Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(122,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.122");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.b (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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 29x^{6} + 282x^{4} + 1061x^{2} + 1331 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 122.4 | ||
Root | \(-1.65816i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.122 |
Dual form | 363.3.b.m.122.5 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.65816i | − | 0.829080i | −0.910031 | − | 0.414540i | \(-0.863943\pi\) | ||
0.910031 | − | 0.414540i | \(-0.136057\pi\) | |||||||
\(3\) | 2.31624 | + | 1.90658i | 0.772079 | + | 0.635527i | ||||
\(4\) | 1.25051 | 0.312627 | ||||||||
\(5\) | − | 0.698503i | − | 0.139701i | −0.997557 | − | 0.0698503i | \(-0.977748\pi\) | ||
0.997557 | − | 0.0698503i | \(-0.0222522\pi\) | |||||||
\(6\) | 3.16141 | − | 3.84069i | 0.526902 | − | 0.640115i | ||||
\(7\) | 2.60911 | 0.372730 | 0.186365 | − | 0.982481i | \(-0.440329\pi\) | ||||
0.186365 | + | 0.982481i | \(0.440329\pi\) | |||||||
\(8\) | − | 8.70618i | − | 1.08827i | ||||||
\(9\) | 1.72990 | + | 8.83218i | 0.192211 | + | 0.981354i | ||||
\(10\) | −1.15823 | −0.115823 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.89647 | + | 2.38419i | 0.241372 | + | 0.198683i | ||||
\(13\) | 17.1169 | 1.31669 | 0.658344 | − | 0.752717i | \(-0.271257\pi\) | ||||
0.658344 | + | 0.752717i | \(0.271257\pi\) | |||||||
\(14\) | − | 4.32632i | − | 0.309023i | ||||||
\(15\) | 1.33175 | − | 1.61790i | 0.0887835 | − | 0.107860i | ||||
\(16\) | −9.43421 | −0.589638 | ||||||||
\(17\) | − | 16.1125i | − | 0.947797i | −0.880579 | − | 0.473898i | \(-0.842846\pi\) | ||
0.880579 | − | 0.473898i | \(-0.157154\pi\) | |||||||
\(18\) | 14.6452 | − | 2.86845i | 0.813620 | − | 0.159359i | ||||
\(19\) | −15.9263 | −0.838229 | −0.419114 | − | 0.907933i | \(-0.637659\pi\) | ||||
−0.419114 | + | 0.907933i | \(0.637659\pi\) | |||||||
\(20\) | − | 0.873483i | − | 0.0436742i | ||||||
\(21\) | 6.04332 | + | 4.97448i | 0.287777 | + | 0.236880i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.1295i | 1.00563i | 0.864395 | + | 0.502814i | \(0.167702\pi\) | ||||
−0.864395 | + | 0.502814i | \(0.832298\pi\) | |||||||
\(24\) | 16.5990 | − | 20.1656i | 0.691626 | − | 0.840232i | ||||
\(25\) | 24.5121 | 0.980484 | ||||||||
\(26\) | − | 28.3826i | − | 1.09164i | ||||||
\(27\) | −12.8324 | + | 23.7556i | −0.475274 | + | 0.879838i | ||||
\(28\) | 3.26271 | 0.116525 | ||||||||
\(29\) | − | 5.36592i | − | 0.185032i | −0.995711 | − | 0.0925158i | \(-0.970509\pi\) | ||
0.995711 | − | 0.0925158i | \(-0.0294909\pi\) | |||||||
\(30\) | −2.68273 | − | 2.20826i | −0.0894245 | − | 0.0736086i | ||||
\(31\) | −4.06259 | −0.131051 | −0.0655257 | − | 0.997851i | \(-0.520872\pi\) | ||||
−0.0655257 | + | 0.997851i | \(0.520872\pi\) | |||||||
\(32\) | − | 19.1813i | − | 0.599415i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −26.7172 | −0.785799 | ||||||||
\(35\) | − | 1.82247i | − | 0.0520706i | ||||||
\(36\) | 2.16325 | + | 11.0447i | 0.0600904 | + | 0.306797i | ||||
\(37\) | 63.5312 | 1.71706 | 0.858529 | − | 0.512765i | \(-0.171379\pi\) | ||||
0.858529 | + | 0.512765i | \(0.171379\pi\) | |||||||
\(38\) | 26.4084i | 0.694958i | ||||||||
\(39\) | 39.6469 | + | 32.6348i | 1.01659 | + | 0.836790i | ||||
\(40\) | −6.08130 | −0.152032 | ||||||||
\(41\) | 67.4378i | 1.64482i | 0.568893 | + | 0.822412i | \(0.307372\pi\) | ||||
−0.568893 | + | 0.822412i | \(0.692628\pi\) | |||||||
\(42\) | 8.24848 | − | 10.0208i | 0.196392 | − | 0.238590i | ||||
\(43\) | −22.6622 | −0.527028 | −0.263514 | − | 0.964656i | \(-0.584882\pi\) | ||||
−0.263514 | + | 0.964656i | \(0.584882\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.16931 | − | 1.20834i | 0.137096 | − | 0.0268521i | ||||
\(46\) | 38.3523 | 0.833746 | ||||||||
\(47\) | − | 73.8208i | − | 1.57066i | −0.619080 | − | 0.785328i | \(-0.712494\pi\) | ||
0.619080 | − | 0.785328i | \(-0.287506\pi\) | |||||||
\(48\) | −21.8519 | − | 17.9871i | −0.455247 | − | 0.374731i | ||||
\(49\) | −42.1925 | −0.861072 | ||||||||
\(50\) | − | 40.6450i | − | 0.812899i | ||||||
\(51\) | 30.7199 | − | 37.3205i | 0.602350 | − | 0.731774i | ||||
\(52\) | 21.4048 | 0.411632 | ||||||||
\(53\) | − | 42.8512i | − | 0.808513i | −0.914646 | − | 0.404256i | \(-0.867530\pi\) | ||
0.914646 | − | 0.404256i | \(-0.132470\pi\) | |||||||
\(54\) | 39.3906 | + | 21.2782i | 0.729456 | + | 0.394040i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 22.7154i | − | 0.405632i | ||||||
\(57\) | −36.8892 | − | 30.3649i | −0.647179 | − | 0.532717i | ||||
\(58\) | −8.89755 | −0.153406 | ||||||||
\(59\) | 28.7381i | 0.487086i | 0.969890 | + | 0.243543i | \(0.0783098\pi\) | ||||
−0.969890 | + | 0.243543i | \(0.921690\pi\) | |||||||
\(60\) | 1.66537 | − | 2.02319i | 0.0277561 | − | 0.0337199i | ||||
\(61\) | −46.3013 | −0.759037 | −0.379519 | − | 0.925184i | \(-0.623910\pi\) | ||||
−0.379519 | + | 0.925184i | \(0.623910\pi\) | |||||||
\(62\) | 6.73643i | 0.108652i | ||||||||
\(63\) | 4.51350 | + | 23.0441i | 0.0716429 | + | 0.365780i | ||||
\(64\) | −69.5425 | −1.08660 | ||||||||
\(65\) | − | 11.9562i | − | 0.183942i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −77.2821 | −1.15346 | −0.576732 | − | 0.816933i | \(-0.695672\pi\) | ||||
−0.576732 | + | 0.816933i | \(0.695672\pi\) | |||||||
\(68\) | − | 20.1489i | − | 0.296307i | ||||||
\(69\) | −44.0982 | + | 53.5733i | −0.639104 | + | 0.776424i | ||||
\(70\) | −3.02195 | −0.0431707 | ||||||||
\(71\) | − | 41.2629i | − | 0.581167i | −0.956850 | − | 0.290584i | \(-0.906151\pi\) | ||
0.956850 | − | 0.290584i | \(-0.0938494\pi\) | |||||||
\(72\) | 76.8946 | − | 15.0608i | 1.06798 | − | 0.209178i | ||||
\(73\) | −56.7729 | −0.777711 | −0.388856 | − | 0.921299i | \(-0.627129\pi\) | ||||
−0.388856 | + | 0.921299i | \(0.627129\pi\) | |||||||
\(74\) | − | 105.345i | − | 1.42358i | ||||||
\(75\) | 56.7758 | + | 46.7343i | 0.757011 | + | 0.623124i | ||||
\(76\) | −19.9160 | −0.262053 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 54.1137 | − | 65.7409i | 0.693766 | − | 0.842831i | ||||
\(79\) | −50.9253 | −0.644624 | −0.322312 | − | 0.946633i | \(-0.604460\pi\) | ||||
−0.322312 | + | 0.946633i | \(0.604460\pi\) | |||||||
\(80\) | 6.58983i | 0.0823728i | ||||||||
\(81\) | −75.0149 | + | 30.5576i | −0.926110 | + | 0.377255i | ||||
\(82\) | 111.823 | 1.36369 | ||||||||
\(83\) | 59.2098i | 0.713371i | 0.934225 | + | 0.356685i | \(0.116093\pi\) | ||||
−0.934225 | + | 0.356685i | \(0.883907\pi\) | |||||||
\(84\) | 7.55721 | + | 6.22062i | 0.0899668 | + | 0.0740550i | ||||
\(85\) | −11.2547 | −0.132408 | ||||||||
\(86\) | 37.5776i | 0.436948i | ||||||||
\(87\) | 10.2306 | − | 12.4287i | 0.117593 | − | 0.142859i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 38.1909i | − | 0.429112i | −0.976712 | − | 0.214556i | \(-0.931170\pi\) | ||
0.976712 | − | 0.214556i | \(-0.0688304\pi\) | |||||||
\(90\) | −2.00362 | − | 10.2297i | −0.0222625 | − | 0.113663i | ||||
\(91\) | 44.6600 | 0.490769 | ||||||||
\(92\) | 28.9235i | 0.314386i | ||||||||
\(93\) | −9.40993 | − | 7.74566i | −0.101182 | − | 0.0832867i | ||||
\(94\) | −122.407 | −1.30220 | ||||||||
\(95\) | 11.1246i | 0.117101i | ||||||||
\(96\) | 36.5707 | − | 44.4284i | 0.380945 | − | 0.462796i | ||||
\(97\) | 16.2924 | 0.167963 | 0.0839815 | − | 0.996467i | \(-0.473236\pi\) | ||||
0.0839815 | + | 0.996467i | \(0.473236\pi\) | |||||||
\(98\) | 69.9620i | 0.713898i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 30.6525 | 0.306525 | ||||||||
\(101\) | 104.194i | 1.03163i | 0.856701 | + | 0.515814i | \(0.172510\pi\) | ||||
−0.856701 | + | 0.515814i | \(0.827490\pi\) | |||||||
\(102\) | −61.8833 | − | 50.9384i | −0.606699 | − | 0.499397i | ||||
\(103\) | 54.4065 | 0.528219 | 0.264109 | − | 0.964493i | \(-0.414922\pi\) | ||||
0.264109 | + | 0.964493i | \(0.414922\pi\) | |||||||
\(104\) | − | 149.023i | − | 1.43291i | ||||||
\(105\) | 3.47469 | − | 4.22128i | 0.0330923 | − | 0.0402026i | ||||
\(106\) | −71.0541 | −0.670321 | ||||||||
\(107\) | 28.4068i | 0.265484i | 0.991151 | + | 0.132742i | \(0.0423782\pi\) | ||||
−0.991151 | + | 0.132742i | \(0.957622\pi\) | |||||||
\(108\) | −16.0470 | + | 29.7066i | −0.148583 | + | 0.275061i | ||||
\(109\) | −41.2540 | −0.378477 | −0.189238 | − | 0.981931i | \(-0.560602\pi\) | ||||
−0.189238 | + | 0.981931i | \(0.560602\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 147.153 | + | 121.127i | 1.32570 | + | 1.09124i | ||||
\(112\) | −24.6149 | −0.219776 | ||||||||
\(113\) | 145.178i | 1.28476i | 0.766386 | + | 0.642381i | \(0.222053\pi\) | ||||
−0.766386 | + | 0.642381i | \(0.777947\pi\) | |||||||
\(114\) | −50.3498 | + | 61.1681i | −0.441665 | + | 0.536563i | ||||
\(115\) | 16.1560 | 0.140487 | ||||||||
\(116\) | − | 6.71012i | − | 0.0578458i | ||||||
\(117\) | 29.6106 | + | 151.180i | 0.253082 | + | 1.29214i | ||||
\(118\) | 47.6524 | 0.403834 | ||||||||
\(119\) | − | 42.0394i | − | 0.353272i | ||||||
\(120\) | −14.0857 | − | 11.5945i | −0.117381 | − | 0.0966207i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 76.7749i | 0.629303i | ||||||||
\(123\) | −128.576 | + | 156.202i | −1.04533 | + | 1.26993i | ||||
\(124\) | −5.08030 | −0.0409702 | ||||||||
\(125\) | − | 34.5844i | − | 0.276675i | ||||||
\(126\) | 38.2109 | − | 7.48411i | 0.303261 | − | 0.0593977i | ||||
\(127\) | −182.781 | −1.43922 | −0.719612 | − | 0.694376i | \(-0.755680\pi\) | ||||
−0.719612 | + | 0.694376i | \(0.755680\pi\) | |||||||
\(128\) | 38.5873i | 0.301464i | ||||||||
\(129\) | −52.4910 | − | 43.2073i | −0.406907 | − | 0.334940i | ||||
\(130\) | −19.8254 | −0.152503 | ||||||||
\(131\) | − | 84.5109i | − | 0.645121i | −0.946549 | − | 0.322561i | \(-0.895456\pi\) | ||
0.946549 | − | 0.322561i | \(-0.104544\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −41.5536 | −0.312433 | ||||||||
\(134\) | 128.146i | 0.956314i | ||||||||
\(135\) | 16.5934 | + | 8.96348i | 0.122914 | + | 0.0663961i | ||||
\(136\) | −140.279 | −1.03146 | ||||||||
\(137\) | 204.373i | 1.49177i | 0.666075 | + | 0.745885i | \(0.267973\pi\) | ||||
−0.666075 | + | 0.745885i | \(0.732027\pi\) | |||||||
\(138\) | 88.8330 | + | 73.1218i | 0.643718 | + | 0.529868i | ||||
\(139\) | −50.2414 | −0.361449 | −0.180724 | − | 0.983534i | \(-0.557844\pi\) | ||||
−0.180724 | + | 0.983534i | \(0.557844\pi\) | |||||||
\(140\) | − | 2.27901i | − | 0.0162787i | ||||||
\(141\) | 140.745 | − | 170.987i | 0.998194 | − | 1.21267i | ||||
\(142\) | −68.4204 | −0.481834 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −16.3203 | − | 83.3246i | −0.113335 | − | 0.578643i | ||||
\(145\) | −3.74811 | −0.0258490 | ||||||||
\(146\) | 94.1385i | 0.644785i | ||||||||
\(147\) | −97.7279 | − | 80.4435i | −0.664816 | − | 0.547235i | ||||
\(148\) | 79.4461 | 0.536798 | ||||||||
\(149\) | 157.402i | 1.05639i | 0.849123 | + | 0.528195i | \(0.177131\pi\) | ||||
−0.849123 | + | 0.528195i | \(0.822869\pi\) | |||||||
\(150\) | 77.4929 | − | 94.1433i | 0.516619 | − | 0.627622i | ||||
\(151\) | −171.381 | −1.13498 | −0.567488 | − | 0.823382i | \(-0.692085\pi\) | ||||
−0.567488 | + | 0.823382i | \(0.692085\pi\) | |||||||
\(152\) | 138.658i | 0.912221i | ||||||||
\(153\) | 142.309 | − | 27.8731i | 0.930124 | − | 0.182177i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.83774i | 0.0183080i | ||||||||
\(156\) | 49.5787 | + | 40.8101i | 0.317812 | + | 0.261603i | ||||
\(157\) | −65.3379 | −0.416165 | −0.208083 | − | 0.978111i | \(-0.566722\pi\) | ||||
−0.208083 | + | 0.978111i | \(0.566722\pi\) | |||||||
\(158\) | 84.4423i | 0.534445i | ||||||||
\(159\) | 81.6992 | − | 99.2534i | 0.513831 | − | 0.624235i | ||||
\(160\) | −13.3982 | −0.0837387 | ||||||||
\(161\) | 60.3473i | 0.374828i | ||||||||
\(162\) | 50.6694 | + | 124.387i | 0.312774 | + | 0.767819i | ||||
\(163\) | −15.4384 | −0.0947144 | −0.0473572 | − | 0.998878i | \(-0.515080\pi\) | ||||
−0.0473572 | + | 0.998878i | \(0.515080\pi\) | |||||||
\(164\) | 84.3314i | 0.514216i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 98.1792 | 0.591441 | ||||||||
\(167\) | − | 154.104i | − | 0.922776i | −0.887198 | − | 0.461388i | \(-0.847352\pi\) | ||
0.887198 | − | 0.461388i | \(-0.152648\pi\) | |||||||
\(168\) | 43.3087 | − | 52.6142i | 0.257790 | − | 0.313180i | ||||
\(169\) | 123.990 | 0.733667 | ||||||||
\(170\) | 18.6620i | 0.109777i | ||||||||
\(171\) | −27.5510 | − | 140.664i | −0.161117 | − | 0.822599i | ||||
\(172\) | −28.3392 | −0.164763 | ||||||||
\(173\) | 25.1030i | 0.145104i | 0.997365 | + | 0.0725520i | \(0.0231143\pi\) | ||||
−0.997365 | + | 0.0725520i | \(0.976886\pi\) | |||||||
\(174\) | −20.6088 | − | 16.9639i | −0.118442 | − | 0.0974936i | ||||
\(175\) | 63.9548 | 0.365456 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −54.7915 | + | 66.5642i | −0.309556 | + | 0.376069i | ||||
\(178\) | −63.3267 | −0.355768 | ||||||||
\(179\) | − | 61.8050i | − | 0.345279i | −0.984985 | − | 0.172640i | \(-0.944770\pi\) | ||
0.984985 | − | 0.172640i | \(-0.0552296\pi\) | |||||||
\(180\) | 7.71476 | − | 1.51104i | 0.0428598 | − | 0.00839467i | ||||
\(181\) | −148.405 | −0.819915 | −0.409958 | − | 0.912105i | \(-0.634456\pi\) | ||||
−0.409958 | + | 0.912105i | \(0.634456\pi\) | |||||||
\(182\) | − | 74.0534i | − | 0.406887i | ||||||
\(183\) | −107.245 | − | 88.2771i | −0.586037 | − | 0.482389i | ||||
\(184\) | 201.369 | 1.09440 | ||||||||
\(185\) | − | 44.3767i | − | 0.239874i | ||||||
\(186\) | −12.8435 | + | 15.6032i | −0.0690513 | + | 0.0838880i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 92.3135i | − | 0.491029i | ||||||
\(189\) | −33.4812 | + | 61.9810i | −0.177149 | + | 0.327942i | ||||
\(190\) | 18.4464 | 0.0970862 | ||||||||
\(191\) | 56.2029i | 0.294256i | 0.989117 | + | 0.147128i | \(0.0470029\pi\) | ||||
−0.989117 | + | 0.147128i | \(0.952997\pi\) | |||||||
\(192\) | −161.077 | − | 132.588i | −0.838942 | − | 0.690564i | ||||
\(193\) | 150.972 | 0.782239 | 0.391119 | − | 0.920340i | \(-0.372088\pi\) | ||||
0.391119 | + | 0.920340i | \(0.372088\pi\) | |||||||
\(194\) | − | 27.0154i | − | 0.139255i | ||||||
\(195\) | 22.7955 | − | 27.6935i | 0.116900 | − | 0.142018i | ||||
\(196\) | −52.7621 | −0.269194 | ||||||||
\(197\) | 22.3374i | 0.113388i | 0.998392 | + | 0.0566938i | \(0.0180559\pi\) | ||||
−0.998392 | + | 0.0566938i | \(0.981944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −150.930 | −0.758444 | −0.379222 | − | 0.925306i | \(-0.623808\pi\) | ||||
−0.379222 | + | 0.925306i | \(0.623808\pi\) | |||||||
\(200\) | − | 213.407i | − | 1.06703i | ||||||
\(201\) | −179.004 | − | 147.344i | −0.890565 | − | 0.733057i | ||||
\(202\) | 172.771 | 0.855302 | ||||||||
\(203\) | − | 14.0003i | − | 0.0689668i | ||||||
\(204\) | 38.4154 | − | 46.6695i | 0.188311 | − | 0.228772i | ||||
\(205\) | 47.1055 | 0.229783 | ||||||||
\(206\) | − | 90.2147i | − | 0.437935i | ||||||
\(207\) | −204.284 | + | 40.0117i | −0.986877 | + | 0.193293i | ||||
\(208\) | −161.485 | −0.776369 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −6.99955 | − | 5.76159i | −0.0333312 | − | 0.0274362i | ||||
\(211\) | 181.578 | 0.860559 | 0.430279 | − | 0.902696i | \(-0.358415\pi\) | ||||
0.430279 | + | 0.902696i | \(0.358415\pi\) | |||||||
\(212\) | − | 53.5857i | − | 0.252763i | ||||||
\(213\) | 78.6710 | − | 95.5745i | 0.369347 | − | 0.448707i | ||||
\(214\) | 47.1030 | 0.220107 | ||||||||
\(215\) | 15.8296i | 0.0736262i | ||||||||
\(216\) | 206.821 | + | 111.721i | 0.957503 | + | 0.517228i | ||||
\(217\) | −10.5998 | −0.0488468 | ||||||||
\(218\) | 68.4057i | 0.313788i | ||||||||
\(219\) | −131.499 | − | 108.242i | −0.600454 | − | 0.494256i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 275.798i | − | 1.24795i | ||||||
\(222\) | 200.848 | − | 244.003i | 0.904722 | − | 1.09911i | ||||
\(223\) | 188.035 | 0.843204 | 0.421602 | − | 0.906781i | \(-0.361468\pi\) | ||||
0.421602 | + | 0.906781i | \(0.361468\pi\) | |||||||
\(224\) | − | 50.0461i | − | 0.223420i | ||||||
\(225\) | 42.4035 | + | 216.495i | 0.188460 | + | 0.962201i | ||||
\(226\) | 240.728 | 1.06517 | ||||||||
\(227\) | − | 429.227i | − | 1.89087i | −0.325815 | − | 0.945434i | \(-0.605639\pi\) | ||
0.325815 | − | 0.945434i | \(-0.394361\pi\) | |||||||
\(228\) | −46.1302 | − | 37.9715i | −0.202325 | − | 0.166541i | ||||
\(229\) | 135.775 | 0.592906 | 0.296453 | − | 0.955047i | \(-0.404196\pi\) | ||||
0.296453 | + | 0.955047i | \(0.404196\pi\) | |||||||
\(230\) | − | 26.7892i | − | 0.116475i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −46.7166 | −0.201365 | ||||||||
\(233\) | − | 326.889i | − | 1.40296i | −0.712690 | − | 0.701479i | \(-0.752523\pi\) | ||
0.712690 | − | 0.701479i | \(-0.247477\pi\) | |||||||
\(234\) | 250.680 | − | 49.0991i | 1.07128 | − | 0.209825i | ||||
\(235\) | −51.5641 | −0.219422 | ||||||||
\(236\) | 35.9372i | 0.152276i | ||||||||
\(237\) | −117.955 | − | 97.0932i | −0.497701 | − | 0.409676i | ||||
\(238\) | −69.7081 | −0.292891 | ||||||||
\(239\) | 93.4530i | 0.391017i | 0.980702 | + | 0.195508i | \(0.0626357\pi\) | ||||
−0.980702 | + | 0.195508i | \(0.937364\pi\) | |||||||
\(240\) | −12.5640 | + | 15.2636i | −0.0523501 | + | 0.0635983i | ||||
\(241\) | 206.766 | 0.857952 | 0.428976 | − | 0.903316i | \(-0.358875\pi\) | ||||
0.428976 | + | 0.903316i | \(0.358875\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −232.013 | − | 72.2432i | −0.954785 | − | 0.297297i | ||||
\(244\) | −57.9001 | −0.237295 | ||||||||
\(245\) | 29.4716i | 0.120292i | ||||||||
\(246\) | 259.007 | + | 213.199i | 1.05288 | + | 0.866661i | ||||
\(247\) | −272.610 | −1.10369 | ||||||||
\(248\) | 35.3697i | 0.142620i | ||||||||
\(249\) | −112.888 | + | 137.144i | −0.453366 | + | 0.550778i | ||||
\(250\) | −57.3464 | −0.229386 | ||||||||
\(251\) | − | 2.79029i | − | 0.0111167i | −0.999985 | − | 0.00555834i | \(-0.998231\pi\) | ||
0.999985 | − | 0.00555834i | \(-0.00176928\pi\) | |||||||
\(252\) | 5.64417 | + | 28.8168i | 0.0223975 | + | 0.114353i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 303.081i | 1.19323i | ||||||||
\(255\) | −26.0685 | − | 21.4579i | −0.102229 | − | 0.0841488i | ||||
\(256\) | −214.186 | −0.836664 | ||||||||
\(257\) | − | 400.206i | − | 1.55722i | −0.627506 | − | 0.778611i | \(-0.715924\pi\) | ||
0.627506 | − | 0.778611i | \(-0.284076\pi\) | |||||||
\(258\) | −71.6446 | + | 87.0385i | −0.277692 | + | 0.337358i | ||||
\(259\) | 165.760 | 0.639999 | ||||||||
\(260\) | − | 14.9514i | − | 0.0575052i | ||||||
\(261\) | 47.3928 | − | 9.28251i | 0.181581 | − | 0.0355652i | ||||
\(262\) | −140.133 | −0.534857 | ||||||||
\(263\) | 379.212i | 1.44187i | 0.693003 | + | 0.720935i | \(0.256287\pi\) | ||||
−0.693003 | + | 0.720935i | \(0.743713\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.9317 | −0.112950 | ||||||||
\(266\) | 68.9025i | 0.259032i | ||||||||
\(267\) | 72.8141 | − | 88.4592i | 0.272712 | − | 0.331308i | ||||
\(268\) | −96.6418 | −0.360604 | ||||||||
\(269\) | − | 31.2008i | − | 0.115988i | −0.998317 | − | 0.0579940i | \(-0.981530\pi\) | ||
0.998317 | − | 0.0579940i | \(-0.0184704\pi\) | |||||||
\(270\) | 14.8629 | − | 27.5145i | 0.0550477 | − | 0.101905i | ||||
\(271\) | 518.106 | 1.91183 | 0.955916 | − | 0.293641i | \(-0.0948672\pi\) | ||||
0.955916 | + | 0.293641i | \(0.0948672\pi\) | |||||||
\(272\) | 152.009i | 0.558857i | ||||||||
\(273\) | 103.443 | + | 85.1479i | 0.378912 | + | 0.311897i | ||||
\(274\) | 338.882 | 1.23680 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −55.1450 | + | 66.9937i | −0.199801 | + | 0.242731i | ||||
\(277\) | 367.958 | 1.32837 | 0.664184 | − | 0.747570i | \(-0.268779\pi\) | ||||
0.664184 | + | 0.747570i | \(0.268779\pi\) | |||||||
\(278\) | 83.3082i | 0.299670i | ||||||||
\(279\) | −7.02789 | − | 35.8816i | −0.0251896 | − | 0.128608i | ||||
\(280\) | −15.8668 | −0.0566670 | ||||||||
\(281\) | − | 320.392i | − | 1.14019i | −0.821580 | − | 0.570093i | \(-0.806907\pi\) | ||
0.821580 | − | 0.570093i | \(-0.193093\pi\) | |||||||
\(282\) | −283.523 | − | 233.378i | −1.00540 | − | 0.827583i | ||||
\(283\) | −160.795 | −0.568180 | −0.284090 | − | 0.958798i | \(-0.591691\pi\) | ||||
−0.284090 | + | 0.958798i | \(0.591691\pi\) | |||||||
\(284\) | − | 51.5995i | − | 0.181688i | ||||||
\(285\) | −21.2100 | + | 25.7672i | −0.0744209 | + | 0.0904113i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 175.953i | 0.613075i | ||||||||
\(288\) | 169.413 | − | 33.1818i | 0.588238 | − | 0.115214i | ||||
\(289\) | 29.3858 | 0.101681 | ||||||||
\(290\) | 6.21497i | 0.0214309i | ||||||||
\(291\) | 37.7371 | + | 31.0628i | 0.129681 | + | 0.106745i | ||||
\(292\) | −70.9949 | −0.243133 | ||||||||
\(293\) | 290.942i | 0.992976i | 0.868043 | + | 0.496488i | \(0.165377\pi\) | ||||
−0.868043 | + | 0.496488i | \(0.834623\pi\) | |||||||
\(294\) | −133.388 | + | 162.048i | −0.453701 | + | 0.551185i | ||||
\(295\) | 20.0737 | 0.0680463 | ||||||||
\(296\) | − | 553.114i | − | 1.86863i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 260.998 | 0.875832 | ||||||||
\(299\) | 395.905i | 1.32410i | ||||||||
\(300\) | 70.9985 | + | 58.4415i | 0.236662 | + | 0.194805i | ||||
\(301\) | −59.1282 | −0.196439 | ||||||||
\(302\) | 284.178i | 0.940986i | ||||||||
\(303\) | −198.655 | + | 241.339i | −0.655627 | + | 0.796498i | ||||
\(304\) | 150.252 | 0.494251 | ||||||||
\(305\) | 32.3416i | 0.106038i | ||||||||
\(306\) | −46.2181 | − | 235.971i | −0.151040 | − | 0.771147i | ||||
\(307\) | −281.800 | −0.917915 | −0.458957 | − | 0.888458i | \(-0.651777\pi\) | ||||
−0.458957 | + | 0.888458i | \(0.651777\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 126.018 | + | 103.730i | 0.407826 | + | 0.335697i | ||||
\(310\) | 4.70542 | 0.0151788 | ||||||||
\(311\) | − | 473.753i | − | 1.52332i | −0.647977 | − | 0.761660i | \(-0.724385\pi\) | ||
0.647977 | − | 0.761660i | \(-0.275615\pi\) | |||||||
\(312\) | 284.125 | − | 345.173i | 0.910656 | − | 1.10632i | ||||
\(313\) | −29.9742 | −0.0957641 | −0.0478820 | − | 0.998853i | \(-0.515247\pi\) | ||||
−0.0478820 | + | 0.998853i | \(0.515247\pi\) | |||||||
\(314\) | 108.341i | 0.345034i | ||||||||
\(315\) | 16.0964 | − | 3.15270i | 0.0510997 | − | 0.0100086i | ||||
\(316\) | −63.6824 | −0.201527 | ||||||||
\(317\) | − | 159.277i | − | 0.502450i | −0.967929 | − | 0.251225i | \(-0.919167\pi\) | ||
0.967929 | − | 0.251225i | \(-0.0808334\pi\) | |||||||
\(318\) | −164.578 | − | 135.470i | −0.517541 | − | 0.426007i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 48.5757i | 0.151799i | ||||||||
\(321\) | −54.1598 | + | 65.7968i | −0.168722 | + | 0.204974i | ||||
\(322\) | 100.065 | 0.310762 | ||||||||
\(323\) | 256.614i | 0.794471i | ||||||||
\(324\) | −93.8066 | + | 38.2125i | −0.289527 | + | 0.117940i | ||||
\(325\) | 419.572 | 1.29099 | ||||||||
\(326\) | 25.5994i | 0.0785258i | ||||||||
\(327\) | −95.5540 | − | 78.6540i | −0.292214 | − | 0.240532i | ||||
\(328\) | 587.125 | 1.79002 | ||||||||
\(329\) | − | 192.607i | − | 0.585431i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 332.709 | 1.00516 | 0.502582 | − | 0.864530i | \(-0.332384\pi\) | ||||
0.502582 | + | 0.864530i | \(0.332384\pi\) | |||||||
\(332\) | 74.0422i | 0.223019i | ||||||||
\(333\) | 109.903 | + | 561.119i | 0.330038 | + | 1.68504i | ||||
\(334\) | −255.528 | −0.765055 | ||||||||
\(335\) | 53.9818i | 0.161140i | ||||||||
\(336\) | −57.0139 | − | 46.9303i | −0.169684 | − | 0.139673i | ||||
\(337\) | 55.4053 | 0.164408 | 0.0822038 | − | 0.996616i | \(-0.473804\pi\) | ||||
0.0822038 | + | 0.996616i | \(0.473804\pi\) | |||||||
\(338\) | − | 205.595i | − | 0.608268i | ||||||
\(339\) | −276.794 | + | 336.267i | −0.816500 | + | 0.991937i | ||||
\(340\) | −14.0740 | −0.0413942 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −233.244 | + | 45.6840i | −0.682000 | + | 0.133579i | ||||
\(343\) | −237.931 | −0.693678 | ||||||||
\(344\) | 197.301i | 0.573550i | ||||||||
\(345\) | 37.4211 | + | 30.8027i | 0.108467 | + | 0.0892832i | ||||
\(346\) | 41.6247 | 0.120303 | ||||||||
\(347\) | − | 138.541i | − | 0.399255i | −0.979872 | − | 0.199627i | \(-0.936027\pi\) | ||
0.979872 | − | 0.199627i | \(-0.0639732\pi\) | |||||||
\(348\) | 12.7934 | − | 15.5422i | 0.0367626 | − | 0.0446615i | ||||
\(349\) | 226.516 | 0.649044 | 0.324522 | − | 0.945878i | \(-0.394797\pi\) | ||||
0.324522 | + | 0.945878i | \(0.394797\pi\) | |||||||
\(350\) | − | 106.047i | − | 0.302992i | ||||||
\(351\) | −219.652 | + | 406.624i | −0.625788 | + | 1.15847i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 258.939i | 0.733538i | 0.930312 | + | 0.366769i | \(0.119536\pi\) | ||||
−0.930312 | + | 0.366769i | \(0.880464\pi\) | |||||||
\(354\) | 110.374 | + | 90.8530i | 0.311791 | + | 0.256647i | ||||
\(355\) | −28.8223 | −0.0811894 | ||||||||
\(356\) | − | 47.7580i | − | 0.134152i | ||||||
\(357\) | 80.1515 | − | 97.3732i | 0.224514 | − | 0.272754i | ||||
\(358\) | −102.482 | −0.286264 | ||||||||
\(359\) | 259.036i | 0.721549i | 0.932653 | + | 0.360774i | \(0.117488\pi\) | ||||
−0.932653 | + | 0.360774i | \(0.882512\pi\) | |||||||
\(360\) | −10.5200 | − | 53.7111i | −0.0292223 | − | 0.149198i | ||||
\(361\) | −107.352 | −0.297373 | ||||||||
\(362\) | 246.079i | 0.679775i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 55.8476 | 0.153428 | ||||||||
\(365\) | 39.6561i | 0.108647i | ||||||||
\(366\) | −146.378 | + | 177.829i | −0.399939 | + | 0.485871i | ||||
\(367\) | −198.777 | −0.541627 | −0.270814 | − | 0.962632i | \(-0.587293\pi\) | ||||
−0.270814 | + | 0.962632i | \(0.587293\pi\) | |||||||
\(368\) | − | 218.208i | − | 0.592957i | ||||||
\(369\) | −595.623 | + | 116.661i | −1.61415 | + | 0.316154i | ||||
\(370\) | −73.5837 | −0.198875 | ||||||||
\(371\) | − | 111.803i | − | 0.301357i | ||||||
\(372\) | −11.7672 | − | 9.68600i | −0.0316322 | − | 0.0260376i | ||||
\(373\) | 670.467 | 1.79750 | 0.898750 | − | 0.438462i | \(-0.144477\pi\) | ||||
0.898750 | + | 0.438462i | \(0.144477\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 65.9379 | − | 80.1056i | 0.175834 | − | 0.213615i | ||||
\(376\) | −642.697 | −1.70930 | ||||||||
\(377\) | − | 91.8481i | − | 0.243629i | ||||||
\(378\) | 102.774 | + | 55.5171i | 0.271890 | + | 0.146871i | ||||
\(379\) | 392.391 | 1.03533 | 0.517666 | − | 0.855583i | \(-0.326801\pi\) | ||||
0.517666 | + | 0.855583i | \(0.326801\pi\) | |||||||
\(380\) | 13.9114i | 0.0366089i | ||||||||
\(381\) | −423.365 | − | 348.488i | −1.11119 | − | 0.914666i | ||||
\(382\) | 93.1933 | 0.243962 | ||||||||
\(383\) | 497.702i | 1.29948i | 0.760155 | + | 0.649741i | \(0.225123\pi\) | ||||
−0.760155 | + | 0.649741i | \(0.774877\pi\) | |||||||
\(384\) | −73.5699 | + | 89.3774i | −0.191588 | + | 0.232754i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 250.336i | − | 0.648538i | ||||||
\(387\) | −39.2034 | − | 200.157i | −0.101301 | − | 0.517201i | ||||
\(388\) | 20.3738 | 0.0525097 | ||||||||
\(389\) | 412.280i | 1.05985i | 0.848046 | + | 0.529923i | \(0.177779\pi\) | ||||
−0.848046 | + | 0.529923i | \(0.822221\pi\) | |||||||
\(390\) | −45.9202 | − | 37.7986i | −0.117744 | − | 0.0969196i | ||||
\(391\) | 372.674 | 0.953131 | ||||||||
\(392\) | 367.336i | 0.937081i | ||||||||
\(393\) | 161.127 | − | 195.747i | 0.409992 | − | 0.498084i | ||||
\(394\) | 37.0389 | 0.0940074 | ||||||||
\(395\) | 35.5715i | 0.0900544i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 171.230 | 0.431310 | 0.215655 | − | 0.976470i | \(-0.430811\pi\) | ||||
0.215655 | + | 0.976470i | \(0.430811\pi\) | |||||||
\(398\) | 250.267i | 0.628810i | ||||||||
\(399\) | −96.2479 | − | 79.2253i | −0.241223 | − | 0.198560i | ||||
\(400\) | −231.252 | −0.578130 | ||||||||
\(401\) | − | 726.019i | − | 1.81052i | −0.424858 | − | 0.905260i | \(-0.639676\pi\) | ||
0.424858 | − | 0.905260i | \(-0.360324\pi\) | |||||||
\(402\) | −244.321 | + | 296.816i | −0.607763 | + | 0.738349i | ||||
\(403\) | −69.5392 | −0.172554 | ||||||||
\(404\) | 130.296i | 0.322514i | ||||||||
\(405\) | 21.3446 | + | 52.3982i | 0.0527027 | + | 0.129378i | ||||
\(406\) | −23.2147 | −0.0571790 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −324.919 | − | 267.453i | −0.796369 | − | 0.655521i | ||||
\(409\) | 301.390 | 0.736896 | 0.368448 | − | 0.929648i | \(-0.379889\pi\) | ||||
0.368448 | + | 0.929648i | \(0.379889\pi\) | |||||||
\(410\) | − | 78.1084i | − | 0.190508i | ||||||
\(411\) | −389.653 | + | 473.375i | −0.948060 | + | 1.15176i | ||||
\(412\) | 68.0357 | 0.165135 | ||||||||
\(413\) | 74.9809i | 0.181552i | ||||||||
\(414\) | 66.3458 | + | 338.735i | 0.160255 | + | 0.818200i | ||||
\(415\) | 41.3582 | 0.0996584 | ||||||||
\(416\) | − | 328.325i | − | 0.789243i | ||||||
\(417\) | −116.371 | − | 95.7892i | −0.279067 | − | 0.229710i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 573.195i | − | 1.36801i | −0.729478 | − | 0.684004i | \(-0.760237\pi\) | ||
0.729478 | − | 0.684004i | \(-0.239763\pi\) | |||||||
\(420\) | 4.34512 | − | 5.27874i | 0.0103455 | − | 0.0125684i | ||||
\(421\) | −559.281 | −1.32846 | −0.664229 | − | 0.747529i | \(-0.731240\pi\) | ||||
−0.664229 | + | 0.747529i | \(0.731240\pi\) | |||||||
\(422\) | − | 301.085i | − | 0.713472i | ||||||
\(423\) | 651.999 | − | 127.703i | 1.54137 | − | 0.301898i | ||||
\(424\) | −373.070 | −0.879882 | ||||||||
\(425\) | − | 394.952i | − | 0.929299i | ||||||
\(426\) | −158.478 | − | 130.449i | −0.372014 | − | 0.306218i | ||||
\(427\) | −120.805 | −0.282916 | ||||||||
\(428\) | 35.5229i | 0.0829973i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 26.2480 | 0.0610420 | ||||||||
\(431\) | 199.847i | 0.463682i | 0.972754 | + | 0.231841i | \(0.0744750\pi\) | ||||
−0.972754 | + | 0.231841i | \(0.925525\pi\) | |||||||
\(432\) | 121.064 | − | 224.115i | 0.280240 | − | 0.518786i | ||||
\(433\) | −103.486 | −0.238999 | −0.119499 | − | 0.992834i | \(-0.538129\pi\) | ||||
−0.119499 | + | 0.992834i | \(0.538129\pi\) | |||||||
\(434\) | 17.5761i | 0.0404979i | ||||||||
\(435\) | −8.68151 | − | 7.14608i | −0.0199575 | − | 0.0164278i | ||||
\(436\) | −51.5884 | −0.118322 | ||||||||
\(437\) | − | 368.368i | − | 0.842947i | ||||||
\(438\) | −179.483 | + | 218.047i | −0.409778 | + | 0.497824i | ||||
\(439\) | −662.550 | −1.50923 | −0.754613 | − | 0.656171i | \(-0.772175\pi\) | ||||
−0.754613 | + | 0.656171i | \(0.772175\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −72.9890 | − | 372.652i | −0.165508 | − | 0.845016i | ||||
\(442\) | −457.316 | −1.03465 | ||||||||
\(443\) | 210.829i | 0.475913i | 0.971276 | + | 0.237956i | \(0.0764775\pi\) | ||||
−0.971276 | + | 0.237956i | \(0.923522\pi\) | |||||||
\(444\) | 184.016 | + | 151.470i | 0.414451 | + | 0.341150i | ||||
\(445\) | −26.6765 | −0.0599472 | ||||||||
\(446\) | − | 311.791i | − | 0.699084i | ||||||
\(447\) | −300.100 | + | 364.581i | −0.671365 | + | 0.815617i | ||||
\(448\) | −181.444 | −0.405009 | ||||||||
\(449\) | − | 239.271i | − | 0.532897i | −0.963849 | − | 0.266448i | \(-0.914150\pi\) | ||
0.963849 | − | 0.266448i | \(-0.0858502\pi\) | |||||||
\(450\) | 358.984 | − | 70.3118i | 0.797742 | − | 0.156248i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 181.546i | 0.401651i | ||||||||
\(453\) | −396.960 | − | 326.752i | −0.876291 | − | 0.721308i | ||||
\(454\) | −711.727 | −1.56768 | ||||||||
\(455\) | − | 31.1952i | − | 0.0685608i | ||||||
\(456\) | −264.362 | + | 321.164i | −0.579741 | + | 0.704307i | ||||
\(457\) | 26.6877 | 0.0583975 | 0.0291988 | − | 0.999574i | \(-0.490704\pi\) | ||||
0.0291988 | + | 0.999574i | \(0.490704\pi\) | |||||||
\(458\) | − | 225.137i | − | 0.491566i | ||||||
\(459\) | 382.764 | + | 206.763i | 0.833908 | + | 0.450463i | ||||
\(460\) | 20.2032 | 0.0439200 | ||||||||
\(461\) | − | 393.125i | − | 0.852766i | −0.904543 | − | 0.426383i | \(-0.859788\pi\) | ||
0.904543 | − | 0.426383i | \(-0.140212\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 106.954 | 0.231002 | 0.115501 | − | 0.993307i | \(-0.463153\pi\) | ||||
0.115501 | + | 0.993307i | \(0.463153\pi\) | |||||||
\(464\) | 50.6232i | 0.109102i | ||||||||
\(465\) | −5.41037 | + | 6.57287i | −0.0116352 | + | 0.0141352i | ||||
\(466\) | −542.035 | −1.16316 | ||||||||
\(467\) | − | 422.909i | − | 0.905588i | −0.891615 | − | 0.452794i | \(-0.850427\pi\) | ||
0.891615 | − | 0.452794i | \(-0.149573\pi\) | |||||||
\(468\) | 37.0283 | + | 189.052i | 0.0791203 | + | 0.403956i | ||||
\(469\) | −201.637 | −0.429931 | ||||||||
\(470\) | 85.5015i | 0.181918i | ||||||||
\(471\) | −151.338 | − | 124.572i | −0.321312 | − | 0.264484i | ||||
\(472\) | 250.199 | 0.530083 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −160.996 | + | 195.588i | −0.339654 | + | 0.412634i | ||||
\(475\) | −390.388 | −0.821870 | ||||||||
\(476\) | − | 52.5706i | − | 0.110442i | ||||||
\(477\) | 378.469 | − | 74.1283i | 0.793437 | − | 0.155405i | ||||
\(478\) | 154.960 | 0.324184 | ||||||||
\(479\) | 539.714i | 1.12675i | 0.826200 | + | 0.563376i | \(0.190498\pi\) | ||||
−0.826200 | + | 0.563376i | \(0.809502\pi\) | |||||||
\(480\) | −31.0334 | − | 25.5447i | −0.0646529 | − | 0.0532182i | ||||
\(481\) | 1087.46 | 2.26083 | ||||||||
\(482\) | − | 342.852i | − | 0.711311i | ||||||
\(483\) | −115.057 | + | 139.779i | −0.238213 | + | 0.289397i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 11.3803i | − | 0.0234645i | ||||||
\(486\) | −119.791 | + | 384.714i | −0.246483 | + | 0.791593i | ||||
\(487\) | 610.646 | 1.25389 | 0.626947 | − | 0.779062i | \(-0.284304\pi\) | ||||
0.626947 | + | 0.779062i | \(0.284304\pi\) | |||||||
\(488\) | 403.107i | 0.826039i | ||||||||
\(489\) | −35.7591 | − | 29.4346i | −0.0731270 | − | 0.0601935i | ||||
\(490\) | 48.8687 | 0.0997320 | ||||||||
\(491\) | 56.8741i | 0.115833i | 0.998321 | + | 0.0579166i | \(0.0184458\pi\) | ||||
−0.998321 | + | 0.0579166i | \(0.981554\pi\) | |||||||
\(492\) | −160.785 | + | 195.331i | −0.326798 | + | 0.397015i | ||||
\(493\) | −86.4586 | −0.175372 | ||||||||
\(494\) | 452.031i | 0.915043i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 38.3274 | 0.0772729 | ||||||||
\(497\) | − | 107.659i | − | 0.216618i | ||||||
\(498\) | 227.406 | + | 187.187i | 0.456639 | + | 0.375877i | ||||
\(499\) | 468.878 | 0.939635 | 0.469818 | − | 0.882763i | \(-0.344320\pi\) | ||||
0.469818 | + | 0.882763i | \(0.344320\pi\) | |||||||
\(500\) | − | 43.2480i | − | 0.0864960i | ||||||
\(501\) | 293.811 | − | 356.940i | 0.586449 | − | 0.712456i | ||||
\(502\) | −4.62674 | −0.00921661 | ||||||||
\(503\) | 458.172i | 0.910879i | 0.890267 | + | 0.455439i | \(0.150518\pi\) | ||||
−0.890267 | + | 0.455439i | \(0.849482\pi\) | |||||||
\(504\) | 200.626 | − | 39.2954i | 0.398068 | − | 0.0779670i | ||||
\(505\) | 72.7802 | 0.144119 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 287.189 | + | 236.396i | 0.566448 | + | 0.466265i | ||||
\(508\) | −228.569 | −0.449940 | ||||||||
\(509\) | 274.849i | 0.539978i | 0.962863 | + | 0.269989i | \(0.0870201\pi\) | ||||
−0.962863 | + | 0.269989i | \(0.912980\pi\) | |||||||
\(510\) | −35.5807 | + | 43.2257i | −0.0697660 | + | 0.0847563i | ||||
\(511\) | −148.127 | −0.289876 | ||||||||
\(512\) | 509.504i | 0.995125i | ||||||||
\(513\) | 204.373 | − | 378.340i | 0.398388 | − | 0.737505i | ||||
\(514\) | −663.606 | −1.29106 | ||||||||
\(515\) | − | 38.0031i | − | 0.0737925i | ||||||
\(516\) | −65.6404 | − | 54.0310i | −0.127210 | − | 0.104711i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 274.856i | − | 0.530610i | ||||||
\(519\) | −47.8609 | + | 58.1444i | −0.0922174 | + | 0.112032i | ||||
\(520\) | −104.093 | −0.200179 | ||||||||
\(521\) | 248.396i | 0.476768i | 0.971171 | + | 0.238384i | \(0.0766177\pi\) | ||||
−0.971171 | + | 0.238384i | \(0.923382\pi\) | |||||||
\(522\) | −15.3919 | − | 78.5848i | −0.0294864 | − | 0.150546i | ||||
\(523\) | 140.587 | 0.268808 | 0.134404 | − | 0.990927i | \(-0.457088\pi\) | ||||
0.134404 | + | 0.990927i | \(0.457088\pi\) | |||||||
\(524\) | − | 105.681i | − | 0.201682i | ||||||
\(525\) | 148.134 | + | 121.935i | 0.282161 | + | 0.232257i | ||||
\(526\) | 628.794 | 1.19543 | ||||||||
\(527\) | 65.4587i | 0.124210i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.97152 | −0.0112883 | ||||||||
\(530\) | 49.6315i | 0.0936444i | ||||||||
\(531\) | −253.820 | + | 49.7141i | −0.478004 | + | 0.0936235i | ||||
\(532\) | −51.9630 | −0.0976749 | ||||||||
\(533\) | 1154.33i | 2.16572i | ||||||||
\(534\) | −146.680 | − | 120.737i | −0.274681 | − | 0.226100i | ||||
\(535\) | 19.8422 | 0.0370883 | ||||||||
\(536\) | 672.832i | 1.25528i | ||||||||
\(537\) | 117.836 | − | 143.155i | 0.219434 | − | 0.266583i | ||||
\(538\) | −51.7358 | −0.0961633 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 20.7501 | + | 11.2089i | 0.0384262 | + | 0.0207572i | ||||
\(541\) | 600.914 | 1.11075 | 0.555373 | − | 0.831601i | \(-0.312576\pi\) | ||||
0.555373 | + | 0.831601i | \(0.312576\pi\) | |||||||
\(542\) | − | 859.103i | − | 1.58506i | ||||||
\(543\) | −343.740 | − | 282.945i | −0.633039 | − | 0.521078i | ||||
\(544\) | −309.060 | −0.568124 | ||||||||
\(545\) | 28.8160i | 0.0528735i | ||||||||
\(546\) | 141.189 | − | 171.525i | 0.258587 | − | 0.314149i | ||||
\(547\) | −620.873 | −1.13505 | −0.567525 | − | 0.823356i | \(-0.692099\pi\) | ||||
−0.567525 | + | 0.823356i | \(0.692099\pi\) | |||||||
\(548\) | 255.569i | 0.466367i | ||||||||
\(549\) | −80.0967 | − | 408.941i | −0.145896 | − | 0.744884i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 85.4594i | 0.155099i | ||||||||
\(552\) | 466.418 | + | 383.926i | 0.844961 | + | 0.695519i | ||||
\(553\) | −132.870 | −0.240271 | ||||||||
\(554\) | − | 610.133i | − | 1.10132i | ||||||
\(555\) | 84.6078 | − | 102.787i | 0.152447 | − | 0.185202i | ||||
\(556\) | −62.8272 | −0.112998 | ||||||||
\(557\) | 540.026i | 0.969526i | 0.874645 | + | 0.484763i | \(0.161094\pi\) | ||||
−0.874645 | + | 0.484763i | \(0.838906\pi\) | |||||||
\(558\) | −59.4974 | + | 11.6534i | −0.106626 | + | 0.0208842i | ||||
\(559\) | −387.908 | −0.693931 | ||||||||
\(560\) | 17.1936i | 0.0307028i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −531.261 | −0.945305 | ||||||||
\(563\) | − | 278.666i | − | 0.494967i | −0.968892 | − | 0.247483i | \(-0.920396\pi\) | ||
0.968892 | − | 0.247483i | \(-0.0796036\pi\) | |||||||
\(564\) | 176.003 | − | 213.820i | 0.312062 | − | 0.379113i | ||||
\(565\) | 101.407 | 0.179482 | ||||||||
\(566\) | 266.624i | 0.471066i | ||||||||
\(567\) | −195.722 | + | 79.7282i | −0.345189 | + | 0.140614i | ||||
\(568\) | −359.242 | −0.632468 | ||||||||
\(569\) | − | 1069.57i | − | 1.87973i | −0.341546 | − | 0.939865i | \(-0.610950\pi\) | ||
0.341546 | − | 0.939865i | \(-0.389050\pi\) | |||||||
\(570\) | 42.7262 | + | 35.1695i | 0.0749582 | + | 0.0617009i | ||||
\(571\) | 470.660 | 0.824274 | 0.412137 | − | 0.911122i | \(-0.364783\pi\) | ||||
0.412137 | + | 0.911122i | \(0.364783\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −107.155 | + | 130.179i | −0.187007 | + | 0.227189i | ||||
\(574\) | 291.757 | 0.508288 | ||||||||
\(575\) | 566.951i | 0.986002i | ||||||||
\(576\) | −120.302 | − | 614.212i | −0.208857 | − | 1.06634i | ||||
\(577\) | 229.146 | 0.397133 | 0.198567 | − | 0.980087i | \(-0.436371\pi\) | ||||
0.198567 | + | 0.980087i | \(0.436371\pi\) | |||||||
\(578\) | − | 48.7263i | − | 0.0843016i | ||||||
\(579\) | 349.687 | + | 287.840i | 0.603950 | + | 0.497134i | ||||
\(580\) | −4.68704 | −0.00808110 | ||||||||
\(581\) | 154.485i | 0.265895i | ||||||||
\(582\) | 51.5071 | − | 62.5741i | 0.0885001 | − | 0.107516i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 494.275i | 0.846361i | ||||||||
\(585\) | 105.600 | − | 20.6831i | 0.180512 | − | 0.0353558i | ||||
\(586\) | 482.428 | 0.823257 | ||||||||
\(587\) | 0.740839i | 0.00126208i | 1.00000 | 0.000631038i | \(0.000200866\pi\) | |||||
−1.00000 | 0.000631038i | \(0.999799\pi\) | ||||||||
\(588\) | −122.209 | − | 100.595i | −0.207839 | − | 0.171080i | ||||
\(589\) | 64.7023 | 0.109851 | ||||||||
\(590\) | − | 33.2853i | − | 0.0564158i | ||||||
\(591\) | −42.5880 | + | 51.7386i | −0.0720608 | + | 0.0875441i | ||||
\(592\) | −599.366 | −1.01244 | ||||||||
\(593\) | − | 498.413i | − | 0.840494i | −0.907410 | − | 0.420247i | \(-0.861943\pi\) | ||
0.907410 | − | 0.420247i | \(-0.138057\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −29.3647 | −0.0493524 | ||||||||
\(596\) | 196.832i | 0.330256i | ||||||||
\(597\) | −349.590 | − | 287.761i | −0.585578 | − | 0.482011i | ||||
\(598\) | 656.474 | 1.09778 | ||||||||
\(599\) | − | 191.403i | − | 0.319537i | −0.987154 | − | 0.159769i | \(-0.948925\pi\) | ||
0.987154 | − | 0.159769i | \(-0.0510748\pi\) | |||||||
\(600\) | 406.877 | − | 494.300i | 0.678128 | − | 0.823834i | ||||
\(601\) | 831.418 | 1.38339 | 0.691696 | − | 0.722189i | \(-0.256864\pi\) | ||||
0.691696 | + | 0.722189i | \(0.256864\pi\) | |||||||
\(602\) | 98.0440i | 0.162864i | ||||||||
\(603\) | −133.690 | − | 682.569i | −0.221709 | − | 1.13196i | ||||
\(604\) | −214.314 | −0.354824 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 400.178 | + | 329.402i | 0.660361 | + | 0.543567i | ||||
\(607\) | 789.695 | 1.30098 | 0.650490 | − | 0.759515i | \(-0.274564\pi\) | ||||
0.650490 | + | 0.759515i | \(0.274564\pi\) | |||||||
\(608\) | 305.488i | 0.502447i | ||||||||
\(609\) | 26.6926 | − | 32.4279i | 0.0438303 | − | 0.0532478i | ||||
\(610\) | 53.6275 | 0.0879140 | ||||||||
\(611\) | − | 1263.59i | − | 2.06806i | ||||||
\(612\) | 177.958 | − | 34.8555i | 0.290782 | − | 0.0569535i | ||||
\(613\) | −277.196 | −0.452196 | −0.226098 | − | 0.974105i | \(-0.572597\pi\) | ||||
−0.226098 | + | 0.974105i | \(0.572597\pi\) | |||||||
\(614\) | 467.269i | 0.761025i | ||||||||
\(615\) | 109.107 | + | 89.8104i | 0.177411 | + | 0.146033i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 928.547i | 1.50494i | 0.658628 | + | 0.752469i | \(0.271137\pi\) | ||||
−0.658628 | + | 0.752469i | \(0.728863\pi\) | |||||||
\(618\) | 172.002 | − | 208.959i | 0.278320 | − | 0.338121i | ||||
\(619\) | 955.674 | 1.54390 | 0.771950 | − | 0.635683i | \(-0.219282\pi\) | ||||
0.771950 | + | 0.635683i | \(0.219282\pi\) | |||||||
\(620\) | 3.54861i | 0.00572356i | ||||||||
\(621\) | −549.454 | − | 296.806i | −0.884790 | − | 0.477949i | ||||
\(622\) | −785.557 | −1.26295 | ||||||||
\(623\) | − | 99.6443i | − | 0.159943i | ||||||
\(624\) | −374.037 | − | 307.884i | −0.599418 | − | 0.493403i | ||||
\(625\) | 588.645 | 0.941832 | ||||||||
\(626\) | 49.7019i | 0.0793961i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −81.7055 | −0.130104 | ||||||||
\(629\) | − | 1023.65i | − | 1.62742i | ||||||
\(630\) | −5.22768 | − | 26.6904i | −0.00829790 | − | 0.0423657i | ||||
\(631\) | −5.25949 | −0.00833517 | −0.00416759 | − | 0.999991i | \(-0.501327\pi\) | ||||
−0.00416759 | + | 0.999991i | \(0.501327\pi\) | |||||||
\(632\) | 443.365i | 0.701527i | ||||||||
\(633\) | 420.577 | + | 346.193i | 0.664419 | + | 0.546908i | ||||
\(634\) | −264.106 | −0.416571 | ||||||||
\(635\) | 127.673i | 0.201061i | ||||||||
\(636\) | 102.165 | − | 124.117i | 0.160637 | − | 0.195153i | ||||
\(637\) | −722.207 | −1.13376 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 364.441 | − | 71.3807i | 0.570330 | − | 0.111707i | ||||
\(640\) | 26.9534 | 0.0421147 | ||||||||
\(641\) | 486.004i | 0.758196i | 0.925356 | + | 0.379098i | \(0.123766\pi\) | ||||
−0.925356 | + | 0.379098i | \(0.876234\pi\) | |||||||
\(642\) | 109.102 | + | 89.8056i | 0.169940 | + | 0.139884i | ||||
\(643\) | −738.878 | −1.14911 | −0.574555 | − | 0.818466i | \(-0.694825\pi\) | ||||
−0.574555 | + | 0.818466i | \(0.694825\pi\) | |||||||
\(644\) | 75.4647i | 0.117181i | ||||||||
\(645\) | −30.1805 | + | 36.6652i | −0.0467914 | + | 0.0568452i | ||||
\(646\) | 425.507 | 0.658680 | ||||||||
\(647\) | 1150.29i | 1.77788i | 0.458027 | + | 0.888938i | \(0.348556\pi\) | ||||
−0.458027 | + | 0.888938i | \(0.651444\pi\) | |||||||
\(648\) | 266.040 | + | 653.093i | 0.410556 | + | 1.00786i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 695.717i | − | 1.07033i | ||||||
\(651\) | −24.5515 | − | 20.2093i | −0.0377136 | − | 0.0310435i | ||||
\(652\) | −19.3059 | −0.0296102 | ||||||||
\(653\) | − | 605.052i | − | 0.926573i | −0.886208 | − | 0.463287i | \(-0.846670\pi\) | ||
0.886208 | − | 0.463287i | \(-0.153330\pi\) | |||||||
\(654\) | −130.421 | + | 158.444i | −0.199420 | + | 0.242269i | ||||
\(655\) | −59.0311 | −0.0901239 | ||||||||
\(656\) | − | 636.222i | − | 0.969850i | ||||||
\(657\) | −98.2116 | − | 501.429i | −0.149485 | − | 0.763209i | ||||
\(658\) | −319.373 | −0.485369 | ||||||||
\(659\) | 956.314i | 1.45116i | 0.688138 | + | 0.725580i | \(0.258428\pi\) | ||||
−0.688138 | + | 0.725580i | \(0.741572\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 57.8747 | 0.0875563 | 0.0437781 | − | 0.999041i | \(-0.486061\pi\) | ||||
0.0437781 | + | 0.999041i | \(0.486061\pi\) | |||||||
\(662\) | − | 551.685i | − | 0.833361i | ||||||
\(663\) | 525.830 | − | 638.812i | 0.793107 | − | 0.963518i | ||||
\(664\) | 515.491 | 0.776342 | ||||||||
\(665\) | 29.0253i | 0.0436471i | ||||||||
\(666\) | 930.425 | − | 182.236i | 1.39703 | − | 0.273628i | ||||
\(667\) | 124.111 | 0.186073 | ||||||||
\(668\) | − | 192.708i | − | 0.288484i | ||||||
\(669\) | 435.532 | + | 358.503i | 0.651020 | + | 0.535879i | ||||
\(670\) | 89.5104 | 0.133598 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 95.4169 | − | 115.919i | 0.141989 | − | 0.172498i | ||||
\(673\) | 851.648 | 1.26545 | 0.632725 | − | 0.774377i | \(-0.281936\pi\) | ||||
0.632725 | + | 0.774377i | \(0.281936\pi\) | |||||||
\(674\) | − | 91.8709i | − | 0.136307i | ||||||
\(675\) | −314.549 | + | 582.300i | −0.465999 | + | 0.862667i | ||||
\(676\) | 155.050 | 0.229364 | ||||||||
\(677\) | 269.729i | 0.398418i | 0.979957 | + | 0.199209i | \(0.0638373\pi\) | ||||
−0.979957 | + | 0.199209i | \(0.936163\pi\) | |||||||
\(678\) | 557.584 | + | 458.968i | 0.822395 | + | 0.676944i | ||||
\(679\) | 42.5087 | 0.0626049 | ||||||||
\(680\) | 97.9852i | 0.144096i | ||||||||
\(681\) | 818.355 | − | 994.191i | 1.20170 | − | 1.45990i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 254.016i | − | 0.371913i | −0.982558 | − | 0.185956i | \(-0.940462\pi\) | ||
0.982558 | − | 0.185956i | \(-0.0595383\pi\) | |||||||
\(684\) | −34.4527 | − | 175.902i | −0.0503695 | − | 0.257166i | ||||
\(685\) | 142.755 | 0.208401 | ||||||||
\(686\) | 394.528i | 0.575114i | ||||||||
\(687\) | 314.488 | + | 258.867i | 0.457770 | + | 0.376808i | ||||
\(688\) | 213.800 | 0.310756 | ||||||||
\(689\) | − | 733.481i | − | 1.06456i | ||||||
\(690\) | 51.0758 | − | 62.0502i | 0.0740229 | − | 0.0899278i | ||||
\(691\) | −378.595 | −0.547894 | −0.273947 | − | 0.961745i | \(-0.588329\pi\) | ||||
−0.273947 | + | 0.961745i | \(0.588329\pi\) | |||||||
\(692\) | 31.3914i | 0.0453634i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −229.724 | −0.331014 | ||||||||
\(695\) | 35.0938i | 0.0504946i | ||||||||
\(696\) | −108.207 | − | 89.0690i | −0.155469 | − | 0.127973i | ||||
\(697\) | 1086.59 | 1.55896 | ||||||||
\(698\) | − | 375.600i | − | 0.538109i | ||||||
\(699\) | 623.241 | − | 757.153i | 0.891618 | − | 1.08319i | ||||
\(700\) | 79.9759 | 0.114251 | ||||||||
\(701\) | − | 319.948i | − | 0.456416i | −0.973612 | − | 0.228208i | \(-0.926713\pi\) | ||
0.973612 | − | 0.228208i | \(-0.0732867\pi\) | |||||||
\(702\) | 674.247 | + | 364.217i | 0.960465 | + | 0.518828i | ||||
\(703\) | −1011.82 | −1.43929 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −119.435 | − | 98.3111i | −0.169411 | − | 0.139448i | ||||
\(706\) | 429.362 | 0.608161 | ||||||||
\(707\) | 271.855i | 0.384519i | ||||||||
\(708\) | −68.5171 | + | 83.2390i | −0.0967756 | + | 0.117569i | ||||
\(709\) | −228.519 | −0.322311 | −0.161156 | − | 0.986929i | \(-0.551522\pi\) | ||||
−0.161156 | + | 0.986929i | \(0.551522\pi\) | |||||||
\(710\) | 47.7919i | 0.0673125i | ||||||||
\(711\) | −88.0958 | − | 449.782i | −0.123904 | − | 0.632604i | ||||
\(712\) | −332.497 | −0.466990 | ||||||||
\(713\) | − | 93.9656i | − | 0.131789i | ||||||
\(714\) | −161.460 | − | 132.904i | −0.226135 | − | 0.186140i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 77.2875i | − | 0.107943i | ||||||
\(717\) | −178.176 | + | 216.459i | −0.248502 | + | 0.301896i | ||||
\(718\) | 429.523 | 0.598222 | ||||||||
\(719\) | − | 805.149i | − | 1.11982i | −0.828554 | − | 0.559909i | \(-0.810836\pi\) | ||
0.828554 | − | 0.559909i | \(-0.189164\pi\) | |||||||
\(720\) | −58.2025 | + | 11.3998i | −0.0808369 | + | 0.0158330i | ||||
\(721\) | 141.953 | 0.196883 | ||||||||
\(722\) | 178.006i | 0.246546i | ||||||||
\(723\) | 478.920 | + | 394.217i | 0.662406 | + | 0.545251i | ||||
\(724\) | −185.581 | −0.256327 | ||||||||
\(725\) | − | 131.530i | − | 0.181420i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1002.31 | −1.37869 | −0.689345 | − | 0.724434i | \(-0.742101\pi\) | ||||
−0.689345 | + | 0.724434i | \(0.742101\pi\) | |||||||
\(728\) | − | 388.818i | − | 0.534090i | ||||||
\(729\) | −399.659 | − | 609.683i | −0.548229 | − | 0.836328i | ||||
\(730\) | 65.7561 | 0.0900768 | ||||||||
\(731\) | 365.146i | 0.499516i | ||||||||
\(732\) | −134.110 | − | 110.391i | −0.183211 | − | 0.150808i | ||||
\(733\) | −724.606 | −0.988548 | −0.494274 | − | 0.869306i | \(-0.664566\pi\) | ||||
−0.494274 | + | 0.869306i | \(0.664566\pi\) | |||||||
\(734\) | 329.604i | 0.449052i | ||||||||
\(735\) | −56.1900 | + | 68.2633i | −0.0764490 | + | 0.0928752i | ||||
\(736\) | 443.653 | 0.602789 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 193.442 | + | 987.637i | 0.262117 | + | 1.33826i | ||||
\(739\) | −860.336 | −1.16419 | −0.582095 | − | 0.813121i | \(-0.697767\pi\) | ||||
−0.582095 | + | 0.813121i | \(0.697767\pi\) | |||||||
\(740\) | − | 55.4934i | − | 0.0749911i | ||||||
\(741\) | −631.430 | − | 519.753i | −0.852132 | − | 0.701422i | ||||
\(742\) | −185.388 | −0.249849 | ||||||||
\(743\) | 390.314i | 0.525322i | 0.964888 | + | 0.262661i | \(0.0846000\pi\) | ||||
−0.964888 | + | 0.262661i | \(0.915400\pi\) | |||||||
\(744\) | −67.4351 | + | 81.9245i | −0.0906386 | + | 0.110114i | ||||
\(745\) | 109.946 | 0.147578 | ||||||||
\(746\) | − | 1111.74i | − | 1.49027i | ||||||
\(747\) | −522.951 | + | 102.427i | −0.700069 | + | 0.137118i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 74.1164i | 0.0989538i | ||||||||
\(750\) | −132.828 | − | 109.336i | −0.177104 | − | 0.145781i | ||||
\(751\) | −863.735 | −1.15011 | −0.575057 | − | 0.818113i | \(-0.695020\pi\) | ||||
−0.575057 | + | 0.818113i | \(0.695020\pi\) | |||||||
\(752\) | 696.441i | 0.926118i | ||||||||
\(753\) | 5.31990 | − | 6.46296i | 0.00706495 | − | 0.00858295i | ||||
\(754\) | −152.299 | −0.201988 | ||||||||
\(755\) | 119.710i | 0.158557i | ||||||||
\(756\) | −41.8684 | + | 77.5077i | −0.0553815 | + | 0.102523i | ||||
\(757\) | −845.429 | −1.11681 | −0.558407 | − | 0.829567i | \(-0.688587\pi\) | ||||
−0.558407 | + | 0.829567i | \(0.688587\pi\) | |||||||
\(758\) | − | 650.647i | − | 0.858373i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 96.8528 | 0.127438 | ||||||||
\(761\) | 175.879i | 0.231116i | 0.993301 | + | 0.115558i | \(0.0368656\pi\) | ||||
−0.993301 | + | 0.115558i | \(0.963134\pi\) | |||||||
\(762\) | −577.848 | + | 702.007i | −0.758331 | + | 0.921269i | ||||
\(763\) | −107.636 | −0.141070 | ||||||||
\(764\) | 70.2821i | 0.0919922i | ||||||||
\(765\) | −19.4695 | − | 99.4033i | −0.0254503 | − | 0.129939i | ||||
\(766\) | 825.269 | 1.07737 | ||||||||
\(767\) | 491.908i | 0.641341i | ||||||||
\(768\) | −496.105 | − | 408.363i | −0.645970 | − | 0.531722i | ||||
\(769\) | 1341.04 | 1.74388 | 0.871941 | − | 0.489611i | \(-0.162861\pi\) | ||||
0.871941 | + | 0.489611i | \(0.162861\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 763.025 | − | 926.972i | 0.989657 | − | 1.20230i | ||||
\(772\) | 188.792 | 0.244549 | ||||||||
\(773\) | − | 784.632i | − | 1.01505i | −0.861637 | − | 0.507524i | \(-0.830561\pi\) | ||
0.861637 | − | 0.507524i | \(-0.169439\pi\) | |||||||
\(774\) | −331.892 | + | 65.0055i | −0.428801 | + | 0.0839864i | ||||
\(775\) | −99.5827 | −0.128494 | ||||||||
\(776\) | − | 141.845i | − | 0.182789i | ||||||
\(777\) | 383.939 | + | 316.034i | 0.494130 | + | 0.406737i | ||||
\(778\) | 683.626 | 0.878696 | ||||||||
\(779\) | − | 1074.04i | − | 1.37874i | ||||||
\(780\) | 28.5060 | − | 34.6309i | 0.0365461 | − | 0.0443986i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 617.954i | − | 0.790222i | ||||||
\(783\) | 127.471 | + | 68.8576i | 0.162798 | + | 0.0879408i | ||||
\(784\) | 398.053 | 0.507721 | ||||||||
\(785\) | 45.6388i | 0.0581386i | ||||||||
\(786\) | −324.580 | − | 267.174i | −0.412952 | − | 0.339916i | ||||
\(787\) | −1448.45 | −1.84047 | −0.920233 | − | 0.391372i | \(-0.872001\pi\) | ||||
−0.920233 | + | 0.391372i | \(0.872001\pi\) | |||||||
\(788\) | 27.9330i | 0.0354480i | ||||||||
\(789\) | −722.998 | + | 878.344i | −0.916347 | + | 1.11324i | ||||
\(790\) | 58.9832 | 0.0746623 | ||||||||
\(791\) | 378.785i | 0.478869i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −792.536 | −0.999415 | ||||||||
\(794\) | − | 283.927i | − | 0.357590i | ||||||
\(795\) | −69.3289 | − | 57.0672i | −0.0872061 | − | 0.0717826i | ||||
\(796\) | −188.739 | −0.237110 | ||||||||
\(797\) | − | 346.393i | − | 0.434621i | −0.976102 | − | 0.217311i | \(-0.930272\pi\) | ||
0.976102 | − | 0.217311i | \(-0.0697285\pi\) | |||||||
\(798\) | −131.368 | + | 159.594i | −0.164622 | + | 0.199993i | ||||
\(799\) | −1189.44 | −1.48866 | ||||||||
\(800\) | − | 470.174i | − | 0.587717i | ||||||
\(801\) | 337.309 | − | 66.0666i | 0.421110 | − | 0.0824801i | ||||
\(802\) | −1203.85 | −1.50107 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −223.845 | − | 184.255i | −0.278414 | − | 0.229173i | ||||
\(805\) | 42.1528 | 0.0523637 | ||||||||
\(806\) | 115.307i | 0.143061i | ||||||||
\(807\) | 59.4868 | − | 72.2683i | 0.0737135 | − | 0.0895518i | ||||
\(808\) | 907.135 | 1.12269 | ||||||||
\(809\) | 523.195i | 0.646718i | 0.946276 | + | 0.323359i | \(0.104812\pi\) | ||||
−0.946276 | + | 0.323359i | \(0.895188\pi\) | |||||||
\(810\) | 86.8845 | − | 35.3928i | 0.107265 | − | 0.0436948i | ||||
\(811\) | −1033.47 | −1.27431 | −0.637156 | − | 0.770735i | \(-0.719889\pi\) | ||||
−0.637156 | + | 0.770735i | \(0.719889\pi\) | |||||||
\(812\) | − | 17.5074i | − | 0.0215609i | ||||||
\(813\) | 1200.06 | + | 987.811i | 1.47608 | + | 1.21502i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.7838i | 0.0132317i | ||||||||
\(816\) | −289.818 | + | 352.089i | −0.355169 | + | 0.431482i | ||||
\(817\) | 360.926 | 0.441770 | ||||||||
\(818\) | − | 499.753i | − | 0.610946i | ||||||
\(819\) | 77.2574 | + | 394.445i | 0.0943314 | + | 0.481618i | ||||
\(820\) | 58.9058 | 0.0718363 | ||||||||
\(821\) | 97.7784i | 0.119097i | 0.998225 | + | 0.0595484i | \(0.0189661\pi\) | ||||
−0.998225 | + | 0.0595484i | \(0.981034\pi\) | |||||||
\(822\) | 784.932 | + | 646.106i | 0.954905 | + | 0.786017i | ||||
\(823\) | 721.665 | 0.876871 | 0.438436 | − | 0.898763i | \(-0.355533\pi\) | ||||
0.438436 | + | 0.898763i | \(0.355533\pi\) | |||||||
\(824\) | − | 473.673i | − | 0.574846i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 124.330 | 0.150521 | ||||||||
\(827\) | 1229.27i | 1.48642i | 0.669059 | + | 0.743209i | \(0.266697\pi\) | ||||
−0.669059 | + | 0.743209i | \(0.733303\pi\) | |||||||
\(828\) | −255.458 | + | 50.0349i | −0.308524 | + | 0.0604286i | ||||
\(829\) | −193.404 | −0.233298 | −0.116649 | − | 0.993173i | \(-0.537215\pi\) | ||||
−0.116649 | + | 0.993173i | \(0.537215\pi\) | |||||||
\(830\) | − | 68.5785i | − | 0.0826248i | ||||||
\(831\) | 852.277 | + | 701.541i | 1.02560 | + | 0.844213i | ||||
\(832\) | −1190.35 | −1.43071 | ||||||||
\(833\) | 679.829i | 0.816122i | ||||||||
\(834\) | −158.834 | + | 192.961i | −0.190448 | + | 0.231369i | ||||
\(835\) | −107.642 | −0.128912 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 52.1329 | − | 96.5094i | 0.0622854 | − | 0.115304i | ||||
\(838\) | −950.449 | −1.13419 | ||||||||
\(839\) | − | 583.289i | − | 0.695220i | −0.937639 | − | 0.347610i | \(-0.886993\pi\) | ||
0.937639 | − | 0.347610i | \(-0.113007\pi\) | |||||||
\(840\) | −36.7512 | − | 30.2513i | −0.0437514 | − | 0.0360134i | ||||
\(841\) | 812.207 | 0.965763 | ||||||||
\(842\) | 927.377i | 1.10140i | ||||||||
\(843\) | 610.853 | − | 742.104i | 0.724618 | − | 0.880313i | ||||
\(844\) | 227.064 | 0.269034 | ||||||||
\(845\) | − | 86.6072i | − | 0.102494i | ||||||
\(846\) | −211.752 | − | 1081.12i | −0.250297 | − | 1.27792i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 404.267i | 0.476730i | ||||||||
\(849\) | −372.439 | − | 306.568i | −0.438679 | − | 0.361093i | ||||
\(850\) | −654.894 | −0.770463 | ||||||||
\(851\) | 1469.44i | 1.72672i | ||||||||
\(852\) | 98.3786 | − | 119.517i | 0.115468 | − | 0.140278i | ||||
\(853\) | −431.225 | −0.505539 | −0.252770 | − | 0.967527i | \(-0.581341\pi\) | ||||
−0.252770 | + | 0.967527i | \(0.581341\pi\) | |||||||
\(854\) | 200.314i | 0.234560i | ||||||||
\(855\) | −98.2546 | + | 19.2445i | −0.114918 | + | 0.0225082i | ||||
\(856\) | 247.314 | 0.288919 | ||||||||
\(857\) | 580.461i | 0.677317i | 0.940909 | + | 0.338659i | \(0.109973\pi\) | ||||
−0.940909 | + | 0.338659i | \(0.890027\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −812.241 | −0.945566 | −0.472783 | − | 0.881179i | \(-0.656751\pi\) | ||||
−0.472783 | + | 0.881179i | \(0.656751\pi\) | |||||||
\(860\) | 19.7951i | 0.0230175i | ||||||||
\(861\) | −335.468 | + | 407.548i | −0.389626 | + | 0.473342i | ||||
\(862\) | 331.378 | 0.384430 | ||||||||
\(863\) | 628.218i | 0.727947i | 0.931409 | + | 0.363973i | \(0.118580\pi\) | ||||
−0.931409 | + | 0.363973i | \(0.881420\pi\) | |||||||
\(864\) | 455.663 | + | 246.142i | 0.527388 | + | 0.284887i | ||||
\(865\) | 17.5345 | 0.0202711 | ||||||||
\(866\) | 171.597i | 0.198149i | ||||||||
\(867\) | 68.0644 | + | 56.0264i | 0.0785057 | + | 0.0646209i | ||||
\(868\) | −13.2551 | −0.0152708 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −11.8493 | + | 14.3953i | −0.0136199 | + | 0.0165464i | ||||
\(871\) | −1322.83 | −1.51875 | ||||||||
\(872\) | 359.164i | 0.411886i | ||||||||
\(873\) | 28.1843 | + | 143.898i | 0.0322844 | + | 0.164831i | ||||
\(874\) | −610.812 | −0.698870 | ||||||||
\(875\) | − | 90.2344i | − | 0.103125i | ||||||
\(876\) | −164.441 | − | 135.357i | −0.187718 | − | 0.154518i | ||||
\(877\) | 1200.80 | 1.36922 | 0.684608 | − | 0.728911i | \(-0.259973\pi\) | ||||
0.684608 | + | 0.728911i | \(0.259973\pi\) | |||||||
\(878\) | 1098.61i | 1.25127i | ||||||||
\(879\) | −554.704 | + | 673.891i | −0.631063 | + | 0.766656i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 131.219i | − | 0.148943i | −0.997223 | − | 0.0744714i | \(-0.976273\pi\) | ||
0.997223 | − | 0.0744714i | \(-0.0237269\pi\) | |||||||
\(882\) | −617.917 | + | 121.027i | −0.700586 | + | 0.137219i | ||||
\(883\) | −127.000 | −0.143828 | −0.0719138 | − | 0.997411i | \(-0.522911\pi\) | ||||
−0.0719138 | + | 0.997411i | \(0.522911\pi\) | |||||||
\(884\) | − | 344.887i | − | 0.390143i | ||||||
\(885\) | 46.4953 | + | 38.2721i | 0.0525371 | + | 0.0432453i | ||||
\(886\) | 349.589 | 0.394570 | ||||||||
\(887\) | 1194.79i | 1.34700i | 0.739189 | + | 0.673499i | \(0.235209\pi\) | ||||
−0.739189 | + | 0.673499i | \(0.764791\pi\) | |||||||
\(888\) | 1054.56 | − | 1281.14i | 1.18756 | − | 1.44273i | ||||
\(889\) | −476.897 | −0.536442 | ||||||||
\(890\) | 44.2339i | 0.0497010i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 235.138 | 0.263608 | ||||||||
\(893\) | 1175.70i | 1.31657i | ||||||||
\(894\) | 604.533 | + | 497.614i | 0.676211 | + | 0.556615i | ||||
\(895\) | −43.1710 | −0.0482357 | ||||||||
\(896\) | 100.679i | 0.112365i | ||||||||
\(897\) | −754.826 | + | 917.011i | −0.841500 | + | 1.02231i | ||||
\(898\) | −396.749 | −0.441814 | ||||||||
\(899\) | 21.7995i | 0.0242487i | ||||||||
\(900\) | 53.0259 | + | 270.729i | 0.0589176 | + | 0.300810i | ||||
\(901\) | −690.442 | −0.766306 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −136.955 | − | 112.733i | −0.151667 | − | 0.124842i | ||||
\(904\) | 1263.95 | 1.39817 | ||||||||
\(905\) | 103.661i | 0.114543i | ||||||||
\(906\) | −541.808 | + | 658.223i | −0.598022 | + | 0.726515i | ||||
\(907\) | 524.583 | 0.578372 | 0.289186 | − | 0.957273i | \(-0.406615\pi\) | ||||
0.289186 | + | 0.957273i | \(0.406615\pi\) | |||||||
\(908\) | − | 536.751i | − | 0.591135i | ||||||
\(909\) | −920.264 | + | 180.246i | −1.01239 | + | 0.198291i | ||||
\(910\) | −51.7265 | −0.0568424 | ||||||||
\(911\) | − | 175.608i | − | 0.192764i | −0.995344 | − | 0.0963822i | \(-0.969273\pi\) | ||
0.995344 | − | 0.0963822i | \(-0.0307271\pi\) | |||||||
\(912\) | 348.020 | + | 286.468i | 0.381601 | + | 0.314110i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 44.2524i | − | 0.0484162i | ||||||
\(915\) | −61.6619 | + | 74.9108i | −0.0673900 | + | 0.0818697i | ||||
\(916\) | 169.788 | 0.185358 | ||||||||
\(917\) | − | 220.498i | − | 0.240456i | ||||||
\(918\) | 342.846 | − | 634.683i | 0.373470 | − | 0.691376i | ||||
\(919\) | −1305.11 | −1.42014 | −0.710070 | − | 0.704131i | \(-0.751337\pi\) | ||||
−0.710070 | + | 0.704131i | \(0.751337\pi\) | |||||||
\(920\) | − | 140.657i | − | 0.152888i | ||||||
\(921\) | −652.715 | − | 537.274i | −0.708702 | − | 0.583359i | ||||
\(922\) | −651.864 | −0.707011 | ||||||||
\(923\) | − | 706.294i | − | 0.765216i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1557.28 | 1.68355 | ||||||||
\(926\) | − | 177.347i | − | 0.191519i | ||||||
\(927\) | 94.1179 | + | 480.528i | 0.101530 | + | 0.518369i | ||||
\(928\) | −102.925 | −0.110911 | ||||||||
\(929\) | − | 1559.50i | − | 1.67869i | −0.543600 | − | 0.839344i | \(-0.682939\pi\) | ||
0.543600 | − | 0.839344i | \(-0.317061\pi\) | |||||||
\(930\) | 10.8989 | + | 8.97126i | 0.0117192 | + | 0.00964652i | ||||
\(931\) | 671.973 | 0.721776 | ||||||||
\(932\) | − | 408.777i | − | 0.438602i | ||||||
\(933\) | 903.247 | − | 1097.32i | 0.968111 | − | 1.17612i | ||||
\(934\) | −701.251 | −0.750804 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1316.20 | − | 257.795i | 1.40620 | − | 0.275422i | ||||
\(937\) | −719.352 | −0.767718 | −0.383859 | − | 0.923392i | \(-0.625405\pi\) | ||||
−0.383859 | + | 0.923392i | \(0.625405\pi\) | |||||||
\(938\) | 334.347i | 0.356447i | ||||||||
\(939\) | −69.4272 | − | 57.1481i | −0.0739374 | − | 0.0608606i | ||||
\(940\) | −64.4813 | −0.0685971 | ||||||||
\(941\) | − | 1173.29i | − | 1.24685i | −0.781882 | − | 0.623426i | \(-0.785740\pi\) | ||
0.781882 | − | 0.623426i | \(-0.214260\pi\) | |||||||
\(942\) | −206.560 | + | 250.943i | −0.219278 | + | 0.266394i | ||||
\(943\) | −1559.80 | −1.65408 | ||||||||
\(944\) | − | 271.121i | − | 0.287205i | ||||||
\(945\) | 43.2940 | + | 23.3867i | 0.0458137 | + | 0.0247478i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 266.119i | 0.281013i | 0.990080 | + | 0.140506i | \(0.0448730\pi\) | ||||
−0.990080 | + | 0.140506i | \(0.955127\pi\) | |||||||
\(948\) | −147.504 | − | 121.416i | −0.155595 | − | 0.128076i | ||||
\(949\) | −971.778 | −1.02400 | ||||||||
\(950\) | 647.326i | 0.681395i | ||||||||
\(951\) | 303.674 | − | 368.922i | 0.319320 | − | 0.387931i | ||||
\(952\) | −366.003 | −0.384457 | ||||||||
\(953\) | 128.153i | 0.134474i | 0.997737 | + | 0.0672369i | \(0.0214183\pi\) | ||||
−0.997737 | + | 0.0672369i | \(0.978582\pi\) | |||||||
\(954\) | −122.917 | − | 627.563i | −0.128843 | − | 0.657822i | ||||
\(955\) | 39.2579 | 0.0411077 | ||||||||
\(956\) | 116.864i | 0.122242i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 894.933 | 0.934168 | ||||||||
\(959\) | 533.231i | 0.556028i | ||||||||
\(960\) | −92.6134 | + | 112.513i | −0.0964723 | + | 0.117201i | ||||
\(961\) | −944.495 | −0.982826 | ||||||||
\(962\) | − | 1803.18i | − | 1.87441i | ||||||
\(963\) | −250.894 | + | 49.1409i | −0.260534 | + | 0.0510290i | ||||
\(964\) | 258.563 | 0.268219 | ||||||||
\(965\) | − | 105.455i | − | 0.109279i | ||||||
\(966\) | 231.775 | + | 190.783i | 0.239933 | + | 0.197498i | ||||
\(967\) | 1324.17 | 1.36936 | 0.684682 | − | 0.728842i | \(-0.259941\pi\) | ||||
0.684682 | + | 0.728842i | \(0.259941\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −489.255 | + | 594.379i | −0.504907 | + | 0.613394i | ||||
\(970\) | −18.8704 | −0.0194540 | ||||||||
\(971\) | − | 584.878i | − | 0.602346i | −0.953570 | − | 0.301173i | \(-0.902622\pi\) | ||
0.953570 | − | 0.301173i | \(-0.0973781\pi\) | |||||||
\(972\) | −290.134 | − | 90.3407i | −0.298491 | − | 0.0929431i | ||||
\(973\) | −131.085 | −0.134723 | ||||||||
\(974\) | − | 1012.55i | − | 1.03958i | ||||||
\(975\) | 971.828 | + | 799.948i | 0.996747 | + | 0.820459i | ||||
\(976\) | 436.816 | 0.447557 | ||||||||
\(977\) | 691.347i | 0.707622i | 0.935317 | + | 0.353811i | \(0.115114\pi\) | ||||
−0.935317 | + | 0.353811i | \(0.884886\pi\) | |||||||
\(978\) | −48.8073 | + | 59.2943i | −0.0499052 | + | 0.0606281i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 36.8545i | 0.0376066i | ||||||||
\(981\) | −71.3653 | − | 364.363i | −0.0727475 | − | 0.371420i | ||||
\(982\) | 94.3064 | 0.0960350 | ||||||||
\(983\) | − | 655.489i | − | 0.666825i | −0.942781 | − | 0.333413i | \(-0.891800\pi\) | ||
0.942781 | − | 0.333413i | \(-0.108200\pi\) | |||||||
\(984\) | 1359.92 | + | 1119.40i | 1.38203 | + | 1.13760i | ||||
\(985\) | 15.6027 | 0.0158403 | ||||||||
\(986\) | 143.362i | 0.145398i | ||||||||
\(987\) | 367.220 | − | 446.123i | 0.372057 | − | 0.451999i | ||||
\(988\) | −340.901 | −0.345042 | ||||||||
\(989\) | − | 524.164i | − | 0.529994i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 95.0559 | 0.0959192 | 0.0479596 | − | 0.998849i | \(-0.484728\pi\) | ||||
0.0479596 | + | 0.998849i | \(0.484728\pi\) | |||||||
\(992\) | 77.9258i | 0.0785542i | ||||||||
\(993\) | 770.633 | + | 634.337i | 0.776066 | + | 0.638809i | ||||
\(994\) | −178.516 | −0.179594 | ||||||||
\(995\) | 105.425i | 0.105955i | ||||||||
\(996\) | −141.167 | + | 171.499i | −0.141734 | + | 0.172188i | ||||
\(997\) | −781.403 | −0.783754 | −0.391877 | − | 0.920018i | \(-0.628174\pi\) | ||||
−0.391877 | + | 0.920018i | \(0.628174\pi\) | |||||||
\(998\) | − | 777.475i | − | 0.779033i | ||||||
\(999\) | −815.258 | + | 1509.22i | −0.816074 | + | 1.51073i |
(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 | 363.3.b.m.122.4 | 8 | ||
3.2 | odd | 2 | inner | 363.3.b.m.122.5 | 8 | ||
11.2 | odd | 10 | 363.3.h.j.323.3 | 16 | |||
11.3 | even | 5 | 363.3.h.o.251.2 | 16 | |||
11.4 | even | 5 | 363.3.h.o.269.3 | 16 | |||
11.5 | even | 5 | 33.3.h.b.14.3 | yes | 16 | ||
11.6 | odd | 10 | 363.3.h.j.245.2 | 16 | |||
11.7 | odd | 10 | 363.3.h.n.269.2 | 16 | |||
11.8 | odd | 10 | 363.3.h.n.251.3 | 16 | |||
11.9 | even | 5 | 33.3.h.b.26.2 | yes | 16 | ||
11.10 | odd | 2 | 363.3.b.l.122.5 | 8 | |||
33.2 | even | 10 | 363.3.h.j.323.2 | 16 | |||
33.5 | odd | 10 | 33.3.h.b.14.2 | ✓ | 16 | ||
33.8 | even | 10 | 363.3.h.n.251.2 | 16 | |||
33.14 | odd | 10 | 363.3.h.o.251.3 | 16 | |||
33.17 | even | 10 | 363.3.h.j.245.3 | 16 | |||
33.20 | odd | 10 | 33.3.h.b.26.3 | yes | 16 | ||
33.26 | odd | 10 | 363.3.h.o.269.2 | 16 | |||
33.29 | even | 10 | 363.3.h.n.269.3 | 16 | |||
33.32 | even | 2 | 363.3.b.l.122.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.h.b.14.2 | ✓ | 16 | 33.5 | odd | 10 | ||
33.3.h.b.14.3 | yes | 16 | 11.5 | even | 5 | ||
33.3.h.b.26.2 | yes | 16 | 11.9 | even | 5 | ||
33.3.h.b.26.3 | yes | 16 | 33.20 | odd | 10 | ||
363.3.b.l.122.4 | 8 | 33.32 | even | 2 | |||
363.3.b.l.122.5 | 8 | 11.10 | odd | 2 | |||
363.3.b.m.122.4 | 8 | 1.1 | even | 1 | trivial | ||
363.3.b.m.122.5 | 8 | 3.2 | odd | 2 | inner | ||
363.3.h.j.245.2 | 16 | 11.6 | odd | 10 | |||
363.3.h.j.245.3 | 16 | 33.17 | even | 10 | |||
363.3.h.j.323.2 | 16 | 33.2 | even | 10 | |||
363.3.h.j.323.3 | 16 | 11.2 | odd | 10 | |||
363.3.h.n.251.2 | 16 | 33.8 | even | 10 | |||
363.3.h.n.251.3 | 16 | 11.8 | odd | 10 | |||
363.3.h.n.269.2 | 16 | 11.7 | odd | 10 | |||
363.3.h.n.269.3 | 16 | 33.29 | even | 10 | |||
363.3.h.o.251.2 | 16 | 11.3 | even | 5 | |||
363.3.h.o.251.3 | 16 | 33.14 | odd | 10 | |||
363.3.h.o.269.2 | 16 | 33.26 | odd | 10 | |||
363.3.h.o.269.3 | 16 | 11.4 | even | 5 |