Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.524942 | −0.371190 | −0.185595 | − | 0.982626i | \(-0.559421\pi\) | ||||
−0.185595 | + | 0.982626i | \(0.559421\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.72444 | −0.862218 | ||||||||
\(5\) | −0.0309405 | −0.0138370 | −0.00691851 | − | 0.999976i | \(-0.502202\pi\) | ||||
−0.00691851 | + | 0.999976i | \(0.502202\pi\) | |||||||
\(6\) | −0.524942 | −0.214307 | ||||||||
\(7\) | 4.53114 | 1.71261 | 0.856305 | − | 0.516470i | \(-0.172754\pi\) | ||||
0.856305 | + | 0.516470i | \(0.172754\pi\) | |||||||
\(8\) | 1.95511 | 0.691236 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.0162420 | 0.00513616 | ||||||||
\(11\) | −5.92549 | −1.78660 | −0.893301 | − | 0.449459i | \(-0.851617\pi\) | ||||
−0.893301 | + | 0.449459i | \(0.851617\pi\) | |||||||
\(12\) | −1.72444 | −0.497802 | ||||||||
\(13\) | 1.49218 | 0.413857 | 0.206929 | − | 0.978356i | \(-0.433653\pi\) | ||||
0.206929 | + | 0.978356i | \(0.433653\pi\) | |||||||
\(14\) | −2.37858 | −0.635703 | ||||||||
\(15\) | −0.0309405 | −0.00798880 | ||||||||
\(16\) | 2.42255 | 0.605638 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −0.524942 | −0.123730 | ||||||||
\(19\) | −0.562629 | −0.129076 | −0.0645380 | − | 0.997915i | \(-0.520557\pi\) | ||||
−0.0645380 | + | 0.997915i | \(0.520557\pi\) | |||||||
\(20\) | 0.0533549 | 0.0119305 | ||||||||
\(21\) | 4.53114 | 0.988776 | ||||||||
\(22\) | 3.11054 | 0.663169 | ||||||||
\(23\) | 2.44586 | 0.509997 | 0.254998 | − | 0.966941i | \(-0.417925\pi\) | ||||
0.254998 | + | 0.966941i | \(0.417925\pi\) | |||||||
\(24\) | 1.95511 | 0.399086 | ||||||||
\(25\) | −4.99904 | −0.999809 | ||||||||
\(26\) | −0.783310 | −0.153620 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −7.81366 | −1.47664 | ||||||||
\(29\) | −2.50610 | −0.465372 | −0.232686 | − | 0.972552i | \(-0.574751\pi\) | ||||
−0.232686 | + | 0.972552i | \(0.574751\pi\) | |||||||
\(30\) | 0.0162420 | 0.00296536 | ||||||||
\(31\) | −4.61927 | −0.829645 | −0.414823 | − | 0.909902i | \(-0.636156\pi\) | ||||
−0.414823 | + | 0.909902i | \(0.636156\pi\) | |||||||
\(32\) | −5.18192 | −0.916043 | ||||||||
\(33\) | −5.92549 | −1.03150 | ||||||||
\(34\) | −0.524942 | −0.0900268 | ||||||||
\(35\) | −0.140196 | −0.0236974 | ||||||||
\(36\) | −1.72444 | −0.287406 | ||||||||
\(37\) | 6.57170 | 1.08038 | 0.540190 | − | 0.841543i | \(-0.318352\pi\) | ||||
0.540190 | + | 0.841543i | \(0.318352\pi\) | |||||||
\(38\) | 0.295347 | 0.0479117 | ||||||||
\(39\) | 1.49218 | 0.238941 | ||||||||
\(40\) | −0.0604922 | −0.00956465 | ||||||||
\(41\) | −0.878038 | −0.137127 | −0.0685633 | − | 0.997647i | \(-0.521841\pi\) | ||||
−0.0685633 | + | 0.997647i | \(0.521841\pi\) | |||||||
\(42\) | −2.37858 | −0.367024 | ||||||||
\(43\) | −10.7343 | −1.63697 | −0.818485 | − | 0.574527i | \(-0.805186\pi\) | ||||
−0.818485 | + | 0.574527i | \(0.805186\pi\) | |||||||
\(44\) | 10.2181 | 1.54044 | ||||||||
\(45\) | −0.0309405 | −0.00461234 | ||||||||
\(46\) | −1.28393 | −0.189306 | ||||||||
\(47\) | −7.87731 | −1.14902 | −0.574512 | − | 0.818496i | \(-0.694808\pi\) | ||||
−0.574512 | + | 0.818496i | \(0.694808\pi\) | |||||||
\(48\) | 2.42255 | 0.349665 | ||||||||
\(49\) | 13.5312 | 1.93303 | ||||||||
\(50\) | 2.62421 | 0.371119 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −2.57318 | −0.356835 | ||||||||
\(53\) | 0.351352 | 0.0482620 | 0.0241310 | − | 0.999709i | \(-0.492318\pi\) | ||||
0.0241310 | + | 0.999709i | \(0.492318\pi\) | |||||||
\(54\) | −0.524942 | −0.0714355 | ||||||||
\(55\) | 0.183338 | 0.0247212 | ||||||||
\(56\) | 8.85889 | 1.18382 | ||||||||
\(57\) | −0.562629 | −0.0745220 | ||||||||
\(58\) | 1.31556 | 0.172741 | ||||||||
\(59\) | −9.83165 | −1.27997 | −0.639986 | − | 0.768387i | \(-0.721060\pi\) | ||||
−0.639986 | + | 0.768387i | \(0.721060\pi\) | |||||||
\(60\) | 0.0533549 | 0.00688809 | ||||||||
\(61\) | −0.530009 | −0.0678607 | −0.0339303 | − | 0.999424i | \(-0.510802\pi\) | ||||
−0.0339303 | + | 0.999424i | \(0.510802\pi\) | |||||||
\(62\) | 2.42485 | 0.307956 | ||||||||
\(63\) | 4.53114 | 0.570870 | ||||||||
\(64\) | −2.12490 | −0.265612 | ||||||||
\(65\) | −0.0461689 | −0.00572655 | ||||||||
\(66\) | 3.11054 | 0.382881 | ||||||||
\(67\) | 1.53198 | 0.187161 | 0.0935805 | − | 0.995612i | \(-0.470169\pi\) | ||||
0.0935805 | + | 0.995612i | \(0.470169\pi\) | |||||||
\(68\) | −1.72444 | −0.209119 | ||||||||
\(69\) | 2.44586 | 0.294447 | ||||||||
\(70\) | 0.0735946 | 0.00879624 | ||||||||
\(71\) | 1.53716 | 0.182427 | 0.0912136 | − | 0.995831i | \(-0.470925\pi\) | ||||
0.0912136 | + | 0.995831i | \(0.470925\pi\) | |||||||
\(72\) | 1.95511 | 0.230412 | ||||||||
\(73\) | −6.42822 | −0.752367 | −0.376183 | − | 0.926545i | \(-0.622764\pi\) | ||||
−0.376183 | + | 0.926545i | \(0.622764\pi\) | |||||||
\(74\) | −3.44976 | −0.401026 | ||||||||
\(75\) | −4.99904 | −0.577240 | ||||||||
\(76\) | 0.970218 | 0.111292 | ||||||||
\(77\) | −26.8492 | −3.05975 | ||||||||
\(78\) | −0.783310 | −0.0886924 | ||||||||
\(79\) | −0.447691 | −0.0503692 | −0.0251846 | − | 0.999683i | \(-0.508017\pi\) | ||||
−0.0251846 | + | 0.999683i | \(0.508017\pi\) | |||||||
\(80\) | −0.0749550 | −0.00838022 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.460919 | 0.0509000 | ||||||||
\(83\) | 4.15544 | 0.456119 | 0.228060 | − | 0.973647i | \(-0.426762\pi\) | ||||
0.228060 | + | 0.973647i | \(0.426762\pi\) | |||||||
\(84\) | −7.81366 | −0.852540 | ||||||||
\(85\) | −0.0309405 | −0.00335597 | ||||||||
\(86\) | 5.63490 | 0.607627 | ||||||||
\(87\) | −2.50610 | −0.268682 | ||||||||
\(88\) | −11.5850 | −1.23496 | ||||||||
\(89\) | −8.61151 | −0.912819 | −0.456409 | − | 0.889770i | \(-0.650865\pi\) | ||||
−0.456409 | + | 0.889770i | \(0.650865\pi\) | |||||||
\(90\) | 0.0162420 | 0.00171205 | ||||||||
\(91\) | 6.76130 | 0.708776 | ||||||||
\(92\) | −4.21773 | −0.439728 | ||||||||
\(93\) | −4.61927 | −0.478996 | ||||||||
\(94\) | 4.13513 | 0.426506 | ||||||||
\(95\) | 0.0174080 | 0.00178603 | ||||||||
\(96\) | −5.18192 | −0.528878 | ||||||||
\(97\) | −13.7697 | −1.39810 | −0.699050 | − | 0.715072i | \(-0.746394\pi\) | ||||
−0.699050 | + | 0.715072i | \(0.746394\pi\) | |||||||
\(98\) | −7.10311 | −0.717522 | ||||||||
\(99\) | −5.92549 | −0.595534 | ||||||||
\(100\) | 8.62053 | 0.862053 | ||||||||
\(101\) | −8.08193 | −0.804182 | −0.402091 | − | 0.915600i | \(-0.631716\pi\) | ||||
−0.402091 | + | 0.915600i | \(0.631716\pi\) | |||||||
\(102\) | −0.524942 | −0.0519770 | ||||||||
\(103\) | 9.81552 | 0.967152 | 0.483576 | − | 0.875302i | \(-0.339338\pi\) | ||||
0.483576 | + | 0.875302i | \(0.339338\pi\) | |||||||
\(104\) | 2.91739 | 0.286073 | ||||||||
\(105\) | −0.140196 | −0.0136817 | ||||||||
\(106\) | −0.184440 | −0.0179143 | ||||||||
\(107\) | −6.78931 | −0.656347 | −0.328174 | − | 0.944617i | \(-0.606433\pi\) | ||||
−0.328174 | + | 0.944617i | \(0.606433\pi\) | |||||||
\(108\) | −1.72444 | −0.165934 | ||||||||
\(109\) | 5.80214 | 0.555744 | 0.277872 | − | 0.960618i | \(-0.410371\pi\) | ||||
0.277872 | + | 0.960618i | \(0.410371\pi\) | |||||||
\(110\) | −0.0962416 | −0.00917627 | ||||||||
\(111\) | 6.57170 | 0.623758 | ||||||||
\(112\) | 10.9769 | 1.03722 | ||||||||
\(113\) | −6.40828 | −0.602841 | −0.301420 | − | 0.953491i | \(-0.597461\pi\) | ||||
−0.301420 | + | 0.953491i | \(0.597461\pi\) | |||||||
\(114\) | 0.295347 | 0.0276618 | ||||||||
\(115\) | −0.0756761 | −0.00705683 | ||||||||
\(116\) | 4.32161 | 0.401252 | ||||||||
\(117\) | 1.49218 | 0.137952 | ||||||||
\(118\) | 5.16104 | 0.475113 | ||||||||
\(119\) | 4.53114 | 0.415369 | ||||||||
\(120\) | −0.0604922 | −0.00552215 | ||||||||
\(121\) | 24.1114 | 2.19195 | ||||||||
\(122\) | 0.278224 | 0.0251892 | ||||||||
\(123\) | −0.878038 | −0.0791700 | ||||||||
\(124\) | 7.96563 | 0.715335 | ||||||||
\(125\) | 0.309375 | 0.0276714 | ||||||||
\(126\) | −2.37858 | −0.211901 | ||||||||
\(127\) | 7.90321 | 0.701297 | 0.350648 | − | 0.936507i | \(-0.385961\pi\) | ||||
0.350648 | + | 0.936507i | \(0.385961\pi\) | |||||||
\(128\) | 11.4793 | 1.01464 | ||||||||
\(129\) | −10.7343 | −0.945105 | ||||||||
\(130\) | 0.0242360 | 0.00212564 | ||||||||
\(131\) | −0.454147 | −0.0396790 | −0.0198395 | − | 0.999803i | \(-0.506316\pi\) | ||||
−0.0198395 | + | 0.999803i | \(0.506316\pi\) | |||||||
\(132\) | 10.2181 | 0.889374 | ||||||||
\(133\) | −2.54935 | −0.221057 | ||||||||
\(134\) | −0.804199 | −0.0694723 | ||||||||
\(135\) | −0.0309405 | −0.00266293 | ||||||||
\(136\) | 1.95511 | 0.167649 | ||||||||
\(137\) | 9.90148 | 0.845940 | 0.422970 | − | 0.906144i | \(-0.360988\pi\) | ||||
0.422970 | + | 0.906144i | \(0.360988\pi\) | |||||||
\(138\) | −1.28393 | −0.109296 | ||||||||
\(139\) | 11.3340 | 0.961334 | 0.480667 | − | 0.876903i | \(-0.340395\pi\) | ||||
0.480667 | + | 0.876903i | \(0.340395\pi\) | |||||||
\(140\) | 0.241759 | 0.0204323 | ||||||||
\(141\) | −7.87731 | −0.663389 | ||||||||
\(142\) | −0.806919 | −0.0677151 | ||||||||
\(143\) | −8.84192 | −0.739399 | ||||||||
\(144\) | 2.42255 | 0.201879 | ||||||||
\(145\) | 0.0775401 | 0.00643935 | ||||||||
\(146\) | 3.37444 | 0.279271 | ||||||||
\(147\) | 13.5312 | 1.11604 | ||||||||
\(148\) | −11.3325 | −0.931524 | ||||||||
\(149\) | −15.8946 | −1.30214 | −0.651068 | − | 0.759019i | \(-0.725679\pi\) | ||||
−0.651068 | + | 0.759019i | \(0.725679\pi\) | |||||||
\(150\) | 2.62421 | 0.214266 | ||||||||
\(151\) | 11.9027 | 0.968631 | 0.484315 | − | 0.874894i | \(-0.339069\pi\) | ||||
0.484315 | + | 0.874894i | \(0.339069\pi\) | |||||||
\(152\) | −1.10000 | −0.0892220 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 14.0943 | 1.13575 | ||||||||
\(155\) | 0.142923 | 0.0114798 | ||||||||
\(156\) | −2.57318 | −0.206019 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 0.235012 | 0.0186965 | ||||||||
\(159\) | 0.351352 | 0.0278641 | ||||||||
\(160\) | 0.160331 | 0.0126753 | ||||||||
\(161\) | 11.0825 | 0.873425 | ||||||||
\(162\) | −0.524942 | −0.0412433 | ||||||||
\(163\) | −0.825261 | −0.0646394 | −0.0323197 | − | 0.999478i | \(-0.510289\pi\) | ||||
−0.0323197 | + | 0.999478i | \(0.510289\pi\) | |||||||
\(164\) | 1.51412 | 0.118233 | ||||||||
\(165\) | 0.183338 | 0.0142728 | ||||||||
\(166\) | −2.18137 | −0.169307 | ||||||||
\(167\) | −20.8423 | −1.61282 | −0.806412 | − | 0.591354i | \(-0.798594\pi\) | ||||
−0.806412 | + | 0.591354i | \(0.798594\pi\) | |||||||
\(168\) | 8.85889 | 0.683478 | ||||||||
\(169\) | −10.7734 | −0.828722 | ||||||||
\(170\) | 0.0162420 | 0.00124570 | ||||||||
\(171\) | −0.562629 | −0.0430253 | ||||||||
\(172\) | 18.5107 | 1.41143 | ||||||||
\(173\) | −7.60663 | −0.578321 | −0.289161 | − | 0.957281i | \(-0.593376\pi\) | ||||
−0.289161 | + | 0.957281i | \(0.593376\pi\) | |||||||
\(174\) | 1.31556 | 0.0997322 | ||||||||
\(175\) | −22.6514 | −1.71228 | ||||||||
\(176\) | −14.3548 | −1.08203 | ||||||||
\(177\) | −9.83165 | −0.738992 | ||||||||
\(178\) | 4.52054 | 0.338829 | ||||||||
\(179\) | 8.25507 | 0.617013 | 0.308507 | − | 0.951222i | \(-0.400171\pi\) | ||||
0.308507 | + | 0.951222i | \(0.400171\pi\) | |||||||
\(180\) | 0.0533549 | 0.00397684 | ||||||||
\(181\) | −12.8556 | −0.955546 | −0.477773 | − | 0.878483i | \(-0.658556\pi\) | ||||
−0.477773 | + | 0.878483i | \(0.658556\pi\) | |||||||
\(182\) | −3.54929 | −0.263091 | ||||||||
\(183\) | −0.530009 | −0.0391794 | ||||||||
\(184\) | 4.78193 | 0.352528 | ||||||||
\(185\) | −0.203332 | −0.0149492 | ||||||||
\(186\) | 2.42485 | 0.177798 | ||||||||
\(187\) | −5.92549 | −0.433315 | ||||||||
\(188\) | 13.5839 | 0.990709 | ||||||||
\(189\) | 4.53114 | 0.329592 | ||||||||
\(190\) | −0.00913820 | −0.000662955 0 | ||||||||
\(191\) | −18.4625 | −1.33590 | −0.667949 | − | 0.744207i | \(-0.732828\pi\) | ||||
−0.667949 | + | 0.744207i | \(0.732828\pi\) | |||||||
\(192\) | −2.12490 | −0.153351 | ||||||||
\(193\) | −18.6825 | −1.34480 | −0.672399 | − | 0.740189i | \(-0.734736\pi\) | ||||
−0.672399 | + | 0.740189i | \(0.734736\pi\) | |||||||
\(194\) | 7.22829 | 0.518961 | ||||||||
\(195\) | −0.0461689 | −0.00330623 | ||||||||
\(196\) | −23.3337 | −1.66670 | ||||||||
\(197\) | 14.4077 | 1.02650 | 0.513252 | − | 0.858238i | \(-0.328441\pi\) | ||||
0.513252 | + | 0.858238i | \(0.328441\pi\) | |||||||
\(198\) | 3.11054 | 0.221056 | ||||||||
\(199\) | 4.63934 | 0.328874 | 0.164437 | − | 0.986388i | \(-0.447419\pi\) | ||||
0.164437 | + | 0.986388i | \(0.447419\pi\) | |||||||
\(200\) | −9.77369 | −0.691104 | ||||||||
\(201\) | 1.53198 | 0.108057 | ||||||||
\(202\) | 4.24254 | 0.298504 | ||||||||
\(203\) | −11.3555 | −0.797000 | ||||||||
\(204\) | −1.72444 | −0.120735 | ||||||||
\(205\) | 0.0271669 | 0.00189742 | ||||||||
\(206\) | −5.15258 | −0.358997 | ||||||||
\(207\) | 2.44586 | 0.169999 | ||||||||
\(208\) | 3.61489 | 0.250648 | ||||||||
\(209\) | 3.33385 | 0.230607 | ||||||||
\(210\) | 0.0735946 | 0.00507851 | ||||||||
\(211\) | −20.8553 | −1.43574 | −0.717869 | − | 0.696178i | \(-0.754883\pi\) | ||||
−0.717869 | + | 0.696178i | \(0.754883\pi\) | |||||||
\(212\) | −0.605885 | −0.0416123 | ||||||||
\(213\) | 1.53716 | 0.105324 | ||||||||
\(214\) | 3.56399 | 0.243629 | ||||||||
\(215\) | 0.332126 | 0.0226508 | ||||||||
\(216\) | 1.95511 | 0.133029 | ||||||||
\(217\) | −20.9306 | −1.42086 | ||||||||
\(218\) | −3.04578 | −0.206287 | ||||||||
\(219\) | −6.42822 | −0.434379 | ||||||||
\(220\) | −0.316154 | −0.0213151 | ||||||||
\(221\) | 1.49218 | 0.100375 | ||||||||
\(222\) | −3.44976 | −0.231533 | ||||||||
\(223\) | −5.38829 | −0.360827 | −0.180413 | − | 0.983591i | \(-0.557744\pi\) | ||||
−0.180413 | + | 0.983591i | \(0.557744\pi\) | |||||||
\(224\) | −23.4800 | −1.56882 | ||||||||
\(225\) | −4.99904 | −0.333270 | ||||||||
\(226\) | 3.36398 | 0.223768 | ||||||||
\(227\) | 15.8982 | 1.05520 | 0.527600 | − | 0.849493i | \(-0.323092\pi\) | ||||
0.527600 | + | 0.849493i | \(0.323092\pi\) | |||||||
\(228\) | 0.970218 | 0.0642542 | ||||||||
\(229\) | 15.6755 | 1.03587 | 0.517934 | − | 0.855421i | \(-0.326701\pi\) | ||||
0.517934 | + | 0.855421i | \(0.326701\pi\) | |||||||
\(230\) | 0.0397255 | 0.00261942 | ||||||||
\(231\) | −26.8492 | −1.76655 | ||||||||
\(232\) | −4.89971 | −0.321682 | ||||||||
\(233\) | −17.1629 | −1.12438 | −0.562190 | − | 0.827008i | \(-0.690041\pi\) | ||||
−0.562190 | + | 0.827008i | \(0.690041\pi\) | |||||||
\(234\) | −0.783310 | −0.0512066 | ||||||||
\(235\) | 0.243728 | 0.0158991 | ||||||||
\(236\) | 16.9541 | 1.10362 | ||||||||
\(237\) | −0.447691 | −0.0290807 | ||||||||
\(238\) | −2.37858 | −0.154181 | ||||||||
\(239\) | −11.7555 | −0.760398 | −0.380199 | − | 0.924905i | \(-0.624144\pi\) | ||||
−0.380199 | + | 0.924905i | \(0.624144\pi\) | |||||||
\(240\) | −0.0749550 | −0.00483832 | ||||||||
\(241\) | 27.8965 | 1.79697 | 0.898485 | − | 0.439005i | \(-0.144669\pi\) | ||||
0.898485 | + | 0.439005i | \(0.144669\pi\) | |||||||
\(242\) | −12.6571 | −0.813628 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.913967 | 0.0585107 | ||||||||
\(245\) | −0.418663 | −0.0267474 | ||||||||
\(246\) | 0.460919 | 0.0293871 | ||||||||
\(247\) | −0.839546 | −0.0534190 | ||||||||
\(248\) | −9.03119 | −0.573481 | ||||||||
\(249\) | 4.15544 | 0.263341 | ||||||||
\(250\) | −0.162404 | −0.0102713 | ||||||||
\(251\) | 4.10976 | 0.259406 | 0.129703 | − | 0.991553i | \(-0.458598\pi\) | ||||
0.129703 | + | 0.991553i | \(0.458598\pi\) | |||||||
\(252\) | −7.81366 | −0.492214 | ||||||||
\(253\) | −14.4929 | −0.911161 | ||||||||
\(254\) | −4.14873 | −0.260314 | ||||||||
\(255\) | −0.0309405 | −0.00193757 | ||||||||
\(256\) | −1.77616 | −0.111010 | ||||||||
\(257\) | 6.27533 | 0.391445 | 0.195722 | − | 0.980659i | \(-0.437295\pi\) | ||||
0.195722 | + | 0.980659i | \(0.437295\pi\) | |||||||
\(258\) | 5.63490 | 0.350814 | ||||||||
\(259\) | 29.7773 | 1.85027 | ||||||||
\(260\) | 0.0796154 | 0.00493754 | ||||||||
\(261\) | −2.50610 | −0.155124 | ||||||||
\(262\) | 0.238401 | 0.0147284 | ||||||||
\(263\) | 17.8354 | 1.09978 | 0.549889 | − | 0.835238i | \(-0.314670\pi\) | ||||
0.549889 | + | 0.835238i | \(0.314670\pi\) | |||||||
\(264\) | −11.5850 | −0.713007 | ||||||||
\(265\) | −0.0108710 | −0.000667801 0 | ||||||||
\(266\) | 1.33826 | 0.0820540 | ||||||||
\(267\) | −8.61151 | −0.527016 | ||||||||
\(268\) | −2.64180 | −0.161374 | ||||||||
\(269\) | 22.4357 | 1.36793 | 0.683965 | − | 0.729515i | \(-0.260254\pi\) | ||||
0.683965 | + | 0.729515i | \(0.260254\pi\) | |||||||
\(270\) | 0.0162420 | 0.000988454 0 | ||||||||
\(271\) | 14.1161 | 0.857495 | 0.428747 | − | 0.903424i | \(-0.358955\pi\) | ||||
0.428747 | + | 0.903424i | \(0.358955\pi\) | |||||||
\(272\) | 2.42255 | 0.146889 | ||||||||
\(273\) | 6.76130 | 0.409212 | ||||||||
\(274\) | −5.19770 | −0.314004 | ||||||||
\(275\) | 29.6218 | 1.78626 | ||||||||
\(276\) | −4.21773 | −0.253877 | ||||||||
\(277\) | 17.8122 | 1.07023 | 0.535117 | − | 0.844778i | \(-0.320267\pi\) | ||||
0.535117 | + | 0.844778i | \(0.320267\pi\) | |||||||
\(278\) | −5.94967 | −0.356838 | ||||||||
\(279\) | −4.61927 | −0.276548 | ||||||||
\(280\) | −0.274098 | −0.0163805 | ||||||||
\(281\) | −16.7597 | −0.999802 | −0.499901 | − | 0.866083i | \(-0.666630\pi\) | ||||
−0.499901 | + | 0.866083i | \(0.666630\pi\) | |||||||
\(282\) | 4.13513 | 0.246243 | ||||||||
\(283\) | 12.2689 | 0.729311 | 0.364656 | − | 0.931142i | \(-0.381187\pi\) | ||||
0.364656 | + | 0.931142i | \(0.381187\pi\) | |||||||
\(284\) | −2.65073 | −0.157292 | ||||||||
\(285\) | 0.0174080 | 0.00103116 | ||||||||
\(286\) | 4.64149 | 0.274457 | ||||||||
\(287\) | −3.97851 | −0.234844 | ||||||||
\(288\) | −5.18192 | −0.305348 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −0.0407040 | −0.00239022 | ||||||||
\(291\) | −13.7697 | −0.807194 | ||||||||
\(292\) | 11.0851 | 0.648704 | ||||||||
\(293\) | −20.0852 | −1.17339 | −0.586696 | − | 0.809807i | \(-0.699572\pi\) | ||||
−0.586696 | + | 0.809807i | \(0.699572\pi\) | |||||||
\(294\) | −7.10311 | −0.414262 | ||||||||
\(295\) | 0.304196 | 0.0177110 | ||||||||
\(296\) | 12.8484 | 0.746799 | ||||||||
\(297\) | −5.92549 | −0.343832 | ||||||||
\(298\) | 8.34374 | 0.483340 | ||||||||
\(299\) | 3.64967 | 0.211066 | ||||||||
\(300\) | 8.62053 | 0.497707 | ||||||||
\(301\) | −48.6388 | −2.80349 | ||||||||
\(302\) | −6.24824 | −0.359546 | ||||||||
\(303\) | −8.08193 | −0.464295 | ||||||||
\(304\) | −1.36300 | −0.0781733 | ||||||||
\(305\) | 0.0163987 | 0.000938989 0 | ||||||||
\(306\) | −0.524942 | −0.0300089 | ||||||||
\(307\) | 19.0510 | 1.08730 | 0.543648 | − | 0.839313i | \(-0.317043\pi\) | ||||
0.543648 | + | 0.839313i | \(0.317043\pi\) | |||||||
\(308\) | 46.2998 | 2.63817 | ||||||||
\(309\) | 9.81552 | 0.558386 | ||||||||
\(310\) | −0.0750260 | −0.00426119 | ||||||||
\(311\) | −0.143909 | −0.00816033 | −0.00408017 | − | 0.999992i | \(-0.501299\pi\) | ||||
−0.00408017 | + | 0.999992i | \(0.501299\pi\) | |||||||
\(312\) | 2.91739 | 0.165165 | ||||||||
\(313\) | −28.3493 | −1.60239 | −0.801197 | − | 0.598400i | \(-0.795803\pi\) | ||||
−0.801197 | + | 0.598400i | \(0.795803\pi\) | |||||||
\(314\) | 0.524942 | 0.0296242 | ||||||||
\(315\) | −0.140196 | −0.00789914 | ||||||||
\(316\) | 0.772015 | 0.0434292 | ||||||||
\(317\) | −9.16101 | −0.514533 | −0.257267 | − | 0.966340i | \(-0.582822\pi\) | ||||
−0.257267 | + | 0.966340i | \(0.582822\pi\) | |||||||
\(318\) | −0.184440 | −0.0103429 | ||||||||
\(319\) | 14.8499 | 0.831434 | ||||||||
\(320\) | 0.0657454 | 0.00367528 | ||||||||
\(321\) | −6.78931 | −0.378942 | ||||||||
\(322\) | −5.81768 | −0.324207 | ||||||||
\(323\) | −0.562629 | −0.0313055 | ||||||||
\(324\) | −1.72444 | −0.0958020 | ||||||||
\(325\) | −7.45949 | −0.413778 | ||||||||
\(326\) | 0.433214 | 0.0239935 | ||||||||
\(327\) | 5.80214 | 0.320859 | ||||||||
\(328\) | −1.71666 | −0.0947868 | ||||||||
\(329\) | −35.6932 | −1.96783 | ||||||||
\(330\) | −0.0962416 | −0.00529792 | ||||||||
\(331\) | 21.5231 | 1.18301 | 0.591507 | − | 0.806300i | \(-0.298533\pi\) | ||||
0.591507 | + | 0.806300i | \(0.298533\pi\) | |||||||
\(332\) | −7.16580 | −0.393274 | ||||||||
\(333\) | 6.57170 | 0.360127 | ||||||||
\(334\) | 10.9410 | 0.598664 | ||||||||
\(335\) | −0.0474002 | −0.00258975 | ||||||||
\(336\) | 10.9769 | 0.598840 | ||||||||
\(337\) | −22.4052 | −1.22049 | −0.610245 | − | 0.792212i | \(-0.708929\pi\) | ||||
−0.610245 | + | 0.792212i | \(0.708929\pi\) | |||||||
\(338\) | 5.65540 | 0.307613 | ||||||||
\(339\) | −6.40828 | −0.348050 | ||||||||
\(340\) | 0.0533549 | 0.00289358 | ||||||||
\(341\) | 27.3714 | 1.48225 | ||||||||
\(342\) | 0.295347 | 0.0159706 | ||||||||
\(343\) | 29.5939 | 1.59792 | ||||||||
\(344\) | −20.9868 | −1.13153 | ||||||||
\(345\) | −0.0756761 | −0.00407426 | ||||||||
\(346\) | 3.99304 | 0.214667 | ||||||||
\(347\) | 23.2977 | 1.25068 | 0.625342 | − | 0.780351i | \(-0.284959\pi\) | ||||
0.625342 | + | 0.780351i | \(0.284959\pi\) | |||||||
\(348\) | 4.32161 | 0.231663 | ||||||||
\(349\) | −15.4419 | −0.826587 | −0.413293 | − | 0.910598i | \(-0.635622\pi\) | ||||
−0.413293 | + | 0.910598i | \(0.635622\pi\) | |||||||
\(350\) | 11.8906 | 0.635582 | ||||||||
\(351\) | 1.49218 | 0.0796469 | ||||||||
\(352\) | 30.7054 | 1.63660 | ||||||||
\(353\) | 10.5563 | 0.561855 | 0.280927 | − | 0.959729i | \(-0.409358\pi\) | ||||
0.280927 | + | 0.959729i | \(0.409358\pi\) | |||||||
\(354\) | 5.16104 | 0.274306 | ||||||||
\(355\) | −0.0475605 | −0.00252425 | ||||||||
\(356\) | 14.8500 | 0.787049 | ||||||||
\(357\) | 4.53114 | 0.239813 | ||||||||
\(358\) | −4.33343 | −0.229029 | ||||||||
\(359\) | −34.4105 | −1.81612 | −0.908058 | − | 0.418844i | \(-0.862435\pi\) | ||||
−0.908058 | + | 0.418844i | \(0.862435\pi\) | |||||||
\(360\) | −0.0604922 | −0.00318822 | ||||||||
\(361\) | −18.6834 | −0.983339 | ||||||||
\(362\) | 6.74842 | 0.354689 | ||||||||
\(363\) | 24.1114 | 1.26552 | ||||||||
\(364\) | −11.6594 | −0.611120 | ||||||||
\(365\) | 0.198893 | 0.0104105 | ||||||||
\(366\) | 0.278224 | 0.0145430 | ||||||||
\(367\) | −33.5629 | −1.75197 | −0.875983 | − | 0.482341i | \(-0.839787\pi\) | ||||
−0.875983 | + | 0.482341i | \(0.839787\pi\) | |||||||
\(368\) | 5.92522 | 0.308873 | ||||||||
\(369\) | −0.878038 | −0.0457088 | ||||||||
\(370\) | 0.106737 | 0.00554901 | ||||||||
\(371\) | 1.59203 | 0.0826539 | ||||||||
\(372\) | 7.96563 | 0.412999 | ||||||||
\(373\) | −0.701734 | −0.0363344 | −0.0181672 | − | 0.999835i | \(-0.505783\pi\) | ||||
−0.0181672 | + | 0.999835i | \(0.505783\pi\) | |||||||
\(374\) | 3.11054 | 0.160842 | ||||||||
\(375\) | 0.309375 | 0.0159761 | ||||||||
\(376\) | −15.4010 | −0.794247 | ||||||||
\(377\) | −3.73957 | −0.192598 | ||||||||
\(378\) | −2.37858 | −0.122341 | ||||||||
\(379\) | −14.4778 | −0.743677 | −0.371839 | − | 0.928297i | \(-0.621272\pi\) | ||||
−0.371839 | + | 0.928297i | \(0.621272\pi\) | |||||||
\(380\) | −0.0300190 | −0.00153994 | ||||||||
\(381\) | 7.90321 | 0.404894 | ||||||||
\(382\) | 9.69172 | 0.495872 | ||||||||
\(383\) | 11.0025 | 0.562204 | 0.281102 | − | 0.959678i | \(-0.409300\pi\) | ||||
0.281102 | + | 0.959678i | \(0.409300\pi\) | |||||||
\(384\) | 11.4793 | 0.585800 | ||||||||
\(385\) | 0.830728 | 0.0423378 | ||||||||
\(386\) | 9.80724 | 0.499175 | ||||||||
\(387\) | −10.7343 | −0.545657 | ||||||||
\(388\) | 23.7450 | 1.20547 | ||||||||
\(389\) | −20.1603 | −1.02217 | −0.511083 | − | 0.859532i | \(-0.670755\pi\) | ||||
−0.511083 | + | 0.859532i | \(0.670755\pi\) | |||||||
\(390\) | 0.0242360 | 0.00122724 | ||||||||
\(391\) | 2.44586 | 0.123692 | ||||||||
\(392\) | 26.4551 | 1.33618 | ||||||||
\(393\) | −0.454147 | −0.0229087 | ||||||||
\(394\) | −7.56318 | −0.381028 | ||||||||
\(395\) | 0.0138518 | 0.000696959 0 | ||||||||
\(396\) | 10.2181 | 0.513480 | ||||||||
\(397\) | 19.5587 | 0.981624 | 0.490812 | − | 0.871266i | \(-0.336700\pi\) | ||||
0.490812 | + | 0.871266i | \(0.336700\pi\) | |||||||
\(398\) | −2.43538 | −0.122075 | ||||||||
\(399\) | −2.54935 | −0.127627 | ||||||||
\(400\) | −12.1104 | −0.605522 | ||||||||
\(401\) | 24.4094 | 1.21895 | 0.609474 | − | 0.792806i | \(-0.291381\pi\) | ||||
0.609474 | + | 0.792806i | \(0.291381\pi\) | |||||||
\(402\) | −0.804199 | −0.0401098 | ||||||||
\(403\) | −6.89280 | −0.343355 | ||||||||
\(404\) | 13.9368 | 0.693380 | ||||||||
\(405\) | −0.0309405 | −0.00153745 | ||||||||
\(406\) | 5.96098 | 0.295838 | ||||||||
\(407\) | −38.9405 | −1.93021 | ||||||||
\(408\) | 1.95511 | 0.0967925 | ||||||||
\(409\) | 0.789075 | 0.0390173 | 0.0195086 | − | 0.999810i | \(-0.493790\pi\) | ||||
0.0195086 | + | 0.999810i | \(0.493790\pi\) | |||||||
\(410\) | −0.0142611 | −0.000704304 0 | ||||||||
\(411\) | 9.90148 | 0.488404 | ||||||||
\(412\) | −16.9262 | −0.833896 | ||||||||
\(413\) | −44.5486 | −2.19209 | ||||||||
\(414\) | −1.28393 | −0.0631019 | ||||||||
\(415\) | −0.128572 | −0.00631133 | ||||||||
\(416\) | −7.73238 | −0.379111 | ||||||||
\(417\) | 11.3340 | 0.555027 | ||||||||
\(418\) | −1.75008 | −0.0855991 | ||||||||
\(419\) | 38.5004 | 1.88087 | 0.940433 | − | 0.339979i | \(-0.110420\pi\) | ||||
0.940433 | + | 0.339979i | \(0.110420\pi\) | |||||||
\(420\) | 0.241759 | 0.0117966 | ||||||||
\(421\) | −7.81654 | −0.380955 | −0.190477 | − | 0.981692i | \(-0.561004\pi\) | ||||
−0.190477 | + | 0.981692i | \(0.561004\pi\) | |||||||
\(422\) | 10.9478 | 0.532932 | ||||||||
\(423\) | −7.87731 | −0.383008 | ||||||||
\(424\) | 0.686933 | 0.0333604 | ||||||||
\(425\) | −4.99904 | −0.242489 | ||||||||
\(426\) | −0.806919 | −0.0390953 | ||||||||
\(427\) | −2.40154 | −0.116219 | ||||||||
\(428\) | 11.7077 | 0.565915 | ||||||||
\(429\) | −8.84192 | −0.426892 | ||||||||
\(430\) | −0.174347 | −0.00840774 | ||||||||
\(431\) | −10.7740 | −0.518965 | −0.259482 | − | 0.965748i | \(-0.583552\pi\) | ||||
−0.259482 | + | 0.965748i | \(0.583552\pi\) | |||||||
\(432\) | 2.42255 | 0.116555 | ||||||||
\(433\) | −12.5623 | −0.603706 | −0.301853 | − | 0.953354i | \(-0.597605\pi\) | ||||
−0.301853 | + | 0.953354i | \(0.597605\pi\) | |||||||
\(434\) | 10.9873 | 0.527408 | ||||||||
\(435\) | 0.0775401 | 0.00371776 | ||||||||
\(436\) | −10.0054 | −0.479173 | ||||||||
\(437\) | −1.37611 | −0.0658283 | ||||||||
\(438\) | 3.37444 | 0.161237 | ||||||||
\(439\) | 0.678118 | 0.0323648 | 0.0161824 | − | 0.999869i | \(-0.494849\pi\) | ||||
0.0161824 | + | 0.999869i | \(0.494849\pi\) | |||||||
\(440\) | 0.358446 | 0.0170882 | ||||||||
\(441\) | 13.5312 | 0.644344 | ||||||||
\(442\) | −0.783310 | −0.0372582 | ||||||||
\(443\) | 3.86683 | 0.183719 | 0.0918594 | − | 0.995772i | \(-0.470719\pi\) | ||||
0.0918594 | + | 0.995772i | \(0.470719\pi\) | |||||||
\(444\) | −11.3325 | −0.537816 | ||||||||
\(445\) | 0.266445 | 0.0126307 | ||||||||
\(446\) | 2.82854 | 0.133935 | ||||||||
\(447\) | −15.8946 | −0.751789 | ||||||||
\(448\) | −9.62821 | −0.454890 | ||||||||
\(449\) | −40.2731 | −1.90061 | −0.950303 | − | 0.311326i | \(-0.899227\pi\) | ||||
−0.950303 | + | 0.311326i | \(0.899227\pi\) | |||||||
\(450\) | 2.62421 | 0.123706 | ||||||||
\(451\) | 5.20280 | 0.244991 | ||||||||
\(452\) | 11.0507 | 0.519780 | ||||||||
\(453\) | 11.9027 | 0.559239 | ||||||||
\(454\) | −8.34563 | −0.391680 | ||||||||
\(455\) | −0.209198 | −0.00980735 | ||||||||
\(456\) | −1.10000 | −0.0515123 | ||||||||
\(457\) | 0.293289 | 0.0137195 | 0.00685973 | − | 0.999976i | \(-0.497816\pi\) | ||||
0.00685973 | + | 0.999976i | \(0.497816\pi\) | |||||||
\(458\) | −8.22874 | −0.384504 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 0.130499 | 0.00608453 | ||||||||
\(461\) | −3.86658 | −0.180085 | −0.0900423 | − | 0.995938i | \(-0.528700\pi\) | ||||
−0.0900423 | + | 0.995938i | \(0.528700\pi\) | |||||||
\(462\) | 14.0943 | 0.655725 | ||||||||
\(463\) | 3.44425 | 0.160068 | 0.0800339 | − | 0.996792i | \(-0.474497\pi\) | ||||
0.0800339 | + | 0.996792i | \(0.474497\pi\) | |||||||
\(464\) | −6.07117 | −0.281847 | ||||||||
\(465\) | 0.142923 | 0.00662787 | ||||||||
\(466\) | 9.00953 | 0.417359 | ||||||||
\(467\) | −28.1616 | −1.30316 | −0.651582 | − | 0.758578i | \(-0.725894\pi\) | ||||
−0.651582 | + | 0.758578i | \(0.725894\pi\) | |||||||
\(468\) | −2.57318 | −0.118945 | ||||||||
\(469\) | 6.94161 | 0.320534 | ||||||||
\(470\) | −0.127943 | −0.00590157 | ||||||||
\(471\) | −1.00000 | −0.0460776 | ||||||||
\(472\) | −19.2220 | −0.884763 | ||||||||
\(473\) | 63.6062 | 2.92462 | ||||||||
\(474\) | 0.235012 | 0.0107944 | ||||||||
\(475\) | 2.81261 | 0.129051 | ||||||||
\(476\) | −7.81366 | −0.358139 | ||||||||
\(477\) | 0.351352 | 0.0160873 | ||||||||
\(478\) | 6.17093 | 0.282252 | ||||||||
\(479\) | −21.2150 | −0.969340 | −0.484670 | − | 0.874697i | \(-0.661060\pi\) | ||||
−0.484670 | + | 0.874697i | \(0.661060\pi\) | |||||||
\(480\) | 0.160331 | 0.00731809 | ||||||||
\(481\) | 9.80619 | 0.447124 | ||||||||
\(482\) | −14.6440 | −0.667017 | ||||||||
\(483\) | 11.0825 | 0.504272 | ||||||||
\(484\) | −41.5786 | −1.88994 | ||||||||
\(485\) | 0.426041 | 0.0193455 | ||||||||
\(486\) | −0.524942 | −0.0238118 | ||||||||
\(487\) | −4.25591 | −0.192853 | −0.0964267 | − | 0.995340i | \(-0.530741\pi\) | ||||
−0.0964267 | + | 0.995340i | \(0.530741\pi\) | |||||||
\(488\) | −1.03623 | −0.0469078 | ||||||||
\(489\) | −0.825261 | −0.0373196 | ||||||||
\(490\) | 0.219774 | 0.00992837 | ||||||||
\(491\) | −6.76995 | −0.305524 | −0.152762 | − | 0.988263i | \(-0.548817\pi\) | ||||
−0.152762 | + | 0.988263i | \(0.548817\pi\) | |||||||
\(492\) | 1.51412 | 0.0682618 | ||||||||
\(493\) | −2.50610 | −0.112869 | ||||||||
\(494\) | 0.440713 | 0.0198286 | ||||||||
\(495\) | 0.183338 | 0.00824041 | ||||||||
\(496\) | −11.1904 | −0.502465 | ||||||||
\(497\) | 6.96508 | 0.312427 | ||||||||
\(498\) | −2.18137 | −0.0977493 | ||||||||
\(499\) | 0.405409 | 0.0181486 | 0.00907431 | − | 0.999959i | \(-0.497112\pi\) | ||||
0.00907431 | + | 0.999959i | \(0.497112\pi\) | |||||||
\(500\) | −0.533498 | −0.0238588 | ||||||||
\(501\) | −20.8423 | −0.931165 | ||||||||
\(502\) | −2.15738 | −0.0962887 | ||||||||
\(503\) | −8.71444 | −0.388558 | −0.194279 | − | 0.980946i | \(-0.562237\pi\) | ||||
−0.194279 | + | 0.980946i | \(0.562237\pi\) | |||||||
\(504\) | 8.85889 | 0.394606 | ||||||||
\(505\) | 0.250059 | 0.0111275 | ||||||||
\(506\) | 7.60793 | 0.338214 | ||||||||
\(507\) | −10.7734 | −0.478463 | ||||||||
\(508\) | −13.6286 | −0.604671 | ||||||||
\(509\) | −17.2021 | −0.762472 | −0.381236 | − | 0.924478i | \(-0.624501\pi\) | ||||
−0.381236 | + | 0.924478i | \(0.624501\pi\) | |||||||
\(510\) | 0.0162420 | 0.000719206 0 | ||||||||
\(511\) | −29.1272 | −1.28851 | ||||||||
\(512\) | −22.0262 | −0.973430 | ||||||||
\(513\) | −0.562629 | −0.0248407 | ||||||||
\(514\) | −3.29418 | −0.145300 | ||||||||
\(515\) | −0.303697 | −0.0133825 | ||||||||
\(516\) | 18.5107 | 0.814887 | ||||||||
\(517\) | 46.6769 | 2.05285 | ||||||||
\(518\) | −15.6313 | −0.686802 | ||||||||
\(519\) | −7.60663 | −0.333894 | ||||||||
\(520\) | −0.0902654 | −0.00395840 | ||||||||
\(521\) | 12.7255 | 0.557514 | 0.278757 | − | 0.960362i | \(-0.410078\pi\) | ||||
0.278757 | + | 0.960362i | \(0.410078\pi\) | |||||||
\(522\) | 1.31556 | 0.0575804 | ||||||||
\(523\) | −27.3908 | −1.19772 | −0.598859 | − | 0.800855i | \(-0.704379\pi\) | ||||
−0.598859 | + | 0.800855i | \(0.704379\pi\) | |||||||
\(524\) | 0.783147 | 0.0342119 | ||||||||
\(525\) | −22.6514 | −0.988587 | ||||||||
\(526\) | −9.36255 | −0.408227 | ||||||||
\(527\) | −4.61927 | −0.201219 | ||||||||
\(528\) | −14.3548 | −0.624713 | ||||||||
\(529\) | −17.0178 | −0.739903 | ||||||||
\(530\) | 0.00570665 | 0.000247881 0 | ||||||||
\(531\) | −9.83165 | −0.426657 | ||||||||
\(532\) | 4.39619 | 0.190599 | ||||||||
\(533\) | −1.31019 | −0.0567508 | ||||||||
\(534\) | 4.52054 | 0.195623 | ||||||||
\(535\) | 0.210065 | 0.00908189 | ||||||||
\(536\) | 2.99519 | 0.129372 | ||||||||
\(537\) | 8.25507 | 0.356233 | ||||||||
\(538\) | −11.7774 | −0.507762 | ||||||||
\(539\) | −80.1792 | −3.45356 | ||||||||
\(540\) | 0.0533549 | 0.00229603 | ||||||||
\(541\) | −16.7552 | −0.720361 | −0.360180 | − | 0.932883i | \(-0.617285\pi\) | ||||
−0.360180 | + | 0.932883i | \(0.617285\pi\) | |||||||
\(542\) | −7.41015 | −0.318293 | ||||||||
\(543\) | −12.8556 | −0.551685 | ||||||||
\(544\) | −5.18192 | −0.222173 | ||||||||
\(545\) | −0.179521 | −0.00768984 | ||||||||
\(546\) | −3.54929 | −0.151895 | ||||||||
\(547\) | 26.2453 | 1.12217 | 0.561084 | − | 0.827759i | \(-0.310385\pi\) | ||||
0.561084 | + | 0.827759i | \(0.310385\pi\) | |||||||
\(548\) | −17.0745 | −0.729385 | ||||||||
\(549\) | −0.530009 | −0.0226202 | ||||||||
\(550\) | −15.5497 | −0.663042 | ||||||||
\(551\) | 1.41001 | 0.0600683 | ||||||||
\(552\) | 4.78193 | 0.203532 | ||||||||
\(553\) | −2.02855 | −0.0862628 | ||||||||
\(554\) | −9.35039 | −0.397260 | ||||||||
\(555\) | −0.203332 | −0.00863095 | ||||||||
\(556\) | −19.5447 | −0.828880 | ||||||||
\(557\) | 15.9331 | 0.675107 | 0.337553 | − | 0.941306i | \(-0.390401\pi\) | ||||
0.337553 | + | 0.941306i | \(0.390401\pi\) | |||||||
\(558\) | 2.42485 | 0.102652 | ||||||||
\(559\) | −16.0176 | −0.677472 | ||||||||
\(560\) | −0.339632 | −0.0143521 | ||||||||
\(561\) | −5.92549 | −0.250174 | ||||||||
\(562\) | 8.79788 | 0.371116 | ||||||||
\(563\) | 13.9202 | 0.586667 | 0.293333 | − | 0.956010i | \(-0.405235\pi\) | ||||
0.293333 | + | 0.956010i | \(0.405235\pi\) | |||||||
\(564\) | 13.5839 | 0.571986 | ||||||||
\(565\) | 0.198276 | 0.00834152 | ||||||||
\(566\) | −6.44047 | −0.270713 | ||||||||
\(567\) | 4.53114 | 0.190290 | ||||||||
\(568\) | 3.00532 | 0.126100 | ||||||||
\(569\) | −10.4683 | −0.438855 | −0.219428 | − | 0.975629i | \(-0.570419\pi\) | ||||
−0.219428 | + | 0.975629i | \(0.570419\pi\) | |||||||
\(570\) | −0.00913820 | −0.000382757 0 | ||||||||
\(571\) | −29.5260 | −1.23563 | −0.617813 | − | 0.786325i | \(-0.711981\pi\) | ||||
−0.617813 | + | 0.786325i | \(0.711981\pi\) | |||||||
\(572\) | 15.2473 | 0.637523 | ||||||||
\(573\) | −18.4625 | −0.771281 | ||||||||
\(574\) | 2.08849 | 0.0871718 | ||||||||
\(575\) | −12.2269 | −0.509899 | ||||||||
\(576\) | −2.12490 | −0.0885374 | ||||||||
\(577\) | −24.6124 | −1.02463 | −0.512313 | − | 0.858799i | \(-0.671211\pi\) | ||||
−0.512313 | + | 0.858799i | \(0.671211\pi\) | |||||||
\(578\) | −0.524942 | −0.0218347 | ||||||||
\(579\) | −18.6825 | −0.776420 | ||||||||
\(580\) | −0.133713 | −0.00555213 | ||||||||
\(581\) | 18.8289 | 0.781154 | ||||||||
\(582\) | 7.22829 | 0.299622 | ||||||||
\(583\) | −2.08193 | −0.0862249 | ||||||||
\(584\) | −12.5679 | −0.520063 | ||||||||
\(585\) | −0.0461689 | −0.00190885 | ||||||||
\(586\) | 10.5436 | 0.435551 | ||||||||
\(587\) | 21.0256 | 0.867819 | 0.433909 | − | 0.900956i | \(-0.357134\pi\) | ||||
0.433909 | + | 0.900956i | \(0.357134\pi\) | |||||||
\(588\) | −23.3337 | −0.962268 | ||||||||
\(589\) | 2.59893 | 0.107087 | ||||||||
\(590\) | −0.159685 | −0.00657414 | ||||||||
\(591\) | 14.4077 | 0.592652 | ||||||||
\(592\) | 15.9203 | 0.654320 | ||||||||
\(593\) | −33.0646 | −1.35780 | −0.678899 | − | 0.734231i | \(-0.737543\pi\) | ||||
−0.678899 | + | 0.734231i | \(0.737543\pi\) | |||||||
\(594\) | 3.11054 | 0.127627 | ||||||||
\(595\) | −0.140196 | −0.00574747 | ||||||||
\(596\) | 27.4092 | 1.12273 | ||||||||
\(597\) | 4.63934 | 0.189876 | ||||||||
\(598\) | −1.91586 | −0.0783455 | ||||||||
\(599\) | −2.05784 | −0.0840811 | −0.0420406 | − | 0.999116i | \(-0.513386\pi\) | ||||
−0.0420406 | + | 0.999116i | \(0.513386\pi\) | |||||||
\(600\) | −9.77369 | −0.399009 | ||||||||
\(601\) | 0.390478 | 0.0159279 | 0.00796397 | − | 0.999968i | \(-0.497465\pi\) | ||||
0.00796397 | + | 0.999968i | \(0.497465\pi\) | |||||||
\(602\) | 25.5325 | 1.04063 | ||||||||
\(603\) | 1.53198 | 0.0623870 | ||||||||
\(604\) | −20.5255 | −0.835171 | ||||||||
\(605\) | −0.746019 | −0.0303300 | ||||||||
\(606\) | 4.24254 | 0.172342 | ||||||||
\(607\) | −0.531510 | −0.0215733 | −0.0107867 | − | 0.999942i | \(-0.503434\pi\) | ||||
−0.0107867 | + | 0.999942i | \(0.503434\pi\) | |||||||
\(608\) | 2.91550 | 0.118239 | ||||||||
\(609\) | −11.3555 | −0.460148 | ||||||||
\(610\) | −0.00860838 | −0.000348543 0 | ||||||||
\(611\) | −11.7544 | −0.475532 | ||||||||
\(612\) | −1.72444 | −0.0697062 | ||||||||
\(613\) | 46.2746 | 1.86901 | 0.934506 | − | 0.355947i | \(-0.115842\pi\) | ||||
0.934506 | + | 0.355947i | \(0.115842\pi\) | |||||||
\(614\) | −10.0006 | −0.403593 | ||||||||
\(615\) | 0.0271669 | 0.00109548 | ||||||||
\(616\) | −52.4932 | −2.11501 | ||||||||
\(617\) | 1.35818 | 0.0546784 | 0.0273392 | − | 0.999626i | \(-0.491297\pi\) | ||||
0.0273392 | + | 0.999626i | \(0.491297\pi\) | |||||||
\(618\) | −5.15258 | −0.207267 | ||||||||
\(619\) | −28.6878 | −1.15306 | −0.576530 | − | 0.817076i | \(-0.695594\pi\) | ||||
−0.576530 | + | 0.817076i | \(0.695594\pi\) | |||||||
\(620\) | −0.246461 | −0.00989810 | ||||||||
\(621\) | 2.44586 | 0.0981489 | ||||||||
\(622\) | 0.0755439 | 0.00302903 | ||||||||
\(623\) | −39.0200 | −1.56330 | ||||||||
\(624\) | 3.61489 | 0.144712 | ||||||||
\(625\) | 24.9856 | 0.999426 | ||||||||
\(626\) | 14.8817 | 0.594793 | ||||||||
\(627\) | 3.33385 | 0.133141 | ||||||||
\(628\) | 1.72444 | 0.0688125 | ||||||||
\(629\) | 6.57170 | 0.262031 | ||||||||
\(630\) | 0.0735946 | 0.00293208 | ||||||||
\(631\) | −37.8397 | −1.50637 | −0.753187 | − | 0.657806i | \(-0.771485\pi\) | ||||
−0.753187 | + | 0.657806i | \(0.771485\pi\) | |||||||
\(632\) | −0.875286 | −0.0348170 | ||||||||
\(633\) | −20.8553 | −0.828924 | ||||||||
\(634\) | 4.80899 | 0.190990 | ||||||||
\(635\) | −0.244529 | −0.00970385 | ||||||||
\(636\) | −0.605885 | −0.0240249 | ||||||||
\(637\) | 20.1911 | 0.800000 | ||||||||
\(638\) | −7.79532 | −0.308620 | ||||||||
\(639\) | 1.53716 | 0.0608091 | ||||||||
\(640\) | −0.355175 | −0.0140395 | ||||||||
\(641\) | −11.5380 | −0.455724 | −0.227862 | − | 0.973693i | \(-0.573174\pi\) | ||||
−0.227862 | + | 0.973693i | \(0.573174\pi\) | |||||||
\(642\) | 3.56399 | 0.140660 | ||||||||
\(643\) | −35.5281 | −1.40109 | −0.700547 | − | 0.713607i | \(-0.747060\pi\) | ||||
−0.700547 | + | 0.713607i | \(0.747060\pi\) | |||||||
\(644\) | −19.1111 | −0.753083 | ||||||||
\(645\) | 0.332126 | 0.0130774 | ||||||||
\(646\) | 0.295347 | 0.0116203 | ||||||||
\(647\) | −17.4723 | −0.686908 | −0.343454 | − | 0.939170i | \(-0.611597\pi\) | ||||
−0.343454 | + | 0.939170i | \(0.611597\pi\) | |||||||
\(648\) | 1.95511 | 0.0768040 | ||||||||
\(649\) | 58.2573 | 2.28680 | ||||||||
\(650\) | 3.91580 | 0.153590 | ||||||||
\(651\) | −20.9306 | −0.820333 | ||||||||
\(652\) | 1.42311 | 0.0557333 | ||||||||
\(653\) | −17.9820 | −0.703689 | −0.351844 | − | 0.936059i | \(-0.614445\pi\) | ||||
−0.351844 | + | 0.936059i | \(0.614445\pi\) | |||||||
\(654\) | −3.04578 | −0.119100 | ||||||||
\(655\) | 0.0140515 | 0.000549039 0 | ||||||||
\(656\) | −2.12709 | −0.0830491 | ||||||||
\(657\) | −6.42822 | −0.250789 | ||||||||
\(658\) | 18.7368 | 0.730438 | ||||||||
\(659\) | −28.2993 | −1.10238 | −0.551192 | − | 0.834379i | \(-0.685827\pi\) | ||||
−0.551192 | + | 0.834379i | \(0.685827\pi\) | |||||||
\(660\) | −0.316154 | −0.0123063 | ||||||||
\(661\) | −10.0576 | −0.391194 | −0.195597 | − | 0.980684i | \(-0.562665\pi\) | ||||
−0.195597 | + | 0.980684i | \(0.562665\pi\) | |||||||
\(662\) | −11.2984 | −0.439123 | ||||||||
\(663\) | 1.49218 | 0.0579516 | ||||||||
\(664\) | 8.12436 | 0.315286 | ||||||||
\(665\) | 0.0788782 | 0.00305877 | ||||||||
\(666\) | −3.44976 | −0.133675 | ||||||||
\(667\) | −6.12957 | −0.237338 | ||||||||
\(668\) | 35.9412 | 1.39061 | ||||||||
\(669\) | −5.38829 | −0.208323 | ||||||||
\(670\) | 0.0248823 | 0.000961289 0 | ||||||||
\(671\) | 3.14056 | 0.121240 | ||||||||
\(672\) | −23.4800 | −0.905761 | ||||||||
\(673\) | −5.54678 | −0.213813 | −0.106906 | − | 0.994269i | \(-0.534094\pi\) | ||||
−0.106906 | + | 0.994269i | \(0.534094\pi\) | |||||||
\(674\) | 11.7614 | 0.453034 | ||||||||
\(675\) | −4.99904 | −0.192413 | ||||||||
\(676\) | 18.5780 | 0.714539 | ||||||||
\(677\) | −19.3559 | −0.743907 | −0.371953 | − | 0.928251i | \(-0.621312\pi\) | ||||
−0.371953 | + | 0.928251i | \(0.621312\pi\) | |||||||
\(678\) | 3.36398 | 0.129193 | ||||||||
\(679\) | −62.3924 | −2.39440 | ||||||||
\(680\) | −0.0604922 | −0.00231977 | ||||||||
\(681\) | 15.8982 | 0.609220 | ||||||||
\(682\) | −14.3684 | −0.550195 | ||||||||
\(683\) | 31.7896 | 1.21640 | 0.608198 | − | 0.793785i | \(-0.291893\pi\) | ||||
0.608198 | + | 0.793785i | \(0.291893\pi\) | |||||||
\(684\) | 0.970218 | 0.0370972 | ||||||||
\(685\) | −0.306357 | −0.0117053 | ||||||||
\(686\) | −15.5351 | −0.593132 | ||||||||
\(687\) | 15.6755 | 0.598059 | ||||||||
\(688\) | −26.0045 | −0.991412 | ||||||||
\(689\) | 0.524282 | 0.0199736 | ||||||||
\(690\) | 0.0397255 | 0.00151233 | ||||||||
\(691\) | 47.2811 | 1.79866 | 0.899329 | − | 0.437273i | \(-0.144056\pi\) | ||||
0.899329 | + | 0.437273i | \(0.144056\pi\) | |||||||
\(692\) | 13.1172 | 0.498639 | ||||||||
\(693\) | −26.8492 | −1.01992 | ||||||||
\(694\) | −12.2299 | −0.464241 | ||||||||
\(695\) | −0.350679 | −0.0133020 | ||||||||
\(696\) | −4.89971 | −0.185723 | ||||||||
\(697\) | −0.878038 | −0.0332581 | ||||||||
\(698\) | 8.10611 | 0.306821 | ||||||||
\(699\) | −17.1629 | −0.649161 | ||||||||
\(700\) | 39.0608 | 1.47636 | ||||||||
\(701\) | −31.4591 | −1.18819 | −0.594096 | − | 0.804394i | \(-0.702490\pi\) | ||||
−0.594096 | + | 0.804394i | \(0.702490\pi\) | |||||||
\(702\) | −0.783310 | −0.0295641 | ||||||||
\(703\) | −3.69743 | −0.139451 | ||||||||
\(704\) | 12.5911 | 0.474543 | ||||||||
\(705\) | 0.243728 | 0.00917932 | ||||||||
\(706\) | −5.54144 | −0.208555 | ||||||||
\(707\) | −36.6204 | −1.37725 | ||||||||
\(708\) | 16.9541 | 0.637172 | ||||||||
\(709\) | −22.0195 | −0.826961 | −0.413480 | − | 0.910513i | \(-0.635687\pi\) | ||||
−0.413480 | + | 0.910513i | \(0.635687\pi\) | |||||||
\(710\) | 0.0249665 | 0.000936975 0 | ||||||||
\(711\) | −0.447691 | −0.0167897 | ||||||||
\(712\) | −16.8365 | −0.630974 | ||||||||
\(713\) | −11.2981 | −0.423116 | ||||||||
\(714\) | −2.37858 | −0.0890163 | ||||||||
\(715\) | 0.273573 | 0.0102311 | ||||||||
\(716\) | −14.2353 | −0.532000 | ||||||||
\(717\) | −11.7555 | −0.439016 | ||||||||
\(718\) | 18.0635 | 0.674124 | ||||||||
\(719\) | −21.6422 | −0.807119 | −0.403560 | − | 0.914953i | \(-0.632227\pi\) | ||||
−0.403560 | + | 0.914953i | \(0.632227\pi\) | |||||||
\(720\) | −0.0749550 | −0.00279341 | ||||||||
\(721\) | 44.4755 | 1.65635 | ||||||||
\(722\) | 9.80772 | 0.365006 | ||||||||
\(723\) | 27.8965 | 1.03748 | ||||||||
\(724\) | 22.1686 | 0.823889 | ||||||||
\(725\) | 12.5281 | 0.465283 | ||||||||
\(726\) | −12.6571 | −0.469749 | ||||||||
\(727\) | −14.8127 | −0.549374 | −0.274687 | − | 0.961534i | \(-0.588574\pi\) | ||||
−0.274687 | + | 0.961534i | \(0.588574\pi\) | |||||||
\(728\) | 13.2191 | 0.489932 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.104407 | −0.00386428 | ||||||||
\(731\) | −10.7343 | −0.397024 | ||||||||
\(732\) | 0.913967 | 0.0337812 | ||||||||
\(733\) | 39.1731 | 1.44689 | 0.723446 | − | 0.690381i | \(-0.242557\pi\) | ||||
0.723446 | + | 0.690381i | \(0.242557\pi\) | |||||||
\(734\) | 17.6185 | 0.650312 | ||||||||
\(735\) | −0.418663 | −0.0154426 | ||||||||
\(736\) | −12.6742 | −0.467179 | ||||||||
\(737\) | −9.07772 | −0.334382 | ||||||||
\(738\) | 0.460919 | 0.0169667 | ||||||||
\(739\) | 43.5631 | 1.60250 | 0.801248 | − | 0.598332i | \(-0.204170\pi\) | ||||
0.801248 | + | 0.598332i | \(0.204170\pi\) | |||||||
\(740\) | 0.350633 | 0.0128895 | ||||||||
\(741\) | −0.839546 | −0.0308415 | ||||||||
\(742\) | −0.835721 | −0.0306803 | ||||||||
\(743\) | 34.4910 | 1.26535 | 0.632676 | − | 0.774416i | \(-0.281956\pi\) | ||||
0.632676 | + | 0.774416i | \(0.281956\pi\) | |||||||
\(744\) | −9.03119 | −0.331099 | ||||||||
\(745\) | 0.491787 | 0.0180177 | ||||||||
\(746\) | 0.368369 | 0.0134870 | ||||||||
\(747\) | 4.15544 | 0.152040 | ||||||||
\(748\) | 10.2181 | 0.373612 | ||||||||
\(749\) | −30.7633 | −1.12407 | ||||||||
\(750\) | −0.162404 | −0.00593016 | ||||||||
\(751\) | −50.4142 | −1.83964 | −0.919820 | − | 0.392341i | \(-0.871665\pi\) | ||||
−0.919820 | + | 0.392341i | \(0.871665\pi\) | |||||||
\(752\) | −19.0832 | −0.695892 | ||||||||
\(753\) | 4.10976 | 0.149768 | ||||||||
\(754\) | 1.96305 | 0.0714902 | ||||||||
\(755\) | −0.368277 | −0.0134030 | ||||||||
\(756\) | −7.81366 | −0.284180 | ||||||||
\(757\) | 0.908233 | 0.0330103 | 0.0165052 | − | 0.999864i | \(-0.494746\pi\) | ||||
0.0165052 | + | 0.999864i | \(0.494746\pi\) | |||||||
\(758\) | 7.60003 | 0.276045 | ||||||||
\(759\) | −14.4929 | −0.526059 | ||||||||
\(760\) | 0.0340346 | 0.00123457 | ||||||||
\(761\) | −12.5656 | −0.455503 | −0.227752 | − | 0.973719i | \(-0.573137\pi\) | ||||
−0.227752 | + | 0.973719i | \(0.573137\pi\) | |||||||
\(762\) | −4.14873 | −0.150292 | ||||||||
\(763\) | 26.2903 | 0.951773 | ||||||||
\(764\) | 31.8374 | 1.15184 | ||||||||
\(765\) | −0.0309405 | −0.00111866 | ||||||||
\(766\) | −5.77569 | −0.208684 | ||||||||
\(767\) | −14.6706 | −0.529726 | ||||||||
\(768\) | −1.77616 | −0.0640918 | ||||||||
\(769\) | 41.0157 | 1.47906 | 0.739532 | − | 0.673121i | \(-0.235047\pi\) | ||||
0.739532 | + | 0.673121i | \(0.235047\pi\) | |||||||
\(770\) | −0.436084 | −0.0157154 | ||||||||
\(771\) | 6.27533 | 0.226001 | ||||||||
\(772\) | 32.2168 | 1.15951 | ||||||||
\(773\) | 11.9536 | 0.429941 | 0.214971 | − | 0.976621i | \(-0.431034\pi\) | ||||
0.214971 | + | 0.976621i | \(0.431034\pi\) | |||||||
\(774\) | 5.63490 | 0.202542 | ||||||||
\(775\) | 23.0919 | 0.829486 | ||||||||
\(776\) | −26.9213 | −0.966418 | ||||||||
\(777\) | 29.7773 | 1.06825 | ||||||||
\(778\) | 10.5830 | 0.379417 | ||||||||
\(779\) | 0.494010 | 0.0176997 | ||||||||
\(780\) | 0.0796154 | 0.00285069 | ||||||||
\(781\) | −9.10842 | −0.325925 | ||||||||
\(782\) | −1.28393 | −0.0459133 | ||||||||
\(783\) | −2.50610 | −0.0895608 | ||||||||
\(784\) | 32.7801 | 1.17072 | ||||||||
\(785\) | 0.0309405 | 0.00110431 | ||||||||
\(786\) | 0.238401 | 0.00850347 | ||||||||
\(787\) | 10.3129 | 0.367613 | 0.183807 | − | 0.982962i | \(-0.441158\pi\) | ||||
0.183807 | + | 0.982962i | \(0.441158\pi\) | |||||||
\(788\) | −24.8451 | −0.885070 | ||||||||
\(789\) | 17.8354 | 0.634957 | ||||||||
\(790\) | −0.00727138 | −0.000258704 0 | ||||||||
\(791\) | −29.0368 | −1.03243 | ||||||||
\(792\) | −11.5850 | −0.411655 | ||||||||
\(793\) | −0.790871 | −0.0280846 | ||||||||
\(794\) | −10.2672 | −0.364369 | ||||||||
\(795\) | −0.0108710 | −0.000385555 0 | ||||||||
\(796\) | −8.00025 | −0.283561 | ||||||||
\(797\) | 43.0865 | 1.52620 | 0.763102 | − | 0.646278i | \(-0.223675\pi\) | ||||
0.763102 | + | 0.646278i | \(0.223675\pi\) | |||||||
\(798\) | 1.33826 | 0.0473739 | ||||||||
\(799\) | −7.87731 | −0.278679 | ||||||||
\(800\) | 25.9047 | 0.915868 | ||||||||
\(801\) | −8.61151 | −0.304273 | ||||||||
\(802\) | −12.8135 | −0.452461 | ||||||||
\(803\) | 38.0904 | 1.34418 | ||||||||
\(804\) | −2.64180 | −0.0931691 | ||||||||
\(805\) | −0.342899 | −0.0120856 | ||||||||
\(806\) | 3.61832 | 0.127450 | ||||||||
\(807\) | 22.4357 | 0.789775 | ||||||||
\(808\) | −15.8011 | −0.555880 | ||||||||
\(809\) | −2.33890 | −0.0822312 | −0.0411156 | − | 0.999154i | \(-0.513091\pi\) | ||||
−0.0411156 | + | 0.999154i | \(0.513091\pi\) | |||||||
\(810\) | 0.0162420 | 0.000570684 0 | ||||||||
\(811\) | −24.1108 | −0.846645 | −0.423323 | − | 0.905979i | \(-0.639136\pi\) | ||||
−0.423323 | + | 0.905979i | \(0.639136\pi\) | |||||||
\(812\) | 19.5818 | 0.687188 | ||||||||
\(813\) | 14.1161 | 0.495075 | ||||||||
\(814\) | 20.4415 | 0.716475 | ||||||||
\(815\) | 0.0255340 | 0.000894417 0 | ||||||||
\(816\) | 2.42255 | 0.0848063 | ||||||||
\(817\) | 6.03945 | 0.211294 | ||||||||
\(818\) | −0.414219 | −0.0144828 | ||||||||
\(819\) | 6.76130 | 0.236259 | ||||||||
\(820\) | −0.0468477 | −0.00163599 | ||||||||
\(821\) | −16.7806 | −0.585647 | −0.292823 | − | 0.956167i | \(-0.594595\pi\) | ||||
−0.292823 | + | 0.956167i | \(0.594595\pi\) | |||||||
\(822\) | −5.19770 | −0.181291 | ||||||||
\(823\) | 44.7104 | 1.55851 | 0.779253 | − | 0.626710i | \(-0.215599\pi\) | ||||
0.779253 | + | 0.626710i | \(0.215599\pi\) | |||||||
\(824\) | 19.1904 | 0.668531 | ||||||||
\(825\) | 29.6218 | 1.03130 | ||||||||
\(826\) | 23.3854 | 0.813683 | ||||||||
\(827\) | 26.2729 | 0.913597 | 0.456798 | − | 0.889570i | \(-0.348996\pi\) | ||||
0.456798 | + | 0.889570i | \(0.348996\pi\) | |||||||
\(828\) | −4.21773 | −0.146576 | ||||||||
\(829\) | 2.93255 | 0.101852 | 0.0509258 | − | 0.998702i | \(-0.483783\pi\) | ||||
0.0509258 | + | 0.998702i | \(0.483783\pi\) | |||||||
\(830\) | 0.0674926 | 0.00234270 | ||||||||
\(831\) | 17.8122 | 0.617900 | ||||||||
\(832\) | −3.17074 | −0.109926 | ||||||||
\(833\) | 13.5312 | 0.468829 | ||||||||
\(834\) | −5.94967 | −0.206020 | ||||||||
\(835\) | 0.644871 | 0.0223167 | ||||||||
\(836\) | −5.74901 | −0.198834 | ||||||||
\(837\) | −4.61927 | −0.159665 | ||||||||
\(838\) | −20.2104 | −0.698158 | ||||||||
\(839\) | −34.5744 | −1.19364 | −0.596821 | − | 0.802374i | \(-0.703570\pi\) | ||||
−0.596821 | + | 0.802374i | \(0.703570\pi\) | |||||||
\(840\) | −0.274098 | −0.00945729 | ||||||||
\(841\) | −22.7194 | −0.783429 | ||||||||
\(842\) | 4.10323 | 0.141407 | ||||||||
\(843\) | −16.7597 | −0.577236 | ||||||||
\(844\) | 35.9637 | 1.23792 | ||||||||
\(845\) | 0.333334 | 0.0114670 | ||||||||
\(846\) | 4.13513 | 0.142169 | ||||||||
\(847\) | 109.252 | 3.75395 | ||||||||
\(848\) | 0.851170 | 0.0292293 | ||||||||
\(849\) | 12.2689 | 0.421068 | ||||||||
\(850\) | 2.62421 | 0.0900095 | ||||||||
\(851\) | 16.0734 | 0.550991 | ||||||||
\(852\) | −2.65073 | −0.0908126 | ||||||||
\(853\) | −53.6615 | −1.83734 | −0.918668 | − | 0.395032i | \(-0.870734\pi\) | ||||
−0.918668 | + | 0.395032i | \(0.870734\pi\) | |||||||
\(854\) | 1.26067 | 0.0431393 | ||||||||
\(855\) | 0.0174080 | 0.000595342 0 | ||||||||
\(856\) | −13.2739 | −0.453691 | ||||||||
\(857\) | −14.4224 | −0.492660 | −0.246330 | − | 0.969186i | \(-0.579225\pi\) | ||||
−0.246330 | + | 0.969186i | \(0.579225\pi\) | |||||||
\(858\) | 4.64149 | 0.158458 | ||||||||
\(859\) | −13.3074 | −0.454043 | −0.227021 | − | 0.973890i | \(-0.572899\pi\) | ||||
−0.227021 | + | 0.973890i | \(0.572899\pi\) | |||||||
\(860\) | −0.572730 | −0.0195299 | ||||||||
\(861\) | −3.97851 | −0.135587 | ||||||||
\(862\) | 5.65572 | 0.192634 | ||||||||
\(863\) | 18.4520 | 0.628113 | 0.314056 | − | 0.949404i | \(-0.398312\pi\) | ||||
0.314056 | + | 0.949404i | \(0.398312\pi\) | |||||||
\(864\) | −5.18192 | −0.176293 | ||||||||
\(865\) | 0.235353 | 0.00800224 | ||||||||
\(866\) | 6.59448 | 0.224089 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 36.0934 | 1.22509 | ||||||||
\(869\) | 2.65279 | 0.0899897 | ||||||||
\(870\) | −0.0407040 | −0.00138000 | ||||||||
\(871\) | 2.28599 | 0.0774580 | ||||||||
\(872\) | 11.3438 | 0.384151 | ||||||||
\(873\) | −13.7697 | −0.466034 | ||||||||
\(874\) | 0.722378 | 0.0244348 | ||||||||
\(875\) | 1.40182 | 0.0473903 | ||||||||
\(876\) | 11.0851 | 0.374530 | ||||||||
\(877\) | −16.1852 | −0.546536 | −0.273268 | − | 0.961938i | \(-0.588105\pi\) | ||||
−0.273268 | + | 0.961938i | \(0.588105\pi\) | |||||||
\(878\) | −0.355973 | −0.0120135 | ||||||||
\(879\) | −20.0852 | −0.677458 | ||||||||
\(880\) | 0.444145 | 0.0149721 | ||||||||
\(881\) | 1.87050 | 0.0630187 | 0.0315093 | − | 0.999503i | \(-0.489969\pi\) | ||||
0.0315093 | + | 0.999503i | \(0.489969\pi\) | |||||||
\(882\) | −7.10311 | −0.239174 | ||||||||
\(883\) | 25.7461 | 0.866426 | 0.433213 | − | 0.901291i | \(-0.357380\pi\) | ||||
0.433213 | + | 0.901291i | \(0.357380\pi\) | |||||||
\(884\) | −2.57318 | −0.0865453 | ||||||||
\(885\) | 0.304196 | 0.0102254 | ||||||||
\(886\) | −2.02986 | −0.0681946 | ||||||||
\(887\) | −9.15777 | −0.307488 | −0.153744 | − | 0.988111i | \(-0.549133\pi\) | ||||
−0.153744 | + | 0.988111i | \(0.549133\pi\) | |||||||
\(888\) | 12.8484 | 0.431164 | ||||||||
\(889\) | 35.8106 | 1.20105 | ||||||||
\(890\) | −0.139868 | −0.00468838 | ||||||||
\(891\) | −5.92549 | −0.198511 | ||||||||
\(892\) | 9.29176 | 0.311111 | ||||||||
\(893\) | 4.43200 | 0.148311 | ||||||||
\(894\) | 8.34374 | 0.279056 | ||||||||
\(895\) | −0.255416 | −0.00853762 | ||||||||
\(896\) | 52.0143 | 1.73768 | ||||||||
\(897\) | 3.64967 | 0.121859 | ||||||||
\(898\) | 21.1410 | 0.705486 | ||||||||
\(899\) | 11.5764 | 0.386093 | ||||||||
\(900\) | 8.62053 | 0.287351 | ||||||||
\(901\) | 0.351352 | 0.0117052 | ||||||||
\(902\) | −2.73117 | −0.0909380 | ||||||||
\(903\) | −48.6388 | −1.61860 | ||||||||
\(904\) | −12.5289 | −0.416705 | ||||||||
\(905\) | 0.397758 | 0.0132219 | ||||||||
\(906\) | −6.24824 | −0.207584 | ||||||||
\(907\) | 30.9045 | 1.02617 | 0.513083 | − | 0.858339i | \(-0.328503\pi\) | ||||
0.513083 | + | 0.858339i | \(0.328503\pi\) | |||||||
\(908\) | −27.4154 | −0.909813 | ||||||||
\(909\) | −8.08193 | −0.268061 | ||||||||
\(910\) | 0.109817 | 0.00364039 | ||||||||
\(911\) | −34.3041 | −1.13655 | −0.568274 | − | 0.822840i | \(-0.692388\pi\) | ||||
−0.568274 | + | 0.822840i | \(0.692388\pi\) | |||||||
\(912\) | −1.36300 | −0.0451334 | ||||||||
\(913\) | −24.6230 | −0.814904 | ||||||||
\(914\) | −0.153959 | −0.00509252 | ||||||||
\(915\) | 0.0163987 | 0.000542126 0 | ||||||||
\(916\) | −27.0314 | −0.893144 | ||||||||
\(917\) | −2.05780 | −0.0679546 | ||||||||
\(918\) | −0.524942 | −0.0173257 | ||||||||
\(919\) | 11.9896 | 0.395502 | 0.197751 | − | 0.980252i | \(-0.436636\pi\) | ||||
0.197751 | + | 0.980252i | \(0.436636\pi\) | |||||||
\(920\) | −0.147955 | −0.00487794 | ||||||||
\(921\) | 19.0510 | 0.627750 | ||||||||
\(922\) | 2.02973 | 0.0668456 | ||||||||
\(923\) | 2.29372 | 0.0754988 | ||||||||
\(924\) | 46.2998 | 1.52315 | ||||||||
\(925\) | −32.8522 | −1.08017 | ||||||||
\(926\) | −1.80803 | −0.0594155 | ||||||||
\(927\) | 9.81552 | 0.322384 | ||||||||
\(928\) | 12.9864 | 0.426301 | ||||||||
\(929\) | 0.926931 | 0.0304116 | 0.0152058 | − | 0.999884i | \(-0.495160\pi\) | ||||
0.0152058 | + | 0.999884i | \(0.495160\pi\) | |||||||
\(930\) | −0.0750260 | −0.00246020 | ||||||||
\(931\) | −7.61306 | −0.249508 | ||||||||
\(932\) | 29.5964 | 0.969461 | ||||||||
\(933\) | −0.143909 | −0.00471137 | ||||||||
\(934\) | 14.7832 | 0.483721 | ||||||||
\(935\) | 0.183338 | 0.00599578 | ||||||||
\(936\) | 2.91739 | 0.0953578 | ||||||||
\(937\) | 27.0705 | 0.884355 | 0.442177 | − | 0.896928i | \(-0.354206\pi\) | ||||
0.442177 | + | 0.896928i | \(0.354206\pi\) | |||||||
\(938\) | −3.64394 | −0.118979 | ||||||||
\(939\) | −28.3493 | −0.925143 | ||||||||
\(940\) | −0.420293 | −0.0137085 | ||||||||
\(941\) | −51.3099 | −1.67266 | −0.836328 | − | 0.548230i | \(-0.815302\pi\) | ||||
−0.836328 | + | 0.548230i | \(0.815302\pi\) | |||||||
\(942\) | 0.524942 | 0.0171035 | ||||||||
\(943\) | −2.14756 | −0.0699341 | ||||||||
\(944\) | −23.8177 | −0.775200 | ||||||||
\(945\) | −0.140196 | −0.00456057 | ||||||||
\(946\) | −33.3895 | −1.08559 | ||||||||
\(947\) | −35.4696 | −1.15261 | −0.576303 | − | 0.817236i | \(-0.695505\pi\) | ||||
−0.576303 | + | 0.817236i | \(0.695505\pi\) | |||||||
\(948\) | 0.772015 | 0.0250739 | ||||||||
\(949\) | −9.59209 | −0.311373 | ||||||||
\(950\) | −1.47645 | −0.0479025 | ||||||||
\(951\) | −9.16101 | −0.297066 | ||||||||
\(952\) | 8.85889 | 0.287118 | ||||||||
\(953\) | −2.18539 | −0.0707916 | −0.0353958 | − | 0.999373i | \(-0.511269\pi\) | ||||
−0.0353958 | + | 0.999373i | \(0.511269\pi\) | |||||||
\(954\) | −0.184440 | −0.00597145 | ||||||||
\(955\) | 0.571238 | 0.0184848 | ||||||||
\(956\) | 20.2716 | 0.655629 | ||||||||
\(957\) | 14.8499 | 0.480029 | ||||||||
\(958\) | 11.1367 | 0.359809 | ||||||||
\(959\) | 44.8650 | 1.44877 | ||||||||
\(960\) | 0.0657454 | 0.00212192 | ||||||||
\(961\) | −9.66235 | −0.311689 | ||||||||
\(962\) | −5.14768 | −0.165968 | ||||||||
\(963\) | −6.78931 | −0.218782 | ||||||||
\(964\) | −48.1057 | −1.54938 | ||||||||
\(965\) | 0.578047 | 0.0186080 | ||||||||
\(966\) | −5.81768 | −0.187181 | ||||||||
\(967\) | 51.2189 | 1.64709 | 0.823544 | − | 0.567253i | \(-0.191994\pi\) | ||||
0.823544 | + | 0.567253i | \(0.191994\pi\) | |||||||
\(968\) | 47.1405 | 1.51515 | ||||||||
\(969\) | −0.562629 | −0.0180742 | ||||||||
\(970\) | −0.223647 | −0.00718087 | ||||||||
\(971\) | 58.8245 | 1.88777 | 0.943884 | − | 0.330277i | \(-0.107142\pi\) | ||||
0.943884 | + | 0.330277i | \(0.107142\pi\) | |||||||
\(972\) | −1.72444 | −0.0553113 | ||||||||
\(973\) | 51.3558 | 1.64639 | ||||||||
\(974\) | 2.23410 | 0.0715853 | ||||||||
\(975\) | −7.45949 | −0.238895 | ||||||||
\(976\) | −1.28397 | −0.0410990 | ||||||||
\(977\) | −50.9504 | −1.63005 | −0.815025 | − | 0.579426i | \(-0.803277\pi\) | ||||
−0.815025 | + | 0.579426i | \(0.803277\pi\) | |||||||
\(978\) | 0.433214 | 0.0138526 | ||||||||
\(979\) | 51.0274 | 1.63084 | ||||||||
\(980\) | 0.721958 | 0.0230621 | ||||||||
\(981\) | 5.80214 | 0.185248 | ||||||||
\(982\) | 3.55383 | 0.113407 | ||||||||
\(983\) | 16.1742 | 0.515877 | 0.257938 | − | 0.966161i | \(-0.416957\pi\) | ||||
0.257938 | + | 0.966161i | \(0.416957\pi\) | |||||||
\(984\) | −1.71666 | −0.0547252 | ||||||||
\(985\) | −0.445780 | −0.0142037 | ||||||||
\(986\) | 1.31556 | 0.0418959 | ||||||||
\(987\) | −35.6932 | −1.13613 | ||||||||
\(988\) | 1.44774 | 0.0460589 | ||||||||
\(989\) | −26.2547 | −0.834850 | ||||||||
\(990\) | −0.0962416 | −0.00305876 | ||||||||
\(991\) | 34.6195 | 1.09973 | 0.549863 | − | 0.835255i | \(-0.314680\pi\) | ||||
0.549863 | + | 0.835255i | \(0.314680\pi\) | |||||||
\(992\) | 23.9367 | 0.759991 | ||||||||
\(993\) | 21.5231 | 0.683014 | ||||||||
\(994\) | −3.65626 | −0.115970 | ||||||||
\(995\) | −0.143544 | −0.00455064 | ||||||||
\(996\) | −7.16580 | −0.227057 | ||||||||
\(997\) | 35.7180 | 1.13120 | 0.565600 | − | 0.824680i | \(-0.308645\pi\) | ||||
0.565600 | + | 0.824680i | \(0.308645\pi\) | |||||||
\(998\) | −0.212816 | −0.00673658 | ||||||||
\(999\) | 6.57170 | 0.207919 |
(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 | 8007.2.a.d.1.18 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.d.1.18 | ✓ | 40 | 1.1 | even | 1 | trivial |