Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(0\) |
Dimension: | \(176\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59269 | −1.83331 | −0.916654 | − | 0.399682i | \(-0.869120\pi\) | ||||
−0.916654 | + | 0.399682i | \(0.869120\pi\) | |||||||
\(3\) | 0.175910 | 0.101562 | 0.0507808 | − | 0.998710i | \(-0.483829\pi\) | ||||
0.0507808 | + | 0.998710i | \(0.483829\pi\) | |||||||
\(4\) | 4.72203 | 2.36102 | ||||||||
\(5\) | 3.23280 | 1.44575 | 0.722876 | − | 0.690978i | \(-0.242820\pi\) | ||||
0.722876 | + | 0.690978i | \(0.242820\pi\) | |||||||
\(6\) | −0.456079 | −0.186193 | ||||||||
\(7\) | 2.53654 | 0.958720 | 0.479360 | − | 0.877618i | \(-0.340869\pi\) | ||||
0.479360 | + | 0.877618i | \(0.340869\pi\) | |||||||
\(8\) | −7.05738 | −2.49516 | ||||||||
\(9\) | −2.96906 | −0.989685 | ||||||||
\(10\) | −8.38164 | −2.65051 | ||||||||
\(11\) | 5.30695 | 1.60011 | 0.800053 | − | 0.599929i | \(-0.204804\pi\) | ||||
0.800053 | + | 0.599929i | \(0.204804\pi\) | |||||||
\(12\) | 0.830651 | 0.239788 | ||||||||
\(13\) | −5.29312 | −1.46805 | −0.734024 | − | 0.679123i | \(-0.762360\pi\) | ||||
−0.734024 | + | 0.679123i | \(0.762360\pi\) | |||||||
\(14\) | −6.57644 | −1.75763 | ||||||||
\(15\) | 0.568680 | 0.146833 | ||||||||
\(16\) | 8.85352 | 2.21338 | ||||||||
\(17\) | 2.29833 | 0.557426 | 0.278713 | − | 0.960374i | \(-0.410092\pi\) | ||||
0.278713 | + | 0.960374i | \(0.410092\pi\) | |||||||
\(18\) | 7.69784 | 1.81440 | ||||||||
\(19\) | −3.46792 | −0.795596 | −0.397798 | − | 0.917473i | \(-0.630225\pi\) | ||||
−0.397798 | + | 0.917473i | \(0.630225\pi\) | |||||||
\(20\) | 15.2654 | 3.41344 | ||||||||
\(21\) | 0.446201 | 0.0973691 | ||||||||
\(22\) | −13.7593 | −2.93349 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.24146 | −0.253412 | ||||||||
\(25\) | 5.45098 | 1.09020 | ||||||||
\(26\) | 13.7234 | 2.69138 | ||||||||
\(27\) | −1.05001 | −0.202075 | ||||||||
\(28\) | 11.9776 | 2.26355 | ||||||||
\(29\) | −8.54620 | −1.58699 | −0.793495 | − | 0.608577i | \(-0.791741\pi\) | ||||
−0.793495 | + | 0.608577i | \(0.791741\pi\) | |||||||
\(30\) | −1.47441 | −0.269189 | ||||||||
\(31\) | 5.22128 | 0.937769 | 0.468885 | − | 0.883259i | \(-0.344656\pi\) | ||||
0.468885 | + | 0.883259i | \(0.344656\pi\) | |||||||
\(32\) | −8.83965 | −1.56264 | ||||||||
\(33\) | 0.933545 | 0.162509 | ||||||||
\(34\) | −5.95884 | −1.02193 | ||||||||
\(35\) | 8.20011 | 1.38607 | ||||||||
\(36\) | −14.0200 | −2.33666 | ||||||||
\(37\) | 9.38807 | 1.54339 | 0.771694 | − | 0.635994i | \(-0.219410\pi\) | ||||
0.771694 | + | 0.635994i | \(0.219410\pi\) | |||||||
\(38\) | 8.99124 | 1.45857 | ||||||||
\(39\) | −0.931112 | −0.149097 | ||||||||
\(40\) | −22.8151 | −3.60738 | ||||||||
\(41\) | 12.6328 | 1.97291 | 0.986454 | − | 0.164040i | \(-0.0524527\pi\) | ||||
0.986454 | + | 0.164040i | \(0.0524527\pi\) | |||||||
\(42\) | −1.15686 | −0.178507 | ||||||||
\(43\) | −3.98512 | −0.607725 | −0.303862 | − | 0.952716i | \(-0.598276\pi\) | ||||
−0.303862 | + | 0.952716i | \(0.598276\pi\) | |||||||
\(44\) | 25.0596 | 3.77788 | ||||||||
\(45\) | −9.59836 | −1.43084 | ||||||||
\(46\) | −2.59269 | −0.382271 | ||||||||
\(47\) | −2.42572 | −0.353827 | −0.176914 | − | 0.984226i | \(-0.556611\pi\) | ||||
−0.176914 | + | 0.984226i | \(0.556611\pi\) | |||||||
\(48\) | 1.55742 | 0.224794 | ||||||||
\(49\) | −0.565990 | −0.0808557 | ||||||||
\(50\) | −14.1327 | −1.99867 | ||||||||
\(51\) | 0.404298 | 0.0566130 | ||||||||
\(52\) | −24.9943 | −3.46609 | ||||||||
\(53\) | 7.85499 | 1.07897 | 0.539483 | − | 0.841996i | \(-0.318620\pi\) | ||||
0.539483 | + | 0.841996i | \(0.318620\pi\) | |||||||
\(54\) | 2.72236 | 0.370466 | ||||||||
\(55\) | 17.1563 | 2.31336 | ||||||||
\(56\) | −17.9013 | −2.39216 | ||||||||
\(57\) | −0.610041 | −0.0808019 | ||||||||
\(58\) | 22.1576 | 2.90944 | ||||||||
\(59\) | 2.47534 | 0.322262 | 0.161131 | − | 0.986933i | \(-0.448486\pi\) | ||||
0.161131 | + | 0.986933i | \(0.448486\pi\) | |||||||
\(60\) | 2.68533 | 0.346674 | ||||||||
\(61\) | −13.0307 | −1.66841 | −0.834206 | − | 0.551453i | \(-0.814074\pi\) | ||||
−0.834206 | + | 0.551453i | \(0.814074\pi\) | |||||||
\(62\) | −13.5371 | −1.71922 | ||||||||
\(63\) | −7.53111 | −0.948831 | ||||||||
\(64\) | 5.21143 | 0.651428 | ||||||||
\(65\) | −17.1116 | −2.12243 | ||||||||
\(66\) | −2.42039 | −0.297929 | ||||||||
\(67\) | 7.45338 | 0.910576 | 0.455288 | − | 0.890344i | \(-0.349536\pi\) | ||||
0.455288 | + | 0.890344i | \(0.349536\pi\) | |||||||
\(68\) | 10.8528 | 1.31609 | ||||||||
\(69\) | 0.175910 | 0.0211770 | ||||||||
\(70\) | −21.2603 | −2.54109 | ||||||||
\(71\) | −3.92447 | −0.465749 | −0.232874 | − | 0.972507i | \(-0.574813\pi\) | ||||
−0.232874 | + | 0.972507i | \(0.574813\pi\) | |||||||
\(72\) | 20.9537 | 2.46942 | ||||||||
\(73\) | −13.8239 | −1.61797 | −0.808985 | − | 0.587830i | \(-0.799982\pi\) | ||||
−0.808985 | + | 0.587830i | \(0.799982\pi\) | |||||||
\(74\) | −24.3403 | −2.82951 | ||||||||
\(75\) | 0.958881 | 0.110722 | ||||||||
\(76\) | −16.3756 | −1.87841 | ||||||||
\(77\) | 13.4613 | 1.53405 | ||||||||
\(78\) | 2.41408 | 0.273341 | ||||||||
\(79\) | 1.45457 | 0.163652 | 0.0818262 | − | 0.996647i | \(-0.473925\pi\) | ||||
0.0818262 | + | 0.996647i | \(0.473925\pi\) | |||||||
\(80\) | 28.6216 | 3.20000 | ||||||||
\(81\) | 8.72246 | 0.969162 | ||||||||
\(82\) | −32.7528 | −3.61695 | ||||||||
\(83\) | 6.69824 | 0.735228 | 0.367614 | − | 0.929979i | \(-0.380175\pi\) | ||||
0.367614 | + | 0.929979i | \(0.380175\pi\) | |||||||
\(84\) | 2.10698 | 0.229890 | ||||||||
\(85\) | 7.43002 | 0.805899 | ||||||||
\(86\) | 10.3322 | 1.11415 | ||||||||
\(87\) | −1.50336 | −0.161177 | ||||||||
\(88\) | −37.4532 | −3.99252 | ||||||||
\(89\) | 15.8078 | 1.67562 | 0.837810 | − | 0.545962i | \(-0.183836\pi\) | ||||
0.837810 | + | 0.545962i | \(0.183836\pi\) | |||||||
\(90\) | 24.8855 | 2.62317 | ||||||||
\(91\) | −13.4262 | −1.40745 | ||||||||
\(92\) | 4.72203 | 0.492306 | ||||||||
\(93\) | 0.918474 | 0.0952413 | ||||||||
\(94\) | 6.28913 | 0.648674 | ||||||||
\(95\) | −11.2111 | −1.15023 | ||||||||
\(96\) | −1.55498 | −0.158705 | ||||||||
\(97\) | 11.9373 | 1.21205 | 0.606023 | − | 0.795447i | \(-0.292764\pi\) | ||||
0.606023 | + | 0.795447i | \(0.292764\pi\) | |||||||
\(98\) | 1.46743 | 0.148233 | ||||||||
\(99\) | −15.7566 | −1.58360 | ||||||||
\(100\) | 25.7397 | 2.57397 | ||||||||
\(101\) | −4.49752 | −0.447520 | −0.223760 | − | 0.974644i | \(-0.571833\pi\) | ||||
−0.223760 | + | 0.974644i | \(0.571833\pi\) | |||||||
\(102\) | −1.04822 | −0.103789 | ||||||||
\(103\) | 6.36534 | 0.627195 | 0.313598 | − | 0.949556i | \(-0.398466\pi\) | ||||
0.313598 | + | 0.949556i | \(0.398466\pi\) | |||||||
\(104\) | 37.3556 | 3.66302 | ||||||||
\(105\) | 1.44248 | 0.140771 | ||||||||
\(106\) | −20.3656 | −1.97808 | ||||||||
\(107\) | −11.3893 | −1.10105 | −0.550525 | − | 0.834819i | \(-0.685572\pi\) | ||||
−0.550525 | + | 0.834819i | \(0.685572\pi\) | |||||||
\(108\) | −4.95820 | −0.477103 | ||||||||
\(109\) | 9.00556 | 0.862576 | 0.431288 | − | 0.902214i | \(-0.358059\pi\) | ||||
0.431288 | + | 0.902214i | \(0.358059\pi\) | |||||||
\(110\) | −44.4810 | −4.24109 | ||||||||
\(111\) | 1.65145 | 0.156749 | ||||||||
\(112\) | 22.4573 | 2.12201 | ||||||||
\(113\) | −12.8681 | −1.21053 | −0.605263 | − | 0.796025i | \(-0.706932\pi\) | ||||
−0.605263 | + | 0.796025i | \(0.706932\pi\) | |||||||
\(114\) | 1.58165 | 0.148135 | ||||||||
\(115\) | 3.23280 | 0.301460 | ||||||||
\(116\) | −40.3554 | −3.74691 | ||||||||
\(117\) | 15.7156 | 1.45291 | ||||||||
\(118\) | −6.41779 | −0.590805 | ||||||||
\(119\) | 5.82978 | 0.534415 | ||||||||
\(120\) | −4.01339 | −0.366371 | ||||||||
\(121\) | 17.1638 | 1.56034 | ||||||||
\(122\) | 33.7846 | 3.05871 | ||||||||
\(123\) | 2.22223 | 0.200371 | ||||||||
\(124\) | 24.6550 | 2.21409 | ||||||||
\(125\) | 1.45794 | 0.130402 | ||||||||
\(126\) | 19.5258 | 1.73950 | ||||||||
\(127\) | 11.0793 | 0.983133 | 0.491566 | − | 0.870840i | \(-0.336424\pi\) | ||||
0.491566 | + | 0.870840i | \(0.336424\pi\) | |||||||
\(128\) | 4.16770 | 0.368376 | ||||||||
\(129\) | −0.701021 | −0.0617214 | ||||||||
\(130\) | 44.3650 | 3.89107 | ||||||||
\(131\) | 17.7650 | 1.55214 | 0.776068 | − | 0.630649i | \(-0.217211\pi\) | ||||
0.776068 | + | 0.630649i | \(0.217211\pi\) | |||||||
\(132\) | 4.40823 | 0.383687 | ||||||||
\(133\) | −8.79650 | −0.762754 | ||||||||
\(134\) | −19.3243 | −1.66937 | ||||||||
\(135\) | −3.39449 | −0.292151 | ||||||||
\(136\) | −16.2202 | −1.39087 | ||||||||
\(137\) | −14.4118 | −1.23129 | −0.615644 | − | 0.788025i | \(-0.711104\pi\) | ||||
−0.615644 | + | 0.788025i | \(0.711104\pi\) | |||||||
\(138\) | −0.456079 | −0.0388240 | ||||||||
\(139\) | −4.54714 | −0.385683 | −0.192842 | − | 0.981230i | \(-0.561770\pi\) | ||||
−0.192842 | + | 0.981230i | \(0.561770\pi\) | |||||||
\(140\) | 38.7212 | 3.27254 | ||||||||
\(141\) | −0.426707 | −0.0359352 | ||||||||
\(142\) | 10.1749 | 0.853860 | ||||||||
\(143\) | −28.0904 | −2.34903 | ||||||||
\(144\) | −26.2866 | −2.19055 | ||||||||
\(145\) | −27.6281 | −2.29439 | ||||||||
\(146\) | 35.8411 | 2.96623 | ||||||||
\(147\) | −0.0995631 | −0.00821182 | ||||||||
\(148\) | 44.3307 | 3.64396 | ||||||||
\(149\) | −23.0896 | −1.89158 | −0.945789 | − | 0.324783i | \(-0.894709\pi\) | ||||
−0.945789 | + | 0.324783i | \(0.894709\pi\) | |||||||
\(150\) | −2.48608 | −0.202987 | ||||||||
\(151\) | −7.98078 | −0.649467 | −0.324733 | − | 0.945806i | \(-0.605275\pi\) | ||||
−0.324733 | + | 0.945806i | \(0.605275\pi\) | |||||||
\(152\) | 24.4744 | 1.98514 | ||||||||
\(153\) | −6.82386 | −0.551676 | ||||||||
\(154\) | −34.9009 | −2.81239 | ||||||||
\(155\) | 16.8793 | 1.35578 | ||||||||
\(156\) | −4.39674 | −0.352021 | ||||||||
\(157\) | 20.5567 | 1.64061 | 0.820303 | − | 0.571929i | \(-0.193805\pi\) | ||||
0.820303 | + | 0.571929i | \(0.193805\pi\) | |||||||
\(158\) | −3.77126 | −0.300025 | ||||||||
\(159\) | 1.38177 | 0.109581 | ||||||||
\(160\) | −28.5768 | −2.25920 | ||||||||
\(161\) | 2.53654 | 0.199907 | ||||||||
\(162\) | −22.6146 | −1.77677 | ||||||||
\(163\) | 12.3571 | 0.967883 | 0.483942 | − | 0.875100i | \(-0.339205\pi\) | ||||
0.483942 | + | 0.875100i | \(0.339205\pi\) | |||||||
\(164\) | 59.6523 | 4.65807 | ||||||||
\(165\) | 3.01796 | 0.234948 | ||||||||
\(166\) | −17.3665 | −1.34790 | ||||||||
\(167\) | 14.0043 | 1.08368 | 0.541841 | − | 0.840481i | \(-0.317727\pi\) | ||||
0.541841 | + | 0.840481i | \(0.317727\pi\) | |||||||
\(168\) | −3.14901 | −0.242951 | ||||||||
\(169\) | 15.0172 | 1.15517 | ||||||||
\(170\) | −19.2637 | −1.47746 | ||||||||
\(171\) | 10.2965 | 0.787389 | ||||||||
\(172\) | −18.8178 | −1.43485 | ||||||||
\(173\) | −3.15493 | −0.239865 | −0.119933 | − | 0.992782i | \(-0.538268\pi\) | ||||
−0.119933 | + | 0.992782i | \(0.538268\pi\) | |||||||
\(174\) | 3.89774 | 0.295487 | ||||||||
\(175\) | 13.8266 | 1.04519 | ||||||||
\(176\) | 46.9852 | 3.54164 | ||||||||
\(177\) | 0.435436 | 0.0327294 | ||||||||
\(178\) | −40.9846 | −3.07193 | ||||||||
\(179\) | 15.3675 | 1.14862 | 0.574312 | − | 0.818637i | \(-0.305270\pi\) | ||||
0.574312 | + | 0.818637i | \(0.305270\pi\) | |||||||
\(180\) | −45.3237 | −3.37823 | ||||||||
\(181\) | −1.71861 | −0.127743 | −0.0638717 | − | 0.997958i | \(-0.520345\pi\) | ||||
−0.0638717 | + | 0.997958i | \(0.520345\pi\) | |||||||
\(182\) | 34.8099 | 2.58028 | ||||||||
\(183\) | −2.29223 | −0.169446 | ||||||||
\(184\) | −7.05738 | −0.520277 | ||||||||
\(185\) | 30.3497 | 2.23136 | ||||||||
\(186\) | −2.38132 | −0.174607 | ||||||||
\(187\) | 12.1971 | 0.891941 | ||||||||
\(188\) | −11.4543 | −0.835392 | ||||||||
\(189\) | −2.66340 | −0.193734 | ||||||||
\(190\) | 29.0669 | 2.10873 | ||||||||
\(191\) | 20.4084 | 1.47670 | 0.738351 | − | 0.674416i | \(-0.235605\pi\) | ||||
0.738351 | + | 0.674416i | \(0.235605\pi\) | |||||||
\(192\) | 0.916741 | 0.0661600 | ||||||||
\(193\) | 8.25880 | 0.594481 | 0.297241 | − | 0.954803i | \(-0.403934\pi\) | ||||
0.297241 | + | 0.954803i | \(0.403934\pi\) | |||||||
\(194\) | −30.9496 | −2.22205 | ||||||||
\(195\) | −3.01010 | −0.215558 | ||||||||
\(196\) | −2.67262 | −0.190902 | ||||||||
\(197\) | −1.27985 | −0.0911852 | −0.0455926 | − | 0.998960i | \(-0.514518\pi\) | ||||
−0.0455926 | + | 0.998960i | \(0.514518\pi\) | |||||||
\(198\) | 40.8521 | 2.90323 | ||||||||
\(199\) | 26.9308 | 1.90908 | 0.954539 | − | 0.298088i | \(-0.0963487\pi\) | ||||
0.954539 | + | 0.298088i | \(0.0963487\pi\) | |||||||
\(200\) | −38.4697 | −2.72022 | ||||||||
\(201\) | 1.31112 | 0.0924794 | ||||||||
\(202\) | 11.6607 | 0.820442 | ||||||||
\(203\) | −21.6777 | −1.52148 | ||||||||
\(204\) | 1.90911 | 0.133664 | ||||||||
\(205\) | 40.8392 | 2.85233 | ||||||||
\(206\) | −16.5033 | −1.14984 | ||||||||
\(207\) | −2.96906 | −0.206364 | ||||||||
\(208\) | −46.8628 | −3.24935 | ||||||||
\(209\) | −18.4041 | −1.27304 | ||||||||
\(210\) | −3.73990 | −0.258077 | ||||||||
\(211\) | 18.0657 | 1.24369 | 0.621847 | − | 0.783139i | \(-0.286382\pi\) | ||||
0.621847 | + | 0.783139i | \(0.286382\pi\) | |||||||
\(212\) | 37.0915 | 2.54746 | ||||||||
\(213\) | −0.690352 | −0.0473021 | ||||||||
\(214\) | 29.5290 | 2.01856 | ||||||||
\(215\) | −12.8831 | −0.878619 | ||||||||
\(216\) | 7.41035 | 0.504211 | ||||||||
\(217\) | 13.2440 | 0.899058 | ||||||||
\(218\) | −23.3486 | −1.58137 | ||||||||
\(219\) | −2.43176 | −0.164323 | ||||||||
\(220\) | 81.0126 | 5.46187 | ||||||||
\(221\) | −12.1653 | −0.818328 | ||||||||
\(222\) | −4.28170 | −0.287369 | ||||||||
\(223\) | 17.3104 | 1.15919 | 0.579595 | − | 0.814904i | \(-0.303211\pi\) | ||||
0.579595 | + | 0.814904i | \(0.303211\pi\) | |||||||
\(224\) | −22.4221 | −1.49814 | ||||||||
\(225\) | −16.1843 | −1.07895 | ||||||||
\(226\) | 33.3629 | 2.21927 | ||||||||
\(227\) | −0.257651 | −0.0171009 | −0.00855045 | − | 0.999963i | \(-0.502722\pi\) | ||||
−0.00855045 | + | 0.999963i | \(0.502722\pi\) | |||||||
\(228\) | −2.88063 | −0.190775 | ||||||||
\(229\) | 1.74044 | 0.115012 | 0.0575058 | − | 0.998345i | \(-0.481685\pi\) | ||||
0.0575058 | + | 0.998345i | \(0.481685\pi\) | |||||||
\(230\) | −8.38164 | −0.552669 | ||||||||
\(231\) | 2.36797 | 0.155801 | ||||||||
\(232\) | 60.3138 | 3.95979 | ||||||||
\(233\) | 7.55104 | 0.494685 | 0.247343 | − | 0.968928i | \(-0.420443\pi\) | ||||
0.247343 | + | 0.968928i | \(0.420443\pi\) | |||||||
\(234\) | −40.7456 | −2.66362 | ||||||||
\(235\) | −7.84186 | −0.511546 | ||||||||
\(236\) | 11.6886 | 0.760866 | ||||||||
\(237\) | 0.255874 | 0.0166208 | ||||||||
\(238\) | −15.1148 | −0.979748 | ||||||||
\(239\) | 15.1585 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(240\) | 5.03482 | 0.324996 | ||||||||
\(241\) | −11.2210 | −0.722809 | −0.361405 | − | 0.932409i | \(-0.617703\pi\) | ||||
−0.361405 | + | 0.932409i | \(0.617703\pi\) | |||||||
\(242\) | −44.5003 | −2.86059 | ||||||||
\(243\) | 4.68441 | 0.300505 | ||||||||
\(244\) | −61.5315 | −3.93915 | ||||||||
\(245\) | −1.82973 | −0.116897 | ||||||||
\(246\) | −5.76154 | −0.367342 | ||||||||
\(247\) | 18.3561 | 1.16797 | ||||||||
\(248\) | −36.8485 | −2.33988 | ||||||||
\(249\) | 1.17829 | 0.0746708 | ||||||||
\(250\) | −3.77998 | −0.239067 | ||||||||
\(251\) | −23.0807 | −1.45684 | −0.728422 | − | 0.685129i | \(-0.759746\pi\) | ||||
−0.728422 | + | 0.685129i | \(0.759746\pi\) | |||||||
\(252\) | −35.5622 | −2.24021 | ||||||||
\(253\) | 5.30695 | 0.333645 | ||||||||
\(254\) | −28.7253 | −1.80238 | ||||||||
\(255\) | 1.30701 | 0.0818483 | ||||||||
\(256\) | −21.2284 | −1.32678 | ||||||||
\(257\) | 30.9575 | 1.93108 | 0.965538 | − | 0.260264i | \(-0.0838095\pi\) | ||||
0.965538 | + | 0.260264i | \(0.0838095\pi\) | |||||||
\(258\) | 1.81753 | 0.113154 | ||||||||
\(259\) | 23.8132 | 1.47968 | ||||||||
\(260\) | −80.8015 | −5.01110 | ||||||||
\(261\) | 25.3741 | 1.57062 | ||||||||
\(262\) | −46.0591 | −2.84554 | ||||||||
\(263\) | 13.8789 | 0.855810 | 0.427905 | − | 0.903824i | \(-0.359252\pi\) | ||||
0.427905 | + | 0.903824i | \(0.359252\pi\) | |||||||
\(264\) | −6.58838 | −0.405487 | ||||||||
\(265\) | 25.3936 | 1.55992 | ||||||||
\(266\) | 22.8066 | 1.39836 | ||||||||
\(267\) | 2.78074 | 0.170178 | ||||||||
\(268\) | 35.1951 | 2.14988 | ||||||||
\(269\) | −6.99772 | −0.426659 | −0.213329 | − | 0.976980i | \(-0.568431\pi\) | ||||
−0.213329 | + | 0.976980i | \(0.568431\pi\) | |||||||
\(270\) | 8.80084 | 0.535602 | ||||||||
\(271\) | −3.13129 | −0.190212 | −0.0951062 | − | 0.995467i | \(-0.530319\pi\) | ||||
−0.0951062 | + | 0.995467i | \(0.530319\pi\) | |||||||
\(272\) | 20.3483 | 1.23379 | ||||||||
\(273\) | −2.36180 | −0.142943 | ||||||||
\(274\) | 37.3654 | 2.25733 | ||||||||
\(275\) | 28.9281 | 1.74443 | ||||||||
\(276\) | 0.830651 | 0.0499993 | ||||||||
\(277\) | −19.4257 | −1.16718 | −0.583590 | − | 0.812049i | \(-0.698352\pi\) | ||||
−0.583590 | + | 0.812049i | \(0.698352\pi\) | |||||||
\(278\) | 11.7893 | 0.707076 | ||||||||
\(279\) | −15.5023 | −0.928097 | ||||||||
\(280\) | −57.8712 | −3.45847 | ||||||||
\(281\) | 11.5559 | 0.689365 | 0.344682 | − | 0.938719i | \(-0.387987\pi\) | ||||
0.344682 | + | 0.938719i | \(0.387987\pi\) | |||||||
\(282\) | 1.10632 | 0.0658804 | ||||||||
\(283\) | 15.8417 | 0.941689 | 0.470844 | − | 0.882216i | \(-0.343949\pi\) | ||||
0.470844 | + | 0.882216i | \(0.343949\pi\) | |||||||
\(284\) | −18.5315 | −1.09964 | ||||||||
\(285\) | −1.97214 | −0.116819 | ||||||||
\(286\) | 72.8296 | 4.30650 | ||||||||
\(287\) | 32.0435 | 1.89147 | ||||||||
\(288\) | 26.2454 | 1.54653 | ||||||||
\(289\) | −11.7177 | −0.689276 | ||||||||
\(290\) | 71.6312 | 4.20633 | ||||||||
\(291\) | 2.09988 | 0.123097 | ||||||||
\(292\) | −65.2770 | −3.82005 | ||||||||
\(293\) | 4.41479 | 0.257915 | 0.128957 | − | 0.991650i | \(-0.458837\pi\) | ||||
0.128957 | + | 0.991650i | \(0.458837\pi\) | |||||||
\(294\) | 0.258136 | 0.0150548 | ||||||||
\(295\) | 8.00228 | 0.465911 | ||||||||
\(296\) | −66.2551 | −3.85100 | ||||||||
\(297\) | −5.57238 | −0.323342 | ||||||||
\(298\) | 59.8642 | 3.46784 | ||||||||
\(299\) | −5.29312 | −0.306109 | ||||||||
\(300\) | 4.52787 | 0.261416 | ||||||||
\(301\) | −10.1084 | −0.582638 | ||||||||
\(302\) | 20.6917 | 1.19067 | ||||||||
\(303\) | −0.791157 | −0.0454508 | ||||||||
\(304\) | −30.7033 | −1.76096 | ||||||||
\(305\) | −42.1257 | −2.41211 | ||||||||
\(306\) | 17.6921 | 1.01139 | ||||||||
\(307\) | 32.0835 | 1.83110 | 0.915550 | − | 0.402204i | \(-0.131756\pi\) | ||||
0.915550 | + | 0.402204i | \(0.131756\pi\) | |||||||
\(308\) | 63.5646 | 3.62193 | ||||||||
\(309\) | 1.11972 | 0.0636989 | ||||||||
\(310\) | −43.7629 | −2.48556 | ||||||||
\(311\) | −4.65407 | −0.263908 | −0.131954 | − | 0.991256i | \(-0.542125\pi\) | ||||
−0.131954 | + | 0.991256i | \(0.542125\pi\) | |||||||
\(312\) | 6.57121 | 0.372021 | ||||||||
\(313\) | −23.7613 | −1.34307 | −0.671534 | − | 0.740974i | \(-0.734364\pi\) | ||||
−0.671534 | + | 0.740974i | \(0.734364\pi\) | |||||||
\(314\) | −53.2972 | −3.00774 | ||||||||
\(315\) | −24.3466 | −1.37177 | ||||||||
\(316\) | 6.86854 | 0.386386 | ||||||||
\(317\) | −7.81222 | −0.438778 | −0.219389 | − | 0.975637i | \(-0.570406\pi\) | ||||
−0.219389 | + | 0.975637i | \(0.570406\pi\) | |||||||
\(318\) | −3.58250 | −0.200896 | ||||||||
\(319\) | −45.3543 | −2.53935 | ||||||||
\(320\) | 16.8475 | 0.941803 | ||||||||
\(321\) | −2.00350 | −0.111824 | ||||||||
\(322\) | −6.57644 | −0.366491 | ||||||||
\(323\) | −7.97041 | −0.443486 | ||||||||
\(324\) | 41.1877 | 2.28821 | ||||||||
\(325\) | −28.8527 | −1.60046 | ||||||||
\(326\) | −32.0381 | −1.77443 | ||||||||
\(327\) | 1.58417 | 0.0876045 | ||||||||
\(328\) | −89.1542 | −4.92272 | ||||||||
\(329\) | −6.15292 | −0.339222 | ||||||||
\(330\) | −7.82463 | −0.430732 | ||||||||
\(331\) | 5.44931 | 0.299521 | 0.149761 | − | 0.988722i | \(-0.452150\pi\) | ||||
0.149761 | + | 0.988722i | \(0.452150\pi\) | |||||||
\(332\) | 31.6293 | 1.73588 | ||||||||
\(333\) | −27.8737 | −1.52747 | ||||||||
\(334\) | −36.3087 | −1.98672 | ||||||||
\(335\) | 24.0953 | 1.31647 | ||||||||
\(336\) | 3.95045 | 0.215515 | ||||||||
\(337\) | −28.3777 | −1.54583 | −0.772916 | − | 0.634508i | \(-0.781203\pi\) | ||||
−0.772916 | + | 0.634508i | \(0.781203\pi\) | |||||||
\(338\) | −38.9348 | −2.11778 | ||||||||
\(339\) | −2.26362 | −0.122943 | ||||||||
\(340\) | 35.0848 | 1.90274 | ||||||||
\(341\) | 27.7091 | 1.50053 | ||||||||
\(342\) | −26.6955 | −1.44353 | ||||||||
\(343\) | −19.1914 | −1.03624 | ||||||||
\(344\) | 28.1245 | 1.51637 | ||||||||
\(345\) | 0.568680 | 0.0306167 | ||||||||
\(346\) | 8.17976 | 0.439747 | ||||||||
\(347\) | 17.5063 | 0.939786 | 0.469893 | − | 0.882723i | \(-0.344292\pi\) | ||||
0.469893 | + | 0.882723i | \(0.344292\pi\) | |||||||
\(348\) | −7.09891 | −0.380542 | ||||||||
\(349\) | −1.00000 | −0.0535288 | ||||||||
\(350\) | −35.8481 | −1.91616 | ||||||||
\(351\) | 5.55786 | 0.296657 | ||||||||
\(352\) | −46.9116 | −2.50040 | ||||||||
\(353\) | −5.20548 | −0.277059 | −0.138530 | − | 0.990358i | \(-0.544238\pi\) | ||||
−0.138530 | + | 0.990358i | \(0.544238\pi\) | |||||||
\(354\) | −1.12895 | −0.0600031 | ||||||||
\(355\) | −12.6870 | −0.673357 | ||||||||
\(356\) | 74.6448 | 3.95616 | ||||||||
\(357\) | 1.02552 | 0.0542760 | ||||||||
\(358\) | −39.8432 | −2.10578 | ||||||||
\(359\) | −19.8325 | −1.04672 | −0.523359 | − | 0.852112i | \(-0.675321\pi\) | ||||
−0.523359 | + | 0.852112i | \(0.675321\pi\) | |||||||
\(360\) | 67.7392 | 3.57017 | ||||||||
\(361\) | −6.97352 | −0.367027 | ||||||||
\(362\) | 4.45582 | 0.234193 | ||||||||
\(363\) | 3.01927 | 0.158471 | ||||||||
\(364\) | −63.3989 | −3.32301 | ||||||||
\(365\) | −44.6900 | −2.33918 | ||||||||
\(366\) | 5.94304 | 0.310647 | ||||||||
\(367\) | 1.83519 | 0.0957960 | 0.0478980 | − | 0.998852i | \(-0.484748\pi\) | ||||
0.0478980 | + | 0.998852i | \(0.484748\pi\) | |||||||
\(368\) | 8.85352 | 0.461522 | ||||||||
\(369\) | −37.5074 | −1.95256 | ||||||||
\(370\) | −78.6874 | −4.09076 | ||||||||
\(371\) | 19.9245 | 1.03443 | ||||||||
\(372\) | 4.33706 | 0.224866 | ||||||||
\(373\) | 24.0662 | 1.24610 | 0.623050 | − | 0.782182i | \(-0.285893\pi\) | ||||
0.623050 | + | 0.782182i | \(0.285893\pi\) | |||||||
\(374\) | −31.6233 | −1.63520 | ||||||||
\(375\) | 0.256466 | 0.0132438 | ||||||||
\(376\) | 17.1192 | 0.882856 | ||||||||
\(377\) | 45.2361 | 2.32978 | ||||||||
\(378\) | 6.90536 | 0.355174 | ||||||||
\(379\) | −1.26215 | −0.0648323 | −0.0324161 | − | 0.999474i | \(-0.510320\pi\) | ||||
−0.0324161 | + | 0.999474i | \(0.510320\pi\) | |||||||
\(380\) | −52.9391 | −2.71572 | ||||||||
\(381\) | 1.94896 | 0.0998485 | ||||||||
\(382\) | −52.9127 | −2.70725 | ||||||||
\(383\) | −15.1001 | −0.771577 | −0.385788 | − | 0.922587i | \(-0.626070\pi\) | ||||
−0.385788 | + | 0.922587i | \(0.626070\pi\) | |||||||
\(384\) | 0.733139 | 0.0374128 | ||||||||
\(385\) | 43.5176 | 2.21786 | ||||||||
\(386\) | −21.4125 | −1.08987 | ||||||||
\(387\) | 11.8320 | 0.601456 | ||||||||
\(388\) | 56.3682 | 2.86166 | ||||||||
\(389\) | −12.3806 | −0.627720 | −0.313860 | − | 0.949469i | \(-0.601622\pi\) | ||||
−0.313860 | + | 0.949469i | \(0.601622\pi\) | |||||||
\(390\) | 7.80424 | 0.395183 | ||||||||
\(391\) | 2.29833 | 0.116231 | ||||||||
\(392\) | 3.99440 | 0.201748 | ||||||||
\(393\) | 3.12504 | 0.157637 | ||||||||
\(394\) | 3.31824 | 0.167171 | ||||||||
\(395\) | 4.70234 | 0.236601 | ||||||||
\(396\) | −74.4034 | −3.73891 | ||||||||
\(397\) | −5.24230 | −0.263103 | −0.131552 | − | 0.991309i | \(-0.541996\pi\) | ||||
−0.131552 | + | 0.991309i | \(0.541996\pi\) | |||||||
\(398\) | −69.8233 | −3.49992 | ||||||||
\(399\) | −1.54739 | −0.0774664 | ||||||||
\(400\) | 48.2604 | 2.41302 | ||||||||
\(401\) | −29.1741 | −1.45689 | −0.728443 | − | 0.685106i | \(-0.759756\pi\) | ||||
−0.728443 | + | 0.685106i | \(0.759756\pi\) | |||||||
\(402\) | −3.39933 | −0.169543 | ||||||||
\(403\) | −27.6369 | −1.37669 | ||||||||
\(404\) | −21.2374 | −1.05660 | ||||||||
\(405\) | 28.1980 | 1.40117 | ||||||||
\(406\) | 56.2036 | 2.78934 | ||||||||
\(407\) | 49.8220 | 2.46959 | ||||||||
\(408\) | −2.85328 | −0.141259 | ||||||||
\(409\) | −16.1404 | −0.798090 | −0.399045 | − | 0.916931i | \(-0.630658\pi\) | ||||
−0.399045 | + | 0.916931i | \(0.630658\pi\) | |||||||
\(410\) | −105.883 | −5.22920 | ||||||||
\(411\) | −2.53518 | −0.125051 | ||||||||
\(412\) | 30.0573 | 1.48082 | ||||||||
\(413\) | 6.27879 | 0.308959 | ||||||||
\(414\) | 7.69784 | 0.378328 | ||||||||
\(415\) | 21.6541 | 1.06296 | ||||||||
\(416\) | 46.7894 | 2.29404 | ||||||||
\(417\) | −0.799886 | −0.0391706 | ||||||||
\(418\) | 47.7161 | 2.33387 | ||||||||
\(419\) | −29.7775 | −1.45473 | −0.727364 | − | 0.686252i | \(-0.759255\pi\) | ||||
−0.727364 | + | 0.686252i | \(0.759255\pi\) | |||||||
\(420\) | 6.81143 | 0.332364 | ||||||||
\(421\) | 32.4816 | 1.58306 | 0.791528 | − | 0.611133i | \(-0.209286\pi\) | ||||
0.791528 | + | 0.611133i | \(0.209286\pi\) | |||||||
\(422\) | −46.8387 | −2.28007 | ||||||||
\(423\) | 7.20209 | 0.350178 | ||||||||
\(424\) | −55.4357 | −2.69219 | ||||||||
\(425\) | 12.5281 | 0.607704 | ||||||||
\(426\) | 1.78987 | 0.0867193 | ||||||||
\(427\) | −33.0529 | −1.59954 | ||||||||
\(428\) | −53.7808 | −2.59960 | ||||||||
\(429\) | −4.94137 | −0.238572 | ||||||||
\(430\) | 33.4018 | 1.61078 | ||||||||
\(431\) | −18.6525 | −0.898459 | −0.449230 | − | 0.893416i | \(-0.648302\pi\) | ||||
−0.449230 | + | 0.893416i | \(0.648302\pi\) | |||||||
\(432\) | −9.29632 | −0.447270 | ||||||||
\(433\) | 39.5864 | 1.90240 | 0.951201 | − | 0.308572i | \(-0.0998512\pi\) | ||||
0.951201 | + | 0.308572i | \(0.0998512\pi\) | |||||||
\(434\) | −34.3374 | −1.64825 | ||||||||
\(435\) | −4.86006 | −0.233022 | ||||||||
\(436\) | 42.5245 | 2.03656 | ||||||||
\(437\) | −3.46792 | −0.165893 | ||||||||
\(438\) | 6.30480 | 0.301255 | ||||||||
\(439\) | −10.9755 | −0.523832 | −0.261916 | − | 0.965091i | \(-0.584354\pi\) | ||||
−0.261916 | + | 0.965091i | \(0.584354\pi\) | |||||||
\(440\) | −121.079 | −5.77219 | ||||||||
\(441\) | 1.68045 | 0.0800217 | ||||||||
\(442\) | 31.5409 | 1.50025 | ||||||||
\(443\) | −33.5263 | −1.59288 | −0.796442 | − | 0.604715i | \(-0.793287\pi\) | ||||
−0.796442 | + | 0.604715i | \(0.793287\pi\) | |||||||
\(444\) | 7.79821 | 0.370087 | ||||||||
\(445\) | 51.1033 | 2.42253 | ||||||||
\(446\) | −44.8805 | −2.12515 | ||||||||
\(447\) | −4.06169 | −0.192111 | ||||||||
\(448\) | 13.2190 | 0.624538 | ||||||||
\(449\) | −9.26977 | −0.437468 | −0.218734 | − | 0.975785i | \(-0.570193\pi\) | ||||
−0.218734 | + | 0.975785i | \(0.570193\pi\) | |||||||
\(450\) | 41.9608 | 1.97805 | ||||||||
\(451\) | 67.0415 | 3.15686 | ||||||||
\(452\) | −60.7634 | −2.85807 | ||||||||
\(453\) | −1.40390 | −0.0659608 | ||||||||
\(454\) | 0.668009 | 0.0313512 | ||||||||
\(455\) | −43.4042 | −2.03482 | ||||||||
\(456\) | 4.30529 | 0.201614 | ||||||||
\(457\) | −1.67842 | −0.0785134 | −0.0392567 | − | 0.999229i | \(-0.512499\pi\) | ||||
−0.0392567 | + | 0.999229i | \(0.512499\pi\) | |||||||
\(458\) | −4.51242 | −0.210851 | ||||||||
\(459\) | −2.41328 | −0.112642 | ||||||||
\(460\) | 15.2654 | 0.711752 | ||||||||
\(461\) | 26.5704 | 1.23751 | 0.618753 | − | 0.785585i | \(-0.287638\pi\) | ||||
0.618753 | + | 0.785585i | \(0.287638\pi\) | |||||||
\(462\) | −6.13940 | −0.285631 | ||||||||
\(463\) | −12.6709 | −0.588868 | −0.294434 | − | 0.955672i | \(-0.595131\pi\) | ||||
−0.294434 | + | 0.955672i | \(0.595131\pi\) | |||||||
\(464\) | −75.6639 | −3.51261 | ||||||||
\(465\) | 2.96924 | 0.137695 | ||||||||
\(466\) | −19.5775 | −0.906910 | ||||||||
\(467\) | 16.2456 | 0.751756 | 0.375878 | − | 0.926669i | \(-0.377341\pi\) | ||||
0.375878 | + | 0.926669i | \(0.377341\pi\) | |||||||
\(468\) | 74.2095 | 3.43033 | ||||||||
\(469\) | 18.9058 | 0.872987 | ||||||||
\(470\) | 20.3315 | 0.937822 | ||||||||
\(471\) | 3.61613 | 0.166623 | ||||||||
\(472\) | −17.4694 | −0.804095 | ||||||||
\(473\) | −21.1488 | −0.972424 | ||||||||
\(474\) | −0.663400 | −0.0304710 | ||||||||
\(475\) | −18.9036 | −0.867356 | ||||||||
\(476\) | 27.5284 | 1.26176 | ||||||||
\(477\) | −23.3219 | −1.06784 | ||||||||
\(478\) | −39.3013 | −1.79760 | ||||||||
\(479\) | −37.6739 | −1.72136 | −0.860681 | − | 0.509144i | \(-0.829962\pi\) | ||||
−0.860681 | + | 0.509144i | \(0.829962\pi\) | |||||||
\(480\) | −5.02694 | −0.229447 | ||||||||
\(481\) | −49.6922 | −2.26577 | ||||||||
\(482\) | 29.0926 | 1.32513 | ||||||||
\(483\) | 0.446201 | 0.0203029 | ||||||||
\(484\) | 81.0478 | 3.68399 | ||||||||
\(485\) | 38.5908 | 1.75232 | ||||||||
\(486\) | −12.1452 | −0.550918 | ||||||||
\(487\) | 7.83577 | 0.355073 | 0.177536 | − | 0.984114i | \(-0.443187\pi\) | ||||
0.177536 | + | 0.984114i | \(0.443187\pi\) | |||||||
\(488\) | 91.9627 | 4.16296 | ||||||||
\(489\) | 2.17373 | 0.0982997 | ||||||||
\(490\) | 4.74392 | 0.214308 | ||||||||
\(491\) | 32.9341 | 1.48630 | 0.743148 | − | 0.669127i | \(-0.233332\pi\) | ||||
0.743148 | + | 0.669127i | \(0.233332\pi\) | |||||||
\(492\) | 10.4934 | 0.473080 | ||||||||
\(493\) | −19.6420 | −0.884629 | ||||||||
\(494\) | −47.5917 | −2.14125 | ||||||||
\(495\) | −50.9380 | −2.28949 | ||||||||
\(496\) | 46.2267 | 2.07564 | ||||||||
\(497\) | −9.95455 | −0.446523 | ||||||||
\(498\) | −3.05493 | −0.136895 | ||||||||
\(499\) | −10.1013 | −0.452198 | −0.226099 | − | 0.974104i | \(-0.572597\pi\) | ||||
−0.226099 | + | 0.974104i | \(0.572597\pi\) | |||||||
\(500\) | 6.88443 | 0.307881 | ||||||||
\(501\) | 2.46349 | 0.110060 | ||||||||
\(502\) | 59.8411 | 2.67084 | ||||||||
\(503\) | 38.1479 | 1.70093 | 0.850465 | − | 0.526031i | \(-0.176321\pi\) | ||||
0.850465 | + | 0.526031i | \(0.176321\pi\) | |||||||
\(504\) | 53.1499 | 2.36749 | ||||||||
\(505\) | −14.5396 | −0.647003 | ||||||||
\(506\) | −13.7593 | −0.611674 | ||||||||
\(507\) | 2.64167 | 0.117320 | ||||||||
\(508\) | 52.3170 | 2.32119 | ||||||||
\(509\) | 17.2125 | 0.762930 | 0.381465 | − | 0.924383i | \(-0.375420\pi\) | ||||
0.381465 | + | 0.924383i | \(0.375420\pi\) | |||||||
\(510\) | −3.38868 | −0.150053 | ||||||||
\(511\) | −35.0649 | −1.55118 | ||||||||
\(512\) | 46.7032 | 2.06401 | ||||||||
\(513\) | 3.64137 | 0.160770 | ||||||||
\(514\) | −80.2631 | −3.54025 | ||||||||
\(515\) | 20.5779 | 0.906768 | ||||||||
\(516\) | −3.31024 | −0.145725 | ||||||||
\(517\) | −12.8732 | −0.566162 | ||||||||
\(518\) | −61.7401 | −2.71270 | ||||||||
\(519\) | −0.554983 | −0.0243611 | ||||||||
\(520\) | 120.763 | 5.29581 | ||||||||
\(521\) | −13.1711 | −0.577037 | −0.288518 | − | 0.957474i | \(-0.593163\pi\) | ||||
−0.288518 | + | 0.957474i | \(0.593163\pi\) | |||||||
\(522\) | −65.7872 | −2.87943 | ||||||||
\(523\) | 39.3267 | 1.71964 | 0.859819 | − | 0.510599i | \(-0.170576\pi\) | ||||
0.859819 | + | 0.510599i | \(0.170576\pi\) | |||||||
\(524\) | 83.8869 | 3.66462 | ||||||||
\(525\) | 2.43223 | 0.106151 | ||||||||
\(526\) | −35.9837 | −1.56896 | ||||||||
\(527\) | 12.0002 | 0.522737 | ||||||||
\(528\) | 8.26515 | 0.359695 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −65.8377 | −2.85981 | ||||||||
\(531\) | −7.34943 | −0.318938 | ||||||||
\(532\) | −41.5374 | −1.80087 | ||||||||
\(533\) | −66.8668 | −2.89632 | ||||||||
\(534\) | −7.20959 | −0.311989 | ||||||||
\(535\) | −36.8195 | −1.59184 | ||||||||
\(536\) | −52.6013 | −2.27203 | ||||||||
\(537\) | 2.70330 | 0.116656 | ||||||||
\(538\) | 18.1429 | 0.782196 | ||||||||
\(539\) | −3.00368 | −0.129378 | ||||||||
\(540\) | −16.0289 | −0.689773 | ||||||||
\(541\) | 3.97101 | 0.170727 | 0.0853636 | − | 0.996350i | \(-0.472795\pi\) | ||||
0.0853636 | + | 0.996350i | \(0.472795\pi\) | |||||||
\(542\) | 8.11846 | 0.348718 | ||||||||
\(543\) | −0.302320 | −0.0129738 | ||||||||
\(544\) | −20.3164 | −0.871059 | ||||||||
\(545\) | 29.1132 | 1.24707 | ||||||||
\(546\) | 6.12341 | 0.262058 | ||||||||
\(547\) | 44.0248 | 1.88236 | 0.941182 | − | 0.337900i | \(-0.109716\pi\) | ||||
0.941182 | + | 0.337900i | \(0.109716\pi\) | |||||||
\(548\) | −68.0532 | −2.90709 | ||||||||
\(549\) | 38.6889 | 1.65120 | ||||||||
\(550\) | −75.0016 | −3.19808 | ||||||||
\(551\) | 29.6376 | 1.26260 | ||||||||
\(552\) | −1.24146 | −0.0528401 | ||||||||
\(553\) | 3.68958 | 0.156897 | ||||||||
\(554\) | 50.3649 | 2.13980 | ||||||||
\(555\) | 5.33881 | 0.226620 | ||||||||
\(556\) | −21.4717 | −0.910604 | ||||||||
\(557\) | −42.4833 | −1.80008 | −0.900038 | − | 0.435812i | \(-0.856461\pi\) | ||||
−0.900038 | + | 0.435812i | \(0.856461\pi\) | |||||||
\(558\) | 40.1925 | 1.70149 | ||||||||
\(559\) | 21.0937 | 0.892169 | ||||||||
\(560\) | 72.5998 | 3.06790 | ||||||||
\(561\) | 2.14559 | 0.0905869 | ||||||||
\(562\) | −29.9607 | −1.26382 | ||||||||
\(563\) | 3.73885 | 0.157574 | 0.0787870 | − | 0.996891i | \(-0.474895\pi\) | ||||
0.0787870 | + | 0.996891i | \(0.474895\pi\) | |||||||
\(564\) | −2.01493 | −0.0848437 | ||||||||
\(565\) | −41.5999 | −1.75012 | ||||||||
\(566\) | −41.0725 | −1.72640 | ||||||||
\(567\) | 22.1248 | 0.929155 | ||||||||
\(568\) | 27.6965 | 1.16212 | ||||||||
\(569\) | −19.7972 | −0.829942 | −0.414971 | − | 0.909835i | \(-0.636208\pi\) | ||||
−0.414971 | + | 0.909835i | \(0.636208\pi\) | |||||||
\(570\) | 5.11314 | 0.214166 | ||||||||
\(571\) | 10.8234 | 0.452946 | 0.226473 | − | 0.974017i | \(-0.427281\pi\) | ||||
0.226473 | + | 0.974017i | \(0.427281\pi\) | |||||||
\(572\) | −132.644 | −5.54611 | ||||||||
\(573\) | 3.59004 | 0.149976 | ||||||||
\(574\) | −83.0787 | −3.46764 | ||||||||
\(575\) | 5.45098 | 0.227322 | ||||||||
\(576\) | −15.4730 | −0.644709 | ||||||||
\(577\) | 31.6089 | 1.31590 | 0.657948 | − | 0.753063i | \(-0.271424\pi\) | ||||
0.657948 | + | 0.753063i | \(0.271424\pi\) | |||||||
\(578\) | 30.3803 | 1.26366 | ||||||||
\(579\) | 1.45280 | 0.0603764 | ||||||||
\(580\) | −130.461 | −5.41710 | ||||||||
\(581\) | 16.9903 | 0.704878 | ||||||||
\(582\) | −5.44434 | −0.225675 | ||||||||
\(583\) | 41.6861 | 1.72646 | ||||||||
\(584\) | 97.5607 | 4.03709 | ||||||||
\(585\) | 50.8053 | 2.10054 | ||||||||
\(586\) | −11.4462 | −0.472837 | ||||||||
\(587\) | −43.1552 | −1.78121 | −0.890604 | − | 0.454780i | \(-0.849718\pi\) | ||||
−0.890604 | + | 0.454780i | \(0.849718\pi\) | |||||||
\(588\) | −0.470140 | −0.0193882 | ||||||||
\(589\) | −18.1070 | −0.746085 | ||||||||
\(590\) | −20.7474 | −0.854157 | ||||||||
\(591\) | −0.225137 | −0.00926091 | ||||||||
\(592\) | 83.1174 | 3.41610 | ||||||||
\(593\) | −2.72270 | −0.111808 | −0.0559040 | − | 0.998436i | \(-0.517804\pi\) | ||||
−0.0559040 | + | 0.998436i | \(0.517804\pi\) | |||||||
\(594\) | 14.4474 | 0.592786 | ||||||||
\(595\) | 18.8465 | 0.772632 | ||||||||
\(596\) | −109.030 | −4.46604 | ||||||||
\(597\) | 4.73740 | 0.193889 | ||||||||
\(598\) | 13.7234 | 0.561192 | ||||||||
\(599\) | −17.0076 | −0.694912 | −0.347456 | − | 0.937696i | \(-0.612954\pi\) | ||||
−0.347456 | + | 0.937696i | \(0.612954\pi\) | |||||||
\(600\) | −6.76718 | −0.276269 | ||||||||
\(601\) | −5.13132 | −0.209311 | −0.104656 | − | 0.994509i | \(-0.533374\pi\) | ||||
−0.104656 | + | 0.994509i | \(0.533374\pi\) | |||||||
\(602\) | 26.2079 | 1.06815 | ||||||||
\(603\) | −22.1295 | −0.901183 | ||||||||
\(604\) | −37.6855 | −1.53340 | ||||||||
\(605\) | 55.4870 | 2.25587 | ||||||||
\(606\) | 2.05122 | 0.0833253 | ||||||||
\(607\) | −27.1784 | −1.10314 | −0.551568 | − | 0.834130i | \(-0.685970\pi\) | ||||
−0.551568 | + | 0.834130i | \(0.685970\pi\) | |||||||
\(608\) | 30.6552 | 1.24323 | ||||||||
\(609\) | −3.81332 | −0.154524 | ||||||||
\(610\) | 109.219 | 4.42214 | ||||||||
\(611\) | 12.8396 | 0.519436 | ||||||||
\(612\) | −32.2225 | −1.30252 | ||||||||
\(613\) | 34.6808 | 1.40075 | 0.700373 | − | 0.713777i | \(-0.253017\pi\) | ||||
0.700373 | + | 0.713777i | \(0.253017\pi\) | |||||||
\(614\) | −83.1824 | −3.35697 | ||||||||
\(615\) | 7.18401 | 0.289687 | ||||||||
\(616\) | −95.0013 | −3.82771 | ||||||||
\(617\) | 18.7244 | 0.753816 | 0.376908 | − | 0.926251i | \(-0.376987\pi\) | ||||
0.376908 | + | 0.926251i | \(0.376987\pi\) | |||||||
\(618\) | −2.90310 | −0.116780 | ||||||||
\(619\) | −3.41941 | −0.137438 | −0.0687189 | − | 0.997636i | \(-0.521891\pi\) | ||||
−0.0687189 | + | 0.997636i | \(0.521891\pi\) | |||||||
\(620\) | 79.7048 | 3.20102 | ||||||||
\(621\) | −1.05001 | −0.0421356 | ||||||||
\(622\) | 12.0666 | 0.483825 | ||||||||
\(623\) | 40.0970 | 1.60645 | ||||||||
\(624\) | −8.24362 | −0.330009 | ||||||||
\(625\) | −22.5417 | −0.901668 | ||||||||
\(626\) | 61.6056 | 2.46225 | ||||||||
\(627\) | −3.23746 | −0.129292 | ||||||||
\(628\) | 97.0696 | 3.87350 | ||||||||
\(629\) | 21.5768 | 0.860325 | ||||||||
\(630\) | 63.1231 | 2.51488 | ||||||||
\(631\) | 7.66016 | 0.304946 | 0.152473 | − | 0.988308i | \(-0.451276\pi\) | ||||
0.152473 | + | 0.988308i | \(0.451276\pi\) | |||||||
\(632\) | −10.2655 | −0.408339 | ||||||||
\(633\) | 3.17793 | 0.126311 | ||||||||
\(634\) | 20.2546 | 0.804415 | ||||||||
\(635\) | 35.8173 | 1.42137 | ||||||||
\(636\) | 6.52476 | 0.258724 | ||||||||
\(637\) | 2.99585 | 0.118700 | ||||||||
\(638\) | 117.590 | 4.65541 | ||||||||
\(639\) | 11.6520 | 0.460945 | ||||||||
\(640\) | 13.4733 | 0.532580 | ||||||||
\(641\) | −32.4635 | −1.28223 | −0.641115 | − | 0.767445i | \(-0.721528\pi\) | ||||
−0.641115 | + | 0.767445i | \(0.721528\pi\) | |||||||
\(642\) | 5.19444 | 0.205008 | ||||||||
\(643\) | −23.6973 | −0.934532 | −0.467266 | − | 0.884117i | \(-0.654761\pi\) | ||||
−0.467266 | + | 0.884117i | \(0.654761\pi\) | |||||||
\(644\) | 11.9776 | 0.471983 | ||||||||
\(645\) | −2.26626 | −0.0892338 | ||||||||
\(646\) | 20.6648 | 0.813045 | ||||||||
\(647\) | 8.69439 | 0.341812 | 0.170906 | − | 0.985287i | \(-0.445331\pi\) | ||||
0.170906 | + | 0.985287i | \(0.445331\pi\) | |||||||
\(648\) | −61.5577 | −2.41821 | ||||||||
\(649\) | 13.1365 | 0.515654 | ||||||||
\(650\) | 74.8061 | 2.93414 | ||||||||
\(651\) | 2.32974 | 0.0913097 | ||||||||
\(652\) | 58.3506 | 2.28519 | ||||||||
\(653\) | 19.3883 | 0.758724 | 0.379362 | − | 0.925248i | \(-0.376144\pi\) | ||||
0.379362 | + | 0.925248i | \(0.376144\pi\) | |||||||
\(654\) | −4.10725 | −0.160606 | ||||||||
\(655\) | 57.4307 | 2.24400 | ||||||||
\(656\) | 111.844 | 4.36679 | ||||||||
\(657\) | 41.0440 | 1.60128 | ||||||||
\(658\) | 15.9526 | 0.621897 | ||||||||
\(659\) | −44.0571 | −1.71622 | −0.858110 | − | 0.513466i | \(-0.828361\pi\) | ||||
−0.858110 | + | 0.513466i | \(0.828361\pi\) | |||||||
\(660\) | 14.2509 | 0.554716 | ||||||||
\(661\) | 4.81955 | 0.187459 | 0.0937293 | − | 0.995598i | \(-0.470121\pi\) | ||||
0.0937293 | + | 0.995598i | \(0.470121\pi\) | |||||||
\(662\) | −14.1284 | −0.549115 | ||||||||
\(663\) | −2.14000 | −0.0831107 | ||||||||
\(664\) | −47.2720 | −1.83451 | ||||||||
\(665\) | −28.4373 | −1.10275 | ||||||||
\(666\) | 72.2678 | 2.80032 | ||||||||
\(667\) | −8.54620 | −0.330910 | ||||||||
\(668\) | 66.1286 | 2.55859 | ||||||||
\(669\) | 3.04507 | 0.117729 | ||||||||
\(670\) | −62.4716 | −2.41349 | ||||||||
\(671\) | −69.1534 | −2.66964 | ||||||||
\(672\) | −3.94426 | −0.152153 | ||||||||
\(673\) | −21.5639 | −0.831226 | −0.415613 | − | 0.909542i | \(-0.636433\pi\) | ||||
−0.415613 | + | 0.909542i | \(0.636433\pi\) | |||||||
\(674\) | 73.5746 | 2.83399 | ||||||||
\(675\) | −5.72361 | −0.220302 | ||||||||
\(676\) | 70.9115 | 2.72737 | ||||||||
\(677\) | −3.86572 | −0.148572 | −0.0742859 | − | 0.997237i | \(-0.523668\pi\) | ||||
−0.0742859 | + | 0.997237i | \(0.523668\pi\) | |||||||
\(678\) | 5.86886 | 0.225392 | ||||||||
\(679\) | 30.2793 | 1.16201 | ||||||||
\(680\) | −52.4365 | −2.01085 | ||||||||
\(681\) | −0.0453233 | −0.00173679 | ||||||||
\(682\) | −71.8410 | −2.75093 | ||||||||
\(683\) | −40.6051 | −1.55371 | −0.776855 | − | 0.629680i | \(-0.783186\pi\) | ||||
−0.776855 | + | 0.629680i | \(0.783186\pi\) | |||||||
\(684\) | 48.6202 | 1.85904 | ||||||||
\(685\) | −46.5906 | −1.78014 | ||||||||
\(686\) | 49.7573 | 1.89974 | ||||||||
\(687\) | 0.306160 | 0.0116807 | ||||||||
\(688\) | −35.2823 | −1.34512 | ||||||||
\(689\) | −41.5775 | −1.58398 | ||||||||
\(690\) | −1.47441 | −0.0561299 | ||||||||
\(691\) | 21.5402 | 0.819426 | 0.409713 | − | 0.912214i | \(-0.365629\pi\) | ||||
0.409713 | + | 0.912214i | \(0.365629\pi\) | |||||||
\(692\) | −14.8977 | −0.566325 | ||||||||
\(693\) | −39.9673 | −1.51823 | ||||||||
\(694\) | −45.3883 | −1.72292 | ||||||||
\(695\) | −14.7000 | −0.557602 | ||||||||
\(696\) | 10.6098 | 0.402163 | ||||||||
\(697\) | 29.0342 | 1.09975 | ||||||||
\(698\) | 2.59269 | 0.0981347 | ||||||||
\(699\) | 1.32830 | 0.0502410 | ||||||||
\(700\) | 65.2897 | 2.46772 | ||||||||
\(701\) | 45.3565 | 1.71309 | 0.856546 | − | 0.516071i | \(-0.172606\pi\) | ||||
0.856546 | + | 0.516071i | \(0.172606\pi\) | |||||||
\(702\) | −14.4098 | −0.543863 | ||||||||
\(703\) | −32.5571 | −1.22791 | ||||||||
\(704\) | 27.6568 | 1.04236 | ||||||||
\(705\) | −1.37946 | −0.0519534 | ||||||||
\(706\) | 13.4962 | 0.507935 | ||||||||
\(707\) | −11.4081 | −0.429046 | ||||||||
\(708\) | 2.05614 | 0.0772747 | ||||||||
\(709\) | −50.5314 | −1.89775 | −0.948873 | − | 0.315658i | \(-0.897775\pi\) | ||||
−0.948873 | + | 0.315658i | \(0.897775\pi\) | |||||||
\(710\) | 32.8935 | 1.23447 | ||||||||
\(711\) | −4.31871 | −0.161964 | ||||||||
\(712\) | −111.561 | −4.18094 | ||||||||
\(713\) | 5.22128 | 0.195538 | ||||||||
\(714\) | −2.65884 | −0.0995047 | ||||||||
\(715\) | −90.8105 | −3.39612 | ||||||||
\(716\) | 72.5660 | 2.71192 | ||||||||
\(717\) | 2.66653 | 0.0995833 | ||||||||
\(718\) | 51.4194 | 1.91896 | ||||||||
\(719\) | 7.97915 | 0.297572 | 0.148786 | − | 0.988869i | \(-0.452463\pi\) | ||||
0.148786 | + | 0.988869i | \(0.452463\pi\) | |||||||
\(720\) | −84.9792 | −3.16699 | ||||||||
\(721\) | 16.1459 | 0.601305 | ||||||||
\(722\) | 18.0802 | 0.672874 | ||||||||
\(723\) | −1.97389 | −0.0734096 | ||||||||
\(724\) | −8.11533 | −0.301604 | ||||||||
\(725\) | −46.5852 | −1.73013 | ||||||||
\(726\) | −7.82803 | −0.290525 | ||||||||
\(727\) | 47.7961 | 1.77266 | 0.886329 | − | 0.463056i | \(-0.153247\pi\) | ||||
0.886329 | + | 0.463056i | \(0.153247\pi\) | |||||||
\(728\) | 94.7537 | 3.51181 | ||||||||
\(729\) | −25.3433 | −0.938642 | ||||||||
\(730\) | 115.867 | 4.28844 | ||||||||
\(731\) | −9.15910 | −0.338761 | ||||||||
\(732\) | −10.8240 | −0.400066 | ||||||||
\(733\) | 6.50357 | 0.240215 | 0.120107 | − | 0.992761i | \(-0.461676\pi\) | ||||
0.120107 | + | 0.992761i | \(0.461676\pi\) | |||||||
\(734\) | −4.75807 | −0.175623 | ||||||||
\(735\) | −0.321867 | −0.0118723 | ||||||||
\(736\) | −8.83965 | −0.325834 | ||||||||
\(737\) | 39.5548 | 1.45702 | ||||||||
\(738\) | 97.2450 | 3.57964 | ||||||||
\(739\) | 15.4770 | 0.569332 | 0.284666 | − | 0.958627i | \(-0.408117\pi\) | ||||
0.284666 | + | 0.958627i | \(0.408117\pi\) | |||||||
\(740\) | 143.312 | 5.26827 | ||||||||
\(741\) | 3.22902 | 0.118621 | ||||||||
\(742\) | −51.6579 | −1.89642 | ||||||||
\(743\) | 36.3789 | 1.33461 | 0.667307 | − | 0.744783i | \(-0.267447\pi\) | ||||
0.667307 | + | 0.744783i | \(0.267447\pi\) | |||||||
\(744\) | −6.48202 | −0.237642 | ||||||||
\(745\) | −74.6442 | −2.73475 | ||||||||
\(746\) | −62.3962 | −2.28449 | ||||||||
\(747\) | −19.8875 | −0.727644 | ||||||||
\(748\) | 57.5951 | 2.10589 | ||||||||
\(749\) | −28.8895 | −1.05560 | ||||||||
\(750\) | −0.664935 | −0.0242800 | ||||||||
\(751\) | −4.14915 | −0.151405 | −0.0757024 | − | 0.997130i | \(-0.524120\pi\) | ||||
−0.0757024 | + | 0.997130i | \(0.524120\pi\) | |||||||
\(752\) | −21.4761 | −0.783154 | ||||||||
\(753\) | −4.06012 | −0.147959 | ||||||||
\(754\) | −117.283 | −4.27120 | ||||||||
\(755\) | −25.8002 | −0.938967 | ||||||||
\(756\) | −12.5767 | −0.457409 | ||||||||
\(757\) | 44.8811 | 1.63123 | 0.815617 | − | 0.578593i | \(-0.196398\pi\) | ||||
0.815617 | + | 0.578593i | \(0.196398\pi\) | |||||||
\(758\) | 3.27236 | 0.118857 | ||||||||
\(759\) | 0.933545 | 0.0338855 | ||||||||
\(760\) | 79.1209 | 2.87002 | ||||||||
\(761\) | −22.8383 | −0.827887 | −0.413944 | − | 0.910302i | \(-0.635849\pi\) | ||||
−0.413944 | + | 0.910302i | \(0.635849\pi\) | |||||||
\(762\) | −5.05306 | −0.183053 | ||||||||
\(763\) | 22.8429 | 0.826969 | ||||||||
\(764\) | 96.3693 | 3.48652 | ||||||||
\(765\) | −22.0602 | −0.797587 | ||||||||
\(766\) | 39.1497 | 1.41454 | ||||||||
\(767\) | −13.1023 | −0.473096 | ||||||||
\(768\) | −3.73428 | −0.134749 | ||||||||
\(769\) | 45.9753 | 1.65791 | 0.828955 | − | 0.559315i | \(-0.188936\pi\) | ||||
0.828955 | + | 0.559315i | \(0.188936\pi\) | |||||||
\(770\) | −112.828 | −4.06602 | ||||||||
\(771\) | 5.44572 | 0.196123 | ||||||||
\(772\) | 38.9983 | 1.40358 | ||||||||
\(773\) | 30.3509 | 1.09164 | 0.545822 | − | 0.837901i | \(-0.316217\pi\) | ||||
0.545822 | + | 0.837901i | \(0.316217\pi\) | |||||||
\(774\) | −30.6768 | −1.10265 | ||||||||
\(775\) | 28.4611 | 1.02235 | ||||||||
\(776\) | −84.2458 | −3.02425 | ||||||||
\(777\) | 4.18897 | 0.150278 | ||||||||
\(778\) | 32.0990 | 1.15080 | ||||||||
\(779\) | −43.8095 | −1.56964 | ||||||||
\(780\) | −14.2138 | −0.508935 | ||||||||
\(781\) | −20.8270 | −0.745248 | ||||||||
\(782\) | −5.95884 | −0.213088 | ||||||||
\(783\) | 8.97364 | 0.320692 | ||||||||
\(784\) | −5.01100 | −0.178964 | ||||||||
\(785\) | 66.4558 | 2.37191 | ||||||||
\(786\) | −8.10225 | −0.288998 | ||||||||
\(787\) | −9.53022 | −0.339716 | −0.169858 | − | 0.985469i | \(-0.554331\pi\) | ||||
−0.169858 | + | 0.985469i | \(0.554331\pi\) | |||||||
\(788\) | −6.04347 | −0.215290 | ||||||||
\(789\) | 2.44143 | 0.0869174 | ||||||||
\(790\) | −12.1917 | −0.433762 | ||||||||
\(791\) | −32.6403 | −1.16056 | ||||||||
\(792\) | 111.201 | 3.95134 | ||||||||
\(793\) | 68.9732 | 2.44931 | ||||||||
\(794\) | 13.5916 | 0.482349 | ||||||||
\(795\) | 4.46698 | 0.158428 | ||||||||
\(796\) | 127.168 | 4.50736 | ||||||||
\(797\) | −5.71014 | −0.202263 | −0.101132 | − | 0.994873i | \(-0.532246\pi\) | ||||
−0.101132 | + | 0.994873i | \(0.532246\pi\) | |||||||
\(798\) | 4.01190 | 0.142020 | ||||||||
\(799\) | −5.57509 | −0.197233 | ||||||||
\(800\) | −48.1848 | −1.70359 | ||||||||
\(801\) | −46.9341 | −1.65834 | ||||||||
\(802\) | 75.6394 | 2.67092 | ||||||||
\(803\) | −73.3630 | −2.58892 | ||||||||
\(804\) | 6.19116 | 0.218345 | ||||||||
\(805\) | 8.20011 | 0.289016 | ||||||||
\(806\) | 71.6538 | 2.52390 | ||||||||
\(807\) | −1.23097 | −0.0433321 | ||||||||
\(808\) | 31.7407 | 1.11663 | ||||||||
\(809\) | −6.76993 | −0.238018 | −0.119009 | − | 0.992893i | \(-0.537972\pi\) | ||||
−0.119009 | + | 0.992893i | \(0.537972\pi\) | |||||||
\(810\) | −73.1085 | −2.56877 | ||||||||
\(811\) | −6.68482 | −0.234736 | −0.117368 | − | 0.993088i | \(-0.537446\pi\) | ||||
−0.117368 | + | 0.993088i | \(0.537446\pi\) | |||||||
\(812\) | −102.363 | −3.59224 | ||||||||
\(813\) | −0.550824 | −0.0193183 | ||||||||
\(814\) | −129.173 | −4.52751 | ||||||||
\(815\) | 39.9480 | 1.39932 | ||||||||
\(816\) | 3.57946 | 0.125306 | ||||||||
\(817\) | 13.8201 | 0.483503 | ||||||||
\(818\) | 41.8470 | 1.46315 | ||||||||
\(819\) | 39.8631 | 1.39293 | ||||||||
\(820\) | 192.844 | 6.73440 | ||||||||
\(821\) | 42.8550 | 1.49565 | 0.747825 | − | 0.663895i | \(-0.231098\pi\) | ||||
0.747825 | + | 0.663895i | \(0.231098\pi\) | |||||||
\(822\) | 6.57294 | 0.229258 | ||||||||
\(823\) | −55.2803 | −1.92695 | −0.963476 | − | 0.267795i | \(-0.913705\pi\) | ||||
−0.963476 | + | 0.267795i | \(0.913705\pi\) | |||||||
\(824\) | −44.9226 | −1.56495 | ||||||||
\(825\) | 5.08874 | 0.177167 | ||||||||
\(826\) | −16.2789 | −0.566417 | ||||||||
\(827\) | 5.62064 | 0.195449 | 0.0977244 | − | 0.995214i | \(-0.468844\pi\) | ||||
0.0977244 | + | 0.995214i | \(0.468844\pi\) | |||||||
\(828\) | −14.0200 | −0.487228 | ||||||||
\(829\) | −7.23925 | −0.251430 | −0.125715 | − | 0.992066i | \(-0.540122\pi\) | ||||
−0.125715 | + | 0.992066i | \(0.540122\pi\) | |||||||
\(830\) | −56.1422 | −1.94873 | ||||||||
\(831\) | −3.41717 | −0.118540 | ||||||||
\(832\) | −27.5847 | −0.956329 | ||||||||
\(833\) | −1.30083 | −0.0450710 | ||||||||
\(834\) | 2.07385 | 0.0718117 | ||||||||
\(835\) | 45.2730 | 1.56674 | ||||||||
\(836\) | −86.9047 | −3.00566 | ||||||||
\(837\) | −5.48242 | −0.189500 | ||||||||
\(838\) | 77.2039 | 2.66696 | ||||||||
\(839\) | 55.5398 | 1.91745 | 0.958724 | − | 0.284339i | \(-0.0917740\pi\) | ||||
0.958724 | + | 0.284339i | \(0.0917740\pi\) | |||||||
\(840\) | −10.1801 | −0.351247 | ||||||||
\(841\) | 44.0376 | 1.51854 | ||||||||
\(842\) | −84.2146 | −2.90223 | ||||||||
\(843\) | 2.03279 | 0.0700129 | ||||||||
\(844\) | 85.3068 | 2.93638 | ||||||||
\(845\) | 48.5475 | 1.67008 | ||||||||
\(846\) | −18.6728 | −0.641984 | ||||||||
\(847\) | 43.5365 | 1.49593 | ||||||||
\(848\) | 69.5443 | 2.38816 | ||||||||
\(849\) | 2.78670 | 0.0956393 | ||||||||
\(850\) | −32.4815 | −1.11411 | ||||||||
\(851\) | 9.38807 | 0.321819 | ||||||||
\(852\) | −3.25986 | −0.111681 | ||||||||
\(853\) | −5.48135 | −0.187678 | −0.0938389 | − | 0.995587i | \(-0.529914\pi\) | ||||
−0.0938389 | + | 0.995587i | \(0.529914\pi\) | |||||||
\(854\) | 85.6958 | 2.93245 | ||||||||
\(855\) | 33.2863 | 1.13837 | ||||||||
\(856\) | 80.3789 | 2.74729 | ||||||||
\(857\) | −29.3810 | −1.00363 | −0.501817 | − | 0.864974i | \(-0.667335\pi\) | ||||
−0.501817 | + | 0.864974i | \(0.667335\pi\) | |||||||
\(858\) | 12.8114 | 0.437375 | ||||||||
\(859\) | −7.37326 | −0.251572 | −0.125786 | − | 0.992057i | \(-0.540145\pi\) | ||||
−0.125786 | + | 0.992057i | \(0.540145\pi\) | |||||||
\(860\) | −60.8343 | −2.07443 | ||||||||
\(861\) | 5.63676 | 0.192100 | ||||||||
\(862\) | 48.3601 | 1.64715 | ||||||||
\(863\) | −37.9220 | −1.29088 | −0.645440 | − | 0.763811i | \(-0.723326\pi\) | ||||
−0.645440 | + | 0.763811i | \(0.723326\pi\) | |||||||
\(864\) | 9.28177 | 0.315772 | ||||||||
\(865\) | −10.1993 | −0.346785 | ||||||||
\(866\) | −102.635 | −3.48769 | ||||||||
\(867\) | −2.06126 | −0.0700039 | ||||||||
\(868\) | 62.5384 | 2.12269 | ||||||||
\(869\) | 7.71936 | 0.261861 | ||||||||
\(870\) | 12.6006 | 0.427201 | ||||||||
\(871\) | −39.4517 | −1.33677 | ||||||||
\(872\) | −63.5557 | −2.15227 | ||||||||
\(873\) | −35.4424 | −1.19954 | ||||||||
\(874\) | 8.99124 | 0.304133 | ||||||||
\(875\) | 3.69811 | 0.125019 | ||||||||
\(876\) | −11.4829 | −0.387970 | ||||||||
\(877\) | 58.8995 | 1.98889 | 0.994447 | − | 0.105235i | \(-0.0335594\pi\) | ||||
0.994447 | + | 0.105235i | \(0.0335594\pi\) | |||||||
\(878\) | 28.4560 | 0.960344 | ||||||||
\(879\) | 0.776605 | 0.0261942 | ||||||||
\(880\) | 151.894 | 5.12034 | ||||||||
\(881\) | −14.0544 | −0.473504 | −0.236752 | − | 0.971570i | \(-0.576083\pi\) | ||||
−0.236752 | + | 0.971570i | \(0.576083\pi\) | |||||||
\(882\) | −4.35690 | −0.146704 | ||||||||
\(883\) | 50.0721 | 1.68506 | 0.842530 | − | 0.538650i | \(-0.181065\pi\) | ||||
0.842530 | + | 0.538650i | \(0.181065\pi\) | |||||||
\(884\) | −57.4450 | −1.93209 | ||||||||
\(885\) | 1.40768 | 0.0473186 | ||||||||
\(886\) | 86.9233 | 2.92024 | ||||||||
\(887\) | −39.1700 | −1.31520 | −0.657599 | − | 0.753368i | \(-0.728428\pi\) | ||||
−0.657599 | + | 0.753368i | \(0.728428\pi\) | |||||||
\(888\) | −11.6549 | −0.391114 | ||||||||
\(889\) | 28.1032 | 0.942549 | ||||||||
\(890\) | −132.495 | −4.44124 | ||||||||
\(891\) | 46.2897 | 1.55076 | ||||||||
\(892\) | 81.7403 | 2.73687 | ||||||||
\(893\) | 8.41220 | 0.281504 | ||||||||
\(894\) | 10.5307 | 0.352199 | ||||||||
\(895\) | 49.6802 | 1.66062 | ||||||||
\(896\) | 10.5715 | 0.353170 | ||||||||
\(897\) | −0.931112 | −0.0310889 | ||||||||
\(898\) | 24.0336 | 0.802013 | ||||||||
\(899\) | −44.6221 | −1.48823 | ||||||||
\(900\) | −76.4226 | −2.54742 | ||||||||
\(901\) | 18.0533 | 0.601444 | ||||||||
\(902\) | −173.818 | −5.78750 | ||||||||
\(903\) | −1.77816 | −0.0591736 | ||||||||
\(904\) | 90.8149 | 3.02046 | ||||||||
\(905\) | −5.55592 | −0.184685 | ||||||||
\(906\) | 3.63987 | 0.120926 | ||||||||
\(907\) | −47.9227 | −1.59125 | −0.795623 | − | 0.605792i | \(-0.792856\pi\) | ||||
−0.795623 | + | 0.605792i | \(0.792856\pi\) | |||||||
\(908\) | −1.21664 | −0.0403755 | ||||||||
\(909\) | 13.3534 | 0.442904 | ||||||||
\(910\) | 112.534 | 3.73045 | ||||||||
\(911\) | −46.2741 | −1.53313 | −0.766565 | − | 0.642167i | \(-0.778036\pi\) | ||||
−0.766565 | + | 0.642167i | \(0.778036\pi\) | |||||||
\(912\) | −5.40101 | −0.178845 | ||||||||
\(913\) | 35.5473 | 1.17644 | ||||||||
\(914\) | 4.35163 | 0.143939 | ||||||||
\(915\) | −7.41031 | −0.244977 | ||||||||
\(916\) | 8.21841 | 0.271544 | ||||||||
\(917\) | 45.0616 | 1.48806 | ||||||||
\(918\) | 6.25687 | 0.206508 | ||||||||
\(919\) | 12.0186 | 0.396458 | 0.198229 | − | 0.980156i | \(-0.436481\pi\) | ||||
0.198229 | + | 0.980156i | \(0.436481\pi\) | |||||||
\(920\) | −22.8151 | −0.752191 | ||||||||
\(921\) | 5.64379 | 0.185969 | ||||||||
\(922\) | −68.8887 | −2.26873 | ||||||||
\(923\) | 20.7727 | 0.683742 | ||||||||
\(924\) | 11.1816 | 0.367848 | ||||||||
\(925\) | 51.1742 | 1.68260 | ||||||||
\(926\) | 32.8517 | 1.07958 | ||||||||
\(927\) | −18.8990 | −0.620726 | ||||||||
\(928\) | 75.5455 | 2.47990 | ||||||||
\(929\) | −3.65244 | −0.119833 | −0.0599164 | − | 0.998203i | \(-0.519083\pi\) | ||||
−0.0599164 | + | 0.998203i | \(0.519083\pi\) | |||||||
\(930\) | −7.69831 | −0.252438 | ||||||||
\(931\) | 1.96281 | 0.0643284 | ||||||||
\(932\) | 35.6563 | 1.16796 | ||||||||
\(933\) | −0.818696 | −0.0268029 | ||||||||
\(934\) | −42.1197 | −1.37820 | ||||||||
\(935\) | 39.4308 | 1.28952 | ||||||||
\(936\) | −110.911 | −3.62523 | ||||||||
\(937\) | −0.787379 | −0.0257226 | −0.0128613 | − | 0.999917i | \(-0.504094\pi\) | ||||
−0.0128613 | + | 0.999917i | \(0.504094\pi\) | |||||||
\(938\) | −49.0168 | −1.60045 | ||||||||
\(939\) | −4.17984 | −0.136404 | ||||||||
\(940\) | −37.0295 | −1.20777 | ||||||||
\(941\) | 22.5297 | 0.734447 | 0.367224 | − | 0.930133i | \(-0.380308\pi\) | ||||
0.367224 | + | 0.930133i | \(0.380308\pi\) | |||||||
\(942\) | −9.37550 | −0.305470 | ||||||||
\(943\) | 12.6328 | 0.411380 | ||||||||
\(944\) | 21.9155 | 0.713288 | ||||||||
\(945\) | −8.61023 | −0.280091 | ||||||||
\(946\) | 54.8323 | 1.78275 | ||||||||
\(947\) | 33.7184 | 1.09570 | 0.547850 | − | 0.836576i | \(-0.315446\pi\) | ||||
0.547850 | + | 0.836576i | \(0.315446\pi\) | |||||||
\(948\) | 1.20824 | 0.0392419 | ||||||||
\(949\) | 73.1718 | 2.37526 | ||||||||
\(950\) | 49.0111 | 1.59013 | ||||||||
\(951\) | −1.37424 | −0.0445629 | ||||||||
\(952\) | −41.1430 | −1.33345 | ||||||||
\(953\) | −3.85626 | −0.124916 | −0.0624582 | − | 0.998048i | \(-0.519894\pi\) | ||||
−0.0624582 | + | 0.998048i | \(0.519894\pi\) | |||||||
\(954\) | 60.4665 | 1.95767 | ||||||||
\(955\) | 65.9763 | 2.13494 | ||||||||
\(956\) | 71.5789 | 2.31503 | ||||||||
\(957\) | −7.97826 | −0.257901 | ||||||||
\(958\) | 97.6766 | 3.15579 | ||||||||
\(959\) | −36.5562 | −1.18046 | ||||||||
\(960\) | 2.96364 | 0.0956510 | ||||||||
\(961\) | −3.73825 | −0.120589 | ||||||||
\(962\) | 128.836 | 4.15385 | ||||||||
\(963\) | 33.8156 | 1.08969 | ||||||||
\(964\) | −52.9860 | −1.70656 | ||||||||
\(965\) | 26.6990 | 0.859472 | ||||||||
\(966\) | −1.15686 | −0.0372214 | ||||||||
\(967\) | −7.05723 | −0.226945 | −0.113473 | − | 0.993541i | \(-0.536197\pi\) | ||||
−0.113473 | + | 0.993541i | \(0.536197\pi\) | |||||||
\(968\) | −121.131 | −3.89330 | ||||||||
\(969\) | −1.40207 | −0.0450411 | ||||||||
\(970\) | −100.054 | −3.21254 | ||||||||
\(971\) | −8.62231 | −0.276703 | −0.138351 | − | 0.990383i | \(-0.544180\pi\) | ||||
−0.138351 | + | 0.990383i | \(0.544180\pi\) | |||||||
\(972\) | 22.1199 | 0.709497 | ||||||||
\(973\) | −11.5340 | −0.369762 | ||||||||
\(974\) | −20.3157 | −0.650957 | ||||||||
\(975\) | −5.07548 | −0.162545 | ||||||||
\(976\) | −115.368 | −3.69283 | ||||||||
\(977\) | 9.03507 | 0.289058 | 0.144529 | − | 0.989501i | \(-0.453833\pi\) | ||||
0.144529 | + | 0.989501i | \(0.453833\pi\) | |||||||
\(978\) | −5.63581 | −0.180213 | ||||||||
\(979\) | 83.8911 | 2.68117 | ||||||||
\(980\) | −8.64004 | −0.275996 | ||||||||
\(981\) | −26.7380 | −0.853679 | ||||||||
\(982\) | −85.3879 | −2.72484 | ||||||||
\(983\) | 13.6514 | 0.435412 | 0.217706 | − | 0.976014i | \(-0.430143\pi\) | ||||
0.217706 | + | 0.976014i | \(0.430143\pi\) | |||||||
\(984\) | −15.6831 | −0.499959 | ||||||||
\(985\) | −4.13748 | −0.131831 | ||||||||
\(986\) | 50.9255 | 1.62180 | ||||||||
\(987\) | −1.08236 | −0.0344518 | ||||||||
\(988\) | 86.6783 | 2.75760 | ||||||||
\(989\) | −3.98512 | −0.126719 | ||||||||
\(990\) | 132.066 | 4.19735 | ||||||||
\(991\) | −31.4355 | −0.998581 | −0.499291 | − | 0.866435i | \(-0.666406\pi\) | ||||
−0.499291 | + | 0.866435i | \(0.666406\pi\) | |||||||
\(992\) | −46.1543 | −1.46540 | ||||||||
\(993\) | 0.958587 | 0.0304198 | ||||||||
\(994\) | 25.8090 | 0.818613 | ||||||||
\(995\) | 87.0620 | 2.76005 | ||||||||
\(996\) | 5.56390 | 0.176299 | ||||||||
\(997\) | 12.7209 | 0.402875 | 0.201437 | − | 0.979501i | \(-0.435439\pi\) | ||||
0.201437 | + | 0.979501i | \(0.435439\pi\) | |||||||
\(998\) | 26.1896 | 0.829017 | ||||||||
\(999\) | −9.85761 | −0.311881 |
(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 | 8027.2.a.f.1.10 | ✓ | 176 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.f.1.10 | ✓ | 176 | 1.1 | even | 1 | trivial |