Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(17,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.n (of order \(6\), degree \(2\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.9 | ||
Character | \(\chi\) | \(=\) | 224.145 |
Dual form | 224.3.n.a.17.9 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.455431 | + | 0.788830i | 0.151810 | + | 0.262943i | 0.931893 | − | 0.362733i | \(-0.118156\pi\) |
−0.780083 | + | 0.625677i | \(0.784823\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.17251 | − | 5.49495i | 0.634503 | − | 1.09899i | −0.352118 | − | 0.935956i | \(-0.614538\pi\) |
0.986620 | − | 0.163035i | \(-0.0521283\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.79106 | − | 5.88455i | −0.541579 | − | 0.840650i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.08516 | − | 7.07571i | 0.453907 | − | 0.786190i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.4442 | + | 6.60732i | −1.04038 | + | 0.600666i | −0.919942 | − | 0.392054i | \(-0.871764\pi\) |
−0.120442 | + | 0.992720i | \(0.538431\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −19.4243 | −1.49418 | −0.747090 | − | 0.664723i | \(-0.768550\pi\) | ||||
−0.747090 | + | 0.664723i | \(0.768550\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.77945 | 0.385296 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 13.7930 | − | 7.96338i | 0.811352 | − | 0.468434i | −0.0360732 | − | 0.999349i | \(-0.511485\pi\) |
0.847425 | + | 0.530915i | \(0.178152\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.22725 | − | 14.2500i | 0.433013 | − | 0.750001i | −0.564118 | − | 0.825694i | \(-0.690784\pi\) |
0.997131 | + | 0.0756934i | \(0.0241170\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.91534 | − | 5.67051i | 0.138826 | − | 0.270024i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 11.9607 | − | 20.7166i | 0.520032 | − | 0.900721i | −0.479697 | − | 0.877434i | \(-0.659254\pi\) |
0.999729 | − | 0.0232870i | \(-0.00741316\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.62967 | − | 13.2150i | −0.305187 | − | 0.528599i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 15.6398 | 0.579252 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 16.6618i | 0.574544i | 0.957849 | + | 0.287272i | \(0.0927483\pi\) | ||||
−0.957849 | + | 0.287272i | \(0.907252\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.1360 | − | 6.42939i | 0.359227 | − | 0.207400i | −0.309515 | − | 0.950895i | \(-0.600167\pi\) |
0.668741 | + | 0.743495i | \(0.266833\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.4241 | − | 6.01837i | −0.315882 | − | 0.182375i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −44.3625 | + | 2.16288i | −1.26750 | + | 0.0617964i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 41.1844 | + | 23.7778i | 1.11309 | + | 0.642644i | 0.939628 | − | 0.342196i | \(-0.111171\pi\) |
0.173463 | + | 0.984840i | \(0.444504\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.84646 | − | 15.3225i | −0.226832 | − | 0.392885i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.49499i | − | 0.158415i | −0.996858 | − | 0.0792073i | \(-0.974761\pi\) | ||
0.996858 | − | 0.0792073i | \(-0.0252389\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 33.2928i | − | 0.774252i | −0.922027 | − | 0.387126i | \(-0.873468\pi\) | ||
0.922027 | − | 0.387126i | \(-0.126532\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −25.9205 | − | 44.8956i | −0.576010 | − | 0.997679i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 18.9713 | + | 10.9531i | 0.403645 | + | 0.233045i | 0.688056 | − | 0.725658i | \(-0.258465\pi\) |
−0.284411 | + | 0.958703i | \(0.591798\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −20.2558 | + | 44.6173i | −0.413383 | + | 0.910557i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.5635 | + | 7.25355i | 0.246343 | + | 0.142226i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −32.2028 | + | 18.5923i | −0.607601 | + | 0.350798i | −0.772026 | − | 0.635591i | \(-0.780756\pi\) |
0.164425 | + | 0.986390i | \(0.447423\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 83.8473i | 1.52450i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.9878 | 0.262944 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 27.3428 | + | 47.3591i | 0.463437 | + | 0.802696i | 0.999129 | − | 0.0417169i | \(-0.0132827\pi\) |
−0.535693 | + | 0.844413i | \(0.679949\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.12340 | + | 8.87399i | −0.0839902 | + | 0.145475i | −0.904960 | − | 0.425496i | \(-0.860100\pi\) |
0.820970 | + | 0.570971i | \(0.193433\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −57.1245 | + | 2.78508i | −0.906737 | + | 0.0442076i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −61.6240 | + | 106.736i | −0.948061 | + | 1.64209i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.8386 | − | 8.56706i | 0.221471 | − | 0.127867i | −0.385160 | − | 0.922850i | \(-0.625854\pi\) |
0.606631 | + | 0.794983i | \(0.292520\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.7892 | 0.315785 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −32.0568 | −0.451505 | −0.225752 | − | 0.974185i | \(-0.572484\pi\) | ||||
−0.225752 | + | 0.974185i | \(0.572484\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 92.8082 | − | 53.5828i | 1.27135 | − | 0.734011i | 0.296104 | − | 0.955156i | \(-0.404313\pi\) |
0.975241 | + | 0.221144i | \(0.0709792\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.94958 | − | 12.0370i | 0.0926611 | − | 0.160494i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 82.2668 | + | 42.2953i | 1.06840 | + | 0.549290i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −29.1542 | + | 50.4965i | −0.369040 | + | 0.639196i | −0.989416 | − | 0.145109i | \(-0.953647\pi\) |
0.620376 | + | 0.784305i | \(0.286980\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −29.6436 | − | 51.3443i | −0.365971 | − | 0.633880i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 36.3441 | 0.437880 | 0.218940 | − | 0.975738i | \(-0.429740\pi\) | ||||
0.218940 | + | 0.975738i | \(0.429740\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 101.056i | − | 1.18889i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.1433 | + | 7.58829i | −0.151072 | + | 0.0872217i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.929882 | + | 0.536867i | 0.0104481 | + | 0.00603222i | 0.505215 | − | 0.862994i | \(-0.331413\pi\) |
−0.494767 | + | 0.869026i | \(0.664747\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 73.6388 | + | 114.303i | 0.809217 | + | 1.25608i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.1434 | + | 5.85629i | 0.109069 | + | 0.0629709i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −52.2021 | − | 90.4167i | −0.549496 | − | 0.951755i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 169.517i | 1.74760i | 0.486286 | + | 0.873799i | \(0.338351\pi\) | ||||
−0.486286 | + | 0.873799i | \(0.661649\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 107.968i | 1.09059i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.0630 | − | 24.3579i | −0.139238 | − | 0.241167i | 0.787971 | − | 0.615713i | \(-0.211132\pi\) |
−0.927208 | + | 0.374546i | \(0.877799\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 144.029 | + | 83.1551i | 1.39834 | + | 0.807331i | 0.994219 | − | 0.107374i | \(-0.0342444\pi\) |
0.404120 | + | 0.914706i | \(0.367578\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −21.9102 | − | 34.0094i | −0.208669 | − | 0.323899i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −171.112 | − | 98.7918i | −1.59918 | − | 0.923288i | −0.991645 | − | 0.128996i | \(-0.958825\pi\) |
−0.607536 | − | 0.794292i | \(-0.707842\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.97643 | − | 5.75990i | 0.0915269 | − | 0.0528431i | −0.453538 | − | 0.891237i | \(-0.649838\pi\) |
0.545065 | + | 0.838394i | \(0.316505\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 43.3167i | 0.390240i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.7908 | −0.130892 | −0.0654460 | − | 0.997856i | \(-0.520847\pi\) | ||||
−0.0654460 | + | 0.997856i | \(0.520847\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −75.8911 | − | 131.447i | −0.659923 | − | 1.14302i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −79.3516 | + | 137.441i | −0.678219 | + | 1.17471i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −99.1509 | − | 50.9758i | −0.833201 | − | 0.428368i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.8135 | − | 46.4423i | 0.221599 | − | 0.383821i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.12345 | − | 2.95802i | 0.0416541 | − | 0.0240490i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 61.8047 | 0.494438 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 70.2656 | 0.553272 | 0.276636 | − | 0.960975i | \(-0.410780\pi\) | ||||
0.276636 | + | 0.960975i | \(0.410780\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 26.2624 | − | 15.1626i | 0.203584 | − | 0.117540i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 71.0646 | − | 123.088i | 0.542478 | − | 0.939600i | −0.456283 | − | 0.889835i | \(-0.650819\pi\) |
0.998761 | − | 0.0497649i | \(-0.0158472\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −115.045 | + | 5.60897i | −0.864999 | + | 0.0421727i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 49.6175 | − | 85.9400i | 0.367537 | − | 0.636593i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −126.537 | − | 219.168i | −0.923626 | − | 1.59977i | −0.793756 | − | 0.608236i | \(-0.791877\pi\) |
−0.129870 | − | 0.991531i | \(-0.541456\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 49.1909 | 0.353892 | 0.176946 | − | 0.984221i | \(-0.443378\pi\) | ||||
0.176946 | + | 0.984221i | \(0.443378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.9535i | 0.141514i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 222.296 | − | 128.343i | 1.55452 | − | 0.897503i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 91.5556 | + | 52.8597i | 0.631418 | + | 0.364549i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −44.4206 | + | 4.34174i | −0.302181 | + | 0.0295356i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −36.1077 | − | 20.8468i | −0.242334 | − | 0.139911i | 0.373915 | − | 0.927463i | \(-0.378015\pi\) |
−0.616249 | + | 0.787551i | \(0.711348\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −48.8145 | − | 84.5492i | −0.323275 | − | 0.559928i | 0.657887 | − | 0.753117i | \(-0.271450\pi\) |
−0.981162 | + | 0.193188i | \(0.938117\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 130.127i | − | 0.850503i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 81.5892i | − | 0.526382i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0827 | − | 24.3919i | −0.0896986 | − | 0.155363i | 0.817685 | − | 0.575666i | \(-0.195257\pi\) |
−0.907384 | + | 0.420303i | \(0.861924\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −29.3324 | − | 16.9350i | −0.184480 | − | 0.106510i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −167.251 | + | 8.15428i | −1.03883 | + | 0.0506477i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 209.952 | + | 121.216i | 1.28805 | + | 0.743655i | 0.978306 | − | 0.207165i | \(-0.0664237\pi\) |
0.309743 | + | 0.950820i | \(0.399757\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −66.1413 | + | 38.1867i | −0.400856 | + | 0.231434i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 60.1108i | − | 0.359945i | −0.983672 | − | 0.179972i | \(-0.942399\pi\) | ||
0.983672 | − | 0.179972i | \(-0.0576008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 208.305 | 1.23257 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −67.2193 | − | 116.427i | −0.393096 | − | 0.680861i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 69.6820 | − | 120.693i | 0.402786 | − | 0.697646i | −0.591275 | − | 0.806470i | \(-0.701375\pi\) |
0.994061 | + | 0.108824i | \(0.0347085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −48.8397 | + | 94.9959i | −0.279084 | + | 0.542834i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −24.9055 | + | 43.1376i | −0.140709 | + | 0.243715i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −252.643 | + | 145.863i | −1.41141 | + | 0.814879i | −0.995522 | − | 0.0945354i | \(-0.969863\pi\) |
−0.415891 | + | 0.909415i | \(0.636530\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 166.844 | 0.921791 | 0.460895 | − | 0.887455i | \(-0.347528\pi\) | ||||
0.460895 | + | 0.887455i | \(0.347528\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.33343 | −0.0510024 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 261.316 | − | 150.871i | 1.41252 | − | 0.815518i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −105.233 | + | 182.269i | −0.562745 | + | 0.974703i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −59.2914 | − | 92.0332i | −0.313711 | − | 0.486948i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −65.6781 | + | 113.758i | −0.343864 | + | 0.595590i | −0.985147 | − | 0.171715i | \(-0.945069\pi\) |
0.641283 | + | 0.767305i | \(0.278403\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 40.7196 | + | 70.5284i | 0.210982 | + | 0.365432i | 0.952022 | − | 0.306029i | \(-0.0990004\pi\) |
−0.741040 | + | 0.671461i | \(0.765667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −112.262 | −0.575702 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.09549i | 0.0106370i | 0.999986 | + | 0.00531851i | \(0.00169294\pi\) | ||||
−0.999986 | + | 0.00531851i | \(0.998307\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 109.937 | − | 63.4721i | 0.552447 | − | 0.318955i | −0.197662 | − | 0.980270i | \(-0.563335\pi\) |
0.750108 | + | 0.661315i | \(0.230001\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.5159 | + | 7.80341i | 0.0672433 | + | 0.0388230i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 98.0469 | − | 63.1657i | 0.482990 | − | 0.311161i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −35.6897 | − | 20.6055i | −0.174096 | − | 0.100514i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −97.7231 | − | 169.261i | −0.472092 | − | 0.817687i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 217.440i | 1.04038i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.16822i | 0.0339726i | 0.999856 | + | 0.0169863i | \(0.00540717\pi\) | ||||
−0.999856 | + | 0.0169863i | \(0.994593\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.5997 | − | 25.2874i | −0.0685432 | − | 0.118720i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −182.943 | − | 105.622i | −0.850896 | − | 0.491265i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −80.0513 | − | 41.1563i | −0.368900 | − | 0.189660i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 84.5355 | + | 48.8066i | 0.386007 | + | 0.222861i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −267.920 | + | 154.683i | −1.21231 | + | 0.699925i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 279.720i | 1.25435i | 0.778878 | + | 0.627175i | \(0.215789\pi\) | ||||
−0.778878 | + | 0.627175i | \(0.784211\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −124.674 | −0.554106 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 152.392 | + | 263.950i | 0.671330 | + | 1.16278i | 0.977527 | + | 0.210809i | \(0.0676098\pi\) |
−0.306198 | + | 0.951968i | \(0.599057\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 207.344 | − | 359.130i | 0.905433 | − | 1.56826i | 0.0850971 | − | 0.996373i | \(-0.472880\pi\) |
0.820335 | − | 0.571883i | \(-0.193787\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.10305 | + | 84.1572i | 0.0177621 | + | 0.364317i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 82.4628 | − | 142.830i | 0.353918 | − | 0.613004i | −0.633014 | − | 0.774140i | \(-0.718183\pi\) |
0.986932 | + | 0.161136i | \(0.0515159\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 120.373 | − | 69.4976i | 0.512227 | − | 0.295735i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −53.1109 | −0.224097 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.1182 | 0.0799926 | 0.0399963 | − | 0.999200i | \(-0.487265\pi\) | ||||
0.0399963 | + | 0.999200i | \(0.487265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −303.376 | + | 175.154i | −1.25882 | + | 0.726780i | −0.972845 | − | 0.231457i | \(-0.925651\pi\) |
−0.285975 | + | 0.958237i | \(0.592317\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 97.3804 | − | 168.668i | 0.400743 | − | 0.694106i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 180.908 | + | 252.854i | 0.738401 | + | 1.03206i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −159.809 | + | 276.797i | −0.647000 | + | 1.12064i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.5522 | + | 28.6693i | 0.0664748 | + | 0.115138i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 88.3204 | 0.351874 | 0.175937 | − | 0.984401i | \(-0.443704\pi\) | ||||
0.175937 | + | 0.984401i | \(0.443704\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 316.114i | 1.24946i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 79.7158 | − | 46.0240i | 0.312611 | − | 0.180486i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 74.5499 | + | 43.0414i | 0.290077 | + | 0.167476i | 0.637977 | − | 0.770056i | \(-0.279772\pi\) |
−0.347899 | + | 0.937532i | \(0.613105\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.2106 | − | 332.495i | −0.0625893 | − | 1.28376i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 117.894 | + | 68.0661i | 0.451701 | + | 0.260789i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 159.605 | + | 276.444i | 0.606863 | + | 1.05112i | 0.991754 | + | 0.128156i | \(0.0409057\pi\) |
−0.384891 | + | 0.922962i | \(0.625761\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 235.937i | 0.890330i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.978025i | 0.00366302i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.7340 | + | 49.7687i | 0.106818 | + | 0.185014i | 0.914479 | − | 0.404632i | \(-0.132601\pi\) |
−0.807662 | + | 0.589646i | \(0.799267\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.7398 | − | 15.4382i | −0.0986709 | − | 0.0569677i | 0.449853 | − | 0.893103i | \(-0.351477\pi\) |
−0.548523 | + | 0.836135i | \(0.684810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −56.6286 | + | 110.146i | −0.207431 | + | 0.403465i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 174.631 | + | 100.823i | 0.635023 | + | 0.366631i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 308.465 | − | 178.092i | 1.11359 | − | 0.642933i | 0.173834 | − | 0.984775i | \(-0.444384\pi\) |
0.939757 | + | 0.341842i | \(0.111051\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 105.060i | − | 0.376561i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −294.160 | −1.04683 | −0.523416 | − | 0.852077i | \(-0.675343\pi\) | ||||
−0.523416 | + | 0.852077i | \(0.675343\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −207.501 | − | 359.402i | −0.733219 | − | 1.26997i | −0.955501 | − | 0.294989i | \(-0.904684\pi\) |
0.222282 | − | 0.974982i | \(-0.428649\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 47.5490 | − | 82.3572i | 0.166838 | − | 0.288973i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −38.2201 | + | 24.6229i | −0.133171 | + | 0.0857940i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.6691 | + | 30.6037i | −0.0611386 | + | 0.105895i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −133.720 | + | 77.2034i | −0.459520 | + | 0.265304i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −370.564 | −1.26472 | −0.632362 | − | 0.774673i | \(-0.717915\pi\) | ||||
−0.632362 | + | 0.774673i | \(0.717915\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 346.981 | 1.17621 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −178.986 | + | 103.337i | −0.602645 | + | 0.347937i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −232.329 | + | 402.406i | −0.777021 | + | 1.34584i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −195.913 | + | 126.215i | −0.650875 | + | 0.419319i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.8095 | − | 22.1867i | 0.0422755 | − | 0.0732233i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32.5081 | + | 56.3057i | 0.106584 | + | 0.184609i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 160.327 | 0.522239 | 0.261120 | − | 0.965306i | \(-0.415908\pi\) | ||||
0.261120 | + | 0.965306i | \(0.415908\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 151.486i | 0.490245i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −409.490 | + | 236.419i | −1.31669 | + | 0.760191i | −0.983195 | − | 0.182561i | \(-0.941561\pi\) |
−0.333495 | + | 0.942752i | \(0.608228\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 200.063 | + | 115.506i | 0.639179 | + | 0.369030i | 0.784298 | − | 0.620384i | \(-0.213023\pi\) |
−0.145119 | + | 0.989414i | \(0.546357\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −165.924 | + | 322.732i | −0.526743 | + | 1.02455i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −195.132 | − | 112.659i | −0.615557 | − | 0.355392i | 0.159580 | − | 0.987185i | \(-0.448986\pi\) |
−0.775137 | + | 0.631793i | \(0.782319\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −110.090 | − | 190.681i | −0.345109 | − | 0.597746i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 179.972i | − | 0.560659i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 262.067i | − | 0.811353i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 148.201 | + | 256.692i | 0.456004 | + | 0.789822i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.08716 | + | 5.24648i | 0.0277895 | + | 0.0160443i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.46732 | − | 153.161i | −0.0226970 | − | 0.465536i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.9257 | − | 10.3494i | −0.0541561 | − | 0.0312671i | 0.472677 | − | 0.881236i | \(-0.343288\pi\) |
−0.526834 | + | 0.849968i | \(0.676621\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 336.490 | − | 194.273i | 1.01048 | − | 0.583401i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 108.716i | − | 0.324527i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.9645 | 0.103752 | 0.0518762 | − | 0.998654i | \(-0.483480\pi\) | ||||
0.0518762 | + | 0.998654i | \(0.483480\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.73619 | − | 11.6674i | −0.0198708 | − | 0.0344172i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −84.9621 | + | 147.159i | −0.249156 | + | 0.431550i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 339.343 | − | 49.9505i | 0.989339 | − | 0.145628i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 69.1264 | − | 119.730i | 0.200366 | − | 0.347045i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 379.958 | − | 219.369i | 1.09498 | − | 0.632188i | 0.160083 | − | 0.987104i | \(-0.448824\pi\) |
0.934898 | + | 0.354916i | \(0.115491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 435.121 | 1.24677 | 0.623383 | − | 0.781917i | \(-0.285758\pi\) | ||||
0.623383 | + | 0.781917i | \(0.285758\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −303.793 | −0.865507 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 243.447 | − | 140.554i | 0.689653 | − | 0.398171i | −0.113829 | − | 0.993500i | \(-0.536312\pi\) |
0.803482 | + | 0.595329i | \(0.202978\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −101.701 | + | 176.151i | −0.286481 | + | 0.496200i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.94514 | − | 101.429i | −0.0138519 | − | 0.284115i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 131.965 | − | 228.570i | 0.367590 | − | 0.636685i | −0.621598 | − | 0.783336i | \(-0.713516\pi\) |
0.989188 | + | 0.146652i | \(0.0468497\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 45.1247 | + | 78.1583i | 0.124999 | + | 0.216505i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 48.8468 | 0.134564 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 679.969i | − | 1.86293i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 134.181 | − | 77.4694i | 0.365615 | − | 0.211088i | −0.305926 | − | 0.952055i | \(-0.598966\pi\) |
0.671541 | + | 0.740967i | \(0.265633\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −45.9567 | − | 26.5331i | −0.124544 | − | 0.0719055i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 231.490 | + | 119.015i | 0.623962 | + | 0.320794i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −506.505 | − | 292.431i | −1.35792 | − | 0.783997i | −0.368579 | − | 0.929597i | \(-0.620155\pi\) |
−0.989344 | + | 0.145600i | \(0.953489\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 28.1478 | + | 48.7534i | 0.0750608 | + | 0.130009i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 323.644i | − | 0.858472i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 128.176i | − | 0.338195i | −0.985599 | − | 0.169098i | \(-0.945915\pi\) | ||
0.985599 | − | 0.169098i | \(-0.0540853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 32.0011 | + | 55.4276i | 0.0839925 | + | 0.145479i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 216.437 | + | 124.960i | 0.565110 | + | 0.326266i | 0.755194 | − | 0.655502i | \(-0.227543\pi\) |
−0.190084 | + | 0.981768i | \(0.560876\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 493.403 | − | 317.870i | 1.28157 | − | 0.825636i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −235.571 | − | 136.007i | −0.608709 | − | 0.351439i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −187.428 | + | 108.212i | −0.481821 | + | 0.278179i | −0.721175 | − | 0.692753i | \(-0.756398\pi\) |
0.239354 | + | 0.970932i | \(0.423064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 380.991i | − | 0.974402i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 129.460 | 0.329415 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 184.984 | + | 320.401i | 0.468314 | + | 0.811143i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −349.941 | + | 606.116i | −0.881463 | + | 1.52674i | −0.0317493 | + | 0.999496i | \(0.510108\pi\) |
−0.849714 | + | 0.527244i | \(0.823226\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −56.8196 | − | 88.1964i | −0.142405 | − | 0.221044i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 90.4903 | − | 156.734i | 0.225662 | − | 0.390858i | −0.730856 | − | 0.682532i | \(-0.760879\pi\) |
0.956518 | + | 0.291674i | \(0.0942123\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −216.310 | + | 124.887i | −0.536749 | + | 0.309892i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −376.179 | −0.928837 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −628.431 | −1.54406 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −310.767 | + | 179.421i | −0.759821 | + | 0.438683i | −0.829232 | − | 0.558905i | \(-0.811222\pi\) |
0.0694104 | + | 0.997588i | \(0.477888\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 115.258 | − | 199.632i | 0.280432 | − | 0.485723i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 175.029 | − | 340.441i | 0.423798 | − | 0.824312i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 115.302 | − | 199.709i | 0.277836 | − | 0.481226i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.4031 | + | 38.8033i | 0.0537245 | + | 0.0930535i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −780.890 | −1.86370 | −0.931849 | − | 0.362846i | \(-0.881805\pi\) | ||||
−0.931849 | + | 0.362846i | \(0.881805\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 114.961i | − | 0.273068i | −0.990635 | − | 0.136534i | \(-0.956404\pi\) | ||
0.990635 | − | 0.136534i | \(-0.0435962\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 155.002 | − | 89.4904i | 0.366435 | − | 0.211561i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −210.472 | − | 121.516i | −0.495228 | − | 0.285920i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 71.6425 | − | 3.49290i | 0.167781 | − | 0.00818010i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 202.482 | + | 116.903i | 0.471985 | + | 0.272501i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 154.856 | + | 268.219i | 0.359295 | + | 0.622317i | 0.987843 | − | 0.155453i | \(-0.0496838\pi\) |
−0.628548 | + | 0.777771i | \(0.716351\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 595.775i | − | 1.37592i | −0.725747 | − | 0.687962i | \(-0.758506\pi\) | ||
0.725747 | − | 0.687962i | \(-0.241494\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 96.2958i | 0.221370i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −196.808 | − | 340.881i | −0.450361 | − | 0.780048i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −698.796 | − | 403.450i | −1.59179 | − | 0.919020i | −0.993000 | − | 0.118113i | \(-0.962315\pi\) |
−0.598789 | − | 0.800907i | \(-0.704351\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 232.951 | + | 325.593i | 0.528233 | + | 0.738306i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −385.214 | − | 222.403i | −0.869557 | − | 0.502039i | −0.00235617 | − | 0.999997i | \(-0.500750\pi\) |
−0.867201 | + | 0.497958i | \(0.834083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.90012 | − | 3.40644i | 0.0132587 | − | 0.00765491i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 37.9772i | − | 0.0849601i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 262.420 | 0.584455 | 0.292228 | − | 0.956349i | \(-0.405604\pi\) | ||||
0.292228 | + | 0.956349i | \(0.405604\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.9145 | + | 74.3302i | 0.0951542 | + | 0.164812i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 44.4633 | − | 77.0127i | 0.0981530 | − | 0.170006i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 861.712 | − | 42.0124i | 1.89387 | − | 0.0923350i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −194.738 | + | 337.296i | −0.426122 | + | 0.738065i | −0.996524 | − | 0.0833004i | \(-0.973454\pi\) |
0.570403 | + | 0.821365i | \(0.306787\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 215.720 | − | 124.546i | 0.469978 | − | 0.271342i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 158.714 | 0.344283 | 0.172141 | − | 0.985072i | \(-0.444931\pi\) | ||||
0.172141 | + | 0.985072i | \(0.444931\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 528.844 | 1.14221 | 0.571106 | − | 0.820877i | \(-0.306515\pi\) | ||||
0.571106 | + | 0.820877i | \(0.306515\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 64.3601 | − | 37.1583i | 0.138409 | − | 0.0799103i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 218.449 | − | 378.365i | 0.467771 | − | 0.810203i | −0.531551 | − | 0.847026i | \(-0.678391\pi\) |
0.999322 | + | 0.0368236i | \(0.0117240\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −106.667 | − | 54.8401i | −0.227435 | − | 0.116930i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.8274 | − | 22.2177i | 0.0272344 | − | 0.0471713i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 219.977 | + | 381.011i | 0.465067 | + | 0.805519i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −251.085 | −0.528600 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 303.811i | 0.636920i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −472.737 | + | 272.935i | −0.986925 | + | 0.569802i | −0.904354 | − | 0.426783i | \(-0.859647\pi\) |
−0.0825716 | + | 0.996585i | \(0.526313\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −799.980 | − | 461.869i | −1.66316 | − | 0.960226i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −82.6039 | − | 128.219i | −0.171023 | − | 0.265464i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 931.488 | + | 537.795i | 1.92059 | + | 1.10886i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 324.115 | + | 561.384i | 0.665534 | + | 1.15274i | 0.979140 | + | 0.203185i | \(0.0651294\pi\) |
−0.313606 | + | 0.949553i | \(0.601537\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 220.822i | 0.451579i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 732.074i | 1.49098i | 0.666514 | + | 0.745492i | \(0.267786\pi\) | ||||
−0.666514 | + | 0.745492i | \(0.732214\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 132.684 | + | 229.815i | 0.269136 | + | 0.466157i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 593.279 | + | 342.530i | 1.19854 | + | 0.691980i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 121.529 | + | 188.640i | 0.244526 | + | 0.379557i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.1264 | − | 13.3520i | −0.0463454 | − | 0.0267575i | 0.476648 | − | 0.879094i | \(-0.341852\pi\) |
−0.522994 | + | 0.852337i | \(0.675185\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 47.4172 | − | 27.3763i | 0.0946451 | − | 0.0546434i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 616.414i | − | 1.22548i | −0.790286 | − | 0.612738i | \(-0.790068\pi\) | ||
0.790286 | − | 0.612738i | \(-0.209932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −178.460 | −0.353387 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 94.8687 | + | 164.317i | 0.187118 | + | 0.324097i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −66.3763 | + | 114.967i | −0.130405 | + | 0.225869i | −0.923833 | − | 0.382796i | \(-0.874961\pi\) |
0.793428 | + | 0.608665i | \(0.208295\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −667.152 | − | 342.999i | −1.30558 | − | 0.671230i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 128.673 | − | 222.868i | 0.250824 | − | 0.434440i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 913.867 | − | 527.621i | 1.77450 | − | 1.02451i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −289.483 | −0.559928 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 126.942 | 0.244589 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −585.480 | + | 338.027i | −1.12376 | + | 0.648804i | −0.942359 | − | 0.334605i | \(-0.891397\pi\) |
−0.181403 | + | 0.983409i | \(0.558064\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 186.224 | − | 322.550i | 0.356069 | − | 0.616730i | −0.631231 | − | 0.775595i | \(-0.717450\pi\) |
0.987300 | + | 0.158865i | \(0.0507833\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −97.1787 | + | 4.73791i | −0.185102 | + | 0.00902459i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 102.399 | − | 177.361i | 0.194306 | − | 0.336548i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6179 | − | 37.4433i | −0.0408656 | − | 0.0707813i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 446.799 | 0.841429 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 126.161i | 0.236700i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1085.71 | + | 626.836i | −2.02937 | + | 1.17166i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −230.123 | − | 132.862i | −0.428534 | − | 0.247414i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −62.9892 | − | 644.447i | −0.116863 | − | 1.19563i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −60.3373 | − | 34.8357i | −0.111529 | − | 0.0643914i | 0.443198 | − | 0.896424i | \(-0.353844\pi\) |
−0.554727 | + | 0.832032i | \(0.687177\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 75.9860 | + | 131.612i | 0.139937 | + | 0.242379i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 73.0934i | − | 0.134116i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 466.463i | 0.852765i | 0.904543 | + | 0.426383i | \(0.140212\pi\) | ||||
−0.904543 | + | 0.426383i | \(0.859788\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 41.8599 | + | 72.5034i | 0.0762475 | + | 0.132065i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 237.430 | + | 137.081i | 0.430908 | + | 0.248785i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 407.674 | − | 19.8760i | 0.737204 | − | 0.0359421i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 238.023 | + | 137.423i | 0.428870 | + | 0.247608i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −118.835 | + | 68.6094i | −0.213348 | + | 0.123177i | −0.602866 | − | 0.797842i | \(-0.705975\pi\) |
0.389518 | + | 0.921019i | \(0.372642\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 646.692i | 1.15687i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −191.706 | −0.341722 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 84.5632 | + | 146.468i | 0.150201 | + | 0.260156i | 0.931301 | − | 0.364250i | \(-0.118675\pi\) |
−0.781100 | + | 0.624406i | \(0.785341\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −46.9240 | + | 81.2747i | −0.0830513 | + | 0.143849i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −189.757 | + | 369.088i | −0.334669 | + | 0.650949i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −372.466 | + | 645.129i | −0.654597 | + | 1.13379i | 0.327398 | + | 0.944887i | \(0.393828\pi\) |
−0.981995 | + | 0.188908i | \(0.939505\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −767.828 | + | 443.306i | −1.34471 | + | 0.776367i | −0.987494 | − | 0.157655i | \(-0.949606\pi\) |
−0.357213 | + | 0.934023i | \(0.616273\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −119.647 | −0.208809 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −365.026 | −0.634827 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −207.900 | + | 120.031i | −0.360311 | + | 0.208026i | −0.669217 | − | 0.743067i | \(-0.733370\pi\) |
0.308906 | + | 0.951093i | \(0.400037\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −37.0900 | + | 64.2417i | −0.0640586 | + | 0.110953i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −137.782 | − | 213.868i | −0.237147 | − | 0.368104i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 245.691 | − | 425.549i | 0.421425 | − | 0.729930i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 503.488 | + | 872.067i | 0.860663 | + | 1.49071i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −190.873 | −0.325168 | −0.162584 | − | 0.986695i | \(-0.551983\pi\) | ||||
−0.162584 | + | 0.986695i | \(0.551983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 211.585i | − | 0.359227i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.65299 | + | 0.954353i | −0.00279693 | + | 0.00161481i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 637.548 | + | 368.089i | 1.07512 | + | 0.620723i | 0.929577 | − | 0.368629i | \(-0.120173\pi\) |
0.145547 | + | 0.989351i | \(0.453506\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −594.667 | + | 383.108i | −0.999441 | + | 0.643879i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 100.137 | + | 57.8144i | 0.167734 | + | 0.0968415i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 558.330 | + | 967.057i | 0.932104 | + | 1.61445i | 0.779718 | + | 0.626131i | \(0.215362\pi\) |
0.152386 | + | 0.988321i | \(0.451304\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 183.100i | 0.304659i | 0.988330 | + | 0.152329i | \(0.0486774\pi\) | ||||
−0.988330 | + | 0.152329i | \(0.951323\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 139.991i | − | 0.232158i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −170.132 | − | 294.678i | −0.281210 | − | 0.487071i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −394.026 | − | 227.491i | −0.649136 | − | 0.374779i | 0.138989 | − | 0.990294i | \(-0.455615\pi\) |
−0.788125 | + | 0.615515i | \(0.788948\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 94.4807 | + | 48.5748i | 0.155141 | + | 0.0797615i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −368.505 | − | 212.757i | −0.603118 | − | 0.348211i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 232.853 | − | 134.438i | 0.379859 | − | 0.219312i | −0.297898 | − | 0.954598i | \(-0.596286\pi\) |
0.677757 | + | 0.735286i | \(0.262952\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 37.5375i | − | 0.0610366i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −184.934 | −0.299731 | −0.149866 | − | 0.988706i | \(-0.547884\pi\) | ||||
−0.149866 | + | 0.988706i | \(0.547884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 496.809 | + | 860.498i | 0.802599 | + | 1.39014i | 0.917900 | + | 0.396812i | \(0.129884\pi\) |
−0.115301 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 187.064 | − | 324.004i | 0.301229 | − | 0.521745i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.366012 | − | 7.50723i | −0.000587499 | − | 0.0120501i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 386.818 | − | 669.988i | 0.618909 | − | 1.07198i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −171.524 | + | 99.0292i | −0.273562 | + | 0.157941i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 757.408 | 1.20415 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −805.857 | −1.27711 | −0.638555 | − | 0.769576i | \(-0.720468\pi\) | ||||
−0.638555 | + | 0.769576i | \(0.720468\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.65451 | + | 3.26463i | −0.00893287 | + | 0.00515740i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 222.918 | − | 386.106i | 0.351053 | − | 0.608041i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 393.455 | − | 866.662i | 0.617669 | − | 1.36054i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −130.957 | + | 226.825i | −0.204941 | + | 0.354969i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.75221 | − | 4.76696i | −0.00429361 | − | 0.00743676i | 0.863871 | − | 0.503714i | \(-0.168033\pi\) |
−0.868164 | + | 0.496277i | \(0.834700\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1024.08 | 1.59266 | 0.796331 | − | 0.604861i | \(-0.206771\pi\) | ||||
0.796331 | + | 0.604861i | \(0.206771\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 192.414i | − | 0.298317i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −395.404 | + | 228.287i | −0.611134 | + | 0.352839i | −0.773409 | − | 0.633907i | \(-0.781450\pi\) |
0.162275 | + | 0.986746i | \(0.448117\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −625.834 | − | 361.325i | −0.964304 | − | 0.556741i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.99255 | − | 81.8908i | −0.00613295 | − | 0.125792i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.4603 | − | 14.1222i | −0.0374584 | − | 0.0216266i | 0.481154 | − | 0.876636i | \(-0.340218\pi\) |
−0.518612 | + | 0.855010i | \(0.673551\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −450.907 | − | 780.994i | −0.688407 | − | 1.19236i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 875.579i | − | 1.33269i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 132.188i | − | 0.200589i | −0.994958 | − | 0.100295i | \(-0.968021\pi\) | ||
0.994958 | − | 0.100295i | \(-0.0319785\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 346.924 | + | 600.889i | 0.524847 | + | 0.909061i | 0.999581 | + | 0.0289321i | \(0.00921065\pi\) |
−0.474735 | + | 0.880129i | \(0.657456\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −244.038 | − | 140.895i | −0.368082 | − | 0.212512i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −334.160 | + | 649.960i | −0.502497 | + | 0.977384i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 345.175 | + | 199.287i | 0.517504 | + | 0.298781i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −220.652 | + | 127.393i | −0.329823 | + | 0.190424i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 135.408i | − | 0.201800i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 532.137 | 0.790694 | 0.395347 | − | 0.918532i | \(-0.370624\pi\) | ||||
0.395347 | + | 0.918532i | \(0.370624\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −119.327 | − | 206.680i | −0.176780 | − | 0.306192i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −143.115 | + | 247.883i | −0.211396 | + | 0.366149i | −0.952152 | − | 0.305626i | \(-0.901134\pi\) |
0.740756 | + | 0.671775i | \(0.234468\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 997.531 | − | 642.649i | 1.46912 | − | 0.946464i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −138.808 | + | 240.423i | −0.203830 | + | 0.353043i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −387.838 | + | 223.918i | −0.567844 | + | 0.327845i | −0.756288 | − | 0.654239i | \(-0.772989\pi\) |
0.188443 | + | 0.982084i | \(0.439656\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1605.76 | −2.34417 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 377.724 | 0.549817 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 625.519 | − | 361.143i | 0.907865 | − | 0.524156i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −510.366 | + | 883.980i | −0.738591 | + | 1.27928i | 0.214539 | + | 0.976715i | \(0.431175\pi\) |
−0.953130 | + | 0.302561i | \(0.902158\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 635.343 | − | 409.313i | 0.916801 | − | 0.590639i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 156.059 | − | 270.302i | 0.224545 | − | 0.388924i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −51.7221 | − | 89.5854i | −0.0742068 | − | 0.128530i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 150.225 | 0.214914 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1311.02i | 1.87021i | 0.354369 | + | 0.935106i | \(0.384696\pi\) | ||||
−0.354369 | + | 0.935106i | \(0.615304\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 677.669 | − | 391.252i | 0.963967 | − | 0.556546i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 109.644 | + | 63.3028i | 0.155523 | + | 0.0897912i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −90.0213 | + | 175.096i | −0.127329 | + | 0.247661i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −465.495 | − | 268.754i | −0.656552 | − | 0.379061i | 0.134410 | − | 0.990926i | \(-0.457086\pi\) |
−0.790962 | + | 0.611865i | \(0.790419\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 238.199 | + | 412.573i | 0.335020 | + | 0.580271i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 307.601i | − | 0.431417i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1628.68i | − | 2.27787i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.70704 | + | 15.0810i | 0.0121437 | + | 0.0210335i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 233.275 | + | 134.681i | 0.324443 | + | 0.187318i | 0.653371 | − | 0.757037i | \(-0.273354\pi\) |
−0.328928 | + | 0.944355i | \(0.606687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −56.6914 | − | 1162.79i | −0.0786288 | − | 1.61275i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −276.334 | − | 159.541i | −0.382204 | − | 0.220666i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 220.185 | − | 127.124i | 0.303703 | − | 0.175343i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 460.316i | − | 0.633172i | −0.948564 | − | 0.316586i | \(-0.897463\pi\) | ||
0.948564 | − | 0.316586i | \(-0.102537\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −356.185 | −0.488594 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −265.124 | − | 459.208i | −0.362686 | − | 0.628191i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.3410 | + | 57.7484i | −0.0454857 | + | 0.0787836i | −0.887872 | − | 0.460091i | \(-0.847817\pi\) |
0.842386 | + | 0.538874i | \(0.181150\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −117.067 | + | 257.863i | −0.159275 | + | 0.350834i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −113.211 | + | 196.087i | −0.153610 | + | 0.266061i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 808.772 | − | 466.944i | 1.09441 | − | 0.631860i | 0.159665 | − | 0.987171i | \(-0.448958\pi\) |
0.934748 | + | 0.355311i | \(0.115625\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −291.128 | −0.392885 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1198.23 | 1.61269 | 0.806345 | − | 0.591446i | \(-0.201443\pi\) | ||||
0.806345 | + | 0.591446i | \(0.201443\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −229.104 | + | 132.273i | −0.307523 | + | 0.177548i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 148.471 | − | 257.160i | 0.198757 | − | 0.344257i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 67.3518 | + | 1381.44i | 0.0899222 | + | 1.84438i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −84.2993 | + | 146.011i | −0.112249 | + | 0.194422i | −0.916677 | − | 0.399629i | \(-0.869139\pi\) |
0.804427 | + | 0.594051i | \(0.202472\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 40.2239 | + | 69.6698i | 0.0534182 | + | 0.0925230i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −619.458 | −0.820474 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 209.207i | − | 0.276364i | −0.990407 | − | 0.138182i | \(-0.955874\pi\) | ||
0.990407 | − | 0.138182i | \(-0.0441259\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −249.360 | + | 143.968i | −0.328538 | + | 0.189681i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 479.127 | + | 276.624i | 0.629602 | + | 0.363501i | 0.780598 | − | 0.625033i | \(-0.214915\pi\) |
−0.150996 | + | 0.988534i | \(0.548248\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −71.7156 | − | 36.8707i | −0.0939916 | − | 0.0483233i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −715.041 | − | 412.829i | −0.934695 | − | 0.539646i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −531.115 | − | 919.919i | −0.692458 | − | 1.19937i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 219.524i | − | 0.285467i | −0.989761 | − | 0.142734i | \(-0.954411\pi\) | ||
0.989761 | − | 0.142734i | \(-0.0455892\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 78.4096i | 0.101699i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −333.337 | − | 577.357i | −0.431225 | − | 0.746904i | 0.565754 | − | 0.824574i | \(-0.308585\pi\) |
−0.996979 | + | 0.0776701i | \(0.975252\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −169.928 | − | 98.1082i | −0.219262 | − | 0.126591i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 254.899 | − | 164.216i | 0.328055 | − | 0.211346i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −92.5538 | − | 53.4359i | −0.118811 | − | 0.0685956i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 366.866 | − | 211.810i | 0.469738 | − | 0.271204i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 260.587i | 0.332806i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −178.710 | −0.227656 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −459.932 | − | 796.626i | −0.584412 | − | 1.01223i | −0.994948 | − | 0.100387i | \(-0.967992\pi\) |
0.410536 | − | 0.911844i | \(-0.365341\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −145.378 | + | 251.803i | −0.184256 | + | 0.319141i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56.0727 | + | 87.0371i | 0.0708884 | + | 0.110034i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 99.5187 | − | 172.371i | 0.125496 | − | 0.217366i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −186.115 | + | 107.453i | −0.234106 | + | 0.135161i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1016.13 | 1.27494 | 0.637470 | − | 0.770476i | \(-0.279981\pi\) | ||||
0.637470 | + | 0.770476i | \(0.279981\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 348.895 | 0.436664 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.59744 | − | 4.38638i | 0.00948494 | − | 0.00547613i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −708.078 | + | 1226.43i | −0.881791 | + | 1.52731i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −485.800 | + | 944.909i | −0.603478 | + | 1.17380i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.1727 | + | 45.3325i | −0.0324321 | + | 0.0561741i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −565.950 | − | 980.254i | −0.699567 | − | 1.21169i | −0.968617 | − | 0.248560i | \(-0.920043\pi\) |
0.269049 | − | 0.963126i | \(-0.413291\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −481.066 | −0.593176 | −0.296588 | − | 0.955006i | \(-0.595849\pi\) | ||||
−0.296588 | + | 0.955006i | \(0.595849\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 28.1242i | − | 0.0345931i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1332.15 | − | 769.117i | 1.63454 | − | 0.943702i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −474.423 | − | 273.908i | −0.580690 | − | 0.335261i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1109.60 | − | 54.0983i | 1.35483 | − | 0.0660541i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −630.185 | − | 363.838i | −0.767582 | − | 0.443164i | 0.0644292 | − | 0.997922i | \(-0.479477\pi\) |
−0.832011 | + | 0.554758i | \(0.812811\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −313.323 | − | 542.692i | −0.380709 | − | 0.659407i | 0.610455 | − | 0.792051i | \(-0.290987\pi\) |
−0.991164 | + | 0.132644i | \(0.957653\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 183.673i | 0.222633i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1468.52i | 1.77572i | 0.460116 | + | 0.887859i | \(0.347808\pi\) | ||||
−0.460116 | + | 0.887859i | \(0.652192\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −409.352 | − | 709.019i | −0.493790 | − | 0.855270i | 0.506184 | − | 0.862425i | \(-0.331056\pi\) |
−0.999974 | + | 0.00715566i | \(0.997722\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 280.969 | + | 162.218i | 0.338110 | + | 0.195208i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 75.9169 | + | 776.710i | 0.0911367 | + | 0.932425i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −330.306 | − | 190.702i | −0.395576 | − | 0.228386i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 174.165 | − | 100.554i | 0.208083 | − | 0.120137i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1108.84i | − | 1.32162i | −0.750555 | − | 0.660808i | \(-0.770214\pi\) | ||
0.750555 | − | 0.660808i | \(-0.229786\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 563.386 | 0.669900 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −133.970 | − | 232.042i | −0.158920 | − | 0.275258i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 660.850 | − | 1144.63i | 0.782072 | − | 1.35459i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −374.943 | + | 18.2802i | −0.442672 | + | 0.0215823i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 189.005 | − | 327.366i | 0.222621 | − | 0.385590i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 985.191 | − | 568.800i | 1.15769 | − | 0.668390i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 610.400 | 0.715592 | 0.357796 | − | 0.933800i | \(-0.383528\pi\) | ||||
0.357796 | + | 0.933800i | \(0.383528\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −853.017 | −0.997680 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 384.614 | − | 222.057i | 0.448791 | − | 0.259110i | −0.258529 | − | 0.966004i | \(-0.583238\pi\) |
0.707319 | + | 0.706894i | \(0.249904\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.7547 | + | 70.5892i | −0.0474443 | + | 0.0821760i | −0.888772 | − | 0.458349i | \(-0.848441\pi\) |
0.841328 | + | 0.540525i | \(0.181774\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −36.8299 | − | 18.9351i | −0.0427757 | − | 0.0219920i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −525.730 | + | 910.592i | −0.609189 | + | 1.05515i | 0.382185 | + | 0.924086i | \(0.375172\pi\) |
−0.991374 | + | 0.131061i | \(0.958162\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −442.134 | − | 765.799i | −0.511138 | − | 0.885317i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −32.1882 | −0.0371259 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 770.524i | − | 0.886679i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −288.230 | + | 166.409i | −0.330918 | + | 0.191056i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1199.45 | + | 692.505i | 1.37395 | + | 0.793248i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −234.305 | − | 363.693i | −0.267777 | − | 0.415649i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1350.68 | + | 779.814i | 1.54011 | + | 0.889183i | 0.998831 | + | 0.0483410i | \(0.0153934\pi\) |
0.541280 | + | 0.840842i | \(0.317940\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −168.767 | − | 292.312i | −0.191998 | − | 0.332551i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1515.22i | 1.71989i | 0.510389 | + | 0.859944i | \(0.329501\pi\) | ||||
−0.510389 | + | 0.859944i | \(0.670499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 763.828i | − | 0.865037i | −0.901625 | − | 0.432519i | \(-0.857625\pi\) | ||
0.901625 | − | 0.432519i | \(-0.142375\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 158.026 | + | 273.709i | 0.178561 | + | 0.309276i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −496.554 | − | 286.686i | −0.559813 | − | 0.323208i | 0.193258 | − | 0.981148i | \(-0.438095\pi\) |
−0.753070 | + | 0.657940i | \(0.771428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −266.381 | − | 413.481i | −0.299641 | − | 0.465108i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 678.496 | + | 391.730i | 0.761500 | + | 0.439652i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 312.163 | − | 180.228i | 0.349567 | − | 0.201823i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1851.01i | 2.06817i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −423.240 | −0.471840 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 107.125 | + | 185.546i | 0.119160 | + | 0.206391i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −296.115 | + | 512.887i | −0.328652 | + | 0.569242i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −188.787 | − | 97.0600i | −0.209067 | − | 0.107486i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 529.315 | − | 916.800i | 0.584878 | − | 1.01304i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −885.036 | + | 510.976i | −0.975784 | + | 0.563369i | −0.900995 | − | 0.433830i | \(-0.857162\pi\) |
−0.0747894 | + | 0.997199i | \(0.523828\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −229.799 | −0.252804 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −630.111 | −0.691669 | −0.345835 | − | 0.938295i | \(-0.612404\pi\) | ||||
−0.345835 | + | 0.938295i | \(0.612404\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −415.930 | + | 240.137i | −0.455564 | + | 0.263020i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −29.6104 | + | 51.2868i | −0.0323611 | + | 0.0560511i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −993.725 | + | 48.4486i | −1.08367 | + | 0.0528339i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −421.489 | + | 730.041i | −0.458639 | + | 0.794386i | −0.998889 | − | 0.0471182i | \(-0.984996\pi\) |
0.540250 | + | 0.841504i | \(0.318330\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 73.0182 | + | 126.471i | 0.0792814 | + | 0.137319i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 622.683 | 0.674630 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 725.668i | − | 0.784506i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1176.76 | − | 679.405i | 1.26943 | − | 0.732907i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 670.867 | + | 387.325i | 0.722139 | + | 0.416927i | 0.815540 | − | 0.578701i | \(-0.196440\pi\) |
−0.0934003 | + | 0.995629i | \(0.529774\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 469.148 | + | 655.723i | 0.503918 | + | 0.704321i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −372.990 | − | 215.346i | −0.399774 | − | 0.230810i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 667.708 | + | 1156.50i | 0.714126 | + | 1.23690i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1586.27i | 1.69293i | 0.532447 | + | 0.846463i | \(0.321273\pi\) | ||||
−0.532447 | + | 0.846463i | \(0.678727\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 210.421i | 0.224090i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 410.023 | + | 710.181i | 0.435731 | + | 0.754708i | 0.997355 | − | 0.0726842i | \(-0.0231565\pi\) |
−0.561624 | + | 0.827393i | \(0.689823\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −134.554 | − | 77.6849i | −0.142687 | − | 0.0823805i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −693.821 | + | 33.8270i | −0.734202 | + | 0.0357957i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 551.949 | + | 318.668i | 0.582839 | + | 0.336502i | 0.762261 | − | 0.647270i | \(-0.224089\pi\) |
−0.179422 | + | 0.983772i | \(0.557423\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1802.74 | + | 1040.81i | −1.89962 | + | 1.09675i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 205.234i | − | 0.215809i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −350.626 | −0.367918 | −0.183959 | − | 0.982934i | \(-0.558891\pi\) | ||||
−0.183959 | + | 0.982934i | \(0.558891\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 416.729 | + | 721.796i | 0.436365 | + | 0.755807i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 100.277 | − | 173.684i | 0.104782 | − | 0.181488i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −809.997 | + | 1575.49i | −0.844627 | + | 1.64285i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −397.826 | + | 689.055i | −0.413971 | + | 0.717019i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1398.04 | + | 807.161i | −1.45176 | + | 0.838174i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 516.734 | 0.535475 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 649.816 | 0.671992 | 0.335996 | − | 0.941863i | \(-0.390927\pi\) | ||||
0.335996 | + | 0.941863i | \(0.390927\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 206.726 | − | 119.354i | 0.213340 | − | 0.123172i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 485.305 | − | 840.573i | 0.499799 | − | 0.865677i | −0.500201 | − | 0.865909i | \(-0.666741\pi\) |
1.00000 | 0.000232071i | \(7.38706e-5\pi\) | ||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −186.486 | − | 289.466i | −0.191660 | − | 0.297499i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −134.991 | + | 233.811i | −0.138452 | + | 0.239807i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 300.437 | + | 520.373i | 0.307510 | + | 0.532623i | 0.977817 | − | 0.209461i | \(-0.0671709\pi\) |
−0.670307 | + | 0.742084i | \(0.733838\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.1890 | −0.0144934 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 94.1205i | − | 0.0959434i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1098.66 | + | 634.311i | −1.11766 | + | 0.645281i | −0.940802 | − | 0.338955i | \(-0.889926\pi\) |
−0.176857 | + | 0.984236i | \(0.556593\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5146 | + | 6.64797i | 0.0116900 | + | 0.00674921i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 117.417 | − | 75.6449i | 0.118964 | − | 0.0766413i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −689.714 | − | 398.207i | −0.697385 | − | 0.402636i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −774.555 | − | 1341.57i | −0.781590 | − | 1.35375i | −0.931015 | − | 0.364980i | \(-0.881076\pi\) |
0.149426 | − | 0.988773i | \(-0.452258\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 18.8538i | − | 0.0189867i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 805.464i | − | 0.809512i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 470.469 | + | 814.876i | 0.471885 | + | 0.817328i | 0.999483 | − | 0.0321661i | \(-0.0102406\pi\) |
−0.527598 | + | 0.849494i | \(0.676907\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 644.116 | + | 371.881i | 0.644761 | + | 0.372253i |
(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 | 224.3.n.a.145.9 | 28 | ||
4.3 | odd | 2 | 56.3.j.a.5.4 | ✓ | 28 | ||
7.2 | even | 3 | 1568.3.h.a.881.12 | 28 | |||
7.3 | odd | 6 | inner | 224.3.n.a.17.6 | 28 | ||
7.5 | odd | 6 | 1568.3.h.a.881.18 | 28 | |||
8.3 | odd | 2 | 56.3.j.a.5.6 | yes | 28 | ||
8.5 | even | 2 | inner | 224.3.n.a.145.6 | 28 | ||
28.3 | even | 6 | 56.3.j.a.45.6 | yes | 28 | ||
28.11 | odd | 6 | 392.3.j.e.325.6 | 28 | |||
28.19 | even | 6 | 392.3.h.a.293.27 | 28 | |||
28.23 | odd | 6 | 392.3.h.a.293.28 | 28 | |||
28.27 | even | 2 | 392.3.j.e.117.4 | 28 | |||
56.3 | even | 6 | 56.3.j.a.45.4 | yes | 28 | ||
56.5 | odd | 6 | 1568.3.h.a.881.11 | 28 | |||
56.11 | odd | 6 | 392.3.j.e.325.4 | 28 | |||
56.19 | even | 6 | 392.3.h.a.293.26 | 28 | |||
56.27 | even | 2 | 392.3.j.e.117.6 | 28 | |||
56.37 | even | 6 | 1568.3.h.a.881.17 | 28 | |||
56.45 | odd | 6 | inner | 224.3.n.a.17.9 | 28 | ||
56.51 | odd | 6 | 392.3.h.a.293.25 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.4 | ✓ | 28 | 4.3 | odd | 2 | ||
56.3.j.a.5.6 | yes | 28 | 8.3 | odd | 2 | ||
56.3.j.a.45.4 | yes | 28 | 56.3 | even | 6 | ||
56.3.j.a.45.6 | yes | 28 | 28.3 | even | 6 | ||
224.3.n.a.17.6 | 28 | 7.3 | odd | 6 | inner | ||
224.3.n.a.17.9 | 28 | 56.45 | odd | 6 | inner | ||
224.3.n.a.145.6 | 28 | 8.5 | even | 2 | inner | ||
224.3.n.a.145.9 | 28 | 1.1 | even | 1 | trivial | ||
392.3.h.a.293.25 | 28 | 56.51 | odd | 6 | |||
392.3.h.a.293.26 | 28 | 56.19 | even | 6 | |||
392.3.h.a.293.27 | 28 | 28.19 | even | 6 | |||
392.3.h.a.293.28 | 28 | 28.23 | odd | 6 | |||
392.3.j.e.117.4 | 28 | 28.27 | even | 2 | |||
392.3.j.e.117.6 | 28 | 56.27 | even | 2 | |||
392.3.j.e.325.4 | 28 | 56.11 | odd | 6 | |||
392.3.j.e.325.6 | 28 | 28.11 | odd | 6 | |||
1568.3.h.a.881.11 | 28 | 56.5 | odd | 6 | |||
1568.3.h.a.881.12 | 28 | 7.2 | even | 3 | |||
1568.3.h.a.881.17 | 28 | 56.37 | even | 6 | |||
1568.3.h.a.881.18 | 28 | 7.5 | odd | 6 |