Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0484532 | −0.0342616 | −0.0171308 | − | 0.999853i | \(-0.505453\pi\) | ||||
−0.0171308 | + | 0.999853i | \(0.505453\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.99765 | −0.998826 | ||||||||
\(5\) | 1.78925 | 0.800175 | 0.400088 | − | 0.916477i | \(-0.368980\pi\) | ||||
0.400088 | + | 0.916477i | \(0.368980\pi\) | |||||||
\(6\) | 0.0484532 | 0.0197809 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.193699 | 0.0684830 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.0866947 | −0.0274153 | ||||||||
\(11\) | 3.36110 | 1.01341 | 0.506705 | − | 0.862119i | \(-0.330863\pi\) | ||||
0.506705 | + | 0.862119i | \(0.330863\pi\) | |||||||
\(12\) | 1.99765 | 0.576673 | ||||||||
\(13\) | −2.05219 | −0.569175 | −0.284588 | − | 0.958650i | \(-0.591857\pi\) | ||||
−0.284588 | + | 0.958650i | \(0.591857\pi\) | |||||||
\(14\) | −0.0484532 | −0.0129497 | ||||||||
\(15\) | −1.78925 | −0.461982 | ||||||||
\(16\) | 3.98592 | 0.996480 | ||||||||
\(17\) | −1.59543 | −0.386949 | −0.193474 | − | 0.981105i | \(-0.561976\pi\) | ||||
−0.193474 | + | 0.981105i | \(0.561976\pi\) | |||||||
\(18\) | −0.0484532 | −0.0114205 | ||||||||
\(19\) | 5.14182 | 1.17961 | 0.589807 | − | 0.807544i | \(-0.299204\pi\) | ||||
0.589807 | + | 0.807544i | \(0.299204\pi\) | |||||||
\(20\) | −3.57429 | −0.799236 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −0.162856 | −0.0347210 | ||||||||
\(23\) | 6.94960 | 1.44909 | 0.724546 | − | 0.689227i | \(-0.242050\pi\) | ||||
0.724546 | + | 0.689227i | \(0.242050\pi\) | |||||||
\(24\) | −0.193699 | −0.0395387 | ||||||||
\(25\) | −1.79860 | −0.359719 | ||||||||
\(26\) | 0.0994352 | 0.0195009 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.99765 | −0.377521 | ||||||||
\(29\) | 4.46629 | 0.829370 | 0.414685 | − | 0.909965i | \(-0.363892\pi\) | ||||
0.414685 | + | 0.909965i | \(0.363892\pi\) | |||||||
\(30\) | 0.0866947 | 0.0158282 | ||||||||
\(31\) | −3.91483 | −0.703124 | −0.351562 | − | 0.936165i | \(-0.614349\pi\) | ||||
−0.351562 | + | 0.936165i | \(0.614349\pi\) | |||||||
\(32\) | −0.580529 | −0.102624 | ||||||||
\(33\) | −3.36110 | −0.585093 | ||||||||
\(34\) | 0.0773037 | 0.0132575 | ||||||||
\(35\) | 1.78925 | 0.302438 | ||||||||
\(36\) | −1.99765 | −0.332942 | ||||||||
\(37\) | −6.88044 | −1.13114 | −0.565568 | − | 0.824701i | \(-0.691343\pi\) | ||||
−0.565568 | + | 0.824701i | \(0.691343\pi\) | |||||||
\(38\) | −0.249138 | −0.0404155 | ||||||||
\(39\) | 2.05219 | 0.328614 | ||||||||
\(40\) | 0.346575 | 0.0547984 | ||||||||
\(41\) | 4.21697 | 0.658581 | 0.329290 | − | 0.944229i | \(-0.393191\pi\) | ||||
0.329290 | + | 0.944229i | \(0.393191\pi\) | |||||||
\(42\) | 0.0484532 | 0.00747649 | ||||||||
\(43\) | 7.27571 | 1.10954 | 0.554768 | − | 0.832005i | \(-0.312807\pi\) | ||||
0.554768 | + | 0.832005i | \(0.312807\pi\) | |||||||
\(44\) | −6.71431 | −1.01222 | ||||||||
\(45\) | 1.78925 | 0.266725 | ||||||||
\(46\) | −0.336730 | −0.0496482 | ||||||||
\(47\) | 4.83673 | 0.705509 | 0.352755 | − | 0.935716i | \(-0.385245\pi\) | ||||
0.352755 | + | 0.935716i | \(0.385245\pi\) | |||||||
\(48\) | −3.98592 | −0.575318 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.0871477 | 0.0123246 | ||||||||
\(51\) | 1.59543 | 0.223405 | ||||||||
\(52\) | 4.09956 | 0.568507 | ||||||||
\(53\) | −12.5504 | −1.72394 | −0.861968 | − | 0.506963i | \(-0.830768\pi\) | ||||
−0.861968 | + | 0.506963i | \(0.830768\pi\) | |||||||
\(54\) | 0.0484532 | 0.00659365 | ||||||||
\(55\) | 6.01384 | 0.810906 | ||||||||
\(56\) | 0.193699 | 0.0258841 | ||||||||
\(57\) | −5.14182 | −0.681051 | ||||||||
\(58\) | −0.216406 | −0.0284155 | ||||||||
\(59\) | 7.29882 | 0.950226 | 0.475113 | − | 0.879925i | \(-0.342407\pi\) | ||||
0.475113 | + | 0.879925i | \(0.342407\pi\) | |||||||
\(60\) | 3.57429 | 0.461439 | ||||||||
\(61\) | 9.05051 | 1.15880 | 0.579400 | − | 0.815043i | \(-0.303287\pi\) | ||||
0.579400 | + | 0.815043i | \(0.303287\pi\) | |||||||
\(62\) | 0.189686 | 0.0240901 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −7.94371 | −0.992964 | ||||||||
\(65\) | −3.67188 | −0.455440 | ||||||||
\(66\) | 0.162856 | 0.0200462 | ||||||||
\(67\) | −12.2508 | −1.49668 | −0.748339 | − | 0.663316i | \(-0.769148\pi\) | ||||
−0.748339 | + | 0.663316i | \(0.769148\pi\) | |||||||
\(68\) | 3.18712 | 0.386495 | ||||||||
\(69\) | −6.94960 | −0.836633 | ||||||||
\(70\) | −0.0866947 | −0.0103620 | ||||||||
\(71\) | −4.67775 | −0.555147 | −0.277574 | − | 0.960704i | \(-0.589530\pi\) | ||||
−0.277574 | + | 0.960704i | \(0.589530\pi\) | |||||||
\(72\) | 0.193699 | 0.0228277 | ||||||||
\(73\) | −10.2723 | −1.20228 | −0.601141 | − | 0.799143i | \(-0.705287\pi\) | ||||
−0.601141 | + | 0.799143i | \(0.705287\pi\) | |||||||
\(74\) | 0.333379 | 0.0387545 | ||||||||
\(75\) | 1.79860 | 0.207684 | ||||||||
\(76\) | −10.2716 | −1.17823 | ||||||||
\(77\) | 3.36110 | 0.383033 | ||||||||
\(78\) | −0.0994352 | −0.0112588 | ||||||||
\(79\) | 8.94904 | 1.00685 | 0.503423 | − | 0.864040i | \(-0.332074\pi\) | ||||
0.503423 | + | 0.864040i | \(0.332074\pi\) | |||||||
\(80\) | 7.13179 | 0.797359 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.204326 | −0.0225640 | ||||||||
\(83\) | −3.69192 | −0.405240 | −0.202620 | − | 0.979257i | \(-0.564946\pi\) | ||||
−0.202620 | + | 0.979257i | \(0.564946\pi\) | |||||||
\(84\) | 1.99765 | 0.217962 | ||||||||
\(85\) | −2.85462 | −0.309627 | ||||||||
\(86\) | −0.352531 | −0.0380144 | ||||||||
\(87\) | −4.46629 | −0.478837 | ||||||||
\(88\) | 0.651042 | 0.0694013 | ||||||||
\(89\) | 1.98084 | 0.209969 | 0.104985 | − | 0.994474i | \(-0.466521\pi\) | ||||
0.104985 | + | 0.994474i | \(0.466521\pi\) | |||||||
\(90\) | −0.0866947 | −0.00913843 | ||||||||
\(91\) | −2.05219 | −0.215128 | ||||||||
\(92\) | −13.8829 | −1.44739 | ||||||||
\(93\) | 3.91483 | 0.405949 | ||||||||
\(94\) | −0.234355 | −0.0241719 | ||||||||
\(95\) | 9.19998 | 0.943899 | ||||||||
\(96\) | 0.580529 | 0.0592500 | ||||||||
\(97\) | 2.08239 | 0.211435 | 0.105718 | − | 0.994396i | \(-0.466286\pi\) | ||||
0.105718 | + | 0.994396i | \(0.466286\pi\) | |||||||
\(98\) | −0.0484532 | −0.00489451 | ||||||||
\(99\) | 3.36110 | 0.337803 | ||||||||
\(100\) | 3.59297 | 0.359297 | ||||||||
\(101\) | 7.02738 | 0.699251 | 0.349625 | − | 0.936890i | \(-0.386309\pi\) | ||||
0.349625 | + | 0.936890i | \(0.386309\pi\) | |||||||
\(102\) | −0.0773037 | −0.00765421 | ||||||||
\(103\) | −1.46585 | −0.144434 | −0.0722171 | − | 0.997389i | \(-0.523007\pi\) | ||||
−0.0722171 | + | 0.997389i | \(0.523007\pi\) | |||||||
\(104\) | −0.397507 | −0.0389788 | ||||||||
\(105\) | −1.78925 | −0.174613 | ||||||||
\(106\) | 0.608109 | 0.0590648 | ||||||||
\(107\) | 3.12126 | 0.301744 | 0.150872 | − | 0.988553i | \(-0.451792\pi\) | ||||
0.150872 | + | 0.988553i | \(0.451792\pi\) | |||||||
\(108\) | 1.99765 | 0.192224 | ||||||||
\(109\) | −5.64099 | −0.540309 | −0.270155 | − | 0.962817i | \(-0.587075\pi\) | ||||
−0.270155 | + | 0.962817i | \(0.587075\pi\) | |||||||
\(110\) | −0.291390 | −0.0277829 | ||||||||
\(111\) | 6.88044 | 0.653062 | ||||||||
\(112\) | 3.98592 | 0.376634 | ||||||||
\(113\) | 6.37340 | 0.599559 | 0.299779 | − | 0.954009i | \(-0.403087\pi\) | ||||
0.299779 | + | 0.954009i | \(0.403087\pi\) | |||||||
\(114\) | 0.249138 | 0.0233339 | ||||||||
\(115\) | 12.4345 | 1.15953 | ||||||||
\(116\) | −8.92210 | −0.828396 | ||||||||
\(117\) | −2.05219 | −0.189725 | ||||||||
\(118\) | −0.353651 | −0.0325562 | ||||||||
\(119\) | −1.59543 | −0.146253 | ||||||||
\(120\) | −0.346575 | −0.0316379 | ||||||||
\(121\) | 0.297008 | 0.0270007 | ||||||||
\(122\) | −0.438526 | −0.0397023 | ||||||||
\(123\) | −4.21697 | −0.380232 | ||||||||
\(124\) | 7.82047 | 0.702299 | ||||||||
\(125\) | −12.1644 | −1.08801 | ||||||||
\(126\) | −0.0484532 | −0.00431655 | ||||||||
\(127\) | 3.93257 | 0.348959 | 0.174480 | − | 0.984661i | \(-0.444176\pi\) | ||||
0.174480 | + | 0.984661i | \(0.444176\pi\) | |||||||
\(128\) | 1.54596 | 0.136644 | ||||||||
\(129\) | −7.27571 | −0.640591 | ||||||||
\(130\) | 0.177914 | 0.0156041 | ||||||||
\(131\) | 12.6893 | 1.10867 | 0.554334 | − | 0.832294i | \(-0.312973\pi\) | ||||
0.554334 | + | 0.832294i | \(0.312973\pi\) | |||||||
\(132\) | 6.71431 | 0.584406 | ||||||||
\(133\) | 5.14182 | 0.445852 | ||||||||
\(134\) | 0.593593 | 0.0512786 | ||||||||
\(135\) | −1.78925 | −0.153994 | ||||||||
\(136\) | −0.309033 | −0.0264994 | ||||||||
\(137\) | 11.4048 | 0.974375 | 0.487188 | − | 0.873297i | \(-0.338023\pi\) | ||||
0.487188 | + | 0.873297i | \(0.338023\pi\) | |||||||
\(138\) | 0.336730 | 0.0286644 | ||||||||
\(139\) | 6.36160 | 0.539584 | 0.269792 | − | 0.962919i | \(-0.413045\pi\) | ||||
0.269792 | + | 0.962919i | \(0.413045\pi\) | |||||||
\(140\) | −3.57429 | −0.302083 | ||||||||
\(141\) | −4.83673 | −0.407326 | ||||||||
\(142\) | 0.226652 | 0.0190202 | ||||||||
\(143\) | −6.89762 | −0.576808 | ||||||||
\(144\) | 3.98592 | 0.332160 | ||||||||
\(145\) | 7.99130 | 0.663641 | ||||||||
\(146\) | 0.497726 | 0.0411921 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 13.7447 | 1.12981 | ||||||||
\(149\) | 15.5309 | 1.27234 | 0.636171 | − | 0.771548i | \(-0.280517\pi\) | ||||
0.636171 | + | 0.771548i | \(0.280517\pi\) | |||||||
\(150\) | −0.0871477 | −0.00711558 | ||||||||
\(151\) | −16.4683 | −1.34017 | −0.670086 | − | 0.742283i | \(-0.733743\pi\) | ||||
−0.670086 | + | 0.742283i | \(0.733743\pi\) | |||||||
\(152\) | 0.995966 | 0.0807835 | ||||||||
\(153\) | −1.59543 | −0.128983 | ||||||||
\(154\) | −0.162856 | −0.0131233 | ||||||||
\(155\) | −7.00460 | −0.562623 | ||||||||
\(156\) | −4.09956 | −0.328228 | ||||||||
\(157\) | −5.87308 | −0.468723 | −0.234361 | − | 0.972150i | \(-0.575300\pi\) | ||||
−0.234361 | + | 0.972150i | \(0.575300\pi\) | |||||||
\(158\) | −0.433610 | −0.0344961 | ||||||||
\(159\) | 12.5504 | 0.995315 | ||||||||
\(160\) | −1.03871 | −0.0821172 | ||||||||
\(161\) | 6.94960 | 0.547705 | ||||||||
\(162\) | −0.0484532 | −0.00380684 | ||||||||
\(163\) | −5.22016 | −0.408875 | −0.204437 | − | 0.978880i | \(-0.565536\pi\) | ||||
−0.204437 | + | 0.978880i | \(0.565536\pi\) | |||||||
\(164\) | −8.42405 | −0.657807 | ||||||||
\(165\) | −6.01384 | −0.468177 | ||||||||
\(166\) | 0.178885 | 0.0138842 | ||||||||
\(167\) | 9.85654 | 0.762722 | 0.381361 | − | 0.924426i | \(-0.375455\pi\) | ||||
0.381361 | + | 0.924426i | \(0.375455\pi\) | |||||||
\(168\) | −0.193699 | −0.0149442 | ||||||||
\(169\) | −8.78851 | −0.676039 | ||||||||
\(170\) | 0.138315 | 0.0106083 | ||||||||
\(171\) | 5.14182 | 0.393205 | ||||||||
\(172\) | −14.5343 | −1.10823 | ||||||||
\(173\) | 5.07979 | 0.386209 | 0.193104 | − | 0.981178i | \(-0.438144\pi\) | ||||
0.193104 | + | 0.981178i | \(0.438144\pi\) | |||||||
\(174\) | 0.216406 | 0.0164057 | ||||||||
\(175\) | −1.79860 | −0.135961 | ||||||||
\(176\) | 13.3971 | 1.00984 | ||||||||
\(177\) | −7.29882 | −0.548613 | ||||||||
\(178\) | −0.0959783 | −0.00719387 | ||||||||
\(179\) | −6.71008 | −0.501535 | −0.250768 | − | 0.968047i | \(-0.580683\pi\) | ||||
−0.250768 | + | 0.968047i | \(0.580683\pi\) | |||||||
\(180\) | −3.57429 | −0.266412 | ||||||||
\(181\) | 15.3178 | 1.13856 | 0.569280 | − | 0.822144i | \(-0.307222\pi\) | ||||
0.569280 | + | 0.822144i | \(0.307222\pi\) | |||||||
\(182\) | 0.0994352 | 0.00737063 | ||||||||
\(183\) | −9.05051 | −0.669033 | ||||||||
\(184\) | 1.34613 | 0.0992381 | ||||||||
\(185\) | −12.3108 | −0.905108 | ||||||||
\(186\) | −0.189686 | −0.0139085 | ||||||||
\(187\) | −5.36240 | −0.392138 | ||||||||
\(188\) | −9.66210 | −0.704681 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −0.445769 | −0.0323395 | ||||||||
\(191\) | −1.00000 | −0.0723575 | ||||||||
\(192\) | 7.94371 | 0.573288 | ||||||||
\(193\) | 24.9357 | 1.79491 | 0.897454 | − | 0.441108i | \(-0.145414\pi\) | ||||
0.897454 | + | 0.441108i | \(0.145414\pi\) | |||||||
\(194\) | −0.100899 | −0.00724410 | ||||||||
\(195\) | 3.67188 | 0.262948 | ||||||||
\(196\) | −1.99765 | −0.142689 | ||||||||
\(197\) | 9.15332 | 0.652147 | 0.326074 | − | 0.945344i | \(-0.394274\pi\) | ||||
0.326074 | + | 0.945344i | \(0.394274\pi\) | |||||||
\(198\) | −0.162856 | −0.0115737 | ||||||||
\(199\) | 14.9381 | 1.05893 | 0.529467 | − | 0.848331i | \(-0.322392\pi\) | ||||
0.529467 | + | 0.848331i | \(0.322392\pi\) | |||||||
\(200\) | −0.348386 | −0.0246346 | ||||||||
\(201\) | 12.2508 | 0.864108 | ||||||||
\(202\) | −0.340499 | −0.0239574 | ||||||||
\(203\) | 4.46629 | 0.313472 | ||||||||
\(204\) | −3.18712 | −0.223143 | ||||||||
\(205\) | 7.54521 | 0.526980 | ||||||||
\(206\) | 0.0710249 | 0.00494854 | ||||||||
\(207\) | 6.94960 | 0.483030 | ||||||||
\(208\) | −8.17987 | −0.567172 | ||||||||
\(209\) | 17.2822 | 1.19543 | ||||||||
\(210\) | 0.0866947 | 0.00598250 | ||||||||
\(211\) | 1.42893 | 0.0983719 | 0.0491859 | − | 0.998790i | \(-0.484337\pi\) | ||||
0.0491859 | + | 0.998790i | \(0.484337\pi\) | |||||||
\(212\) | 25.0714 | 1.72191 | ||||||||
\(213\) | 4.67775 | 0.320514 | ||||||||
\(214\) | −0.151235 | −0.0103382 | ||||||||
\(215\) | 13.0180 | 0.887823 | ||||||||
\(216\) | −0.193699 | −0.0131796 | ||||||||
\(217\) | −3.91483 | −0.265756 | ||||||||
\(218\) | 0.273324 | 0.0185119 | ||||||||
\(219\) | 10.2723 | 0.694137 | ||||||||
\(220\) | −12.0136 | −0.809954 | ||||||||
\(221\) | 3.27413 | 0.220242 | ||||||||
\(222\) | −0.333379 | −0.0223749 | ||||||||
\(223\) | −26.8665 | −1.79912 | −0.899559 | − | 0.436800i | \(-0.856112\pi\) | ||||
−0.899559 | + | 0.436800i | \(0.856112\pi\) | |||||||
\(224\) | −0.580529 | −0.0387882 | ||||||||
\(225\) | −1.79860 | −0.119906 | ||||||||
\(226\) | −0.308811 | −0.0205418 | ||||||||
\(227\) | −7.98868 | −0.530227 | −0.265114 | − | 0.964217i | \(-0.585409\pi\) | ||||
−0.265114 | + | 0.964217i | \(0.585409\pi\) | |||||||
\(228\) | 10.2716 | 0.680251 | ||||||||
\(229\) | 13.2290 | 0.874195 | 0.437097 | − | 0.899414i | \(-0.356006\pi\) | ||||
0.437097 | + | 0.899414i | \(0.356006\pi\) | |||||||
\(230\) | −0.602493 | −0.0397272 | ||||||||
\(231\) | −3.36110 | −0.221144 | ||||||||
\(232\) | 0.865116 | 0.0567977 | ||||||||
\(233\) | 21.9885 | 1.44051 | 0.720257 | − | 0.693707i | \(-0.244024\pi\) | ||||
0.720257 | + | 0.693707i | \(0.244024\pi\) | |||||||
\(234\) | 0.0994352 | 0.00650028 | ||||||||
\(235\) | 8.65410 | 0.564531 | ||||||||
\(236\) | −14.5805 | −0.949111 | ||||||||
\(237\) | −8.94904 | −0.581303 | ||||||||
\(238\) | 0.0773037 | 0.00501086 | ||||||||
\(239\) | 24.0805 | 1.55764 | 0.778818 | − | 0.627250i | \(-0.215820\pi\) | ||||
0.778818 | + | 0.627250i | \(0.215820\pi\) | |||||||
\(240\) | −7.13179 | −0.460355 | ||||||||
\(241\) | 15.8356 | 1.02006 | 0.510032 | − | 0.860156i | \(-0.329634\pi\) | ||||
0.510032 | + | 0.860156i | \(0.329634\pi\) | |||||||
\(242\) | −0.0143910 | −0.000925086 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −18.0798 | −1.15744 | ||||||||
\(245\) | 1.78925 | 0.114311 | ||||||||
\(246\) | 0.204326 | 0.0130273 | ||||||||
\(247\) | −10.5520 | −0.671407 | ||||||||
\(248\) | −0.758299 | −0.0481520 | ||||||||
\(249\) | 3.69192 | 0.233966 | ||||||||
\(250\) | 0.589402 | 0.0372771 | ||||||||
\(251\) | 4.43127 | 0.279699 | 0.139850 | − | 0.990173i | \(-0.455338\pi\) | ||||
0.139850 | + | 0.990173i | \(0.455338\pi\) | |||||||
\(252\) | −1.99765 | −0.125840 | ||||||||
\(253\) | 23.3583 | 1.46852 | ||||||||
\(254\) | −0.190546 | −0.0119559 | ||||||||
\(255\) | 2.85462 | 0.178763 | ||||||||
\(256\) | 15.8125 | 0.988282 | ||||||||
\(257\) | −26.4282 | −1.64855 | −0.824273 | − | 0.566193i | \(-0.808416\pi\) | ||||
−0.824273 | + | 0.566193i | \(0.808416\pi\) | |||||||
\(258\) | 0.352531 | 0.0219476 | ||||||||
\(259\) | −6.88044 | −0.427530 | ||||||||
\(260\) | 7.33513 | 0.454906 | ||||||||
\(261\) | 4.46629 | 0.276457 | ||||||||
\(262\) | −0.614836 | −0.0379847 | ||||||||
\(263\) | 19.5544 | 1.20578 | 0.602889 | − | 0.797825i | \(-0.294016\pi\) | ||||
0.602889 | + | 0.797825i | \(0.294016\pi\) | |||||||
\(264\) | −0.651042 | −0.0400689 | ||||||||
\(265\) | −22.4558 | −1.37945 | ||||||||
\(266\) | −0.249138 | −0.0152756 | ||||||||
\(267\) | −1.98084 | −0.121226 | ||||||||
\(268\) | 24.4729 | 1.49492 | ||||||||
\(269\) | 22.5742 | 1.37637 | 0.688186 | − | 0.725534i | \(-0.258407\pi\) | ||||
0.688186 | + | 0.725534i | \(0.258407\pi\) | |||||||
\(270\) | 0.0866947 | 0.00527607 | ||||||||
\(271\) | 19.5448 | 1.18726 | 0.593631 | − | 0.804737i | \(-0.297694\pi\) | ||||
0.593631 | + | 0.804737i | \(0.297694\pi\) | |||||||
\(272\) | −6.35926 | −0.385587 | ||||||||
\(273\) | 2.05219 | 0.124204 | ||||||||
\(274\) | −0.552598 | −0.0333836 | ||||||||
\(275\) | −6.04527 | −0.364543 | ||||||||
\(276\) | 13.8829 | 0.835651 | ||||||||
\(277\) | 15.9122 | 0.956069 | 0.478035 | − | 0.878341i | \(-0.341349\pi\) | ||||
0.478035 | + | 0.878341i | \(0.341349\pi\) | |||||||
\(278\) | −0.308240 | −0.0184870 | ||||||||
\(279\) | −3.91483 | −0.234375 | ||||||||
\(280\) | 0.346575 | 0.0207118 | ||||||||
\(281\) | −4.72334 | −0.281771 | −0.140886 | − | 0.990026i | \(-0.544995\pi\) | ||||
−0.140886 | + | 0.990026i | \(0.544995\pi\) | |||||||
\(282\) | 0.234355 | 0.0139556 | ||||||||
\(283\) | 1.09143 | 0.0648790 | 0.0324395 | − | 0.999474i | \(-0.489672\pi\) | ||||
0.0324395 | + | 0.999474i | \(0.489672\pi\) | |||||||
\(284\) | 9.34452 | 0.554496 | ||||||||
\(285\) | −9.19998 | −0.544960 | ||||||||
\(286\) | 0.334212 | 0.0197624 | ||||||||
\(287\) | 4.21697 | 0.248920 | ||||||||
\(288\) | −0.580529 | −0.0342080 | ||||||||
\(289\) | −14.4546 | −0.850271 | ||||||||
\(290\) | −0.387204 | −0.0227374 | ||||||||
\(291\) | −2.08239 | −0.122072 | ||||||||
\(292\) | 20.5205 | 1.20087 | ||||||||
\(293\) | −30.6330 | −1.78960 | −0.894799 | − | 0.446468i | \(-0.852682\pi\) | ||||
−0.894799 | + | 0.446468i | \(0.852682\pi\) | |||||||
\(294\) | 0.0484532 | 0.00282585 | ||||||||
\(295\) | 13.0594 | 0.760347 | ||||||||
\(296\) | −1.33273 | −0.0774636 | ||||||||
\(297\) | −3.36110 | −0.195031 | ||||||||
\(298\) | −0.752522 | −0.0435925 | ||||||||
\(299\) | −14.2619 | −0.824787 | ||||||||
\(300\) | −3.59297 | −0.207440 | ||||||||
\(301\) | 7.27571 | 0.419365 | ||||||||
\(302\) | 0.797943 | 0.0459164 | ||||||||
\(303\) | −7.02738 | −0.403713 | ||||||||
\(304\) | 20.4949 | 1.17546 | ||||||||
\(305\) | 16.1936 | 0.927243 | ||||||||
\(306\) | 0.0773037 | 0.00441916 | ||||||||
\(307\) | 21.5884 | 1.23211 | 0.616057 | − | 0.787701i | \(-0.288729\pi\) | ||||
0.616057 | + | 0.787701i | \(0.288729\pi\) | |||||||
\(308\) | −6.71431 | −0.382584 | ||||||||
\(309\) | 1.46585 | 0.0833891 | ||||||||
\(310\) | 0.339395 | 0.0192763 | ||||||||
\(311\) | −11.3055 | −0.641076 | −0.320538 | − | 0.947236i | \(-0.603864\pi\) | ||||
−0.320538 | + | 0.947236i | \(0.603864\pi\) | |||||||
\(312\) | 0.397507 | 0.0225044 | ||||||||
\(313\) | 27.9643 | 1.58063 | 0.790317 | − | 0.612698i | \(-0.209916\pi\) | ||||
0.790317 | + | 0.612698i | \(0.209916\pi\) | |||||||
\(314\) | 0.284569 | 0.0160592 | ||||||||
\(315\) | 1.78925 | 0.100813 | ||||||||
\(316\) | −17.8771 | −1.00566 | ||||||||
\(317\) | −25.2148 | −1.41620 | −0.708102 | − | 0.706110i | \(-0.750448\pi\) | ||||
−0.708102 | + | 0.706110i | \(0.750448\pi\) | |||||||
\(318\) | −0.608109 | −0.0341011 | ||||||||
\(319\) | 15.0117 | 0.840492 | ||||||||
\(320\) | −14.2133 | −0.794545 | ||||||||
\(321\) | −3.12126 | −0.174212 | ||||||||
\(322\) | −0.336730 | −0.0187652 | ||||||||
\(323\) | −8.20342 | −0.456450 | ||||||||
\(324\) | −1.99765 | −0.110981 | ||||||||
\(325\) | 3.69106 | 0.204743 | ||||||||
\(326\) | 0.252934 | 0.0140087 | ||||||||
\(327\) | 5.64099 | 0.311948 | ||||||||
\(328\) | 0.816824 | 0.0451015 | ||||||||
\(329\) | 4.83673 | 0.266657 | ||||||||
\(330\) | 0.291390 | 0.0160405 | ||||||||
\(331\) | 1.93245 | 0.106217 | 0.0531086 | − | 0.998589i | \(-0.483087\pi\) | ||||
0.0531086 | + | 0.998589i | \(0.483087\pi\) | |||||||
\(332\) | 7.37516 | 0.404765 | ||||||||
\(333\) | −6.88044 | −0.377046 | ||||||||
\(334\) | −0.477581 | −0.0261321 | ||||||||
\(335\) | −21.9198 | −1.19761 | ||||||||
\(336\) | −3.98592 | −0.217450 | ||||||||
\(337\) | 23.3954 | 1.27443 | 0.637215 | − | 0.770686i | \(-0.280086\pi\) | ||||
0.637215 | + | 0.770686i | \(0.280086\pi\) | |||||||
\(338\) | 0.425832 | 0.0231622 | ||||||||
\(339\) | −6.37340 | −0.346155 | ||||||||
\(340\) | 5.70254 | 0.309263 | ||||||||
\(341\) | −13.1581 | −0.712553 | ||||||||
\(342\) | −0.249138 | −0.0134718 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 1.40930 | 0.0759843 | ||||||||
\(345\) | −12.4345 | −0.669453 | ||||||||
\(346\) | −0.246132 | −0.0132321 | ||||||||
\(347\) | −3.03197 | −0.162765 | −0.0813824 | − | 0.996683i | \(-0.525933\pi\) | ||||
−0.0813824 | + | 0.996683i | \(0.525933\pi\) | |||||||
\(348\) | 8.92210 | 0.478275 | ||||||||
\(349\) | 17.7162 | 0.948325 | 0.474163 | − | 0.880437i | \(-0.342751\pi\) | ||||
0.474163 | + | 0.880437i | \(0.342751\pi\) | |||||||
\(350\) | 0.0871477 | 0.00465824 | ||||||||
\(351\) | 2.05219 | 0.109538 | ||||||||
\(352\) | −1.95122 | −0.104000 | ||||||||
\(353\) | 28.7717 | 1.53136 | 0.765681 | − | 0.643221i | \(-0.222402\pi\) | ||||
0.765681 | + | 0.643221i | \(0.222402\pi\) | |||||||
\(354\) | 0.353651 | 0.0187964 | ||||||||
\(355\) | −8.36965 | −0.444215 | ||||||||
\(356\) | −3.95704 | −0.209723 | ||||||||
\(357\) | 1.59543 | 0.0844391 | ||||||||
\(358\) | 0.325125 | 0.0171834 | ||||||||
\(359\) | −10.1813 | −0.537351 | −0.268675 | − | 0.963231i | \(-0.586586\pi\) | ||||
−0.268675 | + | 0.963231i | \(0.586586\pi\) | |||||||
\(360\) | 0.346575 | 0.0182661 | ||||||||
\(361\) | 7.43832 | 0.391490 | ||||||||
\(362\) | −0.742194 | −0.0390089 | ||||||||
\(363\) | −0.297008 | −0.0155889 | ||||||||
\(364\) | 4.09956 | 0.214876 | ||||||||
\(365\) | −18.3797 | −0.962036 | ||||||||
\(366\) | 0.438526 | 0.0229221 | ||||||||
\(367\) | 7.63791 | 0.398696 | 0.199348 | − | 0.979929i | \(-0.436118\pi\) | ||||
0.199348 | + | 0.979929i | \(0.436118\pi\) | |||||||
\(368\) | 27.7005 | 1.44399 | ||||||||
\(369\) | 4.21697 | 0.219527 | ||||||||
\(370\) | 0.596498 | 0.0310104 | ||||||||
\(371\) | −12.5504 | −0.651587 | ||||||||
\(372\) | −7.82047 | −0.405472 | ||||||||
\(373\) | −24.9217 | −1.29040 | −0.645199 | − | 0.764014i | \(-0.723226\pi\) | ||||
−0.645199 | + | 0.764014i | \(0.723226\pi\) | |||||||
\(374\) | 0.259826 | 0.0134353 | ||||||||
\(375\) | 12.1644 | 0.628165 | ||||||||
\(376\) | 0.936870 | 0.0483154 | ||||||||
\(377\) | −9.16568 | −0.472057 | ||||||||
\(378\) | 0.0484532 | 0.00249216 | ||||||||
\(379\) | 25.5207 | 1.31091 | 0.655456 | − | 0.755234i | \(-0.272477\pi\) | ||||
0.655456 | + | 0.755234i | \(0.272477\pi\) | |||||||
\(380\) | −18.3784 | −0.942791 | ||||||||
\(381\) | −3.93257 | −0.201472 | ||||||||
\(382\) | 0.0484532 | 0.00247908 | ||||||||
\(383\) | −35.9304 | −1.83596 | −0.917978 | − | 0.396631i | \(-0.870179\pi\) | ||||
−0.917978 | + | 0.396631i | \(0.870179\pi\) | |||||||
\(384\) | −1.54596 | −0.0788917 | ||||||||
\(385\) | 6.01384 | 0.306494 | ||||||||
\(386\) | −1.20821 | −0.0614964 | ||||||||
\(387\) | 7.27571 | 0.369845 | ||||||||
\(388\) | −4.15990 | −0.211187 | ||||||||
\(389\) | 16.2508 | 0.823950 | 0.411975 | − | 0.911195i | \(-0.364839\pi\) | ||||
0.411975 | + | 0.911195i | \(0.364839\pi\) | |||||||
\(390\) | −0.177914 | −0.00900903 | ||||||||
\(391\) | −11.0876 | −0.560724 | ||||||||
\(392\) | 0.193699 | 0.00978328 | ||||||||
\(393\) | −12.6893 | −0.640090 | ||||||||
\(394\) | −0.443508 | −0.0223436 | ||||||||
\(395\) | 16.0120 | 0.805654 | ||||||||
\(396\) | −6.71431 | −0.337407 | ||||||||
\(397\) | 27.0683 | 1.35852 | 0.679259 | − | 0.733898i | \(-0.262301\pi\) | ||||
0.679259 | + | 0.733898i | \(0.262301\pi\) | |||||||
\(398\) | −0.723798 | −0.0362807 | ||||||||
\(399\) | −5.14182 | −0.257413 | ||||||||
\(400\) | −7.16906 | −0.358453 | ||||||||
\(401\) | −11.8162 | −0.590071 | −0.295035 | − | 0.955486i | \(-0.595331\pi\) | ||||
−0.295035 | + | 0.955486i | \(0.595331\pi\) | |||||||
\(402\) | −0.593593 | −0.0296057 | ||||||||
\(403\) | 8.03398 | 0.400201 | ||||||||
\(404\) | −14.0383 | −0.698430 | ||||||||
\(405\) | 1.78925 | 0.0889084 | ||||||||
\(406\) | −0.216406 | −0.0107401 | ||||||||
\(407\) | −23.1259 | −1.14631 | ||||||||
\(408\) | 0.309033 | 0.0152994 | ||||||||
\(409\) | 7.28958 | 0.360446 | 0.180223 | − | 0.983626i | \(-0.442318\pi\) | ||||
0.180223 | + | 0.983626i | \(0.442318\pi\) | |||||||
\(410\) | −0.365589 | −0.0180552 | ||||||||
\(411\) | −11.4048 | −0.562556 | ||||||||
\(412\) | 2.92825 | 0.144265 | ||||||||
\(413\) | 7.29882 | 0.359152 | ||||||||
\(414\) | −0.336730 | −0.0165494 | ||||||||
\(415\) | −6.60575 | −0.324263 | ||||||||
\(416\) | 1.19136 | 0.0584110 | ||||||||
\(417\) | −6.36160 | −0.311529 | ||||||||
\(418\) | −0.837377 | −0.0409575 | ||||||||
\(419\) | −7.22568 | −0.352997 | −0.176499 | − | 0.984301i | \(-0.556477\pi\) | ||||
−0.176499 | + | 0.984301i | \(0.556477\pi\) | |||||||
\(420\) | 3.57429 | 0.174408 | ||||||||
\(421\) | −5.07452 | −0.247317 | −0.123658 | − | 0.992325i | \(-0.539463\pi\) | ||||
−0.123658 | + | 0.992325i | \(0.539463\pi\) | |||||||
\(422\) | −0.0692364 | −0.00337038 | ||||||||
\(423\) | 4.83673 | 0.235170 | ||||||||
\(424\) | −2.43101 | −0.118060 | ||||||||
\(425\) | 2.86954 | 0.139193 | ||||||||
\(426\) | −0.226652 | −0.0109813 | ||||||||
\(427\) | 9.05051 | 0.437985 | ||||||||
\(428\) | −6.23520 | −0.301390 | ||||||||
\(429\) | 6.89762 | 0.333020 | ||||||||
\(430\) | −0.630766 | −0.0304182 | ||||||||
\(431\) | −7.33911 | −0.353513 | −0.176756 | − | 0.984255i | \(-0.556560\pi\) | ||||
−0.176756 | + | 0.984255i | \(0.556560\pi\) | |||||||
\(432\) | −3.98592 | −0.191773 | ||||||||
\(433\) | 5.68241 | 0.273079 | 0.136540 | − | 0.990635i | \(-0.456402\pi\) | ||||
0.136540 | + | 0.990635i | \(0.456402\pi\) | |||||||
\(434\) | 0.189686 | 0.00910522 | ||||||||
\(435\) | −7.99130 | −0.383153 | ||||||||
\(436\) | 11.2687 | 0.539675 | ||||||||
\(437\) | 35.7336 | 1.70937 | ||||||||
\(438\) | −0.497726 | −0.0237822 | ||||||||
\(439\) | 7.65415 | 0.365313 | 0.182656 | − | 0.983177i | \(-0.441530\pi\) | ||||
0.182656 | + | 0.983177i | \(0.441530\pi\) | |||||||
\(440\) | 1.16488 | 0.0555332 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −0.158642 | −0.00754583 | ||||||||
\(443\) | −25.3486 | −1.20435 | −0.602173 | − | 0.798365i | \(-0.705698\pi\) | ||||
−0.602173 | + | 0.798365i | \(0.705698\pi\) | |||||||
\(444\) | −13.7447 | −0.652296 | ||||||||
\(445\) | 3.54422 | 0.168012 | ||||||||
\(446\) | 1.30177 | 0.0616406 | ||||||||
\(447\) | −15.5309 | −0.734587 | ||||||||
\(448\) | −7.94371 | −0.375305 | ||||||||
\(449\) | −26.3344 | −1.24280 | −0.621399 | − | 0.783494i | \(-0.713436\pi\) | ||||
−0.621399 | + | 0.783494i | \(0.713436\pi\) | |||||||
\(450\) | 0.0871477 | 0.00410818 | ||||||||
\(451\) | 14.1737 | 0.667412 | ||||||||
\(452\) | −12.7318 | −0.598855 | ||||||||
\(453\) | 16.4683 | 0.773749 | ||||||||
\(454\) | 0.387077 | 0.0181664 | ||||||||
\(455\) | −3.67188 | −0.172140 | ||||||||
\(456\) | −0.995966 | −0.0466404 | ||||||||
\(457\) | −21.8870 | −1.02383 | −0.511915 | − | 0.859036i | \(-0.671064\pi\) | ||||
−0.511915 | + | 0.859036i | \(0.671064\pi\) | |||||||
\(458\) | −0.640986 | −0.0299513 | ||||||||
\(459\) | 1.59543 | 0.0744683 | ||||||||
\(460\) | −24.8399 | −1.15817 | ||||||||
\(461\) | 2.02297 | 0.0942193 | 0.0471097 | − | 0.998890i | \(-0.484999\pi\) | ||||
0.0471097 | + | 0.998890i | \(0.484999\pi\) | |||||||
\(462\) | 0.162856 | 0.00757675 | ||||||||
\(463\) | 29.8958 | 1.38937 | 0.694687 | − | 0.719312i | \(-0.255543\pi\) | ||||
0.694687 | + | 0.719312i | \(0.255543\pi\) | |||||||
\(464\) | 17.8023 | 0.826450 | ||||||||
\(465\) | 7.00460 | 0.324830 | ||||||||
\(466\) | −1.06541 | −0.0493543 | ||||||||
\(467\) | −29.7906 | −1.37854 | −0.689272 | − | 0.724503i | \(-0.742069\pi\) | ||||
−0.689272 | + | 0.724503i | \(0.742069\pi\) | |||||||
\(468\) | 4.09956 | 0.189502 | ||||||||
\(469\) | −12.2508 | −0.565691 | ||||||||
\(470\) | −0.419319 | −0.0193417 | ||||||||
\(471\) | 5.87308 | 0.270617 | ||||||||
\(472\) | 1.41378 | 0.0650743 | ||||||||
\(473\) | 24.4544 | 1.12441 | ||||||||
\(474\) | 0.433610 | 0.0199164 | ||||||||
\(475\) | −9.24806 | −0.424330 | ||||||||
\(476\) | 3.18712 | 0.146081 | ||||||||
\(477\) | −12.5504 | −0.574645 | ||||||||
\(478\) | −1.16678 | −0.0533671 | ||||||||
\(479\) | −28.7260 | −1.31252 | −0.656262 | − | 0.754533i | \(-0.727863\pi\) | ||||
−0.656262 | + | 0.754533i | \(0.727863\pi\) | |||||||
\(480\) | 1.03871 | 0.0474104 | ||||||||
\(481\) | 14.1200 | 0.643815 | ||||||||
\(482\) | −0.767287 | −0.0349490 | ||||||||
\(483\) | −6.94960 | −0.316218 | ||||||||
\(484\) | −0.593318 | −0.0269690 | ||||||||
\(485\) | 3.72592 | 0.169185 | ||||||||
\(486\) | 0.0484532 | 0.00219788 | ||||||||
\(487\) | 26.6979 | 1.20980 | 0.604898 | − | 0.796303i | \(-0.293214\pi\) | ||||
0.604898 | + | 0.796303i | \(0.293214\pi\) | |||||||
\(488\) | 1.75308 | 0.0793580 | ||||||||
\(489\) | 5.22016 | 0.236064 | ||||||||
\(490\) | −0.0866947 | −0.00391647 | ||||||||
\(491\) | −5.42719 | −0.244926 | −0.122463 | − | 0.992473i | \(-0.539079\pi\) | ||||
−0.122463 | + | 0.992473i | \(0.539079\pi\) | |||||||
\(492\) | 8.42405 | 0.379785 | ||||||||
\(493\) | −7.12566 | −0.320924 | ||||||||
\(494\) | 0.511278 | 0.0230035 | ||||||||
\(495\) | 6.01384 | 0.270302 | ||||||||
\(496\) | −15.6042 | −0.700649 | ||||||||
\(497\) | −4.67775 | −0.209826 | ||||||||
\(498\) | −0.178885 | −0.00801603 | ||||||||
\(499\) | −12.4354 | −0.556684 | −0.278342 | − | 0.960482i | \(-0.589785\pi\) | ||||
−0.278342 | + | 0.960482i | \(0.589785\pi\) | |||||||
\(500\) | 24.3002 | 1.08674 | ||||||||
\(501\) | −9.85654 | −0.440358 | ||||||||
\(502\) | −0.214709 | −0.00958294 | ||||||||
\(503\) | 20.4994 | 0.914021 | 0.457010 | − | 0.889461i | \(-0.348920\pi\) | ||||
0.457010 | + | 0.889461i | \(0.348920\pi\) | |||||||
\(504\) | 0.193699 | 0.00862804 | ||||||||
\(505\) | 12.5737 | 0.559523 | ||||||||
\(506\) | −1.13178 | −0.0503140 | ||||||||
\(507\) | 8.78851 | 0.390312 | ||||||||
\(508\) | −7.85591 | −0.348550 | ||||||||
\(509\) | 42.4578 | 1.88191 | 0.940955 | − | 0.338531i | \(-0.109930\pi\) | ||||
0.940955 | + | 0.338531i | \(0.109930\pi\) | |||||||
\(510\) | −0.138315 | −0.00612471 | ||||||||
\(511\) | −10.2723 | −0.454420 | ||||||||
\(512\) | −3.85808 | −0.170505 | ||||||||
\(513\) | −5.14182 | −0.227017 | ||||||||
\(514\) | 1.28053 | 0.0564818 | ||||||||
\(515\) | −2.62276 | −0.115573 | ||||||||
\(516\) | 14.5343 | 0.639839 | ||||||||
\(517\) | 16.2567 | 0.714971 | ||||||||
\(518\) | 0.333379 | 0.0146478 | ||||||||
\(519\) | −5.07979 | −0.222978 | ||||||||
\(520\) | −0.711239 | −0.0311899 | ||||||||
\(521\) | −5.94373 | −0.260400 | −0.130200 | − | 0.991488i | \(-0.541562\pi\) | ||||
−0.130200 | + | 0.991488i | \(0.541562\pi\) | |||||||
\(522\) | −0.216406 | −0.00947184 | ||||||||
\(523\) | −10.7362 | −0.469460 | −0.234730 | − | 0.972061i | \(-0.575421\pi\) | ||||
−0.234730 | + | 0.972061i | \(0.575421\pi\) | |||||||
\(524\) | −25.3488 | −1.10737 | ||||||||
\(525\) | 1.79860 | 0.0784972 | ||||||||
\(526\) | −0.947475 | −0.0413119 | ||||||||
\(527\) | 6.24584 | 0.272073 | ||||||||
\(528\) | −13.3971 | −0.583033 | ||||||||
\(529\) | 25.2969 | 1.09987 | ||||||||
\(530\) | 1.08806 | 0.0472622 | ||||||||
\(531\) | 7.29882 | 0.316742 | ||||||||
\(532\) | −10.2716 | −0.445329 | ||||||||
\(533\) | −8.65403 | −0.374848 | ||||||||
\(534\) | 0.0959783 | 0.00415339 | ||||||||
\(535\) | 5.58471 | 0.241448 | ||||||||
\(536\) | −2.37298 | −0.102497 | ||||||||
\(537\) | 6.71008 | 0.289561 | ||||||||
\(538\) | −1.09379 | −0.0471567 | ||||||||
\(539\) | 3.36110 | 0.144773 | ||||||||
\(540\) | 3.57429 | 0.153813 | ||||||||
\(541\) | 2.83501 | 0.121887 | 0.0609433 | − | 0.998141i | \(-0.480589\pi\) | ||||
0.0609433 | + | 0.998141i | \(0.480589\pi\) | |||||||
\(542\) | −0.947008 | −0.0406775 | ||||||||
\(543\) | −15.3178 | −0.657348 | ||||||||
\(544\) | 0.926193 | 0.0397102 | ||||||||
\(545\) | −10.0931 | −0.432342 | ||||||||
\(546\) | −0.0994352 | −0.00425543 | ||||||||
\(547\) | −37.5183 | −1.60416 | −0.802082 | − | 0.597214i | \(-0.796274\pi\) | ||||
−0.802082 | + | 0.597214i | \(0.796274\pi\) | |||||||
\(548\) | −22.7828 | −0.973231 | ||||||||
\(549\) | 9.05051 | 0.386267 | ||||||||
\(550\) | 0.292912 | 0.0124898 | ||||||||
\(551\) | 22.9649 | 0.978336 | ||||||||
\(552\) | −1.34613 | −0.0572951 | ||||||||
\(553\) | 8.94904 | 0.380552 | ||||||||
\(554\) | −0.770995 | −0.0327565 | ||||||||
\(555\) | 12.3108 | 0.522564 | ||||||||
\(556\) | −12.7083 | −0.538950 | ||||||||
\(557\) | −25.4342 | −1.07768 | −0.538840 | − | 0.842408i | \(-0.681137\pi\) | ||||
−0.538840 | + | 0.842408i | \(0.681137\pi\) | |||||||
\(558\) | 0.189686 | 0.00803005 | ||||||||
\(559\) | −14.9311 | −0.631520 | ||||||||
\(560\) | 7.13179 | 0.301373 | ||||||||
\(561\) | 5.36240 | 0.226401 | ||||||||
\(562\) | 0.228861 | 0.00965392 | ||||||||
\(563\) | 45.1734 | 1.90383 | 0.951916 | − | 0.306359i | \(-0.0991109\pi\) | ||||
0.951916 | + | 0.306359i | \(0.0991109\pi\) | |||||||
\(564\) | 9.66210 | 0.406848 | ||||||||
\(565\) | 11.4036 | 0.479752 | ||||||||
\(566\) | −0.0528834 | −0.00222286 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −0.906076 | −0.0380181 | ||||||||
\(569\) | 10.4488 | 0.438036 | 0.219018 | − | 0.975721i | \(-0.429715\pi\) | ||||
0.219018 | + | 0.975721i | \(0.429715\pi\) | |||||||
\(570\) | 0.445769 | 0.0186712 | ||||||||
\(571\) | −45.4229 | −1.90089 | −0.950445 | − | 0.310891i | \(-0.899372\pi\) | ||||
−0.950445 | + | 0.310891i | \(0.899372\pi\) | |||||||
\(572\) | 13.7791 | 0.576131 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | −0.204326 | −0.00852840 | ||||||||
\(575\) | −12.4995 | −0.521266 | ||||||||
\(576\) | −7.94371 | −0.330988 | ||||||||
\(577\) | −34.1089 | −1.41997 | −0.709986 | − | 0.704216i | \(-0.751299\pi\) | ||||
−0.709986 | + | 0.704216i | \(0.751299\pi\) | |||||||
\(578\) | 0.700372 | 0.0291316 | ||||||||
\(579\) | −24.9357 | −1.03629 | ||||||||
\(580\) | −15.9638 | −0.662862 | ||||||||
\(581\) | −3.69192 | −0.153166 | ||||||||
\(582\) | 0.100899 | 0.00418238 | ||||||||
\(583\) | −42.1833 | −1.74705 | ||||||||
\(584\) | −1.98973 | −0.0823358 | ||||||||
\(585\) | −3.67188 | −0.151813 | ||||||||
\(586\) | 1.48427 | 0.0613145 | ||||||||
\(587\) | 0.697154 | 0.0287746 | 0.0143873 | − | 0.999896i | \(-0.495420\pi\) | ||||
0.0143873 | + | 0.999896i | \(0.495420\pi\) | |||||||
\(588\) | 1.99765 | 0.0823818 | ||||||||
\(589\) | −20.1294 | −0.829415 | ||||||||
\(590\) | −0.632770 | −0.0260507 | ||||||||
\(591\) | −9.15332 | −0.376517 | ||||||||
\(592\) | −27.4249 | −1.12716 | ||||||||
\(593\) | 15.3082 | 0.628632 | 0.314316 | − | 0.949318i | \(-0.398225\pi\) | ||||
0.314316 | + | 0.949318i | \(0.398225\pi\) | |||||||
\(594\) | 0.162856 | 0.00668207 | ||||||||
\(595\) | −2.85462 | −0.117028 | ||||||||
\(596\) | −31.0254 | −1.27085 | ||||||||
\(597\) | −14.9381 | −0.611375 | ||||||||
\(598\) | 0.691035 | 0.0282585 | ||||||||
\(599\) | −28.1956 | −1.15204 | −0.576021 | − | 0.817435i | \(-0.695396\pi\) | ||||
−0.576021 | + | 0.817435i | \(0.695396\pi\) | |||||||
\(600\) | 0.348386 | 0.0142228 | ||||||||
\(601\) | −17.7830 | −0.725383 | −0.362692 | − | 0.931909i | \(-0.618142\pi\) | ||||
−0.362692 | + | 0.931909i | \(0.618142\pi\) | |||||||
\(602\) | −0.352531 | −0.0143681 | ||||||||
\(603\) | −12.2508 | −0.498893 | ||||||||
\(604\) | 32.8980 | 1.33860 | ||||||||
\(605\) | 0.531420 | 0.0216053 | ||||||||
\(606\) | 0.340499 | 0.0138318 | ||||||||
\(607\) | 29.0832 | 1.18045 | 0.590226 | − | 0.807238i | \(-0.299039\pi\) | ||||
0.590226 | + | 0.807238i | \(0.299039\pi\) | |||||||
\(608\) | −2.98497 | −0.121057 | ||||||||
\(609\) | −4.46629 | −0.180983 | ||||||||
\(610\) | −0.784632 | −0.0317688 | ||||||||
\(611\) | −9.92589 | −0.401559 | ||||||||
\(612\) | 3.18712 | 0.128832 | ||||||||
\(613\) | 24.4517 | 0.987595 | 0.493797 | − | 0.869577i | \(-0.335608\pi\) | ||||
0.493797 | + | 0.869577i | \(0.335608\pi\) | |||||||
\(614\) | −1.04603 | −0.0422142 | ||||||||
\(615\) | −7.54521 | −0.304252 | ||||||||
\(616\) | 0.651042 | 0.0262312 | ||||||||
\(617\) | −42.6450 | −1.71683 | −0.858413 | − | 0.512960i | \(-0.828549\pi\) | ||||
−0.858413 | + | 0.512960i | \(0.828549\pi\) | |||||||
\(618\) | −0.0710249 | −0.00285704 | ||||||||
\(619\) | 12.0403 | 0.483941 | 0.241971 | − | 0.970284i | \(-0.422206\pi\) | ||||
0.241971 | + | 0.970284i | \(0.422206\pi\) | |||||||
\(620\) | 13.9927 | 0.561962 | ||||||||
\(621\) | −6.94960 | −0.278878 | ||||||||
\(622\) | 0.547787 | 0.0219643 | ||||||||
\(623\) | 1.98084 | 0.0793609 | ||||||||
\(624\) | 8.17987 | 0.327457 | ||||||||
\(625\) | −12.7721 | −0.510883 | ||||||||
\(626\) | −1.35496 | −0.0541550 | ||||||||
\(627\) | −17.2822 | −0.690184 | ||||||||
\(628\) | 11.7324 | 0.468172 | ||||||||
\(629\) | 10.9773 | 0.437692 | ||||||||
\(630\) | −0.0866947 | −0.00345400 | ||||||||
\(631\) | 10.4861 | 0.417444 | 0.208722 | − | 0.977975i | \(-0.433070\pi\) | ||||
0.208722 | + | 0.977975i | \(0.433070\pi\) | |||||||
\(632\) | 1.73342 | 0.0689518 | ||||||||
\(633\) | −1.42893 | −0.0567950 | ||||||||
\(634\) | 1.22174 | 0.0485214 | ||||||||
\(635\) | 7.03634 | 0.279229 | ||||||||
\(636\) | −25.0714 | −0.994147 | ||||||||
\(637\) | −2.05219 | −0.0813108 | ||||||||
\(638\) | −0.727363 | −0.0287966 | ||||||||
\(639\) | −4.67775 | −0.185049 | ||||||||
\(640\) | 2.76610 | 0.109340 | ||||||||
\(641\) | −8.60640 | −0.339932 | −0.169966 | − | 0.985450i | \(-0.554366\pi\) | ||||
−0.169966 | + | 0.985450i | \(0.554366\pi\) | |||||||
\(642\) | 0.151235 | 0.00596877 | ||||||||
\(643\) | −33.6841 | −1.32837 | −0.664186 | − | 0.747567i | \(-0.731222\pi\) | ||||
−0.664186 | + | 0.747567i | \(0.731222\pi\) | |||||||
\(644\) | −13.8829 | −0.547062 | ||||||||
\(645\) | −13.0180 | −0.512585 | ||||||||
\(646\) | 0.397482 | 0.0156387 | ||||||||
\(647\) | −40.4104 | −1.58870 | −0.794349 | − | 0.607462i | \(-0.792188\pi\) | ||||
−0.794349 | + | 0.607462i | \(0.792188\pi\) | |||||||
\(648\) | 0.193699 | 0.00760922 | ||||||||
\(649\) | 24.5321 | 0.962969 | ||||||||
\(650\) | −0.178844 | −0.00701483 | ||||||||
\(651\) | 3.91483 | 0.153434 | ||||||||
\(652\) | 10.4281 | 0.408395 | ||||||||
\(653\) | −13.2584 | −0.518842 | −0.259421 | − | 0.965764i | \(-0.583532\pi\) | ||||
−0.259421 | + | 0.965764i | \(0.583532\pi\) | |||||||
\(654\) | −0.273324 | −0.0106878 | ||||||||
\(655\) | 22.7043 | 0.887129 | ||||||||
\(656\) | 16.8085 | 0.656262 | ||||||||
\(657\) | −10.2723 | −0.400760 | ||||||||
\(658\) | −0.234355 | −0.00913611 | ||||||||
\(659\) | 8.43096 | 0.328423 | 0.164212 | − | 0.986425i | \(-0.447492\pi\) | ||||
0.164212 | + | 0.986425i | \(0.447492\pi\) | |||||||
\(660\) | 12.0136 | 0.467627 | ||||||||
\(661\) | −29.5292 | −1.14855 | −0.574276 | − | 0.818662i | \(-0.694716\pi\) | ||||
−0.574276 | + | 0.818662i | \(0.694716\pi\) | |||||||
\(662\) | −0.0936335 | −0.00363917 | ||||||||
\(663\) | −3.27413 | −0.127157 | ||||||||
\(664\) | −0.715121 | −0.0277521 | ||||||||
\(665\) | 9.19998 | 0.356760 | ||||||||
\(666\) | 0.333379 | 0.0129182 | ||||||||
\(667\) | 31.0389 | 1.20183 | ||||||||
\(668\) | −19.6899 | −0.761827 | ||||||||
\(669\) | 26.8665 | 1.03872 | ||||||||
\(670\) | 1.06208 | 0.0410319 | ||||||||
\(671\) | 30.4197 | 1.17434 | ||||||||
\(672\) | 0.580529 | 0.0223944 | ||||||||
\(673\) | 37.0666 | 1.42881 | 0.714406 | − | 0.699732i | \(-0.246697\pi\) | ||||
0.714406 | + | 0.699732i | \(0.246697\pi\) | |||||||
\(674\) | −1.13358 | −0.0436640 | ||||||||
\(675\) | 1.79860 | 0.0692280 | ||||||||
\(676\) | 17.5564 | 0.675246 | ||||||||
\(677\) | −24.9038 | −0.957130 | −0.478565 | − | 0.878052i | \(-0.658843\pi\) | ||||
−0.478565 | + | 0.878052i | \(0.658843\pi\) | |||||||
\(678\) | 0.308811 | 0.0118598 | ||||||||
\(679\) | 2.08239 | 0.0799149 | ||||||||
\(680\) | −0.552937 | −0.0212042 | ||||||||
\(681\) | 7.98868 | 0.306127 | ||||||||
\(682\) | 0.637554 | 0.0244132 | ||||||||
\(683\) | 3.07880 | 0.117807 | 0.0589034 | − | 0.998264i | \(-0.481240\pi\) | ||||
0.0589034 | + | 0.998264i | \(0.481240\pi\) | |||||||
\(684\) | −10.2716 | −0.392743 | ||||||||
\(685\) | 20.4059 | 0.779671 | ||||||||
\(686\) | −0.0484532 | −0.00184995 | ||||||||
\(687\) | −13.2290 | −0.504717 | ||||||||
\(688\) | 29.0004 | 1.10563 | ||||||||
\(689\) | 25.7559 | 0.981222 | ||||||||
\(690\) | 0.602493 | 0.0229365 | ||||||||
\(691\) | 14.6114 | 0.555844 | 0.277922 | − | 0.960604i | \(-0.410354\pi\) | ||||
0.277922 | + | 0.960604i | \(0.410354\pi\) | |||||||
\(692\) | −10.1476 | −0.385756 | ||||||||
\(693\) | 3.36110 | 0.127678 | ||||||||
\(694\) | 0.146909 | 0.00557658 | ||||||||
\(695\) | 11.3825 | 0.431762 | ||||||||
\(696\) | −0.865116 | −0.0327922 | ||||||||
\(697\) | −6.72789 | −0.254837 | ||||||||
\(698\) | −0.858405 | −0.0324911 | ||||||||
\(699\) | −21.9885 | −0.831681 | ||||||||
\(700\) | 3.59297 | 0.135802 | ||||||||
\(701\) | −35.4543 | −1.33909 | −0.669545 | − | 0.742772i | \(-0.733511\pi\) | ||||
−0.669545 | + | 0.742772i | \(0.733511\pi\) | |||||||
\(702\) | −0.0994352 | −0.00375294 | ||||||||
\(703\) | −35.3780 | −1.33431 | ||||||||
\(704\) | −26.6996 | −1.00628 | ||||||||
\(705\) | −8.65410 | −0.325932 | ||||||||
\(706\) | −1.39408 | −0.0524669 | ||||||||
\(707\) | 7.02738 | 0.264292 | ||||||||
\(708\) | 14.5805 | 0.547969 | ||||||||
\(709\) | −4.75894 | −0.178726 | −0.0893629 | − | 0.995999i | \(-0.528483\pi\) | ||||
−0.0893629 | + | 0.995999i | \(0.528483\pi\) | |||||||
\(710\) | 0.405537 | 0.0152195 | ||||||||
\(711\) | 8.94904 | 0.335615 | ||||||||
\(712\) | 0.383688 | 0.0143793 | ||||||||
\(713\) | −27.2065 | −1.01889 | ||||||||
\(714\) | −0.0773037 | −0.00289302 | ||||||||
\(715\) | −12.3415 | −0.461548 | ||||||||
\(716\) | 13.4044 | 0.500946 | ||||||||
\(717\) | −24.0805 | −0.899301 | ||||||||
\(718\) | 0.493319 | 0.0184105 | ||||||||
\(719\) | −4.12971 | −0.154012 | −0.0770061 | − | 0.997031i | \(-0.524536\pi\) | ||||
−0.0770061 | + | 0.997031i | \(0.524536\pi\) | |||||||
\(720\) | 7.13179 | 0.265786 | ||||||||
\(721\) | −1.46585 | −0.0545910 | ||||||||
\(722\) | −0.360410 | −0.0134131 | ||||||||
\(723\) | −15.8356 | −0.588934 | ||||||||
\(724\) | −30.5995 | −1.13722 | ||||||||
\(725\) | −8.03306 | −0.298340 | ||||||||
\(726\) | 0.0143910 | 0.000534099 0 | ||||||||
\(727\) | −14.8186 | −0.549590 | −0.274795 | − | 0.961503i | \(-0.588610\pi\) | ||||
−0.274795 | + | 0.961503i | \(0.588610\pi\) | |||||||
\(728\) | −0.397507 | −0.0147326 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.890554 | 0.0329609 | ||||||||
\(731\) | −11.6079 | −0.429333 | ||||||||
\(732\) | 18.0798 | 0.668248 | ||||||||
\(733\) | 37.2268 | 1.37500 | 0.687501 | − | 0.726183i | \(-0.258708\pi\) | ||||
0.687501 | + | 0.726183i | \(0.258708\pi\) | |||||||
\(734\) | −0.370081 | −0.0136599 | ||||||||
\(735\) | −1.78925 | −0.0659974 | ||||||||
\(736\) | −4.03444 | −0.148711 | ||||||||
\(737\) | −41.1763 | −1.51675 | ||||||||
\(738\) | −0.204326 | −0.00752134 | ||||||||
\(739\) | 25.0811 | 0.922625 | 0.461312 | − | 0.887238i | \(-0.347379\pi\) | ||||
0.461312 | + | 0.887238i | \(0.347379\pi\) | |||||||
\(740\) | 24.5927 | 0.904046 | ||||||||
\(741\) | 10.5520 | 0.387637 | ||||||||
\(742\) | 0.608109 | 0.0223244 | ||||||||
\(743\) | 22.8081 | 0.836747 | 0.418374 | − | 0.908275i | \(-0.362600\pi\) | ||||
0.418374 | + | 0.908275i | \(0.362600\pi\) | |||||||
\(744\) | 0.758299 | 0.0278006 | ||||||||
\(745\) | 27.7886 | 1.01810 | ||||||||
\(746\) | 1.20754 | 0.0442111 | ||||||||
\(747\) | −3.69192 | −0.135080 | ||||||||
\(748\) | 10.7122 | 0.391678 | ||||||||
\(749\) | 3.12126 | 0.114048 | ||||||||
\(750\) | −0.589402 | −0.0215219 | ||||||||
\(751\) | −11.4218 | −0.416788 | −0.208394 | − | 0.978045i | \(-0.566824\pi\) | ||||
−0.208394 | + | 0.978045i | \(0.566824\pi\) | |||||||
\(752\) | 19.2788 | 0.703026 | ||||||||
\(753\) | −4.43127 | −0.161485 | ||||||||
\(754\) | 0.444107 | 0.0161734 | ||||||||
\(755\) | −29.4659 | −1.07237 | ||||||||
\(756\) | 1.99765 | 0.0726539 | ||||||||
\(757\) | −35.8118 | −1.30160 | −0.650801 | − | 0.759249i | \(-0.725567\pi\) | ||||
−0.650801 | + | 0.759249i | \(0.725567\pi\) | |||||||
\(758\) | −1.23656 | −0.0449139 | ||||||||
\(759\) | −23.3583 | −0.847853 | ||||||||
\(760\) | 1.78203 | 0.0646410 | ||||||||
\(761\) | −32.2880 | −1.17044 | −0.585220 | − | 0.810874i | \(-0.698992\pi\) | ||||
−0.585220 | + | 0.810874i | \(0.698992\pi\) | |||||||
\(762\) | 0.190546 | 0.00690274 | ||||||||
\(763\) | −5.64099 | −0.204218 | ||||||||
\(764\) | 1.99765 | 0.0722725 | ||||||||
\(765\) | −2.85462 | −0.103209 | ||||||||
\(766\) | 1.74094 | 0.0629028 | ||||||||
\(767\) | −14.9786 | −0.540845 | ||||||||
\(768\) | −15.8125 | −0.570585 | ||||||||
\(769\) | 39.3988 | 1.42076 | 0.710378 | − | 0.703821i | \(-0.248524\pi\) | ||||
0.710378 | + | 0.703821i | \(0.248524\pi\) | |||||||
\(770\) | −0.291390 | −0.0105010 | ||||||||
\(771\) | 26.4282 | 0.951788 | ||||||||
\(772\) | −49.8128 | −1.79280 | ||||||||
\(773\) | 40.7233 | 1.46472 | 0.732358 | − | 0.680920i | \(-0.238420\pi\) | ||||
0.732358 | + | 0.680920i | \(0.238420\pi\) | |||||||
\(774\) | −0.352531 | −0.0126715 | ||||||||
\(775\) | 7.04120 | 0.252927 | ||||||||
\(776\) | 0.403358 | 0.0144797 | ||||||||
\(777\) | 6.88044 | 0.246834 | ||||||||
\(778\) | −0.787405 | −0.0282298 | ||||||||
\(779\) | 21.6829 | 0.776871 | ||||||||
\(780\) | −7.33513 | −0.262640 | ||||||||
\(781\) | −15.7224 | −0.562592 | ||||||||
\(782\) | 0.537230 | 0.0192113 | ||||||||
\(783\) | −4.46629 | −0.159612 | ||||||||
\(784\) | 3.98592 | 0.142354 | ||||||||
\(785\) | −10.5084 | −0.375060 | ||||||||
\(786\) | 0.614836 | 0.0219305 | ||||||||
\(787\) | −35.2079 | −1.25503 | −0.627513 | − | 0.778606i | \(-0.715927\pi\) | ||||
−0.627513 | + | 0.778606i | \(0.715927\pi\) | |||||||
\(788\) | −18.2852 | −0.651382 | ||||||||
\(789\) | −19.5544 | −0.696156 | ||||||||
\(790\) | −0.775835 | −0.0276030 | ||||||||
\(791\) | 6.37340 | 0.226612 | ||||||||
\(792\) | 0.651042 | 0.0231338 | ||||||||
\(793\) | −18.5734 | −0.659560 | ||||||||
\(794\) | −1.31155 | −0.0465450 | ||||||||
\(795\) | 22.4558 | 0.796427 | ||||||||
\(796\) | −29.8411 | −1.05769 | ||||||||
\(797\) | 9.19566 | 0.325727 | 0.162863 | − | 0.986649i | \(-0.447927\pi\) | ||||
0.162863 | + | 0.986649i | \(0.447927\pi\) | |||||||
\(798\) | 0.249138 | 0.00881938 | ||||||||
\(799\) | −7.71666 | −0.272996 | ||||||||
\(800\) | 1.04414 | 0.0369158 | ||||||||
\(801\) | 1.98084 | 0.0699897 | ||||||||
\(802\) | 0.572531 | 0.0202168 | ||||||||
\(803\) | −34.5262 | −1.21840 | ||||||||
\(804\) | −24.4729 | −0.863093 | ||||||||
\(805\) | 12.4345 | 0.438260 | ||||||||
\(806\) | −0.389272 | −0.0137115 | ||||||||
\(807\) | −22.5742 | −0.794649 | ||||||||
\(808\) | 1.36120 | 0.0478868 | ||||||||
\(809\) | 46.6349 | 1.63960 | 0.819799 | − | 0.572652i | \(-0.194085\pi\) | ||||
0.819799 | + | 0.572652i | \(0.194085\pi\) | |||||||
\(810\) | −0.0866947 | −0.00304614 | ||||||||
\(811\) | −52.8259 | −1.85497 | −0.927485 | − | 0.373861i | \(-0.878034\pi\) | ||||
−0.927485 | + | 0.373861i | \(0.878034\pi\) | |||||||
\(812\) | −8.92210 | −0.313104 | ||||||||
\(813\) | −19.5448 | −0.685466 | ||||||||
\(814\) | 1.12052 | 0.0392743 | ||||||||
\(815\) | −9.34016 | −0.327172 | ||||||||
\(816\) | 6.35926 | 0.222619 | ||||||||
\(817\) | 37.4104 | 1.30882 | ||||||||
\(818\) | −0.353203 | −0.0123495 | ||||||||
\(819\) | −2.05219 | −0.0717094 | ||||||||
\(820\) | −15.0727 | −0.526361 | ||||||||
\(821\) | −55.0376 | −1.92083 | −0.960413 | − | 0.278579i | \(-0.910137\pi\) | ||||
−0.960413 | + | 0.278579i | \(0.910137\pi\) | |||||||
\(822\) | 0.552598 | 0.0192741 | ||||||||
\(823\) | −14.2825 | −0.497857 | −0.248929 | − | 0.968522i | \(-0.580078\pi\) | ||||
−0.248929 | + | 0.968522i | \(0.580078\pi\) | |||||||
\(824\) | −0.283933 | −0.00989128 | ||||||||
\(825\) | 6.04527 | 0.210469 | ||||||||
\(826\) | −0.353651 | −0.0123051 | ||||||||
\(827\) | 29.3836 | 1.02177 | 0.510884 | − | 0.859650i | \(-0.329318\pi\) | ||||
0.510884 | + | 0.859650i | \(0.329318\pi\) | |||||||
\(828\) | −13.8829 | −0.482463 | ||||||||
\(829\) | −13.2860 | −0.461443 | −0.230722 | − | 0.973020i | \(-0.574109\pi\) | ||||
−0.230722 | + | 0.973020i | \(0.574109\pi\) | |||||||
\(830\) | 0.320070 | 0.0111098 | ||||||||
\(831\) | −15.9122 | −0.551987 | ||||||||
\(832\) | 16.3020 | 0.565170 | ||||||||
\(833\) | −1.59543 | −0.0552784 | ||||||||
\(834\) | 0.308240 | 0.0106735 | ||||||||
\(835\) | 17.6358 | 0.610311 | ||||||||
\(836\) | −34.5238 | −1.19403 | ||||||||
\(837\) | 3.91483 | 0.135316 | ||||||||
\(838\) | 0.350107 | 0.0120943 | ||||||||
\(839\) | 6.56697 | 0.226717 | 0.113359 | − | 0.993554i | \(-0.463839\pi\) | ||||
0.113359 | + | 0.993554i | \(0.463839\pi\) | |||||||
\(840\) | −0.346575 | −0.0119580 | ||||||||
\(841\) | −9.05224 | −0.312146 | ||||||||
\(842\) | 0.245877 | 0.00847347 | ||||||||
\(843\) | 4.72334 | 0.162681 | ||||||||
\(844\) | −2.85451 | −0.0982564 | ||||||||
\(845\) | −15.7248 | −0.540950 | ||||||||
\(846\) | −0.234355 | −0.00805729 | ||||||||
\(847\) | 0.297008 | 0.0102053 | ||||||||
\(848\) | −50.0251 | −1.71787 | ||||||||
\(849\) | −1.09143 | −0.0374579 | ||||||||
\(850\) | −0.139038 | −0.00476897 | ||||||||
\(851\) | −47.8163 | −1.63912 | ||||||||
\(852\) | −9.34452 | −0.320138 | ||||||||
\(853\) | −4.41670 | −0.151225 | −0.0756125 | − | 0.997137i | \(-0.524091\pi\) | ||||
−0.0756125 | + | 0.997137i | \(0.524091\pi\) | |||||||
\(854\) | −0.438526 | −0.0150061 | ||||||||
\(855\) | 9.19998 | 0.314633 | ||||||||
\(856\) | 0.604585 | 0.0206643 | ||||||||
\(857\) | 8.88418 | 0.303478 | 0.151739 | − | 0.988421i | \(-0.451513\pi\) | ||||
0.151739 | + | 0.988421i | \(0.451513\pi\) | |||||||
\(858\) | −0.334212 | −0.0114098 | ||||||||
\(859\) | 12.2457 | 0.417818 | 0.208909 | − | 0.977935i | \(-0.433009\pi\) | ||||
0.208909 | + | 0.977935i | \(0.433009\pi\) | |||||||
\(860\) | −26.0055 | −0.886781 | ||||||||
\(861\) | −4.21697 | −0.143714 | ||||||||
\(862\) | 0.355604 | 0.0121119 | ||||||||
\(863\) | −40.1757 | −1.36760 | −0.683798 | − | 0.729671i | \(-0.739673\pi\) | ||||
−0.683798 | + | 0.729671i | \(0.739673\pi\) | |||||||
\(864\) | 0.580529 | 0.0197500 | ||||||||
\(865\) | 9.08899 | 0.309035 | ||||||||
\(866\) | −0.275331 | −0.00935613 | ||||||||
\(867\) | 14.4546 | 0.490904 | ||||||||
\(868\) | 7.82047 | 0.265444 | ||||||||
\(869\) | 30.0787 | 1.02035 | ||||||||
\(870\) | 0.387204 | 0.0131274 | ||||||||
\(871\) | 25.1411 | 0.851873 | ||||||||
\(872\) | −1.09266 | −0.0370020 | ||||||||
\(873\) | 2.08239 | 0.0704784 | ||||||||
\(874\) | −1.73141 | −0.0585657 | ||||||||
\(875\) | −12.1644 | −0.411231 | ||||||||
\(876\) | −20.5205 | −0.693323 | ||||||||
\(877\) | 51.6084 | 1.74269 | 0.871346 | − | 0.490669i | \(-0.163247\pi\) | ||||
0.871346 | + | 0.490669i | \(0.163247\pi\) | |||||||
\(878\) | −0.370868 | −0.0125162 | ||||||||
\(879\) | 30.6330 | 1.03323 | ||||||||
\(880\) | 23.9707 | 0.808052 | ||||||||
\(881\) | 15.9384 | 0.536978 | 0.268489 | − | 0.963283i | \(-0.413476\pi\) | ||||
0.268489 | + | 0.963283i | \(0.413476\pi\) | |||||||
\(882\) | −0.0484532 | −0.00163150 | ||||||||
\(883\) | 8.01850 | 0.269844 | 0.134922 | − | 0.990856i | \(-0.456922\pi\) | ||||
0.134922 | + | 0.990856i | \(0.456922\pi\) | |||||||
\(884\) | −6.54057 | −0.219983 | ||||||||
\(885\) | −13.0594 | −0.438987 | ||||||||
\(886\) | 1.22822 | 0.0412628 | ||||||||
\(887\) | 19.3084 | 0.648312 | 0.324156 | − | 0.946004i | \(-0.394920\pi\) | ||||
0.324156 | + | 0.946004i | \(0.394920\pi\) | |||||||
\(888\) | 1.33273 | 0.0447236 | ||||||||
\(889\) | 3.93257 | 0.131894 | ||||||||
\(890\) | −0.171729 | −0.00575636 | ||||||||
\(891\) | 3.36110 | 0.112601 | ||||||||
\(892\) | 53.6700 | 1.79701 | ||||||||
\(893\) | 24.8696 | 0.832229 | ||||||||
\(894\) | 0.752522 | 0.0251681 | ||||||||
\(895\) | −12.0060 | −0.401316 | ||||||||
\(896\) | 1.54596 | 0.0516467 | ||||||||
\(897\) | 14.2619 | 0.476191 | ||||||||
\(898\) | 1.27599 | 0.0425803 | ||||||||
\(899\) | −17.4848 | −0.583150 | ||||||||
\(900\) | 3.59297 | 0.119766 | ||||||||
\(901\) | 20.0234 | 0.667075 | ||||||||
\(902\) | −0.686760 | −0.0228666 | ||||||||
\(903\) | −7.27571 | −0.242120 | ||||||||
\(904\) | 1.23452 | 0.0410595 | ||||||||
\(905\) | 27.4072 | 0.911048 | ||||||||
\(906\) | −0.797943 | −0.0265099 | ||||||||
\(907\) | −35.8103 | −1.18906 | −0.594531 | − | 0.804073i | \(-0.702662\pi\) | ||||
−0.594531 | + | 0.804073i | \(0.702662\pi\) | |||||||
\(908\) | 15.9586 | 0.529605 | ||||||||
\(909\) | 7.02738 | 0.233084 | ||||||||
\(910\) | 0.177914 | 0.00589780 | ||||||||
\(911\) | 13.2358 | 0.438521 | 0.219260 | − | 0.975666i | \(-0.429636\pi\) | ||||
0.219260 | + | 0.975666i | \(0.429636\pi\) | |||||||
\(912\) | −20.4949 | −0.678653 | ||||||||
\(913\) | −12.4089 | −0.410675 | ||||||||
\(914\) | 1.06049 | 0.0350780 | ||||||||
\(915\) | −16.1936 | −0.535344 | ||||||||
\(916\) | −26.4269 | −0.873169 | ||||||||
\(917\) | 12.6893 | 0.419037 | ||||||||
\(918\) | −0.0773037 | −0.00255140 | ||||||||
\(919\) | 19.3419 | 0.638031 | 0.319015 | − | 0.947750i | \(-0.396648\pi\) | ||||
0.319015 | + | 0.947750i | \(0.396648\pi\) | |||||||
\(920\) | 2.40856 | 0.0794079 | ||||||||
\(921\) | −21.5884 | −0.711362 | ||||||||
\(922\) | −0.0980196 | −0.00322810 | ||||||||
\(923\) | 9.59964 | 0.315976 | ||||||||
\(924\) | 6.71431 | 0.220885 | ||||||||
\(925\) | 12.3751 | 0.406892 | ||||||||
\(926\) | −1.44854 | −0.0476021 | ||||||||
\(927\) | −1.46585 | −0.0481447 | ||||||||
\(928\) | −2.59281 | −0.0851132 | ||||||||
\(929\) | 4.29706 | 0.140982 | 0.0704910 | − | 0.997512i | \(-0.477543\pi\) | ||||
0.0704910 | + | 0.997512i | \(0.477543\pi\) | |||||||
\(930\) | −0.339395 | −0.0111292 | ||||||||
\(931\) | 5.14182 | 0.168516 | ||||||||
\(932\) | −43.9254 | −1.43882 | ||||||||
\(933\) | 11.3055 | 0.370125 | ||||||||
\(934\) | 1.44345 | 0.0472311 | ||||||||
\(935\) | −9.59467 | −0.313779 | ||||||||
\(936\) | −0.397507 | −0.0129929 | ||||||||
\(937\) | −26.3441 | −0.860624 | −0.430312 | − | 0.902680i | \(-0.641596\pi\) | ||||
−0.430312 | + | 0.902680i | \(0.641596\pi\) | |||||||
\(938\) | 0.593593 | 0.0193815 | ||||||||
\(939\) | −27.9643 | −0.912580 | ||||||||
\(940\) | −17.2879 | −0.563869 | ||||||||
\(941\) | 35.9318 | 1.17134 | 0.585671 | − | 0.810549i | \(-0.300831\pi\) | ||||
0.585671 | + | 0.810549i | \(0.300831\pi\) | |||||||
\(942\) | −0.284569 | −0.00927177 | ||||||||
\(943\) | 29.3063 | 0.954343 | ||||||||
\(944\) | 29.0925 | 0.946881 | ||||||||
\(945\) | −1.78925 | −0.0582042 | ||||||||
\(946\) | −1.18489 | −0.0385242 | ||||||||
\(947\) | −16.6353 | −0.540575 | −0.270288 | − | 0.962780i | \(-0.587119\pi\) | ||||
−0.270288 | + | 0.962780i | \(0.587119\pi\) | |||||||
\(948\) | 17.8771 | 0.580621 | ||||||||
\(949\) | 21.0807 | 0.684309 | ||||||||
\(950\) | 0.448098 | 0.0145382 | ||||||||
\(951\) | 25.2148 | 0.817646 | ||||||||
\(952\) | −0.309033 | −0.0100158 | ||||||||
\(953\) | −40.5799 | −1.31451 | −0.657256 | − | 0.753667i | \(-0.728283\pi\) | ||||
−0.657256 | + | 0.753667i | \(0.728283\pi\) | |||||||
\(954\) | 0.608109 | 0.0196883 | ||||||||
\(955\) | −1.78925 | −0.0578987 | ||||||||
\(956\) | −48.1044 | −1.55581 | ||||||||
\(957\) | −15.0117 | −0.485258 | ||||||||
\(958\) | 1.39187 | 0.0449691 | ||||||||
\(959\) | 11.4048 | 0.368279 | ||||||||
\(960\) | 14.2133 | 0.458731 | ||||||||
\(961\) | −15.6741 | −0.505616 | ||||||||
\(962\) | −0.684158 | −0.0220581 | ||||||||
\(963\) | 3.12126 | 0.100581 | ||||||||
\(964\) | −31.6341 | −1.01887 | ||||||||
\(965\) | 44.6161 | 1.43624 | ||||||||
\(966\) | 0.336730 | 0.0108341 | ||||||||
\(967\) | 54.4939 | 1.75241 | 0.876203 | − | 0.481942i | \(-0.160068\pi\) | ||||
0.876203 | + | 0.481942i | \(0.160068\pi\) | |||||||
\(968\) | 0.0575301 | 0.00184909 | ||||||||
\(969\) | 8.20342 | 0.263532 | ||||||||
\(970\) | −0.180533 | −0.00579655 | ||||||||
\(971\) | −18.9209 | −0.607201 | −0.303601 | − | 0.952799i | \(-0.598189\pi\) | ||||
−0.303601 | + | 0.952799i | \(0.598189\pi\) | |||||||
\(972\) | 1.99765 | 0.0640747 | ||||||||
\(973\) | 6.36160 | 0.203943 | ||||||||
\(974\) | −1.29360 | −0.0414496 | ||||||||
\(975\) | −3.69106 | −0.118209 | ||||||||
\(976\) | 36.0746 | 1.15472 | ||||||||
\(977\) | −22.5176 | −0.720402 | −0.360201 | − | 0.932875i | \(-0.617292\pi\) | ||||
−0.360201 | + | 0.932875i | \(0.617292\pi\) | |||||||
\(978\) | −0.252934 | −0.00808793 | ||||||||
\(979\) | 6.65782 | 0.212785 | ||||||||
\(980\) | −3.57429 | −0.114177 | ||||||||
\(981\) | −5.64099 | −0.180103 | ||||||||
\(982\) | 0.262965 | 0.00839154 | ||||||||
\(983\) | 33.4256 | 1.06611 | 0.533055 | − | 0.846080i | \(-0.321044\pi\) | ||||
0.533055 | + | 0.846080i | \(0.321044\pi\) | |||||||
\(984\) | −0.816824 | −0.0260394 | ||||||||
\(985\) | 16.3776 | 0.521832 | ||||||||
\(986\) | 0.345261 | 0.0109953 | ||||||||
\(987\) | −4.83673 | −0.153955 | ||||||||
\(988\) | 21.0792 | 0.670619 | ||||||||
\(989\) | 50.5633 | 1.60782 | ||||||||
\(990\) | −0.291390 | −0.00926098 | ||||||||
\(991\) | −61.5492 | −1.95518 | −0.977588 | − | 0.210529i | \(-0.932481\pi\) | ||||
−0.977588 | + | 0.210529i | \(0.932481\pi\) | |||||||
\(992\) | 2.27267 | 0.0721574 | ||||||||
\(993\) | −1.93245 | −0.0613246 | ||||||||
\(994\) | 0.226652 | 0.00718897 | ||||||||
\(995\) | 26.7279 | 0.847332 | ||||||||
\(996\) | −7.37516 | −0.233691 | ||||||||
\(997\) | 22.1771 | 0.702357 | 0.351179 | − | 0.936309i | \(-0.385781\pi\) | ||||
0.351179 | + | 0.936309i | \(0.385781\pi\) | |||||||
\(998\) | 0.602533 | 0.0190729 | ||||||||
\(999\) | 6.88044 | 0.217687 |
(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 | 4011.2.a.l.1.16 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.l.1.16 | ✓ | 28 | 1.1 | even | 1 | trivial |