Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(199,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, 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("1050.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.q (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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 16.0.22986704741655040229376.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.7 | ||
Root | \(0.337183 + 1.25838i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.199 |
Dual form | 1050.3.q.b.649.7 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | − | 0.707107i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | − | 1.50000i | 0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | −5.76140 | + | 3.97571i | −0.823057 | + | 0.567958i | ||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −1.50000 | − | 2.59808i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.64728 | + | 2.85317i | −0.149753 | + | 0.259379i | −0.931136 | − | 0.364672i | \(-0.881181\pi\) |
0.781383 | + | 0.624051i | \(0.214514\pi\) | |||||||
\(12\) | −1.73205 | − | 3.00000i | −0.144338 | − | 0.250000i | ||||
\(13\) | −7.72850 | −0.594500 | −0.297250 | − | 0.954800i | \(-0.596069\pi\) | ||||
−0.297250 | + | 0.954800i | \(0.596069\pi\) | |||||||
\(14\) | −4.24500 | + | 8.94315i | −0.303214 | + | 0.638797i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | −6.30929 | + | 10.9280i | −0.371135 | + | 0.642824i | −0.989740 | − | 0.142877i | \(-0.954365\pi\) |
0.618606 | + | 0.785702i | \(0.287698\pi\) | |||||||
\(18\) | −3.67423 | − | 2.12132i | −0.204124 | − | 0.117851i | ||||
\(19\) | −1.54304 | + | 0.890872i | −0.0812124 | + | 0.0468880i | −0.540056 | − | 0.841629i | \(-0.681597\pi\) |
0.458844 | + | 0.888517i | \(0.348264\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.974040 | + | 12.0852i | 0.0463829 | + | 0.575484i | ||||
\(22\) | 4.65921i | 0.211782i | ||||||||
\(23\) | −5.85120 | + | 3.37819i | −0.254400 | + | 0.146878i | −0.621777 | − | 0.783194i | \(-0.713589\pi\) |
0.367377 | + | 0.930072i | \(0.380256\pi\) | |||||||
\(24\) | −4.24264 | − | 2.44949i | −0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.46544 | + | 5.46488i | −0.364055 | + | 0.210188i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 1.12472 | + | 13.9547i | 0.0401687 | + | 0.498384i | ||||
\(29\) | −39.2933 | −1.35494 | −0.677471 | − | 0.735550i | \(-0.736924\pi\) | ||||
−0.677471 | + | 0.735550i | \(0.736924\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.46751 | + | 5.46607i | 0.305404 | + | 0.176325i | 0.644868 | − | 0.764294i | \(-0.276912\pi\) |
−0.339464 | + | 0.940619i | \(0.610246\pi\) | |||||||
\(32\) | −4.89898 | − | 2.82843i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 2.85317 | + | 4.94184i | 0.0864598 | + | 0.149753i | ||||
\(34\) | 17.8454i | 0.524864i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −29.7883 | + | 17.1983i | −0.805089 | + | 0.464818i | −0.845248 | − | 0.534375i | \(-0.820547\pi\) |
0.0401585 | + | 0.999193i | \(0.487214\pi\) | |||||||
\(38\) | −1.25988 | + | 2.18218i | −0.0331548 | + | 0.0574258i | ||||
\(39\) | −6.69308 | + | 11.5928i | −0.171617 | + | 0.297250i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18.8536i | 0.459844i | 0.973209 | + | 0.229922i | \(0.0738472\pi\) | ||||
−0.973209 | + | 0.229922i | \(0.926153\pi\) | |||||||
\(42\) | 9.73845 | + | 14.1125i | 0.231868 | + | 0.336012i | ||||
\(43\) | 77.4197i | 1.80046i | 0.435416 | + | 0.900229i | \(0.356601\pi\) | ||||
−0.435416 | + | 0.900229i | \(0.643399\pi\) | |||||||
\(44\) | 3.29456 | + | 5.70635i | 0.0748764 | + | 0.129690i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.77748 | + | 8.27485i | −0.103858 | + | 0.179888i | ||||
\(47\) | −6.44335 | − | 11.1602i | −0.137093 | − | 0.237451i | 0.789302 | − | 0.614005i | \(-0.210442\pi\) |
−0.926395 | + | 0.376553i | \(0.877109\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | 17.3875 | − | 45.8113i | 0.354847 | − | 0.934924i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.9280 | + | 18.9279i | 0.214275 | + | 0.371135i | ||||
\(52\) | −7.72850 | + | 13.3862i | −0.148625 | + | 0.257426i | ||||
\(53\) | 44.7631 | + | 25.8440i | 0.844586 | + | 0.487622i | 0.858821 | − | 0.512276i | \(-0.171198\pi\) |
−0.0142341 | + | 0.999899i | \(0.504531\pi\) | |||||||
\(54\) | −6.36396 | + | 3.67423i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.2450 | + | 16.2957i | 0.200804 | + | 0.290995i | ||||
\(57\) | 3.08607i | 0.0541416i | ||||||||
\(58\) | −48.1243 | + | 27.7846i | −0.829729 | + | 0.479044i | ||||
\(59\) | −97.7973 | − | 56.4633i | −1.65758 | − | 0.957005i | −0.973827 | − | 0.227292i | \(-0.927013\pi\) |
−0.683754 | − | 0.729713i | \(-0.739654\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −22.7184 | + | 13.1165i | −0.372432 | + | 0.215024i | −0.674521 | − | 0.738256i | \(-0.735650\pi\) |
0.302088 | + | 0.953280i | \(0.402316\pi\) | |||||||
\(62\) | 15.4604 | 0.249361 | ||||||||
\(63\) | 18.9713 | + | 9.00500i | 0.301132 | + | 0.142937i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.98882 | + | 4.03500i | 0.105891 | + | 0.0611363i | ||||
\(67\) | −17.2453 | − | 9.95656i | −0.257392 | − | 0.148605i | 0.365752 | − | 0.930712i | \(-0.380812\pi\) |
−0.623144 | + | 0.782107i | \(0.714145\pi\) | |||||||
\(68\) | 12.6186 | + | 21.8560i | 0.185567 | + | 0.321412i | ||||
\(69\) | 11.7024i | 0.169600i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 87.4319 | 1.23144 | 0.615718 | − | 0.787967i | \(-0.288866\pi\) | ||||
0.615718 | + | 0.787967i | \(0.288866\pi\) | |||||||
\(72\) | −7.34847 | + | 4.24264i | −0.102062 | + | 0.0589256i | ||||
\(73\) | −30.4575 | + | 52.7540i | −0.417226 | + | 0.722657i | −0.995659 | − | 0.0930727i | \(-0.970331\pi\) |
0.578433 | + | 0.815730i | \(0.303664\pi\) | |||||||
\(74\) | −24.3220 | + | 42.1270i | −0.328676 | + | 0.569284i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.56349i | 0.0468880i | ||||||||
\(77\) | −1.85274 | − | 22.9874i | −0.0240615 | − | 0.298537i | ||||
\(78\) | 18.9309i | 0.242704i | ||||||||
\(79\) | −17.7888 | − | 30.8112i | −0.225175 | − | 0.390015i | 0.731197 | − | 0.682167i | \(-0.238962\pi\) |
−0.956372 | + | 0.292152i | \(0.905629\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 13.3315 | + | 23.0909i | 0.162580 | + | 0.281596i | ||||
\(83\) | −46.6773 | −0.562377 | −0.281188 | − | 0.959653i | \(-0.590729\pi\) | ||||
−0.281188 | + | 0.959653i | \(0.590729\pi\) | |||||||
\(84\) | 21.9062 | + | 10.3981i | 0.260788 | + | 0.123787i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 54.7440 | + | 94.8194i | 0.636558 | + | 1.10255i | ||||
\(87\) | −34.0290 | + | 58.9399i | −0.391138 | + | 0.677471i | ||||
\(88\) | 8.06999 | + | 4.65921i | 0.0917044 | + | 0.0529456i | ||||
\(89\) | 47.4706 | − | 27.4072i | 0.533378 | − | 0.307946i | −0.209013 | − | 0.977913i | \(-0.567025\pi\) |
0.742391 | + | 0.669967i | \(0.233692\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 44.5270 | − | 30.7263i | 0.489308 | − | 0.337651i | ||||
\(92\) | 13.5128i | 0.146878i | ||||||||
\(93\) | 16.3982 | − | 9.46751i | 0.176325 | − | 0.101801i | ||||
\(94\) | −15.7829 | − | 9.11228i | −0.167903 | − | 0.0969391i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.48528 | + | 4.89898i | −0.0883883 | + | 0.0510310i | ||||
\(97\) | −45.7447 | −0.471595 | −0.235798 | − | 0.971802i | \(-0.575770\pi\) | ||||
−0.235798 | + | 0.971802i | \(0.575770\pi\) | |||||||
\(98\) | −11.0982 | − | 68.4020i | −0.113247 | − | 0.697979i | ||||
\(99\) | 9.88368 | 0.0998352 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 79.2589 | + | 45.7601i | 0.784741 | + | 0.453071i | 0.838108 | − | 0.545504i | \(-0.183662\pi\) |
−0.0533667 | + | 0.998575i | \(0.516995\pi\) | |||||||
\(102\) | 26.7681 | + | 15.4545i | 0.262432 | + | 0.151515i | ||||
\(103\) | −25.2541 | − | 43.7414i | −0.245186 | − | 0.424674i | 0.716998 | − | 0.697075i | \(-0.245516\pi\) |
−0.962184 | + | 0.272401i | \(0.912182\pi\) | |||||||
\(104\) | 21.8595i | 0.210188i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 73.0978 | 0.689602 | ||||||||
\(107\) | −81.3626 | + | 46.9747i | −0.760398 | + | 0.439016i | −0.829439 | − | 0.558598i | \(-0.811340\pi\) |
0.0690404 | + | 0.997614i | \(0.478006\pi\) | |||||||
\(108\) | −5.19615 | + | 9.00000i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 60.3052 | − | 104.452i | 0.553258 | − | 0.958272i | −0.444778 | − | 0.895641i | \(-0.646718\pi\) |
0.998037 | − | 0.0626310i | \(-0.0199491\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 59.5766i | 0.536726i | ||||||||
\(112\) | 25.2951 | + | 12.0067i | 0.225849 | + | 0.107202i | ||||
\(113\) | − | 10.7318i | − | 0.0949713i | −0.998872 | − | 0.0474856i | \(-0.984879\pi\) | ||
0.998872 | − | 0.0474856i | \(-0.0151208\pi\) | |||||||
\(114\) | 2.18218 | + | 3.77965i | 0.0191419 | + | 0.0331548i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −39.2933 | + | 68.0580i | −0.338735 | + | 0.586707i | ||||
\(117\) | 11.5928 | + | 20.0792i | 0.0990834 | + | 0.171617i | ||||
\(118\) | −159.702 | −1.35341 | ||||||||
\(119\) | −7.09622 | − | 88.0446i | −0.0596321 | − | 0.739870i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 55.0729 | + | 95.3891i | 0.455148 | + | 0.788340i | ||||
\(122\) | −18.5495 | + | 32.1286i | −0.152045 | + | 0.263349i | ||||
\(123\) | 28.2804 | + | 16.3277i | 0.229922 | + | 0.132746i | ||||
\(124\) | 18.9350 | − | 10.9321i | 0.152702 | − | 0.0881624i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 29.6025 | − | 2.38590i | 0.234940 | − | 0.0189357i | ||||
\(127\) | − | 117.281i | − | 0.923476i | −0.887016 | − | 0.461738i | \(-0.847226\pi\) | ||
0.887016 | − | 0.461738i | \(-0.152774\pi\) | |||||||
\(128\) | −9.79796 | + | 5.65685i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 116.130 | + | 67.0475i | 0.900229 | + | 0.519748i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 80.2758 | − | 46.3473i | 0.612792 | − | 0.353796i | −0.161265 | − | 0.986911i | \(-0.551557\pi\) |
0.774058 | + | 0.633115i | \(0.218224\pi\) | |||||||
\(132\) | 11.4127 | 0.0864598 | ||||||||
\(133\) | 5.34820 | − | 11.2673i | 0.0402120 | − | 0.0847168i | ||||
\(134\) | −28.1614 | −0.210160 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 30.9091 | + | 17.8454i | 0.227273 | + | 0.131216i | ||||
\(137\) | −23.7932 | − | 13.7370i | −0.173673 | − | 0.100270i | 0.410644 | − | 0.911796i | \(-0.365304\pi\) |
−0.584317 | + | 0.811526i | \(0.698637\pi\) | |||||||
\(138\) | 8.27485 | + | 14.3325i | 0.0599626 | + | 0.103858i | ||||
\(139\) | − | 67.0127i | − | 0.482106i | −0.970512 | − | 0.241053i | \(-0.922507\pi\) | ||
0.970512 | − | 0.241053i | \(-0.0774928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.3204 | −0.158301 | ||||||||
\(142\) | 107.082 | − | 61.8237i | 0.754097 | − | 0.435378i | ||||
\(143\) | 12.7310 | − | 22.0507i | 0.0890280 | − | 0.154201i | ||||
\(144\) | −6.00000 | + | 10.3923i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 86.1469i | 0.590047i | ||||||||
\(147\) | −53.6589 | − | 65.7550i | −0.365027 | − | 0.447313i | ||||
\(148\) | 68.7931i | 0.464818i | ||||||||
\(149\) | 25.5567 | + | 44.2656i | 0.171522 | + | 0.297084i | 0.938952 | − | 0.344048i | \(-0.111798\pi\) |
−0.767430 | + | 0.641132i | \(0.778465\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 82.6090 | − | 143.083i | 0.547079 | − | 0.947569i | −0.451394 | − | 0.892325i | \(-0.649073\pi\) |
0.998473 | − | 0.0552442i | \(-0.0175937\pi\) | |||||||
\(152\) | 2.51977 | + | 4.36436i | 0.0165774 | + | 0.0287129i | ||||
\(153\) | 37.8558 | 0.247423 | ||||||||
\(154\) | −18.5237 | − | 26.8436i | −0.120284 | − | 0.174309i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 13.3862 | + | 23.1855i | 0.0858087 | + | 0.148625i | ||||
\(157\) | −95.4059 | + | 165.248i | −0.607681 | + | 1.05253i | 0.383941 | + | 0.923358i | \(0.374567\pi\) |
−0.991622 | + | 0.129176i | \(0.958767\pi\) | |||||||
\(158\) | −43.5736 | − | 25.1572i | −0.275782 | − | 0.159223i | ||||
\(159\) | 77.5319 | − | 44.7631i | 0.487622 | − | 0.281529i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.2804 | − | 42.7258i | 0.125965 | − | 0.265377i | ||||
\(162\) | 12.7279i | 0.0785674i | ||||||||
\(163\) | −214.949 | + | 124.101i | −1.31871 | + | 0.761356i | −0.983521 | − | 0.180796i | \(-0.942133\pi\) |
−0.335186 | + | 0.942152i | \(0.608799\pi\) | |||||||
\(164\) | 32.6554 | + | 18.8536i | 0.199118 | + | 0.114961i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −57.1678 | + | 33.0058i | −0.344384 | + | 0.198830i | ||||
\(167\) | −29.2974 | −0.175433 | −0.0877167 | − | 0.996145i | \(-0.527957\pi\) | ||||
−0.0877167 | + | 0.996145i | \(0.527957\pi\) | |||||||
\(168\) | 34.1820 | − | 2.75500i | 0.203464 | − | 0.0163988i | ||||
\(169\) | −109.270 | −0.646570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.62911 | + | 2.67262i | 0.0270708 | + | 0.0156293i | ||||
\(172\) | 134.095 | + | 77.4197i | 0.779622 | + | 0.450115i | ||||
\(173\) | 11.5460 | + | 19.9982i | 0.0667397 | + | 0.115597i | 0.897464 | − | 0.441087i | \(-0.145407\pi\) |
−0.830725 | + | 0.556683i | \(0.812074\pi\) | |||||||
\(174\) | 96.2485i | 0.553152i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.1782 | 0.0748764 | ||||||||
\(177\) | −169.390 | + | 97.7973i | −0.957005 | + | 0.552527i | ||||
\(178\) | 38.7596 | − | 67.1336i | 0.217751 | − | 0.377155i | ||||
\(179\) | −104.717 | + | 181.376i | −0.585014 | + | 1.01327i | 0.409860 | + | 0.912148i | \(0.365577\pi\) |
−0.994874 | + | 0.101125i | \(0.967756\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 243.667i | − | 1.34622i | −0.739540 | − | 0.673112i | \(-0.764957\pi\) | ||
0.739540 | − | 0.673112i | \(-0.235043\pi\) | |||||||
\(182\) | 32.8075 | − | 69.1172i | 0.180261 | − | 0.379765i | ||||
\(183\) | 45.4367i | 0.248288i | ||||||||
\(184\) | 9.55497 | + | 16.5497i | 0.0519292 | + | 0.0899440i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 13.3891 | − | 23.1906i | 0.0719843 | − | 0.124681i | ||||
\(187\) | −20.7863 | − | 36.0030i | −0.111157 | − | 0.192529i | ||||
\(188\) | −25.7734 | −0.137093 | ||||||||
\(189\) | 29.9371 | − | 20.6584i | 0.158397 | − | 0.109304i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 118.423 | + | 205.114i | 0.620014 | + | 1.07390i | 0.989483 | + | 0.144653i | \(0.0462064\pi\) |
−0.369468 | + | 0.929243i | \(0.620460\pi\) | |||||||
\(192\) | −6.92820 | + | 12.0000i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −115.088 | − | 66.4460i | −0.596310 | − | 0.344280i | 0.171278 | − | 0.985223i | \(-0.445210\pi\) |
−0.767589 | + | 0.640943i | \(0.778544\pi\) | |||||||
\(194\) | −56.0256 | + | 32.3464i | −0.288792 | + | 0.166734i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −61.9600 | − | 75.9273i | −0.316122 | − | 0.387384i | ||||
\(197\) | − | 105.779i | − | 0.536950i | −0.963287 | − | 0.268475i | \(-0.913480\pi\) | ||
0.963287 | − | 0.268475i | \(-0.0865197\pi\) | |||||||
\(198\) | 12.1050 | − | 6.98882i | 0.0611363 | − | 0.0352971i | ||||
\(199\) | −174.541 | − | 100.771i | −0.877091 | − | 0.506389i | −0.00739279 | − | 0.999973i | \(-0.502353\pi\) |
−0.869698 | + | 0.493584i | \(0.835687\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.8697 | + | 17.2453i | −0.148605 | + | 0.0857973i | ||||
\(202\) | 129.429 | 0.640739 | ||||||||
\(203\) | 226.384 | − | 156.219i | 1.11519 | − | 0.769550i | ||||
\(204\) | 43.7121 | 0.214275 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −61.8597 | − | 35.7147i | −0.300290 | − | 0.173372i | ||||
\(207\) | 17.5536 | + | 10.1346i | 0.0848000 | + | 0.0489593i | ||||
\(208\) | 15.4570 | + | 26.7723i | 0.0743125 | + | 0.128713i | ||||
\(209\) | − | 5.87006i | − | 0.0280864i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 29.6045 | 0.140306 | 0.0701528 | − | 0.997536i | \(-0.477651\pi\) | ||||
0.0701528 | + | 0.997536i | \(0.477651\pi\) | |||||||
\(212\) | 89.5262 | − | 51.6880i | 0.422293 | − | 0.243811i | ||||
\(213\) | 75.7183 | − | 131.148i | 0.355485 | − | 0.615718i | ||||
\(214\) | −66.4323 | + | 115.064i | −0.310431 | + | 0.537683i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | −76.2777 | + | 6.14783i | −0.351510 | + | 0.0283310i | ||||
\(218\) | − | 170.569i | − | 0.782426i | ||||||
\(219\) | 52.7540 | + | 91.3726i | 0.240886 | + | 0.417226i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 48.7614 | − | 84.4572i | 0.220640 | − | 0.382159i | ||||
\(222\) | 42.1270 | + | 72.9661i | 0.189761 | + | 0.328676i | ||||
\(223\) | −328.532 | −1.47324 | −0.736620 | − | 0.676307i | \(-0.763579\pi\) | ||||
−0.736620 | + | 0.676307i | \(0.763579\pi\) | |||||||
\(224\) | 39.4700 | − | 3.18120i | 0.176205 | − | 0.0142018i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.58850 | − | 13.1437i | −0.0335774 | − | 0.0581578i | ||||
\(227\) | −182.228 | + | 315.628i | −0.802766 | + | 1.39043i | 0.115023 | + | 0.993363i | \(0.463306\pi\) |
−0.917789 | + | 0.397069i | \(0.870028\pi\) | |||||||
\(228\) | 5.34523 | + | 3.08607i | 0.0234440 | + | 0.0135354i | ||||
\(229\) | 260.716 | − | 150.525i | 1.13850 | − | 0.657313i | 0.192441 | − | 0.981309i | \(-0.438360\pi\) |
0.946059 | + | 0.323996i | \(0.105026\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −36.0856 | − | 17.1285i | −0.156215 | − | 0.0741496i | ||||
\(232\) | 111.138i | 0.479044i | ||||||||
\(233\) | 244.241 | − | 141.013i | 1.04824 | − | 0.605204i | 0.126087 | − | 0.992019i | \(-0.459758\pi\) |
0.922157 | + | 0.386815i | \(0.126425\pi\) | |||||||
\(234\) | 28.3963 | + | 16.3946i | 0.121352 | + | 0.0700625i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −195.595 | + | 112.927i | −0.828790 | + | 0.478502i | ||||
\(237\) | −61.6224 | −0.260010 | ||||||||
\(238\) | −70.9480 | − | 102.814i | −0.298101 | − | 0.431993i | ||||
\(239\) | −83.0347 | −0.347425 | −0.173713 | − | 0.984796i | \(-0.555576\pi\) | ||||
−0.173713 | + | 0.984796i | \(0.555576\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −287.369 | − | 165.912i | −1.19240 | − | 0.688433i | −0.233551 | − | 0.972345i | \(-0.575035\pi\) |
−0.958851 | + | 0.283911i | \(0.908368\pi\) | |||||||
\(242\) | 134.901 | + | 77.8849i | 0.557440 | + | 0.321838i | ||||
\(243\) | 7.79423 | + | 13.5000i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 52.4658i | 0.215024i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 46.1817 | 0.187731 | ||||||||
\(247\) | 11.9254 | − | 6.88511i | 0.0482808 | − | 0.0278749i | ||||
\(248\) | 15.4604 | − | 26.7782i | 0.0623403 | − | 0.107977i | ||||
\(249\) | −40.4237 | + | 70.0159i | −0.162344 | + | 0.281188i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 419.075i | − | 1.66962i | −0.550537 | − | 0.834811i | \(-0.685577\pi\) | ||
0.550537 | − | 0.834811i | \(-0.314423\pi\) | |||||||
\(252\) | 34.5684 | − | 23.8542i | 0.137176 | − | 0.0946597i | ||||
\(253\) | − | 22.2593i | − | 0.0879815i | ||||||
\(254\) | −82.9305 | − | 143.640i | −0.326498 | − | 0.565511i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −166.979 | − | 289.215i | −0.649722 | − | 1.12535i | −0.983189 | − | 0.182590i | \(-0.941552\pi\) |
0.333467 | − | 0.942762i | \(-0.391781\pi\) | |||||||
\(258\) | 189.639 | 0.735034 | ||||||||
\(259\) | 103.247 | − | 217.516i | 0.398637 | − | 0.839829i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 58.9399 | + | 102.087i | 0.225824 | + | 0.391138i | ||||
\(262\) | 65.5449 | − | 113.527i | 0.250171 | − | 0.433310i | ||||
\(263\) | 176.995 | + | 102.188i | 0.672986 | + | 0.388549i | 0.797207 | − | 0.603706i | \(-0.206310\pi\) |
−0.124221 | + | 0.992255i | \(0.539643\pi\) | |||||||
\(264\) | 13.9776 | − | 8.06999i | 0.0529456 | − | 0.0305681i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.41702 | − | 17.5814i | −0.00532715 | − | 0.0660953i | ||||
\(267\) | − | 94.9412i | − | 0.355585i | ||||||
\(268\) | −34.4905 | + | 19.9131i | −0.128696 | + | 0.0743027i | ||||
\(269\) | 120.768 | + | 69.7257i | 0.448953 | + | 0.259203i | 0.707388 | − | 0.706825i | \(-0.249873\pi\) |
−0.258435 | + | 0.966029i | \(0.583207\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −323.213 | + | 186.607i | −1.19267 | + | 0.688586i | −0.958910 | − | 0.283709i | \(-0.908435\pi\) |
−0.233756 | + | 0.972295i | \(0.575102\pi\) | |||||||
\(272\) | 50.4743 | 0.185567 | ||||||||
\(273\) | −7.52787 | − | 93.4002i | −0.0275746 | − | 0.342125i | ||||
\(274\) | −38.8542 | −0.141804 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 20.2691 | + | 11.7024i | 0.0734389 | + | 0.0424000i | ||||
\(277\) | 430.851 | + | 248.752i | 1.55542 | + | 0.898022i | 0.997685 | + | 0.0680029i | \(0.0216627\pi\) |
0.557735 | + | 0.830019i | \(0.311671\pi\) | |||||||
\(278\) | −47.3852 | − | 82.0735i | −0.170450 | − | 0.295228i | ||||
\(279\) | − | 32.7964i | − | 0.117550i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 292.779 | 1.04192 | 0.520959 | − | 0.853582i | \(-0.325574\pi\) | ||||
0.520959 | + | 0.853582i | \(0.325574\pi\) | |||||||
\(282\) | −27.3368 | + | 15.7829i | −0.0969391 | + | 0.0559678i | ||||
\(283\) | −138.383 | + | 239.686i | −0.488986 | + | 0.846949i | −0.999920 | − | 0.0126714i | \(-0.995966\pi\) |
0.510934 | + | 0.859620i | \(0.329300\pi\) | |||||||
\(284\) | 87.4319 | − | 151.437i | 0.307859 | − | 0.533227i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 36.0087i | − | 0.125905i | ||||||
\(287\) | −74.9565 | − | 108.623i | −0.261172 | − | 0.378478i | ||||
\(288\) | 16.9706i | 0.0589256i | ||||||||
\(289\) | 64.8857 | + | 112.385i | 0.224518 | + | 0.388876i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −39.6161 | + | 68.6171i | −0.136138 | + | 0.235798i | ||||
\(292\) | 60.9150 | + | 105.508i | 0.208613 | + | 0.361329i | ||||
\(293\) | 375.299 | 1.28088 | 0.640442 | − | 0.768006i | \(-0.278751\pi\) | ||||
0.640442 | + | 0.768006i | \(0.278751\pi\) | |||||||
\(294\) | −112.214 | − | 42.5905i | −0.381681 | − | 0.144866i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 48.6441 | + | 84.2540i | 0.164338 | + | 0.284642i | ||||
\(297\) | 8.55952 | − | 14.8255i | 0.0288199 | − | 0.0499176i | ||||
\(298\) | 62.6009 | + | 36.1427i | 0.210070 | + | 0.121284i | ||||
\(299\) | 45.2210 | − | 26.1084i | 0.151241 | − | 0.0873189i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −307.798 | − | 446.046i | −1.02259 | − | 1.48188i | ||||
\(302\) | − | 233.653i | − | 0.773687i | ||||||
\(303\) | 137.280 | − | 79.2589i | 0.453071 | − | 0.261580i | ||||
\(304\) | 6.17214 | + | 3.56349i | 0.0203031 | + | 0.0117220i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 46.3636 | − | 26.7681i | 0.151515 | − | 0.0874773i | ||||
\(307\) | 107.784 | 0.351088 | 0.175544 | − | 0.984472i | \(-0.443832\pi\) | ||||
0.175544 | + | 0.984472i | \(0.443832\pi\) | |||||||
\(308\) | −41.6680 | − | 19.7783i | −0.135286 | − | 0.0642154i | ||||
\(309\) | −87.4828 | −0.283116 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −499.771 | − | 288.543i | −1.60698 | − | 0.927791i | −0.990041 | − | 0.140780i | \(-0.955039\pi\) |
−0.616940 | − | 0.787010i | \(-0.711628\pi\) | |||||||
\(312\) | 32.7893 | + | 18.9309i | 0.105094 | + | 0.0606759i | ||||
\(313\) | −198.637 | − | 344.050i | −0.634624 | − | 1.09920i | −0.986595 | − | 0.163190i | \(-0.947822\pi\) |
0.351971 | − | 0.936011i | \(-0.385512\pi\) | |||||||
\(314\) | 269.849i | 0.859390i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −71.1554 | −0.225175 | ||||||||
\(317\) | 69.6026 | − | 40.1851i | 0.219566 | − | 0.126767i | −0.386183 | − | 0.922422i | \(-0.626207\pi\) |
0.605749 | + | 0.795655i | \(0.292873\pi\) | |||||||
\(318\) | 63.3046 | − | 109.647i | 0.199071 | − | 0.344801i | ||||
\(319\) | 64.7271 | − | 112.111i | 0.202906 | − | 0.351444i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 162.725i | 0.506932i | ||||||||
\(322\) | −5.37336 | − | 66.6686i | −0.0166874 | − | 0.207045i | ||||
\(323\) | − | 22.4831i | − | 0.0696071i | ||||||
\(324\) | 9.00000 | + | 15.5885i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −175.505 | + | 303.984i | −0.538360 | + | 0.932467i | ||||
\(327\) | −104.452 | − | 180.915i | −0.319424 | − | 0.553258i | ||||
\(328\) | 53.3261 | 0.162580 | ||||||||
\(329\) | 81.4925 | + | 38.6816i | 0.247698 | + | 0.117573i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −246.021 | − | 426.121i | −0.743266 | − | 1.28737i | −0.951000 | − | 0.309189i | \(-0.899942\pi\) |
0.207734 | − | 0.978185i | \(-0.433391\pi\) | |||||||
\(332\) | −46.6773 | + | 80.8474i | −0.140594 | + | 0.243516i | ||||
\(333\) | 89.3649 | + | 51.5948i | 0.268363 | + | 0.154939i | ||||
\(334\) | −35.8818 | + | 20.7164i | −0.107431 | + | 0.0620251i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 39.9162 | − | 27.5445i | 0.118798 | − | 0.0819777i | ||||
\(337\) | − | 630.123i | − | 1.86980i | −0.354910 | − | 0.934901i | \(-0.615488\pi\) | ||
0.354910 | − | 0.934901i | \(-0.384512\pi\) | |||||||
\(338\) | −133.828 | + | 77.2657i | −0.395941 | + | 0.228597i | ||||
\(339\) | −16.0976 | − | 9.29397i | −0.0474856 | − | 0.0274159i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.1913 | + | 18.0083i | −0.0914701 | + | 0.0528103i | ||||
\(342\) | 7.55930 | 0.0221032 | ||||||||
\(343\) | 81.9559 | + | 333.065i | 0.238938 | + | 0.971035i | ||||
\(344\) | 218.976 | 0.636558 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 28.2817 | + | 16.3285i | 0.0817391 | + | 0.0471921i | ||||
\(347\) | 372.514 | + | 215.071i | 1.07353 | + | 0.619802i | 0.929143 | − | 0.369720i | \(-0.120546\pi\) |
0.144385 | + | 0.989522i | \(0.453880\pi\) | |||||||
\(348\) | 68.0580 | + | 117.880i | 0.195569 | + | 0.338735i | ||||
\(349\) | 95.1819i | 0.272727i | 0.990659 | + | 0.136364i | \(0.0435416\pi\) | ||||
−0.990659 | + | 0.136364i | \(0.956458\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 40.1585 | 0.114412 | ||||||||
\(352\) | 16.1400 | − | 9.31842i | 0.0458522 | − | 0.0264728i | ||||
\(353\) | 131.469 | − | 227.710i | 0.372432 | − | 0.645071i | −0.617507 | − | 0.786565i | \(-0.711857\pi\) |
0.989939 | + | 0.141494i | \(0.0451906\pi\) | |||||||
\(354\) | −138.306 | + | 239.553i | −0.390696 | + | 0.676704i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 109.629i | − | 0.307946i | ||||||
\(357\) | −138.212 | − | 65.6045i | −0.387150 | − | 0.183766i | ||||
\(358\) | 296.186i | 0.827334i | ||||||||
\(359\) | 149.386 | + | 258.743i | 0.416116 | + | 0.720734i | 0.995545 | − | 0.0942890i | \(-0.0300578\pi\) |
−0.579429 | + | 0.815023i | \(0.696724\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −178.913 | + | 309.886i | −0.495603 | + | 0.858410i | ||||
\(362\) | −172.298 | − | 298.429i | −0.475962 | − | 0.824391i | ||||
\(363\) | 190.778 | 0.525560 | ||||||||
\(364\) | −8.69244 | − | 107.849i | −0.0238803 | − | 0.296289i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 32.1286 | + | 55.6484i | 0.0877831 | + | 0.152045i | ||||
\(367\) | 66.0380 | − | 114.381i | 0.179940 | − | 0.311665i | −0.761920 | − | 0.647671i | \(-0.775743\pi\) |
0.941860 | + | 0.336006i | \(0.109076\pi\) | |||||||
\(368\) | 23.4048 | + | 13.5128i | 0.0636000 | + | 0.0367195i | ||||
\(369\) | 48.9831 | − | 28.2804i | 0.132746 | − | 0.0766407i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −360.646 | + | 29.0674i | −0.972092 | + | 0.0783487i | ||||
\(372\) | − | 37.8701i | − | 0.101801i | ||||||
\(373\) | −9.25597 | + | 5.34394i | −0.0248149 | + | 0.0143269i | −0.512356 | − | 0.858773i | \(-0.671227\pi\) |
0.487541 | + | 0.873100i | \(0.337894\pi\) | |||||||
\(374\) | −50.9159 | − | 29.3963i | −0.136139 | − | 0.0785998i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −31.5659 | + | 18.2246i | −0.0839517 | + | 0.0484696i | ||||
\(377\) | 303.678 | 0.805513 | ||||||||
\(378\) | 22.0577 | − | 46.4700i | 0.0583536 | − | 0.122936i | ||||
\(379\) | −142.918 | −0.377092 | −0.188546 | − | 0.982064i | \(-0.560378\pi\) | ||||
−0.188546 | + | 0.982064i | \(0.560378\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −175.922 | − | 101.569i | −0.461738 | − | 0.266585i | ||||
\(382\) | 290.075 | + | 167.475i | 0.759359 | + | 0.438416i | ||||
\(383\) | 308.507 | + | 534.349i | 0.805500 | + | 1.39517i | 0.915953 | + | 0.401286i | \(0.131437\pi\) |
−0.110452 | + | 0.993881i | \(0.535230\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −187.938 | −0.486885 | ||||||||
\(387\) | 201.142 | − | 116.130i | 0.519748 | − | 0.300076i | ||||
\(388\) | −45.7447 | + | 79.2322i | −0.117899 | + | 0.204207i | ||||
\(389\) | −346.969 | + | 600.968i | −0.891951 | + | 1.54490i | −0.0544171 | + | 0.998518i | \(0.517330\pi\) |
−0.837534 | + | 0.546386i | \(0.816003\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 85.2560i | − | 0.218046i | ||||||
\(392\) | −129.574 | − | 49.1793i | −0.330546 | − | 0.125457i | ||||
\(393\) | − | 160.552i | − | 0.408528i | ||||||
\(394\) | −74.7972 | − | 129.553i | −0.189841 | − | 0.328814i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.88368 | − | 17.1190i | 0.0249588 | − | 0.0432299i | ||||
\(397\) | −279.776 | − | 484.587i | −0.704726 | − | 1.22062i | −0.966790 | − | 0.255571i | \(-0.917737\pi\) |
0.262065 | − | 0.965050i | \(-0.415597\pi\) | |||||||
\(398\) | −285.024 | −0.716142 | ||||||||
\(399\) | −12.2693 | − | 17.7801i | −0.0307502 | − | 0.0445616i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 80.6033 | + | 139.609i | 0.201006 | + | 0.348152i | 0.948853 | − | 0.315719i | \(-0.102246\pi\) |
−0.747847 | + | 0.663871i | \(0.768912\pi\) | |||||||
\(402\) | −24.3885 | + | 42.2421i | −0.0606679 | + | 0.105080i | ||||
\(403\) | −73.1697 | − | 42.2445i | −0.181563 | − | 0.104825i | ||||
\(404\) | 158.518 | − | 91.5203i | 0.392371 | − | 0.226535i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 166.800 | − | 351.406i | 0.410837 | − | 0.865532i | ||||
\(407\) | − | 113.322i | − | 0.278431i | ||||||
\(408\) | 53.5361 | − | 30.9091i | 0.131216 | − | 0.0757576i | ||||
\(409\) | −398.217 | − | 229.911i | −0.973637 | − | 0.562129i | −0.0732937 | − | 0.997310i | \(-0.523351\pi\) |
−0.900343 | + | 0.435181i | \(0.856684\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −41.2111 | + | 23.7932i | −0.100270 | + | 0.0578911i | ||||
\(412\) | −101.016 | −0.245186 | ||||||||
\(413\) | 787.931 | − | 63.5056i | 1.90782 | − | 0.153767i | ||||
\(414\) | 28.6649 | 0.0692389 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 37.8618 | + | 21.8595i | 0.0910139 | + | 0.0525469i | ||||
\(417\) | −100.519 | − | 58.0347i | −0.241053 | − | 0.139172i | ||||
\(418\) | −4.15076 | − | 7.18933i | −0.00993005 | − | 0.0171994i | ||||
\(419\) | − | 93.5818i | − | 0.223346i | −0.993745 | − | 0.111673i | \(-0.964379\pi\) | ||
0.993745 | − | 0.111673i | \(-0.0356208\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 162.957 | 0.387072 | 0.193536 | − | 0.981093i | \(-0.438004\pi\) | ||||
0.193536 | + | 0.981093i | \(0.438004\pi\) | |||||||
\(422\) | 36.2579 | − | 20.9335i | 0.0859193 | − | 0.0496055i | ||||
\(423\) | −19.3301 | + | 33.4806i | −0.0456975 | + | 0.0791504i | ||||
\(424\) | 73.0978 | − | 126.609i | 0.172400 | − | 0.298606i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 214.164i | − | 0.502731i | ||||||
\(427\) | 78.7425 | − | 165.891i | 0.184409 | − | 0.388503i | ||||
\(428\) | 187.899i | 0.439016i | ||||||||
\(429\) | −22.0507 | − | 38.1930i | −0.0514003 | − | 0.0890280i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 165.543 | − | 286.728i | 0.384090 | − | 0.665263i | −0.607553 | − | 0.794279i | \(-0.707849\pi\) |
0.991642 | + | 0.129016i | \(0.0411820\pi\) | |||||||
\(432\) | 10.3923 | + | 18.0000i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −88.4130 | −0.204187 | −0.102094 | − | 0.994775i | \(-0.532554\pi\) | ||||
−0.102094 | + | 0.994775i | \(0.532554\pi\) | |||||||
\(434\) | −89.0735 | + | 61.4660i | −0.205238 | + | 0.141627i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −120.610 | − | 208.903i | −0.276629 | − | 0.479136i | ||||
\(437\) | 6.01907 | − | 10.4253i | 0.0137736 | − | 0.0238566i | ||||
\(438\) | 129.220 | + | 74.6054i | 0.295024 | + | 0.170332i | ||||
\(439\) | 60.4608 | − | 34.9070i | 0.137724 | − | 0.0795149i | −0.429555 | − | 0.903041i | \(-0.641330\pi\) |
0.567279 | + | 0.823526i | \(0.307996\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −145.102 | + | 23.5429i | −0.329031 | + | 0.0533852i | ||||
\(442\) | − | 137.918i | − | 0.312032i | ||||||
\(443\) | −571.953 | + | 330.217i | −1.29109 | + | 0.745411i | −0.978847 | − | 0.204592i | \(-0.934413\pi\) |
−0.312242 | + | 0.950003i | \(0.601080\pi\) | |||||||
\(444\) | 103.190 | + | 59.5766i | 0.232409 | + | 0.134182i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −402.368 | + | 232.307i | −0.902171 | + | 0.520869i | ||||
\(447\) | 88.5311 | 0.198056 | ||||||||
\(448\) | 46.0912 | − | 31.8057i | 0.102882 | − | 0.0709948i | ||||
\(449\) | 560.274 | 1.24783 | 0.623913 | − | 0.781493i | \(-0.285542\pi\) | ||||
0.623913 | + | 0.781493i | \(0.285542\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −53.7926 | − | 31.0572i | −0.119274 | − | 0.0688629i | ||||
\(452\) | −18.5879 | − | 10.7318i | −0.0411238 | − | 0.0237428i | ||||
\(453\) | −143.083 | − | 247.827i | −0.315856 | − | 0.547079i | ||||
\(454\) | 515.418i | 1.13528i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.72873 | 0.0191419 | ||||||||
\(457\) | 159.158 | − | 91.8900i | 0.348267 | − | 0.201072i | −0.315655 | − | 0.948874i | \(-0.602224\pi\) |
0.663922 | + | 0.747802i | \(0.268891\pi\) | |||||||
\(458\) | 212.874 | − | 368.709i | 0.464790 | − | 0.805041i | ||||
\(459\) | 32.7840 | − | 56.7836i | 0.0714249 | − | 0.123712i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.4330i | 0.0616767i | 0.999524 | + | 0.0308384i | \(0.00981771\pi\) | ||||
−0.999524 | + | 0.0308384i | \(0.990182\pi\) | |||||||
\(462\) | −56.3073 | + | 4.53826i | −0.121877 | + | 0.00982307i | ||||
\(463\) | 269.931i | 0.583005i | 0.956570 | + | 0.291503i | \(0.0941552\pi\) | ||||
−0.956570 | + | 0.291503i | \(0.905845\pi\) | |||||||
\(464\) | 78.5866 | + | 136.116i | 0.169368 | + | 0.293353i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 199.422 | − | 345.409i | 0.427944 | − | 0.741221i | ||||
\(467\) | 167.166 | + | 289.539i | 0.357956 | + | 0.619999i | 0.987619 | − | 0.156870i | \(-0.0501403\pi\) |
−0.629663 | + | 0.776868i | \(0.716807\pi\) | |||||||
\(468\) | 46.3710 | 0.0990834 | ||||||||
\(469\) | 138.941 | − | 11.1984i | 0.296250 | − | 0.0238772i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 165.248 | + | 286.218i | 0.350845 | + | 0.607681i | ||||
\(472\) | −159.702 | + | 276.612i | −0.338352 | + | 0.586043i | ||||
\(473\) | −220.892 | − | 127.532i | −0.467002 | − | 0.269624i | ||||
\(474\) | −75.4717 | + | 43.5736i | −0.159223 | + | 0.0919274i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −159.594 | − | 75.7536i | −0.335281 | − | 0.159146i | ||||
\(477\) | − | 155.064i | − | 0.325081i | ||||||
\(478\) | −101.696 | + | 58.7144i | −0.212754 | + | 0.122833i | ||||
\(479\) | −114.560 | − | 66.1412i | −0.239165 | − | 0.138082i | 0.375628 | − | 0.926771i | \(-0.377427\pi\) |
−0.614793 | + | 0.788689i | \(0.710760\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 230.219 | − | 132.917i | 0.478626 | − | 0.276335i | ||||
\(482\) | −469.271 | −0.973592 | ||||||||
\(483\) | −46.5253 | − | 67.4222i | −0.0963257 | − | 0.139591i | ||||
\(484\) | 220.292 | 0.455148 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.0919 | + | 11.0227i | 0.0392837 | + | 0.0226805i | ||||
\(487\) | 447.970 | + | 258.635i | 0.919856 | + | 0.531079i | 0.883589 | − | 0.468263i | \(-0.155120\pi\) |
0.0362667 | + | 0.999342i | \(0.488453\pi\) | |||||||
\(488\) | 37.0989 | + | 64.2573i | 0.0760224 | + | 0.131675i | ||||
\(489\) | 429.898i | 0.879138i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 484.805 | 0.987383 | 0.493692 | − | 0.869637i | \(-0.335647\pi\) | ||||
0.493692 | + | 0.869637i | \(0.335647\pi\) | |||||||
\(492\) | 56.5609 | − | 32.6554i | 0.114961 | − | 0.0663728i | ||||
\(493\) | 247.913 | − | 429.398i | 0.502866 | − | 0.870989i | ||||
\(494\) | 9.73701 | − | 16.8650i | 0.0197105 | − | 0.0341397i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 43.7286i | − | 0.0881624i | ||||||
\(497\) | −503.730 | + | 347.604i | −1.01354 | + | 0.699404i | ||||
\(498\) | 114.336i | 0.229589i | ||||||||
\(499\) | −64.6450 | − | 111.968i | −0.129549 | − | 0.224385i | 0.793953 | − | 0.607979i | \(-0.208020\pi\) |
−0.923502 | + | 0.383594i | \(0.874686\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.3723 | + | 43.9461i | −0.0506432 | + | 0.0877167i | ||||
\(502\) | −296.331 | − | 513.260i | −0.590300 | − | 1.02243i | ||||
\(503\) | −160.905 | −0.319890 | −0.159945 | − | 0.987126i | \(-0.551132\pi\) | ||||
−0.159945 | + | 0.987126i | \(0.551132\pi\) | |||||||
\(504\) | 25.4700 | − | 53.6589i | 0.0505357 | − | 0.106466i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.7397 | − | 27.2620i | −0.0311061 | − | 0.0538774i | ||||
\(507\) | −94.6308 | + | 163.905i | −0.186649 | + | 0.323285i | ||||
\(508\) | −203.137 | − | 117.281i | −0.399877 | − | 0.230869i | ||||
\(509\) | 320.453 | − | 185.014i | 0.629575 | − | 0.363485i | −0.151013 | − | 0.988532i | \(-0.548253\pi\) |
0.780587 | + | 0.625047i | \(0.214920\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.2563 | − | 425.027i | −0.0670378 | − | 0.831755i | ||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 8.01785 | − | 4.62911i | 0.0156293 | − | 0.00902360i | ||||
\(514\) | −409.012 | − | 236.143i | −0.795744 | − | 0.459423i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 232.259 | − | 134.095i | 0.450115 | − | 0.259874i | ||||
\(517\) | 42.4560 | 0.0821200 | ||||||||
\(518\) | −27.3556 | − | 339.408i | −0.0528101 | − | 0.655228i | ||||
\(519\) | 39.9964 | 0.0770644 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 65.1395 | + | 37.6083i | 0.125028 | + | 0.0721849i | 0.561210 | − | 0.827674i | \(-0.310336\pi\) |
−0.436182 | + | 0.899859i | \(0.643670\pi\) | |||||||
\(522\) | 144.373 | + | 83.3537i | 0.276576 | + | 0.159681i | ||||
\(523\) | −468.058 | − | 810.701i | −0.894949 | − | 1.55010i | −0.833867 | − | 0.551965i | \(-0.813878\pi\) |
−0.0610819 | − | 0.998133i | \(-0.519455\pi\) | |||||||
\(524\) | − | 185.389i | − | 0.353796i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 289.032 | 0.549491 | ||||||||
\(527\) | −119.467 | + | 68.9741i | −0.226692 | + | 0.130881i | ||||
\(528\) | 11.4127 | − | 19.7674i | 0.0216149 | − | 0.0374382i | ||||
\(529\) | −241.676 | + | 418.594i | −0.456854 | + | 0.791294i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 338.780i | 0.638003i | ||||||||
\(532\) | −14.1674 | − | 20.5307i | −0.0266304 | − | 0.0385915i | ||||
\(533\) | − | 145.710i | − | 0.273377i | ||||||
\(534\) | −67.1336 | − | 116.279i | −0.125718 | − | 0.217751i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −28.1614 | + | 48.7770i | −0.0525399 | + | 0.0910018i | ||||
\(537\) | 181.376 | + | 314.152i | 0.337758 | + | 0.585014i | ||||
\(538\) | 197.214 | 0.366569 | ||||||||
\(539\) | 102.065 | + | 125.074i | 0.189361 | + | 0.232047i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 304.692 | + | 527.742i | 0.563201 | + | 0.975493i | 0.997215 | + | 0.0745867i | \(0.0237638\pi\) |
−0.434013 | + | 0.900906i | \(0.642903\pi\) | |||||||
\(542\) | −263.902 | + | 457.092i | −0.486904 | + | 0.843343i | ||||
\(543\) | −365.500 | − | 211.021i | −0.673112 | − | 0.388622i | ||||
\(544\) | 61.8182 | − | 35.6907i | 0.113636 | − | 0.0656080i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −75.2637 | − | 109.068i | −0.137846 | − | 0.199759i | ||||
\(547\) | − | 491.361i | − | 0.898283i | −0.893461 | − | 0.449141i | \(-0.851730\pi\) | ||
0.893461 | − | 0.449141i | \(-0.148270\pi\) | |||||||
\(548\) | −47.5865 | + | 27.4741i | −0.0868366 | + | 0.0501351i | ||||
\(549\) | 68.1551 | + | 39.3494i | 0.124144 | + | 0.0716746i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 60.6310 | − | 35.0053i | 0.110038 | − | 0.0635305i | ||||
\(552\) | 33.0994 | 0.0599626 | ||||||||
\(553\) | 224.985 | + | 106.792i | 0.406844 | + | 0.193115i | ||||
\(554\) | 703.577 | 1.27000 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −116.069 | − | 67.0127i | −0.208758 | − | 0.120527i | ||||
\(557\) | 911.250 | + | 526.110i | 1.63600 | + | 0.944543i | 0.982192 | + | 0.187878i | \(0.0601610\pi\) |
0.653803 | + | 0.756665i | \(0.273172\pi\) | |||||||
\(558\) | −23.1906 | − | 40.1673i | −0.0415602 | − | 0.0719843i | ||||
\(559\) | − | 598.339i | − | 1.07037i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −72.0060 | −0.128353 | ||||||||
\(562\) | 358.580 | − | 207.026i | 0.638042 | − | 0.368374i | ||||
\(563\) | −387.269 | + | 670.769i | −0.687866 | + | 1.19142i | 0.284661 | + | 0.958628i | \(0.408119\pi\) |
−0.972527 | + | 0.232791i | \(0.925214\pi\) | |||||||
\(564\) | −22.3204 | + | 38.6601i | −0.0395752 | + | 0.0685463i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 391.406i | 0.691531i | ||||||||
\(567\) | −5.06126 | − | 62.7964i | −0.00892639 | − | 0.110752i | ||||
\(568\) | − | 247.295i | − | 0.435378i | ||||||
\(569\) | 156.525 | + | 271.109i | 0.275088 | + | 0.476466i | 0.970157 | − | 0.242477i | \(-0.0779598\pi\) |
−0.695070 | + | 0.718942i | \(0.744626\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −324.711 | + | 562.416i | −0.568670 | + | 0.984966i | 0.428027 | + | 0.903766i | \(0.359209\pi\) |
−0.996698 | + | 0.0812002i | \(0.974125\pi\) | |||||||
\(572\) | −25.4620 | − | 44.1015i | −0.0445140 | − | 0.0771005i | ||||
\(573\) | 410.228 | 0.715931 | ||||||||
\(574\) | −168.611 | − | 80.0336i | −0.293747 | − | 0.139431i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −514.893 | + | 891.822i | −0.892363 | + | 1.54562i | −0.0553284 | + | 0.998468i | \(0.517621\pi\) |
−0.837035 | + | 0.547150i | \(0.815713\pi\) | |||||||
\(578\) | 158.937 | + | 91.7622i | 0.274977 | + | 0.158758i | ||||
\(579\) | −199.338 | + | 115.088i | −0.344280 | + | 0.198770i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 268.927 | − | 185.575i | 0.462868 | − | 0.319406i | ||||
\(582\) | 112.051i | 0.192528i | ||||||||
\(583\) | −147.475 | + | 85.1445i | −0.252958 | + | 0.146046i | ||||
\(584\) | 149.211 | + | 86.1469i | 0.255498 | + | 0.147512i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 459.646 | − | 265.376i | 0.784378 | − | 0.452861i | ||||
\(587\) | 791.817 | 1.34892 | 0.674461 | − | 0.738311i | \(-0.264376\pi\) | ||||
0.674461 | + | 0.738311i | \(0.264376\pi\) | |||||||
\(588\) | −167.550 | + | 27.1850i | −0.284949 | + | 0.0462329i | ||||
\(589\) | −19.4783 | −0.0330701 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −158.669 | − | 91.6075i | −0.268475 | − | 0.155004i | ||||
\(592\) | 119.153 | + | 68.7931i | 0.201272 | + | 0.116205i | ||||
\(593\) | 42.2509 | + | 73.1807i | 0.0712494 | + | 0.123408i | 0.899449 | − | 0.437025i | \(-0.143968\pi\) |
−0.828200 | + | 0.560433i | \(0.810635\pi\) | |||||||
\(594\) | − | 24.2100i | − | 0.0407575i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 102.227 | 0.171522 | ||||||||
\(597\) | −302.314 | + | 174.541i | −0.506389 | + | 0.292364i | ||||
\(598\) | 36.9228 | − | 63.9522i | 0.0617438 | − | 0.106943i | ||||
\(599\) | −233.463 | + | 404.369i | −0.389754 | + | 0.675074i | −0.992416 | − | 0.122922i | \(-0.960773\pi\) |
0.602662 | + | 0.797997i | \(0.294107\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1095.93i | 1.82351i | 0.410733 | + | 0.911756i | \(0.365273\pi\) | ||||
−0.410733 | + | 0.911756i | \(0.634727\pi\) | |||||||
\(602\) | −692.377 | − | 328.647i | −1.15013 | − | 0.545925i | ||||
\(603\) | 59.7394i | 0.0990702i | ||||||||
\(604\) | −165.218 | − | 286.166i | −0.273540 | − | 0.473785i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 112.089 | − | 194.144i | 0.184965 | − | 0.320369i | ||||
\(607\) | −179.449 | − | 310.815i | −0.295633 | − | 0.512051i | 0.679499 | − | 0.733676i | \(-0.262197\pi\) |
−0.975132 | + | 0.221625i | \(0.928864\pi\) | |||||||
\(608\) | 10.0791 | 0.0165774 | ||||||||
\(609\) | −38.2733 | − | 474.866i | −0.0628461 | − | 0.779747i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 49.7975 | + | 86.2517i | 0.0815016 | + | 0.141165i | ||||
\(612\) | 37.8558 | − | 65.5681i | 0.0618558 | − | 0.107137i | ||||
\(613\) | −400.154 | − | 231.029i | −0.652780 | − | 0.376883i | 0.136741 | − | 0.990607i | \(-0.456337\pi\) |
−0.789520 | + | 0.613724i | \(0.789671\pi\) | |||||||
\(614\) | 132.008 | − | 76.2148i | 0.214996 | − | 0.124128i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −65.0181 | + | 5.24033i | −0.105549 | + | 0.00850703i | ||||
\(617\) | 219.440i | 0.355656i | 0.984062 | + | 0.177828i | \(0.0569071\pi\) | ||||
−0.984062 | + | 0.177828i | \(0.943093\pi\) | |||||||
\(618\) | −107.144 | + | 61.8597i | −0.173372 | + | 0.100097i | ||||
\(619\) | −832.792 | − | 480.813i | −1.34538 | − | 0.776757i | −0.357791 | − | 0.933802i | \(-0.616470\pi\) |
−0.987592 | + | 0.157044i | \(0.949803\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.4037 | − | 17.5536i | 0.0489593 | − | 0.0282667i | ||||
\(622\) | −816.123 | −1.31209 | ||||||||
\(623\) | −164.534 | + | 346.633i | −0.264100 | + | 0.556393i | ||||
\(624\) | 53.5446 | 0.0858087 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −486.560 | − | 280.915i | −0.777252 | − | 0.448747i | ||||
\(627\) | −8.80509 | − | 5.08362i | −0.0140432 | − | 0.00810785i | ||||
\(628\) | 190.812 | + | 330.496i | 0.303840 | + | 0.526267i | ||||
\(629\) | − | 434.036i | − | 0.690041i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 584.721 | 0.926658 | 0.463329 | − | 0.886186i | \(-0.346655\pi\) | ||||
0.463329 | + | 0.886186i | \(0.346655\pi\) | |||||||
\(632\) | −87.1472 | + | 50.3144i | −0.137891 | + | 0.0796115i | ||||
\(633\) | 25.6382 | − | 44.4067i | 0.0405027 | − | 0.0701528i | ||||
\(634\) | 56.8303 | − | 98.4329i | 0.0896376 | − | 0.155257i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 179.052i | − | 0.281529i | ||||||
\(637\) | −134.379 | + | 354.053i | −0.210957 | + | 0.555813i | ||||
\(638\) | − | 183.076i | − | 0.286953i | ||||||
\(639\) | −131.148 | − | 227.155i | −0.205239 | − | 0.355485i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −269.518 | + | 466.819i | −0.420465 | + | 0.728268i | −0.995985 | − | 0.0895205i | \(-0.971467\pi\) |
0.575520 | + | 0.817788i | \(0.304800\pi\) | |||||||
\(642\) | 115.064 | + | 199.297i | 0.179228 | + | 0.310431i | ||||
\(643\) | 150.959 | 0.234773 | 0.117386 | − | 0.993086i | \(-0.462548\pi\) | ||||
0.117386 | + | 0.993086i | \(0.462548\pi\) | |||||||
\(644\) | −53.7228 | − | 77.8525i | −0.0834205 | − | 0.120889i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.8979 | − | 27.5360i | −0.0246098 | − | 0.0426255i | ||||
\(647\) | −225.808 | + | 391.111i | −0.349008 | + | 0.604499i | −0.986073 | − | 0.166310i | \(-0.946815\pi\) |
0.637066 | + | 0.770809i | \(0.280148\pi\) | |||||||
\(648\) | 22.0454 | + | 12.7279i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | 322.199 | − | 186.022i | 0.496454 | − | 0.286628i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −56.8366 | + | 119.741i | −0.0873067 | + | 0.183933i | ||||
\(652\) | 496.404i | 0.761356i | ||||||||
\(653\) | −373.860 | + | 215.848i | −0.572526 | + | 0.330548i | −0.758158 | − | 0.652071i | \(-0.773900\pi\) |
0.185631 | + | 0.982619i | \(0.440567\pi\) | |||||||
\(654\) | −255.853 | − | 147.717i | −0.391213 | − | 0.225867i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 65.3108 | − | 37.7072i | 0.0995592 | − | 0.0574805i | ||||
\(657\) | 182.745 | 0.278151 | ||||||||
\(658\) | 127.160 | − | 10.2488i | 0.193252 | − | 0.0155757i | ||||
\(659\) | 195.185 | 0.296184 | 0.148092 | − | 0.988974i | \(-0.452687\pi\) | ||||
0.148092 | + | 0.988974i | \(0.452687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 596.305 | + | 344.277i | 0.902126 | + | 0.520843i | 0.877889 | − | 0.478863i | \(-0.158951\pi\) |
0.0242368 | + | 0.999706i | \(0.492284\pi\) | |||||||
\(662\) | −602.626 | − | 347.926i | −0.910311 | − | 0.525569i | ||||
\(663\) | −84.4572 | − | 146.284i | −0.127386 | − | 0.220640i | ||||
\(664\) | 132.023i | 0.198830i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 145.932 | 0.219118 | ||||||||
\(667\) | 229.913 | − | 132.740i | 0.344697 | − | 0.199011i | ||||
\(668\) | −29.2974 | + | 50.7445i | −0.0438583 | + | 0.0759649i | ||||
\(669\) | −284.517 | + | 492.799i | −0.425288 | + | 0.736620i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 86.4259i | − | 0.128802i | ||||||
\(672\) | 29.4102 | − | 61.9600i | 0.0437652 | − | 0.0922024i | ||||
\(673\) | − | 200.020i | − | 0.297206i | −0.988897 | − | 0.148603i | \(-0.952522\pi\) | ||
0.988897 | − | 0.148603i | \(-0.0474777\pi\) | |||||||
\(674\) | −445.564 | − | 771.740i | −0.661075 | − | 1.14501i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −109.270 | + | 189.262i | −0.161642 | + | 0.279973i | ||||
\(677\) | 424.807 | + | 735.787i | 0.627484 | + | 1.08683i | 0.988055 | + | 0.154103i | \(0.0492486\pi\) |
−0.360571 | + | 0.932732i | \(0.617418\pi\) | |||||||
\(678\) | −26.2873 | −0.0387719 | ||||||||
\(679\) | 263.554 | − | 181.868i | 0.388150 | − | 0.267846i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 315.628 | + | 546.684i | 0.463477 | + | 0.802766i | ||||
\(682\) | −25.4676 | + | 44.1111i | −0.0373425 | + | 0.0646791i | ||||
\(683\) | −387.988 | − | 224.005i | −0.568064 | − | 0.327972i | 0.188311 | − | 0.982109i | \(-0.439699\pi\) |
−0.756376 | + | 0.654137i | \(0.773032\pi\) | |||||||
\(684\) | 9.25821 | − | 5.34523i | 0.0135354 | − | 0.00781467i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 335.888 | + | 349.968i | 0.489632 | + | 0.510157i | ||||
\(687\) | − | 521.433i | − | 0.759000i | ||||||
\(688\) | 268.190 | − | 154.839i | 0.389811 | − | 0.225057i | ||||
\(689\) | −345.952 | − | 199.735i | −0.502107 | − | 0.289891i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −337.930 | + | 195.104i | −0.489044 | + | 0.282350i | −0.724178 | − | 0.689613i | \(-0.757781\pi\) |
0.235134 | + | 0.971963i | \(0.424447\pi\) | |||||||
\(692\) | 46.1839 | 0.0667397 | ||||||||
\(693\) | −56.9439 | + | 39.2946i | −0.0821701 | + | 0.0567022i | ||||
\(694\) | 608.313 | 0.876532 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 166.707 | + | 96.2485i | 0.239522 | + | 0.138288i | ||||
\(697\) | −206.033 | − | 118.953i | −0.295599 | − | 0.170664i | ||||
\(698\) | 67.3038 | + | 116.574i | 0.0964237 | + | 0.167011i | ||||
\(699\) | − | 488.482i | − | 0.698830i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 989.018 | 1.41087 | 0.705434 | − | 0.708776i | \(-0.250752\pi\) | ||||
0.705434 | + | 0.708776i | \(0.250752\pi\) | |||||||
\(702\) | 49.1839 | − | 28.3963i | 0.0700625 | − | 0.0404506i | ||||
\(703\) | 30.6429 | − | 53.0751i | 0.0435888 | − | 0.0754980i | ||||
\(704\) | 13.1782 | − | 22.8254i | 0.0187191 | − | 0.0324224i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 371.849i | − | 0.526699i | ||||||
\(707\) | −638.571 | + | 51.4676i | −0.903212 | + | 0.0727971i | ||||
\(708\) | 391.189i | 0.552527i | ||||||||
\(709\) | 554.927 | + | 961.161i | 0.782689 | + | 1.35566i | 0.930370 | + | 0.366623i | \(0.119486\pi\) |
−0.147680 | + | 0.989035i | \(0.547181\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −53.3665 | + | 92.4335i | −0.0750584 | + | 0.130005i | ||||
\(712\) | −77.5192 | − | 134.267i | −0.108875 | − | 0.188578i | ||||
\(713\) | −73.8617 | −0.103593 | ||||||||
\(714\) | −215.664 | + | 17.3821i | −0.302051 | + | 0.0243447i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 209.435 | + | 362.752i | 0.292507 | + | 0.506637i | ||||
\(717\) | −71.9101 | + | 124.552i | −0.100293 | + | 0.173713i | ||||
\(718\) | 365.918 | + | 211.263i | 0.509636 | + | 0.294238i | ||||
\(719\) | −936.393 | + | 540.627i | −1.30235 | + | 0.751915i | −0.980807 | − | 0.194979i | \(-0.937536\pi\) |
−0.321547 | + | 0.946894i | \(0.604203\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 319.402 | + | 151.609i | 0.442999 | + | 0.210276i | ||||
\(722\) | 506.042i | 0.700889i | ||||||||
\(723\) | −497.737 | + | 287.369i | −0.688433 | + | 0.397467i | ||||
\(724\) | −422.043 | − | 243.667i | −0.582932 | − | 0.336556i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 233.655 | − | 134.901i | 0.321838 | − | 0.185813i | ||||
\(727\) | 491.493 | 0.676056 | 0.338028 | − | 0.941136i | \(-0.390240\pi\) | ||||
0.338028 | + | 0.941136i | \(0.390240\pi\) | |||||||
\(728\) | −86.9070 | − | 125.941i | −0.119378 | − | 0.172996i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −846.044 | − | 488.464i | −1.15738 | − | 0.668213i | ||||
\(732\) | 78.6988 | + | 45.4367i | 0.107512 | + | 0.0620721i | ||||
\(733\) | 23.3826 | + | 40.4999i | 0.0318999 | + | 0.0552522i | 0.881535 | − | 0.472119i | \(-0.156511\pi\) |
−0.849635 | + | 0.527372i | \(0.823178\pi\) | |||||||
\(734\) | − | 186.784i | − | 0.254474i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 38.2199 | 0.0519292 | ||||||||
\(737\) | 56.8156 | − | 32.8025i | 0.0770903 | − | 0.0445081i | ||||
\(738\) | 39.9946 | − | 69.2726i | 0.0541932 | − | 0.0938653i | ||||
\(739\) | −368.856 | + | 638.878i | −0.499129 | + | 0.864517i | −0.999999 | − | 0.00100544i | \(-0.999680\pi\) |
0.500870 | + | 0.865522i | \(0.333013\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 23.8507i | − | 0.0321872i | ||||||
\(742\) | −421.146 | + | 290.615i | −0.567582 | + | 0.391665i | ||||
\(743\) | 258.593i | 0.348039i | 0.984742 | + | 0.174020i | \(0.0556757\pi\) | ||||
−0.984742 | + | 0.174020i | \(0.944324\pi\) | |||||||
\(744\) | −26.7782 | − | 46.3812i | −0.0359922 | − | 0.0623403i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.55747 | + | 13.0899i | −0.0101307 | + | 0.0175468i | ||||
\(747\) | 70.0159 | + | 121.271i | 0.0937295 | + | 0.162344i | ||||
\(748\) | −83.1454 | −0.111157 | ||||||||
\(749\) | 282.005 | − | 594.114i | 0.376509 | − | 0.793210i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −175.310 | − | 303.645i | −0.233435 | − | 0.404321i | 0.725382 | − | 0.688347i | \(-0.241663\pi\) |
−0.958817 | + | 0.284025i | \(0.908330\pi\) | |||||||
\(752\) | −25.7734 | + | 44.6409i | −0.0342731 | + | 0.0593628i | ||||
\(753\) | −628.613 | − | 362.930i | −0.834811 | − | 0.481978i | ||||
\(754\) | 371.928 | − | 214.733i | 0.493274 | − | 0.284792i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.84424 | − | 72.5110i | −0.00773048 | − | 0.0959140i | ||||
\(757\) | 907.187i | 1.19840i | 0.800600 | + | 0.599199i | \(0.204514\pi\) | ||||
−0.800600 | + | 0.599199i | \(0.795486\pi\) | |||||||
\(758\) | −175.038 | + | 101.058i | −0.230921 | + | 0.133322i | ||||
\(759\) | −33.3890 | − | 19.2771i | −0.0439907 | − | 0.0253981i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1067.66 | − | 616.416i | 1.40297 | − | 0.810007i | 0.408277 | − | 0.912858i | \(-0.366130\pi\) |
0.994697 | + | 0.102851i | \(0.0327965\pi\) | |||||||
\(762\) | −287.280 | −0.377008 | ||||||||
\(763\) | 67.8267 | + | 841.543i | 0.0888948 | + | 1.10294i | ||||
\(764\) | 473.691 | 0.620014 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 755.684 | + | 436.294i | 0.986532 | + | 0.569575i | ||||
\(767\) | 755.826 | + | 436.376i | 0.985432 | + | 0.568939i | ||||
\(768\) | 13.8564 | + | 24.0000i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 685.828i | 0.891844i | 0.895072 | + | 0.445922i | \(0.147124\pi\) | ||||
−0.895072 | + | 0.445922i | \(0.852876\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −578.431 | −0.750235 | ||||||||
\(772\) | −230.176 | + | 132.892i | −0.298155 | + | 0.172140i | ||||
\(773\) | 193.077 | − | 334.420i | 0.249776 | − | 0.432625i | −0.713687 | − | 0.700465i | \(-0.752976\pi\) |
0.963464 | + | 0.267839i | \(0.0863095\pi\) | |||||||
\(774\) | 164.232 | − | 284.458i | 0.212186 | − | 0.367517i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 129.386i | 0.166734i | ||||||||
\(777\) | −236.859 | − | 343.245i | −0.304838 | − | 0.441756i | ||||
\(778\) | 981.376i | 1.26141i | ||||||||
\(779\) | −16.7962 | − | 29.0918i | −0.0215612 | − | 0.0373451i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −144.025 | + | 249.458i | −0.184411 | + | 0.319409i | ||||
\(782\) | −60.2851 | − | 104.417i | −0.0770909 | − | 0.133525i | ||||
\(783\) | 204.174 | 0.260759 | ||||||||
\(784\) | −193.470 | + | 31.3905i | −0.246773 | + | 0.0400389i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −113.527 | − | 196.635i | −0.144437 | − | 0.250171i | ||||
\(787\) | −614.543 | + | 1064.42i | −0.780867 | + | 1.35250i | 0.150570 | + | 0.988599i | \(0.451889\pi\) |
−0.931437 | + | 0.363902i | \(0.881444\pi\) | |||||||
\(788\) | −183.215 | − | 105.779i | −0.232506 | − | 0.134238i | ||||
\(789\) | 306.565 | − | 176.995i | 0.388549 | − | 0.224329i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.6663 | + | 61.8300i | 0.0539397 | + | 0.0781668i | ||||
\(792\) | − | 27.9553i | − | 0.0352971i | ||||||
\(793\) | 175.579 | − | 101.371i | 0.221411 | − | 0.127832i | ||||
\(794\) | −685.309 | − | 395.663i | −0.863109 | − | 0.498316i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −349.082 | + | 201.543i | −0.438545 | + | 0.253194i | ||||
\(797\) | 821.718 | 1.03101 | 0.515507 | − | 0.856886i | \(-0.327604\pi\) | ||||
0.515507 | + | 0.856886i | \(0.327604\pi\) | |||||||
\(798\) | −27.5992 | − | 13.1004i | −0.0345855 | − | 0.0164165i | ||||
\(799\) | 162.612 | 0.203519 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −142.412 | − | 82.2215i | −0.177793 | − | 0.102649i | ||||
\(802\) | 197.437 | + | 113.990i | 0.246181 | + | 0.142132i | ||||
\(803\) | −100.344 | − | 173.801i | −0.124962 | − | 0.216440i | ||||
\(804\) | 68.9811i | 0.0857973i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −119.486 | −0.148245 | ||||||||
\(807\) | 209.177 | − | 120.768i | 0.259203 | − | 0.149651i | ||||
\(808\) | 129.429 | − | 224.178i | 0.160185 | − | 0.277448i | ||||
\(809\) | −216.809 | + | 375.524i | −0.267996 | + | 0.464184i | −0.968344 | − | 0.249618i | \(-0.919695\pi\) |
0.700348 | + | 0.713802i | \(0.253028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1618.04i | 1.99512i | 0.0698416 | + | 0.997558i | \(0.477751\pi\) | ||||
−0.0698416 | + | 0.997558i | \(0.522249\pi\) | |||||||
\(812\) | −44.1941 | − | 548.328i | −0.0544263 | − | 0.675281i | ||||
\(813\) | 646.425i | 0.795111i | ||||||||
\(814\) | −80.1304 | − | 138.790i | −0.0984403 | − | 0.170504i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 43.7121 | − | 75.7115i | 0.0535687 | − | 0.0927837i | ||||
\(817\) | −68.9711 | − | 119.461i | −0.0844199 | − | 0.146220i | ||||
\(818\) | −650.286 | −0.794971 | ||||||||
\(819\) | −146.620 | − | 69.5952i | −0.179023 | − | 0.0849758i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 429.043 | + | 743.125i | 0.522586 | + | 0.905146i | 0.999655 | + | 0.0262799i | \(0.00836612\pi\) |
−0.477068 | + | 0.878866i | \(0.658301\pi\) | |||||||
\(822\) | −33.6487 | + | 58.2813i | −0.0409352 | + | 0.0709018i | ||||
\(823\) | −679.461 | − | 392.287i | −0.825591 | − | 0.476655i | 0.0267498 | − | 0.999642i | \(-0.491484\pi\) |
−0.852341 | + | 0.522987i | \(0.824818\pi\) | |||||||
\(824\) | −123.719 | + | 71.4294i | −0.150145 | + | 0.0866862i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 920.109 | − | 634.929i | 1.11393 | − | 0.768680i | ||||
\(827\) | − | 773.795i | − | 0.935665i | −0.883817 | − | 0.467833i | \(-0.845035\pi\) | ||
0.883817 | − | 0.467833i | \(-0.154965\pi\) | |||||||
\(828\) | 35.1072 | − | 20.2691i | 0.0424000 | − | 0.0244796i | ||||
\(829\) | 573.640 | + | 331.191i | 0.691966 | + | 0.399507i | 0.804348 | − | 0.594158i | \(-0.202515\pi\) |
−0.112382 | + | 0.993665i | \(0.535848\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 746.256 | − | 430.851i | 0.898022 | − | 0.518473i | ||||
\(832\) | 61.8280 | 0.0743125 | ||||||||
\(833\) | 390.924 | + | 479.048i | 0.469296 | + | 0.575087i | ||||
\(834\) | −164.147 | −0.196819 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.1672 | − | 5.87006i | −0.0121618 | − | 0.00702161i | ||||
\(837\) | −49.1946 | − | 28.4025i | −0.0587750 | − | 0.0339337i | ||||
\(838\) | −66.1723 | − | 114.614i | −0.0789646 | − | 0.136771i | ||||
\(839\) | − | 359.133i | − | 0.428049i | −0.976828 | − | 0.214024i | \(-0.931343\pi\) | ||
0.976828 | − | 0.214024i | \(-0.0686572\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 702.963 | 0.835866 | ||||||||
\(842\) | 199.581 | − | 115.228i | 0.237032 | − | 0.136851i | ||||
\(843\) | 253.554 | − | 439.169i | 0.300776 | − | 0.520959i | ||||
\(844\) | 29.6045 | − | 51.2764i | 0.0350764 | − | 0.0607541i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 54.6737i | 0.0646261i | ||||||||
\(847\) | −696.537 | − | 330.621i | −0.822357 | − | 0.390344i | ||||
\(848\) | − | 206.752i | − | 0.243811i | ||||||
\(849\) | 239.686 | + | 415.149i | 0.282316 | + | 0.488986i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 116.198 | − | 201.261i | 0.136543 | − | 0.236500i | ||||
\(852\) | −151.437 | − | 262.296i | −0.177742 | − | 0.307859i | ||||
\(853\) | 1089.78 | 1.27758 | 0.638792 | − | 0.769379i | \(-0.279434\pi\) | ||||
0.638792 | + | 0.769379i | \(0.279434\pi\) | |||||||
\(854\) | −20.8631 | − | 258.853i | −0.0244298 | − | 0.303107i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 132.865 | + | 230.128i | 0.155216 | + | 0.268841i | ||||
\(857\) | 32.4560 | − | 56.2155i | 0.0378717 | − | 0.0655956i | −0.846468 | − | 0.532439i | \(-0.821276\pi\) |
0.884340 | + | 0.466843i | \(0.154609\pi\) | |||||||
\(858\) | −54.0131 | − | 31.1845i | −0.0629523 | − | 0.0363455i | ||||
\(859\) | −250.689 | + | 144.735i | −0.291838 | + | 0.168493i | −0.638770 | − | 0.769397i | \(-0.720557\pi\) |
0.346933 | + | 0.937890i | \(0.387223\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −227.849 | + | 18.3642i | −0.264633 | + | 0.0213289i | ||||
\(862\) | − | 468.225i | − | 0.543185i | ||||||
\(863\) | −812.738 | + | 469.234i | −0.941759 | + | 0.543725i | −0.890511 | − | 0.454961i | \(-0.849653\pi\) |
−0.0512476 | + | 0.998686i | \(0.516320\pi\) | |||||||
\(864\) | 25.4558 | + | 14.6969i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −108.283 | + | 62.5174i | −0.125038 | + | 0.0721910i | ||||
\(867\) | 224.771 | 0.259251 | ||||||||
\(868\) | −65.6293 | + | 138.265i | −0.0756098 | + | 0.159291i | ||||
\(869\) | 117.213 | 0.134882 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 133.280 | + | 76.9493i | 0.153020 | + | 0.0883459i | ||||
\(872\) | −295.434 | − | 170.569i | −0.338800 | − | 0.195606i | ||||
\(873\) | 68.6171 | + | 118.848i | 0.0785992 | + | 0.136138i | ||||
\(874\) | − | 17.0245i | − | 0.0194788i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 211.016 | 0.240886 | ||||||||
\(877\) | 191.465 | − | 110.543i | 0.218318 | − | 0.126046i | −0.386853 | − | 0.922141i | \(-0.626438\pi\) |
0.605171 | + | 0.796095i | \(0.293105\pi\) | |||||||
\(878\) | 49.3660 | − | 85.5044i | 0.0562255 | − | 0.0973855i | ||||
\(879\) | 325.019 | − | 562.949i | 0.369759 | − | 0.640442i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 154.796i | 0.175704i | 0.996134 | + | 0.0878522i | \(0.0280003\pi\) | ||||
−0.996134 | + | 0.0878522i | \(0.972000\pi\) | |||||||
\(882\) | −161.066 | + | 131.437i | −0.182615 | + | 0.149022i | ||||
\(883\) | 1267.40i | 1.43534i | 0.696385 | + | 0.717668i | \(0.254791\pi\) | ||||
−0.696385 | + | 0.717668i | \(0.745209\pi\) | |||||||
\(884\) | −97.5227 | − | 168.914i | −0.110320 | − | 0.191080i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −466.997 | + | 808.863i | −0.527085 | + | 0.912938i | ||||
\(887\) | −828.399 | − | 1434.83i | −0.933934 | − | 1.61762i | −0.776524 | − | 0.630087i | \(-0.783019\pi\) |
−0.157410 | − | 0.987533i | \(-0.550314\pi\) | |||||||
\(888\) | 168.508 | 0.189761 | ||||||||
\(889\) | 466.277 | + | 675.706i | 0.524496 | + | 0.760074i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.8255 | − | 25.6786i | −0.0166392 | − | 0.0288199i | ||||
\(892\) | −328.532 | + | 569.035i | −0.368310 | + | 0.637931i | ||||
\(893\) | 19.8846 | + | 11.4804i | 0.0222672 | + | 0.0128560i | ||||
\(894\) | 108.428 | − | 62.6009i | 0.121284 | − | 0.0700234i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 33.9600 | − | 71.5452i | 0.0379018 | − | 0.0798496i | ||||
\(897\) | − | 90.4420i | − | 0.100827i | ||||||
\(898\) | 686.193 | − | 396.174i | 0.764135 | − | 0.441173i | ||||
\(899\) | −372.010 | − | 214.780i | −0.413804 | − | 0.238910i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −564.847 | + | 326.114i | −0.626911 | + | 0.361947i | ||||
\(902\) | −87.8430 | −0.0973869 | ||||||||
\(903\) | −935.630 | + | 75.4099i | −1.03614 | + | 0.0835105i | ||||
\(904\) | −30.3540 | −0.0335774 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −350.480 | − | 202.350i | −0.386844 | − | 0.223344i | ||||
\(907\) | 637.793 | + | 368.230i | 0.703190 | + | 0.405987i | 0.808534 | − | 0.588449i | \(-0.200261\pi\) |
−0.105345 | + | 0.994436i | \(0.533595\pi\) | |||||||
\(908\) | 364.456 | + | 631.256i | 0.401383 | + | 0.695216i | ||||
\(909\) | − | 274.561i | − | 0.302047i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 197.935 | 0.217273 | 0.108636 | − | 0.994082i | \(-0.465352\pi\) | ||||
0.108636 | + | 0.994082i | \(0.465352\pi\) | |||||||
\(912\) | 10.6905 | − | 6.17214i | 0.0117220 | − | 0.00676770i | ||||
\(913\) | 76.8905 | − | 133.178i | 0.0842175 | − | 0.145869i | ||||
\(914\) | 129.952 | − | 225.084i | 0.142180 | − | 0.246262i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 602.099i | − | 0.657313i | ||||||
\(917\) | −278.238 | + | 586.178i | −0.303422 | + | 0.639235i | ||||
\(918\) | − | 92.7273i | − | 0.101010i | ||||||
\(919\) | 821.091 | + | 1422.17i | 0.893462 | + | 1.54752i | 0.835697 | + | 0.549191i | \(0.185064\pi\) |
0.0577645 | + | 0.998330i | \(0.481603\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 93.3436 | − | 161.676i | 0.101350 | − | 0.175544i | ||||
\(922\) | 20.1051 | + | 34.8231i | 0.0218060 | + | 0.0377691i | ||||
\(923\) | −675.718 | −0.732089 | ||||||||
\(924\) | −65.7531 | + | 45.3735i | −0.0711614 | + | 0.0491055i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 190.870 | + | 330.597i | 0.206123 | + | 0.357016i | ||||
\(927\) | −75.7623 | + | 131.224i | −0.0817285 | + | 0.141558i | ||||
\(928\) | 192.497 | + | 111.138i | 0.207432 | + | 0.119761i | ||||
\(929\) | −1317.18 | + | 760.473i | −1.41784 | + | 0.818593i | −0.996109 | − | 0.0881263i | \(-0.971912\pi\) |
−0.421735 | + | 0.906719i | \(0.638579\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.9825 | + | 86.1785i | 0.0150188 | + | 0.0925655i | ||||
\(932\) | − | 564.050i | − | 0.605204i | ||||||
\(933\) | −865.629 | + | 499.771i | −0.927791 | + | 0.535660i | ||||
\(934\) | 409.471 | + | 236.408i | 0.438405 | + | 0.253113i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 56.7927 | − | 32.7893i | 0.0606759 | − | 0.0350313i | ||||
\(937\) | −682.636 | −0.728534 | −0.364267 | − | 0.931295i | \(-0.618680\pi\) | ||||
−0.364267 | + | 0.931295i | \(0.618680\pi\) | |||||||
\(938\) | 162.249 | − | 111.961i | 0.172974 | − | 0.119362i | ||||
\(939\) | −688.100 | −0.732800 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −248.545 | − | 143.497i | −0.264129 | − | 0.152495i | 0.362088 | − | 0.932144i | \(-0.382064\pi\) |
−0.626216 | + | 0.779649i | \(0.715397\pi\) | |||||||
\(942\) | 404.773 | + | 233.696i | 0.429695 | + | 0.248085i | ||||
\(943\) | −63.6911 | − | 110.316i | −0.0675410 | − | 0.116984i | ||||
\(944\) | 451.706i | 0.478502i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −360.715 | −0.381305 | ||||||||
\(947\) | 415.790 | − | 240.057i | 0.439061 | − | 0.253492i | −0.264139 | − | 0.964485i | \(-0.585088\pi\) |
0.703199 | + | 0.710993i | \(0.251754\pi\) | |||||||
\(948\) | −61.6224 | + | 106.733i | −0.0650025 | + | 0.112588i | ||||
\(949\) | 235.391 | − | 407.709i | 0.248041 | − | 0.429620i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 139.205i | − | 0.146378i | ||||||
\(952\) | −249.028 | + | 20.0711i | −0.261584 | + | 0.0210831i | ||||
\(953\) | − | 1147.30i | − | 1.20388i | −0.798540 | − | 0.601941i | \(-0.794394\pi\) | ||
0.798540 | − | 0.601941i | \(-0.205606\pi\) | |||||||
\(954\) | −109.647 | − | 189.914i | −0.114934 | − | 0.199071i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −83.0347 | + | 143.820i | −0.0868563 | + | 0.150440i | ||||
\(957\) | −112.111 | − | 194.181i | −0.117148 | − | 0.202906i | ||||
\(958\) | −187.076 | −0.195277 | ||||||||
\(959\) | 191.697 | − | 15.4504i | 0.199892 | − | 0.0161109i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −420.744 | − | 728.750i | −0.437819 | − | 0.758325i | ||||
\(962\) | 187.973 | − | 325.579i | 0.195398 | − | 0.338439i | ||||
\(963\) | 244.088 | + | 140.924i | 0.253466 | + | 0.146339i | ||||
\(964\) | −574.737 | + | 331.825i | −0.596201 | + | 0.344217i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −104.656 | − | 49.6767i | −0.108340 | − | 0.0514251i | ||||
\(967\) | − | 1400.07i | − | 1.44785i | −0.689881 | − | 0.723923i | \(-0.742337\pi\) | ||
0.689881 | − | 0.723923i | \(-0.257663\pi\) | |||||||
\(968\) | 269.801 | − | 155.770i | 0.278720 | − | 0.160919i | ||||
\(969\) | −33.7246 | − | 19.4709i | −0.0348035 | − | 0.0200938i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 226.263 | − | 130.633i | 0.233020 | − | 0.134534i | −0.378944 | − | 0.925419i | \(-0.623713\pi\) |
0.611965 | + | 0.790885i | \(0.290379\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | 266.423 | + | 386.087i | 0.273816 | + | 0.396801i | ||||
\(974\) | 731.532 | 0.751059 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 90.8735 | + | 52.4658i | 0.0931081 | + | 0.0537560i | ||||
\(977\) | −675.019 | − | 389.723i | −0.690910 | − | 0.398897i | 0.113043 | − | 0.993590i | \(-0.463940\pi\) |
−0.803953 | + | 0.594693i | \(0.797274\pi\) | |||||||
\(978\) | 303.984 | + | 526.516i | 0.310822 | + | 0.538360i | ||||
\(979\) | 180.589i | 0.184463i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −361.831 | −0.368839 | ||||||||
\(982\) | 593.763 | − | 342.809i | 0.604646 | − | 0.349093i | ||||
\(983\) | −769.118 | + | 1332.15i | −0.782419 | + | 1.35519i | 0.148110 | + | 0.988971i | \(0.452681\pi\) |
−0.930529 | + | 0.366219i | \(0.880652\pi\) | |||||||
\(984\) | 46.1817 | − | 79.9891i | 0.0469327 | − | 0.0812898i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 701.204i | − | 0.711160i | ||||||
\(987\) | 128.597 | − | 88.7395i | 0.130291 | − | 0.0899083i | ||||
\(988\) | − | 27.5404i | − | 0.0278749i | ||||||
\(989\) | −261.539 | − | 452.998i | −0.264448 | − | 0.458037i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −482.270 | + | 835.316i | −0.486650 | + | 0.842902i | −0.999882 | − | 0.0153476i | \(-0.995115\pi\) |
0.513233 | + | 0.858250i | \(0.328448\pi\) | |||||||
\(992\) | −30.9208 | − | 53.5563i | −0.0311701 | − | 0.0539883i | ||||
\(993\) | −852.242 | −0.858250 | ||||||||
\(994\) | −371.148 | + | 781.917i | −0.373389 | + | 0.786637i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 80.8474 | + | 140.032i | 0.0811721 | + | 0.140594i | ||||
\(997\) | −208.868 | + | 361.770i | −0.209496 | + | 0.362858i | −0.951556 | − | 0.307476i | \(-0.900516\pi\) |
0.742060 | + | 0.670334i | \(0.233849\pi\) | |||||||
\(998\) | −158.347 | − | 91.4218i | −0.158664 | − | 0.0916050i | ||||
\(999\) | 154.785 | − | 89.3649i | 0.154939 | − | 0.0894543i |
(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 | 1050.3.q.b.199.7 | 16 | ||
5.2 | odd | 4 | 1050.3.p.c.451.3 | ✓ | 8 | ||
5.3 | odd | 4 | 1050.3.p.d.451.2 | yes | 8 | ||
5.4 | even | 2 | inner | 1050.3.q.b.199.2 | 16 | ||
7.5 | odd | 6 | inner | 1050.3.q.b.649.2 | 16 | ||
35.12 | even | 12 | 1050.3.p.c.901.3 | yes | 8 | ||
35.19 | odd | 6 | inner | 1050.3.q.b.649.7 | 16 | ||
35.33 | even | 12 | 1050.3.p.d.901.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.p.c.451.3 | ✓ | 8 | 5.2 | odd | 4 | ||
1050.3.p.c.901.3 | yes | 8 | 35.12 | even | 12 | ||
1050.3.p.d.451.2 | yes | 8 | 5.3 | odd | 4 | ||
1050.3.p.d.901.2 | yes | 8 | 35.33 | even | 12 | ||
1050.3.q.b.199.2 | 16 | 5.4 | even | 2 | inner | ||
1050.3.q.b.199.7 | 16 | 1.1 | even | 1 | trivial | ||
1050.3.q.b.649.2 | 16 | 7.5 | odd | 6 | inner | ||
1050.3.q.b.649.7 | 16 | 35.19 | odd | 6 | inner |