Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0200112105\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 | ||||||||
\(3\) | 0.822612 | 0.474935 | 0.237468 | − | 0.971395i | \(-0.423683\pi\) | ||||
0.237468 | + | 0.971395i | \(0.423683\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.822612 | 0.335830 | ||||||||
\(7\) | 0.710831 | 0.268669 | 0.134334 | − | 0.990936i | \(-0.457110\pi\) | ||||
0.134334 | + | 0.990936i | \(0.457110\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.32331 | −0.774437 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −4.10210 | −1.23683 | −0.618415 | − | 0.785852i | \(-0.712225\pi\) | ||||
−0.618415 | + | 0.785852i | \(0.712225\pi\) | |||||||
\(12\) | 0.822612 | 0.237468 | ||||||||
\(13\) | 0.532365 | 0.147652 | 0.0738258 | − | 0.997271i | \(-0.476479\pi\) | ||||
0.0738258 | + | 0.997271i | \(0.476479\pi\) | |||||||
\(14\) | 0.710831 | 0.189978 | ||||||||
\(15\) | 0.822612 | 0.212397 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.61575 | 0.391877 | 0.195938 | − | 0.980616i | \(-0.437225\pi\) | ||||
0.195938 | + | 0.980616i | \(0.437225\pi\) | |||||||
\(18\) | −2.32331 | −0.547609 | ||||||||
\(19\) | 7.94642 | 1.82303 | 0.911517 | − | 0.411261i | \(-0.134912\pi\) | ||||
0.911517 | + | 0.411261i | \(0.134912\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.584738 | 0.127600 | ||||||||
\(22\) | −4.10210 | −0.874571 | ||||||||
\(23\) | 6.05858 | 1.26330 | 0.631651 | − | 0.775253i | \(-0.282378\pi\) | ||||
0.631651 | + | 0.775253i | \(0.282378\pi\) | |||||||
\(24\) | 0.822612 | 0.167915 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.532365 | 0.104405 | ||||||||
\(27\) | −4.37902 | −0.842742 | ||||||||
\(28\) | 0.710831 | 0.134334 | ||||||||
\(29\) | −0.915588 | −0.170020 | −0.0850102 | − | 0.996380i | \(-0.527092\pi\) | ||||
−0.0850102 | + | 0.996380i | \(0.527092\pi\) | |||||||
\(30\) | 0.822612 | 0.150188 | ||||||||
\(31\) | −5.17569 | −0.929581 | −0.464790 | − | 0.885421i | \(-0.653870\pi\) | ||||
−0.464790 | + | 0.885421i | \(0.653870\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.37444 | −0.587414 | ||||||||
\(34\) | 1.61575 | 0.277099 | ||||||||
\(35\) | 0.710831 | 0.120152 | ||||||||
\(36\) | −2.32331 | −0.387218 | ||||||||
\(37\) | 10.3629 | 1.70365 | 0.851827 | − | 0.523823i | \(-0.175495\pi\) | ||||
0.851827 | + | 0.523823i | \(0.175495\pi\) | |||||||
\(38\) | 7.94642 | 1.28908 | ||||||||
\(39\) | 0.437930 | 0.0701249 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 6.76575 | 1.05663 | 0.528317 | − | 0.849047i | \(-0.322823\pi\) | ||||
0.528317 | + | 0.849047i | \(0.322823\pi\) | |||||||
\(42\) | 0.584738 | 0.0902270 | ||||||||
\(43\) | 8.64895 | 1.31895 | 0.659476 | − | 0.751725i | \(-0.270778\pi\) | ||||
0.659476 | + | 0.751725i | \(0.270778\pi\) | |||||||
\(44\) | −4.10210 | −0.618415 | ||||||||
\(45\) | −2.32331 | −0.346339 | ||||||||
\(46\) | 6.05858 | 0.893289 | ||||||||
\(47\) | −6.55629 | −0.956333 | −0.478166 | − | 0.878269i | \(-0.658698\pi\) | ||||
−0.478166 | + | 0.878269i | \(0.658698\pi\) | |||||||
\(48\) | 0.822612 | 0.118734 | ||||||||
\(49\) | −6.49472 | −0.927817 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.32913 | 0.186116 | ||||||||
\(52\) | 0.532365 | 0.0738258 | ||||||||
\(53\) | 11.1024 | 1.52503 | 0.762517 | − | 0.646968i | \(-0.223963\pi\) | ||||
0.762517 | + | 0.646968i | \(0.223963\pi\) | |||||||
\(54\) | −4.37902 | −0.595909 | ||||||||
\(55\) | −4.10210 | −0.553127 | ||||||||
\(56\) | 0.710831 | 0.0949888 | ||||||||
\(57\) | 6.53682 | 0.865823 | ||||||||
\(58\) | −0.915588 | −0.120223 | ||||||||
\(59\) | −3.59674 | −0.468255 | −0.234128 | − | 0.972206i | \(-0.575223\pi\) | ||||
−0.234128 | + | 0.972206i | \(0.575223\pi\) | |||||||
\(60\) | 0.822612 | 0.106199 | ||||||||
\(61\) | 4.86048 | 0.622321 | 0.311160 | − | 0.950357i | \(-0.399282\pi\) | ||||
0.311160 | + | 0.950357i | \(0.399282\pi\) | |||||||
\(62\) | −5.17569 | −0.657313 | ||||||||
\(63\) | −1.65148 | −0.208067 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.532365 | 0.0660318 | ||||||||
\(66\) | −3.37444 | −0.415365 | ||||||||
\(67\) | 6.55325 | 0.800607 | 0.400304 | − | 0.916383i | \(-0.368905\pi\) | ||||
0.400304 | + | 0.916383i | \(0.368905\pi\) | |||||||
\(68\) | 1.61575 | 0.195938 | ||||||||
\(69\) | 4.98386 | 0.599987 | ||||||||
\(70\) | 0.710831 | 0.0849606 | ||||||||
\(71\) | 6.01123 | 0.713402 | 0.356701 | − | 0.934219i | \(-0.383902\pi\) | ||||
0.356701 | + | 0.934219i | \(0.383902\pi\) | |||||||
\(72\) | −2.32331 | −0.273805 | ||||||||
\(73\) | 2.41097 | 0.282182 | 0.141091 | − | 0.989997i | \(-0.454939\pi\) | ||||
0.141091 | + | 0.989997i | \(0.454939\pi\) | |||||||
\(74\) | 10.3629 | 1.20467 | ||||||||
\(75\) | 0.822612 | 0.0949870 | ||||||||
\(76\) | 7.94642 | 0.911517 | ||||||||
\(77\) | −2.91590 | −0.332298 | ||||||||
\(78\) | 0.437930 | 0.0495858 | ||||||||
\(79\) | −2.92286 | −0.328847 | −0.164424 | − | 0.986390i | \(-0.552576\pi\) | ||||
−0.164424 | + | 0.986390i | \(0.552576\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 3.36770 | 0.374189 | ||||||||
\(82\) | 6.76575 | 0.747153 | ||||||||
\(83\) | 6.74323 | 0.740166 | 0.370083 | − | 0.928999i | \(-0.379329\pi\) | ||||
0.370083 | + | 0.928999i | \(0.379329\pi\) | |||||||
\(84\) | 0.584738 | 0.0638002 | ||||||||
\(85\) | 1.61575 | 0.175253 | ||||||||
\(86\) | 8.64895 | 0.932640 | ||||||||
\(87\) | −0.753174 | −0.0807487 | ||||||||
\(88\) | −4.10210 | −0.437286 | ||||||||
\(89\) | −4.52594 | −0.479748 | −0.239874 | − | 0.970804i | \(-0.577106\pi\) | ||||
−0.239874 | + | 0.970804i | \(0.577106\pi\) | |||||||
\(90\) | −2.32331 | −0.244898 | ||||||||
\(91\) | 0.378422 | 0.0396694 | ||||||||
\(92\) | 6.05858 | 0.631651 | ||||||||
\(93\) | −4.25758 | −0.441491 | ||||||||
\(94\) | −6.55629 | −0.676230 | ||||||||
\(95\) | 7.94642 | 0.815286 | ||||||||
\(96\) | 0.822612 | 0.0839575 | ||||||||
\(97\) | 1.24039 | 0.125943 | 0.0629714 | − | 0.998015i | \(-0.479942\pi\) | ||||
0.0629714 | + | 0.998015i | \(0.479942\pi\) | |||||||
\(98\) | −6.49472 | −0.656066 | ||||||||
\(99\) | 9.53045 | 0.957847 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −5.27186 | −0.524570 | −0.262285 | − | 0.964990i | \(-0.584476\pi\) | ||||
−0.262285 | + | 0.964990i | \(0.584476\pi\) | |||||||
\(102\) | 1.32913 | 0.131604 | ||||||||
\(103\) | −14.3540 | −1.41434 | −0.707172 | − | 0.707041i | \(-0.750029\pi\) | ||||
−0.707172 | + | 0.707041i | \(0.750029\pi\) | |||||||
\(104\) | 0.532365 | 0.0522027 | ||||||||
\(105\) | 0.584738 | 0.0570646 | ||||||||
\(106\) | 11.1024 | 1.07836 | ||||||||
\(107\) | 4.23982 | 0.409879 | 0.204939 | − | 0.978775i | \(-0.434300\pi\) | ||||
0.204939 | + | 0.978775i | \(0.434300\pi\) | |||||||
\(108\) | −4.37902 | −0.421371 | ||||||||
\(109\) | 0.0957383 | 0.00917007 | 0.00458503 | − | 0.999989i | \(-0.498541\pi\) | ||||
0.00458503 | + | 0.999989i | \(0.498541\pi\) | |||||||
\(110\) | −4.10210 | −0.391120 | ||||||||
\(111\) | 8.52467 | 0.809126 | ||||||||
\(112\) | 0.710831 | 0.0671672 | ||||||||
\(113\) | −8.32289 | −0.782952 | −0.391476 | − | 0.920188i | \(-0.628035\pi\) | ||||
−0.391476 | + | 0.920188i | \(0.628035\pi\) | |||||||
\(114\) | 6.53682 | 0.612230 | ||||||||
\(115\) | 6.05858 | 0.564966 | ||||||||
\(116\) | −0.915588 | −0.0850102 | ||||||||
\(117\) | −1.23685 | −0.114347 | ||||||||
\(118\) | −3.59674 | −0.331107 | ||||||||
\(119\) | 1.14852 | 0.105285 | ||||||||
\(120\) | 0.822612 | 0.0750938 | ||||||||
\(121\) | 5.82724 | 0.529749 | ||||||||
\(122\) | 4.86048 | 0.440047 | ||||||||
\(123\) | 5.56559 | 0.501832 | ||||||||
\(124\) | −5.17569 | −0.464790 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.65148 | −0.147126 | ||||||||
\(127\) | 21.2892 | 1.88911 | 0.944556 | − | 0.328351i | \(-0.106493\pi\) | ||||
0.944556 | + | 0.328351i | \(0.106493\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 7.11473 | 0.626417 | ||||||||
\(130\) | 0.532365 | 0.0466915 | ||||||||
\(131\) | −10.8187 | −0.945237 | −0.472619 | − | 0.881267i | \(-0.656691\pi\) | ||||
−0.472619 | + | 0.881267i | \(0.656691\pi\) | |||||||
\(132\) | −3.37444 | −0.293707 | ||||||||
\(133\) | 5.64857 | 0.489793 | ||||||||
\(134\) | 6.55325 | 0.566115 | ||||||||
\(135\) | −4.37902 | −0.376886 | ||||||||
\(136\) | 1.61575 | 0.138549 | ||||||||
\(137\) | −19.9787 | −1.70690 | −0.853449 | − | 0.521177i | \(-0.825493\pi\) | ||||
−0.853449 | + | 0.521177i | \(0.825493\pi\) | |||||||
\(138\) | 4.98386 | 0.424255 | ||||||||
\(139\) | 11.4197 | 0.968606 | 0.484303 | − | 0.874900i | \(-0.339073\pi\) | ||||
0.484303 | + | 0.874900i | \(0.339073\pi\) | |||||||
\(140\) | 0.710831 | 0.0600762 | ||||||||
\(141\) | −5.39328 | −0.454196 | ||||||||
\(142\) | 6.01123 | 0.504451 | ||||||||
\(143\) | −2.18382 | −0.182620 | ||||||||
\(144\) | −2.32331 | −0.193609 | ||||||||
\(145\) | −0.915588 | −0.0760355 | ||||||||
\(146\) | 2.41097 | 0.199533 | ||||||||
\(147\) | −5.34263 | −0.440653 | ||||||||
\(148\) | 10.3629 | 0.851827 | ||||||||
\(149\) | 2.02784 | 0.166128 | 0.0830638 | − | 0.996544i | \(-0.473529\pi\) | ||||
0.0830638 | + | 0.996544i | \(0.473529\pi\) | |||||||
\(150\) | 0.822612 | 0.0671660 | ||||||||
\(151\) | −7.18615 | −0.584801 | −0.292400 | − | 0.956296i | \(-0.594454\pi\) | ||||
−0.292400 | + | 0.956296i | \(0.594454\pi\) | |||||||
\(152\) | 7.94642 | 0.644540 | ||||||||
\(153\) | −3.75389 | −0.303484 | ||||||||
\(154\) | −2.91590 | −0.234970 | ||||||||
\(155\) | −5.17569 | −0.415721 | ||||||||
\(156\) | 0.437930 | 0.0350625 | ||||||||
\(157\) | 12.0915 | 0.965004 | 0.482502 | − | 0.875895i | \(-0.339728\pi\) | ||||
0.482502 | + | 0.875895i | \(0.339728\pi\) | |||||||
\(158\) | −2.92286 | −0.232530 | ||||||||
\(159\) | 9.13298 | 0.724292 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 4.30663 | 0.339410 | ||||||||
\(162\) | 3.36770 | 0.264591 | ||||||||
\(163\) | 15.2159 | 1.19180 | 0.595900 | − | 0.803059i | \(-0.296796\pi\) | ||||
0.595900 | + | 0.803059i | \(0.296796\pi\) | |||||||
\(164\) | 6.76575 | 0.528317 | ||||||||
\(165\) | −3.37444 | −0.262700 | ||||||||
\(166\) | 6.74323 | 0.523376 | ||||||||
\(167\) | 6.56868 | 0.508300 | 0.254150 | − | 0.967165i | \(-0.418204\pi\) | ||||
0.254150 | + | 0.967165i | \(0.418204\pi\) | |||||||
\(168\) | 0.584738 | 0.0451135 | ||||||||
\(169\) | −12.7166 | −0.978199 | ||||||||
\(170\) | 1.61575 | 0.123922 | ||||||||
\(171\) | −18.4620 | −1.41182 | ||||||||
\(172\) | 8.64895 | 0.659476 | ||||||||
\(173\) | 0.546744 | 0.0415682 | 0.0207841 | − | 0.999784i | \(-0.493384\pi\) | ||||
0.0207841 | + | 0.999784i | \(0.493384\pi\) | |||||||
\(174\) | −0.753174 | −0.0570979 | ||||||||
\(175\) | 0.710831 | 0.0537338 | ||||||||
\(176\) | −4.10210 | −0.309208 | ||||||||
\(177\) | −2.95872 | −0.222391 | ||||||||
\(178\) | −4.52594 | −0.339233 | ||||||||
\(179\) | −0.244179 | −0.0182508 | −0.00912541 | − | 0.999958i | \(-0.502905\pi\) | ||||
−0.00912541 | + | 0.999958i | \(0.502905\pi\) | |||||||
\(180\) | −2.32331 | −0.173169 | ||||||||
\(181\) | −25.9979 | −1.93241 | −0.966204 | − | 0.257777i | \(-0.917010\pi\) | ||||
−0.966204 | + | 0.257777i | \(0.917010\pi\) | |||||||
\(182\) | 0.378422 | 0.0280505 | ||||||||
\(183\) | 3.99829 | 0.295562 | ||||||||
\(184\) | 6.05858 | 0.446645 | ||||||||
\(185\) | 10.3629 | 0.761898 | ||||||||
\(186\) | −4.25758 | −0.312181 | ||||||||
\(187\) | −6.62797 | −0.484685 | ||||||||
\(188\) | −6.55629 | −0.478166 | ||||||||
\(189\) | −3.11274 | −0.226419 | ||||||||
\(190\) | 7.94642 | 0.576494 | ||||||||
\(191\) | −17.9504 | −1.29884 | −0.649421 | − | 0.760429i | \(-0.724989\pi\) | ||||
−0.649421 | + | 0.760429i | \(0.724989\pi\) | |||||||
\(192\) | 0.822612 | 0.0593669 | ||||||||
\(193\) | −11.3687 | −0.818336 | −0.409168 | − | 0.912459i | \(-0.634181\pi\) | ||||
−0.409168 | + | 0.912459i | \(0.634181\pi\) | |||||||
\(194\) | 1.24039 | 0.0890550 | ||||||||
\(195\) | 0.437930 | 0.0313608 | ||||||||
\(196\) | −6.49472 | −0.463909 | ||||||||
\(197\) | 2.14807 | 0.153044 | 0.0765219 | − | 0.997068i | \(-0.475618\pi\) | ||||
0.0765219 | + | 0.997068i | \(0.475618\pi\) | |||||||
\(198\) | 9.53045 | 0.677300 | ||||||||
\(199\) | −21.8261 | −1.54721 | −0.773607 | − | 0.633666i | \(-0.781549\pi\) | ||||
−0.773607 | + | 0.633666i | \(0.781549\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 5.39078 | 0.380236 | ||||||||
\(202\) | −5.27186 | −0.370927 | ||||||||
\(203\) | −0.650829 | −0.0456792 | ||||||||
\(204\) | 1.32913 | 0.0930580 | ||||||||
\(205\) | 6.76575 | 0.472541 | ||||||||
\(206\) | −14.3540 | −1.00009 | ||||||||
\(207\) | −14.0760 | −0.978347 | ||||||||
\(208\) | 0.532365 | 0.0369129 | ||||||||
\(209\) | −32.5970 | −2.25478 | ||||||||
\(210\) | 0.584738 | 0.0403508 | ||||||||
\(211\) | −16.3783 | −1.12753 | −0.563765 | − | 0.825935i | \(-0.690648\pi\) | ||||
−0.563765 | + | 0.825935i | \(0.690648\pi\) | |||||||
\(212\) | 11.1024 | 0.762517 | ||||||||
\(213\) | 4.94491 | 0.338820 | ||||||||
\(214\) | 4.23982 | 0.289828 | ||||||||
\(215\) | 8.64895 | 0.589853 | ||||||||
\(216\) | −4.37902 | −0.297954 | ||||||||
\(217\) | −3.67904 | −0.249749 | ||||||||
\(218\) | 0.0957383 | 0.00648422 | ||||||||
\(219\) | 1.98329 | 0.134018 | ||||||||
\(220\) | −4.10210 | −0.276564 | ||||||||
\(221\) | 0.860169 | 0.0578612 | ||||||||
\(222\) | 8.52467 | 0.572138 | ||||||||
\(223\) | −11.2538 | −0.753607 | −0.376803 | − | 0.926293i | \(-0.622977\pi\) | ||||
−0.376803 | + | 0.926293i | \(0.622977\pi\) | |||||||
\(224\) | 0.710831 | 0.0474944 | ||||||||
\(225\) | −2.32331 | −0.154887 | ||||||||
\(226\) | −8.32289 | −0.553631 | ||||||||
\(227\) | −24.0637 | −1.59716 | −0.798582 | − | 0.601887i | \(-0.794416\pi\) | ||||
−0.798582 | + | 0.601887i | \(0.794416\pi\) | |||||||
\(228\) | 6.53682 | 0.432912 | ||||||||
\(229\) | −6.06411 | −0.400728 | −0.200364 | − | 0.979722i | \(-0.564212\pi\) | ||||
−0.200364 | + | 0.979722i | \(0.564212\pi\) | |||||||
\(230\) | 6.05858 | 0.399491 | ||||||||
\(231\) | −2.39866 | −0.157820 | ||||||||
\(232\) | −0.915588 | −0.0601113 | ||||||||
\(233\) | −23.9664 | −1.57009 | −0.785046 | − | 0.619438i | \(-0.787361\pi\) | ||||
−0.785046 | + | 0.619438i | \(0.787361\pi\) | |||||||
\(234\) | −1.23685 | −0.0808554 | ||||||||
\(235\) | −6.55629 | −0.427685 | ||||||||
\(236\) | −3.59674 | −0.234128 | ||||||||
\(237\) | −2.40438 | −0.156181 | ||||||||
\(238\) | 1.14852 | 0.0744478 | ||||||||
\(239\) | 18.2283 | 1.17909 | 0.589545 | − | 0.807736i | \(-0.299307\pi\) | ||||
0.589545 | + | 0.807736i | \(0.299307\pi\) | |||||||
\(240\) | 0.822612 | 0.0530994 | ||||||||
\(241\) | 25.3760 | 1.63461 | 0.817307 | − | 0.576203i | \(-0.195466\pi\) | ||||
0.817307 | + | 0.576203i | \(0.195466\pi\) | |||||||
\(242\) | 5.82724 | 0.374589 | ||||||||
\(243\) | 15.9074 | 1.02046 | ||||||||
\(244\) | 4.86048 | 0.311160 | ||||||||
\(245\) | −6.49472 | −0.414932 | ||||||||
\(246\) | 5.56559 | 0.354849 | ||||||||
\(247\) | 4.23040 | 0.269174 | ||||||||
\(248\) | −5.17569 | −0.328656 | ||||||||
\(249\) | 5.54706 | 0.351531 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −10.2898 | −0.649489 | −0.324745 | − | 0.945802i | \(-0.605278\pi\) | ||||
−0.324745 | + | 0.945802i | \(0.605278\pi\) | |||||||
\(252\) | −1.65148 | −0.104034 | ||||||||
\(253\) | −24.8529 | −1.56249 | ||||||||
\(254\) | 21.2892 | 1.33580 | ||||||||
\(255\) | 1.32913 | 0.0832336 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.3401 | 1.51829 | 0.759145 | − | 0.650921i | \(-0.225617\pi\) | ||||
0.759145 | + | 0.650921i | \(0.225617\pi\) | |||||||
\(258\) | 7.11473 | 0.442944 | ||||||||
\(259\) | 7.36629 | 0.457719 | ||||||||
\(260\) | 0.532365 | 0.0330159 | ||||||||
\(261\) | 2.12719 | 0.131670 | ||||||||
\(262\) | −10.8187 | −0.668384 | ||||||||
\(263\) | −24.2660 | −1.49630 | −0.748152 | − | 0.663527i | \(-0.769059\pi\) | ||||
−0.748152 | + | 0.663527i | \(0.769059\pi\) | |||||||
\(264\) | −3.37444 | −0.207682 | ||||||||
\(265\) | 11.1024 | 0.682016 | ||||||||
\(266\) | 5.64857 | 0.346336 | ||||||||
\(267\) | −3.72309 | −0.227849 | ||||||||
\(268\) | 6.55325 | 0.400304 | ||||||||
\(269\) | 29.0440 | 1.77084 | 0.885421 | − | 0.464790i | \(-0.153870\pi\) | ||||
0.885421 | + | 0.464790i | \(0.153870\pi\) | |||||||
\(270\) | −4.37902 | −0.266499 | ||||||||
\(271\) | −4.26080 | −0.258825 | −0.129413 | − | 0.991591i | \(-0.541309\pi\) | ||||
−0.129413 | + | 0.991591i | \(0.541309\pi\) | |||||||
\(272\) | 1.61575 | 0.0979692 | ||||||||
\(273\) | 0.311294 | 0.0188404 | ||||||||
\(274\) | −19.9787 | −1.20696 | ||||||||
\(275\) | −4.10210 | −0.247366 | ||||||||
\(276\) | 4.98386 | 0.299993 | ||||||||
\(277\) | 32.2204 | 1.93594 | 0.967968 | − | 0.251075i | \(-0.0807841\pi\) | ||||
0.967968 | + | 0.251075i | \(0.0807841\pi\) | |||||||
\(278\) | 11.4197 | 0.684908 | ||||||||
\(279\) | 12.0247 | 0.719901 | ||||||||
\(280\) | 0.710831 | 0.0424803 | ||||||||
\(281\) | −12.8003 | −0.763602 | −0.381801 | − | 0.924244i | \(-0.624696\pi\) | ||||
−0.381801 | + | 0.924244i | \(0.624696\pi\) | |||||||
\(282\) | −5.39328 | −0.321165 | ||||||||
\(283\) | −6.26449 | −0.372385 | −0.186193 | − | 0.982513i | \(-0.559615\pi\) | ||||
−0.186193 | + | 0.982513i | \(0.559615\pi\) | |||||||
\(284\) | 6.01123 | 0.356701 | ||||||||
\(285\) | 6.53682 | 0.387208 | ||||||||
\(286\) | −2.18382 | −0.129132 | ||||||||
\(287\) | 4.80931 | 0.283885 | ||||||||
\(288\) | −2.32331 | −0.136902 | ||||||||
\(289\) | −14.3894 | −0.846433 | ||||||||
\(290\) | −0.915588 | −0.0537652 | ||||||||
\(291\) | 1.02036 | 0.0598147 | ||||||||
\(292\) | 2.41097 | 0.141091 | ||||||||
\(293\) | 5.23184 | 0.305647 | 0.152824 | − | 0.988253i | \(-0.451163\pi\) | ||||
0.152824 | + | 0.988253i | \(0.451163\pi\) | |||||||
\(294\) | −5.34263 | −0.311589 | ||||||||
\(295\) | −3.59674 | −0.209410 | ||||||||
\(296\) | 10.3629 | 0.602333 | ||||||||
\(297\) | 17.9632 | 1.04233 | ||||||||
\(298\) | 2.02784 | 0.117470 | ||||||||
\(299\) | 3.22538 | 0.186528 | ||||||||
\(300\) | 0.822612 | 0.0474935 | ||||||||
\(301\) | 6.14794 | 0.354361 | ||||||||
\(302\) | −7.18615 | −0.413517 | ||||||||
\(303\) | −4.33670 | −0.249137 | ||||||||
\(304\) | 7.94642 | 0.455759 | ||||||||
\(305\) | 4.86048 | 0.278310 | ||||||||
\(306\) | −3.75389 | −0.214595 | ||||||||
\(307\) | 21.0333 | 1.20044 | 0.600218 | − | 0.799837i | \(-0.295081\pi\) | ||||
0.600218 | + | 0.799837i | \(0.295081\pi\) | |||||||
\(308\) | −2.91590 | −0.166149 | ||||||||
\(309\) | −11.8078 | −0.671722 | ||||||||
\(310\) | −5.17569 | −0.293959 | ||||||||
\(311\) | −23.6109 | −1.33885 | −0.669427 | − | 0.742878i | \(-0.733460\pi\) | ||||
−0.669427 | + | 0.742878i | \(0.733460\pi\) | |||||||
\(312\) | 0.437930 | 0.0247929 | ||||||||
\(313\) | 32.5188 | 1.83807 | 0.919037 | − | 0.394171i | \(-0.128968\pi\) | ||||
0.919037 | + | 0.394171i | \(0.128968\pi\) | |||||||
\(314\) | 12.0915 | 0.682361 | ||||||||
\(315\) | −1.65148 | −0.0930504 | ||||||||
\(316\) | −2.92286 | −0.164424 | ||||||||
\(317\) | −31.4667 | −1.76735 | −0.883674 | − | 0.468102i | \(-0.844938\pi\) | ||||
−0.883674 | + | 0.468102i | \(0.844938\pi\) | |||||||
\(318\) | 9.13298 | 0.512152 | ||||||||
\(319\) | 3.75584 | 0.210286 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 3.48773 | 0.194666 | ||||||||
\(322\) | 4.30663 | 0.239999 | ||||||||
\(323\) | 12.8394 | 0.714405 | ||||||||
\(324\) | 3.36770 | 0.187094 | ||||||||
\(325\) | 0.532365 | 0.0295303 | ||||||||
\(326\) | 15.2159 | 0.842729 | ||||||||
\(327\) | 0.0787555 | 0.00435519 | ||||||||
\(328\) | 6.76575 | 0.373576 | ||||||||
\(329\) | −4.66041 | −0.256937 | ||||||||
\(330\) | −3.37444 | −0.185757 | ||||||||
\(331\) | −20.7862 | −1.14251 | −0.571257 | − | 0.820771i | \(-0.693544\pi\) | ||||
−0.571257 | + | 0.820771i | \(0.693544\pi\) | |||||||
\(332\) | 6.74323 | 0.370083 | ||||||||
\(333\) | −24.0763 | −1.31937 | ||||||||
\(334\) | 6.56868 | 0.359422 | ||||||||
\(335\) | 6.55325 | 0.358042 | ||||||||
\(336\) | 0.584738 | 0.0319001 | ||||||||
\(337\) | 31.6652 | 1.72492 | 0.862458 | − | 0.506129i | \(-0.168924\pi\) | ||||
0.862458 | + | 0.506129i | \(0.168924\pi\) | |||||||
\(338\) | −12.7166 | −0.691691 | ||||||||
\(339\) | −6.84651 | −0.371851 | ||||||||
\(340\) | 1.61575 | 0.0876263 | ||||||||
\(341\) | 21.2312 | 1.14973 | ||||||||
\(342\) | −18.4620 | −0.998311 | ||||||||
\(343\) | −9.59247 | −0.517944 | ||||||||
\(344\) | 8.64895 | 0.466320 | ||||||||
\(345\) | 4.98386 | 0.268322 | ||||||||
\(346\) | 0.546744 | 0.0293931 | ||||||||
\(347\) | 26.5634 | 1.42600 | 0.713000 | − | 0.701164i | \(-0.247336\pi\) | ||||
0.713000 | + | 0.701164i | \(0.247336\pi\) | |||||||
\(348\) | −0.753174 | −0.0403743 | ||||||||
\(349\) | −1.96010 | −0.104922 | −0.0524608 | − | 0.998623i | \(-0.516706\pi\) | ||||
−0.0524608 | + | 0.998623i | \(0.516706\pi\) | |||||||
\(350\) | 0.710831 | 0.0379955 | ||||||||
\(351\) | −2.33124 | −0.124432 | ||||||||
\(352\) | −4.10210 | −0.218643 | ||||||||
\(353\) | 3.30982 | 0.176164 | 0.0880821 | − | 0.996113i | \(-0.471926\pi\) | ||||
0.0880821 | + | 0.996113i | \(0.471926\pi\) | |||||||
\(354\) | −2.95872 | −0.157254 | ||||||||
\(355\) | 6.01123 | 0.319043 | ||||||||
\(356\) | −4.52594 | −0.239874 | ||||||||
\(357\) | 0.944790 | 0.0500036 | ||||||||
\(358\) | −0.244179 | −0.0129053 | ||||||||
\(359\) | −17.1912 | −0.907319 | −0.453659 | − | 0.891175i | \(-0.649882\pi\) | ||||
−0.453659 | + | 0.891175i | \(0.649882\pi\) | |||||||
\(360\) | −2.32331 | −0.122449 | ||||||||
\(361\) | 44.1457 | 2.32346 | ||||||||
\(362\) | −25.9979 | −1.36642 | ||||||||
\(363\) | 4.79356 | 0.251597 | ||||||||
\(364\) | 0.378422 | 0.0198347 | ||||||||
\(365\) | 2.41097 | 0.126196 | ||||||||
\(366\) | 3.99829 | 0.208994 | ||||||||
\(367\) | 6.47995 | 0.338250 | 0.169125 | − | 0.985595i | \(-0.445906\pi\) | ||||
0.169125 | + | 0.985595i | \(0.445906\pi\) | |||||||
\(368\) | 6.05858 | 0.315825 | ||||||||
\(369\) | −15.7189 | −0.818295 | ||||||||
\(370\) | 10.3629 | 0.538743 | ||||||||
\(371\) | 7.89194 | 0.409729 | ||||||||
\(372\) | −4.25758 | −0.220745 | ||||||||
\(373\) | −7.55550 | −0.391209 | −0.195604 | − | 0.980683i | \(-0.562667\pi\) | ||||
−0.195604 | + | 0.980683i | \(0.562667\pi\) | |||||||
\(374\) | −6.62797 | −0.342724 | ||||||||
\(375\) | 0.822612 | 0.0424795 | ||||||||
\(376\) | −6.55629 | −0.338115 | ||||||||
\(377\) | −0.487427 | −0.0251038 | ||||||||
\(378\) | −3.11274 | −0.160102 | ||||||||
\(379\) | 23.0385 | 1.18341 | 0.591705 | − | 0.806155i | \(-0.298455\pi\) | ||||
0.591705 | + | 0.806155i | \(0.298455\pi\) | |||||||
\(380\) | 7.94642 | 0.407643 | ||||||||
\(381\) | 17.5128 | 0.897206 | ||||||||
\(382\) | −17.9504 | −0.918421 | ||||||||
\(383\) | −26.2392 | −1.34076 | −0.670380 | − | 0.742018i | \(-0.733869\pi\) | ||||
−0.670380 | + | 0.742018i | \(0.733869\pi\) | |||||||
\(384\) | 0.822612 | 0.0419787 | ||||||||
\(385\) | −2.91590 | −0.148608 | ||||||||
\(386\) | −11.3687 | −0.578651 | ||||||||
\(387\) | −20.0942 | −1.02144 | ||||||||
\(388\) | 1.24039 | 0.0629714 | ||||||||
\(389\) | −0.818755 | −0.0415125 | −0.0207563 | − | 0.999785i | \(-0.506607\pi\) | ||||
−0.0207563 | + | 0.999785i | \(0.506607\pi\) | |||||||
\(390\) | 0.437930 | 0.0221754 | ||||||||
\(391\) | 9.78915 | 0.495059 | ||||||||
\(392\) | −6.49472 | −0.328033 | ||||||||
\(393\) | −8.89962 | −0.448926 | ||||||||
\(394\) | 2.14807 | 0.108218 | ||||||||
\(395\) | −2.92286 | −0.147065 | ||||||||
\(396\) | 9.53045 | 0.478923 | ||||||||
\(397\) | −36.6154 | −1.83768 | −0.918838 | − | 0.394636i | \(-0.870871\pi\) | ||||
−0.918838 | + | 0.394636i | \(0.870871\pi\) | |||||||
\(398\) | −21.8261 | −1.09404 | ||||||||
\(399\) | 4.64658 | 0.232620 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 5.39078 | 0.268868 | ||||||||
\(403\) | −2.75536 | −0.137254 | ||||||||
\(404\) | −5.27186 | −0.262285 | ||||||||
\(405\) | 3.36770 | 0.167342 | ||||||||
\(406\) | −0.650829 | −0.0323001 | ||||||||
\(407\) | −42.5098 | −2.10713 | ||||||||
\(408\) | 1.32913 | 0.0658020 | ||||||||
\(409\) | 25.7798 | 1.27473 | 0.637365 | − | 0.770562i | \(-0.280024\pi\) | ||||
0.637365 | + | 0.770562i | \(0.280024\pi\) | |||||||
\(410\) | 6.76575 | 0.334137 | ||||||||
\(411\) | −16.4347 | −0.810666 | ||||||||
\(412\) | −14.3540 | −0.707172 | ||||||||
\(413\) | −2.55667 | −0.125806 | ||||||||
\(414\) | −14.0760 | −0.691796 | ||||||||
\(415\) | 6.74323 | 0.331012 | ||||||||
\(416\) | 0.532365 | 0.0261013 | ||||||||
\(417\) | 9.39398 | 0.460025 | ||||||||
\(418\) | −32.5970 | −1.59437 | ||||||||
\(419\) | 32.2101 | 1.57357 | 0.786784 | − | 0.617228i | \(-0.211744\pi\) | ||||
0.786784 | + | 0.617228i | \(0.211744\pi\) | |||||||
\(420\) | 0.584738 | 0.0285323 | ||||||||
\(421\) | −25.7842 | −1.25665 | −0.628323 | − | 0.777952i | \(-0.716258\pi\) | ||||
−0.628323 | + | 0.777952i | \(0.716258\pi\) | |||||||
\(422\) | −16.3783 | −0.797284 | ||||||||
\(423\) | 15.2323 | 0.740619 | ||||||||
\(424\) | 11.1024 | 0.539181 | ||||||||
\(425\) | 1.61575 | 0.0783753 | ||||||||
\(426\) | 4.94491 | 0.239582 | ||||||||
\(427\) | 3.45498 | 0.167198 | ||||||||
\(428\) | 4.23982 | 0.204939 | ||||||||
\(429\) | −1.79643 | −0.0867326 | ||||||||
\(430\) | 8.64895 | 0.417089 | ||||||||
\(431\) | 12.3190 | 0.593387 | 0.296693 | − | 0.954973i | \(-0.404116\pi\) | ||||
0.296693 | + | 0.954973i | \(0.404116\pi\) | |||||||
\(432\) | −4.37902 | −0.210686 | ||||||||
\(433\) | 21.2530 | 1.02135 | 0.510677 | − | 0.859773i | \(-0.329395\pi\) | ||||
0.510677 | + | 0.859773i | \(0.329395\pi\) | |||||||
\(434\) | −3.67904 | −0.176600 | ||||||||
\(435\) | −0.753174 | −0.0361119 | ||||||||
\(436\) | 0.0957383 | 0.00458503 | ||||||||
\(437\) | 48.1441 | 2.30304 | ||||||||
\(438\) | 1.98329 | 0.0947652 | ||||||||
\(439\) | −1.82146 | −0.0869336 | −0.0434668 | − | 0.999055i | \(-0.513840\pi\) | ||||
−0.0434668 | + | 0.999055i | \(0.513840\pi\) | |||||||
\(440\) | −4.10210 | −0.195560 | ||||||||
\(441\) | 15.0892 | 0.718535 | ||||||||
\(442\) | 0.860169 | 0.0409140 | ||||||||
\(443\) | −7.80446 | −0.370801 | −0.185401 | − | 0.982663i | \(-0.559358\pi\) | ||||
−0.185401 | + | 0.982663i | \(0.559358\pi\) | |||||||
\(444\) | 8.52467 | 0.404563 | ||||||||
\(445\) | −4.52594 | −0.214550 | ||||||||
\(446\) | −11.2538 | −0.532881 | ||||||||
\(447\) | 1.66813 | 0.0788998 | ||||||||
\(448\) | 0.710831 | 0.0335836 | ||||||||
\(449\) | −19.1754 | −0.904945 | −0.452473 | − | 0.891778i | \(-0.649458\pi\) | ||||
−0.452473 | + | 0.891778i | \(0.649458\pi\) | |||||||
\(450\) | −2.32331 | −0.109522 | ||||||||
\(451\) | −27.7538 | −1.30688 | ||||||||
\(452\) | −8.32289 | −0.391476 | ||||||||
\(453\) | −5.91142 | −0.277743 | ||||||||
\(454\) | −24.0637 | −1.12936 | ||||||||
\(455\) | 0.378422 | 0.0177407 | ||||||||
\(456\) | 6.53682 | 0.306115 | ||||||||
\(457\) | −7.66012 | −0.358325 | −0.179163 | − | 0.983819i | \(-0.557339\pi\) | ||||
−0.179163 | + | 0.983819i | \(0.557339\pi\) | |||||||
\(458\) | −6.06411 | −0.283357 | ||||||||
\(459\) | −7.07539 | −0.330251 | ||||||||
\(460\) | 6.05858 | 0.282483 | ||||||||
\(461\) | 13.1999 | 0.614782 | 0.307391 | − | 0.951583i | \(-0.400544\pi\) | ||||
0.307391 | + | 0.951583i | \(0.400544\pi\) | |||||||
\(462\) | −2.39866 | −0.111596 | ||||||||
\(463\) | 36.9795 | 1.71858 | 0.859291 | − | 0.511487i | \(-0.170905\pi\) | ||||
0.859291 | + | 0.511487i | \(0.170905\pi\) | |||||||
\(464\) | −0.915588 | −0.0425051 | ||||||||
\(465\) | −4.25758 | −0.197441 | ||||||||
\(466\) | −23.9664 | −1.11022 | ||||||||
\(467\) | −23.2934 | −1.07789 | −0.538945 | − | 0.842341i | \(-0.681177\pi\) | ||||
−0.538945 | + | 0.842341i | \(0.681177\pi\) | |||||||
\(468\) | −1.23685 | −0.0571734 | ||||||||
\(469\) | 4.65826 | 0.215098 | ||||||||
\(470\) | −6.55629 | −0.302419 | ||||||||
\(471\) | 9.94658 | 0.458314 | ||||||||
\(472\) | −3.59674 | −0.165553 | ||||||||
\(473\) | −35.4789 | −1.63132 | ||||||||
\(474\) | −2.40438 | −0.110437 | ||||||||
\(475\) | 7.94642 | 0.364607 | ||||||||
\(476\) | 1.14852 | 0.0526425 | ||||||||
\(477\) | −25.7943 | −1.18104 | ||||||||
\(478\) | 18.2283 | 0.833742 | ||||||||
\(479\) | 32.2728 | 1.47458 | 0.737291 | − | 0.675576i | \(-0.236105\pi\) | ||||
0.737291 | + | 0.675576i | \(0.236105\pi\) | |||||||
\(480\) | 0.822612 | 0.0375469 | ||||||||
\(481\) | 5.51686 | 0.251547 | ||||||||
\(482\) | 25.3760 | 1.15585 | ||||||||
\(483\) | 3.54268 | 0.161198 | ||||||||
\(484\) | 5.82724 | 0.264875 | ||||||||
\(485\) | 1.24039 | 0.0563233 | ||||||||
\(486\) | 15.9074 | 0.721573 | ||||||||
\(487\) | −28.7215 | −1.30149 | −0.650747 | − | 0.759294i | \(-0.725544\pi\) | ||||
−0.650747 | + | 0.759294i | \(0.725544\pi\) | |||||||
\(488\) | 4.86048 | 0.220024 | ||||||||
\(489\) | 12.5168 | 0.566027 | ||||||||
\(490\) | −6.49472 | −0.293402 | ||||||||
\(491\) | 28.6061 | 1.29098 | 0.645488 | − | 0.763771i | \(-0.276654\pi\) | ||||
0.645488 | + | 0.763771i | \(0.276654\pi\) | |||||||
\(492\) | 5.56559 | 0.250916 | ||||||||
\(493\) | −1.47936 | −0.0666271 | ||||||||
\(494\) | 4.23040 | 0.190335 | ||||||||
\(495\) | 9.53045 | 0.428362 | ||||||||
\(496\) | −5.17569 | −0.232395 | ||||||||
\(497\) | 4.27297 | 0.191669 | ||||||||
\(498\) | 5.54706 | 0.248570 | ||||||||
\(499\) | −16.7561 | −0.750104 | −0.375052 | − | 0.927004i | \(-0.622375\pi\) | ||||
−0.375052 | + | 0.927004i | \(0.622375\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 5.40347 | 0.241409 | ||||||||
\(502\) | −10.2898 | −0.459258 | ||||||||
\(503\) | −3.21247 | −0.143237 | −0.0716185 | − | 0.997432i | \(-0.522816\pi\) | ||||
−0.0716185 | + | 0.997432i | \(0.522816\pi\) | |||||||
\(504\) | −1.65148 | −0.0735628 | ||||||||
\(505\) | −5.27186 | −0.234595 | ||||||||
\(506\) | −24.8529 | −1.10485 | ||||||||
\(507\) | −10.4608 | −0.464581 | ||||||||
\(508\) | 21.2892 | 0.944556 | ||||||||
\(509\) | −36.8385 | −1.63284 | −0.816418 | − | 0.577461i | \(-0.804044\pi\) | ||||
−0.816418 | + | 0.577461i | \(0.804044\pi\) | |||||||
\(510\) | 1.32913 | 0.0588551 | ||||||||
\(511\) | 1.71379 | 0.0758136 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −34.7975 | −1.53635 | ||||||||
\(514\) | 24.3401 | 1.07359 | ||||||||
\(515\) | −14.3540 | −0.632514 | ||||||||
\(516\) | 7.11473 | 0.313208 | ||||||||
\(517\) | 26.8946 | 1.18282 | ||||||||
\(518\) | 7.36629 | 0.323656 | ||||||||
\(519\) | 0.449758 | 0.0197422 | ||||||||
\(520\) | 0.532365 | 0.0233458 | ||||||||
\(521\) | 7.30885 | 0.320207 | 0.160103 | − | 0.987100i | \(-0.448817\pi\) | ||||
0.160103 | + | 0.987100i | \(0.448817\pi\) | |||||||
\(522\) | 2.12719 | 0.0931048 | ||||||||
\(523\) | −41.3007 | −1.80595 | −0.902977 | − | 0.429689i | \(-0.858623\pi\) | ||||
−0.902977 | + | 0.429689i | \(0.858623\pi\) | |||||||
\(524\) | −10.8187 | −0.472619 | ||||||||
\(525\) | 0.584738 | 0.0255201 | ||||||||
\(526\) | −24.2660 | −1.05805 | ||||||||
\(527\) | −8.36261 | −0.364281 | ||||||||
\(528\) | −3.37444 | −0.146854 | ||||||||
\(529\) | 13.7064 | 0.595932 | ||||||||
\(530\) | 11.1024 | 0.482258 | ||||||||
\(531\) | 8.35634 | 0.362634 | ||||||||
\(532\) | 5.64857 | 0.244896 | ||||||||
\(533\) | 3.60185 | 0.156014 | ||||||||
\(534\) | −3.72309 | −0.161114 | ||||||||
\(535\) | 4.23982 | 0.183303 | ||||||||
\(536\) | 6.55325 | 0.283057 | ||||||||
\(537\) | −0.200865 | −0.00866795 | ||||||||
\(538\) | 29.0440 | 1.25217 | ||||||||
\(539\) | 26.6420 | 1.14755 | ||||||||
\(540\) | −4.37902 | −0.188443 | ||||||||
\(541\) | 29.4398 | 1.26571 | 0.632857 | − | 0.774269i | \(-0.281882\pi\) | ||||
0.632857 | + | 0.774269i | \(0.281882\pi\) | |||||||
\(542\) | −4.26080 | −0.183017 | ||||||||
\(543\) | −21.3862 | −0.917769 | ||||||||
\(544\) | 1.61575 | 0.0692747 | ||||||||
\(545\) | 0.0957383 | 0.00410098 | ||||||||
\(546\) | 0.311294 | 0.0133222 | ||||||||
\(547\) | 10.2809 | 0.439577 | 0.219789 | − | 0.975547i | \(-0.429463\pi\) | ||||
0.219789 | + | 0.975547i | \(0.429463\pi\) | |||||||
\(548\) | −19.9787 | −0.853449 | ||||||||
\(549\) | −11.2924 | −0.481948 | ||||||||
\(550\) | −4.10210 | −0.174914 | ||||||||
\(551\) | −7.27565 | −0.309953 | ||||||||
\(552\) | 4.98386 | 0.212127 | ||||||||
\(553\) | −2.07766 | −0.0883510 | ||||||||
\(554\) | 32.2204 | 1.36891 | ||||||||
\(555\) | 8.52467 | 0.361852 | ||||||||
\(556\) | 11.4197 | 0.484303 | ||||||||
\(557\) | 6.92435 | 0.293394 | 0.146697 | − | 0.989181i | \(-0.453136\pi\) | ||||
0.146697 | + | 0.989181i | \(0.453136\pi\) | |||||||
\(558\) | 12.0247 | 0.509047 | ||||||||
\(559\) | 4.60440 | 0.194745 | ||||||||
\(560\) | 0.710831 | 0.0300381 | ||||||||
\(561\) | −5.45225 | −0.230194 | ||||||||
\(562\) | −12.8003 | −0.539948 | ||||||||
\(563\) | 2.14831 | 0.0905406 | 0.0452703 | − | 0.998975i | \(-0.485585\pi\) | ||||
0.0452703 | + | 0.998975i | \(0.485585\pi\) | |||||||
\(564\) | −5.39328 | −0.227098 | ||||||||
\(565\) | −8.32289 | −0.350147 | ||||||||
\(566\) | −6.26449 | −0.263316 | ||||||||
\(567\) | 2.39386 | 0.100533 | ||||||||
\(568\) | 6.01123 | 0.252226 | ||||||||
\(569\) | 24.5084 | 1.02745 | 0.513724 | − | 0.857956i | \(-0.328266\pi\) | ||||
0.513724 | + | 0.857956i | \(0.328266\pi\) | |||||||
\(570\) | 6.53682 | 0.273797 | ||||||||
\(571\) | −28.5781 | −1.19596 | −0.597979 | − | 0.801512i | \(-0.704029\pi\) | ||||
−0.597979 | + | 0.801512i | \(0.704029\pi\) | |||||||
\(572\) | −2.18382 | −0.0913099 | ||||||||
\(573\) | −14.7662 | −0.616866 | ||||||||
\(574\) | 4.80931 | 0.200737 | ||||||||
\(575\) | 6.05858 | 0.252660 | ||||||||
\(576\) | −2.32331 | −0.0968046 | ||||||||
\(577\) | 5.64780 | 0.235121 | 0.117561 | − | 0.993066i | \(-0.462493\pi\) | ||||
0.117561 | + | 0.993066i | \(0.462493\pi\) | |||||||
\(578\) | −14.3894 | −0.598518 | ||||||||
\(579\) | −9.35202 | −0.388657 | ||||||||
\(580\) | −0.915588 | −0.0380177 | ||||||||
\(581\) | 4.79330 | 0.198860 | ||||||||
\(582\) | 1.02036 | 0.0422953 | ||||||||
\(583\) | −45.5432 | −1.88621 | ||||||||
\(584\) | 2.41097 | 0.0997664 | ||||||||
\(585\) | −1.23685 | −0.0511374 | ||||||||
\(586\) | 5.23184 | 0.216125 | ||||||||
\(587\) | 16.9563 | 0.699862 | 0.349931 | − | 0.936775i | \(-0.386205\pi\) | ||||
0.349931 | + | 0.936775i | \(0.386205\pi\) | |||||||
\(588\) | −5.34263 | −0.220326 | ||||||||
\(589\) | −41.1282 | −1.69466 | ||||||||
\(590\) | −3.59674 | −0.148075 | ||||||||
\(591\) | 1.76703 | 0.0726859 | ||||||||
\(592\) | 10.3629 | 0.425914 | ||||||||
\(593\) | −35.7935 | −1.46986 | −0.734932 | − | 0.678141i | \(-0.762786\pi\) | ||||
−0.734932 | + | 0.678141i | \(0.762786\pi\) | |||||||
\(594\) | 17.9632 | 0.737038 | ||||||||
\(595\) | 1.14852 | 0.0470849 | ||||||||
\(596\) | 2.02784 | 0.0830638 | ||||||||
\(597\) | −17.9544 | −0.734826 | ||||||||
\(598\) | 3.22538 | 0.131896 | ||||||||
\(599\) | 21.2640 | 0.868823 | 0.434411 | − | 0.900715i | \(-0.356956\pi\) | ||||
0.434411 | + | 0.900715i | \(0.356956\pi\) | |||||||
\(600\) | 0.822612 | 0.0335830 | ||||||||
\(601\) | −37.8926 | −1.54567 | −0.772837 | − | 0.634605i | \(-0.781163\pi\) | ||||
−0.772837 | + | 0.634605i | \(0.781163\pi\) | |||||||
\(602\) | 6.14794 | 0.250571 | ||||||||
\(603\) | −15.2252 | −0.620019 | ||||||||
\(604\) | −7.18615 | −0.292400 | ||||||||
\(605\) | 5.82724 | 0.236911 | ||||||||
\(606\) | −4.33670 | −0.176166 | ||||||||
\(607\) | −29.5517 | −1.19947 | −0.599734 | − | 0.800199i | \(-0.704727\pi\) | ||||
−0.599734 | + | 0.800199i | \(0.704727\pi\) | |||||||
\(608\) | 7.94642 | 0.322270 | ||||||||
\(609\) | −0.535379 | −0.0216947 | ||||||||
\(610\) | 4.86048 | 0.196795 | ||||||||
\(611\) | −3.49034 | −0.141204 | ||||||||
\(612\) | −3.75389 | −0.151742 | ||||||||
\(613\) | −23.3355 | −0.942513 | −0.471256 | − | 0.881996i | \(-0.656199\pi\) | ||||
−0.471256 | + | 0.881996i | \(0.656199\pi\) | |||||||
\(614\) | 21.0333 | 0.848836 | ||||||||
\(615\) | 5.56559 | 0.224426 | ||||||||
\(616\) | −2.91590 | −0.117485 | ||||||||
\(617\) | 30.4230 | 1.22479 | 0.612393 | − | 0.790554i | \(-0.290207\pi\) | ||||
0.612393 | + | 0.790554i | \(0.290207\pi\) | |||||||
\(618\) | −11.8078 | −0.474979 | ||||||||
\(619\) | −31.1594 | −1.25240 | −0.626200 | − | 0.779662i | \(-0.715391\pi\) | ||||
−0.626200 | + | 0.779662i | \(0.715391\pi\) | |||||||
\(620\) | −5.17569 | −0.207861 | ||||||||
\(621\) | −26.5306 | −1.06464 | ||||||||
\(622\) | −23.6109 | −0.946712 | ||||||||
\(623\) | −3.21718 | −0.128893 | ||||||||
\(624\) | 0.437930 | 0.0175312 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 32.5188 | 1.29971 | ||||||||
\(627\) | −26.8147 | −1.07088 | ||||||||
\(628\) | 12.0915 | 0.482502 | ||||||||
\(629\) | 16.7439 | 0.667623 | ||||||||
\(630\) | −1.65148 | −0.0657966 | ||||||||
\(631\) | 14.5621 | 0.579707 | 0.289854 | − | 0.957071i | \(-0.406393\pi\) | ||||
0.289854 | + | 0.957071i | \(0.406393\pi\) | |||||||
\(632\) | −2.92286 | −0.116265 | ||||||||
\(633\) | −13.4730 | −0.535503 | ||||||||
\(634\) | −31.4667 | −1.24970 | ||||||||
\(635\) | 21.2892 | 0.844836 | ||||||||
\(636\) | 9.13298 | 0.362146 | ||||||||
\(637\) | −3.45756 | −0.136994 | ||||||||
\(638\) | 3.75584 | 0.148695 | ||||||||
\(639\) | −13.9659 | −0.552484 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −35.5487 | −1.40409 | −0.702044 | − | 0.712134i | \(-0.747729\pi\) | ||||
−0.702044 | + | 0.712134i | \(0.747729\pi\) | |||||||
\(642\) | 3.48773 | 0.137650 | ||||||||
\(643\) | −23.5931 | −0.930420 | −0.465210 | − | 0.885200i | \(-0.654021\pi\) | ||||
−0.465210 | + | 0.885200i | \(0.654021\pi\) | |||||||
\(644\) | 4.30663 | 0.169705 | ||||||||
\(645\) | 7.11473 | 0.280142 | ||||||||
\(646\) | 12.8394 | 0.505161 | ||||||||
\(647\) | 12.1817 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(648\) | 3.36770 | 0.132296 | ||||||||
\(649\) | 14.7542 | 0.579153 | ||||||||
\(650\) | 0.532365 | 0.0208811 | ||||||||
\(651\) | −3.02642 | −0.118615 | ||||||||
\(652\) | 15.2159 | 0.595900 | ||||||||
\(653\) | −1.86304 | −0.0729063 | −0.0364532 | − | 0.999335i | \(-0.511606\pi\) | ||||
−0.0364532 | + | 0.999335i | \(0.511606\pi\) | |||||||
\(654\) | 0.0787555 | 0.00307958 | ||||||||
\(655\) | −10.8187 | −0.422723 | ||||||||
\(656\) | 6.76575 | 0.264158 | ||||||||
\(657\) | −5.60142 | −0.218532 | ||||||||
\(658\) | −4.66041 | −0.181682 | ||||||||
\(659\) | −48.1507 | −1.87568 | −0.937842 | − | 0.347062i | \(-0.887179\pi\) | ||||
−0.937842 | + | 0.347062i | \(0.887179\pi\) | |||||||
\(660\) | −3.37444 | −0.131350 | ||||||||
\(661\) | −30.8392 | −1.19950 | −0.599752 | − | 0.800186i | \(-0.704734\pi\) | ||||
−0.599752 | + | 0.800186i | \(0.704734\pi\) | |||||||
\(662\) | −20.7862 | −0.807880 | ||||||||
\(663\) | 0.707585 | 0.0274803 | ||||||||
\(664\) | 6.74323 | 0.261688 | ||||||||
\(665\) | 5.64857 | 0.219042 | ||||||||
\(666\) | −24.0763 | −0.932937 | ||||||||
\(667\) | −5.54717 | −0.214787 | ||||||||
\(668\) | 6.56868 | 0.254150 | ||||||||
\(669\) | −9.25747 | −0.357914 | ||||||||
\(670\) | 6.55325 | 0.253174 | ||||||||
\(671\) | −19.9382 | −0.769705 | ||||||||
\(672\) | 0.584738 | 0.0225568 | ||||||||
\(673\) | 29.5955 | 1.14082 | 0.570411 | − | 0.821359i | \(-0.306784\pi\) | ||||
0.570411 | + | 0.821359i | \(0.306784\pi\) | |||||||
\(674\) | 31.6652 | 1.21970 | ||||||||
\(675\) | −4.37902 | −0.168548 | ||||||||
\(676\) | −12.7166 | −0.489100 | ||||||||
\(677\) | −7.41223 | −0.284875 | −0.142438 | − | 0.989804i | \(-0.545494\pi\) | ||||
−0.142438 | + | 0.989804i | \(0.545494\pi\) | |||||||
\(678\) | −6.84651 | −0.262939 | ||||||||
\(679\) | 0.881710 | 0.0338369 | ||||||||
\(680\) | 1.61575 | 0.0619612 | ||||||||
\(681\) | −19.7951 | −0.758549 | ||||||||
\(682\) | 21.2312 | 0.812985 | ||||||||
\(683\) | −13.3379 | −0.510359 | −0.255180 | − | 0.966894i | \(-0.582135\pi\) | ||||
−0.255180 | + | 0.966894i | \(0.582135\pi\) | |||||||
\(684\) | −18.4620 | −0.705912 | ||||||||
\(685\) | −19.9787 | −0.763348 | ||||||||
\(686\) | −9.59247 | −0.366242 | ||||||||
\(687\) | −4.98841 | −0.190320 | ||||||||
\(688\) | 8.64895 | 0.329738 | ||||||||
\(689\) | 5.91054 | 0.225174 | ||||||||
\(690\) | 4.98386 | 0.189732 | ||||||||
\(691\) | −9.88208 | −0.375932 | −0.187966 | − | 0.982176i | \(-0.560190\pi\) | ||||
−0.187966 | + | 0.982176i | \(0.560190\pi\) | |||||||
\(692\) | 0.546744 | 0.0207841 | ||||||||
\(693\) | 6.77454 | 0.257344 | ||||||||
\(694\) | 26.5634 | 1.00833 | ||||||||
\(695\) | 11.4197 | 0.433174 | ||||||||
\(696\) | −0.753174 | −0.0285490 | ||||||||
\(697\) | 10.9318 | 0.414070 | ||||||||
\(698\) | −1.96010 | −0.0741908 | ||||||||
\(699\) | −19.7151 | −0.745692 | ||||||||
\(700\) | 0.710831 | 0.0268669 | ||||||||
\(701\) | −6.23968 | −0.235669 | −0.117835 | − | 0.993033i | \(-0.537595\pi\) | ||||
−0.117835 | + | 0.993033i | \(0.537595\pi\) | |||||||
\(702\) | −2.33124 | −0.0879868 | ||||||||
\(703\) | 82.3482 | 3.10582 | ||||||||
\(704\) | −4.10210 | −0.154604 | ||||||||
\(705\) | −5.39328 | −0.203123 | ||||||||
\(706\) | 3.30982 | 0.124567 | ||||||||
\(707\) | −3.74740 | −0.140936 | ||||||||
\(708\) | −2.95872 | −0.111195 | ||||||||
\(709\) | 39.8810 | 1.49776 | 0.748881 | − | 0.662704i | \(-0.230591\pi\) | ||||
0.748881 | + | 0.662704i | \(0.230591\pi\) | |||||||
\(710\) | 6.01123 | 0.225597 | ||||||||
\(711\) | 6.79070 | 0.254671 | ||||||||
\(712\) | −4.52594 | −0.169617 | ||||||||
\(713\) | −31.3573 | −1.17434 | ||||||||
\(714\) | 0.944790 | 0.0353579 | ||||||||
\(715\) | −2.18382 | −0.0816701 | ||||||||
\(716\) | −0.244179 | −0.00912541 | ||||||||
\(717\) | 14.9948 | 0.559991 | ||||||||
\(718\) | −17.1912 | −0.641571 | ||||||||
\(719\) | 8.66995 | 0.323335 | 0.161667 | − | 0.986845i | \(-0.448313\pi\) | ||||
0.161667 | + | 0.986845i | \(0.448313\pi\) | |||||||
\(720\) | −2.32331 | −0.0865846 | ||||||||
\(721\) | −10.2033 | −0.379990 | ||||||||
\(722\) | 44.1457 | 1.64293 | ||||||||
\(723\) | 20.8746 | 0.776335 | ||||||||
\(724\) | −25.9979 | −0.966204 | ||||||||
\(725\) | −0.915588 | −0.0340041 | ||||||||
\(726\) | 4.79356 | 0.177906 | ||||||||
\(727\) | −31.1141 | −1.15396 | −0.576979 | − | 0.816759i | \(-0.695769\pi\) | ||||
−0.576979 | + | 0.816759i | \(0.695769\pi\) | |||||||
\(728\) | 0.378422 | 0.0140252 | ||||||||
\(729\) | 2.98249 | 0.110463 | ||||||||
\(730\) | 2.41097 | 0.0892338 | ||||||||
\(731\) | 13.9745 | 0.516867 | ||||||||
\(732\) | 3.99829 | 0.147781 | ||||||||
\(733\) | −10.6284 | −0.392570 | −0.196285 | − | 0.980547i | \(-0.562888\pi\) | ||||
−0.196285 | + | 0.980547i | \(0.562888\pi\) | |||||||
\(734\) | 6.47995 | 0.239179 | ||||||||
\(735\) | −5.34263 | −0.197066 | ||||||||
\(736\) | 6.05858 | 0.223322 | ||||||||
\(737\) | −26.8821 | −0.990215 | ||||||||
\(738\) | −15.7189 | −0.578622 | ||||||||
\(739\) | 32.1897 | 1.18412 | 0.592059 | − | 0.805894i | \(-0.298315\pi\) | ||||
0.592059 | + | 0.805894i | \(0.298315\pi\) | |||||||
\(740\) | 10.3629 | 0.380949 | ||||||||
\(741\) | 3.47998 | 0.127840 | ||||||||
\(742\) | 7.89194 | 0.289722 | ||||||||
\(743\) | −40.4608 | −1.48436 | −0.742181 | − | 0.670200i | \(-0.766208\pi\) | ||||
−0.742181 | + | 0.670200i | \(0.766208\pi\) | |||||||
\(744\) | −4.25758 | −0.156091 | ||||||||
\(745\) | 2.02784 | 0.0742945 | ||||||||
\(746\) | −7.55550 | −0.276626 | ||||||||
\(747\) | −15.6666 | −0.573211 | ||||||||
\(748\) | −6.62797 | −0.242343 | ||||||||
\(749\) | 3.01380 | 0.110122 | ||||||||
\(750\) | 0.822612 | 0.0300375 | ||||||||
\(751\) | 27.5477 | 1.00523 | 0.502615 | − | 0.864510i | \(-0.332371\pi\) | ||||
0.502615 | + | 0.864510i | \(0.332371\pi\) | |||||||
\(752\) | −6.55629 | −0.239083 | ||||||||
\(753\) | −8.46455 | −0.308465 | ||||||||
\(754\) | −0.487427 | −0.0177511 | ||||||||
\(755\) | −7.18615 | −0.261531 | ||||||||
\(756\) | −3.11274 | −0.113209 | ||||||||
\(757\) | 11.5209 | 0.418735 | 0.209368 | − | 0.977837i | \(-0.432859\pi\) | ||||
0.209368 | + | 0.977837i | \(0.432859\pi\) | |||||||
\(758\) | 23.0385 | 0.836797 | ||||||||
\(759\) | −20.4443 | −0.742082 | ||||||||
\(760\) | 7.94642 | 0.288247 | ||||||||
\(761\) | 18.7715 | 0.680468 | 0.340234 | − | 0.940341i | \(-0.389494\pi\) | ||||
0.340234 | + | 0.940341i | \(0.389494\pi\) | |||||||
\(762\) | 17.5128 | 0.634420 | ||||||||
\(763\) | 0.0680538 | 0.00246371 | ||||||||
\(764\) | −17.9504 | −0.649421 | ||||||||
\(765\) | −3.75389 | −0.135722 | ||||||||
\(766\) | −26.2392 | −0.948061 | ||||||||
\(767\) | −1.91478 | −0.0691386 | ||||||||
\(768\) | 0.822612 | 0.0296834 | ||||||||
\(769\) | 45.0305 | 1.62384 | 0.811921 | − | 0.583767i | \(-0.198422\pi\) | ||||
0.811921 | + | 0.583767i | \(0.198422\pi\) | |||||||
\(770\) | −2.91590 | −0.105082 | ||||||||
\(771\) | 20.0224 | 0.721090 | ||||||||
\(772\) | −11.3687 | −0.409168 | ||||||||
\(773\) | 26.7052 | 0.960520 | 0.480260 | − | 0.877126i | \(-0.340542\pi\) | ||||
0.480260 | + | 0.877126i | \(0.340542\pi\) | |||||||
\(774\) | −20.0942 | −0.722271 | ||||||||
\(775\) | −5.17569 | −0.185916 | ||||||||
\(776\) | 1.24039 | 0.0445275 | ||||||||
\(777\) | 6.05960 | 0.217387 | ||||||||
\(778\) | −0.818755 | −0.0293538 | ||||||||
\(779\) | 53.7636 | 1.92628 | ||||||||
\(780\) | 0.437930 | 0.0156804 | ||||||||
\(781\) | −24.6587 | −0.882357 | ||||||||
\(782\) | 9.78915 | 0.350059 | ||||||||
\(783\) | 4.00938 | 0.143283 | ||||||||
\(784\) | −6.49472 | −0.231954 | ||||||||
\(785\) | 12.0915 | 0.431563 | ||||||||
\(786\) | −8.89962 | −0.317439 | ||||||||
\(787\) | 45.1456 | 1.60927 | 0.804634 | − | 0.593771i | \(-0.202362\pi\) | ||||
0.804634 | + | 0.593771i | \(0.202362\pi\) | |||||||
\(788\) | 2.14807 | 0.0765219 | ||||||||
\(789\) | −19.9615 | −0.710648 | ||||||||
\(790\) | −2.92286 | −0.103991 | ||||||||
\(791\) | −5.91617 | −0.210355 | ||||||||
\(792\) | 9.53045 | 0.338650 | ||||||||
\(793\) | 2.58755 | 0.0918866 | ||||||||
\(794\) | −36.6154 | −1.29943 | ||||||||
\(795\) | 9.13298 | 0.323913 | ||||||||
\(796\) | −21.8261 | −0.773607 | ||||||||
\(797\) | 17.5910 | 0.623106 | 0.311553 | − | 0.950229i | \(-0.399151\pi\) | ||||
0.311553 | + | 0.950229i | \(0.399151\pi\) | |||||||
\(798\) | 4.64658 | 0.164487 | ||||||||
\(799\) | −10.5933 | −0.374765 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 10.5151 | 0.371535 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | −9.89003 | −0.349011 | ||||||||
\(804\) | 5.39078 | 0.190118 | ||||||||
\(805\) | 4.30663 | 0.151789 | ||||||||
\(806\) | −2.75536 | −0.0970533 | ||||||||
\(807\) | 23.8919 | 0.841035 | ||||||||
\(808\) | −5.27186 | −0.185463 | ||||||||
\(809\) | −30.7415 | −1.08081 | −0.540407 | − | 0.841404i | \(-0.681730\pi\) | ||||
−0.540407 | + | 0.841404i | \(0.681730\pi\) | |||||||
\(810\) | 3.36770 | 0.118329 | ||||||||
\(811\) | 19.8606 | 0.697400 | 0.348700 | − | 0.937234i | \(-0.386623\pi\) | ||||
0.348700 | + | 0.937234i | \(0.386623\pi\) | |||||||
\(812\) | −0.650829 | −0.0228396 | ||||||||
\(813\) | −3.50499 | −0.122925 | ||||||||
\(814\) | −42.5098 | −1.48997 | ||||||||
\(815\) | 15.2159 | 0.532989 | ||||||||
\(816\) | 1.32913 | 0.0465290 | ||||||||
\(817\) | 68.7282 | 2.40450 | ||||||||
\(818\) | 25.7798 | 0.901370 | ||||||||
\(819\) | −0.879191 | −0.0307214 | ||||||||
\(820\) | 6.76575 | 0.236270 | ||||||||
\(821\) | 20.3088 | 0.708781 | 0.354391 | − | 0.935097i | \(-0.384688\pi\) | ||||
0.354391 | + | 0.935097i | \(0.384688\pi\) | |||||||
\(822\) | −16.4347 | −0.573227 | ||||||||
\(823\) | −44.9814 | −1.56795 | −0.783977 | − | 0.620790i | \(-0.786812\pi\) | ||||
−0.783977 | + | 0.620790i | \(0.786812\pi\) | |||||||
\(824\) | −14.3540 | −0.500046 | ||||||||
\(825\) | −3.37444 | −0.117483 | ||||||||
\(826\) | −2.55667 | −0.0889580 | ||||||||
\(827\) | −53.7445 | −1.86888 | −0.934439 | − | 0.356123i | \(-0.884099\pi\) | ||||
−0.934439 | + | 0.356123i | \(0.884099\pi\) | |||||||
\(828\) | −14.0760 | −0.489174 | ||||||||
\(829\) | 21.5647 | 0.748973 | 0.374486 | − | 0.927232i | \(-0.377819\pi\) | ||||
0.374486 | + | 0.927232i | \(0.377819\pi\) | |||||||
\(830\) | 6.74323 | 0.234061 | ||||||||
\(831\) | 26.5049 | 0.919444 | ||||||||
\(832\) | 0.532365 | 0.0184564 | ||||||||
\(833\) | −10.4938 | −0.363590 | ||||||||
\(834\) | 9.39398 | 0.325287 | ||||||||
\(835\) | 6.56868 | 0.227319 | ||||||||
\(836\) | −32.5970 | −1.12739 | ||||||||
\(837\) | 22.6644 | 0.783397 | ||||||||
\(838\) | 32.2101 | 1.11268 | ||||||||
\(839\) | −31.8683 | −1.10022 | −0.550108 | − | 0.835094i | \(-0.685413\pi\) | ||||
−0.550108 | + | 0.835094i | \(0.685413\pi\) | |||||||
\(840\) | 0.584738 | 0.0201754 | ||||||||
\(841\) | −28.1617 | −0.971093 | ||||||||
\(842\) | −25.7842 | −0.888583 | ||||||||
\(843\) | −10.5297 | −0.362662 | ||||||||
\(844\) | −16.3783 | −0.563765 | ||||||||
\(845\) | −12.7166 | −0.437464 | ||||||||
\(846\) | 15.2323 | 0.523697 | ||||||||
\(847\) | 4.14219 | 0.142327 | ||||||||
\(848\) | 11.1024 | 0.381258 | ||||||||
\(849\) | −5.15324 | −0.176859 | ||||||||
\(850\) | 1.61575 | 0.0554197 | ||||||||
\(851\) | 62.7847 | 2.15223 | ||||||||
\(852\) | 4.94491 | 0.169410 | ||||||||
\(853\) | −0.143060 | −0.00489829 | −0.00244915 | − | 0.999997i | \(-0.500780\pi\) | ||||
−0.00244915 | + | 0.999997i | \(0.500780\pi\) | |||||||
\(854\) | 3.45498 | 0.118227 | ||||||||
\(855\) | −18.4620 | −0.631387 | ||||||||
\(856\) | 4.23982 | 0.144914 | ||||||||
\(857\) | 51.9988 | 1.77625 | 0.888123 | − | 0.459605i | \(-0.152009\pi\) | ||||
0.888123 | + | 0.459605i | \(0.152009\pi\) | |||||||
\(858\) | −1.79643 | −0.0613292 | ||||||||
\(859\) | −46.3058 | −1.57993 | −0.789967 | − | 0.613149i | \(-0.789902\pi\) | ||||
−0.789967 | + | 0.613149i | \(0.789902\pi\) | |||||||
\(860\) | 8.64895 | 0.294927 | ||||||||
\(861\) | 3.95619 | 0.134827 | ||||||||
\(862\) | 12.3190 | 0.419588 | ||||||||
\(863\) | −5.47632 | −0.186416 | −0.0932081 | − | 0.995647i | \(-0.529712\pi\) | ||||
−0.0932081 | + | 0.995647i | \(0.529712\pi\) | |||||||
\(864\) | −4.37902 | −0.148977 | ||||||||
\(865\) | 0.546744 | 0.0185899 | ||||||||
\(866\) | 21.2530 | 0.722206 | ||||||||
\(867\) | −11.8369 | −0.402001 | ||||||||
\(868\) | −3.67904 | −0.124875 | ||||||||
\(869\) | 11.9899 | 0.406728 | ||||||||
\(870\) | −0.753174 | −0.0255350 | ||||||||
\(871\) | 3.48872 | 0.118211 | ||||||||
\(872\) | 0.0957383 | 0.00324211 | ||||||||
\(873\) | −2.88182 | −0.0975347 | ||||||||
\(874\) | 48.1441 | 1.62850 | ||||||||
\(875\) | 0.710831 | 0.0240305 | ||||||||
\(876\) | 1.98329 | 0.0670091 | ||||||||
\(877\) | −48.9770 | −1.65384 | −0.826919 | − | 0.562322i | \(-0.809908\pi\) | ||||
−0.826919 | + | 0.562322i | \(0.809908\pi\) | |||||||
\(878\) | −1.82146 | −0.0614713 | ||||||||
\(879\) | 4.30377 | 0.145163 | ||||||||
\(880\) | −4.10210 | −0.138282 | ||||||||
\(881\) | −1.07440 | −0.0361976 | −0.0180988 | − | 0.999836i | \(-0.505761\pi\) | ||||
−0.0180988 | + | 0.999836i | \(0.505761\pi\) | |||||||
\(882\) | 15.0892 | 0.508081 | ||||||||
\(883\) | −41.8301 | −1.40769 | −0.703847 | − | 0.710351i | \(-0.748536\pi\) | ||||
−0.703847 | + | 0.710351i | \(0.748536\pi\) | |||||||
\(884\) | 0.860169 | 0.0289306 | ||||||||
\(885\) | −2.95872 | −0.0994563 | ||||||||
\(886\) | −7.80446 | −0.262196 | ||||||||
\(887\) | −41.8468 | −1.40508 | −0.702539 | − | 0.711646i | \(-0.747950\pi\) | ||||
−0.702539 | + | 0.711646i | \(0.747950\pi\) | |||||||
\(888\) | 8.52467 | 0.286069 | ||||||||
\(889\) | 15.1330 | 0.507546 | ||||||||
\(890\) | −4.52594 | −0.151710 | ||||||||
\(891\) | −13.8146 | −0.462808 | ||||||||
\(892\) | −11.2538 | −0.376803 | ||||||||
\(893\) | −52.0991 | −1.74343 | ||||||||
\(894\) | 1.66813 | 0.0557906 | ||||||||
\(895\) | −0.244179 | −0.00816201 | ||||||||
\(896\) | 0.710831 | 0.0237472 | ||||||||
\(897\) | 2.65323 | 0.0885889 | ||||||||
\(898\) | −19.1754 | −0.639893 | ||||||||
\(899\) | 4.73880 | 0.158048 | ||||||||
\(900\) | −2.32331 | −0.0774437 | ||||||||
\(901\) | 17.9387 | 0.597625 | ||||||||
\(902\) | −27.7538 | −0.924101 | ||||||||
\(903\) | 5.05737 | 0.168299 | ||||||||
\(904\) | −8.32289 | −0.276815 | ||||||||
\(905\) | −25.9979 | −0.864199 | ||||||||
\(906\) | −5.91142 | −0.196394 | ||||||||
\(907\) | 9.29471 | 0.308626 | 0.154313 | − | 0.988022i | \(-0.450684\pi\) | ||||
0.154313 | + | 0.988022i | \(0.450684\pi\) | |||||||
\(908\) | −24.0637 | −0.798582 | ||||||||
\(909\) | 12.2482 | 0.406246 | ||||||||
\(910\) | 0.378422 | 0.0125446 | ||||||||
\(911\) | 5.80056 | 0.192181 | 0.0960905 | − | 0.995373i | \(-0.469366\pi\) | ||||
0.0960905 | + | 0.995373i | \(0.469366\pi\) | |||||||
\(912\) | 6.53682 | 0.216456 | ||||||||
\(913\) | −27.6614 | −0.915459 | ||||||||
\(914\) | −7.66012 | −0.253374 | ||||||||
\(915\) | 3.99829 | 0.132179 | ||||||||
\(916\) | −6.06411 | −0.200364 | ||||||||
\(917\) | −7.69029 | −0.253956 | ||||||||
\(918\) | −7.07539 | −0.233523 | ||||||||
\(919\) | 22.2815 | 0.735000 | 0.367500 | − | 0.930023i | \(-0.380214\pi\) | ||||
0.367500 | + | 0.930023i | \(0.380214\pi\) | |||||||
\(920\) | 6.05858 | 0.199746 | ||||||||
\(921\) | 17.3023 | 0.570129 | ||||||||
\(922\) | 13.1999 | 0.434716 | ||||||||
\(923\) | 3.20017 | 0.105335 | ||||||||
\(924\) | −2.39866 | −0.0789100 | ||||||||
\(925\) | 10.3629 | 0.340731 | ||||||||
\(926\) | 36.9795 | 1.21522 | ||||||||
\(927\) | 33.3489 | 1.09532 | ||||||||
\(928\) | −0.915588 | −0.0300557 | ||||||||
\(929\) | −55.1248 | −1.80859 | −0.904294 | − | 0.426911i | \(-0.859602\pi\) | ||||
−0.904294 | + | 0.426911i | \(0.859602\pi\) | |||||||
\(930\) | −4.25758 | −0.139612 | ||||||||
\(931\) | −51.6098 | −1.69144 | ||||||||
\(932\) | −23.9664 | −0.785046 | ||||||||
\(933\) | −19.4226 | −0.635869 | ||||||||
\(934\) | −23.2934 | −0.762183 | ||||||||
\(935\) | −6.62797 | −0.216758 | ||||||||
\(936\) | −1.23685 | −0.0404277 | ||||||||
\(937\) | 16.3385 | 0.533756 | 0.266878 | − | 0.963730i | \(-0.414008\pi\) | ||||
0.266878 | + | 0.963730i | \(0.414008\pi\) | |||||||
\(938\) | 4.65826 | 0.152097 | ||||||||
\(939\) | 26.7504 | 0.872966 | ||||||||
\(940\) | −6.55629 | −0.213843 | ||||||||
\(941\) | −48.8585 | −1.59274 | −0.796371 | − | 0.604809i | \(-0.793249\pi\) | ||||
−0.796371 | + | 0.604809i | \(0.793249\pi\) | |||||||
\(942\) | 9.94658 | 0.324077 | ||||||||
\(943\) | 40.9909 | 1.33485 | ||||||||
\(944\) | −3.59674 | −0.117064 | ||||||||
\(945\) | −3.11274 | −0.101258 | ||||||||
\(946\) | −35.4789 | −1.15352 | ||||||||
\(947\) | 45.2635 | 1.47086 | 0.735432 | − | 0.677598i | \(-0.236979\pi\) | ||||
0.735432 | + | 0.677598i | \(0.236979\pi\) | |||||||
\(948\) | −2.40438 | −0.0780905 | ||||||||
\(949\) | 1.28351 | 0.0416646 | ||||||||
\(950\) | 7.94642 | 0.257816 | ||||||||
\(951\) | −25.8849 | −0.839376 | ||||||||
\(952\) | 1.14852 | 0.0372239 | ||||||||
\(953\) | 43.3041 | 1.40276 | 0.701378 | − | 0.712789i | \(-0.252568\pi\) | ||||
0.701378 | + | 0.712789i | \(0.252568\pi\) | |||||||
\(954\) | −25.7943 | −0.835123 | ||||||||
\(955\) | −17.9504 | −0.580860 | ||||||||
\(956\) | 18.2283 | 0.589545 | ||||||||
\(957\) | 3.08960 | 0.0998724 | ||||||||
\(958\) | 32.2728 | 1.04269 | ||||||||
\(959\) | −14.2015 | −0.458590 | ||||||||
\(960\) | 0.822612 | 0.0265497 | ||||||||
\(961\) | −4.21227 | −0.135880 | ||||||||
\(962\) | 5.51686 | 0.177871 | ||||||||
\(963\) | −9.85042 | −0.317425 | ||||||||
\(964\) | 25.3760 | 0.817307 | ||||||||
\(965\) | −11.3687 | −0.365971 | ||||||||
\(966\) | 3.54268 | 0.113984 | ||||||||
\(967\) | 33.5978 | 1.08043 | 0.540216 | − | 0.841527i | \(-0.318343\pi\) | ||||
0.540216 | + | 0.841527i | \(0.318343\pi\) | |||||||
\(968\) | 5.82724 | 0.187295 | ||||||||
\(969\) | 10.5619 | 0.339296 | ||||||||
\(970\) | 1.24039 | 0.0398266 | ||||||||
\(971\) | −3.24372 | −0.104096 | −0.0520479 | − | 0.998645i | \(-0.516575\pi\) | ||||
−0.0520479 | + | 0.998645i | \(0.516575\pi\) | |||||||
\(972\) | 15.9074 | 0.510229 | ||||||||
\(973\) | 8.11748 | 0.260234 | ||||||||
\(974\) | −28.7215 | −0.920296 | ||||||||
\(975\) | 0.437930 | 0.0140250 | ||||||||
\(976\) | 4.86048 | 0.155580 | ||||||||
\(977\) | −40.3001 | −1.28931 | −0.644657 | − | 0.764472i | \(-0.723000\pi\) | ||||
−0.644657 | + | 0.764472i | \(0.723000\pi\) | |||||||
\(978\) | 12.5168 | 0.400242 | ||||||||
\(979\) | 18.5658 | 0.593367 | ||||||||
\(980\) | −6.49472 | −0.207466 | ||||||||
\(981\) | −0.222430 | −0.00710164 | ||||||||
\(982\) | 28.6061 | 0.912857 | ||||||||
\(983\) | −4.73686 | −0.151082 | −0.0755412 | − | 0.997143i | \(-0.524068\pi\) | ||||
−0.0755412 | + | 0.997143i | \(0.524068\pi\) | |||||||
\(984\) | 5.56559 | 0.177425 | ||||||||
\(985\) | 2.14807 | 0.0684433 | ||||||||
\(986\) | −1.47936 | −0.0471124 | ||||||||
\(987\) | −3.83371 | −0.122028 | ||||||||
\(988\) | 4.23040 | 0.134587 | ||||||||
\(989\) | 52.4004 | 1.66624 | ||||||||
\(990\) | 9.53045 | 0.302898 | ||||||||
\(991\) | −49.7348 | −1.57988 | −0.789939 | − | 0.613186i | \(-0.789888\pi\) | ||||
−0.789939 | + | 0.613186i | \(0.789888\pi\) | |||||||
\(992\) | −5.17569 | −0.164328 | ||||||||
\(993\) | −17.0990 | −0.542620 | ||||||||
\(994\) | 4.27297 | 0.135530 | ||||||||
\(995\) | −21.8261 | −0.691935 | ||||||||
\(996\) | 5.54706 | 0.175765 | ||||||||
\(997\) | −9.68842 | −0.306835 | −0.153418 | − | 0.988161i | \(-0.549028\pi\) | ||||
−0.153418 | + | 0.988161i | \(0.549028\pi\) | |||||||
\(998\) | −16.7561 | −0.530404 | ||||||||
\(999\) | −45.3794 | −1.43574 |
(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 | 4010.2.a.n.1.13 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.n.1.13 | ✓ | 22 | 1.1 | even | 1 | trivial |