Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1339,2,Mod(1,1339)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1339, 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("1339.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1339 = 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1339.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: | \(10.6919688306\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 1339.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.85697 | 1.31307 | 0.656537 | − | 0.754294i | \(-0.272020\pi\) | ||||
0.656537 | + | 0.754294i | \(0.272020\pi\) | |||||||
\(3\) | −2.04069 | −1.17819 | −0.589096 | − | 0.808063i | \(-0.700516\pi\) | ||||
−0.589096 | + | 0.808063i | \(0.700516\pi\) | |||||||
\(4\) | 1.44833 | 0.724165 | ||||||||
\(5\) | 0.337566 | 0.150964 | 0.0754821 | − | 0.997147i | \(-0.475950\pi\) | ||||
0.0754821 | + | 0.997147i | \(0.475950\pi\) | |||||||
\(6\) | −3.78949 | −1.54705 | ||||||||
\(7\) | −0.868388 | −0.328220 | −0.164110 | − | 0.986442i | \(-0.552475\pi\) | ||||
−0.164110 | + | 0.986442i | \(0.552475\pi\) | |||||||
\(8\) | −1.02443 | −0.362192 | ||||||||
\(9\) | 1.16441 | 0.388135 | ||||||||
\(10\) | 0.626849 | 0.198227 | ||||||||
\(11\) | 4.02651 | 1.21404 | 0.607020 | − | 0.794687i | \(-0.292365\pi\) | ||||
0.607020 | + | 0.794687i | \(0.292365\pi\) | |||||||
\(12\) | −2.95559 | −0.853205 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −1.61257 | −0.430977 | ||||||||
\(15\) | −0.688867 | −0.177865 | ||||||||
\(16\) | −4.79900 | −1.19975 | ||||||||
\(17\) | 4.17665 | 1.01299 | 0.506493 | − | 0.862244i | \(-0.330942\pi\) | ||||
0.506493 | + | 0.862244i | \(0.330942\pi\) | |||||||
\(18\) | 2.16226 | 0.509651 | ||||||||
\(19\) | −6.30143 | −1.44565 | −0.722824 | − | 0.691032i | \(-0.757156\pi\) | ||||
−0.722824 | + | 0.691032i | \(0.757156\pi\) | |||||||
\(20\) | 0.488907 | 0.109323 | ||||||||
\(21\) | 1.77211 | 0.386706 | ||||||||
\(22\) | 7.47711 | 1.59412 | ||||||||
\(23\) | −5.15149 | −1.07416 | −0.537080 | − | 0.843532i | \(-0.680473\pi\) | ||||
−0.537080 | + | 0.843532i | \(0.680473\pi\) | |||||||
\(24\) | 2.09055 | 0.426732 | ||||||||
\(25\) | −4.88605 | −0.977210 | ||||||||
\(26\) | −1.85697 | −0.364181 | ||||||||
\(27\) | 3.74587 | 0.720894 | ||||||||
\(28\) | −1.25771 | −0.237685 | ||||||||
\(29\) | −6.31422 | −1.17252 | −0.586260 | − | 0.810123i | \(-0.699400\pi\) | ||||
−0.586260 | + | 0.810123i | \(0.699400\pi\) | |||||||
\(30\) | −1.27920 | −0.233550 | ||||||||
\(31\) | 0.244159 | 0.0438523 | 0.0219261 | − | 0.999760i | \(-0.493020\pi\) | ||||
0.0219261 | + | 0.999760i | \(0.493020\pi\) | |||||||
\(32\) | −6.86272 | −1.21317 | ||||||||
\(33\) | −8.21686 | −1.43037 | ||||||||
\(34\) | 7.75590 | 1.33013 | ||||||||
\(35\) | −0.293138 | −0.0495494 | ||||||||
\(36\) | 1.68644 | 0.281074 | ||||||||
\(37\) | −6.75531 | −1.11057 | −0.555283 | − | 0.831661i | \(-0.687390\pi\) | ||||
−0.555283 | + | 0.831661i | \(0.687390\pi\) | |||||||
\(38\) | −11.7016 | −1.89824 | ||||||||
\(39\) | 2.04069 | 0.326772 | ||||||||
\(40\) | −0.345814 | −0.0546781 | ||||||||
\(41\) | −1.95590 | −0.305461 | −0.152730 | − | 0.988268i | \(-0.548807\pi\) | ||||
−0.152730 | + | 0.988268i | \(0.548807\pi\) | |||||||
\(42\) | 3.29075 | 0.507774 | ||||||||
\(43\) | 0.258091 | 0.0393584 | 0.0196792 | − | 0.999806i | \(-0.493736\pi\) | ||||
0.0196792 | + | 0.999806i | \(0.493736\pi\) | |||||||
\(44\) | 5.83172 | 0.879165 | ||||||||
\(45\) | 0.393064 | 0.0585945 | ||||||||
\(46\) | −9.56614 | −1.41045 | ||||||||
\(47\) | −4.80034 | −0.700202 | −0.350101 | − | 0.936712i | \(-0.613853\pi\) | ||||
−0.350101 | + | 0.936712i | \(0.613853\pi\) | |||||||
\(48\) | 9.79326 | 1.41354 | ||||||||
\(49\) | −6.24590 | −0.892272 | ||||||||
\(50\) | −9.07324 | −1.28315 | ||||||||
\(51\) | −8.52323 | −1.19349 | ||||||||
\(52\) | −1.44833 | −0.200847 | ||||||||
\(53\) | 4.90729 | 0.674068 | 0.337034 | − | 0.941492i | \(-0.390576\pi\) | ||||
0.337034 | + | 0.941492i | \(0.390576\pi\) | |||||||
\(54\) | 6.95597 | 0.946587 | ||||||||
\(55\) | 1.35921 | 0.183276 | ||||||||
\(56\) | 0.889607 | 0.118879 | ||||||||
\(57\) | 12.8593 | 1.70325 | ||||||||
\(58\) | −11.7253 | −1.53961 | ||||||||
\(59\) | 0.669589 | 0.0871731 | 0.0435865 | − | 0.999050i | \(-0.486122\pi\) | ||||
0.0435865 | + | 0.999050i | \(0.486122\pi\) | |||||||
\(60\) | −0.997706 | −0.128803 | ||||||||
\(61\) | −8.72309 | −1.11688 | −0.558439 | − | 0.829546i | \(-0.688599\pi\) | ||||
−0.558439 | + | 0.829546i | \(0.688599\pi\) | |||||||
\(62\) | 0.453396 | 0.0575813 | ||||||||
\(63\) | −1.01116 | −0.127394 | ||||||||
\(64\) | −3.14585 | −0.393231 | ||||||||
\(65\) | −0.337566 | −0.0418699 | ||||||||
\(66\) | −15.2584 | −1.87818 | ||||||||
\(67\) | 4.50319 | 0.550153 | 0.275076 | − | 0.961422i | \(-0.411297\pi\) | ||||
0.275076 | + | 0.961422i | \(0.411297\pi\) | |||||||
\(68\) | 6.04916 | 0.733568 | ||||||||
\(69\) | 10.5126 | 1.26557 | ||||||||
\(70\) | −0.544349 | −0.0650621 | ||||||||
\(71\) | 11.1310 | 1.32101 | 0.660503 | − | 0.750823i | \(-0.270343\pi\) | ||||
0.660503 | + | 0.750823i | \(0.270343\pi\) | |||||||
\(72\) | −1.19286 | −0.140580 | ||||||||
\(73\) | −13.1290 | −1.53663 | −0.768316 | − | 0.640071i | \(-0.778905\pi\) | ||||
−0.768316 | + | 0.640071i | \(0.778905\pi\) | |||||||
\(74\) | −12.5444 | −1.45826 | ||||||||
\(75\) | 9.97090 | 1.15134 | ||||||||
\(76\) | −9.12655 | −1.04689 | ||||||||
\(77\) | −3.49658 | −0.398472 | ||||||||
\(78\) | 3.78949 | 0.429075 | ||||||||
\(79\) | 0.454458 | 0.0511305 | 0.0255652 | − | 0.999673i | \(-0.491861\pi\) | ||||
0.0255652 | + | 0.999673i | \(0.491861\pi\) | |||||||
\(80\) | −1.61998 | −0.181119 | ||||||||
\(81\) | −11.1374 | −1.23749 | ||||||||
\(82\) | −3.63205 | −0.401093 | ||||||||
\(83\) | 1.72510 | 0.189354 | 0.0946771 | − | 0.995508i | \(-0.469818\pi\) | ||||
0.0946771 | + | 0.995508i | \(0.469818\pi\) | |||||||
\(84\) | 2.56660 | 0.280039 | ||||||||
\(85\) | 1.40989 | 0.152924 | ||||||||
\(86\) | 0.479266 | 0.0516806 | ||||||||
\(87\) | 12.8853 | 1.38145 | ||||||||
\(88\) | −4.12490 | −0.439716 | ||||||||
\(89\) | 4.72748 | 0.501112 | 0.250556 | − | 0.968102i | \(-0.419387\pi\) | ||||
0.250556 | + | 0.968102i | \(0.419387\pi\) | |||||||
\(90\) | 0.729907 | 0.0769390 | ||||||||
\(91\) | 0.868388 | 0.0910318 | ||||||||
\(92\) | −7.46105 | −0.777868 | ||||||||
\(93\) | −0.498253 | −0.0516664 | ||||||||
\(94\) | −8.91408 | −0.919417 | ||||||||
\(95\) | −2.12715 | −0.218241 | ||||||||
\(96\) | 14.0047 | 1.42935 | ||||||||
\(97\) | −7.91621 | −0.803769 | −0.401885 | − | 0.915690i | \(-0.631645\pi\) | ||||
−0.401885 | + | 0.915690i | \(0.631645\pi\) | |||||||
\(98\) | −11.5984 | −1.17162 | ||||||||
\(99\) | 4.68850 | 0.471212 | ||||||||
\(100\) | −7.07661 | −0.707661 | ||||||||
\(101\) | 8.42660 | 0.838478 | 0.419239 | − | 0.907876i | \(-0.362297\pi\) | ||||
0.419239 | + | 0.907876i | \(0.362297\pi\) | |||||||
\(102\) | −15.8274 | −1.56714 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.02443 | 0.100454 | ||||||||
\(105\) | 0.598204 | 0.0583787 | ||||||||
\(106\) | 9.11268 | 0.885102 | ||||||||
\(107\) | 9.57014 | 0.925180 | 0.462590 | − | 0.886572i | \(-0.346920\pi\) | ||||
0.462590 | + | 0.886572i | \(0.346920\pi\) | |||||||
\(108\) | 5.42526 | 0.522046 | ||||||||
\(109\) | −3.36167 | −0.321989 | −0.160995 | − | 0.986955i | \(-0.551470\pi\) | ||||
−0.160995 | + | 0.986955i | \(0.551470\pi\) | |||||||
\(110\) | 2.52402 | 0.240656 | ||||||||
\(111\) | 13.7855 | 1.30846 | ||||||||
\(112\) | 4.16740 | 0.393782 | ||||||||
\(113\) | 8.19635 | 0.771048 | 0.385524 | − | 0.922698i | \(-0.374021\pi\) | ||||
0.385524 | + | 0.922698i | \(0.374021\pi\) | |||||||
\(114\) | 23.8792 | 2.23649 | ||||||||
\(115\) | −1.73897 | −0.162159 | ||||||||
\(116\) | −9.14506 | −0.849098 | ||||||||
\(117\) | −1.16441 | −0.107649 | ||||||||
\(118\) | 1.24341 | 0.114465 | ||||||||
\(119\) | −3.62695 | −0.332482 | ||||||||
\(120\) | 0.705699 | 0.0644212 | ||||||||
\(121\) | 5.21282 | 0.473893 | ||||||||
\(122\) | −16.1985 | −1.46654 | ||||||||
\(123\) | 3.99139 | 0.359891 | ||||||||
\(124\) | 0.353623 | 0.0317563 | ||||||||
\(125\) | −3.33719 | −0.298488 | ||||||||
\(126\) | −1.87769 | −0.167278 | ||||||||
\(127\) | 12.8228 | 1.13784 | 0.568920 | − | 0.822393i | \(-0.307362\pi\) | ||||
0.568920 | + | 0.822393i | \(0.307362\pi\) | |||||||
\(128\) | 7.88370 | 0.696827 | ||||||||
\(129\) | −0.526682 | −0.0463718 | ||||||||
\(130\) | −0.626849 | −0.0549783 | ||||||||
\(131\) | −9.14472 | −0.798978 | −0.399489 | − | 0.916738i | \(-0.630812\pi\) | ||||
−0.399489 | + | 0.916738i | \(0.630812\pi\) | |||||||
\(132\) | −11.9007 | −1.03582 | ||||||||
\(133\) | 5.47209 | 0.474490 | ||||||||
\(134\) | 8.36229 | 0.722392 | ||||||||
\(135\) | 1.26448 | 0.108829 | ||||||||
\(136\) | −4.27870 | −0.366896 | ||||||||
\(137\) | 14.4798 | 1.23710 | 0.618548 | − | 0.785747i | \(-0.287721\pi\) | ||||
0.618548 | + | 0.785747i | \(0.287721\pi\) | |||||||
\(138\) | 19.5215 | 1.66178 | ||||||||
\(139\) | 7.34503 | 0.622997 | 0.311499 | − | 0.950247i | \(-0.399169\pi\) | ||||
0.311499 | + | 0.950247i | \(0.399169\pi\) | |||||||
\(140\) | −0.424561 | −0.0358820 | ||||||||
\(141\) | 9.79600 | 0.824972 | ||||||||
\(142\) | 20.6699 | 1.73458 | ||||||||
\(143\) | −4.02651 | −0.336714 | ||||||||
\(144\) | −5.58799 | −0.465666 | ||||||||
\(145\) | −2.13147 | −0.177009 | ||||||||
\(146\) | −24.3801 | −2.01771 | ||||||||
\(147\) | 12.7459 | 1.05127 | ||||||||
\(148\) | −9.78392 | −0.804233 | ||||||||
\(149\) | 8.17502 | 0.669724 | 0.334862 | − | 0.942267i | \(-0.391310\pi\) | ||||
0.334862 | + | 0.942267i | \(0.391310\pi\) | |||||||
\(150\) | 18.5156 | 1.51180 | ||||||||
\(151\) | 0.616426 | 0.0501641 | 0.0250820 | − | 0.999685i | \(-0.492015\pi\) | ||||
0.0250820 | + | 0.999685i | \(0.492015\pi\) | |||||||
\(152\) | 6.45540 | 0.523602 | ||||||||
\(153\) | 4.86331 | 0.393175 | ||||||||
\(154\) | −6.49303 | −0.523224 | ||||||||
\(155\) | 0.0824198 | 0.00662012 | ||||||||
\(156\) | 2.95559 | 0.236636 | ||||||||
\(157\) | −11.1067 | −0.886414 | −0.443207 | − | 0.896419i | \(-0.646159\pi\) | ||||
−0.443207 | + | 0.896419i | \(0.646159\pi\) | |||||||
\(158\) | 0.843913 | 0.0671381 | ||||||||
\(159\) | −10.0142 | −0.794182 | ||||||||
\(160\) | −2.31662 | −0.183145 | ||||||||
\(161\) | 4.47349 | 0.352560 | ||||||||
\(162\) | −20.6818 | −1.62491 | ||||||||
\(163\) | 7.10016 | 0.556128 | 0.278064 | − | 0.960563i | \(-0.410307\pi\) | ||||
0.278064 | + | 0.960563i | \(0.410307\pi\) | |||||||
\(164\) | −2.83279 | −0.221204 | ||||||||
\(165\) | −2.77373 | −0.215935 | ||||||||
\(166\) | 3.20345 | 0.248636 | ||||||||
\(167\) | −14.4379 | −1.11724 | −0.558618 | − | 0.829425i | \(-0.688668\pi\) | ||||
−0.558618 | + | 0.829425i | \(0.688668\pi\) | |||||||
\(168\) | −1.81541 | −0.140062 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 2.61813 | 0.200801 | ||||||||
\(171\) | −7.33743 | −0.561107 | ||||||||
\(172\) | 0.373800 | 0.0285020 | ||||||||
\(173\) | −20.0730 | −1.52612 | −0.763060 | − | 0.646328i | \(-0.776304\pi\) | ||||
−0.763060 | + | 0.646328i | \(0.776304\pi\) | |||||||
\(174\) | 23.9277 | 1.81395 | ||||||||
\(175\) | 4.24299 | 0.320740 | ||||||||
\(176\) | −19.3232 | −1.45654 | ||||||||
\(177\) | −1.36642 | −0.102707 | ||||||||
\(178\) | 8.77878 | 0.657997 | ||||||||
\(179\) | −10.0573 | −0.751718 | −0.375859 | − | 0.926677i | \(-0.622652\pi\) | ||||
−0.375859 | + | 0.926677i | \(0.622652\pi\) | |||||||
\(180\) | 0.569286 | 0.0424321 | ||||||||
\(181\) | 1.03931 | 0.0772513 | 0.0386256 | − | 0.999254i | \(-0.487702\pi\) | ||||
0.0386256 | + | 0.999254i | \(0.487702\pi\) | |||||||
\(182\) | 1.61257 | 0.119532 | ||||||||
\(183\) | 17.8011 | 1.31590 | ||||||||
\(184\) | 5.27736 | 0.389052 | ||||||||
\(185\) | −2.28036 | −0.167656 | ||||||||
\(186\) | −0.925239 | −0.0678418 | ||||||||
\(187\) | 16.8173 | 1.22980 | ||||||||
\(188\) | −6.95248 | −0.507062 | ||||||||
\(189\) | −3.25287 | −0.236612 | ||||||||
\(190\) | −3.95005 | −0.286567 | ||||||||
\(191\) | 6.31200 | 0.456720 | 0.228360 | − | 0.973577i | \(-0.426664\pi\) | ||||
0.228360 | + | 0.973577i | \(0.426664\pi\) | |||||||
\(192\) | 6.41970 | 0.463302 | ||||||||
\(193\) | 12.7685 | 0.919093 | 0.459547 | − | 0.888154i | \(-0.348012\pi\) | ||||
0.459547 | + | 0.888154i | \(0.348012\pi\) | |||||||
\(194\) | −14.7001 | −1.05541 | ||||||||
\(195\) | 0.688867 | 0.0493308 | ||||||||
\(196\) | −9.04612 | −0.646152 | ||||||||
\(197\) | −8.86713 | −0.631757 | −0.315878 | − | 0.948800i | \(-0.602299\pi\) | ||||
−0.315878 | + | 0.948800i | \(0.602299\pi\) | |||||||
\(198\) | 8.70639 | 0.618736 | ||||||||
\(199\) | −1.52396 | −0.108030 | −0.0540152 | − | 0.998540i | \(-0.517202\pi\) | ||||
−0.0540152 | + | 0.998540i | \(0.517202\pi\) | |||||||
\(200\) | 5.00544 | 0.353938 | ||||||||
\(201\) | −9.18961 | −0.648185 | ||||||||
\(202\) | 15.6479 | 1.10098 | ||||||||
\(203\) | 5.48319 | 0.384845 | ||||||||
\(204\) | −12.3444 | −0.864284 | ||||||||
\(205\) | −0.660247 | −0.0461136 | ||||||||
\(206\) | −1.85697 | −0.129381 | ||||||||
\(207\) | −5.99842 | −0.416919 | ||||||||
\(208\) | 4.79900 | 0.332751 | ||||||||
\(209\) | −25.3728 | −1.75507 | ||||||||
\(210\) | 1.11085 | 0.0766556 | ||||||||
\(211\) | −8.62201 | −0.593564 | −0.296782 | − | 0.954945i | \(-0.595913\pi\) | ||||
−0.296782 | + | 0.954945i | \(0.595913\pi\) | |||||||
\(212\) | 7.10737 | 0.488136 | ||||||||
\(213\) | −22.7149 | −1.55640 | ||||||||
\(214\) | 17.7714 | 1.21483 | ||||||||
\(215\) | 0.0871226 | 0.00594171 | ||||||||
\(216\) | −3.83740 | −0.261102 | ||||||||
\(217\) | −0.212025 | −0.0143932 | ||||||||
\(218\) | −6.24251 | −0.422796 | ||||||||
\(219\) | 26.7922 | 1.81045 | ||||||||
\(220\) | 1.96859 | 0.132722 | ||||||||
\(221\) | −4.17665 | −0.280952 | ||||||||
\(222\) | 25.5992 | 1.71811 | ||||||||
\(223\) | −16.7390 | −1.12092 | −0.560462 | − | 0.828180i | \(-0.689377\pi\) | ||||
−0.560462 | + | 0.828180i | \(0.689377\pi\) | |||||||
\(224\) | 5.95951 | 0.398186 | ||||||||
\(225\) | −5.68935 | −0.379290 | ||||||||
\(226\) | 15.2204 | 1.01244 | ||||||||
\(227\) | −8.60827 | −0.571351 | −0.285676 | − | 0.958326i | \(-0.592218\pi\) | ||||
−0.285676 | + | 0.958326i | \(0.592218\pi\) | |||||||
\(228\) | 18.6244 | 1.23343 | ||||||||
\(229\) | −19.8035 | −1.30865 | −0.654327 | − | 0.756211i | \(-0.727048\pi\) | ||||
−0.654327 | + | 0.756211i | \(0.727048\pi\) | |||||||
\(230\) | −3.22921 | −0.212927 | ||||||||
\(231\) | 7.13543 | 0.469477 | ||||||||
\(232\) | 6.46850 | 0.424678 | ||||||||
\(233\) | 0.298831 | 0.0195771 | 0.00978853 | − | 0.999952i | \(-0.496884\pi\) | ||||
0.00978853 | + | 0.999952i | \(0.496884\pi\) | |||||||
\(234\) | −2.16226 | −0.141352 | ||||||||
\(235\) | −1.62043 | −0.105705 | ||||||||
\(236\) | 0.969786 | 0.0631277 | ||||||||
\(237\) | −0.927406 | −0.0602415 | ||||||||
\(238\) | −6.73513 | −0.436574 | ||||||||
\(239\) | 27.4369 | 1.77475 | 0.887373 | − | 0.461052i | \(-0.152528\pi\) | ||||
0.887373 | + | 0.461052i | \(0.152528\pi\) | |||||||
\(240\) | 3.30587 | 0.213393 | ||||||||
\(241\) | 13.8656 | 0.893161 | 0.446581 | − | 0.894743i | \(-0.352642\pi\) | ||||
0.446581 | + | 0.894743i | \(0.352642\pi\) | |||||||
\(242\) | 9.68004 | 0.622256 | ||||||||
\(243\) | 11.4903 | 0.737102 | ||||||||
\(244\) | −12.6339 | −0.808803 | ||||||||
\(245\) | −2.10840 | −0.134701 | ||||||||
\(246\) | 7.41188 | 0.472564 | ||||||||
\(247\) | 6.30143 | 0.400950 | ||||||||
\(248\) | −0.250125 | −0.0158830 | ||||||||
\(249\) | −3.52039 | −0.223095 | ||||||||
\(250\) | −6.19706 | −0.391937 | ||||||||
\(251\) | 16.9991 | 1.07297 | 0.536485 | − | 0.843910i | \(-0.319752\pi\) | ||||
0.536485 | + | 0.843910i | \(0.319752\pi\) | |||||||
\(252\) | −1.46449 | −0.0922541 | ||||||||
\(253\) | −20.7425 | −1.30407 | ||||||||
\(254\) | 23.8115 | 1.49407 | ||||||||
\(255\) | −2.87715 | −0.180174 | ||||||||
\(256\) | 20.9315 | 1.30822 | ||||||||
\(257\) | 9.17004 | 0.572011 | 0.286006 | − | 0.958228i | \(-0.407672\pi\) | ||||
0.286006 | + | 0.958228i | \(0.407672\pi\) | |||||||
\(258\) | −0.978032 | −0.0608896 | ||||||||
\(259\) | 5.86623 | 0.364510 | ||||||||
\(260\) | −0.488907 | −0.0303207 | ||||||||
\(261\) | −7.35231 | −0.455097 | ||||||||
\(262\) | −16.9815 | −1.04912 | ||||||||
\(263\) | −14.0834 | −0.868420 | −0.434210 | − | 0.900812i | \(-0.642972\pi\) | ||||
−0.434210 | + | 0.900812i | \(0.642972\pi\) | |||||||
\(264\) | 8.41763 | 0.518070 | ||||||||
\(265\) | 1.65653 | 0.101760 | ||||||||
\(266\) | 10.1615 | 0.623041 | ||||||||
\(267\) | −9.64731 | −0.590406 | ||||||||
\(268\) | 6.52211 | 0.398401 | ||||||||
\(269\) | −13.8474 | −0.844292 | −0.422146 | − | 0.906528i | \(-0.638723\pi\) | ||||
−0.422146 | + | 0.906528i | \(0.638723\pi\) | |||||||
\(270\) | 2.34810 | 0.142901 | ||||||||
\(271\) | −15.1319 | −0.919195 | −0.459597 | − | 0.888127i | \(-0.652006\pi\) | ||||
−0.459597 | + | 0.888127i | \(0.652006\pi\) | |||||||
\(272\) | −20.0437 | −1.21533 | ||||||||
\(273\) | −1.77211 | −0.107253 | ||||||||
\(274\) | 26.8886 | 1.62440 | ||||||||
\(275\) | −19.6737 | −1.18637 | ||||||||
\(276\) | 15.2257 | 0.916478 | ||||||||
\(277\) | 31.5583 | 1.89616 | 0.948078 | − | 0.318037i | \(-0.103023\pi\) | ||||
0.948078 | + | 0.318037i | \(0.103023\pi\) | |||||||
\(278\) | 13.6395 | 0.818042 | ||||||||
\(279\) | 0.284300 | 0.0170206 | ||||||||
\(280\) | 0.300301 | 0.0179464 | ||||||||
\(281\) | 6.64836 | 0.396608 | 0.198304 | − | 0.980141i | \(-0.436457\pi\) | ||||
0.198304 | + | 0.980141i | \(0.436457\pi\) | |||||||
\(282\) | 18.1909 | 1.08325 | ||||||||
\(283\) | −18.8468 | −1.12033 | −0.560163 | − | 0.828383i | \(-0.689261\pi\) | ||||
−0.560163 | + | 0.828383i | \(0.689261\pi\) | |||||||
\(284\) | 16.1213 | 0.956626 | ||||||||
\(285\) | 4.34085 | 0.257130 | ||||||||
\(286\) | −7.47711 | −0.442131 | ||||||||
\(287\) | 1.69848 | 0.100258 | ||||||||
\(288\) | −7.99100 | −0.470874 | ||||||||
\(289\) | 0.444366 | 0.0261392 | ||||||||
\(290\) | −3.95806 | −0.232425 | ||||||||
\(291\) | 16.1545 | 0.946994 | ||||||||
\(292\) | −19.0151 | −1.11277 | ||||||||
\(293\) | 19.3011 | 1.12758 | 0.563791 | − | 0.825917i | \(-0.309342\pi\) | ||||
0.563791 | + | 0.825917i | \(0.309342\pi\) | |||||||
\(294\) | 23.6688 | 1.38039 | ||||||||
\(295\) | 0.226031 | 0.0131600 | ||||||||
\(296\) | 6.92037 | 0.402239 | ||||||||
\(297\) | 15.0828 | 0.875194 | ||||||||
\(298\) | 15.1808 | 0.879397 | ||||||||
\(299\) | 5.15149 | 0.297918 | ||||||||
\(300\) | 14.4411 | 0.833760 | ||||||||
\(301\) | −0.224123 | −0.0129182 | ||||||||
\(302\) | 1.14468 | 0.0658692 | ||||||||
\(303\) | −17.1961 | −0.987888 | ||||||||
\(304\) | 30.2406 | 1.73442 | ||||||||
\(305\) | −2.94462 | −0.168608 | ||||||||
\(306\) | 9.03101 | 0.516269 | ||||||||
\(307\) | 20.0124 | 1.14217 | 0.571085 | − | 0.820891i | \(-0.306523\pi\) | ||||
0.571085 | + | 0.820891i | \(0.306523\pi\) | |||||||
\(308\) | −5.06420 | −0.288559 | ||||||||
\(309\) | 2.04069 | 0.116091 | ||||||||
\(310\) | 0.153051 | 0.00869271 | ||||||||
\(311\) | 10.3303 | 0.585780 | 0.292890 | − | 0.956146i | \(-0.405383\pi\) | ||||
0.292890 | + | 0.956146i | \(0.405383\pi\) | |||||||
\(312\) | −2.09055 | −0.118354 | ||||||||
\(313\) | 0.429358 | 0.0242687 | 0.0121344 | − | 0.999926i | \(-0.496137\pi\) | ||||
0.0121344 | + | 0.999926i | \(0.496137\pi\) | |||||||
\(314\) | −20.6249 | −1.16393 | ||||||||
\(315\) | −0.341332 | −0.0192319 | ||||||||
\(316\) | 0.658204 | 0.0370269 | ||||||||
\(317\) | 16.8546 | 0.946647 | 0.473324 | − | 0.880889i | \(-0.343054\pi\) | ||||
0.473324 | + | 0.880889i | \(0.343054\pi\) | |||||||
\(318\) | −18.5961 | −1.04282 | ||||||||
\(319\) | −25.4243 | −1.42349 | ||||||||
\(320\) | −1.06193 | −0.0593638 | ||||||||
\(321\) | −19.5297 | −1.09004 | ||||||||
\(322\) | 8.30713 | 0.462938 | ||||||||
\(323\) | −26.3188 | −1.46442 | ||||||||
\(324\) | −16.1306 | −0.896144 | ||||||||
\(325\) | 4.88605 | 0.271029 | ||||||||
\(326\) | 13.1848 | 0.730237 | ||||||||
\(327\) | 6.86011 | 0.379365 | ||||||||
\(328\) | 2.00370 | 0.110636 | ||||||||
\(329\) | 4.16856 | 0.229820 | ||||||||
\(330\) | −5.15073 | −0.283538 | ||||||||
\(331\) | −15.2855 | −0.840167 | −0.420083 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420083 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(332\) | 2.49851 | 0.137124 | ||||||||
\(333\) | −7.86593 | −0.431050 | ||||||||
\(334\) | −26.8107 | −1.46702 | ||||||||
\(335\) | 1.52013 | 0.0830533 | ||||||||
\(336\) | −8.50436 | −0.463951 | ||||||||
\(337\) | 22.0961 | 1.20365 | 0.601826 | − | 0.798627i | \(-0.294440\pi\) | ||||
0.601826 | + | 0.798627i | \(0.294440\pi\) | |||||||
\(338\) | 1.85697 | 0.101006 | ||||||||
\(339\) | −16.7262 | −0.908442 | ||||||||
\(340\) | 2.04199 | 0.110742 | ||||||||
\(341\) | 0.983110 | 0.0532384 | ||||||||
\(342\) | −13.6254 | −0.736775 | ||||||||
\(343\) | 11.5026 | 0.621081 | ||||||||
\(344\) | −0.264397 | −0.0142553 | ||||||||
\(345\) | 3.54869 | 0.191055 | ||||||||
\(346\) | −37.2748 | −2.00391 | ||||||||
\(347\) | 34.8154 | 1.86899 | 0.934494 | − | 0.355979i | \(-0.115853\pi\) | ||||
0.934494 | + | 0.355979i | \(0.115853\pi\) | |||||||
\(348\) | 18.6622 | 1.00040 | ||||||||
\(349\) | −23.3164 | −1.24810 | −0.624049 | − | 0.781386i | \(-0.714513\pi\) | ||||
−0.624049 | + | 0.781386i | \(0.714513\pi\) | |||||||
\(350\) | 7.87909 | 0.421155 | ||||||||
\(351\) | −3.74587 | −0.199940 | ||||||||
\(352\) | −27.6328 | −1.47284 | ||||||||
\(353\) | −20.4173 | −1.08670 | −0.543351 | − | 0.839506i | \(-0.682845\pi\) | ||||
−0.543351 | + | 0.839506i | \(0.682845\pi\) | |||||||
\(354\) | −2.53740 | −0.134861 | ||||||||
\(355\) | 3.75745 | 0.199424 | ||||||||
\(356\) | 6.84695 | 0.362888 | ||||||||
\(357\) | 7.40147 | 0.391727 | ||||||||
\(358\) | −18.6761 | −0.987062 | ||||||||
\(359\) | 9.98075 | 0.526764 | 0.263382 | − | 0.964692i | \(-0.415162\pi\) | ||||
0.263382 | + | 0.964692i | \(0.415162\pi\) | |||||||
\(360\) | −0.402668 | −0.0212225 | ||||||||
\(361\) | 20.7080 | 1.08990 | ||||||||
\(362\) | 1.92996 | 0.101437 | ||||||||
\(363\) | −10.6377 | −0.558336 | ||||||||
\(364\) | 1.25771 | 0.0659220 | ||||||||
\(365\) | −4.43190 | −0.231976 | ||||||||
\(366\) | 33.0561 | 1.72787 | ||||||||
\(367\) | 18.4927 | 0.965310 | 0.482655 | − | 0.875810i | \(-0.339672\pi\) | ||||
0.482655 | + | 0.875810i | \(0.339672\pi\) | |||||||
\(368\) | 24.7220 | 1.28872 | ||||||||
\(369\) | −2.27747 | −0.118560 | ||||||||
\(370\) | −4.23456 | −0.220144 | ||||||||
\(371\) | −4.26143 | −0.221243 | ||||||||
\(372\) | −0.721634 | −0.0374150 | ||||||||
\(373\) | −38.3755 | −1.98701 | −0.993505 | − | 0.113790i | \(-0.963701\pi\) | ||||
−0.993505 | + | 0.113790i | \(0.963701\pi\) | |||||||
\(374\) | 31.2292 | 1.61482 | ||||||||
\(375\) | 6.81017 | 0.351676 | ||||||||
\(376\) | 4.91764 | 0.253608 | ||||||||
\(377\) | 6.31422 | 0.325199 | ||||||||
\(378\) | −6.04048 | −0.310689 | ||||||||
\(379\) | −13.7059 | −0.704026 | −0.352013 | − | 0.935995i | \(-0.614503\pi\) | ||||
−0.352013 | + | 0.935995i | \(0.614503\pi\) | |||||||
\(380\) | −3.08081 | −0.158042 | ||||||||
\(381\) | −26.1673 | −1.34059 | ||||||||
\(382\) | 11.7212 | 0.599708 | ||||||||
\(383\) | 12.0858 | 0.617555 | 0.308778 | − | 0.951134i | \(-0.400080\pi\) | ||||
0.308778 | + | 0.951134i | \(0.400080\pi\) | |||||||
\(384\) | −16.0882 | −0.820996 | ||||||||
\(385\) | −1.18033 | −0.0601550 | ||||||||
\(386\) | 23.7106 | 1.20684 | ||||||||
\(387\) | 0.300522 | 0.0152764 | ||||||||
\(388\) | −11.4653 | −0.582061 | ||||||||
\(389\) | −30.2130 | −1.53186 | −0.765930 | − | 0.642924i | \(-0.777721\pi\) | ||||
−0.765930 | + | 0.642924i | \(0.777721\pi\) | |||||||
\(390\) | 1.27920 | 0.0647750 | ||||||||
\(391\) | −21.5159 | −1.08811 | ||||||||
\(392\) | 6.39852 | 0.323174 | ||||||||
\(393\) | 18.6615 | 0.941349 | ||||||||
\(394\) | −16.4660 | −0.829544 | ||||||||
\(395\) | 0.153409 | 0.00771887 | ||||||||
\(396\) | 6.79049 | 0.341235 | ||||||||
\(397\) | 22.2128 | 1.11483 | 0.557415 | − | 0.830234i | \(-0.311793\pi\) | ||||
0.557415 | + | 0.830234i | \(0.311793\pi\) | |||||||
\(398\) | −2.82994 | −0.141852 | ||||||||
\(399\) | −11.1668 | −0.559041 | ||||||||
\(400\) | 23.4482 | 1.17241 | ||||||||
\(401\) | −19.3717 | −0.967376 | −0.483688 | − | 0.875240i | \(-0.660703\pi\) | ||||
−0.483688 | + | 0.875240i | \(0.660703\pi\) | |||||||
\(402\) | −17.0648 | −0.851116 | ||||||||
\(403\) | −0.244159 | −0.0121624 | ||||||||
\(404\) | 12.2045 | 0.607196 | ||||||||
\(405\) | −3.75960 | −0.186816 | ||||||||
\(406\) | 10.1821 | 0.505330 | ||||||||
\(407\) | −27.2004 | −1.34827 | ||||||||
\(408\) | 8.73149 | 0.432273 | ||||||||
\(409\) | −11.2165 | −0.554621 | −0.277310 | − | 0.960780i | \(-0.589443\pi\) | ||||
−0.277310 | + | 0.960780i | \(0.589443\pi\) | |||||||
\(410\) | −1.22606 | −0.0605506 | ||||||||
\(411\) | −29.5488 | −1.45754 | ||||||||
\(412\) | −1.44833 | −0.0713541 | ||||||||
\(413\) | −0.581464 | −0.0286120 | ||||||||
\(414\) | −11.1389 | −0.547446 | ||||||||
\(415\) | 0.582335 | 0.0285857 | ||||||||
\(416\) | 6.86272 | 0.336473 | ||||||||
\(417\) | −14.9889 | −0.734010 | ||||||||
\(418\) | −47.1165 | −2.30454 | ||||||||
\(419\) | −29.1424 | −1.42370 | −0.711849 | − | 0.702333i | \(-0.752142\pi\) | ||||
−0.711849 | + | 0.702333i | \(0.752142\pi\) | |||||||
\(420\) | 0.866396 | 0.0422758 | ||||||||
\(421\) | −7.82838 | −0.381532 | −0.190766 | − | 0.981636i | \(-0.561097\pi\) | ||||
−0.190766 | + | 0.981636i | \(0.561097\pi\) | |||||||
\(422\) | −16.0108 | −0.779394 | ||||||||
\(423\) | −5.58955 | −0.271773 | ||||||||
\(424\) | −5.02720 | −0.244142 | ||||||||
\(425\) | −20.4073 | −0.989899 | ||||||||
\(426\) | −42.1808 | −2.04367 | ||||||||
\(427\) | 7.57503 | 0.366581 | ||||||||
\(428\) | 13.8607 | 0.669983 | ||||||||
\(429\) | 8.21686 | 0.396714 | ||||||||
\(430\) | 0.161784 | 0.00780191 | ||||||||
\(431\) | −20.1683 | −0.971474 | −0.485737 | − | 0.874105i | \(-0.661449\pi\) | ||||
−0.485737 | + | 0.874105i | \(0.661449\pi\) | |||||||
\(432\) | −17.9764 | −0.864892 | ||||||||
\(433\) | 13.0824 | 0.628700 | 0.314350 | − | 0.949307i | \(-0.398213\pi\) | ||||
0.314350 | + | 0.949307i | \(0.398213\pi\) | |||||||
\(434\) | −0.393724 | −0.0188993 | ||||||||
\(435\) | 4.34965 | 0.208550 | ||||||||
\(436\) | −4.86880 | −0.233173 | ||||||||
\(437\) | 32.4617 | 1.55286 | ||||||||
\(438\) | 49.7522 | 2.37725 | ||||||||
\(439\) | −7.66674 | −0.365913 | −0.182957 | − | 0.983121i | \(-0.558567\pi\) | ||||
−0.182957 | + | 0.983121i | \(0.558567\pi\) | |||||||
\(440\) | −1.39243 | −0.0663813 | ||||||||
\(441\) | −7.27277 | −0.346322 | ||||||||
\(442\) | −7.75590 | −0.368910 | ||||||||
\(443\) | 14.6959 | 0.698223 | 0.349111 | − | 0.937081i | \(-0.386483\pi\) | ||||
0.349111 | + | 0.937081i | \(0.386483\pi\) | |||||||
\(444\) | 19.9659 | 0.947540 | ||||||||
\(445\) | 1.59584 | 0.0756499 | ||||||||
\(446\) | −31.0837 | −1.47186 | ||||||||
\(447\) | −16.6827 | −0.789063 | ||||||||
\(448\) | 2.73182 | 0.129066 | ||||||||
\(449\) | −31.0829 | −1.46689 | −0.733447 | − | 0.679746i | \(-0.762090\pi\) | ||||
−0.733447 | + | 0.679746i | \(0.762090\pi\) | |||||||
\(450\) | −10.5649 | −0.498036 | ||||||||
\(451\) | −7.87547 | −0.370842 | ||||||||
\(452\) | 11.8710 | 0.558365 | ||||||||
\(453\) | −1.25793 | −0.0591029 | ||||||||
\(454\) | −15.9853 | −0.750226 | ||||||||
\(455\) | 0.293138 | 0.0137425 | ||||||||
\(456\) | −13.1735 | −0.616904 | ||||||||
\(457\) | −16.9808 | −0.794330 | −0.397165 | − | 0.917747i | \(-0.630006\pi\) | ||||
−0.397165 | + | 0.917747i | \(0.630006\pi\) | |||||||
\(458\) | −36.7745 | −1.71836 | ||||||||
\(459\) | 15.6452 | 0.730255 | ||||||||
\(460\) | −2.51860 | −0.117430 | ||||||||
\(461\) | −40.1807 | −1.87140 | −0.935700 | − | 0.352797i | \(-0.885231\pi\) | ||||
−0.935700 | + | 0.352797i | \(0.885231\pi\) | |||||||
\(462\) | 13.2503 | 0.616458 | ||||||||
\(463\) | 7.71807 | 0.358689 | 0.179345 | − | 0.983786i | \(-0.442602\pi\) | ||||
0.179345 | + | 0.983786i | \(0.442602\pi\) | |||||||
\(464\) | 30.3019 | 1.40673 | ||||||||
\(465\) | −0.168193 | −0.00779977 | ||||||||
\(466\) | 0.554919 | 0.0257061 | ||||||||
\(467\) | 16.5007 | 0.763560 | 0.381780 | − | 0.924253i | \(-0.375311\pi\) | ||||
0.381780 | + | 0.924253i | \(0.375311\pi\) | |||||||
\(468\) | −1.68644 | −0.0779559 | ||||||||
\(469\) | −3.91052 | −0.180571 | ||||||||
\(470\) | −3.00909 | −0.138799 | ||||||||
\(471\) | 22.6654 | 1.04437 | ||||||||
\(472\) | −0.685950 | −0.0315734 | ||||||||
\(473\) | 1.03921 | 0.0477827 | ||||||||
\(474\) | −1.72216 | −0.0791016 | ||||||||
\(475\) | 30.7891 | 1.41270 | ||||||||
\(476\) | −5.25302 | −0.240772 | ||||||||
\(477\) | 5.71408 | 0.261630 | ||||||||
\(478\) | 50.9495 | 2.33037 | ||||||||
\(479\) | 29.5562 | 1.35046 | 0.675229 | − | 0.737608i | \(-0.264045\pi\) | ||||
0.675229 | + | 0.737608i | \(0.264045\pi\) | |||||||
\(480\) | 4.72750 | 0.215780 | ||||||||
\(481\) | 6.75531 | 0.308016 | ||||||||
\(482\) | 25.7480 | 1.17279 | ||||||||
\(483\) | −9.12900 | −0.415384 | ||||||||
\(484\) | 7.54988 | 0.343176 | ||||||||
\(485\) | −2.67224 | −0.121340 | ||||||||
\(486\) | 21.3371 | 0.967870 | ||||||||
\(487\) | −24.8359 | −1.12542 | −0.562712 | − | 0.826653i | \(-0.690242\pi\) | ||||
−0.562712 | + | 0.826653i | \(0.690242\pi\) | |||||||
\(488\) | 8.93624 | 0.404524 | ||||||||
\(489\) | −14.4892 | −0.655225 | ||||||||
\(490\) | −3.91524 | −0.176872 | ||||||||
\(491\) | −23.1591 | −1.04515 | −0.522577 | − | 0.852592i | \(-0.675029\pi\) | ||||
−0.522577 | + | 0.852592i | \(0.675029\pi\) | |||||||
\(492\) | 5.78085 | 0.260621 | ||||||||
\(493\) | −26.3722 | −1.18775 | ||||||||
\(494\) | 11.7016 | 0.526478 | ||||||||
\(495\) | 1.58268 | 0.0711361 | ||||||||
\(496\) | −1.17172 | −0.0526118 | ||||||||
\(497\) | −9.66603 | −0.433580 | ||||||||
\(498\) | −6.53724 | −0.292941 | ||||||||
\(499\) | −22.8739 | −1.02397 | −0.511987 | − | 0.858993i | \(-0.671091\pi\) | ||||
−0.511987 | + | 0.858993i | \(0.671091\pi\) | |||||||
\(500\) | −4.83336 | −0.216154 | ||||||||
\(501\) | 29.4632 | 1.31632 | ||||||||
\(502\) | 31.5667 | 1.40889 | ||||||||
\(503\) | −18.4696 | −0.823517 | −0.411759 | − | 0.911293i | \(-0.635085\pi\) | ||||
−0.411759 | + | 0.911293i | \(0.635085\pi\) | |||||||
\(504\) | 1.03586 | 0.0461411 | ||||||||
\(505\) | 2.84453 | 0.126580 | ||||||||
\(506\) | −38.5182 | −1.71234 | ||||||||
\(507\) | −2.04069 | −0.0906301 | ||||||||
\(508\) | 18.5716 | 0.823983 | ||||||||
\(509\) | −2.68795 | −0.119141 | −0.0595706 | − | 0.998224i | \(-0.518973\pi\) | ||||
−0.0595706 | + | 0.998224i | \(0.518973\pi\) | |||||||
\(510\) | −5.34278 | −0.236582 | ||||||||
\(511\) | 11.4011 | 0.504353 | ||||||||
\(512\) | 23.1017 | 1.02096 | ||||||||
\(513\) | −23.6044 | −1.04216 | ||||||||
\(514\) | 17.0285 | 0.751094 | ||||||||
\(515\) | −0.337566 | −0.0148749 | ||||||||
\(516\) | −0.762809 | −0.0335808 | ||||||||
\(517\) | −19.3287 | −0.850073 | ||||||||
\(518\) | 10.8934 | 0.478629 | ||||||||
\(519\) | 40.9627 | 1.79806 | ||||||||
\(520\) | 0.345814 | 0.0151650 | ||||||||
\(521\) | −44.7668 | −1.96127 | −0.980635 | − | 0.195843i | \(-0.937256\pi\) | ||||
−0.980635 | + | 0.195843i | \(0.937256\pi\) | |||||||
\(522\) | −13.6530 | −0.597576 | ||||||||
\(523\) | −2.66249 | −0.116422 | −0.0582112 | − | 0.998304i | \(-0.518540\pi\) | ||||
−0.0582112 | + | 0.998304i | \(0.518540\pi\) | |||||||
\(524\) | −13.2446 | −0.578592 | ||||||||
\(525\) | −8.65861 | −0.377893 | ||||||||
\(526\) | −26.1524 | −1.14030 | ||||||||
\(527\) | 1.01977 | 0.0444217 | ||||||||
\(528\) | 39.4327 | 1.71609 | ||||||||
\(529\) | 3.53781 | 0.153818 | ||||||||
\(530\) | 3.07613 | 0.133619 | ||||||||
\(531\) | 0.779674 | 0.0338350 | ||||||||
\(532\) | 7.92539 | 0.343609 | ||||||||
\(533\) | 1.95590 | 0.0847196 | ||||||||
\(534\) | −17.9148 | −0.775247 | ||||||||
\(535\) | 3.23055 | 0.139669 | ||||||||
\(536\) | −4.61323 | −0.199261 | ||||||||
\(537\) | 20.5238 | 0.885668 | ||||||||
\(538\) | −25.7142 | −1.10862 | ||||||||
\(539\) | −25.1492 | −1.08325 | ||||||||
\(540\) | 1.83138 | 0.0788102 | ||||||||
\(541\) | −17.0596 | −0.733450 | −0.366725 | − | 0.930329i | \(-0.619521\pi\) | ||||
−0.366725 | + | 0.930329i | \(0.619521\pi\) | |||||||
\(542\) | −28.0994 | −1.20697 | ||||||||
\(543\) | −2.12091 | −0.0910168 | ||||||||
\(544\) | −28.6631 | −1.22892 | ||||||||
\(545\) | −1.13478 | −0.0486088 | ||||||||
\(546\) | −3.29075 | −0.140831 | ||||||||
\(547\) | 39.9654 | 1.70880 | 0.854398 | − | 0.519619i | \(-0.173926\pi\) | ||||
0.854398 | + | 0.519619i | \(0.173926\pi\) | |||||||
\(548\) | 20.9716 | 0.895862 | ||||||||
\(549\) | −10.1572 | −0.433500 | ||||||||
\(550\) | −36.5335 | −1.55779 | ||||||||
\(551\) | 39.7886 | 1.69505 | ||||||||
\(552\) | −10.7694 | −0.458378 | ||||||||
\(553\) | −0.394646 | −0.0167820 | ||||||||
\(554\) | 58.6028 | 2.48980 | ||||||||
\(555\) | 4.65351 | 0.197531 | ||||||||
\(556\) | 10.6380 | 0.451153 | ||||||||
\(557\) | −44.0020 | −1.86442 | −0.932212 | − | 0.361913i | \(-0.882124\pi\) | ||||
−0.932212 | + | 0.361913i | \(0.882124\pi\) | |||||||
\(558\) | 0.527937 | 0.0223493 | ||||||||
\(559\) | −0.258091 | −0.0109161 | ||||||||
\(560\) | 1.40677 | 0.0594470 | ||||||||
\(561\) | −34.3189 | −1.44895 | ||||||||
\(562\) | 12.3458 | 0.520776 | ||||||||
\(563\) | 44.7639 | 1.88657 | 0.943286 | − | 0.331980i | \(-0.107717\pi\) | ||||
0.943286 | + | 0.331980i | \(0.107717\pi\) | |||||||
\(564\) | 14.1878 | 0.597416 | ||||||||
\(565\) | 2.76681 | 0.116401 | ||||||||
\(566\) | −34.9979 | −1.47107 | ||||||||
\(567\) | 9.67157 | 0.406168 | ||||||||
\(568\) | −11.4030 | −0.478458 | ||||||||
\(569\) | −17.4692 | −0.732348 | −0.366174 | − | 0.930546i | \(-0.619332\pi\) | ||||
−0.366174 | + | 0.930546i | \(0.619332\pi\) | |||||||
\(570\) | 8.06081 | 0.337630 | ||||||||
\(571\) | 12.0268 | 0.503304 | 0.251652 | − | 0.967818i | \(-0.419026\pi\) | ||||
0.251652 | + | 0.967818i | \(0.419026\pi\) | |||||||
\(572\) | −5.83172 | −0.243836 | ||||||||
\(573\) | −12.8808 | −0.538104 | ||||||||
\(574\) | 3.15403 | 0.131647 | ||||||||
\(575\) | 25.1704 | 1.04968 | ||||||||
\(576\) | −3.66305 | −0.152627 | ||||||||
\(577\) | 15.0401 | 0.626127 | 0.313063 | − | 0.949732i | \(-0.398645\pi\) | ||||
0.313063 | + | 0.949732i | \(0.398645\pi\) | |||||||
\(578\) | 0.825173 | 0.0343227 | ||||||||
\(579\) | −26.0564 | −1.08287 | ||||||||
\(580\) | −3.08706 | −0.128183 | ||||||||
\(581\) | −1.49806 | −0.0621498 | ||||||||
\(582\) | 29.9984 | 1.24347 | ||||||||
\(583\) | 19.7593 | 0.818346 | ||||||||
\(584\) | 13.4498 | 0.556556 | ||||||||
\(585\) | −0.393064 | −0.0162512 | ||||||||
\(586\) | 35.8415 | 1.48060 | ||||||||
\(587\) | −24.0985 | −0.994653 | −0.497327 | − | 0.867563i | \(-0.665685\pi\) | ||||
−0.497327 | + | 0.867563i | \(0.665685\pi\) | |||||||
\(588\) | 18.4603 | 0.761290 | ||||||||
\(589\) | −1.53855 | −0.0633949 | ||||||||
\(590\) | 0.419732 | 0.0172801 | ||||||||
\(591\) | 18.0950 | 0.744331 | ||||||||
\(592\) | 32.4187 | 1.33240 | ||||||||
\(593\) | −30.9840 | −1.27236 | −0.636180 | − | 0.771541i | \(-0.719486\pi\) | ||||
−0.636180 | + | 0.771541i | \(0.719486\pi\) | |||||||
\(594\) | 28.0083 | 1.14919 | ||||||||
\(595\) | −1.22434 | −0.0501929 | ||||||||
\(596\) | 11.8401 | 0.484990 | ||||||||
\(597\) | 3.10992 | 0.127281 | ||||||||
\(598\) | 9.56614 | 0.391189 | ||||||||
\(599\) | 23.7689 | 0.971172 | 0.485586 | − | 0.874189i | \(-0.338606\pi\) | ||||
0.485586 | + | 0.874189i | \(0.338606\pi\) | |||||||
\(600\) | −10.2145 | −0.417007 | ||||||||
\(601\) | −11.2370 | −0.458368 | −0.229184 | − | 0.973383i | \(-0.573606\pi\) | ||||
−0.229184 | + | 0.973383i | \(0.573606\pi\) | |||||||
\(602\) | −0.416189 | −0.0169626 | ||||||||
\(603\) | 5.24355 | 0.213534 | ||||||||
\(604\) | 0.892789 | 0.0363271 | ||||||||
\(605\) | 1.75967 | 0.0715408 | ||||||||
\(606\) | −31.9325 | −1.29717 | ||||||||
\(607\) | −16.3757 | −0.664668 | −0.332334 | − | 0.943162i | \(-0.607836\pi\) | ||||
−0.332334 | + | 0.943162i | \(0.607836\pi\) | |||||||
\(608\) | 43.2450 | 1.75381 | ||||||||
\(609\) | −11.1895 | −0.453421 | ||||||||
\(610\) | −5.46806 | −0.221395 | ||||||||
\(611\) | 4.80034 | 0.194201 | ||||||||
\(612\) | 7.04368 | 0.284724 | ||||||||
\(613\) | −14.6355 | −0.591122 | −0.295561 | − | 0.955324i | \(-0.595506\pi\) | ||||
−0.295561 | + | 0.955324i | \(0.595506\pi\) | |||||||
\(614\) | 37.1625 | 1.49976 | ||||||||
\(615\) | 1.34736 | 0.0543307 | ||||||||
\(616\) | 3.58202 | 0.144324 | ||||||||
\(617\) | 12.9127 | 0.519845 | 0.259923 | − | 0.965629i | \(-0.416303\pi\) | ||||
0.259923 | + | 0.965629i | \(0.416303\pi\) | |||||||
\(618\) | 3.78949 | 0.152436 | ||||||||
\(619\) | −6.77381 | −0.272262 | −0.136131 | − | 0.990691i | \(-0.543467\pi\) | ||||
−0.136131 | + | 0.990691i | \(0.543467\pi\) | |||||||
\(620\) | 0.119371 | 0.00479406 | ||||||||
\(621\) | −19.2968 | −0.774354 | ||||||||
\(622\) | 19.1831 | 0.769173 | ||||||||
\(623\) | −4.10529 | −0.164475 | ||||||||
\(624\) | −9.79326 | −0.392044 | ||||||||
\(625\) | 23.3037 | 0.932149 | ||||||||
\(626\) | 0.797304 | 0.0318667 | ||||||||
\(627\) | 51.7780 | 2.06781 | ||||||||
\(628\) | −16.0862 | −0.641910 | ||||||||
\(629\) | −28.2145 | −1.12499 | ||||||||
\(630\) | −0.633843 | −0.0252529 | ||||||||
\(631\) | −37.5702 | −1.49564 | −0.747822 | − | 0.663899i | \(-0.768900\pi\) | ||||
−0.747822 | + | 0.663899i | \(0.768900\pi\) | |||||||
\(632\) | −0.465562 | −0.0185191 | ||||||||
\(633\) | 17.5948 | 0.699332 | ||||||||
\(634\) | 31.2984 | 1.24302 | ||||||||
\(635\) | 4.32854 | 0.171773 | ||||||||
\(636\) | −14.5039 | −0.575118 | ||||||||
\(637\) | 6.24590 | 0.247472 | ||||||||
\(638\) | −47.2121 | −1.86914 | ||||||||
\(639\) | 12.9610 | 0.512729 | ||||||||
\(640\) | 2.66127 | 0.105196 | ||||||||
\(641\) | 5.76346 | 0.227643 | 0.113822 | − | 0.993501i | \(-0.463691\pi\) | ||||
0.113822 | + | 0.993501i | \(0.463691\pi\) | |||||||
\(642\) | −36.2660 | −1.43130 | ||||||||
\(643\) | 45.6320 | 1.79955 | 0.899776 | − | 0.436352i | \(-0.143730\pi\) | ||||
0.899776 | + | 0.436352i | \(0.143730\pi\) | |||||||
\(644\) | 6.47909 | 0.255312 | ||||||||
\(645\) | −0.177790 | −0.00700048 | ||||||||
\(646\) | −48.8732 | −1.92289 | ||||||||
\(647\) | −20.8063 | −0.817980 | −0.408990 | − | 0.912539i | \(-0.634119\pi\) | ||||
−0.408990 | + | 0.912539i | \(0.634119\pi\) | |||||||
\(648\) | 11.4095 | 0.448208 | ||||||||
\(649\) | 2.69611 | 0.105832 | ||||||||
\(650\) | 9.07324 | 0.355882 | ||||||||
\(651\) | 0.432677 | 0.0169579 | ||||||||
\(652\) | 10.2834 | 0.402728 | ||||||||
\(653\) | −20.2172 | −0.791161 | −0.395581 | − | 0.918431i | \(-0.629457\pi\) | ||||
−0.395581 | + | 0.918431i | \(0.629457\pi\) | |||||||
\(654\) | 12.7390 | 0.498135 | ||||||||
\(655\) | −3.08695 | −0.120617 | ||||||||
\(656\) | 9.38638 | 0.366477 | ||||||||
\(657\) | −15.2875 | −0.596421 | ||||||||
\(658\) | 7.74089 | 0.301771 | ||||||||
\(659\) | −1.16763 | −0.0454845 | −0.0227423 | − | 0.999741i | \(-0.507240\pi\) | ||||
−0.0227423 | + | 0.999741i | \(0.507240\pi\) | |||||||
\(660\) | −4.01728 | −0.156372 | ||||||||
\(661\) | 13.1516 | 0.511540 | 0.255770 | − | 0.966738i | \(-0.417671\pi\) | ||||
0.255770 | + | 0.966738i | \(0.417671\pi\) | |||||||
\(662\) | −28.3847 | −1.10320 | ||||||||
\(663\) | 8.52323 | 0.331015 | ||||||||
\(664\) | −1.76725 | −0.0685826 | ||||||||
\(665\) | 1.84719 | 0.0716310 | ||||||||
\(666\) | −14.6068 | −0.566001 | ||||||||
\(667\) | 32.5276 | 1.25947 | ||||||||
\(668\) | −20.9108 | −0.809063 | ||||||||
\(669\) | 34.1590 | 1.32066 | ||||||||
\(670\) | 2.82282 | 0.109055 | ||||||||
\(671\) | −35.1237 | −1.35593 | ||||||||
\(672\) | −12.1615 | −0.469140 | ||||||||
\(673\) | −3.04069 | −0.117210 | −0.0586050 | − | 0.998281i | \(-0.518665\pi\) | ||||
−0.0586050 | + | 0.998281i | \(0.518665\pi\) | |||||||
\(674\) | 41.0318 | 1.58048 | ||||||||
\(675\) | −18.3025 | −0.704464 | ||||||||
\(676\) | 1.44833 | 0.0557050 | ||||||||
\(677\) | −8.26113 | −0.317501 | −0.158750 | − | 0.987319i | \(-0.550747\pi\) | ||||
−0.158750 | + | 0.987319i | \(0.550747\pi\) | |||||||
\(678\) | −31.0600 | −1.19285 | ||||||||
\(679\) | 6.87434 | 0.263813 | ||||||||
\(680\) | −1.44434 | −0.0553881 | ||||||||
\(681\) | 17.5668 | 0.673161 | ||||||||
\(682\) | 1.82560 | 0.0699060 | ||||||||
\(683\) | 22.9900 | 0.879686 | 0.439843 | − | 0.898075i | \(-0.355034\pi\) | ||||
0.439843 | + | 0.898075i | \(0.355034\pi\) | |||||||
\(684\) | −10.6270 | −0.406334 | ||||||||
\(685\) | 4.88790 | 0.186757 | ||||||||
\(686\) | 21.3599 | 0.815526 | ||||||||
\(687\) | 40.4128 | 1.54185 | ||||||||
\(688\) | −1.23858 | −0.0472203 | ||||||||
\(689\) | −4.90729 | −0.186953 | ||||||||
\(690\) | 6.58980 | 0.250869 | ||||||||
\(691\) | 8.44262 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(692\) | −29.0723 | −1.10516 | ||||||||
\(693\) | −4.07144 | −0.154661 | ||||||||
\(694\) | 64.6510 | 2.45412 | ||||||||
\(695\) | 2.47943 | 0.0940503 | ||||||||
\(696\) | −13.2002 | −0.500352 | ||||||||
\(697\) | −8.16912 | −0.309427 | ||||||||
\(698\) | −43.2978 | −1.63884 | ||||||||
\(699\) | −0.609820 | −0.0230655 | ||||||||
\(700\) | 6.14524 | 0.232268 | ||||||||
\(701\) | 27.1532 | 1.02556 | 0.512781 | − | 0.858519i | \(-0.328615\pi\) | ||||
0.512781 | + | 0.858519i | \(0.328615\pi\) | |||||||
\(702\) | −6.95597 | −0.262536 | ||||||||
\(703\) | 42.5681 | 1.60549 | ||||||||
\(704\) | −12.6668 | −0.477398 | ||||||||
\(705\) | 3.30680 | 0.124541 | ||||||||
\(706\) | −37.9142 | −1.42692 | ||||||||
\(707\) | −7.31756 | −0.275205 | ||||||||
\(708\) | −1.97903 | −0.0743765 | ||||||||
\(709\) | 14.0594 | 0.528014 | 0.264007 | − | 0.964521i | \(-0.414956\pi\) | ||||
0.264007 | + | 0.964521i | \(0.414956\pi\) | |||||||
\(710\) | 6.97746 | 0.261859 | ||||||||
\(711\) | 0.529173 | 0.0198456 | ||||||||
\(712\) | −4.84300 | −0.181499 | ||||||||
\(713\) | −1.25778 | −0.0471043 | ||||||||
\(714\) | 13.7443 | 0.514367 | ||||||||
\(715\) | −1.35921 | −0.0508317 | ||||||||
\(716\) | −14.5663 | −0.544368 | ||||||||
\(717\) | −55.9902 | −2.09099 | ||||||||
\(718\) | 18.5339 | 0.691680 | ||||||||
\(719\) | 30.8032 | 1.14876 | 0.574382 | − | 0.818587i | \(-0.305242\pi\) | ||||
0.574382 | + | 0.818587i | \(0.305242\pi\) | |||||||
\(720\) | −1.88631 | −0.0702988 | ||||||||
\(721\) | 0.868388 | 0.0323405 | ||||||||
\(722\) | 38.4541 | 1.43112 | ||||||||
\(723\) | −28.2953 | −1.05231 | ||||||||
\(724\) | 1.50526 | 0.0559426 | ||||||||
\(725\) | 30.8516 | 1.14580 | ||||||||
\(726\) | −19.7539 | −0.733137 | ||||||||
\(727\) | 19.3629 | 0.718131 | 0.359066 | − | 0.933312i | \(-0.383095\pi\) | ||||
0.359066 | + | 0.933312i | \(0.383095\pi\) | |||||||
\(728\) | −0.889607 | −0.0329710 | ||||||||
\(729\) | 9.96404 | 0.369039 | ||||||||
\(730\) | −8.22989 | −0.304602 | ||||||||
\(731\) | 1.07795 | 0.0398695 | ||||||||
\(732\) | 25.7819 | 0.952925 | ||||||||
\(733\) | −47.4521 | −1.75269 | −0.876343 | − | 0.481689i | \(-0.840024\pi\) | ||||
−0.876343 | + | 0.481689i | \(0.840024\pi\) | |||||||
\(734\) | 34.3403 | 1.26752 | ||||||||
\(735\) | 4.30259 | 0.158704 | ||||||||
\(736\) | 35.3532 | 1.30314 | ||||||||
\(737\) | 18.1322 | 0.667907 | ||||||||
\(738\) | −4.22918 | −0.155678 | ||||||||
\(739\) | 25.8525 | 0.950999 | 0.475499 | − | 0.879716i | \(-0.342267\pi\) | ||||
0.475499 | + | 0.879716i | \(0.342267\pi\) | |||||||
\(740\) | −3.30272 | −0.121410 | ||||||||
\(741\) | −12.8593 | −0.472396 | ||||||||
\(742\) | −7.91335 | −0.290508 | ||||||||
\(743\) | 17.0589 | 0.625829 | 0.312915 | − | 0.949781i | \(-0.398695\pi\) | ||||
0.312915 | + | 0.949781i | \(0.398695\pi\) | |||||||
\(744\) | 0.510427 | 0.0187132 | ||||||||
\(745\) | 2.75961 | 0.101104 | ||||||||
\(746\) | −71.2621 | −2.60909 | ||||||||
\(747\) | 2.00872 | 0.0734950 | ||||||||
\(748\) | 24.3570 | 0.890581 | ||||||||
\(749\) | −8.31060 | −0.303663 | ||||||||
\(750\) | 12.6463 | 0.461776 | ||||||||
\(751\) | 18.1348 | 0.661749 | 0.330875 | − | 0.943675i | \(-0.392656\pi\) | ||||
0.330875 | + | 0.943675i | \(0.392656\pi\) | |||||||
\(752\) | 23.0368 | 0.840067 | ||||||||
\(753\) | −34.6898 | −1.26417 | ||||||||
\(754\) | 11.7253 | 0.427010 | ||||||||
\(755\) | 0.208085 | 0.00757298 | ||||||||
\(756\) | −4.71123 | −0.171346 | ||||||||
\(757\) | 0.447506 | 0.0162649 | 0.00813244 | − | 0.999967i | \(-0.497411\pi\) | ||||
0.00813244 | + | 0.999967i | \(0.497411\pi\) | |||||||
\(758\) | −25.4515 | −0.924438 | ||||||||
\(759\) | 42.3290 | 1.53645 | ||||||||
\(760\) | 2.17913 | 0.0790452 | ||||||||
\(761\) | 39.2873 | 1.42416 | 0.712081 | − | 0.702097i | \(-0.247753\pi\) | ||||
0.712081 | + | 0.702097i | \(0.247753\pi\) | |||||||
\(762\) | −48.5919 | −1.76030 | ||||||||
\(763\) | 2.91923 | 0.105683 | ||||||||
\(764\) | 9.14186 | 0.330741 | ||||||||
\(765\) | 1.64169 | 0.0593554 | ||||||||
\(766\) | 22.4429 | 0.810896 | ||||||||
\(767\) | −0.669589 | −0.0241775 | ||||||||
\(768\) | −42.7146 | −1.54133 | ||||||||
\(769\) | 24.3862 | 0.879388 | 0.439694 | − | 0.898148i | \(-0.355087\pi\) | ||||
0.439694 | + | 0.898148i | \(0.355087\pi\) | |||||||
\(770\) | −2.19183 | −0.0789880 | ||||||||
\(771\) | −18.7132 | −0.673939 | ||||||||
\(772\) | 18.4929 | 0.665575 | ||||||||
\(773\) | 33.8399 | 1.21714 | 0.608568 | − | 0.793502i | \(-0.291744\pi\) | ||||
0.608568 | + | 0.793502i | \(0.291744\pi\) | |||||||
\(774\) | 0.558060 | 0.0200591 | ||||||||
\(775\) | −1.19297 | −0.0428529 | ||||||||
\(776\) | 8.10964 | 0.291119 | ||||||||
\(777\) | −11.9712 | −0.429463 | ||||||||
\(778\) | −56.1045 | −2.01145 | ||||||||
\(779\) | 12.3250 | 0.441589 | ||||||||
\(780\) | 0.997706 | 0.0357236 | ||||||||
\(781\) | 44.8191 | 1.60375 | ||||||||
\(782\) | −39.9544 | −1.42877 | ||||||||
\(783\) | −23.6523 | −0.845263 | ||||||||
\(784\) | 29.9741 | 1.07050 | ||||||||
\(785\) | −3.74926 | −0.133817 | ||||||||
\(786\) | 34.6538 | 1.23606 | ||||||||
\(787\) | −5.07402 | −0.180869 | −0.0904346 | − | 0.995902i | \(-0.528826\pi\) | ||||
−0.0904346 | + | 0.995902i | \(0.528826\pi\) | |||||||
\(788\) | −12.8425 | −0.457496 | ||||||||
\(789\) | 28.7398 | 1.02316 | ||||||||
\(790\) | 0.284876 | 0.0101355 | ||||||||
\(791\) | −7.11761 | −0.253073 | ||||||||
\(792\) | −4.80306 | −0.170669 | ||||||||
\(793\) | 8.72309 | 0.309766 | ||||||||
\(794\) | 41.2485 | 1.46385 | ||||||||
\(795\) | −3.38047 | −0.119893 | ||||||||
\(796\) | −2.20719 | −0.0782319 | ||||||||
\(797\) | −40.4586 | −1.43312 | −0.716558 | − | 0.697527i | \(-0.754284\pi\) | ||||
−0.716558 | + | 0.697527i | \(0.754284\pi\) | |||||||
\(798\) | −20.7364 | −0.734062 | ||||||||
\(799\) | −20.0493 | −0.709294 | ||||||||
\(800\) | 33.5316 | 1.18552 | ||||||||
\(801\) | 5.50471 | 0.194499 | ||||||||
\(802\) | −35.9726 | −1.27024 | ||||||||
\(803\) | −52.8640 | −1.86553 | ||||||||
\(804\) | −13.3096 | −0.469393 | ||||||||
\(805\) | 1.51010 | 0.0532240 | ||||||||
\(806\) | −0.453396 | −0.0159702 | ||||||||
\(807\) | 28.2582 | 0.994737 | ||||||||
\(808\) | −8.63250 | −0.303690 | ||||||||
\(809\) | 33.6236 | 1.18214 | 0.591072 | − | 0.806619i | \(-0.298705\pi\) | ||||
0.591072 | + | 0.806619i | \(0.298705\pi\) | |||||||
\(810\) | −6.98146 | −0.245303 | ||||||||
\(811\) | −31.9444 | −1.12172 | −0.560860 | − | 0.827911i | \(-0.689529\pi\) | ||||
−0.560860 | + | 0.827911i | \(0.689529\pi\) | |||||||
\(812\) | 7.94147 | 0.278691 | ||||||||
\(813\) | 30.8794 | 1.08299 | ||||||||
\(814\) | −50.5102 | −1.77038 | ||||||||
\(815\) | 2.39677 | 0.0839553 | ||||||||
\(816\) | 40.9030 | 1.43189 | ||||||||
\(817\) | −1.62634 | −0.0568984 | ||||||||
\(818\) | −20.8287 | −0.728258 | ||||||||
\(819\) | 1.01116 | 0.0353327 | ||||||||
\(820\) | −0.956255 | −0.0333939 | ||||||||
\(821\) | −52.2211 | −1.82253 | −0.911264 | − | 0.411824i | \(-0.864892\pi\) | ||||
−0.911264 | + | 0.411824i | \(0.864892\pi\) | |||||||
\(822\) | −54.8712 | −1.91385 | ||||||||
\(823\) | 47.2992 | 1.64875 | 0.824374 | − | 0.566046i | \(-0.191527\pi\) | ||||
0.824374 | + | 0.566046i | \(0.191527\pi\) | |||||||
\(824\) | 1.02443 | 0.0356879 | ||||||||
\(825\) | 40.1480 | 1.39777 | ||||||||
\(826\) | −1.07976 | −0.0375696 | ||||||||
\(827\) | −28.6641 | −0.996747 | −0.498374 | − | 0.866962i | \(-0.666069\pi\) | ||||
−0.498374 | + | 0.866962i | \(0.666069\pi\) | |||||||
\(828\) | −8.68769 | −0.301918 | ||||||||
\(829\) | 11.7300 | 0.407399 | 0.203700 | − | 0.979033i | \(-0.434703\pi\) | ||||
0.203700 | + | 0.979033i | \(0.434703\pi\) | |||||||
\(830\) | 1.08138 | 0.0375351 | ||||||||
\(831\) | −64.4007 | −2.23404 | ||||||||
\(832\) | 3.14585 | 0.109063 | ||||||||
\(833\) | −26.0869 | −0.903858 | ||||||||
\(834\) | −27.8339 | −0.963810 | ||||||||
\(835\) | −4.87374 | −0.168663 | ||||||||
\(836\) | −36.7482 | −1.27096 | ||||||||
\(837\) | 0.914589 | 0.0316128 | ||||||||
\(838\) | −54.1164 | −1.86942 | ||||||||
\(839\) | −36.8104 | −1.27084 | −0.635418 | − | 0.772168i | \(-0.719172\pi\) | ||||
−0.635418 | + | 0.772168i | \(0.719172\pi\) | |||||||
\(840\) | −0.612821 | −0.0211443 | ||||||||
\(841\) | 10.8693 | 0.374804 | ||||||||
\(842\) | −14.5370 | −0.500980 | ||||||||
\(843\) | −13.5672 | −0.467280 | ||||||||
\(844\) | −12.4875 | −0.429838 | ||||||||
\(845\) | 0.337566 | 0.0116126 | ||||||||
\(846\) | −10.3796 | −0.356858 | ||||||||
\(847\) | −4.52675 | −0.155541 | ||||||||
\(848\) | −23.5501 | −0.808713 | ||||||||
\(849\) | 38.4604 | 1.31996 | ||||||||
\(850\) | −37.8957 | −1.29981 | ||||||||
\(851\) | 34.7999 | 1.19292 | ||||||||
\(852\) | −32.8986 | −1.12709 | ||||||||
\(853\) | 24.7408 | 0.847108 | 0.423554 | − | 0.905871i | \(-0.360782\pi\) | ||||
0.423554 | + | 0.905871i | \(0.360782\pi\) | |||||||
\(854\) | 14.0666 | 0.481349 | ||||||||
\(855\) | −2.47687 | −0.0847070 | ||||||||
\(856\) | −9.80398 | −0.335093 | ||||||||
\(857\) | 44.5905 | 1.52318 | 0.761592 | − | 0.648057i | \(-0.224418\pi\) | ||||
0.761592 | + | 0.648057i | \(0.224418\pi\) | |||||||
\(858\) | 15.2584 | 0.520915 | ||||||||
\(859\) | −30.3184 | −1.03445 | −0.517225 | − | 0.855849i | \(-0.673035\pi\) | ||||
−0.517225 | + | 0.855849i | \(0.673035\pi\) | |||||||
\(860\) | 0.126182 | 0.00430278 | ||||||||
\(861\) | −3.46608 | −0.118124 | ||||||||
\(862\) | −37.4519 | −1.27562 | ||||||||
\(863\) | 34.3245 | 1.16842 | 0.584210 | − | 0.811603i | \(-0.301405\pi\) | ||||
0.584210 | + | 0.811603i | \(0.301405\pi\) | |||||||
\(864\) | −25.7069 | −0.874566 | ||||||||
\(865\) | −6.77595 | −0.230389 | ||||||||
\(866\) | 24.2936 | 0.825530 | ||||||||
\(867\) | −0.906811 | −0.0307969 | ||||||||
\(868\) | −0.307082 | −0.0104230 | ||||||||
\(869\) | 1.82988 | 0.0620745 | ||||||||
\(870\) | 8.07717 | 0.273842 | ||||||||
\(871\) | −4.50319 | −0.152585 | ||||||||
\(872\) | 3.44381 | 0.116622 | ||||||||
\(873\) | −9.21768 | −0.311971 | ||||||||
\(874\) | 60.2804 | 2.03901 | ||||||||
\(875\) | 2.89798 | 0.0979696 | ||||||||
\(876\) | 38.8039 | 1.31106 | ||||||||
\(877\) | −22.4203 | −0.757080 | −0.378540 | − | 0.925585i | \(-0.623574\pi\) | ||||
−0.378540 | + | 0.925585i | \(0.623574\pi\) | |||||||
\(878\) | −14.2369 | −0.480472 | ||||||||
\(879\) | −39.3875 | −1.32851 | ||||||||
\(880\) | −6.52287 | −0.219886 | ||||||||
\(881\) | −42.0849 | −1.41788 | −0.708939 | − | 0.705270i | \(-0.750826\pi\) | ||||
−0.708939 | + | 0.705270i | \(0.750826\pi\) | |||||||
\(882\) | −13.5053 | −0.454747 | ||||||||
\(883\) | 6.14059 | 0.206647 | 0.103324 | − | 0.994648i | \(-0.467052\pi\) | ||||
0.103324 | + | 0.994648i | \(0.467052\pi\) | |||||||
\(884\) | −6.04916 | −0.203455 | ||||||||
\(885\) | −0.461258 | −0.0155050 | ||||||||
\(886\) | 27.2898 | 0.916819 | ||||||||
\(887\) | 10.8303 | 0.363646 | 0.181823 | − | 0.983331i | \(-0.441800\pi\) | ||||
0.181823 | + | 0.983331i | \(0.441800\pi\) | |||||||
\(888\) | −14.1223 | −0.473914 | ||||||||
\(889\) | −11.1352 | −0.373462 | ||||||||
\(890\) | 2.96342 | 0.0993340 | ||||||||
\(891\) | −44.8448 | −1.50236 | ||||||||
\(892\) | −24.2436 | −0.811734 | ||||||||
\(893\) | 30.2490 | 1.01225 | ||||||||
\(894\) | −30.9792 | −1.03610 | ||||||||
\(895\) | −3.39500 | −0.113482 | ||||||||
\(896\) | −6.84611 | −0.228713 | ||||||||
\(897\) | −10.5126 | −0.351005 | ||||||||
\(898\) | −57.7200 | −1.92614 | ||||||||
\(899\) | −1.54167 | −0.0514177 | ||||||||
\(900\) | −8.24005 | −0.274668 | ||||||||
\(901\) | 20.4960 | 0.682821 | ||||||||
\(902\) | −14.6245 | −0.486943 | ||||||||
\(903\) | 0.457365 | 0.0152201 | ||||||||
\(904\) | −8.39662 | −0.279268 | ||||||||
\(905\) | 0.350836 | 0.0116622 | ||||||||
\(906\) | −2.33594 | −0.0776065 | ||||||||
\(907\) | −14.3673 | −0.477059 | −0.238529 | − | 0.971135i | \(-0.576665\pi\) | ||||
−0.238529 | + | 0.971135i | \(0.576665\pi\) | |||||||
\(908\) | −12.4676 | −0.413752 | ||||||||
\(909\) | 9.81198 | 0.325443 | ||||||||
\(910\) | 0.544349 | 0.0180450 | ||||||||
\(911\) | −35.6324 | −1.18055 | −0.590276 | − | 0.807201i | \(-0.700981\pi\) | ||||
−0.590276 | + | 0.807201i | \(0.700981\pi\) | |||||||
\(912\) | −61.7116 | −2.04347 | ||||||||
\(913\) | 6.94613 | 0.229883 | ||||||||
\(914\) | −31.5329 | −1.04301 | ||||||||
\(915\) | 6.00905 | 0.198653 | ||||||||
\(916\) | −28.6820 | −0.947681 | ||||||||
\(917\) | 7.94117 | 0.262241 | ||||||||
\(918\) | 29.0526 | 0.958879 | ||||||||
\(919\) | −22.6521 | −0.747224 | −0.373612 | − | 0.927585i | \(-0.621881\pi\) | ||||
−0.373612 | + | 0.927585i | \(0.621881\pi\) | |||||||
\(920\) | 1.78146 | 0.0587329 | ||||||||
\(921\) | −40.8392 | −1.34570 | ||||||||
\(922\) | −74.6142 | −2.45729 | ||||||||
\(923\) | −11.1310 | −0.366381 | ||||||||
\(924\) | 10.3344 | 0.339978 | ||||||||
\(925\) | 33.0068 | 1.08526 | ||||||||
\(926\) | 14.3322 | 0.470986 | ||||||||
\(927\) | −1.16441 | −0.0382441 | ||||||||
\(928\) | 43.3327 | 1.42247 | ||||||||
\(929\) | −4.22358 | −0.138571 | −0.0692856 | − | 0.997597i | \(-0.522072\pi\) | ||||
−0.0692856 | + | 0.997597i | \(0.522072\pi\) | |||||||
\(930\) | −0.312329 | −0.0102417 | ||||||||
\(931\) | 39.3581 | 1.28991 | ||||||||
\(932\) | 0.432806 | 0.0141770 | ||||||||
\(933\) | −21.0810 | −0.690161 | ||||||||
\(934\) | 30.6412 | 1.00261 | ||||||||
\(935\) | 5.67696 | 0.185656 | ||||||||
\(936\) | 1.19286 | 0.0389898 | ||||||||
\(937\) | 55.9893 | 1.82909 | 0.914546 | − | 0.404483i | \(-0.132548\pi\) | ||||
0.914546 | + | 0.404483i | \(0.132548\pi\) | |||||||
\(938\) | −7.26171 | −0.237103 | ||||||||
\(939\) | −0.876185 | −0.0285932 | ||||||||
\(940\) | −2.34692 | −0.0765481 | ||||||||
\(941\) | −33.3262 | −1.08640 | −0.543201 | − | 0.839603i | \(-0.682788\pi\) | ||||
−0.543201 | + | 0.839603i | \(0.682788\pi\) | |||||||
\(942\) | 42.0889 | 1.37133 | ||||||||
\(943\) | 10.0758 | 0.328114 | ||||||||
\(944\) | −3.21336 | −0.104586 | ||||||||
\(945\) | −1.09806 | −0.0357199 | ||||||||
\(946\) | 1.92977 | 0.0627423 | ||||||||
\(947\) | −9.46185 | −0.307469 | −0.153734 | − | 0.988112i | \(-0.549130\pi\) | ||||
−0.153734 | + | 0.988112i | \(0.549130\pi\) | |||||||
\(948\) | −1.34319 | −0.0436248 | ||||||||
\(949\) | 13.1290 | 0.426185 | ||||||||
\(950\) | 57.1744 | 1.85498 | ||||||||
\(951\) | −34.3949 | −1.11533 | ||||||||
\(952\) | 3.71557 | 0.120422 | ||||||||
\(953\) | −27.7988 | −0.900492 | −0.450246 | − | 0.892905i | \(-0.648664\pi\) | ||||
−0.450246 | + | 0.892905i | \(0.648664\pi\) | |||||||
\(954\) | 10.6109 | 0.343539 | ||||||||
\(955\) | 2.13072 | 0.0689484 | ||||||||
\(956\) | 39.7377 | 1.28521 | ||||||||
\(957\) | 51.8830 | 1.67714 | ||||||||
\(958\) | 54.8850 | 1.77325 | ||||||||
\(959\) | −12.5741 | −0.406040 | ||||||||
\(960\) | 2.16707 | 0.0699419 | ||||||||
\(961\) | −30.9404 | −0.998077 | ||||||||
\(962\) | 12.5444 | 0.404448 | ||||||||
\(963\) | 11.1435 | 0.359095 | ||||||||
\(964\) | 20.0819 | 0.646796 | ||||||||
\(965\) | 4.31020 | 0.138750 | ||||||||
\(966\) | −16.9523 | −0.545430 | ||||||||
\(967\) | −54.5201 | −1.75325 | −0.876624 | − | 0.481175i | \(-0.840210\pi\) | ||||
−0.876624 | + | 0.481175i | \(0.840210\pi\) | |||||||
\(968\) | −5.34019 | −0.171640 | ||||||||
\(969\) | 53.7085 | 1.72537 | ||||||||
\(970\) | −4.96227 | −0.159329 | ||||||||
\(971\) | −16.2193 | −0.520503 | −0.260251 | − | 0.965541i | \(-0.583805\pi\) | ||||
−0.260251 | + | 0.965541i | \(0.583805\pi\) | |||||||
\(972\) | 16.6417 | 0.533783 | ||||||||
\(973\) | −6.37834 | −0.204480 | ||||||||
\(974\) | −46.1195 | −1.47777 | ||||||||
\(975\) | −9.97090 | −0.319324 | ||||||||
\(976\) | 41.8621 | 1.33997 | ||||||||
\(977\) | −10.4155 | −0.333221 | −0.166610 | − | 0.986023i | \(-0.553282\pi\) | ||||
−0.166610 | + | 0.986023i | \(0.553282\pi\) | |||||||
\(978\) | −26.9060 | −0.860359 | ||||||||
\(979\) | 19.0353 | 0.608370 | ||||||||
\(980\) | −3.05366 | −0.0975457 | ||||||||
\(981\) | −3.91435 | −0.124975 | ||||||||
\(982\) | −43.0057 | −1.37237 | ||||||||
\(983\) | 60.0352 | 1.91483 | 0.957413 | − | 0.288722i | \(-0.0932302\pi\) | ||||
0.957413 | + | 0.288722i | \(0.0932302\pi\) | |||||||
\(984\) | −4.08892 | −0.130350 | ||||||||
\(985\) | −2.99324 | −0.0953726 | ||||||||
\(986\) | −48.9724 | −1.55960 | ||||||||
\(987\) | −8.50673 | −0.270772 | ||||||||
\(988\) | 9.12655 | 0.290354 | ||||||||
\(989\) | −1.32955 | −0.0422772 | ||||||||
\(990\) | 2.93898 | 0.0934070 | ||||||||
\(991\) | 11.7059 | 0.371849 | 0.185925 | − | 0.982564i | \(-0.440472\pi\) | ||||
0.185925 | + | 0.982564i | \(0.440472\pi\) | |||||||
\(992\) | −1.67560 | −0.0532002 | ||||||||
\(993\) | 31.1929 | 0.989878 | ||||||||
\(994\) | −17.9495 | −0.569323 | ||||||||
\(995\) | −0.514436 | −0.0163087 | ||||||||
\(996\) | −5.09868 | −0.161558 | ||||||||
\(997\) | −16.3890 | −0.519045 | −0.259522 | − | 0.965737i | \(-0.583565\pi\) | ||||
−0.259522 | + | 0.965737i | \(0.583565\pi\) | |||||||
\(998\) | −42.4760 | −1.34455 | ||||||||
\(999\) | −25.3045 | −0.800600 |
(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 | 1339.2.a.e.1.17 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1339.2.a.e.1.17 | ✓ | 21 | 1.1 | even | 1 | trivial |