Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(46,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.46");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.h (of order \(5\), degree \(4\), 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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 46.4 | ||
Character | \(\chi\) | \(=\) | 225.46 |
Dual form | 225.4.h.a.181.4 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.177563 | − | 0.546483i | 0.0627781 | − | 0.193211i | −0.914748 | − | 0.404024i | \(-0.867611\pi\) |
0.977526 | + | 0.210813i | \(0.0676112\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 6.20502 | + | 4.50821i | 0.775628 | + | 0.563526i | ||||
\(5\) | 9.45304 | − | 5.96993i | 0.845506 | − | 0.533967i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.67744 | −0.144568 | −0.0722840 | − | 0.997384i | \(-0.523029\pi\) | ||||
−0.0722840 | + | 0.997384i | \(0.523029\pi\) | |||||||
\(8\) | 7.28438 | − | 5.29241i | 0.321927 | − | 0.233894i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.58395 | − | 6.22597i | −0.0500891 | − | 0.196882i | ||||
\(11\) | 19.4804 | − | 59.9545i | 0.533960 | − | 1.64336i | −0.211924 | − | 0.977286i | \(-0.567973\pi\) |
0.745885 | − | 0.666075i | \(-0.232027\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.38017 | + | 13.4808i | 0.0934493 | + | 0.287607i | 0.986846 | − | 0.161660i | \(-0.0516849\pi\) |
−0.893397 | + | 0.449268i | \(0.851685\pi\) | |||||||
\(14\) | −0.475414 | + | 1.46317i | −0.00907569 | + | 0.0279321i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 17.3621 | + | 53.4350i | 0.271282 | + | 0.834922i | ||||
\(17\) | 24.5906 | − | 17.8661i | 0.350829 | − | 0.254892i | −0.398388 | − | 0.917217i | \(-0.630430\pi\) |
0.749217 | + | 0.662325i | \(0.230430\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −22.2647 | + | 16.1762i | −0.268835 | + | 0.195320i | −0.714033 | − | 0.700112i | \(-0.753133\pi\) |
0.445198 | + | 0.895432i | \(0.353133\pi\) | |||||||
\(20\) | 85.5700 | + | 5.57276i | 0.956702 | + | 0.0623054i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −29.3052 | − | 21.2914i | −0.283995 | − | 0.206334i | ||||
\(23\) | −35.9246 | + | 110.565i | −0.325687 | + | 1.00236i | 0.645443 | + | 0.763809i | \(0.276673\pi\) |
−0.971130 | + | 0.238553i | \(0.923327\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 53.7199 | − | 112.868i | 0.429759 | − | 0.902944i | ||||
\(26\) | 8.14478 | 0.0614355 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −16.6135 | − | 12.0704i | −0.112131 | − | 0.0814678i | ||||
\(29\) | −32.5312 | − | 23.6353i | −0.208307 | − | 0.151344i | 0.478740 | − | 0.877956i | \(-0.341093\pi\) |
−0.687047 | + | 0.726613i | \(0.741093\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 180.304 | − | 130.998i | 1.04463 | − | 0.758967i | 0.0734444 | − | 0.997299i | \(-0.476601\pi\) |
0.971184 | + | 0.238333i | \(0.0766008\pi\) | |||||||
\(32\) | 104.316 | 0.576270 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.39715 | − | 16.6107i | −0.0272236 | − | 0.0837857i | ||||
\(35\) | −25.3099 | + | 15.9841i | −0.122233 | + | 0.0771944i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 25.6160 | + | 78.8378i | 0.113817 | + | 0.350293i | 0.991698 | − | 0.128585i | \(-0.0410435\pi\) |
−0.877881 | + | 0.478878i | \(0.841044\pi\) | |||||||
\(38\) | 4.88665 | + | 15.0396i | 0.0208610 | + | 0.0642037i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 37.2642 | − | 93.5166i | 0.147300 | − | 0.369657i | ||||
\(41\) | −44.5269 | − | 137.040i | −0.169608 | − | 0.522000i | 0.829738 | − | 0.558153i | \(-0.188490\pi\) |
−0.999346 | + | 0.0361527i | \(0.988490\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 433.956 | 1.53901 | 0.769507 | − | 0.638638i | \(-0.220502\pi\) | ||||
0.769507 | + | 0.638638i | \(0.220502\pi\) | |||||||
\(44\) | 391.164 | − | 284.197i | 1.34023 | − | 0.973736i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 54.0428 | + | 39.2644i | 0.173221 | + | 0.125853i | ||||
\(47\) | 371.550 | + | 269.947i | 1.15311 | + | 0.837783i | 0.988891 | − | 0.148641i | \(-0.0474898\pi\) |
0.164218 | + | 0.986424i | \(0.447490\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −335.831 | −0.979100 | ||||||||
\(50\) | −52.1418 | − | 49.3982i | −0.147479 | − | 0.139719i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −33.5952 | + | 103.395i | −0.0895925 | + | 0.275737i | ||||
\(53\) | −200.214 | − | 145.464i | −0.518897 | − | 0.377001i | 0.297291 | − | 0.954787i | \(-0.403917\pi\) |
−0.816188 | + | 0.577786i | \(0.803917\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −173.775 | − | 683.049i | −0.426034 | − | 1.67459i | ||||
\(56\) | −19.5034 | + | 14.1701i | −0.0465403 | + | 0.0338135i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −18.6927 | + | 13.5810i | −0.0423184 | + | 0.0307461i | ||||
\(59\) | −95.9388 | − | 295.269i | −0.211698 | − | 0.651539i | −0.999372 | − | 0.0354462i | \(-0.988715\pi\) |
0.787674 | − | 0.616092i | \(-0.211285\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.644333 | − | 1.98305i | 0.00135243 | − | 0.00416236i | −0.950378 | − | 0.311097i | \(-0.899303\pi\) |
0.951730 | + | 0.306935i | \(0.0993034\pi\) | |||||||
\(62\) | −39.5730 | − | 121.793i | −0.0810610 | − | 0.249480i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −120.374 | + | 370.473i | −0.235105 | + | 0.723580i | ||||
\(65\) | 121.885 | + | 101.285i | 0.232585 | + | 0.193275i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −529.476 | + | 384.687i | −0.965460 | + | 0.701448i | −0.954412 | − | 0.298491i | \(-0.903517\pi\) |
−0.0110477 | + | 0.999939i | \(0.503517\pi\) | |||||||
\(68\) | 233.129 | 0.415751 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.24094 | + | 16.6696i | 0.00724127 | + | 0.0284629i | ||||
\(71\) | −734.591 | − | 533.711i | −1.22789 | − | 0.892111i | −0.231156 | − | 0.972917i | \(-0.574251\pi\) |
−0.996730 | + | 0.0808056i | \(0.974251\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −271.486 | + | 835.547i | −0.435274 | + | 1.33964i | 0.457531 | + | 0.889194i | \(0.348734\pi\) |
−0.892805 | + | 0.450443i | \(0.851266\pi\) | |||||||
\(74\) | 47.6320 | 0.0748258 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −211.079 | −0.318584 | ||||||||
\(77\) | −52.1575 | + | 160.524i | −0.0771935 | + | 0.237577i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 921.477 | + | 669.493i | 1.31233 | + | 0.953466i | 0.999994 | + | 0.00349520i | \(0.00111256\pi\) |
0.312339 | + | 0.949971i | \(0.398887\pi\) | |||||||
\(80\) | 483.127 | + | 401.473i | 0.675191 | + | 0.561075i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −82.7962 | −0.111504 | ||||||||
\(83\) | −798.210 | + | 579.934i | −1.05560 | + | 0.766940i | −0.973270 | − | 0.229665i | \(-0.926237\pi\) |
−0.0823324 | + | 0.996605i | \(0.526237\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 125.796 | − | 315.693i | 0.160524 | − | 0.402844i | ||||
\(86\) | 77.0546 | − | 237.150i | 0.0966164 | − | 0.297355i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −175.401 | − | 539.830i | −0.212476 | − | 0.653932i | ||||
\(89\) | −305.549 | + | 940.383i | −0.363911 | + | 1.12000i | 0.586748 | + | 0.809769i | \(0.300408\pi\) |
−0.950660 | + | 0.310235i | \(0.899592\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.7276 | − | 36.0939i | −0.0135098 | − | 0.0415788i | ||||
\(92\) | −721.361 | + | 524.100i | −0.817469 | + | 0.593926i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 213.495 | − | 155.113i | 0.234259 | − | 0.170199i | ||||
\(95\) | −113.898 | + | 285.833i | −0.123007 | + | 0.308693i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1244.20 | − | 903.964i | −1.30236 | − | 0.946223i | −0.302388 | − | 0.953185i | \(-0.597784\pi\) |
−0.999976 | + | 0.00696215i | \(0.997784\pi\) | |||||||
\(98\) | −59.6313 | + | 183.526i | −0.0614660 | + | 0.189173i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 842.166 | − | 458.167i | 0.842166 | − | 0.458167i | ||||
\(101\) | 266.284 | 0.262339 | 0.131170 | − | 0.991360i | \(-0.458127\pi\) | ||||
0.131170 | + | 0.991360i | \(0.458127\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 630.873 | + | 458.356i | 0.603512 | + | 0.438477i | 0.847124 | − | 0.531396i | \(-0.178332\pi\) |
−0.243612 | + | 0.969873i | \(0.578332\pi\) | |||||||
\(104\) | 103.253 | + | 75.0174i | 0.0973534 | + | 0.0707314i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −115.044 | + | 83.5847i | −0.105416 | + | 0.0765893i | ||||
\(107\) | −526.990 | −0.476132 | −0.238066 | − | 0.971249i | \(-0.576513\pi\) | ||||
−0.238066 | + | 0.971249i | \(0.576513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.0367 | − | 55.5114i | −0.0158496 | − | 0.0487800i | 0.942819 | − | 0.333305i | \(-0.108164\pi\) |
−0.958669 | + | 0.284525i | \(0.908164\pi\) | |||||||
\(110\) | −404.131 | − | 26.3191i | −0.350294 | − | 0.0228130i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −46.4858 | − | 143.069i | −0.0392187 | − | 0.120703i | ||||
\(113\) | 14.5997 | + | 44.9333i | 0.0121542 | + | 0.0374068i | 0.956950 | − | 0.290254i | \(-0.0937397\pi\) |
−0.944795 | + | 0.327661i | \(0.893740\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 320.466 | + | 1259.64i | 0.259857 | + | 1.02141i | ||||
\(116\) | −95.3039 | − | 293.315i | −0.0762823 | − | 0.234773i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −178.395 | −0.139174 | ||||||||
\(119\) | −65.8397 | + | 47.8354i | −0.0507186 | + | 0.0368493i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2138.26 | − | 1553.54i | −1.60651 | − | 1.16719i | ||||
\(122\) | −0.969296 | − | 0.704235i | −0.000719311 | − | 0.000522610i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1709.35 | 1.23794 | ||||||||
\(125\) | −165.997 | − | 1387.65i | −0.118778 | − | 0.992921i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −485.405 | + | 1493.92i | −0.339155 | + | 1.04381i | 0.625484 | + | 0.780237i | \(0.284902\pi\) |
−0.964639 | + | 0.263575i | \(0.915098\pi\) | |||||||
\(128\) | 856.231 | + | 622.088i | 0.591257 | + | 0.429573i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 76.9929 | − | 48.6238i | 0.0519440 | − | 0.0328045i | ||||
\(131\) | −2344.50 | + | 1703.38i | −1.56366 | + | 1.13607i | −0.630741 | + | 0.775993i | \(0.717249\pi\) |
−0.932923 | + | 0.360076i | \(0.882751\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 59.6122 | − | 43.3108i | 0.0388649 | − | 0.0282370i | ||||
\(134\) | 116.210 | + | 357.656i | 0.0749177 | + | 0.230573i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 84.5724 | − | 260.287i | 0.0533237 | − | 0.164113i | ||||
\(137\) | −402.958 | − | 1240.18i | −0.251292 | − | 0.773398i | −0.994538 | − | 0.104379i | \(-0.966714\pi\) |
0.743245 | − | 0.669019i | \(-0.233286\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 381.913 | − | 1175.41i | 0.233047 | − | 0.717243i | −0.764328 | − | 0.644828i | \(-0.776929\pi\) |
0.997375 | − | 0.0724158i | \(-0.0230709\pi\) | |||||||
\(140\) | −229.108 | − | 14.9207i | −0.138308 | − | 0.00900736i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −422.101 | + | 306.674i | −0.249450 | + | 0.181236i | ||||
\(143\) | 893.562 | 0.522541 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −448.620 | − | 29.2165i | −0.256937 | − | 0.0167331i | ||||
\(146\) | 408.407 | + | 296.725i | 0.231507 | + | 0.168200i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −196.470 | + | 604.672i | −0.109120 | + | 0.335836i | ||||
\(149\) | 810.211 | 0.445470 | 0.222735 | − | 0.974879i | \(-0.428501\pi\) | ||||
0.222735 | + | 0.974879i | \(0.428501\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3447.19 | −1.85781 | −0.928903 | − | 0.370324i | \(-0.879247\pi\) | ||||
−0.928903 | + | 0.370324i | \(0.879247\pi\) | |||||||
\(152\) | −76.5730 | + | 235.667i | −0.0408611 | + | 0.125758i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 78.4626 | + | 57.0064i | 0.0410565 | + | 0.0298293i | ||||
\(155\) | 922.366 | − | 2314.73i | 0.477976 | − | 1.19951i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −804.338 | −0.408873 | −0.204437 | − | 0.978880i | \(-0.565536\pi\) | ||||
−0.204437 | + | 0.978880i | \(0.565536\pi\) | |||||||
\(158\) | 529.487 | − | 384.695i | 0.266606 | − | 0.193700i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 986.104 | − | 622.760i | 0.487240 | − | 0.307709i | ||||
\(161\) | 96.1858 | − | 296.029i | 0.0470839 | − | 0.144909i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 976.108 | + | 3004.15i | 0.469047 | + | 1.44358i | 0.853821 | + | 0.520567i | \(0.174280\pi\) |
−0.384774 | + | 0.923011i | \(0.625720\pi\) | |||||||
\(164\) | 341.514 | − | 1051.07i | 0.162608 | − | 0.500456i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 175.191 | + | 539.184i | 0.0819126 | + | 0.252101i | ||||
\(167\) | −2278.34 | + | 1655.31i | −1.05571 | + | 0.767018i | −0.973290 | − | 0.229580i | \(-0.926265\pi\) |
−0.0824199 | + | 0.996598i | \(0.526265\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1614.86 | − | 1173.27i | 0.735032 | − | 0.534032i | ||||
\(170\) | −150.184 | − | 124.801i | −0.0677565 | − | 0.0563048i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2692.70 | + | 1956.36i | 1.19370 | + | 0.867276i | ||||
\(173\) | 1133.19 | − | 3487.61i | 0.498006 | − | 1.53270i | −0.314213 | − | 0.949352i | \(-0.601741\pi\) |
0.812219 | − | 0.583352i | \(-0.198259\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −143.832 | + | 302.197i | −0.0621294 | + | 0.130537i | ||||
\(176\) | 3541.89 | 1.51693 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 459.649 | + | 333.955i | 0.193552 | + | 0.140623i | ||||
\(179\) | 1965.97 | + | 1428.36i | 0.820912 | + | 0.596427i | 0.916974 | − | 0.398948i | \(-0.130625\pi\) |
−0.0960617 | + | 0.995375i | \(0.530625\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2655.62 | − | 1929.42i | 1.09056 | − | 0.792336i | 0.111064 | − | 0.993813i | \(-0.464574\pi\) |
0.979493 | + | 0.201477i | \(0.0645743\pi\) | |||||||
\(182\) | −21.8071 | −0.00888160 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 323.465 | + | 995.522i | 0.129599 | + | 0.398863i | ||||
\(185\) | 712.805 | + | 592.331i | 0.283278 | + | 0.235400i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −592.120 | − | 1822.36i | −0.231551 | − | 0.712642i | ||||
\(188\) | 1088.50 | + | 3350.05i | 0.422271 | + | 1.29962i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 135.979 | + | 112.997i | 0.0519208 | + | 0.0431455i | ||||
\(191\) | −659.004 | − | 2028.21i | −0.249654 | − | 0.768355i | −0.994836 | − | 0.101494i | \(-0.967638\pi\) |
0.745183 | − | 0.666861i | \(-0.232362\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3868.32 | −1.44274 | −0.721368 | − | 0.692552i | \(-0.756486\pi\) | ||||
−0.721368 | + | 0.692552i | \(0.756486\pi\) | |||||||
\(194\) | −714.925 | + | 519.423i | −0.264581 | + | 0.192229i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2083.84 | − | 1514.00i | −0.759417 | − | 0.551749i | ||||
\(197\) | −1428.32 | − | 1037.74i | −0.516568 | − | 0.375308i | 0.298742 | − | 0.954334i | \(-0.403433\pi\) |
−0.815309 | + | 0.579026i | \(0.803433\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3952.78 | 1.40807 | 0.704033 | − | 0.710167i | \(-0.251381\pi\) | ||||
0.704033 | + | 0.710167i | \(0.251381\pi\) | |||||||
\(200\) | −206.027 | − | 1106.48i | −0.0728417 | − | 0.391200i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 47.2823 | − | 145.520i | 0.0164692 | − | 0.0506869i | ||||
\(203\) | 87.1002 | + | 63.2820i | 0.0301145 | + | 0.0218794i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1239.03 | − | 1029.62i | −0.422135 | − | 0.350789i | ||||
\(206\) | 362.504 | − | 263.374i | 0.122606 | − | 0.0890784i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −644.296 | + | 468.109i | −0.214778 | + | 0.156046i | ||||
\(209\) | 536.113 | + | 1649.99i | 0.177434 | + | 0.546086i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1472.71 | − | 4532.54i | 0.480501 | − | 1.47883i | −0.357891 | − | 0.933763i | \(-0.616504\pi\) |
0.838392 | − | 0.545067i | \(-0.183496\pi\) | |||||||
\(212\) | −586.551 | − | 1805.22i | −0.190021 | − | 0.584825i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −93.5741 | + | 287.991i | −0.0298906 | + | 0.0919939i | ||||
\(215\) | 4102.20 | − | 2590.69i | 1.30125 | − | 0.821783i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −482.751 | + | 350.739i | −0.151020 | + | 0.109722i | ||||
\(218\) | −33.5387 | −0.0104199 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2001.05 | − | 5021.75i | 0.613231 | − | 1.53894i | ||||
\(221\) | 348.560 | + | 253.244i | 0.106094 | + | 0.0770816i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −679.879 | + | 2092.45i | −0.204162 | + | 0.628345i | 0.795585 | + | 0.605842i | \(0.207164\pi\) |
−0.999747 | + | 0.0225031i | \(0.992836\pi\) | |||||||
\(224\) | −279.300 | −0.0833102 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 27.1477 | 0.00799042 | ||||||||
\(227\) | −301.326 | + | 927.386i | −0.0881045 | + | 0.271158i | −0.985395 | − | 0.170282i | \(-0.945532\pi\) |
0.897291 | + | 0.441440i | \(0.145532\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1289.94 | − | 937.197i | −0.372235 | − | 0.270444i | 0.385902 | − | 0.922540i | \(-0.373890\pi\) |
−0.758137 | + | 0.652095i | \(0.773890\pi\) | |||||||
\(230\) | 745.274 | + | 48.5362i | 0.213661 | + | 0.0139147i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −362.057 | −0.102458 | ||||||||
\(233\) | −3787.94 | + | 2752.10i | −1.06505 | + | 0.773802i | −0.975016 | − | 0.222137i | \(-0.928697\pi\) |
−0.0900318 | + | 0.995939i | \(0.528697\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5123.84 | + | 333.691i | 1.42231 | + | 0.0926282i | ||||
\(236\) | 735.834 | − | 2264.66i | 0.202961 | − | 0.624649i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14.4505 | + | 44.4741i | 0.00393566 | + | 0.0121127i | ||||
\(239\) | −22.3460 | + | 68.7738i | −0.00604787 | + | 0.0186134i | −0.954035 | − | 0.299695i | \(-0.903115\pi\) |
0.947987 | + | 0.318309i | \(0.103115\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 566.484 | + | 1743.46i | 0.151413 | + | 0.466000i | 0.997780 | − | 0.0665998i | \(-0.0212151\pi\) |
−0.846367 | + | 0.532600i | \(0.821215\pi\) | |||||||
\(242\) | −1228.66 | + | 892.672i | −0.326368 | + | 0.237120i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.9381 | − | 9.40010i | 0.00339459 | − | 0.00246631i | ||||
\(245\) | −3174.63 | + | 2004.89i | −0.827835 | + | 0.522807i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −315.591 | − | 229.290i | −0.0812979 | − | 0.0590664i | ||||
\(248\) | 620.103 | − | 1908.48i | 0.158776 | − | 0.488664i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −787.802 | − | 155.681i | −0.199300 | − | 0.0393844i | ||||
\(251\) | 211.935 | 0.0532956 | 0.0266478 | − | 0.999645i | \(-0.491517\pi\) | ||||
0.0266478 | + | 0.999645i | \(0.491517\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5929.02 | + | 4307.69i | 1.47334 | + | 1.07044i | ||||
\(254\) | 730.214 | + | 530.531i | 0.180385 | + | 0.131057i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2029.15 | + | 1474.26i | −0.495398 | + | 0.359927i | ||||
\(257\) | 7074.89 | 1.71720 | 0.858599 | − | 0.512648i | \(-0.171335\pi\) | ||||
0.858599 | + | 0.512648i | \(0.171335\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −68.5851 | − | 211.083i | −0.0164543 | − | 0.0506412i | ||||
\(260\) | 299.686 | + | 1177.96i | 0.0714836 | + | 0.280977i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 514.572 | + | 1583.69i | 0.121337 | + | 0.373437i | ||||
\(263\) | 1562.26 | + | 4808.14i | 0.366286 | + | 1.12731i | 0.949172 | + | 0.314758i | \(0.101923\pi\) |
−0.582886 | + | 0.812554i | \(0.698077\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2761.04 | − | 179.814i | −0.640036 | − | 0.0416825i | ||||
\(266\) | −13.0837 | − | 40.2675i | −0.00301584 | − | 0.00928179i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5019.66 | −1.14412 | ||||||||
\(269\) | 1867.63 | − | 1356.91i | 0.423314 | − | 0.307556i | −0.355656 | − | 0.934617i | \(-0.615742\pi\) |
0.778970 | + | 0.627061i | \(0.215742\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 475.680 | + | 345.602i | 0.106625 | + | 0.0774679i | 0.639820 | − | 0.768525i | \(-0.279009\pi\) |
−0.533195 | + | 0.845992i | \(0.679009\pi\) | |||||||
\(272\) | 1381.62 | + | 1003.81i | 0.307989 | + | 0.223767i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −749.287 | −0.165205 | ||||||||
\(275\) | −5720.46 | − | 5419.47i | −1.25439 | − | 1.18839i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −936.066 | + | 2880.92i | −0.203042 | + | 0.624900i | 0.796746 | + | 0.604315i | \(0.206553\pi\) |
−0.999788 | + | 0.0205857i | \(0.993447\pi\) | |||||||
\(278\) | −574.527 | − | 417.419i | −0.123949 | − | 0.0900543i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −99.7724 | + | 250.385i | −0.0212948 | + | 0.0534405i | ||||
\(281\) | −4977.64 | + | 3616.47i | −1.05673 | + | 0.767759i | −0.973481 | − | 0.228770i | \(-0.926530\pi\) |
−0.0832489 | + | 0.996529i | \(0.526530\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4502.63 | − | 3271.35i | 0.945773 | − | 0.687144i | −0.00403070 | − | 0.999992i | \(-0.501283\pi\) |
0.949803 | + | 0.312848i | \(0.101283\pi\) | |||||||
\(284\) | −2152.07 | − | 6623.38i | −0.449654 | − | 1.38389i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 158.664 | − | 488.316i | 0.0328041 | − | 0.100961i | ||||
\(287\) | 119.218 | + | 366.915i | 0.0245199 | + | 0.0754645i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1232.70 | + | 3793.86i | −0.250906 | + | 0.772209i | ||||
\(290\) | −95.6247 | + | 239.976i | −0.0193630 | + | 0.0485926i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5451.40 | + | 3960.67i | −1.09253 | + | 0.793770i | ||||
\(293\) | −2865.97 | −0.571440 | −0.285720 | − | 0.958313i | \(-0.592233\pi\) | ||||
−0.285720 | + | 0.958313i | \(0.592233\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2669.65 | − | 2218.44i | −0.526892 | − | 0.437840i | ||||
\(296\) | 603.838 | + | 438.714i | 0.118572 | + | 0.0861478i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 143.864 | − | 442.767i | 0.0279658 | − | 0.0860698i | ||||
\(299\) | −1647.85 | −0.318722 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1161.89 | −0.222492 | ||||||||
\(302\) | −612.095 | + | 1883.83i | −0.116629 | + | 0.358948i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1250.94 | − | 908.859i | −0.236007 | − | 0.171469i | ||||
\(305\) | −5.74779 | − | 22.5925i | −0.00107907 | − | 0.00424145i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1957.38 | −0.363888 | −0.181944 | − | 0.983309i | \(-0.558239\pi\) | ||||
−0.181944 | + | 0.983309i | \(0.558239\pi\) | |||||||
\(308\) | −1047.32 | + | 760.920i | −0.193755 | + | 0.140771i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1101.18 | − | 915.069i | −0.201752 | − | 0.167653i | ||||
\(311\) | −1081.33 | + | 3327.99i | −0.197159 | + | 0.606794i | 0.802785 | + | 0.596268i | \(0.203351\pi\) |
−0.999945 | + | 0.0105260i | \(0.996649\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 132.624 | + | 408.176i | 0.0239501 | + | 0.0737107i | 0.962317 | − | 0.271930i | \(-0.0876618\pi\) |
−0.938367 | + | 0.345640i | \(0.887662\pi\) | |||||||
\(314\) | −142.821 | + | 439.557i | −0.0256683 | + | 0.0789989i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2699.57 | + | 8308.43i | 0.480579 | + | 1.47907i | ||||
\(317\) | 3210.73 | − | 2332.73i | 0.568873 | − | 0.413310i | −0.265823 | − | 0.964022i | \(-0.585644\pi\) |
0.834696 | + | 0.550712i | \(0.185644\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2050.77 | + | 1489.97i | −0.359940 | + | 0.261512i | ||||
\(320\) | 1073.80 | + | 4220.72i | 0.187585 | + | 0.737329i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −144.696 | − | 105.128i | −0.0250422 | − | 0.0181942i | ||||
\(323\) | −258.495 | + | 795.566i | −0.0445296 | + | 0.137048i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1756.85 | + | 229.805i | 0.299854 | + | 0.0392225i | ||||
\(326\) | 1815.04 | 0.308361 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1049.62 | − | 762.594i | −0.176694 | − | 0.128376i | ||||
\(329\) | −994.801 | − | 722.765i | −0.166703 | − | 0.121117i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4997.11 | − | 3630.61i | 0.829807 | − | 0.602890i | −0.0896980 | − | 0.995969i | \(-0.528590\pi\) |
0.919505 | + | 0.393079i | \(0.128590\pi\) | |||||||
\(332\) | −7567.38 | −1.25094 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 500.051 | + | 1539.00i | 0.0819209 | + | 0.252127i | ||||
\(335\) | −2708.61 | + | 6797.40i | −0.441752 | + | 1.10860i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2557.17 | − | 7870.15i | −0.413346 | − | 1.27215i | −0.913722 | − | 0.406341i | \(-0.866805\pi\) |
0.500375 | − | 0.865809i | \(-0.333195\pi\) | |||||||
\(338\) | −354.431 | − | 1090.83i | −0.0570370 | − | 0.175542i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2203.78 | − | 1391.77i | 0.351520 | − | 0.221997i | ||||
\(341\) | −4341.55 | − | 13361.9i | −0.689466 | − | 2.12196i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1817.53 | 0.286114 | ||||||||
\(344\) | 3161.10 | − | 2296.67i | 0.495450 | − | 0.359966i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1704.71 | − | 1238.54i | −0.264872 | − | 0.192440i | ||||
\(347\) | 3062.22 | + | 2224.83i | 0.473743 | + | 0.344194i | 0.798898 | − | 0.601466i | \(-0.205417\pi\) |
−0.325156 | + | 0.945661i | \(0.605417\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7094.08 | −1.08807 | −0.544037 | − | 0.839061i | \(-0.683105\pi\) | ||||
−0.544037 | + | 0.839061i | \(0.683105\pi\) | |||||||
\(350\) | 139.606 | + | 132.261i | 0.0213208 | + | 0.0201989i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2032.12 | − | 6254.22i | 0.307706 | − | 0.947020i | ||||
\(353\) | −1416.95 | − | 1029.47i | −0.213644 | − | 0.155222i | 0.475817 | − | 0.879544i | \(-0.342153\pi\) |
−0.689461 | + | 0.724323i | \(0.742153\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10130.3 | − | 659.740i | −1.51454 | − | 0.0986348i | ||||
\(356\) | −6135.38 | + | 4457.62i | −0.913412 | + | 0.663633i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1129.66 | − | 820.744i | 0.166772 | − | 0.121167i | ||||
\(359\) | 101.297 | + | 311.759i | 0.0148920 | + | 0.0458329i | 0.958226 | − | 0.286011i | \(-0.0923293\pi\) |
−0.943334 | + | 0.331844i | \(0.892329\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1885.50 | + | 5802.98i | −0.274895 | + | 0.846039i | ||||
\(362\) | −582.856 | − | 1793.85i | −0.0846250 | − | 0.260449i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 89.9489 | − | 276.834i | 0.0129522 | − | 0.0398628i | ||||
\(365\) | 2421.79 | + | 9519.21i | 0.347294 | + | 1.36509i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4716.67 | − | 3426.86i | 0.670867 | − | 0.487413i | −0.199448 | − | 0.979908i | \(-0.563915\pi\) |
0.870315 | + | 0.492495i | \(0.163915\pi\) | |||||||
\(368\) | −6531.74 | −0.925246 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 450.267 | − | 284.360i | 0.0632656 | − | 0.0399545i | ||||
\(371\) | 536.061 | + | 389.471i | 0.0750159 | + | 0.0545022i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 887.259 | − | 2730.70i | 0.123165 | − | 0.379063i | −0.870397 | − | 0.492350i | \(-0.836138\pi\) |
0.993562 | + | 0.113287i | \(0.0361380\pi\) | |||||||
\(374\) | −1101.03 | −0.152227 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4135.18 | 0.567169 | ||||||||
\(377\) | 176.130 | − | 542.073i | 0.0240615 | − | 0.0740535i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8973.27 | + | 6519.46i | 1.21616 | + | 0.883594i | 0.995776 | − | 0.0918182i | \(-0.0292678\pi\) |
0.220387 | + | 0.975412i | \(0.429268\pi\) | |||||||
\(380\) | −1995.33 | + | 1260.12i | −0.269364 | + | 0.170113i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1225.39 | −0.164127 | ||||||||
\(383\) | 579.752 | − | 421.215i | 0.0773472 | − | 0.0561960i | −0.548440 | − | 0.836190i | \(-0.684778\pi\) |
0.625787 | + | 0.779994i | \(0.284778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 465.272 | + | 1828.82i | 0.0615908 | + | 0.242092i | ||||
\(386\) | −686.872 | + | 2113.97i | −0.0905722 | + | 0.278753i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3645.02 | − | 11218.2i | −0.476928 | − | 1.46783i | ||||
\(389\) | −2338.83 | + | 7198.19i | −0.304842 | + | 0.938207i | 0.674894 | + | 0.737915i | \(0.264189\pi\) |
−0.979736 | + | 0.200293i | \(0.935811\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1091.95 | + | 3360.68i | 0.141234 | + | 0.434673i | ||||
\(392\) | −2446.32 | + | 1777.36i | −0.315199 | + | 0.229005i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −820.724 | + | 596.291i | −0.104943 | + | 0.0762454i | ||||
\(395\) | 12707.6 | + | 827.584i | 1.61870 | + | 0.105418i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −576.649 | − | 418.960i | −0.0728997 | − | 0.0529648i | 0.550739 | − | 0.834678i | \(-0.314346\pi\) |
−0.623638 | + | 0.781713i | \(0.714346\pi\) | |||||||
\(398\) | 701.868 | − | 2160.13i | 0.0883957 | − | 0.272054i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6963.79 | + | 910.899i | 0.870473 | + | 0.113862i | ||||
\(401\) | 5539.33 | 0.689828 | 0.344914 | − | 0.938634i | \(-0.387908\pi\) | ||||
0.344914 | + | 0.938634i | \(0.387908\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2555.72 | + | 1856.84i | 0.315904 | + | 0.229518i | ||||
\(404\) | 1652.30 | + | 1200.47i | 0.203478 | + | 0.147835i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 50.0484 | − | 36.3623i | 0.00611788 | − | 0.00444490i | ||||
\(407\) | 5225.69 | 0.636432 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2701.55 | − | 8314.52i | −0.326609 | − | 1.00520i | −0.970709 | − | 0.240258i | \(-0.922768\pi\) |
0.644100 | − | 0.764941i | \(-0.277232\pi\) | |||||||
\(410\) | −782.676 | + | 494.288i | −0.0942771 | + | 0.0595393i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1848.21 | + | 5688.21i | 0.221007 | + | 0.680190i | ||||
\(413\) | 256.870 | + | 790.564i | 0.0306047 | + | 0.0941916i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4083.35 | + | 10247.4i | −0.482997 | + | 1.21211i | ||||
\(416\) | 456.922 | + | 1406.26i | 0.0538521 | + | 0.165740i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 996.884 | 0.116649 | ||||||||
\(419\) | 2623.21 | − | 1905.87i | 0.305853 | − | 0.222215i | −0.424262 | − | 0.905539i | \(-0.639467\pi\) |
0.730115 | + | 0.683324i | \(0.239467\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1410.17 | + | 1024.55i | 0.163249 | + | 0.118607i | 0.666410 | − | 0.745585i | \(-0.267830\pi\) |
−0.503162 | + | 0.864192i | \(0.667830\pi\) | |||||||
\(422\) | −2215.46 | − | 1609.63i | −0.255561 | − | 0.185676i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2228.29 | −0.255225 | ||||||||
\(425\) | −695.508 | − | 3735.26i | −0.0793813 | − | 0.426321i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.72516 | + | 5.30950i | −0.000195518 | + | 0.000601744i | ||||
\(428\) | −3269.99 | − | 2375.78i | −0.369301 | − | 0.268313i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −687.366 | − | 2701.79i | −0.0770878 | − | 0.303005i | ||||
\(431\) | 5437.70 | − | 3950.72i | 0.607715 | − | 0.441531i | −0.240894 | − | 0.970551i | \(-0.577441\pi\) |
0.848609 | + | 0.529021i | \(0.177441\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4669.15 | − | 3392.34i | 0.518210 | − | 0.376502i | −0.297719 | − | 0.954654i | \(-0.596226\pi\) |
0.815929 | + | 0.578152i | \(0.196226\pi\) | |||||||
\(434\) | 105.954 | + | 326.094i | 0.0117188 | + | 0.0360668i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 138.339 | − | 425.763i | 0.0151955 | − | 0.0467668i | ||||
\(437\) | −988.668 | − | 3042.81i | −0.108225 | − | 0.333083i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1919.93 | + | 5908.95i | −0.208732 | + | 0.642412i | 0.790807 | + | 0.612065i | \(0.209661\pi\) |
−0.999539 | + | 0.0303466i | \(0.990339\pi\) | |||||||
\(440\) | −4880.82 | − | 4055.90i | −0.528827 | − | 0.439449i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 200.285 | − | 145.516i | 0.0215534 | − | 0.0156594i | ||||
\(443\) | 6346.31 | 0.680638 | 0.340319 | − | 0.940310i | \(-0.389465\pi\) | ||||
0.340319 | + | 0.940310i | \(0.389465\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2725.65 | + | 10713.6i | 0.290356 | + | 1.14129i | ||||
\(446\) | 1022.77 | + | 743.085i | 0.108586 | + | 0.0788926i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 322.293 | − | 991.917i | 0.0339887 | − | 0.104606i | ||||
\(449\) | 2732.09 | 0.287161 | 0.143581 | − | 0.989639i | \(-0.454138\pi\) | ||||
0.143581 | + | 0.989639i | \(0.454138\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9083.55 | −0.948399 | ||||||||
\(452\) | −111.977 | + | 344.631i | −0.0116526 | + | 0.0358630i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 453.297 | + | 329.339i | 0.0468596 | + | 0.0340455i | ||||
\(455\) | −326.340 | − | 271.184i | −0.0336243 | − | 0.0279413i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11572.5 | 1.18455 | 0.592276 | − | 0.805735i | \(-0.298230\pi\) | ||||
0.592276 | + | 0.805735i | \(0.298230\pi\) | |||||||
\(458\) | −741.209 | + | 538.520i | −0.0756210 | + | 0.0549419i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3690.22 | + | 9260.81i | −0.374038 | + | 0.938669i | ||||
\(461\) | 1118.62 | − | 3442.75i | 0.113013 | − | 0.347819i | −0.878514 | − | 0.477716i | \(-0.841465\pi\) |
0.991527 | + | 0.129897i | \(0.0414647\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3882.35 | − | 11948.7i | −0.389694 | − | 1.19935i | −0.933018 | − | 0.359831i | \(-0.882834\pi\) |
0.543324 | − | 0.839523i | \(-0.317166\pi\) | |||||||
\(464\) | 698.143 | − | 2148.66i | 0.0698502 | − | 0.214977i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 831.377 | + | 2558.72i | 0.0826455 | + | 0.254357i | ||||
\(467\) | 14107.1 | − | 10249.4i | 1.39786 | − | 1.01561i | 0.402910 | − | 0.915240i | \(-0.367999\pi\) |
0.994951 | − | 0.100366i | \(-0.0320012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1417.64 | − | 1029.97i | 0.139575 | − | 0.101407i | ||||
\(470\) | 1092.16 | − | 2740.84i | 0.107187 | − | 0.268991i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2261.54 | − | 1643.11i | −0.220542 | − | 0.160233i | ||||
\(473\) | 8453.64 | − | 26017.6i | 0.821773 | − | 2.52916i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 629.722 | + | 3381.95i | 0.0608287 | + | 0.326683i | ||||
\(476\) | −624.189 | −0.0601043 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 33.6159 | + | 24.4234i | 0.00321665 | + | 0.00233703i | ||||
\(479\) | −555.095 | − | 403.300i | −0.0529497 | − | 0.0384702i | 0.560996 | − | 0.827819i | \(-0.310418\pi\) |
−0.613945 | + | 0.789349i | \(0.710418\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −950.593 | + | 690.646i | −0.0901108 | + | 0.0654693i | ||||
\(482\) | 1053.36 | 0.0995417 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6264.27 | − | 19279.4i | −0.588305 | − | 1.81062i | ||||
\(485\) | −17158.1 | − | 1117.42i | −1.60641 | − | 0.104618i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1216.53 | + | 3744.08i | 0.113195 | + | 0.348379i | 0.991566 | − | 0.129600i | \(-0.0413694\pi\) |
−0.878371 | + | 0.477979i | \(0.841369\pi\) | |||||||
\(488\) | −5.80157 | − | 17.8554i | −0.000538165 | − | 0.00165630i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 531.942 | + | 2090.88i | 0.0490422 | + | 0.192768i | ||||
\(491\) | 6027.95 | + | 18552.1i | 0.554048 | + | 1.70518i | 0.698445 | + | 0.715664i | \(0.253876\pi\) |
−0.144397 | + | 0.989520i | \(0.546124\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1222.23 | −0.111656 | ||||||||
\(494\) | −181.341 | + | 131.752i | −0.0165160 | + | 0.0119996i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10130.3 | + | 7360.12i | 0.917067 | + | 0.666288i | ||||
\(497\) | 1966.82 | + | 1428.98i | 0.177513 | + | 0.128971i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8132.04 | −0.729539 | −0.364770 | − | 0.931098i | \(-0.618852\pi\) | ||||
−0.364770 | + | 0.931098i | \(0.618852\pi\) | |||||||
\(500\) | 5225.80 | − | 9358.74i | 0.467410 | − | 0.837071i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 37.6318 | − | 115.819i | 0.00334579 | − | 0.0102973i | ||||
\(503\) | 17482.4 | + | 12701.7i | 1.54971 | + | 1.12593i | 0.943860 | + | 0.330345i | \(0.107165\pi\) |
0.605845 | + | 0.795582i | \(0.292835\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2517.20 | − | 1589.70i | 0.221809 | − | 0.140081i | ||||
\(506\) | 3406.86 | − | 2475.23i | 0.299315 | − | 0.217465i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9746.86 | + | 7081.51i | −0.851274 | + | 0.618487i | ||||
\(509\) | −4650.20 | − | 14311.8i | −0.404944 | − | 1.24629i | −0.920942 | − | 0.389699i | \(-0.872579\pi\) |
0.515999 | − | 0.856589i | \(-0.327421\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 726.886 | − | 2237.12i | 0.0629267 | − | 0.193668i | ||||
\(512\) | 3061.77 | + | 9423.15i | 0.264282 | + | 0.813376i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1256.24 | − | 3866.31i | 0.107802 | − | 0.331782i | ||||
\(515\) | 8700.01 | + | 566.590i | 0.744405 | + | 0.0484795i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23422.5 | − | 17017.4i | 1.99250 | − | 1.44763i | ||||
\(518\) | −127.532 | −0.0108174 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1423.90 | + | 92.7318i | 0.120081 | + | 0.00782030i | ||||
\(521\) | 6623.59 | + | 4812.32i | 0.556977 | + | 0.404667i | 0.830351 | − | 0.557240i | \(-0.188140\pi\) |
−0.273375 | + | 0.961908i | \(0.588140\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4169.76 | − | 12833.2i | 0.348625 | − | 1.07296i | −0.610989 | − | 0.791639i | \(-0.709228\pi\) |
0.959614 | − | 0.281319i | \(-0.0907720\pi\) | |||||||
\(524\) | −22226.9 | −1.85303 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2904.97 | 0.240804 | ||||||||
\(527\) | 2093.34 | − | 6442.65i | 0.173031 | − | 0.532535i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1090.64 | − | 792.396i | −0.0896392 | − | 0.0651267i | ||||
\(530\) | −588.525 | + | 1476.94i | −0.0482338 | + | 0.121045i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 565.149 | 0.0460570 | ||||||||
\(533\) | 1652.37 | − | 1200.51i | 0.134281 | − | 0.0975611i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4981.66 | + | 3146.09i | −0.402572 | + | 0.254238i | ||||
\(536\) | −1820.98 | + | 5604.41i | −0.146743 | + | 0.451630i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −409.908 | − | 1261.57i | −0.0328483 | − | 0.101097i | ||||
\(539\) | −6542.13 | + | 20134.6i | −0.522801 | + | 1.60902i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2450.73 | − | 7542.58i | −0.194760 | − | 0.599410i | −0.999979 | − | 0.00643276i | \(-0.997952\pi\) |
0.805219 | − | 0.592977i | \(-0.202048\pi\) | |||||||
\(542\) | 273.329 | − | 198.585i | 0.0216614 | − | 0.0157379i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2565.20 | − | 1863.72i | 0.202172 | − | 0.146887i | ||||
\(545\) | −501.901 | − | 417.073i | −0.0394478 | − | 0.0327806i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11905.8 | + | 8650.05i | 0.930629 | + | 0.676142i | 0.946147 | − | 0.323738i | \(-0.104940\pi\) |
−0.0155174 | + | 0.999880i | \(0.504940\pi\) | |||||||
\(548\) | 3090.62 | − | 9511.95i | 0.240921 | − | 0.741479i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3977.39 | + | 2163.84i | −0.308357 | + | 0.167757i | ||||
\(551\) | 1106.63 | 0.0855606 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2467.20 | − | 1792.52i | −0.189721 | − | 0.137841i | ||||
\(554\) | 1408.16 | + | 1023.09i | 0.107991 | + | 0.0784601i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7668.77 | − | 5571.69i | 0.584943 | − | 0.424986i | ||||
\(557\) | −22711.9 | −1.72771 | −0.863856 | − | 0.503739i | \(-0.831957\pi\) | ||||
−0.863856 | + | 0.503739i | \(0.831957\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1900.80 | + | 5850.06i | 0.143820 | + | 0.442632i | ||||
\(560\) | −1293.54 | − | 1074.92i | −0.0976110 | − | 0.0811134i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1092.49 | + | 3362.35i | 0.0820000 | + | 0.252370i | ||||
\(563\) | −715.529 | − | 2202.17i | −0.0535630 | − | 0.164850i | 0.920697 | − | 0.390279i | \(-0.127622\pi\) |
−0.974260 | + | 0.225429i | \(0.927622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 406.260 | + | 337.597i | 0.0302504 | + | 0.0251377i | ||||
\(566\) | −988.238 | − | 3041.48i | −0.0733900 | − | 0.225871i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8175.66 | −0.603949 | ||||||||
\(569\) | −5246.99 | + | 3812.16i | −0.386582 | + | 0.280868i | −0.764053 | − | 0.645153i | \(-0.776794\pi\) |
0.377472 | + | 0.926021i | \(0.376794\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1237.96 | + | 899.434i | 0.0907307 | + | 0.0659197i | 0.632226 | − | 0.774784i | \(-0.282142\pi\) |
−0.541495 | + | 0.840704i | \(0.682142\pi\) | |||||||
\(572\) | 5544.57 | + | 4028.36i | 0.405297 | + | 0.294466i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 221.682 | 0.0161199 | ||||||||
\(575\) | 10549.3 | + | 9994.25i | 0.765109 | + | 0.724851i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2455.32 | − | 7556.70i | 0.177151 | − | 0.545216i | −0.822574 | − | 0.568658i | \(-0.807463\pi\) |
0.999725 | + | 0.0234424i | \(0.00746262\pi\) | |||||||
\(578\) | 1854.40 | + | 1347.30i | 0.133448 | + | 0.0969556i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2651.98 | − | 2203.76i | −0.189858 | − | 0.157769i | ||||
\(581\) | 2137.16 | − | 1552.74i | 0.152606 | − | 0.110875i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12621.5 | + | 9170.06i | −0.896619 | + | 0.651432i | ||||
\(584\) | 2444.45 | + | 7523.26i | 0.173206 | + | 0.533073i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −508.891 | + | 1566.21i | −0.0358739 | + | 0.110409i | ||||
\(587\) | 863.957 | + | 2658.98i | 0.0607484 | + | 0.186964i | 0.976825 | − | 0.214038i | \(-0.0686618\pi\) |
−0.916077 | + | 0.401003i | \(0.868662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1895.34 | + | 5833.26i | −0.132591 | + | 0.408074i | ||||
\(590\) | −1686.37 | + | 1065.01i | −0.117673 | + | 0.0743145i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3767.95 | + | 2737.58i | −0.261591 | + | 0.190057i | ||||
\(593\) | −18900.9 | −1.30889 | −0.654443 | − | 0.756112i | \(-0.727097\pi\) | ||||
−0.654443 | + | 0.756112i | \(0.727097\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −336.812 | + | 845.248i | −0.0232066 | + | 0.0582383i | ||||
\(596\) | 5027.38 | + | 3652.60i | 0.345519 | + | 0.251034i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −292.598 | + | 900.524i | −0.0200087 | + | 0.0615806i | ||||
\(599\) | −5146.04 | −0.351021 | −0.175511 | − | 0.984478i | \(-0.556158\pi\) | ||||
−0.175511 | + | 0.984478i | \(0.556158\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1011.92 | −0.0686805 | −0.0343403 | − | 0.999410i | \(-0.510933\pi\) | ||||
−0.0343403 | + | 0.999410i | \(0.510933\pi\) | |||||||
\(602\) | −206.309 | + | 634.953i | −0.0139676 | + | 0.0429879i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21389.9 | − | 15540.7i | −1.44096 | − | 1.04692i | ||||
\(605\) | −29487.5 | − | 1920.38i | −1.98155 | − | 0.129049i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10173.3 | 0.680263 | 0.340131 | − | 0.940378i | \(-0.389528\pi\) | ||||
0.340131 | + | 0.940378i | \(0.389528\pi\) | |||||||
\(608\) | −2322.56 | + | 1687.44i | −0.154922 | + | 0.112557i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.3670 | − | 0.870530i | −0.000887238 | − | 5.77815e-5i | ||||
\(611\) | −2011.64 | + | 6191.20i | −0.133195 | + | 0.409933i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6821.12 | + | 20993.3i | 0.449433 | + | 1.38321i | 0.877548 | + | 0.479489i | \(0.159178\pi\) |
−0.428115 | + | 0.903724i | \(0.640822\pi\) | |||||||
\(614\) | −347.559 | + | 1069.68i | −0.0228442 | + | 0.0703071i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 469.626 | + | 1445.36i | 0.0307171 | + | 0.0945376i | ||||
\(617\) | −18690.4 | + | 13579.4i | −1.21953 | + | 0.886039i | −0.996061 | − | 0.0886729i | \(-0.971737\pi\) |
−0.223467 | + | 0.974712i | \(0.571737\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1080.02 | + | 784.684i | −0.0701290 | + | 0.0509517i | −0.622297 | − | 0.782781i | \(-0.713801\pi\) |
0.552168 | + | 0.833733i | \(0.313801\pi\) | |||||||
\(620\) | 16158.6 | − | 10204.7i | 1.04669 | − | 0.661019i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1626.69 | + | 1181.86i | 0.104862 | + | 0.0761868i | ||||
\(623\) | 818.087 | − | 2517.81i | 0.0526099 | − | 0.161917i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9853.35 | − | 12126.5i | −0.630614 | − | 0.776096i | ||||
\(626\) | 246.610 | 0.0157453 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4990.93 | − | 3626.12i | −0.317133 | − | 0.230411i | ||||
\(629\) | 2038.44 | + | 1481.01i | 0.129218 | + | 0.0938820i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5073.00 | − | 3685.75i | 0.320052 | − | 0.232531i | −0.416146 | − | 0.909298i | \(-0.636619\pi\) |
0.736198 | + | 0.676767i | \(0.236619\pi\) | |||||||
\(632\) | 10255.6 | 0.645485 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −704.692 | − | 2168.82i | −0.0441434 | − | 0.135859i | ||||
\(635\) | 4330.06 | + | 17019.9i | 0.270603 | + | 1.06365i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1471.00 | − | 4527.27i | −0.0914962 | − | 0.281596i | ||||
\(638\) | 450.102 | + | 1385.27i | 0.0279306 | + | 0.0859616i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11807.8 | + | 768.986i | 0.729288 | + | 0.0474951i | ||||
\(641\) | −2824.44 | − | 8692.72i | −0.174038 | − | 0.535635i | 0.825550 | − | 0.564329i | \(-0.190865\pi\) |
−0.999588 | + | 0.0286942i | \(0.990865\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12262.8 | −0.752095 | −0.376047 | − | 0.926600i | \(-0.622717\pi\) | ||||
−0.376047 | + | 0.926600i | \(0.622717\pi\) | |||||||
\(644\) | 1931.40 | − | 1403.24i | 0.118180 | − | 0.0858626i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 388.864 | + | 282.527i | 0.0236837 | + | 0.0172072i | ||||
\(647\) | −13172.3 | − | 9570.20i | −0.800394 | − | 0.581520i | 0.110636 | − | 0.993861i | \(-0.464711\pi\) |
−0.911030 | + | 0.412341i | \(0.864711\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19571.7 | −1.18375 | ||||||||
\(650\) | 437.537 | − | 919.284i | 0.0264025 | − | 0.0554728i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7486.58 | + | 23041.3i | −0.449689 | + | 1.38400i | ||||
\(653\) | 3811.13 | + | 2768.95i | 0.228393 | + | 0.165938i | 0.696097 | − | 0.717948i | \(-0.254918\pi\) |
−0.467703 | + | 0.883886i | \(0.654918\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11993.6 | + | 30098.6i | −0.715464 | + | 1.79550i | ||||
\(656\) | 6549.63 | − | 4758.59i | 0.389817 | − | 0.283219i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −571.619 | + | 415.306i | −0.0338663 | + | 0.0246053i | ||||
\(659\) | −5153.02 | − | 15859.4i | −0.304603 | − | 0.937471i | −0.979825 | − | 0.199857i | \(-0.935952\pi\) |
0.675222 | − | 0.737614i | \(-0.264048\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5801.03 | + | 17853.7i | −0.341352 | + | 1.05057i | 0.622156 | + | 0.782894i | \(0.286257\pi\) |
−0.963508 | + | 0.267680i | \(0.913743\pi\) | |||||||
\(662\) | −1096.77 | − | 3375.50i | −0.0643913 | − | 0.198176i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2745.22 | + | 8448.91i | −0.160444 | + | 0.493797i | ||||
\(665\) | 304.954 | − | 765.299i | 0.0177829 | − | 0.0446271i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3781.90 | − | 2747.71i | 0.219544 | − | 0.159508i | ||||
\(668\) | −21599.7 | −1.25107 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3233.72 | + | 2687.18i | 0.186462 | + | 0.154947i | ||||
\(671\) | −106.341 | − | 77.2614i | −0.00611812 | − | 0.00444507i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9259.20 | − | 28496.9i | 0.530336 | − | 1.63221i | −0.223181 | − | 0.974777i | \(-0.571644\pi\) |
0.753517 | − | 0.657429i | \(-0.228356\pi\) | |||||||
\(674\) | −4754.96 | −0.271742 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15309.6 | 0.871052 | ||||||||
\(677\) | 6669.63 | − | 20527.0i | 0.378633 | − | 1.16531i | −0.562362 | − | 0.826891i | \(-0.690107\pi\) |
0.940995 | − | 0.338421i | \(-0.109893\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3331.26 | + | 2420.30i | 0.188280 | + | 0.136793i | ||||
\(680\) | −754.429 | − | 2965.40i | −0.0425456 | − | 0.167232i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8072.96 | −0.453269 | ||||||||
\(683\) | 4810.04 | − | 3494.70i | 0.269474 | − | 0.195784i | −0.444839 | − | 0.895610i | \(-0.646739\pi\) |
0.714313 | + | 0.699826i | \(0.246739\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11213.0 | − | 9317.82i | −0.625438 | − | 0.519731i | ||||
\(686\) | 322.726 | − | 993.248i | 0.0179617 | − | 0.0552804i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7534.37 | + | 23188.4i | 0.417508 | + | 1.28496i | ||||
\(689\) | 1084.00 | − | 3336.20i | 0.0599377 | − | 0.184469i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4660.89 | − | 14344.7i | −0.256597 | − | 0.789725i | −0.993511 | − | 0.113738i | \(-0.963718\pi\) |
0.736914 | − | 0.675987i | \(-0.236282\pi\) | |||||||
\(692\) | 22754.4 | − | 16532.0i | 1.24999 | − | 0.908168i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1759.57 | − | 1278.40i | 0.0962427 | − | 0.0699244i | ||||
\(695\) | −3406.86 | − | 13391.2i | −0.185942 | − | 0.730872i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3543.31 | − | 2574.37i | −0.192557 | − | 0.139901i | ||||
\(698\) | −1259.65 | + | 3876.80i | −0.0683071 | + | 0.210228i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2254.84 | + | 1226.71i | −0.121750 | + | 0.0662363i | ||||
\(701\) | −29869.3 | −1.60934 | −0.804671 | − | 0.593722i | \(-0.797658\pi\) | ||||
−0.804671 | + | 0.593722i | \(0.797658\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1845.63 | − | 1340.93i | −0.0990174 | − | 0.0719403i | ||||
\(704\) | 19866.6 | + | 14433.9i | 1.06357 | + | 0.772726i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −814.186 | + | 591.541i | −0.0434027 | + | 0.0315339i | ||||
\(707\) | −712.959 | −0.0379259 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3546.30 | + | 10914.4i | 0.187848 | + | 0.578136i | 0.999986 | − | 0.00532961i | \(-0.00169648\pi\) |
−0.812138 | + | 0.583465i | \(0.801696\pi\) | |||||||
\(710\) | −2159.31 | + | 5418.91i | −0.114137 | + | 0.286434i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2751.16 | + | 8467.19i | 0.144809 | + | 0.445676i | ||||
\(713\) | 8006.43 | + | 24641.2i | 0.420537 | + | 1.29428i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8446.87 | − | 5334.50i | 0.441811 | − | 0.279020i | ||||
\(716\) | 5759.52 | + | 17726.0i | 0.300619 | + | 0.925211i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 188.358 | 0.00979031 | ||||||||
\(719\) | 7033.06 | − | 5109.81i | 0.364797 | − | 0.265040i | −0.390253 | − | 0.920707i | \(-0.627613\pi\) |
0.755050 | + | 0.655667i | \(0.227613\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1689.12 | − | 1227.22i | −0.0872484 | − | 0.0633897i | ||||
\(722\) | 2836.44 | + | 2060.79i | 0.146207 | + | 0.106225i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 25176.4 | 1.29237 | ||||||||
\(725\) | −4415.24 | + | 2402.05i | −0.226177 | + | 0.123048i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4671.47 | − | 14377.3i | 0.238315 | − | 0.733459i | −0.758349 | − | 0.651849i | \(-0.773994\pi\) |
0.996664 | − | 0.0816103i | \(-0.0260063\pi\) | |||||||
\(728\) | −276.452 | − | 200.854i | −0.0140742 | − | 0.0102255i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5632.11 | + | 366.792i | 0.285553 | + | 0.0185967i | ||||
\(731\) | 10671.2 | − | 7753.11i | 0.539931 | − | 0.392283i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27204.2 | − | 19765.0i | 1.37082 | − | 0.995959i | 0.373148 | − | 0.927772i | \(-0.378278\pi\) |
0.997673 | − | 0.0681872i | \(-0.0217215\pi\) | |||||||
\(734\) | −1035.22 | − | 3186.06i | −0.0520579 | − | 0.160218i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3747.51 | + | 11533.7i | −0.187684 | + | 0.577631i | ||||
\(737\) | 12749.3 | + | 39238.4i | 0.637215 | + | 1.96115i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2946.68 | + | 9068.95i | −0.146678 | + | 0.451430i | −0.997223 | − | 0.0744731i | \(-0.976273\pi\) |
0.850545 | + | 0.525903i | \(0.176273\pi\) | |||||||
\(740\) | 1752.61 | + | 6888.90i | 0.0870640 | + | 0.342218i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 308.024 | − | 223.793i | 0.0152398 | − | 0.0110724i | ||||
\(743\) | −39282.1 | −1.93960 | −0.969798 | − | 0.243909i | \(-0.921570\pi\) | ||||
−0.969798 | + | 0.243909i | \(0.921570\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7658.96 | − | 4836.90i | 0.376648 | − | 0.237866i | ||||
\(746\) | −1334.74 | − | 969.744i | −0.0655070 | − | 0.0475936i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4541.46 | − | 13977.2i | 0.221995 | − | 0.683230i | ||||
\(749\) | 1410.98 | 0.0688333 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15625.4 | 0.759226 | 0.379613 | − | 0.925145i | \(-0.376057\pi\) | ||||
0.379613 | + | 0.925145i | \(0.376057\pi\) | |||||||
\(752\) | −7973.73 | + | 24540.6i | −0.386665 | + | 1.19003i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −264.960 | − | 192.504i | −0.0127974 | − | 0.00929788i | ||||
\(755\) | −32586.4 | + | 20579.5i | −1.57078 | + | 0.992006i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28389.3 | −1.36305 | −0.681524 | − | 0.731796i | \(-0.738682\pi\) | ||||
−0.681524 | + | 0.731796i | \(0.738682\pi\) | |||||||
\(758\) | 5156.10 | − | 3746.13i | 0.247069 | − | 0.179506i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 683.070 | + | 2684.91i | 0.0326021 | + | 0.128147i | ||||
\(761\) | 2807.36 | − | 8640.18i | 0.133728 | − | 0.411572i | −0.861662 | − | 0.507482i | \(-0.830576\pi\) |
0.995390 | + | 0.0959105i | \(0.0305763\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.2922 | + | 148.628i | 0.00229134 | + | 0.00705203i | ||||
\(764\) | 5054.45 | − | 15556.0i | 0.239350 | − | 0.736644i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −127.244 | − | 391.617i | −0.00600198 | − | 0.0184722i | ||||
\(767\) | 3560.23 | − | 2586.66i | 0.167604 | − | 0.121772i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10201.3 | + | 7411.64i | −0.478370 | + | 0.347556i | −0.800694 | − | 0.599073i | \(-0.795536\pi\) |
0.322324 | + | 0.946629i | \(0.395536\pi\) | |||||||
\(770\) | 1082.03 | + | 70.4677i | 0.0506413 | + | 0.00329803i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24003.0 | − | 17439.2i | −1.11903 | − | 0.813020i | ||||
\(773\) | 3920.38 | − | 12065.7i | 0.182415 | − | 0.561414i | −0.817480 | − | 0.575957i | \(-0.804629\pi\) |
0.999894 | + | 0.0145432i | \(0.00462941\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5099.61 | − | 27387.7i | −0.236366 | − | 1.26941i | ||||
\(776\) | −13847.4 | −0.640582 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3518.40 | + | 2556.27i | 0.162135 | + | 0.117798i | ||||
\(779\) | 3208.16 | + | 2330.87i | 0.147554 | + | 0.107204i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −46308.6 | + | 33645.1i | −2.12170 | + | 1.54151i | ||||
\(782\) | 2030.45 | 0.0928499 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5830.73 | − | 17945.1i | −0.265613 | − | 0.817472i | ||||
\(785\) | −7603.43 | + | 4801.84i | −0.345705 | + | 0.218325i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1803.51 | − | 5550.62i | −0.0816875 | − | 0.251408i | 0.901869 | − | 0.432010i | \(-0.142195\pi\) |
−0.983556 | + | 0.180602i | \(0.942195\pi\) | |||||||
\(788\) | −4184.43 | − | 12878.4i | −0.189168 | − | 0.582199i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2708.66 | − | 6797.53i | 0.121987 | − | 0.306133i | ||||
\(791\) | −39.0898 | − | 120.306i | −0.00175711 | − | 0.00540782i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.5554 | 0.00132351 | ||||||||
\(794\) | −331.346 | + | 240.737i | −0.0148099 | + | 0.0107600i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24527.1 | + | 17820.0i | 1.09213 | + | 0.793483i | ||||
\(797\) | −8363.61 | − | 6076.52i | −0.371712 | − | 0.270064i | 0.386209 | − | 0.922411i | \(-0.373784\pi\) |
−0.757920 | + | 0.652347i | \(0.773784\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13959.5 | 0.618089 | ||||||||
\(800\) | 5603.85 | − | 11773.9i | 0.247657 | − | 0.520340i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 983.581 | − | 3027.15i | 0.0433060 | − | 0.133282i | ||||
\(803\) | 44806.2 | + | 32553.6i | 1.96909 | + | 1.43063i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −858.027 | − | 3372.60i | −0.0375670 | − | 0.147663i | ||||
\(806\) | 1468.53 | − | 1066.95i | 0.0641772 | − | 0.0466275i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1939.72 | − | 1409.29i | 0.0844542 | − | 0.0613595i | ||||
\(809\) | −7061.41 | − | 21732.8i | −0.306880 | − | 0.944480i | −0.978969 | − | 0.204009i | \(-0.934603\pi\) |
0.672089 | − | 0.740470i | \(-0.265397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5199.66 | − | 16002.9i | 0.225135 | − | 0.692895i | −0.773142 | − | 0.634232i | \(-0.781316\pi\) |
0.998278 | − | 0.0586630i | \(-0.0186837\pi\) | |||||||
\(812\) | 255.170 | + | 785.333i | 0.0110280 | + | 0.0339406i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 927.891 | − | 2855.75i | 0.0399540 | − | 0.122966i | ||||
\(815\) | 27161.8 | + | 22571.1i | 1.16740 | + | 0.970098i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9661.88 | + | 7019.77i | −0.413741 | + | 0.300600i | ||||
\(818\) | −5023.44 | −0.214719 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3046.48 | − | 11974.6i | −0.129741 | − | 0.509966i | ||||
\(821\) | −31598.7 | − | 22957.8i | −1.34324 | − | 0.975924i | −0.999318 | − | 0.0369280i | \(-0.988243\pi\) |
−0.343927 | − | 0.938996i | \(-0.611757\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4474.49 | − | 13771.0i | 0.189515 | − | 0.583267i | −0.810482 | − | 0.585764i | \(-0.800795\pi\) |
0.999997 | + | 0.00249670i | \(0.000794724\pi\) | |||||||
\(824\) | 7021.32 | 0.296844 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 477.641 | 0.0201202 | ||||||||
\(827\) | 6978.44 | − | 21477.4i | 0.293427 | − | 0.903075i | −0.690318 | − | 0.723506i | \(-0.742530\pi\) |
0.983745 | − | 0.179570i | \(-0.0574705\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24825.2 | + | 18036.5i | 1.04006 | + | 0.755651i | 0.970298 | − | 0.241912i | \(-0.0777746\pi\) |
0.0697666 | + | 0.997563i | \(0.477775\pi\) | |||||||
\(830\) | 4874.98 | + | 4051.04i | 0.203871 | + | 0.169414i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5521.52 | −0.230077 | ||||||||
\(833\) | −8258.29 | + | 6000.00i | −0.343497 | + | 0.249565i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11655.2 | + | 29249.3i | −0.483046 | + | 1.21223i | ||||
\(836\) | −4111.90 | + | 12655.1i | −0.170111 | + | 0.523548i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −575.743 | − | 1771.95i | −0.0237335 | − | 0.0730443i | ||||
\(839\) | −8848.60 | + | 27233.2i | −0.364109 | + | 1.12061i | 0.586428 | + | 0.810002i | \(0.300534\pi\) |
−0.950537 | + | 0.310612i | \(0.899466\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7036.96 | − | 21657.5i | −0.288530 | − | 0.888005i | ||||
\(842\) | 810.295 | − | 588.714i | 0.0331646 | − | 0.0240955i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29571.9 | − | 21485.2i | 1.20605 | − | 0.876247i | ||||
\(845\) | 8261.05 | − | 20731.6i | 0.336318 | − | 0.844009i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5725.05 | + | 4159.49i | 0.232249 | + | 0.168739i | ||||
\(848\) | 4296.74 | − | 13224.0i | 0.173998 | − | 0.535512i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2164.75 | − | 283.161i | −0.0873534 | − | 0.0114263i | ||||
\(851\) | −9636.91 | −0.388189 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25308.6 | + | 18387.8i | 1.01589 | + | 0.738084i | 0.965435 | − | 0.260642i | \(-0.0839343\pi\) |
0.0504504 | + | 0.998727i | \(0.483934\pi\) | |||||||
\(854\) | 2.59523 | + | 1.88554i | 0.000103989 | + | 7.55526e-5i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3838.80 | + | 2789.05i | −0.153280 | + | 0.111364i | ||||
\(857\) | 18790.1 | 0.748958 | 0.374479 | − | 0.927235i | \(-0.377822\pi\) | ||||
0.374479 | + | 0.927235i | \(0.377822\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13511.0 | + | 41582.7i | 0.536659 | + | 1.65167i | 0.740036 | + | 0.672567i | \(0.234808\pi\) |
−0.203377 | + | 0.979101i | \(0.565192\pi\) | |||||||
\(860\) | 37133.6 | + | 2418.33i | 1.47238 | + | 0.0958889i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1193.47 | − | 3673.12i | −0.0471574 | − | 0.145136i | ||||
\(863\) | 1918.14 | + | 5903.42i | 0.0756596 | + | 0.232856i | 0.981733 | − | 0.190265i | \(-0.0609346\pi\) |
−0.906073 | + | 0.423121i | \(0.860935\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10108.7 | − | 39733.6i | −0.397346 | − | 1.56183i | ||||
\(866\) | −1024.79 | − | 3153.97i | −0.0402120 | − | 0.123760i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4576.69 | −0.178966 | ||||||||
\(869\) | 58089.9 | − | 42204.8i | 2.26762 | − | 1.64752i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7505.08 | − | 5452.76i | −0.291963 | − | 0.212124i | ||||
\(872\) | −425.175 | − | 308.908i | −0.0165118 | − | 0.0119965i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1838.39 | −0.0711495 | ||||||||
\(875\) | 444.447 | + | 3715.34i | 0.0171715 | + | 0.143544i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2031.80 | − | 6253.24i | 0.0782315 | − | 0.240772i | −0.904291 | − | 0.426917i | \(-0.859600\pi\) |
0.982522 | + | 0.186145i | \(0.0595996\pi\) | |||||||
\(878\) | 2888.23 | + | 2098.42i | 0.111017 | + | 0.0806588i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 33481.6 | − | 21144.8i | 1.28257 | − | 0.809991i | ||||
\(881\) | 41653.2 | − | 30262.8i | 1.59289 | − | 1.15730i | 0.693217 | − | 0.720729i | \(-0.256193\pi\) |
0.899670 | − | 0.436571i | \(-0.143807\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30274.1 | + | 21995.4i | −1.15380 | + | 0.838285i | −0.988982 | − | 0.148039i | \(-0.952704\pi\) |
−0.164819 | + | 0.986324i | \(0.552704\pi\) | |||||||
\(884\) | 1021.15 | + | 3142.77i | 0.0388517 | + | 0.119573i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1126.87 | − | 3468.15i | 0.0427291 | − | 0.131507i | ||||
\(887\) | −12836.0 | − | 39505.1i | −0.485897 | − | 1.49544i | −0.830678 | − | 0.556753i | \(-0.812047\pi\) |
0.344781 | − | 0.938683i | \(-0.387953\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1299.64 | − | 3999.88i | 0.0490310 | − | 0.150902i | ||||
\(890\) | 6338.77 | + | 412.814i | 0.238737 | + | 0.0155478i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13651.9 | + | 9918.67i | −0.512442 | + | 0.372311i | ||||
\(893\) | −12639.2 | −0.473632 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27111.6 | + | 1765.65i | 1.01256 | + | 0.0659430i | ||||
\(896\) | −2292.50 | − | 1665.60i | −0.0854767 | − | 0.0621025i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 485.119 | − | 1493.04i | 0.0180274 | − | 0.0554827i | ||||
\(899\) | −8961.68 | −0.332468 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7522.27 | −0.278139 | ||||||||
\(902\) | −1612.90 | + | 4964.01i | −0.0595386 | + | 0.183241i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 344.155 | + | 250.043i | 0.0126620 | + | 0.00919947i | ||||
\(905\) | 13585.2 | − | 34092.8i | 0.498991 | − | 1.25225i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14471.6 | −0.529792 | −0.264896 | − | 0.964277i | \(-0.585338\pi\) | ||||
−0.264896 | + | 0.964277i | \(0.585338\pi\) | |||||||
\(908\) | −6050.59 | + | 4396.01i | −0.221141 | + | 0.160668i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −206.144 | + | 130.187i | −0.00750944 | + | 0.00474248i | ||||
\(911\) | 6104.65 | − | 18788.2i | 0.222015 | − | 0.683293i | −0.776565 | − | 0.630037i | \(-0.783040\pi\) |
0.998581 | − | 0.0532566i | \(-0.0169601\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19220.2 | + | 59153.7i | 0.696709 | + | 2.14425i | ||||
\(914\) | 2054.86 | − | 6324.19i | 0.0743639 | − | 0.228868i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3779.03 | − | 11630.7i | −0.136313 | − | 0.419528i | ||||
\(917\) | 6277.25 | − | 4560.69i | 0.226056 | − | 0.164239i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7114.39 | + | 5168.90i | −0.255367 | + | 0.185535i | −0.708102 | − | 0.706110i | \(-0.750448\pi\) |
0.452735 | + | 0.891645i | \(0.350448\pi\) | |||||||
\(920\) | 9000.92 | + | 7479.65i | 0.322556 | + | 0.268040i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1682.78 | − | 1222.61i | −0.0601077 | − | 0.0436708i | ||||
\(923\) | 3977.21 | − | 12240.6i | 0.141833 | − | 0.436516i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10274.3 | + | 1343.94i | 0.365209 | + | 0.0477713i | ||||
\(926\) | −7219.10 | −0.256193 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3393.53 | − | 2465.54i | −0.120041 | − | 0.0872149i | ||||
\(929\) | 25055.7 | + | 18204.0i | 0.884876 | + | 0.642900i | 0.934537 | − | 0.355866i | \(-0.115814\pi\) |
−0.0496611 | + | 0.998766i | \(0.515814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7477.17 | − | 5432.48i | 0.263216 | − | 0.191238i | ||||
\(932\) | −35911.3 | −1.26214 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3096.24 | − | 9529.24i | −0.108471 | − | 0.333840i | ||||
\(935\) | −16476.7 | − | 13691.9i | −0.576305 | − | 0.478902i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8534.11 | − | 26265.3i | −0.297542 | − | 0.915741i | −0.982356 | − | 0.187022i | \(-0.940116\pi\) |
0.684813 | − | 0.728718i | \(-0.259884\pi\) | |||||||
\(938\) | −311.144 | − | 957.601i | −0.0108307 | − | 0.0333335i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 30289.2 | + | 25169.9i | 1.05098 | + | 0.873354i | ||||
\(941\) | 7954.59 | + | 24481.7i | 0.275571 | + | 0.848120i | 0.989068 | + | 0.147462i | \(0.0471104\pi\) |
−0.713497 | + | 0.700659i | \(0.752890\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16751.3 | 0.578472 | ||||||||
\(944\) | 14112.0 | − | 10253.0i | 0.486554 | − | 0.353502i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12717.1 | − | 9239.54i | −0.437072 | − | 0.317551i | ||||
\(947\) | −7972.65 | − | 5792.47i | −0.273576 | − | 0.198764i | 0.442535 | − | 0.896751i | \(-0.354079\pi\) |
−0.716111 | + | 0.697987i | \(0.754079\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12453.0 | −0.425965 | ||||||||
\(950\) | 1960.00 | + | 256.378i | 0.0669375 | + | 0.00875578i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −226.437 | + | 696.902i | −0.00770890 | + | 0.0237255i | ||||
\(953\) | 13751.8 | + | 9991.27i | 0.467434 | + | 0.339611i | 0.796440 | − | 0.604717i | \(-0.206714\pi\) |
−0.329006 | + | 0.944328i | \(0.606714\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18337.8 | − | 15238.5i | −0.621359 | − | 0.516341i | ||||
\(956\) | −448.704 | + | 326.003i | −0.0151801 | + | 0.0110290i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −318.961 | + | 231.739i | −0.0107570 | + | 0.00781538i | ||||
\(959\) | 1078.89 | + | 3320.50i | 0.0363288 | + | 0.111809i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6142.91 | − | 18905.9i | 0.206200 | − | 0.634619i | ||||
\(962\) | 208.636 | + | 642.116i | 0.00699242 | + | 0.0215204i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4344.83 | + | 13372.0i | −0.145164 | + | 0.446767i | ||||
\(965\) | −36567.4 | + | 23093.6i | −1.21984 | + | 0.770373i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35433.3 | + | 25743.8i | −1.17835 | + | 0.856118i | −0.991984 | − | 0.126364i | \(-0.959669\pi\) |
−0.186361 | + | 0.982481i | \(0.559669\pi\) | |||||||
\(968\) | −23797.8 | −0.790177 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3657.29 | + | 9178.18i | −0.121060 | + | 0.303808i | ||||
\(971\) | 10419.1 | + | 7569.90i | 0.344350 | + | 0.250185i | 0.746495 | − | 0.665391i | \(-0.231735\pi\) |
−0.402145 | + | 0.915576i | \(0.631735\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1022.55 | + | 3147.08i | −0.0336910 | + | 0.103690i | ||||
\(974\) | 2262.09 | 0.0744168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 117.151 | 0.00384214 | ||||||||
\(977\) | −13718.8 | + | 42222.0i | −0.449234 | + | 1.38260i | 0.428538 | + | 0.903524i | \(0.359029\pi\) |
−0.877773 | + | 0.479078i | \(0.840971\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 50428.0 | + | 36638.1i | 1.64626 | + | 1.19608i | ||||
\(980\) | −28737.1 | − | 1871.51i | −0.936707 | − | 0.0610032i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11208.8 | 0.364242 | ||||||||
\(983\) | −5150.84 | + | 3742.31i | −0.167127 | + | 0.121425i | −0.668205 | − | 0.743977i | \(-0.732937\pi\) |
0.501078 | + | 0.865402i | \(0.332937\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19697.2 | − | 1282.78i | −0.637163 | − | 0.0414954i | ||||
\(986\) | −217.024 | + | 667.930i | −0.00700958 | + | 0.0215733i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −924.560 | − | 2845.50i | −0.0297714 | − | 0.0916271i | ||||
\(989\) | −15589.7 | + | 47980.1i | −0.501237 | + | 1.54265i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12252.9 | − | 37710.5i | −0.392760 | − | 1.20879i | −0.930692 | − | 0.365804i | \(-0.880794\pi\) |
0.537932 | − | 0.842988i | \(-0.319206\pi\) | |||||||
\(992\) | 18808.6 | − | 13665.2i | 0.601988 | − | 0.437370i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1130.15 | − | 821.100i | 0.0360625 | − | 0.0262009i | ||||
\(995\) | 37365.8 | − | 23597.8i | 1.19053 | − | 0.751860i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27866.6 | + | 20246.3i | 0.885200 | + | 0.643135i | 0.934622 | − | 0.355643i | \(-0.115738\pi\) |
−0.0494223 | + | 0.998778i | \(0.515738\pi\) | |||||||
\(998\) | −1443.95 | + | 4444.02i | −0.0457991 | + | 0.140955i | ||||
\(999\) | 0 | 0 |
(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 | 225.4.h.a.46.4 | 28 | ||
3.2 | odd | 2 | 75.4.g.b.46.4 | yes | 28 | ||
25.6 | even | 5 | inner | 225.4.h.a.181.4 | 28 | ||
75.41 | odd | 10 | 1875.4.a.g.1.7 | 14 | |||
75.56 | odd | 10 | 75.4.g.b.31.4 | ✓ | 28 | ||
75.59 | odd | 10 | 1875.4.a.f.1.8 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.g.b.31.4 | ✓ | 28 | 75.56 | odd | 10 | ||
75.4.g.b.46.4 | yes | 28 | 3.2 | odd | 2 | ||
225.4.h.a.46.4 | 28 | 1.1 | even | 1 | trivial | ||
225.4.h.a.181.4 | 28 | 25.6 | even | 5 | inner | ||
1875.4.a.f.1.8 | 14 | 75.59 | odd | 10 | |||
1875.4.a.g.1.7 | 14 | 75.41 | odd | 10 |