Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(43\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | −0.978925 | −0.565182 | −0.282591 | − | 0.959240i | \(-0.591194\pi\) | ||||
−0.282591 | + | 0.959240i | \(0.591194\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.13476 | −0.954695 | −0.477347 | − | 0.878715i | \(-0.658402\pi\) | ||||
−0.477347 | + | 0.878715i | \(0.658402\pi\) | |||||||
\(6\) | 0.978925 | 0.399644 | ||||||||
\(7\) | 5.08930 | 1.92357 | 0.961787 | − | 0.273799i | \(-0.0882804\pi\) | ||||
0.961787 | + | 0.273799i | \(0.0882804\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.04171 | −0.680569 | ||||||||
\(10\) | 2.13476 | 0.675071 | ||||||||
\(11\) | 5.28067 | 1.59218 | 0.796091 | − | 0.605177i | \(-0.206898\pi\) | ||||
0.796091 | + | 0.605177i | \(0.206898\pi\) | |||||||
\(12\) | −0.978925 | −0.282591 | ||||||||
\(13\) | 1.87541 | 0.520145 | 0.260073 | − | 0.965589i | \(-0.416253\pi\) | ||||
0.260073 | + | 0.965589i | \(0.416253\pi\) | |||||||
\(14\) | −5.08930 | −1.36017 | ||||||||
\(15\) | 2.08977 | 0.539577 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.22020 | 1.26608 | 0.633042 | − | 0.774117i | \(-0.281806\pi\) | ||||
0.633042 | + | 0.774117i | \(0.281806\pi\) | |||||||
\(18\) | 2.04171 | 0.481235 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −2.13476 | −0.477347 | ||||||||
\(21\) | −4.98204 | −1.08717 | ||||||||
\(22\) | −5.28067 | −1.12584 | ||||||||
\(23\) | 6.98184 | 1.45581 | 0.727907 | − | 0.685676i | \(-0.240493\pi\) | ||||
0.727907 | + | 0.685676i | \(0.240493\pi\) | |||||||
\(24\) | 0.978925 | 0.199822 | ||||||||
\(25\) | −0.442792 | −0.0885584 | ||||||||
\(26\) | −1.87541 | −0.367798 | ||||||||
\(27\) | 4.93545 | 0.949828 | ||||||||
\(28\) | 5.08930 | 0.961787 | ||||||||
\(29\) | 1.78976 | 0.332350 | 0.166175 | − | 0.986096i | \(-0.446858\pi\) | ||||
0.166175 | + | 0.986096i | \(0.446858\pi\) | |||||||
\(30\) | −2.08977 | −0.381538 | ||||||||
\(31\) | 5.33522 | 0.958235 | 0.479117 | − | 0.877751i | \(-0.340957\pi\) | ||||
0.479117 | + | 0.877751i | \(0.340957\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.16938 | −0.899873 | ||||||||
\(34\) | −5.22020 | −0.895257 | ||||||||
\(35\) | −10.8644 | −1.83643 | ||||||||
\(36\) | −2.04171 | −0.340284 | ||||||||
\(37\) | 2.19410 | 0.360708 | 0.180354 | − | 0.983602i | \(-0.442276\pi\) | ||||
0.180354 | + | 0.983602i | \(0.442276\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −1.83589 | −0.293977 | ||||||||
\(40\) | 2.13476 | 0.337535 | ||||||||
\(41\) | 3.33373 | 0.520642 | 0.260321 | − | 0.965522i | \(-0.416172\pi\) | ||||
0.260321 | + | 0.965522i | \(0.416172\pi\) | |||||||
\(42\) | 4.98204 | 0.768745 | ||||||||
\(43\) | 5.18624 | 0.790893 | 0.395447 | − | 0.918489i | \(-0.370590\pi\) | ||||
0.395447 | + | 0.918489i | \(0.370590\pi\) | |||||||
\(44\) | 5.28067 | 0.796091 | ||||||||
\(45\) | 4.35856 | 0.649735 | ||||||||
\(46\) | −6.98184 | −1.02942 | ||||||||
\(47\) | 9.99600 | 1.45807 | 0.729033 | − | 0.684479i | \(-0.239970\pi\) | ||||
0.729033 | + | 0.684479i | \(0.239970\pi\) | |||||||
\(48\) | −0.978925 | −0.141296 | ||||||||
\(49\) | 18.9009 | 2.70014 | ||||||||
\(50\) | 0.442792 | 0.0626202 | ||||||||
\(51\) | −5.11018 | −0.715569 | ||||||||
\(52\) | 1.87541 | 0.260073 | ||||||||
\(53\) | −8.83272 | −1.21327 | −0.606633 | − | 0.794982i | \(-0.707480\pi\) | ||||
−0.606633 | + | 0.794982i | \(0.707480\pi\) | |||||||
\(54\) | −4.93545 | −0.671630 | ||||||||
\(55\) | −11.2730 | −1.52005 | ||||||||
\(56\) | −5.08930 | −0.680086 | ||||||||
\(57\) | −0.978925 | −0.129662 | ||||||||
\(58\) | −1.78976 | −0.235007 | ||||||||
\(59\) | 6.70453 | 0.872856 | 0.436428 | − | 0.899739i | \(-0.356243\pi\) | ||||
0.436428 | + | 0.899739i | \(0.356243\pi\) | |||||||
\(60\) | 2.08977 | 0.269788 | ||||||||
\(61\) | 9.23027 | 1.18182 | 0.590908 | − | 0.806739i | \(-0.298770\pi\) | ||||
0.590908 | + | 0.806739i | \(0.298770\pi\) | |||||||
\(62\) | −5.33522 | −0.677574 | ||||||||
\(63\) | −10.3909 | −1.30912 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.00355 | −0.496580 | ||||||||
\(66\) | 5.16938 | 0.636306 | ||||||||
\(67\) | −8.67592 | −1.05993 | −0.529966 | − | 0.848019i | \(-0.677795\pi\) | ||||
−0.529966 | + | 0.848019i | \(0.677795\pi\) | |||||||
\(68\) | 5.22020 | 0.633042 | ||||||||
\(69\) | −6.83469 | −0.822800 | ||||||||
\(70\) | 10.8644 | 1.29855 | ||||||||
\(71\) | −10.4463 | −1.23975 | −0.619874 | − | 0.784701i | \(-0.712816\pi\) | ||||
−0.619874 | + | 0.784701i | \(0.712816\pi\) | |||||||
\(72\) | 2.04171 | 0.240617 | ||||||||
\(73\) | 13.2292 | 1.54836 | 0.774178 | − | 0.632968i | \(-0.218164\pi\) | ||||
0.774178 | + | 0.632968i | \(0.218164\pi\) | |||||||
\(74\) | −2.19410 | −0.255059 | ||||||||
\(75\) | 0.433460 | 0.0500516 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 26.8749 | 3.06268 | ||||||||
\(78\) | 1.83589 | 0.207873 | ||||||||
\(79\) | 7.35322 | 0.827302 | 0.413651 | − | 0.910436i | \(-0.364253\pi\) | ||||
0.413651 | + | 0.910436i | \(0.364253\pi\) | |||||||
\(80\) | −2.13476 | −0.238674 | ||||||||
\(81\) | 1.29368 | 0.143743 | ||||||||
\(82\) | −3.33373 | −0.368149 | ||||||||
\(83\) | 3.29471 | 0.361641 | 0.180820 | − | 0.983516i | \(-0.442125\pi\) | ||||
0.180820 | + | 0.983516i | \(0.442125\pi\) | |||||||
\(84\) | −4.98204 | −0.543585 | ||||||||
\(85\) | −11.1439 | −1.20872 | ||||||||
\(86\) | −5.18624 | −0.559246 | ||||||||
\(87\) | −1.75204 | −0.187838 | ||||||||
\(88\) | −5.28067 | −0.562921 | ||||||||
\(89\) | −5.14339 | −0.545199 | −0.272599 | − | 0.962128i | \(-0.587883\pi\) | ||||
−0.272599 | + | 0.962128i | \(0.587883\pi\) | |||||||
\(90\) | −4.35856 | −0.459432 | ||||||||
\(91\) | 9.54452 | 1.00054 | ||||||||
\(92\) | 6.98184 | 0.727907 | ||||||||
\(93\) | −5.22278 | −0.541577 | ||||||||
\(94\) | −9.99600 | −1.03101 | ||||||||
\(95\) | −2.13476 | −0.219022 | ||||||||
\(96\) | 0.978925 | 0.0999111 | ||||||||
\(97\) | 3.82425 | 0.388294 | 0.194147 | − | 0.980972i | \(-0.437806\pi\) | ||||
0.194147 | + | 0.980972i | \(0.437806\pi\) | |||||||
\(98\) | −18.9009 | −1.90928 | ||||||||
\(99\) | −10.7816 | −1.08359 | ||||||||
\(100\) | −0.442792 | −0.0442792 | ||||||||
\(101\) | −19.0554 | −1.89608 | −0.948040 | − | 0.318151i | \(-0.896938\pi\) | ||||
−0.948040 | + | 0.318151i | \(0.896938\pi\) | |||||||
\(102\) | 5.11018 | 0.505984 | ||||||||
\(103\) | −2.82087 | −0.277949 | −0.138974 | − | 0.990296i | \(-0.544381\pi\) | ||||
−0.138974 | + | 0.990296i | \(0.544381\pi\) | |||||||
\(104\) | −1.87541 | −0.183899 | ||||||||
\(105\) | 10.6355 | 1.03792 | ||||||||
\(106\) | 8.83272 | 0.857909 | ||||||||
\(107\) | −6.38920 | −0.617667 | −0.308834 | − | 0.951116i | \(-0.599939\pi\) | ||||
−0.308834 | + | 0.951116i | \(0.599939\pi\) | |||||||
\(108\) | 4.93545 | 0.474914 | ||||||||
\(109\) | 17.3683 | 1.66358 | 0.831790 | − | 0.555091i | \(-0.187316\pi\) | ||||
0.831790 | + | 0.555091i | \(0.187316\pi\) | |||||||
\(110\) | 11.2730 | 1.07484 | ||||||||
\(111\) | −2.14786 | −0.203866 | ||||||||
\(112\) | 5.08930 | 0.480893 | ||||||||
\(113\) | −9.76251 | −0.918379 | −0.459190 | − | 0.888338i | \(-0.651860\pi\) | ||||
−0.459190 | + | 0.888338i | \(0.651860\pi\) | |||||||
\(114\) | 0.978925 | 0.0916847 | ||||||||
\(115\) | −14.9046 | −1.38986 | ||||||||
\(116\) | 1.78976 | 0.166175 | ||||||||
\(117\) | −3.82904 | −0.353995 | ||||||||
\(118\) | −6.70453 | −0.617202 | ||||||||
\(119\) | 26.5672 | 2.43541 | ||||||||
\(120\) | −2.08977 | −0.190769 | ||||||||
\(121\) | 16.8855 | 1.53504 | ||||||||
\(122\) | −9.23027 | −0.835670 | ||||||||
\(123\) | −3.26347 | −0.294258 | ||||||||
\(124\) | 5.33522 | 0.479117 | ||||||||
\(125\) | 11.6191 | 1.03924 | ||||||||
\(126\) | 10.3909 | 0.925691 | ||||||||
\(127\) | −9.09037 | −0.806640 | −0.403320 | − | 0.915059i | \(-0.632144\pi\) | ||||
−0.403320 | + | 0.915059i | \(0.632144\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.07693 | −0.446999 | ||||||||
\(130\) | 4.00355 | 0.351135 | ||||||||
\(131\) | 0.917354 | 0.0801496 | 0.0400748 | − | 0.999197i | \(-0.487240\pi\) | ||||
0.0400748 | + | 0.999197i | \(0.487240\pi\) | |||||||
\(132\) | −5.16938 | −0.449936 | ||||||||
\(133\) | 5.08930 | 0.441298 | ||||||||
\(134\) | 8.67592 | 0.749485 | ||||||||
\(135\) | −10.5360 | −0.906796 | ||||||||
\(136\) | −5.22020 | −0.447629 | ||||||||
\(137\) | −10.6395 | −0.908990 | −0.454495 | − | 0.890749i | \(-0.650180\pi\) | ||||
−0.454495 | + | 0.890749i | \(0.650180\pi\) | |||||||
\(138\) | 6.83469 | 0.581808 | ||||||||
\(139\) | −3.85031 | −0.326579 | −0.163289 | − | 0.986578i | \(-0.552210\pi\) | ||||
−0.163289 | + | 0.986578i | \(0.552210\pi\) | |||||||
\(140\) | −10.8644 | −0.918213 | ||||||||
\(141\) | −9.78533 | −0.824073 | ||||||||
\(142\) | 10.4463 | 0.876634 | ||||||||
\(143\) | 9.90342 | 0.828165 | ||||||||
\(144\) | −2.04171 | −0.170142 | ||||||||
\(145\) | −3.82071 | −0.317292 | ||||||||
\(146\) | −13.2292 | −1.09485 | ||||||||
\(147\) | −18.5026 | −1.52607 | ||||||||
\(148\) | 2.19410 | 0.180354 | ||||||||
\(149\) | −13.9757 | −1.14493 | −0.572467 | − | 0.819928i | \(-0.694014\pi\) | ||||
−0.572467 | + | 0.819928i | \(0.694014\pi\) | |||||||
\(150\) | −0.433460 | −0.0353919 | ||||||||
\(151\) | 9.97240 | 0.811542 | 0.405771 | − | 0.913975i | \(-0.367003\pi\) | ||||
0.405771 | + | 0.913975i | \(0.367003\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −10.6581 | −0.861658 | ||||||||
\(154\) | −26.8749 | −2.16564 | ||||||||
\(155\) | −11.3894 | −0.914821 | ||||||||
\(156\) | −1.83589 | −0.146988 | ||||||||
\(157\) | −17.5990 | −1.40455 | −0.702276 | − | 0.711904i | \(-0.747833\pi\) | ||||
−0.702276 | + | 0.711904i | \(0.747833\pi\) | |||||||
\(158\) | −7.35322 | −0.584991 | ||||||||
\(159\) | 8.64656 | 0.685717 | ||||||||
\(160\) | 2.13476 | 0.168768 | ||||||||
\(161\) | 35.5326 | 2.80036 | ||||||||
\(162\) | −1.29368 | −0.101641 | ||||||||
\(163\) | −9.78312 | −0.766273 | −0.383137 | − | 0.923692i | \(-0.625156\pi\) | ||||
−0.383137 | + | 0.923692i | \(0.625156\pi\) | |||||||
\(164\) | 3.33373 | 0.260321 | ||||||||
\(165\) | 11.0354 | 0.859104 | ||||||||
\(166\) | −3.29471 | −0.255719 | ||||||||
\(167\) | 0.717227 | 0.0555007 | 0.0277504 | − | 0.999615i | \(-0.491166\pi\) | ||||
0.0277504 | + | 0.999615i | \(0.491166\pi\) | |||||||
\(168\) | 4.98204 | 0.384373 | ||||||||
\(169\) | −9.48284 | −0.729449 | ||||||||
\(170\) | 11.1439 | 0.854697 | ||||||||
\(171\) | −2.04171 | −0.156133 | ||||||||
\(172\) | 5.18624 | 0.395447 | ||||||||
\(173\) | −20.6011 | −1.56627 | −0.783136 | − | 0.621850i | \(-0.786381\pi\) | ||||
−0.783136 | + | 0.621850i | \(0.786381\pi\) | |||||||
\(174\) | 1.75204 | 0.132822 | ||||||||
\(175\) | −2.25350 | −0.170349 | ||||||||
\(176\) | 5.28067 | 0.398045 | ||||||||
\(177\) | −6.56324 | −0.493323 | ||||||||
\(178\) | 5.14339 | 0.385514 | ||||||||
\(179\) | −26.2816 | −1.96438 | −0.982191 | − | 0.187884i | \(-0.939837\pi\) | ||||
−0.982191 | + | 0.187884i | \(0.939837\pi\) | |||||||
\(180\) | 4.35856 | 0.324868 | ||||||||
\(181\) | 7.14860 | 0.531351 | 0.265676 | − | 0.964063i | \(-0.414405\pi\) | ||||
0.265676 | + | 0.964063i | \(0.414405\pi\) | |||||||
\(182\) | −9.54452 | −0.707487 | ||||||||
\(183\) | −9.03574 | −0.667941 | ||||||||
\(184\) | −6.98184 | −0.514708 | ||||||||
\(185\) | −4.68388 | −0.344366 | ||||||||
\(186\) | 5.22278 | 0.382953 | ||||||||
\(187\) | 27.5662 | 2.01584 | ||||||||
\(188\) | 9.99600 | 0.729033 | ||||||||
\(189\) | 25.1180 | 1.82706 | ||||||||
\(190\) | 2.13476 | 0.154872 | ||||||||
\(191\) | −2.34949 | −0.170003 | −0.0850015 | − | 0.996381i | \(-0.527090\pi\) | ||||
−0.0850015 | + | 0.996381i | \(0.527090\pi\) | |||||||
\(192\) | −0.978925 | −0.0706478 | ||||||||
\(193\) | −3.49526 | −0.251594 | −0.125797 | − | 0.992056i | \(-0.540149\pi\) | ||||
−0.125797 | + | 0.992056i | \(0.540149\pi\) | |||||||
\(194\) | −3.82425 | −0.274565 | ||||||||
\(195\) | 3.91918 | 0.280658 | ||||||||
\(196\) | 18.9009 | 1.35007 | ||||||||
\(197\) | 19.8215 | 1.41222 | 0.706112 | − | 0.708100i | \(-0.250448\pi\) | ||||
0.706112 | + | 0.708100i | \(0.250448\pi\) | |||||||
\(198\) | 10.7816 | 0.766213 | ||||||||
\(199\) | −17.8989 | −1.26882 | −0.634408 | − | 0.772998i | \(-0.718756\pi\) | ||||
−0.634408 | + | 0.772998i | \(0.718756\pi\) | |||||||
\(200\) | 0.442792 | 0.0313101 | ||||||||
\(201\) | 8.49307 | 0.599055 | ||||||||
\(202\) | 19.0554 | 1.34073 | ||||||||
\(203\) | 9.10861 | 0.639299 | ||||||||
\(204\) | −5.11018 | −0.357785 | ||||||||
\(205\) | −7.11673 | −0.497054 | ||||||||
\(206\) | 2.82087 | 0.196539 | ||||||||
\(207\) | −14.2549 | −0.990781 | ||||||||
\(208\) | 1.87541 | 0.130036 | ||||||||
\(209\) | 5.28067 | 0.365271 | ||||||||
\(210\) | −10.6355 | −0.733917 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −8.83272 | −0.606633 | ||||||||
\(213\) | 10.2261 | 0.700684 | ||||||||
\(214\) | 6.38920 | 0.436757 | ||||||||
\(215\) | −11.0714 | −0.755062 | ||||||||
\(216\) | −4.93545 | −0.335815 | ||||||||
\(217\) | 27.1525 | 1.84323 | ||||||||
\(218\) | −17.3683 | −1.17633 | ||||||||
\(219\) | −12.9503 | −0.875103 | ||||||||
\(220\) | −11.2730 | −0.760023 | ||||||||
\(221\) | 9.79002 | 0.658548 | ||||||||
\(222\) | 2.14786 | 0.144155 | ||||||||
\(223\) | −15.6798 | −1.04999 | −0.524997 | − | 0.851104i | \(-0.675934\pi\) | ||||
−0.524997 | + | 0.851104i | \(0.675934\pi\) | |||||||
\(224\) | −5.08930 | −0.340043 | ||||||||
\(225\) | 0.904051 | 0.0602701 | ||||||||
\(226\) | 9.76251 | 0.649392 | ||||||||
\(227\) | 6.17225 | 0.409667 | 0.204833 | − | 0.978797i | \(-0.434335\pi\) | ||||
0.204833 | + | 0.978797i | \(0.434335\pi\) | |||||||
\(228\) | −0.978925 | −0.0648309 | ||||||||
\(229\) | 21.8685 | 1.44511 | 0.722555 | − | 0.691314i | \(-0.242968\pi\) | ||||
0.722555 | + | 0.691314i | \(0.242968\pi\) | |||||||
\(230\) | 14.9046 | 0.982778 | ||||||||
\(231\) | −26.3085 | −1.73097 | ||||||||
\(232\) | −1.78976 | −0.117503 | ||||||||
\(233\) | 10.9588 | 0.717934 | 0.358967 | − | 0.933350i | \(-0.383129\pi\) | ||||
0.358967 | + | 0.933350i | \(0.383129\pi\) | |||||||
\(234\) | 3.82904 | 0.250312 | ||||||||
\(235\) | −21.3391 | −1.39201 | ||||||||
\(236\) | 6.70453 | 0.436428 | ||||||||
\(237\) | −7.19825 | −0.467576 | ||||||||
\(238\) | −26.5672 | −1.72209 | ||||||||
\(239\) | 4.07796 | 0.263781 | 0.131891 | − | 0.991264i | \(-0.457895\pi\) | ||||
0.131891 | + | 0.991264i | \(0.457895\pi\) | |||||||
\(240\) | 2.08977 | 0.134894 | ||||||||
\(241\) | 5.48349 | 0.353222 | 0.176611 | − | 0.984281i | \(-0.443486\pi\) | ||||
0.176611 | + | 0.984281i | \(0.443486\pi\) | |||||||
\(242\) | −16.8855 | −1.08544 | ||||||||
\(243\) | −16.0728 | −1.03107 | ||||||||
\(244\) | 9.23027 | 0.590908 | ||||||||
\(245\) | −40.3490 | −2.57780 | ||||||||
\(246\) | 3.26347 | 0.208072 | ||||||||
\(247\) | 1.87541 | 0.119329 | ||||||||
\(248\) | −5.33522 | −0.338787 | ||||||||
\(249\) | −3.22527 | −0.204393 | ||||||||
\(250\) | −11.6191 | −0.734854 | ||||||||
\(251\) | −4.22467 | −0.266659 | −0.133329 | − | 0.991072i | \(-0.542567\pi\) | ||||
−0.133329 | + | 0.991072i | \(0.542567\pi\) | |||||||
\(252\) | −10.3909 | −0.654562 | ||||||||
\(253\) | 36.8688 | 2.31792 | ||||||||
\(254\) | 9.09037 | 0.570380 | ||||||||
\(255\) | 10.9090 | 0.683150 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.8613 | 0.677507 | 0.338753 | − | 0.940875i | \(-0.389995\pi\) | ||||
0.338753 | + | 0.940875i | \(0.389995\pi\) | |||||||
\(258\) | 5.07693 | 0.316076 | ||||||||
\(259\) | 11.1664 | 0.693848 | ||||||||
\(260\) | −4.00355 | −0.248290 | ||||||||
\(261\) | −3.65416 | −0.226187 | ||||||||
\(262\) | −0.917354 | −0.0566743 | ||||||||
\(263\) | −19.4914 | −1.20189 | −0.600944 | − | 0.799291i | \(-0.705209\pi\) | ||||
−0.600944 | + | 0.799291i | \(0.705209\pi\) | |||||||
\(264\) | 5.16938 | 0.318153 | ||||||||
\(265\) | 18.8557 | 1.15830 | ||||||||
\(266\) | −5.08930 | −0.312045 | ||||||||
\(267\) | 5.03500 | 0.308137 | ||||||||
\(268\) | −8.67592 | −0.529966 | ||||||||
\(269\) | 16.9894 | 1.03586 | 0.517931 | − | 0.855423i | \(-0.326703\pi\) | ||||
0.517931 | + | 0.855423i | \(0.326703\pi\) | |||||||
\(270\) | 10.5360 | 0.641201 | ||||||||
\(271\) | −6.65000 | −0.403959 | −0.201979 | − | 0.979390i | \(-0.564737\pi\) | ||||
−0.201979 | + | 0.979390i | \(0.564737\pi\) | |||||||
\(272\) | 5.22020 | 0.316521 | ||||||||
\(273\) | −9.34337 | −0.565486 | ||||||||
\(274\) | 10.6395 | 0.642753 | ||||||||
\(275\) | −2.33824 | −0.141001 | ||||||||
\(276\) | −6.83469 | −0.411400 | ||||||||
\(277\) | −7.22848 | −0.434317 | −0.217159 | − | 0.976136i | \(-0.569679\pi\) | ||||
−0.217159 | + | 0.976136i | \(0.569679\pi\) | |||||||
\(278\) | 3.85031 | 0.230926 | ||||||||
\(279\) | −10.8930 | −0.652144 | ||||||||
\(280\) | 10.8644 | 0.649274 | ||||||||
\(281\) | −22.6400 | −1.35059 | −0.675294 | − | 0.737549i | \(-0.735983\pi\) | ||||
−0.675294 | + | 0.737549i | \(0.735983\pi\) | |||||||
\(282\) | 9.78533 | 0.582708 | ||||||||
\(283\) | −23.6356 | −1.40499 | −0.702496 | − | 0.711688i | \(-0.747931\pi\) | ||||
−0.702496 | + | 0.711688i | \(0.747931\pi\) | |||||||
\(284\) | −10.4463 | −0.619874 | ||||||||
\(285\) | 2.08977 | 0.123787 | ||||||||
\(286\) | −9.90342 | −0.585601 | ||||||||
\(287\) | 16.9664 | 1.00149 | ||||||||
\(288\) | 2.04171 | 0.120309 | ||||||||
\(289\) | 10.2505 | 0.602971 | ||||||||
\(290\) | 3.82071 | 0.224360 | ||||||||
\(291\) | −3.74365 | −0.219457 | ||||||||
\(292\) | 13.2292 | 0.774178 | ||||||||
\(293\) | −18.1258 | −1.05892 | −0.529459 | − | 0.848335i | \(-0.677605\pi\) | ||||
−0.529459 | + | 0.848335i | \(0.677605\pi\) | |||||||
\(294\) | 18.5026 | 1.07909 | ||||||||
\(295\) | −14.3126 | −0.833311 | ||||||||
\(296\) | −2.19410 | −0.127529 | ||||||||
\(297\) | 26.0625 | 1.51230 | ||||||||
\(298\) | 13.9757 | 0.809591 | ||||||||
\(299\) | 13.0938 | 0.757234 | ||||||||
\(300\) | 0.433460 | 0.0250258 | ||||||||
\(301\) | 26.3943 | 1.52134 | ||||||||
\(302\) | −9.97240 | −0.573847 | ||||||||
\(303\) | 18.6538 | 1.07163 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −19.7044 | −1.12827 | ||||||||
\(306\) | 10.6581 | 0.609284 | ||||||||
\(307\) | −30.3152 | −1.73018 | −0.865090 | − | 0.501617i | \(-0.832739\pi\) | ||||
−0.865090 | + | 0.501617i | \(0.832739\pi\) | |||||||
\(308\) | 26.8749 | 1.53134 | ||||||||
\(309\) | 2.76142 | 0.157092 | ||||||||
\(310\) | 11.3894 | 0.646876 | ||||||||
\(311\) | 8.45107 | 0.479216 | 0.239608 | − | 0.970870i | \(-0.422981\pi\) | ||||
0.239608 | + | 0.970870i | \(0.422981\pi\) | |||||||
\(312\) | 1.83589 | 0.103937 | ||||||||
\(313\) | −2.58724 | −0.146240 | −0.0731198 | − | 0.997323i | \(-0.523296\pi\) | ||||
−0.0731198 | + | 0.997323i | \(0.523296\pi\) | |||||||
\(314\) | 17.5990 | 0.993169 | ||||||||
\(315\) | 22.1820 | 1.24981 | ||||||||
\(316\) | 7.35322 | 0.413651 | ||||||||
\(317\) | −16.5315 | −0.928499 | −0.464250 | − | 0.885704i | \(-0.653676\pi\) | ||||
−0.464250 | + | 0.885704i | \(0.653676\pi\) | |||||||
\(318\) | −8.64656 | −0.484875 | ||||||||
\(319\) | 9.45111 | 0.529161 | ||||||||
\(320\) | −2.13476 | −0.119337 | ||||||||
\(321\) | 6.25455 | 0.349095 | ||||||||
\(322\) | −35.5326 | −1.98016 | ||||||||
\(323\) | 5.22020 | 0.290460 | ||||||||
\(324\) | 1.29368 | 0.0718713 | ||||||||
\(325\) | −0.830416 | −0.0460632 | ||||||||
\(326\) | 9.78312 | 0.541837 | ||||||||
\(327\) | −17.0022 | −0.940226 | ||||||||
\(328\) | −3.33373 | −0.184075 | ||||||||
\(329\) | 50.8726 | 2.80470 | ||||||||
\(330\) | −11.0354 | −0.607478 | ||||||||
\(331\) | 3.66999 | 0.201721 | 0.100860 | − | 0.994901i | \(-0.467840\pi\) | ||||
0.100860 | + | 0.994901i | \(0.467840\pi\) | |||||||
\(332\) | 3.29471 | 0.180820 | ||||||||
\(333\) | −4.47971 | −0.245486 | ||||||||
\(334\) | −0.717227 | −0.0392449 | ||||||||
\(335\) | 18.5210 | 1.01191 | ||||||||
\(336\) | −4.98204 | −0.271793 | ||||||||
\(337\) | 14.4640 | 0.787905 | 0.393953 | − | 0.919131i | \(-0.371107\pi\) | ||||
0.393953 | + | 0.919131i | \(0.371107\pi\) | |||||||
\(338\) | 9.48284 | 0.515798 | ||||||||
\(339\) | 9.55676 | 0.519052 | ||||||||
\(340\) | −11.1439 | −0.604362 | ||||||||
\(341\) | 28.1735 | 1.52568 | ||||||||
\(342\) | 2.04171 | 0.110403 | ||||||||
\(343\) | 60.5675 | 3.27034 | ||||||||
\(344\) | −5.18624 | −0.279623 | ||||||||
\(345\) | 14.5904 | 0.785523 | ||||||||
\(346\) | 20.6011 | 1.10752 | ||||||||
\(347\) | −14.7330 | −0.790909 | −0.395455 | − | 0.918486i | \(-0.629413\pi\) | ||||
−0.395455 | + | 0.918486i | \(0.629413\pi\) | |||||||
\(348\) | −1.75204 | −0.0939191 | ||||||||
\(349\) | −28.8350 | −1.54350 | −0.771751 | − | 0.635925i | \(-0.780619\pi\) | ||||
−0.771751 | + | 0.635925i | \(0.780619\pi\) | |||||||
\(350\) | 2.25350 | 0.120455 | ||||||||
\(351\) | 9.25600 | 0.494048 | ||||||||
\(352\) | −5.28067 | −0.281461 | ||||||||
\(353\) | −4.72643 | −0.251563 | −0.125781 | − | 0.992058i | \(-0.540144\pi\) | ||||
−0.125781 | + | 0.992058i | \(0.540144\pi\) | |||||||
\(354\) | 6.56324 | 0.348832 | ||||||||
\(355\) | 22.3004 | 1.18358 | ||||||||
\(356\) | −5.14339 | −0.272599 | ||||||||
\(357\) | −26.0073 | −1.37645 | ||||||||
\(358\) | 26.2816 | 1.38903 | ||||||||
\(359\) | −11.0980 | −0.585730 | −0.292865 | − | 0.956154i | \(-0.594609\pi\) | ||||
−0.292865 | + | 0.956154i | \(0.594609\pi\) | |||||||
\(360\) | −4.35856 | −0.229716 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −7.14860 | −0.375722 | ||||||||
\(363\) | −16.5296 | −0.867578 | ||||||||
\(364\) | 9.54452 | 0.500269 | ||||||||
\(365\) | −28.2411 | −1.47821 | ||||||||
\(366\) | 9.03574 | 0.472306 | ||||||||
\(367\) | −37.1694 | −1.94023 | −0.970114 | − | 0.242648i | \(-0.921984\pi\) | ||||
−0.970114 | + | 0.242648i | \(0.921984\pi\) | |||||||
\(368\) | 6.98184 | 0.363953 | ||||||||
\(369\) | −6.80651 | −0.354333 | ||||||||
\(370\) | 4.68388 | 0.243503 | ||||||||
\(371\) | −44.9523 | −2.33381 | ||||||||
\(372\) | −5.22278 | −0.270789 | ||||||||
\(373\) | 17.7787 | 0.920546 | 0.460273 | − | 0.887777i | \(-0.347752\pi\) | ||||
0.460273 | + | 0.887777i | \(0.347752\pi\) | |||||||
\(374\) | −27.5662 | −1.42541 | ||||||||
\(375\) | −11.3742 | −0.587361 | ||||||||
\(376\) | −9.99600 | −0.515504 | ||||||||
\(377\) | 3.35653 | 0.172870 | ||||||||
\(378\) | −25.1180 | −1.29193 | ||||||||
\(379\) | −1.89896 | −0.0975428 | −0.0487714 | − | 0.998810i | \(-0.515531\pi\) | ||||
−0.0487714 | + | 0.998810i | \(0.515531\pi\) | |||||||
\(380\) | −2.13476 | −0.109511 | ||||||||
\(381\) | 8.89878 | 0.455899 | ||||||||
\(382\) | 2.34949 | 0.120210 | ||||||||
\(383\) | −7.13976 | −0.364825 | −0.182412 | − | 0.983222i | \(-0.558391\pi\) | ||||
−0.182412 | + | 0.983222i | \(0.558391\pi\) | |||||||
\(384\) | 0.978925 | 0.0499555 | ||||||||
\(385\) | −57.3715 | −2.92392 | ||||||||
\(386\) | 3.49526 | 0.177904 | ||||||||
\(387\) | −10.5888 | −0.538257 | ||||||||
\(388\) | 3.82425 | 0.194147 | ||||||||
\(389\) | 16.0209 | 0.812290 | 0.406145 | − | 0.913809i | \(-0.366873\pi\) | ||||
0.406145 | + | 0.913809i | \(0.366873\pi\) | |||||||
\(390\) | −3.91918 | −0.198455 | ||||||||
\(391\) | 36.4466 | 1.84318 | ||||||||
\(392\) | −18.9009 | −0.954642 | ||||||||
\(393\) | −0.898021 | −0.0452992 | ||||||||
\(394\) | −19.8215 | −0.998593 | ||||||||
\(395\) | −15.6974 | −0.789820 | ||||||||
\(396\) | −10.7816 | −0.541794 | ||||||||
\(397\) | 9.33819 | 0.468670 | 0.234335 | − | 0.972156i | \(-0.424709\pi\) | ||||
0.234335 | + | 0.972156i | \(0.424709\pi\) | |||||||
\(398\) | 17.8989 | 0.897189 | ||||||||
\(399\) | −4.98204 | −0.249414 | ||||||||
\(400\) | −0.442792 | −0.0221396 | ||||||||
\(401\) | −26.2078 | −1.30876 | −0.654378 | − | 0.756168i | \(-0.727069\pi\) | ||||
−0.654378 | + | 0.756168i | \(0.727069\pi\) | |||||||
\(402\) | −8.49307 | −0.423596 | ||||||||
\(403\) | 10.0057 | 0.498421 | ||||||||
\(404\) | −19.0554 | −0.948040 | ||||||||
\(405\) | −2.76171 | −0.137230 | ||||||||
\(406\) | −9.10861 | −0.452053 | ||||||||
\(407\) | 11.5863 | 0.574312 | ||||||||
\(408\) | 5.11018 | 0.252992 | ||||||||
\(409\) | 29.1369 | 1.44073 | 0.720364 | − | 0.693597i | \(-0.243975\pi\) | ||||
0.720364 | + | 0.693597i | \(0.243975\pi\) | |||||||
\(410\) | 7.11673 | 0.351470 | ||||||||
\(411\) | 10.4152 | 0.513746 | ||||||||
\(412\) | −2.82087 | −0.138974 | ||||||||
\(413\) | 34.1214 | 1.67900 | ||||||||
\(414\) | 14.2549 | 0.700588 | ||||||||
\(415\) | −7.03341 | −0.345257 | ||||||||
\(416\) | −1.87541 | −0.0919496 | ||||||||
\(417\) | 3.76916 | 0.184577 | ||||||||
\(418\) | −5.28067 | −0.258286 | ||||||||
\(419\) | −0.725090 | −0.0354230 | −0.0177115 | − | 0.999843i | \(-0.505638\pi\) | ||||
−0.0177115 | + | 0.999843i | \(0.505638\pi\) | |||||||
\(420\) | 10.6355 | 0.518958 | ||||||||
\(421\) | 5.90920 | 0.287997 | 0.143998 | − | 0.989578i | \(-0.454004\pi\) | ||||
0.143998 | + | 0.989578i | \(0.454004\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | −20.4089 | −0.992314 | ||||||||
\(424\) | 8.83272 | 0.428955 | ||||||||
\(425\) | −2.31146 | −0.112122 | ||||||||
\(426\) | −10.2261 | −0.495458 | ||||||||
\(427\) | 46.9756 | 2.27331 | ||||||||
\(428\) | −6.38920 | −0.308834 | ||||||||
\(429\) | −9.69470 | −0.468065 | ||||||||
\(430\) | 11.0714 | 0.533909 | ||||||||
\(431\) | 5.64753 | 0.272032 | 0.136016 | − | 0.990707i | \(-0.456570\pi\) | ||||
0.136016 | + | 0.990707i | \(0.456570\pi\) | |||||||
\(432\) | 4.93545 | 0.237457 | ||||||||
\(433\) | −10.5446 | −0.506741 | −0.253370 | − | 0.967369i | \(-0.581539\pi\) | ||||
−0.253370 | + | 0.967369i | \(0.581539\pi\) | |||||||
\(434\) | −27.1525 | −1.30336 | ||||||||
\(435\) | 3.74018 | 0.179328 | ||||||||
\(436\) | 17.3683 | 0.831790 | ||||||||
\(437\) | 6.98184 | 0.333987 | ||||||||
\(438\) | 12.9503 | 0.618791 | ||||||||
\(439\) | −13.3575 | −0.637517 | −0.318758 | − | 0.947836i | \(-0.603266\pi\) | ||||
−0.318758 | + | 0.947836i | \(0.603266\pi\) | |||||||
\(440\) | 11.2730 | 0.537418 | ||||||||
\(441\) | −38.5902 | −1.83763 | ||||||||
\(442\) | −9.79002 | −0.465664 | ||||||||
\(443\) | −16.3288 | −0.775803 | −0.387902 | − | 0.921701i | \(-0.626800\pi\) | ||||
−0.387902 | + | 0.921701i | \(0.626800\pi\) | |||||||
\(444\) | −2.14786 | −0.101933 | ||||||||
\(445\) | 10.9799 | 0.520498 | ||||||||
\(446\) | 15.6798 | 0.742458 | ||||||||
\(447\) | 13.6812 | 0.647097 | ||||||||
\(448\) | 5.08930 | 0.240447 | ||||||||
\(449\) | −1.40367 | −0.0662433 | −0.0331217 | − | 0.999451i | \(-0.510545\pi\) | ||||
−0.0331217 | + | 0.999451i | \(0.510545\pi\) | |||||||
\(450\) | −0.904051 | −0.0426174 | ||||||||
\(451\) | 17.6043 | 0.828956 | ||||||||
\(452\) | −9.76251 | −0.459190 | ||||||||
\(453\) | −9.76223 | −0.458669 | ||||||||
\(454\) | −6.17225 | −0.289678 | ||||||||
\(455\) | −20.3753 | −0.955208 | ||||||||
\(456\) | 0.978925 | 0.0458424 | ||||||||
\(457\) | 26.7909 | 1.25323 | 0.626613 | − | 0.779331i | \(-0.284441\pi\) | ||||
0.626613 | + | 0.779331i | \(0.284441\pi\) | |||||||
\(458\) | −21.8685 | −1.02185 | ||||||||
\(459\) | 25.7641 | 1.20256 | ||||||||
\(460\) | −14.9046 | −0.694929 | ||||||||
\(461\) | −27.7961 | −1.29459 | −0.647296 | − | 0.762239i | \(-0.724100\pi\) | ||||
−0.647296 | + | 0.762239i | \(0.724100\pi\) | |||||||
\(462\) | 26.3085 | 1.22398 | ||||||||
\(463\) | 34.6332 | 1.60954 | 0.804770 | − | 0.593587i | \(-0.202289\pi\) | ||||
0.804770 | + | 0.593587i | \(0.202289\pi\) | |||||||
\(464\) | 1.78976 | 0.0830874 | ||||||||
\(465\) | 11.1494 | 0.517041 | ||||||||
\(466\) | −10.9588 | −0.507656 | ||||||||
\(467\) | 37.5224 | 1.73633 | 0.868166 | − | 0.496275i | \(-0.165299\pi\) | ||||
0.868166 | + | 0.496275i | \(0.165299\pi\) | |||||||
\(468\) | −3.82904 | −0.176997 | ||||||||
\(469\) | −44.1543 | −2.03886 | ||||||||
\(470\) | 21.3391 | 0.984298 | ||||||||
\(471\) | 17.2281 | 0.793829 | ||||||||
\(472\) | −6.70453 | −0.308601 | ||||||||
\(473\) | 27.3868 | 1.25925 | ||||||||
\(474\) | 7.19825 | 0.330626 | ||||||||
\(475\) | −0.442792 | −0.0203167 | ||||||||
\(476\) | 26.5672 | 1.21770 | ||||||||
\(477\) | 18.0338 | 0.825711 | ||||||||
\(478\) | −4.07796 | −0.186522 | ||||||||
\(479\) | −12.3795 | −0.565633 | −0.282817 | − | 0.959174i | \(-0.591269\pi\) | ||||
−0.282817 | + | 0.959174i | \(0.591269\pi\) | |||||||
\(480\) | −2.08977 | −0.0953846 | ||||||||
\(481\) | 4.11484 | 0.187620 | ||||||||
\(482\) | −5.48349 | −0.249766 | ||||||||
\(483\) | −34.7838 | −1.58272 | ||||||||
\(484\) | 16.8855 | 0.767521 | ||||||||
\(485\) | −8.16386 | −0.370702 | ||||||||
\(486\) | 16.0728 | 0.729076 | ||||||||
\(487\) | 24.0676 | 1.09061 | 0.545303 | − | 0.838239i | \(-0.316414\pi\) | ||||
0.545303 | + | 0.838239i | \(0.316414\pi\) | |||||||
\(488\) | −9.23027 | −0.417835 | ||||||||
\(489\) | 9.57694 | 0.433084 | ||||||||
\(490\) | 40.3490 | 1.82278 | ||||||||
\(491\) | 2.95851 | 0.133515 | 0.0667577 | − | 0.997769i | \(-0.478735\pi\) | ||||
0.0667577 | + | 0.997769i | \(0.478735\pi\) | |||||||
\(492\) | −3.26347 | −0.147129 | ||||||||
\(493\) | 9.34289 | 0.420783 | ||||||||
\(494\) | −1.87541 | −0.0843787 | ||||||||
\(495\) | 23.0161 | 1.03450 | ||||||||
\(496\) | 5.33522 | 0.239559 | ||||||||
\(497\) | −53.1643 | −2.38475 | ||||||||
\(498\) | 3.22527 | 0.144528 | ||||||||
\(499\) | −1.40518 | −0.0629046 | −0.0314523 | − | 0.999505i | \(-0.510013\pi\) | ||||
−0.0314523 | + | 0.999505i | \(0.510013\pi\) | |||||||
\(500\) | 11.6191 | 0.519620 | ||||||||
\(501\) | −0.702112 | −0.0313680 | ||||||||
\(502\) | 4.22467 | 0.188556 | ||||||||
\(503\) | 20.9828 | 0.935577 | 0.467789 | − | 0.883840i | \(-0.345051\pi\) | ||||
0.467789 | + | 0.883840i | \(0.345051\pi\) | |||||||
\(504\) | 10.3909 | 0.462845 | ||||||||
\(505\) | 40.6787 | 1.81018 | ||||||||
\(506\) | −36.8688 | −1.63902 | ||||||||
\(507\) | 9.28298 | 0.412272 | ||||||||
\(508\) | −9.09037 | −0.403320 | ||||||||
\(509\) | 34.1506 | 1.51370 | 0.756849 | − | 0.653590i | \(-0.226738\pi\) | ||||
0.756849 | + | 0.653590i | \(0.226738\pi\) | |||||||
\(510\) | −10.9090 | −0.483060 | ||||||||
\(511\) | 67.3271 | 2.97838 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.93545 | 0.217905 | ||||||||
\(514\) | −10.8613 | −0.479070 | ||||||||
\(515\) | 6.02189 | 0.265356 | ||||||||
\(516\) | −5.07693 | −0.223500 | ||||||||
\(517\) | 52.7855 | 2.32151 | ||||||||
\(518\) | −11.1664 | −0.490624 | ||||||||
\(519\) | 20.1669 | 0.885230 | ||||||||
\(520\) | 4.00355 | 0.175567 | ||||||||
\(521\) | −12.1120 | −0.530635 | −0.265317 | − | 0.964161i | \(-0.585477\pi\) | ||||
−0.265317 | + | 0.964161i | \(0.585477\pi\) | |||||||
\(522\) | 3.65416 | 0.159938 | ||||||||
\(523\) | 4.35232 | 0.190314 | 0.0951569 | − | 0.995462i | \(-0.469665\pi\) | ||||
0.0951569 | + | 0.995462i | \(0.469665\pi\) | |||||||
\(524\) | 0.917354 | 0.0400748 | ||||||||
\(525\) | 2.20601 | 0.0962780 | ||||||||
\(526\) | 19.4914 | 0.849864 | ||||||||
\(527\) | 27.8509 | 1.21321 | ||||||||
\(528\) | −5.16938 | −0.224968 | ||||||||
\(529\) | 25.7460 | 1.11939 | ||||||||
\(530\) | −18.8557 | −0.819041 | ||||||||
\(531\) | −13.6887 | −0.594039 | ||||||||
\(532\) | 5.08930 | 0.220649 | ||||||||
\(533\) | 6.25212 | 0.270809 | ||||||||
\(534\) | −5.03500 | −0.217886 | ||||||||
\(535\) | 13.6394 | 0.589683 | ||||||||
\(536\) | 8.67592 | 0.374743 | ||||||||
\(537\) | 25.7278 | 1.11023 | ||||||||
\(538\) | −16.9894 | −0.732465 | ||||||||
\(539\) | 99.8096 | 4.29911 | ||||||||
\(540\) | −10.5360 | −0.453398 | ||||||||
\(541\) | −36.2102 | −1.55680 | −0.778399 | − | 0.627770i | \(-0.783968\pi\) | ||||
−0.778399 | + | 0.627770i | \(0.783968\pi\) | |||||||
\(542\) | 6.65000 | 0.285642 | ||||||||
\(543\) | −6.99794 | −0.300310 | ||||||||
\(544\) | −5.22020 | −0.223814 | ||||||||
\(545\) | −37.0771 | −1.58821 | ||||||||
\(546\) | 9.34337 | 0.399859 | ||||||||
\(547\) | 40.9074 | 1.74907 | 0.874537 | − | 0.484958i | \(-0.161165\pi\) | ||||
0.874537 | + | 0.484958i | \(0.161165\pi\) | |||||||
\(548\) | −10.6395 | −0.454495 | ||||||||
\(549\) | −18.8455 | −0.804306 | ||||||||
\(550\) | 2.33824 | 0.0997028 | ||||||||
\(551\) | 1.78976 | 0.0762462 | ||||||||
\(552\) | 6.83469 | 0.290904 | ||||||||
\(553\) | 37.4227 | 1.59138 | ||||||||
\(554\) | 7.22848 | 0.307109 | ||||||||
\(555\) | 4.58517 | 0.194629 | ||||||||
\(556\) | −3.85031 | −0.163289 | ||||||||
\(557\) | 2.10069 | 0.0890093 | 0.0445046 | − | 0.999009i | \(-0.485829\pi\) | ||||
0.0445046 | + | 0.999009i | \(0.485829\pi\) | |||||||
\(558\) | 10.8930 | 0.461136 | ||||||||
\(559\) | 9.72632 | 0.411379 | ||||||||
\(560\) | −10.8644 | −0.459106 | ||||||||
\(561\) | −26.9852 | −1.13932 | ||||||||
\(562\) | 22.6400 | 0.955010 | ||||||||
\(563\) | −41.5667 | −1.75183 | −0.875913 | − | 0.482469i | \(-0.839740\pi\) | ||||
−0.875913 | + | 0.482469i | \(0.839740\pi\) | |||||||
\(564\) | −9.78533 | −0.412037 | ||||||||
\(565\) | 20.8406 | 0.876772 | ||||||||
\(566\) | 23.6356 | 0.993479 | ||||||||
\(567\) | 6.58394 | 0.276499 | ||||||||
\(568\) | 10.4463 | 0.438317 | ||||||||
\(569\) | 35.9343 | 1.50644 | 0.753222 | − | 0.657767i | \(-0.228499\pi\) | ||||
0.753222 | + | 0.657767i | \(0.228499\pi\) | |||||||
\(570\) | −2.08977 | −0.0875309 | ||||||||
\(571\) | −28.7145 | −1.20166 | −0.600831 | − | 0.799376i | \(-0.705164\pi\) | ||||
−0.600831 | + | 0.799376i | \(0.705164\pi\) | |||||||
\(572\) | 9.90342 | 0.414083 | ||||||||
\(573\) | 2.29997 | 0.0960828 | ||||||||
\(574\) | −16.9664 | −0.708162 | ||||||||
\(575\) | −3.09150 | −0.128924 | ||||||||
\(576\) | −2.04171 | −0.0850711 | ||||||||
\(577\) | 38.4150 | 1.59924 | 0.799618 | − | 0.600509i | \(-0.205035\pi\) | ||||
0.799618 | + | 0.600509i | \(0.205035\pi\) | |||||||
\(578\) | −10.2505 | −0.426365 | ||||||||
\(579\) | 3.42160 | 0.142197 | ||||||||
\(580\) | −3.82071 | −0.158646 | ||||||||
\(581\) | 16.7677 | 0.695643 | ||||||||
\(582\) | 3.74365 | 0.155179 | ||||||||
\(583\) | −46.6426 | −1.93174 | ||||||||
\(584\) | −13.2292 | −0.547426 | ||||||||
\(585\) | 8.17408 | 0.337957 | ||||||||
\(586\) | 18.1258 | 0.748769 | ||||||||
\(587\) | 5.49408 | 0.226765 | 0.113382 | − | 0.993551i | \(-0.463831\pi\) | ||||
0.113382 | + | 0.993551i | \(0.463831\pi\) | |||||||
\(588\) | −18.5026 | −0.763035 | ||||||||
\(589\) | 5.33522 | 0.219834 | ||||||||
\(590\) | 14.3126 | 0.589240 | ||||||||
\(591\) | −19.4038 | −0.798164 | ||||||||
\(592\) | 2.19410 | 0.0901769 | ||||||||
\(593\) | −13.6976 | −0.562494 | −0.281247 | − | 0.959635i | \(-0.590748\pi\) | ||||
−0.281247 | + | 0.959635i | \(0.590748\pi\) | |||||||
\(594\) | −26.0625 | −1.06936 | ||||||||
\(595\) | −56.7146 | −2.32507 | ||||||||
\(596\) | −13.9757 | −0.572467 | ||||||||
\(597\) | 17.5216 | 0.717113 | ||||||||
\(598\) | −13.0938 | −0.535446 | ||||||||
\(599\) | −14.6629 | −0.599108 | −0.299554 | − | 0.954079i | \(-0.596838\pi\) | ||||
−0.299554 | + | 0.954079i | \(0.596838\pi\) | |||||||
\(600\) | −0.433460 | −0.0176959 | ||||||||
\(601\) | 16.9750 | 0.692425 | 0.346213 | − | 0.938156i | \(-0.387468\pi\) | ||||
0.346213 | + | 0.938156i | \(0.387468\pi\) | |||||||
\(602\) | −26.3943 | −1.07575 | ||||||||
\(603\) | 17.7137 | 0.721356 | ||||||||
\(604\) | 9.97240 | 0.405771 | ||||||||
\(605\) | −36.0464 | −1.46550 | ||||||||
\(606\) | −18.6538 | −0.757758 | ||||||||
\(607\) | −43.5340 | −1.76699 | −0.883496 | − | 0.468438i | \(-0.844817\pi\) | ||||
−0.883496 | + | 0.468438i | \(0.844817\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −8.91664 | −0.361321 | ||||||||
\(610\) | 19.7044 | 0.797809 | ||||||||
\(611\) | 18.7466 | 0.758406 | ||||||||
\(612\) | −10.6581 | −0.430829 | ||||||||
\(613\) | −36.8696 | −1.48915 | −0.744574 | − | 0.667540i | \(-0.767347\pi\) | ||||
−0.744574 | + | 0.667540i | \(0.767347\pi\) | |||||||
\(614\) | 30.3152 | 1.22342 | ||||||||
\(615\) | 6.96674 | 0.280926 | ||||||||
\(616\) | −26.8749 | −1.08282 | ||||||||
\(617\) | 5.40290 | 0.217512 | 0.108756 | − | 0.994068i | \(-0.465313\pi\) | ||||
0.108756 | + | 0.994068i | \(0.465313\pi\) | |||||||
\(618\) | −2.76142 | −0.111081 | ||||||||
\(619\) | −7.57463 | −0.304450 | −0.152225 | − | 0.988346i | \(-0.548644\pi\) | ||||
−0.152225 | + | 0.988346i | \(0.548644\pi\) | |||||||
\(620\) | −11.3894 | −0.457411 | ||||||||
\(621\) | 34.4585 | 1.38277 | ||||||||
\(622\) | −8.45107 | −0.338857 | ||||||||
\(623\) | −26.1763 | −1.04873 | ||||||||
\(624\) | −1.83589 | −0.0734942 | ||||||||
\(625\) | −22.5900 | −0.903599 | ||||||||
\(626\) | 2.58724 | 0.103407 | ||||||||
\(627\) | −5.16938 | −0.206445 | ||||||||
\(628\) | −17.5990 | −0.702276 | ||||||||
\(629\) | 11.4536 | 0.456687 | ||||||||
\(630\) | −22.1820 | −0.883752 | ||||||||
\(631\) | −4.57626 | −0.182178 | −0.0910891 | − | 0.995843i | \(-0.529035\pi\) | ||||
−0.0910891 | + | 0.995843i | \(0.529035\pi\) | |||||||
\(632\) | −7.35322 | −0.292495 | ||||||||
\(633\) | 0.978925 | 0.0389088 | ||||||||
\(634\) | 16.5315 | 0.656548 | ||||||||
\(635\) | 19.4058 | 0.770094 | ||||||||
\(636\) | 8.64656 | 0.342859 | ||||||||
\(637\) | 35.4470 | 1.40446 | ||||||||
\(638\) | −9.45111 | −0.374173 | ||||||||
\(639\) | 21.3283 | 0.843734 | ||||||||
\(640\) | 2.13476 | 0.0843839 | ||||||||
\(641\) | −38.7681 | −1.53125 | −0.765624 | − | 0.643289i | \(-0.777570\pi\) | ||||
−0.765624 | + | 0.643289i | \(0.777570\pi\) | |||||||
\(642\) | −6.25455 | −0.246847 | ||||||||
\(643\) | 37.7450 | 1.48852 | 0.744259 | − | 0.667891i | \(-0.232803\pi\) | ||||
0.744259 | + | 0.667891i | \(0.232803\pi\) | |||||||
\(644\) | 35.5326 | 1.40018 | ||||||||
\(645\) | 10.8380 | 0.426748 | ||||||||
\(646\) | −5.22020 | −0.205386 | ||||||||
\(647\) | 22.0464 | 0.866733 | 0.433367 | − | 0.901218i | \(-0.357326\pi\) | ||||
0.433367 | + | 0.901218i | \(0.357326\pi\) | |||||||
\(648\) | −1.29368 | −0.0508207 | ||||||||
\(649\) | 35.4044 | 1.38975 | ||||||||
\(650\) | 0.830416 | 0.0325716 | ||||||||
\(651\) | −26.5803 | −1.04176 | ||||||||
\(652\) | −9.78312 | −0.383137 | ||||||||
\(653\) | −37.6120 | −1.47187 | −0.735935 | − | 0.677052i | \(-0.763257\pi\) | ||||
−0.735935 | + | 0.677052i | \(0.763257\pi\) | |||||||
\(654\) | 17.0022 | 0.664840 | ||||||||
\(655\) | −1.95833 | −0.0765184 | ||||||||
\(656\) | 3.33373 | 0.130160 | ||||||||
\(657\) | −27.0100 | −1.05376 | ||||||||
\(658\) | −50.8726 | −1.98322 | ||||||||
\(659\) | 11.3226 | 0.441067 | 0.220534 | − | 0.975379i | \(-0.429220\pi\) | ||||
0.220534 | + | 0.975379i | \(0.429220\pi\) | |||||||
\(660\) | 11.0354 | 0.429552 | ||||||||
\(661\) | −37.3545 | −1.45292 | −0.726460 | − | 0.687209i | \(-0.758836\pi\) | ||||
−0.726460 | + | 0.687209i | \(0.758836\pi\) | |||||||
\(662\) | −3.66999 | −0.142638 | ||||||||
\(663\) | −9.58369 | −0.372200 | ||||||||
\(664\) | −3.29471 | −0.127859 | ||||||||
\(665\) | −10.8644 | −0.421305 | ||||||||
\(666\) | 4.47971 | 0.173585 | ||||||||
\(667\) | 12.4958 | 0.483839 | ||||||||
\(668\) | 0.717227 | 0.0277504 | ||||||||
\(669\) | 15.3493 | 0.593438 | ||||||||
\(670\) | −18.5210 | −0.715529 | ||||||||
\(671\) | 48.7420 | 1.88166 | ||||||||
\(672\) | 4.98204 | 0.192186 | ||||||||
\(673\) | −8.71929 | −0.336104 | −0.168052 | − | 0.985778i | \(-0.553748\pi\) | ||||
−0.168052 | + | 0.985778i | \(0.553748\pi\) | |||||||
\(674\) | −14.4640 | −0.557133 | ||||||||
\(675\) | −2.18538 | −0.0841152 | ||||||||
\(676\) | −9.48284 | −0.364724 | ||||||||
\(677\) | 22.7762 | 0.875362 | 0.437681 | − | 0.899130i | \(-0.355800\pi\) | ||||
0.437681 | + | 0.899130i | \(0.355800\pi\) | |||||||
\(678\) | −9.55676 | −0.367025 | ||||||||
\(679\) | 19.4627 | 0.746912 | ||||||||
\(680\) | 11.1439 | 0.427349 | ||||||||
\(681\) | −6.04217 | −0.231536 | ||||||||
\(682\) | −28.1735 | −1.07882 | ||||||||
\(683\) | −5.11802 | −0.195836 | −0.0979178 | − | 0.995195i | \(-0.531218\pi\) | ||||
−0.0979178 | + | 0.995195i | \(0.531218\pi\) | |||||||
\(684\) | −2.04171 | −0.0780666 | ||||||||
\(685\) | 22.7127 | 0.867808 | ||||||||
\(686\) | −60.5675 | −2.31248 | ||||||||
\(687\) | −21.4076 | −0.816750 | ||||||||
\(688\) | 5.18624 | 0.197723 | ||||||||
\(689\) | −16.5650 | −0.631075 | ||||||||
\(690\) | −14.5904 | −0.555449 | ||||||||
\(691\) | −3.05694 | −0.116291 | −0.0581457 | − | 0.998308i | \(-0.518519\pi\) | ||||
−0.0581457 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(692\) | −20.6011 | −0.783136 | ||||||||
\(693\) | −54.8706 | −2.08436 | ||||||||
\(694\) | 14.7330 | 0.559257 | ||||||||
\(695\) | 8.21949 | 0.311783 | ||||||||
\(696\) | 1.75204 | 0.0664108 | ||||||||
\(697\) | 17.4028 | 0.659177 | ||||||||
\(698\) | 28.8350 | 1.09142 | ||||||||
\(699\) | −10.7278 | −0.405764 | ||||||||
\(700\) | −2.25350 | −0.0851743 | ||||||||
\(701\) | −1.23988 | −0.0468295 | −0.0234148 | − | 0.999726i | \(-0.507454\pi\) | ||||
−0.0234148 | + | 0.999726i | \(0.507454\pi\) | |||||||
\(702\) | −9.25600 | −0.349345 | ||||||||
\(703\) | 2.19410 | 0.0827520 | ||||||||
\(704\) | 5.28067 | 0.199023 | ||||||||
\(705\) | 20.8893 | 0.786738 | ||||||||
\(706\) | 4.72643 | 0.177882 | ||||||||
\(707\) | −96.9784 | −3.64725 | ||||||||
\(708\) | −6.56324 | −0.246661 | ||||||||
\(709\) | 11.9659 | 0.449388 | 0.224694 | − | 0.974429i | \(-0.427862\pi\) | ||||
0.224694 | + | 0.974429i | \(0.427862\pi\) | |||||||
\(710\) | −22.3004 | −0.836918 | ||||||||
\(711\) | −15.0131 | −0.563036 | ||||||||
\(712\) | 5.14339 | 0.192757 | ||||||||
\(713\) | 37.2497 | 1.39501 | ||||||||
\(714\) | 26.0073 | 0.973297 | ||||||||
\(715\) | −21.1414 | −0.790645 | ||||||||
\(716\) | −26.2816 | −0.982191 | ||||||||
\(717\) | −3.99202 | −0.149085 | ||||||||
\(718\) | 11.0980 | 0.414174 | ||||||||
\(719\) | 12.6319 | 0.471091 | 0.235546 | − | 0.971863i | \(-0.424312\pi\) | ||||
0.235546 | + | 0.971863i | \(0.424312\pi\) | |||||||
\(720\) | 4.35856 | 0.162434 | ||||||||
\(721\) | −14.3563 | −0.534655 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −5.36792 | −0.199635 | ||||||||
\(724\) | 7.14860 | 0.265676 | ||||||||
\(725\) | −0.792490 | −0.0294323 | ||||||||
\(726\) | 16.5296 | 0.613471 | ||||||||
\(727\) | 11.8067 | 0.437887 | 0.218944 | − | 0.975738i | \(-0.429739\pi\) | ||||
0.218944 | + | 0.975738i | \(0.429739\pi\) | |||||||
\(728\) | −9.54452 | −0.353743 | ||||||||
\(729\) | 11.8530 | 0.438999 | ||||||||
\(730\) | 28.2411 | 1.04525 | ||||||||
\(731\) | 27.0732 | 1.00134 | ||||||||
\(732\) | −9.03574 | −0.333971 | ||||||||
\(733\) | 43.1923 | 1.59534 | 0.797671 | − | 0.603093i | \(-0.206065\pi\) | ||||
0.797671 | + | 0.603093i | \(0.206065\pi\) | |||||||
\(734\) | 37.1694 | 1.37195 | ||||||||
\(735\) | 39.4987 | 1.45693 | ||||||||
\(736\) | −6.98184 | −0.257354 | ||||||||
\(737\) | −45.8146 | −1.68760 | ||||||||
\(738\) | 6.80651 | 0.250551 | ||||||||
\(739\) | 36.1192 | 1.32867 | 0.664334 | − | 0.747436i | \(-0.268715\pi\) | ||||
0.664334 | + | 0.747436i | \(0.268715\pi\) | |||||||
\(740\) | −4.68388 | −0.172183 | ||||||||
\(741\) | −1.83589 | −0.0674429 | ||||||||
\(742\) | 44.9523 | 1.65025 | ||||||||
\(743\) | −9.80509 | −0.359714 | −0.179857 | − | 0.983693i | \(-0.557563\pi\) | ||||
−0.179857 | + | 0.983693i | \(0.557563\pi\) | |||||||
\(744\) | 5.22278 | 0.191477 | ||||||||
\(745\) | 29.8348 | 1.09306 | ||||||||
\(746\) | −17.7787 | −0.650924 | ||||||||
\(747\) | −6.72682 | −0.246122 | ||||||||
\(748\) | 27.5662 | 1.00792 | ||||||||
\(749\) | −32.5165 | −1.18813 | ||||||||
\(750\) | 11.3742 | 0.415327 | ||||||||
\(751\) | −6.10985 | −0.222952 | −0.111476 | − | 0.993767i | \(-0.535558\pi\) | ||||
−0.111476 | + | 0.993767i | \(0.535558\pi\) | |||||||
\(752\) | 9.99600 | 0.364517 | ||||||||
\(753\) | 4.13563 | 0.150711 | ||||||||
\(754\) | −3.35653 | −0.122238 | ||||||||
\(755\) | −21.2887 | −0.774775 | ||||||||
\(756\) | 25.1180 | 0.913532 | ||||||||
\(757\) | −44.1144 | −1.60337 | −0.801683 | − | 0.597749i | \(-0.796062\pi\) | ||||
−0.801683 | + | 0.597749i | \(0.796062\pi\) | |||||||
\(758\) | 1.89896 | 0.0689732 | ||||||||
\(759\) | −36.0917 | −1.31005 | ||||||||
\(760\) | 2.13476 | 0.0774360 | ||||||||
\(761\) | −40.7679 | −1.47784 | −0.738918 | − | 0.673796i | \(-0.764663\pi\) | ||||
−0.738918 | + | 0.673796i | \(0.764663\pi\) | |||||||
\(762\) | −8.89878 | −0.322369 | ||||||||
\(763\) | 88.3924 | 3.20002 | ||||||||
\(764\) | −2.34949 | −0.0850015 | ||||||||
\(765\) | 22.7525 | 0.822620 | ||||||||
\(766\) | 7.13976 | 0.257970 | ||||||||
\(767\) | 12.5738 | 0.454012 | ||||||||
\(768\) | −0.978925 | −0.0353239 | ||||||||
\(769\) | −10.0368 | −0.361936 | −0.180968 | − | 0.983489i | \(-0.557923\pi\) | ||||
−0.180968 | + | 0.983489i | \(0.557923\pi\) | |||||||
\(770\) | 57.3715 | 2.06752 | ||||||||
\(771\) | −10.6324 | −0.382915 | ||||||||
\(772\) | −3.49526 | −0.125797 | ||||||||
\(773\) | 6.78116 | 0.243901 | 0.121951 | − | 0.992536i | \(-0.461085\pi\) | ||||
0.121951 | + | 0.992536i | \(0.461085\pi\) | |||||||
\(774\) | 10.5888 | 0.380605 | ||||||||
\(775\) | −2.36239 | −0.0848597 | ||||||||
\(776\) | −3.82425 | −0.137283 | ||||||||
\(777\) | −10.9311 | −0.392151 | ||||||||
\(778\) | −16.0209 | −0.574376 | ||||||||
\(779\) | 3.33373 | 0.119443 | ||||||||
\(780\) | 3.91918 | 0.140329 | ||||||||
\(781\) | −55.1635 | −1.97390 | ||||||||
\(782\) | −36.4466 | −1.30333 | ||||||||
\(783\) | 8.83326 | 0.315675 | ||||||||
\(784\) | 18.9009 | 0.675034 | ||||||||
\(785\) | 37.5697 | 1.34092 | ||||||||
\(786\) | 0.898021 | 0.0320313 | ||||||||
\(787\) | −24.7677 | −0.882874 | −0.441437 | − | 0.897292i | \(-0.645531\pi\) | ||||
−0.441437 | + | 0.897292i | \(0.645531\pi\) | |||||||
\(788\) | 19.8215 | 0.706112 | ||||||||
\(789\) | 19.0806 | 0.679286 | ||||||||
\(790\) | 15.6974 | 0.558487 | ||||||||
\(791\) | −49.6843 | −1.76657 | ||||||||
\(792\) | 10.7816 | 0.383106 | ||||||||
\(793\) | 17.3105 | 0.614715 | ||||||||
\(794\) | −9.33819 | −0.331400 | ||||||||
\(795\) | −18.4584 | −0.654650 | ||||||||
\(796\) | −17.8989 | −0.634408 | ||||||||
\(797\) | −32.5089 | −1.15153 | −0.575763 | − | 0.817617i | \(-0.695295\pi\) | ||||
−0.575763 | + | 0.817617i | \(0.695295\pi\) | |||||||
\(798\) | 4.98204 | 0.176362 | ||||||||
\(799\) | 52.1811 | 1.84604 | ||||||||
\(800\) | 0.442792 | 0.0156551 | ||||||||
\(801\) | 10.5013 | 0.371045 | ||||||||
\(802\) | 26.2078 | 0.925430 | ||||||||
\(803\) | 69.8588 | 2.46526 | ||||||||
\(804\) | 8.49307 | 0.299527 | ||||||||
\(805\) | −75.8537 | −2.67349 | ||||||||
\(806\) | −10.0057 | −0.352437 | ||||||||
\(807\) | −16.6313 | −0.585451 | ||||||||
\(808\) | 19.0554 | 0.670365 | ||||||||
\(809\) | −2.33485 | −0.0820888 | −0.0410444 | − | 0.999157i | \(-0.513069\pi\) | ||||
−0.0410444 | + | 0.999157i | \(0.513069\pi\) | |||||||
\(810\) | 2.76171 | 0.0970364 | ||||||||
\(811\) | 18.8579 | 0.662192 | 0.331096 | − | 0.943597i | \(-0.392582\pi\) | ||||
0.331096 | + | 0.943597i | \(0.392582\pi\) | |||||||
\(812\) | 9.10861 | 0.319649 | ||||||||
\(813\) | 6.50985 | 0.228310 | ||||||||
\(814\) | −11.5863 | −0.406100 | ||||||||
\(815\) | 20.8846 | 0.731557 | ||||||||
\(816\) | −5.11018 | −0.178892 | ||||||||
\(817\) | 5.18624 | 0.181443 | ||||||||
\(818\) | −29.1369 | −1.01875 | ||||||||
\(819\) | −19.4871 | −0.680935 | ||||||||
\(820\) | −7.11673 | −0.248527 | ||||||||
\(821\) | −43.5777 | −1.52087 | −0.760436 | − | 0.649413i | \(-0.775014\pi\) | ||||
−0.760436 | + | 0.649413i | \(0.775014\pi\) | |||||||
\(822\) | −10.4152 | −0.363273 | ||||||||
\(823\) | 35.1308 | 1.22458 | 0.612291 | − | 0.790632i | \(-0.290248\pi\) | ||||
0.612291 | + | 0.790632i | \(0.290248\pi\) | |||||||
\(824\) | 2.82087 | 0.0982697 | ||||||||
\(825\) | 2.28896 | 0.0796913 | ||||||||
\(826\) | −34.1214 | −1.18723 | ||||||||
\(827\) | 49.4794 | 1.72057 | 0.860284 | − | 0.509814i | \(-0.170286\pi\) | ||||
0.860284 | + | 0.509814i | \(0.170286\pi\) | |||||||
\(828\) | −14.2549 | −0.495391 | ||||||||
\(829\) | −6.54886 | −0.227451 | −0.113726 | − | 0.993512i | \(-0.536278\pi\) | ||||
−0.113726 | + | 0.993512i | \(0.536278\pi\) | |||||||
\(830\) | 7.03341 | 0.244133 | ||||||||
\(831\) | 7.07614 | 0.245469 | ||||||||
\(832\) | 1.87541 | 0.0650182 | ||||||||
\(833\) | 98.6668 | 3.41860 | ||||||||
\(834\) | −3.76916 | −0.130515 | ||||||||
\(835\) | −1.53111 | −0.0529862 | ||||||||
\(836\) | 5.28067 | 0.182636 | ||||||||
\(837\) | 26.3317 | 0.910158 | ||||||||
\(838\) | 0.725090 | 0.0250478 | ||||||||
\(839\) | −3.93998 | −0.136023 | −0.0680116 | − | 0.997685i | \(-0.521665\pi\) | ||||
−0.0680116 | + | 0.997685i | \(0.521665\pi\) | |||||||
\(840\) | −10.6355 | −0.366958 | ||||||||
\(841\) | −25.7968 | −0.889544 | ||||||||
\(842\) | −5.90920 | −0.203644 | ||||||||
\(843\) | 22.1628 | 0.763329 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 20.2436 | 0.696401 | ||||||||
\(846\) | 20.4089 | 0.701672 | ||||||||
\(847\) | 85.9351 | 2.95276 | ||||||||
\(848\) | −8.83272 | −0.303317 | ||||||||
\(849\) | 23.1375 | 0.794077 | ||||||||
\(850\) | 2.31146 | 0.0792825 | ||||||||
\(851\) | 15.3188 | 0.525123 | ||||||||
\(852\) | 10.2261 | 0.350342 | ||||||||
\(853\) | −24.5391 | −0.840204 | −0.420102 | − | 0.907477i | \(-0.638006\pi\) | ||||
−0.420102 | + | 0.907477i | \(0.638006\pi\) | |||||||
\(854\) | −46.9756 | −1.60747 | ||||||||
\(855\) | 4.35856 | 0.149059 | ||||||||
\(856\) | 6.38920 | 0.218378 | ||||||||
\(857\) | 11.0934 | 0.378942 | 0.189471 | − | 0.981886i | \(-0.439323\pi\) | ||||
0.189471 | + | 0.981886i | \(0.439323\pi\) | |||||||
\(858\) | 9.69470 | 0.330972 | ||||||||
\(859\) | 0.198137 | 0.00676035 | 0.00338017 | − | 0.999994i | \(-0.498924\pi\) | ||||
0.00338017 | + | 0.999994i | \(0.498924\pi\) | |||||||
\(860\) | −11.0714 | −0.377531 | ||||||||
\(861\) | −16.6088 | −0.566026 | ||||||||
\(862\) | −5.64753 | −0.192356 | ||||||||
\(863\) | −51.2565 | −1.74479 | −0.872396 | − | 0.488799i | \(-0.837435\pi\) | ||||
−0.872396 | + | 0.488799i | \(0.837435\pi\) | |||||||
\(864\) | −4.93545 | −0.167907 | ||||||||
\(865\) | 43.9784 | 1.49531 | ||||||||
\(866\) | 10.5446 | 0.358320 | ||||||||
\(867\) | −10.0345 | −0.340789 | ||||||||
\(868\) | 27.1525 | 0.921617 | ||||||||
\(869\) | 38.8299 | 1.31721 | ||||||||
\(870\) | −3.74018 | −0.126804 | ||||||||
\(871\) | −16.2709 | −0.551318 | ||||||||
\(872\) | −17.3683 | −0.588164 | ||||||||
\(873\) | −7.80800 | −0.264261 | ||||||||
\(874\) | −6.98184 | −0.236164 | ||||||||
\(875\) | 59.1329 | 1.99906 | ||||||||
\(876\) | −12.9503 | −0.437552 | ||||||||
\(877\) | 45.6100 | 1.54014 | 0.770070 | − | 0.637960i | \(-0.220221\pi\) | ||||
0.770070 | + | 0.637960i | \(0.220221\pi\) | |||||||
\(878\) | 13.3575 | 0.450792 | ||||||||
\(879\) | 17.7438 | 0.598482 | ||||||||
\(880\) | −11.2730 | −0.380012 | ||||||||
\(881\) | −18.2693 | −0.615507 | −0.307753 | − | 0.951466i | \(-0.599577\pi\) | ||||
−0.307753 | + | 0.951466i | \(0.599577\pi\) | |||||||
\(882\) | 38.5902 | 1.29940 | ||||||||
\(883\) | −27.1128 | −0.912417 | −0.456209 | − | 0.889873i | \(-0.650793\pi\) | ||||
−0.456209 | + | 0.889873i | \(0.650793\pi\) | |||||||
\(884\) | 9.79002 | 0.329274 | ||||||||
\(885\) | 14.0109 | 0.470973 | ||||||||
\(886\) | 16.3288 | 0.548576 | ||||||||
\(887\) | −13.0938 | −0.439647 | −0.219824 | − | 0.975540i | \(-0.570548\pi\) | ||||
−0.219824 | + | 0.975540i | \(0.570548\pi\) | |||||||
\(888\) | 2.14786 | 0.0720774 | ||||||||
\(889\) | −46.2636 | −1.55163 | ||||||||
\(890\) | −10.9799 | −0.368048 | ||||||||
\(891\) | 6.83151 | 0.228864 | ||||||||
\(892\) | −15.6798 | −0.524997 | ||||||||
\(893\) | 9.99600 | 0.334503 | ||||||||
\(894\) | −13.6812 | −0.457566 | ||||||||
\(895\) | 56.1051 | 1.87539 | ||||||||
\(896\) | −5.08930 | −0.170021 | ||||||||
\(897\) | −12.8179 | −0.427976 | ||||||||
\(898\) | 1.40367 | 0.0468411 | ||||||||
\(899\) | 9.54875 | 0.318469 | ||||||||
\(900\) | 0.904051 | 0.0301350 | ||||||||
\(901\) | −46.1086 | −1.53610 | ||||||||
\(902\) | −17.6043 | −0.586160 | ||||||||
\(903\) | −25.8380 | −0.859836 | ||||||||
\(904\) | 9.76251 | 0.324696 | ||||||||
\(905\) | −15.2606 | −0.507278 | ||||||||
\(906\) | 9.76223 | 0.324328 | ||||||||
\(907\) | 41.6152 | 1.38181 | 0.690905 | − | 0.722946i | \(-0.257212\pi\) | ||||
0.690905 | + | 0.722946i | \(0.257212\pi\) | |||||||
\(908\) | 6.17225 | 0.204833 | ||||||||
\(909\) | 38.9055 | 1.29041 | ||||||||
\(910\) | 20.3753 | 0.675434 | ||||||||
\(911\) | 21.8548 | 0.724083 | 0.362042 | − | 0.932162i | \(-0.382080\pi\) | ||||
0.362042 | + | 0.932162i | \(0.382080\pi\) | |||||||
\(912\) | −0.978925 | −0.0324154 | ||||||||
\(913\) | 17.3982 | 0.575798 | ||||||||
\(914\) | −26.7909 | −0.886164 | ||||||||
\(915\) | 19.2892 | 0.637680 | ||||||||
\(916\) | 21.8685 | 0.722555 | ||||||||
\(917\) | 4.66869 | 0.154174 | ||||||||
\(918\) | −25.7641 | −0.850340 | ||||||||
\(919\) | 15.3017 | 0.504757 | 0.252378 | − | 0.967629i | \(-0.418787\pi\) | ||||
0.252378 | + | 0.967629i | \(0.418787\pi\) | |||||||
\(920\) | 14.9046 | 0.491389 | ||||||||
\(921\) | 29.6763 | 0.977867 | ||||||||
\(922\) | 27.7961 | 0.915415 | ||||||||
\(923\) | −19.5911 | −0.644849 | ||||||||
\(924\) | −26.3085 | −0.865486 | ||||||||
\(925\) | −0.971529 | −0.0319437 | ||||||||
\(926\) | −34.6332 | −1.13812 | ||||||||
\(927\) | 5.75939 | 0.189163 | ||||||||
\(928\) | −1.78976 | −0.0587517 | ||||||||
\(929\) | 30.7509 | 1.00890 | 0.504452 | − | 0.863440i | \(-0.331695\pi\) | ||||
0.504452 | + | 0.863440i | \(0.331695\pi\) | |||||||
\(930\) | −11.1494 | −0.365603 | ||||||||
\(931\) | 18.9009 | 0.619454 | ||||||||
\(932\) | 10.9588 | 0.358967 | ||||||||
\(933\) | −8.27296 | −0.270845 | ||||||||
\(934\) | −37.5224 | −1.22777 | ||||||||
\(935\) | −58.8472 | −1.92451 | ||||||||
\(936\) | 3.82904 | 0.125156 | ||||||||
\(937\) | 21.7682 | 0.711135 | 0.355568 | − | 0.934651i | \(-0.384288\pi\) | ||||
0.355568 | + | 0.934651i | \(0.384288\pi\) | |||||||
\(938\) | 44.1543 | 1.44169 | ||||||||
\(939\) | 2.53272 | 0.0826521 | ||||||||
\(940\) | −21.3391 | −0.696004 | ||||||||
\(941\) | 14.4802 | 0.472041 | 0.236020 | − | 0.971748i | \(-0.424157\pi\) | ||||
0.236020 | + | 0.971748i | \(0.424157\pi\) | |||||||
\(942\) | −17.2281 | −0.561322 | ||||||||
\(943\) | 23.2756 | 0.757957 | ||||||||
\(944\) | 6.70453 | 0.218214 | ||||||||
\(945\) | −53.6209 | −1.74429 | ||||||||
\(946\) | −27.3868 | −0.890421 | ||||||||
\(947\) | −26.3763 | −0.857116 | −0.428558 | − | 0.903514i | \(-0.640978\pi\) | ||||
−0.428558 | + | 0.903514i | \(0.640978\pi\) | |||||||
\(948\) | −7.19825 | −0.233788 | ||||||||
\(949\) | 24.8101 | 0.805370 | ||||||||
\(950\) | 0.442792 | 0.0143661 | ||||||||
\(951\) | 16.1831 | 0.524771 | ||||||||
\(952\) | −26.5672 | −0.861047 | ||||||||
\(953\) | −10.6034 | −0.343478 | −0.171739 | − | 0.985142i | \(-0.554939\pi\) | ||||
−0.171739 | + | 0.985142i | \(0.554939\pi\) | |||||||
\(954\) | −18.0338 | −0.583866 | ||||||||
\(955\) | 5.01560 | 0.162301 | ||||||||
\(956\) | 4.07796 | 0.131891 | ||||||||
\(957\) | −9.25193 | −0.299072 | ||||||||
\(958\) | 12.3795 | 0.399963 | ||||||||
\(959\) | −54.1474 | −1.74851 | ||||||||
\(960\) | 2.08977 | 0.0674471 | ||||||||
\(961\) | −2.53539 | −0.0817866 | ||||||||
\(962\) | −4.11484 | −0.132668 | ||||||||
\(963\) | 13.0449 | 0.420365 | ||||||||
\(964\) | 5.48349 | 0.176611 | ||||||||
\(965\) | 7.46155 | 0.240196 | ||||||||
\(966\) | 34.7838 | 1.11915 | ||||||||
\(967\) | −1.59404 | −0.0512610 | −0.0256305 | − | 0.999671i | \(-0.508159\pi\) | ||||
−0.0256305 | + | 0.999671i | \(0.508159\pi\) | |||||||
\(968\) | −16.8855 | −0.542719 | ||||||||
\(969\) | −5.11018 | −0.164163 | ||||||||
\(970\) | 8.16386 | 0.262126 | ||||||||
\(971\) | −60.1533 | −1.93041 | −0.965206 | − | 0.261490i | \(-0.915786\pi\) | ||||
−0.965206 | + | 0.261490i | \(0.915786\pi\) | |||||||
\(972\) | −16.0728 | −0.515534 | ||||||||
\(973\) | −19.5954 | −0.628198 | ||||||||
\(974\) | −24.0676 | −0.771176 | ||||||||
\(975\) | 0.812915 | 0.0260341 | ||||||||
\(976\) | 9.23027 | 0.295454 | ||||||||
\(977\) | 1.46029 | 0.0467187 | 0.0233594 | − | 0.999727i | \(-0.492564\pi\) | ||||
0.0233594 | + | 0.999727i | \(0.492564\pi\) | |||||||
\(978\) | −9.57694 | −0.306237 | ||||||||
\(979\) | −27.1606 | −0.868055 | ||||||||
\(980\) | −40.3490 | −1.28890 | ||||||||
\(981\) | −35.4609 | −1.13218 | ||||||||
\(982\) | −2.95851 | −0.0944097 | ||||||||
\(983\) | 14.0859 | 0.449271 | 0.224635 | − | 0.974443i | \(-0.427881\pi\) | ||||
0.224635 | + | 0.974443i | \(0.427881\pi\) | |||||||
\(984\) | 3.26347 | 0.104036 | ||||||||
\(985\) | −42.3142 | −1.34824 | ||||||||
\(986\) | −9.34289 | −0.297538 | ||||||||
\(987\) | −49.8005 | −1.58517 | ||||||||
\(988\) | 1.87541 | 0.0596647 | ||||||||
\(989\) | 36.2094 | 1.15139 | ||||||||
\(990\) | −23.0161 | −0.731499 | ||||||||
\(991\) | 39.3962 | 1.25146 | 0.625730 | − | 0.780040i | \(-0.284801\pi\) | ||||
0.625730 | + | 0.780040i | \(0.284801\pi\) | |||||||
\(992\) | −5.33522 | −0.169394 | ||||||||
\(993\) | −3.59264 | −0.114009 | ||||||||
\(994\) | 53.1643 | 1.68627 | ||||||||
\(995\) | 38.2098 | 1.21133 | ||||||||
\(996\) | −3.22527 | −0.102197 | ||||||||
\(997\) | 19.9684 | 0.632406 | 0.316203 | − | 0.948692i | \(-0.397592\pi\) | ||||
0.316203 | + | 0.948692i | \(0.397592\pi\) | |||||||
\(998\) | 1.40518 | 0.0444803 | ||||||||
\(999\) | 10.8289 | 0.342610 |
(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 | 8018.2.a.i.1.18 | ✓ | 43 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.i.1.18 | ✓ | 43 | 1.1 | even | 1 | trivial |