Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4842,2,Mod(1,4842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4842, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4842 = 2 \cdot 3^{2} \cdot 269 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4842.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: | \(38.6635646587\) |
Analytic rank: | \(1\) |
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: | no (minimal twist has level 538) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.90570\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4842.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.90570 | −1.74668 | −0.873342 | − | 0.487108i | \(-0.838052\pi\) | ||||
−0.873342 | + | 0.487108i | \(0.838052\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.487928 | −0.184420 | −0.0922098 | − | 0.995740i | \(-0.529393\pi\) | ||||
−0.0922098 | + | 0.995740i | \(0.529393\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.90570 | −1.23509 | ||||||||
\(11\) | −4.04948 | −1.22096 | −0.610482 | − | 0.792030i | \(-0.709024\pi\) | ||||
−0.610482 | + | 0.792030i | \(0.709024\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.53741 | 0.981101 | 0.490550 | − | 0.871413i | \(-0.336796\pi\) | ||||
0.490550 | + | 0.871413i | \(0.336796\pi\) | |||||||
\(14\) | −0.487928 | −0.130404 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.37296 | 1.54567 | 0.772835 | − | 0.634607i | \(-0.218838\pi\) | ||||
0.772835 | + | 0.634607i | \(0.218838\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 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 | 0 | ||||||||
\(22\) | −4.04948 | −0.863352 | ||||||||
\(23\) | −0.750146 | −0.156416 | −0.0782081 | − | 0.996937i | \(-0.524920\pi\) | ||||
−0.0782081 | + | 0.996937i | \(0.524920\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.2545 | 2.05090 | ||||||||
\(26\) | 3.53741 | 0.693743 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.487928 | −0.0922098 | ||||||||
\(29\) | 4.08193 | 0.757996 | 0.378998 | − | 0.925397i | \(-0.376269\pi\) | ||||
0.378998 | + | 0.925397i | \(0.376269\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.86089 | −1.41186 | −0.705929 | − | 0.708283i | \(-0.749470\pi\) | ||||
−0.705929 | + | 0.708283i | \(0.749470\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.37296 | 1.09295 | ||||||||
\(35\) | 1.90570 | 0.322123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.22571 | −0.694703 | −0.347351 | − | 0.937735i | \(-0.612919\pi\) | ||||
−0.347351 | + | 0.937735i | \(0.612919\pi\) | |||||||
\(38\) | 0.975857 | 0.158305 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.90570 | −0.617546 | ||||||||
\(41\) | 2.07362 | 0.323846 | 0.161923 | − | 0.986803i | \(-0.448230\pi\) | ||||
0.161923 | + | 0.986803i | \(0.448230\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7341 | 1.63694 | 0.818470 | − | 0.574549i | \(-0.194822\pi\) | ||||
0.818470 | + | 0.574549i | \(0.194822\pi\) | |||||||
\(44\) | −4.04948 | −0.610482 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.750146 | −0.110603 | ||||||||
\(47\) | −9.31636 | −1.35893 | −0.679466 | − | 0.733707i | \(-0.737788\pi\) | ||||
−0.679466 | + | 0.733707i | \(0.737788\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.76193 | −0.965989 | ||||||||
\(50\) | 10.2545 | 1.45021 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.53741 | 0.490550 | ||||||||
\(53\) | −11.1231 | −1.52788 | −0.763938 | − | 0.645290i | \(-0.776737\pi\) | ||||
−0.763938 | + | 0.645290i | \(0.776737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.8161 | 2.13264 | ||||||||
\(56\) | −0.487928 | −0.0652022 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.08193 | 0.535984 | ||||||||
\(59\) | 2.98052 | 0.388031 | 0.194015 | − | 0.980998i | \(-0.437849\pi\) | ||||
0.194015 | + | 0.980998i | \(0.437849\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −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 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −13.8161 | −1.71367 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.51207 | 0.429068 | 0.214534 | − | 0.976717i | \(-0.431177\pi\) | ||||
0.214534 | + | 0.976717i | \(0.431177\pi\) | |||||||
\(68\) | 6.37296 | 0.772835 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.90570 | 0.227775 | ||||||||
\(71\) | −14.1349 | −1.67750 | −0.838751 | − | 0.544515i | \(-0.816714\pi\) | ||||
−0.838751 | + | 0.544515i | \(0.816714\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.75828 | −1.14212 | −0.571060 | − | 0.820908i | \(-0.693468\pi\) | ||||
−0.571060 | + | 0.820908i | \(0.693468\pi\) | |||||||
\(74\) | −4.22571 | −0.491229 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.975857 | 0.111938 | ||||||||
\(77\) | 1.97586 | 0.225170 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.29222 | 0.257895 | 0.128948 | − | 0.991651i | \(-0.458840\pi\) | ||||
0.128948 | + | 0.991651i | \(0.458840\pi\) | |||||||
\(80\) | −3.90570 | −0.436671 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.07362 | 0.228994 | ||||||||
\(83\) | 17.1324 | 1.88053 | 0.940265 | − | 0.340444i | \(-0.110578\pi\) | ||||
0.940265 | + | 0.340444i | \(0.110578\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.8909 | −2.69980 | ||||||||
\(86\) | 10.7341 | 1.15749 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.04948 | −0.431676 | ||||||||
\(89\) | −1.86978 | −0.198196 | −0.0990981 | − | 0.995078i | \(-0.531596\pi\) | ||||
−0.0990981 | + | 0.995078i | \(0.531596\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.72600 | −0.180934 | ||||||||
\(92\) | −0.750146 | −0.0782081 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.31636 | −0.960910 | ||||||||
\(95\) | −3.81141 | −0.391042 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.63757 | −0.978547 | −0.489273 | − | 0.872131i | \(-0.662738\pi\) | ||||
−0.489273 | + | 0.872131i | \(0.662738\pi\) | |||||||
\(98\) | −6.76193 | −0.683058 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.2545 | 1.02545 | ||||||||
\(101\) | −5.91748 | −0.588812 | −0.294406 | − | 0.955680i | \(-0.595122\pi\) | ||||
−0.294406 | + | 0.955680i | \(0.595122\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.480814 | 0.0473760 | 0.0236880 | − | 0.999719i | \(-0.492459\pi\) | ||||
0.0236880 | + | 0.999719i | \(0.492459\pi\) | |||||||
\(104\) | 3.53741 | 0.346872 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.1231 | −1.08037 | ||||||||
\(107\) | −3.82496 | −0.369773 | −0.184887 | − | 0.982760i | \(-0.559192\pi\) | ||||
−0.184887 | + | 0.982760i | \(0.559192\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.0866 | −1.63660 | −0.818300 | − | 0.574792i | \(-0.805083\pi\) | ||||
−0.818300 | + | 0.574792i | \(0.805083\pi\) | |||||||
\(110\) | 15.8161 | 1.50800 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.487928 | −0.0461049 | ||||||||
\(113\) | −13.3194 | −1.25299 | −0.626493 | − | 0.779427i | \(-0.715510\pi\) | ||||
−0.626493 | + | 0.779427i | \(0.715510\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.92985 | 0.273210 | ||||||||
\(116\) | 4.08193 | 0.378998 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.98052 | 0.274379 | ||||||||
\(119\) | −3.10955 | −0.285052 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.39830 | 0.490754 | ||||||||
\(122\) | −7.53741 | −0.682405 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.86089 | −0.705929 | ||||||||
\(125\) | −20.5226 | −1.83560 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.18962 | 0.283033 | 0.141516 | − | 0.989936i | \(-0.454802\pi\) | ||||
0.141516 | + | 0.989936i | \(0.454802\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −13.8161 | −1.21175 | ||||||||
\(131\) | 11.5975 | 1.01328 | 0.506638 | − | 0.862159i | \(-0.330888\pi\) | ||||
0.506638 | + | 0.862159i | \(0.330888\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.476148 | −0.0412873 | ||||||||
\(134\) | 3.51207 | 0.303397 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.37296 | 0.546477 | ||||||||
\(137\) | 7.33059 | 0.626295 | 0.313147 | − | 0.949705i | \(-0.398617\pi\) | ||||
0.313147 | + | 0.949705i | \(0.398617\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.1927 | −1.11899 | −0.559494 | − | 0.828834i | \(-0.689005\pi\) | ||||
−0.559494 | + | 0.828834i | \(0.689005\pi\) | |||||||
\(140\) | 1.90570 | 0.161061 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.1349 | −1.18617 | ||||||||
\(143\) | −14.3247 | −1.19789 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.9428 | −1.32398 | ||||||||
\(146\) | −9.75828 | −0.807601 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.22571 | −0.347351 | ||||||||
\(149\) | −19.2132 | −1.57400 | −0.787002 | − | 0.616950i | \(-0.788368\pi\) | ||||
−0.787002 | + | 0.616950i | \(0.788368\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.63637 | −0.295924 | −0.147962 | − | 0.988993i | \(-0.547271\pi\) | ||||
−0.147962 | + | 0.988993i | \(0.547271\pi\) | |||||||
\(152\) | 0.975857 | 0.0791524 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.97586 | 0.159219 | ||||||||
\(155\) | 30.7023 | 2.46607 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.0118 | −1.19807 | −0.599035 | − | 0.800723i | \(-0.704449\pi\) | ||||
−0.599035 | + | 0.800723i | \(0.704449\pi\) | |||||||
\(158\) | 2.29222 | 0.182359 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.90570 | −0.308773 | ||||||||
\(161\) | 0.366017 | 0.0288462 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.77531 | −0.374031 | −0.187016 | − | 0.982357i | \(-0.559882\pi\) | ||||
−0.187016 | + | 0.982357i | \(0.559882\pi\) | |||||||
\(164\) | 2.07362 | 0.161923 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.1324 | 1.32974 | ||||||||
\(167\) | 3.94163 | 0.305012 | 0.152506 | − | 0.988303i | \(-0.451266\pi\) | ||||
0.152506 | + | 0.988303i | \(0.451266\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.486734 | −0.0374411 | ||||||||
\(170\) | −24.8909 | −1.90904 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.7341 | 0.818470 | ||||||||
\(173\) | 24.0607 | 1.82930 | 0.914650 | − | 0.404247i | \(-0.132466\pi\) | ||||
0.914650 | + | 0.404247i | \(0.132466\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.00347 | −0.378227 | ||||||||
\(176\) | −4.04948 | −0.305241 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.86978 | −0.140146 | ||||||||
\(179\) | −17.1745 | −1.28368 | −0.641839 | − | 0.766839i | \(-0.721828\pi\) | ||||
−0.641839 | + | 0.766839i | \(0.721828\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.28875 | −0.541769 | −0.270884 | − | 0.962612i | \(-0.587316\pi\) | ||||
−0.270884 | + | 0.962612i | \(0.587316\pi\) | |||||||
\(182\) | −1.72600 | −0.127940 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.750146 | −0.0553015 | ||||||||
\(185\) | 16.5044 | 1.21343 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.8072 | −1.88721 | ||||||||
\(188\) | −9.31636 | −0.679466 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.81141 | −0.276509 | ||||||||
\(191\) | 6.55038 | 0.473969 | 0.236985 | − | 0.971513i | \(-0.423841\pi\) | ||||
0.236985 | + | 0.971513i | \(0.423841\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.5467 | 1.26304 | 0.631521 | − | 0.775359i | \(-0.282431\pi\) | ||||
0.631521 | + | 0.775359i | \(0.282431\pi\) | |||||||
\(194\) | −9.63757 | −0.691937 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.76193 | −0.482995 | ||||||||
\(197\) | 14.6051 | 1.04057 | 0.520286 | − | 0.853992i | \(-0.325825\pi\) | ||||
0.520286 | + | 0.853992i | \(0.325825\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.64162 | −0.329036 | −0.164518 | − | 0.986374i | \(-0.552607\pi\) | ||||
−0.164518 | + | 0.986374i | \(0.552607\pi\) | |||||||
\(200\) | 10.2545 | 0.725104 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.91748 | −0.416353 | ||||||||
\(203\) | −1.99169 | −0.139789 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.09896 | −0.565656 | ||||||||
\(206\) | 0.480814 | 0.0334999 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.53741 | 0.245275 | ||||||||
\(209\) | −3.95171 | −0.273346 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.7554 | 1.08465 | 0.542324 | − | 0.840169i | \(-0.317545\pi\) | ||||
0.542324 | + | 0.840169i | \(0.317545\pi\) | |||||||
\(212\) | −11.1231 | −0.763938 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.82496 | −0.261469 | ||||||||
\(215\) | −41.9244 | −2.85922 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.83555 | 0.260374 | ||||||||
\(218\) | −17.0866 | −1.15725 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 15.8161 | 1.06632 | ||||||||
\(221\) | 22.5438 | 1.51646 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.8791 | 1.33120 | 0.665602 | − | 0.746307i | \(-0.268175\pi\) | ||||
0.665602 | + | 0.746307i | \(0.268175\pi\) | |||||||
\(224\) | −0.487928 | −0.0326011 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.3194 | −0.885995 | ||||||||
\(227\) | −27.7566 | −1.84227 | −0.921136 | − | 0.389242i | \(-0.872737\pi\) | ||||
−0.921136 | + | 0.389242i | \(0.872737\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.6723 | −1.16782 | −0.583909 | − | 0.811819i | \(-0.698478\pi\) | ||||
−0.583909 | + | 0.811819i | \(0.698478\pi\) | |||||||
\(230\) | 2.92985 | 0.193188 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.08193 | 0.267992 | ||||||||
\(233\) | 1.67230 | 0.109556 | 0.0547779 | − | 0.998499i | \(-0.482555\pi\) | ||||
0.0547779 | + | 0.998499i | \(0.482555\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 36.3870 | 2.37362 | ||||||||
\(236\) | 2.98052 | 0.194015 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.10955 | −0.201562 | ||||||||
\(239\) | 24.0925 | 1.55841 | 0.779206 | − | 0.626768i | \(-0.215623\pi\) | ||||
0.779206 | + | 0.626768i | \(0.215623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.2257 | −1.17402 | −0.587011 | − | 0.809579i | \(-0.699695\pi\) | ||||
−0.587011 | + | 0.809579i | \(0.699695\pi\) | |||||||
\(242\) | 5.39830 | 0.347016 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.53741 | −0.482533 | ||||||||
\(245\) | 26.4101 | 1.68728 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.45200 | 0.219646 | ||||||||
\(248\) | −7.86089 | −0.499167 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −20.5226 | −1.29796 | ||||||||
\(251\) | 1.21740 | 0.0768417 | 0.0384209 | − | 0.999262i | \(-0.487767\pi\) | ||||
0.0384209 | + | 0.999262i | \(0.487767\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.03770 | 0.190979 | ||||||||
\(254\) | 3.18962 | 0.200134 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.7806 | −1.79529 | −0.897644 | − | 0.440722i | \(-0.854723\pi\) | ||||
−0.897644 | + | 0.440722i | \(0.854723\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.06184 | 0.128117 | ||||||||
\(260\) | −13.8161 | −0.856836 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.5975 | 0.716494 | ||||||||
\(263\) | 4.35407 | 0.268483 | 0.134242 | − | 0.990949i | \(-0.457140\pi\) | ||||
0.134242 | + | 0.990949i | \(0.457140\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 43.4436 | 2.66872 | ||||||||
\(266\) | −0.476148 | −0.0291945 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.51207 | 0.214534 | ||||||||
\(269\) | −1.00000 | −0.0609711 | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.6940 | −1.19632 | −0.598162 | − | 0.801375i | \(-0.704102\pi\) | ||||
−0.598162 | + | 0.801375i | \(0.704102\pi\) | |||||||
\(272\) | 6.37296 | 0.386417 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.33059 | 0.442857 | ||||||||
\(275\) | −41.5255 | −2.50408 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.31009 | −0.0787158 | −0.0393579 | − | 0.999225i | \(-0.512531\pi\) | ||||
−0.0393579 | + | 0.999225i | \(0.512531\pi\) | |||||||
\(278\) | −13.1927 | −0.791244 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.90570 | 0.113888 | ||||||||
\(281\) | −7.94749 | −0.474107 | −0.237054 | − | 0.971497i | \(-0.576182\pi\) | ||||
−0.237054 | + | 0.971497i | \(0.576182\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.7544 | 1.23372 | 0.616861 | − | 0.787072i | \(-0.288404\pi\) | ||||
0.616861 | + | 0.787072i | \(0.288404\pi\) | |||||||
\(284\) | −14.1349 | −0.838751 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.3247 | −0.847036 | ||||||||
\(287\) | −1.01178 | −0.0597235 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.6146 | 1.38910 | ||||||||
\(290\) | −15.9428 | −0.936195 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.75828 | −0.571060 | ||||||||
\(293\) | 10.9994 | 0.642593 | 0.321296 | − | 0.946979i | \(-0.395881\pi\) | ||||
0.321296 | + | 0.946979i | \(0.395881\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.6410 | −0.677767 | ||||||||
\(296\) | −4.22571 | −0.245614 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.2132 | −1.11299 | ||||||||
\(299\) | −2.65357 | −0.153460 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.23749 | −0.301884 | ||||||||
\(302\) | −3.63637 | −0.209250 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.975857 | 0.0559692 | ||||||||
\(305\) | 29.4389 | 1.68567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 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 | 0 | ||||||||
\(310\) | 30.7023 | 1.74377 | ||||||||
\(311\) | −9.02476 | −0.511747 | −0.255873 | − | 0.966710i | \(-0.582363\pi\) | ||||
−0.255873 | + | 0.966710i | \(0.582363\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.3481 | 1.94147 | 0.970734 | − | 0.240159i | \(-0.0771995\pi\) | ||||
0.970734 | + | 0.240159i | \(0.0771995\pi\) | |||||||
\(314\) | −15.0118 | −0.847164 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.29222 | 0.128948 | ||||||||
\(317\) | −20.5386 | −1.15356 | −0.576781 | − | 0.816898i | \(-0.695692\pi\) | ||||
−0.576781 | + | 0.816898i | \(0.695692\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.5297 | −0.925486 | ||||||||
\(320\) | −3.90570 | −0.218335 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.366017 | 0.0203974 | ||||||||
\(323\) | 6.21910 | 0.346040 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 36.2744 | 2.01214 | ||||||||
\(326\) | −4.77531 | −0.264480 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.07362 | 0.114497 | ||||||||
\(329\) | 4.54572 | 0.250614 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.30867 | −0.456686 | −0.228343 | − | 0.973581i | \(-0.573331\pi\) | ||||
−0.228343 | + | 0.973581i | \(0.573331\pi\) | |||||||
\(332\) | 17.1324 | 0.940265 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.94163 | 0.215676 | ||||||||
\(335\) | −13.7171 | −0.749446 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.9588 | −0.978276 | −0.489138 | − | 0.872206i | \(-0.662689\pi\) | ||||
−0.489138 | + | 0.872206i | \(0.662689\pi\) | |||||||
\(338\) | −0.486734 | −0.0264748 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −24.8909 | −1.34990 | ||||||||
\(341\) | 31.8325 | 1.72383 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.71483 | 0.362567 | ||||||||
\(344\) | 10.7341 | 0.578746 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.0607 | 1.29351 | ||||||||
\(347\) | −6.69769 | −0.359551 | −0.179775 | − | 0.983708i | \(-0.557537\pi\) | ||||
−0.179775 | + | 0.983708i | \(0.557537\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.974251 | 0.0521505 | 0.0260752 | − | 0.999660i | \(-0.491699\pi\) | ||||
0.0260752 | + | 0.999660i | \(0.491699\pi\) | |||||||
\(350\) | −5.00347 | −0.267447 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.04948 | −0.215838 | ||||||||
\(353\) | −15.8928 | −0.845886 | −0.422943 | − | 0.906156i | \(-0.639003\pi\) | ||||
−0.422943 | + | 0.906156i | \(0.639003\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 55.2067 | 2.93007 | ||||||||
\(356\) | −1.86978 | −0.0990981 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −17.1745 | −0.907698 | ||||||||
\(359\) | 8.66535 | 0.457340 | 0.228670 | − | 0.973504i | \(-0.426562\pi\) | ||||
0.228670 | + | 0.973504i | \(0.426562\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0477 | −0.949879 | ||||||||
\(362\) | −7.28875 | −0.383088 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.72600 | −0.0904671 | ||||||||
\(365\) | 38.1130 | 1.99492 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.50802 | 0.391915 | 0.195958 | − | 0.980612i | \(-0.437218\pi\) | ||||
0.195958 | + | 0.980612i | \(0.437218\pi\) | |||||||
\(368\) | −0.750146 | −0.0391040 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 16.5044 | 0.858022 | ||||||||
\(371\) | 5.42728 | 0.281770 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.14911 | 0.111277 | 0.0556385 | − | 0.998451i | \(-0.482281\pi\) | ||||
0.0556385 | + | 0.998451i | \(0.482281\pi\) | |||||||
\(374\) | −25.8072 | −1.33446 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.31636 | −0.480455 | ||||||||
\(377\) | 14.4395 | 0.743671 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.71644 | 0.396367 | 0.198183 | − | 0.980165i | \(-0.436496\pi\) | ||||
0.198183 | + | 0.980165i | \(0.436496\pi\) | |||||||
\(380\) | −3.81141 | −0.195521 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.55038 | 0.335147 | ||||||||
\(383\) | −1.88104 | −0.0961165 | −0.0480582 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480582 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.71711 | −0.393300 | ||||||||
\(386\) | 17.5467 | 0.893106 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.63757 | −0.489273 | ||||||||
\(389\) | 10.7025 | 0.542640 | 0.271320 | − | 0.962489i | \(-0.412540\pi\) | ||||
0.271320 | + | 0.962489i | \(0.412540\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.78065 | −0.241768 | ||||||||
\(392\) | −6.76193 | −0.341529 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.6051 | 0.735795 | ||||||||
\(395\) | −8.95274 | −0.450461 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 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 | 0 | ||||||||
\(400\) | 10.2545 | 0.512726 | ||||||||
\(401\) | 0.717694 | 0.0358399 | 0.0179200 | − | 0.999839i | \(-0.494296\pi\) | ||||
0.0179200 | + | 0.999839i | \(0.494296\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.8072 | −1.38517 | ||||||||
\(404\) | −5.91748 | −0.294406 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.99169 | −0.0988460 | ||||||||
\(407\) | 17.1119 | 0.848207 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.7906 | −0.583006 | −0.291503 | − | 0.956570i | \(-0.594155\pi\) | ||||
−0.291503 | + | 0.956570i | \(0.594155\pi\) | |||||||
\(410\) | −8.09896 | −0.399979 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.480814 | 0.0236880 | ||||||||
\(413\) | −1.45428 | −0.0715605 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −66.9142 | −3.28469 | ||||||||
\(416\) | 3.53741 | 0.173436 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.95171 | −0.193285 | ||||||||
\(419\) | 7.07076 | 0.345429 | 0.172715 | − | 0.984972i | \(-0.444746\pi\) | ||||
0.172715 | + | 0.984972i | \(0.444746\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.96469 | −0.241964 | −0.120982 | − | 0.992655i | \(-0.538604\pi\) | ||||
−0.120982 | + | 0.992655i | \(0.538604\pi\) | |||||||
\(422\) | 15.7554 | 0.766962 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.1231 | −0.540186 | ||||||||
\(425\) | 65.3516 | 3.17002 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.67772 | 0.177977 | ||||||||
\(428\) | −3.82496 | −0.184887 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −41.9244 | −2.02177 | ||||||||
\(431\) | −25.6140 | −1.23378 | −0.616892 | − | 0.787048i | \(-0.711609\pi\) | ||||
−0.616892 | + | 0.787048i | \(0.711609\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.5767 | −0.988855 | −0.494428 | − | 0.869219i | \(-0.664622\pi\) | ||||
−0.494428 | + | 0.869219i | \(0.664622\pi\) | |||||||
\(434\) | 3.83555 | 0.184112 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.0866 | −0.818300 | ||||||||
\(437\) | −0.732035 | −0.0350180 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.6900 | 0.748843 | 0.374421 | − | 0.927259i | \(-0.377841\pi\) | ||||
0.374421 | + | 0.927259i | \(0.377841\pi\) | |||||||
\(440\) | 15.8161 | 0.754002 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22.5438 | 1.07230 | ||||||||
\(443\) | −29.0018 | −1.37792 | −0.688959 | − | 0.724801i | \(-0.741932\pi\) | ||||
−0.688959 | + | 0.724801i | \(0.741932\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.30281 | 0.346186 | ||||||||
\(446\) | 19.8791 | 0.941303 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.487928 | −0.0230524 | ||||||||
\(449\) | −18.1978 | −0.858805 | −0.429403 | − | 0.903113i | \(-0.641276\pi\) | ||||
−0.429403 | + | 0.903113i | \(0.641276\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.39710 | −0.395404 | ||||||||
\(452\) | −13.3194 | −0.626493 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −27.7566 | −1.30268 | ||||||||
\(455\) | 6.74125 | 0.316035 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.1933 | 1.50594 | 0.752969 | − | 0.658056i | \(-0.228621\pi\) | ||||
0.752969 | + | 0.658056i | \(0.228621\pi\) | |||||||
\(458\) | −17.6723 | −0.825772 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.92985 | 0.136605 | ||||||||
\(461\) | 26.9152 | 1.25357 | 0.626783 | − | 0.779194i | \(-0.284371\pi\) | ||||
0.626783 | + | 0.779194i | \(0.284371\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.2349 | −1.12629 | −0.563145 | − | 0.826358i | \(-0.690409\pi\) | ||||
−0.563145 | + | 0.826358i | \(0.690409\pi\) | |||||||
\(464\) | 4.08193 | 0.189499 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.67230 | 0.0774676 | ||||||||
\(467\) | 17.7628 | 0.821963 | 0.410982 | − | 0.911644i | \(-0.365186\pi\) | ||||
0.410982 | + | 0.911644i | \(0.365186\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.71364 | −0.0791285 | ||||||||
\(470\) | 36.3870 | 1.67841 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.98052 | 0.137190 | ||||||||
\(473\) | −43.4677 | −1.99865 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.0069 | 0.459150 | ||||||||
\(476\) | −3.10955 | −0.142526 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.0925 | 1.10196 | ||||||||
\(479\) | −11.4930 | −0.525130 | −0.262565 | − | 0.964914i | \(-0.584568\pi\) | ||||
−0.262565 | + | 0.964914i | \(0.584568\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.9481 | −0.681573 | ||||||||
\(482\) | −18.2257 | −0.830158 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.39830 | 0.245377 | ||||||||
\(485\) | 37.6415 | 1.70921 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.85514 | 0.265322 | 0.132661 | − | 0.991161i | \(-0.457648\pi\) | ||||
0.132661 | + | 0.991161i | \(0.457648\pi\) | |||||||
\(488\) | −7.53741 | −0.341202 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 26.4101 | 1.19309 | ||||||||
\(491\) | −18.6544 | −0.841862 | −0.420931 | − | 0.907093i | \(-0.638297\pi\) | ||||
−0.420931 | + | 0.907093i | \(0.638297\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.0140 | 1.17161 | ||||||||
\(494\) | 3.45200 | 0.155313 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.86089 | −0.352964 | ||||||||
\(497\) | 6.89681 | 0.309364 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.1119 | 1.57183 | 0.785913 | − | 0.618337i | \(-0.212193\pi\) | ||||
0.785913 | + | 0.618337i | \(0.212193\pi\) | |||||||
\(500\) | −20.5226 | −0.917798 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.21740 | 0.0543353 | ||||||||
\(503\) | −29.7342 | −1.32578 | −0.662892 | − | 0.748715i | \(-0.730671\pi\) | ||||
−0.662892 | + | 0.748715i | \(0.730671\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.1119 | 1.02847 | ||||||||
\(506\) | 3.03770 | 0.135042 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.18962 | 0.141516 | ||||||||
\(509\) | −30.1456 | −1.33618 | −0.668090 | − | 0.744081i | \(-0.732888\pi\) | ||||
−0.668090 | + | 0.744081i | \(0.732888\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.76134 | 0.210629 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −28.7806 | −1.26946 | ||||||||
\(515\) | −1.87792 | −0.0827509 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.7264 | 1.65921 | ||||||||
\(518\) | 2.06184 | 0.0905922 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −13.8161 | −0.605875 | ||||||||
\(521\) | −37.9804 | −1.66395 | −0.831975 | − | 0.554813i | \(-0.812790\pi\) | ||||
−0.831975 | + | 0.554813i | \(0.812790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.1012 | 0.441696 | 0.220848 | − | 0.975308i | \(-0.429117\pi\) | ||||
0.220848 | + | 0.975308i | \(0.429117\pi\) | |||||||
\(524\) | 11.5975 | 0.506638 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.35407 | 0.189846 | ||||||||
\(527\) | −50.0971 | −2.18227 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.4373 | −0.975534 | ||||||||
\(530\) | 43.4436 | 1.88707 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.476148 | −0.0206436 | ||||||||
\(533\) | 7.33526 | 0.317725 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.9392 | 0.645877 | ||||||||
\(536\) | 3.51207 | 0.151698 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.00000 | −0.0431131 | ||||||||
\(539\) | 27.3823 | 1.17944 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.06610 | 0.0458352 | 0.0229176 | − | 0.999737i | \(-0.492704\pi\) | ||||
0.0229176 | + | 0.999737i | \(0.492704\pi\) | |||||||
\(542\) | −19.6940 | −0.845929 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.37296 | 0.273238 | ||||||||
\(545\) | 66.7352 | 2.85862 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.62634 | 0.368836 | 0.184418 | − | 0.982848i | \(-0.440960\pi\) | ||||
0.184418 | + | 0.982848i | \(0.440960\pi\) | |||||||
\(548\) | 7.33059 | 0.313147 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −41.5255 | −1.77065 | ||||||||
\(551\) | 3.98338 | 0.169698 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.11844 | −0.0475609 | ||||||||
\(554\) | −1.31009 | −0.0556605 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.1927 | −0.559494 | ||||||||
\(557\) | −39.3859 | −1.66884 | −0.834418 | − | 0.551132i | \(-0.814196\pi\) | ||||
−0.834418 | + | 0.551132i | \(0.814196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.9710 | 1.60600 | ||||||||
\(560\) | 1.90570 | 0.0805307 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.94749 | −0.335245 | ||||||||
\(563\) | 29.8436 | 1.25776 | 0.628879 | − | 0.777503i | \(-0.283514\pi\) | ||||
0.628879 | + | 0.777503i | \(0.283514\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 52.0217 | 2.18857 | ||||||||
\(566\) | 20.7544 | 0.872373 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.1349 | −0.593087 | ||||||||
\(569\) | −18.1766 | −0.762004 | −0.381002 | − | 0.924574i | \(-0.624421\pi\) | ||||
−0.381002 | + | 0.924574i | \(0.624421\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.4465 | −1.44154 | −0.720771 | − | 0.693173i | \(-0.756212\pi\) | ||||
−0.720771 | + | 0.693173i | \(0.756212\pi\) | |||||||
\(572\) | −14.3247 | −0.598945 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.01178 | −0.0422309 | ||||||||
\(575\) | −7.69238 | −0.320795 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.04440 | 0.251632 | 0.125816 | − | 0.992054i | \(-0.459845\pi\) | ||||
0.125816 | + | 0.992054i | \(0.459845\pi\) | |||||||
\(578\) | 23.6146 | 0.982239 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15.9428 | −0.661990 | ||||||||
\(581\) | −8.35940 | −0.346806 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.0428 | 1.86548 | ||||||||
\(584\) | −9.75828 | −0.403801 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.9994 | 0.454382 | ||||||||
\(587\) | 38.6176 | 1.59392 | 0.796959 | − | 0.604034i | \(-0.206441\pi\) | ||||
0.796959 | + | 0.604034i | \(0.206441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.67110 | −0.316082 | ||||||||
\(590\) | −11.6410 | −0.479254 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.22571 | −0.173676 | ||||||||
\(593\) | 4.06998 | 0.167134 | 0.0835671 | − | 0.996502i | \(-0.473369\pi\) | ||||
0.0835671 | + | 0.996502i | \(0.473369\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.1450 | 0.497895 | ||||||||
\(596\) | −19.2132 | −0.787002 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.65357 | −0.108513 | ||||||||
\(599\) | 18.2628 | 0.746199 | 0.373099 | − | 0.927791i | \(-0.378295\pi\) | ||||
0.373099 | + | 0.927791i | \(0.378295\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.6805 | 1.29228 | 0.646138 | − | 0.763220i | \(-0.276383\pi\) | ||||
0.646138 | + | 0.763220i | \(0.276383\pi\) | |||||||
\(602\) | −5.23749 | −0.213464 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.63637 | −0.147962 | ||||||||
\(605\) | −21.0842 | −0.857193 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.5355 | 1.03645 | 0.518226 | − | 0.855244i | \(-0.326593\pi\) | ||||
0.518226 | + | 0.855244i | \(0.326593\pi\) | |||||||
\(608\) | 0.975857 | 0.0395762 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 29.4389 | 1.19195 | ||||||||
\(611\) | −32.9558 | −1.33325 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.6816 | −0.714154 | −0.357077 | − | 0.934075i | \(-0.616227\pi\) | ||||
−0.357077 | + | 0.934075i | \(0.616227\pi\) | |||||||
\(614\) | 15.1961 | 0.613267 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.97586 | 0.0796095 | ||||||||
\(617\) | −32.8371 | −1.32197 | −0.660986 | − | 0.750398i | \(-0.729862\pi\) | ||||
−0.660986 | + | 0.750398i | \(0.729862\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.5824 | 0.425342 | 0.212671 | − | 0.977124i | \(-0.431784\pi\) | ||||
0.212671 | + | 0.977124i | \(0.431784\pi\) | |||||||
\(620\) | 30.7023 | 1.23303 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.02476 | −0.361860 | ||||||||
\(623\) | 0.912319 | 0.0365513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 28.8826 | 1.15530 | ||||||||
\(626\) | 34.3481 | 1.37282 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.0118 | −0.599035 | ||||||||
\(629\) | −26.9303 | −1.07378 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.902404 | −0.0359241 | −0.0179621 | − | 0.999839i | \(-0.505718\pi\) | ||||
−0.0179621 | + | 0.999839i | \(0.505718\pi\) | |||||||
\(632\) | 2.29222 | 0.0911797 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.5386 | −0.815692 | ||||||||
\(635\) | −12.4577 | −0.494368 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.9197 | −0.947733 | ||||||||
\(638\) | −16.5297 | −0.654418 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.90570 | −0.154386 | ||||||||
\(641\) | 19.2444 | 0.760109 | 0.380055 | − | 0.924964i | \(-0.375905\pi\) | ||||
0.380055 | + | 0.924964i | \(0.375905\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.2804 | 1.35189 | 0.675944 | − | 0.736953i | \(-0.263736\pi\) | ||||
0.675944 | + | 0.736953i | \(0.263736\pi\) | |||||||
\(644\) | 0.366017 | 0.0144231 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.21910 | 0.244687 | ||||||||
\(647\) | 30.2029 | 1.18740 | 0.593698 | − | 0.804688i | \(-0.297667\pi\) | ||||
0.593698 | + | 0.804688i | \(0.297667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.0696 | −0.473772 | ||||||||
\(650\) | 36.2744 | 1.42280 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.77531 | −0.187016 | ||||||||
\(653\) | 21.5877 | 0.844794 | 0.422397 | − | 0.906411i | \(-0.361189\pi\) | ||||
0.422397 | + | 0.906411i | \(0.361189\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −45.2963 | −1.76987 | ||||||||
\(656\) | 2.07362 | 0.0809614 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.54572 | 0.177211 | ||||||||
\(659\) | 21.3740 | 0.832612 | 0.416306 | − | 0.909225i | \(-0.363324\pi\) | ||||
0.416306 | + | 0.909225i | \(0.363324\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.7195 | −0.767000 | −0.383500 | − | 0.923541i | \(-0.625281\pi\) | ||||
−0.383500 | + | 0.923541i | \(0.625281\pi\) | |||||||
\(662\) | −8.30867 | −0.322926 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.1324 | 0.664868 | ||||||||
\(665\) | 1.85969 | 0.0721158 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.06204 | −0.118563 | ||||||||
\(668\) | 3.94163 | 0.152506 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.7171 | −0.529938 | ||||||||
\(671\) | 30.5226 | 1.17831 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.2275 | −0.509883 | −0.254942 | − | 0.966956i | \(-0.582056\pi\) | ||||
−0.254942 | + | 0.966956i | \(0.582056\pi\) | |||||||
\(674\) | −17.9588 | −0.691746 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.486734 | −0.0187205 | ||||||||
\(677\) | 12.7629 | 0.490520 | 0.245260 | − | 0.969457i | \(-0.421127\pi\) | ||||
0.245260 | + | 0.969457i | \(0.421127\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.70244 | 0.180463 | ||||||||
\(680\) | −24.8909 | −0.954522 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 31.8325 | 1.21893 | ||||||||
\(683\) | 3.12345 | 0.119515 | 0.0597577 | − | 0.998213i | \(-0.480967\pi\) | ||||
0.0597577 | + | 0.998213i | \(0.480967\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.6311 | −1.09394 | ||||||||
\(686\) | 6.71483 | 0.256374 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.7341 | 0.409235 | ||||||||
\(689\) | −39.3470 | −1.49900 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.3081 | 0.962767 | 0.481384 | − | 0.876510i | \(-0.340134\pi\) | ||||
0.481384 | + | 0.876510i | \(0.340134\pi\) | |||||||
\(692\) | 24.0607 | 0.914650 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.69769 | −0.254241 | ||||||||
\(695\) | 51.5267 | 1.95452 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.2151 | 0.500559 | ||||||||
\(698\) | 0.974251 | 0.0368759 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.00347 | −0.189113 | ||||||||
\(701\) | 15.5107 | 0.585831 | 0.292916 | − | 0.956138i | \(-0.405374\pi\) | ||||
0.292916 | + | 0.956138i | \(0.405374\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.12369 | −0.155528 | ||||||||
\(704\) | −4.04948 | −0.152621 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.8928 | −0.598132 | ||||||||
\(707\) | 2.88731 | 0.108588 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.24435 | 0.121844 | 0.0609220 | − | 0.998143i | \(-0.480596\pi\) | ||||
0.0609220 | + | 0.998143i | \(0.480596\pi\) | |||||||
\(710\) | 55.2067 | 2.07187 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.86978 | −0.0700730 | ||||||||
\(713\) | 5.89681 | 0.220837 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 55.9479 | 2.09233 | ||||||||
\(716\) | −17.1745 | −0.641839 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.66535 | 0.323388 | ||||||||
\(719\) | −28.5289 | −1.06395 | −0.531974 | − | 0.846761i | \(-0.678549\pi\) | ||||
−0.531974 | + | 0.846761i | \(0.678549\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.234603 | −0.00873707 | ||||||||
\(722\) | −18.0477 | −0.671666 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.28875 | −0.270884 | ||||||||
\(725\) | 41.8583 | 1.55458 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.4941 | 1.05679 | 0.528395 | − | 0.848999i | \(-0.322794\pi\) | ||||
0.528395 | + | 0.848999i | \(0.322794\pi\) | |||||||
\(728\) | −1.72600 | −0.0639699 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 38.1130 | 1.41062 | ||||||||
\(731\) | 68.4082 | 2.53017 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.1617 | 1.15098 | 0.575491 | − | 0.817808i | \(-0.304811\pi\) | ||||
0.575491 | + | 0.817808i | \(0.304811\pi\) | |||||||
\(734\) | 7.50802 | 0.277126 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.750146 | −0.0276507 | ||||||||
\(737\) | −14.2221 | −0.523877 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.7409 | 0.836538 | 0.418269 | − | 0.908323i | \(-0.362637\pi\) | ||||
0.418269 | + | 0.908323i | \(0.362637\pi\) | |||||||
\(740\) | 16.5044 | 0.606713 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.42728 | 0.199242 | ||||||||
\(743\) | −33.4594 | −1.22751 | −0.613753 | − | 0.789498i | \(-0.710341\pi\) | ||||
−0.613753 | + | 0.789498i | \(0.710341\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 75.0410 | 2.74929 | ||||||||
\(746\) | 2.14911 | 0.0786847 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −25.8072 | −0.943604 | ||||||||
\(749\) | 1.86631 | 0.0681934 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.0493 | −1.75334 | −0.876672 | − | 0.481089i | \(-0.840241\pi\) | ||||
−0.876672 | + | 0.481089i | \(0.840241\pi\) | |||||||
\(752\) | −9.31636 | −0.339733 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.4395 | 0.525854 | ||||||||
\(755\) | 14.2026 | 0.516885 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 52.5319 | 1.90930 | 0.954652 | − | 0.297725i | \(-0.0962279\pi\) | ||||
0.954652 | + | 0.297725i | \(0.0962279\pi\) | |||||||
\(758\) | 7.71644 | 0.280274 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.81141 | −0.138254 | ||||||||
\(761\) | −50.4604 | −1.82919 | −0.914594 | − | 0.404373i | \(-0.867490\pi\) | ||||
−0.914594 | + | 0.404373i | \(0.867490\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.33704 | 0.301821 | ||||||||
\(764\) | 6.55038 | 0.236985 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.88104 | −0.0679646 | ||||||||
\(767\) | 10.5433 | 0.380698 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.6684 | −1.39442 | −0.697209 | − | 0.716867i | \(-0.745575\pi\) | ||||
−0.697209 | + | 0.716867i | \(0.745575\pi\) | |||||||
\(770\) | −7.71711 | −0.278105 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.5467 | 0.631521 | ||||||||
\(773\) | 27.8089 | 1.00022 | 0.500108 | − | 0.865963i | \(-0.333294\pi\) | ||||
0.500108 | + | 0.865963i | \(0.333294\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −80.6096 | −2.89558 | ||||||||
\(776\) | −9.63757 | −0.345968 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.7025 | 0.383704 | ||||||||
\(779\) | 2.02356 | 0.0725016 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 57.2390 | 2.04817 | ||||||||
\(782\) | −4.78065 | −0.170956 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.76193 | −0.241497 | ||||||||
\(785\) | 58.6316 | 2.09265 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.0440 | −1.24918 | −0.624592 | − | 0.780951i | \(-0.714735\pi\) | ||||
−0.624592 | + | 0.780951i | \(0.714735\pi\) | |||||||
\(788\) | 14.6051 | 0.520286 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.95274 | −0.318524 | ||||||||
\(791\) | 6.49893 | 0.231075 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.6629 | −0.946827 | ||||||||
\(794\) | 3.84774 | 0.136551 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.64162 | −0.164518 | ||||||||
\(797\) | −44.3028 | −1.56929 | −0.784643 | − | 0.619947i | \(-0.787154\pi\) | ||||
−0.784643 | + | 0.619947i | \(0.787154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −59.3728 | −2.10046 | ||||||||
\(800\) | 10.2545 | 0.362552 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.717694 | 0.0253426 | ||||||||
\(803\) | 39.5160 | 1.39449 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.42956 | −0.0503852 | ||||||||
\(806\) | −27.8072 | −0.979466 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.91748 | −0.208176 | ||||||||
\(809\) | −17.8666 | −0.628157 | −0.314079 | − | 0.949397i | \(-0.601696\pi\) | ||||
−0.314079 | + | 0.949397i | \(0.601696\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.94755 | 0.279076 | 0.139538 | − | 0.990217i | \(-0.455438\pi\) | ||||
0.139538 | + | 0.990217i | \(0.455438\pi\) | |||||||
\(812\) | −1.99169 | −0.0698947 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 17.1119 | 0.599773 | ||||||||
\(815\) | 18.6510 | 0.653314 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4750 | 0.366473 | ||||||||
\(818\) | −11.7906 | −0.412247 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.09896 | −0.282828 | ||||||||
\(821\) | −14.0212 | −0.489342 | −0.244671 | − | 0.969606i | \(-0.578680\pi\) | ||||
−0.244671 | + | 0.969606i | \(0.578680\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −56.0461 | −1.95364 | −0.976822 | − | 0.214052i | \(-0.931334\pi\) | ||||
−0.976822 | + | 0.214052i | \(0.931334\pi\) | |||||||
\(824\) | 0.480814 | 0.0167500 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.45428 | −0.0506009 | ||||||||
\(827\) | −28.6027 | −0.994612 | −0.497306 | − | 0.867575i | \(-0.665677\pi\) | ||||
−0.497306 | + | 0.867575i | \(0.665677\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.08499 | 0.246072 | 0.123036 | − | 0.992402i | \(-0.460737\pi\) | ||||
0.123036 | + | 0.992402i | \(0.460737\pi\) | |||||||
\(830\) | −66.9142 | −2.32263 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.53741 | 0.122638 | ||||||||
\(833\) | −43.0935 | −1.49310 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.3948 | −0.532760 | ||||||||
\(836\) | −3.95171 | −0.136673 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.07076 | 0.244256 | ||||||||
\(839\) | 16.9860 | 0.586423 | 0.293211 | − | 0.956048i | \(-0.405276\pi\) | ||||
0.293211 | + | 0.956048i | \(0.405276\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.3378 | −0.425442 | ||||||||
\(842\) | −4.96469 | −0.171094 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.7554 | 0.542324 | ||||||||
\(845\) | 1.90104 | 0.0653977 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.63398 | −0.0905047 | ||||||||
\(848\) | −11.1231 | −0.381969 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 65.3516 | 2.24154 | ||||||||
\(851\) | 3.16990 | 0.108663 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.5249 | −0.873957 | −0.436979 | − | 0.899472i | \(-0.643951\pi\) | ||||
−0.436979 | + | 0.899472i | \(0.643951\pi\) | |||||||
\(854\) | 3.67772 | 0.125849 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.82496 | −0.130735 | ||||||||
\(857\) | 47.9302 | 1.63726 | 0.818632 | − | 0.574318i | \(-0.194733\pi\) | ||||
0.818632 | + | 0.574318i | \(0.194733\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.23647 | −0.212786 | −0.106393 | − | 0.994324i | \(-0.533930\pi\) | ||||
−0.106393 | + | 0.994324i | \(0.533930\pi\) | |||||||
\(860\) | −41.9244 | −1.42961 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25.6140 | −0.872417 | ||||||||
\(863\) | −8.46337 | −0.288097 | −0.144048 | − | 0.989571i | \(-0.546012\pi\) | ||||
−0.144048 | + | 0.989571i | \(0.546012\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −93.9739 | −3.19521 | ||||||||
\(866\) | −20.5767 | −0.699226 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.83555 | 0.130187 | ||||||||
\(869\) | −9.28231 | −0.314881 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.4236 | 0.420959 | ||||||||
\(872\) | −17.0866 | −0.578625 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.732035 | −0.0247614 | ||||||||
\(875\) | 10.0136 | 0.338520 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.1172 | 1.42220 | 0.711098 | − | 0.703093i | \(-0.248198\pi\) | ||||
0.711098 | + | 0.703093i | \(0.248198\pi\) | |||||||
\(878\) | 15.6900 | 0.529512 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 15.8161 | 0.533160 | ||||||||
\(881\) | 35.0575 | 1.18112 | 0.590558 | − | 0.806995i | \(-0.298908\pi\) | ||||
0.590558 | + | 0.806995i | \(0.298908\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.3854 | 1.66195 | 0.830976 | − | 0.556308i | \(-0.187783\pi\) | ||||
0.830976 | + | 0.556308i | \(0.187783\pi\) | |||||||
\(884\) | 22.5438 | 0.758229 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.0018 | −0.974335 | ||||||||
\(887\) | 20.5875 | 0.691261 | 0.345630 | − | 0.938371i | \(-0.387665\pi\) | ||||
0.345630 | + | 0.938371i | \(0.387665\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.55630 | −0.0521968 | ||||||||
\(890\) | 7.30281 | 0.244791 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.8791 | 0.665602 | ||||||||
\(893\) | −9.09144 | −0.304233 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 67.0783 | 2.24218 | ||||||||
\(896\) | −0.487928 | −0.0163005 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.1978 | −0.607267 | ||||||||
\(899\) | −32.0876 | −1.07018 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −70.8871 | −2.36159 | ||||||||
\(902\) | −8.39710 | −0.279593 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.3194 | −0.442997 | ||||||||
\(905\) | 28.4677 | 0.946298 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −57.1062 | −1.89618 | −0.948090 | − | 0.318003i | \(-0.896988\pi\) | ||||
−0.948090 | + | 0.318003i | \(0.896988\pi\) | |||||||
\(908\) | −27.7566 | −0.921136 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.74125 | 0.223470 | ||||||||
\(911\) | −1.11278 | −0.0368680 | −0.0184340 | − | 0.999830i | \(-0.505868\pi\) | ||||
−0.0184340 | + | 0.999830i | \(0.505868\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −69.3775 | −2.29606 | ||||||||
\(914\) | 32.1933 | 1.06486 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.6723 | −0.583909 | ||||||||
\(917\) | −5.65874 | −0.186868 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.6902 | −0.814453 | −0.407227 | − | 0.913327i | \(-0.633504\pi\) | ||||
−0.407227 | + | 0.913327i | \(0.633504\pi\) | |||||||
\(920\) | 2.92985 | 0.0965942 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 26.9152 | 0.886405 | ||||||||
\(923\) | −50.0009 | −1.64580 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −43.3326 | −1.42477 | ||||||||
\(926\) | −24.2349 | −0.796407 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.08193 | 0.133996 | ||||||||
\(929\) | −53.4317 | −1.75304 | −0.876519 | − | 0.481368i | \(-0.840140\pi\) | ||||
−0.876519 | + | 0.481368i | \(0.840140\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.59867 | −0.216263 | ||||||||
\(932\) | 1.67230 | 0.0547779 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.7628 | 0.581216 | ||||||||
\(935\) | 100.795 | 3.29636 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.01583 | −0.261866 | −0.130933 | − | 0.991391i | \(-0.541797\pi\) | ||||
−0.130933 | + | 0.991391i | \(0.541797\pi\) | |||||||
\(938\) | −1.71364 | −0.0559523 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 36.3870 | 1.18681 | ||||||||
\(941\) | 10.2934 | 0.335556 | 0.167778 | − | 0.985825i | \(-0.446341\pi\) | ||||
0.167778 | + | 0.985825i | \(0.446341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.55552 | −0.0506547 | ||||||||
\(944\) | 2.98052 | 0.0970077 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.4677 | −1.41326 | ||||||||
\(947\) | −42.4848 | −1.38057 | −0.690285 | − | 0.723538i | \(-0.742515\pi\) | ||||
−0.690285 | + | 0.723538i | \(0.742515\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.5190 | −1.12054 | ||||||||
\(950\) | 10.0069 | 0.324668 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.10955 | −0.100781 | ||||||||
\(953\) | −59.0011 | −1.91123 | −0.955617 | − | 0.294612i | \(-0.904809\pi\) | ||||
−0.955617 | + | 0.294612i | \(0.904809\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.5839 | −0.827874 | ||||||||
\(956\) | 24.0925 | 0.779206 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.4930 | −0.371323 | ||||||||
\(959\) | −3.57680 | −0.115501 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.7936 | 0.993341 | ||||||||
\(962\) | −14.9481 | −0.481945 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.2257 | −0.587011 | ||||||||
\(965\) | −68.5324 | −2.20614 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.781747 | −0.0251393 | −0.0125696 | − | 0.999921i | \(-0.504001\pi\) | ||||
−0.0125696 | + | 0.999921i | \(0.504001\pi\) | |||||||
\(968\) | 5.39830 | 0.173508 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 37.6415 | 1.20860 | ||||||||
\(971\) | −51.5702 | −1.65497 | −0.827484 | − | 0.561489i | \(-0.810229\pi\) | ||||
−0.827484 | + | 0.561489i | \(0.810229\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.43708 | 0.206363 | ||||||||
\(974\) | 5.85514 | 0.187611 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.53741 | −0.241267 | ||||||||
\(977\) | −3.02820 | −0.0968806 | −0.0484403 | − | 0.998826i | \(-0.515425\pi\) | ||||
−0.0484403 | + | 0.998826i | \(0.515425\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.57164 | 0.241991 | ||||||||
\(980\) | 26.4101 | 0.843639 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.6544 | −0.595287 | ||||||||
\(983\) | 45.6956 | 1.45746 | 0.728732 | − | 0.684799i | \(-0.240110\pi\) | ||||
0.728732 | + | 0.684799i | \(0.240110\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −57.0432 | −1.81755 | ||||||||
\(986\) | 26.0140 | 0.828454 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.45200 | 0.109823 | ||||||||
\(989\) | −8.05217 | −0.256044 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.3370 | −0.963685 | −0.481843 | − | 0.876258i | \(-0.660032\pi\) | ||||
−0.481843 | + | 0.876258i | \(0.660032\pi\) | |||||||
\(992\) | −7.86089 | −0.249583 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.89681 | 0.218754 | ||||||||
\(995\) | 18.1288 | 0.574721 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.9443 | 0.885004 | 0.442502 | − | 0.896767i | \(-0.354091\pi\) | ||||
0.442502 | + | 0.896767i | \(0.354091\pi\) | |||||||
\(998\) | 35.1119 | 1.11145 | ||||||||
\(999\) | 0 | 0 |
(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 | 4842.2.a.j.1.1 | 4 | ||
3.2 | odd | 2 | 538.2.a.c.1.3 | ✓ | 4 | ||
12.11 | even | 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 | 3.2 | odd | 2 | ||
4304.2.a.e.1.2 | 4 | 12.11 | even | 2 | |||
4842.2.a.j.1.1 | 4 | 1.1 | even | 1 | trivial |