Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(769,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.16 | ||
Character | \(\chi\) | \(=\) | 1155.769 |
Dual form | 1155.2.k.a.769.15 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.17317 | −0.829557 | −0.414779 | − | 0.909922i | \(-0.636141\pi\) | ||||
−0.414779 | + | 0.909922i | \(0.636141\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.623669 | −0.311835 | ||||||||
\(5\) | −2.20931 | + | 0.344884i | −0.988034 | + | 0.154237i | ||||
\(6\) | 1.17317 | 0.478945 | ||||||||
\(7\) | −1.71739 | − | 2.01260i | −0.649113 | − | 0.760692i | ||||
\(8\) | 3.07801 | 1.08824 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.59190 | − | 0.404608i | 0.819631 | − | 0.127948i | ||||
\(11\) | 1.48217 | − | 2.96702i | 0.446890 | − | 0.894589i | ||||
\(12\) | 0.623669 | 0.180038 | ||||||||
\(13\) | 3.43348i | 0.952276i | 0.879371 | + | 0.476138i | \(0.157964\pi\) | ||||
−0.879371 | + | 0.476138i | \(0.842036\pi\) | |||||||
\(14\) | 2.01480 | + | 2.36113i | 0.538477 | + | 0.631037i | ||||
\(15\) | 2.20931 | − | 0.344884i | 0.570442 | − | 0.0890488i | ||||
\(16\) | −2.36370 | −0.590924 | ||||||||
\(17\) | 3.10231i | 0.752420i | 0.926534 | + | 0.376210i | \(0.122773\pi\) | ||||
−0.926534 | + | 0.376210i | \(0.877227\pi\) | |||||||
\(18\) | −1.17317 | −0.276519 | ||||||||
\(19\) | 5.32112 | 1.22075 | 0.610375 | − | 0.792113i | \(-0.291019\pi\) | ||||
0.610375 | + | 0.792113i | \(0.291019\pi\) | |||||||
\(20\) | 1.37788 | − | 0.215094i | 0.308103 | − | 0.0480965i | ||||
\(21\) | 1.71739 | + | 2.01260i | 0.374766 | + | 0.439186i | ||||
\(22\) | −1.73883 | + | 3.48082i | −0.370721 | + | 0.742113i | ||||
\(23\) | − | 5.88666i | − | 1.22745i | −0.789519 | − | 0.613726i | \(-0.789670\pi\) | ||
0.789519 | − | 0.613726i | \(-0.210330\pi\) | |||||||
\(24\) | −3.07801 | −0.628297 | ||||||||
\(25\) | 4.76211 | − | 1.52391i | 0.952422 | − | 0.304783i | ||||
\(26\) | − | 4.02806i | − | 0.789968i | ||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.07109 | + | 1.25520i | 0.202416 | + | 0.237210i | ||||
\(29\) | 5.81504i | 1.07983i | 0.841721 | + | 0.539913i | \(0.181543\pi\) | ||||
−0.841721 | + | 0.539913i | \(0.818457\pi\) | |||||||
\(30\) | −2.59190 | + | 0.404608i | −0.473214 | + | 0.0738711i | ||||
\(31\) | 0.722644i | 0.129791i | 0.997892 | + | 0.0648954i | \(0.0206714\pi\) | ||||
−0.997892 | + | 0.0648954i | \(0.979329\pi\) | |||||||
\(32\) | −3.38301 | −0.598036 | ||||||||
\(33\) | −1.48217 | + | 2.96702i | −0.258012 | + | 0.516491i | ||||
\(34\) | − | 3.63954i | − | 0.624176i | ||||||
\(35\) | 4.48837 | + | 3.85416i | 0.758673 | + | 0.651472i | ||||
\(36\) | −0.623669 | −0.103945 | ||||||||
\(37\) | − | 1.11476i | − | 0.183266i | −0.995793 | − | 0.0916331i | \(-0.970791\pi\) | ||
0.995793 | − | 0.0916331i | \(-0.0292087\pi\) | |||||||
\(38\) | −6.24259 | −1.01268 | ||||||||
\(39\) | − | 3.43348i | − | 0.549797i | ||||||
\(40\) | −6.80029 | + | 1.06156i | −1.07522 | + | 0.167847i | ||||
\(41\) | −3.34512 | −0.522420 | −0.261210 | − | 0.965282i | \(-0.584122\pi\) | ||||
−0.261210 | + | 0.965282i | \(0.584122\pi\) | |||||||
\(42\) | −2.01480 | − | 2.36113i | −0.310890 | − | 0.364330i | ||||
\(43\) | 7.30051 | 1.11332 | 0.556659 | − | 0.830741i | \(-0.312083\pi\) | ||||
0.556659 | + | 0.830741i | \(0.312083\pi\) | |||||||
\(44\) | −0.924381 | + | 1.85044i | −0.139356 | + | 0.278964i | ||||
\(45\) | −2.20931 | + | 0.344884i | −0.329345 | + | 0.0514123i | ||||
\(46\) | 6.90606i | 1.01824i | ||||||||
\(47\) | −6.60481 | −0.963410 | −0.481705 | − | 0.876333i | \(-0.659982\pi\) | ||||
−0.481705 | + | 0.876333i | \(0.659982\pi\) | |||||||
\(48\) | 2.36370 | 0.341170 | ||||||||
\(49\) | −1.10113 | + | 6.91285i | −0.157304 | + | 0.987550i | ||||
\(50\) | −5.58677 | + | 1.78781i | −0.790089 | + | 0.252835i | ||||
\(51\) | − | 3.10231i | − | 0.434410i | ||||||
\(52\) | − | 2.14136i | − | 0.296953i | ||||||
\(53\) | − | 11.7433i | − | 1.61307i | −0.591186 | − | 0.806535i | \(-0.701340\pi\) | ||
0.591186 | − | 0.806535i | \(-0.298660\pi\) | |||||||
\(54\) | 1.17317 | 0.159648 | ||||||||
\(55\) | −2.25129 | + | 7.06624i | −0.303563 | + | 0.952811i | ||||
\(56\) | −5.28616 | − | 6.19481i | −0.706392 | − | 0.827817i | ||||
\(57\) | −5.32112 | −0.704800 | ||||||||
\(58\) | − | 6.82204i | − | 0.895777i | ||||||
\(59\) | − | 14.7567i | − | 1.92116i | −0.278003 | − | 0.960580i | \(-0.589672\pi\) | ||
0.278003 | − | 0.960580i | \(-0.410328\pi\) | |||||||
\(60\) | −1.37788 | + | 0.215094i | −0.177884 | + | 0.0277685i | ||||
\(61\) | −5.25854 | −0.673287 | −0.336643 | − | 0.941632i | \(-0.609292\pi\) | ||||
−0.336643 | + | 0.941632i | \(0.609292\pi\) | |||||||
\(62\) | − | 0.847785i | − | 0.107669i | ||||||
\(63\) | −1.71739 | − | 2.01260i | −0.216371 | − | 0.253564i | ||||
\(64\) | 8.69624 | 1.08703 | ||||||||
\(65\) | −1.18415 | − | 7.58563i | −0.146876 | − | 0.940881i | ||||
\(66\) | 1.73883 | − | 3.48082i | 0.214036 | − | 0.428459i | ||||
\(67\) | − | 1.98202i | − | 0.242142i | −0.992644 | − | 0.121071i | \(-0.961367\pi\) | ||
0.992644 | − | 0.121071i | \(-0.0386329\pi\) | |||||||
\(68\) | − | 1.93481i | − | 0.234631i | ||||||
\(69\) | 5.88666i | 0.708670i | ||||||||
\(70\) | −5.26562 | − | 4.52159i | −0.629363 | − | 0.540433i | ||||
\(71\) | −14.9478 | −1.77398 | −0.886990 | − | 0.461788i | \(-0.847208\pi\) | ||||
−0.886990 | + | 0.461788i | \(0.847208\pi\) | |||||||
\(72\) | 3.07801 | 0.362747 | ||||||||
\(73\) | 7.27698i | 0.851706i | 0.904792 | + | 0.425853i | \(0.140026\pi\) | ||||
−0.904792 | + | 0.425853i | \(0.859974\pi\) | |||||||
\(74\) | 1.30781i | 0.152030i | ||||||||
\(75\) | −4.76211 | + | 1.52391i | −0.549881 | + | 0.175966i | ||||
\(76\) | −3.31862 | −0.380672 | ||||||||
\(77\) | −8.51688 | + | 2.11252i | −0.970589 | + | 0.240744i | ||||
\(78\) | 4.02806i | 0.456088i | ||||||||
\(79\) | − | 11.5312i | − | 1.29736i | −0.761061 | − | 0.648680i | \(-0.775321\pi\) | ||
0.761061 | − | 0.648680i | \(-0.224679\pi\) | |||||||
\(80\) | 5.22214 | − | 0.815202i | 0.583853 | − | 0.0911424i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.92440 | 0.433378 | ||||||||
\(83\) | 7.39391i | 0.811587i | 0.913965 | + | 0.405794i | \(0.133005\pi\) | ||||
−0.913965 | + | 0.405794i | \(0.866995\pi\) | |||||||
\(84\) | −1.07109 | − | 1.25520i | −0.116865 | − | 0.136953i | ||||
\(85\) | −1.06994 | − | 6.85396i | −0.116051 | − | 0.743417i | ||||
\(86\) | −8.56475 | −0.923561 | ||||||||
\(87\) | − | 5.81504i | − | 0.623438i | ||||||
\(88\) | 4.56212 | − | 9.13252i | 0.486324 | − | 0.973529i | ||||
\(89\) | 3.65152i | 0.387060i | 0.981094 | + | 0.193530i | \(0.0619937\pi\) | ||||
−0.981094 | + | 0.193530i | \(0.938006\pi\) | |||||||
\(90\) | 2.59190 | − | 0.404608i | 0.273210 | − | 0.0426495i | ||||
\(91\) | 6.91023 | − | 5.89663i | 0.724389 | − | 0.618135i | ||||
\(92\) | 3.67133i | 0.382762i | ||||||||
\(93\) | − | 0.722644i | − | 0.0749347i | ||||||
\(94\) | 7.74857 | 0.799204 | ||||||||
\(95\) | −11.7560 | + | 1.83517i | −1.20614 | + | 0.188285i | ||||
\(96\) | 3.38301 | 0.345277 | ||||||||
\(97\) | 3.77353 | 0.383144 | 0.191572 | − | 0.981479i | \(-0.438641\pi\) | ||||
0.191572 | + | 0.981479i | \(0.438641\pi\) | |||||||
\(98\) | 1.29181 | − | 8.10996i | 0.130492 | − | 0.819229i | ||||
\(99\) | 1.48217 | − | 2.96702i | 0.148963 | − | 0.298196i | ||||
\(100\) | −2.96998 | + | 0.950419i | −0.296998 | + | 0.0950419i | ||||
\(101\) | −15.2917 | −1.52158 | −0.760791 | − | 0.648997i | \(-0.775189\pi\) | ||||
−0.760791 | + | 0.648997i | \(0.775189\pi\) | |||||||
\(102\) | 3.63954i | 0.360368i | ||||||||
\(103\) | −1.35140 | −0.133158 | −0.0665789 | − | 0.997781i | \(-0.521208\pi\) | ||||
−0.0665789 | + | 0.997781i | \(0.521208\pi\) | |||||||
\(104\) | 10.5683i | 1.03631i | ||||||||
\(105\) | −4.48837 | − | 3.85416i | −0.438020 | − | 0.376127i | ||||
\(106\) | 13.7769i | 1.33813i | ||||||||
\(107\) | −1.77552 | −0.171646 | −0.0858228 | − | 0.996310i | \(-0.527352\pi\) | ||||
−0.0858228 | + | 0.996310i | \(0.527352\pi\) | |||||||
\(108\) | 0.623669 | 0.0600126 | ||||||||
\(109\) | 1.93909i | 0.185731i | 0.995679 | + | 0.0928656i | \(0.0296027\pi\) | ||||
−0.995679 | + | 0.0928656i | \(0.970397\pi\) | |||||||
\(110\) | 2.64114 | − | 8.28991i | 0.251823 | − | 0.790411i | ||||
\(111\) | 1.11476i | 0.105809i | ||||||||
\(112\) | 4.05940 | + | 4.75718i | 0.383577 | + | 0.449511i | ||||
\(113\) | 17.3740i | 1.63441i | 0.576350 | + | 0.817203i | \(0.304477\pi\) | ||||
−0.576350 | + | 0.817203i | \(0.695523\pi\) | |||||||
\(114\) | 6.24259 | 0.584672 | ||||||||
\(115\) | 2.03022 | + | 13.0055i | 0.189319 | + | 1.21276i | ||||
\(116\) | − | 3.62666i | − | 0.336727i | ||||||
\(117\) | 3.43348i | 0.317425i | ||||||||
\(118\) | 17.3122i | 1.59371i | ||||||||
\(119\) | 6.24371 | − | 5.32788i | 0.572360 | − | 0.488406i | ||||
\(120\) | 6.80029 | − | 1.06156i | 0.620779 | − | 0.0969066i | ||||
\(121\) | −6.60637 | − | 8.79522i | −0.600579 | − | 0.799565i | ||||
\(122\) | 6.16916 | 0.558530 | ||||||||
\(123\) | 3.34512 | 0.301620 | ||||||||
\(124\) | − | 0.450691i | − | 0.0404733i | ||||||
\(125\) | −9.99541 | + | 5.00918i | −0.894016 | + | 0.448034i | ||||
\(126\) | 2.01480 | + | 2.36113i | 0.179492 | + | 0.210346i | ||||
\(127\) | 6.23748 | 0.553487 | 0.276743 | − | 0.960944i | \(-0.410745\pi\) | ||||
0.276743 | + | 0.960944i | \(0.410745\pi\) | |||||||
\(128\) | −3.43617 | −0.303717 | ||||||||
\(129\) | −7.30051 | −0.642774 | ||||||||
\(130\) | 1.38922 | + | 8.89924i | 0.121842 | + | 0.780515i | ||||
\(131\) | −2.79723 | −0.244395 | −0.122198 | − | 0.992506i | \(-0.538994\pi\) | ||||
−0.122198 | + | 0.992506i | \(0.538994\pi\) | |||||||
\(132\) | 0.924381 | − | 1.85044i | 0.0804571 | − | 0.161060i | ||||
\(133\) | −9.13845 | − | 10.7093i | −0.792405 | − | 0.928614i | ||||
\(134\) | 2.32525i | 0.200871i | ||||||||
\(135\) | 2.20931 | − | 0.344884i | 0.190147 | − | 0.0296829i | ||||
\(136\) | 9.54894i | 0.818815i | ||||||||
\(137\) | − | 18.1264i | − | 1.54865i | −0.632791 | − | 0.774323i | \(-0.718091\pi\) | ||
0.632791 | − | 0.774323i | \(-0.281909\pi\) | |||||||
\(138\) | − | 6.90606i | − | 0.587882i | ||||||
\(139\) | −12.5540 | −1.06481 | −0.532407 | − | 0.846489i | \(-0.678712\pi\) | ||||
−0.532407 | + | 0.846489i | \(0.678712\pi\) | |||||||
\(140\) | −2.79926 | − | 2.40372i | −0.236581 | − | 0.203152i | ||||
\(141\) | 6.60481 | 0.556225 | ||||||||
\(142\) | 17.5364 | 1.47162 | ||||||||
\(143\) | 10.1872 | + | 5.08899i | 0.851896 | + | 0.425562i | ||||
\(144\) | −2.36370 | −0.196975 | ||||||||
\(145\) | −2.00552 | − | 12.8472i | −0.166549 | − | 1.06690i | ||||
\(146\) | − | 8.53714i | − | 0.706539i | ||||||
\(147\) | 1.10113 | − | 6.91285i | 0.0908194 | − | 0.570162i | ||||
\(148\) | 0.695245i | 0.0571488i | ||||||||
\(149\) | − | 3.14282i | − | 0.257470i | −0.991679 | − | 0.128735i | \(-0.958908\pi\) | ||
0.991679 | − | 0.128735i | \(-0.0410916\pi\) | |||||||
\(150\) | 5.58677 | − | 1.78781i | 0.456158 | − | 0.145974i | ||||
\(151\) | 0.939283i | 0.0764378i | 0.999269 | + | 0.0382189i | \(0.0121684\pi\) | ||||
−0.999269 | + | 0.0382189i | \(0.987832\pi\) | |||||||
\(152\) | 16.3785 | 1.32847 | ||||||||
\(153\) | 3.10231i | 0.250807i | ||||||||
\(154\) | 9.99176 | − | 2.47835i | 0.805159 | − | 0.199711i | ||||
\(155\) | −0.249229 | − | 1.59655i | −0.0200185 | − | 0.128238i | ||||
\(156\) | 2.14136i | 0.171446i | ||||||||
\(157\) | −12.9739 | −1.03543 | −0.517715 | − | 0.855553i | \(-0.673217\pi\) | ||||
−0.517715 | + | 0.855553i | \(0.673217\pi\) | |||||||
\(158\) | 13.5281i | 1.07623i | ||||||||
\(159\) | 11.7433i | 0.931307i | ||||||||
\(160\) | 7.47411 | − | 1.16675i | 0.590880 | − | 0.0922393i | ||||
\(161\) | −11.8475 | + | 10.1097i | −0.933713 | + | 0.796756i | ||||
\(162\) | −1.17317 | −0.0921730 | ||||||||
\(163\) | 9.34655i | 0.732078i | 0.930599 | + | 0.366039i | \(0.119286\pi\) | ||||
−0.930599 | + | 0.366039i | \(0.880714\pi\) | |||||||
\(164\) | 2.08625 | 0.162909 | ||||||||
\(165\) | 2.25129 | − | 7.06624i | 0.175262 | − | 0.550106i | ||||
\(166\) | − | 8.67432i | − | 0.673258i | ||||||
\(167\) | − | 24.2687i | − | 1.87797i | −0.343964 | − | 0.938983i | \(-0.611770\pi\) | ||
0.343964 | − | 0.938983i | \(-0.388230\pi\) | |||||||
\(168\) | 5.28616 | + | 6.19481i | 0.407836 | + | 0.477940i | ||||
\(169\) | 1.21121 | 0.0931702 | ||||||||
\(170\) | 1.25522 | + | 8.04087i | 0.0962710 | + | 0.616707i | ||||
\(171\) | 5.32112 | 0.406916 | ||||||||
\(172\) | −4.55311 | −0.347171 | ||||||||
\(173\) | − | 0.0905291i | − | 0.00688280i | −0.999994 | − | 0.00344140i | \(-0.998905\pi\) | ||
0.999994 | − | 0.00344140i | \(-0.00109543\pi\) | |||||||
\(174\) | 6.82204i | 0.517177i | ||||||||
\(175\) | −11.2454 | − | 6.96707i | −0.850075 | − | 0.526661i | ||||
\(176\) | −3.50339 | + | 7.01313i | −0.264078 | + | 0.528634i | ||||
\(177\) | 14.7567i | 1.10918i | ||||||||
\(178\) | − | 4.28385i | − | 0.321088i | ||||||
\(179\) | −22.0633 | −1.64909 | −0.824543 | − | 0.565799i | \(-0.808568\pi\) | ||||
−0.824543 | + | 0.565799i | \(0.808568\pi\) | |||||||
\(180\) | 1.37788 | − | 0.215094i | 0.102701 | − | 0.0160322i | ||||
\(181\) | − | 5.43785i | − | 0.404192i | −0.979366 | − | 0.202096i | \(-0.935225\pi\) | ||
0.979366 | − | 0.202096i | \(-0.0647753\pi\) | |||||||
\(182\) | −8.10688 | + | 6.91776i | −0.600922 | + | 0.512778i | ||||
\(183\) | 5.25854 | 0.388722 | ||||||||
\(184\) | − | 18.1192i | − | 1.33577i | ||||||
\(185\) | 0.384465 | + | 2.46286i | 0.0282664 | + | 0.181073i | ||||
\(186\) | 0.847785i | 0.0621626i | ||||||||
\(187\) | 9.20460 | + | 4.59813i | 0.673107 | + | 0.336249i | ||||
\(188\) | 4.11922 | 0.300425 | ||||||||
\(189\) | 1.71739 | + | 2.01260i | 0.124922 | + | 0.146395i | ||||
\(190\) | 13.7918 | − | 2.15297i | 1.00056 | − | 0.156193i | ||||
\(191\) | −18.9758 | −1.37304 | −0.686521 | − | 0.727110i | \(-0.740863\pi\) | ||||
−0.686521 | + | 0.727110i | \(0.740863\pi\) | |||||||
\(192\) | −8.69624 | −0.627597 | ||||||||
\(193\) | −16.3232 | −1.17497 | −0.587484 | − | 0.809235i | \(-0.699882\pi\) | ||||
−0.587484 | + | 0.809235i | \(0.699882\pi\) | |||||||
\(194\) | −4.42700 | −0.317840 | ||||||||
\(195\) | 1.18415 | + | 7.58563i | 0.0847990 | + | 0.543218i | ||||
\(196\) | 0.686739 | − | 4.31133i | 0.0490528 | − | 0.307952i | ||||
\(197\) | 16.1111 | 1.14787 | 0.573933 | − | 0.818902i | \(-0.305417\pi\) | ||||
0.573933 | + | 0.818902i | \(0.305417\pi\) | |||||||
\(198\) | −1.73883 | + | 3.48082i | −0.123574 | + | 0.247371i | ||||
\(199\) | 24.4971i | 1.73656i | 0.496078 | + | 0.868278i | \(0.334773\pi\) | ||||
−0.496078 | + | 0.868278i | \(0.665227\pi\) | |||||||
\(200\) | 14.6578 | − | 4.69063i | 1.03647 | − | 0.331677i | ||||
\(201\) | 1.98202i | 0.139801i | ||||||||
\(202\) | 17.9398 | 1.26224 | ||||||||
\(203\) | 11.7034 | − | 9.98670i | 0.821414 | − | 0.700929i | ||||
\(204\) | 1.93481i | 0.135464i | ||||||||
\(205\) | 7.39042 | − | 1.15368i | 0.516169 | − | 0.0805765i | ||||
\(206\) | 1.58543 | 0.110462 | ||||||||
\(207\) | − | 5.88666i | − | 0.409151i | ||||||
\(208\) | − | 8.11571i | − | 0.562723i | ||||||
\(209\) | 7.88678 | − | 15.7879i | 0.545540 | − | 1.09207i | ||||
\(210\) | 5.26562 | + | 4.52159i | 0.363363 | + | 0.312019i | ||||
\(211\) | 13.0894i | 0.901112i | 0.892748 | + | 0.450556i | \(0.148774\pi\) | ||||
−0.892748 | + | 0.450556i | \(0.851226\pi\) | |||||||
\(212\) | 7.32396i | 0.503012i | ||||||||
\(213\) | 14.9478 | 1.02421 | ||||||||
\(214\) | 2.08298 | 0.142390 | ||||||||
\(215\) | −16.1291 | + | 2.51783i | −1.10000 | + | 0.171715i | ||||
\(216\) | −3.07801 | −0.209432 | ||||||||
\(217\) | 1.45439 | − | 1.24106i | 0.0987307 | − | 0.0842489i | ||||
\(218\) | − | 2.27489i | − | 0.154075i | ||||||
\(219\) | − | 7.27698i | − | 0.491733i | ||||||
\(220\) | 1.40406 | − | 4.40700i | 0.0946616 | − | 0.297120i | ||||
\(221\) | −10.6517 | −0.716512 | ||||||||
\(222\) | − | 1.30781i | − | 0.0877744i | ||||||
\(223\) | −4.59749 | −0.307871 | −0.153935 | − | 0.988081i | \(-0.549195\pi\) | ||||
−0.153935 | + | 0.988081i | \(0.549195\pi\) | |||||||
\(224\) | 5.80995 | + | 6.80864i | 0.388193 | + | 0.454921i | ||||
\(225\) | 4.76211 | − | 1.52391i | 0.317474 | − | 0.101594i | ||||
\(226\) | − | 20.3826i | − | 1.35583i | ||||||
\(227\) | 18.9902i | 1.26042i | 0.776424 | + | 0.630211i | \(0.217032\pi\) | ||||
−0.776424 | + | 0.630211i | \(0.782968\pi\) | |||||||
\(228\) | 3.31862 | 0.219781 | ||||||||
\(229\) | − | 19.7583i | − | 1.30566i | −0.757503 | − | 0.652831i | \(-0.773581\pi\) | ||
0.757503 | − | 0.652831i | \(-0.226419\pi\) | |||||||
\(230\) | −2.38179 | − | 15.2576i | −0.157051 | − | 1.00606i | ||||
\(231\) | 8.51688 | − | 2.11252i | 0.560370 | − | 0.138994i | ||||
\(232\) | 17.8988i | 1.17511i | ||||||||
\(233\) | 19.0700 | 1.24932 | 0.624660 | − | 0.780897i | \(-0.285238\pi\) | ||||
0.624660 | + | 0.780897i | \(0.285238\pi\) | |||||||
\(234\) | − | 4.02806i | − | 0.263323i | ||||||
\(235\) | 14.5921 | − | 2.27789i | 0.951882 | − | 0.148593i | ||||
\(236\) | 9.20331i | 0.599085i | ||||||||
\(237\) | 11.5312i | 0.749031i | ||||||||
\(238\) | −7.32494 | + | 6.25051i | −0.474805 | + | 0.405161i | ||||
\(239\) | 23.1560i | 1.49784i | 0.662661 | + | 0.748919i | \(0.269427\pi\) | ||||
−0.662661 | + | 0.748919i | \(0.730573\pi\) | |||||||
\(240\) | −5.22214 | + | 0.815202i | −0.337088 | + | 0.0526211i | ||||
\(241\) | 15.7072 | 1.01179 | 0.505896 | − | 0.862595i | \(-0.331162\pi\) | ||||
0.505896 | + | 0.862595i | \(0.331162\pi\) | |||||||
\(242\) | 7.75041 | + | 10.3183i | 0.498215 | + | 0.663285i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.27959 | 0.209954 | ||||||||
\(245\) | 0.0485958 | − | 15.6524i | 0.00310467 | − | 0.999995i | ||||
\(246\) | −3.92440 | −0.250211 | ||||||||
\(247\) | 18.2700i | 1.16249i | ||||||||
\(248\) | 2.22431i | 0.141244i | ||||||||
\(249\) | − | 7.39391i | − | 0.468570i | ||||||
\(250\) | 11.7263 | − | 5.87662i | 0.741638 | − | 0.371670i | ||||
\(251\) | − | 27.7124i | − | 1.74919i | −0.484854 | − | 0.874595i | \(-0.661127\pi\) | ||
0.484854 | − | 0.874595i | \(-0.338873\pi\) | |||||||
\(252\) | 1.07109 | + | 1.25520i | 0.0674720 | + | 0.0790700i | ||||
\(253\) | −17.4658 | − | 8.72500i | −1.09807 | − | 0.548536i | ||||
\(254\) | −7.31763 | −0.459149 | ||||||||
\(255\) | 1.06994 | + | 6.85396i | 0.0670021 | + | 0.429212i | ||||
\(256\) | −13.3613 | −0.835079 | ||||||||
\(257\) | −8.14674 | −0.508180 | −0.254090 | − | 0.967181i | \(-0.581776\pi\) | ||||
−0.254090 | + | 0.967181i | \(0.581776\pi\) | |||||||
\(258\) | 8.56475 | 0.533218 | ||||||||
\(259\) | −2.24358 | + | 1.91449i | −0.139409 | + | 0.118961i | ||||
\(260\) | 0.738521 | + | 4.73092i | 0.0458011 | + | 0.293399i | ||||
\(261\) | 5.81504i | 0.359942i | ||||||||
\(262\) | 3.28163 | 0.202740 | ||||||||
\(263\) | 11.5514 | 0.712293 | 0.356146 | − | 0.934430i | \(-0.384090\pi\) | ||||
0.356146 | + | 0.934430i | \(0.384090\pi\) | |||||||
\(264\) | −4.56212 | + | 9.13252i | −0.280779 | + | 0.562067i | ||||
\(265\) | 4.05009 | + | 25.9447i | 0.248795 | + | 1.59377i | ||||
\(266\) | 10.7210 | + | 12.5638i | 0.657345 | + | 0.770338i | ||||
\(267\) | − | 3.65152i | − | 0.223469i | ||||||
\(268\) | 1.23613i | 0.0755084i | ||||||||
\(269\) | − | 16.9804i | − | 1.03531i | −0.855589 | − | 0.517656i | \(-0.826805\pi\) | ||
0.855589 | − | 0.517656i | \(-0.173195\pi\) | |||||||
\(270\) | −2.59190 | + | 0.404608i | −0.157738 | + | 0.0246237i | ||||
\(271\) | 18.3679 | 1.11577 | 0.557885 | − | 0.829918i | \(-0.311613\pi\) | ||||
0.557885 | + | 0.829918i | \(0.311613\pi\) | |||||||
\(272\) | − | 7.33292i | − | 0.444623i | ||||||
\(273\) | −6.91023 | + | 5.89663i | −0.418226 | + | 0.356880i | ||||
\(274\) | 21.2654i | 1.28469i | ||||||||
\(275\) | 2.53676 | − | 16.3879i | 0.152972 | − | 0.988230i | ||||
\(276\) | − | 3.67133i | − | 0.220988i | ||||||
\(277\) | −11.6755 | −0.701514 | −0.350757 | − | 0.936467i | \(-0.614076\pi\) | ||||
−0.350757 | + | 0.936467i | \(0.614076\pi\) | |||||||
\(278\) | 14.7280 | 0.883324 | ||||||||
\(279\) | 0.722644i | 0.0432636i | ||||||||
\(280\) | 13.8153 | + | 11.8632i | 0.825620 | + | 0.708959i | ||||
\(281\) | 7.54255i | 0.449951i | 0.974364 | + | 0.224975i | \(0.0722302\pi\) | ||||
−0.974364 | + | 0.224975i | \(0.927770\pi\) | |||||||
\(282\) | −7.74857 | −0.461421 | ||||||||
\(283\) | − | 4.89738i | − | 0.291119i | −0.989350 | − | 0.145559i | \(-0.953502\pi\) | ||
0.989350 | − | 0.145559i | \(-0.0464982\pi\) | |||||||
\(284\) | 9.32250 | 0.553189 | ||||||||
\(285\) | 11.7560 | − | 1.83517i | 0.696366 | − | 0.108706i | ||||
\(286\) | −11.9513 | − | 5.97025i | −0.706696 | − | 0.353028i | ||||
\(287\) | 5.74489 | + | 6.73240i | 0.339110 | + | 0.397401i | ||||
\(288\) | −3.38301 | −0.199345 | ||||||||
\(289\) | 7.37569 | 0.433864 | ||||||||
\(290\) | 2.35281 | + | 15.0720i | 0.138162 | + | 0.885058i | ||||
\(291\) | −3.77353 | −0.221208 | ||||||||
\(292\) | − | 4.53843i | − | 0.265592i | ||||||
\(293\) | − | 7.63128i | − | 0.445824i | −0.974839 | − | 0.222912i | \(-0.928444\pi\) | ||
0.974839 | − | 0.222912i | \(-0.0715563\pi\) | |||||||
\(294\) | −1.29181 | + | 8.10996i | −0.0753399 | + | 0.472982i | ||||
\(295\) | 5.08936 | + | 32.6022i | 0.296314 | + | 1.89817i | ||||
\(296\) | − | 3.43126i | − | 0.199438i | ||||||
\(297\) | −1.48217 | + | 2.96702i | −0.0860040 | + | 0.172164i | ||||
\(298\) | 3.68706i | 0.213586i | ||||||||
\(299\) | 20.2117 | 1.16887 | ||||||||
\(300\) | 2.96998 | − | 0.950419i | 0.171472 | − | 0.0548724i | ||||
\(301\) | −12.5378 | − | 14.6930i | −0.722669 | − | 0.846891i | ||||
\(302\) | − | 1.10194i | − | 0.0634095i | ||||||
\(303\) | 15.2917 | 0.878486 | ||||||||
\(304\) | −12.5775 | −0.721370 | ||||||||
\(305\) | 11.6177 | − | 1.81359i | 0.665230 | − | 0.103846i | ||||
\(306\) | − | 3.63954i | − | 0.208059i | ||||||
\(307\) | − | 29.9896i | − | 1.71160i | −0.517310 | − | 0.855798i | \(-0.673067\pi\) | ||
0.517310 | − | 0.855798i | \(-0.326933\pi\) | |||||||
\(308\) | 5.31172 | − | 1.31752i | 0.302663 | − | 0.0750725i | ||||
\(309\) | 1.35140 | 0.0768787 | ||||||||
\(310\) | 0.292388 | + | 1.87302i | 0.0166065 | + | 0.106380i | ||||
\(311\) | − | 10.3684i | − | 0.587939i | −0.955815 | − | 0.293969i | \(-0.905024\pi\) | ||
0.955815 | − | 0.293969i | \(-0.0949764\pi\) | |||||||
\(312\) | − | 10.5683i | − | 0.598312i | ||||||
\(313\) | −17.3488 | −0.980614 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(314\) | 15.2206 | 0.858948 | ||||||||
\(315\) | 4.48837 | + | 3.85416i | 0.252891 | + | 0.217157i | ||||
\(316\) | 7.19165i | 0.404562i | ||||||||
\(317\) | − | 20.0871i | − | 1.12821i | −0.825704 | − | 0.564103i | \(-0.809222\pi\) | ||
0.825704 | − | 0.564103i | \(-0.190778\pi\) | |||||||
\(318\) | − | 13.7769i | − | 0.772572i | ||||||
\(319\) | 17.2533 | + | 8.61885i | 0.966000 | + | 0.482563i | ||||
\(320\) | −19.2127 | + | 2.99920i | −1.07402 | + | 0.167660i | ||||
\(321\) | 1.77552 | 0.0990996 | ||||||||
\(322\) | 13.8991 | − | 11.8604i | 0.774568 | − | 0.660955i | ||||
\(323\) | 16.5078i | 0.918516i | ||||||||
\(324\) | −0.623669 | −0.0346483 | ||||||||
\(325\) | 5.23233 | + | 16.3506i | 0.290237 | + | 0.906969i | ||||
\(326\) | − | 10.9651i | − | 0.607301i | ||||||
\(327\) | − | 1.93909i | − | 0.107232i | ||||||
\(328\) | −10.2963 | −0.568520 | ||||||||
\(329\) | 11.3430 | + | 13.2928i | 0.625362 | + | 0.732858i | ||||
\(330\) | −2.64114 | + | 8.28991i | −0.145390 | + | 0.456344i | ||||
\(331\) | −17.1491 | −0.942598 | −0.471299 | − | 0.881973i | \(-0.656215\pi\) | ||||
−0.471299 | + | 0.881973i | \(0.656215\pi\) | |||||||
\(332\) | − | 4.61136i | − | 0.253081i | ||||||
\(333\) | − | 1.11476i | − | 0.0610887i | ||||||
\(334\) | 28.4713i | 1.55788i | ||||||||
\(335\) | 0.683568 | + | 4.37890i | 0.0373473 | + | 0.239245i | ||||
\(336\) | −4.05940 | − | 4.75718i | −0.221458 | − | 0.259525i | ||||
\(337\) | −26.9388 | −1.46745 | −0.733724 | − | 0.679448i | \(-0.762219\pi\) | ||||
−0.733724 | + | 0.679448i | \(0.762219\pi\) | |||||||
\(338\) | −1.42096 | −0.0772900 | ||||||||
\(339\) | − | 17.3740i | − | 0.943625i | ||||||
\(340\) | 0.667287 | + | 4.27461i | 0.0361887 | + | 0.231823i | ||||
\(341\) | 2.14410 | + | 1.07108i | 0.116109 | + | 0.0580021i | ||||
\(342\) | −6.24259 | −0.337560 | ||||||||
\(343\) | 15.8039 | − | 9.65595i | 0.853329 | − | 0.521372i | ||||
\(344\) | 22.4711 | 1.21156 | ||||||||
\(345\) | −2.03022 | − | 13.0055i | −0.109303 | − | 0.700190i | ||||
\(346\) | 0.106206i | 0.00570968i | ||||||||
\(347\) | −27.4275 | −1.47238 | −0.736192 | − | 0.676773i | \(-0.763378\pi\) | ||||
−0.736192 | + | 0.676773i | \(0.763378\pi\) | |||||||
\(348\) | 3.62666i | 0.194409i | ||||||||
\(349\) | 3.35671 | 0.179681 | 0.0898403 | − | 0.995956i | \(-0.471364\pi\) | ||||
0.0898403 | + | 0.995956i | \(0.471364\pi\) | |||||||
\(350\) | 13.1928 | + | 8.17356i | 0.705186 | + | 0.436895i | ||||
\(351\) | − | 3.43348i | − | 0.183266i | ||||||
\(352\) | −5.01417 | + | 10.0374i | −0.267256 | + | 0.534997i | ||||
\(353\) | 17.3099 | 0.921312 | 0.460656 | − | 0.887579i | \(-0.347614\pi\) | ||||
0.460656 | + | 0.887579i | \(0.347614\pi\) | |||||||
\(354\) | − | 17.3122i | − | 0.920130i | ||||||
\(355\) | 33.0244 | − | 5.15527i | 1.75275 | − | 0.273613i | ||||
\(356\) | − | 2.27734i | − | 0.120699i | ||||||
\(357\) | −6.24371 | + | 5.32788i | −0.330452 | + | 0.281981i | ||||
\(358\) | 25.8840 | 1.36801 | ||||||||
\(359\) | − | 1.11316i | − | 0.0587501i | −0.999568 | − | 0.0293751i | \(-0.990648\pi\) | ||
0.999568 | − | 0.0293751i | \(-0.00935171\pi\) | |||||||
\(360\) | −6.80029 | + | 1.06156i | −0.358407 | + | 0.0559491i | ||||
\(361\) | 9.31434 | 0.490228 | ||||||||
\(362\) | 6.37952i | 0.335300i | ||||||||
\(363\) | 6.60637 | + | 8.79522i | 0.346745 | + | 0.461629i | ||||
\(364\) | −4.30970 | + | 3.67755i | −0.225890 | + | 0.192756i | ||||
\(365\) | −2.50972 | − | 16.0771i | −0.131365 | − | 0.841514i | ||||
\(366\) | −6.16916 | −0.322467 | ||||||||
\(367\) | 3.68482 | 0.192346 | 0.0961731 | − | 0.995365i | \(-0.469340\pi\) | ||||
0.0961731 | + | 0.995365i | \(0.469340\pi\) | |||||||
\(368\) | 13.9143i | 0.725332i | ||||||||
\(369\) | −3.34512 | −0.174140 | ||||||||
\(370\) | −0.451043 | − | 2.88936i | −0.0234486 | − | 0.150211i | ||||
\(371\) | −23.6346 | + | 20.1679i | −1.22705 | + | 1.04707i | ||||
\(372\) | 0.450691i | 0.0233672i | ||||||||
\(373\) | 4.82270 | 0.249710 | 0.124855 | − | 0.992175i | \(-0.460153\pi\) | ||||
0.124855 | + | 0.992175i | \(0.460153\pi\) | |||||||
\(374\) | −10.7986 | − | 5.39440i | −0.558381 | − | 0.278938i | ||||
\(375\) | 9.99541 | − | 5.00918i | 0.516161 | − | 0.258673i | ||||
\(376\) | −20.3297 | −1.04842 | ||||||||
\(377\) | −19.9658 | −1.02829 | ||||||||
\(378\) | −2.01480 | − | 2.36113i | −0.103630 | − | 0.121443i | ||||
\(379\) | −15.4604 | −0.794148 | −0.397074 | − | 0.917787i | \(-0.629974\pi\) | ||||
−0.397074 | + | 0.917787i | \(0.629974\pi\) | |||||||
\(380\) | 7.33187 | − | 1.14454i | 0.376117 | − | 0.0587137i | ||||
\(381\) | −6.23748 | −0.319556 | ||||||||
\(382\) | 22.2619 | 1.13902 | ||||||||
\(383\) | 4.92470 | 0.251640 | 0.125820 | − | 0.992053i | \(-0.459844\pi\) | ||||
0.125820 | + | 0.992053i | \(0.459844\pi\) | |||||||
\(384\) | 3.43617 | 0.175351 | ||||||||
\(385\) | 18.0879 | − | 7.60456i | 0.921843 | − | 0.387564i | ||||
\(386\) | 19.1499 | 0.974704 | ||||||||
\(387\) | 7.30051 | 0.371106 | ||||||||
\(388\) | −2.35344 | −0.119478 | ||||||||
\(389\) | −8.29383 | −0.420514 | −0.210257 | − | 0.977646i | \(-0.567430\pi\) | ||||
−0.210257 | + | 0.977646i | \(0.567430\pi\) | |||||||
\(390\) | −1.38922 | − | 8.89924i | −0.0703456 | − | 0.450630i | ||||
\(391\) | 18.2622 | 0.923560 | ||||||||
\(392\) | −3.38928 | + | 21.2778i | −0.171185 | + | 1.07469i | ||||
\(393\) | 2.79723 | 0.141102 | ||||||||
\(394\) | −18.9011 | −0.952221 | ||||||||
\(395\) | 3.97693 | + | 25.4760i | 0.200101 | + | 1.28184i | ||||
\(396\) | −0.924381 | + | 1.85044i | −0.0464519 | + | 0.0929880i | ||||
\(397\) | −32.3860 | −1.62541 | −0.812704 | − | 0.582677i | \(-0.802005\pi\) | ||||
−0.812704 | + | 0.582677i | \(0.802005\pi\) | |||||||
\(398\) | − | 28.7393i | − | 1.44057i | ||||||
\(399\) | 9.13845 | + | 10.7093i | 0.457495 | + | 0.536135i | ||||
\(400\) | −11.2562 | + | 3.60207i | −0.562809 | + | 0.180104i | ||||
\(401\) | −18.6858 | −0.933124 | −0.466562 | − | 0.884488i | \(-0.654508\pi\) | ||||
−0.466562 | + | 0.884488i | \(0.654508\pi\) | |||||||
\(402\) | − | 2.32525i | − | 0.115973i | ||||||
\(403\) | −2.48118 | −0.123597 | ||||||||
\(404\) | 9.53698 | 0.474482 | ||||||||
\(405\) | −2.20931 | + | 0.344884i | −0.109782 | + | 0.0171374i | ||||
\(406\) | −13.7300 | + | 11.7161i | −0.681410 | + | 0.581461i | ||||
\(407\) | −3.30753 | − | 1.65227i | −0.163948 | − | 0.0818998i | ||||
\(408\) | − | 9.54894i | − | 0.472743i | ||||||
\(409\) | 7.69234 | 0.380362 | 0.190181 | − | 0.981749i | \(-0.439093\pi\) | ||||
0.190181 | + | 0.981749i | \(0.439093\pi\) | |||||||
\(410\) | −8.67022 | + | 1.35346i | −0.428192 | + | 0.0668429i | ||||
\(411\) | 18.1264i | 0.894111i | ||||||||
\(412\) | 0.842830 | 0.0415232 | ||||||||
\(413\) | −29.6994 | + | 25.3431i | −1.46141 | + | 1.24705i | ||||
\(414\) | 6.90606i | 0.339414i | ||||||||
\(415\) | −2.55004 | − | 16.3354i | −0.125177 | − | 0.801876i | ||||
\(416\) | − | 11.6155i | − | 0.569496i | ||||||
\(417\) | 12.5540 | 0.614771 | ||||||||
\(418\) | −9.25255 | + | 18.5219i | −0.452557 | + | 0.905934i | ||||
\(419\) | 7.32643i | 0.357919i | 0.983856 | + | 0.178960i | \(0.0572732\pi\) | ||||
−0.983856 | + | 0.178960i | \(0.942727\pi\) | |||||||
\(420\) | 2.79926 | + | 2.40372i | 0.136590 | + | 0.117290i | ||||
\(421\) | −1.91887 | −0.0935201 | −0.0467601 | − | 0.998906i | \(-0.514890\pi\) | ||||
−0.0467601 | + | 0.998906i | \(0.514890\pi\) | |||||||
\(422\) | − | 15.3561i | − | 0.747524i | ||||||
\(423\) | −6.60481 | −0.321137 | ||||||||
\(424\) | − | 36.1461i | − | 1.75541i | ||||||
\(425\) | 4.72765 | + | 14.7735i | 0.229325 | + | 0.716621i | ||||
\(426\) | −17.5364 | −0.849639 | ||||||||
\(427\) | 9.03097 | + | 10.5833i | 0.437039 | + | 0.512164i | ||||
\(428\) | 1.10733 | 0.0535251 | ||||||||
\(429\) | −10.1872 | − | 5.08899i | −0.491842 | − | 0.245699i | ||||
\(430\) | 18.9222 | − | 2.95385i | 0.912509 | − | 0.142447i | ||||
\(431\) | 7.47238i | 0.359932i | 0.983673 | + | 0.179966i | \(0.0575988\pi\) | ||||
−0.983673 | + | 0.179966i | \(0.942401\pi\) | |||||||
\(432\) | 2.36370 | 0.113723 | ||||||||
\(433\) | 13.5598 | 0.651644 | 0.325822 | − | 0.945431i | \(-0.394359\pi\) | ||||
0.325822 | + | 0.945431i | \(0.394359\pi\) | |||||||
\(434\) | −1.70625 | + | 1.45598i | −0.0819028 | + | 0.0698893i | ||||
\(435\) | 2.00552 | + | 12.8472i | 0.0961571 | + | 0.615977i | ||||
\(436\) | − | 1.20935i | − | 0.0579175i | ||||||
\(437\) | − | 31.3236i | − | 1.49841i | ||||||
\(438\) | 8.53714i | 0.407920i | ||||||||
\(439\) | −30.6807 | −1.46431 | −0.732156 | − | 0.681137i | \(-0.761486\pi\) | ||||
−0.732156 | + | 0.681137i | \(0.761486\pi\) | |||||||
\(440\) | −6.92949 | + | 21.7500i | −0.330350 | + | 1.03689i | ||||
\(441\) | −1.10113 | + | 6.91285i | −0.0524346 | + | 0.329183i | ||||
\(442\) | 12.4963 | 0.594387 | ||||||||
\(443\) | 29.3213i | 1.39310i | 0.717509 | + | 0.696549i | \(0.245282\pi\) | ||||
−0.717509 | + | 0.696549i | \(0.754718\pi\) | |||||||
\(444\) | − | 0.695245i | − | 0.0329949i | ||||||
\(445\) | −1.25935 | − | 8.06733i | −0.0596990 | − | 0.382428i | ||||
\(446\) | 5.39365 | 0.255397 | ||||||||
\(447\) | 3.14282i | 0.148650i | ||||||||
\(448\) | −14.9349 | − | 17.5021i | −0.705606 | − | 0.826895i | ||||
\(449\) | 14.5550 | 0.686892 | 0.343446 | − | 0.939173i | \(-0.388406\pi\) | ||||
0.343446 | + | 0.939173i | \(0.388406\pi\) | |||||||
\(450\) | −5.58677 | + | 1.78781i | −0.263363 | + | 0.0842783i | ||||
\(451\) | −4.95802 | + | 9.92503i | −0.233464 | + | 0.467352i | ||||
\(452\) | − | 10.8356i | − | 0.509665i | ||||||
\(453\) | − | 0.939283i | − | 0.0441314i | ||||||
\(454\) | − | 22.2787i | − | 1.04559i | ||||||
\(455\) | −13.2332 | + | 15.4107i | −0.620381 | + | 0.722466i | ||||
\(456\) | −16.3785 | −0.766993 | ||||||||
\(457\) | −20.6452 | −0.965741 | −0.482870 | − | 0.875692i | \(-0.660406\pi\) | ||||
−0.482870 | + | 0.875692i | \(0.660406\pi\) | |||||||
\(458\) | 23.1798i | 1.08312i | ||||||||
\(459\) | − | 3.10231i | − | 0.144803i | ||||||
\(460\) | −1.26618 | − | 8.11111i | −0.0590361 | − | 0.378182i | ||||
\(461\) | −7.59495 | −0.353732 | −0.176866 | − | 0.984235i | \(-0.556596\pi\) | ||||
−0.176866 | + | 0.984235i | \(0.556596\pi\) | |||||||
\(462\) | −9.99176 | + | 2.47835i | −0.464859 | + | 0.115303i | ||||
\(463\) | − | 28.5815i | − | 1.32829i | −0.747602 | − | 0.664147i | \(-0.768795\pi\) | ||
0.747602 | − | 0.664147i | \(-0.231205\pi\) | |||||||
\(464\) | − | 13.7450i | − | 0.638095i | ||||||
\(465\) | 0.249229 | + | 1.59655i | 0.0115577 | + | 0.0740380i | ||||
\(466\) | −22.3724 | −1.03638 | ||||||||
\(467\) | 22.0580 | 1.02072 | 0.510360 | − | 0.859961i | \(-0.329512\pi\) | ||||
0.510360 | + | 0.859961i | \(0.329512\pi\) | |||||||
\(468\) | − | 2.14136i | − | 0.0989843i | ||||||
\(469\) | −3.98901 | + | 3.40391i | −0.184196 | + | 0.157178i | ||||
\(470\) | −17.1190 | + | 2.67236i | −0.789640 | + | 0.123267i | ||||
\(471\) | 12.9739 | 0.597806 | ||||||||
\(472\) | − | 45.4214i | − | 2.09069i | ||||||
\(473\) | 10.8206 | − | 21.6607i | 0.497530 | − | 0.995962i | ||||
\(474\) | − | 13.5281i | − | 0.621364i | ||||||
\(475\) | 25.3398 | − | 8.10893i | 1.16267 | − | 0.372063i | ||||
\(476\) | −3.89401 | + | 3.32284i | −0.178482 | + | 0.152302i | ||||
\(477\) | − | 11.7433i | − | 0.537690i | ||||||
\(478\) | − | 27.1660i | − | 1.24254i | ||||||
\(479\) | −30.3084 | −1.38483 | −0.692413 | − | 0.721501i | \(-0.743452\pi\) | ||||
−0.692413 | + | 0.721501i | \(0.743452\pi\) | |||||||
\(480\) | −7.47411 | + | 1.16675i | −0.341145 | + | 0.0532544i | ||||
\(481\) | 3.82752 | 0.174520 | ||||||||
\(482\) | −18.4273 | −0.839339 | ||||||||
\(483\) | 11.8475 | − | 10.1097i | 0.539080 | − | 0.460007i | ||||
\(484\) | 4.12019 | + | 5.48531i | 0.187281 | + | 0.249332i | ||||
\(485\) | −8.33691 | + | 1.30143i | −0.378559 | + | 0.0590950i | ||||
\(486\) | 1.17317 | 0.0532161 | ||||||||
\(487\) | − | 10.1505i | − | 0.459965i | −0.973195 | − | 0.229982i | \(-0.926133\pi\) | ||
0.973195 | − | 0.229982i | \(-0.0738668\pi\) | |||||||
\(488\) | −16.1858 | −0.732699 | ||||||||
\(489\) | − | 9.34655i | − | 0.422665i | ||||||
\(490\) | −0.0570112 | + | 18.3629i | −0.00257550 | + | 0.829553i | ||||
\(491\) | − | 34.2469i | − | 1.54554i | −0.634685 | − | 0.772771i | \(-0.718870\pi\) | ||
0.634685 | − | 0.772771i | \(-0.281130\pi\) | |||||||
\(492\) | −2.08625 | −0.0940554 | ||||||||
\(493\) | −18.0400 | −0.812482 | ||||||||
\(494\) | − | 21.4338i | − | 0.964352i | ||||||
\(495\) | −2.25129 | + | 7.06624i | −0.101188 | + | 0.317604i | ||||
\(496\) | − | 1.70811i | − | 0.0766965i | ||||||
\(497\) | 25.6713 | + | 30.0840i | 1.15151 | + | 1.34945i | ||||
\(498\) | 8.67432i | 0.388706i | ||||||||
\(499\) | 3.09687 | 0.138635 | 0.0693174 | − | 0.997595i | \(-0.477918\pi\) | ||||
0.0693174 | + | 0.997595i | \(0.477918\pi\) | |||||||
\(500\) | 6.23383 | − | 3.12407i | 0.278785 | − | 0.139713i | ||||
\(501\) | 24.2687i | 1.08424i | ||||||||
\(502\) | 32.5114i | 1.45105i | ||||||||
\(503\) | − | 19.8339i | − | 0.884350i | −0.896929 | − | 0.442175i | \(-0.854207\pi\) | ||
0.896929 | − | 0.442175i | \(-0.145793\pi\) | |||||||
\(504\) | −5.28616 | − | 6.19481i | −0.235464 | − | 0.275939i | ||||
\(505\) | 33.7842 | − | 5.27387i | 1.50337 | − | 0.234684i | ||||
\(506\) | 20.4904 | + | 10.2359i | 0.910908 | + | 0.455042i | ||||
\(507\) | −1.21121 | −0.0537918 | ||||||||
\(508\) | −3.89013 | −0.172596 | ||||||||
\(509\) | − | 1.89918i | − | 0.0841798i | −0.999114 | − | 0.0420899i | \(-0.986598\pi\) | ||
0.999114 | − | 0.0420899i | \(-0.0134016\pi\) | |||||||
\(510\) | −1.25522 | − | 8.04087i | −0.0555821 | − | 0.356056i | ||||
\(511\) | 14.6457 | − | 12.4974i | 0.647886 | − | 0.552854i | ||||
\(512\) | 22.5474 | 0.996463 | ||||||||
\(513\) | −5.32112 | −0.234933 | ||||||||
\(514\) | 9.55753 | 0.421564 | ||||||||
\(515\) | 2.98567 | − | 0.466078i | 0.131564 | − | 0.0205379i | ||||
\(516\) | 4.55311 | 0.200439 | ||||||||
\(517\) | −9.78941 | + | 19.5966i | −0.430538 | + | 0.861856i | ||||
\(518\) | 2.63210 | − | 2.24602i | 0.115648 | − | 0.0986846i | ||||
\(519\) | 0.0905291i | 0.00397379i | ||||||||
\(520\) | −3.64484 | − | 23.3487i | −0.159837 | − | 1.02391i | ||||
\(521\) | 8.01305i | 0.351058i | 0.984474 | + | 0.175529i | \(0.0561636\pi\) | ||||
−0.984474 | + | 0.175529i | \(0.943836\pi\) | |||||||
\(522\) | − | 6.82204i | − | 0.298592i | ||||||
\(523\) | − | 5.57803i | − | 0.243910i | −0.992536 | − | 0.121955i | \(-0.961084\pi\) | ||
0.992536 | − | 0.121955i | \(-0.0389164\pi\) | |||||||
\(524\) | 1.74455 | 0.0762109 | ||||||||
\(525\) | 11.2454 | + | 6.96707i | 0.490791 | + | 0.304068i | ||||
\(526\) | −13.5518 | −0.590888 | ||||||||
\(527\) | −2.24186 | −0.0976572 | ||||||||
\(528\) | 3.50339 | − | 7.01313i | 0.152465 | − | 0.305207i | ||||
\(529\) | −11.6527 | −0.506640 | ||||||||
\(530\) | −4.75145 | − | 30.4375i | −0.206390 | − | 1.32212i | ||||
\(531\) | − | 14.7567i | − | 0.640387i | ||||||
\(532\) | 5.69938 | + | 6.67906i | 0.247099 | + | 0.289574i | ||||
\(533\) | − | 11.4854i | − | 0.497488i | ||||||
\(534\) | 4.28385i | 0.185380i | ||||||||
\(535\) | 3.92267 | − | 0.612348i | 0.169592 | − | 0.0264741i | ||||
\(536\) | − | 6.10068i | − | 0.263509i | ||||||
\(537\) | 22.0633 | 0.952100 | ||||||||
\(538\) | 19.9209i | 0.858850i | ||||||||
\(539\) | 18.8785 | + | 13.5130i | 0.813154 | + | 0.582048i | ||||
\(540\) | −1.37788 | + | 0.215094i | −0.0592945 | + | 0.00925617i | ||||
\(541\) | − | 12.9502i | − | 0.556774i | −0.960469 | − | 0.278387i | \(-0.910200\pi\) | ||
0.960469 | − | 0.278387i | \(-0.0897997\pi\) | |||||||
\(542\) | −21.5487 | −0.925595 | ||||||||
\(543\) | 5.43785i | 0.233360i | ||||||||
\(544\) | − | 10.4951i | − | 0.449975i | ||||||
\(545\) | −0.668762 | − | 4.28406i | −0.0286466 | − | 0.183509i | ||||
\(546\) | 8.10688 | − | 6.91776i | 0.346942 | − | 0.296053i | ||||
\(547\) | −9.04582 | −0.386771 | −0.193386 | − | 0.981123i | \(-0.561947\pi\) | ||||
−0.193386 | + | 0.981123i | \(0.561947\pi\) | |||||||
\(548\) | 11.3049i | 0.482922i | ||||||||
\(549\) | −5.25854 | −0.224429 | ||||||||
\(550\) | −2.97605 | + | 19.2259i | −0.126899 | + | 0.819794i | ||||
\(551\) | 30.9425i | 1.31820i | ||||||||
\(552\) | 18.1192i | 0.771205i | ||||||||
\(553\) | −23.2077 | + | 19.8036i | −0.986891 | + | 0.842134i | ||||
\(554\) | 13.6974 | 0.581946 | ||||||||
\(555\) | −0.384465 | − | 2.46286i | −0.0163196 | − | 0.104543i | ||||
\(556\) | 7.82953 | 0.332046 | ||||||||
\(557\) | −35.0800 | −1.48639 | −0.743193 | − | 0.669077i | \(-0.766690\pi\) | ||||
−0.743193 | + | 0.669077i | \(0.766690\pi\) | |||||||
\(558\) | − | 0.847785i | − | 0.0358896i | ||||||
\(559\) | 25.0662i | 1.06019i | ||||||||
\(560\) | −10.6091 | − | 9.11007i | −0.448318 | − | 0.384971i | ||||
\(561\) | −9.20460 | − | 4.59813i | −0.388618 | − | 0.194133i | ||||
\(562\) | − | 8.84870i | − | 0.373260i | ||||||
\(563\) | 0.289494i | 0.0122007i | 0.999981 | + | 0.00610035i | \(0.00194181\pi\) | ||||
−0.999981 | + | 0.00610035i | \(0.998058\pi\) | |||||||
\(564\) | −4.11922 | −0.173450 | ||||||||
\(565\) | −5.99201 | − | 38.3845i | −0.252086 | − | 1.61485i | ||||
\(566\) | 5.74546i | 0.241500i | ||||||||
\(567\) | −1.71739 | − | 2.01260i | −0.0721237 | − | 0.0845213i | ||||
\(568\) | −46.0096 | −1.93052 | ||||||||
\(569\) | 3.15902i | 0.132433i | 0.997805 | + | 0.0662165i | \(0.0210928\pi\) | ||||
−0.997805 | + | 0.0662165i | \(0.978907\pi\) | |||||||
\(570\) | −13.7918 | + | 2.15297i | −0.577676 | + | 0.0901780i | ||||
\(571\) | − | 13.2386i | − | 0.554020i | −0.960867 | − | 0.277010i | \(-0.910656\pi\) | ||
0.960867 | − | 0.277010i | \(-0.0893435\pi\) | |||||||
\(572\) | −6.35344 | − | 3.17384i | −0.265651 | − | 0.132705i | ||||
\(573\) | 18.9758 | 0.792726 | ||||||||
\(574\) | −6.73974 | − | 7.89825i | −0.281311 | − | 0.329667i | ||||
\(575\) | −8.97076 | − | 28.0329i | −0.374106 | − | 1.16905i | ||||
\(576\) | 8.69624 | 0.362343 | ||||||||
\(577\) | −30.8410 | −1.28393 | −0.641964 | − | 0.766734i | \(-0.721880\pi\) | ||||
−0.641964 | + | 0.766734i | \(0.721880\pi\) | |||||||
\(578\) | −8.65294 | −0.359915 | ||||||||
\(579\) | 16.3232 | 0.678369 | ||||||||
\(580\) | 1.25078 | + | 8.01242i | 0.0519358 | + | 0.332698i | ||||
\(581\) | 14.8810 | − | 12.6982i | 0.617368 | − | 0.526812i | ||||
\(582\) | 4.42700 | 0.183505 | ||||||||
\(583\) | −34.8427 | − | 17.4056i | −1.44304 | − | 0.720865i | ||||
\(584\) | 22.3986i | 0.926862i | ||||||||
\(585\) | −1.18415 | − | 7.58563i | −0.0489587 | − | 0.313627i | ||||
\(586\) | 8.95280i | 0.369837i | ||||||||
\(587\) | −35.0865 | −1.44818 | −0.724088 | − | 0.689708i | \(-0.757739\pi\) | ||||
−0.724088 | + | 0.689708i | \(0.757739\pi\) | |||||||
\(588\) | −0.686739 | + | 4.31133i | −0.0283206 | + | 0.177796i | ||||
\(589\) | 3.84528i | 0.158442i | ||||||||
\(590\) | −5.97069 | − | 38.2479i | −0.245809 | − | 1.57464i | ||||
\(591\) | −16.1111 | −0.662721 | ||||||||
\(592\) | 2.63497i | 0.108296i | ||||||||
\(593\) | − | 41.1114i | − | 1.68824i | −0.536151 | − | 0.844122i | \(-0.680122\pi\) | ||
0.536151 | − | 0.844122i | \(-0.319878\pi\) | |||||||
\(594\) | 1.73883 | − | 3.48082i | 0.0713452 | − | 0.142820i | ||||
\(595\) | −11.9568 | + | 13.9243i | −0.490181 | + | 0.570841i | ||||
\(596\) | 1.96008i | 0.0802880i | ||||||||
\(597\) | − | 24.4971i | − | 1.00260i | ||||||
\(598\) | −23.7118 | −0.969648 | ||||||||
\(599\) | 11.6236 | 0.474927 | 0.237464 | − | 0.971396i | \(-0.423684\pi\) | ||||
0.237464 | + | 0.971396i | \(0.423684\pi\) | |||||||
\(600\) | −14.6578 | + | 4.69063i | −0.598404 | + | 0.191494i | ||||
\(601\) | −24.3506 | −0.993282 | −0.496641 | − | 0.867956i | \(-0.665433\pi\) | ||||
−0.496641 | + | 0.867956i | \(0.665433\pi\) | |||||||
\(602\) | 14.7090 | + | 17.2374i | 0.599495 | + | 0.702545i | ||||
\(603\) | − | 1.98202i | − | 0.0807141i | ||||||
\(604\) | − | 0.585802i | − | 0.0238360i | ||||||
\(605\) | 17.6289 | + | 17.1529i | 0.716715 | + | 0.697366i | ||||
\(606\) | −17.9398 | −0.728754 | ||||||||
\(607\) | 14.1378i | 0.573834i | 0.957955 | + | 0.286917i | \(0.0926305\pi\) | ||||
−0.957955 | + | 0.286917i | \(0.907370\pi\) | |||||||
\(608\) | −18.0014 | −0.730052 | ||||||||
\(609\) | −11.7034 | + | 9.98670i | −0.474244 | + | 0.404682i | ||||
\(610\) | −13.6296 | + | 2.12765i | −0.551846 | + | 0.0861460i | ||||
\(611\) | − | 22.6775i | − | 0.917432i | ||||||
\(612\) | − | 1.93481i | − | 0.0782102i | ||||||
\(613\) | 3.49651 | 0.141223 | 0.0706114 | − | 0.997504i | \(-0.477505\pi\) | ||||
0.0706114 | + | 0.997504i | \(0.477505\pi\) | |||||||
\(614\) | 35.1829i | 1.41987i | ||||||||
\(615\) | −7.39042 | + | 1.15368i | −0.298010 | + | 0.0465209i | ||||
\(616\) | −26.2151 | + | 6.50238i | −1.05624 | + | 0.261988i | ||||
\(617\) | 3.42766i | 0.137992i | 0.997617 | + | 0.0689961i | \(0.0219796\pi\) | ||||
−0.997617 | + | 0.0689961i | \(0.978020\pi\) | |||||||
\(618\) | −1.58543 | −0.0637753 | ||||||||
\(619\) | 0.639680i | 0.0257109i | 0.999917 | + | 0.0128555i | \(0.00409213\pi\) | ||||
−0.999917 | + | 0.0128555i | \(0.995908\pi\) | |||||||
\(620\) | 0.155436 | + | 0.995717i | 0.00624247 | + | 0.0399889i | ||||
\(621\) | 5.88666i | 0.236223i | ||||||||
\(622\) | 12.1639i | 0.487729i | ||||||||
\(623\) | 7.34905 | − | 6.27109i | 0.294433 | − | 0.251246i | ||||
\(624\) | 8.11571i | 0.324888i | ||||||||
\(625\) | 20.3554 | − | 14.5141i | 0.814215 | − | 0.580564i | ||||
\(626\) | 20.3531 | 0.813475 | ||||||||
\(627\) | −7.88678 | + | 15.7879i | −0.314968 | + | 0.630506i | ||||
\(628\) | 8.09142 | 0.322883 | ||||||||
\(629\) | 3.45834 | 0.137893 | ||||||||
\(630\) | −5.26562 | − | 4.52159i | −0.209788 | − | 0.180144i | ||||
\(631\) | 44.9853 | 1.79084 | 0.895418 | − | 0.445226i | \(-0.146877\pi\) | ||||
0.895418 | + | 0.445226i | \(0.146877\pi\) | |||||||
\(632\) | − | 35.4931i | − | 1.41184i | ||||||
\(633\) | − | 13.0894i | − | 0.520257i | ||||||
\(634\) | 23.5657i | 0.935912i | ||||||||
\(635\) | −13.7805 | + | 2.15121i | −0.546864 | + | 0.0853682i | ||||
\(636\) | − | 7.32396i | − | 0.290414i | ||||||
\(637\) | −23.7351 | − | 3.78070i | −0.940421 | − | 0.149797i | ||||
\(638\) | −20.2411 | − | 10.1114i | −0.801352 | − | 0.400314i | ||||
\(639\) | −14.9478 | −0.591327 | ||||||||
\(640\) | 7.59156 | − | 1.18508i | 0.300083 | − | 0.0468444i | ||||
\(641\) | 26.6120 | 1.05111 | 0.525556 | − | 0.850759i | \(-0.323857\pi\) | ||||
0.525556 | + | 0.850759i | \(0.323857\pi\) | |||||||
\(642\) | −2.08298 | −0.0822088 | ||||||||
\(643\) | −32.0498 | −1.26392 | −0.631960 | − | 0.775001i | \(-0.717749\pi\) | ||||
−0.631960 | + | 0.775001i | \(0.717749\pi\) | |||||||
\(644\) | 7.38892 | − | 6.30511i | 0.291164 | − | 0.248456i | ||||
\(645\) | 16.1291 | − | 2.51783i | 0.635083 | − | 0.0991396i | ||||
\(646\) | − | 19.3664i | − | 0.761962i | ||||||
\(647\) | −2.30057 | −0.0904447 | −0.0452223 | − | 0.998977i | \(-0.514400\pi\) | ||||
−0.0452223 | + | 0.998977i | \(0.514400\pi\) | |||||||
\(648\) | 3.07801 | 0.120916 | ||||||||
\(649\) | −43.7834 | − | 21.8719i | −1.71865 | − | 0.858547i | ||||
\(650\) | −6.13842 | − | 19.1821i | −0.240768 | − | 0.752382i | ||||
\(651\) | −1.45439 | + | 1.24106i | −0.0570022 | + | 0.0486411i | ||||
\(652\) | − | 5.82916i | − | 0.228287i | ||||||
\(653\) | 30.8146i | 1.20587i | 0.797791 | + | 0.602934i | \(0.206002\pi\) | ||||
−0.797791 | + | 0.602934i | \(0.793998\pi\) | |||||||
\(654\) | 2.27489i | 0.0889551i | ||||||||
\(655\) | 6.17995 | − | 0.964721i | 0.241471 | − | 0.0376948i | ||||
\(656\) | 7.90686 | 0.308711 | ||||||||
\(657\) | 7.27698i | 0.283902i | ||||||||
\(658\) | −13.3073 | − | 15.5948i | −0.518774 | − | 0.607948i | ||||
\(659\) | 42.0492i | 1.63801i | 0.573789 | + | 0.819003i | \(0.305473\pi\) | ||||
−0.573789 | + | 0.819003i | \(0.694527\pi\) | |||||||
\(660\) | −1.40406 | + | 4.40700i | −0.0546529 | + | 0.171542i | ||||
\(661\) | − | 10.9191i | − | 0.424704i | −0.977193 | − | 0.212352i | \(-0.931888\pi\) | ||
0.977193 | − | 0.212352i | \(-0.0681124\pi\) | |||||||
\(662\) | 20.1188 | 0.781939 | ||||||||
\(663\) | 10.6517 | 0.413678 | ||||||||
\(664\) | 22.7586i | 0.883203i | ||||||||
\(665\) | 23.8832 | + | 20.5085i | 0.926149 | + | 0.795284i | ||||
\(666\) | 1.30781i | 0.0506766i | ||||||||
\(667\) | 34.2311 | 1.32543 | ||||||||
\(668\) | 15.1356i | 0.585615i | ||||||||
\(669\) | 4.59749 | 0.177749 | ||||||||
\(670\) | −0.801942 | − | 5.13720i | −0.0309817 | − | 0.198467i | ||||
\(671\) | −7.79402 | + | 15.6022i | −0.300885 | + | 0.602315i | ||||
\(672\) | −5.80995 | − | 6.80864i | −0.224124 | − | 0.262649i | ||||
\(673\) | −16.5791 | −0.639078 | −0.319539 | − | 0.947573i | \(-0.603528\pi\) | ||||
−0.319539 | + | 0.947573i | \(0.603528\pi\) | |||||||
\(674\) | 31.6038 | 1.21733 | ||||||||
\(675\) | −4.76211 | + | 1.52391i | −0.183294 | + | 0.0586555i | ||||
\(676\) | −0.755396 | −0.0290537 | ||||||||
\(677\) | 38.2674i | 1.47074i | 0.677667 | + | 0.735369i | \(0.262991\pi\) | ||||
−0.677667 | + | 0.735369i | \(0.737009\pi\) | |||||||
\(678\) | 20.3826i | 0.782791i | ||||||||
\(679\) | −6.48064 | − | 7.59461i | −0.248704 | − | 0.291455i | ||||
\(680\) | −3.29328 | − | 21.0966i | −0.126292 | − | 0.809017i | ||||
\(681\) | − | 18.9902i | − | 0.727705i | ||||||
\(682\) | −2.51539 | − | 1.25656i | −0.0963194 | − | 0.0481161i | ||||
\(683\) | − | 2.74520i | − | 0.105042i | −0.998620 | − | 0.0525211i | \(-0.983274\pi\) | ||
0.998620 | − | 0.0525211i | \(-0.0167257\pi\) | |||||||
\(684\) | −3.31862 | −0.126891 | ||||||||
\(685\) | 6.25152 | + | 40.0469i | 0.238858 | + | 1.53011i | ||||
\(686\) | −18.5407 | + | 11.3281i | −0.707886 | + | 0.432508i | ||||
\(687\) | 19.7583i | 0.753825i | ||||||||
\(688\) | −17.2562 | −0.657886 | ||||||||
\(689\) | 40.3205 | 1.53609 | ||||||||
\(690\) | 2.38179 | + | 15.2576i | 0.0906732 | + | 0.580848i | ||||
\(691\) | 18.2714i | 0.695079i | 0.937665 | + | 0.347539i | \(0.112983\pi\) | ||||
−0.937665 | + | 0.347539i | \(0.887017\pi\) | |||||||
\(692\) | 0.0564602i | 0.00214630i | ||||||||
\(693\) | −8.51688 | + | 2.11252i | −0.323530 | + | 0.0802481i | ||||
\(694\) | 32.1771 | 1.22143 | ||||||||
\(695\) | 27.7356 | − | 4.32967i | 1.05207 | − | 0.164234i | ||||
\(696\) | − | 17.8988i | − | 0.678451i | ||||||
\(697\) | − | 10.3776i | − | 0.393080i | ||||||
\(698\) | −3.93799 | −0.149055 | ||||||||
\(699\) | −19.0700 | −0.721295 | ||||||||
\(700\) | 7.01344 | + | 4.34515i | 0.265083 | + | 0.164231i | ||||
\(701\) | 8.67328i | 0.327585i | 0.986495 | + | 0.163793i | \(0.0523728\pi\) | ||||
−0.986495 | + | 0.163793i | \(0.947627\pi\) | |||||||
\(702\) | 4.02806i | 0.152029i | ||||||||
\(703\) | − | 5.93180i | − | 0.223722i | ||||||
\(704\) | 12.8893 | − | 25.8019i | 0.485782 | − | 0.972445i | ||||
\(705\) | −14.5921 | + | 2.27789i | −0.549569 | + | 0.0857905i | ||||
\(706\) | −20.3075 | −0.764281 | ||||||||
\(707\) | 26.2619 | + | 30.7761i | 0.987679 | + | 1.15746i | ||||
\(708\) | − | 9.20331i | − | 0.345882i | ||||||
\(709\) | −26.4116 | −0.991907 | −0.495954 | − | 0.868349i | \(-0.665181\pi\) | ||||
−0.495954 | + | 0.868349i | \(0.665181\pi\) | |||||||
\(710\) | −38.7433 | + | 6.04802i | −1.45401 | + | 0.226978i | ||||
\(711\) | − | 11.5312i | − | 0.432453i | ||||||
\(712\) | 11.2394i | 0.421215i | ||||||||
\(713\) | 4.25396 | 0.159312 | ||||||||
\(714\) | 7.32494 | − | 6.25051i | 0.274129 | − | 0.233920i | ||||
\(715\) | −24.2618 | − | 7.72975i | −0.907339 | − | 0.289076i | ||||
\(716\) | 13.7602 | 0.514242 | ||||||||
\(717\) | − | 23.1560i | − | 0.864777i | ||||||
\(718\) | 1.30592i | 0.0487366i | ||||||||
\(719\) | − | 52.5438i | − | 1.95955i | −0.200091 | − | 0.979777i | \(-0.564124\pi\) | ||
0.200091 | − | 0.979777i | \(-0.435876\pi\) | |||||||
\(720\) | 5.22214 | − | 0.815202i | 0.194618 | − | 0.0303808i | ||||
\(721\) | 2.32089 | + | 2.71984i | 0.0864345 | + | 0.101292i | ||||
\(722\) | −10.9273 | −0.406673 | ||||||||
\(723\) | −15.7072 | −0.584158 | ||||||||
\(724\) | 3.39142i | 0.126041i | ||||||||
\(725\) | 8.86162 | + | 27.6918i | 0.329112 | + | 1.02845i | ||||
\(726\) | −7.75041 | − | 10.3183i | −0.287645 | − | 0.382948i | ||||
\(727\) | 30.1240 | 1.11724 | 0.558619 | − | 0.829424i | \(-0.311331\pi\) | ||||
0.558619 | + | 0.829424i | \(0.311331\pi\) | |||||||
\(728\) | 21.2698 | − | 18.1499i | 0.788310 | − | 0.672681i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.94433 | + | 18.8612i | 0.108974 | + | 0.698084i | ||||
\(731\) | 22.6484i | 0.837682i | ||||||||
\(732\) | −3.27959 | −0.121217 | ||||||||
\(733\) | 12.6817i | 0.468408i | 0.972187 | + | 0.234204i | \(0.0752484\pi\) | ||||
−0.972187 | + | 0.234204i | \(0.924752\pi\) | |||||||
\(734\) | −4.32293 | −0.159562 | ||||||||
\(735\) | −0.0485958 | + | 15.6524i | −0.00179248 | + | 0.577347i | ||||
\(736\) | 19.9146i | 0.734061i | ||||||||
\(737\) | −5.88068 | − | 2.93768i | −0.216618 | − | 0.108211i | ||||
\(738\) | 3.92440 | 0.144459 | ||||||||
\(739\) | − | 16.2962i | − | 0.599464i | −0.954023 | − | 0.299732i | \(-0.903103\pi\) | ||
0.954023 | − | 0.299732i | \(-0.0968973\pi\) | |||||||
\(740\) | −0.239779 | − | 1.53601i | −0.00881445 | − | 0.0564649i | ||||
\(741\) | − | 18.2700i | − | 0.671164i | ||||||
\(742\) | 27.7275 | − | 23.6604i | 1.01791 | − | 0.868601i | ||||
\(743\) | −3.73982 | −0.137201 | −0.0686003 | − | 0.997644i | \(-0.521853\pi\) | ||||
−0.0686003 | + | 0.997644i | \(0.521853\pi\) | |||||||
\(744\) | − | 2.22431i | − | 0.0815471i | ||||||
\(745\) | 1.08391 | + | 6.94346i | 0.0397114 | + | 0.254389i | ||||
\(746\) | −5.65786 | −0.207149 | ||||||||
\(747\) | 7.39391i | 0.270529i | ||||||||
\(748\) | −5.74063 | − | 2.86772i | −0.209898 | − | 0.104854i | ||||
\(749\) | 3.04926 | + | 3.57340i | 0.111417 | + | 0.130569i | ||||
\(750\) | −11.7263 | + | 5.87662i | −0.428185 | + | 0.214584i | ||||
\(751\) | −21.8888 | −0.798735 | −0.399367 | − | 0.916791i | \(-0.630770\pi\) | ||||
−0.399367 | + | 0.916791i | \(0.630770\pi\) | |||||||
\(752\) | 15.6118 | 0.569302 | ||||||||
\(753\) | 27.7124i | 1.00990i | ||||||||
\(754\) | 23.4233 | 0.853027 | ||||||||
\(755\) | −0.323944 | − | 2.07517i | −0.0117895 | − | 0.0755231i | ||||
\(756\) | −1.07109 | − | 1.25520i | −0.0389550 | − | 0.0456511i | ||||
\(757\) | − | 49.3842i | − | 1.79490i | −0.441118 | − | 0.897449i | \(-0.645418\pi\) | ||
0.441118 | − | 0.897449i | \(-0.354582\pi\) | |||||||
\(758\) | 18.1377 | 0.658791 | ||||||||
\(759\) | 17.4658 | + | 8.72500i | 0.633969 | + | 0.316697i | ||||
\(760\) | −36.1852 | + | 5.64868i | −1.31257 | + | 0.204899i | ||||
\(761\) | 26.4800 | 0.959898 | 0.479949 | − | 0.877296i | \(-0.340655\pi\) | ||||
0.479949 | + | 0.877296i | \(0.340655\pi\) | |||||||
\(762\) | 7.31763 | 0.265090 | ||||||||
\(763\) | 3.90262 | − | 3.33018i | 0.141284 | − | 0.120561i | ||||
\(764\) | 11.8346 | 0.428162 | ||||||||
\(765\) | −1.06994 | − | 6.85396i | −0.0386837 | − | 0.247806i | ||||
\(766\) | −5.77751 | −0.208750 | ||||||||
\(767\) | 50.6669 | 1.82948 | ||||||||
\(768\) | 13.3613 | 0.482133 | ||||||||
\(769\) | −2.91216 | −0.105015 | −0.0525075 | − | 0.998621i | \(-0.516721\pi\) | ||||
−0.0525075 | + | 0.998621i | \(0.516721\pi\) | |||||||
\(770\) | −21.2202 | + | 8.92145i | −0.764721 | + | 0.321507i | ||||
\(771\) | 8.14674 | 0.293398 | ||||||||
\(772\) | 10.1803 | 0.366396 | ||||||||
\(773\) | −46.6347 | −1.67733 | −0.838666 | − | 0.544646i | \(-0.816664\pi\) | ||||
−0.838666 | + | 0.544646i | \(0.816664\pi\) | |||||||
\(774\) | −8.56475 | −0.307854 | ||||||||
\(775\) | 1.10125 | + | 3.44131i | 0.0395580 | + | 0.123616i | ||||
\(776\) | 11.6150 | 0.416954 | ||||||||
\(777\) | 2.24358 | − | 1.91449i | 0.0804879 | − | 0.0686819i | ||||
\(778\) | 9.73008 | 0.348840 | ||||||||
\(779\) | −17.7998 | −0.637744 | ||||||||
\(780\) | −0.738521 | − | 4.73092i | −0.0264433 | − | 0.169394i | ||||
\(781\) | −22.1552 | + | 44.3505i | −0.792774 | + | 1.58698i | ||||
\(782\) | −21.4247 | −0.766146 | ||||||||
\(783\) | − | 5.81504i | − | 0.207813i | ||||||
\(784\) | 2.60273 | − | 16.3399i | 0.0929546 | − | 0.583567i | ||||
\(785\) | 28.6634 | − | 4.47450i | 1.02304 | − | 0.159702i | ||||
\(786\) | −3.28163 | −0.117052 | ||||||||
\(787\) | − | 23.3539i | − | 0.832478i | −0.909255 | − | 0.416239i | \(-0.863348\pi\) | ||
0.909255 | − | 0.416239i | \(-0.136652\pi\) | |||||||
\(788\) | −10.0480 | −0.357945 | ||||||||
\(789\) | −11.5514 | −0.411242 | ||||||||
\(790\) | −4.66562 | − | 29.8877i | −0.165995 | − | 1.06336i | ||||
\(791\) | 34.9669 | − | 29.8379i | 1.24328 | − | 1.06091i | ||||
\(792\) | 4.56212 | − | 9.13252i | 0.162108 | − | 0.324510i | ||||
\(793\) | − | 18.0551i | − | 0.641155i | ||||||
\(794\) | 37.9943 | 1.34837 | ||||||||
\(795\) | −4.05009 | − | 25.9447i | −0.143642 | − | 0.920163i | ||||
\(796\) | − | 15.2781i | − | 0.541518i | ||||||
\(797\) | 31.0609 | 1.10023 | 0.550117 | − | 0.835087i | \(-0.314583\pi\) | ||||
0.550117 | + | 0.835087i | \(0.314583\pi\) | |||||||
\(798\) | −10.7210 | − | 12.5638i | −0.379518 | − | 0.444755i | ||||
\(799\) | − | 20.4901i | − | 0.724889i | ||||||
\(800\) | −16.1102 | + | 5.15541i | −0.569583 | + | 0.182271i | ||||
\(801\) | 3.65152i | 0.129020i | ||||||||
\(802\) | 21.9216 | 0.774080 | ||||||||
\(803\) | 21.5909 | + | 10.7857i | 0.761927 | + | 0.380619i | ||||
\(804\) | − | 1.23613i | − | 0.0435948i | ||||||
\(805\) | 22.6881 | − | 26.4215i | 0.799651 | − | 0.931235i | ||||
\(806\) | 2.91085 | 0.102530 | ||||||||
\(807\) | 16.9804i | 0.597737i | ||||||||
\(808\) | −47.0681 | −1.65585 | ||||||||
\(809\) | 34.0603i | 1.19750i | 0.800938 | + | 0.598748i | \(0.204335\pi\) | ||||
−0.800938 | + | 0.598748i | \(0.795665\pi\) | |||||||
\(810\) | 2.59190 | − | 0.404608i | 0.0910701 | − | 0.0142165i | ||||
\(811\) | 52.8198 | 1.85475 | 0.927377 | − | 0.374129i | \(-0.122058\pi\) | ||||
0.927377 | + | 0.374129i | \(0.122058\pi\) | |||||||
\(812\) | −7.29902 | + | 6.22840i | −0.256146 | + | 0.218574i | ||||
\(813\) | −18.3679 | −0.644190 | ||||||||
\(814\) | 3.88029 | + | 1.93839i | 0.136004 | + | 0.0679405i | ||||
\(815\) | −3.22348 | − | 20.6494i | −0.112914 | − | 0.723318i | ||||
\(816\) | 7.33292i | 0.256703i | ||||||||
\(817\) | 38.8469 | 1.35908 | ||||||||
\(818\) | −9.02443 | −0.315532 | ||||||||
\(819\) | 6.91023 | − | 5.89663i | 0.241463 | − | 0.206045i | ||||
\(820\) | −4.60918 | + | 0.719515i | −0.160959 | + | 0.0251266i | ||||
\(821\) | − | 7.76941i | − | 0.271154i | −0.990767 | − | 0.135577i | \(-0.956711\pi\) | ||
0.990767 | − | 0.135577i | \(-0.0432888\pi\) | |||||||
\(822\) | − | 21.2654i | − | 0.741716i | ||||||
\(823\) | 1.80568i | 0.0629422i | 0.999505 | + | 0.0314711i | \(0.0100192\pi\) | ||||
−0.999505 | + | 0.0314711i | \(0.989981\pi\) | |||||||
\(824\) | −4.15964 | −0.144908 | ||||||||
\(825\) | −2.53676 | + | 16.3879i | −0.0883185 | + | 0.570555i | ||||
\(826\) | 34.8425 | − | 29.7318i | 1.21232 | − | 1.03450i | ||||
\(827\) | −52.6701 | −1.83152 | −0.915760 | − | 0.401726i | \(-0.868411\pi\) | ||||
−0.915760 | + | 0.401726i | \(0.868411\pi\) | |||||||
\(828\) | 3.67133i | 0.127587i | ||||||||
\(829\) | 7.36227i | 0.255702i | 0.991793 | + | 0.127851i | \(0.0408079\pi\) | ||||
−0.991793 | + | 0.127851i | \(0.959192\pi\) | |||||||
\(830\) | 2.99164 | + | 19.1643i | 0.103841 | + | 0.665202i | ||||
\(831\) | 11.6755 | 0.405019 | ||||||||
\(832\) | 29.8584i | 1.03515i | ||||||||
\(833\) | −21.4458 | − | 3.41603i | −0.743053 | − | 0.118359i | ||||
\(834\) | −14.7280 | −0.509987 | ||||||||
\(835\) | 8.36988 | + | 53.6170i | 0.289652 | + | 1.85549i | ||||
\(836\) | −4.91875 | + | 9.84640i | −0.170118 | + | 0.340545i | ||||
\(837\) | − | 0.722644i | − | 0.0249782i | ||||||
\(838\) | − | 8.59516i | − | 0.296915i | ||||||
\(839\) | − | 17.7190i | − | 0.611728i | −0.952075 | − | 0.305864i | \(-0.901055\pi\) | ||
0.952075 | − | 0.305864i | \(-0.0989454\pi\) | |||||||
\(840\) | −13.8153 | − | 11.8632i | −0.476672 | − | 0.409318i | ||||
\(841\) | −4.81467 | −0.166023 | ||||||||
\(842\) | 2.25117 | 0.0775803 | ||||||||
\(843\) | − | 7.54255i | − | 0.259779i | ||||||
\(844\) | − | 8.16346i | − | 0.280998i | ||||||
\(845\) | −2.67594 | + | 0.417728i | −0.0920553 | + | 0.0143703i | ||||
\(846\) | 7.74857 | 0.266401 | ||||||||
\(847\) | −6.35553 | + | 28.4008i | −0.218379 | + | 0.975864i | ||||
\(848\) | 27.7577i | 0.953203i | ||||||||
\(849\) | 4.89738i | 0.168078i | ||||||||
\(850\) | −5.54634 | − | 17.3319i | −0.190238 | − | 0.594478i | ||||
\(851\) | −6.56224 | −0.224951 | ||||||||
\(852\) | −9.32250 | −0.319384 | ||||||||
\(853\) | 40.5291i | 1.38769i | 0.720125 | + | 0.693844i | \(0.244084\pi\) | ||||
−0.720125 | + | 0.693844i | \(0.755916\pi\) | |||||||
\(854\) | −10.5949 | − | 12.4161i | −0.362549 | − | 0.424869i | ||||
\(855\) | −11.7560 | + | 1.83517i | −0.402047 | + | 0.0627616i | ||||
\(856\) | −5.46506 | −0.186792 | ||||||||
\(857\) | − | 33.2959i | − | 1.13737i | −0.822556 | − | 0.568683i | \(-0.807453\pi\) | ||
0.822556 | − | 0.568683i | \(-0.192547\pi\) | |||||||
\(858\) | 11.9513 | + | 5.97025i | 0.408011 | + | 0.203821i | ||||
\(859\) | − | 49.0304i | − | 1.67289i | −0.548048 | − | 0.836447i | \(-0.684629\pi\) | ||
0.548048 | − | 0.836447i | \(-0.315371\pi\) | |||||||
\(860\) | 10.0592 | − | 1.57030i | 0.343017 | − | 0.0535466i | ||||
\(861\) | −5.74489 | − | 6.73240i | −0.195785 | − | 0.229439i | ||||
\(862\) | − | 8.76638i | − | 0.298584i | ||||||
\(863\) | 10.0731i | 0.342891i | 0.985194 | + | 0.171446i | \(0.0548438\pi\) | ||||
−0.985194 | + | 0.171446i | \(0.945156\pi\) | |||||||
\(864\) | 3.38301 | 0.115092 | ||||||||
\(865\) | 0.0312221 | + | 0.200007i | 0.00106158 | + | 0.00680044i | ||||
\(866\) | −15.9080 | −0.540576 | ||||||||
\(867\) | −7.37569 | −0.250491 | ||||||||
\(868\) | −0.907061 | + | 0.774014i | −0.0307877 | + | 0.0262717i | ||||
\(869\) | −34.2132 | − | 17.0911i | −1.16060 | − | 0.579777i | ||||
\(870\) | −2.35281 | − | 15.0720i | −0.0797679 | − | 0.510989i | ||||
\(871\) | 6.80522 | 0.230586 | ||||||||
\(872\) | 5.96855i | 0.202121i | ||||||||
\(873\) | 3.77353 | 0.127715 | ||||||||
\(874\) | 36.7480i | 1.24302i | ||||||||
\(875\) | 27.2475 | + | 11.5140i | 0.921134 | + | 0.389246i | ||||
\(876\) | 4.53843i | 0.153339i | ||||||||
\(877\) | 15.1073 | 0.510136 | 0.255068 | − | 0.966923i | \(-0.417902\pi\) | ||||
0.255068 | + | 0.966923i | \(0.417902\pi\) | |||||||
\(878\) | 35.9937 | 1.21473 | ||||||||
\(879\) | 7.63128i | 0.257397i | ||||||||
\(880\) | 5.32136 | − | 16.7024i | 0.179383 | − | 0.563039i | ||||
\(881\) | − | 28.6024i | − | 0.963639i | −0.876271 | − | 0.481819i | \(-0.839976\pi\) | ||
0.876271 | − | 0.481819i | \(-0.160024\pi\) | |||||||
\(882\) | 1.29181 | − | 8.10996i | 0.0434975 | − | 0.273076i | ||||
\(883\) | 12.6564i | 0.425921i | 0.977061 | + | 0.212960i | \(0.0683106\pi\) | ||||
−0.977061 | + | 0.212960i | \(0.931689\pi\) | |||||||
\(884\) | 6.64315 | 0.223433 | ||||||||
\(885\) | −5.08936 | − | 32.6022i | −0.171077 | − | 1.09591i | ||||
\(886\) | − | 34.3989i | − | 1.15565i | ||||||
\(887\) | 11.2443i | 0.377547i | 0.982021 | + | 0.188774i | \(0.0604512\pi\) | ||||
−0.982021 | + | 0.188774i | \(0.939549\pi\) | |||||||
\(888\) | 3.43126i | 0.115146i | ||||||||
\(889\) | −10.7122 | − | 12.5536i | −0.359276 | − | 0.421033i | ||||
\(890\) | 1.47743 | + | 9.46436i | 0.0495237 | + | 0.317246i | ||||
\(891\) | 1.48217 | − | 2.96702i | 0.0496544 | − | 0.0993988i | ||||
\(892\) | 2.86732 | 0.0960048 | ||||||||
\(893\) | −35.1450 | −1.17608 | ||||||||
\(894\) | − | 3.68706i | − | 0.123314i | ||||||
\(895\) | 48.7446 | − | 7.60928i | 1.62935 | − | 0.254350i | ||||
\(896\) | 5.90125 | + | 6.91563i | 0.197147 | + | 0.231035i | ||||
\(897\) | −20.2117 | −0.674850 | ||||||||
\(898\) | −17.0755 | −0.569816 | ||||||||
\(899\) | −4.20220 | −0.140151 | ||||||||
\(900\) | −2.96998 | + | 0.950419i | −0.0989994 | + | 0.0316806i | ||||
\(901\) | 36.4314 | 1.21371 | ||||||||
\(902\) | 5.81661 | − | 11.6438i | 0.193672 | − | 0.387695i | ||||
\(903\) | 12.5378 | + | 14.6930i | 0.417233 | + | 0.488953i | ||||
\(904\) | 53.4773i | 1.77863i | ||||||||
\(905\) | 1.87543 | + | 12.0139i | 0.0623413 | + | 0.399355i | ||||
\(906\) | 1.10194i | 0.0366095i | ||||||||
\(907\) | 46.9653i | 1.55946i | 0.626117 | + | 0.779729i | \(0.284643\pi\) | ||||
−0.626117 | + | 0.779729i | \(0.715357\pi\) | |||||||
\(908\) | − | 11.8436i | − | 0.393043i | ||||||
\(909\) | −15.2917 | −0.507194 | ||||||||
\(910\) | 15.5248 | − | 18.0794i | 0.514642 | − | 0.599327i | ||||
\(911\) | 7.80180 | 0.258485 | 0.129243 | − | 0.991613i | \(-0.458745\pi\) | ||||
0.129243 | + | 0.991613i | \(0.458745\pi\) | |||||||
\(912\) | 12.5775 | 0.416483 | ||||||||
\(913\) | 21.9379 | + | 10.9590i | 0.726037 | + | 0.362690i | ||||
\(914\) | 24.2203 | 0.801137 | ||||||||
\(915\) | −11.6177 | + | 1.81359i | −0.384071 | + | 0.0599553i | ||||
\(916\) | 12.3226i | 0.407151i | ||||||||
\(917\) | 4.80394 | + | 5.62971i | 0.158640 | + | 0.185909i | ||||
\(918\) | 3.63954i | 0.120123i | ||||||||
\(919\) | 28.8139i | 0.950484i | 0.879855 | + | 0.475242i | \(0.157639\pi\) | ||||
−0.879855 | + | 0.475242i | \(0.842361\pi\) | |||||||
\(920\) | 6.24903 | + | 40.0310i | 0.206024 | + | 1.31978i | ||||
\(921\) | 29.9896i | 0.988190i | ||||||||
\(922\) | 8.91017 | 0.293441 | ||||||||
\(923\) | − | 51.3231i | − | 1.68932i | ||||||
\(924\) | −5.31172 | + | 1.31752i | −0.174743 | + | 0.0433431i | ||||
\(925\) | −1.69881 | − | 5.30863i | −0.0558564 | − | 0.174547i | ||||
\(926\) | 33.5310i | 1.10190i | ||||||||
\(927\) | −1.35140 | −0.0443859 | ||||||||
\(928\) | − | 19.6723i | − | 0.645775i | ||||||
\(929\) | 0.852646i | 0.0279744i | 0.999902 | + | 0.0139872i | \(0.00445241\pi\) | ||||
−0.999902 | + | 0.0139872i | \(0.995548\pi\) | |||||||
\(930\) | −0.292388 | − | 1.87302i | −0.00958778 | − | 0.0614188i | ||||
\(931\) | −5.85923 | + | 36.7841i | −0.192028 | + | 1.20555i | ||||
\(932\) | −11.8934 | −0.389581 | ||||||||
\(933\) | 10.3684i | 0.339447i | ||||||||
\(934\) | −25.8778 | −0.846746 | ||||||||
\(935\) | −21.9216 | − | 6.98418i | −0.716914 | − | 0.228407i | ||||
\(936\) | 10.5683i | 0.345436i | ||||||||
\(937\) | 16.0248i | 0.523507i | 0.965135 | + | 0.261754i | \(0.0843008\pi\) | ||||
−0.965135 | + | 0.261754i | \(0.915699\pi\) | |||||||
\(938\) | 4.67980 | − | 3.99336i | 0.152801 | − | 0.130388i | ||||
\(939\) | 17.3488 | 0.566157 | ||||||||
\(940\) | −9.10063 | + | 1.42065i | −0.296830 | + | 0.0463366i | ||||
\(941\) | −29.0243 | −0.946164 | −0.473082 | − | 0.881018i | \(-0.656859\pi\) | ||||
−0.473082 | + | 0.881018i | \(0.656859\pi\) | |||||||
\(942\) | −15.2206 | −0.495914 | ||||||||
\(943\) | 19.6916i | 0.641246i | ||||||||
\(944\) | 34.8804i | 1.13526i | ||||||||
\(945\) | −4.48837 | − | 3.85416i | −0.146007 | − | 0.125376i | ||||
\(946\) | −12.6944 | + | 25.4117i | −0.412730 | + | 0.826207i | ||||
\(947\) | 11.9719i | 0.389035i | 0.980899 | + | 0.194518i | \(0.0623142\pi\) | ||||
−0.980899 | + | 0.194518i | \(0.937686\pi\) | |||||||
\(948\) | − | 7.19165i | − | 0.233574i | ||||||
\(949\) | −24.9854 | −0.811059 | ||||||||
\(950\) | −29.7279 | + | 9.51316i | −0.964500 | + | 0.308648i | ||||
\(951\) | 20.0871i | 0.651370i | ||||||||
\(952\) | 19.2182 | − | 16.3993i | 0.622866 | − | 0.531504i | ||||
\(953\) | 27.7753 | 0.899730 | 0.449865 | − | 0.893096i | \(-0.351472\pi\) | ||||
0.449865 | + | 0.893096i | \(0.351472\pi\) | |||||||
\(954\) | 13.7769i | 0.446045i | ||||||||
\(955\) | 41.9235 | − | 6.54446i | 1.35661 | − | 0.211774i | ||||
\(956\) | − | 14.4417i | − | 0.467078i | ||||||
\(957\) | −17.2533 | − | 8.61885i | −0.557720 | − | 0.278608i | ||||
\(958\) | 35.5570 | 1.14879 | ||||||||
\(959\) | −36.4813 | + | 31.1302i | −1.17804 | + | 1.00525i | ||||
\(960\) | 19.2127 | − | 2.99920i | 0.620087 | − | 0.0967987i | ||||
\(961\) | 30.4778 | 0.983154 | ||||||||
\(962\) | −4.49034 | −0.144774 | ||||||||
\(963\) | −1.77552 | −0.0572152 | ||||||||
\(964\) | −9.79612 | −0.315512 | ||||||||
\(965\) | 36.0630 | − | 5.62961i | 1.16091 | − | 0.181224i | ||||
\(966\) | −13.8991 | + | 11.8604i | −0.447197 | + | 0.381602i | ||||
\(967\) | 50.2899 | 1.61722 | 0.808608 | − | 0.588348i | \(-0.200222\pi\) | ||||
0.808608 | + | 0.588348i | \(0.200222\pi\) | |||||||
\(968\) | −20.3345 | − | 27.0718i | −0.653576 | − | 0.870120i | ||||
\(969\) | − | 16.5078i | − | 0.530306i | ||||||
\(970\) | 9.78062 | − | 1.52680i | 0.314037 | − | 0.0490227i | ||||
\(971\) | 43.1696i | 1.38538i | 0.721237 | + | 0.692688i | \(0.243574\pi\) | ||||
−0.721237 | + | 0.692688i | \(0.756426\pi\) | |||||||
\(972\) | 0.623669 | 0.0200042 | ||||||||
\(973\) | 21.5601 | + | 25.2661i | 0.691185 | + | 0.809995i | ||||
\(974\) | 11.9083i | 0.381567i | ||||||||
\(975\) | −5.23233 | − | 16.3506i | −0.167569 | − | 0.523639i | ||||
\(976\) | 12.4296 | 0.397861 | ||||||||
\(977\) | 34.3037i | 1.09747i | 0.835996 | + | 0.548736i | \(0.184891\pi\) | ||||
−0.835996 | + | 0.548736i | \(0.815109\pi\) | |||||||
\(978\) | 10.9651i | 0.350625i | ||||||||
\(979\) | 10.8341 | + | 5.41215i | 0.346260 | + | 0.172973i | ||||
\(980\) | −0.0303077 | + | 9.76192i | −0.000968145 | + | 0.311833i | ||||
\(981\) | 1.93909i | 0.0619104i | ||||||||
\(982\) | 40.1775i | 1.28212i | ||||||||
\(983\) | 50.9060 | 1.62365 | 0.811825 | − | 0.583901i | \(-0.198474\pi\) | ||||
0.811825 | + | 0.583901i | \(0.198474\pi\) | |||||||
\(984\) | 10.2963 | 0.328235 | ||||||||
\(985\) | −35.5944 | + | 5.55646i | −1.13413 | + | 0.177044i | ||||
\(986\) | 21.1641 | 0.674001 | ||||||||
\(987\) | −11.3430 | − | 13.2928i | −0.361053 | − | 0.423116i | ||||
\(988\) | − | 11.3944i | − | 0.362505i | ||||||
\(989\) | − | 42.9756i | − | 1.36654i | ||||||
\(990\) | 2.64114 | − | 8.28991i | 0.0839411 | − | 0.263470i | ||||
\(991\) | 39.1588 | 1.24392 | 0.621960 | − | 0.783049i | \(-0.286336\pi\) | ||||
0.621960 | + | 0.783049i | \(0.286336\pi\) | |||||||
\(992\) | − | 2.44471i | − | 0.0776196i | ||||||
\(993\) | 17.1491 | 0.544209 | ||||||||
\(994\) | −30.1168 | − | 35.2937i | −0.955247 | − | 1.11945i | ||||
\(995\) | −8.44868 | − | 54.1218i | −0.267841 | − | 1.71578i | ||||
\(996\) | 4.61136i | 0.146116i | ||||||||
\(997\) | − | 27.4294i | − | 0.868698i | −0.900745 | − | 0.434349i | \(-0.856978\pi\) | ||
0.900745 | − | 0.434349i | \(-0.143022\pi\) | |||||||
\(998\) | −3.63316 | −0.115006 | ||||||||
\(999\) | 1.11476i | 0.0352696i |
(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 | 1155.2.k.a.769.16 | yes | 48 | |
5.4 | even | 2 | 1155.2.k.b.769.33 | yes | 48 | ||
7.6 | odd | 2 | 1155.2.k.b.769.15 | yes | 48 | ||
11.10 | odd | 2 | inner | 1155.2.k.a.769.33 | yes | 48 | |
35.34 | odd | 2 | inner | 1155.2.k.a.769.34 | yes | 48 | |
55.54 | odd | 2 | 1155.2.k.b.769.16 | yes | 48 | ||
77.76 | even | 2 | 1155.2.k.b.769.34 | yes | 48 | ||
385.384 | even | 2 | inner | 1155.2.k.a.769.15 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.k.a.769.15 | ✓ | 48 | 385.384 | even | 2 | inner | |
1155.2.k.a.769.16 | yes | 48 | 1.1 | even | 1 | trivial | |
1155.2.k.a.769.33 | yes | 48 | 11.10 | odd | 2 | inner | |
1155.2.k.a.769.34 | yes | 48 | 35.34 | odd | 2 | inner | |
1155.2.k.b.769.15 | yes | 48 | 7.6 | odd | 2 | ||
1155.2.k.b.769.16 | yes | 48 | 55.54 | odd | 2 | ||
1155.2.k.b.769.33 | yes | 48 | 5.4 | even | 2 | ||
1155.2.k.b.769.34 | yes | 48 | 77.76 | even | 2 |