Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, 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("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.53 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 | ||||||||
\(3\) | 1.43148 | 0.826464 | 0.413232 | − | 0.910626i | \(-0.364400\pi\) | ||||
0.413232 | + | 0.910626i | \(0.364400\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.803871 | 0.359502 | 0.179751 | − | 0.983712i | \(-0.442471\pi\) | ||||
0.179751 | + | 0.983712i | \(0.442471\pi\) | |||||||
\(6\) | −1.43148 | −0.584399 | ||||||||
\(7\) | −3.58216 | −1.35393 | −0.676964 | − | 0.736016i | \(-0.736705\pi\) | ||||
−0.676964 | + | 0.736016i | \(0.736705\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.950869 | −0.316956 | ||||||||
\(10\) | −0.803871 | −0.254206 | ||||||||
\(11\) | −1.17531 | −0.354370 | −0.177185 | − | 0.984178i | \(-0.556699\pi\) | ||||
−0.177185 | + | 0.984178i | \(0.556699\pi\) | |||||||
\(12\) | 1.43148 | 0.413232 | ||||||||
\(13\) | 4.60600 | 1.27748 | 0.638738 | − | 0.769425i | \(-0.279457\pi\) | ||||
0.638738 | + | 0.769425i | \(0.279457\pi\) | |||||||
\(14\) | 3.58216 | 0.957372 | ||||||||
\(15\) | 1.15072 | 0.297116 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.42510 | 0.345639 | 0.172819 | − | 0.984954i | \(-0.444712\pi\) | ||||
0.172819 | + | 0.984954i | \(0.444712\pi\) | |||||||
\(18\) | 0.950869 | 0.224122 | ||||||||
\(19\) | 7.85309 | 1.80162 | 0.900812 | − | 0.434210i | \(-0.142972\pi\) | ||||
0.900812 | + | 0.434210i | \(0.142972\pi\) | |||||||
\(20\) | 0.803871 | 0.179751 | ||||||||
\(21\) | −5.12778 | −1.11897 | ||||||||
\(22\) | 1.17531 | 0.250577 | ||||||||
\(23\) | −1.12223 | −0.234000 | −0.117000 | − | 0.993132i | \(-0.537328\pi\) | ||||
−0.117000 | + | 0.993132i | \(0.537328\pi\) | |||||||
\(24\) | −1.43148 | −0.292199 | ||||||||
\(25\) | −4.35379 | −0.870758 | ||||||||
\(26\) | −4.60600 | −0.903311 | ||||||||
\(27\) | −5.65558 | −1.08842 | ||||||||
\(28\) | −3.58216 | −0.676964 | ||||||||
\(29\) | −5.21621 | −0.968626 | −0.484313 | − | 0.874895i | \(-0.660930\pi\) | ||||
−0.484313 | + | 0.874895i | \(0.660930\pi\) | |||||||
\(30\) | −1.15072 | −0.210092 | ||||||||
\(31\) | 5.09216 | 0.914579 | 0.457289 | − | 0.889318i | \(-0.348820\pi\) | ||||
0.457289 | + | 0.889318i | \(0.348820\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.68243 | −0.292874 | ||||||||
\(34\) | −1.42510 | −0.244403 | ||||||||
\(35\) | −2.87959 | −0.486740 | ||||||||
\(36\) | −0.950869 | −0.158478 | ||||||||
\(37\) | −3.48843 | −0.573494 | −0.286747 | − | 0.958006i | \(-0.592574\pi\) | ||||
−0.286747 | + | 0.958006i | \(0.592574\pi\) | |||||||
\(38\) | −7.85309 | −1.27394 | ||||||||
\(39\) | 6.59339 | 1.05579 | ||||||||
\(40\) | −0.803871 | −0.127103 | ||||||||
\(41\) | −4.00456 | −0.625407 | −0.312703 | − | 0.949851i | \(-0.601235\pi\) | ||||
−0.312703 | + | 0.949851i | \(0.601235\pi\) | |||||||
\(42\) | 5.12778 | 0.791234 | ||||||||
\(43\) | −1.27939 | −0.195104 | −0.0975522 | − | 0.995230i | \(-0.531101\pi\) | ||||
−0.0975522 | + | 0.995230i | \(0.531101\pi\) | |||||||
\(44\) | −1.17531 | −0.177185 | ||||||||
\(45\) | −0.764376 | −0.113946 | ||||||||
\(46\) | 1.12223 | 0.165463 | ||||||||
\(47\) | 6.62131 | 0.965818 | 0.482909 | − | 0.875671i | \(-0.339580\pi\) | ||||
0.482909 | + | 0.875671i | \(0.339580\pi\) | |||||||
\(48\) | 1.43148 | 0.206616 | ||||||||
\(49\) | 5.83185 | 0.833121 | ||||||||
\(50\) | 4.35379 | 0.615719 | ||||||||
\(51\) | 2.04001 | 0.285658 | ||||||||
\(52\) | 4.60600 | 0.638738 | ||||||||
\(53\) | 12.3592 | 1.69767 | 0.848834 | − | 0.528659i | \(-0.177305\pi\) | ||||
0.848834 | + | 0.528659i | \(0.177305\pi\) | |||||||
\(54\) | 5.65558 | 0.769628 | ||||||||
\(55\) | −0.944799 | −0.127397 | ||||||||
\(56\) | 3.58216 | 0.478686 | ||||||||
\(57\) | 11.2415 | 1.48898 | ||||||||
\(58\) | 5.21621 | 0.684922 | ||||||||
\(59\) | 4.07851 | 0.530977 | 0.265489 | − | 0.964114i | \(-0.414467\pi\) | ||||
0.265489 | + | 0.964114i | \(0.414467\pi\) | |||||||
\(60\) | 1.15072 | 0.148558 | ||||||||
\(61\) | −5.46496 | −0.699717 | −0.349858 | − | 0.936803i | \(-0.613770\pi\) | ||||
−0.349858 | + | 0.936803i | \(0.613770\pi\) | |||||||
\(62\) | −5.09216 | −0.646705 | ||||||||
\(63\) | 3.40616 | 0.429136 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.70263 | 0.459255 | ||||||||
\(66\) | 1.68243 | 0.207093 | ||||||||
\(67\) | −5.10207 | −0.623317 | −0.311659 | − | 0.950194i | \(-0.600885\pi\) | ||||
−0.311659 | + | 0.950194i | \(0.600885\pi\) | |||||||
\(68\) | 1.42510 | 0.172819 | ||||||||
\(69\) | −1.60644 | −0.193393 | ||||||||
\(70\) | 2.87959 | 0.344177 | ||||||||
\(71\) | −6.40788 | −0.760475 | −0.380238 | − | 0.924889i | \(-0.624158\pi\) | ||||
−0.380238 | + | 0.924889i | \(0.624158\pi\) | |||||||
\(72\) | 0.950869 | 0.112061 | ||||||||
\(73\) | −0.792319 | −0.0927339 | −0.0463670 | − | 0.998924i | \(-0.514764\pi\) | ||||
−0.0463670 | + | 0.998924i | \(0.514764\pi\) | |||||||
\(74\) | 3.48843 | 0.405522 | ||||||||
\(75\) | −6.23236 | −0.719651 | ||||||||
\(76\) | 7.85309 | 0.900812 | ||||||||
\(77\) | 4.21015 | 0.479791 | ||||||||
\(78\) | −6.59339 | −0.746555 | ||||||||
\(79\) | 7.21938 | 0.812244 | 0.406122 | − | 0.913819i | \(-0.366881\pi\) | ||||
0.406122 | + | 0.913819i | \(0.366881\pi\) | |||||||
\(80\) | 0.803871 | 0.0898755 | ||||||||
\(81\) | −5.24324 | −0.582582 | ||||||||
\(82\) | 4.00456 | 0.442229 | ||||||||
\(83\) | 6.15613 | 0.675723 | 0.337862 | − | 0.941196i | \(-0.390296\pi\) | ||||
0.337862 | + | 0.941196i | \(0.390296\pi\) | |||||||
\(84\) | −5.12778 | −0.559487 | ||||||||
\(85\) | 1.14560 | 0.124258 | ||||||||
\(86\) | 1.27939 | 0.137960 | ||||||||
\(87\) | −7.46689 | −0.800535 | ||||||||
\(88\) | 1.17531 | 0.125289 | ||||||||
\(89\) | 8.37728 | 0.887990 | 0.443995 | − | 0.896029i | \(-0.353561\pi\) | ||||
0.443995 | + | 0.896029i | \(0.353561\pi\) | |||||||
\(90\) | 0.764376 | 0.0805723 | ||||||||
\(91\) | −16.4994 | −1.72961 | ||||||||
\(92\) | −1.12223 | −0.117000 | ||||||||
\(93\) | 7.28932 | 0.755867 | ||||||||
\(94\) | −6.62131 | −0.682936 | ||||||||
\(95\) | 6.31287 | 0.647687 | ||||||||
\(96\) | −1.43148 | −0.146100 | ||||||||
\(97\) | 6.80739 | 0.691186 | 0.345593 | − | 0.938384i | \(-0.387678\pi\) | ||||
0.345593 | + | 0.938384i | \(0.387678\pi\) | |||||||
\(98\) | −5.83185 | −0.589106 | ||||||||
\(99\) | 1.11757 | 0.112320 | ||||||||
\(100\) | −4.35379 | −0.435379 | ||||||||
\(101\) | 15.1085 | 1.50335 | 0.751676 | − | 0.659532i | \(-0.229246\pi\) | ||||
0.751676 | + | 0.659532i | \(0.229246\pi\) | |||||||
\(102\) | −2.04001 | −0.201991 | ||||||||
\(103\) | 1.93373 | 0.190537 | 0.0952683 | − | 0.995452i | \(-0.469629\pi\) | ||||
0.0952683 | + | 0.995452i | \(0.469629\pi\) | |||||||
\(104\) | −4.60600 | −0.451656 | ||||||||
\(105\) | −4.12207 | −0.402273 | ||||||||
\(106\) | −12.3592 | −1.20043 | ||||||||
\(107\) | 4.83216 | 0.467142 | 0.233571 | − | 0.972340i | \(-0.424959\pi\) | ||||
0.233571 | + | 0.972340i | \(0.424959\pi\) | |||||||
\(108\) | −5.65558 | −0.544209 | ||||||||
\(109\) | −6.80875 | −0.652160 | −0.326080 | − | 0.945342i | \(-0.605728\pi\) | ||||
−0.326080 | + | 0.945342i | \(0.605728\pi\) | |||||||
\(110\) | 0.944799 | 0.0900830 | ||||||||
\(111\) | −4.99361 | −0.473973 | ||||||||
\(112\) | −3.58216 | −0.338482 | ||||||||
\(113\) | 13.9602 | 1.31327 | 0.656635 | − | 0.754209i | \(-0.271979\pi\) | ||||
0.656635 | + | 0.754209i | \(0.271979\pi\) | |||||||
\(114\) | −11.2415 | −1.05287 | ||||||||
\(115\) | −0.902124 | −0.0841235 | ||||||||
\(116\) | −5.21621 | −0.484313 | ||||||||
\(117\) | −4.37971 | −0.404904 | ||||||||
\(118\) | −4.07851 | −0.375458 | ||||||||
\(119\) | −5.10495 | −0.467970 | ||||||||
\(120\) | −1.15072 | −0.105046 | ||||||||
\(121\) | −9.61864 | −0.874422 | ||||||||
\(122\) | 5.46496 | 0.494775 | ||||||||
\(123\) | −5.73244 | −0.516876 | ||||||||
\(124\) | 5.09216 | 0.457289 | ||||||||
\(125\) | −7.51924 | −0.672541 | ||||||||
\(126\) | −3.40616 | −0.303445 | ||||||||
\(127\) | −19.0630 | −1.69157 | −0.845784 | − | 0.533526i | \(-0.820867\pi\) | ||||
−0.845784 | + | 0.533526i | \(0.820867\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.83141 | −0.161247 | ||||||||
\(130\) | −3.70263 | −0.324742 | ||||||||
\(131\) | 1.62818 | 0.142255 | 0.0711274 | − | 0.997467i | \(-0.477340\pi\) | ||||
0.0711274 | + | 0.997467i | \(0.477340\pi\) | |||||||
\(132\) | −1.68243 | −0.146437 | ||||||||
\(133\) | −28.1310 | −2.43927 | ||||||||
\(134\) | 5.10207 | 0.440752 | ||||||||
\(135\) | −4.54636 | −0.391288 | ||||||||
\(136\) | −1.42510 | −0.122202 | ||||||||
\(137\) | 6.36086 | 0.543445 | 0.271723 | − | 0.962376i | \(-0.412407\pi\) | ||||
0.271723 | + | 0.962376i | \(0.412407\pi\) | |||||||
\(138\) | 1.60644 | 0.136749 | ||||||||
\(139\) | 16.7084 | 1.41719 | 0.708595 | − | 0.705616i | \(-0.249329\pi\) | ||||
0.708595 | + | 0.705616i | \(0.249329\pi\) | |||||||
\(140\) | −2.87959 | −0.243370 | ||||||||
\(141\) | 9.47827 | 0.798214 | ||||||||
\(142\) | 6.40788 | 0.537737 | ||||||||
\(143\) | −5.41349 | −0.452699 | ||||||||
\(144\) | −0.950869 | −0.0792391 | ||||||||
\(145\) | −4.19316 | −0.348223 | ||||||||
\(146\) | 0.792319 | 0.0655728 | ||||||||
\(147\) | 8.34817 | 0.688545 | ||||||||
\(148\) | −3.48843 | −0.286747 | ||||||||
\(149\) | 9.78960 | 0.801995 | 0.400998 | − | 0.916079i | \(-0.368664\pi\) | ||||
0.400998 | + | 0.916079i | \(0.368664\pi\) | |||||||
\(150\) | 6.23236 | 0.508870 | ||||||||
\(151\) | −18.6569 | −1.51828 | −0.759138 | − | 0.650929i | \(-0.774379\pi\) | ||||
−0.759138 | + | 0.650929i | \(0.774379\pi\) | |||||||
\(152\) | −7.85309 | −0.636970 | ||||||||
\(153\) | −1.35509 | −0.109552 | ||||||||
\(154\) | −4.21015 | −0.339264 | ||||||||
\(155\) | 4.09344 | 0.328793 | ||||||||
\(156\) | 6.59339 | 0.527894 | ||||||||
\(157\) | 8.84383 | 0.705815 | 0.352907 | − | 0.935658i | \(-0.385193\pi\) | ||||
0.352907 | + | 0.935658i | \(0.385193\pi\) | |||||||
\(158\) | −7.21938 | −0.574343 | ||||||||
\(159\) | 17.6920 | 1.40306 | ||||||||
\(160\) | −0.803871 | −0.0635516 | ||||||||
\(161\) | 4.01999 | 0.316819 | ||||||||
\(162\) | 5.24324 | 0.411948 | ||||||||
\(163\) | −25.4226 | −1.99125 | −0.995625 | − | 0.0934397i | \(-0.970214\pi\) | ||||
−0.995625 | + | 0.0934397i | \(0.970214\pi\) | |||||||
\(164\) | −4.00456 | −0.312703 | ||||||||
\(165\) | −1.35246 | −0.105289 | ||||||||
\(166\) | −6.15613 | −0.477809 | ||||||||
\(167\) | 5.46543 | 0.422928 | 0.211464 | − | 0.977386i | \(-0.432177\pi\) | ||||
0.211464 | + | 0.977386i | \(0.432177\pi\) | |||||||
\(168\) | 5.12778 | 0.395617 | ||||||||
\(169\) | 8.21526 | 0.631943 | ||||||||
\(170\) | −1.14560 | −0.0878635 | ||||||||
\(171\) | −7.46727 | −0.571036 | ||||||||
\(172\) | −1.27939 | −0.0975522 | ||||||||
\(173\) | −18.0771 | −1.37437 | −0.687186 | − | 0.726481i | \(-0.741154\pi\) | ||||
−0.687186 | + | 0.726481i | \(0.741154\pi\) | |||||||
\(174\) | 7.46689 | 0.566064 | ||||||||
\(175\) | 15.5960 | 1.17894 | ||||||||
\(176\) | −1.17531 | −0.0885925 | ||||||||
\(177\) | 5.83831 | 0.438834 | ||||||||
\(178\) | −8.37728 | −0.627903 | ||||||||
\(179\) | −4.58739 | −0.342877 | −0.171439 | − | 0.985195i | \(-0.554842\pi\) | ||||
−0.171439 | + | 0.985195i | \(0.554842\pi\) | |||||||
\(180\) | −0.764376 | −0.0569732 | ||||||||
\(181\) | 19.1771 | 1.42542 | 0.712711 | − | 0.701458i | \(-0.247467\pi\) | ||||
0.712711 | + | 0.701458i | \(0.247467\pi\) | |||||||
\(182\) | 16.4994 | 1.22302 | ||||||||
\(183\) | −7.82298 | −0.578291 | ||||||||
\(184\) | 1.12223 | 0.0827316 | ||||||||
\(185\) | −2.80425 | −0.206172 | ||||||||
\(186\) | −7.28932 | −0.534479 | ||||||||
\(187\) | −1.67494 | −0.122484 | ||||||||
\(188\) | 6.62131 | 0.482909 | ||||||||
\(189\) | 20.2592 | 1.47364 | ||||||||
\(190\) | −6.31287 | −0.457984 | ||||||||
\(191\) | −11.2058 | −0.810826 | −0.405413 | − | 0.914134i | \(-0.632872\pi\) | ||||
−0.405413 | + | 0.914134i | \(0.632872\pi\) | |||||||
\(192\) | 1.43148 | 0.103308 | ||||||||
\(193\) | 22.9269 | 1.65031 | 0.825156 | − | 0.564905i | \(-0.191087\pi\) | ||||
0.825156 | + | 0.564905i | \(0.191087\pi\) | |||||||
\(194\) | −6.80739 | −0.488742 | ||||||||
\(195\) | 5.30024 | 0.379558 | ||||||||
\(196\) | 5.83185 | 0.416561 | ||||||||
\(197\) | 10.4987 | 0.748003 | 0.374001 | − | 0.927428i | \(-0.377986\pi\) | ||||
0.374001 | + | 0.927428i | \(0.377986\pi\) | |||||||
\(198\) | −1.11757 | −0.0794221 | ||||||||
\(199\) | 20.8739 | 1.47971 | 0.739856 | − | 0.672765i | \(-0.234894\pi\) | ||||
0.739856 | + | 0.672765i | \(0.234894\pi\) | |||||||
\(200\) | 4.35379 | 0.307860 | ||||||||
\(201\) | −7.30350 | −0.515149 | ||||||||
\(202\) | −15.1085 | −1.06303 | ||||||||
\(203\) | 18.6853 | 1.31145 | ||||||||
\(204\) | 2.04001 | 0.142829 | ||||||||
\(205\) | −3.21915 | −0.224835 | ||||||||
\(206\) | −1.93373 | −0.134730 | ||||||||
\(207\) | 1.06709 | 0.0741679 | ||||||||
\(208\) | 4.60600 | 0.319369 | ||||||||
\(209\) | −9.22983 | −0.638441 | ||||||||
\(210\) | 4.12207 | 0.284450 | ||||||||
\(211\) | 17.1402 | 1.17998 | 0.589989 | − | 0.807411i | \(-0.299132\pi\) | ||||
0.589989 | + | 0.807411i | \(0.299132\pi\) | |||||||
\(212\) | 12.3592 | 0.848834 | ||||||||
\(213\) | −9.17274 | −0.628506 | ||||||||
\(214\) | −4.83216 | −0.330320 | ||||||||
\(215\) | −1.02846 | −0.0701404 | ||||||||
\(216\) | 5.65558 | 0.384814 | ||||||||
\(217\) | −18.2409 | −1.23827 | ||||||||
\(218\) | 6.80875 | 0.461147 | ||||||||
\(219\) | −1.13419 | −0.0766413 | ||||||||
\(220\) | −0.944799 | −0.0636983 | ||||||||
\(221\) | 6.56404 | 0.441545 | ||||||||
\(222\) | 4.99361 | 0.335149 | ||||||||
\(223\) | 8.10757 | 0.542923 | 0.271461 | − | 0.962449i | \(-0.412493\pi\) | ||||
0.271461 | + | 0.962449i | \(0.412493\pi\) | |||||||
\(224\) | 3.58216 | 0.239343 | ||||||||
\(225\) | 4.13989 | 0.275992 | ||||||||
\(226\) | −13.9602 | −0.928622 | ||||||||
\(227\) | 6.14699 | 0.407990 | 0.203995 | − | 0.978972i | \(-0.434607\pi\) | ||||
0.203995 | + | 0.978972i | \(0.434607\pi\) | |||||||
\(228\) | 11.2415 | 0.744489 | ||||||||
\(229\) | 13.2543 | 0.875870 | 0.437935 | − | 0.899007i | \(-0.355710\pi\) | ||||
0.437935 | + | 0.899007i | \(0.355710\pi\) | |||||||
\(230\) | 0.902124 | 0.0594843 | ||||||||
\(231\) | 6.02674 | 0.396530 | ||||||||
\(232\) | 5.21621 | 0.342461 | ||||||||
\(233\) | 29.9547 | 1.96240 | 0.981198 | − | 0.193003i | \(-0.0618228\pi\) | ||||
0.981198 | + | 0.193003i | \(0.0618228\pi\) | |||||||
\(234\) | 4.37971 | 0.286310 | ||||||||
\(235\) | 5.32268 | 0.347213 | ||||||||
\(236\) | 4.07851 | 0.265489 | ||||||||
\(237\) | 10.3344 | 0.671291 | ||||||||
\(238\) | 5.10495 | 0.330905 | ||||||||
\(239\) | 9.68475 | 0.626454 | 0.313227 | − | 0.949678i | \(-0.398590\pi\) | ||||
0.313227 | + | 0.949678i | \(0.398590\pi\) | |||||||
\(240\) | 1.15072 | 0.0742789 | ||||||||
\(241\) | 23.5432 | 1.51655 | 0.758275 | − | 0.651935i | \(-0.226043\pi\) | ||||
0.758275 | + | 0.651935i | \(0.226043\pi\) | |||||||
\(242\) | 9.61864 | 0.618310 | ||||||||
\(243\) | 9.46117 | 0.606934 | ||||||||
\(244\) | −5.46496 | −0.349858 | ||||||||
\(245\) | 4.68805 | 0.299509 | ||||||||
\(246\) | 5.73244 | 0.365487 | ||||||||
\(247\) | 36.1714 | 2.30153 | ||||||||
\(248\) | −5.09216 | −0.323352 | ||||||||
\(249\) | 8.81237 | 0.558461 | ||||||||
\(250\) | 7.51924 | 0.475558 | ||||||||
\(251\) | 15.0546 | 0.950240 | 0.475120 | − | 0.879921i | \(-0.342405\pi\) | ||||
0.475120 | + | 0.879921i | \(0.342405\pi\) | |||||||
\(252\) | 3.40616 | 0.214568 | ||||||||
\(253\) | 1.31897 | 0.0829226 | ||||||||
\(254\) | 19.0630 | 1.19612 | ||||||||
\(255\) | 1.63990 | 0.102695 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.4035 | −1.83414 | −0.917069 | − | 0.398729i | \(-0.869451\pi\) | ||||
−0.917069 | + | 0.398729i | \(0.869451\pi\) | |||||||
\(258\) | 1.83141 | 0.114019 | ||||||||
\(259\) | 12.4961 | 0.776470 | ||||||||
\(260\) | 3.70263 | 0.229627 | ||||||||
\(261\) | 4.95993 | 0.307012 | ||||||||
\(262\) | −1.62818 | −0.100589 | ||||||||
\(263\) | 20.3220 | 1.25311 | 0.626554 | − | 0.779378i | \(-0.284465\pi\) | ||||
0.626554 | + | 0.779378i | \(0.284465\pi\) | |||||||
\(264\) | 1.68243 | 0.103547 | ||||||||
\(265\) | 9.93521 | 0.610315 | ||||||||
\(266\) | 28.1310 | 1.72482 | ||||||||
\(267\) | 11.9919 | 0.733892 | ||||||||
\(268\) | −5.10207 | −0.311659 | ||||||||
\(269\) | 7.76046 | 0.473164 | 0.236582 | − | 0.971612i | \(-0.423973\pi\) | ||||
0.236582 | + | 0.971612i | \(0.423973\pi\) | |||||||
\(270\) | 4.54636 | 0.276683 | ||||||||
\(271\) | 0.473929 | 0.0287891 | 0.0143946 | − | 0.999896i | \(-0.495418\pi\) | ||||
0.0143946 | + | 0.999896i | \(0.495418\pi\) | |||||||
\(272\) | 1.42510 | 0.0864097 | ||||||||
\(273\) | −23.6186 | −1.42946 | ||||||||
\(274\) | −6.36086 | −0.384274 | ||||||||
\(275\) | 5.11706 | 0.308571 | ||||||||
\(276\) | −1.60644 | −0.0966964 | ||||||||
\(277\) | 6.44464 | 0.387221 | 0.193611 | − | 0.981078i | \(-0.437980\pi\) | ||||
0.193611 | + | 0.981078i | \(0.437980\pi\) | |||||||
\(278\) | −16.7084 | −1.00210 | ||||||||
\(279\) | −4.84198 | −0.289882 | ||||||||
\(280\) | 2.87959 | 0.172088 | ||||||||
\(281\) | −17.6878 | −1.05517 | −0.527583 | − | 0.849504i | \(-0.676901\pi\) | ||||
−0.527583 | + | 0.849504i | \(0.676901\pi\) | |||||||
\(282\) | −9.47827 | −0.564423 | ||||||||
\(283\) | −10.8789 | −0.646684 | −0.323342 | − | 0.946282i | \(-0.604806\pi\) | ||||
−0.323342 | + | 0.946282i | \(0.604806\pi\) | |||||||
\(284\) | −6.40788 | −0.380238 | ||||||||
\(285\) | 9.03674 | 0.535290 | ||||||||
\(286\) | 5.41349 | 0.320106 | ||||||||
\(287\) | 14.3450 | 0.846756 | ||||||||
\(288\) | 0.950869 | 0.0560305 | ||||||||
\(289\) | −14.9691 | −0.880534 | ||||||||
\(290\) | 4.19316 | 0.246231 | ||||||||
\(291\) | 9.74464 | 0.571241 | ||||||||
\(292\) | −0.792319 | −0.0463670 | ||||||||
\(293\) | −9.02055 | −0.526986 | −0.263493 | − | 0.964661i | \(-0.584875\pi\) | ||||
−0.263493 | + | 0.964661i | \(0.584875\pi\) | |||||||
\(294\) | −8.34817 | −0.486875 | ||||||||
\(295\) | 3.27860 | 0.190887 | ||||||||
\(296\) | 3.48843 | 0.202761 | ||||||||
\(297\) | 6.64708 | 0.385702 | ||||||||
\(298\) | −9.78960 | −0.567096 | ||||||||
\(299\) | −5.16897 | −0.298929 | ||||||||
\(300\) | −6.23236 | −0.359825 | ||||||||
\(301\) | 4.58296 | 0.264157 | ||||||||
\(302\) | 18.6569 | 1.07358 | ||||||||
\(303\) | 21.6275 | 1.24247 | ||||||||
\(304\) | 7.85309 | 0.450406 | ||||||||
\(305\) | −4.39312 | −0.251550 | ||||||||
\(306\) | 1.35509 | 0.0774653 | ||||||||
\(307\) | −32.9966 | −1.88321 | −0.941607 | − | 0.336715i | \(-0.890684\pi\) | ||||
−0.941607 | + | 0.336715i | \(0.890684\pi\) | |||||||
\(308\) | 4.21015 | 0.239896 | ||||||||
\(309\) | 2.76810 | 0.157472 | ||||||||
\(310\) | −4.09344 | −0.232492 | ||||||||
\(311\) | 7.35795 | 0.417231 | 0.208616 | − | 0.977998i | \(-0.433104\pi\) | ||||
0.208616 | + | 0.977998i | \(0.433104\pi\) | |||||||
\(312\) | −6.59339 | −0.373277 | ||||||||
\(313\) | 11.9851 | 0.677435 | 0.338718 | − | 0.940888i | \(-0.390007\pi\) | ||||
0.338718 | + | 0.940888i | \(0.390007\pi\) | |||||||
\(314\) | −8.84383 | −0.499086 | ||||||||
\(315\) | 2.73811 | 0.154275 | ||||||||
\(316\) | 7.21938 | 0.406122 | ||||||||
\(317\) | −12.4797 | −0.700927 | −0.350464 | − | 0.936576i | \(-0.613976\pi\) | ||||
−0.350464 | + | 0.936576i | \(0.613976\pi\) | |||||||
\(318\) | −17.6920 | −0.992115 | ||||||||
\(319\) | 6.13067 | 0.343252 | ||||||||
\(320\) | 0.803871 | 0.0449377 | ||||||||
\(321\) | 6.91713 | 0.386077 | ||||||||
\(322\) | −4.01999 | −0.224025 | ||||||||
\(323\) | 11.1915 | 0.622711 | ||||||||
\(324\) | −5.24324 | −0.291291 | ||||||||
\(325\) | −20.0536 | −1.11237 | ||||||||
\(326\) | 25.4226 | 1.40803 | ||||||||
\(327\) | −9.74658 | −0.538987 | ||||||||
\(328\) | 4.00456 | 0.221115 | ||||||||
\(329\) | −23.7186 | −1.30765 | ||||||||
\(330\) | 1.35246 | 0.0744504 | ||||||||
\(331\) | −19.8116 | −1.08894 | −0.544471 | − | 0.838780i | \(-0.683270\pi\) | ||||
−0.544471 | + | 0.838780i | \(0.683270\pi\) | |||||||
\(332\) | 6.15613 | 0.337862 | ||||||||
\(333\) | 3.31704 | 0.181773 | ||||||||
\(334\) | −5.46543 | −0.299055 | ||||||||
\(335\) | −4.10140 | −0.224084 | ||||||||
\(336\) | −5.12778 | −0.279743 | ||||||||
\(337\) | 21.8413 | 1.18977 | 0.594885 | − | 0.803811i | \(-0.297198\pi\) | ||||
0.594885 | + | 0.803811i | \(0.297198\pi\) | |||||||
\(338\) | −8.21526 | −0.446851 | ||||||||
\(339\) | 19.9838 | 1.08537 | ||||||||
\(340\) | 1.14560 | 0.0621289 | ||||||||
\(341\) | −5.98488 | −0.324099 | ||||||||
\(342\) | 7.46727 | 0.403783 | ||||||||
\(343\) | 4.18450 | 0.225942 | ||||||||
\(344\) | 1.27939 | 0.0689798 | ||||||||
\(345\) | −1.29137 | −0.0695251 | ||||||||
\(346\) | 18.0771 | 0.971828 | ||||||||
\(347\) | 0.811855 | 0.0435827 | 0.0217913 | − | 0.999763i | \(-0.493063\pi\) | ||||
0.0217913 | + | 0.999763i | \(0.493063\pi\) | |||||||
\(348\) | −7.46689 | −0.400267 | ||||||||
\(349\) | −11.5066 | −0.615932 | −0.307966 | − | 0.951397i | \(-0.599648\pi\) | ||||
−0.307966 | + | 0.951397i | \(0.599648\pi\) | |||||||
\(350\) | −15.5960 | −0.833639 | ||||||||
\(351\) | −26.0496 | −1.39043 | ||||||||
\(352\) | 1.17531 | 0.0626443 | ||||||||
\(353\) | −10.3775 | −0.552341 | −0.276171 | − | 0.961109i | \(-0.589065\pi\) | ||||
−0.276171 | + | 0.961109i | \(0.589065\pi\) | |||||||
\(354\) | −5.83831 | −0.310302 | ||||||||
\(355\) | −5.15111 | −0.273392 | ||||||||
\(356\) | 8.37728 | 0.443995 | ||||||||
\(357\) | −7.30763 | −0.386761 | ||||||||
\(358\) | 4.58739 | 0.242451 | ||||||||
\(359\) | 1.98848 | 0.104948 | 0.0524740 | − | 0.998622i | \(-0.483289\pi\) | ||||
0.0524740 | + | 0.998622i | \(0.483289\pi\) | |||||||
\(360\) | 0.764376 | 0.0402861 | ||||||||
\(361\) | 42.6711 | 2.24585 | ||||||||
\(362\) | −19.1771 | −1.00793 | ||||||||
\(363\) | −13.7689 | −0.722679 | ||||||||
\(364\) | −16.4994 | −0.864805 | ||||||||
\(365\) | −0.636922 | −0.0333380 | ||||||||
\(366\) | 7.82298 | 0.408914 | ||||||||
\(367\) | 33.8501 | 1.76696 | 0.883481 | − | 0.468467i | \(-0.155193\pi\) | ||||
0.883481 | + | 0.468467i | \(0.155193\pi\) | |||||||
\(368\) | −1.12223 | −0.0585000 | ||||||||
\(369\) | 3.80781 | 0.198227 | ||||||||
\(370\) | 2.80425 | 0.145786 | ||||||||
\(371\) | −44.2726 | −2.29852 | ||||||||
\(372\) | 7.28932 | 0.377933 | ||||||||
\(373\) | −17.3730 | −0.899542 | −0.449771 | − | 0.893144i | \(-0.648494\pi\) | ||||
−0.449771 | + | 0.893144i | \(0.648494\pi\) | |||||||
\(374\) | 1.67494 | 0.0866092 | ||||||||
\(375\) | −10.7636 | −0.555831 | ||||||||
\(376\) | −6.62131 | −0.341468 | ||||||||
\(377\) | −24.0259 | −1.23740 | ||||||||
\(378\) | −20.2592 | −1.04202 | ||||||||
\(379\) | 14.8045 | 0.760457 | 0.380229 | − | 0.924893i | \(-0.375845\pi\) | ||||
0.380229 | + | 0.924893i | \(0.375845\pi\) | |||||||
\(380\) | 6.31287 | 0.323843 | ||||||||
\(381\) | −27.2883 | −1.39802 | ||||||||
\(382\) | 11.2058 | 0.573340 | ||||||||
\(383\) | 17.7812 | 0.908578 | 0.454289 | − | 0.890854i | \(-0.349893\pi\) | ||||
0.454289 | + | 0.890854i | \(0.349893\pi\) | |||||||
\(384\) | −1.43148 | −0.0730498 | ||||||||
\(385\) | 3.38442 | 0.172486 | ||||||||
\(386\) | −22.9269 | −1.16695 | ||||||||
\(387\) | 1.21653 | 0.0618396 | ||||||||
\(388\) | 6.80739 | 0.345593 | ||||||||
\(389\) | −21.2040 | −1.07508 | −0.537542 | − | 0.843237i | \(-0.680647\pi\) | ||||
−0.537542 | + | 0.843237i | \(0.680647\pi\) | |||||||
\(390\) | −5.30024 | −0.268388 | ||||||||
\(391\) | −1.59929 | −0.0808795 | ||||||||
\(392\) | −5.83185 | −0.294553 | ||||||||
\(393\) | 2.33071 | 0.117569 | ||||||||
\(394\) | −10.4987 | −0.528918 | ||||||||
\(395\) | 5.80345 | 0.292003 | ||||||||
\(396\) | 1.11757 | 0.0561599 | ||||||||
\(397\) | 26.7934 | 1.34472 | 0.672362 | − | 0.740223i | \(-0.265280\pi\) | ||||
0.672362 | + | 0.740223i | \(0.265280\pi\) | |||||||
\(398\) | −20.8739 | −1.04631 | ||||||||
\(399\) | −40.2689 | −2.01597 | ||||||||
\(400\) | −4.35379 | −0.217690 | ||||||||
\(401\) | 19.3584 | 0.966710 | 0.483355 | − | 0.875424i | \(-0.339418\pi\) | ||||
0.483355 | + | 0.875424i | \(0.339418\pi\) | |||||||
\(402\) | 7.30350 | 0.364266 | ||||||||
\(403\) | 23.4545 | 1.16835 | ||||||||
\(404\) | 15.1085 | 0.751676 | ||||||||
\(405\) | −4.21489 | −0.209439 | ||||||||
\(406\) | −18.6853 | −0.927335 | ||||||||
\(407\) | 4.09999 | 0.203229 | ||||||||
\(408\) | −2.04001 | −0.100995 | ||||||||
\(409\) | 5.17694 | 0.255983 | 0.127992 | − | 0.991775i | \(-0.459147\pi\) | ||||
0.127992 | + | 0.991775i | \(0.459147\pi\) | |||||||
\(410\) | 3.21915 | 0.158982 | ||||||||
\(411\) | 9.10544 | 0.449138 | ||||||||
\(412\) | 1.93373 | 0.0952683 | ||||||||
\(413\) | −14.6099 | −0.718905 | ||||||||
\(414\) | −1.06709 | −0.0524446 | ||||||||
\(415\) | 4.94874 | 0.242924 | ||||||||
\(416\) | −4.60600 | −0.225828 | ||||||||
\(417\) | 23.9177 | 1.17126 | ||||||||
\(418\) | 9.22983 | 0.451446 | ||||||||
\(419\) | 13.5001 | 0.659523 | 0.329761 | − | 0.944064i | \(-0.393032\pi\) | ||||
0.329761 | + | 0.944064i | \(0.393032\pi\) | |||||||
\(420\) | −4.12207 | −0.201137 | ||||||||
\(421\) | −20.3494 | −0.991767 | −0.495884 | − | 0.868389i | \(-0.665156\pi\) | ||||
−0.495884 | + | 0.868389i | \(0.665156\pi\) | |||||||
\(422\) | −17.1402 | −0.834371 | ||||||||
\(423\) | −6.29600 | −0.306122 | ||||||||
\(424\) | −12.3592 | −0.600217 | ||||||||
\(425\) | −6.20461 | −0.300968 | ||||||||
\(426\) | 9.17274 | 0.444421 | ||||||||
\(427\) | 19.5764 | 0.947366 | ||||||||
\(428\) | 4.83216 | 0.233571 | ||||||||
\(429\) | −7.74929 | −0.374139 | ||||||||
\(430\) | 1.02846 | 0.0495968 | ||||||||
\(431\) | 0.00245142 | 0.000118081 0 | 5.90404e−5 | − | 1.00000i | \(-0.499981\pi\) | ||||
5.90404e−5 | 1.00000i | \(0.499981\pi\) | ||||||||
\(432\) | −5.65558 | −0.272104 | ||||||||
\(433\) | 13.4348 | 0.645638 | 0.322819 | − | 0.946461i | \(-0.395370\pi\) | ||||
0.322819 | + | 0.946461i | \(0.395370\pi\) | |||||||
\(434\) | 18.2409 | 0.875592 | ||||||||
\(435\) | −6.00242 | −0.287794 | ||||||||
\(436\) | −6.80875 | −0.326080 | ||||||||
\(437\) | −8.81294 | −0.421580 | ||||||||
\(438\) | 1.13419 | 0.0541936 | ||||||||
\(439\) | 29.4126 | 1.40379 | 0.701894 | − | 0.712281i | \(-0.252338\pi\) | ||||
0.701894 | + | 0.712281i | \(0.252338\pi\) | |||||||
\(440\) | 0.944799 | 0.0450415 | ||||||||
\(441\) | −5.54533 | −0.264063 | ||||||||
\(442\) | −6.56404 | −0.312219 | ||||||||
\(443\) | 25.2124 | 1.19788 | 0.598940 | − | 0.800794i | \(-0.295589\pi\) | ||||
0.598940 | + | 0.800794i | \(0.295589\pi\) | |||||||
\(444\) | −4.99361 | −0.236986 | ||||||||
\(445\) | 6.73425 | 0.319234 | ||||||||
\(446\) | −8.10757 | −0.383904 | ||||||||
\(447\) | 14.0136 | 0.662821 | ||||||||
\(448\) | −3.58216 | −0.169241 | ||||||||
\(449\) | −6.24356 | −0.294652 | −0.147326 | − | 0.989088i | \(-0.547067\pi\) | ||||
−0.147326 | + | 0.989088i | \(0.547067\pi\) | |||||||
\(450\) | −4.13989 | −0.195156 | ||||||||
\(451\) | 4.70660 | 0.221625 | ||||||||
\(452\) | 13.9602 | 0.656635 | ||||||||
\(453\) | −26.7070 | −1.25480 | ||||||||
\(454\) | −6.14699 | −0.288493 | ||||||||
\(455\) | −13.2634 | −0.621798 | ||||||||
\(456\) | −11.2415 | −0.526433 | ||||||||
\(457\) | 22.7691 | 1.06509 | 0.532546 | − | 0.846401i | \(-0.321235\pi\) | ||||
0.532546 | + | 0.846401i | \(0.321235\pi\) | |||||||
\(458\) | −13.2543 | −0.619334 | ||||||||
\(459\) | −8.05980 | −0.376199 | ||||||||
\(460\) | −0.902124 | −0.0420618 | ||||||||
\(461\) | −23.9176 | −1.11395 | −0.556976 | − | 0.830529i | \(-0.688038\pi\) | ||||
−0.556976 | + | 0.830529i | \(0.688038\pi\) | |||||||
\(462\) | −6.02674 | −0.280389 | ||||||||
\(463\) | 30.7084 | 1.42714 | 0.713570 | − | 0.700584i | \(-0.247077\pi\) | ||||
0.713570 | + | 0.700584i | \(0.247077\pi\) | |||||||
\(464\) | −5.21621 | −0.242156 | ||||||||
\(465\) | 5.85967 | 0.271736 | ||||||||
\(466\) | −29.9547 | −1.38762 | ||||||||
\(467\) | 23.7542 | 1.09921 | 0.549606 | − | 0.835424i | \(-0.314778\pi\) | ||||
0.549606 | + | 0.835424i | \(0.314778\pi\) | |||||||
\(468\) | −4.37971 | −0.202452 | ||||||||
\(469\) | 18.2764 | 0.843926 | ||||||||
\(470\) | −5.32268 | −0.245517 | ||||||||
\(471\) | 12.6598 | 0.583331 | ||||||||
\(472\) | −4.07851 | −0.187729 | ||||||||
\(473\) | 1.50368 | 0.0691391 | ||||||||
\(474\) | −10.3344 | −0.474674 | ||||||||
\(475\) | −34.1907 | −1.56878 | ||||||||
\(476\) | −5.10495 | −0.233985 | ||||||||
\(477\) | −11.7520 | −0.538087 | ||||||||
\(478\) | −9.68475 | −0.442970 | ||||||||
\(479\) | 39.1600 | 1.78926 | 0.894632 | − | 0.446803i | \(-0.147438\pi\) | ||||
0.894632 | + | 0.446803i | \(0.147438\pi\) | |||||||
\(480\) | −1.15072 | −0.0525231 | ||||||||
\(481\) | −16.0677 | −0.732625 | ||||||||
\(482\) | −23.5432 | −1.07236 | ||||||||
\(483\) | 5.75453 | 0.261840 | ||||||||
\(484\) | −9.61864 | −0.437211 | ||||||||
\(485\) | 5.47226 | 0.248483 | ||||||||
\(486\) | −9.46117 | −0.429167 | ||||||||
\(487\) | −29.7377 | −1.34754 | −0.673771 | − | 0.738940i | \(-0.735327\pi\) | ||||
−0.673771 | + | 0.738940i | \(0.735327\pi\) | |||||||
\(488\) | 5.46496 | 0.247387 | ||||||||
\(489\) | −36.3919 | −1.64570 | ||||||||
\(490\) | −4.68805 | −0.211785 | ||||||||
\(491\) | 29.0228 | 1.30978 | 0.654891 | − | 0.755723i | \(-0.272714\pi\) | ||||
0.654891 | + | 0.755723i | \(0.272714\pi\) | |||||||
\(492\) | −5.73244 | −0.258438 | ||||||||
\(493\) | −7.43365 | −0.334795 | ||||||||
\(494\) | −36.1714 | −1.62743 | ||||||||
\(495\) | 0.898380 | 0.0403792 | ||||||||
\(496\) | 5.09216 | 0.228645 | ||||||||
\(497\) | 22.9540 | 1.02963 | ||||||||
\(498\) | −8.81237 | −0.394892 | ||||||||
\(499\) | −34.3533 | −1.53786 | −0.768932 | − | 0.639330i | \(-0.779212\pi\) | ||||
−0.768932 | + | 0.639330i | \(0.779212\pi\) | |||||||
\(500\) | −7.51924 | −0.336271 | ||||||||
\(501\) | 7.82365 | 0.349535 | ||||||||
\(502\) | −15.0546 | −0.671921 | ||||||||
\(503\) | 13.4589 | 0.600103 | 0.300052 | − | 0.953923i | \(-0.402996\pi\) | ||||
0.300052 | + | 0.953923i | \(0.402996\pi\) | |||||||
\(504\) | −3.40616 | −0.151723 | ||||||||
\(505\) | 12.1453 | 0.540458 | ||||||||
\(506\) | −1.31897 | −0.0586351 | ||||||||
\(507\) | 11.7600 | 0.522278 | ||||||||
\(508\) | −19.0630 | −0.845784 | ||||||||
\(509\) | 27.1714 | 1.20435 | 0.602176 | − | 0.798363i | \(-0.294301\pi\) | ||||
0.602176 | + | 0.798363i | \(0.294301\pi\) | |||||||
\(510\) | −1.63990 | −0.0726161 | ||||||||
\(511\) | 2.83821 | 0.125555 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −44.4138 | −1.96092 | ||||||||
\(514\) | 29.4035 | 1.29693 | ||||||||
\(515\) | 1.55447 | 0.0684982 | ||||||||
\(516\) | −1.83141 | −0.0806234 | ||||||||
\(517\) | −7.78211 | −0.342257 | ||||||||
\(518\) | −12.4961 | −0.549047 | ||||||||
\(519\) | −25.8769 | −1.13587 | ||||||||
\(520\) | −3.70263 | −0.162371 | ||||||||
\(521\) | −10.6612 | −0.467077 | −0.233539 | − | 0.972348i | \(-0.575031\pi\) | ||||
−0.233539 | + | 0.972348i | \(0.575031\pi\) | |||||||
\(522\) | −4.95993 | −0.217090 | ||||||||
\(523\) | 35.0878 | 1.53428 | 0.767140 | − | 0.641480i | \(-0.221679\pi\) | ||||
0.767140 | + | 0.641480i | \(0.221679\pi\) | |||||||
\(524\) | 1.62818 | 0.0711274 | ||||||||
\(525\) | 22.3253 | 0.974356 | ||||||||
\(526\) | −20.3220 | −0.886081 | ||||||||
\(527\) | 7.25686 | 0.316114 | ||||||||
\(528\) | −1.68243 | −0.0732185 | ||||||||
\(529\) | −21.7406 | −0.945244 | ||||||||
\(530\) | −9.93521 | −0.431558 | ||||||||
\(531\) | −3.87813 | −0.168297 | ||||||||
\(532\) | −28.1310 | −1.21963 | ||||||||
\(533\) | −18.4450 | −0.798942 | ||||||||
\(534\) | −11.9919 | −0.518940 | ||||||||
\(535\) | 3.88443 | 0.167939 | ||||||||
\(536\) | 5.10207 | 0.220376 | ||||||||
\(537\) | −6.56674 | −0.283376 | ||||||||
\(538\) | −7.76046 | −0.334577 | ||||||||
\(539\) | −6.85424 | −0.295233 | ||||||||
\(540\) | −4.54636 | −0.195644 | ||||||||
\(541\) | −43.6364 | −1.87607 | −0.938037 | − | 0.346535i | \(-0.887358\pi\) | ||||
−0.938037 | + | 0.346535i | \(0.887358\pi\) | |||||||
\(542\) | −0.473929 | −0.0203570 | ||||||||
\(543\) | 27.4516 | 1.17806 | ||||||||
\(544\) | −1.42510 | −0.0611009 | ||||||||
\(545\) | −5.47335 | −0.234453 | ||||||||
\(546\) | 23.6186 | 1.01078 | ||||||||
\(547\) | 17.6908 | 0.756403 | 0.378202 | − | 0.925723i | \(-0.376543\pi\) | ||||
0.378202 | + | 0.925723i | \(0.376543\pi\) | |||||||
\(548\) | 6.36086 | 0.271723 | ||||||||
\(549\) | 5.19647 | 0.221780 | ||||||||
\(550\) | −5.11706 | −0.218192 | ||||||||
\(551\) | −40.9634 | −1.74510 | ||||||||
\(552\) | 1.60644 | 0.0683747 | ||||||||
\(553\) | −25.8610 | −1.09972 | ||||||||
\(554\) | −6.44464 | −0.273807 | ||||||||
\(555\) | −4.01422 | −0.170394 | ||||||||
\(556\) | 16.7084 | 0.708595 | ||||||||
\(557\) | 28.2587 | 1.19736 | 0.598679 | − | 0.800989i | \(-0.295693\pi\) | ||||
0.598679 | + | 0.800989i | \(0.295693\pi\) | |||||||
\(558\) | 4.84198 | 0.204977 | ||||||||
\(559\) | −5.89285 | −0.249241 | ||||||||
\(560\) | −2.87959 | −0.121685 | ||||||||
\(561\) | −2.39764 | −0.101229 | ||||||||
\(562\) | 17.6878 | 0.746114 | ||||||||
\(563\) | 32.2465 | 1.35903 | 0.679514 | − | 0.733663i | \(-0.262191\pi\) | ||||
0.679514 | + | 0.733663i | \(0.262191\pi\) | |||||||
\(564\) | 9.47827 | 0.399107 | ||||||||
\(565\) | 11.2222 | 0.472123 | ||||||||
\(566\) | 10.8789 | 0.457274 | ||||||||
\(567\) | 18.7821 | 0.788774 | ||||||||
\(568\) | 6.40788 | 0.268869 | ||||||||
\(569\) | −32.0928 | −1.34540 | −0.672699 | − | 0.739916i | \(-0.734865\pi\) | ||||
−0.672699 | + | 0.739916i | \(0.734865\pi\) | |||||||
\(570\) | −9.03674 | −0.378507 | ||||||||
\(571\) | −4.02161 | −0.168299 | −0.0841496 | − | 0.996453i | \(-0.526817\pi\) | ||||
−0.0841496 | + | 0.996453i | \(0.526817\pi\) | |||||||
\(572\) | −5.41349 | −0.226349 | ||||||||
\(573\) | −16.0409 | −0.670119 | ||||||||
\(574\) | −14.3450 | −0.598747 | ||||||||
\(575\) | 4.88594 | 0.203758 | ||||||||
\(576\) | −0.950869 | −0.0396196 | ||||||||
\(577\) | −15.4175 | −0.641839 | −0.320920 | − | 0.947106i | \(-0.603992\pi\) | ||||
−0.320920 | + | 0.947106i | \(0.603992\pi\) | |||||||
\(578\) | 14.9691 | 0.622631 | ||||||||
\(579\) | 32.8193 | 1.36392 | ||||||||
\(580\) | −4.19316 | −0.174111 | ||||||||
\(581\) | −22.0522 | −0.914881 | ||||||||
\(582\) | −9.74464 | −0.403928 | ||||||||
\(583\) | −14.5259 | −0.601603 | ||||||||
\(584\) | 0.792319 | 0.0327864 | ||||||||
\(585\) | −3.52072 | −0.145564 | ||||||||
\(586\) | 9.02055 | 0.372635 | ||||||||
\(587\) | 34.4441 | 1.42166 | 0.710831 | − | 0.703363i | \(-0.248319\pi\) | ||||
0.710831 | + | 0.703363i | \(0.248319\pi\) | |||||||
\(588\) | 8.34817 | 0.344273 | ||||||||
\(589\) | 39.9892 | 1.64773 | ||||||||
\(590\) | −3.27860 | −0.134978 | ||||||||
\(591\) | 15.0287 | 0.618198 | ||||||||
\(592\) | −3.48843 | −0.143374 | ||||||||
\(593\) | −33.7207 | −1.38474 | −0.692371 | − | 0.721542i | \(-0.743434\pi\) | ||||
−0.692371 | + | 0.721542i | \(0.743434\pi\) | |||||||
\(594\) | −6.64708 | −0.272733 | ||||||||
\(595\) | −4.10372 | −0.168236 | ||||||||
\(596\) | 9.78960 | 0.400998 | ||||||||
\(597\) | 29.8806 | 1.22293 | ||||||||
\(598\) | 5.16897 | 0.211375 | ||||||||
\(599\) | −27.4060 | −1.11978 | −0.559888 | − | 0.828568i | \(-0.689156\pi\) | ||||
−0.559888 | + | 0.828568i | \(0.689156\pi\) | |||||||
\(600\) | 6.23236 | 0.254435 | ||||||||
\(601\) | −31.4801 | −1.28410 | −0.642049 | − | 0.766663i | \(-0.721915\pi\) | ||||
−0.642049 | + | 0.766663i | \(0.721915\pi\) | |||||||
\(602\) | −4.58296 | −0.186787 | ||||||||
\(603\) | 4.85140 | 0.197564 | ||||||||
\(604\) | −18.6569 | −0.759138 | ||||||||
\(605\) | −7.73214 | −0.314356 | ||||||||
\(606\) | −21.6275 | −0.878557 | ||||||||
\(607\) | −45.0275 | −1.82761 | −0.913806 | − | 0.406151i | \(-0.866871\pi\) | ||||
−0.913806 | + | 0.406151i | \(0.866871\pi\) | |||||||
\(608\) | −7.85309 | −0.318485 | ||||||||
\(609\) | 26.7476 | 1.08387 | ||||||||
\(610\) | 4.39312 | 0.177872 | ||||||||
\(611\) | 30.4978 | 1.23381 | ||||||||
\(612\) | −1.35509 | −0.0547762 | ||||||||
\(613\) | −15.0761 | −0.608919 | −0.304459 | − | 0.952525i | \(-0.598476\pi\) | ||||
−0.304459 | + | 0.952525i | \(0.598476\pi\) | |||||||
\(614\) | 32.9966 | 1.33163 | ||||||||
\(615\) | −4.60814 | −0.185818 | ||||||||
\(616\) | −4.21015 | −0.169632 | ||||||||
\(617\) | 33.3062 | 1.34086 | 0.670429 | − | 0.741974i | \(-0.266110\pi\) | ||||
0.670429 | + | 0.741974i | \(0.266110\pi\) | |||||||
\(618\) | −2.76810 | −0.111349 | ||||||||
\(619\) | 32.7845 | 1.31772 | 0.658860 | − | 0.752266i | \(-0.271039\pi\) | ||||
0.658860 | + | 0.752266i | \(0.271039\pi\) | |||||||
\(620\) | 4.09344 | 0.164396 | ||||||||
\(621\) | 6.34684 | 0.254690 | ||||||||
\(622\) | −7.35795 | −0.295027 | ||||||||
\(623\) | −30.0087 | −1.20227 | ||||||||
\(624\) | 6.59339 | 0.263947 | ||||||||
\(625\) | 15.7245 | 0.628979 | ||||||||
\(626\) | −11.9851 | −0.479019 | ||||||||
\(627\) | −13.2123 | −0.527649 | ||||||||
\(628\) | 8.84383 | 0.352907 | ||||||||
\(629\) | −4.97138 | −0.198222 | ||||||||
\(630\) | −2.73811 | −0.109089 | ||||||||
\(631\) | −22.4125 | −0.892227 | −0.446114 | − | 0.894976i | \(-0.647192\pi\) | ||||
−0.446114 | + | 0.894976i | \(0.647192\pi\) | |||||||
\(632\) | −7.21938 | −0.287172 | ||||||||
\(633\) | 24.5358 | 0.975211 | ||||||||
\(634\) | 12.4797 | 0.495630 | ||||||||
\(635\) | −15.3242 | −0.608122 | ||||||||
\(636\) | 17.6920 | 0.701532 | ||||||||
\(637\) | 26.8615 | 1.06429 | ||||||||
\(638\) | −6.13067 | −0.242716 | ||||||||
\(639\) | 6.09306 | 0.241038 | ||||||||
\(640\) | −0.803871 | −0.0317758 | ||||||||
\(641\) | −34.4552 | −1.36090 | −0.680450 | − | 0.732795i | \(-0.738216\pi\) | ||||
−0.680450 | + | 0.732795i | \(0.738216\pi\) | |||||||
\(642\) | −6.91713 | −0.272997 | ||||||||
\(643\) | −41.9310 | −1.65360 | −0.826798 | − | 0.562499i | \(-0.809840\pi\) | ||||
−0.826798 | + | 0.562499i | \(0.809840\pi\) | |||||||
\(644\) | 4.01999 | 0.158410 | ||||||||
\(645\) | −1.47222 | −0.0579686 | ||||||||
\(646\) | −11.1915 | −0.440323 | ||||||||
\(647\) | −31.9677 | −1.25678 | −0.628390 | − | 0.777899i | \(-0.716286\pi\) | ||||
−0.628390 | + | 0.777899i | \(0.716286\pi\) | |||||||
\(648\) | 5.24324 | 0.205974 | ||||||||
\(649\) | −4.79353 | −0.188162 | ||||||||
\(650\) | 20.0536 | 0.786566 | ||||||||
\(651\) | −26.1115 | −1.02339 | ||||||||
\(652\) | −25.4226 | −0.995625 | ||||||||
\(653\) | 43.3264 | 1.69549 | 0.847747 | − | 0.530400i | \(-0.177958\pi\) | ||||
0.847747 | + | 0.530400i | \(0.177958\pi\) | |||||||
\(654\) | 9.74658 | 0.381121 | ||||||||
\(655\) | 1.30885 | 0.0511409 | ||||||||
\(656\) | −4.00456 | −0.156352 | ||||||||
\(657\) | 0.753392 | 0.0293926 | ||||||||
\(658\) | 23.7186 | 0.924647 | ||||||||
\(659\) | −4.10123 | −0.159761 | −0.0798806 | − | 0.996804i | \(-0.525454\pi\) | ||||
−0.0798806 | + | 0.996804i | \(0.525454\pi\) | |||||||
\(660\) | −1.35246 | −0.0526444 | ||||||||
\(661\) | −33.8905 | −1.31819 | −0.659094 | − | 0.752061i | \(-0.729060\pi\) | ||||
−0.659094 | + | 0.752061i | \(0.729060\pi\) | |||||||
\(662\) | 19.8116 | 0.769998 | ||||||||
\(663\) | 9.39628 | 0.364921 | ||||||||
\(664\) | −6.15613 | −0.238904 | ||||||||
\(665\) | −22.6137 | −0.876922 | ||||||||
\(666\) | −3.31704 | −0.128533 | ||||||||
\(667\) | 5.85376 | 0.226659 | ||||||||
\(668\) | 5.46543 | 0.211464 | ||||||||
\(669\) | 11.6058 | 0.448707 | ||||||||
\(670\) | 4.10140 | 0.158451 | ||||||||
\(671\) | 6.42304 | 0.247959 | ||||||||
\(672\) | 5.12778 | 0.197808 | ||||||||
\(673\) | −33.8252 | −1.30387 | −0.651933 | − | 0.758276i | \(-0.726042\pi\) | ||||
−0.651933 | + | 0.758276i | \(0.726042\pi\) | |||||||
\(674\) | −21.8413 | −0.841294 | ||||||||
\(675\) | 24.6232 | 0.947749 | ||||||||
\(676\) | 8.21526 | 0.315972 | ||||||||
\(677\) | −19.0158 | −0.730838 | −0.365419 | − | 0.930843i | \(-0.619074\pi\) | ||||
−0.365419 | + | 0.930843i | \(0.619074\pi\) | |||||||
\(678\) | −19.9838 | −0.767473 | ||||||||
\(679\) | −24.3852 | −0.935816 | ||||||||
\(680\) | −1.14560 | −0.0439318 | ||||||||
\(681\) | 8.79929 | 0.337189 | ||||||||
\(682\) | 5.98488 | 0.229173 | ||||||||
\(683\) | −21.2328 | −0.812452 | −0.406226 | − | 0.913773i | \(-0.633155\pi\) | ||||
−0.406226 | + | 0.913773i | \(0.633155\pi\) | |||||||
\(684\) | −7.46727 | −0.285518 | ||||||||
\(685\) | 5.11331 | 0.195370 | ||||||||
\(686\) | −4.18450 | −0.159765 | ||||||||
\(687\) | 18.9733 | 0.723876 | ||||||||
\(688\) | −1.27939 | −0.0487761 | ||||||||
\(689\) | 56.9266 | 2.16873 | ||||||||
\(690\) | 1.29137 | 0.0491617 | ||||||||
\(691\) | 51.5610 | 1.96147 | 0.980736 | − | 0.195339i | \(-0.0625806\pi\) | ||||
0.980736 | + | 0.195339i | \(0.0625806\pi\) | |||||||
\(692\) | −18.0771 | −0.687186 | ||||||||
\(693\) | −4.00330 | −0.152073 | ||||||||
\(694\) | −0.811855 | −0.0308176 | ||||||||
\(695\) | 13.4314 | 0.509482 | ||||||||
\(696\) | 7.46689 | 0.283032 | ||||||||
\(697\) | −5.70691 | −0.216165 | ||||||||
\(698\) | 11.5066 | 0.435530 | ||||||||
\(699\) | 42.8795 | 1.62185 | ||||||||
\(700\) | 15.5960 | 0.589472 | ||||||||
\(701\) | 24.8228 | 0.937546 | 0.468773 | − | 0.883319i | \(-0.344696\pi\) | ||||
0.468773 | + | 0.883319i | \(0.344696\pi\) | |||||||
\(702\) | 26.0496 | 0.983180 | ||||||||
\(703\) | −27.3950 | −1.03322 | ||||||||
\(704\) | −1.17531 | −0.0442962 | ||||||||
\(705\) | 7.61930 | 0.286959 | ||||||||
\(706\) | 10.3775 | 0.390564 | ||||||||
\(707\) | −54.1210 | −2.03543 | ||||||||
\(708\) | 5.83831 | 0.219417 | ||||||||
\(709\) | −0.620603 | −0.0233072 | −0.0116536 | − | 0.999932i | \(-0.503710\pi\) | ||||
−0.0116536 | + | 0.999932i | \(0.503710\pi\) | |||||||
\(710\) | 5.15111 | 0.193318 | ||||||||
\(711\) | −6.86469 | −0.257446 | ||||||||
\(712\) | −8.37728 | −0.313952 | ||||||||
\(713\) | −5.71455 | −0.214012 | ||||||||
\(714\) | 7.30763 | 0.273481 | ||||||||
\(715\) | −4.35175 | −0.162746 | ||||||||
\(716\) | −4.58739 | −0.171439 | ||||||||
\(717\) | 13.8635 | 0.517742 | ||||||||
\(718\) | −1.98848 | −0.0742094 | ||||||||
\(719\) | 34.9883 | 1.30484 | 0.652422 | − | 0.757856i | \(-0.273753\pi\) | ||||
0.652422 | + | 0.757856i | \(0.273753\pi\) | |||||||
\(720\) | −0.764376 | −0.0284866 | ||||||||
\(721\) | −6.92694 | −0.257973 | ||||||||
\(722\) | −42.6711 | −1.58805 | ||||||||
\(723\) | 33.7016 | 1.25337 | ||||||||
\(724\) | 19.1771 | 0.712711 | ||||||||
\(725\) | 22.7103 | 0.843439 | ||||||||
\(726\) | 13.7689 | 0.511011 | ||||||||
\(727\) | 42.4243 | 1.57343 | 0.786715 | − | 0.617316i | \(-0.211780\pi\) | ||||
0.786715 | + | 0.617316i | \(0.211780\pi\) | |||||||
\(728\) | 16.4994 | 0.611509 | ||||||||
\(729\) | 29.2732 | 1.08419 | ||||||||
\(730\) | 0.636922 | 0.0235735 | ||||||||
\(731\) | −1.82326 | −0.0674356 | ||||||||
\(732\) | −7.82298 | −0.289146 | ||||||||
\(733\) | −27.3968 | −1.01192 | −0.505962 | − | 0.862555i | \(-0.668863\pi\) | ||||
−0.505962 | + | 0.862555i | \(0.668863\pi\) | |||||||
\(734\) | −33.8501 | −1.24943 | ||||||||
\(735\) | 6.71085 | 0.247533 | ||||||||
\(736\) | 1.12223 | 0.0413658 | ||||||||
\(737\) | 5.99652 | 0.220885 | ||||||||
\(738\) | −3.80781 | −0.140167 | ||||||||
\(739\) | 40.9798 | 1.50747 | 0.753733 | − | 0.657180i | \(-0.228251\pi\) | ||||
0.753733 | + | 0.657180i | \(0.228251\pi\) | |||||||
\(740\) | −2.80425 | −0.103086 | ||||||||
\(741\) | 51.7785 | 1.90213 | ||||||||
\(742\) | 44.2726 | 1.62530 | ||||||||
\(743\) | 1.95166 | 0.0715995 | 0.0357998 | − | 0.999359i | \(-0.488602\pi\) | ||||
0.0357998 | + | 0.999359i | \(0.488602\pi\) | |||||||
\(744\) | −7.28932 | −0.267239 | ||||||||
\(745\) | 7.86957 | 0.288319 | ||||||||
\(746\) | 17.3730 | 0.636072 | ||||||||
\(747\) | −5.85368 | −0.214175 | ||||||||
\(748\) | −1.67494 | −0.0612420 | ||||||||
\(749\) | −17.3096 | −0.632477 | ||||||||
\(750\) | 10.7636 | 0.393032 | ||||||||
\(751\) | 26.8155 | 0.978511 | 0.489256 | − | 0.872140i | \(-0.337268\pi\) | ||||
0.489256 | + | 0.872140i | \(0.337268\pi\) | |||||||
\(752\) | 6.62131 | 0.241454 | ||||||||
\(753\) | 21.5504 | 0.785340 | ||||||||
\(754\) | 24.0259 | 0.874971 | ||||||||
\(755\) | −14.9977 | −0.545823 | ||||||||
\(756\) | 20.2592 | 0.736820 | ||||||||
\(757\) | −6.13139 | −0.222849 | −0.111425 | − | 0.993773i | \(-0.535541\pi\) | ||||
−0.111425 | + | 0.993773i | \(0.535541\pi\) | |||||||
\(758\) | −14.8045 | −0.537725 | ||||||||
\(759\) | 1.88807 | 0.0685326 | ||||||||
\(760\) | −6.31287 | −0.228992 | ||||||||
\(761\) | 5.93684 | 0.215210 | 0.107605 | − | 0.994194i | \(-0.465682\pi\) | ||||
0.107605 | + | 0.994194i | \(0.465682\pi\) | |||||||
\(762\) | 27.2883 | 0.988550 | ||||||||
\(763\) | 24.3900 | 0.882978 | ||||||||
\(764\) | −11.2058 | −0.405413 | ||||||||
\(765\) | −1.08932 | −0.0393843 | ||||||||
\(766\) | −17.7812 | −0.642462 | ||||||||
\(767\) | 18.7856 | 0.678310 | ||||||||
\(768\) | 1.43148 | 0.0516540 | ||||||||
\(769\) | −13.3517 | −0.481473 | −0.240737 | − | 0.970591i | \(-0.577389\pi\) | ||||
−0.240737 | + | 0.970591i | \(0.577389\pi\) | |||||||
\(770\) | −3.38442 | −0.121966 | ||||||||
\(771\) | −42.0904 | −1.51585 | ||||||||
\(772\) | 22.9269 | 0.825156 | ||||||||
\(773\) | 39.3531 | 1.41543 | 0.707716 | − | 0.706497i | \(-0.249726\pi\) | ||||
0.707716 | + | 0.706497i | \(0.249726\pi\) | |||||||
\(774\) | −1.21653 | −0.0437272 | ||||||||
\(775\) | −22.1702 | −0.796377 | ||||||||
\(776\) | −6.80739 | −0.244371 | ||||||||
\(777\) | 17.8879 | 0.641725 | ||||||||
\(778\) | 21.2040 | 0.760200 | ||||||||
\(779\) | −31.4482 | −1.12675 | ||||||||
\(780\) | 5.30024 | 0.189779 | ||||||||
\(781\) | 7.53126 | 0.269490 | ||||||||
\(782\) | 1.59929 | 0.0571905 | ||||||||
\(783\) | 29.5007 | 1.05427 | ||||||||
\(784\) | 5.83185 | 0.208280 | ||||||||
\(785\) | 7.10930 | 0.253742 | ||||||||
\(786\) | −2.33071 | −0.0831336 | ||||||||
\(787\) | 3.95473 | 0.140971 | 0.0704854 | − | 0.997513i | \(-0.477545\pi\) | ||||
0.0704854 | + | 0.997513i | \(0.477545\pi\) | |||||||
\(788\) | 10.4987 | 0.374001 | ||||||||
\(789\) | 29.0905 | 1.03565 | ||||||||
\(790\) | −5.80345 | −0.206477 | ||||||||
\(791\) | −50.0078 | −1.77807 | ||||||||
\(792\) | −1.11757 | −0.0397111 | ||||||||
\(793\) | −25.1716 | −0.893871 | ||||||||
\(794\) | −26.7934 | −0.950863 | ||||||||
\(795\) | 14.2220 | 0.504404 | ||||||||
\(796\) | 20.8739 | 0.739856 | ||||||||
\(797\) | 22.4915 | 0.796691 | 0.398346 | − | 0.917235i | \(-0.369584\pi\) | ||||
0.398346 | + | 0.917235i | \(0.369584\pi\) | |||||||
\(798\) | 40.2689 | 1.42550 | ||||||||
\(799\) | 9.43607 | 0.333824 | ||||||||
\(800\) | 4.35379 | 0.153930 | ||||||||
\(801\) | −7.96570 | −0.281454 | ||||||||
\(802\) | −19.3584 | −0.683567 | ||||||||
\(803\) | 0.931222 | 0.0328621 | ||||||||
\(804\) | −7.30350 | −0.257575 | ||||||||
\(805\) | 3.23155 | 0.113897 | ||||||||
\(806\) | −23.4545 | −0.826149 | ||||||||
\(807\) | 11.1089 | 0.391053 | ||||||||
\(808\) | −15.1085 | −0.531515 | ||||||||
\(809\) | −44.7344 | −1.57278 | −0.786388 | − | 0.617733i | \(-0.788051\pi\) | ||||
−0.786388 | + | 0.617733i | \(0.788051\pi\) | |||||||
\(810\) | 4.21489 | 0.148096 | ||||||||
\(811\) | 1.74111 | 0.0611387 | 0.0305694 | − | 0.999533i | \(-0.490268\pi\) | ||||
0.0305694 | + | 0.999533i | \(0.490268\pi\) | |||||||
\(812\) | 18.6853 | 0.655725 | ||||||||
\(813\) | 0.678419 | 0.0237932 | ||||||||
\(814\) | −4.09999 | −0.143705 | ||||||||
\(815\) | −20.4365 | −0.715858 | ||||||||
\(816\) | 2.04001 | 0.0714145 | ||||||||
\(817\) | −10.0471 | −0.351505 | ||||||||
\(818\) | −5.17694 | −0.181007 | ||||||||
\(819\) | 15.6888 | 0.548211 | ||||||||
\(820\) | −3.21915 | −0.112417 | ||||||||
\(821\) | 27.5669 | 0.962091 | 0.481045 | − | 0.876696i | \(-0.340257\pi\) | ||||
0.481045 | + | 0.876696i | \(0.340257\pi\) | |||||||
\(822\) | −9.10544 | −0.317589 | ||||||||
\(823\) | −22.7791 | −0.794031 | −0.397015 | − | 0.917812i | \(-0.629954\pi\) | ||||
−0.397015 | + | 0.917812i | \(0.629954\pi\) | |||||||
\(824\) | −1.93373 | −0.0673648 | ||||||||
\(825\) | 7.32497 | 0.255023 | ||||||||
\(826\) | 14.6099 | 0.508343 | ||||||||
\(827\) | 40.8914 | 1.42193 | 0.710966 | − | 0.703226i | \(-0.248258\pi\) | ||||
0.710966 | + | 0.703226i | \(0.248258\pi\) | |||||||
\(828\) | 1.06709 | 0.0370839 | ||||||||
\(829\) | 0.833934 | 0.0289637 | 0.0144819 | − | 0.999895i | \(-0.495390\pi\) | ||||
0.0144819 | + | 0.999895i | \(0.495390\pi\) | |||||||
\(830\) | −4.94874 | −0.171773 | ||||||||
\(831\) | 9.22537 | 0.320024 | ||||||||
\(832\) | 4.60600 | 0.159684 | ||||||||
\(833\) | 8.31100 | 0.287959 | ||||||||
\(834\) | −23.9177 | −0.828204 | ||||||||
\(835\) | 4.39350 | 0.152043 | ||||||||
\(836\) | −9.22983 | −0.319220 | ||||||||
\(837\) | −28.7991 | −0.995444 | ||||||||
\(838\) | −13.5001 | −0.466353 | ||||||||
\(839\) | 28.1092 | 0.970439 | 0.485219 | − | 0.874393i | \(-0.338740\pi\) | ||||
0.485219 | + | 0.874393i | \(0.338740\pi\) | |||||||
\(840\) | 4.12207 | 0.142225 | ||||||||
\(841\) | −1.79116 | −0.0617640 | ||||||||
\(842\) | 20.3494 | 0.701285 | ||||||||
\(843\) | −25.3197 | −0.872057 | ||||||||
\(844\) | 17.1402 | 0.589989 | ||||||||
\(845\) | 6.60401 | 0.227185 | ||||||||
\(846\) | 6.29600 | 0.216461 | ||||||||
\(847\) | 34.4555 | 1.18390 | ||||||||
\(848\) | 12.3592 | 0.424417 | ||||||||
\(849\) | −15.5729 | −0.534461 | ||||||||
\(850\) | 6.20461 | 0.212816 | ||||||||
\(851\) | 3.91480 | 0.134198 | ||||||||
\(852\) | −9.17274 | −0.314253 | ||||||||
\(853\) | 32.2317 | 1.10359 | 0.551796 | − | 0.833979i | \(-0.313943\pi\) | ||||
0.551796 | + | 0.833979i | \(0.313943\pi\) | |||||||
\(854\) | −19.5764 | −0.669889 | ||||||||
\(855\) | −6.00272 | −0.205289 | ||||||||
\(856\) | −4.83216 | −0.165160 | ||||||||
\(857\) | 16.3053 | 0.556977 | 0.278489 | − | 0.960440i | \(-0.410167\pi\) | ||||
0.278489 | + | 0.960440i | \(0.410167\pi\) | |||||||
\(858\) | 7.74929 | 0.264557 | ||||||||
\(859\) | −46.6831 | −1.59281 | −0.796404 | − | 0.604766i | \(-0.793267\pi\) | ||||
−0.796404 | + | 0.604766i | \(0.793267\pi\) | |||||||
\(860\) | −1.02846 | −0.0350702 | ||||||||
\(861\) | 20.5345 | 0.699813 | ||||||||
\(862\) | −0.00245142 | −8.34958e−5 0 | ||||||||
\(863\) | 11.4098 | 0.388395 | 0.194198 | − | 0.980962i | \(-0.437790\pi\) | ||||
0.194198 | + | 0.980962i | \(0.437790\pi\) | |||||||
\(864\) | 5.65558 | 0.192407 | ||||||||
\(865\) | −14.5316 | −0.494090 | ||||||||
\(866\) | −13.4348 | −0.456535 | ||||||||
\(867\) | −21.4279 | −0.727730 | ||||||||
\(868\) | −18.2409 | −0.619137 | ||||||||
\(869\) | −8.48502 | −0.287835 | ||||||||
\(870\) | 6.00242 | 0.203501 | ||||||||
\(871\) | −23.5001 | −0.796272 | ||||||||
\(872\) | 6.80875 | 0.230573 | ||||||||
\(873\) | −6.47294 | −0.219076 | ||||||||
\(874\) | 8.81294 | 0.298102 | ||||||||
\(875\) | 26.9351 | 0.910572 | ||||||||
\(876\) | −1.13419 | −0.0383206 | ||||||||
\(877\) | −33.4478 | −1.12945 | −0.564725 | − | 0.825279i | \(-0.691018\pi\) | ||||
−0.564725 | + | 0.825279i | \(0.691018\pi\) | |||||||
\(878\) | −29.4126 | −0.992628 | ||||||||
\(879\) | −12.9127 | −0.435535 | ||||||||
\(880\) | −0.944799 | −0.0318492 | ||||||||
\(881\) | −34.5471 | −1.16392 | −0.581961 | − | 0.813217i | \(-0.697714\pi\) | ||||
−0.581961 | + | 0.813217i | \(0.697714\pi\) | |||||||
\(882\) | 5.54533 | 0.186721 | ||||||||
\(883\) | −26.6240 | −0.895968 | −0.447984 | − | 0.894041i | \(-0.647858\pi\) | ||||
−0.447984 | + | 0.894041i | \(0.647858\pi\) | |||||||
\(884\) | 6.56404 | 0.220772 | ||||||||
\(885\) | 4.69324 | 0.157762 | ||||||||
\(886\) | −25.2124 | −0.847028 | ||||||||
\(887\) | 17.5073 | 0.587839 | 0.293920 | − | 0.955830i | \(-0.405040\pi\) | ||||
0.293920 | + | 0.955830i | \(0.405040\pi\) | |||||||
\(888\) | 4.99361 | 0.167575 | ||||||||
\(889\) | 68.2867 | 2.29026 | ||||||||
\(890\) | −6.73425 | −0.225732 | ||||||||
\(891\) | 6.16244 | 0.206450 | ||||||||
\(892\) | 8.10757 | 0.271461 | ||||||||
\(893\) | 51.9978 | 1.74004 | ||||||||
\(894\) | −14.0136 | −0.468685 | ||||||||
\(895\) | −3.68767 | −0.123265 | ||||||||
\(896\) | 3.58216 | 0.119671 | ||||||||
\(897\) | −7.39927 | −0.247055 | ||||||||
\(898\) | 6.24356 | 0.208350 | ||||||||
\(899\) | −26.5618 | −0.885885 | ||||||||
\(900\) | 4.13989 | 0.137996 | ||||||||
\(901\) | 17.6132 | 0.586780 | ||||||||
\(902\) | −4.70660 | −0.156713 | ||||||||
\(903\) | 6.56041 | 0.218317 | ||||||||
\(904\) | −13.9602 | −0.464311 | ||||||||
\(905\) | 15.4159 | 0.512442 | ||||||||
\(906\) | 26.7070 | 0.887279 | ||||||||
\(907\) | −19.3253 | −0.641687 | −0.320843 | − | 0.947132i | \(-0.603966\pi\) | ||||
−0.320843 | + | 0.947132i | \(0.603966\pi\) | |||||||
\(908\) | 6.14699 | 0.203995 | ||||||||
\(909\) | −14.3662 | −0.476497 | ||||||||
\(910\) | 13.2634 | 0.439678 | ||||||||
\(911\) | 17.4940 | 0.579601 | 0.289800 | − | 0.957087i | \(-0.406411\pi\) | ||||
0.289800 | + | 0.957087i | \(0.406411\pi\) | |||||||
\(912\) | 11.2415 | 0.372244 | ||||||||
\(913\) | −7.23538 | −0.239456 | ||||||||
\(914\) | −22.7691 | −0.753134 | ||||||||
\(915\) | −6.28866 | −0.207897 | ||||||||
\(916\) | 13.2543 | 0.437935 | ||||||||
\(917\) | −5.83240 | −0.192603 | ||||||||
\(918\) | 8.05980 | 0.266013 | ||||||||
\(919\) | −26.9194 | −0.887990 | −0.443995 | − | 0.896029i | \(-0.646439\pi\) | ||||
−0.443995 | + | 0.896029i | \(0.646439\pi\) | |||||||
\(920\) | 0.902124 | 0.0297422 | ||||||||
\(921\) | −47.2339 | −1.55641 | ||||||||
\(922\) | 23.9176 | 0.787683 | ||||||||
\(923\) | −29.5147 | −0.971488 | ||||||||
\(924\) | 6.02674 | 0.198265 | ||||||||
\(925\) | 15.1879 | 0.499375 | ||||||||
\(926\) | −30.7084 | −1.00914 | ||||||||
\(927\) | −1.83873 | −0.0603918 | ||||||||
\(928\) | 5.21621 | 0.171230 | ||||||||
\(929\) | −21.0988 | −0.692230 | −0.346115 | − | 0.938192i | \(-0.612499\pi\) | ||||
−0.346115 | + | 0.938192i | \(0.612499\pi\) | |||||||
\(930\) | −5.85967 | −0.192146 | ||||||||
\(931\) | 45.7980 | 1.50097 | ||||||||
\(932\) | 29.9547 | 0.981198 | ||||||||
\(933\) | 10.5328 | 0.344827 | ||||||||
\(934\) | −23.7542 | −0.777261 | ||||||||
\(935\) | −1.34644 | −0.0440332 | ||||||||
\(936\) | 4.37971 | 0.143155 | ||||||||
\(937\) | −24.9317 | −0.814483 | −0.407242 | − | 0.913320i | \(-0.633509\pi\) | ||||
−0.407242 | + | 0.913320i | \(0.633509\pi\) | |||||||
\(938\) | −18.2764 | −0.596746 | ||||||||
\(939\) | 17.1563 | 0.559876 | ||||||||
\(940\) | 5.32268 | 0.173607 | ||||||||
\(941\) | 10.5116 | 0.342668 | 0.171334 | − | 0.985213i | \(-0.445192\pi\) | ||||
0.171334 | + | 0.985213i | \(0.445192\pi\) | |||||||
\(942\) | −12.6598 | −0.412477 | ||||||||
\(943\) | 4.49402 | 0.146345 | ||||||||
\(944\) | 4.07851 | 0.132744 | ||||||||
\(945\) | 16.2858 | 0.529776 | ||||||||
\(946\) | −1.50368 | −0.0488888 | ||||||||
\(947\) | −17.0994 | −0.555655 | −0.277828 | − | 0.960631i | \(-0.589614\pi\) | ||||
−0.277828 | + | 0.960631i | \(0.589614\pi\) | |||||||
\(948\) | 10.3344 | 0.335645 | ||||||||
\(949\) | −3.64942 | −0.118465 | ||||||||
\(950\) | 34.1907 | 1.10929 | ||||||||
\(951\) | −17.8644 | −0.579291 | ||||||||
\(952\) | 5.10495 | 0.165452 | ||||||||
\(953\) | −30.2850 | −0.981027 | −0.490514 | − | 0.871434i | \(-0.663191\pi\) | ||||
−0.490514 | + | 0.871434i | \(0.663191\pi\) | |||||||
\(954\) | 11.7520 | 0.380485 | ||||||||
\(955\) | −9.00804 | −0.291493 | ||||||||
\(956\) | 9.68475 | 0.313227 | ||||||||
\(957\) | 8.77593 | 0.283685 | ||||||||
\(958\) | −39.1600 | −1.26520 | ||||||||
\(959\) | −22.7856 | −0.735786 | ||||||||
\(960\) | 1.15072 | 0.0371394 | ||||||||
\(961\) | −5.06992 | −0.163546 | ||||||||
\(962\) | 16.0677 | 0.518044 | ||||||||
\(963\) | −4.59475 | −0.148064 | ||||||||
\(964\) | 23.5432 | 0.758275 | ||||||||
\(965\) | 18.4302 | 0.593290 | ||||||||
\(966\) | −5.75453 | −0.185149 | ||||||||
\(967\) | 18.8905 | 0.607476 | 0.303738 | − | 0.952756i | \(-0.401765\pi\) | ||||
0.303738 | + | 0.952756i | \(0.401765\pi\) | |||||||
\(968\) | 9.61864 | 0.309155 | ||||||||
\(969\) | 16.0204 | 0.514648 | ||||||||
\(970\) | −5.47226 | −0.175704 | ||||||||
\(971\) | −49.0867 | −1.57527 | −0.787633 | − | 0.616144i | \(-0.788694\pi\) | ||||
−0.787633 | + | 0.616144i | \(0.788694\pi\) | |||||||
\(972\) | 9.46117 | 0.303467 | ||||||||
\(973\) | −59.8522 | −1.91877 | ||||||||
\(974\) | 29.7377 | 0.952856 | ||||||||
\(975\) | −28.7063 | −0.919336 | ||||||||
\(976\) | −5.46496 | −0.174929 | ||||||||
\(977\) | −17.6020 | −0.563137 | −0.281568 | − | 0.959541i | \(-0.590855\pi\) | ||||
−0.281568 | + | 0.959541i | \(0.590855\pi\) | |||||||
\(978\) | 36.3919 | 1.16368 | ||||||||
\(979\) | −9.84591 | −0.314677 | ||||||||
\(980\) | 4.68805 | 0.149754 | ||||||||
\(981\) | 6.47423 | 0.206706 | ||||||||
\(982\) | −29.0228 | −0.926156 | ||||||||
\(983\) | −3.69837 | −0.117960 | −0.0589799 | − | 0.998259i | \(-0.518785\pi\) | ||||
−0.0589799 | + | 0.998259i | \(0.518785\pi\) | |||||||
\(984\) | 5.73244 | 0.182743 | ||||||||
\(985\) | 8.43961 | 0.268908 | ||||||||
\(986\) | 7.43365 | 0.236736 | ||||||||
\(987\) | −33.9526 | −1.08072 | ||||||||
\(988\) | 36.1714 | 1.15076 | ||||||||
\(989\) | 1.43576 | 0.0456545 | ||||||||
\(990\) | −0.898380 | −0.0285524 | ||||||||
\(991\) | 22.2776 | 0.707671 | 0.353836 | − | 0.935308i | \(-0.384877\pi\) | ||||
0.353836 | + | 0.935308i | \(0.384877\pi\) | |||||||
\(992\) | −5.09216 | −0.161676 | ||||||||
\(993\) | −28.3598 | −0.899972 | ||||||||
\(994\) | −22.9540 | −0.728058 | ||||||||
\(995\) | 16.7799 | 0.531959 | ||||||||
\(996\) | 8.81237 | 0.279231 | ||||||||
\(997\) | −42.8107 | −1.35583 | −0.677915 | − | 0.735141i | \(-0.737116\pi\) | ||||
−0.677915 | + | 0.735141i | \(0.737116\pi\) | |||||||
\(998\) | 34.3533 | 1.08743 | ||||||||
\(999\) | 19.7291 | 0.624201 |
(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 | 8002.2.a.e.1.53 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.53 | ✓ | 77 | 1.1 | even | 1 | trivial |