Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(122,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.122");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.j (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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 122.6 | ||
Character | \(\chi\) | \(=\) | 429.122 |
Dual form | 429.2.j.a.320.6 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70776 | − | 1.70776i | −1.20757 | − | 1.20757i | −0.971813 | − | 0.235753i | \(-0.924244\pi\) |
−0.235753 | − | 0.971813i | \(-0.575756\pi\) | |||||||
\(3\) | 0.636556 | − | 1.61084i | 0.367516 | − | 0.930017i | ||||
\(4\) | 3.83287i | 1.91643i | ||||||||
\(5\) | 0.490801 | + | 0.490801i | 0.219493 | + | 0.219493i | 0.808285 | − | 0.588792i | \(-0.200396\pi\) |
−0.588792 | + | 0.808285i | \(0.700396\pi\) | |||||||
\(6\) | −3.83800 | + | 1.66383i | −1.56686 | + | 0.679257i | ||||
\(7\) | −0.206749 | − | 0.206749i | −0.0781438 | − | 0.0781438i | 0.666955 | − | 0.745098i | \(-0.267597\pi\) |
−0.745098 | + | 0.666955i | \(0.767597\pi\) | |||||||
\(8\) | 3.13009 | − | 3.13009i | 1.10665 | − | 1.10665i | ||||
\(9\) | −2.18959 | − | 2.05078i | −0.729864 | − | 0.683592i | ||||
\(10\) | − | 1.67634i | − | 0.530104i | ||||||
\(11\) | −0.707107 | + | 0.707107i | −0.213201 | + | 0.213201i | ||||
\(12\) | 6.17412 | + | 2.43984i | 1.78232 | + | 0.704320i | ||||
\(13\) | −3.34311 | − | 1.35040i | −0.927213 | − | 0.374535i | ||||
\(14\) | 0.706154i | 0.188728i | ||||||||
\(15\) | 1.10302 | − | 0.478178i | 0.284799 | − | 0.123465i | ||||
\(16\) | −3.02513 | −0.756281 | ||||||||
\(17\) | −7.70465 | −1.86865 | −0.934326 | − | 0.356419i | \(-0.883998\pi\) | ||||
−0.934326 | + | 0.356419i | \(0.883998\pi\) | |||||||
\(18\) | 0.237061 | + | 7.24152i | 0.0558758 | + | 1.70684i | ||||
\(19\) | −2.28456 | + | 2.28456i | −0.524113 | + | 0.524113i | −0.918811 | − | 0.394698i | \(-0.870849\pi\) |
0.394698 | + | 0.918811i | \(0.370849\pi\) | |||||||
\(20\) | −1.88117 | + | 1.88117i | −0.420643 | + | 0.420643i | ||||
\(21\) | −0.464646 | + | 0.201432i | −0.101394 | + | 0.0439560i | ||||
\(22\) | 2.41513 | 0.514908 | ||||||||
\(23\) | −5.93163 | −1.23683 | −0.618415 | − | 0.785852i | \(-0.712225\pi\) | ||||
−0.618415 | + | 0.785852i | \(0.712225\pi\) | |||||||
\(24\) | −3.04958 | − | 7.03454i | −0.622494 | − | 1.43592i | ||||
\(25\) | − | 4.51823i | − | 0.903646i | ||||||
\(26\) | 3.40306 | + | 8.01539i | 0.667395 | + | 1.57195i | ||||
\(27\) | −4.69727 | + | 2.22164i | −0.903989 | + | 0.427555i | ||||
\(28\) | 0.792441 | − | 0.792441i | 0.149757 | − | 0.149757i | ||||
\(29\) | − | 3.81466i | − | 0.708364i | −0.935176 | − | 0.354182i | \(-0.884759\pi\) | ||
0.935176 | − | 0.354182i | \(-0.115241\pi\) | |||||||
\(30\) | −2.70031 | − | 1.06708i | −0.493006 | − | 0.194822i | ||||
\(31\) | 0.609361 | − | 0.609361i | 0.109444 | − | 0.109444i | −0.650264 | − | 0.759708i | \(-0.725342\pi\) |
0.759708 | + | 0.650264i | \(0.225342\pi\) | |||||||
\(32\) | −1.09400 | − | 1.09400i | −0.193393 | − | 0.193393i | ||||
\(33\) | 0.688920 | + | 1.58915i | 0.119926 | + | 0.276635i | ||||
\(34\) | 13.1577 | + | 13.1577i | 2.25652 | + | 2.25652i | ||||
\(35\) | − | 0.202945i | − | 0.0343040i | ||||||
\(36\) | 7.86035 | − | 8.39241i | 1.31006 | − | 1.39873i | ||||
\(37\) | 2.18188 | + | 2.18188i | 0.358699 | + | 0.358699i | 0.863333 | − | 0.504634i | \(-0.168373\pi\) |
−0.504634 | + | 0.863333i | \(0.668373\pi\) | |||||||
\(38\) | 7.80293 | 1.26580 | ||||||||
\(39\) | −4.30336 | + | 4.52560i | −0.689089 | + | 0.724676i | ||||
\(40\) | 3.07250 | 0.485805 | ||||||||
\(41\) | 5.44677 | + | 5.44677i | 0.850643 | + | 0.850643i | 0.990212 | − | 0.139570i | \(-0.0445719\pi\) |
−0.139570 | + | 0.990212i | \(0.544572\pi\) | |||||||
\(42\) | 1.13750 | + | 0.449507i | 0.175520 | + | 0.0693604i | ||||
\(43\) | − | 5.00836i | − | 0.763768i | −0.924210 | − | 0.381884i | \(-0.875275\pi\) | ||
0.924210 | − | 0.381884i | \(-0.124725\pi\) | |||||||
\(44\) | −2.71025 | − | 2.71025i | −0.408585 | − | 0.408585i | ||||
\(45\) | −0.0681301 | − | 2.08118i | −0.0101562 | − | 0.310244i | ||||
\(46\) | 10.1298 | + | 10.1298i | 1.49355 | + | 1.49355i | ||||
\(47\) | 6.31754 | − | 6.31754i | 0.921508 | − | 0.921508i | −0.0756279 | − | 0.997136i | \(-0.524096\pi\) |
0.997136 | + | 0.0756279i | \(0.0240961\pi\) | |||||||
\(48\) | −1.92566 | + | 4.87298i | −0.277946 | + | 0.703355i | ||||
\(49\) | − | 6.91451i | − | 0.987787i | ||||||
\(50\) | −7.71603 | + | 7.71603i | −1.09121 | + | 1.09121i | ||||
\(51\) | −4.90445 | + | 12.4109i | −0.686760 | + | 1.73788i | ||||
\(52\) | 5.17592 | − | 12.8137i | 0.717771 | − | 1.77694i | ||||
\(53\) | 7.19003i | 0.987627i | 0.869568 | + | 0.493813i | \(0.164397\pi\) | ||||
−0.869568 | + | 0.493813i | \(0.835603\pi\) | |||||||
\(54\) | 11.8158 | + | 4.22777i | 1.60793 | + | 0.575327i | ||||
\(55\) | −0.694098 | −0.0935921 | ||||||||
\(56\) | −1.29429 | −0.172956 | ||||||||
\(57\) | 2.22580 | + | 5.13430i | 0.294814 | + | 0.680054i | ||||
\(58\) | −6.51451 | + | 6.51451i | −0.855397 | + | 0.855397i | ||||
\(59\) | 0.134466 | − | 0.134466i | 0.0175060 | − | 0.0175060i | −0.698300 | − | 0.715806i | \(-0.746060\pi\) |
0.715806 | + | 0.698300i | \(0.246060\pi\) | |||||||
\(60\) | 1.83279 | + | 4.22774i | 0.236612 | + | 0.545799i | ||||
\(61\) | 2.61118 | 0.334327 | 0.167163 | − | 0.985929i | \(-0.446539\pi\) | ||||
0.167163 | + | 0.985929i | \(0.446539\pi\) | |||||||
\(62\) | −2.08128 | −0.264323 | ||||||||
\(63\) | 0.0286997 | + | 0.876692i | 0.00361582 | + | 0.110453i | ||||
\(64\) | 9.78681i | 1.22335i | ||||||||
\(65\) | −0.978024 | − | 2.30358i | −0.121309 | − | 0.285724i | ||||
\(66\) | 1.53737 | − | 3.89038i | 0.189237 | − | 0.478873i | ||||
\(67\) | 2.48830 | − | 2.48830i | 0.303994 | − | 0.303994i | −0.538580 | − | 0.842574i | \(-0.681039\pi\) |
0.842574 | + | 0.538580i | \(0.181039\pi\) | |||||||
\(68\) | − | 29.5309i | − | 3.58115i | ||||||
\(69\) | −3.77582 | + | 9.55488i | −0.454555 | + | 1.15027i | ||||
\(70\) | −0.346581 | + | 0.346581i | −0.0414244 | + | 0.0414244i | ||||
\(71\) | 5.16561 | + | 5.16561i | 0.613045 | + | 0.613045i | 0.943738 | − | 0.330693i | \(-0.107283\pi\) |
−0.330693 | + | 0.943738i | \(0.607283\pi\) | |||||||
\(72\) | −13.2727 | + | 0.434501i | −1.56421 | + | 0.0512064i | ||||
\(73\) | 0.488464 | + | 0.488464i | 0.0571704 | + | 0.0571704i | 0.735114 | − | 0.677944i | \(-0.237129\pi\) |
−0.677944 | + | 0.735114i | \(0.737129\pi\) | |||||||
\(74\) | − | 7.45225i | − | 0.866307i | ||||||
\(75\) | −7.27813 | − | 2.87611i | −0.840406 | − | 0.332104i | ||||
\(76\) | −8.75640 | − | 8.75640i | −1.00443 | − | 1.00443i | ||||
\(77\) | 0.292387 | 0.0333206 | ||||||||
\(78\) | 15.0777 | − | 0.379533i | 1.70722 | − | 0.0429736i | ||||
\(79\) | −4.88091 | −0.549145 | −0.274573 | − | 0.961566i | \(-0.588536\pi\) | ||||
−0.274573 | + | 0.961566i | \(0.588536\pi\) | |||||||
\(80\) | −1.48474 | − | 1.48474i | −0.165998 | − | 0.165998i | ||||
\(81\) | 0.588623 | + | 8.98073i | 0.0654026 | + | 0.997859i | ||||
\(82\) | − | 18.6035i | − | 2.05441i | ||||||
\(83\) | −12.2258 | − | 12.2258i | −1.34195 | − | 1.34195i | −0.894115 | − | 0.447837i | \(-0.852195\pi\) |
−0.447837 | − | 0.894115i | \(-0.647805\pi\) | |||||||
\(84\) | −0.772060 | − | 1.78093i | −0.0842387 | − | 0.194315i | ||||
\(85\) | −3.78145 | − | 3.78145i | −0.410156 | − | 0.410156i | ||||
\(86\) | −8.55306 | + | 8.55306i | −0.922300 | + | 0.922300i | ||||
\(87\) | −6.14479 | − | 2.42824i | −0.658791 | − | 0.260335i | ||||
\(88\) | 4.42661i | 0.471879i | ||||||||
\(89\) | 5.33030 | − | 5.33030i | 0.565010 | − | 0.565010i | −0.365716 | − | 0.930726i | \(-0.619176\pi\) |
0.930726 | + | 0.365716i | \(0.119176\pi\) | |||||||
\(90\) | −3.43780 | + | 3.67049i | −0.362375 | + | 0.386904i | ||||
\(91\) | 0.411991 | + | 0.970380i | 0.0431884 | + | 0.101724i | ||||
\(92\) | − | 22.7351i | − | 2.37030i | ||||||
\(93\) | −0.593688 | − | 1.36947i | −0.0615626 | − | 0.142008i | ||||
\(94\) | −21.5776 | −2.22556 | ||||||||
\(95\) | −2.24253 | −0.230078 | ||||||||
\(96\) | −2.45864 | + | 1.06586i | −0.250934 | + | 0.108784i | ||||
\(97\) | −3.91936 | + | 3.91936i | −0.397951 | + | 0.397951i | −0.877510 | − | 0.479559i | \(-0.840797\pi\) |
0.479559 | + | 0.877510i | \(0.340797\pi\) | |||||||
\(98\) | −11.8083 | + | 11.8083i | −1.19282 | + | 1.19282i | ||||
\(99\) | 2.99839 | − | 0.0981564i | 0.301350 | − | 0.00986509i | ||||
\(100\) | 17.3178 | 1.73178 | ||||||||
\(101\) | 7.48913 | 0.745196 | 0.372598 | − | 0.927993i | \(-0.378467\pi\) | ||||
0.372598 | + | 0.927993i | \(0.378467\pi\) | |||||||
\(102\) | 29.5705 | − | 12.8193i | 2.92791 | − | 1.26930i | ||||
\(103\) | − | 13.1275i | − | 1.29349i | −0.762706 | − | 0.646745i | \(-0.776130\pi\) | ||
0.762706 | − | 0.646745i | \(-0.223870\pi\) | |||||||
\(104\) | −14.6911 | + | 6.23735i | −1.44058 | + | 0.611623i | ||||
\(105\) | −0.326912 | − | 0.129186i | −0.0319033 | − | 0.0126073i | ||||
\(106\) | 12.2788 | − | 12.2788i | 1.19262 | − | 1.19262i | ||||
\(107\) | − | 13.1793i | − | 1.27409i | −0.770828 | − | 0.637043i | \(-0.780157\pi\) | ||
0.770828 | − | 0.637043i | \(-0.219843\pi\) | |||||||
\(108\) | −8.51525 | − | 18.0040i | −0.819380 | − | 1.73243i | ||||
\(109\) | −9.34026 | + | 9.34026i | −0.894634 | + | 0.894634i | −0.994955 | − | 0.100321i | \(-0.968013\pi\) |
0.100321 | + | 0.994955i | \(0.468013\pi\) | |||||||
\(110\) | 1.18535 | + | 1.18535i | 0.113019 | + | 0.113019i | ||||
\(111\) | 4.90355 | − | 2.12577i | 0.465424 | − | 0.201769i | ||||
\(112\) | 0.625442 | + | 0.625442i | 0.0590987 | + | 0.0590987i | ||||
\(113\) | 12.4461i | 1.17083i | 0.810733 | + | 0.585416i | \(0.199069\pi\) | ||||
−0.810733 | + | 0.585416i | \(0.800931\pi\) | |||||||
\(114\) | 4.96701 | − | 12.5693i | 0.465203 | − | 1.17722i | ||||
\(115\) | −2.91125 | − | 2.91125i | −0.271475 | − | 0.271475i | ||||
\(116\) | 14.6211 | 1.35753 | ||||||||
\(117\) | 4.55067 | + | 9.81282i | 0.420710 | + | 0.907195i | ||||
\(118\) | −0.459271 | −0.0422793 | ||||||||
\(119\) | 1.59293 | + | 1.59293i | 0.146024 | + | 0.146024i | ||||
\(120\) | 1.95582 | − | 4.94930i | 0.178541 | − | 0.451807i | ||||
\(121\) | − | 1.00000i | − | 0.0909091i | ||||||
\(122\) | −4.45925 | − | 4.45925i | −0.403722 | − | 0.403722i | ||||
\(123\) | 12.2410 | − | 5.30668i | 1.10374 | − | 0.478487i | ||||
\(124\) | 2.33560 | + | 2.33560i | 0.209743 | + | 0.209743i | ||||
\(125\) | 4.67156 | − | 4.67156i | 0.417837 | − | 0.417837i | ||||
\(126\) | 1.44817 | − | 1.54619i | 0.129013 | − | 0.137745i | ||||
\(127\) | − | 15.3653i | − | 1.36345i | −0.731607 | − | 0.681727i | \(-0.761229\pi\) | ||
0.731607 | − | 0.681727i | \(-0.238771\pi\) | |||||||
\(128\) | 14.5255 | − | 14.5255i | 1.28388 | − | 1.28388i | ||||
\(129\) | −8.06765 | − | 3.18810i | −0.710317 | − | 0.280697i | ||||
\(130\) | −2.26373 | + | 5.60419i | −0.198543 | + | 0.491520i | ||||
\(131\) | 5.15162i | 0.450099i | 0.974347 | + | 0.225050i | \(0.0722544\pi\) | ||||
−0.974347 | + | 0.225050i | \(0.927746\pi\) | |||||||
\(132\) | −6.09099 | + | 2.64054i | −0.530152 | + | 0.229829i | ||||
\(133\) | 0.944660 | 0.0819124 | ||||||||
\(134\) | −8.49881 | −0.734186 | ||||||||
\(135\) | −3.39581 | − | 1.21504i | −0.292265 | − | 0.104574i | ||||
\(136\) | −24.1162 | + | 24.1162i | −2.06795 | + | 2.06795i | ||||
\(137\) | −6.36931 | + | 6.36931i | −0.544167 | + | 0.544167i | −0.924748 | − | 0.380581i | \(-0.875724\pi\) |
0.380581 | + | 0.924748i | \(0.375724\pi\) | |||||||
\(138\) | 22.7656 | − | 9.86924i | 1.93794 | − | 0.840126i | ||||
\(139\) | −3.12234 | −0.264833 | −0.132417 | − | 0.991194i | \(-0.542274\pi\) | ||||
−0.132417 | + | 0.991194i | \(0.542274\pi\) | |||||||
\(140\) | 0.777862 | 0.0657413 | ||||||||
\(141\) | −6.15506 | − | 14.1980i | −0.518349 | − | 1.19569i | ||||
\(142\) | − | 17.6432i | − | 1.48059i | ||||||
\(143\) | 3.31882 | − | 1.40906i | 0.277534 | − | 0.117831i | ||||
\(144\) | 6.62379 | + | 6.20386i | 0.551983 | + | 0.516988i | ||||
\(145\) | 1.87224 | − | 1.87224i | 0.155481 | − | 0.155481i | ||||
\(146\) | − | 1.66835i | − | 0.138074i | ||||||
\(147\) | −11.1381 | − | 4.40148i | −0.918659 | − | 0.363028i | ||||
\(148\) | −8.36286 | + | 8.36286i | −0.687423 | + | 0.687423i | ||||
\(149\) | 1.16939 | + | 1.16939i | 0.0958001 | + | 0.0958001i | 0.753383 | − | 0.657582i | \(-0.228421\pi\) |
−0.657582 | + | 0.753383i | \(0.728421\pi\) | |||||||
\(150\) | 7.51758 | + | 17.3410i | 0.613808 | + | 1.41588i | ||||
\(151\) | −2.50991 | − | 2.50991i | −0.204253 | − | 0.204253i | 0.597566 | − | 0.801819i | \(-0.296134\pi\) |
−0.801819 | + | 0.597566i | \(0.796134\pi\) | |||||||
\(152\) | 14.3017i | 1.16002i | ||||||||
\(153\) | 16.8700 | + | 15.8005i | 1.36386 | + | 1.27740i | ||||
\(154\) | −0.499326 | − | 0.499326i | −0.0402369 | − | 0.0402369i | ||||
\(155\) | 0.598150 | 0.0480445 | ||||||||
\(156\) | −17.3460 | − | 16.4942i | −1.38879 | − | 1.32059i | ||||
\(157\) | −14.5015 | −1.15734 | −0.578672 | − | 0.815560i | \(-0.696429\pi\) | ||||
−0.578672 | + | 0.815560i | \(0.696429\pi\) | |||||||
\(158\) | 8.33541 | + | 8.33541i | 0.663129 | + | 0.663129i | ||||
\(159\) | 11.5820 | + | 4.57686i | 0.918510 | + | 0.362969i | ||||
\(160\) | − | 1.07387i | − | 0.0848969i | ||||||
\(161\) | 1.22636 | + | 1.22636i | 0.0966506 | + | 0.0966506i | ||||
\(162\) | 14.3317 | − | 16.3421i | 1.12600 | − | 1.28396i | ||||
\(163\) | 14.9820 | + | 14.9820i | 1.17348 | + | 1.17348i | 0.981375 | + | 0.192103i | \(0.0615307\pi\) |
0.192103 | + | 0.981375i | \(0.438469\pi\) | |||||||
\(164\) | −20.8767 | + | 20.8767i | −1.63020 | + | 1.63020i | ||||
\(165\) | −0.441832 | + | 1.11808i | −0.0343966 | + | 0.0870423i | ||||
\(166\) | 41.7573i | 3.24099i | ||||||||
\(167\) | −2.44130 | + | 2.44130i | −0.188914 | + | 0.188914i | −0.795226 | − | 0.606313i | \(-0.792648\pi\) |
0.606313 | + | 0.795226i | \(0.292648\pi\) | |||||||
\(168\) | −0.823886 | + | 2.08488i | −0.0635642 | + | 0.160852i | ||||
\(169\) | 9.35282 | + | 9.02911i | 0.719447 | + | 0.694547i | ||||
\(170\) | 12.9156i | 0.990581i | ||||||||
\(171\) | 9.68736 | − | 0.317129i | 0.740811 | − | 0.0242514i | ||||
\(172\) | 19.1964 | 1.46371 | ||||||||
\(173\) | 11.4929 | 0.873787 | 0.436893 | − | 0.899513i | \(-0.356079\pi\) | ||||
0.436893 | + | 0.899513i | \(0.356079\pi\) | |||||||
\(174\) | 6.34696 | + | 14.6407i | 0.481162 | + | 1.10991i | ||||
\(175\) | −0.934140 | + | 0.934140i | −0.0706143 | + | 0.0706143i | ||||
\(176\) | 2.13909 | − | 2.13909i | 0.161240 | − | 0.161240i | ||||
\(177\) | −0.131008 | − | 0.302199i | −0.00984715 | − | 0.0227146i | ||||
\(178\) | −18.2057 | −1.36457 | ||||||||
\(179\) | −24.7845 | −1.85248 | −0.926241 | − | 0.376932i | \(-0.876979\pi\) | ||||
−0.926241 | + | 0.376932i | \(0.876979\pi\) | |||||||
\(180\) | 7.97687 | − | 0.261134i | 0.594561 | − | 0.0194638i | ||||
\(181\) | − | 18.5500i | − | 1.37881i | −0.724377 | − | 0.689404i | \(-0.757873\pi\) | ||
0.724377 | − | 0.689404i | \(-0.242127\pi\) | |||||||
\(182\) | 0.953594 | − | 2.36075i | 0.0706851 | − | 0.174991i | ||||
\(183\) | 1.66216 | − | 4.20618i | 0.122870 | − | 0.310930i | ||||
\(184\) | −18.5665 | + | 18.5665i | −1.36874 | + | 1.36874i | ||||
\(185\) | 2.14174i | 0.157464i | ||||||||
\(186\) | −1.32485 | + | 3.35260i | −0.0971428 | + | 0.245825i | ||||
\(187\) | 5.44801 | − | 5.44801i | 0.398398 | − | 0.398398i | ||||
\(188\) | 24.2143 | + | 24.2143i | 1.76601 | + | 1.76601i | ||||
\(189\) | 1.43048 | + | 0.511834i | 0.104052 | + | 0.0372304i | ||||
\(190\) | 3.82969 | + | 3.82969i | 0.277835 | + | 0.277835i | ||||
\(191\) | − | 12.5407i | − | 0.907413i | −0.891151 | − | 0.453707i | \(-0.850101\pi\) | ||
0.891151 | − | 0.453707i | \(-0.149899\pi\) | |||||||
\(192\) | 15.7650 | + | 6.22986i | 1.13774 | + | 0.449601i | ||||
\(193\) | −10.9222 | − | 10.9222i | −0.786200 | − | 0.786200i | 0.194669 | − | 0.980869i | \(-0.437637\pi\) |
−0.980869 | + | 0.194669i | \(0.937637\pi\) | |||||||
\(194\) | 13.3866 | 0.961103 | ||||||||
\(195\) | −4.33327 | + | 0.109076i | −0.310312 | + | 0.00781108i | ||||
\(196\) | 26.5024 | 1.89303 | ||||||||
\(197\) | 8.01738 | + | 8.01738i | 0.571215 | + | 0.571215i | 0.932468 | − | 0.361253i | \(-0.117651\pi\) |
−0.361253 | + | 0.932468i | \(0.617651\pi\) | |||||||
\(198\) | −5.28815 | − | 4.95290i | −0.375813 | − | 0.351987i | ||||
\(199\) | − | 7.96039i | − | 0.564297i | −0.959371 | − | 0.282149i | \(-0.908953\pi\) | ||
0.959371 | − | 0.282149i | \(-0.0910471\pi\) | |||||||
\(200\) | −14.1425 | − | 14.1425i | −1.00002 | − | 1.00002i | ||||
\(201\) | −2.42430 | − | 5.59218i | −0.170997 | − | 0.394442i | ||||
\(202\) | −12.7896 | − | 12.7896i | −0.899874 | − | 0.899874i | ||||
\(203\) | −0.788677 | + | 0.788677i | −0.0553543 | + | 0.0553543i | ||||
\(204\) | −47.5695 | − | 18.7981i | −3.33053 | − | 1.31613i | ||||
\(205\) | 5.34656i | 0.373420i | ||||||||
\(206\) | −22.4186 | + | 22.4186i | −1.56198 | + | 1.56198i | ||||
\(207\) | 12.9878 | + | 12.1644i | 0.902717 | + | 0.845488i | ||||
\(208\) | 10.1133 | + | 4.08514i | 0.701234 | + | 0.283254i | ||||
\(209\) | − | 3.23085i | − | 0.223483i | ||||||
\(210\) | 0.337667 | + | 0.778904i | 0.0233013 | + | 0.0537495i | ||||
\(211\) | 3.06592 | 0.211067 | 0.105533 | − | 0.994416i | \(-0.466345\pi\) | ||||
0.105533 | + | 0.994416i | \(0.466345\pi\) | |||||||
\(212\) | −27.5584 | −1.89272 | ||||||||
\(213\) | 11.6092 | − | 5.03275i | 0.795446 | − | 0.344839i | ||||
\(214\) | −22.5070 | + | 22.5070i | −1.53854 | + | 1.53854i | ||||
\(215\) | 2.45811 | − | 2.45811i | 0.167642 | − | 0.167642i | ||||
\(216\) | −7.74893 | + | 21.6568i | −0.527248 | + | 1.47356i | ||||
\(217\) | −0.251969 | −0.0171048 | ||||||||
\(218\) | 31.9018 | 2.16066 | ||||||||
\(219\) | 1.09777 | − | 0.475901i | 0.0741804 | − | 0.0321584i | ||||
\(220\) | − | 2.66038i | − | 0.179363i | ||||||
\(221\) | 25.7575 | + | 10.4044i | 1.73264 | + | 0.699875i | ||||
\(222\) | −12.0044 | − | 4.74378i | −0.805680 | − | 0.318382i | ||||
\(223\) | −10.6166 | + | 10.6166i | −0.710937 | + | 0.710937i | −0.966731 | − | 0.255794i | \(-0.917663\pi\) |
0.255794 | + | 0.966731i | \(0.417663\pi\) | |||||||
\(224\) | 0.452366i | 0.0302250i | ||||||||
\(225\) | −9.26588 | + | 9.89308i | −0.617725 | + | 0.659538i | ||||
\(226\) | 21.2550 | − | 21.2550i | 1.41386 | − | 1.41386i | ||||
\(227\) | 14.5721 | + | 14.5721i | 0.967185 | + | 0.967185i | 0.999478 | − | 0.0322931i | \(-0.0102810\pi\) |
−0.0322931 | + | 0.999478i | \(0.510281\pi\) | |||||||
\(228\) | −19.6791 | + | 8.53119i | −1.30328 | + | 0.564992i | ||||
\(229\) | −15.2204 | − | 15.2204i | −1.00579 | − | 1.00579i | −0.999983 | − | 0.00580798i | \(-0.998151\pi\) |
−0.00580798 | − | 0.999983i | \(-0.501849\pi\) | |||||||
\(230\) | 9.94341i | 0.655649i | ||||||||
\(231\) | 0.186121 | − | 0.470988i | 0.0122459 | − | 0.0309888i | ||||
\(232\) | −11.9402 | − | 11.9402i | −0.783913 | − | 0.783913i | ||||
\(233\) | 13.0759 | 0.856632 | 0.428316 | − | 0.903629i | \(-0.359107\pi\) | ||||
0.428316 | + | 0.903629i | \(0.359107\pi\) | |||||||
\(234\) | 8.98646 | − | 24.5293i | 0.587463 | − | 1.60353i | ||||
\(235\) | 6.20131 | 0.404529 | ||||||||
\(236\) | 0.515391 | + | 0.515391i | 0.0335491 | + | 0.0335491i | ||||
\(237\) | −3.10698 | + | 7.86235i | −0.201820 | + | 0.510715i | ||||
\(238\) | − | 5.44067i | − | 0.352666i | ||||||
\(239\) | −12.6577 | − | 12.6577i | −0.818758 | − | 0.818758i | 0.167170 | − | 0.985928i | \(-0.446537\pi\) |
−0.985928 | + | 0.167170i | \(0.946537\pi\) | |||||||
\(240\) | −3.33678 | + | 1.44655i | −0.215388 | + | 0.0933743i | ||||
\(241\) | 11.0145 | + | 11.0145i | 0.709507 | + | 0.709507i | 0.966432 | − | 0.256924i | \(-0.0827091\pi\) |
−0.256924 | + | 0.966432i | \(0.582709\pi\) | |||||||
\(242\) | −1.70776 | + | 1.70776i | −0.109779 | + | 0.109779i | ||||
\(243\) | 14.8412 | + | 4.76857i | 0.952062 | + | 0.305904i | ||||
\(244\) | 10.0083i | 0.640715i | ||||||||
\(245\) | 3.39365 | − | 3.39365i | 0.216812 | − | 0.216812i | ||||
\(246\) | −29.9672 | − | 11.8422i | −1.91064 | − | 0.755030i | ||||
\(247\) | 10.7226 | − | 4.55246i | 0.682263 | − | 0.289666i | ||||
\(248\) | − | 3.81470i | − | 0.242234i | ||||||
\(249\) | −27.4761 | + | 11.9113i | −1.74123 | + | 0.754850i | ||||
\(250\) | −15.9558 | −1.00913 | ||||||||
\(251\) | 1.23189 | 0.0777564 | 0.0388782 | − | 0.999244i | \(-0.487622\pi\) | ||||
0.0388782 | + | 0.999244i | \(0.487622\pi\) | |||||||
\(252\) | −3.36024 | + | 0.110002i | −0.211675 | + | 0.00692948i | ||||
\(253\) | 4.19429 | − | 4.19429i | 0.263693 | − | 0.263693i | ||||
\(254\) | −26.2403 | + | 26.2403i | −1.64646 | + | 1.64646i | ||||
\(255\) | −8.49841 | + | 3.68419i | −0.532191 | + | 0.230713i | ||||
\(256\) | −30.0384 | −1.87740 | ||||||||
\(257\) | −3.07858 | −0.192036 | −0.0960182 | − | 0.995380i | \(-0.530611\pi\) | ||||
−0.0960182 | + | 0.995380i | \(0.530611\pi\) | |||||||
\(258\) | 8.33308 | + | 19.2221i | 0.518795 | + | 1.19672i | ||||
\(259\) | − | 0.902205i | − | 0.0560603i | ||||||
\(260\) | 8.82933 | − | 3.74863i | 0.547572 | − | 0.232480i | ||||
\(261\) | −7.82301 | + | 8.35254i | −0.484232 | + | 0.517009i | ||||
\(262\) | 8.79771 | − | 8.79771i | 0.543524 | − | 0.543524i | ||||
\(263\) | 0.738856i | 0.0455598i | 0.999741 | + | 0.0227799i | \(0.00725170\pi\) | ||||
−0.999741 | + | 0.0227799i | \(0.992748\pi\) | |||||||
\(264\) | 7.13055 | + | 2.81779i | 0.438855 | + | 0.173423i | ||||
\(265\) | −3.52887 | + | 3.52887i | −0.216777 | + | 0.216777i | ||||
\(266\) | −1.61325 | − | 1.61325i | −0.0989146 | − | 0.0989146i | ||||
\(267\) | −5.19320 | − | 11.9793i | −0.317819 | − | 0.733120i | ||||
\(268\) | 9.53731 | + | 9.53731i | 0.582584 | + | 0.582584i | ||||
\(269\) | − | 32.4101i | − | 1.97608i | −0.154210 | − | 0.988038i | \(-0.549283\pi\) | ||
0.154210 | − | 0.988038i | \(-0.450717\pi\) | |||||||
\(270\) | 3.72422 | + | 7.87421i | 0.226649 | + | 0.479209i | ||||
\(271\) | −12.1407 | − | 12.1407i | −0.737497 | − | 0.737497i | 0.234596 | − | 0.972093i | \(-0.424623\pi\) |
−0.972093 | + | 0.234596i | \(0.924623\pi\) | |||||||
\(272\) | 23.3075 | 1.41323 | ||||||||
\(273\) | 1.82538 | − | 0.0459480i | 0.110477 | − | 0.00278090i | ||||
\(274\) | 21.7545 | 1.31423 | ||||||||
\(275\) | 3.19487 | + | 3.19487i | 0.192658 | + | 0.192658i | ||||
\(276\) | −36.6226 | − | 14.4722i | −2.20442 | − | 0.871124i | ||||
\(277\) | 28.1478i | 1.69124i | 0.533786 | + | 0.845620i | \(0.320769\pi\) | ||||
−0.533786 | + | 0.845620i | \(0.679231\pi\) | |||||||
\(278\) | 5.33219 | + | 5.33219i | 0.319803 | + | 0.319803i | ||||
\(279\) | −2.58391 | + | 0.0845879i | −0.154695 | + | 0.00506414i | ||||
\(280\) | −0.635237 | − | 0.635237i | −0.0379627 | − | 0.0379627i | ||||
\(281\) | 13.0914 | − | 13.0914i | 0.780965 | − | 0.780965i | −0.199029 | − | 0.979994i | \(-0.563779\pi\) |
0.979994 | + | 0.199029i | \(0.0637788\pi\) | |||||||
\(282\) | −13.7354 | + | 34.7581i | −0.817931 | + | 2.06981i | ||||
\(283\) | 18.4563i | 1.09711i | 0.836113 | + | 0.548557i | \(0.184823\pi\) | ||||
−0.836113 | + | 0.548557i | \(0.815177\pi\) | |||||||
\(284\) | −19.7991 | + | 19.7991i | −1.17486 | + | 1.17486i | ||||
\(285\) | −1.42749 | + | 3.61234i | −0.0845574 | + | 0.213977i | ||||
\(286\) | −8.07406 | − | 3.26141i | −0.477429 | − | 0.192851i | ||||
\(287\) | − | 2.25223i | − | 0.132945i | ||||||
\(288\) | 0.151862 | + | 4.63895i | 0.00894857 | + | 0.273353i | ||||
\(289\) | 42.3617 | 2.49186 | ||||||||
\(290\) | −6.39465 | −0.375507 | ||||||||
\(291\) | 3.81856 | + | 8.80834i | 0.223848 | + | 0.516354i | ||||
\(292\) | −1.87222 | + | 1.87222i | −0.109563 | + | 0.109563i | ||||
\(293\) | 17.5261 | − | 17.5261i | 1.02389 | − | 1.02389i | 0.0241777 | − | 0.999708i | \(-0.492303\pi\) |
0.999708 | − | 0.0241777i | \(-0.00769675\pi\) | |||||||
\(294\) | 11.5046 | + | 26.5379i | 0.670962 | + | 1.54772i | ||||
\(295\) | 0.131992 | 0.00768489 | ||||||||
\(296\) | 13.6590 | 0.793912 | ||||||||
\(297\) | 1.75053 | − | 4.89241i | 0.101576 | − | 0.283886i | ||||
\(298\) | − | 3.99406i | − | 0.231370i | ||||||
\(299\) | 19.8301 | + | 8.01009i | 1.14680 | + | 0.463236i | ||||
\(300\) | 11.0237 | − | 27.8961i | 0.636456 | − | 1.61058i | ||||
\(301\) | −1.03547 | + | 1.03547i | −0.0596837 | + | 0.0596837i | ||||
\(302\) | 8.57261i | 0.493299i | ||||||||
\(303\) | 4.76725 | − | 12.0638i | 0.273872 | − | 0.693045i | ||||
\(304\) | 6.91107 | − | 6.91107i | 0.396377 | − | 0.396377i | ||||
\(305\) | 1.28157 | + | 1.28157i | 0.0733824 | + | 0.0733824i | ||||
\(306\) | −1.82647 | − | 55.7934i | −0.104412 | − | 3.18949i | ||||
\(307\) | −13.7811 | − | 13.7811i | −0.786529 | − | 0.786529i | 0.194395 | − | 0.980923i | \(-0.437726\pi\) |
−0.980923 | + | 0.194395i | \(0.937726\pi\) | |||||||
\(308\) | 1.12068i | 0.0638567i | ||||||||
\(309\) | −21.1463 | − | 8.35639i | −1.20297 | − | 0.475379i | ||||
\(310\) | −1.02149 | − | 1.02149i | −0.0580170 | − | 0.0580170i | ||||
\(311\) | −12.7746 | −0.724383 | −0.362192 | − | 0.932104i | \(-0.617971\pi\) | ||||
−0.362192 | + | 0.932104i | \(0.617971\pi\) | |||||||
\(312\) | 0.695632 | + | 27.6354i | 0.0393824 | + | 1.56455i | ||||
\(313\) | 5.00198 | 0.282728 | 0.141364 | − | 0.989958i | \(-0.454851\pi\) | ||||
0.141364 | + | 0.989958i | \(0.454851\pi\) | |||||||
\(314\) | 24.7650 | + | 24.7650i | 1.39757 | + | 1.39757i | ||||
\(315\) | −0.416196 | + | 0.444367i | −0.0234500 | + | 0.0250373i | ||||
\(316\) | − | 18.7079i | − | 1.05240i | ||||||
\(317\) | −4.15600 | − | 4.15600i | −0.233424 | − | 0.233424i | 0.580696 | − | 0.814120i | \(-0.302780\pi\) |
−0.814120 | + | 0.580696i | \(0.802780\pi\) | |||||||
\(318\) | −11.9630 | − | 27.5953i | −0.670853 | − | 1.54747i | ||||
\(319\) | 2.69737 | + | 2.69737i | 0.151024 | + | 0.151024i | ||||
\(320\) | −4.80338 | + | 4.80338i | −0.268517 | + | 0.268517i | ||||
\(321\) | −21.2296 | − | 8.38934i | −1.18492 | − | 0.468247i | ||||
\(322\) | − | 4.18864i | − | 0.233424i | ||||||
\(323\) | 17.6017 | − | 17.6017i | 0.979385 | − | 0.979385i | ||||
\(324\) | −34.4219 | + | 2.25611i | −1.91233 | + | 0.125340i | ||||
\(325\) | −6.10144 | + | 15.1050i | −0.338447 | + | 0.837872i | ||||
\(326\) | − | 51.1711i | − | 2.83410i | ||||||
\(327\) | 9.10003 | + | 20.9912i | 0.503233 | + | 1.16082i | ||||
\(328\) | 34.0977 | 1.88273 | ||||||||
\(329\) | −2.61229 | −0.144020 | ||||||||
\(330\) | 2.66395 | − | 1.15486i | 0.146645 | − | 0.0635731i | ||||
\(331\) | 17.3835 | − | 17.3835i | 0.955486 | − | 0.955486i | −0.0435644 | − | 0.999051i | \(-0.513871\pi\) |
0.999051 | + | 0.0435644i | \(0.0138714\pi\) | |||||||
\(332\) | 46.8597 | − | 46.8597i | 2.57176 | − | 2.57176i | ||||
\(333\) | −0.302876 | − | 9.25199i | −0.0165975 | − | 0.507006i | ||||
\(334\) | 8.33830 | 0.456251 | ||||||||
\(335\) | 2.44252 | 0.133449 | ||||||||
\(336\) | 1.40561 | − | 0.609356i | 0.0766825 | − | 0.0332431i | ||||
\(337\) | 16.8962i | 0.920397i | 0.887816 | + | 0.460199i | \(0.152222\pi\) | ||||
−0.887816 | + | 0.460199i | \(0.847778\pi\) | |||||||
\(338\) | −0.552811 | − | 31.3919i | −0.0300690 | − | 1.70749i | ||||
\(339\) | 20.0487 | + | 7.92266i | 1.08889 | + | 0.430300i | ||||
\(340\) | 14.4938 | − | 14.4938i | 0.786036 | − | 0.786036i | ||||
\(341\) | 0.861766i | 0.0466672i | ||||||||
\(342\) | −17.0852 | − | 16.0021i | −0.923864 | − | 0.865293i | ||||
\(343\) | −2.87681 | + | 2.87681i | −0.155333 | + | 0.155333i | ||||
\(344\) | −15.6766 | − | 15.6766i | −0.845226 | − | 0.845226i | ||||
\(345\) | −6.54272 | + | 2.83637i | −0.352248 | + | 0.152705i | ||||
\(346\) | −19.6270 | − | 19.6270i | −1.05516 | − | 1.05516i | ||||
\(347\) | − | 16.2445i | − | 0.872051i | −0.899934 | − | 0.436025i | \(-0.856386\pi\) | ||
0.899934 | − | 0.436025i | \(-0.143614\pi\) | |||||||
\(348\) | 9.30714 | − | 23.5522i | 0.498915 | − | 1.26253i | ||||
\(349\) | 16.4776 | + | 16.4776i | 0.882027 | + | 0.882027i | 0.993740 | − | 0.111713i | \(-0.0356338\pi\) |
−0.111713 | + | 0.993740i | \(0.535634\pi\) | |||||||
\(350\) | 3.19057 | 0.170543 | ||||||||
\(351\) | 18.7036 | − | 1.08398i | 0.998325 | − | 0.0578588i | ||||
\(352\) | 1.54715 | 0.0824631 | ||||||||
\(353\) | −7.48343 | − | 7.48343i | −0.398303 | − | 0.398303i | 0.479331 | − | 0.877634i | \(-0.340879\pi\) |
−0.877634 | + | 0.479331i | \(0.840879\pi\) | |||||||
\(354\) | −0.292352 | + | 0.739811i | −0.0155383 | + | 0.0393205i | ||||
\(355\) | 5.07057i | 0.269118i | ||||||||
\(356\) | 20.4303 | + | 20.4303i | 1.08280 | + | 1.08280i | ||||
\(357\) | 3.57994 | − | 1.55196i | 0.189470 | − | 0.0821384i | ||||
\(358\) | 42.3259 | + | 42.3259i | 2.23699 | + | 2.23699i | ||||
\(359\) | 3.64309 | − | 3.64309i | 0.192275 | − | 0.192275i | −0.604404 | − | 0.796678i | \(-0.706589\pi\) |
0.796678 | + | 0.604404i | \(0.206589\pi\) | |||||||
\(360\) | −6.72752 | − | 6.30102i | −0.354572 | − | 0.332093i | ||||
\(361\) | 8.56161i | 0.450611i | ||||||||
\(362\) | −31.6788 | + | 31.6788i | −1.66500 | + | 1.66500i | ||||
\(363\) | −1.61084 | − | 0.636556i | −0.0845470 | − | 0.0334106i | ||||
\(364\) | −3.71934 | + | 1.57911i | −0.194946 | + | 0.0827676i | ||||
\(365\) | 0.479477i | 0.0250970i | ||||||||
\(366\) | −10.0217 | + | 4.34456i | −0.523842 | + | 0.227094i | ||||
\(367\) | 7.14984 | 0.373219 | 0.186609 | − | 0.982434i | \(-0.440250\pi\) | ||||
0.186609 | + | 0.982434i | \(0.440250\pi\) | |||||||
\(368\) | 17.9439 | 0.935391 | ||||||||
\(369\) | −0.756089 | − | 23.0963i | −0.0393604 | − | 1.20235i | ||||
\(370\) | 3.65757 | − | 3.65757i | 0.190148 | − | 0.190148i | ||||
\(371\) | 1.48653 | − | 1.48653i | 0.0771769 | − | 0.0771769i | ||||
\(372\) | 5.24901 | − | 2.27553i | 0.272148 | − | 0.117981i | ||||
\(373\) | −3.35659 | −0.173798 | −0.0868988 | − | 0.996217i | \(-0.527696\pi\) | ||||
−0.0868988 | + | 0.996217i | \(0.527696\pi\) | |||||||
\(374\) | −18.6078 | −0.962184 | ||||||||
\(375\) | −4.55141 | − | 10.4988i | −0.235034 | − | 0.542157i | ||||
\(376\) | − | 39.5489i | − | 2.03958i | ||||||
\(377\) | −5.15133 | + | 12.7528i | −0.265307 | + | 0.656804i | ||||
\(378\) | −1.56882 | − | 3.31699i | −0.0806914 | − | 0.170608i | ||||
\(379\) | 2.65048 | − | 2.65048i | 0.136146 | − | 0.136146i | −0.635749 | − | 0.771896i | \(-0.719309\pi\) |
0.771896 | + | 0.635749i | \(0.219309\pi\) | |||||||
\(380\) | − | 8.59530i | − | 0.440929i | ||||||
\(381\) | −24.7511 | − | 9.78091i | −1.26804 | − | 0.501091i | ||||
\(382\) | −21.4165 | + | 21.4165i | −1.09576 | + | 1.09576i | ||||
\(383\) | −20.2101 | − | 20.2101i | −1.03269 | − | 1.03269i | −0.999447 | − | 0.0332396i | \(-0.989418\pi\) |
−0.0332396 | − | 0.999447i | \(-0.510582\pi\) | |||||||
\(384\) | −14.1519 | − | 32.6445i | −0.722187 | − | 1.66588i | ||||
\(385\) | 0.143504 | + | 0.143504i | 0.00731364 | + | 0.00731364i | ||||
\(386\) | 37.3051i | 1.89878i | ||||||||
\(387\) | −10.2710 | + | 10.9663i | −0.522106 | + | 0.557447i | ||||
\(388\) | −15.0224 | − | 15.0224i | −0.762646 | − | 0.762646i | ||||
\(389\) | −38.1102 | −1.93226 | −0.966132 | − | 0.258049i | \(-0.916920\pi\) | ||||
−0.966132 | + | 0.258049i | \(0.916920\pi\) | |||||||
\(390\) | 7.58644 | + | 7.21389i | 0.384154 | + | 0.365289i | ||||
\(391\) | 45.7011 | 2.31120 | ||||||||
\(392\) | −21.6430 | − | 21.6430i | −1.09314 | − | 1.09314i | ||||
\(393\) | 8.29842 | + | 3.27930i | 0.418600 | + | 0.165419i | ||||
\(394\) | − | 27.3835i | − | 1.37956i | ||||||
\(395\) | −2.39556 | − | 2.39556i | −0.120534 | − | 0.120534i | ||||
\(396\) | 0.376220 | + | 11.4924i | 0.0189058 | + | 0.577517i | ||||
\(397\) | −24.4808 | − | 24.4808i | −1.22866 | − | 1.22866i | −0.964472 | − | 0.264183i | \(-0.914898\pi\) |
−0.264183 | − | 0.964472i | \(-0.585102\pi\) | |||||||
\(398\) | −13.5944 | + | 13.5944i | −0.681426 | + | 0.681426i | ||||
\(399\) | 0.601329 | − | 1.52169i | 0.0301041 | − | 0.0761799i | ||||
\(400\) | 13.6682i | 0.683411i | ||||||||
\(401\) | −22.1907 | + | 22.1907i | −1.10815 | + | 1.10815i | −0.114756 | + | 0.993394i | \(0.536609\pi\) |
−0.993394 | + | 0.114756i | \(0.963391\pi\) | |||||||
\(402\) | −5.40998 | + | 13.6902i | −0.269825 | + | 0.682805i | ||||
\(403\) | −2.86004 | + | 1.21428i | −0.142469 | + | 0.0604875i | ||||
\(404\) | 28.7048i | 1.42812i | ||||||||
\(405\) | −4.11886 | + | 4.69665i | −0.204668 | + | 0.233378i | ||||
\(406\) | 2.69374 | 0.133688 | ||||||||
\(407\) | −3.08565 | −0.152950 | ||||||||
\(408\) | 23.4960 | + | 54.1987i | 1.16322 | + | 2.68323i | ||||
\(409\) | −25.4319 | + | 25.4319i | −1.25753 | + | 1.25753i | −0.305256 | + | 0.952270i | \(0.598742\pi\) |
−0.952270 | + | 0.305256i | \(0.901258\pi\) | |||||||
\(410\) | 9.13063 | − | 9.13063i | 0.450929 | − | 0.450929i | ||||
\(411\) | 6.20549 | + | 14.3143i | 0.306094 | + | 0.706074i | ||||
\(412\) | 50.3159 | 2.47889 | ||||||||
\(413\) | −0.0556015 | −0.00273597 | ||||||||
\(414\) | −1.40616 | − | 42.9540i | −0.0691088 | − | 2.11107i | ||||
\(415\) | − | 12.0008i | − | 0.589098i | ||||||
\(416\) | 2.18002 | + | 5.13469i | 0.106884 | + | 0.251749i | ||||
\(417\) | −1.98754 | + | 5.02957i | −0.0973304 | + | 0.246299i | ||||
\(418\) | −5.51751 | + | 5.51751i | −0.269870 | + | 0.269870i | ||||
\(419\) | 0.526677i | 0.0257298i | 0.999917 | + | 0.0128649i | \(0.00409514\pi\) | ||||
−0.999917 | + | 0.0128649i | \(0.995905\pi\) | |||||||
\(420\) | 0.495153 | − | 1.25301i | 0.0241610 | − | 0.0611406i | ||||
\(421\) | −15.4532 | + | 15.4532i | −0.753144 | + | 0.753144i | −0.975065 | − | 0.221921i | \(-0.928767\pi\) |
0.221921 | + | 0.975065i | \(0.428767\pi\) | |||||||
\(422\) | −5.23584 | − | 5.23584i | −0.254877 | − | 0.254877i | ||||
\(423\) | −26.7887 | + | 0.876964i | −1.30251 | + | 0.0426395i | ||||
\(424\) | 22.5054 | + | 22.5054i | 1.09296 | + | 1.09296i | ||||
\(425\) | 34.8114i | 1.68860i | ||||||||
\(426\) | −28.4203 | − | 11.2309i | −1.37697 | − | 0.544139i | ||||
\(427\) | −0.539858 | − | 0.539858i | −0.0261256 | − | 0.0261256i | ||||
\(428\) | 50.5143 | 2.44170 | ||||||||
\(429\) | −0.157148 | − | 6.24302i | −0.00758716 | − | 0.301416i | ||||
\(430\) | −8.39570 | −0.404877 | ||||||||
\(431\) | −10.0651 | − | 10.0651i | −0.484817 | − | 0.484817i | 0.421849 | − | 0.906666i | \(-0.361381\pi\) |
−0.906666 | + | 0.421849i | \(0.861381\pi\) | |||||||
\(432\) | 14.2098 | − | 6.72074i | 0.683671 | − | 0.323352i | ||||
\(433\) | 11.4494i | 0.550224i | 0.961412 | + | 0.275112i | \(0.0887150\pi\) | ||||
−0.961412 | + | 0.275112i | \(0.911285\pi\) | |||||||
\(434\) | 0.430302 | + | 0.430302i | 0.0206552 | + | 0.0206552i | ||||
\(435\) | −1.82408 | − | 4.20766i | −0.0874582 | − | 0.201742i | ||||
\(436\) | −35.7999 | − | 35.7999i | −1.71451 | − | 1.71451i | ||||
\(437\) | 13.5511 | − | 13.5511i | 0.648239 | − | 0.648239i | ||||
\(438\) | −2.68745 | − | 1.06200i | −0.128411 | − | 0.0507444i | ||||
\(439\) | 3.61495i | 0.172532i | 0.996272 | + | 0.0862661i | \(0.0274935\pi\) | ||||
−0.996272 | + | 0.0862661i | \(0.972506\pi\) | |||||||
\(440\) | −2.17259 | + | 2.17259i | −0.103574 | + | 0.103574i | ||||
\(441\) | −14.1801 | + | 15.1400i | −0.675244 | + | 0.720950i | ||||
\(442\) | −26.2194 | − | 61.7558i | −1.24713 | − | 2.93742i | ||||
\(443\) | 10.0361i | 0.476830i | 0.971163 | + | 0.238415i | \(0.0766278\pi\) | ||||
−0.971163 | + | 0.238415i | \(0.923372\pi\) | |||||||
\(444\) | 8.14778 | + | 18.7946i | 0.386676 | + | 0.891955i | ||||
\(445\) | 5.23223 | 0.248032 | ||||||||
\(446\) | 36.2610 | 1.71701 | ||||||||
\(447\) | 2.62808 | − | 1.13931i | 0.124304 | − | 0.0538877i | ||||
\(448\) | 2.02341 | − | 2.02341i | 0.0955973 | − | 0.0955973i | ||||
\(449\) | −14.0855 | + | 14.0855i | −0.664737 | + | 0.664737i | −0.956493 | − | 0.291755i | \(-0.905761\pi\) |
0.291755 | + | 0.956493i | \(0.405761\pi\) | |||||||
\(450\) | 32.7188 | − | 1.07109i | 1.54238 | − | 0.0504919i | ||||
\(451\) | −7.70290 | −0.362715 | ||||||||
\(452\) | −47.7043 | −2.24382 | ||||||||
\(453\) | −5.64074 | + | 2.44535i | −0.265025 | + | 0.114893i | ||||
\(454\) | − | 49.7713i | − | 2.33588i | ||||||
\(455\) | −0.274058 | + | 0.678469i | −0.0128480 | + | 0.0318071i | ||||
\(456\) | 23.0377 | + | 9.10385i | 1.07884 | + | 0.426327i | ||||
\(457\) | 5.29636 | − | 5.29636i | 0.247753 | − | 0.247753i | −0.572295 | − | 0.820048i | \(-0.693947\pi\) |
0.820048 | + | 0.572295i | \(0.193947\pi\) | |||||||
\(458\) | 51.9854i | 2.42912i | ||||||||
\(459\) | 36.1908 | − | 17.1170i | 1.68924 | − | 0.798951i | ||||
\(460\) | 11.1584 | − | 11.1584i | 0.520264 | − | 0.520264i | ||||
\(461\) | 18.5585 | + | 18.5585i | 0.864354 | + | 0.864354i | 0.991840 | − | 0.127486i | \(-0.0406908\pi\) |
−0.127486 | + | 0.991840i | \(0.540691\pi\) | |||||||
\(462\) | −1.12218 | + | 0.486484i | −0.0522087 | + | 0.0226333i | ||||
\(463\) | −7.18404 | − | 7.18404i | −0.333871 | − | 0.333871i | 0.520184 | − | 0.854054i | \(-0.325863\pi\) |
−0.854054 | + | 0.520184i | \(0.825863\pi\) | |||||||
\(464\) | 11.5398i | 0.535723i | ||||||||
\(465\) | 0.380756 | − | 0.963522i | 0.0176571 | − | 0.0446822i | ||||
\(466\) | −22.3305 | − | 22.3305i | −1.03444 | − | 1.03444i | ||||
\(467\) | 8.04940 | 0.372482 | 0.186241 | − | 0.982504i | \(-0.440370\pi\) | ||||
0.186241 | + | 0.982504i | \(0.440370\pi\) | |||||||
\(468\) | −37.6112 | + | 17.4421i | −1.73858 | + | 0.806262i | ||||
\(469\) | −1.02891 | −0.0475105 | ||||||||
\(470\) | −10.5903 | − | 10.5903i | −0.488496 | − | 0.488496i | ||||
\(471\) | −9.23102 | + | 23.3595i | −0.425343 | + | 1.07635i | ||||
\(472\) | − | 0.841782i | − | 0.0387462i | ||||||
\(473\) | 3.54145 | + | 3.54145i | 0.162836 | + | 0.162836i | ||||
\(474\) | 18.7329 | − | 8.12103i | 0.860433 | − | 0.373011i | ||||
\(475\) | 10.3221 | + | 10.3221i | 0.473613 | + | 0.473613i | ||||
\(476\) | −6.10548 | + | 6.10548i | −0.279844 | + | 0.279844i | ||||
\(477\) | 14.7452 | − | 15.7432i | 0.675134 | − | 0.720833i | ||||
\(478\) | 43.2325i | 1.97741i | ||||||||
\(479\) | −29.7250 | + | 29.7250i | −1.35817 | + | 1.35817i | −0.481999 | + | 0.876172i | \(0.660089\pi\) |
−0.876172 | + | 0.481999i | \(0.839911\pi\) | |||||||
\(480\) | −1.72983 | − | 0.683579i | −0.0789555 | − | 0.0312010i | ||||
\(481\) | −4.34786 | − | 10.2407i | −0.198245 | − | 0.466936i | ||||
\(482\) | − | 37.6202i | − | 1.71355i | ||||||
\(483\) | 2.75611 | − | 1.19482i | 0.125407 | − | 0.0543661i | ||||
\(484\) | 3.83287 | 0.174221 | ||||||||
\(485\) | −3.84725 | −0.174695 | ||||||||
\(486\) | −17.2016 | − | 33.4887i | −0.780280 | − | 1.51908i | ||||
\(487\) | −6.16106 | + | 6.16106i | −0.279184 | + | 0.279184i | −0.832783 | − | 0.553599i | \(-0.813254\pi\) |
0.553599 | + | 0.832783i | \(0.313254\pi\) | |||||||
\(488\) | 8.17321 | − | 8.17321i | 0.369984 | − | 0.369984i | ||||
\(489\) | 33.6704 | − | 14.5966i | 1.52263 | − | 0.660082i | ||||
\(490\) | −11.5911 | −0.523630 | ||||||||
\(491\) | −24.6292 | −1.11150 | −0.555750 | − | 0.831349i | \(-0.687569\pi\) | ||||
−0.555750 | + | 0.831349i | \(0.687569\pi\) | |||||||
\(492\) | 20.3398 | + | 46.9182i | 0.916989 | + | 2.11524i | ||||
\(493\) | 29.3906i | 1.32369i | ||||||||
\(494\) | −26.0861 | − | 10.5371i | −1.17367 | − | 0.474087i | ||||
\(495\) | 1.51979 | + | 1.42344i | 0.0683095 | + | 0.0639789i | ||||
\(496\) | −1.84339 | + | 1.84339i | −0.0827708 | + | 0.0827708i | ||||
\(497\) | − | 2.13597i | − | 0.0958114i | ||||||
\(498\) | 67.2641 | + | 26.5809i | 3.01418 | + | 1.19112i | ||||
\(499\) | 23.1951 | − | 23.1951i | 1.03835 | − | 1.03835i | 0.0391187 | − | 0.999235i | \(-0.487545\pi\) |
0.999235 | − | 0.0391187i | \(-0.0124551\pi\) | |||||||
\(500\) | 17.9054 | + | 17.9054i | 0.800756 | + | 0.800756i | ||||
\(501\) | 2.37851 | + | 5.48656i | 0.106264 | + | 0.245122i | ||||
\(502\) | −2.10377 | − | 2.10377i | −0.0938960 | − | 0.0938960i | ||||
\(503\) | − | 5.48591i | − | 0.244605i | −0.992493 | − | 0.122302i | \(-0.960972\pi\) | ||
0.992493 | − | 0.122302i | \(-0.0390277\pi\) | |||||||
\(504\) | 2.83396 | + | 2.65429i | 0.126234 | + | 0.118232i | ||||
\(505\) | 3.67567 | + | 3.67567i | 0.163565 | + | 0.163565i | ||||
\(506\) | −14.3257 | −0.636853 | ||||||||
\(507\) | 20.4980 | − | 9.31832i | 0.910349 | − | 0.413841i | ||||
\(508\) | 58.8933 | 2.61297 | ||||||||
\(509\) | −4.06978 | − | 4.06978i | −0.180390 | − | 0.180390i | 0.611136 | − | 0.791526i | \(-0.290713\pi\) |
−0.791526 | + | 0.611136i | \(0.790713\pi\) | |||||||
\(510\) | 20.8049 | + | 8.22151i | 0.921257 | + | 0.364054i | ||||
\(511\) | − | 0.201979i | − | 0.00893502i | ||||||
\(512\) | 22.2473 | + | 22.2473i | 0.983201 | + | 0.983201i | ||||
\(513\) | 5.65571 | − | 15.8066i | 0.249706 | − | 0.697880i | ||||
\(514\) | 5.25746 | + | 5.25746i | 0.231897 | + | 0.231897i | ||||
\(515\) | 6.44299 | − | 6.44299i | 0.283912 | − | 0.283912i | ||||
\(516\) | 12.2196 | − | 30.9222i | 0.537937 | − | 1.36128i | ||||
\(517\) | 8.93435i | 0.392932i | ||||||||
\(518\) | −1.54075 | + | 1.54075i | −0.0676965 | + | 0.0676965i | ||||
\(519\) | 7.31586 | − | 18.5131i | 0.321131 | − | 0.812637i | ||||
\(520\) | −10.2717 | − | 4.14912i | −0.450445 | − | 0.181951i | ||||
\(521\) | 28.4799i | 1.24773i | 0.781534 | + | 0.623863i | \(0.214438\pi\) | ||||
−0.781534 | + | 0.623863i | \(0.785562\pi\) | |||||||
\(522\) | 27.6239 | − | 0.904306i | 1.20907 | − | 0.0395804i | ||||
\(523\) | 36.3221 | 1.58826 | 0.794128 | − | 0.607751i | \(-0.207928\pi\) | ||||
0.794128 | + | 0.607751i | \(0.207928\pi\) | |||||||
\(524\) | −19.7455 | −0.862585 | ||||||||
\(525\) | 0.910114 | + | 2.09938i | 0.0397206 | + | 0.0916244i | ||||
\(526\) | 1.26179 | − | 1.26179i | 0.0550165 | − | 0.0550165i | ||||
\(527\) | −4.69491 | + | 4.69491i | −0.204514 | + | 0.204514i | ||||
\(528\) | −2.08407 | − | 4.80737i | −0.0906975 | − | 0.209214i | ||||
\(529\) | 12.1842 | 0.529748 | ||||||||
\(530\) | 12.0529 | 0.523545 | ||||||||
\(531\) | −0.570187 | + | 0.0186658i | −0.0247440 | + | 0.000810028i | ||||
\(532\) | 3.62075i | 0.156980i | ||||||||
\(533\) | −10.8538 | − | 25.5645i | −0.470132 | − | 1.10732i | ||||
\(534\) | −11.5890 | + | 29.3264i | −0.501503 | + | 1.26908i | ||||
\(535\) | 6.46839 | − | 6.46839i | 0.279653 | − | 0.279653i | ||||
\(536\) | − | 15.5772i | − | 0.672832i | ||||||
\(537\) | −15.7767 | + | 39.9238i | −0.680817 | + | 1.72284i | ||||
\(538\) | −55.3485 | + | 55.3485i | −2.38624 | + | 2.38624i | ||||
\(539\) | 4.88930 | + | 4.88930i | 0.210597 | + | 0.210597i | ||||
\(540\) | 4.65709 | − | 13.0157i | 0.200409 | − | 0.560105i | ||||
\(541\) | 12.3828 | + | 12.3828i | 0.532377 | + | 0.532377i | 0.921279 | − | 0.388902i | \(-0.127146\pi\) |
−0.388902 | + | 0.921279i | \(0.627146\pi\) | |||||||
\(542\) | 41.4668i | 1.78115i | ||||||||
\(543\) | −29.8810 | − | 11.8081i | −1.28231 | − | 0.506734i | ||||
\(544\) | 8.42886 | + | 8.42886i | 0.361385 | + | 0.361385i | ||||
\(545\) | −9.16842 | −0.392732 | ||||||||
\(546\) | −3.19577 | − | 3.03884i | −0.136766 | − | 0.130050i | ||||
\(547\) | 6.37191 | 0.272443 | 0.136222 | − | 0.990678i | \(-0.456504\pi\) | ||||
0.136222 | + | 0.990678i | \(0.456504\pi\) | |||||||
\(548\) | −24.4127 | − | 24.4127i | −1.04286 | − | 1.04286i | ||||
\(549\) | −5.71741 | − | 5.35494i | −0.244013 | − | 0.228543i | ||||
\(550\) | − | 10.9121i | − | 0.465294i | ||||||
\(551\) | 8.71480 | + | 8.71480i | 0.371263 | + | 0.371263i | ||||
\(552\) | 18.0890 | + | 41.7263i | 0.769919 | + | 1.77599i | ||||
\(553\) | 1.00912 | + | 1.00912i | 0.0429123 | + | 0.0429123i | ||||
\(554\) | 48.0697 | − | 48.0697i | 2.04228 | − | 2.04228i | ||||
\(555\) | 3.45000 | + | 1.36334i | 0.146444 | + | 0.0578705i | ||||
\(556\) | − | 11.9675i | − | 0.507535i | ||||||
\(557\) | 12.9428 | − | 12.9428i | 0.548405 | − | 0.548405i | −0.377574 | − | 0.925979i | \(-0.623242\pi\) |
0.925979 | + | 0.377574i | \(0.123242\pi\) | |||||||
\(558\) | 4.55715 | + | 4.26824i | 0.192920 | + | 0.180689i | ||||
\(559\) | −6.76331 | + | 16.7435i | −0.286058 | + | 0.708175i | ||||
\(560\) | 0.613935i | 0.0259435i | ||||||||
\(561\) | −5.30789 | − | 12.2438i | −0.224099 | − | 0.516935i | ||||
\(562\) | −44.7137 | −1.88613 | ||||||||
\(563\) | 20.5332 | 0.865372 | 0.432686 | − | 0.901545i | \(-0.357566\pi\) | ||||
0.432686 | + | 0.901545i | \(0.357566\pi\) | |||||||
\(564\) | 54.4190 | − | 23.5915i | 2.29145 | − | 0.993382i | ||||
\(565\) | −6.10857 | + | 6.10857i | −0.256990 | + | 0.256990i | ||||
\(566\) | 31.5189 | − | 31.5189i | 1.32484 | − | 1.32484i | ||||
\(567\) | 1.73506 | − | 1.97845i | 0.0728657 | − | 0.0830873i | ||||
\(568\) | 32.3376 | 1.35686 | ||||||||
\(569\) | 19.1130 | 0.801257 | 0.400629 | − | 0.916241i | \(-0.368792\pi\) | ||||
0.400629 | + | 0.916241i | \(0.368792\pi\) | |||||||
\(570\) | 8.60681 | − | 3.73119i | 0.360500 | − | 0.156282i | ||||
\(571\) | 45.6854i | 1.91188i | 0.293569 | + | 0.955938i | \(0.405157\pi\) | ||||
−0.293569 | + | 0.955938i | \(0.594843\pi\) | |||||||
\(572\) | 5.40073 | + | 12.7206i | 0.225816 | + | 0.531874i | ||||
\(573\) | −20.2010 | − | 7.98286i | −0.843910 | − | 0.333489i | ||||
\(574\) | −3.84626 | + | 3.84626i | −0.160540 | + | 0.160540i | ||||
\(575\) | 26.8004i | 1.11766i | ||||||||
\(576\) | 20.0706 | − | 21.4291i | 0.836274 | − | 0.892880i | ||||
\(577\) | −25.0351 | + | 25.0351i | −1.04222 | + | 1.04222i | −0.0431553 | + | 0.999068i | \(0.513741\pi\) |
−0.999068 | + | 0.0431553i | \(0.986259\pi\) | |||||||
\(578\) | −72.3434 | − | 72.3434i | −3.00909 | − | 3.00909i | ||||
\(579\) | −24.5466 | + | 10.6413i | −1.02012 | + | 0.442238i | ||||
\(580\) | 7.17604 | + | 7.17604i | 0.297969 | + | 0.297969i | ||||
\(581\) | 5.05533i | 0.209730i | ||||||||
\(582\) | 8.52134 | − | 21.5637i | 0.353221 | − | 0.893843i | ||||
\(583\) | −5.08412 | − | 5.08412i | −0.210563 | − | 0.210563i | ||||
\(584\) | 3.05787 | 0.126536 | ||||||||
\(585\) | −2.58266 | + | 7.04962i | −0.106780 | + | 0.291466i | ||||
\(586\) | −59.8606 | −2.47282 | ||||||||
\(587\) | −27.2706 | − | 27.2706i | −1.12558 | − | 1.12558i | −0.990887 | − | 0.134692i | \(-0.956995\pi\) |
−0.134692 | − | 0.990887i | \(-0.543005\pi\) | |||||||
\(588\) | 16.8703 | − | 42.6910i | 0.695718 | − | 1.76055i | ||||
\(589\) | 2.78424i | 0.114722i | ||||||||
\(590\) | −0.225411 | − | 0.225411i | −0.00928002 | − | 0.00928002i | ||||
\(591\) | 18.0182 | − | 7.81118i | 0.741170 | − | 0.321309i | ||||
\(592\) | −6.60047 | − | 6.60047i | −0.271278 | − | 0.271278i | ||||
\(593\) | 12.9483 | − | 12.9483i | 0.531722 | − | 0.531722i | −0.389363 | − | 0.921084i | \(-0.627305\pi\) |
0.921084 | + | 0.389363i | \(0.127305\pi\) | |||||||
\(594\) | −11.3445 | + | 5.36555i | −0.465471 | + | 0.220151i | ||||
\(595\) | 1.56362i | 0.0641023i | ||||||||
\(596\) | −4.48211 | + | 4.48211i | −0.183594 | + | 0.183594i | ||||
\(597\) | −12.8229 | − | 5.06724i | −0.524806 | − | 0.207388i | ||||
\(598\) | −20.1857 | − | 47.5443i | −0.825454 | − | 1.94423i | ||||
\(599\) | − | 28.2602i | − | 1.15468i | −0.816504 | − | 0.577340i | \(-0.804091\pi\) | ||
0.816504 | − | 0.577340i | \(-0.195909\pi\) | |||||||
\(600\) | −31.7837 | + | 13.7787i | −1.29756 | + | 0.562514i | ||||
\(601\) | −13.5389 | −0.552264 | −0.276132 | − | 0.961120i | \(-0.589053\pi\) | ||||
−0.276132 | + | 0.961120i | \(0.589053\pi\) | |||||||
\(602\) | 3.53668 | 0.144144 | ||||||||
\(603\) | −10.5513 | + | 0.345411i | −0.429682 | + | 0.0140662i | ||||
\(604\) | 9.62013 | − | 9.62013i | 0.391437 | − | 0.391437i | ||||
\(605\) | 0.490801 | − | 0.490801i | 0.0199539 | − | 0.0199539i | ||||
\(606\) | −28.7433 | + | 12.4607i | −1.16762 | + | 0.506180i | ||||
\(607\) | −34.4697 | −1.39908 | −0.699542 | − | 0.714592i | \(-0.746612\pi\) | ||||
−0.699542 | + | 0.714592i | \(0.746612\pi\) | |||||||
\(608\) | 4.99859 | 0.202720 | ||||||||
\(609\) | 0.768392 | + | 1.77247i | 0.0311368 | + | 0.0718240i | ||||
\(610\) | − | 4.37721i | − | 0.177228i | ||||||
\(611\) | −29.6515 | + | 12.5890i | −1.19957 | + | 0.509297i | ||||
\(612\) | −60.5613 | + | 64.6606i | −2.44804 | + | 2.61375i | ||||
\(613\) | 21.9672 | − | 21.9672i | 0.887246 | − | 0.887246i | −0.107011 | − | 0.994258i | \(-0.534128\pi\) |
0.994258 | + | 0.107011i | \(0.0341281\pi\) | |||||||
\(614\) | 47.0695i | 1.89957i | ||||||||
\(615\) | 8.61244 | + | 3.40339i | 0.347287 | + | 0.137238i | ||||
\(616\) | 0.915198 | − | 0.915198i | 0.0368744 | − | 0.0368744i | ||||
\(617\) | 30.7830 | + | 30.7830i | 1.23928 | + | 1.23928i | 0.960297 | + | 0.278979i | \(0.0899960\pi\) |
0.278979 | + | 0.960297i | \(0.410004\pi\) | |||||||
\(618\) | 21.8420 | + | 50.3833i | 0.878613 | + | 2.02672i | ||||
\(619\) | −3.05526 | − | 3.05526i | −0.122801 | − | 0.122801i | 0.643035 | − | 0.765836i | \(-0.277675\pi\) |
−0.765836 | + | 0.643035i | \(0.777675\pi\) | |||||||
\(620\) | 2.29263i | 0.0920741i | ||||||||
\(621\) | 27.8624 | − | 13.1779i | 1.11808 | − | 0.528812i | ||||
\(622\) | 21.8160 | + | 21.8160i | 0.874741 | + | 0.874741i | ||||
\(623\) | −2.20407 | −0.0883041 | ||||||||
\(624\) | 13.0182 | − | 13.6905i | 0.521146 | − | 0.548059i | ||||
\(625\) | −18.0055 | −0.720221 | ||||||||
\(626\) | −8.54216 | − | 8.54216i | −0.341413 | − | 0.341413i | ||||
\(627\) | −5.20437 | − | 2.05662i | −0.207843 | − | 0.0821334i | ||||
\(628\) | − | 55.5822i | − | 2.21797i | ||||||
\(629\) | −16.8106 | − | 16.8106i | −0.670284 | − | 0.670284i | ||||
\(630\) | 1.46963 | − | 0.0481104i | 0.0585516 | − | 0.00191676i | ||||
\(631\) | 17.2385 | + | 17.2385i | 0.686256 | + | 0.686256i | 0.961402 | − | 0.275147i | \(-0.0887264\pi\) |
−0.275147 | + | 0.961402i | \(0.588726\pi\) | |||||||
\(632\) | −15.2777 | + | 15.2777i | −0.607714 | + | 0.607714i | ||||
\(633\) | 1.95163 | − | 4.93870i | 0.0775704 | − | 0.196296i | ||||
\(634\) | 14.1949i | 0.563750i | ||||||||
\(635\) | 7.54133 | − | 7.54133i | 0.299268 | − | 0.299268i | ||||
\(636\) | −17.5425 | + | 44.3921i | −0.695605 | + | 1.76026i | ||||
\(637\) | −9.33738 | + | 23.1160i | −0.369961 | + | 0.915889i | ||||
\(638\) | − | 9.21290i | − | 0.364742i | ||||||
\(639\) | −0.717060 | − | 21.9041i | −0.0283665 | − | 0.866513i | ||||
\(640\) | 14.2583 | 0.563607 | ||||||||
\(641\) | 7.92897 | 0.313175 | 0.156588 | − | 0.987664i | \(-0.449951\pi\) | ||||
0.156588 | + | 0.987664i | \(0.449951\pi\) | |||||||
\(642\) | 21.9281 | + | 50.5820i | 0.865433 | + | 1.99631i | ||||
\(643\) | −17.1643 | + | 17.1643i | −0.676894 | + | 0.676894i | −0.959296 | − | 0.282402i | \(-0.908869\pi\) |
0.282402 | + | 0.959296i | \(0.408869\pi\) | |||||||
\(644\) | −4.70047 | + | 4.70047i | −0.185224 | + | 0.185224i | ||||
\(645\) | −2.39489 | − | 5.52434i | −0.0942986 | − | 0.217521i | ||||
\(646\) | −60.1189 | −2.36535 | ||||||||
\(647\) | 16.6296 | 0.653777 | 0.326889 | − | 0.945063i | \(-0.394000\pi\) | ||||
0.326889 | + | 0.945063i | \(0.394000\pi\) | |||||||
\(648\) | 29.9529 | + | 26.2680i | 1.17666 | + | 1.03191i | ||||
\(649\) | 0.190164i | 0.00746459i | ||||||||
\(650\) | 36.2153 | − | 15.3758i | 1.42048 | − | 0.603089i | ||||
\(651\) | −0.160393 | + | 0.405882i | −0.00628629 | + | 0.0159078i | ||||
\(652\) | −57.4238 | + | 57.4238i | −2.24889 | + | 2.24889i | ||||
\(653\) | 23.9169i | 0.935942i | 0.883744 | + | 0.467971i | \(0.155015\pi\) | ||||
−0.883744 | + | 0.467971i | \(0.844985\pi\) | |||||||
\(654\) | 20.3073 | − | 51.3886i | 0.794077 | − | 2.00945i | ||||
\(655\) | −2.52842 | + | 2.52842i | −0.0987936 | + | 0.0987936i | ||||
\(656\) | −16.4772 | − | 16.4772i | −0.643325 | − | 0.643325i | ||||
\(657\) | −0.0678057 | − | 2.07127i | −0.00264535 | − | 0.0808078i | ||||
\(658\) | 4.46116 | + | 4.46116i | 0.173914 | + | 0.173914i | ||||
\(659\) | − | 46.0117i | − | 1.79236i | −0.443690 | − | 0.896180i | \(-0.646331\pi\) | ||
0.443690 | − | 0.896180i | \(-0.353669\pi\) | |||||||
\(660\) | −4.28544 | − | 1.69348i | −0.166811 | − | 0.0659188i | ||||
\(661\) | −2.99437 | − | 2.99437i | −0.116468 | − | 0.116468i | 0.646471 | − | 0.762939i | \(-0.276244\pi\) |
−0.762939 | + | 0.646471i | \(0.776244\pi\) | |||||||
\(662\) | −59.3737 | −2.30763 | ||||||||
\(663\) | 33.1559 | − | 34.8682i | 1.28767 | − | 1.35417i | ||||
\(664\) | −76.5354 | −2.97015 | ||||||||
\(665\) | 0.463640 | + | 0.463640i | 0.0179792 | + | 0.0179792i | ||||
\(666\) | −15.2829 | + | 16.3174i | −0.592201 | + | 0.632286i | ||||
\(667\) | 22.6271i | 0.876126i | ||||||||
\(668\) | −9.35718 | − | 9.35718i | −0.362040 | − | 0.362040i | ||||
\(669\) | 10.3435 | + | 23.8596i | 0.399903 | + | 0.922465i | ||||
\(670\) | −4.17123 | − | 4.17123i | −0.161149 | − | 0.161149i | ||||
\(671\) | −1.84638 | + | 1.84638i | −0.0712787 | + | 0.0712787i | ||||
\(672\) | 0.728687 | + | 0.287956i | 0.0281097 | + | 0.0111082i | ||||
\(673\) | − | 36.5964i | − | 1.41069i | −0.708865 | − | 0.705344i | \(-0.750792\pi\) | ||
0.708865 | − | 0.705344i | \(-0.249208\pi\) | |||||||
\(674\) | 28.8547 | − | 28.8547i | 1.11144 | − | 1.11144i | ||||
\(675\) | 10.0379 | + | 21.2233i | 0.386358 | + | 0.816886i | ||||
\(676\) | −34.6074 | + | 35.8481i | −1.33105 | + | 1.37877i | ||||
\(677\) | − | 33.1807i | − | 1.27524i | −0.770352 | − | 0.637619i | \(-0.779919\pi\) | ||
0.770352 | − | 0.637619i | \(-0.220081\pi\) | |||||||
\(678\) | −20.7083 | − | 47.7682i | −0.795297 | − | 1.83453i | ||||
\(679\) | 1.62065 | 0.0621947 | ||||||||
\(680\) | −23.6725 | −0.907801 | ||||||||
\(681\) | 32.7493 | − | 14.1973i | 1.25496 | − | 0.544043i | ||||
\(682\) | 1.47169 | − | 1.47169i | 0.0563538 | − | 0.0563538i | ||||
\(683\) | −2.90156 | + | 2.90156i | −0.111025 | + | 0.111025i | −0.760437 | − | 0.649412i | \(-0.775015\pi\) |
0.649412 | + | 0.760437i | \(0.275015\pi\) | |||||||
\(684\) | 1.21551 | + | 37.1304i | 0.0464763 | + | 1.41971i | ||||
\(685\) | −6.25213 | −0.238881 | ||||||||
\(686\) | 9.82579 | 0.375150 | ||||||||
\(687\) | −34.2062 | + | 14.8289i | −1.30505 | + | 0.565759i | ||||
\(688\) | 15.1509i | 0.577624i | ||||||||
\(689\) | 9.70945 | − | 24.0371i | 0.369901 | − | 0.915740i | ||||
\(690\) | 16.0172 | + | 6.32954i | 0.609765 | + | 0.240962i | ||||
\(691\) | 10.6714 | − | 10.6714i | 0.405960 | − | 0.405960i | −0.474367 | − | 0.880327i | \(-0.657323\pi\) |
0.880327 | + | 0.474367i | \(0.157323\pi\) | |||||||
\(692\) | 44.0506i | 1.67455i | ||||||||
\(693\) | −0.640209 | − | 0.599621i | −0.0243195 | − | 0.0227777i | ||||
\(694\) | −27.7417 | + | 27.7417i | −1.05306 | + | 1.05306i | ||||
\(695\) | −1.53245 | − | 1.53245i | −0.0581290 | − | 0.0581290i | ||||
\(696\) | −26.8344 | + | 11.6331i | −1.01715 | + | 0.440952i | ||||
\(697\) | −41.9655 | − | 41.9655i | −1.58956 | − | 1.58956i | ||||
\(698\) | − | 56.2796i | − | 2.13021i | ||||||
\(699\) | 8.32356 | − | 21.0632i | 0.314826 | − | 0.796682i | ||||
\(700\) | −3.58043 | − | 3.58043i | −0.135328 | − | 0.135328i | ||||
\(701\) | 39.1347 | 1.47810 | 0.739049 | − | 0.673651i | \(-0.235275\pi\) | ||||
0.739049 | + | 0.673651i | \(0.235275\pi\) | |||||||
\(702\) | −33.7924 | − | 30.0900i | −1.27541 | − | 1.13568i | ||||
\(703\) | −9.96927 | −0.375998 | ||||||||
\(704\) | −6.92032 | − | 6.92032i | −0.260819 | − | 0.260819i | ||||
\(705\) | 3.94749 | − | 9.98930i | 0.148671 | − | 0.376219i | ||||
\(706\) | 25.5598i | 0.961954i | ||||||||
\(707\) | −1.54837 | − | 1.54837i | −0.0582325 | − | 0.0582325i | ||||
\(708\) | 1.15829 | − | 0.502135i | 0.0435311 | − | 0.0188714i | ||||
\(709\) | 2.37210 | + | 2.37210i | 0.0890862 | + | 0.0890862i | 0.750246 | − | 0.661159i | \(-0.229935\pi\) |
−0.661159 | + | 0.750246i | \(0.729935\pi\) | |||||||
\(710\) | 8.65931 | − | 8.65931i | 0.324978 | − | 0.324978i | ||||
\(711\) | 10.6872 | + | 10.0097i | 0.400801 | + | 0.375392i | ||||
\(712\) | − | 33.3686i | − | 1.25054i | ||||||
\(713\) | −3.61450 | + | 3.61450i | −0.135364 | + | 0.135364i | ||||
\(714\) | −8.76404 | − | 3.46329i | −0.327986 | − | 0.129611i | ||||
\(715\) | 2.32045 | + | 0.937312i | 0.0867798 | + | 0.0350535i | ||||
\(716\) | − | 94.9957i | − | 3.55016i | ||||||
\(717\) | −28.4468 | + | 12.3321i | −1.06237 | + | 0.460552i | ||||
\(718\) | −12.4430 | −0.464369 | ||||||||
\(719\) | 4.95664 | 0.184851 | 0.0924257 | − | 0.995720i | \(-0.470538\pi\) | ||||
0.0924257 | + | 0.995720i | \(0.470538\pi\) | |||||||
\(720\) | 0.206102 | + | 6.29582i | 0.00768098 | + | 0.234632i | ||||
\(721\) | −2.71410 | + | 2.71410i | −0.101078 | + | 0.101078i | ||||
\(722\) | 14.6211 | − | 14.6211i | 0.544142 | − | 0.544142i | ||||
\(723\) | 24.7540 | − | 10.7312i | 0.920609 | − | 0.399099i | ||||
\(724\) | 71.0995 | 2.64239 | ||||||||
\(725\) | −17.2355 | −0.640110 | ||||||||
\(726\) | 1.66383 | + | 3.83800i | 0.0617507 | + | 0.142442i | ||||
\(727\) | − | 25.3584i | − | 0.940491i | −0.882536 | − | 0.470245i | \(-0.844165\pi\) | ||
0.882536 | − | 0.470245i | \(-0.155835\pi\) | |||||||
\(728\) | 4.32694 | + | 1.74781i | 0.160367 | + | 0.0647781i | ||||
\(729\) | 17.1286 | − | 20.8713i | 0.634394 | − | 0.773010i | ||||
\(730\) | 0.818830 | − | 0.818830i | 0.0303063 | − | 0.0303063i | ||||
\(731\) | 38.5877i | 1.42722i | ||||||||
\(732\) | 16.1217 | + | 6.37084i | 0.595876 | + | 0.235473i | ||||
\(733\) | 12.4432 | − | 12.4432i | 0.459599 | − | 0.459599i | −0.438925 | − | 0.898524i | \(-0.644641\pi\) |
0.898524 | + | 0.438925i | \(0.144641\pi\) | |||||||
\(734\) | −12.2102 | − | 12.2102i | −0.450686 | − | 0.450686i | ||||
\(735\) | −3.30637 | − | 7.62686i | −0.121957 | − | 0.281321i | ||||
\(736\) | 6.48918 | + | 6.48918i | 0.239194 | + | 0.239194i | ||||
\(737\) | 3.51898i | 0.129623i | ||||||||
\(738\) | −38.1517 | + | 40.7341i | −1.40438 | + | 1.49944i | ||||
\(739\) | 9.98888 | + | 9.98888i | 0.367447 | + | 0.367447i | 0.866545 | − | 0.499098i | \(-0.166335\pi\) |
−0.499098 | + | 0.866545i | \(0.666335\pi\) | |||||||
\(740\) | −8.20901 | −0.301769 | ||||||||
\(741\) | −0.507721 | − | 20.1703i | −0.0186516 | − | 0.740973i | ||||
\(742\) | −5.07727 | −0.186392 | ||||||||
\(743\) | 23.8013 | + | 23.8013i | 0.873184 | + | 0.873184i | 0.992818 | − | 0.119634i | \(-0.0381720\pi\) |
−0.119634 | + | 0.992818i | \(0.538172\pi\) | |||||||
\(744\) | −6.14487 | − | 2.42827i | −0.225282 | − | 0.0890249i | ||||
\(745\) | 1.14788i | 0.0420549i | ||||||||
\(746\) | 5.73224 | + | 5.73224i | 0.209872 | + | 0.209872i | ||||
\(747\) | 1.69711 | + | 51.8418i | 0.0620940 | + | 1.89679i | ||||
\(748\) | 20.8815 | + | 20.8815i | 0.763503 | + | 0.763503i | ||||
\(749\) | −2.72480 | + | 2.72480i | −0.0995620 | + | 0.0995620i | ||||
\(750\) | −10.1567 | + | 25.7021i | −0.370872 | + | 0.938509i | ||||
\(751\) | − | 44.5125i | − | 1.62428i | −0.583459 | − | 0.812142i | \(-0.698301\pi\) | ||
0.583459 | − | 0.812142i | \(-0.301699\pi\) | |||||||
\(752\) | −19.1114 | + | 19.1114i | −0.696920 | + | 0.696920i | ||||
\(753\) | 0.784169 | − | 1.98438i | 0.0285767 | − | 0.0723148i | ||||
\(754\) | 30.5760 | − | 12.9815i | 1.11351 | − | 0.472759i | ||||
\(755\) | − | 2.46373i | − | 0.0896643i | ||||||
\(756\) | −1.96179 | + | 5.48283i | −0.0713496 | + | 0.199409i | ||||
\(757\) | −7.13372 | −0.259280 | −0.129640 | − | 0.991561i | \(-0.541382\pi\) | ||||
−0.129640 | + | 0.991561i | \(0.541382\pi\) | |||||||
\(758\) | −9.05277 | −0.328811 | ||||||||
\(759\) | −4.08642 | − | 9.42623i | −0.148328 | − | 0.342150i | ||||
\(760\) | −7.01930 | + | 7.01930i | −0.254617 | + | 0.254617i | ||||
\(761\) | −15.8503 | + | 15.8503i | −0.574571 | + | 0.574571i | −0.933403 | − | 0.358831i | \(-0.883175\pi\) |
0.358831 | + | 0.933403i | \(0.383175\pi\) | |||||||
\(762\) | 25.5654 | + | 58.9722i | 0.926136 | + | 2.13634i | ||||
\(763\) | 3.86218 | 0.139820 | ||||||||
\(764\) | 48.0668 | 1.73900 | ||||||||
\(765\) | 0.524919 | + | 16.0347i | 0.0189785 | + | 0.579738i | ||||
\(766\) | 69.0278i | 2.49408i | ||||||||
\(767\) | −0.631120 | + | 0.267952i | −0.0227884 | + | 0.00967519i | ||||
\(768\) | −19.1211 | + | 48.3870i | −0.689975 | + | 1.74602i | ||||
\(769\) | 25.8917 | − | 25.8917i | 0.933680 | − | 0.933680i | −0.0642540 | − | 0.997934i | \(-0.520467\pi\) |
0.997934 | + | 0.0642540i | \(0.0204668\pi\) | |||||||
\(770\) | − | 0.490140i | − | 0.0176634i | ||||||
\(771\) | −1.95969 | + | 4.95909i | −0.0705765 | + | 0.178597i | ||||
\(772\) | 41.8635 | − | 41.8635i | 1.50670 | − | 1.50670i | ||||
\(773\) | 13.5883 | + | 13.5883i | 0.488739 | + | 0.488739i | 0.907908 | − | 0.419169i | \(-0.137679\pi\) |
−0.419169 | + | 0.907908i | \(0.637679\pi\) | |||||||
\(774\) | 36.2681 | − | 1.18729i | 1.30363 | − | 0.0426761i | ||||
\(775\) | −2.75323 | − | 2.75323i | −0.0988989 | − | 0.0988989i | ||||
\(776\) | 24.5359i | 0.880787i | ||||||||
\(777\) | −1.45330 | − | 0.574304i | −0.0521370 | − | 0.0206030i | ||||
\(778\) | 65.0829 | + | 65.0829i | 2.33334 | + | 2.33334i | ||||
\(779\) | −24.8869 | −0.891666 | ||||||||
\(780\) | −0.418073 | − | 16.6088i | −0.0149694 | − | 0.594691i | ||||
\(781\) | −7.30528 | −0.261403 | ||||||||
\(782\) | −78.0464 | − | 78.0464i | −2.79093 | − | 2.79093i | ||||
\(783\) | 8.47479 | + | 17.9185i | 0.302864 | + | 0.640354i | ||||
\(784\) | 20.9173i | 0.747045i | ||||||||
\(785\) | −7.11735 | − | 7.11735i | −0.254029 | − | 0.254029i | ||||
\(786\) | −8.57144 | − | 19.7719i | −0.305733 | − | 0.705241i | ||||
\(787\) | −10.0432 | − | 10.0432i | −0.358003 | − | 0.358003i | 0.505073 | − | 0.863076i | \(-0.331465\pi\) |
−0.863076 | + | 0.505073i | \(0.831465\pi\) | |||||||
\(788\) | −30.7295 | + | 30.7295i | −1.09469 | + | 1.09469i | ||||
\(789\) | 1.19018 | + | 0.470324i | 0.0423714 | + | 0.0167440i | ||||
\(790\) | 8.18205i | 0.291104i | ||||||||
\(791\) | 2.57322 | − | 2.57322i | 0.0914933 | − | 0.0914933i | ||||
\(792\) | 9.07800 | − | 9.69247i | 0.322573 | − | 0.344407i | ||||
\(793\) | −8.72946 | − | 3.52614i | −0.309992 | − | 0.125217i | ||||
\(794\) | 83.6145i | 2.96737i | ||||||||
\(795\) | 3.43811 | + | 7.93077i | 0.121937 | + | 0.281275i | ||||
\(796\) | 30.5111 | 1.08144 | ||||||||
\(797\) | 9.35059 | 0.331215 | 0.165608 | − | 0.986192i | \(-0.447042\pi\) | ||||
0.165608 | + | 0.986192i | \(0.447042\pi\) | |||||||
\(798\) | −3.62560 | + | 1.57176i | −0.128345 | + | 0.0556396i | ||||
\(799\) | −48.6745 | + | 48.6745i | −1.72198 | + | 1.72198i | ||||
\(800\) | −4.94293 | + | 4.94293i | −0.174759 | + | 0.174759i | ||||
\(801\) | −22.6024 | + | 0.739921i | −0.798617 | + | 0.0261438i | ||||
\(802\) | 75.7926 | 2.67633 | ||||||||
\(803\) | −0.690792 | −0.0243775 | ||||||||
\(804\) | 21.4341 | − | 9.29202i | 0.755922 | − | 0.327704i | ||||
\(805\) | 1.20380i | 0.0424282i | ||||||||
\(806\) | 6.95795 | + | 2.81057i | 0.245083 | + | 0.0989980i | ||||
\(807\) | −52.2073 | − | 20.6308i | −1.83778 | − | 0.726240i | ||||
\(808\) | 23.4416 | − | 23.4416i | 0.824674 | − | 0.824674i | ||||
\(809\) | − | 8.55554i | − | 0.300797i | −0.988625 | − | 0.150398i | \(-0.951944\pi\) | ||
0.988625 | − | 0.150398i | \(-0.0480556\pi\) | |||||||
\(810\) | 15.0547 | − | 0.986731i | 0.528970 | − | 0.0346702i | ||||
\(811\) | 28.7824 | − | 28.7824i | 1.01069 | − | 1.01069i | 0.0107441 | − | 0.999942i | \(-0.496580\pi\) |
0.999942 | − | 0.0107441i | \(-0.00342003\pi\) | |||||||
\(812\) | −3.02289 | − | 3.02289i | −0.106083 | − | 0.106083i | ||||
\(813\) | −27.2850 | + | 11.8285i | −0.956927 | + | 0.414843i | ||||
\(814\) | 5.26954 | + | 5.26954i | 0.184697 | + | 0.184697i | ||||
\(815\) | 14.7063i | 0.515140i | ||||||||
\(816\) | 14.8366 | − | 37.5446i | 0.519384 | − | 1.31433i | ||||
\(817\) | 11.4419 | + | 11.4419i | 0.400301 | + | 0.400301i | ||||
\(818\) | 86.8630 | 3.03709 | ||||||||
\(819\) | 1.08794 | − | 2.96964i | 0.0380158 | − | 0.103768i | ||||
\(820\) | −20.4927 | −0.715634 | ||||||||
\(821\) | 28.8221 | + | 28.8221i | 1.00590 | + | 1.00590i | 0.999982 | + | 0.00591632i | \(0.00188323\pi\) |
0.00591632 | + | 0.999982i | \(0.498117\pi\) | |||||||
\(822\) | 13.8479 | − | 35.0429i | 0.483002 | − | 1.22226i | ||||
\(823\) | − | 35.9860i | − | 1.25439i | −0.778861 | − | 0.627197i | \(-0.784202\pi\) | ||
0.778861 | − | 0.627197i | \(-0.215798\pi\) | |||||||
\(824\) | −41.0902 | − | 41.0902i | −1.43145 | − | 1.43145i | ||||
\(825\) | 7.18013 | − | 3.11270i | 0.249980 | − | 0.108370i | ||||
\(826\) | 0.0949539 | + | 0.0949539i | 0.00330387 | + | 0.00330387i | ||||
\(827\) | 21.6443 | − | 21.6443i | 0.752647 | − | 0.752647i | −0.222326 | − | 0.974972i | \(-0.571365\pi\) |
0.974972 | + | 0.222326i | \(0.0713648\pi\) | |||||||
\(828\) | −46.6247 | + | 49.7806i | −1.62032 | + | 1.73000i | ||||
\(829\) | − | 16.5762i | − | 0.575714i | −0.957673 | − | 0.287857i | \(-0.907057\pi\) | ||
0.957673 | − | 0.287857i | \(-0.0929428\pi\) | |||||||
\(830\) | −20.4945 | + | 20.4945i | −0.711375 | + | 0.711375i | ||||
\(831\) | 45.3416 | + | 17.9177i | 1.57288 | + | 0.621558i | ||||
\(832\) | 13.2162 | − | 32.7184i | 0.458188 | − | 1.13431i | ||||
\(833\) | 53.2739i | 1.84583i | ||||||||
\(834\) | 11.9835 | − | 5.19505i | 0.414956 | − | 0.179890i | ||||
\(835\) | −2.39639 | −0.0829304 | ||||||||
\(836\) | 12.3834 | 0.428289 | ||||||||
\(837\) | −1.50855 | + | 4.21611i | −0.0521431 | + | 0.145730i | ||||
\(838\) | 0.899436 | − | 0.899436i | 0.0310705 | − | 0.0310705i | ||||
\(839\) | 19.9818 | − | 19.9818i | 0.689847 | − | 0.689847i | −0.272351 | − | 0.962198i | \(-0.587801\pi\) |
0.962198 | + | 0.272351i | \(0.0878012\pi\) | |||||||
\(840\) | −1.42763 | + | 0.618899i | −0.0492578 | + | 0.0213540i | ||||
\(841\) | 14.4484 | 0.498220 | ||||||||
\(842\) | 52.7807 | 1.81894 | ||||||||
\(843\) | −12.7546 | − | 29.4214i | −0.439293 | − | 1.01333i | ||||
\(844\) | 11.7513i | 0.404495i | ||||||||
\(845\) | 0.158875 | + | 9.02187i | 0.00546548 | + | 0.310362i | ||||
\(846\) | 47.2462 | + | 44.2510i | 1.62436 | + | 1.52138i | ||||
\(847\) | −0.206749 | + | 0.206749i | −0.00710398 | + | 0.00710398i | ||||
\(848\) | − | 21.7507i | − | 0.746924i | ||||||
\(849\) | 29.7301 | + | 11.7485i | 1.02034 | + | 0.403207i | ||||
\(850\) | 59.4494 | − | 59.4494i | 2.03910 | − | 2.03910i | ||||
\(851\) | −12.9421 | − | 12.9421i | −0.443650 | − | 0.443650i | ||||
\(852\) | 19.2899 | + | 44.4963i | 0.660860 | + | 1.52442i | ||||
\(853\) | −1.18725 | − | 1.18725i | −0.0406508 | − | 0.0406508i | 0.686489 | − | 0.727140i | \(-0.259151\pi\) |
−0.727140 | + | 0.686489i | \(0.759151\pi\) | |||||||
\(854\) | 1.84389i | 0.0630967i | ||||||||
\(855\) | 4.91021 | + | 4.59892i | 0.167926 | + | 0.157280i | ||||
\(856\) | −41.2522 | − | 41.2522i | −1.40997 | − | 1.40997i | ||||
\(857\) | −43.2926 | −1.47885 | −0.739424 | − | 0.673240i | \(-0.764902\pi\) | ||||
−0.739424 | + | 0.673240i | \(0.764902\pi\) | |||||||
\(858\) | −10.3932 | + | 10.9299i | −0.354818 | + | 0.373142i | ||||
\(859\) | 25.3908 | 0.866322 | 0.433161 | − | 0.901317i | \(-0.357398\pi\) | ||||
0.433161 | + | 0.901317i | \(0.357398\pi\) | |||||||
\(860\) | 9.42160 | + | 9.42160i | 0.321274 | + | 0.321274i | ||||
\(861\) | −3.62797 | − | 1.43367i | −0.123641 | − | 0.0488594i | ||||
\(862\) | 34.3774i | 1.17090i | ||||||||
\(863\) | −24.3693 | − | 24.3693i | −0.829539 | − | 0.829539i | 0.157914 | − | 0.987453i | \(-0.449523\pi\) |
−0.987453 | + | 0.157914i | \(0.949523\pi\) | |||||||
\(864\) | 7.56926 | + | 2.70833i | 0.257512 | + | 0.0921392i | ||||
\(865\) | 5.64071 | + | 5.64071i | 0.191790 | + | 0.191790i | ||||
\(866\) | 19.5528 | − | 19.5528i | 0.664432 | − | 0.664432i | ||||
\(867\) | 26.9656 | − | 68.2377i | 0.915799 | − | 2.31747i | ||||
\(868\) | − | 0.965765i | − | 0.0327802i | ||||||
\(869\) | 3.45133 | − | 3.45133i | 0.117078 | − | 0.117078i | ||||
\(870\) | −4.07056 | + | 10.3007i | −0.138005 | + | 0.349228i | ||||
\(871\) | −11.6789 | + | 4.95845i | −0.395723 | + | 0.168011i | ||||
\(872\) | 58.4717i | 1.98010i | ||||||||
\(873\) | 16.6195 | − | 0.544063i | 0.562486 | − | 0.0184137i | ||||
\(874\) | −46.2841 | −1.56558 | ||||||||
\(875\) | −1.93168 | −0.0653027 | ||||||||
\(876\) | 1.82406 | + | 4.20761i | 0.0616294 | + | 0.142162i | ||||
\(877\) | −15.7593 | + | 15.7593i | −0.532155 | + | 0.532155i | −0.921213 | − | 0.389058i | \(-0.872801\pi\) |
0.389058 | + | 0.921213i | \(0.372801\pi\) | |||||||
\(878\) | 6.17346 | − | 6.17346i | 0.208344 | − | 0.208344i | ||||
\(879\) | −17.0753 | − | 39.3880i | −0.575937 | − | 1.32853i | ||||
\(880\) | 2.09973 | 0.0707820 | ||||||||
\(881\) | 14.4374 | 0.486409 | 0.243205 | − | 0.969975i | \(-0.421801\pi\) | ||||
0.243205 | + | 0.969975i | \(0.421801\pi\) | |||||||
\(882\) | 50.0715 | − | 1.63916i | 1.68600 | − | 0.0551934i | ||||
\(883\) | 25.0665i | 0.843555i | 0.906699 | + | 0.421778i | \(0.138594\pi\) | ||||
−0.906699 | + | 0.421778i | \(0.861406\pi\) | |||||||
\(884\) | −39.8786 | + | 98.7251i | −1.34126 | + | 3.32049i | ||||
\(885\) | 0.0840206 | − | 0.212618i | 0.00282432 | − | 0.00714708i | ||||
\(886\) | 17.1392 | − | 17.1392i | 0.575804 | − | 0.575804i | ||||
\(887\) | 36.6379i | 1.23018i | 0.788457 | + | 0.615091i | \(0.210881\pi\) | ||||
−0.788457 | + | 0.615091i | \(0.789119\pi\) | |||||||
\(888\) | 8.69471 | − | 22.0024i | 0.291775 | − | 0.738351i | ||||
\(889\) | −3.17677 | + | 3.17677i | −0.106545 | + | 0.106545i | ||||
\(890\) | −8.93538 | − | 8.93538i | −0.299514 | − | 0.299514i | ||||
\(891\) | −6.76656 | − | 5.93412i | −0.226688 | − | 0.198800i | ||||
\(892\) | −40.6918 | − | 40.6918i | −1.36246 | − | 1.36246i | ||||
\(893\) | 28.8656i | 0.965949i | ||||||||
\(894\) | −6.43379 | − | 2.54245i | −0.215178 | − | 0.0850322i | ||||
\(895\) | −12.1643 | − | 12.1643i | −0.406607 | − | 0.406607i | ||||
\(896\) | −6.00627 | −0.200655 | ||||||||
\(897\) | 25.5259 | − | 26.8442i | 0.852286 | − | 0.896301i | ||||
\(898\) | 48.1093 | 1.60543 | ||||||||
\(899\) | −2.32450 | − | 2.32450i | −0.0775265 | − | 0.0775265i | ||||
\(900\) | −37.9188 | − | 35.5149i | −1.26396 | − | 1.18383i | ||||
\(901\) | − | 55.3967i | − | 1.84553i | ||||||
\(902\) | 13.1547 | + | 13.1547i | 0.438003 | + | 0.438003i | ||||
\(903\) | 1.00884 | + | 2.32712i | 0.0335722 | + | 0.0774416i | ||||
\(904\) | 38.9575 | + | 38.9575i | 1.29571 | + | 1.29571i | ||||
\(905\) | 9.10434 | − | 9.10434i | 0.302638 | − | 0.302638i | ||||
\(906\) | 13.8091 | + | 5.45695i | 0.458776 | + | 0.181295i | ||||
\(907\) | 3.87488i | 0.128663i | 0.997929 | + | 0.0643317i | \(0.0204916\pi\) | ||||
−0.997929 | + | 0.0643317i | \(0.979508\pi\) | |||||||
\(908\) | −55.8530 | + | 55.8530i | −1.85355 | + | 1.85355i | ||||
\(909\) | −16.3981 | − | 15.3585i | −0.543892 | − | 0.509411i | ||||
\(910\) | 1.62669 | − | 0.690636i | 0.0539241 | − | 0.0228943i | ||||
\(911\) | − | 1.41239i | − | 0.0467945i | −0.999726 | − | 0.0233973i | \(-0.992552\pi\) | ||
0.999726 | − | 0.0233973i | \(-0.00744826\pi\) | |||||||
\(912\) | −6.73332 | − | 15.5319i | −0.222963 | − | 0.514312i | ||||
\(913\) | 17.2898 | 0.572210 | ||||||||
\(914\) | −18.0898 | −0.598357 | ||||||||
\(915\) | 2.88019 | − | 1.24861i | 0.0952161 | − | 0.0412777i | ||||
\(916\) | 58.3377 | − | 58.3377i | 1.92753 | − | 1.92753i | ||||
\(917\) | 1.06509 | − | 1.06509i | 0.0351725 | − | 0.0351725i | ||||
\(918\) | −91.0367 | − | 32.5735i | −3.00466 | − | 1.07509i | ||||
\(919\) | −58.2892 | −1.92278 | −0.961391 | − | 0.275186i | \(-0.911261\pi\) | ||||
−0.961391 | + | 0.275186i | \(0.911261\pi\) | |||||||
\(920\) | −18.2249 | −0.600858 | ||||||||
\(921\) | −30.9716 | + | 13.4267i | −1.02055 | + | 0.442423i | ||||
\(922\) | − | 63.3867i | − | 2.08753i | ||||||
\(923\) | −10.2936 | − | 24.2449i | −0.338817 | − | 0.798030i | ||||
\(924\) | 1.80523 | + | 0.713377i | 0.0593879 | + | 0.0234684i | ||||
\(925\) | 9.85825 | − | 9.85825i | 0.324137 | − | 0.324137i | ||||
\(926\) | 24.5372i | 0.806342i | ||||||||
\(927\) | −26.9216 | + | 28.7439i | −0.884220 | + | 0.944072i | ||||
\(928\) | −4.17322 | + | 4.17322i | −0.136993 | + | 0.136993i | ||||
\(929\) | −22.0972 | − | 22.0972i | −0.724986 | − | 0.724986i | 0.244630 | − | 0.969616i | \(-0.421333\pi\) |
−0.969616 | + | 0.244630i | \(0.921333\pi\) | |||||||
\(930\) | −2.29570 | + | 0.995222i | −0.0752789 | + | 0.0326346i | ||||
\(931\) | 15.7966 | + | 15.7966i | 0.517712 | + | 0.517712i | ||||
\(932\) | 50.1182i | 1.64168i | ||||||||
\(933\) | −8.13178 | + | 20.5779i | −0.266223 | + | 0.673689i | ||||
\(934\) | −13.7464 | − | 13.7464i | −0.449796 | − | 0.449796i | ||||
\(935\) | 5.34778 | 0.174891 | ||||||||
\(936\) | 44.9590 | + | 16.4710i | 1.46953 | + | 0.538370i | ||||
\(937\) | −19.6838 | −0.643042 | −0.321521 | − | 0.946902i | \(-0.604194\pi\) | ||||
−0.321521 | + | 0.946902i | \(0.604194\pi\) | |||||||
\(938\) | 1.75712 | + | 1.75712i | 0.0573721 | + | 0.0573721i | ||||
\(939\) | 3.18404 | − | 8.05737i | 0.103907 | − | 0.262942i | ||||
\(940\) | 23.7688i | 0.775253i | ||||||||
\(941\) | −15.1802 | − | 15.1802i | −0.494860 | − | 0.494860i | 0.414974 | − | 0.909833i | \(-0.363791\pi\) |
−0.909833 | + | 0.414974i | \(0.863791\pi\) | |||||||
\(942\) | 55.6567 | − | 24.1281i | 1.81339 | − | 0.786135i | ||||
\(943\) | −32.3082 | − | 32.3082i | −1.05210 | − | 1.05210i | ||||
\(944\) | −0.406777 | + | 0.406777i | −0.0132395 | + | 0.0132395i | ||||
\(945\) | 0.450871 | + | 0.953288i | 0.0146668 | + | 0.0310105i | ||||
\(946\) | − | 12.0959i | − | 0.393270i | ||||||
\(947\) | 37.5296 | − | 37.5296i | 1.21955 | − | 1.21955i | 0.251759 | − | 0.967790i | \(-0.418991\pi\) |
0.967790 | − | 0.251759i | \(-0.0810092\pi\) | |||||||
\(948\) | −30.1353 | − | 11.9086i | −0.978750 | − | 0.386774i | ||||
\(949\) | −0.973366 | − | 2.29261i | −0.0315968 | − | 0.0744214i | ||||
\(950\) | − | 35.2554i | − | 1.14384i | ||||||
\(951\) | −9.34016 | + | 4.04911i | −0.302875 | + | 0.131301i | ||||
\(952\) | 9.97202 | 0.323195 | ||||||||
\(953\) | −32.6456 | −1.05749 | −0.528747 | − | 0.848780i | \(-0.677338\pi\) | ||||
−0.528747 | + | 0.848780i | \(0.677338\pi\) | |||||||
\(954\) | −52.0667 | + | 1.70447i | −1.68572 | + | 0.0551844i | ||||
\(955\) | 6.15499 | − | 6.15499i | 0.199171 | − | 0.199171i | ||||
\(956\) | 48.5152 | − | 48.5152i | 1.56910 | − | 1.56910i | ||||
\(957\) | 6.06205 | − | 2.62800i | 0.195958 | − | 0.0849510i | ||||
\(958\) | 101.526 | 3.28016 | ||||||||
\(959\) | 2.63370 | 0.0850465 | ||||||||
\(960\) | 4.67984 | + | 10.7951i | 0.151041 | + | 0.348410i | ||||
\(961\) | 30.2574i | 0.976044i | ||||||||
\(962\) | −10.0636 | + | 24.9137i | −0.324462 | + | 0.803251i | ||||
\(963\) | −27.0277 | + | 28.8572i | −0.870956 | + | 0.929910i | ||||
\(964\) | −42.2172 | + | 42.2172i | −1.35972 | + | 1.35972i | ||||
\(965\) | − | 10.7213i | − | 0.345131i | ||||||
\(966\) | −6.74722 | − | 2.66631i | −0.217088 | − | 0.0857870i | ||||
\(967\) | 2.99860 | − | 2.99860i | 0.0964286 | − | 0.0964286i | −0.657247 | − | 0.753675i | \(-0.728279\pi\) |
0.753675 | + | 0.657247i | \(0.228279\pi\) | |||||||
\(968\) | −3.13009 | − | 3.13009i | −0.100605 | − | 0.100605i | ||||
\(969\) | −17.1490 | − | 39.5580i | −0.550905 | − | 1.27078i | ||||
\(970\) | 6.57017 | + | 6.57017i | 0.210955 | + | 0.210955i | ||||
\(971\) | 11.5308i | 0.370042i | 0.982735 | + | 0.185021i | \(0.0592353\pi\) | ||||
−0.982735 | + | 0.185021i | \(0.940765\pi\) | |||||||
\(972\) | −18.2773 | + | 56.8843i | −0.586244 | + | 1.82456i | ||||
\(973\) | 0.645540 | + | 0.645540i | 0.0206951 | + | 0.0206951i | ||||
\(974\) | 21.0432 | 0.674267 | ||||||||
\(975\) | 20.4477 | + | 19.4436i | 0.654851 | + | 0.622693i | ||||
\(976\) | −7.89914 | −0.252845 | ||||||||
\(977\) | −0.512393 | − | 0.512393i | −0.0163929 | − | 0.0163929i | 0.698863 | − | 0.715256i | \(-0.253690\pi\) |
−0.715256 | + | 0.698863i | \(0.753690\pi\) | |||||||
\(978\) | −82.4283 | − | 32.5733i | −2.63577 | − | 1.04158i | ||||
\(979\) | 7.53818i | 0.240921i | ||||||||
\(980\) | 13.0074 | + | 13.0074i | 0.415506 | + | 0.415506i | ||||
\(981\) | 39.6061 | − | 1.29656i | 1.26453 | − | 0.0413960i | ||||
\(982\) | 42.0607 | + | 42.0607i | 1.34221 | + | 1.34221i | ||||
\(983\) | −29.5660 | + | 29.5660i | −0.943009 | + | 0.943009i | −0.998461 | − | 0.0554528i | \(-0.982340\pi\) |
0.0554528 | + | 0.998461i | \(0.482340\pi\) | |||||||
\(984\) | 21.7051 | − | 54.9259i | 0.691935 | − | 1.75097i | ||||
\(985\) | 7.86988i | 0.250755i | ||||||||
\(986\) | 50.1920 | − | 50.1920i | 1.59844 | − | 1.59844i | ||||
\(987\) | −1.66287 | + | 4.20798i | −0.0529298 | + | 0.133941i | ||||
\(988\) | 17.4490 | + | 41.0983i | 0.555125 | + | 1.30751i | ||||
\(989\) | 29.7077i | 0.944651i | ||||||||
\(990\) | −0.164543 | − | 5.02632i | −0.00522953 | − | 0.159747i | ||||
\(991\) | 19.5779 | 0.621913 | 0.310956 | − | 0.950424i | \(-0.399351\pi\) | ||||
0.310956 | + | 0.950424i | \(0.399351\pi\) | |||||||
\(992\) | −1.33328 | −0.0423316 | ||||||||
\(993\) | −16.9365 | − | 39.0677i | −0.537462 | − | 1.23978i | ||||
\(994\) | −3.64772 | + | 3.64772i | −0.115699 | + | 0.115699i | ||||
\(995\) | 3.90697 | − | 3.90697i | 0.123859 | − | 0.123859i | ||||
\(996\) | −45.6545 | − | 105.312i | −1.44662 | − | 3.33695i | ||||
\(997\) | 44.3850 | 1.40569 | 0.702843 | − | 0.711345i | \(-0.251914\pi\) | ||||
0.702843 | + | 0.711345i | \(0.251914\pi\) | |||||||
\(998\) | −79.2230 | −2.50776 | ||||||||
\(999\) | −15.0962 | − | 5.40153i | −0.477624 | − | 0.170897i |
(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 | 429.2.j.a.122.6 | ✓ | 96 | |
3.2 | odd | 2 | inner | 429.2.j.a.122.43 | yes | 96 | |
13.8 | odd | 4 | inner | 429.2.j.a.320.43 | yes | 96 | |
39.8 | even | 4 | inner | 429.2.j.a.320.6 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.j.a.122.6 | ✓ | 96 | 1.1 | even | 1 | trivial | |
429.2.j.a.122.43 | yes | 96 | 3.2 | odd | 2 | inner | |
429.2.j.a.320.6 | yes | 96 | 39.8 | even | 4 | inner | |
429.2.j.a.320.43 | yes | 96 | 13.8 | odd | 4 | inner |