Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(461,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.461");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.g (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 461.2 | ||
Character | \(\chi\) | \(=\) | 690.461 |
Dual form | 690.3.g.a.461.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | 2.78199 | + | 1.12272i | 0.927332 | + | 0.374241i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | −1.58777 | + | 3.93433i | −0.264628 | + | 0.655722i | ||||
\(7\) | 9.71289 | 1.38756 | 0.693778 | − | 0.720189i | \(-0.255945\pi\) | ||||
0.693778 | + | 0.720189i | \(0.255945\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 6.47899 | + | 6.24682i | 0.719888 | + | 0.694091i | ||||
\(10\) | −3.16228 | −0.316228 | ||||||||
\(11\) | − | 16.7924i | − | 1.52658i | −0.646056 | − | 0.763290i | \(-0.723583\pi\) | ||
0.646056 | − | 0.763290i | \(-0.276417\pi\) | |||||||
\(12\) | −5.56399 | − | 2.24544i | −0.463666 | − | 0.187120i | ||||
\(13\) | 14.2200 | 1.09384 | 0.546921 | − | 0.837184i | \(-0.315800\pi\) | ||||
0.546921 | + | 0.837184i | \(0.315800\pi\) | |||||||
\(14\) | 13.7361i | 0.981150i | ||||||||
\(15\) | −2.51048 | + | 6.22073i | −0.167366 | + | 0.414715i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 8.32060i | − | 0.489447i | −0.969593 | − | 0.244724i | \(-0.921303\pi\) | ||
0.969593 | − | 0.244724i | \(-0.0786972\pi\) | |||||||
\(18\) | −8.83433 | + | 9.16267i | −0.490796 | + | 0.509037i | ||||
\(19\) | 18.7748 | 0.988148 | 0.494074 | − | 0.869420i | \(-0.335507\pi\) | ||||
0.494074 | + | 0.869420i | \(0.335507\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | 27.0212 | + | 10.9049i | 1.28672 | + | 0.519280i | ||||
\(22\) | 23.7480 | 1.07946 | ||||||||
\(23\) | − | 4.79583i | − | 0.208514i | ||||||
\(24\) | 3.17554 | − | 7.86867i | 0.132314 | − | 0.327861i | ||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 20.1101i | 0.773464i | ||||||||
\(27\) | 11.0111 | + | 24.6527i | 0.407818 | + | 0.913063i | ||||
\(28\) | −19.4258 | −0.693778 | ||||||||
\(29\) | − | 8.35888i | − | 0.288237i | −0.989560 | − | 0.144119i | \(-0.953965\pi\) | ||
0.989560 | − | 0.144119i | \(-0.0460347\pi\) | |||||||
\(30\) | −8.79744 | − | 3.55036i | −0.293248 | − | 0.118345i | ||||
\(31\) | 12.7798 | 0.412252 | 0.206126 | − | 0.978526i | \(-0.433914\pi\) | ||||
0.206126 | + | 0.978526i | \(0.433914\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | 18.8532 | − | 46.7163i | 0.571309 | − | 1.41565i | ||||
\(34\) | 11.7671 | 0.346091 | ||||||||
\(35\) | 21.7187i | 0.620534i | ||||||||
\(36\) | −12.9580 | − | 12.4936i | −0.359944 | − | 0.347045i | ||||
\(37\) | −48.4043 | −1.30823 | −0.654113 | − | 0.756397i | \(-0.726958\pi\) | ||||
−0.654113 | + | 0.756397i | \(0.726958\pi\) | |||||||
\(38\) | 26.5516i | 0.698726i | ||||||||
\(39\) | 39.5598 | + | 15.9651i | 1.01435 | + | 0.409361i | ||||
\(40\) | 6.32456 | 0.158114 | ||||||||
\(41\) | − | 33.7058i | − | 0.822093i | −0.911614 | − | 0.411046i | \(-0.865163\pi\) | ||
0.911614 | − | 0.411046i | \(-0.134837\pi\) | |||||||
\(42\) | −15.4218 | + | 38.2138i | −0.367186 | + | 0.909852i | ||||
\(43\) | −41.8569 | −0.973417 | −0.486709 | − | 0.873564i | \(-0.661803\pi\) | ||||
−0.486709 | + | 0.873564i | \(0.661803\pi\) | |||||||
\(44\) | 33.5848i | 0.763290i | ||||||||
\(45\) | −13.9683 | + | 14.4875i | −0.310407 | + | 0.321944i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | 25.4461i | 0.541406i | 0.962663 | + | 0.270703i | \(0.0872561\pi\) | ||||
−0.962663 | + | 0.270703i | \(0.912744\pi\) | |||||||
\(48\) | 11.1280 | + | 4.49089i | 0.231833 | + | 0.0935602i | ||||
\(49\) | 45.3403 | 0.925312 | ||||||||
\(50\) | − | 7.07107i | − | 0.141421i | ||||||
\(51\) | 9.34172 | − | 23.1479i | 0.183171 | − | 0.453880i | ||||
\(52\) | −28.4399 | −0.546921 | ||||||||
\(53\) | 64.6839i | 1.22045i | 0.792228 | + | 0.610225i | \(0.208921\pi\) | ||||
−0.792228 | + | 0.610225i | \(0.791079\pi\) | |||||||
\(54\) | −34.8642 | + | 15.5720i | −0.645633 | + | 0.288371i | ||||
\(55\) | 37.5489 | 0.682707 | ||||||||
\(56\) | − | 27.4722i | − | 0.490575i | ||||||
\(57\) | 52.2314 | + | 21.0789i | 0.916341 | + | 0.369805i | ||||
\(58\) | 11.8212 | 0.203815 | ||||||||
\(59\) | 35.0667i | 0.594351i | 0.954823 | + | 0.297175i | \(0.0960446\pi\) | ||||
−0.954823 | + | 0.297175i | \(0.903955\pi\) | |||||||
\(60\) | 5.02097 | − | 12.4415i | 0.0836828 | − | 0.207358i | ||||
\(61\) | −57.1839 | −0.937441 | −0.468721 | − | 0.883347i | \(-0.655285\pi\) | ||||
−0.468721 | + | 0.883347i | \(0.655285\pi\) | |||||||
\(62\) | 18.0734i | 0.291506i | ||||||||
\(63\) | 62.9297 | + | 60.6746i | 0.998884 | + | 0.963090i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 31.7968i | 0.489181i | ||||||||
\(66\) | 66.0668 | + | 26.6624i | 1.00101 | + | 0.403976i | ||||
\(67\) | −61.2135 | −0.913634 | −0.456817 | − | 0.889561i | \(-0.651011\pi\) | ||||
−0.456817 | + | 0.889561i | \(0.651011\pi\) | |||||||
\(68\) | 16.6412i | 0.244724i | ||||||||
\(69\) | 5.38439 | − | 13.3420i | 0.0780346 | − | 0.193362i | ||||
\(70\) | −30.7149 | −0.438784 | ||||||||
\(71\) | 99.0489i | 1.39505i | 0.716558 | + | 0.697527i | \(0.245716\pi\) | ||||
−0.716558 | + | 0.697527i | \(0.754284\pi\) | |||||||
\(72\) | 17.6687 | − | 18.3253i | 0.245398 | − | 0.254519i | ||||
\(73\) | 1.71337 | 0.0234709 | 0.0117354 | − | 0.999931i | \(-0.496264\pi\) | ||||
0.0117354 | + | 0.999931i | \(0.496264\pi\) | |||||||
\(74\) | − | 68.4541i | − | 0.925055i | ||||||
\(75\) | −13.9100 | − | 5.61361i | −0.185466 | − | 0.0748482i | ||||
\(76\) | −37.5496 | −0.494074 | ||||||||
\(77\) | − | 163.103i | − | 2.11822i | ||||||
\(78\) | −22.5780 | + | 55.9461i | −0.289462 | + | 0.717257i | ||||
\(79\) | 118.909 | 1.50517 | 0.752586 | − | 0.658493i | \(-0.228806\pi\) | ||||
0.752586 | + | 0.658493i | \(0.228806\pi\) | |||||||
\(80\) | 8.94427i | 0.111803i | ||||||||
\(81\) | 2.95460 | + | 80.9461i | 0.0364765 | + | 0.999335i | ||||
\(82\) | 47.6672 | 0.581307 | ||||||||
\(83\) | 13.2505i | 0.159645i | 0.996809 | + | 0.0798226i | \(0.0254354\pi\) | ||||
−0.996809 | + | 0.0798226i | \(0.974565\pi\) | |||||||
\(84\) | −54.0424 | − | 21.8098i | −0.643362 | − | 0.259640i | ||||
\(85\) | 18.6054 | 0.218887 | ||||||||
\(86\) | − | 59.1947i | − | 0.688310i | ||||||
\(87\) | 9.38470 | − | 23.2544i | 0.107870 | − | 0.267292i | ||||
\(88\) | −47.4960 | −0.539728 | ||||||||
\(89\) | − | 145.864i | − | 1.63892i | −0.573133 | − | 0.819462i | \(-0.694272\pi\) | ||
0.573133 | − | 0.819462i | \(-0.305728\pi\) | |||||||
\(90\) | −20.4884 | − | 19.7542i | −0.227648 | − | 0.219491i | ||||
\(91\) | 138.117 | 1.51777 | ||||||||
\(92\) | 9.59166i | 0.104257i | ||||||||
\(93\) | 35.5533 | + | 14.3482i | 0.382294 | + | 0.154281i | ||||
\(94\) | −35.9862 | −0.382832 | ||||||||
\(95\) | 41.9818i | 0.441913i | ||||||||
\(96\) | −6.35108 | + | 15.7373i | −0.0661570 | + | 0.163931i | ||||
\(97\) | −166.157 | −1.71296 | −0.856478 | − | 0.516183i | \(-0.827352\pi\) | ||||
−0.856478 | + | 0.516183i | \(0.827352\pi\) | |||||||
\(98\) | 64.1208i | 0.654294i | ||||||||
\(99\) | 104.899 | − | 108.798i | 1.05958 | − | 1.09897i | ||||
\(100\) | 10.0000 | 0.100000 | ||||||||
\(101\) | 101.312i | 1.00309i | 0.865131 | + | 0.501546i | \(0.167235\pi\) | ||||
−0.865131 | + | 0.501546i | \(0.832765\pi\) | |||||||
\(102\) | 32.7360 | + | 13.2112i | 0.320941 | + | 0.129521i | ||||
\(103\) | −156.509 | −1.51951 | −0.759754 | − | 0.650210i | \(-0.774681\pi\) | ||||
−0.759754 | + | 0.650210i | \(0.774681\pi\) | |||||||
\(104\) | − | 40.2201i | − | 0.386732i | ||||||
\(105\) | −24.3841 | + | 60.4213i | −0.232229 | + | 0.575441i | ||||
\(106\) | −91.4768 | −0.862989 | ||||||||
\(107\) | − | 49.5970i | − | 0.463523i | −0.972773 | − | 0.231762i | \(-0.925551\pi\) | ||
0.972773 | − | 0.231762i | \(-0.0744489\pi\) | |||||||
\(108\) | −22.0221 | − | 49.3054i | −0.203909 | − | 0.456532i | ||||
\(109\) | −9.54244 | −0.0875453 | −0.0437727 | − | 0.999042i | \(-0.513938\pi\) | ||||
−0.0437727 | + | 0.999042i | \(0.513938\pi\) | |||||||
\(110\) | 53.1022i | 0.482747i | ||||||||
\(111\) | −134.661 | − | 54.3446i | −1.21316 | − | 0.489591i | ||||
\(112\) | 38.8516 | 0.346889 | ||||||||
\(113\) | 194.702i | 1.72303i | 0.507736 | + | 0.861513i | \(0.330483\pi\) | ||||
−0.507736 | + | 0.861513i | \(0.669517\pi\) | |||||||
\(114\) | −29.8101 | + | 73.8664i | −0.261492 | + | 0.647951i | ||||
\(115\) | 10.7238 | 0.0932505 | ||||||||
\(116\) | 16.7178i | 0.144119i | ||||||||
\(117\) | 92.1309 | + | 88.8294i | 0.787444 | + | 0.759226i | ||||
\(118\) | −49.5918 | −0.420269 | ||||||||
\(119\) | − | 80.8171i | − | 0.679135i | ||||||
\(120\) | 17.5949 | + | 7.10072i | 0.146624 | + | 0.0591727i | ||||
\(121\) | −160.984 | −1.33045 | ||||||||
\(122\) | − | 80.8703i | − | 0.662871i | ||||||
\(123\) | 37.8423 | − | 93.7694i | 0.307661 | − | 0.762353i | ||||
\(124\) | −25.5596 | −0.206126 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | −85.8069 | + | 88.9961i | −0.681007 | + | 0.706318i | ||||
\(127\) | 91.5991 | 0.721253 | 0.360626 | − | 0.932710i | \(-0.382563\pi\) | ||||
0.360626 | + | 0.932710i | \(0.382563\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | −116.446 | − | 46.9937i | −0.902681 | − | 0.364292i | ||||
\(130\) | −44.9675 | −0.345903 | ||||||||
\(131\) | − | 137.955i | − | 1.05309i | −0.850148 | − | 0.526544i | \(-0.823488\pi\) | ||
0.850148 | − | 0.526544i | \(-0.176512\pi\) | |||||||
\(132\) | −37.7064 | + | 93.4326i | −0.285654 | + | 0.707823i | ||||
\(133\) | 182.358 | 1.37111 | ||||||||
\(134\) | − | 86.5689i | − | 0.646037i | ||||||
\(135\) | −55.1251 | + | 24.6215i | −0.408334 | + | 0.182382i | ||||
\(136\) | −23.5342 | −0.173046 | ||||||||
\(137\) | 60.6857i | 0.442961i | 0.975165 | + | 0.221481i | \(0.0710889\pi\) | ||||
−0.975165 | + | 0.221481i | \(0.928911\pi\) | |||||||
\(138\) | 18.8684 | + | 7.61467i | 0.136728 | + | 0.0551788i | ||||
\(139\) | 107.481 | 0.773243 | 0.386622 | − | 0.922238i | \(-0.373642\pi\) | ||||
0.386622 | + | 0.922238i | \(0.373642\pi\) | |||||||
\(140\) | − | 43.4374i | − | 0.310267i | ||||||
\(141\) | −28.5689 | + | 70.7908i | −0.202616 | + | 0.502063i | ||||
\(142\) | −140.076 | −0.986453 | ||||||||
\(143\) | − | 238.787i | − | 1.66984i | ||||||
\(144\) | 25.9160 | + | 24.9873i | 0.179972 | + | 0.173523i | ||||
\(145\) | 18.6910 | 0.128904 | ||||||||
\(146\) | 2.42308i | 0.0165964i | ||||||||
\(147\) | 126.136 | + | 50.9045i | 0.858071 | + | 0.346289i | ||||
\(148\) | 96.8087 | 0.654113 | ||||||||
\(149\) | − | 34.1446i | − | 0.229158i | −0.993414 | − | 0.114579i | \(-0.963448\pi\) | ||
0.993414 | − | 0.114579i | \(-0.0365520\pi\) | |||||||
\(150\) | 7.93885 | − | 19.6717i | 0.0529256 | − | 0.131144i | ||||
\(151\) | −153.941 | −1.01947 | −0.509737 | − | 0.860330i | \(-0.670257\pi\) | ||||
−0.509737 | + | 0.860330i | \(0.670257\pi\) | |||||||
\(152\) | − | 53.1032i | − | 0.349363i | ||||||
\(153\) | 51.9773 | − | 53.9091i | 0.339721 | − | 0.352347i | ||||
\(154\) | 230.662 | 1.49780 | ||||||||
\(155\) | 28.5765i | 0.184364i | ||||||||
\(156\) | −79.1197 | − | 31.9301i | −0.507177 | − | 0.204680i | ||||
\(157\) | 68.3351 | 0.435255 | 0.217628 | − | 0.976032i | \(-0.430168\pi\) | ||||
0.217628 | + | 0.976032i | \(0.430168\pi\) | |||||||
\(158\) | 168.162i | 1.06432i | ||||||||
\(159\) | −72.6220 | + | 179.950i | −0.456742 | + | 1.13176i | ||||
\(160\) | −12.6491 | −0.0790569 | ||||||||
\(161\) | − | 46.5814i | − | 0.289325i | ||||||
\(162\) | −114.475 | + | 4.17844i | −0.706636 | + | 0.0257928i | ||||
\(163\) | 160.804 | 0.986527 | 0.493264 | − | 0.869880i | \(-0.335804\pi\) | ||||
0.493264 | + | 0.869880i | \(0.335804\pi\) | |||||||
\(164\) | 67.4116i | 0.411046i | ||||||||
\(165\) | 104.461 | + | 42.1570i | 0.633096 | + | 0.255497i | ||||
\(166\) | −18.7391 | −0.112886 | ||||||||
\(167\) | 203.880i | 1.22084i | 0.792078 | + | 0.610420i | \(0.208999\pi\) | ||||
−0.792078 | + | 0.610420i | \(0.791001\pi\) | |||||||
\(168\) | 30.8437 | − | 76.4275i | 0.183593 | − | 0.454926i | ||||
\(169\) | 33.2072 | 0.196492 | ||||||||
\(170\) | 26.3120i | 0.154777i | ||||||||
\(171\) | 121.642 | + | 117.283i | 0.711356 | + | 0.685864i | ||||
\(172\) | 83.7139 | 0.486709 | ||||||||
\(173\) | − | 38.3584i | − | 0.221725i | −0.993836 | − | 0.110863i | \(-0.964639\pi\) | ||
0.993836 | − | 0.110863i | \(-0.0353613\pi\) | |||||||
\(174\) | 32.8866 | + | 13.2720i | 0.189004 | + | 0.0762757i | ||||
\(175\) | −48.5645 | −0.277511 | ||||||||
\(176\) | − | 67.1695i | − | 0.381645i | ||||||
\(177\) | −39.3702 | + | 97.5553i | −0.222430 | + | 0.551160i | ||||
\(178\) | 206.283 | 1.15889 | ||||||||
\(179\) | 36.4722i | 0.203755i | 0.994797 | + | 0.101878i | \(0.0324850\pi\) | ||||
−0.994797 | + | 0.101878i | \(0.967515\pi\) | |||||||
\(180\) | 27.9366 | − | 28.9749i | 0.155203 | − | 0.160972i | ||||
\(181\) | −340.697 | −1.88231 | −0.941153 | − | 0.337981i | \(-0.890256\pi\) | ||||
−0.941153 | + | 0.337981i | \(0.890256\pi\) | |||||||
\(182\) | 195.327i | 1.07322i | ||||||||
\(183\) | −159.085 | − | 64.2016i | −0.869319 | − | 0.350829i | ||||
\(184\) | −13.5647 | −0.0737210 | ||||||||
\(185\) | − | 108.235i | − | 0.585056i | ||||||
\(186\) | −20.2914 | + | 50.2800i | −0.109093 | + | 0.270323i | ||||
\(187\) | −139.723 | −0.747180 | ||||||||
\(188\) | − | 50.8921i | − | 0.270703i | ||||||
\(189\) | 106.949 | + | 239.449i | 0.565870 | + | 1.26693i | ||||
\(190\) | −59.3712 | −0.312480 | ||||||||
\(191\) | − | 187.221i | − | 0.980216i | −0.871662 | − | 0.490108i | \(-0.836957\pi\) | ||
0.871662 | − | 0.490108i | \(-0.163043\pi\) | |||||||
\(192\) | −22.2560 | − | 8.98178i | −0.115916 | − | 0.0467801i | ||||
\(193\) | 375.100 | 1.94352 | 0.971760 | − | 0.235970i | \(-0.0758266\pi\) | ||||
0.971760 | + | 0.235970i | \(0.0758266\pi\) | |||||||
\(194\) | − | 234.981i | − | 1.21124i | ||||||
\(195\) | −35.6990 | + | 88.4585i | −0.183072 | + | 0.453633i | ||||
\(196\) | −90.6806 | −0.462656 | ||||||||
\(197\) | − | 199.478i | − | 1.01258i | −0.862363 | − | 0.506290i | \(-0.831016\pi\) | ||
0.862363 | − | 0.506290i | \(-0.168984\pi\) | |||||||
\(198\) | 153.863 | + | 148.349i | 0.777086 | + | 0.749240i | ||||
\(199\) | 331.088 | 1.66376 | 0.831880 | − | 0.554955i | \(-0.187265\pi\) | ||||
0.831880 | + | 0.554955i | \(0.187265\pi\) | |||||||
\(200\) | 14.1421i | 0.0707107i | ||||||||
\(201\) | −170.296 | − | 68.7257i | −0.847242 | − | 0.341919i | ||||
\(202\) | −143.277 | −0.709293 | ||||||||
\(203\) | − | 81.1889i | − | 0.399945i | ||||||
\(204\) | −18.6834 | + | 46.2957i | −0.0915855 | + | 0.226940i | ||||
\(205\) | 75.3685 | 0.367651 | ||||||||
\(206\) | − | 221.338i | − | 1.07445i | ||||||
\(207\) | 29.9587 | − | 31.0721i | 0.144728 | − | 0.150107i | ||||
\(208\) | 56.8798 | 0.273461 | ||||||||
\(209\) | − | 315.274i | − | 1.50849i | ||||||
\(210\) | −85.4486 | − | 34.4843i | −0.406898 | − | 0.164211i | ||||
\(211\) | −327.623 | −1.55272 | −0.776358 | − | 0.630293i | \(-0.782935\pi\) | ||||
−0.776358 | + | 0.630293i | \(0.782935\pi\) | |||||||
\(212\) | − | 129.368i | − | 0.610225i | ||||||
\(213\) | −111.204 | + | 275.553i | −0.522086 | + | 1.29368i | ||||
\(214\) | 70.1407 | 0.327760 | ||||||||
\(215\) | − | 93.5950i | − | 0.435325i | ||||||
\(216\) | 69.7284 | − | 31.1440i | 0.322817 | − | 0.144185i | ||||
\(217\) | 124.129 | 0.572022 | ||||||||
\(218\) | − | 13.4950i | − | 0.0619039i | ||||||
\(219\) | 4.76660 | + | 1.92364i | 0.0217653 | + | 0.00878376i | ||||
\(220\) | −75.0978 | −0.341354 | ||||||||
\(221\) | − | 118.319i | − | 0.535378i | ||||||
\(222\) | 76.8549 | − | 190.439i | 0.346193 | − | 0.857833i | ||||
\(223\) | −397.757 | −1.78366 | −0.891832 | − | 0.452367i | \(-0.850580\pi\) | ||||
−0.891832 | + | 0.452367i | \(0.850580\pi\) | |||||||
\(224\) | 54.9444i | 0.245288i | ||||||||
\(225\) | −32.3949 | − | 31.2341i | −0.143978 | − | 0.138818i | ||||
\(226\) | −275.350 | −1.21836 | ||||||||
\(227\) | − | 76.3503i | − | 0.336345i | −0.985758 | − | 0.168172i | \(-0.946213\pi\) | ||
0.985758 | − | 0.168172i | \(-0.0537865\pi\) | |||||||
\(228\) | −104.463 | − | 42.1578i | −0.458171 | − | 0.184903i | ||||
\(229\) | −95.0705 | −0.415155 | −0.207578 | − | 0.978219i | \(-0.566558\pi\) | ||||
−0.207578 | + | 0.978219i | \(0.566558\pi\) | |||||||
\(230\) | 15.1658i | 0.0659380i | ||||||||
\(231\) | 183.119 | − | 453.751i | 0.792723 | − | 1.96429i | ||||
\(232\) | −23.6425 | −0.101907 | ||||||||
\(233\) | − | 372.400i | − | 1.59828i | −0.601144 | − | 0.799141i | \(-0.705288\pi\) | ||
0.601144 | − | 0.799141i | \(-0.294712\pi\) | |||||||
\(234\) | −125.624 | + | 130.293i | −0.536854 | + | 0.556807i | ||||
\(235\) | −56.8991 | −0.242124 | ||||||||
\(236\) | − | 70.1334i | − | 0.297175i | ||||||
\(237\) | 330.803 | + | 133.501i | 1.39579 | + | 0.563297i | ||||
\(238\) | 114.293 | 0.480221 | ||||||||
\(239\) | − | 337.680i | − | 1.41289i | −0.707770 | − | 0.706443i | \(-0.750299\pi\) | ||
0.707770 | − | 0.706443i | \(-0.249701\pi\) | |||||||
\(240\) | −10.0419 | + | 24.8829i | −0.0418414 | + | 0.103679i | ||||
\(241\) | 127.860 | 0.530539 | 0.265270 | − | 0.964174i | \(-0.414539\pi\) | ||||
0.265270 | + | 0.964174i | \(0.414539\pi\) | |||||||
\(242\) | − | 227.666i | − | 0.940768i | ||||||
\(243\) | −82.6603 | + | 228.509i | −0.340166 | + | 0.940365i | ||||
\(244\) | 114.368 | 0.468721 | ||||||||
\(245\) | 101.384i | 0.413812i | ||||||||
\(246\) | 132.610 | + | 53.5170i | 0.539065 | + | 0.217549i | ||||
\(247\) | 266.977 | 1.08088 | ||||||||
\(248\) | − | 36.1467i | − | 0.145753i | ||||||
\(249\) | −14.8767 | + | 36.8630i | −0.0597457 | + | 0.148044i | ||||
\(250\) | 15.8114 | 0.0632456 | ||||||||
\(251\) | 117.132i | 0.466662i | 0.972397 | + | 0.233331i | \(0.0749625\pi\) | ||||
−0.972397 | + | 0.233331i | \(0.925037\pi\) | |||||||
\(252\) | −125.859 | − | 121.349i | −0.499442 | − | 0.481545i | ||||
\(253\) | −80.5334 | −0.318314 | ||||||||
\(254\) | 129.541i | 0.510003i | ||||||||
\(255\) | 51.7602 | + | 20.8887i | 0.202981 | + | 0.0819166i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 95.1801i | − | 0.370351i | −0.982706 | − | 0.185175i | \(-0.940715\pi\) | ||
0.982706 | − | 0.185175i | \(-0.0592853\pi\) | |||||||
\(258\) | 66.4592 | − | 164.679i | 0.257594 | − | 0.638292i | ||||
\(259\) | −470.146 | −1.81524 | ||||||||
\(260\) | − | 63.5936i | − | 0.244591i | ||||||
\(261\) | 52.2164 | − | 54.1571i | 0.200063 | − | 0.207498i | ||||
\(262\) | 195.097 | 0.744646 | ||||||||
\(263\) | − | 189.537i | − | 0.720673i | −0.932822 | − | 0.360336i | \(-0.882662\pi\) | ||
0.932822 | − | 0.360336i | \(-0.117338\pi\) | |||||||
\(264\) | −132.134 | − | 53.3248i | −0.500506 | − | 0.201988i | ||||
\(265\) | −144.638 | −0.545802 | ||||||||
\(266\) | 257.893i | 0.969522i | ||||||||
\(267\) | 163.765 | − | 405.794i | 0.613352 | − | 1.51983i | ||||
\(268\) | 122.427 | 0.456817 | ||||||||
\(269\) | 44.1590i | 0.164160i | 0.996626 | + | 0.0820799i | \(0.0261563\pi\) | ||||
−0.996626 | + | 0.0820799i | \(0.973844\pi\) | |||||||
\(270\) | −34.8201 | − | 77.9587i | −0.128963 | − | 0.288736i | ||||
\(271\) | −198.521 | −0.732548 | −0.366274 | − | 0.930507i | \(-0.619367\pi\) | ||||
−0.366274 | + | 0.930507i | \(0.619367\pi\) | |||||||
\(272\) | − | 33.2824i | − | 0.122362i | ||||||
\(273\) | 384.240 | + | 155.067i | 1.40747 | + | 0.568011i | ||||
\(274\) | −85.8225 | −0.313221 | ||||||||
\(275\) | 83.9619i | 0.305316i | ||||||||
\(276\) | −10.7688 | + | 26.6840i | −0.0390173 | + | 0.0966810i | ||||
\(277\) | 516.578 | 1.86490 | 0.932452 | − | 0.361295i | \(-0.117665\pi\) | ||||
0.932452 | + | 0.361295i | \(0.117665\pi\) | |||||||
\(278\) | 152.001i | 0.546766i | ||||||||
\(279\) | 82.8002 | + | 79.8330i | 0.296775 | + | 0.286140i | ||||
\(280\) | 61.4297 | 0.219392 | ||||||||
\(281\) | − | 263.794i | − | 0.938769i | −0.882994 | − | 0.469385i | \(-0.844476\pi\) | ||
0.882994 | − | 0.469385i | \(-0.155524\pi\) | |||||||
\(282\) | −100.113 | − | 40.4025i | −0.355012 | − | 0.143271i | ||||
\(283\) | 100.543 | 0.355277 | 0.177639 | − | 0.984096i | \(-0.443154\pi\) | ||||
0.177639 | + | 0.984096i | \(0.443154\pi\) | |||||||
\(284\) | − | 198.098i | − | 0.697527i | ||||||
\(285\) | −47.1339 | + | 116.793i | −0.165382 | + | 0.409800i | ||||
\(286\) | 337.696 | 1.18075 | ||||||||
\(287\) | − | 327.381i | − | 1.14070i | ||||||
\(288\) | −35.3373 | + | 36.6507i | −0.122699 | + | 0.127259i | ||||
\(289\) | 219.768 | 0.760442 | ||||||||
\(290\) | 26.4331i | 0.0911486i | ||||||||
\(291\) | −462.247 | − | 186.548i | −1.58848 | − | 0.641058i | ||||
\(292\) | −3.42675 | −0.0117354 | ||||||||
\(293\) | − | 334.768i | − | 1.14255i | −0.820758 | − | 0.571276i | \(-0.806449\pi\) | ||
0.820758 | − | 0.571276i | \(-0.193551\pi\) | |||||||
\(294\) | −71.9899 | + | 178.384i | −0.244864 | + | 0.606748i | ||||
\(295\) | −78.4115 | −0.265802 | ||||||||
\(296\) | 136.908i | 0.462527i | ||||||||
\(297\) | 413.978 | − | 184.902i | 1.39386 | − | 0.622566i | ||||
\(298\) | 48.2878 | 0.162039 | ||||||||
\(299\) | − | 68.1965i | − | 0.228082i | ||||||
\(300\) | 27.8199 | + | 11.2272i | 0.0927332 | + | 0.0374241i | ||||
\(301\) | −406.552 | −1.35067 | ||||||||
\(302\) | − | 217.705i | − | 0.720878i | ||||||
\(303\) | −113.746 | + | 281.850i | −0.375398 | + | 0.930199i | ||||
\(304\) | 75.0993 | 0.247037 | ||||||||
\(305\) | − | 127.867i | − | 0.419236i | ||||||
\(306\) | 76.2389 | + | 73.5069i | 0.249147 | + | 0.240219i | ||||
\(307\) | −273.175 | −0.889819 | −0.444910 | − | 0.895575i | \(-0.646764\pi\) | ||||
−0.444910 | + | 0.895575i | \(0.646764\pi\) | |||||||
\(308\) | 326.205i | 1.05911i | ||||||||
\(309\) | −435.408 | − | 175.717i | −1.40909 | − | 0.568662i | ||||
\(310\) | −40.4133 | −0.130365 | ||||||||
\(311\) | 364.172i | 1.17097i | 0.810683 | + | 0.585485i | \(0.199096\pi\) | ||||
−0.810683 | + | 0.585485i | \(0.800904\pi\) | |||||||
\(312\) | 45.1560 | − | 111.892i | 0.144731 | − | 0.358629i | ||||
\(313\) | −499.143 | −1.59471 | −0.797354 | − | 0.603512i | \(-0.793767\pi\) | ||||
−0.797354 | + | 0.603512i | \(0.793767\pi\) | |||||||
\(314\) | 96.6404i | 0.307772i | ||||||||
\(315\) | −135.673 | + | 140.715i | −0.430707 | + | 0.446715i | ||||
\(316\) | −237.817 | −0.752586 | ||||||||
\(317\) | 609.173i | 1.92168i | 0.277099 | + | 0.960841i | \(0.410627\pi\) | ||||
−0.277099 | + | 0.960841i | \(0.589373\pi\) | |||||||
\(318\) | −254.488 | − | 102.703i | −0.800277 | − | 0.322966i | ||||
\(319\) | −140.366 | −0.440017 | ||||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | 55.6836 | − | 137.979i | 0.173469 | − | 0.429840i | ||||
\(322\) | 65.8760 | 0.204584 | ||||||||
\(323\) | − | 156.218i | − | 0.483646i | ||||||
\(324\) | −5.90920 | − | 161.892i | −0.0182383 | − | 0.499667i | ||||
\(325\) | −71.0998 | −0.218769 | ||||||||
\(326\) | 227.411i | 0.697580i | ||||||||
\(327\) | −26.5470 | − | 10.7135i | −0.0811835 | − | 0.0327630i | ||||
\(328\) | −95.3344 | −0.290654 | ||||||||
\(329\) | 247.155i | 0.751231i | ||||||||
\(330\) | −59.6190 | + | 147.730i | −0.180664 | + | 0.447667i | ||||
\(331\) | 212.610 | 0.642326 | 0.321163 | − | 0.947024i | \(-0.395926\pi\) | ||||
0.321163 | + | 0.947024i | \(0.395926\pi\) | |||||||
\(332\) | − | 26.5011i | − | 0.0798226i | ||||||
\(333\) | −313.611 | − | 302.373i | −0.941775 | − | 0.908027i | ||||
\(334\) | −288.330 | −0.863265 | ||||||||
\(335\) | − | 136.877i | − | 0.408589i | ||||||
\(336\) | 108.085 | + | 43.6195i | 0.321681 | + | 0.129820i | ||||
\(337\) | 186.428 | 0.553199 | 0.276600 | − | 0.960985i | \(-0.410792\pi\) | ||||
0.276600 | + | 0.960985i | \(0.410792\pi\) | |||||||
\(338\) | 46.9620i | 0.138941i | ||||||||
\(339\) | −218.596 | + | 541.660i | −0.644826 | + | 1.59782i | ||||
\(340\) | −37.2109 | −0.109444 | ||||||||
\(341\) | − | 214.603i | − | 0.629335i | ||||||
\(342\) | −165.863 | + | 172.028i | −0.484979 | + | 0.503005i | ||||
\(343\) | −35.5465 | −0.103634 | ||||||||
\(344\) | 118.389i | 0.344155i | ||||||||
\(345\) | 29.8336 | + | 12.0399i | 0.0864741 | + | 0.0348981i | ||||
\(346\) | 54.2470 | 0.156783 | ||||||||
\(347\) | − | 144.932i | − | 0.417672i | −0.977951 | − | 0.208836i | \(-0.933033\pi\) | ||
0.977951 | − | 0.208836i | \(-0.0669674\pi\) | |||||||
\(348\) | −18.7694 | + | 46.5087i | −0.0539351 | + | 0.133646i | ||||
\(349\) | 217.428 | 0.623003 | 0.311502 | − | 0.950246i | \(-0.399168\pi\) | ||||
0.311502 | + | 0.950246i | \(0.399168\pi\) | |||||||
\(350\) | − | 68.6805i | − | 0.196230i | ||||||
\(351\) | 156.577 | + | 350.560i | 0.446088 | + | 0.998748i | ||||
\(352\) | 94.9921 | 0.269864 | ||||||||
\(353\) | 252.766i | 0.716052i | 0.933712 | + | 0.358026i | \(0.116550\pi\) | ||||
−0.933712 | + | 0.358026i | \(0.883450\pi\) | |||||||
\(354\) | −137.964 | − | 55.6778i | −0.389729 | − | 0.157282i | ||||
\(355\) | −221.480 | −0.623887 | ||||||||
\(356\) | 291.729i | 0.819462i | ||||||||
\(357\) | 90.7352 | − | 224.833i | 0.254160 | − | 0.629784i | ||||
\(358\) | −51.5795 | −0.144077 | ||||||||
\(359\) | 310.853i | 0.865887i | 0.901421 | + | 0.432943i | \(0.142525\pi\) | ||||
−0.901421 | + | 0.432943i | \(0.857475\pi\) | |||||||
\(360\) | 40.9767 | + | 39.5083i | 0.113824 | + | 0.109745i | ||||
\(361\) | −8.50620 | −0.0235629 | ||||||||
\(362\) | − | 481.819i | − | 1.33099i | ||||||
\(363\) | −447.857 | − | 180.740i | −1.23377 | − | 0.497907i | ||||
\(364\) | −276.234 | −0.758884 | ||||||||
\(365\) | 3.83122i | 0.0104965i | ||||||||
\(366\) | 90.7948 | − | 224.981i | 0.248073 | − | 0.614701i | ||||
\(367\) | 578.070 | 1.57512 | 0.787561 | − | 0.616237i | \(-0.211344\pi\) | ||||
0.787561 | + | 0.616237i | \(0.211344\pi\) | |||||||
\(368\) | − | 19.1833i | − | 0.0521286i | ||||||
\(369\) | 210.554 | − | 218.380i | 0.570607 | − | 0.591814i | ||||
\(370\) | 153.068 | 0.413697 | ||||||||
\(371\) | 628.267i | 1.69344i | ||||||||
\(372\) | −71.1067 | − | 28.6963i | −0.191147 | − | 0.0771407i | ||||
\(373\) | 547.166 | 1.46693 | 0.733466 | − | 0.679726i | \(-0.237901\pi\) | ||||
0.733466 | + | 0.679726i | \(0.237901\pi\) | |||||||
\(374\) | − | 197.598i | − | 0.528336i | ||||||
\(375\) | 12.5524 | − | 31.1036i | 0.0334731 | − | 0.0829431i | ||||
\(376\) | 71.9723 | 0.191416 | ||||||||
\(377\) | − | 118.863i | − | 0.315286i | ||||||
\(378\) | −338.632 | + | 151.249i | −0.895852 | + | 0.400130i | ||||
\(379\) | −176.439 | −0.465539 | −0.232769 | − | 0.972532i | \(-0.574779\pi\) | ||||
−0.232769 | + | 0.972532i | \(0.574779\pi\) | |||||||
\(380\) | − | 83.9635i | − | 0.220957i | ||||||
\(381\) | 254.828 | + | 102.840i | 0.668841 | + | 0.269922i | ||||
\(382\) | 264.771 | 0.693118 | ||||||||
\(383\) | 102.841i | 0.268513i | 0.990947 | + | 0.134257i | \(0.0428646\pi\) | ||||
−0.990947 | + | 0.134257i | \(0.957135\pi\) | |||||||
\(384\) | 12.7022 | − | 31.4747i | 0.0330785 | − | 0.0819653i | ||||
\(385\) | 364.708 | 0.947295 | ||||||||
\(386\) | 530.471i | 1.37428i | ||||||||
\(387\) | −271.191 | − | 261.473i | −0.700751 | − | 0.675640i | ||||
\(388\) | 332.314 | 0.856478 | ||||||||
\(389\) | − | 225.716i | − | 0.580248i | −0.956989 | − | 0.290124i | \(-0.906304\pi\) | ||
0.956989 | − | 0.290124i | \(-0.0936965\pi\) | |||||||
\(390\) | −125.099 | − | 50.4860i | −0.320767 | − | 0.129451i | ||||
\(391\) | −39.9042 | −0.102057 | ||||||||
\(392\) | − | 128.242i | − | 0.327147i | ||||||
\(393\) | 154.885 | − | 383.789i | 0.394108 | − | 0.976562i | ||||
\(394\) | 282.105 | 0.716002 | ||||||||
\(395\) | 265.888i | 0.673134i | ||||||||
\(396\) | −209.798 | + | 217.595i | −0.529792 | + | 0.549483i | ||||
\(397\) | 267.452 | 0.673682 | 0.336841 | − | 0.941562i | \(-0.390642\pi\) | ||||
0.336841 | + | 0.941562i | \(0.390642\pi\) | |||||||
\(398\) | 468.230i | 1.17646i | ||||||||
\(399\) | 507.318 | + | 204.737i | 1.27147 | + | 0.513126i | ||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 440.820i | 1.09930i | 0.835395 | + | 0.549651i | \(0.185239\pi\) | ||||
−0.835395 | + | 0.549651i | \(0.814761\pi\) | |||||||
\(402\) | 97.1929 | − | 240.834i | 0.241773 | − | 0.599090i | ||||
\(403\) | 181.728 | 0.450938 | ||||||||
\(404\) | − | 202.625i | − | 0.501546i | ||||||
\(405\) | −181.001 | + | 6.60669i | −0.446916 | + | 0.0163128i | ||||
\(406\) | 114.818 | 0.282804 | ||||||||
\(407\) | 812.824i | 1.99711i | ||||||||
\(408\) | −65.4720 | − | 26.4224i | −0.160471 | − | 0.0647607i | ||||
\(409\) | 62.7728 | 0.153479 | 0.0767393 | − | 0.997051i | \(-0.475549\pi\) | ||||
0.0767393 | + | 0.997051i | \(0.475549\pi\) | |||||||
\(410\) | 106.587i | 0.259969i | ||||||||
\(411\) | −68.1332 | + | 168.827i | −0.165774 | + | 0.410772i | ||||
\(412\) | 313.019 | 0.759754 | ||||||||
\(413\) | 340.599i | 0.824695i | ||||||||
\(414\) | 43.9426 | + | 42.3680i | 0.106142 | + | 0.102338i | ||||
\(415\) | −29.6291 | −0.0713955 | ||||||||
\(416\) | 80.4402i | 0.193366i | ||||||||
\(417\) | 299.011 | + | 120.671i | 0.717053 | + | 0.289379i | ||||
\(418\) | 445.865 | 1.06666 | ||||||||
\(419\) | 678.217i | 1.61866i | 0.587357 | + | 0.809328i | \(0.300168\pi\) | ||||
−0.587357 | + | 0.809328i | \(0.699832\pi\) | |||||||
\(420\) | 48.7681 | − | 120.843i | 0.116115 | − | 0.287720i | ||||
\(421\) | 104.952 | 0.249293 | 0.124646 | − | 0.992201i | \(-0.460220\pi\) | ||||
0.124646 | + | 0.992201i | \(0.460220\pi\) | |||||||
\(422\) | − | 463.329i | − | 1.09794i | ||||||
\(423\) | −158.957 | + | 164.865i | −0.375785 | + | 0.389751i | ||||
\(424\) | 182.954 | 0.431494 | ||||||||
\(425\) | 41.6030i | 0.0978894i | ||||||||
\(426\) | −389.691 | − | 157.267i | −0.914769 | − | 0.369171i | ||||
\(427\) | −555.421 | −1.30075 | ||||||||
\(428\) | 99.1940i | 0.231762i | ||||||||
\(429\) | 268.091 | − | 664.304i | 0.624922 | − | 1.54849i | ||||
\(430\) | 132.363 | 0.307822 | ||||||||
\(431\) | − | 155.310i | − | 0.360349i | −0.983635 | − | 0.180174i | \(-0.942334\pi\) | ||
0.983635 | − | 0.180174i | \(-0.0576662\pi\) | |||||||
\(432\) | 44.0443 | + | 98.6109i | 0.101954 | + | 0.228266i | ||||
\(433\) | −618.290 | −1.42792 | −0.713961 | − | 0.700185i | \(-0.753101\pi\) | ||||
−0.713961 | + | 0.700185i | \(0.753101\pi\) | |||||||
\(434\) | 175.545i | 0.404481i | ||||||||
\(435\) | 51.9983 | + | 20.9848i | 0.119536 | + | 0.0482410i | ||||
\(436\) | 19.0849 | 0.0437727 | ||||||||
\(437\) | − | 90.0409i | − | 0.206043i | ||||||
\(438\) | −2.72044 | + | 6.74099i | −0.00621106 | + | 0.0153904i | ||||
\(439\) | −103.321 | −0.235356 | −0.117678 | − | 0.993052i | \(-0.537545\pi\) | ||||
−0.117678 | + | 0.993052i | \(0.537545\pi\) | |||||||
\(440\) | − | 106.204i | − | 0.241374i | ||||||
\(441\) | 293.759 | + | 283.232i | 0.666121 | + | 0.642250i | ||||
\(442\) | 167.328 | 0.378570 | ||||||||
\(443\) | 190.496i | 0.430013i | 0.976613 | + | 0.215006i | \(0.0689772\pi\) | ||||
−0.976613 | + | 0.215006i | \(0.931023\pi\) | |||||||
\(444\) | 269.321 | + | 108.689i | 0.606579 | + | 0.244796i | ||||
\(445\) | 326.162 | 0.732949 | ||||||||
\(446\) | − | 562.513i | − | 1.26124i | ||||||
\(447\) | 38.3349 | − | 94.9901i | 0.0857604 | − | 0.212506i | ||||
\(448\) | −77.7031 | −0.173445 | ||||||||
\(449\) | − | 2.15568i | − | 0.00480107i | −0.999997 | − | 0.00240053i | \(-0.999236\pi\) | ||
0.999997 | − | 0.00240053i | \(-0.000764114\pi\) | |||||||
\(450\) | 44.1717 | − | 45.8134i | 0.0981592 | − | 0.101807i | ||||
\(451\) | −566.001 | −1.25499 | ||||||||
\(452\) | − | 389.404i | − | 0.861513i | ||||||
\(453\) | −428.262 | − | 172.833i | −0.945391 | − | 0.381529i | ||||
\(454\) | 107.976 | 0.237832 | ||||||||
\(455\) | 308.839i | 0.678767i | ||||||||
\(456\) | 59.6202 | − | 147.733i | 0.130746 | − | 0.323976i | ||||
\(457\) | −400.938 | −0.877326 | −0.438663 | − | 0.898652i | \(-0.644548\pi\) | ||||
−0.438663 | + | 0.898652i | \(0.644548\pi\) | |||||||
\(458\) | − | 134.450i | − | 0.293559i | ||||||
\(459\) | 205.125 | − | 91.6187i | 0.446896 | − | 0.199605i | ||||
\(460\) | −21.4476 | −0.0466252 | ||||||||
\(461\) | 416.867i | 0.904266i | 0.891951 | + | 0.452133i | \(0.149337\pi\) | ||||
−0.891951 | + | 0.452133i | \(0.850663\pi\) | |||||||
\(462\) | 641.700 | + | 258.969i | 1.38896 | + | 0.560540i | ||||
\(463\) | −211.974 | −0.457827 | −0.228913 | − | 0.973447i | \(-0.573517\pi\) | ||||
−0.228913 | + | 0.973447i | \(0.573517\pi\) | |||||||
\(464\) | − | 33.4355i | − | 0.0720593i | ||||||
\(465\) | −32.0835 | + | 79.4997i | −0.0689967 | + | 0.170967i | ||||
\(466\) | 526.652 | 1.13016 | ||||||||
\(467\) | 536.033i | 1.14782i | 0.818918 | + | 0.573911i | \(0.194574\pi\) | ||||
−0.818918 | + | 0.573911i | \(0.805426\pi\) | |||||||
\(468\) | −184.262 | − | 177.659i | −0.393722 | − | 0.379613i | ||||
\(469\) | −594.560 | −1.26772 | ||||||||
\(470\) | − | 80.4675i | − | 0.171208i | ||||||
\(471\) | 190.108 | + | 76.7214i | 0.403626 | + | 0.162890i | ||||
\(472\) | 99.1836 | 0.210135 | ||||||||
\(473\) | 702.878i | 1.48600i | ||||||||
\(474\) | −188.800 | + | 467.826i | −0.398311 | + | 0.986976i | ||||
\(475\) | −93.8741 | −0.197630 | ||||||||
\(476\) | 161.634i | 0.339568i | ||||||||
\(477\) | −404.068 | + | 419.086i | −0.847103 | + | 0.878587i | ||||
\(478\) | 477.551 | 0.999061 | ||||||||
\(479\) | 143.758i | 0.300120i | 0.988677 | + | 0.150060i | \(0.0479467\pi\) | ||||
−0.988677 | + | 0.150060i | \(0.952053\pi\) | |||||||
\(480\) | −35.1898 | − | 14.2014i | −0.0733120 | − | 0.0295863i | ||||
\(481\) | −688.307 | −1.43099 | ||||||||
\(482\) | 180.821i | 0.375148i | ||||||||
\(483\) | 52.2980 | − | 129.589i | 0.108277 | − | 0.268301i | ||||
\(484\) | 321.968 | 0.665223 | ||||||||
\(485\) | − | 371.538i | − | 0.766058i | ||||||
\(486\) | −323.160 | − | 116.899i | −0.664939 | − | 0.240534i | ||||
\(487\) | −454.474 | −0.933211 | −0.466605 | − | 0.884466i | \(-0.654523\pi\) | ||||
−0.466605 | + | 0.884466i | \(0.654523\pi\) | |||||||
\(488\) | 161.741i | 0.331435i | ||||||||
\(489\) | 447.356 | + | 180.538i | 0.914838 | + | 0.369199i | ||||
\(490\) | −143.379 | −0.292609 | ||||||||
\(491\) | 414.443i | 0.844079i | 0.906577 | + | 0.422039i | \(0.138686\pi\) | ||||
−0.906577 | + | 0.422039i | \(0.861314\pi\) | |||||||
\(492\) | −75.6845 | + | 187.539i | −0.153830 | + | 0.381176i | ||||
\(493\) | −69.5509 | −0.141077 | ||||||||
\(494\) | 377.563i | 0.764297i | ||||||||
\(495\) | 243.279 | + | 234.561i | 0.491473 | + | 0.473861i | ||||
\(496\) | 51.1192 | 0.103063 | ||||||||
\(497\) | 962.051i | 1.93572i | ||||||||
\(498\) | −52.1321 | − | 21.0388i | −0.104683 | − | 0.0422466i | ||||
\(499\) | −408.192 | −0.818021 | −0.409010 | − | 0.912530i | \(-0.634126\pi\) | ||||
−0.409010 | + | 0.912530i | \(0.634126\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | −228.901 | + | 567.194i | −0.456888 | + | 1.13212i | ||||
\(502\) | −165.650 | −0.329980 | ||||||||
\(503\) | − | 541.009i | − | 1.07556i | −0.843084 | − | 0.537782i | \(-0.819262\pi\) | ||
0.843084 | − | 0.537782i | \(-0.180738\pi\) | |||||||
\(504\) | 171.614 | − | 177.992i | 0.340504 | − | 0.353159i | ||||
\(505\) | −226.541 | −0.448596 | ||||||||
\(506\) | − | 113.891i | − | 0.225082i | ||||||
\(507\) | 92.3821 | + | 37.2824i | 0.182213 | + | 0.0735353i | ||||
\(508\) | −183.198 | −0.360626 | ||||||||
\(509\) | − | 508.935i | − | 0.999872i | −0.866062 | − | 0.499936i | \(-0.833357\pi\) | ||
0.866062 | − | 0.499936i | \(-0.166643\pi\) | |||||||
\(510\) | −29.5411 | + | 73.2000i | −0.0579238 | + | 0.143529i | ||||
\(511\) | 16.6418 | 0.0325672 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 206.731 | + | 462.850i | 0.402984 | + | 0.902242i | ||||
\(514\) | 134.605 | 0.261877 | ||||||||
\(515\) | − | 349.966i | − | 0.679545i | ||||||
\(516\) | 232.892 | + | 93.9874i | 0.451340 | + | 0.182146i | ||||
\(517\) | 427.300 | 0.826499 | ||||||||
\(518\) | − | 664.887i | − | 1.28357i | ||||||
\(519\) | 43.0659 | − | 106.713i | 0.0829786 | − | 0.205613i | ||||
\(520\) | 89.9349 | 0.172952 | ||||||||
\(521\) | − | 326.505i | − | 0.626689i | −0.949640 | − | 0.313344i | \(-0.898551\pi\) | ||
0.949640 | − | 0.313344i | \(-0.101449\pi\) | |||||||
\(522\) | 76.5897 | + | 73.8451i | 0.146724 | + | 0.141466i | ||||
\(523\) | 651.561 | 1.24581 | 0.622907 | − | 0.782296i | \(-0.285951\pi\) | ||||
0.622907 | + | 0.782296i | \(0.285951\pi\) | |||||||
\(524\) | 275.909i | 0.526544i | ||||||||
\(525\) | −135.106 | − | 54.5244i | −0.257345 | − | 0.103856i | ||||
\(526\) | 268.046 | 0.509592 | ||||||||
\(527\) | − | 106.336i | − | 0.201775i | ||||||
\(528\) | 75.4127 | − | 186.865i | 0.142827 | − | 0.353911i | ||||
\(529\) | −23.0000 | −0.0434783 | ||||||||
\(530\) | − | 204.548i | − | 0.385940i | ||||||
\(531\) | −219.055 | + | 227.197i | −0.412533 | + | 0.427866i | ||||
\(532\) | −364.716 | −0.685556 | ||||||||
\(533\) | − | 479.295i | − | 0.899240i | ||||||
\(534\) | 573.879 | + | 231.599i | 1.07468 | + | 0.433706i | ||||
\(535\) | 110.902 | 0.207294 | ||||||||
\(536\) | 173.138i | 0.323018i | ||||||||
\(537\) | −40.9482 | + | 101.465i | −0.0762535 | + | 0.188949i | ||||
\(538\) | −62.4502 | −0.116078 | ||||||||
\(539\) | − | 761.371i | − | 1.41256i | ||||||
\(540\) | 110.250 | − | 49.2430i | 0.204167 | − | 0.0911908i | ||||
\(541\) | −561.296 | −1.03752 | −0.518758 | − | 0.854921i | \(-0.673605\pi\) | ||||
−0.518758 | + | 0.854921i | \(0.673605\pi\) | |||||||
\(542\) | − | 280.751i | − | 0.517990i | ||||||
\(543\) | −947.818 | − | 382.509i | −1.74552 | − | 0.704436i | ||||
\(544\) | 47.0684 | 0.0865228 | ||||||||
\(545\) | − | 21.3375i | − | 0.0391514i | ||||||
\(546\) | −219.298 | + | 543.398i | −0.401644 | + | 0.995235i | ||||
\(547\) | −539.069 | −0.985500 | −0.492750 | − | 0.870171i | \(-0.664008\pi\) | ||||
−0.492750 | + | 0.870171i | \(0.664008\pi\) | |||||||
\(548\) | − | 121.371i | − | 0.221481i | ||||||
\(549\) | −370.494 | − | 357.217i | −0.674852 | − | 0.650669i | ||||
\(550\) | −118.740 | −0.215891 | ||||||||
\(551\) | − | 156.936i | − | 0.284821i | ||||||
\(552\) | −37.7368 | − | 15.2293i | −0.0683638 | − | 0.0275894i | ||||
\(553\) | 1154.95 | 2.08851 | ||||||||
\(554\) | 730.552i | 1.31869i | ||||||||
\(555\) | 121.518 | − | 301.110i | 0.218952 | − | 0.542541i | ||||
\(556\) | −214.962 | −0.386622 | ||||||||
\(557\) | − | 613.984i | − | 1.10231i | −0.834404 | − | 0.551153i | \(-0.814188\pi\) | ||
0.834404 | − | 0.551153i | \(-0.185812\pi\) | |||||||
\(558\) | −112.901 | + | 117.097i | −0.202331 | + | 0.209851i | ||||
\(559\) | −595.204 | −1.06477 | ||||||||
\(560\) | 86.8747i | 0.155133i | ||||||||
\(561\) | −388.708 | − | 156.870i | −0.692884 | − | 0.279625i | ||||
\(562\) | 373.061 | 0.663810 | ||||||||
\(563\) | 522.289i | 0.927689i | 0.885917 | + | 0.463844i | \(0.153530\pi\) | ||||
−0.885917 | + | 0.463844i | \(0.846470\pi\) | |||||||
\(564\) | 57.1377 | − | 141.582i | 0.101308 | − | 0.251031i | ||||
\(565\) | −435.367 | −0.770560 | ||||||||
\(566\) | 142.190i | 0.251219i | ||||||||
\(567\) | 28.6977 | + | 786.221i | 0.0506132 | + | 1.38663i | ||||
\(568\) | 280.153 | 0.493226 | ||||||||
\(569\) | − | 835.117i | − | 1.46769i | −0.679316 | − | 0.733846i | \(-0.737723\pi\) | ||
0.679316 | − | 0.733846i | \(-0.262277\pi\) | |||||||
\(570\) | −165.170 | − | 66.6574i | −0.289773 | − | 0.116943i | ||||
\(571\) | −973.842 | −1.70550 | −0.852752 | − | 0.522316i | \(-0.825068\pi\) | ||||
−0.852752 | + | 0.522316i | \(0.825068\pi\) | |||||||
\(572\) | 477.574i | 0.834919i | ||||||||
\(573\) | 210.198 | − | 520.849i | 0.366837 | − | 0.908986i | ||||
\(574\) | 462.986 | 0.806596 | ||||||||
\(575\) | 23.9792i | 0.0417029i | ||||||||
\(576\) | −51.8319 | − | 49.9745i | −0.0899860 | − | 0.0867613i | ||||
\(577\) | 556.066 | 0.963719 | 0.481859 | − | 0.876249i | \(-0.339962\pi\) | ||||
0.481859 | + | 0.876249i | \(0.339962\pi\) | |||||||
\(578\) | 310.798i | 0.537713i | ||||||||
\(579\) | 1043.52 | + | 421.133i | 1.80229 | + | 0.727345i | ||||
\(580\) | −37.3821 | −0.0644518 | ||||||||
\(581\) | 128.701i | 0.221517i | ||||||||
\(582\) | 263.819 | − | 653.716i | 0.453297 | − | 1.12322i | ||||
\(583\) | 1086.20 | 1.86312 | ||||||||
\(584\) | − | 4.84616i | − | 0.00829821i | ||||||
\(585\) | −198.629 | + | 206.011i | −0.339536 | + | 0.352156i | ||||
\(586\) | 473.433 | 0.807906 | ||||||||
\(587\) | 455.905i | 0.776669i | 0.921519 | + | 0.388334i | \(0.126949\pi\) | ||||
−0.921519 | + | 0.388334i | \(0.873051\pi\) | |||||||
\(588\) | −252.273 | − | 101.809i | −0.429035 | − | 0.173145i | ||||
\(589\) | 239.938 | 0.407366 | ||||||||
\(590\) | − | 110.891i | − | 0.187950i | ||||||
\(591\) | 223.959 | − | 554.948i | 0.378949 | − | 0.938998i | ||||
\(592\) | −193.617 | −0.327056 | ||||||||
\(593\) | 1016.74i | 1.71457i | 0.514842 | + | 0.857285i | \(0.327851\pi\) | ||||
−0.514842 | + | 0.857285i | \(0.672149\pi\) | |||||||
\(594\) | 261.491 | + | 585.453i | 0.440221 | + | 0.985611i | ||||
\(595\) | 180.713 | 0.303719 | ||||||||
\(596\) | 68.2892i | 0.114579i | ||||||||
\(597\) | 921.086 | + | 371.720i | 1.54286 | + | 0.622647i | ||||
\(598\) | 96.4444 | 0.161278 | ||||||||
\(599\) | − | 6.66161i | − | 0.0111212i | −0.999985 | − | 0.00556061i | \(-0.998230\pi\) | ||
0.999985 | − | 0.00556061i | \(-0.00177001\pi\) | |||||||
\(600\) | −15.8777 | + | 39.3433i | −0.0264628 | + | 0.0655722i | ||||
\(601\) | 451.786 | 0.751724 | 0.375862 | − | 0.926676i | \(-0.377347\pi\) | ||||
0.375862 | + | 0.926676i | \(0.377347\pi\) | |||||||
\(602\) | − | 574.951i | − | 0.955069i | ||||||
\(603\) | −396.601 | − | 382.389i | −0.657714 | − | 0.634145i | ||||
\(604\) | 307.881 | 0.509737 | ||||||||
\(605\) | − | 359.971i | − | 0.594994i | ||||||
\(606\) | −398.596 | − | 160.861i | −0.657750 | − | 0.265446i | ||||
\(607\) | −263.050 | −0.433361 | −0.216680 | − | 0.976243i | \(-0.569523\pi\) | ||||
−0.216680 | + | 0.976243i | \(0.569523\pi\) | |||||||
\(608\) | 106.206i | 0.174682i | ||||||||
\(609\) | 91.1526 | − | 225.867i | 0.149676 | − | 0.370882i | ||||
\(610\) | 180.831 | 0.296445 | ||||||||
\(611\) | 361.842i | 0.592213i | ||||||||
\(612\) | −103.955 | + | 107.818i | −0.169860 | + | 0.176173i | ||||
\(613\) | 613.976 | 1.00159 | 0.500796 | − | 0.865565i | \(-0.333041\pi\) | ||||
0.500796 | + | 0.865565i | \(0.333041\pi\) | |||||||
\(614\) | − | 386.327i | − | 0.629197i | ||||||
\(615\) | 209.675 | + | 84.6179i | 0.340934 | + | 0.137590i | ||||
\(616\) | −461.324 | −0.748902 | ||||||||
\(617\) | 1142.79i | 1.85217i | 0.377316 | + | 0.926084i | \(0.376847\pi\) | ||||
−0.377316 | + | 0.926084i | \(0.623153\pi\) | |||||||
\(618\) | 248.501 | − | 615.760i | 0.402105 | − | 0.996376i | ||||
\(619\) | −590.671 | −0.954234 | −0.477117 | − | 0.878840i | \(-0.658318\pi\) | ||||
−0.477117 | + | 0.878840i | \(0.658318\pi\) | |||||||
\(620\) | − | 57.1530i | − | 0.0921822i | ||||||
\(621\) | 118.230 | − | 52.8073i | 0.190387 | − | 0.0850358i | ||||
\(622\) | −515.017 | −0.828001 | ||||||||
\(623\) | − | 1416.76i | − | 2.27410i | ||||||
\(624\) | 158.239 | + | 63.8603i | 0.253589 | + | 0.102340i | ||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 705.895i | − | 1.12763i | ||||||
\(627\) | 353.965 | − | 877.090i | 0.564538 | − | 1.39887i | ||||
\(628\) | −136.670 | −0.217628 | ||||||||
\(629\) | 402.753i | 0.640307i | ||||||||
\(630\) | −199.001 | − | 191.870i | −0.315875 | − | 0.304556i | ||||
\(631\) | 316.818 | 0.502089 | 0.251044 | − | 0.967976i | \(-0.419226\pi\) | ||||
0.251044 | + | 0.967976i | \(0.419226\pi\) | |||||||
\(632\) | − | 336.324i | − | 0.532159i | ||||||
\(633\) | −911.445 | − | 367.830i | −1.43988 | − | 0.581089i | ||||
\(634\) | −861.501 | −1.35883 | ||||||||
\(635\) | 204.822i | 0.322554i | ||||||||
\(636\) | 145.244 | − | 359.900i | 0.228371 | − | 0.565881i | ||||
\(637\) | 644.737 | 1.01215 | ||||||||
\(638\) | − | 198.507i | − | 0.311139i | ||||||
\(639\) | −618.740 | + | 641.737i | −0.968294 | + | 1.00428i | ||||
\(640\) | 25.2982 | 0.0395285 | ||||||||
\(641\) | − | 617.453i | − | 0.963265i | −0.876373 | − | 0.481633i | \(-0.840044\pi\) | ||
0.876373 | − | 0.481633i | \(-0.159956\pi\) | |||||||
\(642\) | 195.131 | + | 78.7486i | 0.303943 | + | 0.122661i | ||||
\(643\) | −465.627 | −0.724148 | −0.362074 | − | 0.932149i | \(-0.617931\pi\) | ||||
−0.362074 | + | 0.932149i | \(0.617931\pi\) | |||||||
\(644\) | 93.1628i | 0.144663i | ||||||||
\(645\) | 105.081 | − | 260.381i | 0.162917 | − | 0.403691i | ||||
\(646\) | 220.925 | 0.341990 | ||||||||
\(647\) | − | 439.316i | − | 0.679005i | −0.940605 | − | 0.339503i | \(-0.889741\pi\) | ||
0.940605 | − | 0.339503i | \(-0.110259\pi\) | |||||||
\(648\) | 228.950 | − | 8.35687i | 0.353318 | − | 0.0128964i | ||||
\(649\) | 588.853 | 0.907324 | ||||||||
\(650\) | − | 100.550i | − | 0.154693i | ||||||
\(651\) | 345.326 | + | 139.362i | 0.530454 | + | 0.214074i | ||||
\(652\) | −321.608 | −0.493264 | ||||||||
\(653\) | 1275.64i | 1.95350i | 0.214377 | + | 0.976751i | \(0.431228\pi\) | ||||
−0.214377 | + | 0.976751i | \(0.568772\pi\) | |||||||
\(654\) | 15.1512 | − | 37.5431i | 0.0231670 | − | 0.0574054i | ||||
\(655\) | 308.476 | 0.470955 | ||||||||
\(656\) | − | 134.823i | − | 0.205523i | ||||||
\(657\) | 11.1009 | + | 10.7031i | 0.0168964 | + | 0.0162909i | ||||
\(658\) | −349.530 | −0.531200 | ||||||||
\(659\) | − | 1058.48i | − | 1.60619i | −0.595851 | − | 0.803095i | \(-0.703185\pi\) | ||
0.595851 | − | 0.803095i | \(-0.296815\pi\) | |||||||
\(660\) | −208.922 | − | 84.3140i | −0.316548 | − | 0.127748i | ||||
\(661\) | 74.3586 | 0.112494 | 0.0562470 | − | 0.998417i | \(-0.482087\pi\) | ||||
0.0562470 | + | 0.998417i | \(0.482087\pi\) | |||||||
\(662\) | 300.676i | 0.454193i | ||||||||
\(663\) | 132.839 | − | 329.162i | 0.200360 | − | 0.496473i | ||||
\(664\) | 37.4782 | 0.0564431 | ||||||||
\(665\) | 407.764i | 0.613180i | ||||||||
\(666\) | 427.620 | − | 443.513i | 0.642072 | − | 0.665936i | ||||
\(667\) | −40.0878 | −0.0601016 | ||||||||
\(668\) | − | 407.761i | − | 0.610420i | ||||||
\(669\) | −1106.56 | − | 446.571i | −1.65405 | − | 0.667520i | ||||
\(670\) | 193.574 | 0.288916 | ||||||||
\(671\) | 960.254i | 1.43108i | ||||||||
\(672\) | −61.6873 | + | 152.855i | −0.0917966 | + | 0.227463i | ||||
\(673\) | 495.673 | 0.736513 | 0.368256 | − | 0.929724i | \(-0.379955\pi\) | ||||
0.368256 | + | 0.929724i | \(0.379955\pi\) | |||||||
\(674\) | 263.649i | 0.391171i | ||||||||
\(675\) | −55.0554 | − | 123.264i | −0.0815635 | − | 0.182613i | ||||
\(676\) | −66.4143 | −0.0982460 | ||||||||
\(677\) | − | 179.621i | − | 0.265319i | −0.991162 | − | 0.132660i | \(-0.957648\pi\) | ||
0.991162 | − | 0.132660i | \(-0.0423517\pi\) | |||||||
\(678\) | −766.022 | − | 309.142i | −1.12983 | − | 0.455961i | ||||
\(679\) | −1613.86 | −2.37682 | ||||||||
\(680\) | − | 52.6241i | − | 0.0773884i | ||||||
\(681\) | 85.7201 | − | 212.406i | 0.125874 | − | 0.311903i | ||||
\(682\) | 303.495 | 0.445007 | ||||||||
\(683\) | 144.842i | 0.212067i | 0.994363 | + | 0.106034i | \(0.0338151\pi\) | ||||
−0.994363 | + | 0.106034i | \(0.966185\pi\) | |||||||
\(684\) | −243.284 | − | 234.566i | −0.355678 | − | 0.342932i | ||||
\(685\) | −135.697 | −0.198098 | ||||||||
\(686\) | − | 50.2704i | − | 0.0732804i | ||||||
\(687\) | −264.486 | − | 106.738i | −0.384986 | − | 0.155368i | ||||
\(688\) | −167.428 | −0.243354 | ||||||||
\(689\) | 919.802i | 1.33498i | ||||||||
\(690\) | −17.0269 | + | 42.1910i | −0.0246767 | + | 0.0611464i | ||||
\(691\) | −877.963 | −1.27057 | −0.635284 | − | 0.772278i | \(-0.719117\pi\) | ||||
−0.635284 | + | 0.772278i | \(0.719117\pi\) | |||||||
\(692\) | 76.7169i | 0.110863i | ||||||||
\(693\) | 1018.87 | − | 1056.74i | 1.47023 | − | 1.52488i | ||||
\(694\) | 204.965 | 0.295338 | ||||||||
\(695\) | 240.334i | 0.345805i | ||||||||
\(696\) | −65.7733 | − | 26.5439i | −0.0945018 | − | 0.0381379i | ||||
\(697\) | −280.452 | −0.402371 | ||||||||
\(698\) | 307.490i | 0.440530i | ||||||||
\(699\) | 418.101 | − | 1036.01i | 0.598142 | − | 1.48214i | ||||
\(700\) | 97.1289 | 0.138756 | ||||||||
\(701\) | − | 1173.42i | − | 1.67393i | −0.547259 | − | 0.836964i | \(-0.684329\pi\) | ||
0.547259 | − | 0.836964i | \(-0.315671\pi\) | |||||||
\(702\) | −495.767 | + | 221.433i | −0.706221 | + | 0.315432i | ||||
\(703\) | −908.783 | −1.29272 | ||||||||
\(704\) | 134.339i | 0.190823i | ||||||||
\(705\) | −158.293 | − | 63.8819i | −0.224529 | − | 0.0906127i | ||||
\(706\) | −357.466 | −0.506325 | ||||||||
\(707\) | 984.035i | 1.39185i | ||||||||
\(708\) | 78.7403 | − | 195.111i | 0.111215 | − | 0.275580i | ||||
\(709\) | 1123.63 | 1.58481 | 0.792407 | − | 0.609993i | \(-0.208828\pi\) | ||||
0.792407 | + | 0.609993i | \(0.208828\pi\) | |||||||
\(710\) | − | 313.220i | − | 0.441155i | ||||||
\(711\) | 770.408 | + | 742.800i | 1.08356 | + | 1.04473i | ||||
\(712\) | −412.566 | −0.579447 | ||||||||
\(713\) | − | 61.2898i | − | 0.0859604i | ||||||
\(714\) | 317.961 | + | 128.319i | 0.445324 | + | 0.179718i | ||||
\(715\) | 533.944 | 0.746775 | ||||||||
\(716\) | − | 72.9444i | − | 0.101878i | ||||||
\(717\) | 379.120 | − | 939.423i | 0.528759 | − | 1.31021i | ||||
\(718\) | −439.613 | −0.612274 | ||||||||
\(719\) | − | 1040.78i | − | 1.44753i | −0.690044 | − | 0.723767i | \(-0.742409\pi\) | ||
0.690044 | − | 0.723767i | \(-0.257591\pi\) | |||||||
\(720\) | −55.8732 | + | 57.9498i | −0.0776017 | + | 0.0804859i | ||||
\(721\) | −1520.16 | −2.10840 | ||||||||
\(722\) | − | 12.0296i | − | 0.0166615i | ||||||
\(723\) | 355.706 | + | 143.551i | 0.491986 | + | 0.198549i | ||||
\(724\) | 681.395 | 0.941153 | ||||||||
\(725\) | 41.7944i | 0.0576475i | ||||||||
\(726\) | 255.606 | − | 633.365i | 0.352074 | − | 0.872404i | ||||
\(727\) | 501.507 | 0.689831 | 0.344916 | − | 0.938634i | \(-0.387908\pi\) | ||||
0.344916 | + | 0.938634i | \(0.387908\pi\) | |||||||
\(728\) | − | 390.654i | − | 0.536612i | ||||||
\(729\) | −486.512 | + | 542.906i | −0.667370 | + | 0.744727i | ||||
\(730\) | −5.41817 | −0.00742215 | ||||||||
\(731\) | 348.275i | 0.476436i | ||||||||
\(732\) | 318.171 | + | 128.403i | 0.434659 | + | 0.175414i | ||||
\(733\) | −110.721 | −0.151052 | −0.0755261 | − | 0.997144i | \(-0.524064\pi\) | ||||
−0.0755261 | + | 0.997144i | \(0.524064\pi\) | |||||||
\(734\) | 817.514i | 1.11378i | ||||||||
\(735\) | −113.826 | + | 282.050i | −0.154865 | + | 0.383741i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | 1027.92i | 1.39474i | ||||||||
\(738\) | 308.835 | + | 297.768i | 0.418476 | + | 0.403480i | ||||
\(739\) | −637.166 | −0.862200 | −0.431100 | − | 0.902304i | \(-0.641874\pi\) | ||||
−0.431100 | + | 0.902304i | \(0.641874\pi\) | |||||||
\(740\) | 216.471i | 0.292528i | ||||||||
\(741\) | 742.729 | + | 299.741i | 1.00233 | + | 0.404509i | ||||
\(742\) | −888.504 | −1.19745 | ||||||||
\(743\) | 174.168i | 0.234412i | 0.993108 | + | 0.117206i | \(0.0373937\pi\) | ||||
−0.993108 | + | 0.117206i | \(0.962606\pi\) | |||||||
\(744\) | 40.5827 | − | 100.560i | 0.0545467 | − | 0.135161i | ||||
\(745\) | 76.3497 | 0.102483 | ||||||||
\(746\) | 773.809i | 1.03728i | ||||||||
\(747\) | −82.7737 | + | 85.8502i | −0.110808 | + | 0.114927i | ||||
\(748\) | 279.445 | 0.373590 | ||||||||
\(749\) | − | 481.730i | − | 0.643164i | ||||||
\(750\) | 43.9872 | + | 17.7518i | 0.0586496 | + | 0.0236691i | ||||
\(751\) | 1041.90 | 1.38735 | 0.693676 | − | 0.720287i | \(-0.255990\pi\) | ||||
0.693676 | + | 0.720287i | \(0.255990\pi\) | |||||||
\(752\) | 101.784i | 0.135351i | ||||||||
\(753\) | −131.507 | + | 325.861i | −0.174644 | + | 0.432750i | ||||
\(754\) | 168.098 | 0.222941 | ||||||||
\(755\) | − | 344.222i | − | 0.455923i | ||||||
\(756\) | −213.899 | − | 478.898i | −0.282935 | − | 0.633463i | ||||
\(757\) | 1352.49 | 1.78664 | 0.893321 | − | 0.449419i | \(-0.148369\pi\) | ||||
0.893321 | + | 0.449419i | \(0.148369\pi\) | |||||||
\(758\) | − | 249.523i | − | 0.329186i | ||||||
\(759\) | −224.044 | − | 90.4167i | −0.295183 | − | 0.119126i | ||||
\(760\) | 118.742 | 0.156240 | ||||||||
\(761\) | − | 786.105i | − | 1.03299i | −0.856290 | − | 0.516495i | \(-0.827237\pi\) | ||
0.856290 | − | 0.516495i | \(-0.172763\pi\) | |||||||
\(762\) | −145.438 | + | 360.382i | −0.190864 | + | 0.472942i | ||||
\(763\) | −92.6847 | −0.121474 | ||||||||
\(764\) | 374.443i | 0.490108i | ||||||||
\(765\) | 120.544 | + | 116.225i | 0.157574 | + | 0.151928i | ||||
\(766\) | −145.438 | −0.189867 | ||||||||
\(767\) | 498.647i | 0.650126i | ||||||||
\(768\) | 44.5119 | + | 17.9636i | 0.0579582 | + | 0.0233900i | ||||
\(769\) | 273.919 | 0.356202 | 0.178101 | − | 0.984012i | \(-0.443005\pi\) | ||||
0.178101 | + | 0.984012i | \(0.443005\pi\) | |||||||
\(770\) | 515.776i | 0.669839i | ||||||||
\(771\) | 106.861 | − | 264.790i | 0.138600 | − | 0.343438i | ||||
\(772\) | −750.199 | −0.971760 | ||||||||
\(773\) | − | 396.276i | − | 0.512647i | −0.966591 | − | 0.256324i | \(-0.917489\pi\) | ||
0.966591 | − | 0.256324i | \(-0.0825113\pi\) | |||||||
\(774\) | 369.778 | − | 383.522i | 0.477749 | − | 0.495506i | ||||
\(775\) | −63.8990 | −0.0824503 | ||||||||
\(776\) | 469.962i | 0.605622i | ||||||||
\(777\) | −1307.94 | − | 527.843i | −1.68333 | − | 0.679335i | ||||
\(778\) | 319.211 | 0.410297 | ||||||||
\(779\) | − | 632.820i | − | 0.812350i | ||||||
\(780\) | 71.3979 | − | 176.917i | 0.0915358 | − | 0.226817i | ||||
\(781\) | 1663.27 | 2.12966 | ||||||||
\(782\) | − | 56.4331i | − | 0.0721650i | ||||||
\(783\) | 206.069 | − | 92.0403i | 0.263179 | − | 0.117548i | ||||
\(784\) | 181.361 | 0.231328 | ||||||||
\(785\) | 152.802i | 0.194652i | ||||||||
\(786\) | 542.759 | + | 219.040i | 0.690533 | + | 0.278677i | ||||
\(787\) | −755.682 | −0.960206 | −0.480103 | − | 0.877212i | \(-0.659401\pi\) | ||||
−0.480103 | + | 0.877212i | \(0.659401\pi\) | |||||||
\(788\) | 398.957i | 0.506290i | ||||||||
\(789\) | 212.797 | − | 527.291i | 0.269705 | − | 0.668302i | ||||
\(790\) | −376.022 | −0.475977 | ||||||||
\(791\) | 1891.12i | 2.39079i | ||||||||
\(792\) | −307.726 | − | 296.699i | −0.388543 | − | 0.374620i | ||||
\(793\) | −813.153 | −1.02541 | ||||||||
\(794\) | 378.234i | 0.476365i | ||||||||
\(795\) | −402.381 | − | 162.388i | −0.506139 | − | 0.204261i | ||||
\(796\) | −662.177 | −0.831880 | ||||||||
\(797\) | − | 396.840i | − | 0.497917i | −0.968514 | − | 0.248958i | \(-0.919912\pi\) | ||
0.968514 | − | 0.248958i | \(-0.0800883\pi\) | |||||||
\(798\) | −289.542 | + | 717.457i | −0.362835 | + | 0.899068i | ||||
\(799\) | 211.727 | 0.264989 | ||||||||
\(800\) | − | 28.2843i | − | 0.0353553i | ||||||
\(801\) | 911.187 | − | 945.053i | 1.13756 | − | 1.17984i | ||||
\(802\) | −623.413 | −0.777323 | ||||||||
\(803\) | − | 28.7716i | − | 0.0358302i | ||||||
\(804\) | 340.591 | + | 137.451i | 0.423621 | + | 0.170960i | ||||
\(805\) | 104.159 | 0.129390 | ||||||||
\(806\) | 257.002i | 0.318862i | ||||||||
\(807\) | −49.5783 | + | 122.850i | −0.0614353 | + | 0.152230i | ||||
\(808\) | 286.554 | 0.354647 | ||||||||
\(809\) | 902.391i | 1.11544i | 0.830029 | + | 0.557720i | \(0.188324\pi\) | ||||
−0.830029 | + | 0.557720i | \(0.811676\pi\) | |||||||
\(810\) | −9.34327 | − | 255.974i | −0.0115349 | − | 0.316017i | ||||
\(811\) | 137.716 | 0.169810 | 0.0849049 | − | 0.996389i | \(-0.472941\pi\) | ||||
0.0849049 | + | 0.996389i | \(0.472941\pi\) | |||||||
\(812\) | 162.378i | 0.199973i | ||||||||
\(813\) | −552.283 | − | 222.884i | −0.679315 | − | 0.274149i | ||||
\(814\) | −1149.51 | −1.41217 | ||||||||
\(815\) | 359.569i | 0.441188i | ||||||||
\(816\) | 37.3669 | − | 92.5915i | 0.0457928 | − | 0.113470i | ||||
\(817\) | −785.856 | −0.961881 | ||||||||
\(818\) | 88.7741i | 0.108526i | ||||||||
\(819\) | 894.858 | + | 862.791i | 1.09262 | + | 1.05347i | ||||
\(820\) | −150.737 | −0.183826 | ||||||||
\(821\) | − | 69.2262i | − | 0.0843194i | −0.999111 | − | 0.0421597i | \(-0.986576\pi\) | ||
0.999111 | − | 0.0421597i | \(-0.0134238\pi\) | |||||||
\(822\) | −238.758 | − | 96.3548i | −0.290460 | − | 0.117220i | ||||
\(823\) | 850.393 | 1.03328 | 0.516642 | − | 0.856201i | \(-0.327182\pi\) | ||||
0.516642 | + | 0.856201i | \(0.327182\pi\) | |||||||
\(824\) | 442.675i | 0.537227i | ||||||||
\(825\) | −94.2659 | + | 233.582i | −0.114262 | + | 0.283129i | ||||
\(826\) | −481.680 | −0.583147 | ||||||||
\(827\) | − | 1439.96i | − | 1.74118i | −0.492006 | − | 0.870592i | \(-0.663736\pi\) | ||
0.492006 | − | 0.870592i | \(-0.336264\pi\) | |||||||
\(828\) | −59.9173 | + | 62.1443i | −0.0723639 | + | 0.0750535i | ||||
\(829\) | 782.251 | 0.943608 | 0.471804 | − | 0.881704i | \(-0.343603\pi\) | ||||
0.471804 | + | 0.881704i | \(0.343603\pi\) | |||||||
\(830\) | − | 41.9019i | − | 0.0504842i | ||||||
\(831\) | 1437.12 | + | 579.974i | 1.72938 | + | 0.697923i | ||||
\(832\) | −113.760 | −0.136730 | ||||||||
\(833\) | − | 377.258i | − | 0.452891i | ||||||
\(834\) | −170.655 | + | 422.866i | −0.204622 | + | 0.507033i | ||||
\(835\) | −455.890 | −0.545976 | ||||||||
\(836\) | 630.548i | 0.754244i | ||||||||
\(837\) | 140.719 | + | 315.057i | 0.168123 | + | 0.376412i | ||||
\(838\) | −959.143 | −1.14456 | ||||||||
\(839\) | 249.787i | 0.297720i | 0.988858 | + | 0.148860i | \(0.0475604\pi\) | ||||
−0.988858 | + | 0.148860i | \(0.952440\pi\) | |||||||
\(840\) | 170.897 | + | 68.9685i | 0.203449 | + | 0.0821054i | ||||
\(841\) | 771.129 | 0.916919 | ||||||||
\(842\) | 148.425i | 0.176277i | ||||||||
\(843\) | 296.168 | − | 733.874i | 0.351326 | − | 0.870550i | ||||
\(844\) | 655.246 | 0.776358 | ||||||||
\(845\) | 74.2535i | 0.0878739i | ||||||||
\(846\) | −233.154 | − | 224.799i | −0.275596 | − | 0.265720i | ||||
\(847\) | −1563.62 | −1.84607 | ||||||||
\(848\) | 258.735i | 0.305113i | ||||||||
\(849\) | 279.711 | + | 112.882i | 0.329460 | + | 0.132959i | ||||
\(850\) | −58.8355 | −0.0692183 | ||||||||
\(851\) | 232.139i | 0.272784i | ||||||||
\(852\) | 222.409 | − | 551.107i | 0.261043 | − | 0.646839i | ||||
\(853\) | 213.094 | 0.249817 | 0.124909 | − | 0.992168i | \(-0.460136\pi\) | ||||
0.124909 | + | 0.992168i | \(0.460136\pi\) | |||||||
\(854\) | − | 785.484i | − | 0.919771i | ||||||
\(855\) | −262.252 | + | 271.999i | −0.306728 | + | 0.318128i | ||||
\(856\) | −140.281 | −0.163880 | ||||||||
\(857\) | 347.089i | 0.405005i | 0.979282 | + | 0.202503i | \(0.0649075\pi\) | ||||
−0.979282 | + | 0.202503i | \(0.935093\pi\) | |||||||
\(858\) | 939.468 | + | 379.139i | 1.09495 | + | 0.441886i | ||||
\(859\) | −629.153 | −0.732425 | −0.366212 | − | 0.930531i | \(-0.619346\pi\) | ||||
−0.366212 | + | 0.930531i | \(0.619346\pi\) | |||||||
\(860\) | 187.190i | 0.217663i | ||||||||
\(861\) | 367.558 | − | 910.772i | 0.426896 | − | 1.05781i | ||||
\(862\) | 219.642 | 0.254805 | ||||||||
\(863\) | 434.058i | 0.502964i | 0.967862 | + | 0.251482i | \(0.0809179\pi\) | ||||
−0.967862 | + | 0.251482i | \(0.919082\pi\) | |||||||
\(864\) | −139.457 | + | 62.2880i | −0.161408 | + | 0.0720926i | ||||
\(865\) | 85.7721 | 0.0991585 | ||||||||
\(866\) | − | 874.395i | − | 1.00969i | ||||||
\(867\) | 611.392 | + | 246.738i | 0.705181 | + | 0.284588i | ||||
\(868\) | −248.258 | −0.286011 | ||||||||
\(869\) | − | 1996.76i | − | 2.29777i | ||||||
\(870\) | −29.6770 | + | 73.5368i | −0.0341115 | + | 0.0845250i | ||||
\(871\) | −870.453 | −0.999372 | ||||||||
\(872\) | 26.9901i | 0.0309519i | ||||||||
\(873\) | −1076.53 | − | 1037.95i | −1.23314 | − | 1.18895i | ||||
\(874\) | 127.337 | 0.145695 | ||||||||
\(875\) | − | 108.593i | − | 0.124107i | ||||||
\(876\) | −9.53320 | − | 3.84729i | −0.0108826 | − | 0.00439188i | ||||
\(877\) | −1239.84 | −1.41373 | −0.706864 | − | 0.707350i | \(-0.749891\pi\) | ||||
−0.706864 | + | 0.707350i | \(0.749891\pi\) | |||||||
\(878\) | − | 146.118i | − | 0.166422i | ||||||
\(879\) | 375.851 | − | 931.322i | 0.427589 | − | 1.05952i | ||||
\(880\) | 150.196 | 0.170677 | ||||||||
\(881\) | − | 1441.46i | − | 1.63617i | −0.575100 | − | 0.818083i | \(-0.695037\pi\) | ||
0.575100 | − | 0.818083i | \(-0.304963\pi\) | |||||||
\(882\) | −400.551 | + | 415.438i | −0.454139 | + | 0.471018i | ||||
\(883\) | −1682.05 | −1.90493 | −0.952464 | − | 0.304652i | \(-0.901460\pi\) | ||||
−0.952464 | + | 0.304652i | \(0.901460\pi\) | |||||||
\(884\) | 236.637i | 0.267689i | ||||||||
\(885\) | −218.140 | − | 88.0343i | −0.246486 | − | 0.0994738i | ||||
\(886\) | −269.401 | −0.304065 | ||||||||
\(887\) | − | 65.3052i | − | 0.0736249i | −0.999322 | − | 0.0368124i | \(-0.988280\pi\) | ||
0.999322 | − | 0.0368124i | \(-0.0117204\pi\) | |||||||
\(888\) | −153.710 | + | 380.878i | −0.173097 | + | 0.428916i | ||||
\(889\) | 889.692 | 1.00078 | ||||||||
\(890\) | 461.263i | 0.518273i | ||||||||
\(891\) | 1359.28 | − | 49.6148i | 1.52556 | − | 0.0556844i | ||||
\(892\) | 795.514 | 0.891832 | ||||||||
\(893\) | 477.745i | 0.534989i | ||||||||
\(894\) | 134.336 | + | 54.2137i | 0.150264 | + | 0.0606418i | ||||
\(895\) | −81.5543 | −0.0911221 | ||||||||
\(896\) | − | 109.889i | − | 0.122644i | ||||||
\(897\) | 76.5658 | − | 189.722i | 0.0853576 | − | 0.211508i | ||||
\(898\) | 3.04859 | 0.00339487 | ||||||||
\(899\) | − | 106.825i | − | 0.118826i | ||||||
\(900\) | 64.7899 | + | 62.4682i | 0.0719888 | + | 0.0694091i | ||||
\(901\) | 538.209 | 0.597346 | ||||||||
\(902\) | − | 800.446i | − | 0.887412i | ||||||
\(903\) | −1131.03 | − | 456.445i | −1.25252 | − | 0.505476i | ||||
\(904\) | 550.700 | 0.609181 | ||||||||
\(905\) | − | 761.823i | − | 0.841793i | ||||||
\(906\) | 244.422 | − | 605.654i | 0.269782 | − | 0.668493i | ||||
\(907\) | −951.333 | −1.04888 | −0.524439 | − | 0.851448i | \(-0.675725\pi\) | ||||
−0.524439 | + | 0.851448i | \(0.675725\pi\) | |||||||
\(908\) | 152.701i | 0.168172i | ||||||||
\(909\) | −632.879 | + | 656.401i | −0.696237 | + | 0.722113i | ||||
\(910\) | −436.764 | −0.479960 | ||||||||
\(911\) | − | 381.220i | − | 0.418463i | −0.977866 | − | 0.209231i | \(-0.932904\pi\) | ||
0.977866 | − | 0.209231i | \(-0.0670962\pi\) | |||||||
\(912\) | 208.926 | + | 84.3156i | 0.229085 | + | 0.0924513i | ||||
\(913\) | 222.508 | 0.243711 | ||||||||
\(914\) | − | 567.012i | − | 0.620363i | ||||||
\(915\) | 143.559 | − | 355.726i | 0.156895 | − | 0.388771i | ||||
\(916\) | 190.141 | 0.207578 | ||||||||
\(917\) | − | 1339.94i | − | 1.46122i | ||||||
\(918\) | 129.568 | + | 290.091i | 0.141142 | + | 0.316003i | ||||
\(919\) | 1499.36 | 1.63151 | 0.815757 | − | 0.578395i | \(-0.196321\pi\) | ||||
0.815757 | + | 0.578395i | \(0.196321\pi\) | |||||||
\(920\) | − | 30.3315i | − | 0.0329690i | ||||||
\(921\) | −759.970 | − | 306.699i | −0.825158 | − | 0.333007i | ||||
\(922\) | −589.538 | −0.639413 | ||||||||
\(923\) | 1408.47i | 1.52597i | ||||||||
\(924\) | −366.238 | + | 907.501i | −0.396361 | + | 0.982144i | ||||
\(925\) | 242.022 | 0.261645 | ||||||||
\(926\) | − | 299.776i | − | 0.323732i | ||||||
\(927\) | −1014.02 | − | 977.685i | −1.09388 | − | 1.05468i | ||||
\(928\) | 47.2850 | 0.0509536 | ||||||||
\(929\) | − | 925.130i | − | 0.995834i | −0.867225 | − | 0.497917i | \(-0.834098\pi\) | ||
0.867225 | − | 0.497917i | \(-0.165902\pi\) | |||||||
\(930\) | −112.429 | − | 45.3729i | −0.120892 | − | 0.0487880i | ||||
\(931\) | 851.255 | 0.914345 | ||||||||
\(932\) | 744.799i | 0.799141i | ||||||||
\(933\) | −408.864 | + | 1013.12i | −0.438225 | + | 1.08588i | ||||
\(934\) | −758.064 | −0.811632 | ||||||||
\(935\) | − | 312.429i | − | 0.334149i | ||||||
\(936\) | 251.248 | − | 260.586i | 0.268427 | − | 0.278403i | ||||
\(937\) | 1474.31 | 1.57344 | 0.786718 | − | 0.617313i | \(-0.211779\pi\) | ||||
0.786718 | + | 0.617313i | \(0.211779\pi\) | |||||||
\(938\) | − | 840.835i | − | 0.896412i | ||||||
\(939\) | −1388.61 | − | 560.399i | −1.47882 | − | 0.596805i | ||||
\(940\) | 113.798 | 0.121062 | ||||||||
\(941\) | − | 1018.88i | − | 1.08276i | −0.840777 | − | 0.541381i | \(-0.817902\pi\) | ||
0.840777 | − | 0.541381i | \(-0.182098\pi\) | |||||||
\(942\) | −108.500 | + | 268.853i | −0.115181 | + | 0.285407i | ||||
\(943\) | −161.647 | −0.171418 | ||||||||
\(944\) | 140.267i | 0.148588i | ||||||||
\(945\) | −535.425 | + | 239.146i | −0.566587 | + | 0.253065i | ||||
\(946\) | −994.019 | −1.05076 | ||||||||
\(947\) | 741.719i | 0.783230i | 0.920129 | + | 0.391615i | \(0.128084\pi\) | ||||
−0.920129 | + | 0.391615i | \(0.871916\pi\) | |||||||
\(948\) | −661.607 | − | 267.003i | −0.697897 | − | 0.281649i | ||||
\(949\) | 24.3641 | 0.0256735 | ||||||||
\(950\) | − | 132.758i | − | 0.139745i | ||||||
\(951\) | −683.933 | + | 1694.72i | −0.719172 | + | 1.78204i | ||||
\(952\) | −228.585 | −0.240111 | ||||||||
\(953\) | − | 184.758i | − | 0.193870i | −0.995291 | − | 0.0969352i | \(-0.969096\pi\) | ||
0.995291 | − | 0.0969352i | \(-0.0309039\pi\) | |||||||
\(954\) | −592.677 | − | 571.439i | −0.621255 | − | 0.598992i | ||||
\(955\) | 418.640 | 0.438366 | ||||||||
\(956\) | 675.359i | 0.706443i | ||||||||
\(957\) | −390.496 | − | 157.592i | −0.408042 | − | 0.164672i | ||||
\(958\) | −203.304 | −0.212217 | ||||||||
\(959\) | 589.433i | 0.614633i | ||||||||
\(960\) | 20.0839 | − | 49.7658i | 0.0209207 | − | 0.0518394i | ||||
\(961\) | −797.677 | −0.830049 | ||||||||
\(962\) | − | 973.414i | − | 1.01186i | ||||||
\(963\) | 309.823 | − | 321.338i | 0.321727 | − | 0.333685i | ||||
\(964\) | −255.720 | −0.265270 | ||||||||
\(965\) | 838.748i | 0.869169i | ||||||||
\(966\) | 183.267 | + | 73.9605i | 0.189717 | + | 0.0765637i | ||||
\(967\) | 615.373 | 0.636373 | 0.318187 | − | 0.948028i | \(-0.396926\pi\) | ||||
0.318187 | + | 0.948028i | \(0.396926\pi\) | |||||||
\(968\) | 455.332i | 0.470384i | ||||||||
\(969\) | 175.389 | − | 434.597i | 0.181000 | − | 0.448500i | ||||
\(970\) | 525.434 | 0.541684 | ||||||||
\(971\) | − | 22.2504i | − | 0.0229149i | −0.999934 | − | 0.0114574i | \(-0.996353\pi\) | ||
0.999934 | − | 0.0114574i | \(-0.00364710\pi\) | |||||||
\(972\) | 165.321 | − | 457.018i | 0.170083 | − | 0.470183i | ||||
\(973\) | 1043.95 | 1.07292 | ||||||||
\(974\) | − | 642.723i | − | 0.659880i | ||||||
\(975\) | −197.799 | − | 79.8253i | −0.202871 | − | 0.0818721i | ||||
\(976\) | −228.736 | −0.234360 | ||||||||
\(977\) | 981.189i | 1.00429i | 0.864784 | + | 0.502144i | \(0.167455\pi\) | ||||
−0.864784 | + | 0.502144i | \(0.832545\pi\) | |||||||
\(978\) | −255.320 | + | 632.657i | −0.261063 | + | 0.646888i | ||||
\(979\) | −2449.41 | −2.50195 | ||||||||
\(980\) | − | 202.768i | − | 0.206906i | ||||||
\(981\) | −61.8254 | − | 59.6098i | −0.0630228 | − | 0.0607644i | ||||
\(982\) | −586.111 | −0.596854 | ||||||||
\(983\) | − | 1186.61i | − | 1.20713i | −0.797312 | − | 0.603567i | \(-0.793746\pi\) | ||
0.797312 | − | 0.603567i | \(-0.206254\pi\) | |||||||
\(984\) | −265.220 | − | 107.034i | −0.269532 | − | 0.108774i | ||||
\(985\) | 446.047 | 0.452840 | ||||||||
\(986\) | − | 98.3598i | − | 0.0997564i | ||||||
\(987\) | −277.486 | + | 687.584i | −0.281141 | + | 0.696640i | ||||
\(988\) | −533.954 | −0.540439 | ||||||||
\(989\) | 200.739i | 0.202972i | ||||||||
\(990\) | −331.719 | + | 344.048i | −0.335070 | + | 0.347524i | ||||
\(991\) | −579.495 | −0.584758 | −0.292379 | − | 0.956303i | \(-0.594447\pi\) | ||||
−0.292379 | + | 0.956303i | \(0.594447\pi\) | |||||||
\(992\) | 72.2935i | 0.0728765i | ||||||||
\(993\) | 591.480 | + | 238.702i | 0.595649 | + | 0.240385i | ||||
\(994\) | −1360.55 | −1.36876 | ||||||||
\(995\) | 740.336i | 0.744056i | ||||||||
\(996\) | 29.7534 | − | 73.7259i | 0.0298729 | − | 0.0740220i | ||||
\(997\) | −1032.17 | −1.03528 | −0.517640 | − | 0.855599i | \(-0.673189\pi\) | ||||
−0.517640 | + | 0.855599i | \(0.673189\pi\) | |||||||
\(998\) | − | 577.271i | − | 0.578428i | ||||||
\(999\) | −532.984 | − | 1193.30i | −0.533517 | − | 1.19449i |
(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 | 690.3.g.a.461.2 | yes | 56 | |
3.2 | odd | 2 | inner | 690.3.g.a.461.1 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.g.a.461.1 | ✓ | 56 | 3.2 | odd | 2 | inner | |
690.3.g.a.461.2 | yes | 56 | 1.1 | even | 1 | trivial |