Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(74\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.21900 | −1.56907 | −0.784533 | − | 0.620087i | \(-0.787097\pi\) | ||||
−0.784533 | + | 0.620087i | \(0.787097\pi\) | |||||||
\(3\) | −1.42344 | −0.821826 | −0.410913 | − | 0.911675i | \(-0.634790\pi\) | ||||
−0.410913 | + | 0.911675i | \(0.634790\pi\) | |||||||
\(4\) | 2.92394 | 1.46197 | ||||||||
\(5\) | −3.24388 | −1.45071 | −0.725353 | − | 0.688377i | \(-0.758323\pi\) | ||||
−0.725353 | + | 0.688377i | \(0.758323\pi\) | |||||||
\(6\) | 3.15861 | 1.28950 | ||||||||
\(7\) | 4.34231 | 1.64124 | 0.820620 | − | 0.571475i | \(-0.193628\pi\) | ||||
0.820620 | + | 0.571475i | \(0.193628\pi\) | |||||||
\(8\) | −2.05022 | −0.724863 | ||||||||
\(9\) | −0.973808 | −0.324603 | ||||||||
\(10\) | 7.19815 | 2.27625 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −4.16207 | −1.20148 | ||||||||
\(13\) | −2.33927 | −0.648797 | −0.324399 | − | 0.945920i | \(-0.605162\pi\) | ||||
−0.324399 | + | 0.945920i | \(0.605162\pi\) | |||||||
\(14\) | −9.63557 | −2.57521 | ||||||||
\(15\) | 4.61748 | 1.19223 | ||||||||
\(16\) | −1.29845 | −0.324613 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 2.16088 | 0.509323 | ||||||||
\(19\) | 0.168561 | 0.0386704 | 0.0193352 | − | 0.999813i | \(-0.493845\pi\) | ||||
0.0193352 | + | 0.999813i | \(0.493845\pi\) | |||||||
\(20\) | −9.48490 | −2.12089 | ||||||||
\(21\) | −6.18104 | −1.34881 | ||||||||
\(22\) | 2.21900 | 0.473091 | ||||||||
\(23\) | −0.985765 | −0.205546 | −0.102773 | − | 0.994705i | \(-0.532772\pi\) | ||||
−0.102773 | + | 0.994705i | \(0.532772\pi\) | |||||||
\(24\) | 2.91837 | 0.595711 | ||||||||
\(25\) | 5.52274 | 1.10455 | ||||||||
\(26\) | 5.19083 | 1.01801 | ||||||||
\(27\) | 5.65649 | 1.08859 | ||||||||
\(28\) | 12.6967 | 2.39944 | ||||||||
\(29\) | −0.164955 | −0.0306314 | −0.0153157 | − | 0.999883i | \(-0.504875\pi\) | ||||
−0.0153157 | + | 0.999883i | \(0.504875\pi\) | |||||||
\(30\) | −10.2462 | −1.87068 | ||||||||
\(31\) | −2.02106 | −0.362993 | −0.181497 | − | 0.983392i | \(-0.558094\pi\) | ||||
−0.181497 | + | 0.983392i | \(0.558094\pi\) | |||||||
\(32\) | 6.98170 | 1.23420 | ||||||||
\(33\) | 1.42344 | 0.247790 | ||||||||
\(34\) | 2.21900 | 0.380555 | ||||||||
\(35\) | −14.0859 | −2.38096 | ||||||||
\(36\) | −2.84736 | −0.474560 | ||||||||
\(37\) | 9.45602 | 1.55456 | 0.777280 | − | 0.629154i | \(-0.216599\pi\) | ||||
0.777280 | + | 0.629154i | \(0.216599\pi\) | |||||||
\(38\) | −0.374035 | −0.0606765 | ||||||||
\(39\) | 3.32982 | 0.533198 | ||||||||
\(40\) | 6.65066 | 1.05156 | ||||||||
\(41\) | −5.59501 | −0.873793 | −0.436897 | − | 0.899512i | \(-0.643922\pi\) | ||||
−0.436897 | + | 0.899512i | \(0.643922\pi\) | |||||||
\(42\) | 13.7157 | 2.11638 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −2.92394 | −0.440801 | ||||||||
\(45\) | 3.15891 | 0.470903 | ||||||||
\(46\) | 2.18741 | 0.322516 | ||||||||
\(47\) | −7.32264 | −1.06812 | −0.534059 | − | 0.845447i | \(-0.679334\pi\) | ||||
−0.534059 | + | 0.845447i | \(0.679334\pi\) | |||||||
\(48\) | 1.84827 | 0.266775 | ||||||||
\(49\) | 11.8557 | 1.69367 | ||||||||
\(50\) | −12.2549 | −1.73311 | ||||||||
\(51\) | 1.42344 | 0.199322 | ||||||||
\(52\) | −6.83989 | −0.948522 | ||||||||
\(53\) | −2.00710 | −0.275697 | −0.137848 | − | 0.990453i | \(-0.544019\pi\) | ||||
−0.137848 | + | 0.990453i | \(0.544019\pi\) | |||||||
\(54\) | −12.5517 | −1.70807 | ||||||||
\(55\) | 3.24388 | 0.437404 | ||||||||
\(56\) | −8.90270 | −1.18967 | ||||||||
\(57\) | −0.239936 | −0.0317804 | ||||||||
\(58\) | 0.366034 | 0.0480627 | ||||||||
\(59\) | 3.01087 | 0.391982 | 0.195991 | − | 0.980606i | \(-0.437208\pi\) | ||||
0.195991 | + | 0.980606i | \(0.437208\pi\) | |||||||
\(60\) | 13.5012 | 1.74300 | ||||||||
\(61\) | 6.96961 | 0.892367 | 0.446184 | − | 0.894941i | \(-0.352783\pi\) | ||||
0.446184 | + | 0.894941i | \(0.352783\pi\) | |||||||
\(62\) | 4.48473 | 0.569561 | ||||||||
\(63\) | −4.22858 | −0.532751 | ||||||||
\(64\) | −12.8955 | −1.61193 | ||||||||
\(65\) | 7.58831 | 0.941214 | ||||||||
\(66\) | −3.15861 | −0.388799 | ||||||||
\(67\) | −6.46785 | −0.790173 | −0.395087 | − | 0.918644i | \(-0.629285\pi\) | ||||
−0.395087 | + | 0.918644i | \(0.629285\pi\) | |||||||
\(68\) | −2.92394 | −0.354580 | ||||||||
\(69\) | 1.40318 | 0.168923 | ||||||||
\(70\) | 31.2566 | 3.73588 | ||||||||
\(71\) | 10.3156 | 1.22424 | 0.612119 | − | 0.790766i | \(-0.290317\pi\) | ||||
0.612119 | + | 0.790766i | \(0.290317\pi\) | |||||||
\(72\) | 1.99652 | 0.235292 | ||||||||
\(73\) | −3.32324 | −0.388956 | −0.194478 | − | 0.980907i | \(-0.562301\pi\) | ||||
−0.194478 | + | 0.980907i | \(0.562301\pi\) | |||||||
\(74\) | −20.9829 | −2.43921 | ||||||||
\(75\) | −7.86130 | −0.907745 | ||||||||
\(76\) | 0.492861 | 0.0565351 | ||||||||
\(77\) | −4.34231 | −0.494852 | ||||||||
\(78\) | −7.38886 | −0.836623 | ||||||||
\(79\) | 16.8936 | 1.90068 | 0.950339 | − | 0.311217i | \(-0.100737\pi\) | ||||
0.950339 | + | 0.311217i | \(0.100737\pi\) | |||||||
\(80\) | 4.21201 | 0.470917 | ||||||||
\(81\) | −5.13027 | −0.570030 | ||||||||
\(82\) | 12.4153 | 1.37104 | ||||||||
\(83\) | −15.1788 | −1.66609 | −0.833043 | − | 0.553209i | \(-0.813403\pi\) | ||||
−0.833043 | + | 0.553209i | \(0.813403\pi\) | |||||||
\(84\) | −18.0730 | −1.97192 | ||||||||
\(85\) | 3.24388 | 0.351848 | ||||||||
\(86\) | 2.21900 | 0.239280 | ||||||||
\(87\) | 0.234804 | 0.0251736 | ||||||||
\(88\) | 2.05022 | 0.218554 | ||||||||
\(89\) | −13.5804 | −1.43952 | −0.719759 | − | 0.694225i | \(-0.755747\pi\) | ||||
−0.719759 | + | 0.694225i | \(0.755747\pi\) | |||||||
\(90\) | −7.00962 | −0.738879 | ||||||||
\(91\) | −10.1578 | −1.06483 | ||||||||
\(92\) | −2.88232 | −0.300502 | ||||||||
\(93\) | 2.87687 | 0.298317 | ||||||||
\(94\) | 16.2489 | 1.67595 | ||||||||
\(95\) | −0.546790 | −0.0560994 | ||||||||
\(96\) | −9.93805 | −1.01430 | ||||||||
\(97\) | 9.61282 | 0.976034 | 0.488017 | − | 0.872834i | \(-0.337720\pi\) | ||||
0.488017 | + | 0.872834i | \(0.337720\pi\) | |||||||
\(98\) | −26.3077 | −2.65748 | ||||||||
\(99\) | 0.973808 | 0.0978714 | ||||||||
\(100\) | 16.1482 | 1.61482 | ||||||||
\(101\) | 17.8966 | 1.78078 | 0.890388 | − | 0.455203i | \(-0.150433\pi\) | ||||
0.890388 | + | 0.455203i | \(0.150433\pi\) | |||||||
\(102\) | −3.15861 | −0.312749 | ||||||||
\(103\) | −8.07670 | −0.795821 | −0.397911 | − | 0.917424i | \(-0.630265\pi\) | ||||
−0.397911 | + | 0.917424i | \(0.630265\pi\) | |||||||
\(104\) | 4.79602 | 0.470289 | ||||||||
\(105\) | 20.0505 | 1.95673 | ||||||||
\(106\) | 4.45375 | 0.432587 | ||||||||
\(107\) | −1.69407 | −0.163772 | −0.0818861 | − | 0.996642i | \(-0.526094\pi\) | ||||
−0.0818861 | + | 0.996642i | \(0.526094\pi\) | |||||||
\(108\) | 16.5392 | 1.59149 | ||||||||
\(109\) | −14.5207 | −1.39083 | −0.695413 | − | 0.718610i | \(-0.744779\pi\) | ||||
−0.695413 | + | 0.718610i | \(0.744779\pi\) | |||||||
\(110\) | −7.19815 | −0.686316 | ||||||||
\(111\) | −13.4601 | −1.27758 | ||||||||
\(112\) | −5.63828 | −0.532767 | ||||||||
\(113\) | −13.6497 | −1.28406 | −0.642028 | − | 0.766681i | \(-0.721907\pi\) | ||||
−0.642028 | + | 0.766681i | \(0.721907\pi\) | |||||||
\(114\) | 0.532418 | 0.0498655 | ||||||||
\(115\) | 3.19770 | 0.298187 | ||||||||
\(116\) | −0.482319 | −0.0447822 | ||||||||
\(117\) | 2.27800 | 0.210601 | ||||||||
\(118\) | −6.68111 | −0.615046 | ||||||||
\(119\) | −4.34231 | −0.398059 | ||||||||
\(120\) | −9.46685 | −0.864201 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −15.4655 | −1.40018 | ||||||||
\(123\) | 7.96418 | 0.718106 | ||||||||
\(124\) | −5.90946 | −0.530686 | ||||||||
\(125\) | −1.69569 | −0.151667 | ||||||||
\(126\) | 9.38320 | 0.835922 | ||||||||
\(127\) | 11.1503 | 0.989430 | 0.494715 | − | 0.869055i | \(-0.335272\pi\) | ||||
0.494715 | + | 0.869055i | \(0.335272\pi\) | |||||||
\(128\) | 14.6516 | 1.29503 | ||||||||
\(129\) | 1.42344 | 0.125327 | ||||||||
\(130\) | −16.8384 | −1.47683 | ||||||||
\(131\) | 21.5713 | 1.88469 | 0.942347 | − | 0.334639i | \(-0.108614\pi\) | ||||
0.942347 | + | 0.334639i | \(0.108614\pi\) | |||||||
\(132\) | 4.16207 | 0.362261 | ||||||||
\(133\) | 0.731942 | 0.0634675 | ||||||||
\(134\) | 14.3521 | 1.23983 | ||||||||
\(135\) | −18.3490 | −1.57923 | ||||||||
\(136\) | 2.05022 | 0.175805 | ||||||||
\(137\) | −21.9329 | −1.87385 | −0.936925 | − | 0.349531i | \(-0.886341\pi\) | ||||
−0.936925 | + | 0.349531i | \(0.886341\pi\) | |||||||
\(138\) | −3.11365 | −0.265052 | ||||||||
\(139\) | −9.26739 | −0.786050 | −0.393025 | − | 0.919528i | \(-0.628571\pi\) | ||||
−0.393025 | + | 0.919528i | \(0.628571\pi\) | |||||||
\(140\) | −41.1864 | −3.48089 | ||||||||
\(141\) | 10.4234 | 0.877806 | ||||||||
\(142\) | −22.8903 | −1.92091 | ||||||||
\(143\) | 2.33927 | 0.195620 | ||||||||
\(144\) | 1.26444 | 0.105370 | ||||||||
\(145\) | 0.535094 | 0.0444371 | ||||||||
\(146\) | 7.37427 | 0.610299 | ||||||||
\(147\) | −16.8759 | −1.39190 | ||||||||
\(148\) | 27.6489 | 2.27272 | ||||||||
\(149\) | 6.26008 | 0.512846 | 0.256423 | − | 0.966565i | \(-0.417456\pi\) | ||||
0.256423 | + | 0.966565i | \(0.417456\pi\) | |||||||
\(150\) | 17.4442 | 1.42431 | ||||||||
\(151\) | −2.44911 | −0.199306 | −0.0996530 | − | 0.995022i | \(-0.531773\pi\) | ||||
−0.0996530 | + | 0.995022i | \(0.531773\pi\) | |||||||
\(152\) | −0.345586 | −0.0280308 | ||||||||
\(153\) | 0.973808 | 0.0787277 | ||||||||
\(154\) | 9.63557 | 0.776456 | ||||||||
\(155\) | 6.55607 | 0.526597 | ||||||||
\(156\) | 9.73620 | 0.779520 | ||||||||
\(157\) | 5.17777 | 0.413231 | 0.206615 | − | 0.978422i | \(-0.433755\pi\) | ||||
0.206615 | + | 0.978422i | \(0.433755\pi\) | |||||||
\(158\) | −37.4868 | −2.98229 | ||||||||
\(159\) | 2.85700 | 0.226575 | ||||||||
\(160\) | −22.6478 | −1.79046 | ||||||||
\(161\) | −4.28050 | −0.337350 | ||||||||
\(162\) | 11.3841 | 0.894415 | ||||||||
\(163\) | −5.60922 | −0.439348 | −0.219674 | − | 0.975573i | \(-0.570499\pi\) | ||||
−0.219674 | + | 0.975573i | \(0.570499\pi\) | |||||||
\(164\) | −16.3595 | −1.27746 | ||||||||
\(165\) | −4.61748 | −0.359470 | ||||||||
\(166\) | 33.6816 | 2.61420 | ||||||||
\(167\) | 0.291785 | 0.0225790 | 0.0112895 | − | 0.999936i | \(-0.496406\pi\) | ||||
0.0112895 | + | 0.999936i | \(0.496406\pi\) | |||||||
\(168\) | 12.6725 | 0.977704 | ||||||||
\(169\) | −7.52781 | −0.579062 | ||||||||
\(170\) | −7.19815 | −0.552073 | ||||||||
\(171\) | −0.164146 | −0.0125525 | ||||||||
\(172\) | −2.92394 | −0.222948 | ||||||||
\(173\) | 15.5846 | 1.18488 | 0.592438 | − | 0.805616i | \(-0.298166\pi\) | ||||
0.592438 | + | 0.805616i | \(0.298166\pi\) | |||||||
\(174\) | −0.521029 | −0.0394991 | ||||||||
\(175\) | 23.9814 | 1.81283 | ||||||||
\(176\) | 1.29845 | 0.0978744 | ||||||||
\(177\) | −4.28580 | −0.322141 | ||||||||
\(178\) | 30.1348 | 2.25870 | ||||||||
\(179\) | −1.74084 | −0.130117 | −0.0650584 | − | 0.997881i | \(-0.520723\pi\) | ||||
−0.0650584 | + | 0.997881i | \(0.520723\pi\) | |||||||
\(180\) | 9.23648 | 0.688447 | ||||||||
\(181\) | 9.83878 | 0.731311 | 0.365655 | − | 0.930750i | \(-0.380845\pi\) | ||||
0.365655 | + | 0.930750i | \(0.380845\pi\) | |||||||
\(182\) | 22.5402 | 1.67079 | ||||||||
\(183\) | −9.92085 | −0.733370 | ||||||||
\(184\) | 2.02104 | 0.148993 | ||||||||
\(185\) | −30.6742 | −2.25521 | ||||||||
\(186\) | −6.38376 | −0.468080 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −21.4110 | −1.56156 | ||||||||
\(189\) | 24.5623 | 1.78664 | ||||||||
\(190\) | 1.21332 | 0.0880238 | ||||||||
\(191\) | 9.64636 | 0.697986 | 0.348993 | − | 0.937125i | \(-0.386524\pi\) | ||||
0.348993 | + | 0.937125i | \(0.386524\pi\) | |||||||
\(192\) | 18.3560 | 1.32473 | ||||||||
\(193\) | 5.68852 | 0.409468 | 0.204734 | − | 0.978818i | \(-0.434367\pi\) | ||||
0.204734 | + | 0.978818i | \(0.434367\pi\) | |||||||
\(194\) | −21.3308 | −1.53146 | ||||||||
\(195\) | −10.8015 | −0.773513 | ||||||||
\(196\) | 34.6653 | 2.47609 | ||||||||
\(197\) | −10.8928 | −0.776081 | −0.388040 | − | 0.921642i | \(-0.626848\pi\) | ||||
−0.388040 | + | 0.921642i | \(0.626848\pi\) | |||||||
\(198\) | −2.16088 | −0.153567 | ||||||||
\(199\) | −8.27232 | −0.586409 | −0.293205 | − | 0.956050i | \(-0.594722\pi\) | ||||
−0.293205 | + | 0.956050i | \(0.594722\pi\) | |||||||
\(200\) | −11.3228 | −0.800645 | ||||||||
\(201\) | 9.20661 | 0.649384 | ||||||||
\(202\) | −39.7124 | −2.79416 | ||||||||
\(203\) | −0.716286 | −0.0502734 | ||||||||
\(204\) | 4.16207 | 0.291403 | ||||||||
\(205\) | 18.1495 | 1.26762 | ||||||||
\(206\) | 17.9222 | 1.24870 | ||||||||
\(207\) | 0.959946 | 0.0667208 | ||||||||
\(208\) | 3.03743 | 0.210608 | ||||||||
\(209\) | −0.168561 | −0.0116596 | ||||||||
\(210\) | −44.4920 | −3.07024 | ||||||||
\(211\) | 18.0157 | 1.24025 | 0.620126 | − | 0.784502i | \(-0.287081\pi\) | ||||
0.620126 | + | 0.784502i | \(0.287081\pi\) | |||||||
\(212\) | −5.86865 | −0.403060 | ||||||||
\(213\) | −14.6837 | −1.00611 | ||||||||
\(214\) | 3.75914 | 0.256970 | ||||||||
\(215\) | 3.24388 | 0.221231 | ||||||||
\(216\) | −11.5971 | −0.789080 | ||||||||
\(217\) | −8.77608 | −0.595759 | ||||||||
\(218\) | 32.2213 | 2.18230 | ||||||||
\(219\) | 4.73045 | 0.319654 | ||||||||
\(220\) | 9.48490 | 0.639472 | ||||||||
\(221\) | 2.33927 | 0.157356 | ||||||||
\(222\) | 29.8679 | 2.00460 | ||||||||
\(223\) | 14.8218 | 0.992539 | 0.496269 | − | 0.868169i | \(-0.334703\pi\) | ||||
0.496269 | + | 0.868169i | \(0.334703\pi\) | |||||||
\(224\) | 30.3167 | 2.02562 | ||||||||
\(225\) | −5.37809 | −0.358539 | ||||||||
\(226\) | 30.2886 | 2.01477 | ||||||||
\(227\) | 20.7575 | 1.37772 | 0.688861 | − | 0.724893i | \(-0.258111\pi\) | ||||
0.688861 | + | 0.724893i | \(0.258111\pi\) | |||||||
\(228\) | −0.701560 | −0.0464619 | ||||||||
\(229\) | −13.6355 | −0.901061 | −0.450530 | − | 0.892761i | \(-0.648765\pi\) | ||||
−0.450530 | + | 0.892761i | \(0.648765\pi\) | |||||||
\(230\) | −7.09568 | −0.467875 | ||||||||
\(231\) | 6.18104 | 0.406682 | ||||||||
\(232\) | 0.338194 | 0.0222035 | ||||||||
\(233\) | −4.77207 | −0.312628 | −0.156314 | − | 0.987707i | \(-0.549961\pi\) | ||||
−0.156314 | + | 0.987707i | \(0.549961\pi\) | |||||||
\(234\) | −5.05488 | −0.330448 | ||||||||
\(235\) | 23.7538 | 1.54952 | ||||||||
\(236\) | 8.80361 | 0.573066 | ||||||||
\(237\) | −24.0471 | −1.56203 | ||||||||
\(238\) | 9.63557 | 0.624581 | ||||||||
\(239\) | −12.8869 | −0.833585 | −0.416793 | − | 0.909002i | \(-0.636846\pi\) | ||||
−0.416793 | + | 0.909002i | \(0.636846\pi\) | |||||||
\(240\) | −5.99556 | −0.387012 | ||||||||
\(241\) | 7.31671 | 0.471311 | 0.235656 | − | 0.971837i | \(-0.424276\pi\) | ||||
0.235656 | + | 0.971837i | \(0.424276\pi\) | |||||||
\(242\) | −2.21900 | −0.142642 | ||||||||
\(243\) | −9.66682 | −0.620127 | ||||||||
\(244\) | 20.3787 | 1.30461 | ||||||||
\(245\) | −38.4583 | −2.45701 | ||||||||
\(246\) | −17.6725 | −1.12676 | ||||||||
\(247\) | −0.394309 | −0.0250893 | ||||||||
\(248\) | 4.14362 | 0.263120 | ||||||||
\(249\) | 21.6061 | 1.36923 | ||||||||
\(250\) | 3.76273 | 0.237976 | ||||||||
\(251\) | 4.82277 | 0.304411 | 0.152205 | − | 0.988349i | \(-0.451362\pi\) | ||||
0.152205 | + | 0.988349i | \(0.451362\pi\) | |||||||
\(252\) | −12.3641 | −0.778866 | ||||||||
\(253\) | 0.985765 | 0.0619745 | ||||||||
\(254\) | −24.7425 | −1.55248 | ||||||||
\(255\) | −4.61748 | −0.289158 | ||||||||
\(256\) | −6.72084 | −0.420053 | ||||||||
\(257\) | 25.9570 | 1.61915 | 0.809576 | − | 0.587016i | \(-0.199697\pi\) | ||||
0.809576 | + | 0.587016i | \(0.199697\pi\) | |||||||
\(258\) | −3.15861 | −0.196647 | ||||||||
\(259\) | 41.0610 | 2.55141 | ||||||||
\(260\) | 22.1878 | 1.37603 | ||||||||
\(261\) | 0.160635 | 0.00994303 | ||||||||
\(262\) | −47.8666 | −2.95721 | ||||||||
\(263\) | 23.7089 | 1.46195 | 0.730977 | − | 0.682402i | \(-0.239065\pi\) | ||||
0.730977 | + | 0.682402i | \(0.239065\pi\) | |||||||
\(264\) | −2.91837 | −0.179614 | ||||||||
\(265\) | 6.51079 | 0.399955 | ||||||||
\(266\) | −1.62418 | −0.0995847 | ||||||||
\(267\) | 19.3309 | 1.18303 | ||||||||
\(268\) | −18.9116 | −1.15521 | ||||||||
\(269\) | 14.9628 | 0.912299 | 0.456149 | − | 0.889903i | \(-0.349228\pi\) | ||||
0.456149 | + | 0.889903i | \(0.349228\pi\) | |||||||
\(270\) | 40.7163 | 2.47791 | ||||||||
\(271\) | 24.2901 | 1.47552 | 0.737758 | − | 0.675065i | \(-0.235885\pi\) | ||||
0.737758 | + | 0.675065i | \(0.235885\pi\) | |||||||
\(272\) | 1.29845 | 0.0787301 | ||||||||
\(273\) | 14.4591 | 0.875106 | ||||||||
\(274\) | 48.6689 | 2.94020 | ||||||||
\(275\) | −5.52274 | −0.333034 | ||||||||
\(276\) | 4.10282 | 0.246961 | ||||||||
\(277\) | 9.35781 | 0.562256 | 0.281128 | − | 0.959670i | \(-0.409291\pi\) | ||||
0.281128 | + | 0.959670i | \(0.409291\pi\) | |||||||
\(278\) | 20.5643 | 1.23337 | ||||||||
\(279\) | 1.96813 | 0.117829 | ||||||||
\(280\) | 28.8793 | 1.72587 | ||||||||
\(281\) | −31.2948 | −1.86689 | −0.933445 | − | 0.358721i | \(-0.883213\pi\) | ||||
−0.933445 | + | 0.358721i | \(0.883213\pi\) | |||||||
\(282\) | −23.1294 | −1.37734 | ||||||||
\(283\) | 6.46574 | 0.384348 | 0.192174 | − | 0.981361i | \(-0.438446\pi\) | ||||
0.192174 | + | 0.981361i | \(0.438446\pi\) | |||||||
\(284\) | 30.1622 | 1.78980 | ||||||||
\(285\) | 0.778324 | 0.0461039 | ||||||||
\(286\) | −5.19083 | −0.306940 | ||||||||
\(287\) | −24.2953 | −1.43410 | ||||||||
\(288\) | −6.79884 | −0.400625 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −1.18737 | −0.0697248 | ||||||||
\(291\) | −13.6833 | −0.802129 | ||||||||
\(292\) | −9.71697 | −0.568643 | ||||||||
\(293\) | 30.3716 | 1.77433 | 0.887165 | − | 0.461453i | \(-0.152672\pi\) | ||||
0.887165 | + | 0.461453i | \(0.152672\pi\) | |||||||
\(294\) | 37.4475 | 2.18398 | ||||||||
\(295\) | −9.76689 | −0.568650 | ||||||||
\(296\) | −19.3869 | −1.12684 | ||||||||
\(297\) | −5.65649 | −0.328223 | ||||||||
\(298\) | −13.8911 | −0.804689 | ||||||||
\(299\) | 2.30597 | 0.133358 | ||||||||
\(300\) | −22.9860 | −1.32710 | ||||||||
\(301\) | −4.34231 | −0.250287 | ||||||||
\(302\) | 5.43457 | 0.312724 | ||||||||
\(303\) | −25.4748 | −1.46349 | ||||||||
\(304\) | −0.218868 | −0.0125529 | ||||||||
\(305\) | −22.6086 | −1.29456 | ||||||||
\(306\) | −2.16088 | −0.123529 | ||||||||
\(307\) | 24.6632 | 1.40761 | 0.703803 | − | 0.710396i | \(-0.251484\pi\) | ||||
0.703803 | + | 0.710396i | \(0.251484\pi\) | |||||||
\(308\) | −12.6967 | −0.723460 | ||||||||
\(309\) | 11.4967 | 0.654026 | ||||||||
\(310\) | −14.5479 | −0.826265 | ||||||||
\(311\) | 5.99308 | 0.339836 | 0.169918 | − | 0.985458i | \(-0.445650\pi\) | ||||
0.169918 | + | 0.985458i | \(0.445650\pi\) | |||||||
\(312\) | −6.82687 | −0.386495 | ||||||||
\(313\) | −23.0932 | −1.30530 | −0.652652 | − | 0.757658i | \(-0.726343\pi\) | ||||
−0.652652 | + | 0.757658i | \(0.726343\pi\) | |||||||
\(314\) | −11.4894 | −0.648387 | ||||||||
\(315\) | 13.7170 | 0.772865 | ||||||||
\(316\) | 49.3959 | 2.77873 | ||||||||
\(317\) | 25.1608 | 1.41317 | 0.706586 | − | 0.707627i | \(-0.250234\pi\) | ||||
0.706586 | + | 0.707627i | \(0.250234\pi\) | |||||||
\(318\) | −6.33966 | −0.355511 | ||||||||
\(319\) | 0.164955 | 0.00923571 | ||||||||
\(320\) | 41.8313 | 2.33844 | ||||||||
\(321\) | 2.41142 | 0.134592 | ||||||||
\(322\) | 9.49840 | 0.529325 | ||||||||
\(323\) | −0.168561 | −0.00937896 | ||||||||
\(324\) | −15.0006 | −0.833367 | ||||||||
\(325\) | −12.9192 | −0.716627 | ||||||||
\(326\) | 12.4468 | 0.689367 | ||||||||
\(327\) | 20.6693 | 1.14302 | ||||||||
\(328\) | 11.4710 | 0.633380 | ||||||||
\(329\) | −31.7972 | −1.75304 | ||||||||
\(330\) | 10.2462 | 0.564032 | ||||||||
\(331\) | −1.95642 | −0.107535 | −0.0537673 | − | 0.998553i | \(-0.517123\pi\) | ||||
−0.0537673 | + | 0.998553i | \(0.517123\pi\) | |||||||
\(332\) | −44.3818 | −2.43577 | ||||||||
\(333\) | −9.20836 | −0.504615 | ||||||||
\(334\) | −0.647469 | −0.0354279 | ||||||||
\(335\) | 20.9809 | 1.14631 | ||||||||
\(336\) | 8.02577 | 0.437842 | ||||||||
\(337\) | 0.349007 | 0.0190116 | 0.00950581 | − | 0.999955i | \(-0.496974\pi\) | ||||
0.00950581 | + | 0.999955i | \(0.496974\pi\) | |||||||
\(338\) | 16.7042 | 0.908587 | ||||||||
\(339\) | 19.4296 | 1.05527 | ||||||||
\(340\) | 9.48490 | 0.514391 | ||||||||
\(341\) | 2.02106 | 0.109447 | ||||||||
\(342\) | 0.364239 | 0.0196958 | ||||||||
\(343\) | 21.0848 | 1.13847 | ||||||||
\(344\) | 2.05022 | 0.110541 | ||||||||
\(345\) | −4.55174 | −0.245058 | ||||||||
\(346\) | −34.5822 | −1.85915 | ||||||||
\(347\) | −5.08045 | −0.272733 | −0.136366 | − | 0.990658i | \(-0.543542\pi\) | ||||
−0.136366 | + | 0.990658i | \(0.543542\pi\) | |||||||
\(348\) | 0.686554 | 0.0368031 | ||||||||
\(349\) | −32.3442 | −1.73135 | −0.865673 | − | 0.500610i | \(-0.833109\pi\) | ||||
−0.865673 | + | 0.500610i | \(0.833109\pi\) | |||||||
\(350\) | −53.2147 | −2.84445 | ||||||||
\(351\) | −13.2321 | −0.706276 | ||||||||
\(352\) | −6.98170 | −0.372126 | ||||||||
\(353\) | 5.66174 | 0.301344 | 0.150672 | − | 0.988584i | \(-0.451856\pi\) | ||||
0.150672 | + | 0.988584i | \(0.451856\pi\) | |||||||
\(354\) | 9.51018 | 0.505460 | ||||||||
\(355\) | −33.4626 | −1.77601 | ||||||||
\(356\) | −39.7082 | −2.10453 | ||||||||
\(357\) | 6.18104 | 0.327135 | ||||||||
\(358\) | 3.86292 | 0.204162 | ||||||||
\(359\) | 6.37066 | 0.336231 | 0.168115 | − | 0.985767i | \(-0.446232\pi\) | ||||
0.168115 | + | 0.985767i | \(0.446232\pi\) | |||||||
\(360\) | −6.47647 | −0.341340 | ||||||||
\(361\) | −18.9716 | −0.998505 | ||||||||
\(362\) | −21.8322 | −1.14748 | ||||||||
\(363\) | −1.42344 | −0.0747114 | ||||||||
\(364\) | −29.7009 | −1.55675 | ||||||||
\(365\) | 10.7802 | 0.564261 | ||||||||
\(366\) | 22.0143 | 1.15071 | ||||||||
\(367\) | −8.19238 | −0.427639 | −0.213819 | − | 0.976873i | \(-0.568590\pi\) | ||||
−0.213819 | + | 0.976873i | \(0.568590\pi\) | |||||||
\(368\) | 1.27997 | 0.0667229 | ||||||||
\(369\) | 5.44846 | 0.283636 | ||||||||
\(370\) | 68.0659 | 3.53858 | ||||||||
\(371\) | −8.71546 | −0.452484 | ||||||||
\(372\) | 8.41179 | 0.436131 | ||||||||
\(373\) | −0.765166 | −0.0396188 | −0.0198094 | − | 0.999804i | \(-0.506306\pi\) | ||||
−0.0198094 | + | 0.999804i | \(0.506306\pi\) | |||||||
\(374\) | −2.21900 | −0.114742 | ||||||||
\(375\) | 2.41372 | 0.124644 | ||||||||
\(376\) | 15.0130 | 0.774239 | ||||||||
\(377\) | 0.385875 | 0.0198735 | ||||||||
\(378\) | −54.5035 | −2.80336 | ||||||||
\(379\) | −33.4549 | −1.71846 | −0.859231 | − | 0.511587i | \(-0.829058\pi\) | ||||
−0.859231 | + | 0.511587i | \(0.829058\pi\) | |||||||
\(380\) | −1.59878 | −0.0820157 | ||||||||
\(381\) | −15.8718 | −0.813139 | ||||||||
\(382\) | −21.4052 | −1.09519 | ||||||||
\(383\) | 19.3524 | 0.988864 | 0.494432 | − | 0.869216i | \(-0.335376\pi\) | ||||
0.494432 | + | 0.869216i | \(0.335376\pi\) | |||||||
\(384\) | −20.8557 | −1.06429 | ||||||||
\(385\) | 14.0859 | 0.717885 | ||||||||
\(386\) | −12.6228 | −0.642483 | ||||||||
\(387\) | 0.973808 | 0.0495015 | ||||||||
\(388\) | 28.1073 | 1.42693 | ||||||||
\(389\) | −11.0838 | −0.561972 | −0.280986 | − | 0.959712i | \(-0.590662\pi\) | ||||
−0.280986 | + | 0.959712i | \(0.590662\pi\) | |||||||
\(390\) | 23.9685 | 1.21369 | ||||||||
\(391\) | 0.985765 | 0.0498523 | ||||||||
\(392\) | −24.3067 | −1.22768 | ||||||||
\(393\) | −30.7055 | −1.54889 | ||||||||
\(394\) | 24.1711 | 1.21772 | ||||||||
\(395\) | −54.8007 | −2.75732 | ||||||||
\(396\) | 2.84736 | 0.143085 | ||||||||
\(397\) | 21.4575 | 1.07692 | 0.538460 | − | 0.842651i | \(-0.319006\pi\) | ||||
0.538460 | + | 0.842651i | \(0.319006\pi\) | |||||||
\(398\) | 18.3562 | 0.920115 | ||||||||
\(399\) | −1.04188 | −0.0521592 | ||||||||
\(400\) | −7.17100 | −0.358550 | ||||||||
\(401\) | 3.91375 | 0.195443 | 0.0977216 | − | 0.995214i | \(-0.468845\pi\) | ||||
0.0977216 | + | 0.995214i | \(0.468845\pi\) | |||||||
\(402\) | −20.4294 | −1.01893 | ||||||||
\(403\) | 4.72781 | 0.235509 | ||||||||
\(404\) | 52.3285 | 2.60344 | ||||||||
\(405\) | 16.6420 | 0.826946 | ||||||||
\(406\) | 1.58944 | 0.0788824 | ||||||||
\(407\) | −9.45602 | −0.468718 | ||||||||
\(408\) | −2.91837 | −0.144481 | ||||||||
\(409\) | −16.9893 | −0.840067 | −0.420033 | − | 0.907509i | \(-0.637982\pi\) | ||||
−0.420033 | + | 0.907509i | \(0.637982\pi\) | |||||||
\(410\) | −40.2737 | −1.98898 | ||||||||
\(411\) | 31.2202 | 1.53998 | ||||||||
\(412\) | −23.6158 | −1.16347 | ||||||||
\(413\) | 13.0741 | 0.643336 | ||||||||
\(414\) | −2.13012 | −0.104689 | ||||||||
\(415\) | 49.2380 | 2.41700 | ||||||||
\(416\) | −16.3321 | −0.800746 | ||||||||
\(417\) | 13.1916 | 0.645996 | ||||||||
\(418\) | 0.374035 | 0.0182947 | ||||||||
\(419\) | −10.3589 | −0.506066 | −0.253033 | − | 0.967458i | \(-0.581428\pi\) | ||||
−0.253033 | + | 0.967458i | \(0.581428\pi\) | |||||||
\(420\) | 58.6265 | 2.86068 | ||||||||
\(421\) | −33.5034 | −1.63286 | −0.816429 | − | 0.577446i | \(-0.804049\pi\) | ||||
−0.816429 | + | 0.577446i | \(0.804049\pi\) | |||||||
\(422\) | −39.9768 | −1.94604 | ||||||||
\(423\) | 7.13085 | 0.346714 | ||||||||
\(424\) | 4.11500 | 0.199842 | ||||||||
\(425\) | −5.52274 | −0.267892 | ||||||||
\(426\) | 32.5830 | 1.57865 | ||||||||
\(427\) | 30.2642 | 1.46459 | ||||||||
\(428\) | −4.95337 | −0.239430 | ||||||||
\(429\) | −3.32982 | −0.160765 | ||||||||
\(430\) | −7.19815 | −0.347126 | ||||||||
\(431\) | −20.9487 | −1.00906 | −0.504532 | − | 0.863393i | \(-0.668335\pi\) | ||||
−0.504532 | + | 0.863393i | \(0.668335\pi\) | |||||||
\(432\) | −7.34468 | −0.353371 | ||||||||
\(433\) | −10.7961 | −0.518828 | −0.259414 | − | 0.965766i | \(-0.583529\pi\) | ||||
−0.259414 | + | 0.965766i | \(0.583529\pi\) | |||||||
\(434\) | 19.4741 | 0.934786 | ||||||||
\(435\) | −0.761676 | −0.0365196 | ||||||||
\(436\) | −42.4575 | −2.03335 | ||||||||
\(437\) | −0.166161 | −0.00794856 | ||||||||
\(438\) | −10.4969 | −0.501559 | ||||||||
\(439\) | 14.5954 | 0.696601 | 0.348301 | − | 0.937383i | \(-0.386759\pi\) | ||||
0.348301 | + | 0.937383i | \(0.386759\pi\) | |||||||
\(440\) | −6.65066 | −0.317058 | ||||||||
\(441\) | −11.5452 | −0.549769 | ||||||||
\(442\) | −5.19083 | −0.246903 | ||||||||
\(443\) | 21.2294 | 1.00864 | 0.504320 | − | 0.863517i | \(-0.331743\pi\) | ||||
0.504320 | + | 0.863517i | \(0.331743\pi\) | |||||||
\(444\) | −39.3566 | −1.86778 | ||||||||
\(445\) | 44.0531 | 2.08832 | ||||||||
\(446\) | −32.8894 | −1.55736 | ||||||||
\(447\) | −8.91087 | −0.421470 | ||||||||
\(448\) | −55.9961 | −2.64557 | ||||||||
\(449\) | −37.2701 | −1.75888 | −0.879442 | − | 0.476006i | \(-0.842084\pi\) | ||||
−0.879442 | + | 0.476006i | \(0.842084\pi\) | |||||||
\(450\) | 11.9340 | 0.562572 | ||||||||
\(451\) | 5.59501 | 0.263459 | ||||||||
\(452\) | −39.9110 | −1.87725 | ||||||||
\(453\) | 3.48618 | 0.163795 | ||||||||
\(454\) | −46.0607 | −2.16174 | ||||||||
\(455\) | 32.9508 | 1.54476 | ||||||||
\(456\) | 0.491923 | 0.0230364 | ||||||||
\(457\) | 7.90582 | 0.369819 | 0.184909 | − | 0.982756i | \(-0.440801\pi\) | ||||
0.184909 | + | 0.982756i | \(0.440801\pi\) | |||||||
\(458\) | 30.2572 | 1.41382 | ||||||||
\(459\) | −5.65649 | −0.264022 | ||||||||
\(460\) | 9.34988 | 0.435941 | ||||||||
\(461\) | 39.3929 | 1.83471 | 0.917355 | − | 0.398069i | \(-0.130320\pi\) | ||||
0.917355 | + | 0.398069i | \(0.130320\pi\) | |||||||
\(462\) | −13.7157 | −0.638112 | ||||||||
\(463\) | −14.1083 | −0.655670 | −0.327835 | − | 0.944735i | \(-0.606319\pi\) | ||||
−0.327835 | + | 0.944735i | \(0.606319\pi\) | |||||||
\(464\) | 0.214186 | 0.00994333 | ||||||||
\(465\) | −9.33220 | −0.432771 | ||||||||
\(466\) | 10.5892 | 0.490535 | ||||||||
\(467\) | −16.3544 | −0.756792 | −0.378396 | − | 0.925644i | \(-0.623524\pi\) | ||||
−0.378396 | + | 0.925644i | \(0.623524\pi\) | |||||||
\(468\) | 6.66074 | 0.307893 | ||||||||
\(469\) | −28.0854 | −1.29686 | ||||||||
\(470\) | −52.7095 | −2.43131 | ||||||||
\(471\) | −7.37026 | −0.339604 | ||||||||
\(472\) | −6.17295 | −0.284133 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 53.3604 | 2.45092 | ||||||||
\(475\) | 0.930915 | 0.0427133 | ||||||||
\(476\) | −12.6967 | −0.581951 | ||||||||
\(477\) | 1.95453 | 0.0894919 | ||||||||
\(478\) | 28.5960 | 1.30795 | ||||||||
\(479\) | −27.5008 | −1.25654 | −0.628272 | − | 0.777994i | \(-0.716238\pi\) | ||||
−0.628272 | + | 0.777994i | \(0.716238\pi\) | |||||||
\(480\) | 32.2378 | 1.47145 | ||||||||
\(481\) | −22.1202 | −1.00859 | ||||||||
\(482\) | −16.2358 | −0.739518 | ||||||||
\(483\) | 6.09305 | 0.277243 | ||||||||
\(484\) | 2.92394 | 0.132906 | ||||||||
\(485\) | −31.1828 | −1.41594 | ||||||||
\(486\) | 21.4506 | 0.973021 | ||||||||
\(487\) | 35.0151 | 1.58668 | 0.793342 | − | 0.608776i | \(-0.208339\pi\) | ||||
0.793342 | + | 0.608776i | \(0.208339\pi\) | |||||||
\(488\) | −14.2892 | −0.646844 | ||||||||
\(489\) | 7.98441 | 0.361067 | ||||||||
\(490\) | 85.3389 | 3.85522 | ||||||||
\(491\) | 5.81085 | 0.262240 | 0.131120 | − | 0.991367i | \(-0.458143\pi\) | ||||
0.131120 | + | 0.991367i | \(0.458143\pi\) | |||||||
\(492\) | 23.2868 | 1.04985 | ||||||||
\(493\) | 0.164955 | 0.00742920 | ||||||||
\(494\) | 0.874970 | 0.0393667 | ||||||||
\(495\) | −3.15891 | −0.141983 | ||||||||
\(496\) | 2.62425 | 0.117832 | ||||||||
\(497\) | 44.7936 | 2.00927 | ||||||||
\(498\) | −47.9438 | −2.14842 | ||||||||
\(499\) | 35.4872 | 1.58862 | 0.794312 | − | 0.607510i | \(-0.207831\pi\) | ||||
0.794312 | + | 0.607510i | \(0.207831\pi\) | |||||||
\(500\) | −4.95810 | −0.221733 | ||||||||
\(501\) | −0.415339 | −0.0185560 | ||||||||
\(502\) | −10.7017 | −0.477641 | ||||||||
\(503\) | −38.0822 | −1.69800 | −0.849001 | − | 0.528392i | \(-0.822795\pi\) | ||||
−0.849001 | + | 0.528392i | \(0.822795\pi\) | |||||||
\(504\) | 8.66952 | 0.386171 | ||||||||
\(505\) | −58.0543 | −2.58338 | ||||||||
\(506\) | −2.18741 | −0.0972421 | ||||||||
\(507\) | 10.7154 | 0.475888 | ||||||||
\(508\) | 32.6029 | 1.44652 | ||||||||
\(509\) | −20.6921 | −0.917163 | −0.458582 | − | 0.888652i | \(-0.651642\pi\) | ||||
−0.458582 | + | 0.888652i | \(0.651642\pi\) | |||||||
\(510\) | 10.2462 | 0.453707 | ||||||||
\(511\) | −14.4306 | −0.638371 | ||||||||
\(512\) | −14.3896 | −0.635937 | ||||||||
\(513\) | 0.953461 | 0.0420964 | ||||||||
\(514\) | −57.5984 | −2.54056 | ||||||||
\(515\) | 26.1998 | 1.15450 | ||||||||
\(516\) | 4.16207 | 0.183225 | ||||||||
\(517\) | 7.32264 | 0.322050 | ||||||||
\(518\) | −91.1142 | −4.00333 | ||||||||
\(519\) | −22.1838 | −0.973761 | ||||||||
\(520\) | −15.5577 | −0.682251 | ||||||||
\(521\) | −22.0626 | −0.966578 | −0.483289 | − | 0.875461i | \(-0.660558\pi\) | ||||
−0.483289 | + | 0.875461i | \(0.660558\pi\) | |||||||
\(522\) | −0.356447 | −0.0156013 | ||||||||
\(523\) | −4.39028 | −0.191974 | −0.0959868 | − | 0.995383i | \(-0.530601\pi\) | ||||
−0.0959868 | + | 0.995383i | \(0.530601\pi\) | |||||||
\(524\) | 63.0732 | 2.75537 | ||||||||
\(525\) | −34.1362 | −1.48983 | ||||||||
\(526\) | −52.6099 | −2.29390 | ||||||||
\(527\) | 2.02106 | 0.0880388 | ||||||||
\(528\) | −1.84827 | −0.0804357 | ||||||||
\(529\) | −22.0283 | −0.957751 | ||||||||
\(530\) | −14.4474 | −0.627556 | ||||||||
\(531\) | −2.93201 | −0.127238 | ||||||||
\(532\) | 2.14016 | 0.0927876 | ||||||||
\(533\) | 13.0882 | 0.566915 | ||||||||
\(534\) | −42.8952 | −1.85626 | ||||||||
\(535\) | 5.49537 | 0.237585 | ||||||||
\(536\) | 13.2605 | 0.572767 | ||||||||
\(537\) | 2.47799 | 0.106933 | ||||||||
\(538\) | −33.2024 | −1.43146 | ||||||||
\(539\) | −11.8557 | −0.510660 | ||||||||
\(540\) | −53.6513 | −2.30878 | ||||||||
\(541\) | −4.27903 | −0.183970 | −0.0919850 | − | 0.995760i | \(-0.529321\pi\) | ||||
−0.0919850 | + | 0.995760i | \(0.529321\pi\) | |||||||
\(542\) | −53.8995 | −2.31518 | ||||||||
\(543\) | −14.0049 | −0.601010 | ||||||||
\(544\) | −6.98170 | −0.299338 | ||||||||
\(545\) | 47.1032 | 2.01768 | ||||||||
\(546\) | −32.0847 | −1.37310 | ||||||||
\(547\) | 21.4055 | 0.915235 | 0.457617 | − | 0.889149i | \(-0.348703\pi\) | ||||
0.457617 | + | 0.889149i | \(0.348703\pi\) | |||||||
\(548\) | −64.1304 | −2.73951 | ||||||||
\(549\) | −6.78707 | −0.289665 | ||||||||
\(550\) | 12.2549 | 0.522552 | ||||||||
\(551\) | −0.0278049 | −0.00118453 | ||||||||
\(552\) | −2.87683 | −0.122446 | ||||||||
\(553\) | 73.3572 | 3.11947 | ||||||||
\(554\) | −20.7649 | −0.882218 | ||||||||
\(555\) | 43.6630 | 1.85339 | ||||||||
\(556\) | −27.0973 | −1.14918 | ||||||||
\(557\) | 10.6371 | 0.450708 | 0.225354 | − | 0.974277i | \(-0.427646\pi\) | ||||
0.225354 | + | 0.974277i | \(0.427646\pi\) | |||||||
\(558\) | −4.36726 | −0.184881 | ||||||||
\(559\) | 2.33927 | 0.0989406 | ||||||||
\(560\) | 18.2899 | 0.772888 | ||||||||
\(561\) | −1.42344 | −0.0600978 | ||||||||
\(562\) | 69.4430 | 2.92928 | ||||||||
\(563\) | 8.95936 | 0.377592 | 0.188796 | − | 0.982016i | \(-0.439541\pi\) | ||||
0.188796 | + | 0.982016i | \(0.439541\pi\) | |||||||
\(564\) | 30.4773 | 1.28333 | ||||||||
\(565\) | 44.2780 | 1.86279 | ||||||||
\(566\) | −14.3474 | −0.603068 | ||||||||
\(567\) | −22.2772 | −0.935556 | ||||||||
\(568\) | −21.1493 | −0.887404 | ||||||||
\(569\) | −40.1706 | −1.68404 | −0.842019 | − | 0.539448i | \(-0.818633\pi\) | ||||
−0.842019 | + | 0.539448i | \(0.818633\pi\) | |||||||
\(570\) | −1.72710 | −0.0723402 | ||||||||
\(571\) | −17.0870 | −0.715069 | −0.357534 | − | 0.933900i | \(-0.616382\pi\) | ||||
−0.357534 | + | 0.933900i | \(0.616382\pi\) | |||||||
\(572\) | 6.83989 | 0.285990 | ||||||||
\(573\) | −13.7311 | −0.573623 | ||||||||
\(574\) | 53.9111 | 2.25021 | ||||||||
\(575\) | −5.44412 | −0.227035 | ||||||||
\(576\) | 12.5577 | 0.523238 | ||||||||
\(577\) | −13.8811 | −0.577880 | −0.288940 | − | 0.957347i | \(-0.593303\pi\) | ||||
−0.288940 | + | 0.957347i | \(0.593303\pi\) | |||||||
\(578\) | −2.21900 | −0.0922980 | ||||||||
\(579\) | −8.09728 | −0.336511 | ||||||||
\(580\) | 1.56458 | 0.0649658 | ||||||||
\(581\) | −65.9109 | −2.73444 | ||||||||
\(582\) | 30.3632 | 1.25859 | ||||||||
\(583\) | 2.00710 | 0.0831257 | ||||||||
\(584\) | 6.81339 | 0.281940 | ||||||||
\(585\) | −7.38956 | −0.305521 | ||||||||
\(586\) | −67.3945 | −2.78404 | ||||||||
\(587\) | −27.8595 | −1.14988 | −0.574942 | − | 0.818194i | \(-0.694975\pi\) | ||||
−0.574942 | + | 0.818194i | \(0.694975\pi\) | |||||||
\(588\) | −49.3441 | −2.03492 | ||||||||
\(589\) | −0.340671 | −0.0140371 | ||||||||
\(590\) | 21.6727 | 0.892251 | ||||||||
\(591\) | 15.5053 | 0.637803 | ||||||||
\(592\) | −12.2782 | −0.504630 | ||||||||
\(593\) | 0.353922 | 0.0145338 | 0.00726692 | − | 0.999974i | \(-0.497687\pi\) | ||||
0.00726692 | + | 0.999974i | \(0.497687\pi\) | |||||||
\(594\) | 12.5517 | 0.515004 | ||||||||
\(595\) | 14.0859 | 0.577467 | ||||||||
\(596\) | 18.3041 | 0.749765 | ||||||||
\(597\) | 11.7752 | 0.481926 | ||||||||
\(598\) | −5.11694 | −0.209247 | ||||||||
\(599\) | −40.0065 | −1.63462 | −0.817311 | − | 0.576196i | \(-0.804536\pi\) | ||||
−0.817311 | + | 0.576196i | \(0.804536\pi\) | |||||||
\(600\) | 16.1174 | 0.657991 | ||||||||
\(601\) | 9.80601 | 0.399995 | 0.199998 | − | 0.979796i | \(-0.435907\pi\) | ||||
0.199998 | + | 0.979796i | \(0.435907\pi\) | |||||||
\(602\) | 9.63557 | 0.392717 | ||||||||
\(603\) | 6.29844 | 0.256492 | ||||||||
\(604\) | −7.16106 | −0.291380 | ||||||||
\(605\) | −3.24388 | −0.131882 | ||||||||
\(606\) | 56.5284 | 2.29631 | ||||||||
\(607\) | 43.3038 | 1.75765 | 0.878824 | − | 0.477147i | \(-0.158329\pi\) | ||||
0.878824 | + | 0.477147i | \(0.158329\pi\) | |||||||
\(608\) | 1.17684 | 0.0477271 | ||||||||
\(609\) | 1.01959 | 0.0413160 | ||||||||
\(610\) | 50.1683 | 2.03126 | ||||||||
\(611\) | 17.1297 | 0.692992 | ||||||||
\(612\) | 2.84736 | 0.115098 | ||||||||
\(613\) | 3.97962 | 0.160735 | 0.0803677 | − | 0.996765i | \(-0.474391\pi\) | ||||
0.0803677 | + | 0.996765i | \(0.474391\pi\) | |||||||
\(614\) | −54.7276 | −2.20863 | ||||||||
\(615\) | −25.8348 | −1.04176 | ||||||||
\(616\) | 8.90270 | 0.358700 | ||||||||
\(617\) | −24.9581 | −1.00478 | −0.502388 | − | 0.864642i | \(-0.667545\pi\) | ||||
−0.502388 | + | 0.864642i | \(0.667545\pi\) | |||||||
\(618\) | −25.5112 | −1.02621 | ||||||||
\(619\) | 9.98236 | 0.401225 | 0.200612 | − | 0.979671i | \(-0.435707\pi\) | ||||
0.200612 | + | 0.979671i | \(0.435707\pi\) | |||||||
\(620\) | 19.1696 | 0.769869 | ||||||||
\(621\) | −5.57597 | −0.223756 | ||||||||
\(622\) | −13.2986 | −0.533226 | ||||||||
\(623\) | −58.9702 | −2.36259 | ||||||||
\(624\) | −4.32361 | −0.173083 | ||||||||
\(625\) | −22.1131 | −0.884523 | ||||||||
\(626\) | 51.2436 | 2.04811 | ||||||||
\(627\) | 0.239936 | 0.00958214 | ||||||||
\(628\) | 15.1395 | 0.604131 | ||||||||
\(629\) | −9.45602 | −0.377036 | ||||||||
\(630\) | −30.4379 | −1.21268 | ||||||||
\(631\) | 31.2136 | 1.24259 | 0.621296 | − | 0.783576i | \(-0.286606\pi\) | ||||
0.621296 | + | 0.783576i | \(0.286606\pi\) | |||||||
\(632\) | −34.6356 | −1.37773 | ||||||||
\(633\) | −25.6443 | −1.01927 | ||||||||
\(634\) | −55.8317 | −2.21736 | ||||||||
\(635\) | −36.1702 | −1.43537 | ||||||||
\(636\) | 8.35369 | 0.331245 | ||||||||
\(637\) | −27.7336 | −1.09885 | ||||||||
\(638\) | −0.366034 | −0.0144914 | ||||||||
\(639\) | −10.0454 | −0.397391 | ||||||||
\(640\) | −47.5279 | −1.87870 | ||||||||
\(641\) | 12.4159 | 0.490397 | 0.245198 | − | 0.969473i | \(-0.421147\pi\) | ||||
0.245198 | + | 0.969473i | \(0.421147\pi\) | |||||||
\(642\) | −5.35093 | −0.211184 | ||||||||
\(643\) | 26.7222 | 1.05382 | 0.526910 | − | 0.849921i | \(-0.323351\pi\) | ||||
0.526910 | + | 0.849921i | \(0.323351\pi\) | |||||||
\(644\) | −12.5159 | −0.493196 | ||||||||
\(645\) | −4.61748 | −0.181813 | ||||||||
\(646\) | 0.374035 | 0.0147162 | ||||||||
\(647\) | −30.5218 | −1.19993 | −0.599967 | − | 0.800025i | \(-0.704820\pi\) | ||||
−0.599967 | + | 0.800025i | \(0.704820\pi\) | |||||||
\(648\) | 10.5182 | 0.413194 | ||||||||
\(649\) | −3.01087 | −0.118187 | ||||||||
\(650\) | 28.6676 | 1.12444 | ||||||||
\(651\) | 12.4923 | 0.489610 | ||||||||
\(652\) | −16.4010 | −0.642314 | ||||||||
\(653\) | 1.07982 | 0.0422566 | 0.0211283 | − | 0.999777i | \(-0.493274\pi\) | ||||
0.0211283 | + | 0.999777i | \(0.493274\pi\) | |||||||
\(654\) | −45.8652 | −1.79347 | ||||||||
\(655\) | −69.9746 | −2.73414 | ||||||||
\(656\) | 7.26484 | 0.283644 | ||||||||
\(657\) | 3.23620 | 0.126256 | ||||||||
\(658\) | 70.5579 | 2.75063 | ||||||||
\(659\) | 8.32386 | 0.324252 | 0.162126 | − | 0.986770i | \(-0.448165\pi\) | ||||
0.162126 | + | 0.986770i | \(0.448165\pi\) | |||||||
\(660\) | −13.5012 | −0.525535 | ||||||||
\(661\) | 31.1013 | 1.20970 | 0.604850 | − | 0.796340i | \(-0.293233\pi\) | ||||
0.604850 | + | 0.796340i | \(0.293233\pi\) | |||||||
\(662\) | 4.34129 | 0.168729 | ||||||||
\(663\) | −3.32982 | −0.129320 | ||||||||
\(664\) | 31.1198 | 1.20768 | ||||||||
\(665\) | −2.37433 | −0.0920726 | ||||||||
\(666\) | 20.4333 | 0.791774 | ||||||||
\(667\) | 0.162607 | 0.00629616 | ||||||||
\(668\) | 0.853162 | 0.0330098 | ||||||||
\(669\) | −21.0979 | −0.815694 | ||||||||
\(670\) | −46.5565 | −1.79863 | ||||||||
\(671\) | −6.96961 | −0.269059 | ||||||||
\(672\) | −43.1541 | −1.66471 | ||||||||
\(673\) | −35.9020 | −1.38392 | −0.691961 | − | 0.721935i | \(-0.743253\pi\) | ||||
−0.691961 | + | 0.721935i | \(0.743253\pi\) | |||||||
\(674\) | −0.774445 | −0.0298305 | ||||||||
\(675\) | 31.2393 | 1.20240 | ||||||||
\(676\) | −22.0109 | −0.846572 | ||||||||
\(677\) | 9.10901 | 0.350088 | 0.175044 | − | 0.984561i | \(-0.443993\pi\) | ||||
0.175044 | + | 0.984561i | \(0.443993\pi\) | |||||||
\(678\) | −43.1142 | −1.65579 | ||||||||
\(679\) | 41.7418 | 1.60191 | ||||||||
\(680\) | −6.65066 | −0.255041 | ||||||||
\(681\) | −29.5471 | −1.13225 | ||||||||
\(682\) | −4.48473 | −0.171729 | ||||||||
\(683\) | −25.4418 | −0.973503 | −0.486751 | − | 0.873541i | \(-0.661818\pi\) | ||||
−0.486751 | + | 0.873541i | \(0.661818\pi\) | |||||||
\(684\) | −0.479952 | −0.0183514 | ||||||||
\(685\) | 71.1475 | 2.71840 | ||||||||
\(686\) | −46.7871 | −1.78634 | ||||||||
\(687\) | 19.4094 | 0.740515 | ||||||||
\(688\) | 1.29845 | 0.0495030 | ||||||||
\(689\) | 4.69516 | 0.178871 | ||||||||
\(690\) | 10.1003 | 0.384512 | ||||||||
\(691\) | 38.0233 | 1.44648 | 0.723238 | − | 0.690599i | \(-0.242653\pi\) | ||||
0.723238 | + | 0.690599i | \(0.242653\pi\) | |||||||
\(692\) | 45.5684 | 1.73225 | ||||||||
\(693\) | 4.22858 | 0.160630 | ||||||||
\(694\) | 11.2735 | 0.427936 | ||||||||
\(695\) | 30.0623 | 1.14033 | ||||||||
\(696\) | −0.481400 | −0.0182474 | ||||||||
\(697\) | 5.59501 | 0.211926 | ||||||||
\(698\) | 71.7717 | 2.71660 | ||||||||
\(699\) | 6.79277 | 0.256926 | ||||||||
\(700\) | 70.1203 | 2.65030 | ||||||||
\(701\) | −38.7308 | −1.46284 | −0.731422 | − | 0.681925i | \(-0.761143\pi\) | ||||
−0.731422 | + | 0.681925i | \(0.761143\pi\) | |||||||
\(702\) | 29.3619 | 1.10819 | ||||||||
\(703\) | 1.59391 | 0.0601156 | ||||||||
\(704\) | 12.8955 | 0.486016 | ||||||||
\(705\) | −33.8121 | −1.27344 | ||||||||
\(706\) | −12.5634 | −0.472829 | ||||||||
\(707\) | 77.7125 | 2.92268 | ||||||||
\(708\) | −12.5314 | −0.470960 | ||||||||
\(709\) | 20.8392 | 0.782632 | 0.391316 | − | 0.920256i | \(-0.372020\pi\) | ||||
0.391316 | + | 0.920256i | \(0.372020\pi\) | |||||||
\(710\) | 74.2533 | 2.78668 | ||||||||
\(711\) | −16.4511 | −0.616965 | ||||||||
\(712\) | 27.8428 | 1.04345 | ||||||||
\(713\) | 1.99229 | 0.0746119 | ||||||||
\(714\) | −13.7157 | −0.513297 | ||||||||
\(715\) | −7.58831 | −0.283787 | ||||||||
\(716\) | −5.09012 | −0.190227 | ||||||||
\(717\) | 18.3438 | 0.685062 | ||||||||
\(718\) | −14.1365 | −0.527568 | ||||||||
\(719\) | −7.75544 | −0.289229 | −0.144615 | − | 0.989488i | \(-0.546194\pi\) | ||||
−0.144615 | + | 0.989488i | \(0.546194\pi\) | |||||||
\(720\) | −4.10169 | −0.152861 | ||||||||
\(721\) | −35.0716 | −1.30613 | ||||||||
\(722\) | 42.0979 | 1.56672 | ||||||||
\(723\) | −10.4149 | −0.387335 | ||||||||
\(724\) | 28.7680 | 1.06915 | ||||||||
\(725\) | −0.911003 | −0.0338338 | ||||||||
\(726\) | 3.15861 | 0.117227 | ||||||||
\(727\) | 50.5169 | 1.87357 | 0.936783 | − | 0.349910i | \(-0.113788\pi\) | ||||
0.936783 | + | 0.349910i | \(0.113788\pi\) | |||||||
\(728\) | 20.8258 | 0.771857 | ||||||||
\(729\) | 29.1510 | 1.07967 | ||||||||
\(730\) | −23.9212 | −0.885364 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −29.0080 | −1.07217 | ||||||||
\(733\) | −0.907654 | −0.0335250 | −0.0167625 | − | 0.999859i | \(-0.505336\pi\) | ||||
−0.0167625 | + | 0.999859i | \(0.505336\pi\) | |||||||
\(734\) | 18.1789 | 0.670994 | ||||||||
\(735\) | 54.7433 | 2.01924 | ||||||||
\(736\) | −6.88231 | −0.253685 | ||||||||
\(737\) | 6.46785 | 0.238246 | ||||||||
\(738\) | −12.0901 | −0.445043 | ||||||||
\(739\) | 34.5219 | 1.26991 | 0.634954 | − | 0.772550i | \(-0.281019\pi\) | ||||
0.634954 | + | 0.772550i | \(0.281019\pi\) | |||||||
\(740\) | −89.6895 | −3.29705 | ||||||||
\(741\) | 0.561276 | 0.0206190 | ||||||||
\(742\) | 19.3396 | 0.709978 | ||||||||
\(743\) | 4.82868 | 0.177147 | 0.0885736 | − | 0.996070i | \(-0.471769\pi\) | ||||
0.0885736 | + | 0.996070i | \(0.471769\pi\) | |||||||
\(744\) | −5.89821 | −0.216239 | ||||||||
\(745\) | −20.3069 | −0.743988 | ||||||||
\(746\) | 1.69790 | 0.0621645 | ||||||||
\(747\) | 14.7812 | 0.540816 | ||||||||
\(748\) | 2.92394 | 0.106910 | ||||||||
\(749\) | −7.35620 | −0.268790 | ||||||||
\(750\) | −5.35604 | −0.195575 | ||||||||
\(751\) | −15.1984 | −0.554598 | −0.277299 | − | 0.960784i | \(-0.589439\pi\) | ||||
−0.277299 | + | 0.960784i | \(0.589439\pi\) | |||||||
\(752\) | 9.50809 | 0.346724 | ||||||||
\(753\) | −6.86494 | −0.250172 | ||||||||
\(754\) | −0.856254 | −0.0311829 | ||||||||
\(755\) | 7.94462 | 0.289134 | ||||||||
\(756\) | 71.8186 | 2.61202 | ||||||||
\(757\) | 5.94453 | 0.216057 | 0.108029 | − | 0.994148i | \(-0.465546\pi\) | ||||
0.108029 | + | 0.994148i | \(0.465546\pi\) | |||||||
\(758\) | 74.2363 | 2.69638 | ||||||||
\(759\) | −1.40318 | −0.0509322 | ||||||||
\(760\) | 1.12104 | 0.0406644 | ||||||||
\(761\) | −1.82834 | −0.0662772 | −0.0331386 | − | 0.999451i | \(-0.510550\pi\) | ||||
−0.0331386 | + | 0.999451i | \(0.510550\pi\) | |||||||
\(762\) | 35.2195 | 1.27587 | ||||||||
\(763\) | −63.0532 | −2.28268 | ||||||||
\(764\) | 28.2054 | 1.02044 | ||||||||
\(765\) | −3.15891 | −0.114211 | ||||||||
\(766\) | −42.9430 | −1.55159 | ||||||||
\(767\) | −7.04324 | −0.254317 | ||||||||
\(768\) | 9.56674 | 0.345210 | ||||||||
\(769\) | −5.30186 | −0.191190 | −0.0955950 | − | 0.995420i | \(-0.530475\pi\) | ||||
−0.0955950 | + | 0.995420i | \(0.530475\pi\) | |||||||
\(770\) | −31.2566 | −1.12641 | ||||||||
\(771\) | −36.9483 | −1.33066 | ||||||||
\(772\) | 16.6329 | 0.598631 | ||||||||
\(773\) | −0.739334 | −0.0265920 | −0.0132960 | − | 0.999912i | \(-0.504232\pi\) | ||||
−0.0132960 | + | 0.999912i | \(0.504232\pi\) | |||||||
\(774\) | −2.16088 | −0.0776711 | ||||||||
\(775\) | −11.1618 | −0.400943 | ||||||||
\(776\) | −19.7084 | −0.707490 | ||||||||
\(777\) | −58.4480 | −2.09681 | ||||||||
\(778\) | 24.5950 | 0.881772 | ||||||||
\(779\) | −0.943098 | −0.0337900 | ||||||||
\(780\) | −31.5830 | −1.13085 | ||||||||
\(781\) | −10.3156 | −0.369121 | ||||||||
\(782\) | −2.18741 | −0.0782215 | ||||||||
\(783\) | −0.933067 | −0.0333451 | ||||||||
\(784\) | −15.3940 | −0.549786 | ||||||||
\(785\) | −16.7960 | −0.599476 | ||||||||
\(786\) | 68.1354 | 2.43031 | ||||||||
\(787\) | −40.0836 | −1.42883 | −0.714413 | − | 0.699724i | \(-0.753306\pi\) | ||||
−0.714413 | + | 0.699724i | \(0.753306\pi\) | |||||||
\(788\) | −31.8499 | −1.13461 | ||||||||
\(789\) | −33.7483 | −1.20147 | ||||||||
\(790\) | 121.603 | 4.32643 | ||||||||
\(791\) | −59.2713 | −2.10744 | ||||||||
\(792\) | −1.99652 | −0.0709433 | ||||||||
\(793\) | −16.3038 | −0.578965 | ||||||||
\(794\) | −47.6140 | −1.68976 | ||||||||
\(795\) | −9.26775 | −0.328693 | ||||||||
\(796\) | −24.1878 | −0.857313 | ||||||||
\(797\) | 11.3744 | 0.402903 | 0.201452 | − | 0.979498i | \(-0.435434\pi\) | ||||
0.201452 | + | 0.979498i | \(0.435434\pi\) | |||||||
\(798\) | 2.31192 | 0.0818412 | ||||||||
\(799\) | 7.32264 | 0.259057 | ||||||||
\(800\) | 38.5581 | 1.36323 | ||||||||
\(801\) | 13.2247 | 0.467271 | ||||||||
\(802\) | −8.68459 | −0.306663 | ||||||||
\(803\) | 3.32324 | 0.117275 | ||||||||
\(804\) | 26.9196 | 0.949381 | ||||||||
\(805\) | 13.8854 | 0.489396 | ||||||||
\(806\) | −10.4910 | −0.369529 | ||||||||
\(807\) | −21.2987 | −0.749750 | ||||||||
\(808\) | −36.6919 | −1.29082 | ||||||||
\(809\) | −8.25575 | −0.290257 | −0.145128 | − | 0.989413i | \(-0.546360\pi\) | ||||
−0.145128 | + | 0.989413i | \(0.546360\pi\) | |||||||
\(810\) | −36.9285 | −1.29753 | ||||||||
\(811\) | −30.8723 | −1.08407 | −0.542036 | − | 0.840355i | \(-0.682346\pi\) | ||||
−0.542036 | + | 0.840355i | \(0.682346\pi\) | |||||||
\(812\) | −2.09438 | −0.0734983 | ||||||||
\(813\) | −34.5755 | −1.21262 | ||||||||
\(814\) | 20.9829 | 0.735449 | ||||||||
\(815\) | 18.1956 | 0.637365 | ||||||||
\(816\) | −1.84827 | −0.0647024 | ||||||||
\(817\) | −0.168561 | −0.00589719 | ||||||||
\(818\) | 37.6992 | 1.31812 | ||||||||
\(819\) | 9.89179 | 0.345647 | ||||||||
\(820\) | 53.0681 | 1.85322 | ||||||||
\(821\) | 6.02126 | 0.210143 | 0.105072 | − | 0.994465i | \(-0.466493\pi\) | ||||
0.105072 | + | 0.994465i | \(0.466493\pi\) | |||||||
\(822\) | −69.2774 | −2.41633 | ||||||||
\(823\) | −30.1880 | −1.05229 | −0.526144 | − | 0.850395i | \(-0.676363\pi\) | ||||
−0.526144 | + | 0.850395i | \(0.676363\pi\) | |||||||
\(824\) | 16.5590 | 0.576861 | ||||||||
\(825\) | 7.86130 | 0.273695 | ||||||||
\(826\) | −29.0115 | −1.00944 | ||||||||
\(827\) | −15.1863 | −0.528078 | −0.264039 | − | 0.964512i | \(-0.585055\pi\) | ||||
−0.264039 | + | 0.964512i | \(0.585055\pi\) | |||||||
\(828\) | 2.80683 | 0.0975439 | ||||||||
\(829\) | −34.7492 | −1.20689 | −0.603445 | − | 0.797404i | \(-0.706206\pi\) | ||||
−0.603445 | + | 0.797404i | \(0.706206\pi\) | |||||||
\(830\) | −109.259 | −3.79243 | ||||||||
\(831\) | −13.3203 | −0.462077 | ||||||||
\(832\) | 30.1660 | 1.04582 | ||||||||
\(833\) | −11.8557 | −0.410775 | ||||||||
\(834\) | −29.2721 | −1.01361 | ||||||||
\(835\) | −0.946514 | −0.0327555 | ||||||||
\(836\) | −0.492861 | −0.0170460 | ||||||||
\(837\) | −11.4321 | −0.395152 | ||||||||
\(838\) | 22.9864 | 0.794051 | ||||||||
\(839\) | −31.6224 | −1.09173 | −0.545863 | − | 0.837875i | \(-0.683798\pi\) | ||||
−0.545863 | + | 0.837875i | \(0.683798\pi\) | |||||||
\(840\) | −41.1080 | −1.41836 | ||||||||
\(841\) | −28.9728 | −0.999062 | ||||||||
\(842\) | 74.3440 | 2.56206 | ||||||||
\(843\) | 44.5464 | 1.53426 | ||||||||
\(844\) | 52.6769 | 1.81321 | ||||||||
\(845\) | 24.4193 | 0.840049 | ||||||||
\(846\) | −15.8233 | −0.544017 | ||||||||
\(847\) | 4.34231 | 0.149204 | ||||||||
\(848\) | 2.60612 | 0.0894946 | ||||||||
\(849\) | −9.20362 | −0.315867 | ||||||||
\(850\) | 12.2549 | 0.420341 | ||||||||
\(851\) | −9.32141 | −0.319534 | ||||||||
\(852\) | −42.9342 | −1.47090 | ||||||||
\(853\) | −50.8142 | −1.73985 | −0.869923 | − | 0.493187i | \(-0.835832\pi\) | ||||
−0.869923 | + | 0.493187i | \(0.835832\pi\) | |||||||
\(854\) | −67.1562 | −2.29804 | ||||||||
\(855\) | 0.532468 | 0.0182100 | ||||||||
\(856\) | 3.47323 | 0.118712 | ||||||||
\(857\) | −52.4053 | −1.79013 | −0.895066 | − | 0.445933i | \(-0.852872\pi\) | ||||
−0.895066 | + | 0.445933i | \(0.852872\pi\) | |||||||
\(858\) | 7.38886 | 0.252251 | ||||||||
\(859\) | −18.1811 | −0.620331 | −0.310165 | − | 0.950683i | \(-0.600384\pi\) | ||||
−0.310165 | + | 0.950683i | \(0.600384\pi\) | |||||||
\(860\) | 9.48490 | 0.323433 | ||||||||
\(861\) | 34.5829 | 1.17858 | ||||||||
\(862\) | 46.4851 | 1.58329 | ||||||||
\(863\) | −23.2488 | −0.791399 | −0.395699 | − | 0.918380i | \(-0.629498\pi\) | ||||
−0.395699 | + | 0.918380i | \(0.629498\pi\) | |||||||
\(864\) | 39.4919 | 1.34354 | ||||||||
\(865\) | −50.5545 | −1.71891 | ||||||||
\(866\) | 23.9565 | 0.814076 | ||||||||
\(867\) | −1.42344 | −0.0483427 | ||||||||
\(868\) | −25.6607 | −0.870982 | ||||||||
\(869\) | −16.8936 | −0.573076 | ||||||||
\(870\) | 1.69016 | 0.0573016 | ||||||||
\(871\) | 15.1300 | 0.512662 | ||||||||
\(872\) | 29.7706 | 1.00816 | ||||||||
\(873\) | −9.36104 | −0.316823 | ||||||||
\(874\) | 0.368711 | 0.0124718 | ||||||||
\(875\) | −7.36322 | −0.248922 | ||||||||
\(876\) | 13.8316 | 0.467325 | ||||||||
\(877\) | −49.2444 | −1.66286 | −0.831432 | − | 0.555626i | \(-0.812478\pi\) | ||||
−0.831432 | + | 0.555626i | \(0.812478\pi\) | |||||||
\(878\) | −32.3872 | −1.09301 | ||||||||
\(879\) | −43.2323 | −1.45819 | ||||||||
\(880\) | −4.21201 | −0.141987 | ||||||||
\(881\) | 17.8498 | 0.601375 | 0.300687 | − | 0.953723i | \(-0.402784\pi\) | ||||
0.300687 | + | 0.953723i | \(0.402784\pi\) | |||||||
\(882\) | 25.6186 | 0.862624 | ||||||||
\(883\) | 11.7793 | 0.396404 | 0.198202 | − | 0.980161i | \(-0.436490\pi\) | ||||
0.198202 | + | 0.980161i | \(0.436490\pi\) | |||||||
\(884\) | 6.83989 | 0.230050 | ||||||||
\(885\) | 13.9026 | 0.467331 | ||||||||
\(886\) | −47.1080 | −1.58262 | ||||||||
\(887\) | 44.1033 | 1.48084 | 0.740422 | − | 0.672142i | \(-0.234626\pi\) | ||||
0.740422 | + | 0.672142i | \(0.234626\pi\) | |||||||
\(888\) | 27.5962 | 0.926068 | ||||||||
\(889\) | 48.4181 | 1.62389 | ||||||||
\(890\) | −97.7536 | −3.27671 | ||||||||
\(891\) | 5.13027 | 0.171871 | ||||||||
\(892\) | 43.3380 | 1.45106 | ||||||||
\(893\) | −1.23431 | −0.0413046 | ||||||||
\(894\) | 19.7732 | 0.661314 | ||||||||
\(895\) | 5.64708 | 0.188761 | ||||||||
\(896\) | 63.6217 | 2.12545 | ||||||||
\(897\) | −3.28242 | −0.109597 | ||||||||
\(898\) | 82.7021 | 2.75981 | ||||||||
\(899\) | 0.333384 | 0.0111190 | ||||||||
\(900\) | −15.7252 | −0.524174 | ||||||||
\(901\) | 2.00710 | 0.0668663 | ||||||||
\(902\) | −12.4153 | −0.413384 | ||||||||
\(903\) | 6.18104 | 0.205692 | ||||||||
\(904\) | 27.9849 | 0.930765 | ||||||||
\(905\) | −31.9158 | −1.06092 | ||||||||
\(906\) | −7.73581 | −0.257005 | ||||||||
\(907\) | −55.7734 | −1.85193 | −0.925963 | − | 0.377615i | \(-0.876744\pi\) | ||||
−0.925963 | + | 0.377615i | \(0.876744\pi\) | |||||||
\(908\) | 60.6936 | 2.01419 | ||||||||
\(909\) | −17.4278 | −0.578045 | ||||||||
\(910\) | −73.1177 | −2.42383 | ||||||||
\(911\) | 49.7052 | 1.64681 | 0.823403 | − | 0.567457i | \(-0.192073\pi\) | ||||
0.823403 | + | 0.567457i | \(0.192073\pi\) | |||||||
\(912\) | 0.311546 | 0.0103163 | ||||||||
\(913\) | 15.1788 | 0.502344 | ||||||||
\(914\) | −17.5430 | −0.580270 | ||||||||
\(915\) | 32.1820 | 1.06390 | ||||||||
\(916\) | −39.8695 | −1.31732 | ||||||||
\(917\) | 93.6693 | 3.09323 | ||||||||
\(918\) | 12.5517 | 0.414269 | ||||||||
\(919\) | −12.9447 | −0.427006 | −0.213503 | − | 0.976942i | \(-0.568487\pi\) | ||||
−0.213503 | + | 0.976942i | \(0.568487\pi\) | |||||||
\(920\) | −6.55599 | −0.216145 | ||||||||
\(921\) | −35.1067 | −1.15681 | ||||||||
\(922\) | −87.4127 | −2.87878 | ||||||||
\(923\) | −24.1310 | −0.794282 | ||||||||
\(924\) | 18.0730 | 0.594558 | ||||||||
\(925\) | 52.2231 | 1.71709 | ||||||||
\(926\) | 31.3063 | 1.02879 | ||||||||
\(927\) | 7.86516 | 0.258326 | ||||||||
\(928\) | −1.15167 | −0.0378053 | ||||||||
\(929\) | −31.3268 | −1.02780 | −0.513899 | − | 0.857851i | \(-0.671799\pi\) | ||||
−0.513899 | + | 0.857851i | \(0.671799\pi\) | |||||||
\(930\) | 20.7081 | 0.679046 | ||||||||
\(931\) | 1.99840 | 0.0654949 | ||||||||
\(932\) | −13.9532 | −0.457054 | ||||||||
\(933\) | −8.53081 | −0.279286 | ||||||||
\(934\) | 36.2904 | 1.18746 | ||||||||
\(935\) | −3.24388 | −0.106086 | ||||||||
\(936\) | −4.67041 | −0.152657 | ||||||||
\(937\) | −33.6348 | −1.09880 | −0.549401 | − | 0.835559i | \(-0.685144\pi\) | ||||
−0.549401 | + | 0.835559i | \(0.685144\pi\) | |||||||
\(938\) | 62.3214 | 2.03486 | ||||||||
\(939\) | 32.8718 | 1.07273 | ||||||||
\(940\) | 69.4546 | 2.26536 | ||||||||
\(941\) | 10.7913 | 0.351787 | 0.175894 | − | 0.984409i | \(-0.443719\pi\) | ||||
0.175894 | + | 0.984409i | \(0.443719\pi\) | |||||||
\(942\) | 16.3546 | 0.532861 | ||||||||
\(943\) | 5.51536 | 0.179605 | ||||||||
\(944\) | −3.90947 | −0.127242 | ||||||||
\(945\) | −79.6769 | −2.59189 | ||||||||
\(946\) | −2.21900 | −0.0721458 | ||||||||
\(947\) | −36.8685 | −1.19807 | −0.599033 | − | 0.800724i | \(-0.704448\pi\) | ||||
−0.599033 | + | 0.800724i | \(0.704448\pi\) | |||||||
\(948\) | −70.3122 | −2.28364 | ||||||||
\(949\) | 7.77397 | 0.252354 | ||||||||
\(950\) | −2.06570 | −0.0670201 | ||||||||
\(951\) | −35.8150 | −1.16138 | ||||||||
\(952\) | 8.90270 | 0.288538 | ||||||||
\(953\) | −24.7583 | −0.802000 | −0.401000 | − | 0.916078i | \(-0.631337\pi\) | ||||
−0.401000 | + | 0.916078i | \(0.631337\pi\) | |||||||
\(954\) | −4.33710 | −0.140419 | ||||||||
\(955\) | −31.2916 | −1.01257 | ||||||||
\(956\) | −37.6806 | −1.21868 | ||||||||
\(957\) | −0.234804 | −0.00759014 | ||||||||
\(958\) | 61.0242 | 1.97160 | ||||||||
\(959\) | −95.2393 | −3.07544 | ||||||||
\(960\) | −59.5445 | −1.92179 | ||||||||
\(961\) | −26.9153 | −0.868236 | ||||||||
\(962\) | 49.0846 | 1.58255 | ||||||||
\(963\) | 1.64970 | 0.0531609 | ||||||||
\(964\) | 21.3936 | 0.689043 | ||||||||
\(965\) | −18.4528 | −0.594018 | ||||||||
\(966\) | −13.5204 | −0.435013 | ||||||||
\(967\) | −26.4393 | −0.850232 | −0.425116 | − | 0.905139i | \(-0.639767\pi\) | ||||
−0.425116 | + | 0.905139i | \(0.639767\pi\) | |||||||
\(968\) | −2.05022 | −0.0658966 | ||||||||
\(969\) | 0.239936 | 0.00770787 | ||||||||
\(970\) | 69.1945 | 2.22170 | ||||||||
\(971\) | 12.3613 | 0.396692 | 0.198346 | − | 0.980132i | \(-0.436443\pi\) | ||||
0.198346 | + | 0.980132i | \(0.436443\pi\) | |||||||
\(972\) | −28.2652 | −0.906607 | ||||||||
\(973\) | −40.2419 | −1.29010 | ||||||||
\(974\) | −77.6983 | −2.48961 | ||||||||
\(975\) | 18.3897 | 0.588942 | ||||||||
\(976\) | −9.04970 | −0.289674 | ||||||||
\(977\) | −8.22409 | −0.263112 | −0.131556 | − | 0.991309i | \(-0.541997\pi\) | ||||
−0.131556 | + | 0.991309i | \(0.541997\pi\) | |||||||
\(978\) | −17.7174 | −0.566539 | ||||||||
\(979\) | 13.5804 | 0.434031 | ||||||||
\(980\) | −112.450 | −3.59208 | ||||||||
\(981\) | 14.1403 | 0.451466 | ||||||||
\(982\) | −12.8942 | −0.411472 | ||||||||
\(983\) | −36.9045 | −1.17707 | −0.588535 | − | 0.808471i | \(-0.700295\pi\) | ||||
−0.588535 | + | 0.808471i | \(0.700295\pi\) | |||||||
\(984\) | −16.3283 | −0.520528 | ||||||||
\(985\) | 35.3349 | 1.12586 | ||||||||
\(986\) | −0.366034 | −0.0116569 | ||||||||
\(987\) | 45.2615 | 1.44069 | ||||||||
\(988\) | −1.15294 | −0.0366798 | ||||||||
\(989\) | 0.985765 | 0.0313455 | ||||||||
\(990\) | 7.00962 | 0.222780 | ||||||||
\(991\) | −31.6841 | −1.00648 | −0.503239 | − | 0.864147i | \(-0.667858\pi\) | ||||
−0.503239 | + | 0.864147i | \(0.667858\pi\) | |||||||
\(992\) | −14.1104 | −0.448007 | ||||||||
\(993\) | 2.78486 | 0.0883747 | ||||||||
\(994\) | −99.3968 | −3.15267 | ||||||||
\(995\) | 26.8344 | 0.850707 | ||||||||
\(996\) | 63.1750 | 2.00178 | ||||||||
\(997\) | 21.2341 | 0.672489 | 0.336245 | − | 0.941775i | \(-0.390843\pi\) | ||||
0.336245 | + | 0.941775i | \(0.390843\pi\) | |||||||
\(998\) | −78.7459 | −2.49266 | ||||||||
\(999\) | 53.4879 | 1.69228 |
(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 | 8041.2.a.h.1.11 | ✓ | 74 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.h.1.11 | ✓ | 74 | 1.1 | even | 1 | trivial |