Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(493,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.493");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.f (of order \(4\), degree \(2\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 493.8 | ||
Character | \(\chi\) | \(=\) | 950.493 |
Dual form | 950.2.f.d.607.8 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 1.91489 | − | 1.91489i | 1.10556 | − | 1.10556i | 0.111833 | − | 0.993727i | \(-0.464328\pi\) |
0.993727 | − | 0.111833i | \(-0.0356723\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.70806 | −1.10556 | ||||||||
\(7\) | 2.95447 | − | 2.95447i | 1.11668 | − | 1.11668i | 0.124459 | − | 0.992225i | \(-0.460280\pi\) |
0.992225 | − | 0.124459i | \(-0.0397195\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 4.33358i | − | 1.44453i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.90336 | −1.17691 | −0.588453 | − | 0.808531i | \(-0.700263\pi\) | ||||
−0.588453 | + | 0.808531i | \(0.700263\pi\) | |||||||
\(12\) | 1.91489 | + | 1.91489i | 0.552780 | + | 0.552780i | ||||
\(13\) | −4.27208 | + | 4.27208i | −1.18486 | + | 1.18486i | −0.206394 | + | 0.978469i | \(0.566173\pi\) |
−0.978469 | + | 0.206394i | \(0.933827\pi\) | |||||||
\(14\) | −4.17825 | −1.11668 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.82166 | − | 3.82166i | 0.926888 | − | 0.926888i | −0.0706153 | − | 0.997504i | \(-0.522496\pi\) |
0.997504 | + | 0.0706153i | \(0.0224963\pi\) | |||||||
\(18\) | −3.06430 | + | 3.06430i | −0.722263 | + | 0.722263i | ||||
\(19\) | −0.797842 | − | 4.28526i | −0.183037 | − | 0.983106i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 11.3149i | − | 2.46912i | ||||||
\(22\) | 2.76009 | + | 2.76009i | 0.588453 | + | 0.588453i | ||||
\(23\) | −4.44500 | − | 4.44500i | −0.926846 | − | 0.926846i | 0.0706544 | − | 0.997501i | \(-0.477491\pi\) |
−0.997501 | + | 0.0706544i | \(0.977491\pi\) | |||||||
\(24\) | − | 2.70806i | − | 0.552780i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.04164 | 1.18486 | ||||||||
\(27\) | −2.55366 | − | 2.55366i | −0.491451 | − | 0.491451i | ||||
\(28\) | 2.95447 | + | 2.95447i | 0.558342 | + | 0.558342i | ||||
\(29\) | 2.10793 | 0.391433 | 0.195716 | − | 0.980661i | \(-0.437297\pi\) | ||||
0.195716 | + | 0.980661i | \(0.437297\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46410i | 0.622171i | 0.950382 | + | 0.311086i | \(0.100693\pi\) | ||||
−0.950382 | + | 0.311086i | \(0.899307\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −7.47449 | + | 7.47449i | −1.30114 | + | 1.30114i | ||||
\(34\) | −5.40464 | −0.926888 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.33358 | 0.722263 | ||||||||
\(37\) | −1.05164 | − | 1.05164i | −0.172888 | − | 0.172888i | 0.615359 | − | 0.788247i | \(-0.289011\pi\) |
−0.788247 | + | 0.615359i | \(0.789011\pi\) | |||||||
\(38\) | −2.46598 | + | 3.59430i | −0.400034 | + | 0.583072i | ||||
\(39\) | 16.3611i | 2.61987i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.48808i | − | 1.01327i | −0.862161 | − | 0.506634i | \(-0.830890\pi\) | ||
0.862161 | − | 0.506634i | \(-0.169110\pi\) | |||||||
\(42\) | −8.00087 | + | 8.00087i | −1.23456 | + | 1.23456i | ||||
\(43\) | 6.63336 | + | 6.63336i | 1.01158 | + | 1.01158i | 0.999932 | + | 0.0116460i | \(0.00370711\pi\) |
0.0116460 | + | 0.999932i | \(0.496293\pi\) | |||||||
\(44\) | − | 3.90336i | − | 0.588453i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.28618i | 0.926846i | ||||||||
\(47\) | 2.35306 | − | 2.35306i | 0.343230 | − | 0.343230i | −0.514350 | − | 0.857580i | \(-0.671967\pi\) |
0.857580 | + | 0.514350i | \(0.171967\pi\) | |||||||
\(48\) | −1.91489 | + | 1.91489i | −0.276390 | + | 0.276390i | ||||
\(49\) | − | 10.4578i | − | 1.49397i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 14.6361i | − | 2.04946i | ||||||
\(52\) | −4.27208 | − | 4.27208i | −0.592431 | − | 0.592431i | ||||
\(53\) | 3.83975 | − | 3.83975i | 0.527430 | − | 0.527430i | −0.392375 | − | 0.919805i | \(-0.628347\pi\) |
0.919805 | + | 0.392375i | \(0.128347\pi\) | |||||||
\(54\) | 3.61142i | 0.491451i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 4.17825i | − | 0.558342i | ||||||
\(57\) | −9.73356 | − | 6.67801i | −1.28924 | − | 0.884524i | ||||
\(58\) | −1.49053 | − | 1.49053i | −0.195716 | − | 0.195716i | ||||
\(59\) | 14.9154 | 1.94182 | 0.970910 | − | 0.239443i | \(-0.0769648\pi\) | ||||
0.970910 | + | 0.239443i | \(0.0769648\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 2.44949 | − | 2.44949i | 0.311086 | − | 0.311086i | ||||
\(63\) | −12.8034 | − | 12.8034i | −1.61308 | − | 1.61308i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.5705 | 1.30114 | ||||||||
\(67\) | 4.04760 | + | 4.04760i | 0.494494 | + | 0.494494i | 0.909719 | − | 0.415225i | \(-0.136297\pi\) |
−0.415225 | + | 0.909719i | \(0.636297\pi\) | |||||||
\(68\) | 3.82166 | + | 3.82166i | 0.463444 | + | 0.463444i | ||||
\(69\) | −17.0233 | −2.04937 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.70103i | 0.201875i | 0.994893 | + | 0.100937i | \(0.0321842\pi\) | ||||
−0.994893 | + | 0.100937i | \(0.967816\pi\) | |||||||
\(72\) | −3.06430 | − | 3.06430i | −0.361132 | − | 0.361132i | ||||
\(73\) | 5.04174 | + | 5.04174i | 0.590091 | + | 0.590091i | 0.937656 | − | 0.347565i | \(-0.112991\pi\) |
−0.347565 | + | 0.937656i | \(0.612991\pi\) | |||||||
\(74\) | 1.48724i | 0.172888i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.28526 | − | 0.797842i | 0.491553 | − | 0.0915187i | ||||
\(77\) | −11.5323 | + | 11.5323i | −1.31423 | + | 1.31423i | ||||
\(78\) | 11.5691 | − | 11.5691i | 1.30994 | − | 1.30994i | ||||
\(79\) | −11.8206 | −1.32992 | −0.664961 | − | 0.746878i | \(-0.731552\pi\) | ||||
−0.664961 | + | 0.746878i | \(0.731552\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.22082 | 0.357869 | ||||||||
\(82\) | −4.58776 | + | 4.58776i | −0.506634 | + | 0.506634i | ||||
\(83\) | 2.04560 | + | 2.04560i | 0.224534 | + | 0.224534i | 0.810404 | − | 0.585871i | \(-0.199247\pi\) |
−0.585871 | + | 0.810404i | \(0.699247\pi\) | |||||||
\(84\) | 11.3149 | 1.23456 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 9.38099i | − | 1.01158i | ||||||
\(87\) | 4.03645 | − | 4.03645i | 0.432753 | − | 0.432753i | ||||
\(88\) | −2.76009 | + | 2.76009i | −0.294227 | + | 0.294227i | ||||
\(89\) | −10.9767 | −1.16353 | −0.581763 | − | 0.813359i | \(-0.697637\pi\) | ||||
−0.581763 | + | 0.813359i | \(0.697637\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.2435i | 2.64623i | ||||||||
\(92\) | 4.44500 | − | 4.44500i | 0.463423 | − | 0.463423i | ||||
\(93\) | 6.63336 | + | 6.63336i | 0.687848 | + | 0.687848i | ||||
\(94\) | −3.32773 | −0.343230 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.70806 | 0.276390 | ||||||||
\(97\) | −3.35802 | − | 3.35802i | −0.340955 | − | 0.340955i | 0.515771 | − | 0.856726i | \(-0.327505\pi\) |
−0.856726 | + | 0.515771i | \(0.827505\pi\) | |||||||
\(98\) | −7.39475 | + | 7.39475i | −0.746983 | + | 0.746983i | ||||
\(99\) | 16.9155i | 1.70007i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | −10.3493 | + | 10.3493i | −1.02473 | + | 1.02473i | ||||
\(103\) | 0.884622 | − | 0.884622i | 0.0871644 | − | 0.0871644i | −0.662180 | − | 0.749345i | \(-0.730369\pi\) |
0.749345 | + | 0.662180i | \(0.230369\pi\) | |||||||
\(104\) | 6.04164i | 0.592431i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.43022 | −0.527430 | ||||||||
\(107\) | 4.87001 | + | 4.87001i | 0.470802 | + | 0.470802i | 0.902174 | − | 0.431372i | \(-0.141970\pi\) |
−0.431372 | + | 0.902174i | \(0.641970\pi\) | |||||||
\(108\) | 2.55366 | − | 2.55366i | 0.245726 | − | 0.245726i | ||||
\(109\) | 0.310347 | 0.0297259 | 0.0148629 | − | 0.999890i | \(-0.495269\pi\) | ||||
0.0148629 | + | 0.999890i | \(0.495269\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.02753 | −0.382276 | ||||||||
\(112\) | −2.95447 | + | 2.95447i | −0.279171 | + | 0.279171i | ||||
\(113\) | −7.00273 | + | 7.00273i | −0.658762 | + | 0.658762i | −0.955087 | − | 0.296326i | \(-0.904239\pi\) |
0.296326 | + | 0.955087i | \(0.404239\pi\) | |||||||
\(114\) | 2.16060 | + | 11.6047i | 0.202359 | + | 1.08688i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.10793i | 0.195716i | ||||||||
\(117\) | 18.5134 | + | 18.5134i | 1.71157 | + | 1.71157i | ||||
\(118\) | −10.5468 | − | 10.5468i | −0.970910 | − | 0.970910i | ||||
\(119\) | − | 22.5819i | − | 2.07008i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.23619 | 0.385109 | ||||||||
\(122\) | 1.41421 | + | 1.41421i | 0.128037 | + | 0.128037i | ||||
\(123\) | −12.4239 | − | 12.4239i | −1.12023 | − | 1.12023i | ||||
\(124\) | −3.46410 | −0.311086 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 18.1068i | 1.61308i | ||||||||
\(127\) | 13.6515 | + | 13.6515i | 1.21137 | + | 1.21137i | 0.970575 | + | 0.240798i | \(0.0774091\pi\) |
0.240798 | + | 0.970575i | \(0.422591\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 25.4043 | 2.23672 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.667162 | −0.0582902 | −0.0291451 | − | 0.999575i | \(-0.509278\pi\) | ||||
−0.0291451 | + | 0.999575i | \(0.509278\pi\) | |||||||
\(132\) | −7.47449 | − | 7.47449i | −0.650570 | − | 0.650570i | ||||
\(133\) | −15.0179 | − | 10.3035i | −1.30221 | − | 0.893423i | ||||
\(134\) | − | 5.72418i | − | 0.494494i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 5.40464i | − | 0.463444i | ||||||
\(137\) | 9.46015 | − | 9.46015i | 0.808235 | − | 0.808235i | −0.176132 | − | 0.984367i | \(-0.556358\pi\) |
0.984367 | + | 0.176132i | \(0.0563585\pi\) | |||||||
\(138\) | 12.0373 | + | 12.0373i | 1.02468 | + | 1.02468i | ||||
\(139\) | 20.3772i | 1.72837i | 0.503171 | + | 0.864187i | \(0.332167\pi\) | ||||
−0.503171 | + | 0.864187i | \(0.667833\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 9.01170i | − | 0.758922i | ||||||
\(142\) | 1.20281 | − | 1.20281i | 0.100937 | − | 0.100937i | ||||
\(143\) | 16.6755 | − | 16.6755i | 1.39447 | − | 1.39447i | ||||
\(144\) | 4.33358i | 0.361132i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 7.13010i | − | 0.590091i | ||||||
\(147\) | −20.0254 | − | 20.0254i | −1.65167 | − | 1.65167i | ||||
\(148\) | 1.05164 | − | 1.05164i | 0.0864441 | − | 0.0864441i | ||||
\(149\) | − | 1.80671i | − | 0.148012i | −0.997258 | − | 0.0740059i | \(-0.976422\pi\) | ||
0.997258 | − | 0.0740059i | \(-0.0235784\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.32069i | 0.514370i | 0.966362 | + | 0.257185i | \(0.0827950\pi\) | ||||
−0.966362 | + | 0.257185i | \(0.917205\pi\) | |||||||
\(152\) | −3.59430 | − | 2.46598i | −0.291536 | − | 0.200017i | ||||
\(153\) | −16.5615 | − | 16.5615i | −1.33892 | − | 1.33892i | ||||
\(154\) | 16.3092 | 1.31423 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −16.3611 | −1.30994 | ||||||||
\(157\) | 10.8172 | − | 10.8172i | 0.863309 | − | 0.863309i | −0.128412 | − | 0.991721i | \(-0.540988\pi\) |
0.991721 | + | 0.128412i | \(0.0409879\pi\) | |||||||
\(158\) | 8.35842 | + | 8.35842i | 0.664961 | + | 0.664961i | ||||
\(159\) | − | 14.7054i | − | 1.16621i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −26.2652 | −2.06999 | ||||||||
\(162\) | −2.27746 | − | 2.27746i | −0.178934 | − | 0.178934i | ||||
\(163\) | 11.9456 | + | 11.9456i | 0.935648 | + | 0.935648i | 0.998051 | − | 0.0624032i | \(-0.0198765\pi\) |
−0.0624032 | + | 0.998051i | \(0.519876\pi\) | |||||||
\(164\) | 6.48808 | 0.506634 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 2.89291i | − | 0.224534i | ||||||
\(167\) | 7.71843 | + | 7.71843i | 0.597270 | + | 0.597270i | 0.939585 | − | 0.342315i | \(-0.111211\pi\) |
−0.342315 | + | 0.939585i | \(0.611211\pi\) | |||||||
\(168\) | −8.00087 | − | 8.00087i | −0.617281 | − | 0.617281i | ||||
\(169\) | − | 23.5014i | − | 1.80780i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.5705 | + | 3.45751i | −1.42012 | + | 0.264403i | ||||
\(172\) | −6.63336 | + | 6.63336i | −0.505789 | + | 0.505789i | ||||
\(173\) | −2.36527 | + | 2.36527i | −0.179828 | + | 0.179828i | −0.791281 | − | 0.611453i | \(-0.790585\pi\) |
0.611453 | + | 0.791281i | \(0.290585\pi\) | |||||||
\(174\) | −5.70840 | −0.432753 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.90336 | 0.294227 | ||||||||
\(177\) | 28.5613 | − | 28.5613i | 2.14680 | − | 2.14680i | ||||
\(178\) | 7.76168 | + | 7.76168i | 0.581763 | + | 0.581763i | ||||
\(179\) | −9.68475 | −0.723872 | −0.361936 | − | 0.932203i | \(-0.617884\pi\) | ||||
−0.361936 | + | 0.932203i | \(0.617884\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.1370i | 1.05080i | 0.850857 | + | 0.525398i | \(0.176084\pi\) | ||||
−0.850857 | + | 0.525398i | \(0.823916\pi\) | |||||||
\(182\) | 17.8498 | − | 17.8498i | 1.32312 | − | 1.32312i | ||||
\(183\) | −3.82977 | + | 3.82977i | −0.283105 | + | 0.283105i | ||||
\(184\) | −6.28618 | −0.463423 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 9.38099i | − | 0.687848i | ||||||
\(187\) | −14.9173 | + | 14.9173i | −1.09086 | + | 1.09086i | ||||
\(188\) | 2.35306 | + | 2.35306i | 0.171615 | + | 0.171615i | ||||
\(189\) | −15.0894 | −1.09759 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.0275325 | −0.00199218 | −0.000996089 | − | 1.00000i | \(-0.500317\pi\) | ||||
−0.000996089 | 1.00000i | \(0.500317\pi\) | ||||||||
\(192\) | −1.91489 | − | 1.91489i | −0.138195 | − | 0.138195i | ||||
\(193\) | 16.8244 | − | 16.8244i | 1.21105 | − | 1.21105i | 0.240368 | − | 0.970682i | \(-0.422732\pi\) |
0.970682 | − | 0.240368i | \(-0.0772680\pi\) | |||||||
\(194\) | 4.74896i | 0.340955i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.4578 | 0.746983 | ||||||||
\(197\) | 12.3494 | − | 12.3494i | 0.879861 | − | 0.879861i | −0.113658 | − | 0.993520i | \(-0.536257\pi\) |
0.993520 | + | 0.113658i | \(0.0362569\pi\) | |||||||
\(198\) | 11.9611 | − | 11.9611i | 0.850037 | − | 0.850037i | ||||
\(199\) | 5.01141i | 0.355250i | 0.984098 | + | 0.177625i | \(0.0568414\pi\) | ||||
−0.984098 | + | 0.177625i | \(0.943159\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.5014 | 1.09339 | ||||||||
\(202\) | 4.24264 | + | 4.24264i | 0.298511 | + | 0.298511i | ||||
\(203\) | 6.22781 | − | 6.22781i | 0.437107 | − | 0.437107i | ||||
\(204\) | 14.6361 | 1.02473 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.25104 | −0.0871644 | ||||||||
\(207\) | −19.2628 | + | 19.2628i | −1.33885 | + | 1.33885i | ||||
\(208\) | 4.27208 | − | 4.27208i | 0.296216 | − | 0.296216i | ||||
\(209\) | 3.11426 | + | 16.7269i | 0.215418 | + | 1.15702i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 19.5714i | − | 1.34735i | −0.739028 | − | 0.673675i | \(-0.764715\pi\) | ||
0.739028 | − | 0.673675i | \(-0.235285\pi\) | |||||||
\(212\) | 3.83975 | + | 3.83975i | 0.263715 | + | 0.263715i | ||||
\(213\) | 3.25727 | + | 3.25727i | 0.223185 | + | 0.223185i | ||||
\(214\) | − | 6.88724i | − | 0.470802i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.61142 | −0.245726 | ||||||||
\(217\) | 10.2346 | + | 10.2346i | 0.694768 | + | 0.694768i | ||||
\(218\) | −0.219449 | − | 0.219449i | −0.0148629 | − | 0.0148629i | ||||
\(219\) | 19.3087 | 1.30476 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.6529i | 2.19647i | ||||||||
\(222\) | 2.84790 | + | 2.84790i | 0.191138 | + | 0.191138i | ||||
\(223\) | 7.65955 | − | 7.65955i | 0.512921 | − | 0.512921i | −0.402499 | − | 0.915420i | \(-0.631858\pi\) |
0.915420 | + | 0.402499i | \(0.131858\pi\) | |||||||
\(224\) | 4.17825 | 0.279171 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.90336 | 0.658762 | ||||||||
\(227\) | −17.0784 | − | 17.0784i | −1.13353 | − | 1.13353i | −0.989586 | − | 0.143945i | \(-0.954021\pi\) |
−0.143945 | − | 0.989586i | \(-0.545979\pi\) | |||||||
\(228\) | 6.67801 | − | 9.73356i | 0.442262 | − | 0.644621i | ||||
\(229\) | 17.5812i | 1.16180i | 0.813976 | + | 0.580899i | \(0.197299\pi\) | ||||
−0.813976 | + | 0.580899i | \(0.802701\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 44.1662i | 2.90593i | ||||||||
\(232\) | 1.49053 | − | 1.49053i | 0.0978582 | − | 0.0978582i | ||||
\(233\) | 10.7208 | + | 10.7208i | 0.702343 | + | 0.702343i | 0.964913 | − | 0.262570i | \(-0.0845699\pi\) |
−0.262570 | + | 0.964913i | \(0.584570\pi\) | |||||||
\(234\) | − | 26.1819i | − | 1.71157i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 14.9154i | 0.970910i | ||||||||
\(237\) | −22.6351 | + | 22.6351i | −1.47031 | + | 1.47031i | ||||
\(238\) | −15.9678 | + | 15.9678i | −1.03504 | + | 1.03504i | ||||
\(239\) | − | 2.88649i | − | 0.186712i | −0.995633 | − | 0.0933559i | \(-0.970241\pi\) | ||
0.995633 | − | 0.0933559i | \(-0.0297594\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 2.89291i | − | 0.186349i | −0.995650 | − | 0.0931744i | \(-0.970299\pi\) | ||
0.995650 | − | 0.0931744i | \(-0.0297014\pi\) | |||||||
\(242\) | −2.99544 | − | 2.99544i | −0.192554 | − | 0.192554i | ||||
\(243\) | 13.8285 | − | 13.8285i | 0.887097 | − | 0.887097i | ||||
\(244\) | − | 2.00000i | − | 0.128037i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 17.5701i | 1.12023i | ||||||||
\(247\) | 21.7154 | + | 14.8985i | 1.38172 | + | 0.947972i | ||||
\(248\) | 2.44949 | + | 2.44949i | 0.155543 | + | 0.155543i | ||||
\(249\) | 7.83417 | 0.496471 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.3772 | 0.781244 | 0.390622 | − | 0.920551i | \(-0.372260\pi\) | ||||
0.390622 | + | 0.920551i | \(0.372260\pi\) | |||||||
\(252\) | 12.8034 | − | 12.8034i | 0.806540 | − | 0.806540i | ||||
\(253\) | 17.3504 | + | 17.3504i | 1.09081 | + | 1.09081i | ||||
\(254\) | − | 19.3061i | − | 1.21137i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.79772 | − | 6.79772i | −0.424030 | − | 0.424030i | 0.462559 | − | 0.886589i | \(-0.346931\pi\) |
−0.886589 | + | 0.462559i | \(0.846931\pi\) | |||||||
\(258\) | −17.9635 | − | 17.9635i | −1.11836 | − | 1.11836i | ||||
\(259\) | −6.21406 | −0.386123 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 9.13489i | − | 0.565435i | ||||||
\(262\) | 0.471755 | + | 0.471755i | 0.0291451 | + | 0.0291451i | ||||
\(263\) | −14.2674 | − | 14.2674i | −0.879763 | − | 0.879763i | 0.113747 | − | 0.993510i | \(-0.463715\pi\) |
−0.993510 | + | 0.113747i | \(0.963715\pi\) | |||||||
\(264\) | 10.5705i | 0.650570i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.33358 | + | 17.9049i | 0.204395 | + | 1.09782i | ||||
\(267\) | −21.0191 | + | 21.0191i | −1.28635 | + | 1.28635i | ||||
\(268\) | −4.04760 | + | 4.04760i | −0.247247 | + | 0.247247i | ||||
\(269\) | 20.4577 | 1.24733 | 0.623664 | − | 0.781692i | \(-0.285643\pi\) | ||||
0.623664 | + | 0.781692i | \(0.285643\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.414105 | −0.0251551 | −0.0125775 | − | 0.999921i | \(-0.504004\pi\) | ||||
−0.0125775 | + | 0.999921i | \(0.504004\pi\) | |||||||
\(272\) | −3.82166 | + | 3.82166i | −0.231722 | + | 0.231722i | ||||
\(273\) | 48.3384 | + | 48.3384i | 2.92557 | + | 2.92557i | ||||
\(274\) | −13.3787 | −0.808235 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 17.0233i | − | 1.02468i | ||||||
\(277\) | 8.26575 | − | 8.26575i | 0.496641 | − | 0.496641i | −0.413750 | − | 0.910391i | \(-0.635781\pi\) |
0.910391 | + | 0.413750i | \(0.135781\pi\) | |||||||
\(278\) | 14.4089 | − | 14.4089i | 0.864187 | − | 0.864187i | ||||
\(279\) | 15.0120 | 0.898743 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 23.6412i | − | 1.41032i | −0.709050 | − | 0.705158i | \(-0.750876\pi\) | ||
0.709050 | − | 0.705158i | \(-0.249124\pi\) | |||||||
\(282\) | −6.37223 | + | 6.37223i | −0.379461 | + | 0.379461i | ||||
\(283\) | 17.0281 | + | 17.0281i | 1.01221 | + | 1.01221i | 0.999924 | + | 0.0122889i | \(0.00391178\pi\) |
0.0122889 | + | 0.999924i | \(0.496088\pi\) | |||||||
\(284\) | −1.70103 | −0.100937 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.5827 | −1.39447 | ||||||||
\(287\) | −19.1688 | − | 19.1688i | −1.13150 | − | 1.13150i | ||||
\(288\) | 3.06430 | − | 3.06430i | 0.180566 | − | 0.180566i | ||||
\(289\) | − | 12.2101i | − | 0.718244i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.8604 | −0.753893 | ||||||||
\(292\) | −5.04174 | + | 5.04174i | −0.295046 | + | 0.295046i | ||||
\(293\) | −15.7814 | + | 15.7814i | −0.921957 | + | 0.921957i | −0.997168 | − | 0.0752111i | \(-0.976037\pi\) |
0.0752111 | + | 0.997168i | \(0.476037\pi\) | |||||||
\(294\) | 28.3202i | 1.65167i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.48724 | −0.0864441 | ||||||||
\(297\) | 9.96783 | + | 9.96783i | 0.578392 | + | 0.578392i | ||||
\(298\) | −1.27754 | + | 1.27754i | −0.0740059 | + | 0.0740059i | ||||
\(299\) | 37.9788 | 2.19637 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 39.1961 | 2.25923 | ||||||||
\(302\) | 4.46940 | − | 4.46940i | 0.257185 | − | 0.257185i | ||||
\(303\) | −11.4893 | + | 11.4893i | −0.660044 | + | 0.660044i | ||||
\(304\) | 0.797842 | + | 4.28526i | 0.0457594 | + | 0.245776i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 23.4215i | 1.33892i | ||||||||
\(307\) | 0.784894 | + | 0.784894i | 0.0447962 | + | 0.0447962i | 0.729150 | − | 0.684354i | \(-0.239916\pi\) |
−0.684354 | + | 0.729150i | \(0.739916\pi\) | |||||||
\(308\) | −11.5323 | − | 11.5323i | −0.657116 | − | 0.657116i | ||||
\(309\) | − | 3.38790i | − | 0.192731i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.6786 | 0.889050 | 0.444525 | − | 0.895766i | \(-0.353372\pi\) | ||||
0.444525 | + | 0.895766i | \(0.353372\pi\) | |||||||
\(312\) | 11.5691 | + | 11.5691i | 0.654969 | + | 0.654969i | ||||
\(313\) | −3.46164 | − | 3.46164i | −0.195663 | − | 0.195663i | 0.602475 | − | 0.798138i | \(-0.294181\pi\) |
−0.798138 | + | 0.602475i | \(0.794181\pi\) | |||||||
\(314\) | −15.2979 | −0.863309 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 11.8206i | − | 0.664961i | ||||||
\(317\) | −12.7474 | − | 12.7474i | −0.715965 | − | 0.715965i | 0.251812 | − | 0.967776i | \(-0.418974\pi\) |
−0.967776 | + | 0.251812i | \(0.918974\pi\) | |||||||
\(318\) | −10.3983 | + | 10.3983i | −0.583106 | + | 0.583106i | ||||
\(319\) | −8.22801 | −0.460680 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.6510 | 1.04100 | ||||||||
\(322\) | 18.5723 | + | 18.5723i | 1.03499 | + | 1.03499i | ||||
\(323\) | −19.4259 | − | 13.3277i | −1.08088 | − | 0.741574i | ||||
\(324\) | 3.22082i | 0.178934i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 16.8936i | − | 0.935648i | ||||||
\(327\) | 0.594280 | − | 0.594280i | 0.0328638 | − | 0.0328638i | ||||
\(328\) | −4.58776 | − | 4.58776i | −0.253317 | − | 0.253317i | ||||
\(329\) | − | 13.9041i | − | 0.766558i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 8.59601i | − | 0.472479i | −0.971695 | − | 0.236240i | \(-0.924085\pi\) | ||
0.971695 | − | 0.236240i | \(-0.0759151\pi\) | |||||||
\(332\) | −2.04560 | + | 2.04560i | −0.112267 | + | 0.112267i | ||||
\(333\) | −4.55736 | + | 4.55736i | −0.249742 | + | 0.249742i | ||||
\(334\) | − | 10.9155i | − | 0.597270i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 11.3149i | 0.617281i | ||||||||
\(337\) | 2.01319 | + | 2.01319i | 0.109666 | + | 0.109666i | 0.759810 | − | 0.650145i | \(-0.225292\pi\) |
−0.650145 | + | 0.759810i | \(0.725292\pi\) | |||||||
\(338\) | −16.6180 | + | 16.6180i | −0.903900 | + | 0.903900i | ||||
\(339\) | 26.8189i | 1.45660i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 13.5216i | − | 0.732237i | ||||||
\(342\) | 15.5762 | + | 10.6865i | 0.842263 | + | 0.577860i | ||||
\(343\) | −10.2158 | − | 10.2158i | −0.551603 | − | 0.551603i | ||||
\(344\) | 9.38099 | 0.505789 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.34499 | 0.179828 | ||||||||
\(347\) | −4.87329 | + | 4.87329i | −0.261612 | + | 0.261612i | −0.825709 | − | 0.564097i | \(-0.809225\pi\) |
0.564097 | + | 0.825709i | \(0.309225\pi\) | |||||||
\(348\) | 4.03645 | + | 4.03645i | 0.216376 | + | 0.216376i | ||||
\(349\) | − | 21.9692i | − | 1.17599i | −0.808866 | − | 0.587993i | \(-0.799918\pi\) | ||
0.808866 | − | 0.587993i | \(-0.200082\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.8189 | 1.16461 | ||||||||
\(352\) | −2.76009 | − | 2.76009i | −0.147113 | − | 0.147113i | ||||
\(353\) | 2.66894 | + | 2.66894i | 0.142053 | + | 0.142053i | 0.774557 | − | 0.632504i | \(-0.217973\pi\) |
−0.632504 | + | 0.774557i | \(0.717973\pi\) | |||||||
\(354\) | −40.3918 | −2.14680 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 10.9767i | − | 0.581763i | ||||||
\(357\) | −43.2418 | − | 43.2418i | −2.28860 | − | 2.28860i | ||||
\(358\) | 6.84815 | + | 6.84815i | 0.361936 | + | 0.361936i | ||||
\(359\) | 3.01612i | 0.159185i | 0.996827 | + | 0.0795923i | \(0.0253619\pi\) | ||||
−0.996827 | + | 0.0795923i | \(0.974638\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7269 | + | 6.83792i | −0.932995 | + | 0.359890i | ||||
\(362\) | 9.99638 | − | 9.99638i | 0.525398 | − | 0.525398i | ||||
\(363\) | 8.11183 | − | 8.11183i | 0.425761 | − | 0.425761i | ||||
\(364\) | −25.2435 | −1.32312 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.41612 | 0.283105 | ||||||||
\(367\) | −24.8917 | + | 24.8917i | −1.29934 | + | 1.29934i | −0.370510 | + | 0.928829i | \(0.620817\pi\) |
−0.928829 | + | 0.370510i | \(0.879183\pi\) | |||||||
\(368\) | 4.44500 | + | 4.44500i | 0.231712 | + | 0.231712i | ||||
\(369\) | −28.1166 | −1.46369 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 22.6888i | − | 1.17795i | ||||||
\(372\) | −6.63336 | + | 6.63336i | −0.343924 | + | 0.343924i | ||||
\(373\) | −20.0368 | + | 20.0368i | −1.03747 | + | 1.03747i | −0.0381967 | + | 0.999270i | \(0.512161\pi\) |
−0.999270 | + | 0.0381967i | \(0.987839\pi\) | |||||||
\(374\) | 21.0962 | 1.09086 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 3.32773i | − | 0.171615i | ||||||
\(377\) | −9.00526 | + | 9.00526i | −0.463794 | + | 0.463794i | ||||
\(378\) | 10.6698 | + | 10.6698i | 0.548796 | + | 0.548796i | ||||
\(379\) | 7.82292 | 0.401836 | 0.200918 | − | 0.979608i | \(-0.435607\pi\) | ||||
0.200918 | + | 0.979608i | \(0.435607\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 52.2821 | 2.67849 | ||||||||
\(382\) | 0.0194684 | + | 0.0194684i | 0.000996089 | + | 0.000996089i | ||||
\(383\) | −17.0323 | + | 17.0323i | −0.870310 | + | 0.870310i | −0.992506 | − | 0.122196i | \(-0.961006\pi\) |
0.122196 | + | 0.992506i | \(0.461006\pi\) | |||||||
\(384\) | 2.70806i | 0.138195i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.7933 | −1.21105 | ||||||||
\(387\) | 28.7462 | − | 28.7462i | 1.46125 | − | 1.46125i | ||||
\(388\) | 3.35802 | − | 3.35802i | 0.170478 | − | 0.170478i | ||||
\(389\) | 31.3894i | 1.59151i | 0.605622 | + | 0.795753i | \(0.292924\pi\) | ||||
−0.605622 | + | 0.795753i | \(0.707076\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.9745 | −1.71817 | ||||||||
\(392\) | −7.39475 | − | 7.39475i | −0.373491 | − | 0.373491i | ||||
\(393\) | −1.27754 | + | 1.27754i | −0.0644433 | + | 0.0644433i | ||||
\(394\) | −17.4648 | −0.879861 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −16.9155 | −0.850037 | ||||||||
\(397\) | −3.50332 | + | 3.50332i | −0.175827 | + | 0.175827i | −0.789534 | − | 0.613707i | \(-0.789678\pi\) |
0.613707 | + | 0.789534i | \(0.289678\pi\) | |||||||
\(398\) | 3.54360 | − | 3.54360i | 0.177625 | − | 0.177625i | ||||
\(399\) | −48.4875 | + | 9.02753i | −2.42741 | + | 0.451942i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.27222i | 0.113469i | 0.998389 | + | 0.0567345i | \(0.0180689\pi\) | ||||
−0.998389 | + | 0.0567345i | \(0.981931\pi\) | |||||||
\(402\) | −10.9612 | − | 10.9612i | −0.546693 | − | 0.546693i | ||||
\(403\) | −14.7989 | − | 14.7989i | −0.737187 | − | 0.737187i | ||||
\(404\) | − | 6.00000i | − | 0.298511i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.80746 | −0.437107 | ||||||||
\(407\) | 4.10492 | + | 4.10492i | 0.203473 | + | 0.203473i | ||||
\(408\) | −10.3493 | − | 10.3493i | −0.512365 | − | 0.512365i | ||||
\(409\) | −10.2870 | −0.508657 | −0.254329 | − | 0.967118i | \(-0.581855\pi\) | ||||
−0.254329 | + | 0.967118i | \(0.581855\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 36.2302i | − | 1.78710i | ||||||
\(412\) | 0.884622 | + | 0.884622i | 0.0435822 | + | 0.0435822i | ||||
\(413\) | 44.0671 | − | 44.0671i | 2.16840 | − | 2.16840i | ||||
\(414\) | 27.2417 | 1.33885 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.04164 | −0.296216 | ||||||||
\(417\) | 39.0201 | + | 39.0201i | 1.91082 | + | 1.91082i | ||||
\(418\) | 9.62559 | − | 14.0298i | 0.470803 | − | 0.686221i | ||||
\(419\) | 35.2927i | 1.72416i | 0.506769 | + | 0.862082i | \(0.330840\pi\) | ||||
−0.506769 | + | 0.862082i | \(0.669160\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.6067i | 1.15052i | 0.817971 | + | 0.575260i | \(0.195099\pi\) | ||||
−0.817971 | + | 0.575260i | \(0.804901\pi\) | |||||||
\(422\) | −13.8391 | + | 13.8391i | −0.673675 | + | 0.673675i | ||||
\(423\) | −10.1972 | − | 10.1972i | −0.495804 | − | 0.495804i | ||||
\(424\) | − | 5.43022i | − | 0.263715i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 4.60648i | − | 0.223185i | ||||||
\(427\) | −5.90894 | + | 5.90894i | −0.285953 | + | 0.285953i | ||||
\(428\) | −4.87001 | + | 4.87001i | −0.235401 | + | 0.235401i | ||||
\(429\) | − | 63.8633i | − | 3.08335i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.05927i | 0.340033i | 0.985441 | + | 0.170016i | \(0.0543821\pi\) | ||||
−0.985441 | + | 0.170016i | \(0.945618\pi\) | |||||||
\(432\) | 2.55366 | + | 2.55366i | 0.122863 | + | 0.122863i | ||||
\(433\) | 12.8930 | − | 12.8930i | 0.619600 | − | 0.619600i | −0.325829 | − | 0.945429i | \(-0.605643\pi\) |
0.945429 | + | 0.325829i | \(0.105643\pi\) | |||||||
\(434\) | − | 14.4739i | − | 0.694768i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.310347i | 0.0148629i | ||||||||
\(437\) | −15.5016 | + | 22.5944i | −0.741541 | + | 1.08084i | ||||
\(438\) | −13.6533 | − | 13.6533i | −0.652382 | − | 0.652382i | ||||
\(439\) | −31.1306 | −1.48578 | −0.742892 | − | 0.669412i | \(-0.766546\pi\) | ||||
−0.742892 | + | 0.669412i | \(0.766546\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −45.3195 | −2.15807 | ||||||||
\(442\) | 23.0891 | − | 23.0891i | 1.09824 | − | 1.09824i | ||||
\(443\) | −14.1929 | − | 14.1929i | −0.674324 | − | 0.674324i | 0.284386 | − | 0.958710i | \(-0.408210\pi\) |
−0.958710 | + | 0.284386i | \(0.908210\pi\) | |||||||
\(444\) | − | 4.02753i | − | 0.191138i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.8322 | −0.512921 | ||||||||
\(447\) | −3.45965 | − | 3.45965i | −0.163636 | − | 0.163636i | ||||
\(448\) | −2.95447 | − | 2.95447i | −0.139585 | − | 0.139585i | ||||
\(449\) | −8.10691 | −0.382589 | −0.191294 | − | 0.981533i | \(-0.561269\pi\) | ||||
−0.191294 | + | 0.981533i | \(0.561269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.3253i | 1.19252i | ||||||||
\(452\) | −7.00273 | − | 7.00273i | −0.329381 | − | 0.329381i | ||||
\(453\) | 12.1034 | + | 12.1034i | 0.568667 | + | 0.568667i | ||||
\(454\) | 24.1525i | 1.13353i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.6047 | + | 2.16060i | −0.543441 | + | 0.101179i | ||||
\(457\) | 8.09821 | − | 8.09821i | 0.378818 | − | 0.378818i | −0.491858 | − | 0.870676i | \(-0.663682\pi\) |
0.870676 | + | 0.491858i | \(0.163682\pi\) | |||||||
\(458\) | 12.4318 | − | 12.4318i | 0.580899 | − | 0.580899i | ||||
\(459\) | −19.5184 | −0.911041 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.4201 | −1.37023 | −0.685116 | − | 0.728434i | \(-0.740249\pi\) | ||||
−0.685116 | + | 0.728434i | \(0.740249\pi\) | |||||||
\(462\) | 31.2303 | − | 31.2303i | 1.45296 | − | 1.45296i | ||||
\(463\) | −16.1908 | − | 16.1908i | −0.752452 | − | 0.752452i | 0.222484 | − | 0.974936i | \(-0.428583\pi\) |
−0.974936 | + | 0.222484i | \(0.928583\pi\) | |||||||
\(464\) | −2.10793 | −0.0978582 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 15.1615i | − | 0.702343i | ||||||
\(467\) | 26.2293 | − | 26.2293i | 1.21375 | − | 1.21375i | 0.243961 | − | 0.969785i | \(-0.421553\pi\) |
0.969785 | − | 0.243961i | \(-0.0784470\pi\) | |||||||
\(468\) | −18.5134 | + | 18.5134i | −0.855783 | + | 0.855783i | ||||
\(469\) | 23.9170 | 1.10439 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 41.4275i | − | 1.90888i | ||||||
\(472\) | 10.5468 | − | 10.5468i | 0.485455 | − | 0.485455i | ||||
\(473\) | −25.8924 | − | 25.8924i | −1.19053 | − | 1.19053i | ||||
\(474\) | 32.0109 | 1.47031 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 22.5819 | 1.03504 | ||||||||
\(477\) | −16.6399 | − | 16.6399i | −0.761887 | − | 0.761887i | ||||
\(478\) | −2.04106 | + | 2.04106i | −0.0933559 | + | 0.0933559i | ||||
\(479\) | 26.9048i | 1.22931i | 0.788795 | + | 0.614657i | \(0.210705\pi\) | ||||
−0.788795 | + | 0.614657i | \(0.789295\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.98537 | 0.409697 | ||||||||
\(482\) | −2.04560 | + | 2.04560i | −0.0931744 | + | 0.0931744i | ||||
\(483\) | −50.2949 | + | 50.2949i | −2.28850 | + | 2.28850i | ||||
\(484\) | 4.23619i | 0.192554i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.5564 | −0.887097 | ||||||||
\(487\) | 26.8151 | + | 26.8151i | 1.21511 | + | 1.21511i | 0.969325 | + | 0.245781i | \(0.0790445\pi\) |
0.245781 | + | 0.969325i | \(0.420955\pi\) | |||||||
\(488\) | −1.41421 | + | 1.41421i | −0.0640184 | + | 0.0640184i | ||||
\(489\) | 45.7488 | 2.06883 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.8604 | 0.490125 | 0.245063 | − | 0.969507i | \(-0.421191\pi\) | ||||
0.245063 | + | 0.969507i | \(0.421191\pi\) | |||||||
\(492\) | 12.4239 | − | 12.4239i | 0.560114 | − | 0.560114i | ||||
\(493\) | 8.05579 | − | 8.05579i | 0.362815 | − | 0.362815i | ||||
\(494\) | −4.82027 | − | 25.8900i | −0.216874 | − | 1.16485i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 3.46410i | − | 0.155543i | ||||||
\(497\) | 5.02563 | + | 5.02563i | 0.225430 | + | 0.225430i | ||||
\(498\) | −5.53960 | − | 5.53960i | −0.248235 | − | 0.248235i | ||||
\(499\) | − | 19.5827i | − | 0.876641i | −0.898819 | − | 0.438320i | \(-0.855574\pi\) | ||
0.898819 | − | 0.438320i | \(-0.144426\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29.5598 | 1.32064 | ||||||||
\(502\) | −8.75203 | − | 8.75203i | −0.390622 | − | 0.390622i | ||||
\(503\) | −8.89712 | − | 8.89712i | −0.396703 | − | 0.396703i | 0.480365 | − | 0.877068i | \(-0.340504\pi\) |
−0.877068 | + | 0.480365i | \(0.840504\pi\) | |||||||
\(504\) | −18.1068 | −0.806540 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 24.5372i | − | 1.09081i | ||||||
\(507\) | −45.0025 | − | 45.0025i | −1.99863 | − | 1.99863i | ||||
\(508\) | −13.6515 | + | 13.6515i | −0.605687 | + | 0.605687i | ||||
\(509\) | 37.2433 | 1.65078 | 0.825391 | − | 0.564561i | \(-0.190955\pi\) | ||||
0.825391 | + | 0.564561i | \(0.190955\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.7913 | 1.31789 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −8.90567 | + | 12.9805i | −0.393195 | + | 0.573103i | ||||
\(514\) | 9.61343i | 0.424030i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 25.4043i | 1.11836i | ||||||||
\(517\) | −9.18485 | + | 9.18485i | −0.403949 | + | 0.403949i | ||||
\(518\) | 4.39400 | + | 4.39400i | 0.193061 | + | 0.193061i | ||||
\(519\) | 9.05844i | 0.397621i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 10.7039i | − | 0.468948i | −0.972122 | − | 0.234474i | \(-0.924663\pi\) | ||
0.972122 | − | 0.234474i | \(-0.0753368\pi\) | |||||||
\(522\) | −6.45934 | + | 6.45934i | −0.282718 | + | 0.282718i | ||||
\(523\) | −28.4254 | + | 28.4254i | −1.24295 | + | 1.24295i | −0.284185 | + | 0.958769i | \(0.591723\pi\) |
−0.958769 | + | 0.284185i | \(0.908277\pi\) | |||||||
\(524\) | − | 0.667162i | − | 0.0291451i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.1771i | 0.879763i | ||||||||
\(527\) | 13.2386 | + | 13.2386i | 0.576683 | + | 0.576683i | ||||
\(528\) | 7.47449 | − | 7.47449i | 0.325285 | − | 0.325285i | ||||
\(529\) | 16.5160i | 0.718089i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 64.6371i | − | 2.80501i | ||||||
\(532\) | 10.3035 | − | 15.0179i | 0.446712 | − | 0.651107i | ||||
\(533\) | 27.7176 | + | 27.7176i | 1.20058 | + | 1.20058i | ||||
\(534\) | 29.7255 | 1.28635 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.72418 | 0.247247 | ||||||||
\(537\) | −18.5452 | + | 18.5452i | −0.800284 | + | 0.800284i | ||||
\(538\) | −14.4658 | − | 14.4658i | −0.623664 | − | 0.623664i | ||||
\(539\) | 40.8204i | 1.75826i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.2484 | −0.612584 | −0.306292 | − | 0.951938i | \(-0.599088\pi\) | ||||
−0.306292 | + | 0.951938i | \(0.599088\pi\) | |||||||
\(542\) | 0.292816 | + | 0.292816i | 0.0125775 | + | 0.0125775i | ||||
\(543\) | 27.0708 | + | 27.0708i | 1.16172 | + | 1.16172i | ||||
\(544\) | 5.40464 | 0.231722 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 68.3608i | − | 2.92557i | ||||||
\(547\) | −12.9130 | − | 12.9130i | −0.552119 | − | 0.552119i | 0.374933 | − | 0.927052i | \(-0.377666\pi\) |
−0.927052 | + | 0.374933i | \(0.877666\pi\) | |||||||
\(548\) | 9.46015 | + | 9.46015i | 0.404117 | + | 0.404117i | ||||
\(549\) | 8.66716i | 0.369905i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.68180 | − | 9.03303i | −0.0716469 | − | 0.384820i | ||||
\(552\) | −12.0373 | + | 12.0373i | −0.512342 | + | 0.512342i | ||||
\(553\) | −34.9236 | + | 34.9236i | −1.48510 | + | 1.48510i | ||||
\(554\) | −11.6895 | −0.496641 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.3772 | −0.864187 | ||||||||
\(557\) | −0.294848 | + | 0.294848i | −0.0124931 | + | 0.0124931i | −0.713326 | − | 0.700833i | \(-0.752812\pi\) |
0.700833 | + | 0.713326i | \(0.252812\pi\) | |||||||
\(558\) | −10.6151 | − | 10.6151i | −0.449371 | − | 0.449371i | ||||
\(559\) | −56.6766 | −2.39716 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 57.1299i | 2.41202i | ||||||||
\(562\) | −16.7168 | + | 16.7168i | −0.705158 | + | 0.705158i | ||||
\(563\) | 32.5972 | − | 32.5972i | 1.37381 | − | 1.37381i | 0.519091 | − | 0.854719i | \(-0.326271\pi\) |
0.854719 | − | 0.519091i | \(-0.173729\pi\) | |||||||
\(564\) | 9.01170 | 0.379461 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 24.0813i | − | 1.01221i | ||||||
\(567\) | 9.51580 | − | 9.51580i | 0.399626 | − | 0.399626i | ||||
\(568\) | 1.20281 | + | 1.20281i | 0.0504687 | + | 0.0504687i | ||||
\(569\) | −24.2387 | −1.01614 | −0.508070 | − | 0.861315i | \(-0.669641\pi\) | ||||
−0.508070 | + | 0.861315i | \(0.669641\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.8082 | −1.33113 | −0.665566 | − | 0.746339i | \(-0.731810\pi\) | ||||
−0.665566 | + | 0.746339i | \(0.731810\pi\) | |||||||
\(572\) | 16.6755 | + | 16.6755i | 0.697236 | + | 0.697236i | ||||
\(573\) | −0.0527215 | + | 0.0527215i | −0.00220247 | + | 0.00220247i | ||||
\(574\) | 27.1088i | 1.13150i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.33358 | −0.180566 | ||||||||
\(577\) | −20.9508 | + | 20.9508i | −0.872194 | + | 0.872194i | −0.992711 | − | 0.120518i | \(-0.961545\pi\) |
0.120518 | + | 0.992711i | \(0.461545\pi\) | |||||||
\(578\) | −8.63388 | + | 8.63388i | −0.359122 | + | 0.359122i | ||||
\(579\) | − | 64.4338i | − | 2.67778i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0873 | 0.501466 | ||||||||
\(582\) | 9.09371 | + | 9.09371i | 0.376946 | + | 0.376946i | ||||
\(583\) | −14.9879 | + | 14.9879i | −0.620736 | + | 0.620736i | ||||
\(584\) | 7.13010 | 0.295046 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.3182 | 0.921957 | ||||||||
\(587\) | −5.45185 | + | 5.45185i | −0.225022 | + | 0.225022i | −0.810609 | − | 0.585587i | \(-0.800864\pi\) |
0.585587 | + | 0.810609i | \(0.300864\pi\) | |||||||
\(588\) | 20.0254 | − | 20.0254i | 0.825834 | − | 0.825834i | ||||
\(589\) | 14.8446 | − | 2.76381i | 0.611660 | − | 0.113881i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 47.2956i | − | 1.94548i | ||||||
\(592\) | 1.05164 | + | 1.05164i | 0.0432220 | + | 0.0432220i | ||||
\(593\) | −5.88700 | − | 5.88700i | −0.241750 | − | 0.241750i | 0.575824 | − | 0.817574i | \(-0.304681\pi\) |
−0.817574 | + | 0.575824i | \(0.804681\pi\) | |||||||
\(594\) | − | 14.0966i | − | 0.578392i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.80671 | 0.0740059 | ||||||||
\(597\) | 9.59629 | + | 9.59629i | 0.392750 | + | 0.392750i | ||||
\(598\) | −26.8551 | − | 26.8551i | −1.09819 | − | 1.09819i | ||||
\(599\) | −20.8668 | −0.852595 | −0.426297 | − | 0.904583i | \(-0.640182\pi\) | ||||
−0.426297 | + | 0.904583i | \(0.640182\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0125i | 0.530790i | 0.964140 | + | 0.265395i | \(0.0855024\pi\) | ||||
−0.964140 | + | 0.265395i | \(0.914498\pi\) | |||||||
\(602\) | −27.7158 | − | 27.7158i | −1.12961 | − | 1.12961i | ||||
\(603\) | 17.5406 | − | 17.5406i | 0.714309 | − | 0.714309i | ||||
\(604\) | −6.32069 | −0.257185 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 16.2484 | 0.660044 | ||||||||
\(607\) | −31.0710 | − | 31.0710i | −1.26113 | − | 1.26113i | −0.950544 | − | 0.310589i | \(-0.899474\pi\) |
−0.310589 | − | 0.950544i | \(-0.600526\pi\) | |||||||
\(608\) | 2.46598 | − | 3.59430i | 0.100009 | − | 0.145768i | ||||
\(609\) | − | 23.8511i | − | 0.966496i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.1050i | 0.813360i | ||||||||
\(612\) | 16.5615 | − | 16.5615i | 0.669458 | − | 0.669458i | ||||
\(613\) | 1.48834 | + | 1.48834i | 0.0601134 | + | 0.0601134i | 0.736524 | − | 0.676411i | \(-0.236466\pi\) |
−0.676411 | + | 0.736524i | \(0.736466\pi\) | |||||||
\(614\) | − | 1.11001i | − | 0.0447962i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.3092i | 0.657116i | ||||||||
\(617\) | 22.9244 | − | 22.9244i | 0.922901 | − | 0.922901i | −0.0743326 | − | 0.997234i | \(-0.523683\pi\) |
0.997234 | + | 0.0743326i | \(0.0236827\pi\) | |||||||
\(618\) | −2.39561 | + | 2.39561i | −0.0963655 | + | 0.0963655i | ||||
\(619\) | 4.72223i | 0.189802i | 0.995487 | + | 0.0949012i | \(0.0302535\pi\) | ||||
−0.995487 | + | 0.0949012i | \(0.969746\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.7020i | 0.911000i | ||||||||
\(622\) | −11.0864 | − | 11.0864i | −0.444525 | − | 0.444525i | ||||
\(623\) | −32.4302 | + | 32.4302i | −1.29929 | + | 1.29929i | ||||
\(624\) | − | 16.3611i | − | 0.654969i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.89550i | 0.195663i | ||||||||
\(627\) | 37.9936 | + | 26.0667i | 1.51732 | + | 1.04100i | ||||
\(628\) | 10.8172 | + | 10.8172i | 0.431655 | + | 0.431655i | ||||
\(629\) | −8.03800 | −0.320496 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.04291 | 0.240564 | 0.120282 | − | 0.992740i | \(-0.461620\pi\) | ||||
0.120282 | + | 0.992740i | \(0.461620\pi\) | |||||||
\(632\) | −8.35842 | + | 8.35842i | −0.332480 | + | 0.332480i | ||||
\(633\) | −37.4770 | − | 37.4770i | −1.48958 | − | 1.48958i | ||||
\(634\) | 18.0275i | 0.715965i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.7054 | 0.583106 | ||||||||
\(637\) | 44.6764 | + | 44.6764i | 1.77014 | + | 1.77014i | ||||
\(638\) | 5.81808 | + | 5.81808i | 0.230340 | + | 0.230340i | ||||
\(639\) | 7.37154 | 0.291614 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.5348i | 0.534593i | 0.963614 | + | 0.267296i | \(0.0861302\pi\) | ||||
−0.963614 | + | 0.267296i | \(0.913870\pi\) | |||||||
\(642\) | −13.1883 | − | 13.1883i | −0.520500 | − | 0.520500i | ||||
\(643\) | −5.37736 | − | 5.37736i | −0.212062 | − | 0.212062i | 0.593081 | − | 0.805143i | \(-0.297912\pi\) |
−0.805143 | + | 0.593081i | \(0.797912\pi\) | |||||||
\(644\) | − | 26.2652i | − | 1.03499i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.31205 | + | 23.1603i | 0.169655 | + | 0.911229i | ||||
\(647\) | −25.3967 | + | 25.3967i | −0.998448 | + | 0.998448i | −0.999999 | − | 0.00155076i | \(-0.999506\pi\) |
0.00155076 | + | 0.999999i | \(0.499506\pi\) | |||||||
\(648\) | 2.27746 | − | 2.27746i | 0.0894672 | − | 0.0894672i | ||||
\(649\) | −58.2202 | −2.28534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 39.1961 | 1.53622 | ||||||||
\(652\) | −11.9456 | + | 11.9456i | −0.467824 | + | 0.467824i | ||||
\(653\) | 18.9735 | + | 18.9735i | 0.742490 | + | 0.742490i | 0.973057 | − | 0.230567i | \(-0.0740580\pi\) |
−0.230567 | + | 0.973057i | \(0.574058\pi\) | |||||||
\(654\) | −0.840439 | −0.0328638 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.48808i | 0.253317i | ||||||||
\(657\) | 21.8488 | − | 21.8488i | 0.852403 | − | 0.852403i | ||||
\(658\) | −9.83168 | + | 9.83168i | −0.383279 | + | 0.383279i | ||||
\(659\) | −30.5839 | −1.19138 | −0.595689 | − | 0.803215i | \(-0.703121\pi\) | ||||
−0.595689 | + | 0.803215i | \(0.703121\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 34.7263i | − | 1.35070i | −0.737499 | − | 0.675349i | \(-0.763993\pi\) | ||
0.737499 | − | 0.675349i | \(-0.236007\pi\) | |||||||
\(662\) | −6.07830 | + | 6.07830i | −0.236240 | + | 0.236240i | ||||
\(663\) | 62.5266 | + | 62.5266i | 2.42833 | + | 2.42833i | ||||
\(664\) | 2.89291 | 0.112267 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.44507 | 0.249742 | ||||||||
\(667\) | −9.36975 | − | 9.36975i | −0.362798 | − | 0.362798i | ||||
\(668\) | −7.71843 | + | 7.71843i | −0.298635 | + | 0.298635i | ||||
\(669\) | − | 29.3343i | − | 1.13413i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.80671 | 0.301375 | ||||||||
\(672\) | 8.00087 | − | 8.00087i | 0.308640 | − | 0.308640i | ||||
\(673\) | 31.9784 | − | 31.9784i | 1.23268 | − | 1.23268i | 0.269746 | − | 0.962931i | \(-0.413060\pi\) |
0.962931 | − | 0.269746i | \(-0.0869398\pi\) | |||||||
\(674\) | − | 2.84708i | − | 0.109666i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.5014 | 0.903900 | ||||||||
\(677\) | 8.41642 | + | 8.41642i | 0.323469 | + | 0.323469i | 0.850096 | − | 0.526627i | \(-0.176544\pi\) |
−0.526627 | + | 0.850096i | \(0.676544\pi\) | |||||||
\(678\) | 18.9638 | − | 18.9638i | 0.728301 | − | 0.728301i | ||||
\(679\) | −19.8423 | −0.761478 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −65.4063 | −2.50637 | ||||||||
\(682\) | −9.56123 | + | 9.56123i | −0.366119 | + | 0.366119i | ||||
\(683\) | 7.28467 | − | 7.28467i | 0.278740 | − | 0.278740i | −0.553866 | − | 0.832606i | \(-0.686848\pi\) |
0.832606 | + | 0.553866i | \(0.186848\pi\) | |||||||
\(684\) | −3.45751 | − | 18.5705i | −0.132201 | − | 0.710062i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14.4474i | 0.551603i | ||||||||
\(687\) | 33.6660 | + | 33.6660i | 1.28444 | + | 1.28444i | ||||
\(688\) | −6.63336 | − | 6.63336i | −0.252895 | − | 0.252895i | ||||
\(689\) | 32.8075i | 1.24986i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1517 | 0.462273 | 0.231136 | − | 0.972921i | \(-0.425756\pi\) | ||||
0.231136 | + | 0.972921i | \(0.425756\pi\) | |||||||
\(692\) | −2.36527 | − | 2.36527i | −0.0899140 | − | 0.0899140i | ||||
\(693\) | 49.9763 | + | 49.9763i | 1.89844 | + | 1.89844i | ||||
\(694\) | 6.89188 | 0.261612 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 5.70840i | − | 0.216376i | ||||||
\(697\) | −24.7952 | − | 24.7952i | −0.939186 | − | 0.939186i | ||||
\(698\) | −15.5346 | + | 15.5346i | −0.587993 | + | 0.587993i | ||||
\(699\) | 41.0583 | 1.55297 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.2161 | −0.612474 | −0.306237 | − | 0.951955i | \(-0.599070\pi\) | ||||
−0.306237 | + | 0.951955i | \(0.599070\pi\) | |||||||
\(702\) | −15.4283 | − | 15.4283i | −0.582303 | − | 0.582303i | ||||
\(703\) | −3.66750 | + | 5.34558i | −0.138322 | + | 0.201612i | ||||
\(704\) | 3.90336i | 0.147113i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 3.77445i | − | 0.142053i | ||||||
\(707\) | −17.7268 | + | 17.7268i | −0.666685 | + | 0.666685i | ||||
\(708\) | 28.5613 | + | 28.5613i | 1.07340 | + | 1.07340i | ||||
\(709\) | 22.0228i | 0.827085i | 0.910485 | + | 0.413542i | \(0.135709\pi\) | ||||
−0.910485 | + | 0.413542i | \(0.864291\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 51.2255i | 1.92111i | ||||||||
\(712\) | −7.76168 | + | 7.76168i | −0.290881 | + | 0.290881i | ||||
\(713\) | 15.3979 | − | 15.3979i | 0.576657 | − | 0.576657i | ||||
\(714\) | 61.1532i | 2.28860i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 9.68475i | − | 0.361936i | ||||||
\(717\) | −5.52731 | − | 5.52731i | −0.206421 | − | 0.206421i | ||||
\(718\) | 2.13272 | − | 2.13272i | 0.0795923 | − | 0.0795923i | ||||
\(719\) | − | 0.0275325i | − | 0.00102679i | −1.00000 | 0.000513394i | \(-0.999837\pi\) | |||
1.00000 | 0.000513394i | \(-0.000163418\pi\) | ||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 5.22718i | − | 0.194670i | ||||||
\(722\) | 17.3699 | + | 7.69967i | 0.646443 | + | 0.286552i | ||||
\(723\) | −5.53960 | − | 5.53960i | −0.206020 | − | 0.206020i | ||||
\(724\) | −14.1370 | −0.525398 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −11.4719 | −0.425761 | ||||||||
\(727\) | 23.0328 | − | 23.0328i | 0.854239 | − | 0.854239i | −0.136413 | − | 0.990652i | \(-0.543558\pi\) |
0.990652 | + | 0.136413i | \(0.0435575\pi\) | |||||||
\(728\) | 17.8498 | + | 17.8498i | 0.661559 | + | 0.661559i | ||||
\(729\) | − | 43.2975i | − | 1.60361i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.7009 | 1.87524 | ||||||||
\(732\) | −3.82977 | − | 3.82977i | −0.141552 | − | 0.141552i | ||||
\(733\) | −2.78821 | − | 2.78821i | −0.102985 | − | 0.102985i | 0.653737 | − | 0.756722i | \(-0.273200\pi\) |
−0.756722 | + | 0.653737i | \(0.773200\pi\) | |||||||
\(734\) | 35.2022 | 1.29934 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.28618i | − | 0.231712i | ||||||
\(737\) | −15.7992 | − | 15.7992i | −0.581973 | − | 0.581973i | ||||
\(738\) | 19.8814 | + | 19.8814i | 0.731846 | + | 0.731846i | ||||
\(739\) | − | 26.4431i | − | 0.972726i | −0.873757 | − | 0.486363i | \(-0.838323\pi\) | ||
0.873757 | − | 0.486363i | \(-0.161677\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 70.1116 | − | 13.0536i | 2.57561 | − | 0.479535i | ||||
\(742\) | −16.0434 | + | 16.0434i | −0.588973 | + | 0.588973i | ||||
\(743\) | −17.9302 | + | 17.9302i | −0.657796 | + | 0.657796i | −0.954858 | − | 0.297062i | \(-0.903993\pi\) |
0.297062 | + | 0.954858i | \(0.403993\pi\) | |||||||
\(744\) | 9.38099 | 0.343924 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 28.3363 | 1.03747 | ||||||||
\(747\) | 8.86476 | − | 8.86476i | 0.324345 | − | 0.324345i | ||||
\(748\) | −14.9173 | − | 14.9173i | −0.545430 | − | 0.545430i | ||||
\(749\) | 28.7766 | 1.05147 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 53.4720i | 1.95122i | 0.219508 | + | 0.975611i | \(0.429555\pi\) | ||||
−0.219508 | + | 0.975611i | \(0.570445\pi\) | |||||||
\(752\) | −2.35306 | + | 2.35306i | −0.0858074 | + | 0.0858074i | ||||
\(753\) | 23.7010 | − | 23.7010i | 0.863712 | − | 0.863712i | ||||
\(754\) | 12.7354 | 0.463794 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 15.0894i | − | 0.548796i | ||||||
\(757\) | −8.12170 | + | 8.12170i | −0.295188 | + | 0.295188i | −0.839126 | − | 0.543938i | \(-0.816933\pi\) |
0.543938 | + | 0.839126i | \(0.316933\pi\) | |||||||
\(758\) | −5.53164 | − | 5.53164i | −0.200918 | − | 0.200918i | ||||
\(759\) | 66.4482 | 2.41192 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.5881 | −0.565069 | −0.282535 | − | 0.959257i | \(-0.591175\pi\) | ||||
−0.282535 | + | 0.959257i | \(0.591175\pi\) | |||||||
\(762\) | −36.9690 | − | 36.9690i | −1.33925 | − | 1.33925i | ||||
\(763\) | 0.916911 | − | 0.916911i | 0.0331944 | − | 0.0331944i | ||||
\(764\) | − | 0.0275325i | − | 0.000996089i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0873 | 0.870310 | ||||||||
\(767\) | −63.7199 | + | 63.7199i | −2.30079 | + | 2.30079i | ||||
\(768\) | 1.91489 | − | 1.91489i | 0.0690975 | − | 0.0690975i | ||||
\(769\) | 2.64037i | 0.0952143i | 0.998866 | + | 0.0476071i | \(0.0151596\pi\) | ||||
−0.998866 | + | 0.0476071i | \(0.984840\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.0337 | −0.937582 | ||||||||
\(772\) | 16.8244 | + | 16.8244i | 0.605525 | + | 0.605525i | ||||
\(773\) | 4.26211 | − | 4.26211i | 0.153297 | − | 0.153297i | −0.626292 | − | 0.779589i | \(-0.715428\pi\) |
0.779589 | + | 0.626292i | \(0.215428\pi\) | |||||||
\(774\) | −40.6533 | −1.46125 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.74896 | −0.170478 | ||||||||
\(777\) | −11.8992 | + | 11.8992i | −0.426882 | + | 0.426882i | ||||
\(778\) | 22.1956 | − | 22.1956i | 0.795753 | − | 0.795753i | ||||
\(779\) | −27.8031 | + | 5.17646i | −0.996149 | + | 0.185466i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 6.63972i | − | 0.237588i | ||||||
\(782\) | 24.0236 | + | 24.0236i | 0.859083 | + | 0.859083i | ||||
\(783\) | −5.38293 | − | 5.38293i | −0.192370 | − | 0.192370i | ||||
\(784\) | 10.4578i | 0.373491i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.80671 | 0.0644433 | ||||||||
\(787\) | 5.97579 | + | 5.97579i | 0.213014 | + | 0.213014i | 0.805546 | − | 0.592533i | \(-0.201872\pi\) |
−0.592533 | + | 0.805546i | \(0.701872\pi\) | |||||||
\(788\) | 12.3494 | + | 12.3494i | 0.439931 | + | 0.439931i | ||||
\(789\) | −54.6408 | −1.94526 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 41.3787i | 1.47126i | ||||||||
\(792\) | 11.9611 | + | 11.9611i | 0.425018 | + | 0.425018i | ||||
\(793\) | 8.54417 | − | 8.54417i | 0.303412 | − | 0.303412i | ||||
\(794\) | 4.95444 | 0.175827 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.01141 | −0.177625 | ||||||||
\(797\) | 15.7814 | + | 15.7814i | 0.559004 | + | 0.559004i | 0.929024 | − | 0.370020i | \(-0.120649\pi\) |
−0.370020 | + | 0.929024i | \(0.620649\pi\) | |||||||
\(798\) | 40.6692 | + | 27.9024i | 1.43968 | + | 0.987733i | ||||
\(799\) | − | 17.9852i | − | 0.636271i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 47.5683i | 1.68074i | ||||||||
\(802\) | 1.60670 | − | 1.60670i | 0.0567345 | − | 0.0567345i | ||||
\(803\) | −19.6797 | − | 19.6797i | −0.694482 | − | 0.694482i | ||||
\(804\) | 15.5014i | 0.546693i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.9289i | 0.737187i | ||||||||
\(807\) | 39.1742 | − | 39.1742i | 1.37900 | − | 1.37900i | ||||
\(808\) | −4.24264 | + | 4.24264i | −0.149256 | + | 0.149256i | ||||
\(809\) | 24.1847i | 0.850288i | 0.905126 | + | 0.425144i | \(0.139777\pi\) | ||||
−0.905126 | + | 0.425144i | \(0.860223\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.38279i | − | 0.259245i | −0.991563 | − | 0.129622i | \(-0.958623\pi\) | ||
0.991563 | − | 0.129622i | \(-0.0413765\pi\) | |||||||
\(812\) | 6.22781 | + | 6.22781i | 0.218553 | + | 0.218553i | ||||
\(813\) | −0.792964 | + | 0.792964i | −0.0278105 | + | 0.0278105i | ||||
\(814\) | − | 5.80523i | − | 0.203473i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 14.6361i | 0.512365i | ||||||||
\(817\) | 23.1333 | − | 33.7180i | 0.809332 | − | 1.17965i | ||||
\(818\) | 7.27398 | + | 7.27398i | 0.254329 | + | 0.254329i | ||||
\(819\) | 109.395 | 3.82256 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.9921 | 1.11653 | 0.558266 | − | 0.829662i | \(-0.311467\pi\) | ||||
0.558266 | + | 0.829662i | \(0.311467\pi\) | |||||||
\(822\) | −25.6186 | + | 25.6186i | −0.893552 | + | 0.893552i | ||||
\(823\) | 4.20827 | + | 4.20827i | 0.146691 | + | 0.146691i | 0.776638 | − | 0.629947i | \(-0.216923\pi\) |
−0.629947 | + | 0.776638i | \(0.716923\pi\) | |||||||
\(824\) | − | 1.25104i | − | 0.0435822i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −62.3203 | −2.16840 | ||||||||
\(827\) | −9.72213 | − | 9.72213i | −0.338072 | − | 0.338072i | 0.517569 | − | 0.855641i | \(-0.326837\pi\) |
−0.855641 | + | 0.517569i | \(0.826837\pi\) | |||||||
\(828\) | −19.2628 | − | 19.2628i | −0.669427 | − | 0.669427i | ||||
\(829\) | −6.70058 | −0.232721 | −0.116360 | − | 0.993207i | \(-0.537123\pi\) | ||||
−0.116360 | + | 0.993207i | \(0.537123\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 31.6559i | − | 1.09813i | ||||||
\(832\) | 4.27208 | + | 4.27208i | 0.148108 | + | 0.148108i | ||||
\(833\) | −39.9660 | − | 39.9660i | −1.38474 | − | 1.38474i | ||||
\(834\) | − | 55.1827i | − | 1.91082i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −16.7269 | + | 3.11426i | −0.578512 | + | 0.107709i | ||||
\(837\) | 8.84612 | − | 8.84612i | 0.305767 | − | 0.305767i | ||||
\(838\) | 24.9557 | − | 24.9557i | 0.862082 | − | 0.862082i | ||||
\(839\) | −15.1405 | −0.522707 | −0.261353 | − | 0.965243i | \(-0.584169\pi\) | ||||
−0.261353 | + | 0.965243i | \(0.584169\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.5566 | −0.846780 | ||||||||
\(842\) | 16.6924 | − | 16.6924i | 0.575260 | − | 0.575260i | ||||
\(843\) | −45.2702 | − | 45.2702i | −1.55919 | − | 1.55919i | ||||
\(844\) | 19.5714 | 0.673675 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14.4210i | 0.495804i | ||||||||
\(847\) | 12.5157 | − | 12.5157i | 0.430045 | − | 0.430045i | ||||
\(848\) | −3.83975 | + | 3.83975i | −0.131857 | + | 0.131857i | ||||
\(849\) | 65.2136 | 2.23813 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.34906i | 0.320481i | ||||||||
\(852\) | −3.25727 | + | 3.25727i | −0.111592 | + | 0.111592i | ||||
\(853\) | −36.0415 | − | 36.0415i | −1.23404 | − | 1.23404i | −0.962400 | − | 0.271637i | \(-0.912435\pi\) |
−0.271637 | − | 0.962400i | \(-0.587565\pi\) | |||||||
\(854\) | 8.35650 | 0.285953 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.88724 | 0.235401 | ||||||||
\(857\) | −11.2682 | − | 11.2682i | −0.384913 | − | 0.384913i | 0.487955 | − | 0.872869i | \(-0.337743\pi\) |
−0.872869 | + | 0.487955i | \(0.837743\pi\) | |||||||
\(858\) | −45.1581 | + | 45.1581i | −1.54167 | + | 1.54167i | ||||
\(859\) | − | 30.5383i | − | 1.04195i | −0.853571 | − | 0.520976i | \(-0.825568\pi\) | ||
0.853571 | − | 0.520976i | \(-0.174432\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −73.4122 | −2.50188 | ||||||||
\(862\) | 4.99166 | − | 4.99166i | 0.170016 | − | 0.170016i | ||||
\(863\) | 31.6472 | − | 31.6472i | 1.07728 | − | 1.07728i | 0.0805325 | − | 0.996752i | \(-0.474338\pi\) |
0.996752 | − | 0.0805325i | \(-0.0256621\pi\) | |||||||
\(864\) | − | 3.61142i | − | 0.122863i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −18.2335 | −0.619600 | ||||||||
\(867\) | −23.3810 | − | 23.3810i | −0.794062 | − | 0.794062i | ||||
\(868\) | −10.2346 | + | 10.2346i | −0.347384 | + | 0.347384i | ||||
\(869\) | 46.1400 | 1.56519 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.5834 | −1.17181 | ||||||||
\(872\) | 0.219449 | − | 0.219449i | 0.00743147 | − | 0.00743147i | ||||
\(873\) | −14.5522 | + | 14.5522i | −0.492519 | + | 0.492519i | ||||
\(874\) | 26.9379 | − | 5.01538i | 0.911188 | − | 0.169648i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19.3087i | 0.652382i | ||||||||
\(877\) | −15.4991 | − | 15.4991i | −0.523367 | − | 0.523367i | 0.395220 | − | 0.918587i | \(-0.370668\pi\) |
−0.918587 | + | 0.395220i | \(0.870668\pi\) | |||||||
\(878\) | 22.0127 | + | 22.0127i | 0.742892 | + | 0.742892i | ||||
\(879\) | 60.4390i | 2.03856i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.90484 | −0.0978666 | −0.0489333 | − | 0.998802i | \(-0.515582\pi\) | ||||
−0.0489333 | + | 0.998802i | \(0.515582\pi\) | |||||||
\(882\) | 32.0458 | + | 32.0458i | 1.07904 | + | 1.07904i | ||||
\(883\) | 34.0836 | + | 34.0836i | 1.14701 | + | 1.14701i | 0.987139 | + | 0.159867i | \(0.0511066\pi\) |
0.159867 | + | 0.987139i | \(0.448893\pi\) | |||||||
\(884\) | −32.6529 | −1.09824 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.0718i | 0.674324i | ||||||||
\(887\) | 18.7588 | + | 18.7588i | 0.629859 | + | 0.629859i | 0.948032 | − | 0.318174i | \(-0.103070\pi\) |
−0.318174 | + | 0.948032i | \(0.603070\pi\) | |||||||
\(888\) | −2.84790 | + | 2.84790i | −0.0955691 | + | 0.0955691i | ||||
\(889\) | 80.6657 | 2.70544 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.5720 | −0.421178 | ||||||||
\(892\) | 7.65955 | + | 7.65955i | 0.256461 | + | 0.256461i | ||||
\(893\) | −11.9609 | − | 8.20612i | −0.400255 | − | 0.274607i | ||||
\(894\) | 4.89269i | 0.163636i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.17825i | 0.139585i | ||||||||
\(897\) | 72.7251 | − | 72.7251i | 2.42822 | − | 2.42822i | ||||
\(898\) | 5.73245 | + | 5.73245i | 0.191294 | + | 0.191294i | ||||
\(899\) | 7.30209i | 0.243538i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 29.3484i | − | 0.977737i | ||||||
\(902\) | 17.9077 | − | 17.9077i | 0.596261 | − | 0.596261i | ||||
\(903\) | 75.0561 | − | 75.0561i | 2.49771 | − | 2.49771i | ||||
\(904\) | 9.90336i | 0.329381i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 17.1168i | − | 0.568667i | ||||||
\(907\) | 34.9725 | + | 34.9725i | 1.16124 | + | 1.16124i | 0.984204 | + | 0.177038i | \(0.0566516\pi\) |
0.177038 | + | 0.984204i | \(0.443348\pi\) | |||||||
\(908\) | 17.0784 | − | 17.0784i | 0.566765 | − | 0.566765i | ||||
\(909\) | 26.0015i | 0.862415i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.12932i | − | 0.103679i | −0.998655 | − | 0.0518395i | \(-0.983492\pi\) | ||
0.998655 | − | 0.0518395i | \(-0.0165084\pi\) | |||||||
\(912\) | 9.73356 | + | 6.67801i | 0.322310 | + | 0.221131i | ||||
\(913\) | −7.98470 | − | 7.98470i | −0.264255 | − | 0.264255i | ||||
\(914\) | −11.4526 | −0.378818 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.5812 | −0.580899 | ||||||||
\(917\) | −1.97111 | + | 1.97111i | −0.0650917 | + | 0.0650917i | ||||
\(918\) | 13.8016 | + | 13.8016i | 0.455521 | + | 0.455521i | ||||
\(919\) | 24.2860i | 0.801120i | 0.916271 | + | 0.400560i | \(0.131184\pi\) | ||||
−0.916271 | + | 0.400560i | \(0.868816\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.00596 | 0.0990499 | ||||||||
\(922\) | 20.8032 | + | 20.8032i | 0.685116 | + | 0.685116i | ||||
\(923\) | −7.26693 | − | 7.26693i | −0.239194 | − | 0.239194i | ||||
\(924\) | −44.1662 | −1.45296 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 22.8973i | 0.752452i | ||||||||
\(927\) | −3.83358 | − | 3.83358i | −0.125911 | − | 0.125911i | ||||
\(928\) | 1.49053 | + | 1.49053i | 0.0489291 | + | 0.0489291i | ||||
\(929\) | 19.3296i | 0.634184i | 0.948395 | + | 0.317092i | \(0.102706\pi\) | ||||
−0.948395 | + | 0.317092i | \(0.897294\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.8142 | + | 8.34364i | −1.46873 | + | 0.273452i | ||||
\(932\) | −10.7208 | + | 10.7208i | −0.351172 | + | 0.351172i | ||||
\(933\) | 30.0227 | − | 30.0227i | 0.982899 | − | 0.982899i | ||||
\(934\) | −37.0938 | −1.21375 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 26.1819 | 0.855783 | ||||||||
\(937\) | 7.03506 | − | 7.03506i | 0.229825 | − | 0.229825i | −0.582794 | − | 0.812620i | \(-0.698041\pi\) |
0.812620 | + | 0.582794i | \(0.198041\pi\) | |||||||
\(938\) | −16.9119 | − | 16.9119i | −0.552193 | − | 0.552193i | ||||
\(939\) | −13.2573 | −0.432636 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.3091i | 0.499063i | 0.968367 | + | 0.249532i | \(0.0802767\pi\) | ||||
−0.968367 | + | 0.249532i | \(0.919723\pi\) | |||||||
\(942\) | −29.2937 | + | 29.2937i | −0.954440 | + | 0.954440i | ||||
\(943\) | −28.8395 | + | 28.8395i | −0.939143 | + | 0.939143i | ||||
\(944\) | −14.9154 | −0.485455 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 36.6174i | 1.19053i | ||||||||
\(947\) | 3.75429 | − | 3.75429i | 0.121998 | − | 0.121998i | −0.643472 | − | 0.765470i | \(-0.722507\pi\) |
0.765470 | + | 0.643472i | \(0.222507\pi\) | |||||||
\(948\) | −22.6351 | − | 22.6351i | −0.735154 | − | 0.735154i | ||||
\(949\) | −43.0775 | −1.39836 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −48.8196 | −1.58308 | ||||||||
\(952\) | −15.9678 | − | 15.9678i | −0.517521 | − | 0.517521i | ||||
\(953\) | −24.3463 | + | 24.3463i | −0.788653 | + | 0.788653i | −0.981273 | − | 0.192621i | \(-0.938301\pi\) |
0.192621 | + | 0.981273i | \(0.438301\pi\) | |||||||
\(954\) | 23.5323i | 0.761887i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.88649 | 0.0933559 | ||||||||
\(957\) | −15.7557 | + | 15.7557i | −0.509309 | + | 0.509309i | ||||
\(958\) | 19.0246 | − | 19.0246i | 0.614657 | − | 0.614657i | ||||
\(959\) | − | 55.8994i | − | 1.80509i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | −6.35361 | − | 6.35361i | −0.204849 | − | 0.204849i | ||||
\(963\) | 21.1046 | − | 21.1046i | 0.680086 | − | 0.680086i | ||||
\(964\) | 2.89291 | 0.0931744 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 71.1277 | 2.28850 | ||||||||
\(967\) | 17.4994 | − | 17.4994i | 0.562743 | − | 0.562743i | −0.367343 | − | 0.930086i | \(-0.619732\pi\) |
0.930086 | + | 0.367343i | \(0.119732\pi\) | |||||||
\(968\) | 2.99544 | − | 2.99544i | 0.0962772 | − | 0.0962772i | ||||
\(969\) | −62.7194 | + | 11.6773i | −2.01484 | + | 0.375128i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.33148i | 0.299462i | 0.988727 | + | 0.149731i | \(0.0478407\pi\) | ||||
−0.988727 | + | 0.149731i | \(0.952159\pi\) | |||||||
\(972\) | 13.8285 | + | 13.8285i | 0.443548 | + | 0.443548i | ||||
\(973\) | 60.2039 | + | 60.2039i | 1.93005 | + | 1.93005i | ||||
\(974\) | − | 37.9222i | − | 1.21511i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | −9.53501 | − | 9.53501i | −0.305052 | − | 0.305052i | 0.537935 | − | 0.842987i | \(-0.319205\pi\) |
−0.842987 | + | 0.537935i | \(0.819205\pi\) | |||||||
\(978\) | −32.3493 | − | 32.3493i | −1.03442 | − | 1.03442i | ||||
\(979\) | 42.8459 | 1.36936 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1.34492i | − | 0.0429399i | ||||||
\(982\) | −7.67950 | − | 7.67950i | −0.245063 | − | 0.245063i | ||||
\(983\) | −17.6028 | + | 17.6028i | −0.561443 | + | 0.561443i | −0.929717 | − | 0.368274i | \(-0.879949\pi\) |
0.368274 | + | 0.929717i | \(0.379949\pi\) | |||||||
\(984\) | −17.5701 | −0.560114 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11.3926 | −0.362815 | ||||||||
\(987\) | −26.6248 | − | 26.6248i | −0.847476 | − | 0.847476i | ||||
\(988\) | −14.8985 | + | 21.7154i | −0.473986 | + | 0.690860i | ||||
\(989\) | − | 58.9706i | − | 1.87516i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 31.0484i | − | 0.986286i | −0.869948 | − | 0.493143i | \(-0.835848\pi\) | ||
0.869948 | − | 0.493143i | \(-0.164152\pi\) | |||||||
\(992\) | −2.44949 | + | 2.44949i | −0.0777714 | + | 0.0777714i | ||||
\(993\) | −16.4604 | − | 16.4604i | −0.522354 | − | 0.522354i | ||||
\(994\) | − | 7.10731i | − | 0.225430i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.83417i | 0.248235i | ||||||||
\(997\) | −12.3889 | + | 12.3889i | −0.392361 | + | 0.392361i | −0.875528 | − | 0.483167i | \(-0.839486\pi\) |
0.483167 | + | 0.875528i | \(0.339486\pi\) | |||||||
\(998\) | −13.8470 | + | 13.8470i | −0.438320 | + | 0.438320i | ||||
\(999\) | 5.37104i | 0.169932i |
(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 | 950.2.f.d.493.8 | yes | 32 | |
5.2 | odd | 4 | inner | 950.2.f.d.607.10 | yes | 32 | |
5.3 | odd | 4 | inner | 950.2.f.d.607.7 | yes | 32 | |
5.4 | even | 2 | inner | 950.2.f.d.493.9 | yes | 32 | |
19.18 | odd | 2 | inner | 950.2.f.d.493.10 | yes | 32 | |
95.18 | even | 4 | inner | 950.2.f.d.607.9 | yes | 32 | |
95.37 | even | 4 | inner | 950.2.f.d.607.8 | yes | 32 | |
95.94 | odd | 2 | inner | 950.2.f.d.493.7 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.f.d.493.7 | ✓ | 32 | 95.94 | odd | 2 | inner | |
950.2.f.d.493.8 | yes | 32 | 1.1 | even | 1 | trivial | |
950.2.f.d.493.9 | yes | 32 | 5.4 | even | 2 | inner | |
950.2.f.d.493.10 | yes | 32 | 19.18 | odd | 2 | inner | |
950.2.f.d.607.7 | yes | 32 | 5.3 | odd | 4 | inner | |
950.2.f.d.607.8 | yes | 32 | 95.37 | even | 4 | inner | |
950.2.f.d.607.9 | yes | 32 | 95.18 | even | 4 | inner | |
950.2.f.d.607.10 | yes | 32 | 5.2 | odd | 4 | inner |