Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [538,2,Mod(1,538)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(538, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("538.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 538 = 2 \cdot 269 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 538.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: | \(4.29595162874\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4913.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.344151\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 538.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.34415 | 0.776046 | 0.388023 | − | 0.921650i | \(-0.373158\pi\) | ||||
0.388023 | + | 0.921650i | \(0.373158\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.90570 | 1.74668 | 0.873342 | − | 0.487108i | \(-0.161948\pi\) | ||||
0.873342 | + | 0.487108i | \(0.161948\pi\) | |||||||
\(6\) | −1.34415 | −0.548747 | ||||||||
\(7\) | −0.487928 | −0.184420 | −0.0922098 | − | 0.995740i | \(-0.529393\pi\) | ||||
−0.0922098 | + | 0.995740i | \(0.529393\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.19326 | −0.397753 | ||||||||
\(10\) | −3.90570 | −1.23509 | ||||||||
\(11\) | 4.04948 | 1.22096 | 0.610482 | − | 0.792030i | \(-0.290976\pi\) | ||||
0.610482 | + | 0.792030i | \(0.290976\pi\) | |||||||
\(12\) | 1.34415 | 0.388023 | ||||||||
\(13\) | 3.53741 | 0.981101 | 0.490550 | − | 0.871413i | \(-0.336796\pi\) | ||||
0.490550 | + | 0.871413i | \(0.336796\pi\) | |||||||
\(14\) | 0.487928 | 0.130404 | ||||||||
\(15\) | 5.24985 | 1.35551 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.37296 | −1.54567 | −0.772835 | − | 0.634607i | \(-0.781162\pi\) | ||||
−0.772835 | + | 0.634607i | \(0.781162\pi\) | |||||||
\(18\) | 1.19326 | 0.281254 | ||||||||
\(19\) | 0.975857 | 0.223877 | 0.111938 | − | 0.993715i | \(-0.464294\pi\) | ||||
0.111938 | + | 0.993715i | \(0.464294\pi\) | |||||||
\(20\) | 3.90570 | 0.873342 | ||||||||
\(21\) | −0.655849 | −0.143118 | ||||||||
\(22\) | −4.04948 | −0.863352 | ||||||||
\(23\) | 0.750146 | 0.156416 | 0.0782081 | − | 0.996937i | \(-0.475080\pi\) | ||||
0.0782081 | + | 0.996937i | \(0.475080\pi\) | |||||||
\(24\) | −1.34415 | −0.274374 | ||||||||
\(25\) | 10.2545 | 2.05090 | ||||||||
\(26\) | −3.53741 | −0.693743 | ||||||||
\(27\) | −5.63637 | −1.08472 | ||||||||
\(28\) | −0.487928 | −0.0922098 | ||||||||
\(29\) | −4.08193 | −0.757996 | −0.378998 | − | 0.925397i | \(-0.623731\pi\) | ||||
−0.378998 | + | 0.925397i | \(0.623731\pi\) | |||||||
\(30\) | −5.24985 | −0.958488 | ||||||||
\(31\) | −7.86089 | −1.41186 | −0.705929 | − | 0.708283i | \(-0.749470\pi\) | ||||
−0.705929 | + | 0.708283i | \(0.749470\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.44311 | 0.947524 | ||||||||
\(34\) | 6.37296 | 1.09295 | ||||||||
\(35\) | −1.90570 | −0.322123 | ||||||||
\(36\) | −1.19326 | −0.198876 | ||||||||
\(37\) | −4.22571 | −0.694703 | −0.347351 | − | 0.937735i | \(-0.612919\pi\) | ||||
−0.347351 | + | 0.937735i | \(0.612919\pi\) | |||||||
\(38\) | −0.975857 | −0.158305 | ||||||||
\(39\) | 4.75481 | 0.761379 | ||||||||
\(40\) | −3.90570 | −0.617546 | ||||||||
\(41\) | −2.07362 | −0.323846 | −0.161923 | − | 0.986803i | \(-0.551770\pi\) | ||||
−0.161923 | + | 0.986803i | \(0.551770\pi\) | |||||||
\(42\) | 0.655849 | 0.101200 | ||||||||
\(43\) | 10.7341 | 1.63694 | 0.818470 | − | 0.574549i | \(-0.194822\pi\) | ||||
0.818470 | + | 0.574549i | \(0.194822\pi\) | |||||||
\(44\) | 4.04948 | 0.610482 | ||||||||
\(45\) | −4.66052 | −0.694749 | ||||||||
\(46\) | −0.750146 | −0.110603 | ||||||||
\(47\) | 9.31636 | 1.35893 | 0.679466 | − | 0.733707i | \(-0.262212\pi\) | ||||
0.679466 | + | 0.733707i | \(0.262212\pi\) | |||||||
\(48\) | 1.34415 | 0.194011 | ||||||||
\(49\) | −6.76193 | −0.965989 | ||||||||
\(50\) | −10.2545 | −1.45021 | ||||||||
\(51\) | −8.56622 | −1.19951 | ||||||||
\(52\) | 3.53741 | 0.490550 | ||||||||
\(53\) | 11.1231 | 1.52788 | 0.763938 | − | 0.645290i | \(-0.223263\pi\) | ||||
0.763938 | + | 0.645290i | \(0.223263\pi\) | |||||||
\(54\) | 5.63637 | 0.767013 | ||||||||
\(55\) | 15.8161 | 2.13264 | ||||||||
\(56\) | 0.487928 | 0.0652022 | ||||||||
\(57\) | 1.31170 | 0.173739 | ||||||||
\(58\) | 4.08193 | 0.535984 | ||||||||
\(59\) | −2.98052 | −0.388031 | −0.194015 | − | 0.980998i | \(-0.562151\pi\) | ||||
−0.194015 | + | 0.980998i | \(0.562151\pi\) | |||||||
\(60\) | 5.24985 | 0.677753 | ||||||||
\(61\) | −7.53741 | −0.965066 | −0.482533 | − | 0.875878i | \(-0.660283\pi\) | ||||
−0.482533 | + | 0.875878i | \(0.660283\pi\) | |||||||
\(62\) | 7.86089 | 0.998334 | ||||||||
\(63\) | 0.582225 | 0.0733534 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 13.8161 | 1.71367 | ||||||||
\(66\) | −5.44311 | −0.670001 | ||||||||
\(67\) | 3.51207 | 0.429068 | 0.214534 | − | 0.976717i | \(-0.431177\pi\) | ||||
0.214534 | + | 0.976717i | \(0.431177\pi\) | |||||||
\(68\) | −6.37296 | −0.772835 | ||||||||
\(69\) | 1.00831 | 0.121386 | ||||||||
\(70\) | 1.90570 | 0.227775 | ||||||||
\(71\) | 14.1349 | 1.67750 | 0.838751 | − | 0.544515i | \(-0.183286\pi\) | ||||
0.838751 | + | 0.544515i | \(0.183286\pi\) | |||||||
\(72\) | 1.19326 | 0.140627 | ||||||||
\(73\) | −9.75828 | −1.14212 | −0.571060 | − | 0.820908i | \(-0.693468\pi\) | ||||
−0.571060 | + | 0.820908i | \(0.693468\pi\) | |||||||
\(74\) | 4.22571 | 0.491229 | ||||||||
\(75\) | 13.7836 | 1.59160 | ||||||||
\(76\) | 0.975857 | 0.111938 | ||||||||
\(77\) | −1.97586 | −0.225170 | ||||||||
\(78\) | −4.75481 | −0.538376 | ||||||||
\(79\) | 2.29222 | 0.257895 | 0.128948 | − | 0.991651i | \(-0.458840\pi\) | ||||
0.128948 | + | 0.991651i | \(0.458840\pi\) | |||||||
\(80\) | 3.90570 | 0.436671 | ||||||||
\(81\) | −3.99636 | −0.444040 | ||||||||
\(82\) | 2.07362 | 0.228994 | ||||||||
\(83\) | −17.1324 | −1.88053 | −0.940265 | − | 0.340444i | \(-0.889422\pi\) | ||||
−0.940265 | + | 0.340444i | \(0.889422\pi\) | |||||||
\(84\) | −0.655849 | −0.0715590 | ||||||||
\(85\) | −24.8909 | −2.69980 | ||||||||
\(86\) | −10.7341 | −1.15749 | ||||||||
\(87\) | −5.48673 | −0.588240 | ||||||||
\(88\) | −4.04948 | −0.431676 | ||||||||
\(89\) | 1.86978 | 0.198196 | 0.0990981 | − | 0.995078i | \(-0.468404\pi\) | ||||
0.0990981 | + | 0.995078i | \(0.468404\pi\) | |||||||
\(90\) | 4.66052 | 0.491261 | ||||||||
\(91\) | −1.72600 | −0.180934 | ||||||||
\(92\) | 0.750146 | 0.0782081 | ||||||||
\(93\) | −10.5662 | −1.09567 | ||||||||
\(94\) | −9.31636 | −0.960910 | ||||||||
\(95\) | 3.81141 | 0.391042 | ||||||||
\(96\) | −1.34415 | −0.137187 | ||||||||
\(97\) | −9.63757 | −0.978547 | −0.489273 | − | 0.872131i | \(-0.662738\pi\) | ||||
−0.489273 | + | 0.872131i | \(0.662738\pi\) | |||||||
\(98\) | 6.76193 | 0.683058 | ||||||||
\(99\) | −4.83208 | −0.485642 | ||||||||
\(100\) | 10.2545 | 1.02545 | ||||||||
\(101\) | 5.91748 | 0.588812 | 0.294406 | − | 0.955680i | \(-0.404878\pi\) | ||||
0.294406 | + | 0.955680i | \(0.404878\pi\) | |||||||
\(102\) | 8.56622 | 0.848182 | ||||||||
\(103\) | 0.480814 | 0.0473760 | 0.0236880 | − | 0.999719i | \(-0.492459\pi\) | ||||
0.0236880 | + | 0.999719i | \(0.492459\pi\) | |||||||
\(104\) | −3.53741 | −0.346872 | ||||||||
\(105\) | −2.56155 | −0.249982 | ||||||||
\(106\) | −11.1231 | −1.08037 | ||||||||
\(107\) | 3.82496 | 0.369773 | 0.184887 | − | 0.982760i | \(-0.440808\pi\) | ||||
0.184887 | + | 0.982760i | \(0.440808\pi\) | |||||||
\(108\) | −5.63637 | −0.542360 | ||||||||
\(109\) | −17.0866 | −1.63660 | −0.818300 | − | 0.574792i | \(-0.805083\pi\) | ||||
−0.818300 | + | 0.574792i | \(0.805083\pi\) | |||||||
\(110\) | −15.8161 | −1.50800 | ||||||||
\(111\) | −5.67999 | −0.539121 | ||||||||
\(112\) | −0.487928 | −0.0461049 | ||||||||
\(113\) | 13.3194 | 1.25299 | 0.626493 | − | 0.779427i | \(-0.284490\pi\) | ||||
0.626493 | + | 0.779427i | \(0.284490\pi\) | |||||||
\(114\) | −1.31170 | −0.122852 | ||||||||
\(115\) | 2.92985 | 0.273210 | ||||||||
\(116\) | −4.08193 | −0.378998 | ||||||||
\(117\) | −4.22105 | −0.390236 | ||||||||
\(118\) | 2.98052 | 0.274379 | ||||||||
\(119\) | 3.10955 | 0.285052 | ||||||||
\(120\) | −5.24985 | −0.479244 | ||||||||
\(121\) | 5.39830 | 0.490754 | ||||||||
\(122\) | 7.53741 | 0.682405 | ||||||||
\(123\) | −2.78726 | −0.251319 | ||||||||
\(124\) | −7.86089 | −0.705929 | ||||||||
\(125\) | 20.5226 | 1.83560 | ||||||||
\(126\) | −0.582225 | −0.0518687 | ||||||||
\(127\) | 3.18962 | 0.283033 | 0.141516 | − | 0.989936i | \(-0.454802\pi\) | ||||
0.141516 | + | 0.989936i | \(0.454802\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 14.4283 | 1.27034 | ||||||||
\(130\) | −13.8161 | −1.21175 | ||||||||
\(131\) | −11.5975 | −1.01328 | −0.506638 | − | 0.862159i | \(-0.669112\pi\) | ||||
−0.506638 | + | 0.862159i | \(0.669112\pi\) | |||||||
\(132\) | 5.44311 | 0.473762 | ||||||||
\(133\) | −0.476148 | −0.0412873 | ||||||||
\(134\) | −3.51207 | −0.303397 | ||||||||
\(135\) | −22.0140 | −1.89466 | ||||||||
\(136\) | 6.37296 | 0.546477 | ||||||||
\(137\) | −7.33059 | −0.626295 | −0.313147 | − | 0.949705i | \(-0.601383\pi\) | ||||
−0.313147 | + | 0.949705i | \(0.601383\pi\) | |||||||
\(138\) | −1.00831 | −0.0858330 | ||||||||
\(139\) | −13.1927 | −1.11899 | −0.559494 | − | 0.828834i | \(-0.689005\pi\) | ||||
−0.559494 | + | 0.828834i | \(0.689005\pi\) | |||||||
\(140\) | −1.90570 | −0.161061 | ||||||||
\(141\) | 12.5226 | 1.05459 | ||||||||
\(142\) | −14.1349 | −1.18617 | ||||||||
\(143\) | 14.3247 | 1.19789 | ||||||||
\(144\) | −1.19326 | −0.0994382 | ||||||||
\(145\) | −15.9428 | −1.32398 | ||||||||
\(146\) | 9.75828 | 0.807601 | ||||||||
\(147\) | −9.08905 | −0.749652 | ||||||||
\(148\) | −4.22571 | −0.347351 | ||||||||
\(149\) | 19.2132 | 1.57400 | 0.787002 | − | 0.616950i | \(-0.211632\pi\) | ||||
0.787002 | + | 0.616950i | \(0.211632\pi\) | |||||||
\(150\) | −13.7836 | −1.12543 | ||||||||
\(151\) | −3.63637 | −0.295924 | −0.147962 | − | 0.988993i | \(-0.547271\pi\) | ||||
−0.147962 | + | 0.988993i | \(0.547271\pi\) | |||||||
\(152\) | −0.975857 | −0.0791524 | ||||||||
\(153\) | 7.60459 | 0.614795 | ||||||||
\(154\) | 1.97586 | 0.159219 | ||||||||
\(155\) | −30.7023 | −2.46607 | ||||||||
\(156\) | 4.75481 | 0.380690 | ||||||||
\(157\) | −15.0118 | −1.19807 | −0.599035 | − | 0.800723i | \(-0.704449\pi\) | ||||
−0.599035 | + | 0.800723i | \(0.704449\pi\) | |||||||
\(158\) | −2.29222 | −0.182359 | ||||||||
\(159\) | 14.9511 | 1.18570 | ||||||||
\(160\) | −3.90570 | −0.308773 | ||||||||
\(161\) | −0.366017 | −0.0288462 | ||||||||
\(162\) | 3.99636 | 0.313983 | ||||||||
\(163\) | −4.77531 | −0.374031 | −0.187016 | − | 0.982357i | \(-0.559882\pi\) | ||||
−0.187016 | + | 0.982357i | \(0.559882\pi\) | |||||||
\(164\) | −2.07362 | −0.161923 | ||||||||
\(165\) | 21.2592 | 1.65503 | ||||||||
\(166\) | 17.1324 | 1.32974 | ||||||||
\(167\) | −3.94163 | −0.305012 | −0.152506 | − | 0.988303i | \(-0.548734\pi\) | ||||
−0.152506 | + | 0.988303i | \(0.548734\pi\) | |||||||
\(168\) | 0.655849 | 0.0505999 | ||||||||
\(169\) | −0.486734 | −0.0374411 | ||||||||
\(170\) | 24.8909 | 1.90904 | ||||||||
\(171\) | −1.16445 | −0.0890477 | ||||||||
\(172\) | 10.7341 | 0.818470 | ||||||||
\(173\) | −24.0607 | −1.82930 | −0.914650 | − | 0.404247i | \(-0.867534\pi\) | ||||
−0.914650 | + | 0.404247i | \(0.867534\pi\) | |||||||
\(174\) | 5.48673 | 0.415948 | ||||||||
\(175\) | −5.00347 | −0.378227 | ||||||||
\(176\) | 4.04948 | 0.305241 | ||||||||
\(177\) | −4.00627 | −0.301130 | ||||||||
\(178\) | −1.86978 | −0.140146 | ||||||||
\(179\) | 17.1745 | 1.28368 | 0.641839 | − | 0.766839i | \(-0.278172\pi\) | ||||
0.641839 | + | 0.766839i | \(0.278172\pi\) | |||||||
\(180\) | −4.66052 | −0.347374 | ||||||||
\(181\) | −7.28875 | −0.541769 | −0.270884 | − | 0.962612i | \(-0.587316\pi\) | ||||
−0.270884 | + | 0.962612i | \(0.587316\pi\) | |||||||
\(182\) | 1.72600 | 0.127940 | ||||||||
\(183\) | −10.1314 | −0.748936 | ||||||||
\(184\) | −0.750146 | −0.0553015 | ||||||||
\(185\) | −16.5044 | −1.21343 | ||||||||
\(186\) | 10.5662 | 0.774753 | ||||||||
\(187\) | −25.8072 | −1.88721 | ||||||||
\(188\) | 9.31636 | 0.679466 | ||||||||
\(189\) | 2.75015 | 0.200044 | ||||||||
\(190\) | −3.81141 | −0.276509 | ||||||||
\(191\) | −6.55038 | −0.473969 | −0.236985 | − | 0.971513i | \(-0.576159\pi\) | ||||
−0.236985 | + | 0.971513i | \(0.576159\pi\) | |||||||
\(192\) | 1.34415 | 0.0970057 | ||||||||
\(193\) | 17.5467 | 1.26304 | 0.631521 | − | 0.775359i | \(-0.282431\pi\) | ||||
0.631521 | + | 0.775359i | \(0.282431\pi\) | |||||||
\(194\) | 9.63757 | 0.691937 | ||||||||
\(195\) | 18.5709 | 1.32989 | ||||||||
\(196\) | −6.76193 | −0.482995 | ||||||||
\(197\) | −14.6051 | −1.04057 | −0.520286 | − | 0.853992i | \(-0.674175\pi\) | ||||
−0.520286 | + | 0.853992i | \(0.674175\pi\) | |||||||
\(198\) | 4.83208 | 0.343401 | ||||||||
\(199\) | −4.64162 | −0.329036 | −0.164518 | − | 0.986374i | \(-0.552607\pi\) | ||||
−0.164518 | + | 0.986374i | \(0.552607\pi\) | |||||||
\(200\) | −10.2545 | −0.725104 | ||||||||
\(201\) | 4.72075 | 0.332976 | ||||||||
\(202\) | −5.91748 | −0.416353 | ||||||||
\(203\) | 1.99169 | 0.139789 | ||||||||
\(204\) | −8.56622 | −0.599755 | ||||||||
\(205\) | −8.09896 | −0.565656 | ||||||||
\(206\) | −0.480814 | −0.0334999 | ||||||||
\(207\) | −0.895118 | −0.0622150 | ||||||||
\(208\) | 3.53741 | 0.245275 | ||||||||
\(209\) | 3.95171 | 0.273346 | ||||||||
\(210\) | 2.56155 | 0.176764 | ||||||||
\(211\) | 15.7554 | 1.08465 | 0.542324 | − | 0.840169i | \(-0.317545\pi\) | ||||
0.542324 | + | 0.840169i | \(0.317545\pi\) | |||||||
\(212\) | 11.1231 | 0.763938 | ||||||||
\(213\) | 18.9994 | 1.30182 | ||||||||
\(214\) | −3.82496 | −0.261469 | ||||||||
\(215\) | 41.9244 | 2.85922 | ||||||||
\(216\) | 5.63637 | 0.383507 | ||||||||
\(217\) | 3.83555 | 0.260374 | ||||||||
\(218\) | 17.0866 | 1.15725 | ||||||||
\(219\) | −13.1166 | −0.886338 | ||||||||
\(220\) | 15.8161 | 1.06632 | ||||||||
\(221\) | −22.5438 | −1.51646 | ||||||||
\(222\) | 5.67999 | 0.381216 | ||||||||
\(223\) | 19.8791 | 1.33120 | 0.665602 | − | 0.746307i | \(-0.268175\pi\) | ||||
0.665602 | + | 0.746307i | \(0.268175\pi\) | |||||||
\(224\) | 0.487928 | 0.0326011 | ||||||||
\(225\) | −12.2363 | −0.815753 | ||||||||
\(226\) | −13.3194 | −0.885995 | ||||||||
\(227\) | 27.7566 | 1.84227 | 0.921136 | − | 0.389242i | \(-0.127263\pi\) | ||||
0.921136 | + | 0.389242i | \(0.127263\pi\) | |||||||
\(228\) | 1.31170 | 0.0868694 | ||||||||
\(229\) | −17.6723 | −1.16782 | −0.583909 | − | 0.811819i | \(-0.698478\pi\) | ||||
−0.583909 | + | 0.811819i | \(0.698478\pi\) | |||||||
\(230\) | −2.92985 | −0.193188 | ||||||||
\(231\) | −2.65585 | −0.174742 | ||||||||
\(232\) | 4.08193 | 0.267992 | ||||||||
\(233\) | −1.67230 | −0.109556 | −0.0547779 | − | 0.998499i | \(-0.517445\pi\) | ||||
−0.0547779 | + | 0.998499i | \(0.517445\pi\) | |||||||
\(234\) | 4.22105 | 0.275938 | ||||||||
\(235\) | 36.3870 | 2.37362 | ||||||||
\(236\) | −2.98052 | −0.194015 | ||||||||
\(237\) | 3.08109 | 0.200138 | ||||||||
\(238\) | −3.10955 | −0.201562 | ||||||||
\(239\) | −24.0925 | −1.55841 | −0.779206 | − | 0.626768i | \(-0.784377\pi\) | ||||
−0.779206 | + | 0.626768i | \(0.784377\pi\) | |||||||
\(240\) | 5.24985 | 0.338877 | ||||||||
\(241\) | −18.2257 | −1.17402 | −0.587011 | − | 0.809579i | \(-0.699695\pi\) | ||||
−0.587011 | + | 0.809579i | \(0.699695\pi\) | |||||||
\(242\) | −5.39830 | −0.347016 | ||||||||
\(243\) | 11.5374 | 0.740125 | ||||||||
\(244\) | −7.53741 | −0.482533 | ||||||||
\(245\) | −26.4101 | −1.68728 | ||||||||
\(246\) | 2.78726 | 0.177709 | ||||||||
\(247\) | 3.45200 | 0.219646 | ||||||||
\(248\) | 7.86089 | 0.499167 | ||||||||
\(249\) | −23.0286 | −1.45938 | ||||||||
\(250\) | −20.5226 | −1.29796 | ||||||||
\(251\) | −1.21740 | −0.0768417 | −0.0384209 | − | 0.999262i | \(-0.512233\pi\) | ||||
−0.0384209 | + | 0.999262i | \(0.512233\pi\) | |||||||
\(252\) | 0.582225 | 0.0366767 | ||||||||
\(253\) | 3.03770 | 0.190979 | ||||||||
\(254\) | −3.18962 | −0.200134 | ||||||||
\(255\) | −33.4571 | −2.09517 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 28.7806 | 1.79529 | 0.897644 | − | 0.440722i | \(-0.145277\pi\) | ||||
0.897644 | + | 0.440722i | \(0.145277\pi\) | |||||||
\(258\) | −14.4283 | −0.898267 | ||||||||
\(259\) | 2.06184 | 0.128117 | ||||||||
\(260\) | 13.8161 | 0.856836 | ||||||||
\(261\) | 4.87080 | 0.301495 | ||||||||
\(262\) | 11.5975 | 0.716494 | ||||||||
\(263\) | −4.35407 | −0.268483 | −0.134242 | − | 0.990949i | \(-0.542860\pi\) | ||||
−0.134242 | + | 0.990949i | \(0.542860\pi\) | |||||||
\(264\) | −5.44311 | −0.335000 | ||||||||
\(265\) | 43.4436 | 2.66872 | ||||||||
\(266\) | 0.476148 | 0.0291945 | ||||||||
\(267\) | 2.51327 | 0.153809 | ||||||||
\(268\) | 3.51207 | 0.214534 | ||||||||
\(269\) | 1.00000 | 0.0609711 | ||||||||
\(270\) | 22.0140 | 1.33973 | ||||||||
\(271\) | −19.6940 | −1.19632 | −0.598162 | − | 0.801375i | \(-0.704102\pi\) | ||||
−0.598162 | + | 0.801375i | \(0.704102\pi\) | |||||||
\(272\) | −6.37296 | −0.386417 | ||||||||
\(273\) | −2.32001 | −0.140413 | ||||||||
\(274\) | 7.33059 | 0.442857 | ||||||||
\(275\) | 41.5255 | 2.50408 | ||||||||
\(276\) | 1.00831 | 0.0606931 | ||||||||
\(277\) | −1.31009 | −0.0787158 | −0.0393579 | − | 0.999225i | \(-0.512531\pi\) | ||||
−0.0393579 | + | 0.999225i | \(0.512531\pi\) | |||||||
\(278\) | 13.1927 | 0.791244 | ||||||||
\(279\) | 9.38007 | 0.561570 | ||||||||
\(280\) | 1.90570 | 0.113888 | ||||||||
\(281\) | 7.94749 | 0.474107 | 0.237054 | − | 0.971497i | \(-0.423818\pi\) | ||||
0.237054 | + | 0.971497i | \(0.423818\pi\) | |||||||
\(282\) | −12.5226 | −0.745710 | ||||||||
\(283\) | 20.7544 | 1.23372 | 0.616861 | − | 0.787072i | \(-0.288404\pi\) | ||||
0.616861 | + | 0.787072i | \(0.288404\pi\) | |||||||
\(284\) | 14.1349 | 0.838751 | ||||||||
\(285\) | 5.12311 | 0.303467 | ||||||||
\(286\) | −14.3247 | −0.847036 | ||||||||
\(287\) | 1.01178 | 0.0597235 | ||||||||
\(288\) | 1.19326 | 0.0703134 | ||||||||
\(289\) | 23.6146 | 1.38910 | ||||||||
\(290\) | 15.9428 | 0.936195 | ||||||||
\(291\) | −12.9543 | −0.759397 | ||||||||
\(292\) | −9.75828 | −0.571060 | ||||||||
\(293\) | −10.9994 | −0.642593 | −0.321296 | − | 0.946979i | \(-0.604119\pi\) | ||||
−0.321296 | + | 0.946979i | \(0.604119\pi\) | |||||||
\(294\) | 9.08905 | 0.530084 | ||||||||
\(295\) | −11.6410 | −0.677767 | ||||||||
\(296\) | 4.22571 | 0.245614 | ||||||||
\(297\) | −22.8244 | −1.32440 | ||||||||
\(298\) | −19.2132 | −1.11299 | ||||||||
\(299\) | 2.65357 | 0.153460 | ||||||||
\(300\) | 13.7836 | 0.795798 | ||||||||
\(301\) | −5.23749 | −0.301884 | ||||||||
\(302\) | 3.63637 | 0.209250 | ||||||||
\(303\) | 7.95399 | 0.456945 | ||||||||
\(304\) | 0.975857 | 0.0559692 | ||||||||
\(305\) | −29.4389 | −1.68567 | ||||||||
\(306\) | −7.60459 | −0.434726 | ||||||||
\(307\) | 15.1961 | 0.867290 | 0.433645 | − | 0.901084i | \(-0.357227\pi\) | ||||
0.433645 | + | 0.901084i | \(0.357227\pi\) | |||||||
\(308\) | −1.97586 | −0.112585 | ||||||||
\(309\) | 0.646287 | 0.0367660 | ||||||||
\(310\) | 30.7023 | 1.74377 | ||||||||
\(311\) | 9.02476 | 0.511747 | 0.255873 | − | 0.966710i | \(-0.417637\pi\) | ||||
0.255873 | + | 0.966710i | \(0.417637\pi\) | |||||||
\(312\) | −4.75481 | −0.269188 | ||||||||
\(313\) | 34.3481 | 1.94147 | 0.970734 | − | 0.240159i | \(-0.0771995\pi\) | ||||
0.970734 | + | 0.240159i | \(0.0771995\pi\) | |||||||
\(314\) | 15.0118 | 0.847164 | ||||||||
\(315\) | 2.27400 | 0.128125 | ||||||||
\(316\) | 2.29222 | 0.128948 | ||||||||
\(317\) | 20.5386 | 1.15356 | 0.576781 | − | 0.816898i | \(-0.304308\pi\) | ||||
0.576781 | + | 0.816898i | \(0.304308\pi\) | |||||||
\(318\) | −14.9511 | −0.838418 | ||||||||
\(319\) | −16.5297 | −0.925486 | ||||||||
\(320\) | 3.90570 | 0.218335 | ||||||||
\(321\) | 5.14133 | 0.286961 | ||||||||
\(322\) | 0.366017 | 0.0203974 | ||||||||
\(323\) | −6.21910 | −0.346040 | ||||||||
\(324\) | −3.99636 | −0.222020 | ||||||||
\(325\) | 36.2744 | 2.01214 | ||||||||
\(326\) | 4.77531 | 0.264480 | ||||||||
\(327\) | −22.9670 | −1.27008 | ||||||||
\(328\) | 2.07362 | 0.114497 | ||||||||
\(329\) | −4.54572 | −0.250614 | ||||||||
\(330\) | −21.2592 | −1.17028 | ||||||||
\(331\) | −8.30867 | −0.456686 | −0.228343 | − | 0.973581i | \(-0.573331\pi\) | ||||
−0.228343 | + | 0.973581i | \(0.573331\pi\) | |||||||
\(332\) | −17.1324 | −0.940265 | ||||||||
\(333\) | 5.04237 | 0.276320 | ||||||||
\(334\) | 3.94163 | 0.215676 | ||||||||
\(335\) | 13.7171 | 0.749446 | ||||||||
\(336\) | −0.655849 | −0.0357795 | ||||||||
\(337\) | −17.9588 | −0.978276 | −0.489138 | − | 0.872206i | \(-0.662689\pi\) | ||||
−0.489138 | + | 0.872206i | \(0.662689\pi\) | |||||||
\(338\) | 0.486734 | 0.0264748 | ||||||||
\(339\) | 17.9033 | 0.972375 | ||||||||
\(340\) | −24.8909 | −1.34990 | ||||||||
\(341\) | −31.8325 | −1.72383 | ||||||||
\(342\) | 1.16445 | 0.0629662 | ||||||||
\(343\) | 6.71483 | 0.362567 | ||||||||
\(344\) | −10.7341 | −0.578746 | ||||||||
\(345\) | 3.93816 | 0.212023 | ||||||||
\(346\) | 24.0607 | 1.29351 | ||||||||
\(347\) | 6.69769 | 0.359551 | 0.179775 | − | 0.983708i | \(-0.442463\pi\) | ||||
0.179775 | + | 0.983708i | \(0.442463\pi\) | |||||||
\(348\) | −5.48673 | −0.294120 | ||||||||
\(349\) | 0.974251 | 0.0521505 | 0.0260752 | − | 0.999660i | \(-0.491699\pi\) | ||||
0.0260752 | + | 0.999660i | \(0.491699\pi\) | |||||||
\(350\) | 5.00347 | 0.267447 | ||||||||
\(351\) | −19.9382 | −1.06422 | ||||||||
\(352\) | −4.04948 | −0.215838 | ||||||||
\(353\) | 15.8928 | 0.845886 | 0.422943 | − | 0.906156i | \(-0.360997\pi\) | ||||
0.422943 | + | 0.906156i | \(0.360997\pi\) | |||||||
\(354\) | 4.00627 | 0.212931 | ||||||||
\(355\) | 55.2067 | 2.93007 | ||||||||
\(356\) | 1.86978 | 0.0990981 | ||||||||
\(357\) | 4.17970 | 0.221213 | ||||||||
\(358\) | −17.1745 | −0.907698 | ||||||||
\(359\) | −8.66535 | −0.457340 | −0.228670 | − | 0.973504i | \(-0.573438\pi\) | ||||
−0.228670 | + | 0.973504i | \(0.573438\pi\) | |||||||
\(360\) | 4.66052 | 0.245631 | ||||||||
\(361\) | −18.0477 | −0.949879 | ||||||||
\(362\) | 7.28875 | 0.383088 | ||||||||
\(363\) | 7.25613 | 0.380848 | ||||||||
\(364\) | −1.72600 | −0.0904671 | ||||||||
\(365\) | −38.1130 | −1.99492 | ||||||||
\(366\) | 10.1314 | 0.529578 | ||||||||
\(367\) | 7.50802 | 0.391915 | 0.195958 | − | 0.980612i | \(-0.437218\pi\) | ||||
0.195958 | + | 0.980612i | \(0.437218\pi\) | |||||||
\(368\) | 0.750146 | 0.0391040 | ||||||||
\(369\) | 2.47437 | 0.128811 | ||||||||
\(370\) | 16.5044 | 0.858022 | ||||||||
\(371\) | −5.42728 | −0.281770 | ||||||||
\(372\) | −10.5662 | −0.547833 | ||||||||
\(373\) | 2.14911 | 0.111277 | 0.0556385 | − | 0.998451i | \(-0.482281\pi\) | ||||
0.0556385 | + | 0.998451i | \(0.482281\pi\) | |||||||
\(374\) | 25.8072 | 1.33446 | ||||||||
\(375\) | 27.5855 | 1.42451 | ||||||||
\(376\) | −9.31636 | −0.480455 | ||||||||
\(377\) | −14.4395 | −0.743671 | ||||||||
\(378\) | −2.75015 | −0.141452 | ||||||||
\(379\) | 7.71644 | 0.396367 | 0.198183 | − | 0.980165i | \(-0.436496\pi\) | ||||
0.198183 | + | 0.980165i | \(0.436496\pi\) | |||||||
\(380\) | 3.81141 | 0.195521 | ||||||||
\(381\) | 4.28732 | 0.219646 | ||||||||
\(382\) | 6.55038 | 0.335147 | ||||||||
\(383\) | 1.88104 | 0.0961165 | 0.0480582 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480582 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(384\) | −1.34415 | −0.0685934 | ||||||||
\(385\) | −7.71711 | −0.393300 | ||||||||
\(386\) | −17.5467 | −0.893106 | ||||||||
\(387\) | −12.8086 | −0.651098 | ||||||||
\(388\) | −9.63757 | −0.489273 | ||||||||
\(389\) | −10.7025 | −0.542640 | −0.271320 | − | 0.962489i | \(-0.587460\pi\) | ||||
−0.271320 | + | 0.962489i | \(0.587460\pi\) | |||||||
\(390\) | −18.5709 | −0.940373 | ||||||||
\(391\) | −4.78065 | −0.241768 | ||||||||
\(392\) | 6.76193 | 0.341529 | ||||||||
\(393\) | −15.5888 | −0.786349 | ||||||||
\(394\) | 14.6051 | 0.735795 | ||||||||
\(395\) | 8.95274 | 0.450461 | ||||||||
\(396\) | −4.83208 | −0.242821 | ||||||||
\(397\) | 3.84774 | 0.193113 | 0.0965563 | − | 0.995328i | \(-0.469217\pi\) | ||||
0.0965563 | + | 0.995328i | \(0.469217\pi\) | |||||||
\(398\) | 4.64162 | 0.232663 | ||||||||
\(399\) | −0.640015 | −0.0320408 | ||||||||
\(400\) | 10.2545 | 0.512726 | ||||||||
\(401\) | −0.717694 | −0.0358399 | −0.0179200 | − | 0.999839i | \(-0.505704\pi\) | ||||
−0.0179200 | + | 0.999839i | \(0.505704\pi\) | |||||||
\(402\) | −4.72075 | −0.235450 | ||||||||
\(403\) | −27.8072 | −1.38517 | ||||||||
\(404\) | 5.91748 | 0.294406 | ||||||||
\(405\) | −15.6086 | −0.775597 | ||||||||
\(406\) | −1.99169 | −0.0988460 | ||||||||
\(407\) | −17.1119 | −0.848207 | ||||||||
\(408\) | 8.56622 | 0.424091 | ||||||||
\(409\) | −11.7906 | −0.583006 | −0.291503 | − | 0.956570i | \(-0.594155\pi\) | ||||
−0.291503 | + | 0.956570i | \(0.594155\pi\) | |||||||
\(410\) | 8.09896 | 0.399979 | ||||||||
\(411\) | −9.85342 | −0.486033 | ||||||||
\(412\) | 0.480814 | 0.0236880 | ||||||||
\(413\) | 1.45428 | 0.0715605 | ||||||||
\(414\) | 0.895118 | 0.0439926 | ||||||||
\(415\) | −66.9142 | −3.28469 | ||||||||
\(416\) | −3.53741 | −0.173436 | ||||||||
\(417\) | −17.7329 | −0.868386 | ||||||||
\(418\) | −3.95171 | −0.193285 | ||||||||
\(419\) | −7.07076 | −0.345429 | −0.172715 | − | 0.984972i | \(-0.555254\pi\) | ||||
−0.172715 | + | 0.984972i | \(0.555254\pi\) | |||||||
\(420\) | −2.56155 | −0.124991 | ||||||||
\(421\) | −4.96469 | −0.241964 | −0.120982 | − | 0.992655i | \(-0.538604\pi\) | ||||
−0.120982 | + | 0.992655i | \(0.538604\pi\) | |||||||
\(422\) | −15.7554 | −0.766962 | ||||||||
\(423\) | −11.1168 | −0.540519 | ||||||||
\(424\) | −11.1231 | −0.540186 | ||||||||
\(425\) | −65.3516 | −3.17002 | ||||||||
\(426\) | −18.9994 | −0.920525 | ||||||||
\(427\) | 3.67772 | 0.177977 | ||||||||
\(428\) | 3.82496 | 0.184887 | ||||||||
\(429\) | 19.2545 | 0.929617 | ||||||||
\(430\) | −41.9244 | −2.02177 | ||||||||
\(431\) | 25.6140 | 1.23378 | 0.616892 | − | 0.787048i | \(-0.288391\pi\) | ||||
0.616892 | + | 0.787048i | \(0.288391\pi\) | |||||||
\(432\) | −5.63637 | −0.271180 | ||||||||
\(433\) | −20.5767 | −0.988855 | −0.494428 | − | 0.869219i | \(-0.664622\pi\) | ||||
−0.494428 | + | 0.869219i | \(0.664622\pi\) | |||||||
\(434\) | −3.83555 | −0.184112 | ||||||||
\(435\) | −21.4296 | −1.02747 | ||||||||
\(436\) | −17.0866 | −0.818300 | ||||||||
\(437\) | 0.732035 | 0.0350180 | ||||||||
\(438\) | 13.1166 | 0.626736 | ||||||||
\(439\) | 15.6900 | 0.748843 | 0.374421 | − | 0.927259i | \(-0.377841\pi\) | ||||
0.374421 | + | 0.927259i | \(0.377841\pi\) | |||||||
\(440\) | −15.8161 | −0.754002 | ||||||||
\(441\) | 8.06873 | 0.384225 | ||||||||
\(442\) | 22.5438 | 1.07230 | ||||||||
\(443\) | 29.0018 | 1.37792 | 0.688959 | − | 0.724801i | \(-0.258068\pi\) | ||||
0.688959 | + | 0.724801i | \(0.258068\pi\) | |||||||
\(444\) | −5.67999 | −0.269561 | ||||||||
\(445\) | 7.30281 | 0.346186 | ||||||||
\(446\) | −19.8791 | −0.941303 | ||||||||
\(447\) | 25.8254 | 1.22150 | ||||||||
\(448\) | −0.487928 | −0.0230524 | ||||||||
\(449\) | 18.1978 | 0.858805 | 0.429403 | − | 0.903113i | \(-0.358724\pi\) | ||||
0.429403 | + | 0.903113i | \(0.358724\pi\) | |||||||
\(450\) | 12.2363 | 0.576825 | ||||||||
\(451\) | −8.39710 | −0.395404 | ||||||||
\(452\) | 13.3194 | 0.626493 | ||||||||
\(453\) | −4.88783 | −0.229650 | ||||||||
\(454\) | −27.7566 | −1.30268 | ||||||||
\(455\) | −6.74125 | −0.316035 | ||||||||
\(456\) | −1.31170 | −0.0614259 | ||||||||
\(457\) | 32.1933 | 1.50594 | 0.752969 | − | 0.658056i | \(-0.228621\pi\) | ||||
0.752969 | + | 0.658056i | \(0.228621\pi\) | |||||||
\(458\) | 17.6723 | 0.825772 | ||||||||
\(459\) | 35.9204 | 1.67662 | ||||||||
\(460\) | 2.92985 | 0.136605 | ||||||||
\(461\) | −26.9152 | −1.25357 | −0.626783 | − | 0.779194i | \(-0.715629\pi\) | ||||
−0.626783 | + | 0.779194i | \(0.715629\pi\) | |||||||
\(462\) | 2.65585 | 0.123561 | ||||||||
\(463\) | −24.2349 | −1.12629 | −0.563145 | − | 0.826358i | \(-0.690409\pi\) | ||||
−0.563145 | + | 0.826358i | \(0.690409\pi\) | |||||||
\(464\) | −4.08193 | −0.189499 | ||||||||
\(465\) | −41.2685 | −1.91378 | ||||||||
\(466\) | 1.67230 | 0.0774676 | ||||||||
\(467\) | −17.7628 | −0.821963 | −0.410982 | − | 0.911644i | \(-0.634814\pi\) | ||||
−0.410982 | + | 0.911644i | \(0.634814\pi\) | |||||||
\(468\) | −4.22105 | −0.195118 | ||||||||
\(469\) | −1.71364 | −0.0791285 | ||||||||
\(470\) | −36.3870 | −1.67841 | ||||||||
\(471\) | −20.1781 | −0.929758 | ||||||||
\(472\) | 2.98052 | 0.137190 | ||||||||
\(473\) | 43.4677 | 1.99865 | ||||||||
\(474\) | −3.08109 | −0.141519 | ||||||||
\(475\) | 10.0069 | 0.459150 | ||||||||
\(476\) | 3.10955 | 0.142526 | ||||||||
\(477\) | −13.2727 | −0.607717 | ||||||||
\(478\) | 24.0925 | 1.10196 | ||||||||
\(479\) | 11.4930 | 0.525130 | 0.262565 | − | 0.964914i | \(-0.415432\pi\) | ||||
0.262565 | + | 0.964914i | \(0.415432\pi\) | |||||||
\(480\) | −5.24985 | −0.239622 | ||||||||
\(481\) | −14.9481 | −0.681573 | ||||||||
\(482\) | 18.2257 | 0.830158 | ||||||||
\(483\) | −0.491983 | −0.0223860 | ||||||||
\(484\) | 5.39830 | 0.245377 | ||||||||
\(485\) | −37.6415 | −1.70921 | ||||||||
\(486\) | −11.5374 | −0.523348 | ||||||||
\(487\) | 5.85514 | 0.265322 | 0.132661 | − | 0.991161i | \(-0.457648\pi\) | ||||
0.132661 | + | 0.991161i | \(0.457648\pi\) | |||||||
\(488\) | 7.53741 | 0.341202 | ||||||||
\(489\) | −6.41874 | −0.290265 | ||||||||
\(490\) | 26.4101 | 1.19309 | ||||||||
\(491\) | 18.6544 | 0.841862 | 0.420931 | − | 0.907093i | \(-0.361703\pi\) | ||||
0.420931 | + | 0.907093i | \(0.361703\pi\) | |||||||
\(492\) | −2.78726 | −0.125660 | ||||||||
\(493\) | 26.0140 | 1.17161 | ||||||||
\(494\) | −3.45200 | −0.155313 | ||||||||
\(495\) | −18.8727 | −0.848263 | ||||||||
\(496\) | −7.86089 | −0.352964 | ||||||||
\(497\) | −6.89681 | −0.309364 | ||||||||
\(498\) | 23.0286 | 1.03194 | ||||||||
\(499\) | 35.1119 | 1.57183 | 0.785913 | − | 0.618337i | \(-0.212193\pi\) | ||||
0.785913 | + | 0.618337i | \(0.212193\pi\) | |||||||
\(500\) | 20.5226 | 0.917798 | ||||||||
\(501\) | −5.29814 | −0.236703 | ||||||||
\(502\) | 1.21740 | 0.0543353 | ||||||||
\(503\) | 29.7342 | 1.32578 | 0.662892 | − | 0.748715i | \(-0.269329\pi\) | ||||
0.662892 | + | 0.748715i | \(0.269329\pi\) | |||||||
\(504\) | −0.582225 | −0.0259344 | ||||||||
\(505\) | 23.1119 | 1.02847 | ||||||||
\(506\) | −3.03770 | −0.135042 | ||||||||
\(507\) | −0.654243 | −0.0290560 | ||||||||
\(508\) | 3.18962 | 0.141516 | ||||||||
\(509\) | 30.1456 | 1.33618 | 0.668090 | − | 0.744081i | \(-0.267112\pi\) | ||||
0.668090 | + | 0.744081i | \(0.267112\pi\) | |||||||
\(510\) | 33.4571 | 1.48151 | ||||||||
\(511\) | 4.76134 | 0.210629 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.50029 | −0.242844 | ||||||||
\(514\) | −28.7806 | −1.26946 | ||||||||
\(515\) | 1.87792 | 0.0827509 | ||||||||
\(516\) | 14.4283 | 0.635171 | ||||||||
\(517\) | 37.7264 | 1.65921 | ||||||||
\(518\) | −2.06184 | −0.0905922 | ||||||||
\(519\) | −32.3412 | −1.41962 | ||||||||
\(520\) | −13.8161 | −0.605875 | ||||||||
\(521\) | 37.9804 | 1.66395 | 0.831975 | − | 0.554813i | \(-0.187210\pi\) | ||||
0.831975 | + | 0.554813i | \(0.187210\pi\) | |||||||
\(522\) | −4.87080 | −0.213189 | ||||||||
\(523\) | 10.1012 | 0.441696 | 0.220848 | − | 0.975308i | \(-0.429117\pi\) | ||||
0.220848 | + | 0.975308i | \(0.429117\pi\) | |||||||
\(524\) | −11.5975 | −0.506638 | ||||||||
\(525\) | −6.72542 | −0.293521 | ||||||||
\(526\) | 4.35407 | 0.189846 | ||||||||
\(527\) | 50.0971 | 2.18227 | ||||||||
\(528\) | 5.44311 | 0.236881 | ||||||||
\(529\) | −22.4373 | −0.975534 | ||||||||
\(530\) | −43.4436 | −1.88707 | ||||||||
\(531\) | 3.55653 | 0.154340 | ||||||||
\(532\) | −0.476148 | −0.0206436 | ||||||||
\(533\) | −7.33526 | −0.317725 | ||||||||
\(534\) | −2.51327 | −0.108760 | ||||||||
\(535\) | 14.9392 | 0.645877 | ||||||||
\(536\) | −3.51207 | −0.151698 | ||||||||
\(537\) | 23.0851 | 0.996194 | ||||||||
\(538\) | −1.00000 | −0.0431131 | ||||||||
\(539\) | −27.3823 | −1.17944 | ||||||||
\(540\) | −22.0140 | −0.947332 | ||||||||
\(541\) | 1.06610 | 0.0458352 | 0.0229176 | − | 0.999737i | \(-0.492704\pi\) | ||||
0.0229176 | + | 0.999737i | \(0.492704\pi\) | |||||||
\(542\) | 19.6940 | 0.845929 | ||||||||
\(543\) | −9.79718 | −0.420437 | ||||||||
\(544\) | 6.37296 | 0.273238 | ||||||||
\(545\) | −66.7352 | −2.85862 | ||||||||
\(546\) | 2.32001 | 0.0992872 | ||||||||
\(547\) | 8.62634 | 0.368836 | 0.184418 | − | 0.982848i | \(-0.440960\pi\) | ||||
0.184418 | + | 0.982848i | \(0.440960\pi\) | |||||||
\(548\) | −7.33059 | −0.313147 | ||||||||
\(549\) | 8.99408 | 0.383858 | ||||||||
\(550\) | −41.5255 | −1.77065 | ||||||||
\(551\) | −3.98338 | −0.169698 | ||||||||
\(552\) | −1.00831 | −0.0429165 | ||||||||
\(553\) | −1.11844 | −0.0475609 | ||||||||
\(554\) | 1.31009 | 0.0556605 | ||||||||
\(555\) | −22.1844 | −0.941674 | ||||||||
\(556\) | −13.1927 | −0.559494 | ||||||||
\(557\) | 39.3859 | 1.66884 | 0.834418 | − | 0.551132i | \(-0.185804\pi\) | ||||
0.834418 | + | 0.551132i | \(0.185804\pi\) | |||||||
\(558\) | −9.38007 | −0.397090 | ||||||||
\(559\) | 37.9710 | 1.60600 | ||||||||
\(560\) | −1.90570 | −0.0805307 | ||||||||
\(561\) | −34.6887 | −1.46456 | ||||||||
\(562\) | −7.94749 | −0.335245 | ||||||||
\(563\) | −29.8436 | −1.25776 | −0.628879 | − | 0.777503i | \(-0.716486\pi\) | ||||
−0.628879 | + | 0.777503i | \(0.716486\pi\) | |||||||
\(564\) | 12.5226 | 0.527297 | ||||||||
\(565\) | 52.0217 | 2.18857 | ||||||||
\(566\) | −20.7544 | −0.872373 | ||||||||
\(567\) | 1.94994 | 0.0818896 | ||||||||
\(568\) | −14.1349 | −0.593087 | ||||||||
\(569\) | 18.1766 | 0.762004 | 0.381002 | − | 0.924574i | \(-0.375579\pi\) | ||||
0.381002 | + | 0.924574i | \(0.375579\pi\) | |||||||
\(570\) | −5.12311 | −0.214583 | ||||||||
\(571\) | −34.4465 | −1.44154 | −0.720771 | − | 0.693173i | \(-0.756212\pi\) | ||||
−0.720771 | + | 0.693173i | \(0.756212\pi\) | |||||||
\(572\) | 14.3247 | 0.598945 | ||||||||
\(573\) | −8.80470 | −0.367822 | ||||||||
\(574\) | −1.01178 | −0.0422309 | ||||||||
\(575\) | 7.69238 | 0.320795 | ||||||||
\(576\) | −1.19326 | −0.0497191 | ||||||||
\(577\) | 6.04440 | 0.251632 | 0.125816 | − | 0.992054i | \(-0.459845\pi\) | ||||
0.125816 | + | 0.992054i | \(0.459845\pi\) | |||||||
\(578\) | −23.6146 | −0.982239 | ||||||||
\(579\) | 23.5855 | 0.980178 | ||||||||
\(580\) | −15.9428 | −0.661990 | ||||||||
\(581\) | 8.35940 | 0.346806 | ||||||||
\(582\) | 12.9543 | 0.536975 | ||||||||
\(583\) | 45.0428 | 1.86548 | ||||||||
\(584\) | 9.75828 | 0.403801 | ||||||||
\(585\) | −16.4862 | −0.681618 | ||||||||
\(586\) | 10.9994 | 0.454382 | ||||||||
\(587\) | −38.6176 | −1.59392 | −0.796959 | − | 0.604034i | \(-0.793559\pi\) | ||||
−0.796959 | + | 0.604034i | \(0.793559\pi\) | |||||||
\(588\) | −9.08905 | −0.374826 | ||||||||
\(589\) | −7.67110 | −0.316082 | ||||||||
\(590\) | 11.6410 | 0.479254 | ||||||||
\(591\) | −19.6315 | −0.807531 | ||||||||
\(592\) | −4.22571 | −0.173676 | ||||||||
\(593\) | −4.06998 | −0.167134 | −0.0835671 | − | 0.996502i | \(-0.526631\pi\) | ||||
−0.0835671 | + | 0.996502i | \(0.526631\pi\) | |||||||
\(594\) | 22.8244 | 0.936496 | ||||||||
\(595\) | 12.1450 | 0.497895 | ||||||||
\(596\) | 19.2132 | 0.787002 | ||||||||
\(597\) | −6.23904 | −0.255347 | ||||||||
\(598\) | −2.65357 | −0.108513 | ||||||||
\(599\) | −18.2628 | −0.746199 | −0.373099 | − | 0.927791i | \(-0.621705\pi\) | ||||
−0.373099 | + | 0.927791i | \(0.621705\pi\) | |||||||
\(600\) | −13.7836 | −0.562714 | ||||||||
\(601\) | 31.6805 | 1.29228 | 0.646138 | − | 0.763220i | \(-0.276383\pi\) | ||||
0.646138 | + | 0.763220i | \(0.276383\pi\) | |||||||
\(602\) | 5.23749 | 0.213464 | ||||||||
\(603\) | −4.19081 | −0.170663 | ||||||||
\(604\) | −3.63637 | −0.147962 | ||||||||
\(605\) | 21.0842 | 0.857193 | ||||||||
\(606\) | −7.95399 | −0.323109 | ||||||||
\(607\) | 25.5355 | 1.03645 | 0.518226 | − | 0.855244i | \(-0.326593\pi\) | ||||
0.518226 | + | 0.855244i | \(0.326593\pi\) | |||||||
\(608\) | −0.975857 | −0.0395762 | ||||||||
\(609\) | 2.67713 | 0.108483 | ||||||||
\(610\) | 29.4389 | 1.19195 | ||||||||
\(611\) | 32.9558 | 1.33325 | ||||||||
\(612\) | 7.60459 | 0.307397 | ||||||||
\(613\) | −17.6816 | −0.714154 | −0.357077 | − | 0.934075i | \(-0.616227\pi\) | ||||
−0.357077 | + | 0.934075i | \(0.616227\pi\) | |||||||
\(614\) | −15.1961 | −0.613267 | ||||||||
\(615\) | −10.8862 | −0.438975 | ||||||||
\(616\) | 1.97586 | 0.0796095 | ||||||||
\(617\) | 32.8371 | 1.32197 | 0.660986 | − | 0.750398i | \(-0.270138\pi\) | ||||
0.660986 | + | 0.750398i | \(0.270138\pi\) | |||||||
\(618\) | −0.646287 | −0.0259975 | ||||||||
\(619\) | 10.5824 | 0.425342 | 0.212671 | − | 0.977124i | \(-0.431784\pi\) | ||||
0.212671 | + | 0.977124i | \(0.431784\pi\) | |||||||
\(620\) | −30.7023 | −1.23303 | ||||||||
\(621\) | −4.22810 | −0.169668 | ||||||||
\(622\) | −9.02476 | −0.361860 | ||||||||
\(623\) | −0.912319 | −0.0365513 | ||||||||
\(624\) | 4.75481 | 0.190345 | ||||||||
\(625\) | 28.8826 | 1.15530 | ||||||||
\(626\) | −34.3481 | −1.37282 | ||||||||
\(627\) | 5.31170 | 0.212129 | ||||||||
\(628\) | −15.0118 | −0.599035 | ||||||||
\(629\) | 26.9303 | 1.07378 | ||||||||
\(630\) | −2.27400 | −0.0905982 | ||||||||
\(631\) | −0.902404 | −0.0359241 | −0.0179621 | − | 0.999839i | \(-0.505718\pi\) | ||||
−0.0179621 | + | 0.999839i | \(0.505718\pi\) | |||||||
\(632\) | −2.29222 | −0.0911797 | ||||||||
\(633\) | 21.1777 | 0.841737 | ||||||||
\(634\) | −20.5386 | −0.815692 | ||||||||
\(635\) | 12.4577 | 0.494368 | ||||||||
\(636\) | 14.9511 | 0.592851 | ||||||||
\(637\) | −23.9197 | −0.947733 | ||||||||
\(638\) | 16.5297 | 0.654418 | ||||||||
\(639\) | −16.8666 | −0.667231 | ||||||||
\(640\) | −3.90570 | −0.154386 | ||||||||
\(641\) | −19.2444 | −0.760109 | −0.380055 | − | 0.924964i | \(-0.624095\pi\) | ||||
−0.380055 | + | 0.924964i | \(0.624095\pi\) | |||||||
\(642\) | −5.14133 | −0.202912 | ||||||||
\(643\) | 34.2804 | 1.35189 | 0.675944 | − | 0.736953i | \(-0.263736\pi\) | ||||
0.675944 | + | 0.736953i | \(0.263736\pi\) | |||||||
\(644\) | −0.366017 | −0.0144231 | ||||||||
\(645\) | 56.3527 | 2.21888 | ||||||||
\(646\) | 6.21910 | 0.244687 | ||||||||
\(647\) | −30.2029 | −1.18740 | −0.593698 | − | 0.804688i | \(-0.702333\pi\) | ||||
−0.593698 | + | 0.804688i | \(0.702333\pi\) | |||||||
\(648\) | 3.99636 | 0.156992 | ||||||||
\(649\) | −12.0696 | −0.473772 | ||||||||
\(650\) | −36.2744 | −1.42280 | ||||||||
\(651\) | 5.15556 | 0.202062 | ||||||||
\(652\) | −4.77531 | −0.187016 | ||||||||
\(653\) | −21.5877 | −0.844794 | −0.422397 | − | 0.906411i | \(-0.638811\pi\) | ||||
−0.422397 | + | 0.906411i | \(0.638811\pi\) | |||||||
\(654\) | 22.9670 | 0.898079 | ||||||||
\(655\) | −45.2963 | −1.76987 | ||||||||
\(656\) | −2.07362 | −0.0809614 | ||||||||
\(657\) | 11.6442 | 0.454282 | ||||||||
\(658\) | 4.54572 | 0.177211 | ||||||||
\(659\) | −21.3740 | −0.832612 | −0.416306 | − | 0.909225i | \(-0.636676\pi\) | ||||
−0.416306 | + | 0.909225i | \(0.636676\pi\) | |||||||
\(660\) | 21.2592 | 0.827513 | ||||||||
\(661\) | −19.7195 | −0.767000 | −0.383500 | − | 0.923541i | \(-0.625281\pi\) | ||||
−0.383500 | + | 0.923541i | \(0.625281\pi\) | |||||||
\(662\) | 8.30867 | 0.322926 | ||||||||
\(663\) | −30.3022 | −1.17684 | ||||||||
\(664\) | 17.1324 | 0.664868 | ||||||||
\(665\) | −1.85969 | −0.0721158 | ||||||||
\(666\) | −5.04237 | −0.195388 | ||||||||
\(667\) | −3.06204 | −0.118563 | ||||||||
\(668\) | −3.94163 | −0.152506 | ||||||||
\(669\) | 26.7205 | 1.03308 | ||||||||
\(670\) | −13.7171 | −0.529938 | ||||||||
\(671\) | −30.5226 | −1.17831 | ||||||||
\(672\) | 0.655849 | 0.0252999 | ||||||||
\(673\) | −13.2275 | −0.509883 | −0.254942 | − | 0.966956i | \(-0.582056\pi\) | ||||
−0.254942 | + | 0.966956i | \(0.582056\pi\) | |||||||
\(674\) | 17.9588 | 0.691746 | ||||||||
\(675\) | −57.7983 | −2.22466 | ||||||||
\(676\) | −0.486734 | −0.0187205 | ||||||||
\(677\) | −12.7629 | −0.490520 | −0.245260 | − | 0.969457i | \(-0.578873\pi\) | ||||
−0.245260 | + | 0.969457i | \(0.578873\pi\) | |||||||
\(678\) | −17.9033 | −0.687573 | ||||||||
\(679\) | 4.70244 | 0.180463 | ||||||||
\(680\) | 24.8909 | 0.954522 | ||||||||
\(681\) | 37.3091 | 1.42969 | ||||||||
\(682\) | 31.8325 | 1.21893 | ||||||||
\(683\) | −3.12345 | −0.119515 | −0.0597577 | − | 0.998213i | \(-0.519033\pi\) | ||||
−0.0597577 | + | 0.998213i | \(0.519033\pi\) | |||||||
\(684\) | −1.16445 | −0.0445238 | ||||||||
\(685\) | −28.6311 | −1.09394 | ||||||||
\(686\) | −6.71483 | −0.256374 | ||||||||
\(687\) | −23.7542 | −0.906280 | ||||||||
\(688\) | 10.7341 | 0.409235 | ||||||||
\(689\) | 39.3470 | 1.49900 | ||||||||
\(690\) | −3.93816 | −0.149923 | ||||||||
\(691\) | 25.3081 | 0.962767 | 0.481384 | − | 0.876510i | \(-0.340134\pi\) | ||||
0.481384 | + | 0.876510i | \(0.340134\pi\) | |||||||
\(692\) | −24.0607 | −0.914650 | ||||||||
\(693\) | 2.35771 | 0.0895619 | ||||||||
\(694\) | −6.69769 | −0.254241 | ||||||||
\(695\) | −51.5267 | −1.95452 | ||||||||
\(696\) | 5.48673 | 0.207974 | ||||||||
\(697\) | 13.2151 | 0.500559 | ||||||||
\(698\) | −0.974251 | −0.0368759 | ||||||||
\(699\) | −2.24782 | −0.0850202 | ||||||||
\(700\) | −5.00347 | −0.189113 | ||||||||
\(701\) | −15.5107 | −0.585831 | −0.292916 | − | 0.956138i | \(-0.594626\pi\) | ||||
−0.292916 | + | 0.956138i | \(0.594626\pi\) | |||||||
\(702\) | 19.9382 | 0.752517 | ||||||||
\(703\) | −4.12369 | −0.155528 | ||||||||
\(704\) | 4.04948 | 0.152621 | ||||||||
\(705\) | 48.9096 | 1.84204 | ||||||||
\(706\) | −15.8928 | −0.598132 | ||||||||
\(707\) | −2.88731 | −0.108588 | ||||||||
\(708\) | −4.00627 | −0.150565 | ||||||||
\(709\) | 3.24435 | 0.121844 | 0.0609220 | − | 0.998143i | \(-0.480596\pi\) | ||||
0.0609220 | + | 0.998143i | \(0.480596\pi\) | |||||||
\(710\) | −55.2067 | −2.07187 | ||||||||
\(711\) | −2.73521 | −0.102579 | ||||||||
\(712\) | −1.86978 | −0.0700730 | ||||||||
\(713\) | −5.89681 | −0.220837 | ||||||||
\(714\) | −4.17970 | −0.156421 | ||||||||
\(715\) | 55.9479 | 2.09233 | ||||||||
\(716\) | 17.1745 | 0.641839 | ||||||||
\(717\) | −32.3839 | −1.20940 | ||||||||
\(718\) | 8.66535 | 0.323388 | ||||||||
\(719\) | 28.5289 | 1.06395 | 0.531974 | − | 0.846761i | \(-0.321451\pi\) | ||||
0.531974 | + | 0.846761i | \(0.321451\pi\) | |||||||
\(720\) | −4.66052 | −0.173687 | ||||||||
\(721\) | −0.234603 | −0.00873707 | ||||||||
\(722\) | 18.0477 | 0.671666 | ||||||||
\(723\) | −24.4981 | −0.911094 | ||||||||
\(724\) | −7.28875 | −0.270884 | ||||||||
\(725\) | −41.8583 | −1.55458 | ||||||||
\(726\) | −7.25613 | −0.269300 | ||||||||
\(727\) | 28.4941 | 1.05679 | 0.528395 | − | 0.848999i | \(-0.322794\pi\) | ||||
0.528395 | + | 0.848999i | \(0.322794\pi\) | |||||||
\(728\) | 1.72600 | 0.0639699 | ||||||||
\(729\) | 27.4971 | 1.01841 | ||||||||
\(730\) | 38.1130 | 1.41062 | ||||||||
\(731\) | −68.4082 | −2.53017 | ||||||||
\(732\) | −10.1314 | −0.374468 | ||||||||
\(733\) | 31.1617 | 1.15098 | 0.575491 | − | 0.817808i | \(-0.304811\pi\) | ||||
0.575491 | + | 0.817808i | \(0.304811\pi\) | |||||||
\(734\) | −7.50802 | −0.277126 | ||||||||
\(735\) | −35.4991 | −1.30940 | ||||||||
\(736\) | −0.750146 | −0.0276507 | ||||||||
\(737\) | 14.2221 | 0.523877 | ||||||||
\(738\) | −2.47437 | −0.0910828 | ||||||||
\(739\) | 22.7409 | 0.836538 | 0.418269 | − | 0.908323i | \(-0.362637\pi\) | ||||
0.418269 | + | 0.908323i | \(0.362637\pi\) | |||||||
\(740\) | −16.5044 | −0.606713 | ||||||||
\(741\) | 4.64001 | 0.170455 | ||||||||
\(742\) | 5.42728 | 0.199242 | ||||||||
\(743\) | 33.4594 | 1.22751 | 0.613753 | − | 0.789498i | \(-0.289659\pi\) | ||||
0.613753 | + | 0.789498i | \(0.289659\pi\) | |||||||
\(744\) | 10.5662 | 0.387376 | ||||||||
\(745\) | 75.0410 | 2.74929 | ||||||||
\(746\) | −2.14911 | −0.0786847 | ||||||||
\(747\) | 20.4434 | 0.747986 | ||||||||
\(748\) | −25.8072 | −0.943604 | ||||||||
\(749\) | −1.86631 | −0.0681934 | ||||||||
\(750\) | −27.5855 | −1.00728 | ||||||||
\(751\) | −48.0493 | −1.75334 | −0.876672 | − | 0.481089i | \(-0.840241\pi\) | ||||
−0.876672 | + | 0.481089i | \(0.840241\pi\) | |||||||
\(752\) | 9.31636 | 0.339733 | ||||||||
\(753\) | −1.63637 | −0.0596327 | ||||||||
\(754\) | 14.4395 | 0.525854 | ||||||||
\(755\) | −14.2026 | −0.516885 | ||||||||
\(756\) | 2.75015 | 0.100022 | ||||||||
\(757\) | 52.5319 | 1.90930 | 0.954652 | − | 0.297725i | \(-0.0962279\pi\) | ||||
0.954652 | + | 0.297725i | \(0.0962279\pi\) | |||||||
\(758\) | −7.71644 | −0.280274 | ||||||||
\(759\) | 4.08313 | 0.148208 | ||||||||
\(760\) | −3.81141 | −0.138254 | ||||||||
\(761\) | 50.4604 | 1.82919 | 0.914594 | − | 0.404373i | \(-0.132510\pi\) | ||||
0.914594 | + | 0.404373i | \(0.132510\pi\) | |||||||
\(762\) | −4.28732 | −0.155313 | ||||||||
\(763\) | 8.33704 | 0.301821 | ||||||||
\(764\) | −6.55038 | −0.236985 | ||||||||
\(765\) | 29.7013 | 1.07385 | ||||||||
\(766\) | −1.88104 | −0.0679646 | ||||||||
\(767\) | −10.5433 | −0.380698 | ||||||||
\(768\) | 1.34415 | 0.0485029 | ||||||||
\(769\) | −38.6684 | −1.39442 | −0.697209 | − | 0.716867i | \(-0.745575\pi\) | ||||
−0.697209 | + | 0.716867i | \(0.745575\pi\) | |||||||
\(770\) | 7.71711 | 0.278105 | ||||||||
\(771\) | 38.6855 | 1.39323 | ||||||||
\(772\) | 17.5467 | 0.631521 | ||||||||
\(773\) | −27.8089 | −1.00022 | −0.500108 | − | 0.865963i | \(-0.666706\pi\) | ||||
−0.500108 | + | 0.865963i | \(0.666706\pi\) | |||||||
\(774\) | 12.8086 | 0.460396 | ||||||||
\(775\) | −80.6096 | −2.89558 | ||||||||
\(776\) | 9.63757 | 0.345968 | ||||||||
\(777\) | 2.77143 | 0.0994245 | ||||||||
\(778\) | 10.7025 | 0.383704 | ||||||||
\(779\) | −2.02356 | −0.0725016 | ||||||||
\(780\) | 18.5709 | 0.664944 | ||||||||
\(781\) | 57.2390 | 2.04817 | ||||||||
\(782\) | 4.78065 | 0.170956 | ||||||||
\(783\) | 23.0073 | 0.822214 | ||||||||
\(784\) | −6.76193 | −0.241497 | ||||||||
\(785\) | −58.6316 | −2.09265 | ||||||||
\(786\) | 15.5888 | 0.556033 | ||||||||
\(787\) | −35.0440 | −1.24918 | −0.624592 | − | 0.780951i | \(-0.714735\pi\) | ||||
−0.624592 | + | 0.780951i | \(0.714735\pi\) | |||||||
\(788\) | −14.6051 | −0.520286 | ||||||||
\(789\) | −5.85252 | −0.208355 | ||||||||
\(790\) | −8.95274 | −0.318524 | ||||||||
\(791\) | −6.49893 | −0.231075 | ||||||||
\(792\) | 4.83208 | 0.171700 | ||||||||
\(793\) | −26.6629 | −0.946827 | ||||||||
\(794\) | −3.84774 | −0.136551 | ||||||||
\(795\) | 58.3947 | 2.07105 | ||||||||
\(796\) | −4.64162 | −0.164518 | ||||||||
\(797\) | 44.3028 | 1.56929 | 0.784643 | − | 0.619947i | \(-0.212846\pi\) | ||||
0.784643 | + | 0.619947i | \(0.212846\pi\) | |||||||
\(798\) | 0.640015 | 0.0226563 | ||||||||
\(799\) | −59.3728 | −2.10046 | ||||||||
\(800\) | −10.2545 | −0.362552 | ||||||||
\(801\) | −2.23113 | −0.0788332 | ||||||||
\(802\) | 0.717694 | 0.0253426 | ||||||||
\(803\) | −39.5160 | −1.39449 | ||||||||
\(804\) | 4.72075 | 0.166488 | ||||||||
\(805\) | −1.42956 | −0.0503852 | ||||||||
\(806\) | 27.8072 | 0.979466 | ||||||||
\(807\) | 1.34415 | 0.0473163 | ||||||||
\(808\) | −5.91748 | −0.208176 | ||||||||
\(809\) | 17.8666 | 0.628157 | 0.314079 | − | 0.949397i | \(-0.398304\pi\) | ||||
0.314079 | + | 0.949397i | \(0.398304\pi\) | |||||||
\(810\) | 15.6086 | 0.548430 | ||||||||
\(811\) | 7.94755 | 0.279076 | 0.139538 | − | 0.990217i | \(-0.455438\pi\) | ||||
0.139538 | + | 0.990217i | \(0.455438\pi\) | |||||||
\(812\) | 1.99169 | 0.0698947 | ||||||||
\(813\) | −26.4717 | −0.928403 | ||||||||
\(814\) | 17.1119 | 0.599773 | ||||||||
\(815\) | −18.6510 | −0.653314 | ||||||||
\(816\) | −8.56622 | −0.299878 | ||||||||
\(817\) | 10.4750 | 0.366473 | ||||||||
\(818\) | 11.7906 | 0.412247 | ||||||||
\(819\) | 2.05957 | 0.0719671 | ||||||||
\(820\) | −8.09896 | −0.282828 | ||||||||
\(821\) | 14.0212 | 0.489342 | 0.244671 | − | 0.969606i | \(-0.421320\pi\) | ||||
0.244671 | + | 0.969606i | \(0.421320\pi\) | |||||||
\(822\) | 9.85342 | 0.343678 | ||||||||
\(823\) | −56.0461 | −1.95364 | −0.976822 | − | 0.214052i | \(-0.931334\pi\) | ||||
−0.976822 | + | 0.214052i | \(0.931334\pi\) | |||||||
\(824\) | −0.480814 | −0.0167500 | ||||||||
\(825\) | 55.8165 | 1.94328 | ||||||||
\(826\) | −1.45428 | −0.0506009 | ||||||||
\(827\) | 28.6027 | 0.994612 | 0.497306 | − | 0.867575i | \(-0.334323\pi\) | ||||
0.497306 | + | 0.867575i | \(0.334323\pi\) | |||||||
\(828\) | −0.895118 | −0.0311075 | ||||||||
\(829\) | 7.08499 | 0.246072 | 0.123036 | − | 0.992402i | \(-0.460737\pi\) | ||||
0.123036 | + | 0.992402i | \(0.460737\pi\) | |||||||
\(830\) | 66.9142 | 2.32263 | ||||||||
\(831\) | −1.76096 | −0.0610871 | ||||||||
\(832\) | 3.53741 | 0.122638 | ||||||||
\(833\) | 43.0935 | 1.49310 | ||||||||
\(834\) | 17.7329 | 0.614042 | ||||||||
\(835\) | −15.3948 | −0.532760 | ||||||||
\(836\) | 3.95171 | 0.136673 | ||||||||
\(837\) | 44.3069 | 1.53147 | ||||||||
\(838\) | 7.07076 | 0.244256 | ||||||||
\(839\) | −16.9860 | −0.586423 | −0.293211 | − | 0.956048i | \(-0.594724\pi\) | ||||
−0.293211 | + | 0.956048i | \(0.594724\pi\) | |||||||
\(840\) | 2.56155 | 0.0883820 | ||||||||
\(841\) | −12.3378 | −0.425442 | ||||||||
\(842\) | 4.96469 | 0.171094 | ||||||||
\(843\) | 10.6826 | 0.367929 | ||||||||
\(844\) | 15.7554 | 0.542324 | ||||||||
\(845\) | −1.90104 | −0.0653977 | ||||||||
\(846\) | 11.1168 | 0.382205 | ||||||||
\(847\) | −2.63398 | −0.0905047 | ||||||||
\(848\) | 11.1231 | 0.381969 | ||||||||
\(849\) | 27.8970 | 0.957424 | ||||||||
\(850\) | 65.3516 | 2.24154 | ||||||||
\(851\) | −3.16990 | −0.108663 | ||||||||
\(852\) | 18.9994 | 0.650909 | ||||||||
\(853\) | −25.5249 | −0.873957 | −0.436979 | − | 0.899472i | \(-0.643951\pi\) | ||||
−0.436979 | + | 0.899472i | \(0.643951\pi\) | |||||||
\(854\) | −3.67772 | −0.125849 | ||||||||
\(855\) | −4.54800 | −0.155538 | ||||||||
\(856\) | −3.82496 | −0.130735 | ||||||||
\(857\) | −47.9302 | −1.63726 | −0.818632 | − | 0.574318i | \(-0.805267\pi\) | ||||
−0.818632 | + | 0.574318i | \(0.805267\pi\) | |||||||
\(858\) | −19.2545 | −0.657338 | ||||||||
\(859\) | −6.23647 | −0.212786 | −0.106393 | − | 0.994324i | \(-0.533930\pi\) | ||||
−0.106393 | + | 0.994324i | \(0.533930\pi\) | |||||||
\(860\) | 41.9244 | 1.42961 | ||||||||
\(861\) | 1.35999 | 0.0463482 | ||||||||
\(862\) | −25.6140 | −0.872417 | ||||||||
\(863\) | 8.46337 | 0.288097 | 0.144048 | − | 0.989571i | \(-0.453988\pi\) | ||||
0.144048 | + | 0.989571i | \(0.453988\pi\) | |||||||
\(864\) | 5.63637 | 0.191753 | ||||||||
\(865\) | −93.9739 | −3.19521 | ||||||||
\(866\) | 20.5767 | 0.699226 | ||||||||
\(867\) | 31.7416 | 1.07800 | ||||||||
\(868\) | 3.83555 | 0.130187 | ||||||||
\(869\) | 9.28231 | 0.314881 | ||||||||
\(870\) | 21.4296 | 0.726530 | ||||||||
\(871\) | 12.4236 | 0.420959 | ||||||||
\(872\) | 17.0866 | 0.578625 | ||||||||
\(873\) | 11.5001 | 0.389220 | ||||||||
\(874\) | −0.732035 | −0.0247614 | ||||||||
\(875\) | −10.0136 | −0.338520 | ||||||||
\(876\) | −13.1166 | −0.443169 | ||||||||
\(877\) | 42.1172 | 1.42220 | 0.711098 | − | 0.703093i | \(-0.248198\pi\) | ||||
0.711098 | + | 0.703093i | \(0.248198\pi\) | |||||||
\(878\) | −15.6900 | −0.529512 | ||||||||
\(879\) | −14.7849 | −0.498681 | ||||||||
\(880\) | 15.8161 | 0.533160 | ||||||||
\(881\) | −35.0575 | −1.18112 | −0.590558 | − | 0.806995i | \(-0.701092\pi\) | ||||
−0.590558 | + | 0.806995i | \(0.701092\pi\) | |||||||
\(882\) | −8.06873 | −0.271688 | ||||||||
\(883\) | 49.3854 | 1.66195 | 0.830976 | − | 0.556308i | \(-0.187783\pi\) | ||||
0.830976 | + | 0.556308i | \(0.187783\pi\) | |||||||
\(884\) | −22.5438 | −0.758229 | ||||||||
\(885\) | −15.6473 | −0.525979 | ||||||||
\(886\) | −29.0018 | −0.974335 | ||||||||
\(887\) | −20.5875 | −0.691261 | −0.345630 | − | 0.938371i | \(-0.612335\pi\) | ||||
−0.345630 | + | 0.938371i | \(0.612335\pi\) | |||||||
\(888\) | 5.67999 | 0.190608 | ||||||||
\(889\) | −1.55630 | −0.0521968 | ||||||||
\(890\) | −7.30281 | −0.244791 | ||||||||
\(891\) | −16.1832 | −0.542157 | ||||||||
\(892\) | 19.8791 | 0.665602 | ||||||||
\(893\) | 9.09144 | 0.304233 | ||||||||
\(894\) | −25.8254 | −0.863731 | ||||||||
\(895\) | 67.0783 | 2.24218 | ||||||||
\(896\) | 0.487928 | 0.0163005 | ||||||||
\(897\) | 3.56680 | 0.119092 | ||||||||
\(898\) | −18.1978 | −0.607267 | ||||||||
\(899\) | 32.0876 | 1.07018 | ||||||||
\(900\) | −12.2363 | −0.407877 | ||||||||
\(901\) | −70.8871 | −2.36159 | ||||||||
\(902\) | 8.39710 | 0.279593 | ||||||||
\(903\) | −7.03998 | −0.234276 | ||||||||
\(904\) | −13.3194 | −0.442997 | ||||||||
\(905\) | −28.4677 | −0.946298 | ||||||||
\(906\) | 4.88783 | 0.162387 | ||||||||
\(907\) | −57.1062 | −1.89618 | −0.948090 | − | 0.318003i | \(-0.896988\pi\) | ||||
−0.948090 | + | 0.318003i | \(0.896988\pi\) | |||||||
\(908\) | 27.7566 | 0.921136 | ||||||||
\(909\) | −7.06109 | −0.234202 | ||||||||
\(910\) | 6.74125 | 0.223470 | ||||||||
\(911\) | 1.11278 | 0.0368680 | 0.0184340 | − | 0.999830i | \(-0.494132\pi\) | ||||
0.0184340 | + | 0.999830i | \(0.494132\pi\) | |||||||
\(912\) | 1.31170 | 0.0434347 | ||||||||
\(913\) | −69.3775 | −2.29606 | ||||||||
\(914\) | −32.1933 | −1.06486 | ||||||||
\(915\) | −39.5703 | −1.30815 | ||||||||
\(916\) | −17.6723 | −0.583909 | ||||||||
\(917\) | 5.65874 | 0.186868 | ||||||||
\(918\) | −35.9204 | −1.18555 | ||||||||
\(919\) | −24.6902 | −0.814453 | −0.407227 | − | 0.913327i | \(-0.633504\pi\) | ||||
−0.407227 | + | 0.913327i | \(0.633504\pi\) | |||||||
\(920\) | −2.92985 | −0.0965942 | ||||||||
\(921\) | 20.4259 | 0.673057 | ||||||||
\(922\) | 26.9152 | 0.886405 | ||||||||
\(923\) | 50.0009 | 1.64580 | ||||||||
\(924\) | −2.65585 | −0.0873710 | ||||||||
\(925\) | −43.3326 | −1.42477 | ||||||||
\(926\) | 24.2349 | 0.796407 | ||||||||
\(927\) | −0.573736 | −0.0188440 | ||||||||
\(928\) | 4.08193 | 0.133996 | ||||||||
\(929\) | 53.4317 | 1.75304 | 0.876519 | − | 0.481368i | \(-0.159860\pi\) | ||||
0.876519 | + | 0.481368i | \(0.159860\pi\) | |||||||
\(930\) | 41.2685 | 1.35325 | ||||||||
\(931\) | −6.59867 | −0.216263 | ||||||||
\(932\) | −1.67230 | −0.0547779 | ||||||||
\(933\) | 12.1306 | 0.397139 | ||||||||
\(934\) | 17.7628 | 0.581216 | ||||||||
\(935\) | −100.795 | −3.29636 | ||||||||
\(936\) | 4.22105 | 0.137969 | ||||||||
\(937\) | −8.01583 | −0.261866 | −0.130933 | − | 0.991391i | \(-0.541797\pi\) | ||||
−0.130933 | + | 0.991391i | \(0.541797\pi\) | |||||||
\(938\) | 1.71364 | 0.0559523 | ||||||||
\(939\) | 46.1690 | 1.50667 | ||||||||
\(940\) | 36.3870 | 1.18681 | ||||||||
\(941\) | −10.2934 | −0.335556 | −0.167778 | − | 0.985825i | \(-0.553659\pi\) | ||||
−0.167778 | + | 0.985825i | \(0.553659\pi\) | |||||||
\(942\) | 20.1781 | 0.657438 | ||||||||
\(943\) | −1.55552 | −0.0506547 | ||||||||
\(944\) | −2.98052 | −0.0970077 | ||||||||
\(945\) | 10.7413 | 0.349413 | ||||||||
\(946\) | −43.4677 | −1.41326 | ||||||||
\(947\) | 42.4848 | 1.38057 | 0.690285 | − | 0.723538i | \(-0.257485\pi\) | ||||
0.690285 | + | 0.723538i | \(0.257485\pi\) | |||||||
\(948\) | 3.08109 | 0.100069 | ||||||||
\(949\) | −34.5190 | −1.12054 | ||||||||
\(950\) | −10.0069 | −0.324668 | ||||||||
\(951\) | 27.6070 | 0.895218 | ||||||||
\(952\) | −3.10955 | −0.100781 | ||||||||
\(953\) | 59.0011 | 1.91123 | 0.955617 | − | 0.294612i | \(-0.0951905\pi\) | ||||
0.955617 | + | 0.294612i | \(0.0951905\pi\) | |||||||
\(954\) | 13.2727 | 0.429721 | ||||||||
\(955\) | −25.5839 | −0.827874 | ||||||||
\(956\) | −24.0925 | −0.779206 | ||||||||
\(957\) | −22.2184 | −0.718220 | ||||||||
\(958\) | −11.4930 | −0.371323 | ||||||||
\(959\) | 3.57680 | 0.115501 | ||||||||
\(960\) | 5.24985 | 0.169438 | ||||||||
\(961\) | 30.7936 | 0.993341 | ||||||||
\(962\) | 14.9481 | 0.481945 | ||||||||
\(963\) | −4.56417 | −0.147078 | ||||||||
\(964\) | −18.2257 | −0.587011 | ||||||||
\(965\) | 68.5324 | 2.20614 | ||||||||
\(966\) | 0.491983 | 0.0158293 | ||||||||
\(967\) | −0.781747 | −0.0251393 | −0.0125696 | − | 0.999921i | \(-0.504001\pi\) | ||||
−0.0125696 | + | 0.999921i | \(0.504001\pi\) | |||||||
\(968\) | −5.39830 | −0.173508 | ||||||||
\(969\) | −8.35940 | −0.268543 | ||||||||
\(970\) | 37.6415 | 1.20860 | ||||||||
\(971\) | 51.5702 | 1.65497 | 0.827484 | − | 0.561489i | \(-0.189771\pi\) | ||||
0.827484 | + | 0.561489i | \(0.189771\pi\) | |||||||
\(972\) | 11.5374 | 0.370063 | ||||||||
\(973\) | 6.43708 | 0.206363 | ||||||||
\(974\) | −5.85514 | −0.187611 | ||||||||
\(975\) | 48.7583 | 1.56152 | ||||||||
\(976\) | −7.53741 | −0.241267 | ||||||||
\(977\) | 3.02820 | 0.0968806 | 0.0484403 | − | 0.998826i | \(-0.484575\pi\) | ||||
0.0484403 | + | 0.998826i | \(0.484575\pi\) | |||||||
\(978\) | 6.41874 | 0.205249 | ||||||||
\(979\) | 7.57164 | 0.241991 | ||||||||
\(980\) | −26.4101 | −0.843639 | ||||||||
\(981\) | 20.3887 | 0.650962 | ||||||||
\(982\) | −18.6544 | −0.595287 | ||||||||
\(983\) | −45.6956 | −1.45746 | −0.728732 | − | 0.684799i | \(-0.759890\pi\) | ||||
−0.728732 | + | 0.684799i | \(0.759890\pi\) | |||||||
\(984\) | 2.78726 | 0.0888547 | ||||||||
\(985\) | −57.0432 | −1.81755 | ||||||||
\(986\) | −26.0140 | −0.828454 | ||||||||
\(987\) | −6.11013 | −0.194488 | ||||||||
\(988\) | 3.45200 | 0.109823 | ||||||||
\(989\) | 8.05217 | 0.256044 | ||||||||
\(990\) | 18.8727 | 0.599813 | ||||||||
\(991\) | −30.3370 | −0.963685 | −0.481843 | − | 0.876258i | \(-0.660032\pi\) | ||||
−0.481843 | + | 0.876258i | \(0.660032\pi\) | |||||||
\(992\) | 7.86089 | 0.249583 | ||||||||
\(993\) | −11.1681 | −0.354409 | ||||||||
\(994\) | 6.89681 | 0.218754 | ||||||||
\(995\) | −18.1288 | −0.574721 | ||||||||
\(996\) | −23.0286 | −0.729688 | ||||||||
\(997\) | 27.9443 | 0.885004 | 0.442502 | − | 0.896767i | \(-0.354091\pi\) | ||||
0.442502 | + | 0.896767i | \(0.354091\pi\) | |||||||
\(998\) | −35.1119 | −1.11145 | ||||||||
\(999\) | 23.8177 | 0.753558 |
(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 | 538.2.a.c.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 4842.2.a.j.1.1 | 4 | |||
4.3 | odd | 2 | 4304.2.a.e.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
538.2.a.c.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4304.2.a.e.1.2 | 4 | 4.3 | odd | 2 | |||
4842.2.a.j.1.1 | 4 | 3.2 | odd | 2 |