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 | 493.7 | ||
Character | \(\chi\) | \(=\) | 950.493 |
Dual form | 950.2.f.d.607.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | \(0.539720\pi\) |
−0.992225 | + | 0.124459i | \(0.960280\pi\) | |||||||
\(8\) | 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 | −0.997504 | − | 0.0706153i | \(-0.977504\pi\) |
0.0706153 | + | 0.997504i | \(0.477504\pi\) | |||||||
\(18\) | −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 | 0.997501 | − | 0.0706544i | \(-0.0225087\pi\) |
−0.0706544 | + | 0.997501i | \(0.522509\pi\) | |||||||
\(24\) | − | 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 | \(-0.562703\pi\) | ||||
−0.195716 | + | 0.980661i | \(0.562703\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46410i | − | 0.622171i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(32\) | 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 | \(0.789011\pi\) | |||||||
\(38\) | −3.59430 | + | 2.46598i | −0.583072 | + | 0.400034i | ||||
\(39\) | 16.3611i | 2.61987i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.48808i | 1.01327i | 0.862161 | + | 0.506634i | \(0.169110\pi\) | ||||
−0.862161 | + | 0.506634i | \(0.830890\pi\) | |||||||
\(42\) | 8.00087 | − | 8.00087i | 1.23456 | − | 1.23456i | ||||
\(43\) | −6.63336 | − | 6.63336i | −1.01158 | − | 1.01158i | −0.999932 | − | 0.0116460i | \(-0.996293\pi\) |
−0.0116460 | − | 0.999932i | \(-0.503707\pi\) | |||||||
\(44\) | − | 3.90336i | − | 0.588453i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 6.28618i | − | 0.926846i | ||||||
\(47\) | −2.35306 | + | 2.35306i | −0.343230 | + | 0.343230i | −0.857580 | − | 0.514350i | \(-0.828033\pi\) |
0.514350 | + | 0.857580i | \(0.328033\pi\) | |||||||
\(48\) | −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 | ||||||||
\(57\) | −6.67801 | − | 9.73356i | −0.884524 | − | 1.28924i | ||||
\(58\) | 1.49053 | + | 1.49053i | 0.195716 | + | 0.195716i | ||||
\(59\) | −14.9154 | −1.94182 | −0.970910 | − | 0.239443i | \(-0.923035\pi\) | ||||
−0.970910 | + | 0.239443i | \(0.923035\pi\) | |||||||
\(60\) | 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 | \(-0.967816\pi\) | ||
0.994893 | − | 0.100937i | \(-0.0321842\pi\) | |||||||
\(72\) | −3.06430 | − | 3.06430i | −0.361132 | − | 0.361132i | ||||
\(73\) | −5.04174 | − | 5.04174i | −0.590091 | − | 0.590091i | 0.347565 | − | 0.937656i | \(-0.387009\pi\) |
−0.937656 | + | 0.347565i | \(0.887009\pi\) | |||||||
\(74\) | 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 | \(-0.268448\pi\) | ||||
0.664961 | + | 0.746878i | \(0.268448\pi\) | |||||||
\(80\) | 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 | 0.585871 | − | 0.810404i | \(-0.300753\pi\) |
−0.810404 | + | 0.585871i | \(0.800753\pi\) | |||||||
\(84\) | −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 | \(-0.302363\pi\) | ||||
0.581763 | + | 0.813359i | \(0.302363\pi\) | |||||||
\(90\) | 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 | \(-0.504731\pi\) | ||||
−0.0148629 | + | 0.999890i | \(0.504731\pi\) | |||||||
\(110\) | 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 | ||||
\(133\) | 10.3035 | + | 15.0179i | 0.893423 | + | 1.30221i | ||||
\(134\) | − | 5.72418i | − | 0.494494i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.40464i | 0.463444i | ||||||||
\(137\) | −9.46015 | + | 9.46015i | −0.808235 | + | 0.808235i | −0.984367 | − | 0.176132i | \(-0.943642\pi\) |
0.176132 | + | 0.984367i | \(0.443642\pi\) | |||||||
\(138\) | −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 | \(-0.917205\pi\) | ||
0.966362 | − | 0.257185i | \(-0.0827950\pi\) | |||||||
\(152\) | −2.46598 | − | 3.59430i | −0.200017 | − | 0.291536i | ||||
\(153\) | 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 | −0.991721 | − | 0.128412i | \(-0.959012\pi\) |
0.128412 | + | 0.991721i | \(0.459012\pi\) | |||||||
\(158\) | −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 | 0.0624032 | − | 0.998051i | \(-0.480124\pi\) |
−0.998051 | + | 0.0624032i | \(0.980124\pi\) | |||||||
\(164\) | −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 | \(-0.382116\pi\) | ||||
0.361936 | + | 0.932203i | \(0.382116\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.1370i | − | 1.05080i | −0.850857 | − | 0.525398i | \(-0.823916\pi\) | ||
0.850857 | − | 0.525398i | \(-0.176084\pi\) | |||||||
\(182\) | −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 | −0.993520 | − | 0.113658i | \(-0.963743\pi\) |
0.113658 | + | 0.993520i | \(0.463743\pi\) | |||||||
\(198\) | 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 | \(0.235285\pi\) | ||||
−0.739028 | + | 0.673675i | \(0.764715\pi\) | |||||||
\(212\) | 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 | \(-0.545979\pi\) | |||||||
\(228\) | 9.73356 | − | 6.67801i | 0.644621 | − | 0.442262i | ||||
\(229\) | 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 | 0.262570 | − | 0.964913i | \(-0.415430\pi\) |
−0.964913 | + | 0.262570i | \(0.915430\pi\) | |||||||
\(234\) | − | 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 | \(0.0297014\pi\) | ||||
−0.995650 | + | 0.0931744i | \(0.970299\pi\) | |||||||
\(242\) | −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 | ||||||
\(247\) | 14.8985 | + | 21.7154i | 0.947972 | + | 1.38172i | ||||
\(248\) | −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 | 0.993510 | − | 0.113747i | \(-0.0362852\pi\) |
−0.113747 | + | 0.993510i | \(0.536285\pi\) | |||||||
\(264\) | 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 | \(-0.714357\pi\) | ||||
−0.623664 | + | 0.781692i | \(0.714357\pi\) | |||||||
\(270\) | 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 | −0.910391 | − | 0.413750i | \(-0.864219\pi\) |
0.413750 | + | 0.910391i | \(0.364219\pi\) | |||||||
\(278\) | 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 | \(0.249124\pi\) | ||||
−0.709050 | + | 0.705158i | \(0.750876\pi\) | |||||||
\(282\) | 6.37223 | − | 6.37223i | 0.379461 | − | 0.379461i | ||||
\(283\) | −17.0281 | − | 17.0281i | −1.01221 | − | 1.01221i | −0.999924 | − | 0.0122889i | \(-0.996088\pi\) |
−0.0122889 | − | 0.999924i | \(-0.503912\pi\) | |||||||
\(284\) | 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 | 0.798138 | − | 0.602475i | \(-0.205819\pi\) |
−0.602475 | + | 0.798138i | \(0.705819\pi\) | |||||||
\(314\) | 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 | ||||
\(323\) | 13.3277 | + | 19.4259i | 0.741574 | + | 1.08088i | ||||
\(324\) | 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 | \(0.0759151\pi\) | ||||
−0.971695 | + | 0.236240i | \(0.924085\pi\) | |||||||
\(332\) | 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 | ||||||||
\(342\) | 10.6865 | + | 15.5762i | 0.577860 | + | 0.842263i | ||||
\(343\) | 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 | −0.564097 | − | 0.825709i | \(-0.690775\pi\) |
0.825709 | + | 0.564097i | \(0.190775\pi\) | |||||||
\(348\) | −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 | 0.632504 | − | 0.774557i | \(-0.282027\pi\) |
−0.774557 | + | 0.632504i | \(0.782027\pi\) | |||||||
\(354\) | 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 | \(-0.379183\pi\) |
0.928829 | − | 0.370510i | \(-0.120817\pi\) | |||||||
\(368\) | −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 | \(-0.564393\pi\) | ||||
−0.200918 | + | 0.979608i | \(0.564393\pi\) | |||||||
\(380\) | 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 | −0.613707 | − | 0.789534i | \(-0.710322\pi\) |
0.789534 | + | 0.613707i | \(0.210322\pi\) | |||||||
\(398\) | 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 | \(-0.981931\pi\) | ||
0.998389 | − | 0.0567345i | \(-0.0180689\pi\) | |||||||
\(402\) | −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 | \(-0.418145\pi\) | ||||
0.254329 | + | 0.967118i | \(0.418145\pi\) | |||||||
\(410\) | 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 | ||||
\(418\) | 14.0298 | − | 9.62559i | 0.686221 | − | 0.470803i | ||||
\(419\) | 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 | \(-0.804901\pi\) | ||
0.817971 | − | 0.575260i | \(-0.195099\pi\) | |||||||
\(422\) | 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 | \(-0.945618\pi\) | ||
0.985441 | − | 0.170016i | \(-0.0543821\pi\) | |||||||
\(432\) | 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 | ||||||
\(437\) | 22.5944 | − | 15.5016i | 1.08084 | − | 0.741541i | ||||
\(438\) | 13.6533 | + | 13.6533i | 0.652382 | + | 0.652382i | ||||
\(439\) | 31.1306 | 1.48578 | 0.742892 | − | 0.669412i | \(-0.233454\pi\) | ||||
0.742892 | + | 0.669412i | \(0.233454\pi\) | |||||||
\(440\) | 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 | 0.958710 | − | 0.284386i | \(-0.0917898\pi\) |
−0.284386 | + | 0.958710i | \(0.591790\pi\) | |||||||
\(444\) | − | 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 | \(-0.438731\pi\) | ||||
0.191294 | + | 0.981533i | \(0.438731\pi\) | |||||||
\(450\) | 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 | −0.870676 | − | 0.491858i | \(-0.836318\pi\) |
0.491858 | + | 0.870676i | \(0.336318\pi\) | |||||||
\(458\) | 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 | 0.974936 | − | 0.222484i | \(-0.0714165\pi\) |
−0.222484 | + | 0.974936i | \(0.571417\pi\) | |||||||
\(464\) | 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 | \(0.578447\pi\) |
−0.969785 | + | 0.243961i | \(0.921553\pi\) | |||||||
\(468\) | −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 | 0.877068 | − | 0.480365i | \(-0.159496\pi\) |
−0.480365 | + | 0.877068i | \(0.659496\pi\) | |||||||
\(504\) | 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 | \(-0.809045\pi\) | ||||
−0.825391 | + | 0.564561i | \(0.809045\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.7913 | 1.31789 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −12.9805 | + | 8.90567i | −0.573103 | + | 0.393195i | ||||
\(514\) | 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 | \(0.0753368\pi\) | ||||
−0.972122 | + | 0.234474i | \(0.924663\pi\) | |||||||
\(522\) | 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 | ||||||||
\(532\) | −15.0179 | + | 10.3035i | −0.651107 | + | 0.446712i | ||||
\(533\) | −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 | −0.700833 | − | 0.713326i | \(-0.747188\pi\) |
0.713326 | + | 0.700833i | \(0.247188\pi\) | |||||||
\(558\) | 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 | \(-0.330359\pi\) | ||||
0.508070 | + | 0.861315i | \(0.330359\pi\) | |||||||
\(570\) | 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 | −0.120518 | − | 0.992711i | \(-0.538455\pi\) |
0.992711 | + | 0.120518i | \(0.0384554\pi\) | |||||||
\(578\) | −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 | −0.585587 | − | 0.810609i | \(-0.699136\pi\) |
0.810609 | + | 0.585587i | \(0.199136\pi\) | |||||||
\(588\) | 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 | 0.817574 | − | 0.575824i | \(-0.195319\pi\) |
−0.575824 | + | 0.817574i | \(0.695319\pi\) | |||||||
\(594\) | − | 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 | \(-0.359818\pi\) | ||||
0.426297 | + | 0.904583i | \(0.359818\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.0125i | − | 0.530790i | −0.964140 | − | 0.265395i | \(-0.914498\pi\) | ||
0.964140 | − | 0.265395i | \(-0.0855024\pi\) | |||||||
\(602\) | −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 | \(-0.600526\pi\) | |||||||
\(608\) | 3.59430 | − | 2.46598i | 0.145768 | − | 0.100009i | ||||
\(609\) | − | 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 | 0.676411 | − | 0.736524i | \(-0.263534\pi\) |
−0.736524 | + | 0.676411i | \(0.763534\pi\) | |||||||
\(614\) | − | 1.11001i | − | 0.0447962i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 16.3092i | − | 0.657116i | ||||||
\(617\) | −22.9244 | + | 22.9244i | −0.922901 | + | 0.922901i | −0.997234 | − | 0.0743326i | \(-0.976317\pi\) |
0.0743326 | + | 0.997234i | \(0.476317\pi\) | |||||||
\(618\) | −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 | ||||||
\(627\) | 26.0667 | + | 37.9936i | 1.04100 | + | 1.51732i | ||||
\(628\) | −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 | \(-0.913870\pi\) | ||
0.963614 | − | 0.267296i | \(-0.0861302\pi\) | |||||||
\(642\) | −13.1883 | − | 13.1883i | −0.520500 | − | 0.520500i | ||||
\(643\) | 5.37736 | + | 5.37736i | 0.212062 | + | 0.212062i | 0.805143 | − | 0.593081i | \(-0.202088\pi\) |
−0.593081 | + | 0.805143i | \(0.702088\pi\) | |||||||
\(644\) | − | 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 | −0.00155076 | − | 0.999999i | \(-0.500494\pi\) |
0.999999 | + | 0.00155076i | \(0.000493622\pi\) | |||||||
\(648\) | 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 | 0.230567 | − | 0.973057i | \(-0.425942\pi\) |
−0.973057 | + | 0.230567i | \(0.925942\pi\) | |||||||
\(654\) | 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 | \(-0.296879\pi\) | ||||
0.595689 | + | 0.803215i | \(0.296879\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.7263i | 1.35070i | 0.737499 | + | 0.675349i | \(0.236007\pi\) | ||||
−0.737499 | + | 0.675349i | \(0.763993\pi\) | |||||||
\(662\) | 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 | ||||
\(703\) | −5.34558 | + | 3.66750i | −0.201612 | + | 0.138322i | ||||
\(704\) | 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 | ||||||||
\(722\) | 7.69967 | + | 17.3699i | 0.286552 | + | 0.646443i | ||||
\(723\) | 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 | −0.990652 | − | 0.136413i | \(-0.956442\pi\) |
0.136413 | + | 0.990652i | \(0.456442\pi\) | |||||||
\(728\) | −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 | 0.756722 | − | 0.653737i | \(-0.226800\pi\) |
−0.653737 | + | 0.756722i | \(0.726800\pi\) | |||||||
\(734\) | −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 | \(-0.570445\pi\) | ||
0.219508 | − | 0.975611i | \(-0.429555\pi\) | |||||||
\(752\) | 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 | −0.543938 | − | 0.839126i | \(-0.683067\pi\) |
0.839126 | + | 0.543938i | \(0.183067\pi\) | |||||||
\(758\) | 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 | \(0.620649\pi\) | |||||||
\(798\) | −27.9024 | − | 40.6692i | −0.987733 | − | 1.43968i | ||||
\(799\) | − | 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 | \(0.0413765\pi\) | ||||
−0.991563 | + | 0.129622i | \(0.958623\pi\) | |||||||
\(812\) | 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 | ||||||
\(817\) | −33.7180 | + | 23.1333i | −1.17965 | + | 0.809332i | ||||
\(818\) | −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 | 0.629947 | − | 0.776638i | \(-0.283077\pi\) |
−0.776638 | + | 0.629947i | \(0.783077\pi\) | |||||||
\(824\) | − | 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 | \(-0.462877\pi\) | ||||
0.116360 | + | 0.993207i | \(0.462877\pi\) | |||||||
\(830\) | 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 | \(-0.415831\pi\) | ||||
0.261353 | + | 0.965243i | \(0.415831\pi\) | |||||||
\(840\) | 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 | \(0.0875651\pi\) |
0.271637 | + | 0.962400i | \(0.412435\pi\) | |||||||
\(854\) | −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 | \(-0.948893\pi\) |
−0.159867 | − | 0.987139i | \(-0.551107\pi\) | |||||||
\(884\) | 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 | ||||
\(893\) | 8.20612 | + | 11.9609i | 0.274607 | + | 0.400255i | ||||
\(894\) | 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 | \(0.0165084\pi\) | ||||
−0.998655 | + | 0.0518395i | \(0.983492\pi\) | |||||||
\(912\) | 6.67801 | + | 9.73356i | 0.221131 | + | 0.322310i | ||||
\(913\) | 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 | −0.812620 | − | 0.582794i | \(-0.801959\pi\) |
0.582794 | + | 0.812620i | \(0.301959\pi\) | |||||||
\(938\) | 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 | \(-0.919723\pi\) | ||
0.968367 | − | 0.249532i | \(-0.0802767\pi\) | |||||||
\(942\) | 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 | −0.765470 | − | 0.643472i | \(-0.777493\pi\) |
0.643472 | + | 0.765470i | \(0.277493\pi\) | |||||||
\(948\) | 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 | −0.930086 | − | 0.367343i | \(-0.880268\pi\) |
0.367343 | + | 0.930086i | \(0.380268\pi\) | |||||||
\(968\) | 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 | \(-0.952159\pi\) | ||
0.988727 | − | 0.149731i | \(-0.0478407\pi\) | |||||||
\(972\) | 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 | ||||
\(988\) | −21.7154 | + | 14.8985i | −0.690860 | + | 0.473986i | ||||
\(989\) | − | 58.9706i | − | 1.87516i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.0484i | 0.986286i | 0.869948 | + | 0.493143i | \(0.164152\pi\) | ||||
−0.869948 | + | 0.493143i | \(0.835848\pi\) | |||||||
\(992\) | 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 | −0.483167 | − | 0.875528i | \(-0.660514\pi\) |
0.875528 | + | 0.483167i | \(0.160514\pi\) | |||||||
\(998\) | −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.493.7 | ✓ | 32 | |
5.2 | odd | 4 | inner | 950.2.f.d.607.9 | yes | 32 | |
5.3 | odd | 4 | inner | 950.2.f.d.607.8 | yes | 32 | |
5.4 | even | 2 | inner | 950.2.f.d.493.10 | yes | 32 | |
19.18 | odd | 2 | inner | 950.2.f.d.493.9 | yes | 32 | |
95.18 | even | 4 | inner | 950.2.f.d.607.10 | yes | 32 | |
95.37 | even | 4 | inner | 950.2.f.d.607.7 | yes | 32 | |
95.94 | odd | 2 | inner | 950.2.f.d.493.8 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.f.d.493.7 | ✓ | 32 | 1.1 | even | 1 | trivial | |
950.2.f.d.493.8 | yes | 32 | 95.94 | odd | 2 | inner | |
950.2.f.d.493.9 | yes | 32 | 19.18 | odd | 2 | inner | |
950.2.f.d.493.10 | yes | 32 | 5.4 | even | 2 | inner | |
950.2.f.d.607.7 | yes | 32 | 95.37 | even | 4 | inner | |
950.2.f.d.607.8 | yes | 32 | 5.3 | odd | 4 | inner | |
950.2.f.d.607.9 | yes | 32 | 5.2 | odd | 4 | inner | |
950.2.f.d.607.10 | yes | 32 | 95.18 | even | 4 | inner |