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: | \(0\) |
Dimension: | \(82\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.26888 | −1.60434 | −0.802169 | − | 0.597097i | \(-0.796321\pi\) | ||||
−0.802169 | + | 0.597097i | \(0.796321\pi\) | |||||||
\(3\) | 0.654424 | 0.377832 | 0.188916 | − | 0.981993i | \(-0.439503\pi\) | ||||
0.188916 | + | 0.981993i | \(0.439503\pi\) | |||||||
\(4\) | 3.14780 | 1.57390 | ||||||||
\(5\) | −0.968068 | −0.432933 | −0.216467 | − | 0.976290i | \(-0.569453\pi\) | ||||
−0.216467 | + | 0.976290i | \(0.569453\pi\) | |||||||
\(6\) | −1.48481 | −0.606170 | ||||||||
\(7\) | 1.81018 | 0.684185 | 0.342092 | − | 0.939666i | \(-0.388864\pi\) | ||||
0.342092 | + | 0.939666i | \(0.388864\pi\) | |||||||
\(8\) | −2.60421 | −0.920727 | ||||||||
\(9\) | −2.57173 | −0.857243 | ||||||||
\(10\) | 2.19643 | 0.694571 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.05999 | 0.594669 | ||||||||
\(13\) | 3.55823 | 0.986876 | 0.493438 | − | 0.869781i | \(-0.335740\pi\) | ||||
0.493438 | + | 0.869781i | \(0.335740\pi\) | |||||||
\(14\) | −4.10708 | −1.09766 | ||||||||
\(15\) | −0.633527 | −0.163576 | ||||||||
\(16\) | −0.386967 | −0.0967417 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 5.83493 | 1.37531 | ||||||||
\(19\) | −4.84794 | −1.11219 | −0.556097 | − | 0.831117i | \(-0.687702\pi\) | ||||
−0.556097 | + | 0.831117i | \(0.687702\pi\) | |||||||
\(20\) | −3.04728 | −0.681393 | ||||||||
\(21\) | 1.18463 | 0.258507 | ||||||||
\(22\) | −2.26888 | −0.483726 | ||||||||
\(23\) | −7.36907 | −1.53656 | −0.768279 | − | 0.640115i | \(-0.778887\pi\) | ||||
−0.768279 | + | 0.640115i | \(0.778887\pi\) | |||||||
\(24\) | −1.70426 | −0.347880 | ||||||||
\(25\) | −4.06284 | −0.812569 | ||||||||
\(26\) | −8.07319 | −1.58328 | ||||||||
\(27\) | −3.64627 | −0.701726 | ||||||||
\(28\) | 5.69809 | 1.07684 | ||||||||
\(29\) | 7.99930 | 1.48543 | 0.742716 | − | 0.669606i | \(-0.233537\pi\) | ||||
0.742716 | + | 0.669606i | \(0.233537\pi\) | |||||||
\(30\) | 1.43739 | 0.262431 | ||||||||
\(31\) | −2.59561 | −0.466186 | −0.233093 | − | 0.972454i | \(-0.574885\pi\) | ||||
−0.233093 | + | 0.972454i | \(0.574885\pi\) | |||||||
\(32\) | 6.08640 | 1.07593 | ||||||||
\(33\) | 0.654424 | 0.113921 | ||||||||
\(34\) | −2.26888 | −0.389109 | ||||||||
\(35\) | −1.75238 | −0.296206 | ||||||||
\(36\) | −8.09528 | −1.34921 | ||||||||
\(37\) | −7.56763 | −1.24411 | −0.622055 | − | 0.782973i | \(-0.713702\pi\) | ||||
−0.622055 | + | 0.782973i | \(0.713702\pi\) | |||||||
\(38\) | 10.9994 | 1.78434 | ||||||||
\(39\) | 2.32859 | 0.372873 | ||||||||
\(40\) | 2.52105 | 0.398613 | ||||||||
\(41\) | 1.85905 | 0.290335 | 0.145167 | − | 0.989407i | \(-0.453628\pi\) | ||||
0.145167 | + | 0.989407i | \(0.453628\pi\) | |||||||
\(42\) | −2.68777 | −0.414732 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 3.14780 | 0.474548 | ||||||||
\(45\) | 2.48961 | 0.371129 | ||||||||
\(46\) | 16.7195 | 2.46516 | ||||||||
\(47\) | −3.71881 | −0.542444 | −0.271222 | − | 0.962517i | \(-0.587428\pi\) | ||||
−0.271222 | + | 0.962517i | \(0.587428\pi\) | |||||||
\(48\) | −0.253240 | −0.0365521 | ||||||||
\(49\) | −3.72324 | −0.531891 | ||||||||
\(50\) | 9.21809 | 1.30363 | ||||||||
\(51\) | 0.654424 | 0.0916377 | ||||||||
\(52\) | 11.2006 | 1.55324 | ||||||||
\(53\) | −8.29080 | −1.13883 | −0.569415 | − | 0.822050i | \(-0.692830\pi\) | ||||
−0.569415 | + | 0.822050i | \(0.692830\pi\) | |||||||
\(54\) | 8.27294 | 1.12580 | ||||||||
\(55\) | −0.968068 | −0.130534 | ||||||||
\(56\) | −4.71409 | −0.629947 | ||||||||
\(57\) | −3.17261 | −0.420223 | ||||||||
\(58\) | −18.1494 | −2.38314 | ||||||||
\(59\) | −4.79436 | −0.624173 | −0.312086 | − | 0.950054i | \(-0.601028\pi\) | ||||
−0.312086 | + | 0.950054i | \(0.601028\pi\) | |||||||
\(60\) | −1.99421 | −0.257452 | ||||||||
\(61\) | 14.1516 | 1.81193 | 0.905966 | − | 0.423352i | \(-0.139146\pi\) | ||||
0.905966 | + | 0.423352i | \(0.139146\pi\) | |||||||
\(62\) | 5.88912 | 0.747919 | ||||||||
\(63\) | −4.65530 | −0.586513 | ||||||||
\(64\) | −13.0353 | −1.62942 | ||||||||
\(65\) | −3.44461 | −0.427252 | ||||||||
\(66\) | −1.48481 | −0.182767 | ||||||||
\(67\) | −4.30268 | −0.525656 | −0.262828 | − | 0.964843i | \(-0.584655\pi\) | ||||
−0.262828 | + | 0.964843i | \(0.584655\pi\) | |||||||
\(68\) | 3.14780 | 0.381726 | ||||||||
\(69\) | −4.82250 | −0.580560 | ||||||||
\(70\) | 3.97593 | 0.475215 | ||||||||
\(71\) | 14.1314 | 1.67708 | 0.838542 | − | 0.544837i | \(-0.183409\pi\) | ||||
0.838542 | + | 0.544837i | \(0.183409\pi\) | |||||||
\(72\) | 6.69732 | 0.789287 | ||||||||
\(73\) | 2.83925 | 0.332309 | 0.166155 | − | 0.986100i | \(-0.446865\pi\) | ||||
0.166155 | + | 0.986100i | \(0.446865\pi\) | |||||||
\(74\) | 17.1700 | 1.99597 | ||||||||
\(75\) | −2.65882 | −0.307014 | ||||||||
\(76\) | −15.2603 | −1.75048 | ||||||||
\(77\) | 1.81018 | 0.206289 | ||||||||
\(78\) | −5.28329 | −0.598214 | ||||||||
\(79\) | 0.315578 | 0.0355053 | 0.0177526 | − | 0.999842i | \(-0.494349\pi\) | ||||
0.0177526 | + | 0.999842i | \(0.494349\pi\) | |||||||
\(80\) | 0.374610 | 0.0418827 | ||||||||
\(81\) | 5.32898 | 0.592109 | ||||||||
\(82\) | −4.21795 | −0.465795 | ||||||||
\(83\) | 9.58463 | 1.05205 | 0.526025 | − | 0.850469i | \(-0.323682\pi\) | ||||
0.526025 | + | 0.850469i | \(0.323682\pi\) | |||||||
\(84\) | 3.72896 | 0.406863 | ||||||||
\(85\) | −0.968068 | −0.105002 | ||||||||
\(86\) | −2.26888 | −0.244659 | ||||||||
\(87\) | 5.23493 | 0.561244 | ||||||||
\(88\) | −2.60421 | −0.277610 | ||||||||
\(89\) | 13.9904 | 1.48298 | 0.741488 | − | 0.670966i | \(-0.234120\pi\) | ||||
0.741488 | + | 0.670966i | \(0.234120\pi\) | |||||||
\(90\) | −5.64862 | −0.595416 | ||||||||
\(91\) | 6.44105 | 0.675206 | ||||||||
\(92\) | −23.1963 | −2.41839 | ||||||||
\(93\) | −1.69863 | −0.176140 | ||||||||
\(94\) | 8.43751 | 0.870263 | ||||||||
\(95\) | 4.69314 | 0.481506 | ||||||||
\(96\) | 3.98308 | 0.406522 | ||||||||
\(97\) | 17.3930 | 1.76600 | 0.882998 | − | 0.469377i | \(-0.155522\pi\) | ||||
0.882998 | + | 0.469377i | \(0.155522\pi\) | |||||||
\(98\) | 8.44757 | 0.853333 | ||||||||
\(99\) | −2.57173 | −0.258469 | ||||||||
\(100\) | −12.7890 | −1.27890 | ||||||||
\(101\) | −17.5068 | −1.74199 | −0.870994 | − | 0.491294i | \(-0.836524\pi\) | ||||
−0.870994 | + | 0.491294i | \(0.836524\pi\) | |||||||
\(102\) | −1.48481 | −0.147018 | ||||||||
\(103\) | 8.82769 | 0.869818 | 0.434909 | − | 0.900474i | \(-0.356781\pi\) | ||||
0.434909 | + | 0.900474i | \(0.356781\pi\) | |||||||
\(104\) | −9.26638 | −0.908644 | ||||||||
\(105\) | −1.14680 | −0.111916 | ||||||||
\(106\) | 18.8108 | 1.82707 | ||||||||
\(107\) | 10.9388 | 1.05749 | 0.528745 | − | 0.848781i | \(-0.322663\pi\) | ||||
0.528745 | + | 0.848781i | \(0.322663\pi\) | |||||||
\(108\) | −11.4777 | −1.10444 | ||||||||
\(109\) | −14.5544 | −1.39406 | −0.697031 | − | 0.717041i | \(-0.745496\pi\) | ||||
−0.697031 | + | 0.717041i | \(0.745496\pi\) | |||||||
\(110\) | 2.19643 | 0.209421 | ||||||||
\(111\) | −4.95244 | −0.470064 | ||||||||
\(112\) | −0.700480 | −0.0661892 | ||||||||
\(113\) | 9.18926 | 0.864453 | 0.432227 | − | 0.901765i | \(-0.357728\pi\) | ||||
0.432227 | + | 0.901765i | \(0.357728\pi\) | |||||||
\(114\) | 7.19826 | 0.674179 | ||||||||
\(115\) | 7.13377 | 0.665227 | ||||||||
\(116\) | 25.1802 | 2.33792 | ||||||||
\(117\) | −9.15081 | −0.845993 | ||||||||
\(118\) | 10.8778 | 1.00138 | ||||||||
\(119\) | 1.81018 | 0.165939 | ||||||||
\(120\) | 1.64984 | 0.150609 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −32.1083 | −2.90695 | ||||||||
\(123\) | 1.21661 | 0.109698 | ||||||||
\(124\) | −8.17046 | −0.733729 | ||||||||
\(125\) | 8.77345 | 0.784721 | ||||||||
\(126\) | 10.5623 | 0.940964 | ||||||||
\(127\) | 6.42299 | 0.569948 | 0.284974 | − | 0.958535i | \(-0.408015\pi\) | ||||
0.284974 | + | 0.958535i | \(0.408015\pi\) | |||||||
\(128\) | 17.4028 | 1.53820 | ||||||||
\(129\) | 0.654424 | 0.0576188 | ||||||||
\(130\) | 7.81540 | 0.685456 | ||||||||
\(131\) | 10.0152 | 0.875036 | 0.437518 | − | 0.899210i | \(-0.355858\pi\) | ||||
0.437518 | + | 0.899210i | \(0.355858\pi\) | |||||||
\(132\) | 2.05999 | 0.179299 | ||||||||
\(133\) | −8.77566 | −0.760946 | ||||||||
\(134\) | 9.76224 | 0.843329 | ||||||||
\(135\) | 3.52984 | 0.303800 | ||||||||
\(136\) | −2.60421 | −0.223309 | ||||||||
\(137\) | −20.1159 | −1.71861 | −0.859307 | − | 0.511461i | \(-0.829104\pi\) | ||||
−0.859307 | + | 0.511461i | \(0.829104\pi\) | |||||||
\(138\) | 10.9416 | 0.931415 | ||||||||
\(139\) | −22.4797 | −1.90670 | −0.953350 | − | 0.301867i | \(-0.902390\pi\) | ||||
−0.953350 | + | 0.301867i | \(0.902390\pi\) | |||||||
\(140\) | −5.51614 | −0.466199 | ||||||||
\(141\) | −2.43368 | −0.204953 | ||||||||
\(142\) | −32.0623 | −2.69061 | ||||||||
\(143\) | 3.55823 | 0.297554 | ||||||||
\(144\) | 0.995174 | 0.0829311 | ||||||||
\(145\) | −7.74387 | −0.643093 | ||||||||
\(146\) | −6.44190 | −0.533136 | ||||||||
\(147\) | −2.43658 | −0.200965 | ||||||||
\(148\) | −23.8214 | −1.95810 | ||||||||
\(149\) | 6.68632 | 0.547764 | 0.273882 | − | 0.961763i | \(-0.411692\pi\) | ||||
0.273882 | + | 0.961763i | \(0.411692\pi\) | |||||||
\(150\) | 6.03254 | 0.492555 | ||||||||
\(151\) | −21.1487 | −1.72106 | −0.860528 | − | 0.509404i | \(-0.829866\pi\) | ||||
−0.860528 | + | 0.509404i | \(0.829866\pi\) | |||||||
\(152\) | 12.6251 | 1.02403 | ||||||||
\(153\) | −2.57173 | −0.207912 | ||||||||
\(154\) | −4.10708 | −0.330958 | ||||||||
\(155\) | 2.51273 | 0.201827 | ||||||||
\(156\) | 7.32994 | 0.586865 | ||||||||
\(157\) | 16.1279 | 1.28715 | 0.643575 | − | 0.765383i | \(-0.277450\pi\) | ||||
0.643575 | + | 0.765383i | \(0.277450\pi\) | |||||||
\(158\) | −0.716007 | −0.0569624 | ||||||||
\(159\) | −5.42570 | −0.430286 | ||||||||
\(160\) | −5.89205 | −0.465807 | ||||||||
\(161\) | −13.3394 | −1.05129 | ||||||||
\(162\) | −12.0908 | −0.949942 | ||||||||
\(163\) | 12.9992 | 1.01818 | 0.509089 | − | 0.860714i | \(-0.329983\pi\) | ||||
0.509089 | + | 0.860714i | \(0.329983\pi\) | |||||||
\(164\) | 5.85191 | 0.456957 | ||||||||
\(165\) | −0.633527 | −0.0493200 | ||||||||
\(166\) | −21.7463 | −1.68784 | ||||||||
\(167\) | 24.9283 | 1.92901 | 0.964505 | − | 0.264065i | \(-0.0850633\pi\) | ||||
0.964505 | + | 0.264065i | \(0.0850633\pi\) | |||||||
\(168\) | −3.08502 | −0.238014 | ||||||||
\(169\) | −0.338981 | −0.0260754 | ||||||||
\(170\) | 2.19643 | 0.168458 | ||||||||
\(171\) | 12.4676 | 0.953421 | ||||||||
\(172\) | 3.14780 | 0.240017 | ||||||||
\(173\) | 9.67419 | 0.735515 | 0.367758 | − | 0.929922i | \(-0.380126\pi\) | ||||
0.367758 | + | 0.929922i | \(0.380126\pi\) | |||||||
\(174\) | −11.8774 | −0.900424 | ||||||||
\(175\) | −7.35449 | −0.555947 | ||||||||
\(176\) | −0.386967 | −0.0291687 | ||||||||
\(177\) | −3.13755 | −0.235832 | ||||||||
\(178\) | −31.7424 | −2.37919 | ||||||||
\(179\) | −14.1103 | −1.05465 | −0.527326 | − | 0.849663i | \(-0.676805\pi\) | ||||
−0.527326 | + | 0.849663i | \(0.676805\pi\) | |||||||
\(180\) | 7.83679 | 0.584120 | ||||||||
\(181\) | −4.06005 | −0.301781 | −0.150890 | − | 0.988550i | \(-0.548214\pi\) | ||||
−0.150890 | + | 0.988550i | \(0.548214\pi\) | |||||||
\(182\) | −14.6139 | −1.08326 | ||||||||
\(183\) | 9.26117 | 0.684605 | ||||||||
\(184\) | 19.1906 | 1.41475 | ||||||||
\(185\) | 7.32598 | 0.538617 | ||||||||
\(186\) | 3.85398 | 0.282588 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −11.7061 | −0.853752 | ||||||||
\(189\) | −6.60042 | −0.480110 | ||||||||
\(190\) | −10.6482 | −0.772498 | ||||||||
\(191\) | 6.78214 | 0.490738 | 0.245369 | − | 0.969430i | \(-0.421091\pi\) | ||||
0.245369 | + | 0.969430i | \(0.421091\pi\) | |||||||
\(192\) | −8.53064 | −0.615646 | ||||||||
\(193\) | −19.9960 | −1.43934 | −0.719671 | − | 0.694315i | \(-0.755707\pi\) | ||||
−0.719671 | + | 0.694315i | \(0.755707\pi\) | |||||||
\(194\) | −39.4626 | −2.83325 | ||||||||
\(195\) | −2.25424 | −0.161429 | ||||||||
\(196\) | −11.7200 | −0.837143 | ||||||||
\(197\) | 7.21511 | 0.514055 | 0.257028 | − | 0.966404i | \(-0.417257\pi\) | ||||
0.257028 | + | 0.966404i | \(0.417257\pi\) | |||||||
\(198\) | 5.83493 | 0.414671 | ||||||||
\(199\) | 22.2752 | 1.57905 | 0.789523 | − | 0.613721i | \(-0.210328\pi\) | ||||
0.789523 | + | 0.613721i | \(0.210328\pi\) | |||||||
\(200\) | 10.5805 | 0.748154 | ||||||||
\(201\) | −2.81578 | −0.198609 | ||||||||
\(202\) | 39.7206 | 2.79474 | ||||||||
\(203\) | 14.4802 | 1.01631 | ||||||||
\(204\) | 2.05999 | 0.144228 | ||||||||
\(205\) | −1.79969 | −0.125696 | ||||||||
\(206\) | −20.0289 | −1.39548 | ||||||||
\(207\) | 18.9513 | 1.31720 | ||||||||
\(208\) | −1.37692 | −0.0954721 | ||||||||
\(209\) | −4.84794 | −0.335339 | ||||||||
\(210\) | 2.60195 | 0.179551 | ||||||||
\(211\) | 18.0658 | 1.24370 | 0.621852 | − | 0.783135i | \(-0.286381\pi\) | ||||
0.621852 | + | 0.783135i | \(0.286381\pi\) | |||||||
\(212\) | −26.0978 | −1.79240 | ||||||||
\(213\) | 9.24790 | 0.633655 | ||||||||
\(214\) | −24.8187 | −1.69657 | ||||||||
\(215\) | −0.968068 | −0.0660217 | ||||||||
\(216\) | 9.49566 | 0.646098 | ||||||||
\(217\) | −4.69853 | −0.318957 | ||||||||
\(218\) | 33.0222 | 2.23655 | ||||||||
\(219\) | 1.85807 | 0.125557 | ||||||||
\(220\) | −3.04728 | −0.205448 | ||||||||
\(221\) | 3.55823 | 0.239353 | ||||||||
\(222\) | 11.2365 | 0.754142 | ||||||||
\(223\) | −13.6552 | −0.914420 | −0.457210 | − | 0.889359i | \(-0.651151\pi\) | ||||
−0.457210 | + | 0.889359i | \(0.651151\pi\) | |||||||
\(224\) | 11.0175 | 0.736137 | ||||||||
\(225\) | 10.4485 | 0.696569 | ||||||||
\(226\) | −20.8493 | −1.38687 | ||||||||
\(227\) | 24.1755 | 1.60459 | 0.802293 | − | 0.596931i | \(-0.203613\pi\) | ||||
0.802293 | + | 0.596931i | \(0.203613\pi\) | |||||||
\(228\) | −9.98673 | −0.661388 | ||||||||
\(229\) | 3.55989 | 0.235244 | 0.117622 | − | 0.993058i | \(-0.462473\pi\) | ||||
0.117622 | + | 0.993058i | \(0.462473\pi\) | |||||||
\(230\) | −16.1856 | −1.06725 | ||||||||
\(231\) | 1.18463 | 0.0779427 | ||||||||
\(232\) | −20.8319 | −1.36768 | ||||||||
\(233\) | −4.44301 | −0.291071 | −0.145536 | − | 0.989353i | \(-0.546491\pi\) | ||||
−0.145536 | + | 0.989353i | \(0.546491\pi\) | |||||||
\(234\) | 20.7621 | 1.35726 | ||||||||
\(235\) | 3.60006 | 0.234842 | ||||||||
\(236\) | −15.0917 | −0.982385 | ||||||||
\(237\) | 0.206522 | 0.0134150 | ||||||||
\(238\) | −4.10708 | −0.266222 | ||||||||
\(239\) | 12.0797 | 0.781371 | 0.390686 | − | 0.920524i | \(-0.372238\pi\) | ||||
0.390686 | + | 0.920524i | \(0.372238\pi\) | |||||||
\(240\) | 0.245154 | 0.0158246 | ||||||||
\(241\) | −13.6638 | −0.880165 | −0.440082 | − | 0.897957i | \(-0.645051\pi\) | ||||
−0.440082 | + | 0.897957i | \(0.645051\pi\) | |||||||
\(242\) | −2.26888 | −0.145849 | ||||||||
\(243\) | 14.4262 | 0.925443 | ||||||||
\(244\) | 44.5465 | 2.85180 | ||||||||
\(245\) | 3.60435 | 0.230274 | ||||||||
\(246\) | −2.76033 | −0.175992 | ||||||||
\(247\) | −17.2501 | −1.09760 | ||||||||
\(248\) | 6.75952 | 0.429230 | ||||||||
\(249\) | 6.27241 | 0.397498 | ||||||||
\(250\) | −19.9059 | −1.25896 | ||||||||
\(251\) | 15.9799 | 1.00864 | 0.504322 | − | 0.863516i | \(-0.331742\pi\) | ||||
0.504322 | + | 0.863516i | \(0.331742\pi\) | |||||||
\(252\) | −14.6539 | −0.923111 | ||||||||
\(253\) | −7.36907 | −0.463290 | ||||||||
\(254\) | −14.5730 | −0.914389 | ||||||||
\(255\) | −0.633527 | −0.0396730 | ||||||||
\(256\) | −13.4141 | −0.838379 | ||||||||
\(257\) | −13.6291 | −0.850160 | −0.425080 | − | 0.905156i | \(-0.639754\pi\) | ||||
−0.425080 | + | 0.905156i | \(0.639754\pi\) | |||||||
\(258\) | −1.48481 | −0.0924400 | ||||||||
\(259\) | −13.6988 | −0.851201 | ||||||||
\(260\) | −10.8429 | −0.672451 | ||||||||
\(261\) | −20.5720 | −1.27338 | ||||||||
\(262\) | −22.7233 | −1.40385 | ||||||||
\(263\) | −28.3881 | −1.75049 | −0.875244 | − | 0.483682i | \(-0.839299\pi\) | ||||
−0.875244 | + | 0.483682i | \(0.839299\pi\) | |||||||
\(264\) | −1.70426 | −0.104890 | ||||||||
\(265\) | 8.02606 | 0.493037 | ||||||||
\(266\) | 19.9109 | 1.22081 | ||||||||
\(267\) | 9.15563 | 0.560316 | ||||||||
\(268\) | −13.5440 | −0.827329 | ||||||||
\(269\) | 21.8036 | 1.32939 | 0.664694 | − | 0.747116i | \(-0.268562\pi\) | ||||
0.664694 | + | 0.747116i | \(0.268562\pi\) | |||||||
\(270\) | −8.00877 | −0.487398 | ||||||||
\(271\) | 15.1598 | 0.920894 | 0.460447 | − | 0.887687i | \(-0.347689\pi\) | ||||
0.460447 | + | 0.887687i | \(0.347689\pi\) | |||||||
\(272\) | −0.386967 | −0.0234633 | ||||||||
\(273\) | 4.21518 | 0.255114 | ||||||||
\(274\) | 45.6404 | 2.75724 | ||||||||
\(275\) | −4.06284 | −0.244999 | ||||||||
\(276\) | −15.1802 | −0.913743 | ||||||||
\(277\) | 25.0059 | 1.50246 | 0.751230 | − | 0.660041i | \(-0.229461\pi\) | ||||
0.751230 | + | 0.660041i | \(0.229461\pi\) | |||||||
\(278\) | 51.0036 | 3.05899 | ||||||||
\(279\) | 6.67521 | 0.399634 | ||||||||
\(280\) | 4.56357 | 0.272725 | ||||||||
\(281\) | 19.1877 | 1.14464 | 0.572322 | − | 0.820029i | \(-0.306043\pi\) | ||||
0.572322 | + | 0.820029i | \(0.306043\pi\) | |||||||
\(282\) | 5.52171 | 0.328813 | ||||||||
\(283\) | 12.2974 | 0.731003 | 0.365501 | − | 0.930811i | \(-0.380898\pi\) | ||||
0.365501 | + | 0.930811i | \(0.380898\pi\) | |||||||
\(284\) | 44.4826 | 2.63956 | ||||||||
\(285\) | 3.07130 | 0.181928 | ||||||||
\(286\) | −8.07319 | −0.477378 | ||||||||
\(287\) | 3.36522 | 0.198642 | ||||||||
\(288\) | −15.6526 | −0.922337 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 17.5699 | 1.03174 | ||||||||
\(291\) | 11.3824 | 0.667249 | ||||||||
\(292\) | 8.93738 | 0.523021 | ||||||||
\(293\) | 15.6074 | 0.911796 | 0.455898 | − | 0.890032i | \(-0.349318\pi\) | ||||
0.455898 | + | 0.890032i | \(0.349318\pi\) | |||||||
\(294\) | 5.52829 | 0.322416 | ||||||||
\(295\) | 4.64127 | 0.270225 | ||||||||
\(296\) | 19.7077 | 1.14549 | ||||||||
\(297\) | −3.64627 | −0.211578 | ||||||||
\(298\) | −15.1704 | −0.878799 | ||||||||
\(299\) | −26.2209 | −1.51639 | ||||||||
\(300\) | −8.36943 | −0.483209 | ||||||||
\(301\) | 1.81018 | 0.104337 | ||||||||
\(302\) | 47.9837 | 2.76115 | ||||||||
\(303\) | −11.4568 | −0.658178 | ||||||||
\(304\) | 1.87599 | 0.107596 | ||||||||
\(305\) | −13.6997 | −0.784445 | ||||||||
\(306\) | 5.83493 | 0.333561 | ||||||||
\(307\) | −9.02362 | −0.515005 | −0.257503 | − | 0.966278i | \(-0.582900\pi\) | ||||
−0.257503 | + | 0.966278i | \(0.582900\pi\) | |||||||
\(308\) | 5.69809 | 0.324679 | ||||||||
\(309\) | 5.77705 | 0.328645 | ||||||||
\(310\) | −5.70107 | −0.323799 | ||||||||
\(311\) | 8.48774 | 0.481296 | 0.240648 | − | 0.970613i | \(-0.422640\pi\) | ||||
0.240648 | + | 0.970613i | \(0.422640\pi\) | |||||||
\(312\) | −6.06414 | −0.343314 | ||||||||
\(313\) | 10.3944 | 0.587523 | 0.293762 | − | 0.955879i | \(-0.405093\pi\) | ||||
0.293762 | + | 0.955879i | \(0.405093\pi\) | |||||||
\(314\) | −36.5923 | −2.06502 | ||||||||
\(315\) | 4.50665 | 0.253921 | ||||||||
\(316\) | 0.993375 | 0.0558817 | ||||||||
\(317\) | −31.8125 | −1.78677 | −0.893384 | − | 0.449293i | \(-0.851676\pi\) | ||||
−0.893384 | + | 0.449293i | \(0.851676\pi\) | |||||||
\(318\) | 12.3102 | 0.690324 | ||||||||
\(319\) | 7.99930 | 0.447875 | ||||||||
\(320\) | 12.6191 | 0.705430 | ||||||||
\(321\) | 7.15858 | 0.399553 | ||||||||
\(322\) | 30.2654 | 1.68662 | ||||||||
\(323\) | −4.84794 | −0.269747 | ||||||||
\(324\) | 16.7745 | 0.931919 | ||||||||
\(325\) | −14.4565 | −0.801905 | ||||||||
\(326\) | −29.4936 | −1.63350 | ||||||||
\(327\) | −9.52477 | −0.526721 | ||||||||
\(328\) | −4.84135 | −0.267319 | ||||||||
\(329\) | −6.73172 | −0.371132 | ||||||||
\(330\) | 1.43739 | 0.0791260 | ||||||||
\(331\) | 4.20246 | 0.230988 | 0.115494 | − | 0.993308i | \(-0.463155\pi\) | ||||
0.115494 | + | 0.993308i | \(0.463155\pi\) | |||||||
\(332\) | 30.1705 | 1.65582 | ||||||||
\(333\) | 19.4619 | 1.06650 | ||||||||
\(334\) | −56.5592 | −3.09478 | ||||||||
\(335\) | 4.16529 | 0.227574 | ||||||||
\(336\) | −0.458411 | −0.0250084 | ||||||||
\(337\) | 18.7531 | 1.02154 | 0.510772 | − | 0.859716i | \(-0.329360\pi\) | ||||
0.510772 | + | 0.859716i | \(0.329360\pi\) | |||||||
\(338\) | 0.769105 | 0.0418338 | ||||||||
\(339\) | 6.01367 | 0.326618 | ||||||||
\(340\) | −3.04728 | −0.165262 | ||||||||
\(341\) | −2.59561 | −0.140560 | ||||||||
\(342\) | −28.2874 | −1.52961 | ||||||||
\(343\) | −19.4110 | −1.04810 | ||||||||
\(344\) | −2.60421 | −0.140410 | ||||||||
\(345\) | 4.66851 | 0.251344 | ||||||||
\(346\) | −21.9495 | −1.18001 | ||||||||
\(347\) | 19.5899 | 1.05164 | 0.525819 | − | 0.850596i | \(-0.323759\pi\) | ||||
0.525819 | + | 0.850596i | \(0.323759\pi\) | |||||||
\(348\) | 16.4785 | 0.883341 | ||||||||
\(349\) | −21.4986 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(350\) | 16.6864 | 0.891927 | ||||||||
\(351\) | −12.9743 | −0.692516 | ||||||||
\(352\) | 6.08640 | 0.324406 | ||||||||
\(353\) | −7.00756 | −0.372975 | −0.186487 | − | 0.982457i | \(-0.559710\pi\) | ||||
−0.186487 | + | 0.982457i | \(0.559710\pi\) | |||||||
\(354\) | 7.11870 | 0.378355 | ||||||||
\(355\) | −13.6801 | −0.726065 | ||||||||
\(356\) | 44.0388 | 2.33405 | ||||||||
\(357\) | 1.18463 | 0.0626971 | ||||||||
\(358\) | 32.0145 | 1.69202 | ||||||||
\(359\) | −2.25680 | −0.119109 | −0.0595547 | − | 0.998225i | \(-0.518968\pi\) | ||||
−0.0595547 | + | 0.998225i | \(0.518968\pi\) | |||||||
\(360\) | −6.48347 | −0.341709 | ||||||||
\(361\) | 4.50256 | 0.236977 | ||||||||
\(362\) | 9.21174 | 0.484158 | ||||||||
\(363\) | 0.654424 | 0.0343483 | ||||||||
\(364\) | 20.2751 | 1.06271 | ||||||||
\(365\) | −2.74859 | −0.143868 | ||||||||
\(366\) | −21.0124 | −1.09834 | ||||||||
\(367\) | −19.8758 | −1.03751 | −0.518753 | − | 0.854924i | \(-0.673604\pi\) | ||||
−0.518753 | + | 0.854924i | \(0.673604\pi\) | |||||||
\(368\) | 2.85159 | 0.148649 | ||||||||
\(369\) | −4.78097 | −0.248887 | ||||||||
\(370\) | −16.6217 | −0.864123 | ||||||||
\(371\) | −15.0079 | −0.779170 | ||||||||
\(372\) | −5.34694 | −0.277226 | ||||||||
\(373\) | −15.3983 | −0.797294 | −0.398647 | − | 0.917104i | \(-0.630520\pi\) | ||||
−0.398647 | + | 0.917104i | \(0.630520\pi\) | |||||||
\(374\) | −2.26888 | −0.117321 | ||||||||
\(375\) | 5.74156 | 0.296493 | ||||||||
\(376\) | 9.68455 | 0.499443 | ||||||||
\(377\) | 28.4634 | 1.46594 | ||||||||
\(378\) | 14.9755 | 0.770258 | ||||||||
\(379\) | −34.2454 | −1.75907 | −0.879533 | − | 0.475838i | \(-0.842145\pi\) | ||||
−0.879533 | + | 0.475838i | \(0.842145\pi\) | |||||||
\(380\) | 14.7731 | 0.757842 | ||||||||
\(381\) | 4.20336 | 0.215345 | ||||||||
\(382\) | −15.3878 | −0.787310 | ||||||||
\(383\) | 29.4784 | 1.50628 | 0.753138 | − | 0.657862i | \(-0.228539\pi\) | ||||
0.753138 | + | 0.657862i | \(0.228539\pi\) | |||||||
\(384\) | 11.3888 | 0.581182 | ||||||||
\(385\) | −1.75238 | −0.0893096 | ||||||||
\(386\) | 45.3684 | 2.30919 | ||||||||
\(387\) | −2.57173 | −0.130728 | ||||||||
\(388\) | 54.7498 | 2.77950 | ||||||||
\(389\) | −11.9208 | −0.604407 | −0.302203 | − | 0.953243i | \(-0.597722\pi\) | ||||
−0.302203 | + | 0.953243i | \(0.597722\pi\) | |||||||
\(390\) | 5.11458 | 0.258987 | ||||||||
\(391\) | −7.36907 | −0.372670 | ||||||||
\(392\) | 9.69610 | 0.489727 | ||||||||
\(393\) | 6.55421 | 0.330616 | ||||||||
\(394\) | −16.3702 | −0.824718 | ||||||||
\(395\) | −0.305501 | −0.0153714 | ||||||||
\(396\) | −8.09528 | −0.406803 | ||||||||
\(397\) | −6.38995 | −0.320703 | −0.160351 | − | 0.987060i | \(-0.551263\pi\) | ||||
−0.160351 | + | 0.987060i | \(0.551263\pi\) | |||||||
\(398\) | −50.5396 | −2.53332 | ||||||||
\(399\) | −5.74300 | −0.287510 | ||||||||
\(400\) | 1.57219 | 0.0786093 | ||||||||
\(401\) | 2.67473 | 0.133570 | 0.0667848 | − | 0.997767i | \(-0.478726\pi\) | ||||
0.0667848 | + | 0.997767i | \(0.478726\pi\) | |||||||
\(402\) | 6.38865 | 0.318637 | ||||||||
\(403\) | −9.23579 | −0.460067 | ||||||||
\(404\) | −55.1077 | −2.74171 | ||||||||
\(405\) | −5.15882 | −0.256344 | ||||||||
\(406\) | −32.8538 | −1.63050 | ||||||||
\(407\) | −7.56763 | −0.375113 | ||||||||
\(408\) | −1.70426 | −0.0843733 | ||||||||
\(409\) | 3.75111 | 0.185481 | 0.0927403 | − | 0.995690i | \(-0.470437\pi\) | ||||
0.0927403 | + | 0.995690i | \(0.470437\pi\) | |||||||
\(410\) | 4.08326 | 0.201658 | ||||||||
\(411\) | −13.1643 | −0.649347 | ||||||||
\(412\) | 27.7878 | 1.36900 | ||||||||
\(413\) | −8.67867 | −0.427049 | ||||||||
\(414\) | −42.9981 | −2.11324 | ||||||||
\(415\) | −9.27858 | −0.455468 | ||||||||
\(416\) | 21.6568 | 1.06181 | ||||||||
\(417\) | −14.7112 | −0.720412 | ||||||||
\(418\) | 10.9994 | 0.537997 | ||||||||
\(419\) | −26.5650 | −1.29778 | −0.648892 | − | 0.760881i | \(-0.724767\pi\) | ||||
−0.648892 | + | 0.760881i | \(0.724767\pi\) | |||||||
\(420\) | −3.60989 | −0.176145 | ||||||||
\(421\) | −19.5653 | −0.953553 | −0.476777 | − | 0.879024i | \(-0.658195\pi\) | ||||
−0.476777 | + | 0.879024i | \(0.658195\pi\) | |||||||
\(422\) | −40.9891 | −1.99532 | ||||||||
\(423\) | 9.56377 | 0.465006 | ||||||||
\(424\) | 21.5910 | 1.04855 | ||||||||
\(425\) | −4.06284 | −0.197077 | ||||||||
\(426\) | −20.9823 | −1.01660 | ||||||||
\(427\) | 25.6170 | 1.23970 | ||||||||
\(428\) | 34.4330 | 1.66438 | ||||||||
\(429\) | 2.32859 | 0.112426 | ||||||||
\(430\) | 2.19643 | 0.105921 | ||||||||
\(431\) | 34.0784 | 1.64150 | 0.820750 | − | 0.571287i | \(-0.193556\pi\) | ||||
0.820750 | + | 0.571287i | \(0.193556\pi\) | |||||||
\(432\) | 1.41099 | 0.0678861 | ||||||||
\(433\) | −7.36781 | −0.354074 | −0.177037 | − | 0.984204i | \(-0.556651\pi\) | ||||
−0.177037 | + | 0.984204i | \(0.556651\pi\) | |||||||
\(434\) | 10.6604 | 0.511715 | ||||||||
\(435\) | −5.06777 | −0.242981 | ||||||||
\(436\) | −45.8144 | −2.19411 | ||||||||
\(437\) | 35.7248 | 1.70895 | ||||||||
\(438\) | −4.21574 | −0.201436 | ||||||||
\(439\) | −6.48225 | −0.309381 | −0.154691 | − | 0.987963i | \(-0.549438\pi\) | ||||
−0.154691 | + | 0.987963i | \(0.549438\pi\) | |||||||
\(440\) | 2.52105 | 0.120186 | ||||||||
\(441\) | 9.57516 | 0.455960 | ||||||||
\(442\) | −8.07319 | −0.384002 | ||||||||
\(443\) | −10.8793 | −0.516893 | −0.258447 | − | 0.966026i | \(-0.583211\pi\) | ||||
−0.258447 | + | 0.966026i | \(0.583211\pi\) | |||||||
\(444\) | −15.5893 | −0.739834 | ||||||||
\(445\) | −13.5436 | −0.642030 | ||||||||
\(446\) | 30.9820 | 1.46704 | ||||||||
\(447\) | 4.37569 | 0.206963 | ||||||||
\(448\) | −23.5964 | −1.11482 | ||||||||
\(449\) | −20.0663 | −0.946987 | −0.473494 | − | 0.880797i | \(-0.657007\pi\) | ||||
−0.473494 | + | 0.880797i | \(0.657007\pi\) | |||||||
\(450\) | −23.7064 | −1.11753 | ||||||||
\(451\) | 1.85905 | 0.0875392 | ||||||||
\(452\) | 28.9259 | 1.36056 | ||||||||
\(453\) | −13.8402 | −0.650269 | ||||||||
\(454\) | −54.8513 | −2.57430 | ||||||||
\(455\) | −6.23538 | −0.292319 | ||||||||
\(456\) | 8.26214 | 0.386910 | ||||||||
\(457\) | 2.75446 | 0.128848 | 0.0644241 | − | 0.997923i | \(-0.479479\pi\) | ||||
0.0644241 | + | 0.997923i | \(0.479479\pi\) | |||||||
\(458\) | −8.07695 | −0.377411 | ||||||||
\(459\) | −3.64627 | −0.170193 | ||||||||
\(460\) | 22.4556 | 1.04700 | ||||||||
\(461\) | 17.8701 | 0.832296 | 0.416148 | − | 0.909297i | \(-0.363380\pi\) | ||||
0.416148 | + | 0.909297i | \(0.363380\pi\) | |||||||
\(462\) | −2.68777 | −0.125046 | ||||||||
\(463\) | −15.5482 | −0.722587 | −0.361294 | − | 0.932452i | \(-0.617665\pi\) | ||||
−0.361294 | + | 0.932452i | \(0.617665\pi\) | |||||||
\(464\) | −3.09546 | −0.143703 | ||||||||
\(465\) | 1.64439 | 0.0762568 | ||||||||
\(466\) | 10.0806 | 0.466977 | ||||||||
\(467\) | −8.86413 | −0.410183 | −0.205091 | − | 0.978743i | \(-0.565749\pi\) | ||||
−0.205091 | + | 0.978743i | \(0.565749\pi\) | |||||||
\(468\) | −28.8049 | −1.33151 | ||||||||
\(469\) | −7.78863 | −0.359646 | ||||||||
\(470\) | −8.16809 | −0.376766 | ||||||||
\(471\) | 10.5545 | 0.486326 | ||||||||
\(472\) | 12.4855 | 0.574693 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −0.468572 | −0.0215222 | ||||||||
\(475\) | 19.6964 | 0.903735 | ||||||||
\(476\) | 5.69809 | 0.261171 | ||||||||
\(477\) | 21.3217 | 0.976254 | ||||||||
\(478\) | −27.4073 | −1.25358 | ||||||||
\(479\) | 39.4044 | 1.80044 | 0.900218 | − | 0.435440i | \(-0.143407\pi\) | ||||
0.900218 | + | 0.435440i | \(0.143407\pi\) | |||||||
\(480\) | −3.85590 | −0.175997 | ||||||||
\(481\) | −26.9274 | −1.22778 | ||||||||
\(482\) | 31.0015 | 1.41208 | ||||||||
\(483\) | −8.72960 | −0.397211 | ||||||||
\(484\) | 3.14780 | 0.143082 | ||||||||
\(485\) | −16.8377 | −0.764558 | ||||||||
\(486\) | −32.7313 | −1.48472 | ||||||||
\(487\) | 26.3199 | 1.19267 | 0.596335 | − | 0.802736i | \(-0.296623\pi\) | ||||
0.596335 | + | 0.802736i | \(0.296623\pi\) | |||||||
\(488\) | −36.8538 | −1.66829 | ||||||||
\(489\) | 8.50700 | 0.384700 | ||||||||
\(490\) | −8.17782 | −0.369436 | ||||||||
\(491\) | 10.5119 | 0.474394 | 0.237197 | − | 0.971462i | \(-0.423771\pi\) | ||||
0.237197 | + | 0.971462i | \(0.423771\pi\) | |||||||
\(492\) | 3.82963 | 0.172653 | ||||||||
\(493\) | 7.99930 | 0.360270 | ||||||||
\(494\) | 39.1384 | 1.76092 | ||||||||
\(495\) | 2.48961 | 0.111900 | ||||||||
\(496\) | 1.00442 | 0.0450996 | ||||||||
\(497\) | 25.5803 | 1.14743 | ||||||||
\(498\) | −14.2313 | −0.637721 | ||||||||
\(499\) | 27.3220 | 1.22310 | 0.611550 | − | 0.791206i | \(-0.290546\pi\) | ||||
0.611550 | + | 0.791206i | \(0.290546\pi\) | |||||||
\(500\) | 27.6170 | 1.23507 | ||||||||
\(501\) | 16.3137 | 0.728841 | ||||||||
\(502\) | −36.2565 | −1.61821 | ||||||||
\(503\) | 4.46103 | 0.198907 | 0.0994537 | − | 0.995042i | \(-0.468290\pi\) | ||||
0.0994537 | + | 0.995042i | \(0.468290\pi\) | |||||||
\(504\) | 12.1234 | 0.540018 | ||||||||
\(505\) | 16.9477 | 0.754164 | ||||||||
\(506\) | 16.7195 | 0.743273 | ||||||||
\(507\) | −0.221837 | −0.00985213 | ||||||||
\(508\) | 20.2183 | 0.897041 | ||||||||
\(509\) | 10.2339 | 0.453612 | 0.226806 | − | 0.973940i | \(-0.427172\pi\) | ||||
0.226806 | + | 0.973940i | \(0.427172\pi\) | |||||||
\(510\) | 1.43739 | 0.0636489 | ||||||||
\(511\) | 5.13956 | 0.227361 | ||||||||
\(512\) | −4.37072 | −0.193160 | ||||||||
\(513\) | 17.6769 | 0.780455 | ||||||||
\(514\) | 30.9227 | 1.36394 | ||||||||
\(515\) | −8.54580 | −0.376573 | ||||||||
\(516\) | 2.05999 | 0.0906862 | ||||||||
\(517\) | −3.71881 | −0.163553 | ||||||||
\(518\) | 31.0808 | 1.36561 | ||||||||
\(519\) | 6.33102 | 0.277901 | ||||||||
\(520\) | 8.97049 | 0.393382 | ||||||||
\(521\) | 23.7011 | 1.03837 | 0.519183 | − | 0.854663i | \(-0.326236\pi\) | ||||
0.519183 | + | 0.854663i | \(0.326236\pi\) | |||||||
\(522\) | 46.6754 | 2.04293 | ||||||||
\(523\) | −38.7691 | −1.69526 | −0.847628 | − | 0.530591i | \(-0.821970\pi\) | ||||
−0.847628 | + | 0.530591i | \(0.821970\pi\) | |||||||
\(524\) | 31.5260 | 1.37722 | ||||||||
\(525\) | −4.81295 | −0.210054 | ||||||||
\(526\) | 64.4092 | 2.80837 | ||||||||
\(527\) | −2.59561 | −0.113067 | ||||||||
\(528\) | −0.253240 | −0.0110209 | ||||||||
\(529\) | 31.3032 | 1.36101 | ||||||||
\(530\) | −18.2101 | −0.790998 | ||||||||
\(531\) | 12.3298 | 0.535068 | ||||||||
\(532\) | −27.6240 | −1.19765 | ||||||||
\(533\) | 6.61493 | 0.286524 | ||||||||
\(534\) | −20.7730 | −0.898935 | ||||||||
\(535\) | −10.5895 | −0.457822 | ||||||||
\(536\) | 11.2051 | 0.483986 | ||||||||
\(537\) | −9.23411 | −0.398481 | ||||||||
\(538\) | −49.4696 | −2.13279 | ||||||||
\(539\) | −3.72324 | −0.160371 | ||||||||
\(540\) | 11.1112 | 0.478151 | ||||||||
\(541\) | −11.3462 | −0.487812 | −0.243906 | − | 0.969799i | \(-0.578429\pi\) | ||||
−0.243906 | + | 0.969799i | \(0.578429\pi\) | |||||||
\(542\) | −34.3958 | −1.47742 | ||||||||
\(543\) | −2.65699 | −0.114022 | ||||||||
\(544\) | 6.08640 | 0.260952 | ||||||||
\(545\) | 14.0897 | 0.603536 | ||||||||
\(546\) | −9.56371 | −0.409289 | ||||||||
\(547\) | 18.4261 | 0.787842 | 0.393921 | − | 0.919144i | \(-0.371118\pi\) | ||||
0.393921 | + | 0.919144i | \(0.371118\pi\) | |||||||
\(548\) | −63.3206 | −2.70492 | ||||||||
\(549\) | −36.3942 | −1.55327 | ||||||||
\(550\) | 9.21809 | 0.393061 | ||||||||
\(551\) | −38.7802 | −1.65209 | ||||||||
\(552\) | 12.5588 | 0.534538 | ||||||||
\(553\) | 0.571253 | 0.0242922 | ||||||||
\(554\) | −56.7353 | −2.41045 | ||||||||
\(555\) | 4.79430 | 0.203507 | ||||||||
\(556\) | −70.7614 | −3.00095 | ||||||||
\(557\) | −0.497729 | −0.0210895 | −0.0105447 | − | 0.999944i | \(-0.503357\pi\) | ||||
−0.0105447 | + | 0.999944i | \(0.503357\pi\) | |||||||
\(558\) | −15.1452 | −0.641148 | ||||||||
\(559\) | 3.55823 | 0.150497 | ||||||||
\(560\) | 0.678113 | 0.0286555 | ||||||||
\(561\) | 0.654424 | 0.0276298 | ||||||||
\(562\) | −43.5346 | −1.83640 | ||||||||
\(563\) | 23.0984 | 0.973480 | 0.486740 | − | 0.873547i | \(-0.338186\pi\) | ||||
0.486740 | + | 0.873547i | \(0.338186\pi\) | |||||||
\(564\) | −7.66072 | −0.322575 | ||||||||
\(565\) | −8.89584 | −0.374251 | ||||||||
\(566\) | −27.9012 | −1.17277 | ||||||||
\(567\) | 9.64643 | 0.405112 | ||||||||
\(568\) | −36.8010 | −1.54414 | ||||||||
\(569\) | −5.81738 | −0.243877 | −0.121939 | − | 0.992538i | \(-0.538911\pi\) | ||||
−0.121939 | + | 0.992538i | \(0.538911\pi\) | |||||||
\(570\) | −6.96841 | −0.291874 | ||||||||
\(571\) | −22.2688 | −0.931920 | −0.465960 | − | 0.884806i | \(-0.654291\pi\) | ||||
−0.465960 | + | 0.884806i | \(0.654291\pi\) | |||||||
\(572\) | 11.2006 | 0.468320 | ||||||||
\(573\) | 4.43839 | 0.185417 | ||||||||
\(574\) | −7.63526 | −0.318690 | ||||||||
\(575\) | 29.9394 | 1.24856 | ||||||||
\(576\) | 33.5234 | 1.39681 | ||||||||
\(577\) | −14.5687 | −0.606504 | −0.303252 | − | 0.952910i | \(-0.598072\pi\) | ||||
−0.303252 | + | 0.952910i | \(0.598072\pi\) | |||||||
\(578\) | −2.26888 | −0.0943728 | ||||||||
\(579\) | −13.0858 | −0.543829 | ||||||||
\(580\) | −24.3761 | −1.01216 | ||||||||
\(581\) | 17.3499 | 0.719797 | ||||||||
\(582\) | −25.8253 | −1.07049 | ||||||||
\(583\) | −8.29080 | −0.343370 | ||||||||
\(584\) | −7.39400 | −0.305966 | ||||||||
\(585\) | 8.85861 | 0.366258 | ||||||||
\(586\) | −35.4113 | −1.46283 | ||||||||
\(587\) | 28.5016 | 1.17639 | 0.588193 | − | 0.808720i | \(-0.299839\pi\) | ||||
0.588193 | + | 0.808720i | \(0.299839\pi\) | |||||||
\(588\) | −7.66985 | −0.316299 | ||||||||
\(589\) | 12.5834 | 0.518489 | ||||||||
\(590\) | −10.5305 | −0.433532 | ||||||||
\(591\) | 4.72174 | 0.194226 | ||||||||
\(592\) | 2.92842 | 0.120357 | ||||||||
\(593\) | 40.9865 | 1.68312 | 0.841558 | − | 0.540167i | \(-0.181639\pi\) | ||||
0.841558 | + | 0.540167i | \(0.181639\pi\) | |||||||
\(594\) | 8.27294 | 0.339443 | ||||||||
\(595\) | −1.75238 | −0.0718406 | ||||||||
\(596\) | 21.0472 | 0.862126 | ||||||||
\(597\) | 14.5774 | 0.596614 | ||||||||
\(598\) | 59.4919 | 2.43280 | ||||||||
\(599\) | 8.64990 | 0.353425 | 0.176713 | − | 0.984262i | \(-0.443454\pi\) | ||||
0.176713 | + | 0.984262i | \(0.443454\pi\) | |||||||
\(600\) | 6.92413 | 0.282676 | ||||||||
\(601\) | 1.52981 | 0.0624024 | 0.0312012 | − | 0.999513i | \(-0.490067\pi\) | ||||
0.0312012 | + | 0.999513i | \(0.490067\pi\) | |||||||
\(602\) | −4.10708 | −0.167392 | ||||||||
\(603\) | 11.0653 | 0.450615 | ||||||||
\(604\) | −66.5718 | −2.70877 | ||||||||
\(605\) | −0.968068 | −0.0393576 | ||||||||
\(606\) | 25.9941 | 1.05594 | ||||||||
\(607\) | −19.8845 | −0.807088 | −0.403544 | − | 0.914960i | \(-0.632222\pi\) | ||||
−0.403544 | + | 0.914960i | \(0.632222\pi\) | |||||||
\(608\) | −29.5065 | −1.19665 | ||||||||
\(609\) | 9.47618 | 0.383994 | ||||||||
\(610\) | 31.0830 | 1.25852 | ||||||||
\(611\) | −13.2324 | −0.535325 | ||||||||
\(612\) | −8.09528 | −0.327232 | ||||||||
\(613\) | −22.9660 | −0.927586 | −0.463793 | − | 0.885943i | \(-0.653512\pi\) | ||||
−0.463793 | + | 0.885943i | \(0.653512\pi\) | |||||||
\(614\) | 20.4735 | 0.826242 | ||||||||
\(615\) | −1.17776 | −0.0474918 | ||||||||
\(616\) | −4.71409 | −0.189936 | ||||||||
\(617\) | −42.0033 | −1.69099 | −0.845494 | − | 0.533985i | \(-0.820694\pi\) | ||||
−0.845494 | + | 0.533985i | \(0.820694\pi\) | |||||||
\(618\) | −13.1074 | −0.527257 | ||||||||
\(619\) | 17.8147 | 0.716033 | 0.358017 | − | 0.933715i | \(-0.383453\pi\) | ||||
0.358017 | + | 0.933715i | \(0.383453\pi\) | |||||||
\(620\) | 7.90956 | 0.317656 | ||||||||
\(621\) | 26.8696 | 1.07824 | ||||||||
\(622\) | −19.2576 | −0.772160 | ||||||||
\(623\) | 25.3251 | 1.01463 | ||||||||
\(624\) | −0.901088 | −0.0360724 | ||||||||
\(625\) | 11.8209 | 0.472837 | ||||||||
\(626\) | −23.5835 | −0.942586 | ||||||||
\(627\) | −3.17261 | −0.126702 | ||||||||
\(628\) | 50.7675 | 2.02584 | ||||||||
\(629\) | −7.56763 | −0.301741 | ||||||||
\(630\) | −10.2250 | −0.407375 | ||||||||
\(631\) | −40.0166 | −1.59304 | −0.796519 | − | 0.604614i | \(-0.793327\pi\) | ||||
−0.796519 | + | 0.604614i | \(0.793327\pi\) | |||||||
\(632\) | −0.821831 | −0.0326907 | ||||||||
\(633\) | 11.8227 | 0.469911 | ||||||||
\(634\) | 72.1786 | 2.86658 | ||||||||
\(635\) | −6.21789 | −0.246750 | ||||||||
\(636\) | −17.0790 | −0.677227 | ||||||||
\(637\) | −13.2482 | −0.524911 | ||||||||
\(638\) | −18.1494 | −0.718542 | ||||||||
\(639\) | −36.3420 | −1.43767 | ||||||||
\(640\) | −16.8471 | −0.665940 | ||||||||
\(641\) | −24.7790 | −0.978710 | −0.489355 | − | 0.872085i | \(-0.662768\pi\) | ||||
−0.489355 | + | 0.872085i | \(0.662768\pi\) | |||||||
\(642\) | −16.2419 | −0.641018 | ||||||||
\(643\) | 33.7086 | 1.32934 | 0.664668 | − | 0.747139i | \(-0.268573\pi\) | ||||
0.664668 | + | 0.747139i | \(0.268573\pi\) | |||||||
\(644\) | −41.9896 | −1.65462 | ||||||||
\(645\) | −0.633527 | −0.0249451 | ||||||||
\(646\) | 10.9994 | 0.432765 | ||||||||
\(647\) | 13.0771 | 0.514112 | 0.257056 | − | 0.966396i | \(-0.417247\pi\) | ||||
0.257056 | + | 0.966396i | \(0.417247\pi\) | |||||||
\(648\) | −13.8778 | −0.545171 | ||||||||
\(649\) | −4.79436 | −0.188195 | ||||||||
\(650\) | 32.8001 | 1.28653 | ||||||||
\(651\) | −3.07483 | −0.120512 | ||||||||
\(652\) | 40.9189 | 1.60251 | ||||||||
\(653\) | −1.62862 | −0.0637329 | −0.0318665 | − | 0.999492i | \(-0.510145\pi\) | ||||
−0.0318665 | + | 0.999492i | \(0.510145\pi\) | |||||||
\(654\) | 21.6105 | 0.845038 | ||||||||
\(655\) | −9.69544 | −0.378832 | ||||||||
\(656\) | −0.719390 | −0.0280875 | ||||||||
\(657\) | −7.30178 | −0.284870 | ||||||||
\(658\) | 15.2734 | 0.595421 | ||||||||
\(659\) | 18.9684 | 0.738902 | 0.369451 | − | 0.929250i | \(-0.379546\pi\) | ||||
0.369451 | + | 0.929250i | \(0.379546\pi\) | |||||||
\(660\) | −1.99421 | −0.0776247 | ||||||||
\(661\) | −15.6090 | −0.607121 | −0.303561 | − | 0.952812i | \(-0.598176\pi\) | ||||
−0.303561 | + | 0.952812i | \(0.598176\pi\) | |||||||
\(662\) | −9.53485 | −0.370583 | ||||||||
\(663\) | 2.32859 | 0.0904350 | ||||||||
\(664\) | −24.9604 | −0.968651 | ||||||||
\(665\) | 8.49544 | 0.329439 | ||||||||
\(666\) | −44.1566 | −1.71103 | ||||||||
\(667\) | −58.9474 | −2.28245 | ||||||||
\(668\) | 78.4692 | 3.03607 | ||||||||
\(669\) | −8.93629 | −0.345497 | ||||||||
\(670\) | −9.45052 | −0.365105 | ||||||||
\(671\) | 14.1516 | 0.546318 | ||||||||
\(672\) | 7.21011 | 0.278136 | ||||||||
\(673\) | 36.4052 | 1.40332 | 0.701659 | − | 0.712513i | \(-0.252443\pi\) | ||||
0.701659 | + | 0.712513i | \(0.252443\pi\) | |||||||
\(674\) | −42.5483 | −1.63890 | ||||||||
\(675\) | 14.8142 | 0.570200 | ||||||||
\(676\) | −1.06704 | −0.0410401 | ||||||||
\(677\) | −0.0296180 | −0.00113831 | −0.000569156 | − | 1.00000i | \(-0.500181\pi\) | ||||
−0.000569156 | 1.00000i | \(0.500181\pi\) | ||||||||
\(678\) | −13.6443 | −0.524005 | ||||||||
\(679\) | 31.4846 | 1.20827 | ||||||||
\(680\) | 2.52105 | 0.0966780 | ||||||||
\(681\) | 15.8210 | 0.606264 | ||||||||
\(682\) | 5.88912 | 0.225506 | ||||||||
\(683\) | −36.6564 | −1.40262 | −0.701309 | − | 0.712858i | \(-0.747401\pi\) | ||||
−0.701309 | + | 0.712858i | \(0.747401\pi\) | |||||||
\(684\) | 39.2455 | 1.50059 | ||||||||
\(685\) | 19.4735 | 0.744045 | ||||||||
\(686\) | 44.0412 | 1.68150 | ||||||||
\(687\) | 2.32968 | 0.0888828 | ||||||||
\(688\) | −0.386967 | −0.0147530 | ||||||||
\(689\) | −29.5006 | −1.12388 | ||||||||
\(690\) | −10.5923 | −0.403241 | ||||||||
\(691\) | 13.4801 | 0.512805 | 0.256403 | − | 0.966570i | \(-0.417463\pi\) | ||||
0.256403 | + | 0.966570i | \(0.417463\pi\) | |||||||
\(692\) | 30.4524 | 1.15763 | ||||||||
\(693\) | −4.65530 | −0.176840 | ||||||||
\(694\) | −44.4470 | −1.68718 | ||||||||
\(695\) | 21.7618 | 0.825474 | ||||||||
\(696\) | −13.6329 | −0.516752 | ||||||||
\(697\) | 1.85905 | 0.0704165 | ||||||||
\(698\) | 48.7775 | 1.84626 | ||||||||
\(699\) | −2.90761 | −0.109976 | ||||||||
\(700\) | −23.1504 | −0.875004 | ||||||||
\(701\) | −15.7723 | −0.595713 | −0.297856 | − | 0.954611i | \(-0.596272\pi\) | ||||
−0.297856 | + | 0.954611i | \(0.596272\pi\) | |||||||
\(702\) | 29.4370 | 1.11103 | ||||||||
\(703\) | 36.6874 | 1.38369 | ||||||||
\(704\) | −13.0353 | −0.491288 | ||||||||
\(705\) | 2.35597 | 0.0887308 | ||||||||
\(706\) | 15.8993 | 0.598378 | ||||||||
\(707\) | −31.6904 | −1.19184 | ||||||||
\(708\) | −9.87636 | −0.371176 | ||||||||
\(709\) | 27.8722 | 1.04676 | 0.523381 | − | 0.852099i | \(-0.324670\pi\) | ||||
0.523381 | + | 0.852099i | \(0.324670\pi\) | |||||||
\(710\) | 31.0385 | 1.16485 | ||||||||
\(711\) | −0.811581 | −0.0304366 | ||||||||
\(712\) | −36.4338 | −1.36542 | ||||||||
\(713\) | 19.1272 | 0.716321 | ||||||||
\(714\) | −2.68777 | −0.100587 | ||||||||
\(715\) | −3.44461 | −0.128821 | ||||||||
\(716\) | −44.4163 | −1.65992 | ||||||||
\(717\) | 7.90525 | 0.295227 | ||||||||
\(718\) | 5.12040 | 0.191092 | ||||||||
\(719\) | 5.58871 | 0.208424 | 0.104212 | − | 0.994555i | \(-0.466768\pi\) | ||||
0.104212 | + | 0.994555i | \(0.466768\pi\) | |||||||
\(720\) | −0.963396 | −0.0359037 | ||||||||
\(721\) | 15.9797 | 0.595116 | ||||||||
\(722\) | −10.2158 | −0.380191 | ||||||||
\(723\) | −8.94194 | −0.332554 | ||||||||
\(724\) | −12.7802 | −0.474972 | ||||||||
\(725\) | −32.4999 | −1.20702 | ||||||||
\(726\) | −1.48481 | −0.0551063 | ||||||||
\(727\) | 30.6023 | 1.13498 | 0.567488 | − | 0.823382i | \(-0.307915\pi\) | ||||
0.567488 | + | 0.823382i | \(0.307915\pi\) | |||||||
\(728\) | −16.7738 | −0.621680 | ||||||||
\(729\) | −6.54607 | −0.242447 | ||||||||
\(730\) | 6.23620 | 0.230812 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 29.1523 | 1.07750 | ||||||||
\(733\) | 34.0003 | 1.25583 | 0.627914 | − | 0.778283i | \(-0.283909\pi\) | ||||
0.627914 | + | 0.778283i | \(0.283909\pi\) | |||||||
\(734\) | 45.0956 | 1.66451 | ||||||||
\(735\) | 2.35877 | 0.0870047 | ||||||||
\(736\) | −44.8511 | −1.65323 | ||||||||
\(737\) | −4.30268 | −0.158491 | ||||||||
\(738\) | 10.8474 | 0.399299 | ||||||||
\(739\) | 40.7938 | 1.50062 | 0.750312 | − | 0.661084i | \(-0.229903\pi\) | ||||
0.750312 | + | 0.661084i | \(0.229903\pi\) | |||||||
\(740\) | 23.0607 | 0.847728 | ||||||||
\(741\) | −11.2889 | −0.414708 | ||||||||
\(742\) | 34.0510 | 1.25005 | ||||||||
\(743\) | −21.7604 | −0.798313 | −0.399157 | − | 0.916883i | \(-0.630697\pi\) | ||||
−0.399157 | + | 0.916883i | \(0.630697\pi\) | |||||||
\(744\) | 4.42359 | 0.162177 | ||||||||
\(745\) | −6.47281 | −0.237145 | ||||||||
\(746\) | 34.9368 | 1.27913 | ||||||||
\(747\) | −24.6491 | −0.901863 | ||||||||
\(748\) | 3.14780 | 0.115095 | ||||||||
\(749\) | 19.8011 | 0.723518 | ||||||||
\(750\) | −13.0269 | −0.475674 | ||||||||
\(751\) | 16.4297 | 0.599528 | 0.299764 | − | 0.954013i | \(-0.403092\pi\) | ||||
0.299764 | + | 0.954013i | \(0.403092\pi\) | |||||||
\(752\) | 1.43905 | 0.0524769 | ||||||||
\(753\) | 10.4576 | 0.381098 | ||||||||
\(754\) | −64.5798 | −2.35186 | ||||||||
\(755\) | 20.4734 | 0.745102 | ||||||||
\(756\) | −20.7768 | −0.755644 | ||||||||
\(757\) | 36.0582 | 1.31056 | 0.655279 | − | 0.755387i | \(-0.272551\pi\) | ||||
0.655279 | + | 0.755387i | \(0.272551\pi\) | |||||||
\(758\) | 77.6984 | 2.82213 | ||||||||
\(759\) | −4.82250 | −0.175046 | ||||||||
\(760\) | −12.2219 | −0.443336 | ||||||||
\(761\) | 19.7761 | 0.716885 | 0.358442 | − | 0.933552i | \(-0.383308\pi\) | ||||
0.358442 | + | 0.933552i | \(0.383308\pi\) | |||||||
\(762\) | −9.53690 | −0.345485 | ||||||||
\(763\) | −26.3462 | −0.953796 | ||||||||
\(764\) | 21.3488 | 0.772372 | ||||||||
\(765\) | 2.48961 | 0.0900120 | ||||||||
\(766\) | −66.8829 | −2.41658 | ||||||||
\(767\) | −17.0595 | −0.615981 | ||||||||
\(768\) | −8.77849 | −0.316766 | ||||||||
\(769\) | −16.3780 | −0.590605 | −0.295302 | − | 0.955404i | \(-0.595420\pi\) | ||||
−0.295302 | + | 0.955404i | \(0.595420\pi\) | |||||||
\(770\) | 3.97593 | 0.143283 | ||||||||
\(771\) | −8.91921 | −0.321218 | ||||||||
\(772\) | −62.9433 | −2.26538 | ||||||||
\(773\) | 2.86226 | 0.102948 | 0.0514742 | − | 0.998674i | \(-0.483608\pi\) | ||||
0.0514742 | + | 0.998674i | \(0.483608\pi\) | |||||||
\(774\) | 5.83493 | 0.209732 | ||||||||
\(775\) | 10.5456 | 0.378808 | ||||||||
\(776\) | −45.2951 | −1.62600 | ||||||||
\(777\) | −8.96481 | −0.321611 | ||||||||
\(778\) | 27.0467 | 0.969672 | ||||||||
\(779\) | −9.01256 | −0.322909 | ||||||||
\(780\) | −7.09588 | −0.254073 | ||||||||
\(781\) | 14.1314 | 0.505660 | ||||||||
\(782\) | 16.7195 | 0.597888 | ||||||||
\(783\) | −29.1676 | −1.04237 | ||||||||
\(784\) | 1.44077 | 0.0514561 | ||||||||
\(785\) | −15.6130 | −0.557250 | ||||||||
\(786\) | −14.8707 | −0.530420 | ||||||||
\(787\) | 47.8343 | 1.70511 | 0.852554 | − | 0.522639i | \(-0.175052\pi\) | ||||
0.852554 | + | 0.522639i | \(0.175052\pi\) | |||||||
\(788\) | 22.7117 | 0.809071 | ||||||||
\(789\) | −18.5779 | −0.661390 | ||||||||
\(790\) | 0.693143 | 0.0246609 | ||||||||
\(791\) | 16.6342 | 0.591446 | ||||||||
\(792\) | 6.69732 | 0.237979 | ||||||||
\(793\) | 50.3548 | 1.78815 | ||||||||
\(794\) | 14.4980 | 0.514515 | ||||||||
\(795\) | 5.25245 | 0.186285 | ||||||||
\(796\) | 70.1178 | 2.48526 | ||||||||
\(797\) | 31.3080 | 1.10899 | 0.554494 | − | 0.832188i | \(-0.312912\pi\) | ||||
0.554494 | + | 0.832188i | \(0.312912\pi\) | |||||||
\(798\) | 13.0302 | 0.461263 | ||||||||
\(799\) | −3.71881 | −0.131562 | ||||||||
\(800\) | −24.7281 | −0.874270 | ||||||||
\(801\) | −35.9794 | −1.27127 | ||||||||
\(802\) | −6.06863 | −0.214291 | ||||||||
\(803\) | 2.83925 | 0.100195 | ||||||||
\(804\) | −8.86349 | −0.312591 | ||||||||
\(805\) | 12.9134 | 0.455138 | ||||||||
\(806\) | 20.9549 | 0.738103 | ||||||||
\(807\) | 14.2688 | 0.502285 | ||||||||
\(808\) | 45.5913 | 1.60389 | ||||||||
\(809\) | −7.12766 | −0.250595 | −0.125298 | − | 0.992119i | \(-0.539989\pi\) | ||||
−0.125298 | + | 0.992119i | \(0.539989\pi\) | |||||||
\(810\) | 11.7047 | 0.411262 | ||||||||
\(811\) | 43.1598 | 1.51555 | 0.757773 | − | 0.652518i | \(-0.226287\pi\) | ||||
0.757773 | + | 0.652518i | \(0.226287\pi\) | |||||||
\(812\) | 45.5807 | 1.59957 | ||||||||
\(813\) | 9.92095 | 0.347943 | ||||||||
\(814\) | 17.1700 | 0.601808 | ||||||||
\(815\) | −12.5841 | −0.440803 | ||||||||
\(816\) | −0.253240 | −0.00886518 | ||||||||
\(817\) | −4.84794 | −0.169608 | ||||||||
\(818\) | −8.51081 | −0.297574 | ||||||||
\(819\) | −16.5646 | −0.578815 | ||||||||
\(820\) | −5.66505 | −0.197832 | ||||||||
\(821\) | 17.8483 | 0.622911 | 0.311456 | − | 0.950261i | \(-0.399184\pi\) | ||||
0.311456 | + | 0.950261i | \(0.399184\pi\) | |||||||
\(822\) | 29.8681 | 1.04177 | ||||||||
\(823\) | −28.9802 | −1.01019 | −0.505094 | − | 0.863065i | \(-0.668542\pi\) | ||||
−0.505094 | + | 0.863065i | \(0.668542\pi\) | |||||||
\(824\) | −22.9891 | −0.800865 | ||||||||
\(825\) | −2.65882 | −0.0925683 | ||||||||
\(826\) | 19.6908 | 0.685131 | ||||||||
\(827\) | 30.6810 | 1.06688 | 0.533441 | − | 0.845838i | \(-0.320899\pi\) | ||||
0.533441 | + | 0.845838i | \(0.320899\pi\) | |||||||
\(828\) | 59.6547 | 2.07314 | ||||||||
\(829\) | 31.1394 | 1.08151 | 0.540757 | − | 0.841179i | \(-0.318138\pi\) | ||||
0.540757 | + | 0.841179i | \(0.318138\pi\) | |||||||
\(830\) | 21.0519 | 0.730724 | ||||||||
\(831\) | 16.3645 | 0.567677 | ||||||||
\(832\) | −46.3828 | −1.60803 | ||||||||
\(833\) | −3.72324 | −0.129003 | ||||||||
\(834\) | 33.3779 | 1.15578 | ||||||||
\(835\) | −24.1323 | −0.835133 | ||||||||
\(836\) | −15.2603 | −0.527790 | ||||||||
\(837\) | 9.46431 | 0.327134 | ||||||||
\(838\) | 60.2726 | 2.08208 | ||||||||
\(839\) | −51.9366 | −1.79305 | −0.896525 | − | 0.442993i | \(-0.853917\pi\) | ||||
−0.896525 | + | 0.442993i | \(0.853917\pi\) | |||||||
\(840\) | 2.98651 | 0.103044 | ||||||||
\(841\) | 34.9888 | 1.20651 | ||||||||
\(842\) | 44.3912 | 1.52982 | ||||||||
\(843\) | 12.5569 | 0.432483 | ||||||||
\(844\) | 56.8676 | 1.95746 | ||||||||
\(845\) | 0.328156 | 0.0112889 | ||||||||
\(846\) | −21.6990 | −0.746027 | ||||||||
\(847\) | 1.81018 | 0.0621986 | ||||||||
\(848\) | 3.20827 | 0.110172 | ||||||||
\(849\) | 8.04769 | 0.276196 | ||||||||
\(850\) | 9.21809 | 0.316178 | ||||||||
\(851\) | 55.7664 | 1.91165 | ||||||||
\(852\) | 29.1105 | 0.997309 | ||||||||
\(853\) | −7.03745 | −0.240958 | −0.120479 | − | 0.992716i | \(-0.538443\pi\) | ||||
−0.120479 | + | 0.992716i | \(0.538443\pi\) | |||||||
\(854\) | −58.1219 | −1.98889 | ||||||||
\(855\) | −12.0695 | −0.412768 | ||||||||
\(856\) | −28.4868 | −0.973659 | ||||||||
\(857\) | 32.9687 | 1.12619 | 0.563094 | − | 0.826393i | \(-0.309611\pi\) | ||||
0.563094 | + | 0.826393i | \(0.309611\pi\) | |||||||
\(858\) | −5.28329 | −0.180368 | ||||||||
\(859\) | −22.6709 | −0.773520 | −0.386760 | − | 0.922180i | \(-0.626406\pi\) | ||||
−0.386760 | + | 0.922180i | \(0.626406\pi\) | |||||||
\(860\) | −3.04728 | −0.103911 | ||||||||
\(861\) | 2.20228 | 0.0750535 | ||||||||
\(862\) | −77.3198 | −2.63352 | ||||||||
\(863\) | −41.5480 | −1.41431 | −0.707155 | − | 0.707058i | \(-0.750022\pi\) | ||||
−0.707155 | + | 0.707058i | \(0.750022\pi\) | |||||||
\(864\) | −22.1927 | −0.755010 | ||||||||
\(865\) | −9.36528 | −0.318429 | ||||||||
\(866\) | 16.7166 | 0.568054 | ||||||||
\(867\) | 0.654424 | 0.0222254 | ||||||||
\(868\) | −14.7900 | −0.502006 | ||||||||
\(869\) | 0.315578 | 0.0107052 | ||||||||
\(870\) | 11.4981 | 0.389824 | ||||||||
\(871\) | −15.3099 | −0.518757 | ||||||||
\(872\) | 37.9028 | 1.28355 | ||||||||
\(873\) | −44.7302 | −1.51389 | ||||||||
\(874\) | −81.0552 | −2.74173 | ||||||||
\(875\) | 15.8815 | 0.536894 | ||||||||
\(876\) | 5.84884 | 0.197614 | ||||||||
\(877\) | 42.8331 | 1.44637 | 0.723185 | − | 0.690655i | \(-0.242678\pi\) | ||||
0.723185 | + | 0.690655i | \(0.242678\pi\) | |||||||
\(878\) | 14.7074 | 0.496352 | ||||||||
\(879\) | 10.2139 | 0.344506 | ||||||||
\(880\) | 0.374610 | 0.0126281 | ||||||||
\(881\) | 28.0970 | 0.946612 | 0.473306 | − | 0.880898i | \(-0.343061\pi\) | ||||
0.473306 | + | 0.880898i | \(0.343061\pi\) | |||||||
\(882\) | −21.7249 | −0.731514 | ||||||||
\(883\) | 29.1559 | 0.981172 | 0.490586 | − | 0.871393i | \(-0.336783\pi\) | ||||
0.490586 | + | 0.871393i | \(0.336783\pi\) | |||||||
\(884\) | 11.2006 | 0.376717 | ||||||||
\(885\) | 3.03736 | 0.102100 | ||||||||
\(886\) | 24.6839 | 0.829271 | ||||||||
\(887\) | −43.5924 | −1.46369 | −0.731845 | − | 0.681471i | \(-0.761341\pi\) | ||||
−0.731845 | + | 0.681471i | \(0.761341\pi\) | |||||||
\(888\) | 12.8972 | 0.432801 | ||||||||
\(889\) | 11.6268 | 0.389950 | ||||||||
\(890\) | 30.7288 | 1.03003 | ||||||||
\(891\) | 5.32898 | 0.178528 | ||||||||
\(892\) | −42.9838 | −1.43920 | ||||||||
\(893\) | 18.0286 | 0.603303 | ||||||||
\(894\) | −9.92789 | −0.332038 | ||||||||
\(895\) | 13.6597 | 0.456594 | ||||||||
\(896\) | 31.5022 | 1.05242 | ||||||||
\(897\) | −17.1596 | −0.572941 | ||||||||
\(898\) | 45.5280 | 1.51929 | ||||||||
\(899\) | −20.7631 | −0.692487 | ||||||||
\(900\) | 32.8899 | 1.09633 | ||||||||
\(901\) | −8.29080 | −0.276207 | ||||||||
\(902\) | −4.21795 | −0.140442 | ||||||||
\(903\) | 1.18463 | 0.0394219 | ||||||||
\(904\) | −23.9308 | −0.795926 | ||||||||
\(905\) | 3.93040 | 0.130651 | ||||||||
\(906\) | 31.4017 | 1.04325 | ||||||||
\(907\) | −16.2688 | −0.540195 | −0.270098 | − | 0.962833i | \(-0.587056\pi\) | ||||
−0.270098 | + | 0.962833i | \(0.587056\pi\) | |||||||
\(908\) | 76.0996 | 2.52546 | ||||||||
\(909\) | 45.0226 | 1.49331 | ||||||||
\(910\) | 14.1473 | 0.468978 | ||||||||
\(911\) | −11.0011 | −0.364484 | −0.182242 | − | 0.983254i | \(-0.558335\pi\) | ||||
−0.182242 | + | 0.983254i | \(0.558335\pi\) | |||||||
\(912\) | 1.22769 | 0.0406530 | ||||||||
\(913\) | 9.58463 | 0.317205 | ||||||||
\(914\) | −6.24952 | −0.206716 | ||||||||
\(915\) | −8.96544 | −0.296388 | ||||||||
\(916\) | 11.2058 | 0.370251 | ||||||||
\(917\) | 18.1294 | 0.598686 | ||||||||
\(918\) | 8.27294 | 0.273048 | ||||||||
\(919\) | 11.3109 | 0.373111 | 0.186556 | − | 0.982444i | \(-0.440268\pi\) | ||||
0.186556 | + | 0.982444i | \(0.440268\pi\) | |||||||
\(920\) | −18.5778 | −0.612493 | ||||||||
\(921\) | −5.90527 | −0.194585 | ||||||||
\(922\) | −40.5451 | −1.33528 | ||||||||
\(923\) | 50.2826 | 1.65507 | ||||||||
\(924\) | 3.72896 | 0.122674 | ||||||||
\(925\) | 30.7461 | 1.01093 | ||||||||
\(926\) | 35.2770 | 1.15927 | ||||||||
\(927\) | −22.7024 | −0.745645 | ||||||||
\(928\) | 48.6869 | 1.59823 | ||||||||
\(929\) | 51.7569 | 1.69809 | 0.849044 | − | 0.528322i | \(-0.177179\pi\) | ||||
0.849044 | + | 0.528322i | \(0.177179\pi\) | |||||||
\(930\) | −3.73092 | −0.122342 | ||||||||
\(931\) | 18.0501 | 0.591567 | ||||||||
\(932\) | −13.9857 | −0.458117 | ||||||||
\(933\) | 5.55458 | 0.181849 | ||||||||
\(934\) | 20.1116 | 0.658072 | ||||||||
\(935\) | −0.968068 | −0.0316592 | ||||||||
\(936\) | 23.8306 | 0.778928 | ||||||||
\(937\) | 13.0178 | 0.425272 | 0.212636 | − | 0.977132i | \(-0.431795\pi\) | ||||
0.212636 | + | 0.977132i | \(0.431795\pi\) | |||||||
\(938\) | 17.6714 | 0.576993 | ||||||||
\(939\) | 6.80231 | 0.221985 | ||||||||
\(940\) | 11.3323 | 0.369618 | ||||||||
\(941\) | −27.7311 | −0.904009 | −0.452004 | − | 0.892016i | \(-0.649291\pi\) | ||||
−0.452004 | + | 0.892016i | \(0.649291\pi\) | |||||||
\(942\) | −23.9469 | −0.780231 | ||||||||
\(943\) | −13.6995 | −0.446116 | ||||||||
\(944\) | 1.85526 | 0.0603835 | ||||||||
\(945\) | 6.38966 | 0.207856 | ||||||||
\(946\) | −2.26888 | −0.0737675 | ||||||||
\(947\) | 12.6634 | 0.411504 | 0.205752 | − | 0.978604i | \(-0.434036\pi\) | ||||
0.205752 | + | 0.978604i | \(0.434036\pi\) | |||||||
\(948\) | 0.650088 | 0.0211139 | ||||||||
\(949\) | 10.1027 | 0.327948 | ||||||||
\(950\) | −44.6888 | −1.44990 | ||||||||
\(951\) | −20.8189 | −0.675098 | ||||||||
\(952\) | −4.71409 | −0.152785 | ||||||||
\(953\) | 53.2090 | 1.72361 | 0.861805 | − | 0.507240i | \(-0.169334\pi\) | ||||
0.861805 | + | 0.507240i | \(0.169334\pi\) | |||||||
\(954\) | −48.3763 | −1.56624 | ||||||||
\(955\) | −6.56557 | −0.212457 | ||||||||
\(956\) | 38.0245 | 1.22980 | ||||||||
\(957\) | 5.23493 | 0.169221 | ||||||||
\(958\) | −89.4038 | −2.88851 | ||||||||
\(959\) | −36.4134 | −1.17585 | ||||||||
\(960\) | 8.25825 | 0.266534 | ||||||||
\(961\) | −24.2628 | −0.782671 | ||||||||
\(962\) | 61.0949 | 1.96978 | ||||||||
\(963\) | −28.1315 | −0.906525 | ||||||||
\(964\) | −43.0110 | −1.38529 | ||||||||
\(965\) | 19.3575 | 0.623139 | ||||||||
\(966\) | 19.8064 | 0.637260 | ||||||||
\(967\) | −28.9666 | −0.931502 | −0.465751 | − | 0.884916i | \(-0.654216\pi\) | ||||
−0.465751 | + | 0.884916i | \(0.654216\pi\) | |||||||
\(968\) | −2.60421 | −0.0837025 | ||||||||
\(969\) | −3.17261 | −0.101919 | ||||||||
\(970\) | 38.2025 | 1.22661 | ||||||||
\(971\) | 3.85560 | 0.123732 | 0.0618661 | − | 0.998084i | \(-0.480295\pi\) | ||||
0.0618661 | + | 0.998084i | \(0.480295\pi\) | |||||||
\(972\) | 45.4108 | 1.45655 | ||||||||
\(973\) | −40.6923 | −1.30453 | ||||||||
\(974\) | −59.7166 | −1.91344 | ||||||||
\(975\) | −9.46071 | −0.302985 | ||||||||
\(976\) | −5.47621 | −0.175289 | ||||||||
\(977\) | −54.2208 | −1.73468 | −0.867339 | − | 0.497719i | \(-0.834171\pi\) | ||||
−0.867339 | + | 0.497719i | \(0.834171\pi\) | |||||||
\(978\) | −19.3013 | −0.617188 | ||||||||
\(979\) | 13.9904 | 0.447134 | ||||||||
\(980\) | 11.3458 | 0.362427 | ||||||||
\(981\) | 37.4301 | 1.19505 | ||||||||
\(982\) | −23.8501 | −0.761087 | ||||||||
\(983\) | −22.7208 | −0.724680 | −0.362340 | − | 0.932046i | \(-0.618022\pi\) | ||||
−0.362340 | + | 0.932046i | \(0.618022\pi\) | |||||||
\(984\) | −3.16830 | −0.101002 | ||||||||
\(985\) | −6.98472 | −0.222552 | ||||||||
\(986\) | −18.1494 | −0.577995 | ||||||||
\(987\) | −4.40540 | −0.140225 | ||||||||
\(988\) | −54.2999 | −1.72751 | ||||||||
\(989\) | −7.36907 | −0.234323 | ||||||||
\(990\) | −5.64862 | −0.179525 | ||||||||
\(991\) | −12.2064 | −0.387750 | −0.193875 | − | 0.981026i | \(-0.562106\pi\) | ||||
−0.193875 | + | 0.981026i | \(0.562106\pi\) | |||||||
\(992\) | −15.7979 | −0.501585 | ||||||||
\(993\) | 2.75019 | 0.0872746 | ||||||||
\(994\) | −58.0386 | −1.84087 | ||||||||
\(995\) | −21.5639 | −0.683622 | ||||||||
\(996\) | 19.7443 | 0.625622 | ||||||||
\(997\) | 15.7306 | 0.498192 | 0.249096 | − | 0.968479i | \(-0.419866\pi\) | ||||
0.249096 | + | 0.968479i | \(0.419866\pi\) | |||||||
\(998\) | −61.9902 | −1.96226 | ||||||||
\(999\) | 27.5936 | 0.873024 |
(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.j.1.11 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.j.1.11 | ✓ | 82 | 1.1 | even | 1 | trivial |