Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(288,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.288");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.b (of order \(2\), degree \(1\), not 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: | \(17.0515519917\) |
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: | \( x^{8} + 43x^{6} + 505x^{4} + 1528x^{2} + 1296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.5 | ||
Root | \(1.58184i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.d.288.6 |
$q$-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 \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.58184 | 0.559265 | 0.279632 | − | 0.960107i | \(-0.409787\pi\) | ||||
0.279632 | + | 0.960107i | \(0.409787\pi\) | |||||||
\(3\) | − 4.98387i | − 0.959146i | −0.877502 | − | 0.479573i | \(-0.840792\pi\) | ||||
0.877502 | − | 0.479573i | \(-0.159208\pi\) | |||||||
\(4\) | −5.49778 | −0.687223 | ||||||||
\(5\) | − 14.4471i | − 1.29219i | −0.763259 | − | 0.646093i | \(-0.776402\pi\) | ||||
0.763259 | − | 0.646093i | \(-0.223598\pi\) | |||||||
\(6\) | − 7.88368i | − 0.536417i | ||||||||
\(7\) | − 29.4104i | − 1.58801i | −0.607910 | − | 0.794006i | \(-0.707992\pi\) | ||||
0.607910 | − | 0.794006i | \(-0.292008\pi\) | |||||||
\(8\) | −21.3513 | −0.943604 | ||||||||
\(9\) | 2.16104 | 0.0800385 | ||||||||
\(10\) | − 22.8530i | − 0.722674i | ||||||||
\(11\) | 13.5324i | 0.370923i | 0.982651 | + | 0.185462i | \(0.0593781\pi\) | ||||
−0.982651 | + | 0.185462i | \(0.940622\pi\) | |||||||
\(12\) | 27.4002i | 0.659147i | ||||||||
\(13\) | 45.7656 | 0.976391 | 0.488196 | − | 0.872734i | \(-0.337655\pi\) | ||||
0.488196 | + | 0.872734i | \(0.337655\pi\) | |||||||
\(14\) | − 46.5225i | − 0.888119i | ||||||||
\(15\) | −72.0024 | −1.23940 | ||||||||
\(16\) | 10.2079 | 0.159498 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 3.41842 | 0.0447627 | ||||||||
\(19\) | −113.386 | −1.36908 | −0.684539 | − | 0.728976i | \(-0.739996\pi\) | ||||
−0.684539 | + | 0.728976i | \(0.739996\pi\) | |||||||
\(20\) | 79.4269i | 0.888020i | ||||||||
\(21\) | −146.578 | −1.52314 | ||||||||
\(22\) | 21.4060i | 0.207444i | ||||||||
\(23\) | 144.513i | 1.31013i | 0.755573 | + | 0.655065i | \(0.227359\pi\) | ||||
−0.755573 | + | 0.655065i | \(0.772641\pi\) | |||||||
\(24\) | 106.412i | 0.905055i | ||||||||
\(25\) | −83.7182 | −0.669745 | ||||||||
\(26\) | 72.3938 | 0.546061 | ||||||||
\(27\) | − 145.335i | − 1.03591i | ||||||||
\(28\) | 161.692i | 1.09132i | ||||||||
\(29\) | 1.26688i | 0.00811217i | 0.999992 | + | 0.00405608i | \(0.00129109\pi\) | ||||
−0.999992 | + | 0.00405608i | \(0.998709\pi\) | |||||||
\(30\) | −113.896 | −0.693150 | ||||||||
\(31\) | 30.0858i | 0.174309i | 0.996195 | + | 0.0871544i | \(0.0277773\pi\) | ||||
−0.996195 | + | 0.0871544i | \(0.972223\pi\) | |||||||
\(32\) | 186.958 | 1.03281 | ||||||||
\(33\) | 67.4435 | 0.355770 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −424.894 | −2.05201 | ||||||||
\(36\) | −11.8809 | −0.0550043 | ||||||||
\(37\) | − 398.512i | − 1.77067i | −0.464950 | − | 0.885337i | \(-0.653928\pi\) | ||||
0.464950 | − | 0.885337i | \(-0.346072\pi\) | |||||||
\(38\) | −179.358 | −0.765677 | ||||||||
\(39\) | − 228.090i | − 0.936502i | ||||||||
\(40\) | 308.464i | 1.21931i | ||||||||
\(41\) | 184.595i | 0.703143i | 0.936161 | + | 0.351571i | \(0.114353\pi\) | ||||
−0.936161 | + | 0.351571i | \(0.885647\pi\) | |||||||
\(42\) | −231.862 | −0.851836 | ||||||||
\(43\) | −135.605 | −0.480921 | −0.240460 | − | 0.970659i | \(-0.577298\pi\) | ||||
−0.240460 | + | 0.970659i | \(0.577298\pi\) | |||||||
\(44\) | − 74.3979i | − 0.254907i | ||||||||
\(45\) | − 31.2207i | − 0.103425i | ||||||||
\(46\) | 228.596i | 0.732709i | ||||||||
\(47\) | 247.542 | 0.768249 | 0.384124 | − | 0.923281i | \(-0.374503\pi\) | ||||
0.384124 | + | 0.923281i | \(0.374503\pi\) | |||||||
\(48\) | − 50.8748i | − 0.152982i | ||||||||
\(49\) | −521.971 | −1.52178 | ||||||||
\(50\) | −132.429 | −0.374565 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −251.609 | −0.670998 | ||||||||
\(53\) | 635.182 | 1.64621 | 0.823103 | − | 0.567892i | \(-0.192241\pi\) | ||||
0.823103 | + | 0.567892i | \(0.192241\pi\) | |||||||
\(54\) | − 229.896i | − 0.579351i | ||||||||
\(55\) | 195.503 | 0.479302 | ||||||||
\(56\) | 627.951i | 1.49845i | ||||||||
\(57\) | 565.100i | 1.31315i | ||||||||
\(58\) | 2.00399i | 0.00453685i | ||||||||
\(59\) | −625.420 | −1.38005 | −0.690023 | − | 0.723788i | \(-0.742400\pi\) | ||||
−0.690023 | + | 0.723788i | \(0.742400\pi\) | |||||||
\(60\) | 395.853 | 0.851741 | ||||||||
\(61\) | − 166.873i | − 0.350261i | −0.984545 | − | 0.175130i | \(-0.943965\pi\) | ||||
0.984545 | − | 0.175130i | \(-0.0560347\pi\) | |||||||
\(62\) | 47.5909i | 0.0974847i | ||||||||
\(63\) | − 63.5570i | − 0.127102i | ||||||||
\(64\) | 214.074 | 0.418114 | ||||||||
\(65\) | − 661.179i | − 1.26168i | ||||||||
\(66\) | 106.685 | 0.198970 | ||||||||
\(67\) | 159.984 | 0.291719 | 0.145859 | − | 0.989305i | \(-0.453405\pi\) | ||||
0.145859 | + | 0.989305i | \(0.453405\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 720.232 | 1.25661 | ||||||||
\(70\) | −672.115 | −1.14762 | ||||||||
\(71\) | − 19.4559i | − 0.0325211i | −0.999868 | − | 0.0162605i | \(-0.994824\pi\) | ||||
0.999868 | − | 0.0162605i | \(-0.00517611\pi\) | |||||||
\(72\) | −46.1411 | −0.0755247 | ||||||||
\(73\) | − 336.039i | − 0.538772i | −0.963032 | − | 0.269386i | \(-0.913179\pi\) | ||||
0.963032 | − | 0.269386i | \(-0.0868207\pi\) | |||||||
\(74\) | − 630.382i | − 0.990276i | ||||||||
\(75\) | 417.241i | 0.642384i | ||||||||
\(76\) | 623.370 | 0.940862 | ||||||||
\(77\) | 397.992 | 0.589031 | ||||||||
\(78\) | − 360.801i | − 0.523753i | ||||||||
\(79\) | 1072.15i | 1.52691i | 0.645859 | + | 0.763457i | \(0.276500\pi\) | ||||
−0.645859 | + | 0.763457i | \(0.723500\pi\) | |||||||
\(80\) | − 147.474i | − 0.206101i | ||||||||
\(81\) | −665.982 | −0.913555 | ||||||||
\(82\) | 291.999i | 0.393243i | ||||||||
\(83\) | −47.1944 | −0.0624128 | −0.0312064 | − | 0.999513i | \(-0.509935\pi\) | ||||
−0.0312064 | + | 0.999513i | \(0.509935\pi\) | |||||||
\(84\) | 805.852 | 1.04673 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −214.506 | −0.268962 | ||||||||
\(87\) | 6.31394 | 0.00778075 | ||||||||
\(88\) | − 288.934i | − 0.350005i | ||||||||
\(89\) | −626.312 | −0.745944 | −0.372972 | − | 0.927843i | \(-0.621661\pi\) | ||||
−0.372972 | + | 0.927843i | \(0.621661\pi\) | |||||||
\(90\) | − 49.3862i | − 0.0578418i | ||||||||
\(91\) | − 1345.98i | − 1.55052i | ||||||||
\(92\) | − 794.499i | − 0.900351i | ||||||||
\(93\) | 149.944 | 0.167188 | ||||||||
\(94\) | 391.572 | 0.429655 | ||||||||
\(95\) | 1638.09i | 1.76910i | ||||||||
\(96\) | − 931.774i | − 0.990612i | ||||||||
\(97\) | − 692.045i | − 0.724398i | −0.932101 | − | 0.362199i | \(-0.882026\pi\) | ||||
0.932101 | − | 0.362199i | \(-0.117974\pi\) | |||||||
\(98\) | −825.674 | −0.851079 | ||||||||
\(99\) | 29.2439i | 0.0296882i | ||||||||
\(100\) | 460.264 | 0.460264 | ||||||||
\(101\) | −551.668 | −0.543496 | −0.271748 | − | 0.962369i | \(-0.587602\pi\) | ||||
−0.271748 | + | 0.962369i | \(0.587602\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −175.990 | −0.168358 | −0.0841789 | − | 0.996451i | \(-0.526827\pi\) | ||||
−0.0841789 | + | 0.996451i | \(0.526827\pi\) | |||||||
\(104\) | −977.156 | −0.921327 | ||||||||
\(105\) | 2117.62i | 1.96817i | ||||||||
\(106\) | 1004.76 | 0.920665 | ||||||||
\(107\) | − 148.521i | − 0.134188i | −0.997747 | − | 0.0670938i | \(-0.978627\pi\) | ||||
0.997747 | − | 0.0670938i | \(-0.0213727\pi\) | |||||||
\(108\) | 799.019i | 0.711904i | ||||||||
\(109\) | − 703.114i | − 0.617854i | −0.951086 | − | 0.308927i | \(-0.900030\pi\) | ||||
0.951086 | − | 0.308927i | \(-0.0999699\pi\) | |||||||
\(110\) | 309.254 | 0.268057 | ||||||||
\(111\) | −1986.13 | −1.69834 | ||||||||
\(112\) | − 300.218i | − 0.253285i | ||||||||
\(113\) | − 1987.05i | − 1.65421i | −0.562048 | − | 0.827104i | \(-0.689986\pi\) | ||||
0.562048 | − | 0.827104i | \(-0.310014\pi\) | |||||||
\(114\) | 893.898i | 0.734396i | ||||||||
\(115\) | 2087.79 | 1.69293 | ||||||||
\(116\) | − 6.96500i | − 0.00557487i | ||||||||
\(117\) | 98.9012 | 0.0781489 | ||||||||
\(118\) | −989.314 | −0.771811 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1537.35 | 1.16950 | ||||||||
\(121\) | 1147.88 | 0.862416 | ||||||||
\(122\) | − 263.966i | − 0.195888i | ||||||||
\(123\) | 919.996 | 0.674417 | ||||||||
\(124\) | − 165.405i | − 0.119789i | ||||||||
\(125\) | − 596.402i | − 0.426750i | ||||||||
\(126\) | − 100.537i | − 0.0710837i | ||||||||
\(127\) | 1561.88 | 1.09130 | 0.545649 | − | 0.838014i | \(-0.316283\pi\) | ||||
0.545649 | + | 0.838014i | \(0.316283\pi\) | |||||||
\(128\) | −1157.03 | −0.798970 | ||||||||
\(129\) | 675.838i | 0.461273i | ||||||||
\(130\) | − 1045.88i | − 0.705613i | ||||||||
\(131\) | − 1317.70i | − 0.878839i | −0.898282 | − | 0.439419i | \(-0.855184\pi\) | ||||
0.898282 | − | 0.439419i | \(-0.144816\pi\) | |||||||
\(132\) | −370.790 | −0.244493 | ||||||||
\(133\) | 3334.72i | 2.17411i | ||||||||
\(134\) | 253.069 | 0.163148 | ||||||||
\(135\) | −2099.66 | −1.33859 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 485.214 | 0.302588 | 0.151294 | − | 0.988489i | \(-0.451656\pi\) | ||||
0.151294 | + | 0.988489i | \(0.451656\pi\) | |||||||
\(138\) | 1139.29 | 0.702775 | ||||||||
\(139\) | 1016.66i | 0.620376i | 0.950675 | + | 0.310188i | \(0.100392\pi\) | ||||
−0.950675 | + | 0.310188i | \(0.899608\pi\) | |||||||
\(140\) | 2335.98 | 1.41019 | ||||||||
\(141\) | − 1233.72i | − 0.736863i | ||||||||
\(142\) | − 30.7762i | − 0.0181879i | ||||||||
\(143\) | 619.316i | 0.362166i | ||||||||
\(144\) | 22.0596 | 0.0127660 | ||||||||
\(145\) | 18.3026 | 0.0104824 | ||||||||
\(146\) | − 531.559i | − 0.301316i | ||||||||
\(147\) | 2601.44i | 1.45961i | ||||||||
\(148\) | 2190.93i | 1.21685i | ||||||||
\(149\) | −1322.91 | −0.727364 | −0.363682 | − | 0.931523i | \(-0.618481\pi\) | ||||
−0.363682 | + | 0.931523i | \(0.618481\pi\) | |||||||
\(150\) | 660.008i | 0.359263i | ||||||||
\(151\) | 1467.32 | 0.790785 | 0.395392 | − | 0.918512i | \(-0.370609\pi\) | ||||
0.395392 | + | 0.918512i | \(0.370609\pi\) | |||||||
\(152\) | 2420.94 | 1.29187 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 629.559 | 0.329424 | ||||||||
\(155\) | 434.652 | 0.225239 | ||||||||
\(156\) | 1253.99i | 0.643586i | ||||||||
\(157\) | −3403.23 | −1.72998 | −0.864991 | − | 0.501788i | \(-0.832676\pi\) | ||||
−0.864991 | + | 0.501788i | \(0.832676\pi\) | |||||||
\(158\) | 1695.97i | 0.853949i | ||||||||
\(159\) | − 3165.66i | − 1.57895i | ||||||||
\(160\) | − 2701.00i | − 1.33458i | ||||||||
\(161\) | 4250.17 | 2.08050 | ||||||||
\(162\) | −1053.48 | −0.510919 | ||||||||
\(163\) | − 378.056i | − 0.181667i | −0.995866 | − | 0.0908333i | \(-0.971047\pi\) | ||||
0.995866 | − | 0.0908333i | \(-0.0289530\pi\) | |||||||
\(164\) | − 1014.86i | − 0.483216i | ||||||||
\(165\) | − 974.362i | − 0.459721i | ||||||||
\(166\) | −74.6540 | −0.0349053 | ||||||||
\(167\) | − 572.418i | − 0.265240i | −0.991167 | − | 0.132620i | \(-0.957661\pi\) | ||||
0.991167 | − | 0.132620i | \(-0.0423390\pi\) | |||||||
\(168\) | 3129.63 | 1.43724 | ||||||||
\(169\) | −102.512 | −0.0466601 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −245.031 | −0.109579 | ||||||||
\(172\) | 745.528 | 0.330500 | ||||||||
\(173\) | − 3321.64i | − 1.45977i | −0.683571 | − | 0.729884i | \(-0.739574\pi\) | ||||
0.683571 | − | 0.729884i | \(-0.260426\pi\) | |||||||
\(174\) | 9.98764 | 0.00435150 | ||||||||
\(175\) | 2462.18i | 1.06356i | ||||||||
\(176\) | 138.137i | 0.0591616i | ||||||||
\(177\) | 3117.01i | 1.32367i | ||||||||
\(178\) | −990.726 | −0.417180 | ||||||||
\(179\) | 2093.76 | 0.874273 | 0.437137 | − | 0.899395i | \(-0.355993\pi\) | ||||
0.437137 | + | 0.899395i | \(0.355993\pi\) | |||||||
\(180\) | 171.645i | 0.0710758i | ||||||||
\(181\) | − 682.032i | − 0.280083i | −0.990146 | − | 0.140042i | \(-0.955276\pi\) | ||||
0.990146 | − | 0.140042i | \(-0.0447236\pi\) | |||||||
\(182\) | − 2129.13i | − 0.867152i | ||||||||
\(183\) | −831.673 | −0.335951 | ||||||||
\(184\) | − 3085.54i | − 1.23624i | ||||||||
\(185\) | −5757.33 | −2.28804 | ||||||||
\(186\) | 237.187 | 0.0935021 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1360.93 | −0.527958 | ||||||||
\(189\) | −4274.35 | −1.64504 | ||||||||
\(190\) | 2591.20i | 0.989398i | ||||||||
\(191\) | 1921.15 | 0.727799 | 0.363900 | − | 0.931438i | \(-0.381445\pi\) | ||||
0.363900 | + | 0.931438i | \(0.381445\pi\) | |||||||
\(192\) | − 1066.92i | − 0.401032i | ||||||||
\(193\) | 69.6893i | 0.0259914i | 0.999916 | + | 0.0129957i | \(0.00413678\pi\) | ||||
−0.999916 | + | 0.0129957i | \(0.995863\pi\) | |||||||
\(194\) | − 1094.70i | − 0.405130i | ||||||||
\(195\) | −3295.23 | −1.21014 | ||||||||
\(196\) | 2869.68 | 1.04580 | ||||||||
\(197\) | 3043.10i | 1.10057i | 0.834977 | + | 0.550285i | \(0.185481\pi\) | ||||
−0.834977 | + | 0.550285i | \(0.814519\pi\) | |||||||
\(198\) | 46.2592i | 0.0166035i | ||||||||
\(199\) | − 1255.72i | − 0.447315i | −0.974668 | − | 0.223657i | \(-0.928200\pi\) | ||||
0.974668 | − | 0.223657i | \(-0.0717997\pi\) | |||||||
\(200\) | 1787.49 | 0.631975 | ||||||||
\(201\) | − 797.340i | − 0.279801i | ||||||||
\(202\) | −872.651 | −0.303958 | ||||||||
\(203\) | 37.2593 | 0.0128822 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2666.85 | 0.908591 | ||||||||
\(206\) | −278.389 | −0.0941566 | ||||||||
\(207\) | 312.297i | 0.104861i | ||||||||
\(208\) | 467.170 | 0.155733 | ||||||||
\(209\) | − 1534.38i | − 0.507823i | ||||||||
\(210\) | 3349.73i | 1.10073i | ||||||||
\(211\) | 1060.15i | 0.345894i | 0.984931 | + | 0.172947i | \(0.0553289\pi\) | ||||
−0.984931 | + | 0.172947i | \(0.944671\pi\) | |||||||
\(212\) | −3492.09 | −1.13131 | ||||||||
\(213\) | −96.9658 | −0.0311924 | ||||||||
\(214\) | − 234.937i | − 0.0750464i | ||||||||
\(215\) | 1959.10i | 0.621439i | ||||||||
\(216\) | 3103.09i | 0.977494i | ||||||||
\(217\) | 884.835 | 0.276804 | ||||||||
\(218\) | − 1112.21i | − 0.345544i | ||||||||
\(219\) | −1674.77 | −0.516761 | ||||||||
\(220\) | −1074.83 | −0.329387 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3141.74 | −0.949819 | ||||||||
\(223\) | 1398.85 | 0.420064 | 0.210032 | − | 0.977695i | \(-0.432643\pi\) | ||||
0.210032 | + | 0.977695i | \(0.432643\pi\) | |||||||
\(224\) | − 5498.50i | − 1.64011i | ||||||||
\(225\) | −180.918 | −0.0536054 | ||||||||
\(226\) | − 3143.19i | − 0.925141i | ||||||||
\(227\) | 2436.65i | 0.712451i | 0.934400 | + | 0.356226i | \(0.115937\pi\) | ||||
−0.934400 | + | 0.356226i | \(0.884063\pi\) | |||||||
\(228\) | − 3106.80i | − 0.902424i | ||||||||
\(229\) | −5027.28 | −1.45071 | −0.725354 | − | 0.688376i | \(-0.758324\pi\) | ||||
−0.725354 | + | 0.688376i | \(0.758324\pi\) | |||||||
\(230\) | 3302.54 | 0.946797 | ||||||||
\(231\) | − 1983.54i | − 0.564967i | ||||||||
\(232\) | − 27.0495i | − 0.00765467i | ||||||||
\(233\) | 891.120i | 0.250555i | 0.992122 | + | 0.125277i | \(0.0399821\pi\) | ||||
−0.992122 | + | 0.125277i | \(0.960018\pi\) | |||||||
\(234\) | 156.446 | 0.0437059 | ||||||||
\(235\) | − 3576.26i | − 0.992721i | ||||||||
\(236\) | 3438.42 | 0.948399 | ||||||||
\(237\) | 5343.45 | 1.46453 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −161.975 | −0.0438382 | −0.0219191 | − | 0.999760i | \(-0.506978\pi\) | ||||
−0.0219191 | + | 0.999760i | \(0.506978\pi\) | |||||||
\(240\) | −734.992 | −0.197681 | ||||||||
\(241\) | − 3467.39i | − 0.926782i | −0.886154 | − | 0.463391i | \(-0.846633\pi\) | ||||
0.886154 | − | 0.463391i | \(-0.153367\pi\) | |||||||
\(242\) | 1815.75 | 0.482319 | ||||||||
\(243\) | − 604.873i | − 0.159682i | ||||||||
\(244\) | 917.432i | 0.240707i | ||||||||
\(245\) | 7540.96i | 1.96642i | ||||||||
\(246\) | 1455.29 | 0.377177 | ||||||||
\(247\) | −5189.17 | −1.33676 | ||||||||
\(248\) | − 642.372i | − 0.164478i | ||||||||
\(249\) | 235.211i | 0.0598630i | ||||||||
\(250\) | − 943.412i | − 0.238666i | ||||||||
\(251\) | −4328.65 | −1.08853 | −0.544267 | − | 0.838912i | \(-0.683192\pi\) | ||||
−0.544267 | + | 0.838912i | \(0.683192\pi\) | |||||||
\(252\) | 349.423i | 0.0873474i | ||||||||
\(253\) | −1955.60 | −0.485958 | ||||||||
\(254\) | 2470.65 | 0.610324 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3542.83 | −0.864950 | ||||||||
\(257\) | 4567.47 | 1.10860 | 0.554301 | − | 0.832316i | \(-0.312986\pi\) | ||||
0.554301 | + | 0.832316i | \(0.312986\pi\) | |||||||
\(258\) | 1069.07i | 0.257974i | ||||||||
\(259\) | −11720.4 | −2.81185 | ||||||||
\(260\) | 3635.02i | 0.867055i | ||||||||
\(261\) | 2.73777i | 0 0.000649285i | ||||||||
\(262\) | − 2084.39i | − 0.491504i | ||||||||
\(263\) | −4711.02 | −1.10454 | −0.552270 | − | 0.833665i | \(-0.686238\pi\) | ||||
−0.552270 | + | 0.833665i | \(0.686238\pi\) | |||||||
\(264\) | −1440.01 | −0.335706 | ||||||||
\(265\) | − 9176.52i | − 2.12721i | ||||||||
\(266\) | 5274.99i | 1.21590i | ||||||||
\(267\) | 3121.46i | 0.715469i | ||||||||
\(268\) | −879.558 | −0.200476 | ||||||||
\(269\) | 3659.09i | 0.829362i | 0.909967 | + | 0.414681i | \(0.136107\pi\) | ||||
−0.909967 | + | 0.414681i | \(0.863893\pi\) | |||||||
\(270\) | −3321.33 | −0.748629 | ||||||||
\(271\) | −7702.43 | −1.72653 | −0.863264 | − | 0.504753i | \(-0.831584\pi\) | ||||
−0.863264 | + | 0.504753i | \(0.831584\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6708.21 | −1.48718 | ||||||||
\(274\) | 767.530 | 0.169227 | ||||||||
\(275\) | − 1132.90i | − 0.248424i | ||||||||
\(276\) | −3959.68 | −0.863568 | ||||||||
\(277\) | 3252.61i | 0.705526i | 0.935713 | + | 0.352763i | \(0.114758\pi\) | ||||
−0.935713 | + | 0.352763i | \(0.885242\pi\) | |||||||
\(278\) | 1608.20i | 0.346954i | ||||||||
\(279\) | 65.0166i | 0.0139514i | ||||||||
\(280\) | 9072.06 | 1.93628 | ||||||||
\(281\) | 6839.31 | 1.45195 | 0.725977 | − | 0.687719i | \(-0.241388\pi\) | ||||
0.725977 | + | 0.687719i | \(0.241388\pi\) | |||||||
\(282\) | − 1951.54i | − 0.412101i | ||||||||
\(283\) | 3131.30i | 0.657726i | 0.944378 | + | 0.328863i | \(0.106665\pi\) | ||||
−0.944378 | + | 0.328863i | \(0.893335\pi\) | |||||||
\(284\) | 106.965i | 0.0223492i | ||||||||
\(285\) | 8164.05 | 1.69683 | ||||||||
\(286\) | 979.659i | 0.202547i | ||||||||
\(287\) | 5429.00 | 1.11660 | ||||||||
\(288\) | 404.023 | 0.0826642 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 28.9519 | 0.00586245 | ||||||||
\(291\) | −3449.06 | −0.694803 | ||||||||
\(292\) | 1847.47i | 0.370256i | ||||||||
\(293\) | 5396.03 | 1.07590 | 0.537951 | − | 0.842976i | \(-0.319198\pi\) | ||||
0.537951 | + | 0.842976i | \(0.319198\pi\) | |||||||
\(294\) | 4115.05i | 0.816309i | ||||||||
\(295\) | 9035.49i | 1.78328i | ||||||||
\(296\) | 8508.76i | 1.67082i | ||||||||
\(297\) | 1966.72 | 0.384245 | ||||||||
\(298\) | −2092.64 | −0.406789 | ||||||||
\(299\) | 6613.70i | 1.27920i | ||||||||
\(300\) | − 2293.90i | − 0.441461i | ||||||||
\(301\) | 3988.20i | 0.763708i | ||||||||
\(302\) | 2321.06 | 0.442258 | ||||||||
\(303\) | 2749.44i | 0.521292i | ||||||||
\(304\) | −1157.43 | −0.218365 | ||||||||
\(305\) | −2410.83 | −0.452602 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2156.62 | 0.400927 | 0.200463 | − | 0.979701i | \(-0.435755\pi\) | ||||
0.200463 | + | 0.979701i | \(0.435755\pi\) | |||||||
\(308\) | −2188.07 | −0.404795 | ||||||||
\(309\) | 877.113i | 0.161480i | ||||||||
\(310\) | 687.550 | 0.125968 | ||||||||
\(311\) | − 2729.42i | − 0.497656i | −0.968548 | − | 0.248828i | \(-0.919955\pi\) | ||||
0.968548 | − | 0.248828i | \(-0.0800454\pi\) | |||||||
\(312\) | 4870.02i | 0.883687i | ||||||||
\(313\) | − 5014.77i | − 0.905595i | −0.891613 | − | 0.452798i | \(-0.850426\pi\) | ||||
0.891613 | − | 0.452798i | \(-0.149574\pi\) | |||||||
\(314\) | −5383.36 | −0.967518 | ||||||||
\(315\) | −918.213 | −0.164240 | ||||||||
\(316\) | − 5894.44i | − 1.04933i | ||||||||
\(317\) | − 1164.53i | − 0.206329i | −0.994664 | − | 0.103165i | \(-0.967103\pi\) | ||||
0.994664 | − | 0.103165i | \(-0.0328968\pi\) | |||||||
\(318\) | − 5007.57i | − 0.883052i | ||||||||
\(319\) | −17.1438 | −0.00300899 | ||||||||
\(320\) | − 3092.75i | − 0.540281i | ||||||||
\(321\) | −740.210 | −0.128706 | ||||||||
\(322\) | 6723.09 | 1.16355 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 3661.42 | 0.627816 | ||||||||
\(325\) | −3831.41 | −0.653934 | ||||||||
\(326\) | − 598.024i | − 0.101600i | ||||||||
\(327\) | −3504.23 | −0.592612 | ||||||||
\(328\) | − 3941.34i | − 0.663488i | ||||||||
\(329\) | − 7280.30i | − 1.21999i | ||||||||
\(330\) | − 1541.28i | − 0.257106i | ||||||||
\(331\) | −2144.03 | −0.356032 | −0.178016 | − | 0.984028i | \(-0.556968\pi\) | ||||
−0.178016 | + | 0.984028i | \(0.556968\pi\) | |||||||
\(332\) | 259.465 | 0.0428915 | ||||||||
\(333\) | − 861.200i | − 0.141722i | ||||||||
\(334\) | − 905.474i | − 0.148339i | ||||||||
\(335\) | − 2311.30i | − 0.376955i | ||||||||
\(336\) | −1496.25 | −0.242937 | ||||||||
\(337\) | 1955.09i | 0.316025i | 0.987437 | + | 0.158012i | \(0.0505086\pi\) | ||||
−0.987437 | + | 0.158012i | \(0.949491\pi\) | |||||||
\(338\) | −162.158 | −0.0260954 | ||||||||
\(339\) | −9903.18 | −1.58663 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −407.132 | −0.0646552 | ||||||||
\(342\) | −387.600 | −0.0612836 | ||||||||
\(343\) | 5263.61i | 0.828595i | ||||||||
\(344\) | 2895.35 | 0.453799 | ||||||||
\(345\) | − 10405.3i | − 1.62377i | ||||||||
\(346\) | − 5254.31i | − 0.816397i | ||||||||
\(347\) | − 10906.7i | − 1.68732i | −0.536875 | − | 0.843662i | \(-0.680395\pi\) | ||||
0.536875 | − | 0.843662i | \(-0.319605\pi\) | |||||||
\(348\) | −34.7127 | −0.00534711 | ||||||||
\(349\) | −9245.27 | −1.41802 | −0.709009 | − | 0.705200i | \(-0.750857\pi\) | ||||
−0.709009 | + | 0.705200i | \(0.750857\pi\) | |||||||
\(350\) | 3894.78i | 0.594814i | ||||||||
\(351\) | − 6651.33i | − 1.01146i | ||||||||
\(352\) | 2529.98i | 0.383092i | ||||||||
\(353\) | −4026.13 | −0.607051 | −0.303526 | − | 0.952823i | \(-0.598164\pi\) | ||||
−0.303526 | + | 0.952823i | \(0.598164\pi\) | |||||||
\(354\) | 4930.61i | 0.740280i | ||||||||
\(355\) | −281.081 | −0.0420233 | ||||||||
\(356\) | 3443.33 | 0.512630 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3311.99 | 0.488950 | ||||||||
\(359\) | 10382.3 | 1.52634 | 0.763171 | − | 0.646197i | \(-0.223641\pi\) | ||||
0.763171 | + | 0.646197i | \(0.223641\pi\) | |||||||
\(360\) | 666.604i | 0.0975919i | ||||||||
\(361\) | 5997.34 | 0.874375 | ||||||||
\(362\) | − 1078.87i | − 0.156641i | ||||||||
\(363\) | − 5720.86i | − 0.827183i | ||||||||
\(364\) | 7399.92i | 1.06555i | ||||||||
\(365\) | −4854.78 | −0.696194 | ||||||||
\(366\) | −1315.57 | −0.187886 | ||||||||
\(367\) | 12159.2i | 1.72945i | 0.502249 | + | 0.864723i | \(0.332506\pi\) | ||||
−0.502249 | + | 0.864723i | \(0.667494\pi\) | |||||||
\(368\) | 1475.17i | 0.208963i | ||||||||
\(369\) | 398.916i | 0.0562785i | ||||||||
\(370\) | −9107.18 | −1.27962 | ||||||||
\(371\) | − 18680.9i | − 2.61419i | ||||||||
\(372\) | −824.358 | −0.114895 | ||||||||
\(373\) | 11494.5 | 1.59561 | 0.797807 | − | 0.602913i | \(-0.205993\pi\) | ||||
0.797807 | + | 0.602913i | \(0.205993\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2972.39 | −0.409316 | ||||||||
\(376\) | −5285.35 | −0.724923 | ||||||||
\(377\) | 57.9793i | 0.00792065i | ||||||||
\(378\) | −6761.34 | −0.920016 | ||||||||
\(379\) | 1085.96i | 0.147182i | 0.997289 | + | 0.0735908i | \(0.0234459\pi\) | ||||
−0.997289 | + | 0.0735908i | \(0.976554\pi\) | |||||||
\(380\) | − 9005.88i | − 1.21577i | ||||||||
\(381\) | − 7784.23i | − 1.04671i | ||||||||
\(382\) | 3038.95 | 0.407032 | ||||||||
\(383\) | 8246.14 | 1.10015 | 0.550076 | − | 0.835115i | \(-0.314599\pi\) | ||||
0.550076 | + | 0.835115i | \(0.314599\pi\) | |||||||
\(384\) | 5766.50i | 0.766329i | ||||||||
\(385\) | − 5749.82i | − 0.761138i | ||||||||
\(386\) | 110.237i | 0.0145361i | ||||||||
\(387\) | −293.048 | −0.0384922 | ||||||||
\(388\) | 3804.72i | 0.497823i | ||||||||
\(389\) | 3801.18 | 0.495443 | 0.247722 | − | 0.968831i | \(-0.420318\pi\) | ||||
0.247722 | + | 0.968831i | \(0.420318\pi\) | |||||||
\(390\) | −5212.53 | −0.676786 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 11144.8 | 1.43596 | ||||||||
\(393\) | −6567.24 | −0.842935 | ||||||||
\(394\) | 4813.70i | 0.615510i | ||||||||
\(395\) | 15489.4 | 1.97306 | ||||||||
\(396\) | − 160.777i | − 0.0204024i | ||||||||
\(397\) | − 8372.90i | − 1.05850i | −0.848466 | − | 0.529249i | \(-0.822474\pi\) | ||||
0.848466 | − | 0.529249i | \(-0.177526\pi\) | |||||||
\(398\) | − 1986.35i | − 0.250167i | ||||||||
\(399\) | 16619.8 | 2.08529 | ||||||||
\(400\) | −854.586 | −0.106823 | ||||||||
\(401\) | − 2173.63i | − 0.270688i | −0.990799 | − | 0.135344i | \(-0.956786\pi\) | ||||
0.990799 | − | 0.135344i | \(-0.0432139\pi\) | |||||||
\(402\) | − 1261.26i | − 0.156483i | ||||||||
\(403\) | 1376.89i | 0.170194i | ||||||||
\(404\) | 3032.95 | 0.373503 | ||||||||
\(405\) | 9621.49i | 1.18048i | ||||||||
\(406\) | 58.9382 | 0.00720457 | ||||||||
\(407\) | 5392.80 | 0.656785 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4538.13 | 0.548646 | 0.274323 | − | 0.961638i | \(-0.411546\pi\) | ||||
0.274323 | + | 0.961638i | \(0.411546\pi\) | |||||||
\(410\) | 4218.54 | 0.508143 | ||||||||
\(411\) | − 2418.24i | − 0.290227i | ||||||||
\(412\) | 967.557 | 0.115699 | ||||||||
\(413\) | 18393.8i | 2.19153i | ||||||||
\(414\) | 494.005i | 0.0586449i | ||||||||
\(415\) | 681.822i | 0.0806490i | ||||||||
\(416\) | 8556.23 | 1.00842 | ||||||||
\(417\) | 5066.91 | 0.595031 | ||||||||
\(418\) | − 2427.14i | − 0.284008i | ||||||||
\(419\) | 4239.67i | 0.494323i | 0.968974 | + | 0.247161i | \(0.0794978\pi\) | ||||
−0.968974 | + | 0.247161i | \(0.920502\pi\) | |||||||
\(420\) | − 11642.2i | − 1.35257i | ||||||||
\(421\) | 14001.6 | 1.62090 | 0.810448 | − | 0.585811i | \(-0.199224\pi\) | ||||
0.810448 | + | 0.585811i | \(0.199224\pi\) | |||||||
\(422\) | 1676.98i | 0.193446i | ||||||||
\(423\) | 534.948 | 0.0614895 | ||||||||
\(424\) | −13562.0 | −1.55337 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −153.384 | −0.0174448 | ||||||||
\(427\) | −4907.80 | −0.556218 | ||||||||
\(428\) | 816.537i | 0.0922168i | ||||||||
\(429\) | 3086.59 | 0.347371 | ||||||||
\(430\) | 3098.98i | 0.347549i | ||||||||
\(431\) | 6401.94i | 0.715477i | 0.933822 | + | 0.357738i | \(0.116452\pi\) | ||||
−0.933822 | + | 0.357738i | \(0.883548\pi\) | |||||||
\(432\) | − 1483.56i | − 0.165227i | ||||||||
\(433\) | −13.2865 | −0.00147462 | −0.000737310 | − | 1.00000i | \(-0.500235\pi\) | ||||
−0.000737310 | 1.00000i | \(0.500235\pi\) | ||||||||
\(434\) | 1399.67 | 0.154807 | ||||||||
\(435\) | − 91.2180i | − 0.0100542i | ||||||||
\(436\) | 3865.57i | 0.424603i | ||||||||
\(437\) | − 16385.7i | − 1.79367i | ||||||||
\(438\) | −2649.22 | −0.289006 | ||||||||
\(439\) | 14294.8i | 1.55410i | 0.629437 | + | 0.777052i | \(0.283286\pi\) | ||||
−0.629437 | + | 0.777052i | \(0.716714\pi\) | |||||||
\(440\) | −4174.25 | −0.452272 | ||||||||
\(441\) | −1128.00 | −0.121801 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16530.3 | 1.77286 | 0.886430 | − | 0.462862i | \(-0.153177\pi\) | ||||
0.886430 | + | 0.462862i | \(0.153177\pi\) | |||||||
\(444\) | 10919.3 | 1.16713 | ||||||||
\(445\) | 9048.39i | 0.963898i | ||||||||
\(446\) | 2212.76 | 0.234927 | ||||||||
\(447\) | 6593.22i | 0.697648i | ||||||||
\(448\) | − 6296.01i | − 0.663970i | ||||||||
\(449\) | 16571.9i | 1.74182i | 0.491443 | + | 0.870910i | \(0.336470\pi\) | ||||
−0.491443 | + | 0.870910i | \(0.663530\pi\) | |||||||
\(450\) | −286.184 | −0.0299796 | ||||||||
\(451\) | −2498.00 | −0.260812 | ||||||||
\(452\) | 10924.4i | 1.13681i | ||||||||
\(453\) | − 7312.91i | − 0.758478i | ||||||||
\(454\) | 3854.40i | 0.398449i | ||||||||
\(455\) | −19445.5 | −2.00356 | ||||||||
\(456\) | − 12065.6i | − 1.23909i | ||||||||
\(457\) | 14718.1 | 1.50653 | 0.753263 | − | 0.657719i | \(-0.228479\pi\) | ||||
0.753263 | + | 0.657719i | \(0.228479\pi\) | |||||||
\(458\) | −7952.35 | −0.811329 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −11478.2 | −1.16342 | ||||||||
\(461\) | 15330.5 | 1.54884 | 0.774419 | − | 0.632672i | \(-0.218042\pi\) | ||||
0.774419 | + | 0.632672i | \(0.218042\pi\) | |||||||
\(462\) | − 3137.64i | − 0.315966i | ||||||||
\(463\) | 11158.0 | 1.11999 | 0.559993 | − | 0.828497i | \(-0.310804\pi\) | ||||
0.559993 | + | 0.828497i | \(0.310804\pi\) | |||||||
\(464\) | 12.9321i | 0.00129388i | ||||||||
\(465\) | − 2166.25i | − 0.216037i | ||||||||
\(466\) | 1409.61i | 0.140126i | ||||||||
\(467\) | 14748.4 | 1.46140 | 0.730700 | − | 0.682699i | \(-0.239194\pi\) | ||||
0.730700 | + | 0.682699i | \(0.239194\pi\) | |||||||
\(468\) | −543.737 | −0.0537057 | ||||||||
\(469\) | − 4705.19i | − 0.463253i | ||||||||
\(470\) | − 5657.07i | − 0.555194i | ||||||||
\(471\) | 16961.2i | 1.65931i | ||||||||
\(472\) | 13353.5 | 1.30222 | ||||||||
\(473\) | − 1835.06i | − 0.178385i | ||||||||
\(474\) | 8452.48 | 0.819062 | ||||||||
\(475\) | 9492.45 | 0.916934 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1372.65 | 0.131760 | ||||||||
\(478\) | −256.219 | −0.0245171 | ||||||||
\(479\) | − 14914.1i | − 1.42264i | −0.702868 | − | 0.711320i | \(-0.748098\pi\) | ||||
0.702868 | − | 0.711320i | \(-0.251902\pi\) | |||||||
\(480\) | −13461.4 | −1.28006 | ||||||||
\(481\) | − 18238.1i | − 1.72887i | ||||||||
\(482\) | − 5484.86i | − 0.518317i | ||||||||
\(483\) | − 21182.3i | − 1.99550i | ||||||||
\(484\) | −6310.77 | −0.592672 | ||||||||
\(485\) | −9998.04 | −0.936057 | ||||||||
\(486\) | − 956.813i | − 0.0893043i | ||||||||
\(487\) | 3034.34i | 0.282339i | 0.989985 | + | 0.141169i | \(0.0450862\pi\) | ||||
−0.989985 | + | 0.141169i | \(0.954914\pi\) | |||||||
\(488\) | 3562.96i | 0.330507i | ||||||||
\(489\) | −1884.18 | −0.174245 | ||||||||
\(490\) | 11928.6i | 1.09975i | ||||||||
\(491\) | −10032.0 | −0.922073 | −0.461036 | − | 0.887381i | \(-0.652522\pi\) | ||||
−0.461036 | + | 0.887381i | \(0.652522\pi\) | |||||||
\(492\) | −5057.94 | −0.463475 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −8208.43 | −0.747601 | ||||||||
\(495\) | 422.490 | 0.0383626 | ||||||||
\(496\) | 307.112i | 0.0278019i | ||||||||
\(497\) | −572.207 | −0.0516438 | ||||||||
\(498\) | 372.066i | 0.0334793i | ||||||||
\(499\) | 13921.2i | 1.24890i | 0.781066 | + | 0.624449i | \(0.214676\pi\) | ||||
−0.781066 | + | 0.624449i | \(0.785324\pi\) | |||||||
\(500\) | 3278.89i | 0.293273i | ||||||||
\(501\) | −2852.86 | −0.254404 | ||||||||
\(502\) | −6847.23 | −0.608779 | ||||||||
\(503\) | − 10270.2i | − 0.910387i | −0.890392 | − | 0.455194i | \(-0.849570\pi\) | ||||
0.890392 | − | 0.455194i | \(-0.150430\pi\) | |||||||
\(504\) | 1357.03i | 0.119934i | ||||||||
\(505\) | 7970.00i | 0.702298i | ||||||||
\(506\) | −3093.44 | −0.271779 | ||||||||
\(507\) | 510.908i | 0.0447539i | ||||||||
\(508\) | −8586.90 | −0.749965 | ||||||||
\(509\) | 18020.5 | 1.56924 | 0.784621 | − | 0.619975i | \(-0.212857\pi\) | ||||
0.784621 | + | 0.619975i | \(0.212857\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9883.03 | −0.855576 | ||||||||
\(512\) | 3652.06 | 0.315234 | ||||||||
\(513\) | 16478.9i | 1.41825i | ||||||||
\(514\) | 7225.00 | 0.620002 | ||||||||
\(515\) | 2542.55i | 0.217550i | ||||||||
\(516\) | − 3715.61i | − 0.316998i | ||||||||
\(517\) | 3349.82i | 0.284962i | ||||||||
\(518\) | −18539.8 | −1.57257 | ||||||||
\(519\) | −16554.6 | −1.40013 | ||||||||
\(520\) | 14117.1i | 1.19053i | ||||||||
\(521\) | − 18326.3i | − 1.54106i | −0.637405 | − | 0.770529i | \(-0.719992\pi\) | ||||
0.637405 | − | 0.770529i | \(-0.280008\pi\) | |||||||
\(522\) | 4.33071i | 0 0.000363122i | ||||||||
\(523\) | −15369.6 | −1.28502 | −0.642512 | − | 0.766276i | \(-0.722108\pi\) | ||||
−0.642512 | + | 0.766276i | \(0.722108\pi\) | |||||||
\(524\) | 7244.42i | 0.603958i | ||||||||
\(525\) | 12271.2 | 1.02011 | ||||||||
\(526\) | −7452.09 | −0.617731 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 688.455 | 0.0567447 | ||||||||
\(529\) | −8716.90 | −0.716438 | ||||||||
\(530\) | − 14515.8i | − 1.18967i | ||||||||
\(531\) | −1351.56 | −0.110457 | ||||||||
\(532\) | − 18333.6i | − 1.49410i | ||||||||
\(533\) | 8448.08i | 0.686542i | ||||||||
\(534\) | 4937.65i | 0.400137i | ||||||||
\(535\) | −2145.70 | −0.173395 | ||||||||
\(536\) | −3415.87 | −0.275267 | ||||||||
\(537\) | − 10435.0i | − 0.838556i | ||||||||
\(538\) | 5788.09i | 0.463833i | ||||||||
\(539\) | − 7063.50i | − 0.564464i | ||||||||
\(540\) | 11543.5 | 0.919913 | ||||||||
\(541\) | − 18606.9i | − 1.47870i | −0.673323 | − | 0.739348i | \(-0.735134\pi\) | ||||
0.673323 | − | 0.739348i | \(-0.264866\pi\) | |||||||
\(542\) | −12184.0 | −0.965586 | ||||||||
\(543\) | −3399.16 | −0.268641 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10157.9 | −0.798382 | ||||||||
\(546\) | −10611.3 | −0.831725 | ||||||||
\(547\) | 3946.20i | 0.308459i | 0.988035 | + | 0.154230i | \(0.0492896\pi\) | ||||
−0.988035 | + | 0.154230i | \(0.950710\pi\) | |||||||
\(548\) | −2667.60 | −0.207946 | ||||||||
\(549\) | − 360.619i | − 0.0280343i | ||||||||
\(550\) | − 1792.07i | − 0.138935i | ||||||||
\(551\) | − 143.646i | − 0.0111062i | ||||||||
\(552\) | −15377.9 | −1.18574 | ||||||||
\(553\) | 31532.3 | 2.42476 | ||||||||
\(554\) | 5145.11i | 0.394576i | ||||||||
\(555\) | 28693.8i | 2.19457i | ||||||||
\(556\) | − 5589.39i | − 0.426336i | ||||||||
\(557\) | 14883.1 | 1.13217 | 0.566084 | − | 0.824347i | \(-0.308458\pi\) | ||||
0.566084 | + | 0.824347i | \(0.308458\pi\) | |||||||
\(558\) | 102.846i | 0.00780253i | ||||||||
\(559\) | −6206.05 | −0.469567 | ||||||||
\(560\) | −4337.27 | −0.327291 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10818.7 | 0.812027 | ||||||||
\(563\) | −25751.7 | −1.92771 | −0.963857 | − | 0.266420i | \(-0.914159\pi\) | ||||
−0.963857 | + | 0.266420i | \(0.914159\pi\) | |||||||
\(564\) | 6782.71i | 0.506389i | ||||||||
\(565\) | −28707.0 | −2.13755 | ||||||||
\(566\) | 4953.22i | 0.367843i | ||||||||
\(567\) | 19586.8i | 1.45074i | ||||||||
\(568\) | 415.410i | 0.0306870i | ||||||||
\(569\) | 2194.88 | 0.161712 | 0.0808561 | − | 0.996726i | \(-0.474235\pi\) | ||||
0.0808561 | + | 0.996726i | \(0.474235\pi\) | |||||||
\(570\) | 12914.2 | 0.948977 | ||||||||
\(571\) | − 5227.87i | − 0.383151i | −0.981478 | − | 0.191576i | \(-0.938640\pi\) | ||||
0.981478 | − | 0.191576i | \(-0.0613598\pi\) | |||||||
\(572\) | − 3404.86i | − 0.248889i | ||||||||
\(573\) | − 9574.77i | − 0.698066i | ||||||||
\(574\) | 8587.81 | 0.624474 | ||||||||
\(575\) | − 12098.3i | − 0.877453i | ||||||||
\(576\) | 462.623 | 0.0334652 | ||||||||
\(577\) | −6527.86 | −0.470985 | −0.235492 | − | 0.971876i | \(-0.575670\pi\) | ||||
−0.235492 | + | 0.971876i | \(0.575670\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 347.323 | 0.0249296 | ||||||||
\(580\) | −100.624 | −0.00720376 | ||||||||
\(581\) | 1388.01i | 0.0991122i | ||||||||
\(582\) | −5455.87 | −0.388579 | ||||||||
\(583\) | 8595.50i | 0.610617i | ||||||||
\(584\) | 7174.87i | 0.508387i | ||||||||
\(585\) | − 1428.83i | − 0.100983i | ||||||||
\(586\) | 8535.65 | 0.601714 | ||||||||
\(587\) | 6648.24 | 0.467465 | 0.233733 | − | 0.972301i | \(-0.424906\pi\) | ||||
0.233733 | + | 0.972301i | \(0.424906\pi\) | |||||||
\(588\) | − 14302.1i | − 1.00308i | ||||||||
\(589\) | − 3411.30i | − 0.238642i | ||||||||
\(590\) | 14292.7i | 0.997324i | ||||||||
\(591\) | 15166.4 | 1.05561 | ||||||||
\(592\) | − 4067.96i | − 0.282419i | ||||||||
\(593\) | 1450.60 | 0.100453 | 0.0502267 | − | 0.998738i | \(-0.484006\pi\) | ||||
0.0502267 | + | 0.998738i | \(0.484006\pi\) | |||||||
\(594\) | 3111.04 | 0.214895 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7273.09 | 0.499861 | ||||||||
\(597\) | −6258.35 | −0.429040 | ||||||||
\(598\) | 10461.8i | 0.715411i | ||||||||
\(599\) | −10070.9 | −0.686957 | −0.343479 | − | 0.939161i | \(-0.611605\pi\) | ||||
−0.343479 | + | 0.939161i | \(0.611605\pi\) | |||||||
\(600\) | − 8908.64i | − 0.606156i | ||||||||
\(601\) | 9209.45i | 0.625060i | 0.949908 | + | 0.312530i | \(0.101177\pi\) | ||||
−0.949908 | + | 0.312530i | \(0.898823\pi\) | |||||||
\(602\) | 6308.69i | 0.427115i | ||||||||
\(603\) | 345.732 | 0.0233487 | ||||||||
\(604\) | −8066.99 | −0.543445 | ||||||||
\(605\) | − 16583.5i | − 1.11440i | ||||||||
\(606\) | 4349.18i | 0.291540i | ||||||||
\(607\) | 5813.89i | 0.388762i | 0.980926 | + | 0.194381i | \(0.0622698\pi\) | ||||
−0.980926 | + | 0.194381i | \(0.937730\pi\) | |||||||
\(608\) | −21198.4 | −1.41399 | ||||||||
\(609\) | − 185.695i | − 0.0123559i | ||||||||
\(610\) | −3813.54 | −0.253124 | ||||||||
\(611\) | 11328.9 | 0.750111 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23778.5 | −1.56673 | −0.783365 | − | 0.621562i | \(-0.786498\pi\) | ||||
−0.783365 | + | 0.621562i | \(0.786498\pi\) | |||||||
\(614\) | 3411.42 | 0.224224 | ||||||||
\(615\) | − 13291.3i | − 0.871472i | ||||||||
\(616\) | −8497.65 | −0.555812 | ||||||||
\(617\) | 19716.9i | 1.28650i | 0.765655 | + | 0.643251i | \(0.222415\pi\) | ||||
−0.765655 | + | 0.643251i | \(0.777585\pi\) | |||||||
\(618\) | 1387.45i | 0.0903099i | ||||||||
\(619\) | − 6184.28i | − 0.401562i | −0.979636 | − | 0.200781i | \(-0.935652\pi\) | ||||
0.979636 | − | 0.200781i | \(-0.0643480\pi\) | |||||||
\(620\) | −2389.62 | −0.154790 | ||||||||
\(621\) | 21002.7 | 1.35718 | ||||||||
\(622\) | − 4317.50i | − 0.278322i | ||||||||
\(623\) | 18420.1i | 1.18457i | ||||||||
\(624\) | − 2328.31i | − 0.149370i | ||||||||
\(625\) | −19081.0 | −1.22119 | ||||||||
\(626\) | − 7932.56i | − 0.506468i | ||||||||
\(627\) | −7647.13 | −0.487077 | ||||||||
\(628\) | 18710.2 | 1.18888 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1452.47 | −0.0918534 | ||||||||
\(631\) | −14216.8 | −0.896926 | −0.448463 | − | 0.893801i | \(-0.648028\pi\) | ||||
−0.448463 | + | 0.893801i | \(0.648028\pi\) | |||||||
\(632\) | − 22891.8i | − 1.44080i | ||||||||
\(633\) | 5283.64 | 0.331763 | ||||||||
\(634\) | − 1842.09i | − 0.115393i | ||||||||
\(635\) | − 22564.7i | − 1.41016i | ||||||||
\(636\) | 17404.1i | 1.08509i | ||||||||
\(637\) | −23888.3 | −1.48585 | ||||||||
\(638\) | −27.1187 | −0.00168282 | ||||||||
\(639\) | − 42.0450i | − 0.00260294i | ||||||||
\(640\) | 16715.7i | 1.03242i | ||||||||
\(641\) | 14249.8i | 0.878058i | 0.898473 | + | 0.439029i | \(0.144677\pi\) | ||||
−0.898473 | + | 0.439029i | \(0.855323\pi\) | |||||||
\(642\) | −1170.89 | −0.0719805 | ||||||||
\(643\) | 1767.83i | 0.108424i | 0.998529 | + | 0.0542118i | \(0.0172646\pi\) | ||||
−0.998529 | + | 0.0542118i | \(0.982735\pi\) | |||||||
\(644\) | −23366.5 | −1.42977 | ||||||||
\(645\) | 9763.89 | 0.596051 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14274.5 | −0.867369 | −0.433685 | − | 0.901065i | \(-0.642787\pi\) | ||||
−0.433685 | + | 0.901065i | \(0.642787\pi\) | |||||||
\(648\) | 14219.6 | 0.862035 | ||||||||
\(649\) | − 8463.40i | − 0.511891i | ||||||||
\(650\) | −6060.68 | −0.365722 | ||||||||
\(651\) | − 4409.90i | − 0.265496i | ||||||||
\(652\) | 2078.47i | 0.124845i | ||||||||
\(653\) | − 14516.1i | − 0.869924i | −0.900449 | − | 0.434962i | \(-0.856762\pi\) | ||||
0.900449 | − | 0.434962i | \(-0.143238\pi\) | |||||||
\(654\) | −5543.13 | −0.331427 | ||||||||
\(655\) | −19036.9 | −1.13562 | ||||||||
\(656\) | 1884.32i | 0.112150i | ||||||||
\(657\) | − 726.193i | − 0.0431225i | ||||||||
\(658\) | − 11516.3i | − 0.682296i | ||||||||
\(659\) | 23248.8 | 1.37427 | 0.687135 | − | 0.726530i | \(-0.258868\pi\) | ||||
0.687135 | + | 0.726530i | \(0.258868\pi\) | |||||||
\(660\) | 5356.83i | 0.315931i | ||||||||
\(661\) | 28695.7 | 1.68855 | 0.844277 | − | 0.535907i | \(-0.180030\pi\) | ||||
0.844277 | + | 0.535907i | \(0.180030\pi\) | |||||||
\(662\) | −3391.51 | −0.199116 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1007.66 | 0.0588930 | ||||||||
\(665\) | 48177.0 | 2.80936 | ||||||||
\(666\) | − 1362.28i | − 0.0792602i | ||||||||
\(667\) | −183.079 | −0.0106280 | ||||||||
\(668\) | 3147.03i | 0.182279i | ||||||||
\(669\) | − 6971.71i | − 0.402903i | ||||||||
\(670\) | − 3656.11i | − 0.210818i | ||||||||
\(671\) | 2258.18 | 0.129920 | ||||||||
\(672\) | −27403.8 | −1.57310 | ||||||||
\(673\) | 6852.55i | 0.392491i | 0.980555 | + | 0.196246i | \(0.0628750\pi\) | ||||
−0.980555 | + | 0.196246i | \(0.937125\pi\) | |||||||
\(674\) | 3092.63i | 0.176742i | ||||||||
\(675\) | 12167.2i | 0.693799i | ||||||||
\(676\) | 563.590 | 0.0320659 | ||||||||
\(677\) | − 2123.19i | − 0.120533i | −0.998182 | − | 0.0602665i | \(-0.980805\pi\) | ||||
0.998182 | − | 0.0602665i | \(-0.0191951\pi\) | |||||||
\(678\) | −15665.2 | −0.887345 | ||||||||
\(679\) | −20353.3 | −1.15035 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12144.0 | 0.683345 | ||||||||
\(682\) | −644.017 | −0.0361594 | ||||||||
\(683\) | − 4035.12i | − 0.226061i | −0.993592 | − | 0.113030i | \(-0.963944\pi\) | ||||
0.993592 | − | 0.113030i | \(-0.0360558\pi\) | |||||||
\(684\) | 1347.13 | 0.0753052 | ||||||||
\(685\) | − 7009.92i | − 0.391001i | ||||||||
\(686\) | 8326.18i | 0.463404i | ||||||||
\(687\) | 25055.3i | 1.39144i | ||||||||
\(688\) | −1384.24 | −0.0767060 | ||||||||
\(689\) | 29069.5 | 1.60734 | ||||||||
\(690\) | − 16459.4i | − 0.908116i | ||||||||
\(691\) | − 20015.0i | − 1.10189i | −0.834540 | − | 0.550947i | \(-0.814267\pi\) | ||||
0.834540 | − | 0.550947i | \(-0.185733\pi\) | |||||||
\(692\) | 18261.7i | 1.00319i | ||||||||
\(693\) | 860.076 | 0.0471451 | ||||||||
\(694\) | − 17252.6i | − 0.943661i | ||||||||
\(695\) | 14687.8 | 0.801641 | ||||||||
\(696\) | −134.811 | −0.00734195 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −14624.5 | −0.793047 | ||||||||
\(699\) | 4441.23 | 0.240319 | ||||||||
\(700\) | − 13536.6i | − 0.730905i | ||||||||
\(701\) | 19025.4 | 1.02508 | 0.512539 | − | 0.858664i | \(-0.328705\pi\) | ||||
0.512539 | + | 0.858664i | \(0.328705\pi\) | |||||||
\(702\) | − 10521.3i | − 0.565673i | ||||||||
\(703\) | 45185.6i | 2.42419i | ||||||||
\(704\) | 2896.93i | 0.155088i | ||||||||
\(705\) | −17823.6 | −0.952164 | ||||||||
\(706\) | −6368.69 | −0.339502 | ||||||||
\(707\) | 16224.8i | 0.863077i | ||||||||
\(708\) | − 17136.6i | − 0.909653i | ||||||||
\(709\) | − 11992.4i | − 0.635237i | −0.948219 | − | 0.317619i | \(-0.897117\pi\) | ||||
0.948219 | − | 0.317619i | \(-0.102883\pi\) | |||||||
\(710\) | −444.626 | −0.0235021 | ||||||||
\(711\) | 2316.96i | 0.122212i | ||||||||
\(712\) | 13372.6 | 0.703876 | ||||||||
\(713\) | −4347.78 | −0.228367 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8947.31 | 0.467987 | ||||||||
\(716\) | −11511.0 | −0.600821 | ||||||||
\(717\) | 807.265i | 0.0420472i | ||||||||
\(718\) | 16423.1 | 0.853629 | ||||||||
\(719\) | − 12005.7i | − 0.622721i | −0.950292 | − | 0.311361i | \(-0.899215\pi\) | ||||
0.950292 | − | 0.311361i | \(-0.100785\pi\) | |||||||
\(720\) | − 318.697i | − 0.0164960i | ||||||||
\(721\) | 5175.95i | 0.267354i | ||||||||
\(722\) | 9486.83 | 0.489007 | ||||||||
\(723\) | −17281.0 | −0.888919 | ||||||||
\(724\) | 3749.66i | 0.192479i | ||||||||
\(725\) | − 106.060i | − 0.00543309i | ||||||||
\(726\) | − 9049.49i | − 0.462614i | ||||||||
\(727\) | −22403.9 | −1.14294 | −0.571468 | − | 0.820624i | \(-0.693626\pi\) | ||||
−0.571468 | + | 0.820624i | \(0.693626\pi\) | |||||||
\(728\) | 28738.5i | 1.46308i | ||||||||
\(729\) | −20996.1 | −1.06671 | ||||||||
\(730\) | −7679.48 | −0.389357 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 4572.36 | 0.230873 | ||||||||
\(733\) | 17400.5 | 0.876810 | 0.438405 | − | 0.898777i | \(-0.355543\pi\) | ||||
0.438405 | + | 0.898777i | \(0.355543\pi\) | |||||||
\(734\) | 19233.9i | 0.967218i | ||||||||
\(735\) | 37583.2 | 1.88609 | ||||||||
\(736\) | 27017.8i | 1.35311i | ||||||||
\(737\) | 2164.96i | 0.108205i | ||||||||
\(738\) | 631.022i | 0.0314746i | ||||||||
\(739\) | 7691.26 | 0.382852 | 0.191426 | − | 0.981507i | \(-0.438689\pi\) | ||||
0.191426 | + | 0.981507i | \(0.438689\pi\) | |||||||
\(740\) | 31652.6 | 1.57239 | ||||||||
\(741\) | 25862.1i | 1.28214i | ||||||||
\(742\) | − 29550.3i | − 1.46203i | ||||||||
\(743\) | − 33377.5i | − 1.64805i | −0.566551 | − | 0.824027i | \(-0.691723\pi\) | ||||
0.566551 | − | 0.824027i | \(-0.308277\pi\) | |||||||
\(744\) | −3201.50 | −0.157759 | ||||||||
\(745\) | 19112.2i | 0.939890i | ||||||||
\(746\) | 18182.5 | 0.892371 | ||||||||
\(747\) | −101.989 | −0.00499543 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4368.06 | −0.213092 | ||||||||
\(750\) | −4701.84 | −0.228916 | ||||||||
\(751\) | − 30285.6i | − 1.47155i | −0.677224 | − | 0.735777i | \(-0.736817\pi\) | ||||
0.677224 | − | 0.735777i | \(-0.263183\pi\) | |||||||
\(752\) | 2526.88 | 0.122534 | ||||||||
\(753\) | 21573.4i | 1.04406i | ||||||||
\(754\) | 91.7139i | 0.00442974i | ||||||||
\(755\) | − 21198.4i | − 1.02184i | ||||||||
\(756\) | 23499.5 | 1.13051 | ||||||||
\(757\) | 13809.3 | 0.663023 | 0.331511 | − | 0.943451i | \(-0.392441\pi\) | ||||
0.331511 | + | 0.943451i | \(0.392441\pi\) | |||||||
\(758\) | 1717.81i | 0.0823135i | ||||||||
\(759\) | 9746.44i | 0.466104i | ||||||||
\(760\) | − 34975.5i | − 1.66933i | ||||||||
\(761\) | 33269.2 | 1.58477 | 0.792383 | − | 0.610023i | \(-0.208840\pi\) | ||||
0.792383 | + | 0.610023i | \(0.208840\pi\) | |||||||
\(762\) | − 12313.4i | − 0.585390i | ||||||||
\(763\) | −20678.8 | −0.981159 | ||||||||
\(764\) | −10562.1 | −0.500160 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13044.1 | 0.615276 | ||||||||
\(767\) | −28622.7 | −1.34746 | ||||||||
\(768\) | 17657.0i | 0.829613i | ||||||||
\(769\) | −22932.1 | −1.07536 | −0.537681 | − | 0.843148i | \(-0.680700\pi\) | ||||
−0.537681 | + | 0.843148i | \(0.680700\pi\) | |||||||
\(770\) | − 9095.29i | − 0.425677i | ||||||||
\(771\) | − 22763.7i | − 1.06331i | ||||||||
\(772\) | − 383.137i | − 0.0178619i | ||||||||
\(773\) | −3142.46 | −0.146218 | −0.0731090 | − | 0.997324i | \(-0.523292\pi\) | ||||
−0.0731090 | + | 0.997324i | \(0.523292\pi\) | |||||||
\(774\) | −463.555 | −0.0215273 | ||||||||
\(775\) | − 2518.73i | − 0.116742i | ||||||||
\(776\) | 14776.1i | 0.683545i | ||||||||
\(777\) | 58412.9i | 2.69698i | ||||||||
\(778\) | 6012.85 | 0.277084 | ||||||||
\(779\) | − 20930.4i | − 0.962657i | ||||||||
\(780\) | 18116.5 | 0.831633 | ||||||||
\(781\) | 263.285 | 0.0120628 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 184.121 | 0.00840351 | ||||||||
\(784\) | −5328.22 | −0.242721 | ||||||||
\(785\) | 49166.7i | 2.23546i | ||||||||
\(786\) | −10388.3 | −0.471424 | ||||||||
\(787\) | 11712.3i | 0.530492i | 0.964181 | + | 0.265246i | \(0.0854532\pi\) | ||||
−0.964181 | + | 0.265246i | \(0.914547\pi\) | |||||||
\(788\) | − 16730.3i | − 0.756337i | ||||||||
\(789\) | 23479.1i | 1.05942i | ||||||||
\(790\) | 24501.8 | 1.10346 | ||||||||
\(791\) | −58439.8 | −2.62690 | ||||||||
\(792\) | − 624.397i | − 0.0280139i | ||||||||
\(793\) | − 7637.04i | − 0.341991i | ||||||||
\(794\) | − 13244.6i | − 0.591981i | ||||||||
\(795\) | −45734.6 | −2.04030 | ||||||||
\(796\) | 6903.68i | 0.307405i | ||||||||
\(797\) | 12691.2 | 0.564045 | 0.282022 | − | 0.959408i | \(-0.408995\pi\) | ||||
0.282022 | + | 0.959408i | \(0.408995\pi\) | |||||||
\(798\) | 26289.9 | 1.16623 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −15651.8 | −0.691717 | ||||||||
\(801\) | −1353.49 | −0.0597042 | ||||||||
\(802\) | − 3438.33i | − 0.151386i | ||||||||
\(803\) | 4547.39 | 0.199843 | ||||||||
\(804\) | 4383.60i | 0.192286i | ||||||||
\(805\) | − 61402.6i | − 2.68839i | ||||||||
\(806\) | 2178.03i | 0.0951832i | ||||||||
\(807\) | 18236.4 | 0.795480 | ||||||||
\(808\) | 11778.9 | 0.512845 | ||||||||
\(809\) | 22034.9i | 0.957610i | 0.877921 | + | 0.478805i | \(0.158930\pi\) | ||||
−0.877921 | + | 0.478805i | \(0.841070\pi\) | |||||||
\(810\) | 15219.7i | 0.660203i | ||||||||
\(811\) | − 2987.60i | − 0.129357i | −0.997906 | − | 0.0646787i | \(-0.979398\pi\) | ||||
0.997906 | − | 0.0646787i | \(-0.0206023\pi\) | |||||||
\(812\) | −204.843 | −0.00885295 | ||||||||
\(813\) | 38387.9i | 1.65599i | ||||||||
\(814\) | 8530.55 | 0.367316 | ||||||||
\(815\) | −5461.81 | −0.234747 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15375.7 | 0.658418 | ||||||||
\(818\) | 7178.59 | 0.306838 | ||||||||
\(819\) | − 2908.72i | − 0.124101i | ||||||||
\(820\) | −14661.8 | −0.624405 | ||||||||
\(821\) | − 39918.9i | − 1.69693i | −0.529251 | − | 0.848465i | \(-0.677527\pi\) | ||||
0.529251 | − | 0.848465i | \(-0.322473\pi\) | |||||||
\(822\) | − 3825.27i | − 0.162313i | ||||||||
\(823\) | − 15017.3i | − 0.636050i | −0.948082 | − | 0.318025i | \(-0.896980\pi\) | ||||
0.948082 | − | 0.318025i | \(-0.103020\pi\) | |||||||
\(824\) | 3757.63 | 0.158863 | ||||||||
\(825\) | −5646.25 | −0.238275 | ||||||||
\(826\) | 29096.1i | 1.22564i | ||||||||
\(827\) | − 3898.57i | − 0.163926i | −0.996635 | − | 0.0819628i | \(-0.973881\pi\) | ||||
0.996635 | − | 0.0819628i | \(-0.0261189\pi\) | |||||||
\(828\) | − 1716.94i | − 0.0720627i | ||||||||
\(829\) | −4410.66 | −0.184787 | −0.0923937 | − | 0.995723i | \(-0.529452\pi\) | ||||
−0.0923937 | + | 0.995723i | \(0.529452\pi\) | |||||||
\(830\) | 1078.53i | 0.0451041i | ||||||||
\(831\) | 16210.6 | 0.676702 | ||||||||
\(832\) | 9797.23 | 0.408243 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8015.05 | 0.332780 | ||||||||
\(835\) | −8269.77 | −0.342739 | ||||||||
\(836\) | 8435.67i | 0.348988i | ||||||||
\(837\) | 4372.52 | 0.180569 | ||||||||
\(838\) | 6706.47i | 0.276457i | ||||||||
\(839\) | − 29154.8i | − 1.19969i | −0.800118 | − | 0.599843i | \(-0.795230\pi\) | ||||
0.800118 | − | 0.599843i | \(-0.204770\pi\) | |||||||
\(840\) | − 45214.0i | − 1.85718i | ||||||||
\(841\) | 24387.4 | 0.999934 | ||||||||
\(842\) | 22148.3 | 0.906510 | ||||||||
\(843\) | − 34086.2i | − 1.39264i | ||||||||
\(844\) | − 5828.46i | − 0.237706i | ||||||||
\(845\) | 1481.00i | 0.0602936i | ||||||||
\(846\) | 846.202 | 0.0343889 | ||||||||
\(847\) | − 33759.5i | − 1.36953i | ||||||||
\(848\) | 6483.86 | 0.262567 | ||||||||
\(849\) | 15606.0 | 0.630856 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 57590.0 | 2.31981 | ||||||||
\(852\) | 533.097 | 0.0214362 | ||||||||
\(853\) | 24310.2i | 0.975808i | 0.872897 | + | 0.487904i | \(0.162238\pi\) | ||||
−0.872897 | + | 0.487904i | \(0.837762\pi\) | |||||||
\(854\) | −7763.35 | −0.311073 | ||||||||
\(855\) | 3539.99i | 0.141596i | ||||||||
\(856\) | 3171.12i | 0.126620i | ||||||||
\(857\) | − 13081.1i | − 0.521403i | −0.965419 | − | 0.260701i | \(-0.916046\pi\) | ||||
0.965419 | − | 0.260701i | \(-0.0839538\pi\) | |||||||
\(858\) | 4882.49 | 0.194272 | ||||||||
\(859\) | −1740.97 | −0.0691514 | −0.0345757 | − | 0.999402i | \(-0.511008\pi\) | ||||
−0.0345757 | + | 0.999402i | \(0.511008\pi\) | |||||||
\(860\) | − 10770.7i | − 0.427067i | ||||||||
\(861\) | − 27057.4i | − 1.07098i | ||||||||
\(862\) | 10126.8i | 0.400141i | ||||||||
\(863\) | −15561.9 | −0.613826 | −0.306913 | − | 0.951738i | \(-0.599296\pi\) | ||||
−0.306913 | + | 0.951738i | \(0.599296\pi\) | |||||||
\(864\) | − 27171.5i | − 1.06990i | ||||||||
\(865\) | −47988.0 | −1.88629 | ||||||||
\(866\) | −21.0172 | −0.000824703 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4864.63 | −0.190226 | ||||||||
\(869\) | −14508.7 | −0.566368 | ||||||||
\(870\) | − 144.292i | − 0.00562295i | ||||||||
\(871\) | 7321.76 | 0.284832 | ||||||||
\(872\) | 15012.4i | 0.583010i | ||||||||
\(873\) | − 1495.54i | − 0.0579797i | ||||||||
\(874\) | − 25919.5i | − 1.00314i | ||||||||
\(875\) | −17540.4 | −0.677685 | ||||||||
\(876\) | 9207.54 | 0.355130 | ||||||||
\(877\) | − 32043.6i | − 1.23379i | −0.787045 | − | 0.616895i | \(-0.788390\pi\) | ||||
0.787045 | − | 0.616895i | \(-0.211610\pi\) | |||||||
\(878\) | 22612.0i | 0.869156i | ||||||||
\(879\) | − 26893.1i | − 1.03195i | ||||||||
\(880\) | 1995.67 | 0.0764478 | ||||||||
\(881\) | 38673.0i | 1.47892i | 0.673202 | + | 0.739458i | \(0.264918\pi\) | ||||
−0.673202 | + | 0.739458i | \(0.735082\pi\) | |||||||
\(882\) | −1784.31 | −0.0681191 | ||||||||
\(883\) | −45977.4 | −1.75228 | −0.876140 | − | 0.482056i | \(-0.839890\pi\) | ||||
−0.876140 | + | 0.482056i | \(0.839890\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 45031.7 | 1.71042 | ||||||||
\(886\) | 26148.3 | 0.991499 | ||||||||
\(887\) | 5325.60i | 0.201596i | 0.994907 | + | 0.100798i | \(0.0321396\pi\) | ||||
−0.994907 | + | 0.100798i | \(0.967860\pi\) | |||||||
\(888\) | 42406.5 | 1.60256 | ||||||||
\(889\) | − 45935.6i | − 1.73299i | ||||||||
\(890\) | 14313.1i | 0.539074i | ||||||||
\(891\) | − 9012.30i | − 0.338859i | ||||||||
\(892\) | −7690.60 | −0.288677 | ||||||||
\(893\) | −28067.7 | −1.05179 | ||||||||
\(894\) | 10429.4i | 0.390170i | ||||||||
\(895\) | − 30248.7i | − 1.12972i | ||||||||
\(896\) | 34028.8i | 1.26877i | ||||||||
\(897\) | 32961.8 | 1.22694 | ||||||||
\(898\) | 26214.1i | 0.974139i | ||||||||
\(899\) | −38.1150 | −0.00141402 | ||||||||
\(900\) | 994.649 | 0.0368389 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −3951.44 | −0.145863 | ||||||||
\(903\) | 19876.7 | 0.732507 | ||||||||
\(904\) | 42426.1i | 1.56092i | ||||||||
\(905\) | −9853.37 | −0.361919 | ||||||||
\(906\) | − 11567.9i | − 0.424190i | ||||||||
\(907\) | − 12188.4i | − 0.446207i | −0.974795 | − | 0.223104i | \(-0.928381\pi\) | ||||
0.974795 | − | 0.223104i | \(-0.0716189\pi\) | |||||||
\(908\) | − 13396.2i | − 0.489613i | ||||||||
\(909\) | −1192.18 | −0.0435006 | ||||||||
\(910\) | −30759.7 | −1.12052 | ||||||||
\(911\) | 24738.8i | 0.899707i | 0.893102 | + | 0.449854i | \(0.148524\pi\) | ||||
−0.893102 | + | 0.449854i | \(0.851476\pi\) | |||||||
\(912\) | 5768.48i | 0.209444i | ||||||||
\(913\) | − 638.652i | − 0.0231504i | ||||||||
\(914\) | 23281.6 | 0.842547 | ||||||||
\(915\) | 12015.3i | 0.434111i | ||||||||
\(916\) | 27638.9 | 0.996959 | ||||||||
\(917\) | −38754.0 | −1.39561 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1584.70 | 0.0568820 | 0.0284410 | − | 0.999595i | \(-0.490946\pi\) | ||||
0.0284410 | + | 0.999595i | \(0.490946\pi\) | |||||||
\(920\) | −44577.0 | −1.59746 | ||||||||
\(921\) | − 10748.3i | − 0.384548i | ||||||||
\(922\) | 24250.5 | 0.866211 | ||||||||
\(923\) | − 890.412i | − 0.0317533i | ||||||||
\(924\) | 10905.1i | 0.388258i | ||||||||
\(925\) | 33362.7i | 1.18590i | ||||||||
\(926\) | 17650.1 | 0.626369 | ||||||||
\(927\) | −380.322 | −0.0134751 | ||||||||
\(928\) | 236.852i | 0.00837829i | ||||||||
\(929\) | − 7266.92i | − 0.256642i | −0.991733 | − | 0.128321i | \(-0.959041\pi\) | ||||
0.991733 | − | 0.128321i | \(-0.0409587\pi\) | |||||||
\(930\) | − 3426.66i | − 0.120822i | ||||||||
\(931\) | 59184.1 | 2.08344 | ||||||||
\(932\) | − 4899.19i | − 0.172187i | ||||||||
\(933\) | −13603.1 | −0.477325 | ||||||||
\(934\) | 23329.6 | 0.817310 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2111.67 | −0.0737416 | ||||||||
\(937\) | 3617.62 | 0.126129 | 0.0630643 | − | 0.998009i | \(-0.479913\pi\) | ||||
0.0630643 | + | 0.998009i | \(0.479913\pi\) | |||||||
\(938\) | − 7442.86i | − 0.259081i | ||||||||
\(939\) | −24992.9 | −0.868598 | ||||||||
\(940\) | 19661.5i | 0.682220i | ||||||||
\(941\) | 35841.7i | 1.24166i | 0.783944 | + | 0.620832i | \(0.213205\pi\) | ||||
−0.783944 | + | 0.620832i | \(0.786795\pi\) | |||||||
\(942\) | 26830.0i | 0.927991i | ||||||||
\(943\) | −26676.3 | −0.921208 | ||||||||
\(944\) | −6384.21 | −0.220115 | ||||||||
\(945\) | 61751.9i | 2.12570i | ||||||||
\(946\) | − 2902.77i | − 0.0997643i | ||||||||
\(947\) | − 33544.8i | − 1.15107i | −0.817778 | − | 0.575534i | \(-0.804794\pi\) | ||||
0.817778 | − | 0.575534i | \(-0.195206\pi\) | |||||||
\(948\) | −29377.1 | −1.00646 | ||||||||
\(949\) | − 15379.0i | − 0.526052i | ||||||||
\(950\) | 15015.5 | 0.512809 | ||||||||
\(951\) | −5803.85 | −0.197900 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51190.9 | −1.74002 | −0.870008 | − | 0.493038i | \(-0.835886\pi\) | ||||
−0.870008 | + | 0.493038i | \(0.835886\pi\) | |||||||
\(954\) | 2171.32 | 0.0736886 | ||||||||
\(955\) | − 27755.0i | − 0.940452i | ||||||||
\(956\) | 890.506 | 0.0301266 | ||||||||
\(957\) | 85.4425i | 0.00288606i | ||||||||
\(958\) | − 23591.8i | − 0.795633i | ||||||||
\(959\) | − 14270.3i | − 0.480514i | ||||||||
\(960\) | −15413.9 | −0.518209 | ||||||||
\(961\) | 28885.8 | 0.969616 | ||||||||
\(962\) | − 28849.8i | − 0.966896i | ||||||||
\(963\) | − 320.960i | − 0.0107402i | ||||||||
\(964\) | 19063.0i | 0.636906i | ||||||||
\(965\) | 1006.81 | 0.0335858 | ||||||||
\(966\) | − 33507.0i | − 1.11602i | ||||||||
\(967\) | −11754.1 | −0.390885 | −0.195442 | − | 0.980715i | \(-0.562614\pi\) | ||||
−0.195442 | + | 0.980715i | \(0.562614\pi\) | |||||||
\(968\) | −24508.7 | −0.813779 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15815.3 | −0.523503 | ||||||||
\(971\) | 16608.7 | 0.548919 | 0.274459 | − | 0.961599i | \(-0.411501\pi\) | ||||
0.274459 | + | 0.961599i | \(0.411501\pi\) | |||||||
\(972\) | 3325.46i | 0.109737i | ||||||||
\(973\) | 29900.4 | 0.985164 | ||||||||
\(974\) | 4799.84i | 0.157902i | ||||||||
\(975\) | 19095.3i | 0.627218i | ||||||||
\(976\) | − 1703.42i | − 0.0558659i | ||||||||
\(977\) | 47963.6 | 1.57062 | 0.785308 | − | 0.619105i | \(-0.212504\pi\) | ||||
0.785308 | + | 0.619105i | \(0.212504\pi\) | |||||||
\(978\) | −2980.48 | −0.0974490 | ||||||||
\(979\) | − 8475.48i | − 0.276688i | ||||||||
\(980\) | − 41458.5i | − 1.35137i | ||||||||
\(981\) | − 1519.46i | − 0.0494521i | ||||||||
\(982\) | −15869.0 | −0.515683 | ||||||||
\(983\) | 49858.2i | 1.61773i | 0.587993 | + | 0.808866i | \(0.299918\pi\) | ||||
−0.587993 | + | 0.808866i | \(0.700082\pi\) | |||||||
\(984\) | −19643.1 | −0.636382 | ||||||||
\(985\) | 43964.0 | 1.42214 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −36284.1 | −1.17015 | ||||||||
\(988\) | 28528.9 | 0.918649 | ||||||||
\(989\) | − 19596.7i | − 0.630068i | ||||||||
\(990\) | 668.311 | 0.0214549 | ||||||||
\(991\) | 50467.6i | 1.61772i | 0.588005 | + | 0.808858i | \(0.299914\pi\) | ||||
−0.588005 | + | 0.808858i | \(0.700086\pi\) | |||||||
\(992\) | 5624.78i | 0.180027i | ||||||||
\(993\) | 10685.6i | 0.341487i | ||||||||
\(994\) | −905.139 | −0.0288826 | ||||||||
\(995\) | −18141.5 | −0.578014 | ||||||||
\(996\) | − 1293.14i | − 0.0411392i | ||||||||
\(997\) | 40927.6i | 1.30009i | 0.759895 | + | 0.650046i | \(0.225250\pi\) | ||||
−0.759895 | + | 0.650046i | \(0.774750\pi\) | |||||||
\(998\) | 22021.2i | 0.698465i | ||||||||
\(999\) | −57917.6 | −1.83427 |
(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 | 289.4.b.d.288.5 | 8 | ||
17.4 | even | 4 | 289.4.a.d.1.2 | yes | 4 | ||
17.13 | even | 4 | 289.4.a.c.1.2 | ✓ | 4 | ||
17.16 | even | 2 | inner | 289.4.b.d.288.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.c.1.2 | ✓ | 4 | 17.13 | even | 4 | ||
289.4.a.d.1.2 | yes | 4 | 17.4 | even | 4 | ||
289.4.b.d.288.5 | 8 | 1.1 | even | 1 | trivial | ||
289.4.b.d.288.6 | 8 | 17.16 | even | 2 | inner |