Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, 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("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 16x^{6} - 4x^{5} + 75x^{4} + 32x^{3} - 90x^{2} - 28x - 2 \) |
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 | 1.8 | ||
Root | \(-2.75320\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-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 | ||||||||
\(3\) | 3.37860 | 1.95063 | 0.975317 | − | 0.220810i | \(-0.0708701\pi\) | ||||
0.975317 | + | 0.220810i | \(0.0708701\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.17017 | −1.86496 | −0.932478 | − | 0.361228i | \(-0.882358\pi\) | ||||
−0.932478 | + | 0.361228i | \(0.882358\pi\) | |||||||
\(6\) | −3.37860 | −1.37931 | ||||||||
\(7\) | 3.60700 | 1.36332 | 0.681660 | − | 0.731669i | \(-0.261258\pi\) | ||||
0.681660 | + | 0.731669i | \(0.261258\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 8.41492 | 2.80497 | ||||||||
\(10\) | 4.17017 | 1.31872 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.37860 | 0.975317 | ||||||||
\(13\) | 0.669426 | 0.185665 | 0.0928326 | − | 0.995682i | \(-0.470408\pi\) | ||||
0.0928326 | + | 0.995682i | \(0.470408\pi\) | |||||||
\(14\) | −3.60700 | −0.964012 | ||||||||
\(15\) | −14.0893 | −3.63784 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.10493 | −0.995592 | −0.497796 | − | 0.867294i | \(-0.665857\pi\) | ||||
−0.497796 | + | 0.867294i | \(0.665857\pi\) | |||||||
\(18\) | −8.41492 | −1.98341 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −4.17017 | −0.932478 | ||||||||
\(21\) | 12.1866 | 2.65934 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.35872 | 1.32589 | 0.662943 | − | 0.748670i | \(-0.269307\pi\) | ||||
0.662943 | + | 0.748670i | \(0.269307\pi\) | |||||||
\(24\) | −3.37860 | −0.689653 | ||||||||
\(25\) | 12.3903 | 2.47806 | ||||||||
\(26\) | −0.669426 | −0.131285 | ||||||||
\(27\) | 18.2948 | 3.52084 | ||||||||
\(28\) | 3.60700 | 0.681660 | ||||||||
\(29\) | −3.27213 | −0.607619 | −0.303809 | − | 0.952733i | \(-0.598259\pi\) | ||||
−0.303809 | + | 0.952733i | \(0.598259\pi\) | |||||||
\(30\) | 14.0893 | 2.57234 | ||||||||
\(31\) | −1.55576 | −0.279423 | −0.139712 | − | 0.990192i | \(-0.544618\pi\) | ||||
−0.139712 | + | 0.990192i | \(0.544618\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.10493 | 0.703990 | ||||||||
\(35\) | −15.0418 | −2.54253 | ||||||||
\(36\) | 8.41492 | 1.40249 | ||||||||
\(37\) | 3.51430 | 0.577747 | 0.288873 | − | 0.957367i | \(-0.406719\pi\) | ||||
0.288873 | + | 0.957367i | \(0.406719\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 2.26172 | 0.362165 | ||||||||
\(40\) | 4.17017 | 0.659361 | ||||||||
\(41\) | −7.30933 | −1.14153 | −0.570763 | − | 0.821115i | \(-0.693352\pi\) | ||||
−0.570763 | + | 0.821115i | \(0.693352\pi\) | |||||||
\(42\) | −12.1866 | −1.88044 | ||||||||
\(43\) | 6.04669 | 0.922112 | 0.461056 | − | 0.887371i | \(-0.347471\pi\) | ||||
0.461056 | + | 0.887371i | \(0.347471\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −35.0916 | −5.23115 | ||||||||
\(46\) | −6.35872 | −0.937543 | ||||||||
\(47\) | 0.862845 | 0.125859 | 0.0629294 | − | 0.998018i | \(-0.479956\pi\) | ||||
0.0629294 | + | 0.998018i | \(0.479956\pi\) | |||||||
\(48\) | 3.37860 | 0.487658 | ||||||||
\(49\) | 6.01048 | 0.858640 | ||||||||
\(50\) | −12.3903 | −1.75225 | ||||||||
\(51\) | −13.8689 | −1.94204 | ||||||||
\(52\) | 0.669426 | 0.0928326 | ||||||||
\(53\) | 6.79423 | 0.933260 | 0.466630 | − | 0.884453i | \(-0.345468\pi\) | ||||
0.466630 | + | 0.884453i | \(0.345468\pi\) | |||||||
\(54\) | −18.2948 | −2.48961 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.60700 | −0.482006 | ||||||||
\(57\) | 3.37860 | 0.447506 | ||||||||
\(58\) | 3.27213 | 0.429651 | ||||||||
\(59\) | −9.41317 | −1.22549 | −0.612745 | − | 0.790280i | \(-0.709935\pi\) | ||||
−0.612745 | + | 0.790280i | \(0.709935\pi\) | |||||||
\(60\) | −14.0893 | −1.81892 | ||||||||
\(61\) | 4.40660 | 0.564207 | 0.282103 | − | 0.959384i | \(-0.408968\pi\) | ||||
0.282103 | + | 0.959384i | \(0.408968\pi\) | |||||||
\(62\) | 1.55576 | 0.197582 | ||||||||
\(63\) | 30.3526 | 3.82407 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.79162 | −0.346257 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.80340 | 0.220320 | 0.110160 | − | 0.993914i | \(-0.464864\pi\) | ||||
0.110160 | + | 0.993914i | \(0.464864\pi\) | |||||||
\(68\) | −4.10493 | −0.497796 | ||||||||
\(69\) | 21.4836 | 2.58632 | ||||||||
\(70\) | 15.0418 | 1.79784 | ||||||||
\(71\) | 11.9933 | 1.42334 | 0.711669 | − | 0.702514i | \(-0.247939\pi\) | ||||
0.711669 | + | 0.702514i | \(0.247939\pi\) | |||||||
\(72\) | −8.41492 | −0.991707 | ||||||||
\(73\) | −9.91252 | −1.16017 | −0.580087 | − | 0.814555i | \(-0.696981\pi\) | ||||
−0.580087 | + | 0.814555i | \(0.696981\pi\) | |||||||
\(74\) | −3.51430 | −0.408529 | ||||||||
\(75\) | 41.8618 | 4.83378 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.26172 | −0.256089 | ||||||||
\(79\) | −1.04552 | −0.117630 | −0.0588152 | − | 0.998269i | \(-0.518732\pi\) | ||||
−0.0588152 | + | 0.998269i | \(0.518732\pi\) | |||||||
\(80\) | −4.17017 | −0.466239 | ||||||||
\(81\) | 36.5661 | 4.06290 | ||||||||
\(82\) | 7.30933 | 0.807180 | ||||||||
\(83\) | −0.503831 | −0.0553026 | −0.0276513 | − | 0.999618i | \(-0.508803\pi\) | ||||
−0.0276513 | + | 0.999618i | \(0.508803\pi\) | |||||||
\(84\) | 12.1866 | 1.32967 | ||||||||
\(85\) | 17.1183 | 1.85674 | ||||||||
\(86\) | −6.04669 | −0.652032 | ||||||||
\(87\) | −11.0552 | −1.18524 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.23674 | 0.873093 | 0.436546 | − | 0.899682i | \(-0.356201\pi\) | ||||
0.436546 | + | 0.899682i | \(0.356201\pi\) | |||||||
\(90\) | 35.0916 | 3.69898 | ||||||||
\(91\) | 2.41462 | 0.253121 | ||||||||
\(92\) | 6.35872 | 0.662943 | ||||||||
\(93\) | −5.25629 | −0.545052 | ||||||||
\(94\) | −0.862845 | −0.0889957 | ||||||||
\(95\) | −4.17017 | −0.427850 | ||||||||
\(96\) | −3.37860 | −0.344827 | ||||||||
\(97\) | 0.809369 | 0.0821790 | 0.0410895 | − | 0.999155i | \(-0.486917\pi\) | ||||
0.0410895 | + | 0.999155i | \(0.486917\pi\) | |||||||
\(98\) | −6.01048 | −0.607150 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.3903 | 1.23903 | ||||||||
\(101\) | 12.0493 | 1.19895 | 0.599475 | − | 0.800393i | \(-0.295376\pi\) | ||||
0.599475 | + | 0.800393i | \(0.295376\pi\) | |||||||
\(102\) | 13.8689 | 1.37323 | ||||||||
\(103\) | 5.64096 | 0.555820 | 0.277910 | − | 0.960607i | \(-0.410358\pi\) | ||||
0.277910 | + | 0.960607i | \(0.410358\pi\) | |||||||
\(104\) | −0.669426 | −0.0656426 | ||||||||
\(105\) | −50.8202 | −4.95954 | ||||||||
\(106\) | −6.79423 | −0.659914 | ||||||||
\(107\) | −15.1059 | −1.46034 | −0.730172 | − | 0.683264i | \(-0.760560\pi\) | ||||
−0.730172 | + | 0.683264i | \(0.760560\pi\) | |||||||
\(108\) | 18.2948 | 1.76042 | ||||||||
\(109\) | 11.6030 | 1.11137 | 0.555685 | − | 0.831393i | \(-0.312456\pi\) | ||||
0.555685 | + | 0.831393i | \(0.312456\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.8734 | 1.12697 | ||||||||
\(112\) | 3.60700 | 0.340830 | ||||||||
\(113\) | −6.03660 | −0.567876 | −0.283938 | − | 0.958843i | \(-0.591641\pi\) | ||||
−0.283938 | + | 0.958843i | \(0.591641\pi\) | |||||||
\(114\) | −3.37860 | −0.316435 | ||||||||
\(115\) | −26.5169 | −2.47272 | ||||||||
\(116\) | −3.27213 | −0.303809 | ||||||||
\(117\) | 5.63316 | 0.520786 | ||||||||
\(118\) | 9.41317 | 0.866553 | ||||||||
\(119\) | −14.8065 | −1.35731 | ||||||||
\(120\) | 14.0893 | 1.28617 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −4.40660 | −0.398954 | ||||||||
\(123\) | −24.6953 | −2.22670 | ||||||||
\(124\) | −1.55576 | −0.139712 | ||||||||
\(125\) | −30.8187 | −2.75651 | ||||||||
\(126\) | −30.3526 | −2.70403 | ||||||||
\(127\) | 7.06535 | 0.626949 | 0.313474 | − | 0.949597i | \(-0.398507\pi\) | ||||
0.313474 | + | 0.949597i | \(0.398507\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 20.4293 | 1.79870 | ||||||||
\(130\) | 2.79162 | 0.244841 | ||||||||
\(131\) | 3.26224 | 0.285023 | 0.142512 | − | 0.989793i | \(-0.454482\pi\) | ||||
0.142512 | + | 0.989793i | \(0.454482\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.60700 | 0.312767 | ||||||||
\(134\) | −1.80340 | −0.155790 | ||||||||
\(135\) | −76.2924 | −6.56621 | ||||||||
\(136\) | 4.10493 | 0.351995 | ||||||||
\(137\) | 1.25379 | 0.107118 | 0.0535592 | − | 0.998565i | \(-0.482943\pi\) | ||||
0.0535592 | + | 0.998565i | \(0.482943\pi\) | |||||||
\(138\) | −21.4836 | −1.82880 | ||||||||
\(139\) | −1.52427 | −0.129287 | −0.0646433 | − | 0.997908i | \(-0.520591\pi\) | ||||
−0.0646433 | + | 0.997908i | \(0.520591\pi\) | |||||||
\(140\) | −15.0418 | −1.27127 | ||||||||
\(141\) | 2.91521 | 0.245505 | ||||||||
\(142\) | −11.9933 | −1.00645 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 8.41492 | 0.701243 | ||||||||
\(145\) | 13.6453 | 1.13318 | ||||||||
\(146\) | 9.91252 | 0.820366 | ||||||||
\(147\) | 20.3070 | 1.67489 | ||||||||
\(148\) | 3.51430 | 0.288873 | ||||||||
\(149\) | 15.6872 | 1.28515 | 0.642575 | − | 0.766223i | \(-0.277866\pi\) | ||||
0.642575 | + | 0.766223i | \(0.277866\pi\) | |||||||
\(150\) | −41.8618 | −3.41800 | ||||||||
\(151\) | −18.9865 | −1.54510 | −0.772548 | − | 0.634957i | \(-0.781018\pi\) | ||||
−0.772548 | + | 0.634957i | \(0.781018\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −34.5427 | −2.79261 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.48779 | 0.521112 | ||||||||
\(156\) | 2.26172 | 0.181082 | ||||||||
\(157\) | −8.89570 | −0.709954 | −0.354977 | − | 0.934875i | \(-0.615511\pi\) | ||||
−0.354977 | + | 0.934875i | \(0.615511\pi\) | |||||||
\(158\) | 1.04552 | 0.0831772 | ||||||||
\(159\) | 22.9550 | 1.82045 | ||||||||
\(160\) | 4.17017 | 0.329681 | ||||||||
\(161\) | 22.9359 | 1.80761 | ||||||||
\(162\) | −36.5661 | −2.87290 | ||||||||
\(163\) | −4.84499 | −0.379489 | −0.189744 | − | 0.981834i | \(-0.560766\pi\) | ||||
−0.189744 | + | 0.981834i | \(0.560766\pi\) | |||||||
\(164\) | −7.30933 | −0.570763 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.503831 | 0.0391049 | ||||||||
\(167\) | 4.61536 | 0.357148 | 0.178574 | − | 0.983927i | \(-0.442852\pi\) | ||||
0.178574 | + | 0.983927i | \(0.442852\pi\) | |||||||
\(168\) | −12.1866 | −0.940218 | ||||||||
\(169\) | −12.5519 | −0.965528 | ||||||||
\(170\) | −17.1183 | −1.31291 | ||||||||
\(171\) | 8.41492 | 0.643505 | ||||||||
\(172\) | 6.04669 | 0.461056 | ||||||||
\(173\) | 9.33836 | 0.709982 | 0.354991 | − | 0.934870i | \(-0.384484\pi\) | ||||
0.354991 | + | 0.934870i | \(0.384484\pi\) | |||||||
\(174\) | 11.0552 | 0.838092 | ||||||||
\(175\) | 44.6918 | 3.37839 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −31.8033 | −2.39048 | ||||||||
\(178\) | −8.23674 | −0.617370 | ||||||||
\(179\) | 16.7881 | 1.25480 | 0.627401 | − | 0.778696i | \(-0.284119\pi\) | ||||
0.627401 | + | 0.778696i | \(0.284119\pi\) | |||||||
\(180\) | −35.0916 | −2.61557 | ||||||||
\(181\) | 17.5877 | 1.30729 | 0.653643 | − | 0.756803i | \(-0.273240\pi\) | ||||
0.653643 | + | 0.756803i | \(0.273240\pi\) | |||||||
\(182\) | −2.41462 | −0.178984 | ||||||||
\(183\) | 14.8881 | 1.10056 | ||||||||
\(184\) | −6.35872 | −0.468771 | ||||||||
\(185\) | −14.6552 | −1.07747 | ||||||||
\(186\) | 5.25629 | 0.385410 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.862845 | 0.0629294 | ||||||||
\(189\) | 65.9895 | 4.80003 | ||||||||
\(190\) | 4.17017 | 0.302536 | ||||||||
\(191\) | −2.76249 | −0.199887 | −0.0999435 | − | 0.994993i | \(-0.531866\pi\) | ||||
−0.0999435 | + | 0.994993i | \(0.531866\pi\) | |||||||
\(192\) | 3.37860 | 0.243829 | ||||||||
\(193\) | −21.4775 | −1.54598 | −0.772991 | − | 0.634417i | \(-0.781240\pi\) | ||||
−0.772991 | + | 0.634417i | \(0.781240\pi\) | |||||||
\(194\) | −0.809369 | −0.0581093 | ||||||||
\(195\) | −9.43175 | −0.675421 | ||||||||
\(196\) | 6.01048 | 0.429320 | ||||||||
\(197\) | 18.9032 | 1.34680 | 0.673399 | − | 0.739280i | \(-0.264834\pi\) | ||||
0.673399 | + | 0.739280i | \(0.264834\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.76283 | 0.550292 | 0.275146 | − | 0.961402i | \(-0.411274\pi\) | ||||
0.275146 | + | 0.961402i | \(0.411274\pi\) | |||||||
\(200\) | −12.3903 | −0.876126 | ||||||||
\(201\) | 6.09296 | 0.429764 | ||||||||
\(202\) | −12.0493 | −0.847786 | ||||||||
\(203\) | −11.8026 | −0.828378 | ||||||||
\(204\) | −13.8689 | −0.971018 | ||||||||
\(205\) | 30.4811 | 2.12889 | ||||||||
\(206\) | −5.64096 | −0.393024 | ||||||||
\(207\) | 53.5081 | 3.71907 | ||||||||
\(208\) | 0.669426 | 0.0464163 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 50.8202 | 3.50693 | ||||||||
\(211\) | 6.88377 | 0.473898 | 0.236949 | − | 0.971522i | \(-0.423853\pi\) | ||||
0.236949 | + | 0.971522i | \(0.423853\pi\) | |||||||
\(212\) | 6.79423 | 0.466630 | ||||||||
\(213\) | 40.5204 | 2.77641 | ||||||||
\(214\) | 15.1059 | 1.03262 | ||||||||
\(215\) | −25.2157 | −1.71970 | ||||||||
\(216\) | −18.2948 | −1.24480 | ||||||||
\(217\) | −5.61164 | −0.380943 | ||||||||
\(218\) | −11.6030 | −0.785857 | ||||||||
\(219\) | −33.4904 | −2.26307 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.74795 | −0.184847 | ||||||||
\(222\) | −11.8734 | −0.796890 | ||||||||
\(223\) | 14.5212 | 0.972409 | 0.486204 | − | 0.873845i | \(-0.338381\pi\) | ||||
0.486204 | + | 0.873845i | \(0.338381\pi\) | |||||||
\(224\) | −3.60700 | −0.241003 | ||||||||
\(225\) | 104.263 | 6.95088 | ||||||||
\(226\) | 6.03660 | 0.401549 | ||||||||
\(227\) | 18.1073 | 1.20182 | 0.600912 | − | 0.799315i | \(-0.294804\pi\) | ||||
0.600912 | + | 0.799315i | \(0.294804\pi\) | |||||||
\(228\) | 3.37860 | 0.223753 | ||||||||
\(229\) | −25.3580 | −1.67570 | −0.837850 | − | 0.545900i | \(-0.816188\pi\) | ||||
−0.837850 | + | 0.545900i | \(0.816188\pi\) | |||||||
\(230\) | 26.5169 | 1.74848 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.27213 | 0.214826 | ||||||||
\(233\) | 21.9886 | 1.44052 | 0.720261 | − | 0.693704i | \(-0.244022\pi\) | ||||
0.720261 | + | 0.693704i | \(0.244022\pi\) | |||||||
\(234\) | −5.63316 | −0.368251 | ||||||||
\(235\) | −3.59821 | −0.234721 | ||||||||
\(236\) | −9.41317 | −0.612745 | ||||||||
\(237\) | −3.53240 | −0.229454 | ||||||||
\(238\) | 14.8065 | 0.959764 | ||||||||
\(239\) | −15.2971 | −0.989488 | −0.494744 | − | 0.869039i | \(-0.664738\pi\) | ||||
−0.494744 | + | 0.869039i | \(0.664738\pi\) | |||||||
\(240\) | −14.0893 | −0.909461 | ||||||||
\(241\) | −16.0409 | −1.03328 | −0.516642 | − | 0.856201i | \(-0.672818\pi\) | ||||
−0.516642 | + | 0.856201i | \(0.672818\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 68.6575 | 4.40438 | ||||||||
\(244\) | 4.40660 | 0.282103 | ||||||||
\(245\) | −25.0647 | −1.60133 | ||||||||
\(246\) | 24.6953 | 1.57451 | ||||||||
\(247\) | 0.669426 | 0.0425945 | ||||||||
\(248\) | 1.55576 | 0.0987910 | ||||||||
\(249\) | −1.70224 | −0.107875 | ||||||||
\(250\) | 30.8187 | 1.94915 | ||||||||
\(251\) | −6.91197 | −0.436279 | −0.218140 | − | 0.975918i | \(-0.569999\pi\) | ||||
−0.218140 | + | 0.975918i | \(0.569999\pi\) | |||||||
\(252\) | 30.3526 | 1.91204 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −7.06535 | −0.443320 | ||||||||
\(255\) | 57.8357 | 3.62181 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.7512 | −1.54394 | −0.771968 | − | 0.635661i | \(-0.780727\pi\) | ||||
−0.771968 | + | 0.635661i | \(0.780727\pi\) | |||||||
\(258\) | −20.4293 | −1.27187 | ||||||||
\(259\) | 12.6761 | 0.787654 | ||||||||
\(260\) | −2.79162 | −0.173129 | ||||||||
\(261\) | −27.5347 | −1.70435 | ||||||||
\(262\) | −3.26224 | −0.201542 | ||||||||
\(263\) | −16.8155 | −1.03689 | −0.518444 | − | 0.855112i | \(-0.673488\pi\) | ||||
−0.518444 | + | 0.855112i | \(0.673488\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −28.3331 | −1.74049 | ||||||||
\(266\) | −3.60700 | −0.221160 | ||||||||
\(267\) | 27.8286 | 1.70308 | ||||||||
\(268\) | 1.80340 | 0.110160 | ||||||||
\(269\) | 17.8288 | 1.08704 | 0.543521 | − | 0.839395i | \(-0.317091\pi\) | ||||
0.543521 | + | 0.839395i | \(0.317091\pi\) | |||||||
\(270\) | 76.2924 | 4.64301 | ||||||||
\(271\) | 30.2063 | 1.83490 | 0.917450 | − | 0.397850i | \(-0.130244\pi\) | ||||
0.917450 | + | 0.397850i | \(0.130244\pi\) | |||||||
\(272\) | −4.10493 | −0.248898 | ||||||||
\(273\) | 8.15803 | 0.493747 | ||||||||
\(274\) | −1.25379 | −0.0757441 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 21.4836 | 1.29316 | ||||||||
\(277\) | −32.7642 | −1.96861 | −0.984306 | − | 0.176473i | \(-0.943531\pi\) | ||||
−0.984306 | + | 0.176473i | \(0.943531\pi\) | |||||||
\(278\) | 1.52427 | 0.0914194 | ||||||||
\(279\) | −13.0916 | −0.783774 | ||||||||
\(280\) | 15.0418 | 0.898920 | ||||||||
\(281\) | 9.70846 | 0.579158 | 0.289579 | − | 0.957154i | \(-0.406485\pi\) | ||||
0.289579 | + | 0.957154i | \(0.406485\pi\) | |||||||
\(282\) | −2.91521 | −0.173598 | ||||||||
\(283\) | −14.5739 | −0.866326 | −0.433163 | − | 0.901316i | \(-0.642603\pi\) | ||||
−0.433163 | + | 0.901316i | \(0.642603\pi\) | |||||||
\(284\) | 11.9933 | 0.711669 | ||||||||
\(285\) | −14.0893 | −0.834579 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.3648 | −1.55626 | ||||||||
\(288\) | −8.41492 | −0.495854 | ||||||||
\(289\) | −0.149526 | −0.00879562 | ||||||||
\(290\) | −13.6453 | −0.801281 | ||||||||
\(291\) | 2.73453 | 0.160301 | ||||||||
\(292\) | −9.91252 | −0.580087 | ||||||||
\(293\) | 10.5241 | 0.614824 | 0.307412 | − | 0.951576i | \(-0.400537\pi\) | ||||
0.307412 | + | 0.951576i | \(0.400537\pi\) | |||||||
\(294\) | −20.3070 | −1.18433 | ||||||||
\(295\) | 39.2545 | 2.28549 | ||||||||
\(296\) | −3.51430 | −0.204264 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.6872 | −0.908738 | ||||||||
\(299\) | 4.25669 | 0.246171 | ||||||||
\(300\) | 41.8618 | 2.41689 | ||||||||
\(301\) | 21.8104 | 1.25713 | ||||||||
\(302\) | 18.9865 | 1.09255 | ||||||||
\(303\) | 40.7097 | 2.33871 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −18.3762 | −1.05222 | ||||||||
\(306\) | 34.5427 | 1.97467 | ||||||||
\(307\) | 21.4131 | 1.22211 | 0.611054 | − | 0.791589i | \(-0.290746\pi\) | ||||
0.611054 | + | 0.791589i | \(0.290746\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.0585 | 1.08420 | ||||||||
\(310\) | −6.48779 | −0.368482 | ||||||||
\(311\) | 8.91440 | 0.505489 | 0.252745 | − | 0.967533i | \(-0.418667\pi\) | ||||
0.252745 | + | 0.967533i | \(0.418667\pi\) | |||||||
\(312\) | −2.26172 | −0.128045 | ||||||||
\(313\) | −29.2280 | −1.65206 | −0.826031 | − | 0.563624i | \(-0.809407\pi\) | ||||
−0.826031 | + | 0.563624i | \(0.809407\pi\) | |||||||
\(314\) | 8.89570 | 0.502014 | ||||||||
\(315\) | −126.576 | −7.13173 | ||||||||
\(316\) | −1.04552 | −0.0588152 | ||||||||
\(317\) | −3.86251 | −0.216940 | −0.108470 | − | 0.994100i | \(-0.534595\pi\) | ||||
−0.108470 | + | 0.994100i | \(0.534595\pi\) | |||||||
\(318\) | −22.9550 | −1.28725 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −4.17017 | −0.233119 | ||||||||
\(321\) | −51.0368 | −2.84860 | ||||||||
\(322\) | −22.9359 | −1.27817 | ||||||||
\(323\) | −4.10493 | −0.228405 | ||||||||
\(324\) | 36.5661 | 2.03145 | ||||||||
\(325\) | 8.29438 | 0.460089 | ||||||||
\(326\) | 4.84499 | 0.268339 | ||||||||
\(327\) | 39.2020 | 2.16788 | ||||||||
\(328\) | 7.30933 | 0.403590 | ||||||||
\(329\) | 3.11229 | 0.171586 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.7968 | 1.69275 | 0.846373 | − | 0.532590i | \(-0.178781\pi\) | ||||
0.846373 | + | 0.532590i | \(0.178781\pi\) | |||||||
\(332\) | −0.503831 | −0.0276513 | ||||||||
\(333\) | 29.5725 | 1.62056 | ||||||||
\(334\) | −4.61536 | −0.252542 | ||||||||
\(335\) | −7.52048 | −0.410888 | ||||||||
\(336\) | 12.1866 | 0.664834 | ||||||||
\(337\) | 16.0941 | 0.876704 | 0.438352 | − | 0.898803i | \(-0.355562\pi\) | ||||
0.438352 | + | 0.898803i | \(0.355562\pi\) | |||||||
\(338\) | 12.5519 | 0.682732 | ||||||||
\(339\) | −20.3953 | −1.10772 | ||||||||
\(340\) | 17.1183 | 0.928368 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −8.41492 | −0.455027 | ||||||||
\(343\) | −3.56920 | −0.192719 | ||||||||
\(344\) | −6.04669 | −0.326016 | ||||||||
\(345\) | −89.5900 | −4.82337 | ||||||||
\(346\) | −9.33836 | −0.502033 | ||||||||
\(347\) | 31.7933 | 1.70676 | 0.853378 | − | 0.521292i | \(-0.174550\pi\) | ||||
0.853378 | + | 0.521292i | \(0.174550\pi\) | |||||||
\(348\) | −11.0552 | −0.592621 | ||||||||
\(349\) | −11.5331 | −0.617350 | −0.308675 | − | 0.951168i | \(-0.599886\pi\) | ||||
−0.308675 | + | 0.951168i | \(0.599886\pi\) | |||||||
\(350\) | −44.6918 | −2.38888 | ||||||||
\(351\) | 12.2470 | 0.653697 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.56825 | −0.189919 | −0.0949593 | − | 0.995481i | \(-0.530272\pi\) | ||||
−0.0949593 | + | 0.995481i | \(0.530272\pi\) | |||||||
\(354\) | 31.8033 | 1.69033 | ||||||||
\(355\) | −50.0139 | −2.65446 | ||||||||
\(356\) | 8.23674 | 0.436546 | ||||||||
\(357\) | −50.0252 | −2.64762 | ||||||||
\(358\) | −16.7881 | −0.887279 | ||||||||
\(359\) | −21.8282 | −1.15205 | −0.576025 | − | 0.817432i | \(-0.695397\pi\) | ||||
−0.576025 | + | 0.817432i | \(0.695397\pi\) | |||||||
\(360\) | 35.0916 | 1.84949 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −17.5877 | −0.924391 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.41462 | 0.126561 | ||||||||
\(365\) | 41.3369 | 2.16367 | ||||||||
\(366\) | −14.8881 | −0.778214 | ||||||||
\(367\) | 7.86931 | 0.410774 | 0.205387 | − | 0.978681i | \(-0.434155\pi\) | ||||
0.205387 | + | 0.978681i | \(0.434155\pi\) | |||||||
\(368\) | 6.35872 | 0.331471 | ||||||||
\(369\) | −61.5074 | −3.20195 | ||||||||
\(370\) | 14.6552 | 0.761888 | ||||||||
\(371\) | 24.5068 | 1.27233 | ||||||||
\(372\) | −5.25629 | −0.272526 | ||||||||
\(373\) | 2.90718 | 0.150528 | 0.0752639 | − | 0.997164i | \(-0.476020\pi\) | ||||
0.0752639 | + | 0.997164i | \(0.476020\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −104.124 | −5.37695 | ||||||||
\(376\) | −0.862845 | −0.0444978 | ||||||||
\(377\) | −2.19045 | −0.112814 | ||||||||
\(378\) | −65.9895 | −3.39413 | ||||||||
\(379\) | 4.89402 | 0.251389 | 0.125694 | − | 0.992069i | \(-0.459884\pi\) | ||||
0.125694 | + | 0.992069i | \(0.459884\pi\) | |||||||
\(380\) | −4.17017 | −0.213925 | ||||||||
\(381\) | 23.8710 | 1.22295 | ||||||||
\(382\) | 2.76249 | 0.141341 | ||||||||
\(383\) | −12.3879 | −0.632994 | −0.316497 | − | 0.948593i | \(-0.602507\pi\) | ||||
−0.316497 | + | 0.948593i | \(0.602507\pi\) | |||||||
\(384\) | −3.37860 | −0.172413 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.4775 | 1.09317 | ||||||||
\(387\) | 50.8824 | 2.58650 | ||||||||
\(388\) | 0.809369 | 0.0410895 | ||||||||
\(389\) | −13.7527 | −0.697291 | −0.348645 | − | 0.937255i | \(-0.613358\pi\) | ||||
−0.348645 | + | 0.937255i | \(0.613358\pi\) | |||||||
\(390\) | 9.43175 | 0.477595 | ||||||||
\(391\) | −26.1021 | −1.32004 | ||||||||
\(392\) | −6.01048 | −0.303575 | ||||||||
\(393\) | 11.0218 | 0.555975 | ||||||||
\(394\) | −18.9032 | −0.952330 | ||||||||
\(395\) | 4.36000 | 0.219375 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0289 | 0.503338 | 0.251669 | − | 0.967813i | \(-0.419021\pi\) | ||||
0.251669 | + | 0.967813i | \(0.419021\pi\) | |||||||
\(398\) | −7.76283 | −0.389115 | ||||||||
\(399\) | 12.1866 | 0.610094 | ||||||||
\(400\) | 12.3903 | 0.619515 | ||||||||
\(401\) | 22.2869 | 1.11296 | 0.556479 | − | 0.830862i | \(-0.312152\pi\) | ||||
0.556479 | + | 0.830862i | \(0.312152\pi\) | |||||||
\(402\) | −6.09296 | −0.303889 | ||||||||
\(403\) | −1.04147 | −0.0518792 | ||||||||
\(404\) | 12.0493 | 0.599475 | ||||||||
\(405\) | −152.487 | −7.57712 | ||||||||
\(406\) | 11.8026 | 0.585752 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 13.8689 | 0.686613 | ||||||||
\(409\) | −5.88120 | −0.290807 | −0.145403 | − | 0.989372i | \(-0.546448\pi\) | ||||
−0.145403 | + | 0.989372i | \(0.546448\pi\) | |||||||
\(410\) | −30.4811 | −1.50536 | ||||||||
\(411\) | 4.23604 | 0.208949 | ||||||||
\(412\) | 5.64096 | 0.277910 | ||||||||
\(413\) | −33.9534 | −1.67074 | ||||||||
\(414\) | −53.5081 | −2.62978 | ||||||||
\(415\) | 2.10106 | 0.103137 | ||||||||
\(416\) | −0.669426 | −0.0328213 | ||||||||
\(417\) | −5.14988 | −0.252191 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.24502 | 0.158530 | 0.0792648 | − | 0.996854i | \(-0.474743\pi\) | ||||
0.0792648 | + | 0.996854i | \(0.474743\pi\) | |||||||
\(420\) | −50.8202 | −2.47977 | ||||||||
\(421\) | −19.2545 | −0.938405 | −0.469203 | − | 0.883091i | \(-0.655459\pi\) | ||||
−0.469203 | + | 0.883091i | \(0.655459\pi\) | |||||||
\(422\) | −6.88377 | −0.335097 | ||||||||
\(423\) | 7.26077 | 0.353031 | ||||||||
\(424\) | −6.79423 | −0.329957 | ||||||||
\(425\) | −50.8613 | −2.46714 | ||||||||
\(426\) | −40.5204 | −1.96322 | ||||||||
\(427\) | 15.8946 | 0.769194 | ||||||||
\(428\) | −15.1059 | −0.730172 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 25.2157 | 1.21601 | ||||||||
\(431\) | 23.7828 | 1.14558 | 0.572789 | − | 0.819703i | \(-0.305861\pi\) | ||||
0.572789 | + | 0.819703i | \(0.305861\pi\) | |||||||
\(432\) | 18.2948 | 0.880210 | ||||||||
\(433\) | −17.1402 | −0.823707 | −0.411853 | − | 0.911250i | \(-0.635118\pi\) | ||||
−0.411853 | + | 0.911250i | \(0.635118\pi\) | |||||||
\(434\) | 5.61164 | 0.269367 | ||||||||
\(435\) | 46.1020 | 2.21042 | ||||||||
\(436\) | 11.6030 | 0.555685 | ||||||||
\(437\) | 6.35872 | 0.304179 | ||||||||
\(438\) | 33.4904 | 1.60023 | ||||||||
\(439\) | 0.144467 | 0.00689503 | 0.00344752 | − | 0.999994i | \(-0.498903\pi\) | ||||
0.00344752 | + | 0.999994i | \(0.498903\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 50.5777 | 2.40846 | ||||||||
\(442\) | 2.74795 | 0.130707 | ||||||||
\(443\) | −19.6940 | −0.935692 | −0.467846 | − | 0.883810i | \(-0.654970\pi\) | ||||
−0.467846 | + | 0.883810i | \(0.654970\pi\) | |||||||
\(444\) | 11.8734 | 0.563486 | ||||||||
\(445\) | −34.3486 | −1.62828 | ||||||||
\(446\) | −14.5212 | −0.687597 | ||||||||
\(447\) | 53.0009 | 2.50686 | ||||||||
\(448\) | 3.60700 | 0.170415 | ||||||||
\(449\) | −30.0122 | −1.41636 | −0.708182 | − | 0.706030i | \(-0.750484\pi\) | ||||
−0.708182 | + | 0.706030i | \(0.750484\pi\) | |||||||
\(450\) | −104.263 | −4.91502 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.03660 | −0.283938 | ||||||||
\(453\) | −64.1476 | −3.01392 | ||||||||
\(454\) | −18.1073 | −0.849817 | ||||||||
\(455\) | −10.0694 | −0.472060 | ||||||||
\(456\) | −3.37860 | −0.158217 | ||||||||
\(457\) | −0.810437 | −0.0379106 | −0.0189553 | − | 0.999820i | \(-0.506034\pi\) | ||||
−0.0189553 | + | 0.999820i | \(0.506034\pi\) | |||||||
\(458\) | 25.3580 | 1.18490 | ||||||||
\(459\) | −75.0990 | −3.50532 | ||||||||
\(460\) | −26.5169 | −1.23636 | ||||||||
\(461\) | −29.4451 | −1.37139 | −0.685697 | − | 0.727888i | \(-0.740502\pi\) | ||||
−0.685697 | + | 0.727888i | \(0.740502\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.9830 | 1.16106 | 0.580529 | − | 0.814239i | \(-0.302846\pi\) | ||||
0.580529 | + | 0.814239i | \(0.302846\pi\) | |||||||
\(464\) | −3.27213 | −0.151905 | ||||||||
\(465\) | 21.9196 | 1.01650 | ||||||||
\(466\) | −21.9886 | −1.01860 | ||||||||
\(467\) | −21.6826 | −1.00335 | −0.501676 | − | 0.865056i | \(-0.667283\pi\) | ||||
−0.501676 | + | 0.865056i | \(0.667283\pi\) | |||||||
\(468\) | 5.63316 | 0.260393 | ||||||||
\(469\) | 6.50487 | 0.300367 | ||||||||
\(470\) | 3.59821 | 0.165973 | ||||||||
\(471\) | −30.0550 | −1.38486 | ||||||||
\(472\) | 9.41317 | 0.433276 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.53240 | 0.162248 | ||||||||
\(475\) | 12.3903 | 0.568506 | ||||||||
\(476\) | −14.8065 | −0.678655 | ||||||||
\(477\) | 57.1729 | 2.61777 | ||||||||
\(478\) | 15.2971 | 0.699674 | ||||||||
\(479\) | −30.8590 | −1.40998 | −0.704992 | − | 0.709215i | \(-0.749049\pi\) | ||||
−0.704992 | + | 0.709215i | \(0.749049\pi\) | |||||||
\(480\) | 14.0893 | 0.643086 | ||||||||
\(481\) | 2.35256 | 0.107268 | ||||||||
\(482\) | 16.0409 | 0.730643 | ||||||||
\(483\) | 77.4913 | 3.52598 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.37520 | −0.153260 | ||||||||
\(486\) | −68.6575 | −3.11437 | ||||||||
\(487\) | −5.68001 | −0.257386 | −0.128693 | − | 0.991685i | \(-0.541078\pi\) | ||||
−0.128693 | + | 0.991685i | \(0.541078\pi\) | |||||||
\(488\) | −4.40660 | −0.199477 | ||||||||
\(489\) | −16.3693 | −0.740244 | ||||||||
\(490\) | 25.0647 | 1.13231 | ||||||||
\(491\) | −29.9204 | −1.35029 | −0.675145 | − | 0.737685i | \(-0.735919\pi\) | ||||
−0.675145 | + | 0.737685i | \(0.735919\pi\) | |||||||
\(492\) | −24.6953 | −1.11335 | ||||||||
\(493\) | 13.4319 | 0.604941 | ||||||||
\(494\) | −0.669426 | −0.0301189 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.55576 | −0.0698558 | ||||||||
\(497\) | 43.2598 | 1.94047 | ||||||||
\(498\) | 1.70224 | 0.0762793 | ||||||||
\(499\) | −2.89019 | −0.129383 | −0.0646913 | − | 0.997905i | \(-0.520606\pi\) | ||||
−0.0646913 | + | 0.997905i | \(0.520606\pi\) | |||||||
\(500\) | −30.8187 | −1.37826 | ||||||||
\(501\) | 15.5935 | 0.696664 | ||||||||
\(502\) | 6.91197 | 0.308496 | ||||||||
\(503\) | 27.9653 | 1.24691 | 0.623456 | − | 0.781858i | \(-0.285728\pi\) | ||||
0.623456 | + | 0.781858i | \(0.285728\pi\) | |||||||
\(504\) | −30.3526 | −1.35201 | ||||||||
\(505\) | −50.2476 | −2.23599 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −42.4077 | −1.88339 | ||||||||
\(508\) | 7.06535 | 0.313474 | ||||||||
\(509\) | −34.7436 | −1.53998 | −0.769992 | − | 0.638054i | \(-0.779740\pi\) | ||||
−0.769992 | + | 0.638054i | \(0.779740\pi\) | |||||||
\(510\) | −57.8357 | −2.56101 | ||||||||
\(511\) | −35.7545 | −1.58169 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 18.2948 | 0.807736 | ||||||||
\(514\) | 24.7512 | 1.09173 | ||||||||
\(515\) | −23.5237 | −1.03658 | ||||||||
\(516\) | 20.4293 | 0.899351 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −12.6761 | −0.556955 | ||||||||
\(519\) | 31.5506 | 1.38492 | ||||||||
\(520\) | 2.79162 | 0.122420 | ||||||||
\(521\) | 26.9219 | 1.17947 | 0.589734 | − | 0.807597i | \(-0.299232\pi\) | ||||
0.589734 | + | 0.807597i | \(0.299232\pi\) | |||||||
\(522\) | 27.5347 | 1.20516 | ||||||||
\(523\) | 2.23979 | 0.0979394 | 0.0489697 | − | 0.998800i | \(-0.484406\pi\) | ||||
0.0489697 | + | 0.998800i | \(0.484406\pi\) | |||||||
\(524\) | 3.26224 | 0.142512 | ||||||||
\(525\) | 150.996 | 6.58999 | ||||||||
\(526\) | 16.8155 | 0.733190 | ||||||||
\(527\) | 6.38630 | 0.278192 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.4334 | 0.757973 | ||||||||
\(530\) | 28.3331 | 1.23071 | ||||||||
\(531\) | −79.2110 | −3.43747 | ||||||||
\(532\) | 3.60700 | 0.156383 | ||||||||
\(533\) | −4.89305 | −0.211942 | ||||||||
\(534\) | −27.8286 | −1.20426 | ||||||||
\(535\) | 62.9942 | 2.72348 | ||||||||
\(536\) | −1.80340 | −0.0778950 | ||||||||
\(537\) | 56.7203 | 2.44766 | ||||||||
\(538\) | −17.8288 | −0.768655 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −76.2924 | −3.28310 | ||||||||
\(541\) | 9.52299 | 0.409425 | 0.204713 | − | 0.978822i | \(-0.434374\pi\) | ||||
0.204713 | + | 0.978822i | \(0.434374\pi\) | |||||||
\(542\) | −30.2063 | −1.29747 | ||||||||
\(543\) | 59.4219 | 2.55004 | ||||||||
\(544\) | 4.10493 | 0.175998 | ||||||||
\(545\) | −48.3866 | −2.07265 | ||||||||
\(546\) | −8.15803 | −0.349132 | ||||||||
\(547\) | 17.0265 | 0.727999 | 0.364000 | − | 0.931399i | \(-0.381411\pi\) | ||||
0.364000 | + | 0.931399i | \(0.381411\pi\) | |||||||
\(548\) | 1.25379 | 0.0535592 | ||||||||
\(549\) | 37.0811 | 1.58258 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.27213 | −0.139397 | ||||||||
\(552\) | −21.4836 | −0.914401 | ||||||||
\(553\) | −3.77120 | −0.160368 | ||||||||
\(554\) | 32.7642 | 1.39202 | ||||||||
\(555\) | −49.5140 | −2.10175 | ||||||||
\(556\) | −1.52427 | −0.0646433 | ||||||||
\(557\) | 14.4105 | 0.610593 | 0.305296 | − | 0.952257i | \(-0.401244\pi\) | ||||
0.305296 | + | 0.952257i | \(0.401244\pi\) | |||||||
\(558\) | 13.0916 | 0.554212 | ||||||||
\(559\) | 4.04781 | 0.171204 | ||||||||
\(560\) | −15.0418 | −0.635633 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.70846 | −0.409527 | ||||||||
\(563\) | 14.3589 | 0.605156 | 0.302578 | − | 0.953125i | \(-0.402153\pi\) | ||||
0.302578 | + | 0.953125i | \(0.402153\pi\) | |||||||
\(564\) | 2.91521 | 0.122752 | ||||||||
\(565\) | 25.1736 | 1.05906 | ||||||||
\(566\) | 14.5739 | 0.612585 | ||||||||
\(567\) | 131.894 | 5.53902 | ||||||||
\(568\) | −11.9933 | −0.503226 | ||||||||
\(569\) | −27.8880 | −1.16912 | −0.584562 | − | 0.811349i | \(-0.698734\pi\) | ||||
−0.584562 | + | 0.811349i | \(0.698734\pi\) | |||||||
\(570\) | 14.0893 | 0.590136 | ||||||||
\(571\) | 40.1622 | 1.68073 | 0.840367 | − | 0.542018i | \(-0.182340\pi\) | ||||
0.840367 | + | 0.542018i | \(0.182340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.33335 | −0.389906 | ||||||||
\(574\) | 26.3648 | 1.10044 | ||||||||
\(575\) | 78.7864 | 3.28562 | ||||||||
\(576\) | 8.41492 | 0.350621 | ||||||||
\(577\) | 3.68171 | 0.153271 | 0.0766357 | − | 0.997059i | \(-0.475582\pi\) | ||||
0.0766357 | + | 0.997059i | \(0.475582\pi\) | |||||||
\(578\) | 0.149526 | 0.00621944 | ||||||||
\(579\) | −72.5637 | −3.01564 | ||||||||
\(580\) | 13.6453 | 0.566591 | ||||||||
\(581\) | −1.81732 | −0.0753952 | ||||||||
\(582\) | −2.73453 | −0.113350 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 9.91252 | 0.410183 | ||||||||
\(585\) | −23.4912 | −0.971242 | ||||||||
\(586\) | −10.5241 | −0.434746 | ||||||||
\(587\) | −44.1246 | −1.82122 | −0.910608 | − | 0.413272i | \(-0.864386\pi\) | ||||
−0.910608 | + | 0.413272i | \(0.864386\pi\) | |||||||
\(588\) | 20.3070 | 0.837446 | ||||||||
\(589\) | −1.55576 | −0.0641041 | ||||||||
\(590\) | −39.2545 | −1.61608 | ||||||||
\(591\) | 63.8663 | 2.62711 | ||||||||
\(592\) | 3.51430 | 0.144437 | ||||||||
\(593\) | 2.42622 | 0.0996330 | 0.0498165 | − | 0.998758i | \(-0.484136\pi\) | ||||
0.0498165 | + | 0.998758i | \(0.484136\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 61.7456 | 2.53132 | ||||||||
\(596\) | 15.6872 | 0.642575 | ||||||||
\(597\) | 26.2275 | 1.07342 | ||||||||
\(598\) | −4.25669 | −0.174069 | ||||||||
\(599\) | 30.0748 | 1.22882 | 0.614412 | − | 0.788986i | \(-0.289393\pi\) | ||||
0.614412 | + | 0.788986i | \(0.289393\pi\) | |||||||
\(600\) | −41.8618 | −1.70900 | ||||||||
\(601\) | −43.6023 | −1.77858 | −0.889288 | − | 0.457348i | \(-0.848799\pi\) | ||||
−0.889288 | + | 0.457348i | \(0.848799\pi\) | |||||||
\(602\) | −21.8104 | −0.888927 | ||||||||
\(603\) | 15.1755 | 0.617992 | ||||||||
\(604\) | −18.9865 | −0.772548 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −40.7097 | −1.65372 | ||||||||
\(607\) | 3.95907 | 0.160694 | 0.0803468 | − | 0.996767i | \(-0.474397\pi\) | ||||
0.0803468 | + | 0.996767i | \(0.474397\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −39.8761 | −1.61586 | ||||||||
\(610\) | 18.3762 | 0.744032 | ||||||||
\(611\) | 0.577611 | 0.0233676 | ||||||||
\(612\) | −34.5427 | −1.39630 | ||||||||
\(613\) | −33.3417 | −1.34666 | −0.673329 | − | 0.739343i | \(-0.735136\pi\) | ||||
−0.673329 | + | 0.739343i | \(0.735136\pi\) | |||||||
\(614\) | −21.4131 | −0.864161 | ||||||||
\(615\) | 102.983 | 4.15269 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.8084 | −1.88443 | −0.942217 | − | 0.335004i | \(-0.891262\pi\) | ||||
−0.942217 | + | 0.335004i | \(0.891262\pi\) | |||||||
\(618\) | −19.0585 | −0.766646 | ||||||||
\(619\) | −3.44952 | −0.138648 | −0.0693239 | − | 0.997594i | \(-0.522084\pi\) | ||||
−0.0693239 | + | 0.997594i | \(0.522084\pi\) | |||||||
\(620\) | 6.48779 | 0.260556 | ||||||||
\(621\) | 116.332 | 4.66823 | ||||||||
\(622\) | −8.91440 | −0.357435 | ||||||||
\(623\) | 29.7100 | 1.19030 | ||||||||
\(624\) | 2.26172 | 0.0905412 | ||||||||
\(625\) | 66.5679 | 2.66271 | ||||||||
\(626\) | 29.2280 | 1.16818 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.89570 | −0.354977 | ||||||||
\(629\) | −14.4260 | −0.575200 | ||||||||
\(630\) | 126.576 | 5.04289 | ||||||||
\(631\) | −3.45479 | −0.137533 | −0.0687665 | − | 0.997633i | \(-0.521906\pi\) | ||||
−0.0687665 | + | 0.997633i | \(0.521906\pi\) | |||||||
\(632\) | 1.04552 | 0.0415886 | ||||||||
\(633\) | 23.2575 | 0.924402 | ||||||||
\(634\) | 3.86251 | 0.153400 | ||||||||
\(635\) | −29.4637 | −1.16923 | ||||||||
\(636\) | 22.9550 | 0.910224 | ||||||||
\(637\) | 4.02357 | 0.159420 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 100.922 | 3.99243 | ||||||||
\(640\) | 4.17017 | 0.164840 | ||||||||
\(641\) | 4.16142 | 0.164366 | 0.0821831 | − | 0.996617i | \(-0.473811\pi\) | ||||
0.0821831 | + | 0.996617i | \(0.473811\pi\) | |||||||
\(642\) | 51.0368 | 2.01426 | ||||||||
\(643\) | −27.0695 | −1.06752 | −0.533759 | − | 0.845637i | \(-0.679221\pi\) | ||||
−0.533759 | + | 0.845637i | \(0.679221\pi\) | |||||||
\(644\) | 22.9359 | 0.903803 | ||||||||
\(645\) | −85.1937 | −3.35450 | ||||||||
\(646\) | 4.10493 | 0.161506 | ||||||||
\(647\) | −4.31680 | −0.169711 | −0.0848554 | − | 0.996393i | \(-0.527043\pi\) | ||||
−0.0848554 | + | 0.996393i | \(0.527043\pi\) | |||||||
\(648\) | −36.5661 | −1.43645 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −8.29438 | −0.325332 | ||||||||
\(651\) | −18.9595 | −0.743080 | ||||||||
\(652\) | −4.84499 | −0.189744 | ||||||||
\(653\) | −5.85277 | −0.229037 | −0.114518 | − | 0.993421i | \(-0.536532\pi\) | ||||
−0.114518 | + | 0.993421i | \(0.536532\pi\) | |||||||
\(654\) | −39.2020 | −1.53292 | ||||||||
\(655\) | −13.6041 | −0.531555 | ||||||||
\(656\) | −7.30933 | −0.285381 | ||||||||
\(657\) | −83.4131 | −3.25425 | ||||||||
\(658\) | −3.11229 | −0.121330 | ||||||||
\(659\) | −16.4116 | −0.639307 | −0.319653 | − | 0.947535i | \(-0.603566\pi\) | ||||
−0.319653 | + | 0.947535i | \(0.603566\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.8425 | −1.00516 | −0.502578 | − | 0.864532i | \(-0.667615\pi\) | ||||
−0.502578 | + | 0.864532i | \(0.667615\pi\) | |||||||
\(662\) | −30.7968 | −1.19695 | ||||||||
\(663\) | −9.28421 | −0.360569 | ||||||||
\(664\) | 0.503831 | 0.0195524 | ||||||||
\(665\) | −15.0418 | −0.583296 | ||||||||
\(666\) | −29.5725 | −1.14591 | ||||||||
\(667\) | −20.8066 | −0.805633 | ||||||||
\(668\) | 4.61536 | 0.178574 | ||||||||
\(669\) | 49.0611 | 1.89681 | ||||||||
\(670\) | 7.52048 | 0.290541 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −12.1866 | −0.470109 | ||||||||
\(673\) | −4.23989 | −0.163436 | −0.0817178 | − | 0.996656i | \(-0.526041\pi\) | ||||
−0.0817178 | + | 0.996656i | \(0.526041\pi\) | |||||||
\(674\) | −16.0941 | −0.619923 | ||||||||
\(675\) | 226.678 | 8.72484 | ||||||||
\(676\) | −12.5519 | −0.482764 | ||||||||
\(677\) | −49.7388 | −1.91162 | −0.955809 | − | 0.293988i | \(-0.905017\pi\) | ||||
−0.955809 | + | 0.293988i | \(0.905017\pi\) | |||||||
\(678\) | 20.3953 | 0.783275 | ||||||||
\(679\) | 2.91940 | 0.112036 | ||||||||
\(680\) | −17.1183 | −0.656455 | ||||||||
\(681\) | 61.1772 | 2.34432 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.4329 | 1.47059 | 0.735297 | − | 0.677745i | \(-0.237043\pi\) | ||||
0.735297 | + | 0.677745i | \(0.237043\pi\) | |||||||
\(684\) | 8.41492 | 0.321752 | ||||||||
\(685\) | −5.22851 | −0.199771 | ||||||||
\(686\) | 3.56920 | 0.136273 | ||||||||
\(687\) | −85.6743 | −3.26868 | ||||||||
\(688\) | 6.04669 | 0.230528 | ||||||||
\(689\) | 4.54823 | 0.173274 | ||||||||
\(690\) | 89.5900 | 3.41063 | ||||||||
\(691\) | 26.5880 | 1.01145 | 0.505727 | − | 0.862693i | \(-0.331224\pi\) | ||||
0.505727 | + | 0.862693i | \(0.331224\pi\) | |||||||
\(692\) | 9.33836 | 0.354991 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −31.7933 | −1.20686 | ||||||||
\(695\) | 6.35644 | 0.241114 | ||||||||
\(696\) | 11.0552 | 0.419046 | ||||||||
\(697\) | 30.0043 | 1.13649 | ||||||||
\(698\) | 11.5331 | 0.436532 | ||||||||
\(699\) | 74.2906 | 2.80993 | ||||||||
\(700\) | 44.6918 | 1.68919 | ||||||||
\(701\) | 14.6368 | 0.552826 | 0.276413 | − | 0.961039i | \(-0.410854\pi\) | ||||
0.276413 | + | 0.961039i | \(0.410854\pi\) | |||||||
\(702\) | −12.2470 | −0.462234 | ||||||||
\(703\) | 3.51430 | 0.132544 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.1569 | −0.457855 | ||||||||
\(706\) | 3.56825 | 0.134293 | ||||||||
\(707\) | 43.4619 | 1.63455 | ||||||||
\(708\) | −31.8033 | −1.19524 | ||||||||
\(709\) | 14.7490 | 0.553911 | 0.276956 | − | 0.960883i | \(-0.410674\pi\) | ||||
0.276956 | + | 0.960883i | \(0.410674\pi\) | |||||||
\(710\) | 50.0139 | 1.87699 | ||||||||
\(711\) | −8.79798 | −0.329950 | ||||||||
\(712\) | −8.23674 | −0.308685 | ||||||||
\(713\) | −9.89266 | −0.370483 | ||||||||
\(714\) | 50.0252 | 1.87215 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.7881 | 0.627401 | ||||||||
\(717\) | −51.6828 | −1.93013 | ||||||||
\(718\) | 21.8282 | 0.814622 | ||||||||
\(719\) | 8.82348 | 0.329060 | 0.164530 | − | 0.986372i | \(-0.447389\pi\) | ||||
0.164530 | + | 0.986372i | \(0.447389\pi\) | |||||||
\(720\) | −35.0916 | −1.30779 | ||||||||
\(721\) | 20.3470 | 0.757760 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −54.1957 | −2.01556 | ||||||||
\(724\) | 17.5877 | 0.653643 | ||||||||
\(725\) | −40.5426 | −1.50571 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.938013 | 0.0347890 | 0.0173945 | − | 0.999849i | \(-0.494463\pi\) | ||||
0.0173945 | + | 0.999849i | \(0.494463\pi\) | |||||||
\(728\) | −2.41462 | −0.0894918 | ||||||||
\(729\) | 122.268 | 4.52844 | ||||||||
\(730\) | −41.3369 | −1.52995 | ||||||||
\(731\) | −24.8213 | −0.918048 | ||||||||
\(732\) | 14.8881 | 0.550280 | ||||||||
\(733\) | −2.58558 | −0.0955007 | −0.0477504 | − | 0.998859i | \(-0.515205\pi\) | ||||
−0.0477504 | + | 0.998859i | \(0.515205\pi\) | |||||||
\(734\) | −7.86931 | −0.290461 | ||||||||
\(735\) | −84.6835 | −3.12360 | ||||||||
\(736\) | −6.35872 | −0.234386 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 61.5074 | 2.26412 | ||||||||
\(739\) | 1.56553 | 0.0575888 | 0.0287944 | − | 0.999585i | \(-0.490833\pi\) | ||||
0.0287944 | + | 0.999585i | \(0.490833\pi\) | |||||||
\(740\) | −14.6552 | −0.538736 | ||||||||
\(741\) | 2.26172 | 0.0830863 | ||||||||
\(742\) | −24.5068 | −0.899674 | ||||||||
\(743\) | −35.3325 | −1.29623 | −0.648113 | − | 0.761545i | \(-0.724441\pi\) | ||||
−0.648113 | + | 0.761545i | \(0.724441\pi\) | |||||||
\(744\) | 5.25629 | 0.192705 | ||||||||
\(745\) | −65.4184 | −2.39675 | ||||||||
\(746\) | −2.90718 | −0.106439 | ||||||||
\(747\) | −4.23970 | −0.155122 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −54.4871 | −1.99092 | ||||||||
\(750\) | 104.124 | 3.80208 | ||||||||
\(751\) | −11.3947 | −0.415799 | −0.207900 | − | 0.978150i | \(-0.566663\pi\) | ||||
−0.207900 | + | 0.978150i | \(0.566663\pi\) | |||||||
\(752\) | 0.862845 | 0.0314647 | ||||||||
\(753\) | −23.3527 | −0.851021 | ||||||||
\(754\) | 2.19045 | 0.0797713 | ||||||||
\(755\) | 79.1767 | 2.88153 | ||||||||
\(756\) | 65.9895 | 2.40001 | ||||||||
\(757\) | −6.68211 | −0.242865 | −0.121433 | − | 0.992600i | \(-0.538749\pi\) | ||||
−0.121433 | + | 0.992600i | \(0.538749\pi\) | |||||||
\(758\) | −4.89402 | −0.177759 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.17017 | 0.151268 | ||||||||
\(761\) | −2.33169 | −0.0845239 | −0.0422619 | − | 0.999107i | \(-0.513456\pi\) | ||||
−0.0422619 | + | 0.999107i | \(0.513456\pi\) | |||||||
\(762\) | −23.8710 | −0.864754 | ||||||||
\(763\) | 41.8522 | 1.51515 | ||||||||
\(764\) | −2.76249 | −0.0999435 | ||||||||
\(765\) | 144.049 | 5.20809 | ||||||||
\(766\) | 12.3879 | 0.447594 | ||||||||
\(767\) | −6.30142 | −0.227531 | ||||||||
\(768\) | 3.37860 | 0.121915 | ||||||||
\(769\) | −28.8994 | −1.04214 | −0.521070 | − | 0.853514i | \(-0.674467\pi\) | ||||
−0.521070 | + | 0.853514i | \(0.674467\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −83.6242 | −3.01165 | ||||||||
\(772\) | −21.4775 | −0.772991 | ||||||||
\(773\) | −25.5506 | −0.918991 | −0.459495 | − | 0.888180i | \(-0.651970\pi\) | ||||
−0.459495 | + | 0.888180i | \(0.651970\pi\) | |||||||
\(774\) | −50.8824 | −1.82893 | ||||||||
\(775\) | −19.2763 | −0.692427 | ||||||||
\(776\) | −0.809369 | −0.0290546 | ||||||||
\(777\) | 42.8274 | 1.53642 | ||||||||
\(778\) | 13.7527 | 0.493059 | ||||||||
\(779\) | −7.30933 | −0.261884 | ||||||||
\(780\) | −9.43175 | −0.337711 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 26.1021 | 0.933411 | ||||||||
\(783\) | −59.8630 | −2.13933 | ||||||||
\(784\) | 6.01048 | 0.214660 | ||||||||
\(785\) | 37.0966 | 1.32403 | ||||||||
\(786\) | −11.0218 | −0.393134 | ||||||||
\(787\) | −10.5042 | −0.374436 | −0.187218 | − | 0.982318i | \(-0.559947\pi\) | ||||
−0.187218 | + | 0.982318i | \(0.559947\pi\) | |||||||
\(788\) | 18.9032 | 0.673399 | ||||||||
\(789\) | −56.8128 | −2.02259 | ||||||||
\(790\) | −4.36000 | −0.155122 | ||||||||
\(791\) | −21.7741 | −0.774196 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.94989 | 0.104754 | ||||||||
\(794\) | −10.0289 | −0.355914 | ||||||||
\(795\) | −95.7261 | −3.39505 | ||||||||
\(796\) | 7.76283 | 0.275146 | ||||||||
\(797\) | −6.50041 | −0.230256 | −0.115128 | − | 0.993351i | \(-0.536728\pi\) | ||||
−0.115128 | + | 0.993351i | \(0.536728\pi\) | |||||||
\(798\) | −12.1866 | −0.431401 | ||||||||
\(799\) | −3.54192 | −0.125304 | ||||||||
\(800\) | −12.3903 | −0.438063 | ||||||||
\(801\) | 69.3115 | 2.44900 | ||||||||
\(802\) | −22.2869 | −0.786979 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 6.09296 | 0.214882 | ||||||||
\(805\) | −95.6467 | −3.37110 | ||||||||
\(806\) | 1.04147 | 0.0366841 | ||||||||
\(807\) | 60.2364 | 2.12042 | ||||||||
\(808\) | −12.0493 | −0.423893 | ||||||||
\(809\) | 30.5543 | 1.07423 | 0.537116 | − | 0.843509i | \(-0.319514\pi\) | ||||
0.537116 | + | 0.843509i | \(0.319514\pi\) | |||||||
\(810\) | 152.487 | 5.35783 | ||||||||
\(811\) | −5.81000 | −0.204017 | −0.102008 | − | 0.994784i | \(-0.532527\pi\) | ||||
−0.102008 | + | 0.994784i | \(0.532527\pi\) | |||||||
\(812\) | −11.8026 | −0.414189 | ||||||||
\(813\) | 102.055 | 3.57922 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.2044 | 0.707730 | ||||||||
\(816\) | −13.8689 | −0.485509 | ||||||||
\(817\) | 6.04669 | 0.211547 | ||||||||
\(818\) | 5.88120 | 0.205631 | ||||||||
\(819\) | 20.3188 | 0.709997 | ||||||||
\(820\) | 30.4811 | 1.06445 | ||||||||
\(821\) | 43.0690 | 1.50312 | 0.751559 | − | 0.659666i | \(-0.229302\pi\) | ||||
0.751559 | + | 0.659666i | \(0.229302\pi\) | |||||||
\(822\) | −4.23604 | −0.147749 | ||||||||
\(823\) | −20.6760 | −0.720722 | −0.360361 | − | 0.932813i | \(-0.617346\pi\) | ||||
−0.360361 | + | 0.932813i | \(0.617346\pi\) | |||||||
\(824\) | −5.64096 | −0.196512 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.9534 | 1.18139 | ||||||||
\(827\) | −35.8535 | −1.24675 | −0.623374 | − | 0.781924i | \(-0.714239\pi\) | ||||
−0.623374 | + | 0.781924i | \(0.714239\pi\) | |||||||
\(828\) | 53.5081 | 1.85954 | ||||||||
\(829\) | 10.6519 | 0.369956 | 0.184978 | − | 0.982743i | \(-0.440779\pi\) | ||||
0.184978 | + | 0.982743i | \(0.440779\pi\) | |||||||
\(830\) | −2.10106 | −0.0729288 | ||||||||
\(831\) | −110.697 | −3.84004 | ||||||||
\(832\) | 0.669426 | 0.0232082 | ||||||||
\(833\) | −24.6726 | −0.854856 | ||||||||
\(834\) | 5.14988 | 0.178326 | ||||||||
\(835\) | −19.2468 | −0.666064 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.4624 | −0.983804 | ||||||||
\(838\) | −3.24502 | −0.112097 | ||||||||
\(839\) | −46.8329 | −1.61685 | −0.808425 | − | 0.588599i | \(-0.799680\pi\) | ||||
−0.808425 | + | 0.588599i | \(0.799680\pi\) | |||||||
\(840\) | 50.8202 | 1.75346 | ||||||||
\(841\) | −18.2932 | −0.630799 | ||||||||
\(842\) | 19.2545 | 0.663553 | ||||||||
\(843\) | 32.8010 | 1.12973 | ||||||||
\(844\) | 6.88377 | 0.236949 | ||||||||
\(845\) | 52.3434 | 1.80067 | ||||||||
\(846\) | −7.26077 | −0.249630 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.79423 | 0.233315 | ||||||||
\(849\) | −49.2392 | −1.68988 | ||||||||
\(850\) | 50.8613 | 1.74453 | ||||||||
\(851\) | 22.3464 | 0.766026 | ||||||||
\(852\) | 40.5204 | 1.38821 | ||||||||
\(853\) | −35.3351 | −1.20985 | −0.604926 | − | 0.796282i | \(-0.706797\pi\) | ||||
−0.604926 | + | 0.796282i | \(0.706797\pi\) | |||||||
\(854\) | −15.8946 | −0.543902 | ||||||||
\(855\) | −35.0916 | −1.20011 | ||||||||
\(856\) | 15.1059 | 0.516309 | ||||||||
\(857\) | 4.94229 | 0.168826 | 0.0844128 | − | 0.996431i | \(-0.473099\pi\) | ||||
0.0844128 | + | 0.996431i | \(0.473099\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.1131 | 0.345054 | 0.172527 | − | 0.985005i | \(-0.444807\pi\) | ||||
0.172527 | + | 0.985005i | \(0.444807\pi\) | |||||||
\(860\) | −25.2157 | −0.859849 | ||||||||
\(861\) | −89.0760 | −3.03570 | ||||||||
\(862\) | −23.7828 | −0.810046 | ||||||||
\(863\) | 12.9844 | 0.441995 | 0.220998 | − | 0.975274i | \(-0.429069\pi\) | ||||
0.220998 | + | 0.975274i | \(0.429069\pi\) | |||||||
\(864\) | −18.2948 | −0.622402 | ||||||||
\(865\) | −38.9425 | −1.32409 | ||||||||
\(866\) | 17.1402 | 0.582449 | ||||||||
\(867\) | −0.505186 | −0.0171570 | ||||||||
\(868\) | −5.61164 | −0.190471 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −46.1020 | −1.56300 | ||||||||
\(871\) | 1.20724 | 0.0409058 | ||||||||
\(872\) | −11.6030 | −0.392929 | ||||||||
\(873\) | 6.81077 | 0.230510 | ||||||||
\(874\) | −6.35872 | −0.215087 | ||||||||
\(875\) | −111.163 | −3.75801 | ||||||||
\(876\) | −33.4904 | −1.13154 | ||||||||
\(877\) | −44.8363 | −1.51401 | −0.757007 | − | 0.653407i | \(-0.773339\pi\) | ||||
−0.757007 | + | 0.653407i | \(0.773339\pi\) | |||||||
\(878\) | −0.144467 | −0.00487552 | ||||||||
\(879\) | 35.5567 | 1.19930 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.0954 | −0.710722 | −0.355361 | − | 0.934729i | \(-0.615642\pi\) | ||||
−0.355361 | + | 0.934729i | \(0.615642\pi\) | |||||||
\(882\) | −50.5777 | −1.70304 | ||||||||
\(883\) | 53.8142 | 1.81099 | 0.905496 | − | 0.424355i | \(-0.139499\pi\) | ||||
0.905496 | + | 0.424355i | \(0.139499\pi\) | |||||||
\(884\) | −2.74795 | −0.0924235 | ||||||||
\(885\) | 132.625 | 4.45814 | ||||||||
\(886\) | 19.6940 | 0.661634 | ||||||||
\(887\) | 28.4930 | 0.956701 | 0.478351 | − | 0.878169i | \(-0.341235\pi\) | ||||
0.478351 | + | 0.878169i | \(0.341235\pi\) | |||||||
\(888\) | −11.8734 | −0.398445 | ||||||||
\(889\) | 25.4848 | 0.854731 | ||||||||
\(890\) | 34.3486 | 1.15137 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.5212 | 0.486204 | ||||||||
\(893\) | 0.862845 | 0.0288740 | ||||||||
\(894\) | −53.0009 | −1.77261 | ||||||||
\(895\) | −70.0092 | −2.34015 | ||||||||
\(896\) | −3.60700 | −0.120502 | ||||||||
\(897\) | 14.3816 | 0.480189 | ||||||||
\(898\) | 30.0122 | 1.00152 | ||||||||
\(899\) | 5.09065 | 0.169783 | ||||||||
\(900\) | 104.263 | 3.47544 | ||||||||
\(901\) | −27.8899 | −0.929146 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 73.6887 | 2.45221 | ||||||||
\(904\) | 6.03660 | 0.200774 | ||||||||
\(905\) | −73.3438 | −2.43803 | ||||||||
\(906\) | 64.1476 | 2.13116 | ||||||||
\(907\) | −19.0581 | −0.632815 | −0.316408 | − | 0.948623i | \(-0.602477\pi\) | ||||
−0.316408 | + | 0.948623i | \(0.602477\pi\) | |||||||
\(908\) | 18.1073 | 0.600912 | ||||||||
\(909\) | 101.394 | 3.36302 | ||||||||
\(910\) | 10.0694 | 0.333796 | ||||||||
\(911\) | −8.41671 | −0.278858 | −0.139429 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139429 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(912\) | 3.37860 | 0.111877 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.810437 | 0.0268069 | ||||||||
\(915\) | −62.0859 | −2.05250 | ||||||||
\(916\) | −25.3580 | −0.837850 | ||||||||
\(917\) | 11.7669 | 0.388577 | ||||||||
\(918\) | 75.0990 | 2.47864 | ||||||||
\(919\) | 10.5289 | 0.347315 | 0.173658 | − | 0.984806i | \(-0.444441\pi\) | ||||
0.173658 | + | 0.984806i | \(0.444441\pi\) | |||||||
\(920\) | 26.5169 | 0.874238 | ||||||||
\(921\) | 72.3461 | 2.38388 | ||||||||
\(922\) | 29.4451 | 0.969721 | ||||||||
\(923\) | 8.02860 | 0.264265 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.5432 | 1.43169 | ||||||||
\(926\) | −24.9830 | −0.820992 | ||||||||
\(927\) | 47.4682 | 1.55906 | ||||||||
\(928\) | 3.27213 | 0.107413 | ||||||||
\(929\) | −19.5004 | −0.639787 | −0.319893 | − | 0.947454i | \(-0.603647\pi\) | ||||
−0.319893 | + | 0.947454i | \(0.603647\pi\) | |||||||
\(930\) | −21.9196 | −0.718773 | ||||||||
\(931\) | 6.01048 | 0.196986 | ||||||||
\(932\) | 21.9886 | 0.720261 | ||||||||
\(933\) | 30.1182 | 0.986024 | ||||||||
\(934\) | 21.6826 | 0.709477 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.63316 | −0.184126 | ||||||||
\(937\) | −46.4018 | −1.51588 | −0.757941 | − | 0.652323i | \(-0.773794\pi\) | ||||
−0.757941 | + | 0.652323i | \(0.773794\pi\) | |||||||
\(938\) | −6.50487 | −0.212392 | ||||||||
\(939\) | −98.7495 | −3.22257 | ||||||||
\(940\) | −3.59821 | −0.117361 | ||||||||
\(941\) | 17.4235 | 0.567991 | 0.283996 | − | 0.958826i | \(-0.408340\pi\) | ||||
0.283996 | + | 0.958826i | \(0.408340\pi\) | |||||||
\(942\) | 30.0550 | 0.979245 | ||||||||
\(943\) | −46.4780 | −1.51353 | ||||||||
\(944\) | −9.41317 | −0.306373 | ||||||||
\(945\) | −275.187 | −8.95184 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.8103 | −0.611254 | −0.305627 | − | 0.952151i | \(-0.598866\pi\) | ||||
−0.305627 | + | 0.952151i | \(0.598866\pi\) | |||||||
\(948\) | −3.53240 | −0.114727 | ||||||||
\(949\) | −6.63570 | −0.215404 | ||||||||
\(950\) | −12.3903 | −0.401994 | ||||||||
\(951\) | −13.0499 | −0.423171 | ||||||||
\(952\) | 14.8065 | 0.479882 | ||||||||
\(953\) | −54.4674 | −1.76437 | −0.882187 | − | 0.470900i | \(-0.843929\pi\) | ||||
−0.882187 | + | 0.470900i | \(0.843929\pi\) | |||||||
\(954\) | −57.1729 | −1.85104 | ||||||||
\(955\) | 11.5201 | 0.372780 | ||||||||
\(956\) | −15.2971 | −0.494744 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.8590 | 0.997009 | ||||||||
\(959\) | 4.52242 | 0.146037 | ||||||||
\(960\) | −14.0893 | −0.454731 | ||||||||
\(961\) | −28.5796 | −0.921923 | ||||||||
\(962\) | −2.35256 | −0.0758496 | ||||||||
\(963\) | −127.115 | −4.09622 | ||||||||
\(964\) | −16.0409 | −0.516642 | ||||||||
\(965\) | 89.5646 | 2.88319 | ||||||||
\(966\) | −77.4913 | −2.49324 | ||||||||
\(967\) | −51.7050 | −1.66272 | −0.831361 | − | 0.555733i | \(-0.812438\pi\) | ||||
−0.831361 | + | 0.555733i | \(0.812438\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.8689 | −0.445534 | ||||||||
\(970\) | 3.37520 | 0.108371 | ||||||||
\(971\) | 41.0651 | 1.31784 | 0.658920 | − | 0.752213i | \(-0.271013\pi\) | ||||
0.658920 | + | 0.752213i | \(0.271013\pi\) | |||||||
\(972\) | 68.6575 | 2.20219 | ||||||||
\(973\) | −5.49803 | −0.176259 | ||||||||
\(974\) | 5.68001 | 0.181999 | ||||||||
\(975\) | 28.0234 | 0.897466 | ||||||||
\(976\) | 4.40660 | 0.141052 | ||||||||
\(977\) | −15.0675 | −0.482052 | −0.241026 | − | 0.970519i | \(-0.577484\pi\) | ||||
−0.241026 | + | 0.970519i | \(0.577484\pi\) | |||||||
\(978\) | 16.3693 | 0.523431 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −25.0647 | −0.800663 | ||||||||
\(981\) | 97.6386 | 3.11736 | ||||||||
\(982\) | 29.9204 | 0.954799 | ||||||||
\(983\) | −24.2754 | −0.774263 | −0.387132 | − | 0.922024i | \(-0.626534\pi\) | ||||
−0.387132 | + | 0.922024i | \(0.626534\pi\) | |||||||
\(984\) | 24.6953 | 0.787257 | ||||||||
\(985\) | −78.8295 | −2.51172 | ||||||||
\(986\) | −13.4319 | −0.427758 | ||||||||
\(987\) | 10.5152 | 0.334701 | ||||||||
\(988\) | 0.669426 | 0.0212973 | ||||||||
\(989\) | 38.4492 | 1.22261 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.0803 | −0.574339 | −0.287169 | − | 0.957880i | \(-0.592714\pi\) | ||||
−0.287169 | + | 0.957880i | \(0.592714\pi\) | |||||||
\(992\) | 1.55576 | 0.0493955 | ||||||||
\(993\) | 104.050 | 3.30193 | ||||||||
\(994\) | −43.2598 | −1.37212 | ||||||||
\(995\) | −32.3723 | −1.02627 | ||||||||
\(996\) | −1.70224 | −0.0539376 | ||||||||
\(997\) | −17.0357 | −0.539527 | −0.269764 | − | 0.962927i | \(-0.586946\pi\) | ||||
−0.269764 | + | 0.962927i | \(0.586946\pi\) | |||||||
\(998\) | 2.89019 | 0.0914873 | ||||||||
\(999\) | 64.2934 | 2.03415 |
(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 | 4598.2.a.by.1.8 | ✓ | 8 | |
11.10 | odd | 2 | 4598.2.a.cb.1.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.by.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial | |
4598.2.a.cb.1.8 | yes | 8 | 11.10 | odd | 2 |