0.684824\pi\) | |||||||
\(258\) | −5.40050 | −0.336220 | ||||||||
\(259\) | 14.7754 | 0.918099 | ||||||||
\(260\) | 6.49020 | 0.402505 | ||||||||
\(261\) | −8.58748 | −0.531551 | ||||||||
\(262\) | −14.9845 | −0.925746 | ||||||||
\(263\) | 19.4248 | 1.19778 | 0.598891 | − | 0.800830i | \(-0.295608\pi\) | ||||
0.598891 | + | 0.800830i | \(0.295608\pi\) | |||||||
\(264\) | −18.3619 | −1.13010 | ||||||||
\(265\) | −2.37912 | −0.146148 | ||||||||
\(266\) | 4.94522 | 0.303211 | ||||||||
\(267\) | −49.8279 | −3.04942 | ||||||||
\(268\) | −14.0409 | −0.857684 | ||||||||
\(269\) | 11.6592 | 0.710873 | 0.355437 | − | 0.934700i | \(-0.384332\pi\) | ||||
0.355437 | + | 0.934700i | \(0.384332\pi\) | |||||||
\(270\) | −8.11104 | −0.493622 | ||||||||
\(271\) | −12.7256 | −0.773025 | −0.386512 | − | 0.922284i | \(-0.626320\pi\) | ||||
−0.386512 | + | 0.922284i | \(0.626320\pi\) | |||||||
\(272\) | −6.53706 | −0.396367 | ||||||||
\(273\) | 37.9054 | 2.29414 | ||||||||
\(274\) | 19.9718 | 1.20654 | ||||||||
\(275\) | 18.5886 | 1.12093 | ||||||||
\(276\) | 6.18050 | 0.372023 | ||||||||
\(277\) | −12.1068 | −0.727429 | −0.363714 | − | 0.931511i | \(-0.618492\pi\) | ||||
−0.363714 | + | 0.931511i | \(0.618492\pi\) | |||||||
\(278\) | −21.5488 | −1.29241 | ||||||||
\(279\) | −27.5459 | −1.64913 | ||||||||
\(280\) | 4.43572 | 0.265085 | ||||||||
\(281\) | 23.7004 | 1.41385 | 0.706924 | − | 0.707290i | \(-0.250082\pi\) | ||||
0.706924 | + | 0.707290i | \(0.250082\pi\) | |||||||
\(282\) | 20.1412 | 1.19939 | ||||||||
\(283\) | 30.9156 | 1.83774 | 0.918870 | − | 0.394560i | \(-0.129103\pi\) | ||||
0.918870 | + | 0.394560i | \(0.129103\pi\) | |||||||
\(284\) | −7.17329 | −0.425656 | ||||||||
\(285\) | −6.74275 | −0.399406 | ||||||||
\(286\) | −28.8466 | −1.70574 | ||||||||
\(287\) | −20.0110 | −1.18121 | ||||||||
\(288\) | −4.96334 | −0.292467 | ||||||||
\(289\) | 25.7331 | 1.51371 | ||||||||
\(290\) | −2.53295 | −0.148740 | ||||||||
\(291\) | −39.5351 | −2.31759 | ||||||||
\(292\) | −14.9201 | −0.873131 | ||||||||
\(293\) | 18.0475 | 1.05434 | 0.527172 | − | 0.849758i | \(-0.323252\pi\) | ||||
0.527172 | + | 0.849758i | \(0.323252\pi\) | |||||||
\(294\) | 6.15288 | 0.358843 | ||||||||
\(295\) | 15.9771 | 0.930224 | ||||||||
\(296\) | −4.87651 | −0.283441 | ||||||||
\(297\) | 36.0507 | 2.09187 | ||||||||
\(298\) | 23.6769 | 1.37156 | ||||||||
\(299\) | 9.70957 | 0.561519 | ||||||||
\(300\) | 8.06163 | 0.465439 | ||||||||
\(301\) | −5.79851 | −0.334221 | ||||||||
\(302\) | −9.82987 | −0.565646 | ||||||||
\(303\) | 49.2504 | 2.82936 | ||||||||
\(304\) | −1.63213 | −0.0936091 | ||||||||
\(305\) | −5.46400 | −0.312868 | ||||||||
\(306\) | 32.4456 | 1.85479 | ||||||||
\(307\) | 14.2676 | 0.814298 | 0.407149 | − | 0.913362i | \(-0.366523\pi\) | ||||
0.407149 | + | 0.913362i | \(0.366523\pi\) | |||||||
\(308\) | −19.7152 | −1.12338 | ||||||||
\(309\) | −24.2969 | −1.38220 | ||||||||
\(310\) | −8.12488 | −0.461462 | ||||||||
\(311\) | 27.8016 | 1.57648 | 0.788242 | − | 0.615366i | \(-0.210992\pi\) | ||||
0.788242 | + | 0.615366i | \(0.210992\pi\) | |||||||
\(312\) | −12.5104 | −0.708262 | ||||||||
\(313\) | −14.5793 | −0.824070 | −0.412035 | − | 0.911168i | \(-0.635182\pi\) | ||||
−0.412035 | + | 0.911168i | \(0.635182\pi\) | |||||||
\(314\) | 9.91111 | 0.559316 | ||||||||
\(315\) | −22.0160 | −1.24046 | ||||||||
\(316\) | 1.93882 | 0.109067 | ||||||||
\(317\) | −10.6348 | −0.597310 | −0.298655 | − | 0.954361i | \(-0.596538\pi\) | ||||
−0.298655 | + | 0.954361i | \(0.596538\pi\) | |||||||
\(318\) | 4.58596 | 0.257168 | ||||||||
\(319\) | 11.2580 | 0.630329 | ||||||||
\(320\) | −1.46398 | −0.0818388 | ||||||||
\(321\) | 52.8923 | 2.95216 | ||||||||
\(322\) | 6.63600 | 0.369810 | ||||||||
\(323\) | 10.6693 | 0.593658 | ||||||||
\(324\) | 0.744700 | 0.0413722 | ||||||||
\(325\) | 12.6648 | 0.702518 | ||||||||
\(326\) | 11.5771 | 0.641195 | ||||||||
\(327\) | 37.7572 | 2.08798 | ||||||||
\(328\) | 6.60449 | 0.364672 | ||||||||
\(329\) | 21.6256 | 1.19226 | ||||||||
\(330\) | 26.8815 | 1.47978 | ||||||||
\(331\) | −10.1390 | −0.557289 | −0.278644 | − | 0.960394i | \(-0.589885\pi\) | ||||
−0.278644 | + | 0.960394i | \(0.589885\pi\) | |||||||
\(332\) | −3.85911 | −0.211796 | ||||||||
\(333\) | 24.2038 | 1.32636 | ||||||||
\(334\) | 0.324636 | 0.0177633 | ||||||||
\(335\) | 20.5555 | 1.12307 | ||||||||
\(336\) | −8.55023 | −0.466453 | ||||||||
\(337\) | −0.725346 | −0.0395121 | −0.0197561 | − | 0.999805i | \(-0.506289\pi\) | ||||
−0.0197561 | + | 0.999805i | \(0.506289\pi\) | |||||||
\(338\) | −6.65383 | −0.361920 | ||||||||
\(339\) | 25.7507 | 1.39859 | ||||||||
\(340\) | 9.57010 | 0.519012 | ||||||||
\(341\) | 36.1122 | 1.95558 | ||||||||
\(342\) | 8.10082 | 0.438042 | ||||||||
\(343\) | −14.6030 | −0.788490 | ||||||||
\(344\) | 1.91376 | 0.103183 | ||||||||
\(345\) | −9.04812 | −0.487134 | ||||||||
\(346\) | 5.38821 | 0.289672 | ||||||||
\(347\) | 5.00784 | 0.268835 | 0.134418 | − | 0.990925i | \(-0.457084\pi\) | ||||
0.134418 | + | 0.990925i | \(0.457084\pi\) | |||||||
\(348\) | 4.88247 | 0.261728 | ||||||||
\(349\) | −20.8257 | −1.11477 | −0.557387 | − | 0.830253i | \(-0.688196\pi\) | ||||
−0.557387 | + | 0.830253i | \(0.688196\pi\) | |||||||
\(350\) | 8.65577 | 0.462670 | ||||||||
\(351\) | 24.5621 | 1.31103 | ||||||||
\(352\) | 6.50685 | 0.346816 | ||||||||
\(353\) | −7.66220 | −0.407818 | −0.203909 | − | 0.978990i | \(-0.565365\pi\) | ||||
−0.203909 | + | 0.978990i | \(0.565365\pi\) | |||||||
\(354\) | −30.7973 | −1.63686 | ||||||||
\(355\) | 10.5015 | 0.557363 | ||||||||
\(356\) | 17.6573 | 0.935836 | ||||||||
\(357\) | 55.8933 | 2.95819 | ||||||||
\(358\) | −14.8329 | −0.783942 | ||||||||
\(359\) | 0.236658 | 0.0124903 | 0.00624517 | − | 0.999980i | \(-0.498012\pi\) | ||||
0.00624517 | + | 0.999980i | \(0.498012\pi\) | |||||||
\(360\) | 7.26621 | 0.382963 | ||||||||
\(361\) | −16.3361 | −0.859797 | ||||||||
\(362\) | 8.95412 | 0.470618 | ||||||||
\(363\) | −88.4371 | −4.64175 | ||||||||
\(364\) | −13.4324 | −0.704049 | ||||||||
\(365\) | 21.8426 | 1.14330 | ||||||||
\(366\) | 10.5323 | 0.550533 | ||||||||
\(367\) | 29.6537 | 1.54791 | 0.773954 | − | 0.633241i | \(-0.218276\pi\) | ||||
0.773954 | + | 0.633241i | \(0.218276\pi\) | |||||||
\(368\) | −2.19016 | −0.114170 | ||||||||
\(369\) | −32.7803 | −1.70648 | ||||||||
\(370\) | 7.13910 | 0.371144 | ||||||||
\(371\) | 4.92394 | 0.255638 | ||||||||
\(372\) | 15.6614 | 0.812005 | ||||||||
\(373\) | −21.5425 | −1.11543 | −0.557715 | − | 0.830033i | \(-0.688322\pi\) | ||||
−0.557715 | + | 0.830033i | \(0.688322\pi\) | |||||||
\(374\) | −42.5357 | −2.19947 | ||||||||
\(375\) | −32.4583 | −1.67614 | ||||||||
\(376\) | −7.13736 | −0.368081 | ||||||||
\(377\) | 7.67035 | 0.395043 | ||||||||
\(378\) | 16.7870 | 0.863429 | ||||||||
\(379\) | −1.63867 | −0.0841728 | −0.0420864 | − | 0.999114i | \(-0.513400\pi\) | ||||
−0.0420864 | + | 0.999114i | \(0.513400\pi\) | |||||||
\(380\) | 2.38940 | 0.122574 | ||||||||
\(381\) | 55.3616 | 2.83626 | ||||||||
\(382\) | −19.7490 | −1.01045 | ||||||||
\(383\) | −14.3630 | −0.733914 | −0.366957 | − | 0.930238i | \(-0.619600\pi\) | ||||
−0.366957 | + | 0.930238i | \(0.619600\pi\) | |||||||
\(384\) | 2.82194 | 0.144006 | ||||||||
\(385\) | 28.8626 | 1.47097 | ||||||||
\(386\) | −5.61538 | −0.285815 | ||||||||
\(387\) | −9.49861 | −0.482842 | ||||||||
\(388\) | 14.0099 | 0.711246 | ||||||||
\(389\) | 10.0688 | 0.510507 | 0.255253 | − | 0.966874i | \(-0.417841\pi\) | ||||
0.255253 | + | 0.966874i | \(0.417841\pi\) | |||||||
\(390\) | 18.3149 | 0.927413 | ||||||||
\(391\) | 14.3172 | 0.724053 | ||||||||
\(392\) | −2.18037 | −0.110126 | ||||||||
\(393\) | −42.2853 | −2.13301 | ||||||||
\(394\) | 15.3217 | 0.771894 | ||||||||
\(395\) | −2.83839 | −0.142815 | ||||||||
\(396\) | −32.2957 | −1.62292 | ||||||||
\(397\) | 15.5768 | 0.781777 | 0.390888 | − | 0.920438i | \(-0.372168\pi\) | ||||
0.390888 | + | 0.920438i | \(0.372168\pi\) | |||||||
\(398\) | −2.13728 | −0.107132 | ||||||||
\(399\) | 13.9551 | 0.698629 | ||||||||
\(400\) | −2.85677 | −0.142839 | ||||||||
\(401\) | −25.0146 | −1.24917 | −0.624584 | − | 0.780957i | \(-0.714732\pi\) | ||||
−0.624584 | + | 0.780957i | \(0.714732\pi\) | |||||||
\(402\) | −39.6225 | −1.97619 | ||||||||
\(403\) | 24.6040 | 1.22561 | ||||||||
\(404\) | −17.4527 | −0.868303 | ||||||||
\(405\) | −1.09022 | −0.0541736 | ||||||||
\(406\) | 5.24230 | 0.260171 | ||||||||
\(407\) | −31.7307 | −1.57283 | ||||||||
\(408\) | −18.4472 | −0.913271 | ||||||||
\(409\) | 0.455269 | 0.0225116 | 0.0112558 | − | 0.999937i | \(-0.496417\pi\) | ||||
0.0112558 | + | 0.999937i | \(0.496417\pi\) | |||||||
\(410\) | −9.66883 | −0.477509 | ||||||||
\(411\) | 56.3591 | 2.77999 | ||||||||
\(412\) | 8.61001 | 0.424185 | ||||||||
\(413\) | −33.0670 | −1.62712 | ||||||||
\(414\) | 10.8705 | 0.534257 | ||||||||
\(415\) | 5.64964 | 0.277330 | ||||||||
\(416\) | 4.43326 | 0.217359 | ||||||||
\(417\) | −60.8094 | −2.97785 | ||||||||
\(418\) | −10.6200 | −0.519443 | ||||||||
\(419\) | −3.12795 | −0.152810 | −0.0764051 | − | 0.997077i | \(-0.524344\pi\) | ||||
−0.0764051 | + | 0.997077i | \(0.524344\pi\) | |||||||
\(420\) | 12.5173 | 0.610784 | ||||||||
\(421\) | −11.3086 | −0.551147 | −0.275573 | − | 0.961280i | \(-0.588868\pi\) | ||||
−0.275573 | + | 0.961280i | \(0.588868\pi\) | |||||||
\(422\) | −9.11310 | −0.443619 | ||||||||
\(423\) | 35.4251 | 1.72243 | ||||||||
\(424\) | −1.62511 | −0.0789223 | ||||||||
\(425\) | 18.6749 | 0.905865 | ||||||||
\(426\) | −20.2426 | −0.980756 | ||||||||
\(427\) | 11.3086 | 0.547259 | ||||||||
\(428\) | −18.7433 | −0.905990 | ||||||||
\(429\) | −81.4033 | −3.93019 | ||||||||
\(430\) | −2.80169 | −0.135110 | ||||||||
\(431\) | −17.3422 | −0.835346 | −0.417673 | − | 0.908597i | \(-0.637154\pi\) | ||||
−0.417673 | + | 0.908597i | \(0.637154\pi\) | |||||||
\(432\) | −5.54041 | −0.266563 | ||||||||
\(433\) | 23.7963 | 1.14358 | 0.571789 | − | 0.820400i | \(-0.306249\pi\) | ||||
0.571789 | + | 0.820400i | \(0.306249\pi\) | |||||||
\(434\) | 16.8156 | 0.807175 | ||||||||
\(435\) | −7.14782 | −0.342712 | ||||||||
\(436\) | −13.3799 | −0.640780 | ||||||||
\(437\) | 3.57463 | 0.170998 | ||||||||
\(438\) | −42.1035 | −2.01178 | ||||||||
\(439\) | 1.12925 | 0.0538962 | 0.0269481 | − | 0.999637i | \(-0.491421\pi\) | ||||
0.0269481 | + | 0.999637i | \(0.491421\pi\) | |||||||
\(440\) | −9.52588 | −0.454129 | ||||||||
\(441\) | 10.8219 | 0.515330 | ||||||||
\(442\) | −28.9805 | −1.37846 | ||||||||
\(443\) | 2.94603 | 0.139970 | 0.0699852 | − | 0.997548i | \(-0.477705\pi\) | ||||
0.0699852 | + | 0.997548i | \(0.477705\pi\) | |||||||
\(444\) | −13.7612 | −0.653078 | ||||||||
\(445\) | −25.8499 | −1.22540 | ||||||||
\(446\) | −2.83838 | −0.134401 | ||||||||
\(447\) | 66.8146 | 3.16022 | ||||||||
\(448\) | 3.02991 | 0.143150 | ||||||||
\(449\) | 18.2475 | 0.861151 | 0.430576 | − | 0.902554i | \(-0.358311\pi\) | ||||
0.430576 | + | 0.902554i | \(0.358311\pi\) | |||||||
\(450\) | 14.1791 | 0.668410 | ||||||||
\(451\) | 42.9745 | 2.02359 | ||||||||
\(452\) | −9.12519 | −0.429213 | ||||||||
\(453\) | −27.7393 | −1.30331 | ||||||||
\(454\) | 12.8931 | 0.605102 | ||||||||
\(455\) | 19.6647 | 0.921897 | ||||||||
\(456\) | −4.60577 | −0.215685 | ||||||||
\(457\) | −30.3549 | −1.41994 | −0.709970 | − | 0.704232i | \(-0.751292\pi\) | ||||
−0.709970 | + | 0.704232i | \(0.751292\pi\) | |||||||
\(458\) | 4.75894 | 0.222371 | ||||||||
\(459\) | 36.2180 | 1.69051 | ||||||||
\(460\) | 3.20635 | 0.149497 | ||||||||
\(461\) | 15.2365 | 0.709633 | 0.354817 | − | 0.934936i | \(-0.384543\pi\) | ||||
0.354817 | + | 0.934936i | \(0.384543\pi\) | |||||||
\(462\) | −55.6351 | −2.58838 | ||||||||
\(463\) | 34.5415 | 1.60528 | 0.802641 | − | 0.596463i | \(-0.203428\pi\) | ||||
0.802641 | + | 0.596463i | \(0.203428\pi\) | |||||||
\(464\) | −1.73018 | −0.0803217 | ||||||||
\(465\) | −22.9279 | −1.06326 | ||||||||
\(466\) | 24.6821 | 1.14338 | ||||||||
\(467\) | −3.04551 | −0.140929 | −0.0704647 | − | 0.997514i | \(-0.522448\pi\) | ||||
−0.0704647 | + | 0.997514i | \(0.522448\pi\) | |||||||
\(468\) | −22.0038 | −1.01713 | ||||||||
\(469\) | −42.5427 | −1.96444 | ||||||||
\(470\) | 10.4489 | 0.481973 | ||||||||
\(471\) | 27.9685 | 1.28872 | ||||||||
\(472\) | 10.9135 | 0.502335 | ||||||||
\(473\) | 12.4525 | 0.572568 | ||||||||
\(474\) | 5.47124 | 0.251303 | ||||||||
\(475\) | 4.66263 | 0.213936 | ||||||||
\(476\) | −19.8067 | −0.907839 | ||||||||
\(477\) | 8.06597 | 0.369315 | ||||||||
\(478\) | −4.15919 | −0.190237 | ||||||||
\(479\) | −38.6905 | −1.76781 | −0.883907 | − | 0.467663i | \(-0.845096\pi\) | ||||
−0.883907 | + | 0.467663i | \(0.845096\pi\) | |||||||
\(480\) | −4.13125 | −0.188565 | ||||||||
\(481\) | −21.6188 | −0.985735 | ||||||||
\(482\) | −21.2315 | −0.967067 | ||||||||
\(483\) | 18.7264 | 0.852080 | ||||||||
\(484\) | 31.3391 | 1.42451 | ||||||||
\(485\) | −20.5102 | −0.931321 | ||||||||
\(486\) | −14.5197 | −0.658629 | ||||||||
\(487\) | −4.11267 | −0.186363 | −0.0931814 | − | 0.995649i | \(-0.529704\pi\) | ||||
−0.0931814 | + | 0.995649i | \(0.529704\pi\) | |||||||
\(488\) | −3.73230 | −0.168953 | ||||||||
\(489\) | 32.6698 | 1.47738 | ||||||||
\(490\) | 3.19202 | 0.144201 | ||||||||
\(491\) | 14.2410 | 0.642688 | 0.321344 | − | 0.946963i | \(-0.395865\pi\) | ||||
0.321344 | + | 0.946963i | \(0.395865\pi\) | |||||||
\(492\) | 18.6375 | 0.840242 | ||||||||
\(493\) | 11.3103 | 0.509390 | ||||||||
\(494\) | −7.23567 | −0.325548 | ||||||||
\(495\) | 47.2802 | 2.12509 | ||||||||
\(496\) | −5.54987 | −0.249196 | ||||||||
\(497\) | −21.7344 | −0.974923 | ||||||||
\(498\) | −10.8902 | −0.488000 | ||||||||
\(499\) | −8.77860 | −0.392984 | −0.196492 | − | 0.980505i | \(-0.562955\pi\) | ||||
−0.196492 | + | 0.980505i | \(0.562955\pi\) | |||||||
\(500\) | 11.5021 | 0.514391 | ||||||||
\(501\) | 0.916103 | 0.0409285 | ||||||||
\(502\) | 14.0693 | 0.627944 | ||||||||
\(503\) | −13.7681 | −0.613891 | −0.306946 | − | 0.951727i | \(-0.599307\pi\) | ||||
−0.306946 | + | 0.951727i | \(0.599307\pi\) | |||||||
\(504\) | −15.0385 | −0.669867 | ||||||||
\(505\) | 25.5503 | 1.13697 | ||||||||
\(506\) | −14.2511 | −0.633537 | ||||||||
\(507\) | −18.7767 | −0.833902 | ||||||||
\(508\) | −19.6183 | −0.870420 | ||||||||
\(509\) | −28.3985 | −1.25874 | −0.629371 | − | 0.777105i | \(-0.716688\pi\) | ||||
−0.629371 | + | 0.777105i | \(0.716688\pi\) | |||||||
\(510\) | 27.0062 | 1.19586 | ||||||||
\(511\) | −45.2065 | −1.99982 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 9.04268 | 0.399244 | ||||||||
\(514\) | 17.5882 | 0.775783 | ||||||||
\(515\) | −12.6048 | −0.555436 | ||||||||
\(516\) | 5.40050 | 0.237744 | ||||||||
\(517\) | −46.4417 | −2.04251 | ||||||||
\(518\) | −14.7754 | −0.649194 | ||||||||
\(519\) | 15.2052 | 0.667434 | ||||||||
\(520\) | −6.49020 | −0.284614 | ||||||||
\(521\) | −25.1560 | −1.10211 | −0.551053 | − | 0.834470i | \(-0.685774\pi\) | ||||
−0.551053 | + | 0.834470i | \(0.685774\pi\) | |||||||
\(522\) | 8.58748 | 0.375864 | ||||||||
\(523\) | −14.5445 | −0.635987 | −0.317993 | − | 0.948093i | \(-0.603009\pi\) | ||||
−0.317993 | + | 0.948093i | \(0.603009\pi\) | |||||||
\(524\) | 14.9845 | 0.654601 | ||||||||
\(525\) | 24.4261 | 1.06604 | ||||||||
\(526\) | −19.4248 | −0.846960 | ||||||||
\(527\) | 36.2798 | 1.58037 | ||||||||
\(528\) | 18.3619 | 0.799101 | ||||||||
\(529\) | −18.2032 | −0.791443 | ||||||||
\(530\) | 2.37912 | 0.103342 | ||||||||
\(531\) | −54.1674 | −2.35067 | ||||||||
\(532\) | −4.94522 | −0.214402 | ||||||||
\(533\) | 29.2795 | 1.26823 | ||||||||
\(534\) | 49.8279 | 2.15626 | ||||||||
\(535\) | 27.4397 | 1.18632 | ||||||||
\(536\) | 14.0409 | 0.606474 | ||||||||
\(537\) | −41.8575 | −1.80628 | ||||||||
\(538\) | −11.6592 | −0.502663 | ||||||||
\(539\) | −14.1874 | −0.611094 | ||||||||
\(540\) | 8.11104 | 0.349044 | ||||||||
\(541\) | 8.27359 | 0.355709 | 0.177855 | − | 0.984057i | \(-0.443084\pi\) | ||||
0.177855 | + | 0.984057i | \(0.443084\pi\) | |||||||
\(542\) | 12.7256 | 0.546611 | ||||||||
\(543\) | 25.2680 | 1.08435 | ||||||||
\(544\) | 6.53706 | 0.280274 | ||||||||
\(545\) | 19.5878 | 0.839051 | ||||||||
\(546\) | −37.9054 | −1.62220 | ||||||||
\(547\) | −23.8217 | −1.01854 | −0.509271 | − | 0.860606i | \(-0.670085\pi\) | ||||
−0.509271 | + | 0.860606i | \(0.670085\pi\) | |||||||
\(548\) | −19.9718 | −0.853152 | ||||||||
\(549\) | 18.5247 | 0.790614 | ||||||||
\(550\) | −18.5886 | −0.792620 | ||||||||
\(551\) | 2.82388 | 0.120302 | ||||||||
\(552\) | −6.18050 | −0.263060 | ||||||||
\(553\) | 5.87447 | 0.249808 | ||||||||
\(554\) | 12.1068 | 0.514370 | ||||||||
\(555\) | 20.1461 | 0.855154 | ||||||||
\(556\) | 21.5488 | 0.913873 | ||||||||
\(557\) | −24.3767 | −1.03287 | −0.516436 | − | 0.856326i | \(-0.672742\pi\) | ||||
−0.516436 | + | 0.856326i | \(0.672742\pi\) | |||||||
\(558\) | 27.5459 | 1.16611 | ||||||||
\(559\) | 8.48418 | 0.358843 | ||||||||
\(560\) | −4.43572 | −0.187444 | ||||||||
\(561\) | −120.033 | −5.06780 | ||||||||
\(562\) | −23.7004 | −0.999741 | ||||||||
\(563\) | 9.84571 | 0.414947 | 0.207474 | − | 0.978241i | \(-0.433476\pi\) | ||||
0.207474 | + | 0.978241i | \(0.433476\pi\) | |||||||
\(564\) | −20.1412 | −0.848097 | ||||||||
\(565\) | 13.3591 | 0.562020 | ||||||||
\(566\) | −30.9156 | −1.29948 | ||||||||
\(567\) | 2.25638 | 0.0947589 | ||||||||
\(568\) | 7.17329 | 0.300984 | ||||||||
\(569\) | −2.95663 | −0.123948 | −0.0619741 | − | 0.998078i | \(-0.519740\pi\) | ||||
−0.0619741 | + | 0.998078i | \(0.519740\pi\) | |||||||
\(570\) | 6.74275 | 0.282423 | ||||||||
\(571\) | −28.3270 | −1.18545 | −0.592723 | − | 0.805406i | \(-0.701947\pi\) | ||||
−0.592723 | + | 0.805406i | \(0.701947\pi\) | |||||||
\(572\) | 28.8466 | 1.20614 | ||||||||
\(573\) | −55.7305 | −2.32817 | ||||||||
\(574\) | 20.0110 | 0.835245 | ||||||||
\(575\) | 6.25679 | 0.260926 | ||||||||
\(576\) | 4.96334 | 0.206806 | ||||||||
\(577\) | −19.7791 | −0.823415 | −0.411708 | − | 0.911316i | \(-0.635067\pi\) | ||||
−0.411708 | + | 0.911316i | \(0.635067\pi\) | |||||||
\(578\) | −25.7331 | −1.07036 | ||||||||
\(579\) | −15.8462 | −0.658548 | ||||||||
\(580\) | 2.53295 | 0.105175 | ||||||||
\(581\) | −11.6928 | −0.485097 | ||||||||
\(582\) | 39.5351 | 1.63878 | ||||||||
\(583\) | −10.5743 | −0.437945 | ||||||||
\(584\) | 14.9201 | 0.617397 | ||||||||
\(585\) | 32.2130 | 1.33184 | ||||||||
\(586\) | −18.0475 | −0.745534 | ||||||||
\(587\) | 40.1016 | 1.65517 | 0.827585 | − | 0.561341i | \(-0.189714\pi\) | ||||
0.827585 | + | 0.561341i | \(0.189714\pi\) | |||||||
\(588\) | −6.15288 | −0.253741 | ||||||||
\(589\) | 9.05811 | 0.373233 | ||||||||
\(590\) | −15.9771 | −0.657768 | ||||||||
\(591\) | 43.2368 | 1.77852 | ||||||||
\(592\) | 4.87651 | 0.200423 | ||||||||
\(593\) | 31.0164 | 1.27369 | 0.636845 | − | 0.770992i | \(-0.280239\pi\) | ||||
0.636845 | + | 0.770992i | \(0.280239\pi\) | |||||||
\(594\) | −36.0507 | −1.47918 | ||||||||
\(595\) | 28.9966 | 1.18874 | ||||||||
\(596\) | −23.6769 | −0.969842 | ||||||||
\(597\) | −6.03128 | −0.246844 | ||||||||
\(598\) | −9.70957 | −0.397054 | ||||||||
\(599\) | −10.3984 | −0.424868 | −0.212434 | − | 0.977175i | \(-0.568139\pi\) | ||||
−0.212434 | + | 0.977175i | \(0.568139\pi\) | |||||||
\(600\) | −8.06163 | −0.329115 | ||||||||
\(601\) | 42.9806 | 1.75321 | 0.876607 | − | 0.481207i | \(-0.159802\pi\) | ||||
0.876607 | + | 0.481207i | \(0.159802\pi\) | |||||||
\(602\) | 5.79851 | 0.236330 | ||||||||
\(603\) | −69.6897 | −2.83798 | ||||||||
\(604\) | 9.82987 | 0.399972 | ||||||||
\(605\) | −45.8798 | −1.86528 | ||||||||
\(606\) | −49.2504 | −2.00066 | ||||||||
\(607\) | 33.3003 | 1.35162 | 0.675808 | − | 0.737078i | \(-0.263795\pi\) | ||||
0.675808 | + | 0.737078i | \(0.263795\pi\) | |||||||
\(608\) | 1.63213 | 0.0661917 | ||||||||
\(609\) | 14.7935 | 0.599461 | ||||||||
\(610\) | 5.46400 | 0.221231 | ||||||||
\(611\) | −31.6418 | −1.28009 | ||||||||
\(612\) | −32.4456 | −1.31154 | ||||||||
\(613\) | 2.63315 | 0.106352 | 0.0531759 | − | 0.998585i | \(-0.483066\pi\) | ||||
0.0531759 | + | 0.998585i | \(0.483066\pi\) | |||||||
\(614\) | −14.2676 | −0.575795 | ||||||||
\(615\) | −27.2848 | −1.10023 | ||||||||
\(616\) | 19.7152 | 0.794348 | ||||||||
\(617\) | 35.6454 | 1.43503 | 0.717516 | − | 0.696542i | \(-0.245279\pi\) | ||||
0.717516 | + | 0.696542i | \(0.245279\pi\) | |||||||
\(618\) | 24.2969 | 0.977365 | ||||||||
\(619\) | 33.9716 | 1.36544 | 0.682718 | − | 0.730682i | \(-0.260798\pi\) | ||||
0.682718 | + | 0.730682i | \(0.260798\pi\) | |||||||
\(620\) | 8.12488 | 0.326303 | ||||||||
\(621\) | 12.1344 | 0.486937 | ||||||||
\(622\) | −27.8016 | −1.11474 | ||||||||
\(623\) | 53.5001 | 2.14344 | ||||||||
\(624\) | 12.5104 | 0.500817 | ||||||||
\(625\) | −2.55500 | −0.102200 | ||||||||
\(626\) | 14.5793 | 0.582706 | ||||||||
\(627\) | −29.9691 | −1.19685 | ||||||||
\(628\) | −9.91111 | −0.395496 | ||||||||
\(629\) | −31.8780 | −1.27106 | ||||||||
\(630\) | 22.0160 | 0.877138 | ||||||||
\(631\) | 32.0822 | 1.27717 | 0.638586 | − | 0.769550i | \(-0.279520\pi\) | ||||
0.638586 | + | 0.769550i | \(0.279520\pi\) | |||||||
\(632\) | −1.93882 | −0.0771223 | ||||||||
\(633\) | −25.7166 | −1.02214 | ||||||||
\(634\) | 10.6348 | 0.422362 | ||||||||
\(635\) | 28.7207 | 1.13975 | ||||||||
\(636\) | −4.58596 | −0.181845 | ||||||||
\(637\) | −9.66618 | −0.382988 | ||||||||
\(638\) | −11.2580 | −0.445710 | ||||||||
\(639\) | −35.6034 | −1.40845 | ||||||||
\(640\) | 1.46398 | 0.0578688 | ||||||||
\(641\) | 43.3843 | 1.71358 | 0.856788 | − | 0.515668i | \(-0.172456\pi\) | ||||
0.856788 | + | 0.515668i | \(0.172456\pi\) | |||||||
\(642\) | −52.8923 | −2.08749 | ||||||||
\(643\) | −37.9867 | −1.49805 | −0.749026 | − | 0.662541i | \(-0.769478\pi\) | ||||
−0.749026 | + | 0.662541i | \(0.769478\pi\) | |||||||
\(644\) | −6.63600 | −0.261495 | ||||||||
\(645\) | −7.90621 | −0.311307 | ||||||||
\(646\) | −10.6693 | −0.419779 | ||||||||
\(647\) | 20.3732 | 0.800953 | 0.400477 | − | 0.916307i | \(-0.368845\pi\) | ||||
0.400477 | + | 0.916307i | \(0.368845\pi\) | |||||||
\(648\) | −0.744700 | −0.0292546 | ||||||||
\(649\) | 71.0126 | 2.78749 | ||||||||
\(650\) | −12.6648 | −0.496755 | ||||||||
\(651\) | 47.4526 | 1.85982 | ||||||||
\(652\) | −11.5771 | −0.453393 | ||||||||
\(653\) | 43.5596 | 1.70462 | 0.852310 | − | 0.523036i | \(-0.175201\pi\) | ||||
0.852310 | + | 0.523036i | \(0.175201\pi\) | |||||||
\(654\) | −37.7572 | −1.47642 | ||||||||
\(655\) | −21.9370 | −0.857148 | ||||||||
\(656\) | −6.60449 | −0.257862 | ||||||||
\(657\) | −74.0533 | −2.88910 | ||||||||
\(658\) | −21.6256 | −0.843052 | ||||||||
\(659\) | 13.1273 | 0.511369 | 0.255684 | − | 0.966760i | \(-0.417699\pi\) | ||||
0.255684 | + | 0.966760i | \(0.417699\pi\) | |||||||
\(660\) | −26.8815 | −1.04636 | ||||||||
\(661\) | 1.46238 | 0.0568799 | 0.0284400 | − | 0.999596i | \(-0.490946\pi\) | ||||
0.0284400 | + | 0.999596i | \(0.490946\pi\) | |||||||
\(662\) | 10.1390 | 0.394063 | ||||||||
\(663\) | −81.7812 | −3.17612 | ||||||||
\(664\) | 3.85911 | 0.149762 | ||||||||
\(665\) | 7.23968 | 0.280743 | ||||||||
\(666\) | −24.2038 | −0.937876 | ||||||||
\(667\) | 3.78938 | 0.146725 | ||||||||
\(668\) | −0.324636 | −0.0125606 | ||||||||
\(669\) | −8.00973 | −0.309674 | ||||||||
\(670\) | −20.5555 | −0.794130 | ||||||||
\(671\) | −24.2855 | −0.937533 | ||||||||
\(672\) | 8.55023 | 0.329832 | ||||||||
\(673\) | −14.6230 | −0.563675 | −0.281837 | − | 0.959462i | \(-0.590944\pi\) | ||||
−0.281837 | + | 0.959462i | \(0.590944\pi\) | |||||||
\(674\) | 0.725346 | 0.0279393 | ||||||||
\(675\) | 15.8277 | 0.609208 | ||||||||
\(676\) | 6.65383 | 0.255916 | ||||||||
\(677\) | −42.6209 | −1.63805 | −0.819026 | − | 0.573756i | \(-0.805486\pi\) | ||||
−0.819026 | + | 0.573756i | \(0.805486\pi\) | |||||||
\(678\) | −25.7507 | −0.988950 | ||||||||
\(679\) | 42.4489 | 1.62904 | ||||||||
\(680\) | −9.57010 | −0.366997 | ||||||||
\(681\) | 36.3835 | 1.39422 | ||||||||
\(682\) | −36.1122 | −1.38281 | ||||||||
\(683\) | −2.62888 | −0.100591 | −0.0502957 | − | 0.998734i | \(-0.516016\pi\) | ||||
−0.0502957 | + | 0.998734i | \(0.516016\pi\) | |||||||
\(684\) | −8.10082 | −0.309742 | ||||||||
\(685\) | 29.2382 | 1.11714 | ||||||||
\(686\) | 14.6030 | 0.557547 | ||||||||
\(687\) | 13.4294 | 0.512365 | ||||||||
\(688\) | −1.91376 | −0.0729613 | ||||||||
\(689\) | −7.20454 | −0.274471 | ||||||||
\(690\) | 9.04812 | 0.344456 | ||||||||
\(691\) | −8.97368 | −0.341375 | −0.170687 | − | 0.985325i | \(-0.554599\pi\) | ||||
−0.170687 | + | 0.985325i | \(0.554599\pi\) | |||||||
\(692\) | −5.38821 | −0.204829 | ||||||||
\(693\) | −97.8532 | −3.71714 | ||||||||
\(694\) | −5.00784 | −0.190095 | ||||||||
\(695\) | −31.5470 | −1.19664 | ||||||||
\(696\) | −4.88247 | −0.185069 | ||||||||
\(697\) | 43.1740 | 1.63533 | ||||||||
\(698\) | 20.8257 | 0.788264 | ||||||||
\(699\) | 69.6515 | 2.63446 | ||||||||
\(700\) | −8.65577 | −0.327157 | ||||||||
\(701\) | 9.80744 | 0.370422 | 0.185211 | − | 0.982699i | \(-0.440703\pi\) | ||||
0.185211 | + | 0.982699i | \(0.440703\pi\) | |||||||
\(702\) | −24.5621 | −0.927037 | ||||||||
\(703\) | −7.95910 | −0.300183 | ||||||||
\(704\) | −6.50685 | −0.245236 | ||||||||
\(705\) | 29.4862 | 1.11052 | ||||||||
\(706\) | 7.66220 | 0.288371 | ||||||||
\(707\) | −52.8801 | −1.98876 | ||||||||
\(708\) | 30.7973 | 1.15743 | ||||||||
\(709\) | 34.8451 | 1.30864 | 0.654318 | − | 0.756219i | \(-0.272956\pi\) | ||||
0.654318 | + | 0.756219i | \(0.272956\pi\) | |||||||
\(710\) | −10.5015 | −0.394115 | ||||||||
\(711\) | 9.62304 | 0.360892 | ||||||||
\(712\) | −17.6573 | −0.661736 | ||||||||
\(713\) | 12.1551 | 0.455213 | ||||||||
\(714\) | −55.8933 | −2.09176 | ||||||||
\(715\) | −42.2308 | −1.57934 | ||||||||
\(716\) | 14.8329 | 0.554331 | ||||||||
\(717\) | −11.7370 | −0.438325 | ||||||||
\(718\) | −0.236658 | −0.00883200 | ||||||||
\(719\) | −5.44164 | −0.202939 | −0.101469 | − | 0.994839i | \(-0.532354\pi\) | ||||
−0.101469 | + | 0.994839i | \(0.532354\pi\) | |||||||
\(720\) | −7.26621 | −0.270796 | ||||||||
\(721\) | 26.0876 | 0.971552 | ||||||||
\(722\) | 16.3361 | 0.607968 | ||||||||
\(723\) | −59.9139 | −2.22822 | ||||||||
\(724\) | −8.95412 | −0.332777 | ||||||||
\(725\) | 4.94274 | 0.183569 | ||||||||
\(726\) | 88.4371 | 3.28221 | ||||||||
\(727\) | −29.1055 | −1.07946 | −0.539732 | − | 0.841837i | \(-0.681474\pi\) | ||||
−0.539732 | + | 0.841837i | \(0.681474\pi\) | |||||||
\(728\) | 13.4324 | 0.497838 | ||||||||
\(729\) | −43.2079 | −1.60029 | ||||||||
\(730\) | −21.8426 | −0.808432 | ||||||||
\(731\) | 12.5103 | 0.462711 | ||||||||
\(732\) | −10.5323 | −0.389286 | ||||||||
\(733\) | −23.7742 | −0.878121 | −0.439061 | − | 0.898457i | \(-0.644689\pi\) | ||||
−0.439061 | + | 0.898457i | \(0.644689\pi\) | |||||||
\(734\) | −29.6537 | −1.09454 | ||||||||
\(735\) | 9.00768 | 0.332253 | ||||||||
\(736\) | 2.19016 | 0.0807305 | ||||||||
\(737\) | 91.3621 | 3.36537 | ||||||||
\(738\) | 32.7803 | 1.20666 | ||||||||
\(739\) | −10.0885 | −0.371112 | −0.185556 | − | 0.982634i | \(-0.559409\pi\) | ||||
−0.185556 | + | 0.982634i | \(0.559409\pi\) | |||||||
\(740\) | −7.13910 | −0.262438 | ||||||||
\(741\) | −20.4186 | −0.750096 | ||||||||
\(742\) | −4.92394 | −0.180764 | ||||||||
\(743\) | 6.05747 | 0.222227 | 0.111113 | − | 0.993808i | \(-0.464558\pi\) | ||||
0.111113 | + | 0.993808i | \(0.464558\pi\) | |||||||
\(744\) | −15.6614 | −0.574174 | ||||||||
\(745\) | 34.6624 | 1.26993 | ||||||||
\(746\) | 21.5425 | 0.788728 | ||||||||
\(747\) | −19.1540 | −0.700810 | ||||||||
\(748\) | 42.5357 | 1.55526 | ||||||||
\(749\) | −56.7905 | −2.07508 | ||||||||
\(750\) | 32.4583 | 1.18521 | ||||||||
\(751\) | −0.00557344 | −0.000203378 0 | −0.000101689 | − | 1.00000i | \(-0.500032\pi\) | ||||
−0.000101689 | 1.00000i | \(0.500032\pi\) | ||||||||
\(752\) | 7.13736 | 0.260273 | ||||||||
\(753\) | 39.7027 | 1.44685 | ||||||||
\(754\) | −7.67035 | −0.279338 | ||||||||
\(755\) | −14.3907 | −0.523731 | ||||||||
\(756\) | −16.7870 | −0.610536 | ||||||||
\(757\) | −48.1829 | −1.75124 | −0.875620 | − | 0.483001i | \(-0.839547\pi\) | ||||
−0.875620 | + | 0.483001i | \(0.839547\pi\) | |||||||
\(758\) | 1.63867 | 0.0595192 | ||||||||
\(759\) | −40.2156 | −1.45974 | ||||||||
\(760\) | −2.38940 | −0.0866727 | ||||||||
\(761\) | 27.1909 | 0.985671 | 0.492835 | − | 0.870123i | \(-0.335960\pi\) | ||||
0.492835 | + | 0.870123i | \(0.335960\pi\) | |||||||
\(762\) | −55.3616 | −2.00554 | ||||||||
\(763\) | −40.5399 | −1.46764 | ||||||||
\(764\) | 19.7490 | 0.714494 | ||||||||
\(765\) | 47.4996 | 1.71735 | ||||||||
\(766\) | 14.3630 | 0.518955 | ||||||||
\(767\) | 48.3825 | 1.74699 | ||||||||
\(768\) | −2.82194 | −0.101828 | ||||||||
\(769\) | −2.59541 | −0.0935928 | −0.0467964 | − | 0.998904i | \(-0.514901\pi\) | ||||
−0.0467964 | + | 0.998904i | \(0.514901\pi\) | |||||||
\(770\) | −28.8626 | −1.04014 | ||||||||
\(771\) | 49.6329 | 1.78748 | ||||||||
\(772\) | 5.61538 | 0.202102 | ||||||||
\(773\) | 10.5331 | 0.378849 | 0.189424 | − | 0.981895i | \(-0.439338\pi\) | ||||
0.189424 | + | 0.981895i | \(0.439338\pi\) | |||||||
\(774\) | 9.49861 | 0.341421 | ||||||||
\(775\) | 15.8547 | 0.569518 | ||||||||
\(776\) | −14.0099 | −0.502927 | ||||||||
\(777\) | −41.6953 | −1.49581 | ||||||||
\(778\) | −10.0688 | −0.360983 | ||||||||
\(779\) | 10.7794 | 0.386212 | ||||||||
\(780\) | −18.3149 | −0.655780 | ||||||||
\(781\) | 46.6755 | 1.67018 | ||||||||
\(782\) | −14.3172 | −0.511983 | ||||||||
\(783\) | 9.58593 | 0.342573 | ||||||||
\(784\) | 2.18037 | 0.0778705 | ||||||||
\(785\) | 14.5096 | 0.517871 | ||||||||
\(786\) | 42.2853 | 1.50827 | ||||||||
\(787\) | −5.41002 | −0.192846 | −0.0964232 | − | 0.995340i | \(-0.530740\pi\) | ||||
−0.0964232 | + | 0.995340i | \(0.530740\pi\) | |||||||
\(788\) | −15.3217 | −0.545811 | ||||||||
\(789\) | −54.8155 | −1.95148 | ||||||||
\(790\) | 2.83839 | 0.100986 | ||||||||
\(791\) | −27.6485 | −0.983068 | ||||||||
\(792\) | 32.2957 | 1.14758 | ||||||||
\(793\) | −16.5463 | −0.587576 | ||||||||
\(794\) | −15.5768 | −0.552799 | ||||||||
\(795\) | 6.71374 | 0.238112 | ||||||||
\(796\) | 2.13728 | 0.0757540 | ||||||||
\(797\) | 27.6755 | 0.980315 | 0.490158 | − | 0.871634i | \(-0.336939\pi\) | ||||
0.490158 | + | 0.871634i | \(0.336939\pi\) | |||||||
\(798\) | −13.9551 | −0.494005 | ||||||||
\(799\) | −46.6573 | −1.65062 | ||||||||
\(800\) | 2.85677 | 0.101002 | ||||||||
\(801\) | 87.6392 | 3.09658 | ||||||||
\(802\) | 25.0146 | 0.883296 | ||||||||
\(803\) | 97.0827 | 3.42597 | ||||||||
\(804\) | 39.6225 | 1.39738 | ||||||||
\(805\) | 9.71496 | 0.342407 | ||||||||
\(806\) | −24.6040 | −0.866640 | ||||||||
\(807\) | −32.9015 | −1.15819 | ||||||||
\(808\) | 17.4527 | 0.613983 | ||||||||
\(809\) | 2.24454 | 0.0789137 | 0.0394569 | − | 0.999221i | \(-0.487437\pi\) | ||||
0.0394569 | + | 0.999221i | \(0.487437\pi\) | |||||||
\(810\) | 1.09022 | 0.0383065 | ||||||||
\(811\) | 40.3802 | 1.41794 | 0.708970 | − | 0.705239i | \(-0.249160\pi\) | ||||
0.708970 | + | 0.705239i | \(0.249160\pi\) | |||||||
\(812\) | −5.24230 | −0.183969 | ||||||||
\(813\) | 35.9108 | 1.25945 | ||||||||
\(814\) | 31.7307 | 1.11216 | ||||||||
\(815\) | 16.9486 | 0.593683 | ||||||||
\(816\) | 18.4472 | 0.645780 | ||||||||
\(817\) | 3.12350 | 0.109277 | ||||||||
\(818\) | −0.455269 | −0.0159181 | ||||||||
\(819\) | −66.6695 | −2.32962 | ||||||||
\(820\) | 9.66883 | 0.337650 | ||||||||
\(821\) | −4.76420 | −0.166272 | −0.0831359 | − | 0.996538i | \(-0.526494\pi\) | ||||
−0.0831359 | + | 0.996538i | \(0.526494\pi\) | |||||||
\(822\) | −56.3591 | −1.96575 | ||||||||
\(823\) | −17.5536 | −0.611878 | −0.305939 | − | 0.952051i | \(-0.598970\pi\) | ||||
−0.305939 | + | 0.952051i | \(0.598970\pi\) | |||||||
\(824\) | −8.61001 | −0.299944 | ||||||||
\(825\) | −52.4559 | −1.82628 | ||||||||
\(826\) | 33.0670 | 1.15055 | ||||||||
\(827\) | −0.515239 | −0.0179166 | −0.00895830 | − | 0.999960i | \(-0.502852\pi\) | ||||
−0.00895830 | + | 0.999960i | \(0.502852\pi\) | |||||||
\(828\) | −10.8705 | −0.377776 | ||||||||
\(829\) | 5.53341 | 0.192183 | 0.0960916 | − | 0.995373i | \(-0.469366\pi\) | ||||
0.0960916 | + | 0.995373i | \(0.469366\pi\) | |||||||
\(830\) | −5.64964 | −0.196102 | ||||||||
\(831\) | 34.1647 | 1.18516 | ||||||||
\(832\) | −4.43326 | −0.153696 | ||||||||
\(833\) | −14.2532 | −0.493845 | ||||||||
\(834\) | 60.8094 | 2.10566 | ||||||||
\(835\) | 0.475260 | 0.0164470 | ||||||||
\(836\) | 10.6200 | 0.367302 | ||||||||
\(837\) | 30.7486 | 1.06283 | ||||||||
\(838\) | 3.12795 | 0.108053 | ||||||||
\(839\) | 39.2550 | 1.35523 | 0.677617 | − | 0.735415i | \(-0.263013\pi\) | ||||
0.677617 | + | 0.735415i | \(0.263013\pi\) | |||||||
\(840\) | −12.5173 | −0.431889 | ||||||||
\(841\) | −26.0065 | −0.896775 | ||||||||
\(842\) | 11.3086 | 0.389719 | ||||||||
\(843\) | −66.8811 | −2.30351 | ||||||||
\(844\) | 9.11310 | 0.313686 | ||||||||
\(845\) | −9.74105 | −0.335102 | ||||||||
\(846\) | −35.4251 | −1.21794 | ||||||||
\(847\) | 94.9549 | 3.26269 | ||||||||
\(848\) | 1.62511 | 0.0558065 | ||||||||
\(849\) | −87.2419 | −2.99413 | ||||||||
\(850\) | −18.6749 | −0.640543 | ||||||||
\(851\) | −10.6803 | −0.366118 | ||||||||
\(852\) | 20.2426 | 0.693499 | ||||||||
\(853\) | −55.4202 | −1.89755 | −0.948776 | − | 0.315950i | \(-0.897677\pi\) | ||||
−0.948776 | + | 0.315950i | \(0.897677\pi\) | |||||||
\(854\) | −11.3086 | −0.386971 | ||||||||
\(855\) | 11.8594 | 0.405583 | ||||||||
\(856\) | 18.7433 | 0.640631 | ||||||||
\(857\) | −15.8070 | −0.539958 | −0.269979 | − | 0.962866i | \(-0.587017\pi\) | ||||
−0.269979 | + | 0.962866i | \(0.587017\pi\) | |||||||
\(858\) | 81.4033 | 2.77906 | ||||||||
\(859\) | 24.9610 | 0.851659 | 0.425829 | − | 0.904804i | \(-0.359982\pi\) | ||||
0.425829 | + | 0.904804i | \(0.359982\pi\) | |||||||
\(860\) | 2.80169 | 0.0955370 | ||||||||
\(861\) | 56.4699 | 1.92449 | ||||||||
\(862\) | 17.3422 | 0.590679 | ||||||||
\(863\) | 27.8446 | 0.947841 | 0.473921 | − | 0.880568i | \(-0.342838\pi\) | ||||
0.473921 | + | 0.880568i | \(0.342838\pi\) | |||||||
\(864\) | 5.54041 | 0.188489 | ||||||||
\(865\) | 7.88821 | 0.268207 | ||||||||
\(866\) | −23.7963 | −0.808632 | ||||||||
\(867\) | −72.6172 | −2.46621 | ||||||||
\(868\) | −16.8156 | −0.570759 | ||||||||
\(869\) | −12.6156 | −0.427957 | ||||||||
\(870\) | 7.14782 | 0.242334 | ||||||||
\(871\) | 62.2470 | 2.10916 | ||||||||
\(872\) | 13.3799 | 0.453100 | ||||||||
\(873\) | 69.5360 | 2.35344 | ||||||||
\(874\) | −3.57463 | −0.120914 | ||||||||
\(875\) | 34.8505 | 1.17816 | ||||||||
\(876\) | 42.1035 | 1.42255 | ||||||||
\(877\) | −34.6702 | −1.17073 | −0.585365 | − | 0.810770i | \(-0.699049\pi\) | ||||
−0.585365 | + | 0.810770i | \(0.699049\pi\) | |||||||
\(878\) | −1.12925 | −0.0381104 | ||||||||
\(879\) | −50.9289 | −1.71779 | ||||||||
\(880\) | 9.52588 | 0.321117 | ||||||||
\(881\) | −13.7252 | −0.462415 | −0.231208 | − | 0.972904i | \(-0.574268\pi\) | ||||
−0.231208 | + | 0.972904i | \(0.574268\pi\) | |||||||
\(882\) | −10.8219 | −0.364393 | ||||||||
\(883\) | 17.1895 | 0.578472 | 0.289236 | − | 0.957258i | \(-0.406599\pi\) | ||||
0.289236 | + | 0.957258i | \(0.406599\pi\) | |||||||
\(884\) | 28.9805 | 0.974720 | ||||||||
\(885\) | −45.0865 | −1.51557 | ||||||||
\(886\) | −2.94603 | −0.0989740 | ||||||||
\(887\) | −37.9003 | −1.27257 | −0.636284 | − | 0.771455i | \(-0.719529\pi\) | ||||
−0.636284 | + | 0.771455i | \(0.719529\pi\) | |||||||
\(888\) | 13.7612 | 0.461796 | ||||||||
\(889\) | −59.4417 | −1.99361 | ||||||||
\(890\) | 25.8499 | 0.866491 | ||||||||
\(891\) | −4.84565 | −0.162335 | ||||||||
\(892\) | 2.83838 | 0.0950359 | ||||||||
\(893\) | −11.6491 | −0.389822 | ||||||||
\(894\) | −66.8146 | −2.23462 | ||||||||
\(895\) | −21.7150 | −0.725852 | ||||||||
\(896\) | −3.02991 | −0.101222 | ||||||||
\(897\) | −27.3998 | −0.914853 | ||||||||
\(898\) | −18.2475 | −0.608926 | ||||||||
\(899\) | 9.60228 | 0.320254 | ||||||||
\(900\) | −14.1791 | −0.472637 | ||||||||
\(901\) | −10.6234 | −0.353918 | ||||||||
\(902\) | −42.9745 | −1.43089 | ||||||||
\(903\) | 16.3630 | 0.544528 | ||||||||
\(904\) | 9.12519 | 0.303499 | ||||||||
\(905\) | 13.1086 | 0.435746 | ||||||||
\(906\) | 27.7393 | 0.921577 | ||||||||
\(907\) | 21.7126 | 0.720954 | 0.360477 | − | 0.932768i | \(-0.382614\pi\) | ||||
0.360477 | + | 0.932768i | \(0.382614\pi\) | |||||||
\(908\) | −12.8931 | −0.427872 | ||||||||
\(909\) | −86.6235 | −2.87312 | ||||||||
\(910\) | −19.6647 | −0.651879 | ||||||||
\(911\) | −20.1146 | −0.666427 | −0.333214 | − | 0.942851i | \(-0.608133\pi\) | ||||
−0.333214 | + | 0.942851i | \(0.608133\pi\) | |||||||
\(912\) | 4.60577 | 0.152512 | ||||||||
\(913\) | 25.1106 | 0.831041 | ||||||||
\(914\) | 30.3549 | 1.00405 | ||||||||
\(915\) | 15.4191 | 0.509739 | ||||||||
\(916\) | −4.75894 | −0.157240 | ||||||||
\(917\) | 45.4018 | 1.49930 | ||||||||
\(918\) | −36.2180 | −1.19537 | ||||||||
\(919\) | −39.0670 | −1.28870 | −0.644350 | − | 0.764730i | \(-0.722872\pi\) | ||||
−0.644350 | + | 0.764730i | \(0.722872\pi\) | |||||||
\(920\) | −3.20635 | −0.105710 | ||||||||
\(921\) | −40.2624 | −1.32669 | ||||||||
\(922\) | −15.2365 | −0.501786 | ||||||||
\(923\) | 31.8011 | 1.04674 | ||||||||
\(924\) | 55.6351 | 1.83026 | ||||||||
\(925\) | −13.9311 | −0.458051 | ||||||||
\(926\) | −34.5415 | −1.13511 | ||||||||
\(927\) | 42.7344 | 1.40358 | ||||||||
\(928\) | 1.73018 | 0.0567960 | ||||||||
\(929\) | −38.3293 | −1.25754 | −0.628772 | − | 0.777590i | \(-0.716442\pi\) | ||||
−0.628772 | + | 0.777590i | \(0.716442\pi\) | |||||||
\(930\) | 22.9279 | 0.751836 | ||||||||
\(931\) | −3.55866 | −0.116630 | ||||||||
\(932\) | −24.6821 | −0.808490 | ||||||||
\(933\) | −78.4544 | −2.56848 | ||||||||
\(934\) | 3.04551 | 0.0996522 | ||||||||
\(935\) | −62.2712 | −2.03649 | ||||||||
\(936\) | 22.0038 | 0.719216 | ||||||||
\(937\) | −45.0104 | −1.47043 | −0.735213 | − | 0.677836i | \(-0.762918\pi\) | ||||
−0.735213 | + | 0.677836i | \(0.762918\pi\) | |||||||
\(938\) | 42.5427 | 1.38907 | ||||||||
\(939\) | 41.1419 | 1.34261 | ||||||||
\(940\) | −10.4489 | −0.340806 | ||||||||
\(941\) | 11.5345 | 0.376015 | 0.188007 | − | 0.982168i | \(-0.439797\pi\) | ||||
0.188007 | + | 0.982168i | \(0.439797\pi\) | |||||||
\(942\) | −27.9685 | −0.911265 | ||||||||
\(943\) | 14.4649 | 0.471042 | ||||||||
\(944\) | −10.9135 | −0.355205 | ||||||||
\(945\) | 24.5757 | 0.799449 | ||||||||
\(946\) | −12.4525 | −0.404867 | ||||||||
\(947\) | −4.38393 | −0.142458 | −0.0712292 | − | 0.997460i | \(-0.522692\pi\) | ||||
−0.0712292 | + | 0.997460i | \(0.522692\pi\) | |||||||
\(948\) | −5.47124 | −0.177698 | ||||||||
\(949\) | 66.1446 | 2.14714 | ||||||||
\(950\) | −4.66263 | −0.151276 | ||||||||
\(951\) | 30.0108 | 0.973165 | ||||||||
\(952\) | 19.8067 | 0.641939 | ||||||||
\(953\) | −1.59541 | −0.0516804 | −0.0258402 | − | 0.999666i | \(-0.508226\pi\) | ||||
−0.0258402 | + | 0.999666i | \(0.508226\pi\) | |||||||
\(954\) | −8.06597 | −0.261145 | ||||||||
\(955\) | −28.9121 | −0.935573 | ||||||||
\(956\) | 4.15919 | 0.134518 | ||||||||
\(957\) | −31.7695 | −1.02696 | ||||||||
\(958\) | 38.6905 | 1.25003 | ||||||||
\(959\) | −60.5128 | −1.95406 | ||||||||
\(960\) | 4.13125 | 0.133336 | ||||||||
\(961\) | −0.198974 | −0.00641851 | ||||||||
\(962\) | 21.6188 | 0.697020 | ||||||||
\(963\) | −93.0291 | −2.99782 | ||||||||
\(964\) | 21.2315 | 0.683820 | ||||||||
\(965\) | −8.22078 | −0.264636 | ||||||||
\(966\) | −18.7264 | −0.602512 | ||||||||
\(967\) | −30.4189 | −0.978205 | −0.489102 | − | 0.872226i | \(-0.662676\pi\) | ||||
−0.489102 | + | 0.872226i | \(0.662676\pi\) | |||||||
\(968\) | −31.3391 | −1.00728 | ||||||||
\(969\) | −30.1082 | −0.967215 | ||||||||
\(970\) | 20.5102 | 0.658543 | ||||||||
\(971\) | 7.67415 | 0.246275 | 0.123138 | − | 0.992390i | \(-0.460704\pi\) | ||||
0.123138 | + | 0.992390i | \(0.460704\pi\) | |||||||
\(972\) | 14.5197 | 0.465721 | ||||||||
\(973\) | 65.2910 | 2.09313 | ||||||||
\(974\) | 4.11267 | 0.131778 | ||||||||
\(975\) | −35.7393 | −1.14458 | ||||||||
\(976\) | 3.73230 | 0.119468 | ||||||||
\(977\) | −16.2904 | −0.521177 | −0.260589 | − | 0.965450i | \(-0.583917\pi\) | ||||
−0.260589 | + | 0.965450i | \(0.583917\pi\) | |||||||
\(978\) | −32.6698 | −1.04466 | ||||||||
\(979\) | −114.894 | −3.67201 | ||||||||
\(980\) | −3.19202 | −0.101965 | ||||||||
\(981\) | −66.4089 | −2.12027 | ||||||||
\(982\) | −14.2410 | −0.454449 | ||||||||
\(983\) | −60.3337 | −1.92434 | −0.962172 | − | 0.272441i | \(-0.912169\pi\) | ||||
−0.962172 | + | 0.272441i | \(0.912169\pi\) | |||||||
\(984\) | −18.6375 | −0.594141 | ||||||||
\(985\) | 22.4305 | 0.714697 | ||||||||
\(986\) | −11.3103 | −0.360193 | ||||||||
\(987\) | −61.0260 | −1.94248 | ||||||||
\(988\) | 7.23567 | 0.230197 | ||||||||
\(989\) | 4.19144 | 0.133280 | ||||||||
\(990\) | −47.2802 | −1.50266 | ||||||||
\(991\) | −41.1911 | −1.30848 | −0.654240 | − | 0.756287i | \(-0.727011\pi\) | ||||
−0.654240 | + | 0.756287i | \(0.727011\pi\) | |||||||
\(992\) | 5.54987 | 0.176208 | ||||||||
\(993\) | 28.6116 | 0.907961 | ||||||||
\(994\) | 21.7344 | 0.689374 | ||||||||
\(995\) | −3.12893 | −0.0991939 | ||||||||
\(996\) | 10.8902 | 0.345068 | ||||||||
\(997\) | −24.8164 | −0.785943 | −0.392971 | − | 0.919551i | \(-0.628553\pi\) | ||||
−0.392971 | + | 0.919551i | \(0.628553\pi\) | |||||||
\(998\) | 8.77860 | 0.277882 | ||||||||
\(999\) | −27.0179 | −0.854808 |
(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 | 4034.2.a.c.1.3 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.c.1.3 | ✓ | 49 | 1.1 | even | 1 | trivial |