Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.446265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 4x^{6} - 7x^{5} + 19x^{4} + 21x^{3} + 36x^{2} + 27x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 729.2 | ||
Root | \(-0.711597 + 2.19007i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.729 |
Dual form | 847.2.f.r.323.2 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.86298 | − | 1.35354i | 1.31733 | − | 0.957096i | 0.317368 | − | 0.948303i | \(-0.397201\pi\) |
0.999961 | − | 0.00879304i | \(-0.00279895\pi\) | |||||||
\(3\) | −0.711597 | − | 2.19007i | −0.410841 | − | 1.26444i | −0.915919 | − | 0.401364i | \(-0.868536\pi\) |
0.505078 | − | 0.863074i | \(-0.331464\pi\) | |||||||
\(4\) | 1.02061 | − | 3.14113i | 0.510307 | − | 1.57056i | ||||
\(5\) | −2.91695 | − | 2.11929i | −1.30450 | − | 0.947775i | −0.304512 | − | 0.952509i | \(-0.598493\pi\) |
−0.999989 | + | 0.00473329i | \(0.998493\pi\) | |||||||
\(6\) | −4.29004 | − | 3.11689i | −1.75140 | − | 1.27247i | ||||
\(7\) | 0.309017 | − | 0.951057i | 0.116797 | − | 0.359466i | ||||
\(8\) | −0.927051 | − | 2.85317i | −0.327762 | − | 1.00875i | ||||
\(9\) | −1.86298 | + | 1.35354i | −0.620995 | + | 0.451179i | ||||
\(10\) | −8.30278 | −2.62557 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −7.60555 | −2.19553 | ||||||||
\(13\) | 5.34400 | − | 3.88265i | 1.48216 | − | 1.07685i | 0.505307 | − | 0.862940i | \(-0.331379\pi\) |
0.976853 | − | 0.213912i | \(-0.0686207\pi\) | |||||||
\(14\) | −0.711597 | − | 2.19007i | −0.190182 | − | 0.585321i | ||||
\(15\) | −2.56570 | + | 7.89641i | −0.662461 | + | 2.03884i | ||||
\(16\) | −0.244951 | − | 0.177967i | −0.0612377 | − | 0.0444918i | ||||
\(17\) | 2.18210 | + | 1.58539i | 0.529237 | + | 0.384513i | 0.820072 | − | 0.572260i | \(-0.193933\pi\) |
−0.290835 | + | 0.956773i | \(0.593933\pi\) | |||||||
\(18\) | −1.63865 | + | 5.04324i | −0.386233 | + | 1.18870i | ||||
\(19\) | 0.927051 | + | 2.85317i | 0.212680 | + | 0.654562i | 0.999310 | + | 0.0371374i | \(0.0118239\pi\) |
−0.786630 | + | 0.617425i | \(0.788176\pi\) | |||||||
\(20\) | −9.63404 | + | 6.99954i | −2.15424 | + | 1.56514i | ||||
\(21\) | −2.30278 | −0.502507 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.69722 | −0.562410 | −0.281205 | − | 0.959648i | \(-0.590734\pi\) | ||||
−0.281205 | + | 0.959648i | \(0.590734\pi\) | |||||||
\(24\) | −5.58895 | + | 4.06061i | −1.14084 | + | 0.828869i | ||||
\(25\) | 2.47214 | + | 7.60845i | 0.494427 | + | 1.52169i | ||||
\(26\) | 4.70049 | − | 14.4666i | 0.921842 | − | 2.83714i | ||||
\(27\) | −1.29892 | − | 0.943719i | −0.249977 | − | 0.181619i | ||||
\(28\) | −2.67200 | − | 1.94132i | −0.504961 | − | 0.366876i | ||||
\(29\) | −1.45152 | + | 4.46733i | −0.269541 | + | 0.829562i | 0.721071 | + | 0.692861i | \(0.243650\pi\) |
−0.990612 | + | 0.136701i | \(0.956350\pi\) | |||||||
\(30\) | 5.90823 | + | 18.1837i | 1.07869 | + | 3.31987i | ||||
\(31\) | −0.809017 | + | 0.587785i | −0.145304 | + | 0.105569i | −0.658062 | − | 0.752964i | \(-0.728624\pi\) |
0.512758 | + | 0.858533i | \(0.328624\pi\) | |||||||
\(32\) | 5.30278 | 0.937407 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.21110 | 1.06520 | ||||||||
\(35\) | −2.91695 | + | 2.11929i | −0.493055 | + | 0.358225i | ||||
\(36\) | 2.35024 | + | 7.23331i | 0.391707 | + | 1.20555i | ||||
\(37\) | −1.61032 | + | 4.95605i | −0.264735 | + | 0.814770i | 0.727020 | + | 0.686617i | \(0.240905\pi\) |
−0.991754 | + | 0.128153i | \(0.959095\pi\) | |||||||
\(38\) | 5.58895 | + | 4.06061i | 0.906648 | + | 0.658718i | ||||
\(39\) | −12.3060 | − | 8.94086i | −1.97054 | − | 1.43168i | ||||
\(40\) | −3.34253 | + | 10.2872i | −0.528500 | + | 1.62656i | ||||
\(41\) | −2.16312 | − | 6.65740i | −0.337822 | − | 1.03971i | −0.965315 | − | 0.261088i | \(-0.915919\pi\) |
0.627493 | − | 0.778623i | \(-0.284081\pi\) | |||||||
\(42\) | −4.29004 | + | 3.11689i | −0.661967 | + | 0.480947i | ||||
\(43\) | −1.69722 | −0.258824 | −0.129412 | − | 0.991591i | \(-0.541309\pi\) | ||||
−0.129412 | + | 0.991591i | \(0.541309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.30278 | 1.23770 | ||||||||
\(46\) | −5.02489 | + | 3.65079i | −0.740879 | + | 0.538280i | ||||
\(47\) | −0.589705 | − | 1.81493i | −0.0860174 | − | 0.264734i | 0.898791 | − | 0.438377i | \(-0.144446\pi\) |
−0.984809 | + | 0.173642i | \(0.944446\pi\) | |||||||
\(48\) | −0.215454 | + | 0.663100i | −0.0310981 | + | 0.0957102i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | 14.9039 | + | 10.8283i | 2.10773 | + | 1.53135i | ||||
\(51\) | 1.91934 | − | 5.90711i | 0.268761 | − | 0.827161i | ||||
\(52\) | −6.74172 | − | 20.7489i | −0.934908 | − | 2.87735i | ||||
\(53\) | 10.4431 | − | 7.58732i | 1.43446 | − | 1.04220i | 0.445301 | − | 0.895381i | \(-0.353097\pi\) |
0.989164 | − | 0.146818i | \(-0.0469031\pi\) | |||||||
\(54\) | −3.69722 | −0.503129 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | 5.58895 | − | 4.06061i | 0.740275 | − | 0.537841i | ||||
\(58\) | 3.34253 | + | 10.2872i | 0.438896 | + | 1.35078i | ||||
\(59\) | 2.06956 | − | 6.36944i | 0.269433 | − | 0.829230i | −0.721206 | − | 0.692721i | \(-0.756412\pi\) |
0.990639 | − | 0.136509i | \(-0.0435883\pi\) | |||||||
\(60\) | 22.1850 | + | 16.1184i | 2.86408 | + | 2.08087i | ||||
\(61\) | −3.48102 | − | 2.52911i | −0.445699 | − | 0.323819i | 0.342196 | − | 0.939628i | \(-0.388829\pi\) |
−0.787895 | + | 0.615809i | \(0.788829\pi\) | |||||||
\(62\) | −0.711597 | + | 2.19007i | −0.0903729 | + | 0.278139i | ||||
\(63\) | 0.711597 | + | 2.19007i | 0.0896528 | + | 0.275923i | ||||
\(64\) | 10.3689 | − | 7.53344i | 1.29611 | − | 0.941680i | ||||
\(65\) | −23.8167 | −2.95409 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.51388 | 1.04014 | 0.520068 | − | 0.854125i | \(-0.325907\pi\) | ||||
0.520068 | + | 0.854125i | \(0.325907\pi\) | |||||||
\(68\) | 7.20699 | − | 5.23618i | 0.873976 | − | 0.634980i | ||||
\(69\) | 1.91934 | + | 5.90711i | 0.231061 | + | 0.711132i | ||||
\(70\) | −2.56570 | + | 7.89641i | −0.306660 | + | 0.943801i | ||||
\(71\) | 3.48102 | + | 2.52911i | 0.413121 | + | 0.300150i | 0.774864 | − | 0.632128i | \(-0.217818\pi\) |
−0.361743 | + | 0.932278i | \(0.617818\pi\) | |||||||
\(72\) | 5.58895 | + | 4.06061i | 0.658665 | + | 0.478548i | ||||
\(73\) | 1.54508 | − | 4.75528i | 0.180839 | − | 0.556564i | −0.819013 | − | 0.573774i | \(-0.805479\pi\) |
0.999852 | + | 0.0172107i | \(0.00547861\pi\) | |||||||
\(74\) | 3.70820 | + | 11.4127i | 0.431070 | + | 1.32670i | ||||
\(75\) | 14.9039 | − | 10.8283i | 1.72095 | − | 1.25034i | ||||
\(76\) | 9.90833 | 1.13656 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −35.0278 | −3.96611 | ||||||||
\(79\) | −6.71709 | + | 4.88025i | −0.755731 | + | 0.549071i | −0.897598 | − | 0.440815i | \(-0.854690\pi\) |
0.141867 | + | 0.989886i | \(0.454690\pi\) | |||||||
\(80\) | 0.337346 | + | 1.03824i | 0.0377164 | + | 0.116079i | ||||
\(81\) | −3.27730 | + | 10.0865i | −0.364144 | + | 1.12072i | ||||
\(82\) | −13.0409 | − | 9.47476i | −1.44013 | − | 1.04631i | ||||
\(83\) | 2.42705 | + | 1.76336i | 0.266403 | + | 0.193553i | 0.712965 | − | 0.701199i | \(-0.247352\pi\) |
−0.446562 | + | 0.894753i | \(0.647352\pi\) | |||||||
\(84\) | −2.35024 | + | 7.23331i | −0.256433 | + | 0.789219i | ||||
\(85\) | −3.00518 | − | 9.24901i | −0.325958 | − | 1.00320i | ||||
\(86\) | −3.16190 | + | 2.29726i | −0.340957 | + | 0.247720i | ||||
\(87\) | 10.8167 | 1.15967 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.7250 | −1.56084 | −0.780422 | − | 0.625253i | \(-0.784996\pi\) | ||||
−0.780422 | + | 0.625253i | \(0.784996\pi\) | |||||||
\(90\) | 15.4679 | − | 11.2381i | 1.63046 | − | 1.18460i | ||||
\(91\) | −2.04123 | − | 6.28225i | −0.213979 | − | 0.658559i | ||||
\(92\) | −2.75282 | + | 8.47232i | −0.287002 | + | 0.883301i | ||||
\(93\) | 1.86298 | + | 1.35354i | 0.193183 | + | 0.140355i | ||||
\(94\) | −3.55518 | − | 2.58299i | −0.366689 | − | 0.266415i | ||||
\(95\) | 3.34253 | − | 10.2872i | 0.342936 | − | 1.05545i | ||||
\(96\) | −3.77344 | − | 11.6134i | −0.385125 | − | 1.18529i | ||||
\(97\) | 2.91695 | − | 2.11929i | 0.296172 | − | 0.215181i | −0.429769 | − | 0.902939i | \(-0.641405\pi\) |
0.725940 | + | 0.687758i | \(0.241405\pi\) | |||||||
\(98\) | −2.30278 | −0.232615 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 26.4222 | 2.64222 | ||||||||
\(101\) | −4.29004 | + | 3.11689i | −0.426874 | + | 0.310142i | −0.780398 | − | 0.625283i | \(-0.784983\pi\) |
0.353523 | + | 0.935426i | \(0.384983\pi\) | |||||||
\(102\) | −4.41980 | − | 13.6027i | −0.437625 | − | 1.34687i | ||||
\(103\) | −4.41980 | + | 13.6027i | −0.435496 | + | 1.34032i | 0.457082 | + | 0.889425i | \(0.348895\pi\) |
−0.892578 | + | 0.450894i | \(0.851105\pi\) | |||||||
\(104\) | −16.0320 | − | 11.6479i | −1.57207 | − | 1.14217i | ||||
\(105\) | 6.71709 | + | 4.88025i | 0.655521 | + | 0.476264i | ||||
\(106\) | 9.18552 | − | 28.2701i | 0.892177 | − | 2.74584i | ||||
\(107\) | −3.83010 | − | 11.7878i | −0.370269 | − | 1.13957i | −0.946615 | − | 0.322366i | \(-0.895522\pi\) |
0.576346 | − | 0.817206i | \(-0.304478\pi\) | |||||||
\(108\) | −4.29004 | + | 3.11689i | −0.412809 | + | 0.299923i | ||||
\(109\) | 8.00000 | 0.766261 | 0.383131 | − | 0.923694i | \(-0.374846\pi\) | ||||
0.383131 | + | 0.923694i | \(0.374846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0000 | 1.13899 | ||||||||
\(112\) | −0.244951 | + | 0.177967i | −0.0231457 | + | 0.0168163i | ||||
\(113\) | −3.30562 | − | 10.1737i | −0.310967 | − | 0.957058i | −0.977383 | − | 0.211478i | \(-0.932172\pi\) |
0.666416 | − | 0.745580i | \(-0.267828\pi\) | |||||||
\(114\) | 4.91594 | − | 15.1297i | 0.460420 | − | 1.41703i | ||||
\(115\) | 7.86767 | + | 5.71620i | 0.733664 | + | 0.533038i | ||||
\(116\) | 12.5510 | + | 9.11883i | 1.16533 | + | 0.846662i | ||||
\(117\) | −4.70049 | + | 14.4666i | −0.434560 | + | 1.33744i | ||||
\(118\) | −4.76572 | − | 14.6674i | −0.438720 | − | 1.35024i | ||||
\(119\) | 2.18210 | − | 1.58539i | 0.200033 | − | 0.145332i | ||||
\(120\) | 24.9083 | 2.27381 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −9.90833 | −0.897058 | ||||||||
\(123\) | −13.0409 | + | 9.47476i | −1.17586 | + | 0.854311i | ||||
\(124\) | 1.02061 | + | 3.14113i | 0.0916538 | + | 0.282081i | ||||
\(125\) | 3.34253 | − | 10.2872i | 0.298965 | − | 0.920120i | ||||
\(126\) | 4.29004 | + | 3.11689i | 0.382187 | + | 0.277675i | ||||
\(127\) | 1.61803 | + | 1.17557i | 0.143577 | + | 0.104315i | 0.657255 | − | 0.753668i | \(-0.271717\pi\) |
−0.513678 | + | 0.857983i | \(0.671717\pi\) | |||||||
\(128\) | 5.84299 | − | 17.9829i | 0.516453 | − | 1.58948i | ||||
\(129\) | 1.20774 | + | 3.71704i | 0.106336 | + | 0.327267i | ||||
\(130\) | −44.3701 | + | 32.2367i | −3.89151 | + | 2.82735i | ||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | 0.260133 | ||||||||
\(134\) | 15.8612 | − | 11.5239i | 1.37020 | − | 0.995509i | ||||
\(135\) | 1.78887 | + | 5.50557i | 0.153961 | + | 0.473844i | ||||
\(136\) | 2.50046 | − | 7.69564i | 0.214413 | − | 0.659896i | ||||
\(137\) | 8.18679 | + | 5.94805i | 0.699445 | + | 0.508176i | 0.879751 | − | 0.475434i | \(-0.157709\pi\) |
−0.180307 | + | 0.983610i | \(0.557709\pi\) | |||||||
\(138\) | 11.5712 | + | 8.40696i | 0.985005 | + | 0.715648i | ||||
\(139\) | −6.67648 | + | 20.5481i | −0.566292 | + | 1.74287i | 0.0977898 | + | 0.995207i | \(0.468823\pi\) |
−0.664082 | + | 0.747660i | \(0.731177\pi\) | |||||||
\(140\) | 3.67988 | + | 11.3255i | 0.311006 | + | 0.957179i | ||||
\(141\) | −3.55518 | + | 2.58299i | −0.299400 | + | 0.217527i | ||||
\(142\) | 9.90833 | 0.831488 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.697224 | 0.0581020 | ||||||||
\(145\) | 13.7016 | − | 9.95478i | 1.13785 | − | 0.826699i | ||||
\(146\) | −3.55798 | − | 10.9503i | −0.294461 | − | 0.906257i | ||||
\(147\) | −0.711597 | + | 2.19007i | −0.0586915 | + | 0.180634i | ||||
\(148\) | 13.9241 | + | 10.1164i | 1.14455 | + | 0.831566i | ||||
\(149\) | −3.97092 | − | 2.88504i | −0.325310 | − | 0.236352i | 0.413128 | − | 0.910673i | \(-0.364436\pi\) |
−0.738438 | + | 0.674321i | \(0.764436\pi\) | |||||||
\(150\) | 13.1092 | − | 40.3459i | 1.07036 | − | 3.29423i | ||||
\(151\) | 0.0652343 | + | 0.200770i | 0.00530869 | + | 0.0163385i | 0.953676 | − | 0.300836i | \(-0.0972658\pi\) |
−0.948367 | + | 0.317175i | \(0.897266\pi\) | |||||||
\(152\) | 7.28115 | − | 5.29007i | 0.590579 | − | 0.429081i | ||||
\(153\) | −6.21110 | −0.502138 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.60555 | 0.289605 | ||||||||
\(156\) | −40.6441 | + | 29.5297i | −3.25413 | + | 2.36426i | ||||
\(157\) | 2.22835 | + | 6.85817i | 0.177842 | + | 0.547341i | 0.999752 | − | 0.0222763i | \(-0.00709134\pi\) |
−0.821910 | + | 0.569618i | \(0.807091\pi\) | |||||||
\(158\) | −5.90823 | + | 18.1837i | −0.470033 | + | 1.44661i | ||||
\(159\) | −24.0480 | − | 17.4719i | −1.90713 | − | 1.38561i | ||||
\(160\) | −15.4679 | − | 11.2381i | −1.22285 | − | 0.888451i | ||||
\(161\) | −0.833488 | + | 2.56521i | −0.0656881 | + | 0.202167i | ||||
\(162\) | 7.54688 | + | 23.2269i | 0.592939 | + | 1.82488i | ||||
\(163\) | −2.27872 | + | 1.65559i | −0.178483 | + | 0.129676i | −0.673440 | − | 0.739242i | \(-0.735184\pi\) |
0.494957 | + | 0.868918i | \(0.335184\pi\) | |||||||
\(164\) | −23.1194 | −1.80532 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.90833 | 0.536190 | ||||||||
\(167\) | −4.21587 | + | 3.06301i | −0.326234 | + | 0.237023i | −0.738831 | − | 0.673891i | \(-0.764622\pi\) |
0.412597 | + | 0.910914i | \(0.364622\pi\) | |||||||
\(168\) | 2.13479 | + | 6.57021i | 0.164703 | + | 0.506903i | ||||
\(169\) | 9.46621 | − | 29.1340i | 0.728170 | − | 2.24108i | ||||
\(170\) | −18.1175 | − | 13.1631i | −1.38955 | − | 1.00957i | ||||
\(171\) | −5.58895 | − | 4.06061i | −0.427398 | − | 0.310523i | ||||
\(172\) | −1.73221 | + | 5.33120i | −0.132080 | + | 0.406500i | ||||
\(173\) | 0.402580 | + | 1.23901i | 0.0306076 | + | 0.0942004i | 0.965193 | − | 0.261538i | \(-0.0842295\pi\) |
−0.934586 | + | 0.355738i | \(0.884230\pi\) | |||||||
\(174\) | 20.1513 | − | 14.6407i | 1.52766 | − | 1.10991i | ||||
\(175\) | 8.00000 | 0.604743 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.4222 | −1.15920 | ||||||||
\(178\) | −27.4324 | + | 19.9308i | −2.05615 | + | 1.49388i | ||||
\(179\) | −1.97599 | − | 6.08148i | −0.147693 | − | 0.454551i | 0.849655 | − | 0.527339i | \(-0.176810\pi\) |
−0.997347 | + | 0.0727880i | \(0.976810\pi\) | |||||||
\(180\) | 8.47393 | − | 26.0801i | 0.631609 | − | 1.94389i | ||||
\(181\) | 20.3962 | + | 14.8187i | 1.51604 | + | 1.10147i | 0.963408 | + | 0.268040i | \(0.0863760\pi\) |
0.552631 | + | 0.833426i | \(0.313624\pi\) | |||||||
\(182\) | −12.3060 | − | 8.94086i | −0.912184 | − | 0.662741i | ||||
\(183\) | −3.06184 | + | 9.42338i | −0.226338 | + | 0.696596i | ||||
\(184\) | 2.50046 | + | 7.69564i | 0.184337 | + | 0.567330i | ||||
\(185\) | 15.2005 | − | 11.0438i | 1.11757 | − | 0.811959i | ||||
\(186\) | 5.30278 | 0.388818 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.30278 | −0.459677 | ||||||||
\(189\) | −1.29892 | + | 0.943719i | −0.0944824 | + | 0.0686455i | ||||
\(190\) | −7.69710 | − | 23.6892i | −0.558406 | − | 1.71860i | ||||
\(191\) | −8.28680 | + | 25.5042i | −0.599612 | + | 1.84542i | −0.0693311 | + | 0.997594i | \(0.522086\pi\) |
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(192\) | −23.8772 | − | 17.3478i | −1.72319 | − | 1.25197i | ||||
\(193\) | −1.71465 | − | 1.24577i | −0.123424 | − | 0.0896724i | 0.524361 | − | 0.851496i | \(-0.324304\pi\) |
−0.647784 | + | 0.761824i | \(0.724304\pi\) | |||||||
\(194\) | 2.56570 | − | 7.89641i | 0.184206 | − | 0.566929i | ||||
\(195\) | 16.9479 | + | 52.1601i | 1.21366 | + | 3.73526i | ||||
\(196\) | −2.67200 | + | 1.94132i | −0.190857 | + | 0.138666i | ||||
\(197\) | 10.6056 | 0.755614 | 0.377807 | − | 0.925884i | \(-0.376678\pi\) | ||||
0.377807 | + | 0.925884i | \(0.376678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.4222 | 1.37680 | 0.688402 | − | 0.725330i | \(-0.258313\pi\) | ||||
0.688402 | + | 0.725330i | \(0.258313\pi\) | |||||||
\(200\) | 19.4164 | − | 14.1068i | 1.37295 | − | 0.997505i | ||||
\(201\) | −6.05845 | − | 18.6460i | −0.427330 | − | 1.31519i | ||||
\(202\) | −3.77344 | + | 11.6134i | −0.265498 | + | 0.817119i | ||||
\(203\) | 3.80013 | + | 2.76096i | 0.266717 | + | 0.193781i | ||||
\(204\) | −16.5961 | − | 12.0578i | −1.16196 | − | 0.844212i | ||||
\(205\) | −7.79924 | + | 24.0036i | −0.544722 | + | 1.67648i | ||||
\(206\) | 10.1778 | + | 31.3241i | 0.709122 | + | 2.18245i | ||||
\(207\) | 5.02489 | − | 3.65079i | 0.349254 | − | 0.253748i | ||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 19.1194 | 1.31937 | ||||||||
\(211\) | 12.5510 | − | 9.11883i | 0.864046 | − | 0.627766i | −0.0649368 | − | 0.997889i | \(-0.520685\pi\) |
0.928983 | + | 0.370123i | \(0.120685\pi\) | |||||||
\(212\) | −13.1744 | − | 40.5467i | −0.904823 | − | 2.78476i | ||||
\(213\) | 3.06184 | − | 9.42338i | 0.209794 | − | 0.645679i | ||||
\(214\) | −23.0907 | − | 16.7764i | −1.57845 | − | 1.14681i | ||||
\(215\) | 4.95072 | + | 3.59691i | 0.337636 | + | 0.245307i | ||||
\(216\) | −1.48843 | + | 4.58091i | −0.101275 | + | 0.311691i | ||||
\(217\) | 0.309017 | + | 0.951057i | 0.0209774 | + | 0.0645619i | ||||
\(218\) | 14.9039 | − | 10.8283i | 1.00942 | − | 0.733385i | ||||
\(219\) | −11.5139 | −0.778036 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.8167 | 1.19848 | ||||||||
\(222\) | 22.3558 | − | 16.2425i | 1.50042 | − | 1.09012i | ||||
\(223\) | 4.29791 | + | 13.2276i | 0.287809 | + | 0.885786i | 0.985543 | + | 0.169428i | \(0.0541921\pi\) |
−0.697733 | + | 0.716358i | \(0.745808\pi\) | |||||||
\(224\) | 1.63865 | − | 5.04324i | 0.109487 | − | 0.336966i | ||||
\(225\) | −14.9039 | − | 10.8283i | −0.993592 | − | 0.721887i | ||||
\(226\) | −19.9288 | − | 14.4791i | −1.32564 | − | 0.963135i | ||||
\(227\) | −2.01290 | + | 6.19507i | −0.133601 | + | 0.411181i | −0.995370 | − | 0.0961200i | \(-0.969357\pi\) |
0.861769 | + | 0.507301i | \(0.169357\pi\) | |||||||
\(228\) | −7.05073 | − | 21.6999i | −0.466946 | − | 1.43711i | ||||
\(229\) | 2.10794 | − | 1.53150i | 0.139296 | − | 0.101205i | −0.515955 | − | 0.856616i | \(-0.672563\pi\) |
0.655251 | + | 0.755411i | \(0.272563\pi\) | |||||||
\(230\) | 22.3944 | 1.47665 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.0917 | 0.925164 | ||||||||
\(233\) | 14.5623 | − | 10.5801i | 0.954008 | − | 0.693128i | 0.00225687 | − | 0.999997i | \(-0.499282\pi\) |
0.951752 | + | 0.306870i | \(0.0992816\pi\) | |||||||
\(234\) | 10.8242 | + | 33.3134i | 0.707598 | + | 2.17776i | ||||
\(235\) | −2.12621 | + | 6.54381i | −0.138699 | + | 0.426871i | ||||
\(236\) | −17.8950 | − | 13.0015i | −1.16486 | − | 0.846324i | ||||
\(237\) | 15.4679 | + | 11.2381i | 1.00475 | + | 0.729994i | ||||
\(238\) | 1.91934 | − | 5.90711i | 0.124412 | − | 0.382901i | ||||
\(239\) | −8.13658 | − | 25.0418i | −0.526312 | − | 1.61982i | −0.761707 | − | 0.647921i | \(-0.775639\pi\) |
0.235396 | − | 0.971900i | \(-0.424361\pi\) | |||||||
\(240\) | 2.03377 | − | 1.47762i | 0.131279 | − | 0.0953800i | ||||
\(241\) | −0.486122 | −0.0313139 | −0.0156569 | − | 0.999877i | \(-0.504984\pi\) | ||||
−0.0156569 | + | 0.999877i | \(0.504984\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.6056 | 1.25770 | ||||||||
\(244\) | −11.4970 | + | 8.35308i | −0.736022 | + | 0.534751i | ||||
\(245\) | 1.11418 | + | 3.42908i | 0.0711821 | + | 0.219076i | ||||
\(246\) | −11.4705 | + | 35.3027i | −0.731335 | + | 2.25082i | ||||
\(247\) | 16.0320 | + | 11.6479i | 1.02009 | + | 0.741140i | ||||
\(248\) | 2.42705 | + | 1.76336i | 0.154118 | + | 0.111973i | ||||
\(249\) | 2.13479 | − | 6.57021i | 0.135287 | − | 0.416370i | ||||
\(250\) | −7.69710 | − | 23.6892i | −0.486807 | − | 1.49824i | ||||
\(251\) | −3.55518 | + | 2.58299i | −0.224401 | + | 0.163037i | −0.694306 | − | 0.719680i | \(-0.744288\pi\) |
0.469904 | + | 0.882717i | \(0.344288\pi\) | |||||||
\(252\) | 7.60555 | 0.479105 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 4.60555 | 0.288978 | ||||||||
\(255\) | −18.1175 | + | 13.1631i | −1.13456 | + | 0.824307i | ||||
\(256\) | −5.53398 | − | 17.0318i | −0.345874 | − | 1.06449i | ||||
\(257\) | 2.00432 | − | 6.16867i | 0.125026 | − | 0.384791i | −0.868880 | − | 0.495023i | \(-0.835160\pi\) |
0.993906 | + | 0.110232i | \(0.0351595\pi\) | |||||||
\(258\) | 7.28115 | + | 5.29007i | 0.453305 | + | 0.329345i | ||||
\(259\) | 4.21587 | + | 3.06301i | 0.261961 | + | 0.190326i | ||||
\(260\) | −24.3076 | + | 74.8111i | −1.50749 | + | 4.63959i | ||||
\(261\) | −3.34253 | − | 10.2872i | −0.206897 | − | 0.636765i | ||||
\(262\) | 11.1779 | − | 8.12123i | 0.690573 | − | 0.501731i | ||||
\(263\) | −20.2389 | −1.24798 | −0.623991 | − | 0.781432i | \(-0.714490\pi\) | ||||
−0.623991 | + | 0.781432i | \(0.714490\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −46.5416 | −2.85903 | ||||||||
\(266\) | 5.58895 | − | 4.06061i | 0.342681 | − | 0.248972i | ||||
\(267\) | 10.4782 | + | 32.2487i | 0.641258 | + | 1.97359i | ||||
\(268\) | 8.68938 | − | 26.7432i | 0.530788 | − | 1.63360i | ||||
\(269\) | −13.0409 | − | 9.47476i | −0.795117 | − | 0.577686i | 0.114360 | − | 0.993439i | \(-0.463518\pi\) |
−0.909478 | + | 0.415753i | \(0.863518\pi\) | |||||||
\(270\) | 10.7846 | + | 7.83549i | 0.656331 | + | 0.476853i | ||||
\(271\) | 8.81127 | − | 27.1183i | 0.535247 | − | 1.64732i | −0.207869 | − | 0.978157i | \(-0.566653\pi\) |
0.743115 | − | 0.669163i | \(-0.233347\pi\) | |||||||
\(272\) | −0.252360 | − | 0.776684i | −0.0153016 | − | 0.0470934i | ||||
\(273\) | −12.3060 | + | 8.94086i | −0.744795 | + | 0.541126i | ||||
\(274\) | 23.3028 | 1.40777 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 20.5139 | 1.23479 | ||||||||
\(277\) | 24.2188 | − | 17.5960i | 1.45517 | − | 1.05724i | 0.470577 | − | 0.882359i | \(-0.344046\pi\) |
0.984589 | − | 0.174882i | \(-0.0559543\pi\) | |||||||
\(278\) | 15.3744 | + | 47.3177i | 0.922098 | + | 2.83792i | ||||
\(279\) | 0.711597 | − | 2.19007i | 0.0426022 | − | 0.131116i | ||||
\(280\) | 8.75086 | + | 6.35787i | 0.522964 | + | 0.379955i | ||||
\(281\) | 5.17322 | + | 3.75856i | 0.308608 | + | 0.224217i | 0.731299 | − | 0.682057i | \(-0.238914\pi\) |
−0.422691 | + | 0.906274i | \(0.638914\pi\) | |||||||
\(282\) | −3.12708 | + | 9.62415i | −0.186215 | + | 0.573110i | ||||
\(283\) | −1.35796 | − | 4.17937i | −0.0807223 | − | 0.248438i | 0.902548 | − | 0.430589i | \(-0.141694\pi\) |
−0.983271 | + | 0.182151i | \(0.941694\pi\) | |||||||
\(284\) | 11.4970 | − | 8.35308i | 0.682223 | − | 0.495664i | ||||
\(285\) | −24.9083 | −1.47544 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.00000 | −0.413197 | ||||||||
\(288\) | −9.87899 | + | 7.17751i | −0.582125 | + | 0.422939i | ||||
\(289\) | −3.00518 | − | 9.24901i | −0.176776 | − | 0.544059i | ||||
\(290\) | 12.0517 | − | 37.0912i | 0.707698 | − | 2.17807i | ||||
\(291\) | −6.71709 | − | 4.88025i | −0.393763 | − | 0.286085i | ||||
\(292\) | −13.3600 | − | 9.70661i | −0.781835 | − | 0.568037i | ||||
\(293\) | −1.48843 | + | 4.58091i | −0.0869549 | + | 0.267620i | −0.985074 | − | 0.172133i | \(-0.944934\pi\) |
0.898119 | + | 0.439753i | \(0.144934\pi\) | |||||||
\(294\) | 1.63865 | + | 5.04324i | 0.0955679 | + | 0.294128i | ||||
\(295\) | −19.5355 | + | 14.1934i | −1.13740 | + | 0.826369i | ||||
\(296\) | 15.6333 | 0.908668 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.3028 | −0.654752 | ||||||||
\(299\) | −14.4140 | + | 10.4724i | −0.833582 | + | 0.605633i | ||||
\(300\) | −18.8020 | − | 57.8665i | −1.08553 | − | 3.34092i | ||||
\(301\) | −0.524471 | + | 1.61416i | −0.0302300 | + | 0.0930384i | ||||
\(302\) | 0.393281 | + | 0.285735i | 0.0226308 | + | 0.0164422i | ||||
\(303\) | 9.87899 | + | 7.17751i | 0.567533 | + | 0.412337i | ||||
\(304\) | 0.280688 | − | 0.863870i | 0.0160986 | − | 0.0495464i | ||||
\(305\) | 4.79405 | + | 14.7546i | 0.274507 | + | 0.844845i | ||||
\(306\) | −11.5712 | + | 8.40696i | −0.661481 | + | 0.480594i | ||||
\(307\) | 16.6333 | 0.949313 | 0.474657 | − | 0.880171i | \(-0.342572\pi\) | ||||
0.474657 | + | 0.880171i | \(0.342572\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 32.9361 | 1.87367 | ||||||||
\(310\) | 6.71709 | − | 4.88025i | 0.381505 | − | 0.277180i | ||||
\(311\) | 1.97599 | + | 6.08148i | 0.112048 | + | 0.344849i | 0.991320 | − | 0.131471i | \(-0.0419702\pi\) |
−0.879272 | + | 0.476321i | \(0.841970\pi\) | |||||||
\(312\) | −14.1015 | + | 43.3999i | −0.798338 | + | 2.45703i | ||||
\(313\) | −12.3802 | − | 8.99475i | −0.699771 | − | 0.508413i | 0.180087 | − | 0.983651i | \(-0.442362\pi\) |
−0.879857 | + | 0.475238i | \(0.842362\pi\) | |||||||
\(314\) | 13.4342 | + | 9.76050i | 0.758134 | + | 0.550817i | ||||
\(315\) | 2.56570 | − | 7.89641i | 0.144561 | − | 0.444912i | ||||
\(316\) | 8.47393 | + | 26.0801i | 0.476696 | + | 1.46712i | ||||
\(317\) | −13.9982 | + | 10.1703i | −0.786219 | + | 0.571222i | −0.906839 | − | 0.421477i | \(-0.861512\pi\) |
0.120620 | + | 0.992699i | \(0.461512\pi\) | |||||||
\(318\) | −68.4500 | −3.83848 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −46.2111 | −2.58328 | ||||||||
\(321\) | −23.0907 | + | 16.7764i | −1.28880 | + | 0.936365i | ||||
\(322\) | 1.91934 | + | 5.90711i | 0.106960 | + | 0.329190i | ||||
\(323\) | −2.50046 | + | 7.69564i | −0.139130 | + | 0.428197i | ||||
\(324\) | 28.3381 | + | 20.5888i | 1.57434 | + | 1.14382i | ||||
\(325\) | 42.7520 | + | 31.0612i | 2.37146 | + | 1.72296i | ||||
\(326\) | −2.00432 | + | 6.16867i | −0.111009 | + | 0.341651i | ||||
\(327\) | −5.69277 | − | 17.5206i | −0.314811 | − | 0.968889i | ||||
\(328\) | −16.9894 | + | 12.3435i | −0.938080 | + | 0.681555i | ||||
\(329\) | −1.90833 | −0.105209 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.8167 | 1.30908 | 0.654541 | − | 0.756027i | \(-0.272862\pi\) | ||||
0.654541 | + | 0.756027i | \(0.272862\pi\) | |||||||
\(332\) | 8.01600 | − | 5.82397i | 0.439935 | − | 0.319632i | ||||
\(333\) | −3.70820 | − | 11.4127i | −0.203208 | − | 0.625411i | ||||
\(334\) | −3.70820 | + | 11.4127i | −0.202904 | + | 0.624474i | ||||
\(335\) | −24.8346 | − | 18.0434i | −1.35686 | − | 0.985815i | ||||
\(336\) | 0.564066 | + | 0.409818i | 0.0307723 | + | 0.0223574i | ||||
\(337\) | −3.64297 | + | 11.2119i | −0.198445 | + | 0.610752i | 0.801474 | + | 0.598030i | \(0.204050\pi\) |
−0.999919 | + | 0.0127217i | \(0.995950\pi\) | |||||||
\(338\) | −21.7986 | − | 67.0891i | −1.18569 | − | 3.64916i | ||||
\(339\) | −19.9288 | + | 14.4791i | −1.08238 | + | 0.786396i | ||||
\(340\) | −32.1194 | −1.74192 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −15.9083 | −0.860224 | ||||||||
\(343\) | −0.809017 | + | 0.587785i | −0.0436828 | + | 0.0317374i | ||||
\(344\) | 1.57341 | + | 4.84247i | 0.0848328 | + | 0.261088i | ||||
\(345\) | 6.92027 | − | 21.2984i | 0.372575 | − | 1.14667i | ||||
\(346\) | 2.42705 | + | 1.76336i | 0.130479 | + | 0.0947986i | ||||
\(347\) | 7.77105 | + | 5.64600i | 0.417172 | + | 0.303093i | 0.776499 | − | 0.630119i | \(-0.216994\pi\) |
−0.359327 | + | 0.933212i | \(0.616994\pi\) | |||||||
\(348\) | 11.0396 | − | 33.9765i | 0.591786 | − | 1.82133i | ||||
\(349\) | 1.45152 | + | 4.46733i | 0.0776982 | + | 0.239130i | 0.982360 | − | 0.187000i | \(-0.0598764\pi\) |
−0.904662 | + | 0.426130i | \(0.859876\pi\) | |||||||
\(350\) | 14.9039 | − | 10.8283i | 0.796646 | − | 0.578797i | ||||
\(351\) | −10.6056 | −0.566082 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.09167 | 0.271002 | 0.135501 | − | 0.990777i | \(-0.456736\pi\) | ||||
0.135501 | + | 0.990777i | \(0.456736\pi\) | |||||||
\(354\) | −28.7313 | + | 20.8745i | −1.52705 | + | 1.10947i | ||||
\(355\) | −4.79405 | − | 14.7546i | −0.254442 | − | 0.783092i | ||||
\(356\) | −15.0285 | + | 46.2530i | −0.796510 | + | 2.45141i | ||||
\(357\) | −5.02489 | − | 3.65079i | −0.265945 | − | 0.193221i | ||||
\(358\) | −11.9128 | − | 8.65513i | −0.629609 | − | 0.457438i | ||||
\(359\) | 10.4868 | − | 32.2751i | 0.553474 | − | 1.70342i | −0.146467 | − | 0.989216i | \(-0.546790\pi\) |
0.699941 | − | 0.714201i | \(-0.253210\pi\) | |||||||
\(360\) | −7.69710 | − | 23.6892i | −0.405673 | − | 1.24853i | ||||
\(361\) | 8.09017 | − | 5.87785i | 0.425798 | − | 0.309361i | ||||
\(362\) | 58.0555 | 3.05133 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −21.8167 | −1.14350 | ||||||||
\(365\) | −14.5848 | + | 10.5964i | −0.763401 | + | 0.554644i | ||||
\(366\) | 7.05073 | + | 21.6999i | 0.368548 | + | 1.13427i | ||||
\(367\) | −5.44899 | + | 16.7703i | −0.284435 | + | 0.875401i | 0.702132 | + | 0.712046i | \(0.252231\pi\) |
−0.986567 | + | 0.163355i | \(0.947769\pi\) | |||||||
\(368\) | 0.660687 | + | 0.480017i | 0.0344407 | + | 0.0250226i | ||||
\(369\) | 13.0409 | + | 9.47476i | 0.678882 | + | 0.493236i | ||||
\(370\) | 13.3701 | − | 41.1490i | 0.695079 | − | 2.13923i | ||||
\(371\) | −3.98889 | − | 12.2765i | −0.207093 | − | 0.637367i | ||||
\(372\) | 6.15302 | − | 4.47043i | 0.319019 | − | 0.231781i | ||||
\(373\) | 20.1194 | 1.04174 | 0.520872 | − | 0.853635i | \(-0.325607\pi\) | ||||
0.520872 | + | 0.853635i | \(0.325607\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −24.9083 | −1.28626 | ||||||||
\(376\) | −4.63161 | + | 3.36506i | −0.238857 | + | 0.173540i | ||||
\(377\) | 9.58810 | + | 29.5091i | 0.493812 | + | 1.51980i | ||||
\(378\) | −1.14251 | + | 3.51627i | −0.0587641 | + | 0.180857i | ||||
\(379\) | 12.7959 | + | 9.29680i | 0.657283 | + | 0.477544i | 0.865744 | − | 0.500486i | \(-0.166845\pi\) |
−0.208461 | + | 0.978031i | \(0.566845\pi\) | |||||||
\(380\) | −28.9021 | − | 20.9986i | −1.48265 | − | 1.07721i | ||||
\(381\) | 1.42319 | − | 4.38014i | 0.0729124 | − | 0.224401i | ||||
\(382\) | 19.0826 | + | 58.7303i | 0.976353 | + | 3.00491i | ||||
\(383\) | −31.2550 | + | 22.7081i | −1.59706 | + | 1.16033i | −0.704185 | + | 0.710016i | \(0.748687\pi\) |
−0.892871 | + | 0.450313i | \(0.851313\pi\) | |||||||
\(384\) | −43.5416 | −2.22197 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.88057 | −0.248414 | ||||||||
\(387\) | 3.16190 | − | 2.29726i | 0.160729 | − | 0.116776i | ||||
\(388\) | −3.67988 | − | 11.3255i | −0.186817 | − | 0.574965i | ||||
\(389\) | −2.41548 | + | 7.43408i | −0.122470 | + | 0.376923i | −0.993432 | − | 0.114428i | \(-0.963497\pi\) |
0.870962 | + | 0.491350i | \(0.163497\pi\) | |||||||
\(390\) | 102.174 | + | 74.2340i | 5.17380 | + | 3.75898i | ||||
\(391\) | −5.88561 | − | 4.27615i | −0.297648 | − | 0.216254i | ||||
\(392\) | −0.927051 | + | 2.85317i | −0.0468231 | + | 0.144107i | ||||
\(393\) | −4.26958 | − | 13.1404i | −0.215372 | − | 0.662846i | ||||
\(394\) | 19.7580 | − | 14.3550i | 0.995393 | − | 0.723195i | ||||
\(395\) | 29.9361 | 1.50625 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.2111 | 1.51625 | 0.758126 | − | 0.652108i | \(-0.226115\pi\) | ||||
0.758126 | + | 0.652108i | \(0.226115\pi\) | |||||||
\(398\) | 36.1833 | − | 26.2887i | 1.81370 | − | 1.31773i | ||||
\(399\) | −2.13479 | − | 6.57021i | −0.106873 | − | 0.328922i | ||||
\(400\) | 0.748503 | − | 2.30365i | 0.0374251 | − | 0.115183i | ||||
\(401\) | 17.1601 | + | 12.4676i | 0.856937 | + | 0.622601i | 0.927050 | − | 0.374938i | \(-0.122336\pi\) |
−0.0701132 | + | 0.997539i | \(0.522336\pi\) | |||||||
\(402\) | −36.5248 | − | 26.5369i | −1.82169 | − | 1.32354i | ||||
\(403\) | −2.04123 | + | 6.28225i | −0.101681 | + | 0.312941i | ||||
\(404\) | 5.41209 | + | 16.6567i | 0.269261 | + | 0.828701i | ||||
\(405\) | 30.9359 | − | 22.4762i | 1.53722 | − | 1.11685i | ||||
\(406\) | 10.8167 | 0.536822 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −18.6333 | −0.922486 | ||||||||
\(409\) | 16.6702 | − | 12.1116i | 0.824290 | − | 0.598882i | −0.0936478 | − | 0.995605i | \(-0.529853\pi\) |
0.917938 | + | 0.396723i | \(0.129853\pi\) | |||||||
\(410\) | 17.9599 | + | 55.2749i | 0.886976 | + | 2.72983i | ||||
\(411\) | 7.20095 | − | 22.1623i | 0.355197 | − | 1.09318i | ||||
\(412\) | 38.2170 | + | 27.7663i | 1.88282 | + | 1.36795i | ||||
\(413\) | −5.41817 | − | 3.93653i | −0.266611 | − | 0.193704i | ||||
\(414\) | 4.41980 | − | 13.6027i | 0.217221 | − | 0.668539i | ||||
\(415\) | −3.34253 | − | 10.2872i | −0.164078 | − | 0.504981i | ||||
\(416\) | 28.3381 | − | 20.5888i | 1.38939 | − | 1.00945i | ||||
\(417\) | 49.7527 | 2.43640 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −38.4222 | −1.87705 | −0.938524 | − | 0.345215i | \(-0.887806\pi\) | ||||
−0.938524 | + | 0.345215i | \(0.887806\pi\) | |||||||
\(420\) | 22.1850 | − | 16.1184i | 1.08252 | − | 0.786496i | ||||
\(421\) | −6.74172 | − | 20.7489i | −0.328571 | − | 1.01124i | −0.969803 | − | 0.243891i | \(-0.921576\pi\) |
0.641232 | − | 0.767347i | \(-0.278424\pi\) | |||||||
\(422\) | 11.0396 | − | 33.9765i | 0.537401 | − | 1.65395i | ||||
\(423\) | 3.55518 | + | 2.58299i | 0.172859 | + | 0.125589i | ||||
\(424\) | −31.3292 | − | 22.7620i | −1.52148 | − | 1.10542i | ||||
\(425\) | −6.66791 | + | 20.5217i | −0.323441 | + | 0.995449i | ||||
\(426\) | −7.05073 | − | 21.6999i | −0.341609 | − | 1.05136i | ||||
\(427\) | −3.48102 | + | 2.52911i | −0.168458 | + | 0.122392i | ||||
\(428\) | −40.9361 | −1.97872 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.0917 | 0.679561 | ||||||||
\(431\) | −2.52367 | + | 1.83355i | −0.121561 | + | 0.0883192i | −0.646905 | − | 0.762571i | \(-0.723937\pi\) |
0.525344 | + | 0.850890i | \(0.323937\pi\) | |||||||
\(432\) | 0.150220 | + | 0.462329i | 0.00722746 | + | 0.0222438i | ||||
\(433\) | 9.00698 | − | 27.7206i | 0.432848 | − | 1.33217i | −0.462429 | − | 0.886657i | \(-0.653022\pi\) |
0.895276 | − | 0.445511i | \(-0.146978\pi\) | |||||||
\(434\) | 1.86298 | + | 1.35354i | 0.0894261 | + | 0.0649719i | ||||
\(435\) | −31.5517 | − | 22.9236i | −1.51279 | − | 1.09910i | ||||
\(436\) | 8.16491 | − | 25.1290i | 0.391028 | − | 1.20346i | ||||
\(437\) | −2.50046 | − | 7.69564i | −0.119613 | − | 0.368132i | ||||
\(438\) | −21.4502 | + | 15.5845i | −1.02493 | + | 0.744655i | ||||
\(439\) | −27.7250 | −1.32324 | −0.661621 | − | 0.749839i | \(-0.730131\pi\) | ||||
−0.661621 | + | 0.749839i | \(0.730131\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.30278 | 0.109656 | ||||||||
\(442\) | 33.1922 | − | 24.1155i | 1.57879 | − | 1.14706i | ||||
\(443\) | 8.32371 | + | 25.6177i | 0.395471 | + | 1.21714i | 0.928594 | + | 0.371097i | \(0.121018\pi\) |
−0.533123 | + | 0.846038i | \(0.678982\pi\) | |||||||
\(444\) | 12.2474 | − | 37.6935i | 0.581234 | − | 1.78886i | ||||
\(445\) | 42.9521 | + | 31.2065i | 2.03612 | + | 1.47933i | ||||
\(446\) | 25.9110 | + | 18.8254i | 1.22692 | + | 0.891411i | ||||
\(447\) | −3.49275 | + | 10.7496i | −0.165201 | + | 0.508438i | ||||
\(448\) | −3.96056 | − | 12.1894i | −0.187119 | − | 0.575893i | ||||
\(449\) | −32.6281 | + | 23.7057i | −1.53981 | + | 1.11874i | −0.589363 | + | 0.807868i | \(0.700621\pi\) |
−0.950452 | + | 0.310872i | \(0.899379\pi\) | |||||||
\(450\) | −42.4222 | −1.99980 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −35.3305 | −1.66181 | ||||||||
\(453\) | 0.393281 | − | 0.285735i | 0.0184779 | − | 0.0134250i | ||||
\(454\) | 4.63525 | + | 14.2658i | 0.217543 | + | 0.669529i | ||||
\(455\) | −7.35975 | + | 22.6510i | −0.345030 | + | 1.06189i | ||||
\(456\) | −16.7669 | − | 12.1818i | −0.785180 | − | 0.570467i | ||||
\(457\) | 17.0860 | + | 12.4137i | 0.799248 | + | 0.580688i | 0.910694 | − | 0.413083i | \(-0.135548\pi\) |
−0.111445 | + | 0.993771i | \(0.535548\pi\) | |||||||
\(458\) | 1.85410 | − | 5.70634i | 0.0866365 | − | 0.266640i | ||||
\(459\) | −1.33821 | − | 4.11858i | −0.0624622 | − | 0.192239i | ||||
\(460\) | 25.9852 | − | 18.8793i | 1.21156 | − | 0.880253i | ||||
\(461\) | −8.09167 | −0.376867 | −0.188433 | − | 0.982086i | \(-0.560341\pi\) | ||||
−0.188433 | + | 0.982086i | \(0.560341\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.8167 | −1.43217 | −0.716086 | − | 0.698012i | \(-0.754068\pi\) | ||||
−0.716086 | + | 0.698012i | \(0.754068\pi\) | |||||||
\(464\) | 1.15059 | − | 0.835951i | 0.0534147 | − | 0.0388081i | ||||
\(465\) | −2.56570 | − | 7.89641i | −0.118981 | − | 0.366187i | ||||
\(466\) | 12.8087 | − | 39.4213i | 0.593354 | − | 1.82615i | ||||
\(467\) | 10.9554 | + | 7.95957i | 0.506956 | + | 0.368325i | 0.811668 | − | 0.584120i | \(-0.198560\pi\) |
−0.304712 | + | 0.952445i | \(0.598560\pi\) | |||||||
\(468\) | 40.6441 | + | 29.5297i | 1.87877 | + | 1.36501i | ||||
\(469\) | 2.63093 | − | 8.09718i | 0.121485 | − | 0.373893i | ||||
\(470\) | 4.89619 | + | 15.0689i | 0.225844 | + | 0.695078i | ||||
\(471\) | 13.4342 | − | 9.76050i | 0.619014 | − | 0.449740i | ||||
\(472\) | −20.0917 | −0.924794 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 44.0278 | 2.02226 | ||||||||
\(475\) | −19.4164 | + | 14.1068i | −0.890886 | + | 0.647266i | ||||
\(476\) | −2.75282 | − | 8.47232i | −0.126175 | − | 0.388328i | ||||
\(477\) | −9.18552 | + | 28.2701i | −0.420576 | + | 1.29440i | ||||
\(478\) | −49.0534 | − | 35.6394i | −2.24365 | − | 1.63011i | ||||
\(479\) | −23.1648 | − | 16.8302i | −1.05843 | − | 0.768993i | −0.0846313 | − | 0.996412i | \(-0.526971\pi\) |
−0.973797 | + | 0.227419i | \(0.926971\pi\) | |||||||
\(480\) | −13.6053 | + | 41.8729i | −0.620995 | + | 1.91123i | ||||
\(481\) | 10.6370 | + | 32.7375i | 0.485008 | + | 1.49270i | ||||
\(482\) | −0.905637 | + | 0.657984i | −0.0412507 | + | 0.0299704i | ||||
\(483\) | 6.21110 | 0.282615 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.0000 | −0.590300 | ||||||||
\(486\) | 36.5248 | − | 26.5369i | 1.65680 | − | 1.20374i | ||||
\(487\) | −0.870394 | − | 2.67880i | −0.0394413 | − | 0.121388i | 0.929397 | − | 0.369081i | \(-0.120328\pi\) |
−0.968839 | + | 0.247693i | \(0.920328\pi\) | |||||||
\(488\) | −3.98889 | + | 12.2765i | −0.180569 | + | 0.555733i | ||||
\(489\) | 5.24738 | + | 3.81245i | 0.237295 | + | 0.172405i | ||||
\(490\) | 6.71709 | + | 4.88025i | 0.303447 | + | 0.220467i | ||||
\(491\) | 3.92366 | − | 12.0758i | 0.177072 | − | 0.544972i | −0.822650 | − | 0.568548i | \(-0.807505\pi\) |
0.999722 | + | 0.0235761i | \(0.00750521\pi\) | |||||||
\(492\) | 16.4517 | + | 50.6332i | 0.741700 | + | 2.28272i | ||||
\(493\) | −10.2498 | + | 7.44693i | −0.461628 | + | 0.335393i | ||||
\(494\) | 45.6333 | 2.05314 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.302776 | 0.0135950 | ||||||||
\(497\) | 3.48102 | − | 2.52911i | 0.156145 | − | 0.113446i | ||||
\(498\) | −4.91594 | − | 15.1297i | −0.220289 | − | 0.677979i | ||||
\(499\) | 0.898722 | − | 2.76598i | 0.0402323 | − | 0.123822i | −0.928923 | − | 0.370273i | \(-0.879264\pi\) |
0.969155 | + | 0.246450i | \(0.0792642\pi\) | |||||||
\(500\) | −28.9021 | − | 20.9986i | −1.29254 | − | 0.939087i | ||||
\(501\) | 9.70820 | + | 7.05342i | 0.433731 | + | 0.315124i | ||||
\(502\) | −3.12708 | + | 9.62415i | −0.139568 | + | 0.429547i | ||||
\(503\) | −1.72363 | − | 5.30480i | −0.0768530 | − | 0.236529i | 0.905248 | − | 0.424883i | \(-0.139685\pi\) |
−0.982101 | + | 0.188354i | \(0.939685\pi\) | |||||||
\(504\) | 5.58895 | − | 4.06061i | 0.248952 | − | 0.180874i | ||||
\(505\) | 19.1194 | 0.850803 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −70.5416 | −3.13286 | ||||||||
\(508\) | 5.34400 | − | 3.88265i | 0.237102 | − | 0.172265i | ||||
\(509\) | 6.89194 | + | 21.2112i | 0.305480 | + | 0.940170i | 0.979498 | + | 0.201455i | \(0.0645670\pi\) |
−0.674018 | + | 0.738715i | \(0.735433\pi\) | |||||||
\(510\) | −15.9358 | + | 49.0454i | −0.705650 | + | 2.17177i | ||||
\(511\) | −4.04508 | − | 2.93893i | −0.178944 | − | 0.130010i | ||||
\(512\) | −2.76862 | − | 2.01152i | −0.122357 | − | 0.0888975i | ||||
\(513\) | 1.48843 | − | 4.58091i | 0.0657157 | − | 0.202252i | ||||
\(514\) | −4.61550 | − | 14.2051i | −0.203581 | − | 0.626558i | ||||
\(515\) | 41.7205 | − | 30.3117i | 1.83843 | − | 1.33569i | ||||
\(516\) | 12.9083 | 0.568257 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 12.0000 | 0.527250 | ||||||||
\(519\) | 2.42705 | − | 1.76336i | 0.106536 | − | 0.0774027i | ||||
\(520\) | 22.0793 | + | 67.9530i | 0.968239 | + | 2.97993i | ||||
\(521\) | 2.29359 | − | 7.05894i | 0.100484 | − | 0.309258i | −0.888160 | − | 0.459534i | \(-0.848016\pi\) |
0.988644 | + | 0.150277i | \(0.0480164\pi\) | |||||||
\(522\) | −20.1513 | − | 14.6407i | −0.881997 | − | 0.640808i | ||||
\(523\) | −36.0349 | − | 26.1809i | −1.57570 | − | 1.14481i | −0.921427 | − | 0.388551i | \(-0.872976\pi\) |
−0.654271 | − | 0.756260i | \(-0.727024\pi\) | |||||||
\(524\) | 6.12368 | − | 18.8468i | 0.267514 | − | 0.823324i | ||||
\(525\) | −5.69277 | − | 17.5206i | −0.248453 | − | 0.764660i | ||||
\(526\) | −37.7047 | + | 27.3941i | −1.64400 | + | 1.19444i | ||||
\(527\) | −2.69722 | −0.117493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7250 | −0.683695 | ||||||||
\(530\) | −86.7063 | + | 62.9959i | −3.76628 | + | 2.73636i | ||||
\(531\) | 4.76572 | + | 14.6674i | 0.206815 | + | 0.636510i | ||||
\(532\) | 3.06184 | − | 9.42338i | 0.132748 | − | 0.408555i | ||||
\(533\) | −37.4080 | − | 27.1785i | −1.62032 | − | 1.17723i | ||||
\(534\) | 63.1707 | + | 45.8962i | 2.73366 | + | 1.98612i | ||||
\(535\) | −13.8096 | + | 42.5016i | −0.597041 | + | 1.83750i | ||||
\(536\) | −7.89280 | − | 24.2915i | −0.340917 | − | 1.04923i | ||||
\(537\) | −11.9128 | + | 8.65513i | −0.514074 | + | 0.373496i | ||||
\(538\) | −37.1194 | −1.60033 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 19.1194 | 0.822769 | ||||||||
\(541\) | −26.2077 | + | 19.0410i | −1.12676 | + | 0.818636i | −0.985219 | − | 0.171297i | \(-0.945204\pi\) |
−0.141536 | + | 0.989933i | \(0.545204\pi\) | |||||||
\(542\) | −20.2904 | − | 62.4474i | −0.871547 | − | 2.68234i | ||||
\(543\) | 17.9401 | − | 55.2141i | 0.769885 | − | 2.36946i | ||||
\(544\) | 11.5712 | + | 8.40696i | 0.496111 | + | 0.360445i | ||||
\(545\) | −23.3356 | − | 16.9543i | −0.999588 | − | 0.726243i | ||||
\(546\) | −10.8242 | + | 33.3134i | −0.463232 | + | 1.42568i | ||||
\(547\) | 9.25076 | + | 28.4709i | 0.395534 | + | 1.21733i | 0.928545 | + | 0.371220i | \(0.121060\pi\) |
−0.533011 | + | 0.846108i | \(0.678940\pi\) | |||||||
\(548\) | 27.0391 | − | 19.6451i | 1.15505 | − | 0.839196i | ||||
\(549\) | 9.90833 | 0.422877 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.0917 | −0.600325 | ||||||||
\(552\) | 15.0747 | − | 10.9524i | 0.641620 | − | 0.466164i | ||||
\(553\) | 2.56570 | + | 7.89641i | 0.109105 | + | 0.335789i | ||||
\(554\) | 21.3024 | − | 65.5621i | 0.905053 | − | 2.78547i | ||||
\(555\) | −35.0034 | − | 25.4315i | −1.48581 | − | 1.07951i | ||||
\(556\) | 57.7301 | + | 41.9433i | 2.44830 | + | 1.77879i | ||||
\(557\) | −2.23693 | + | 6.88456i | −0.0947818 | + | 0.291708i | −0.987197 | − | 0.159507i | \(-0.949009\pi\) |
0.892415 | + | 0.451216i | \(0.149009\pi\) | |||||||
\(558\) | −1.63865 | − | 5.04324i | −0.0693695 | − | 0.213497i | ||||
\(559\) | −9.06997 | + | 6.58972i | −0.383619 | + | 0.278715i | ||||
\(560\) | 1.09167 | 0.0461316 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.7250 | 0.621136 | ||||||||
\(563\) | −0.244951 | + | 0.177967i | −0.0103234 | + | 0.00750042i | −0.592935 | − | 0.805250i | \(-0.702031\pi\) |
0.582612 | + | 0.812751i | \(0.302031\pi\) | |||||||
\(564\) | 4.48504 | + | 13.8035i | 0.188854 | + | 0.581233i | ||||
\(565\) | −11.9186 | + | 36.6817i | −0.501419 | + | 1.54321i | ||||
\(566\) | −8.18679 | − | 5.94805i | −0.344116 | − | 0.250015i | ||||
\(567\) | 8.58007 | + | 6.23379i | 0.360329 | + | 0.261794i | ||||
\(568\) | 3.98889 | − | 12.2765i | 0.167370 | − | 0.515113i | ||||
\(569\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(570\) | −46.4038 | + | 33.7144i | −1.94364 | + | 1.41214i | ||||
\(571\) | −25.8444 | −1.08155 | −0.540777 | − | 0.841166i | \(-0.681870\pi\) | ||||
−0.540777 | + | 0.841166i | \(0.681870\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 61.7527 | 2.57976 | ||||||||
\(574\) | −13.0409 | + | 9.47476i | −0.544316 | + | 0.395469i | ||||
\(575\) | −6.66791 | − | 20.5217i | −0.278071 | − | 0.855814i | ||||
\(576\) | −9.12029 | + | 28.0694i | −0.380012 | + | 1.16956i | ||||
\(577\) | −1.78882 | − | 1.29965i | −0.0744695 | − | 0.0541053i | 0.549928 | − | 0.835212i | \(-0.314655\pi\) |
−0.624397 | + | 0.781107i | \(0.714655\pi\) | |||||||
\(578\) | −18.1175 | − | 13.1631i | −0.753588 | − | 0.547514i | ||||
\(579\) | −1.50818 | + | 4.64170i | −0.0626778 | + | 0.192902i | ||||
\(580\) | −17.2852 | − | 53.1984i | −0.717729 | − | 2.20894i | ||||
\(581\) | 2.42705 | − | 1.76336i | 0.100691 | − | 0.0731563i | ||||
\(582\) | −19.1194 | −0.792526 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −15.0000 | −0.620704 | ||||||||
\(585\) | 44.3701 | − | 32.2367i | 1.83448 | − | 1.33282i | ||||
\(586\) | 3.42752 | + | 10.5488i | 0.141589 | + | 0.435767i | ||||
\(587\) | −4.20435 | + | 12.9396i | −0.173532 | + | 0.534076i | −0.999563 | − | 0.0295476i | \(-0.990593\pi\) |
0.826031 | + | 0.563624i | \(0.190593\pi\) | |||||||
\(588\) | 6.15302 | + | 4.47043i | 0.253746 | + | 0.184357i | ||||
\(589\) | −2.42705 | − | 1.76336i | −0.100005 | − | 0.0726578i | ||||
\(590\) | −17.1831 | + | 52.8840i | −0.707415 | + | 2.17720i | ||||
\(591\) | −7.54688 | − | 23.2269i | −0.310437 | − | 0.955427i | ||||
\(592\) | 1.27646 | − | 0.927405i | 0.0524623 | − | 0.0381161i | ||||
\(593\) | −22.6056 | −0.928299 | −0.464149 | − | 0.885757i | \(-0.653640\pi\) | ||||
−0.464149 | + | 0.885757i | \(0.653640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.72498 | −0.398685 | ||||||||
\(596\) | −13.1151 | + | 9.52865i | −0.537214 | + | 0.390309i | ||||
\(597\) | −13.8208 | − | 42.5360i | −0.565647 | − | 1.74088i | ||||
\(598\) | −12.6783 | + | 39.0197i | −0.518453 | + | 1.59563i | ||||
\(599\) | 11.9645 | + | 8.69270i | 0.488855 | + | 0.355174i | 0.804744 | − | 0.593622i | \(-0.202303\pi\) |
−0.315889 | + | 0.948796i | \(0.602303\pi\) | |||||||
\(600\) | −44.7116 | − | 32.4849i | −1.82534 | − | 1.32619i | ||||
\(601\) | 1.79744 | − | 5.53197i | 0.0733193 | − | 0.225654i | −0.907681 | − | 0.419662i | \(-0.862149\pi\) |
0.981000 | + | 0.194008i | \(0.0621488\pi\) | |||||||
\(602\) | 1.20774 | + | 3.71704i | 0.0492238 | + | 0.151495i | ||||
\(603\) | −15.8612 | + | 11.5239i | −0.645919 | + | 0.469288i | ||||
\(604\) | 0.697224 | 0.0283697 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 28.1194 | 1.14227 | ||||||||
\(607\) | −16.6185 | + | 12.0741i | −0.674525 | + | 0.490071i | −0.871537 | − | 0.490330i | \(-0.836876\pi\) |
0.197012 | + | 0.980401i | \(0.436876\pi\) | |||||||
\(608\) | 4.91594 | + | 15.1297i | 0.199368 | + | 0.613591i | ||||
\(609\) | 3.34253 | − | 10.2872i | 0.135446 | − | 0.416860i | ||||
\(610\) | 28.9021 | + | 20.9986i | 1.17021 | + | 0.850209i | ||||
\(611\) | −10.1981 | − | 7.40936i | −0.412571 | − | 0.299751i | ||||
\(612\) | −6.33914 | + | 19.5099i | −0.256244 | + | 0.788639i | ||||
\(613\) | 10.2147 | + | 31.4377i | 0.412568 | + | 1.26976i | 0.914408 | + | 0.404794i | \(0.132657\pi\) |
−0.501839 | + | 0.864961i | \(0.667343\pi\) | |||||||
\(614\) | 30.9876 | − | 22.5138i | 1.25056 | − | 0.908583i | ||||
\(615\) | 58.1194 | 2.34360 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.6333 | 0.870924 | 0.435462 | − | 0.900207i | \(-0.356585\pi\) | ||||
0.435462 | + | 0.900207i | \(0.356585\pi\) | |||||||
\(618\) | 61.3594 | − | 44.5802i | 2.46824 | − | 1.79328i | ||||
\(619\) | 12.3040 | + | 37.8679i | 0.494540 | + | 1.52204i | 0.817672 | + | 0.575685i | \(0.195264\pi\) |
−0.323131 | + | 0.946354i | \(0.604736\pi\) | |||||||
\(620\) | 3.67988 | − | 11.3255i | 0.147787 | − | 0.454843i | ||||
\(621\) | 3.50347 | + | 2.54542i | 0.140590 | + | 0.102144i | ||||
\(622\) | 11.9128 | + | 8.65513i | 0.477658 | + | 0.347039i | ||||
\(623\) | −4.55027 | + | 14.0043i | −0.182303 | + | 0.561070i | ||||
\(624\) | 1.42319 | + | 4.38014i | 0.0569733 | + | 0.175346i | ||||
\(625\) | 0.809017 | − | 0.587785i | 0.0323607 | − | 0.0235114i | ||||
\(626\) | −35.2389 | −1.40843 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.8167 | 0.950388 | ||||||||
\(629\) | −11.3711 | + | 8.26162i | −0.453397 | + | 0.329412i | ||||
\(630\) | −5.90823 | − | 18.1837i | −0.235389 | − | 0.724454i | ||||
\(631\) | −9.59668 | + | 29.5355i | −0.382038 | + | 1.17579i | 0.556569 | + | 0.830802i | \(0.312118\pi\) |
−0.938606 | + | 0.344990i | \(0.887882\pi\) | |||||||
\(632\) | 20.1513 | + | 14.6407i | 0.801574 | + | 0.582378i | ||||
\(633\) | −28.9021 | − | 20.9986i | −1.14876 | − | 0.834620i | ||||
\(634\) | −12.3126 | + | 37.8943i | −0.488996 | + | 1.50497i | ||||
\(635\) | −2.22835 | − | 6.85817i | −0.0884295 | − | 0.272158i | ||||
\(636\) | −79.4252 | + | 57.7058i | −3.14941 | + | 2.28818i | ||||
\(637\) | −6.60555 | −0.261721 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.90833 | −0.391967 | ||||||||
\(640\) | −55.1547 | + | 40.0722i | −2.18018 | + | 1.58399i | ||||
\(641\) | −8.90484 | − | 27.4063i | −0.351720 | − | 1.08248i | −0.957887 | − | 0.287145i | \(-0.907294\pi\) |
0.606167 | − | 0.795337i | \(-0.292706\pi\) | |||||||
\(642\) | −20.3101 | + | 62.5082i | −0.801577 | + | 2.46700i | ||||
\(643\) | 1.00226 | + | 0.728183i | 0.0395252 | + | 0.0287167i | 0.607372 | − | 0.794417i | \(-0.292224\pi\) |
−0.567847 | + | 0.823134i | \(0.692224\pi\) | |||||||
\(644\) | 7.20699 | + | 5.23618i | 0.283995 | + | 0.206335i | ||||
\(645\) | 4.35457 | − | 13.4020i | 0.171461 | − | 0.527702i | ||||
\(646\) | 5.75801 | + | 17.7213i | 0.226546 | + | 0.697236i | ||||
\(647\) | −8.58007 | + | 6.23379i | −0.337317 | + | 0.245075i | −0.743529 | − | 0.668704i | \(-0.766850\pi\) |
0.406212 | + | 0.913779i | \(0.366850\pi\) | |||||||
\(648\) | 31.8167 | 1.24988 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 121.689 | 4.77303 | ||||||||
\(651\) | 1.86298 | − | 1.35354i | 0.0730161 | − | 0.0530493i | ||||
\(652\) | 2.87472 | + | 8.84747i | 0.112583 | + | 0.346493i | ||||
\(653\) | −2.10646 | + | 6.48302i | −0.0824322 | + | 0.253700i | −0.983775 | − | 0.179406i | \(-0.942582\pi\) |
0.901343 | + | 0.433106i | \(0.142582\pi\) | |||||||
\(654\) | −34.3203 | − | 24.9351i | −1.34203 | − | 0.975041i | ||||
\(655\) | −17.5017 | − | 12.7157i | −0.683849 | − | 0.496845i | ||||
\(656\) | −0.654940 | + | 2.01570i | −0.0255711 | + | 0.0786998i | ||||
\(657\) | 3.55798 | + | 10.9503i | 0.138810 | + | 0.427214i | ||||
\(658\) | −3.55518 | + | 2.58299i | −0.138595 | + | 0.100696i | ||||
\(659\) | −4.63331 | −0.180488 | −0.0902440 | − | 0.995920i | \(-0.528765\pi\) | ||||
−0.0902440 | + | 0.995920i | \(0.528765\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.3028 | −0.711895 | −0.355948 | − | 0.934506i | \(-0.615842\pi\) | ||||
−0.355948 | + | 0.934506i | \(0.615842\pi\) | |||||||
\(662\) | 44.3701 | − | 32.2367i | 1.72449 | − | 1.25292i | ||||
\(663\) | −12.6783 | − | 39.0197i | −0.492383 | − | 1.51540i | ||||
\(664\) | 2.78115 | − | 8.55951i | 0.107930 | − | 0.332173i | ||||
\(665\) | −8.75086 | − | 6.35787i | −0.339344 | − | 0.246548i | ||||
\(666\) | −22.3558 | − | 16.2425i | −0.866270 | − | 0.629382i | ||||
\(667\) | 3.91508 | − | 12.0494i | 0.151593 | − | 0.466554i | ||||
\(668\) | 5.31852 | + | 16.3687i | 0.205780 | + | 0.633325i | ||||
\(669\) | 25.9110 | − | 18.8254i | 1.00178 | − | 0.727834i | ||||
\(670\) | −70.6888 | −2.73095 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −12.2111 | −0.471054 | ||||||||
\(673\) | −6.81371 | + | 4.95045i | −0.262649 | + | 0.190826i | −0.711314 | − | 0.702874i | \(-0.751900\pi\) |
0.448665 | + | 0.893700i | \(0.351900\pi\) | |||||||
\(674\) | 8.38894 | + | 25.8185i | 0.323130 | + | 0.994492i | ||||
\(675\) | 3.96914 | − | 12.2158i | 0.152772 | − | 0.470185i | ||||
\(676\) | −81.8522 | − | 59.4691i | −3.14816 | − | 2.28727i | ||||
\(677\) | 8.33512 | + | 6.05582i | 0.320345 | + | 0.232744i | 0.736323 | − | 0.676631i | \(-0.236561\pi\) |
−0.415978 | + | 0.909375i | \(0.636561\pi\) | |||||||
\(678\) | −17.5290 | + | 53.9487i | −0.673197 | + | 2.07189i | ||||
\(679\) | −1.11418 | − | 3.42908i | −0.0427582 | − | 0.131596i | ||||
\(680\) | −23.6030 | + | 17.1486i | −0.905135 | + | 0.657619i | ||||
\(681\) | 15.0000 | 0.574801 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.6972 | 0.600638 | 0.300319 | − | 0.953839i | \(-0.402907\pi\) | ||||
0.300319 | + | 0.953839i | \(0.402907\pi\) | |||||||
\(684\) | −18.4591 | + | 13.4113i | −0.705800 | + | 0.512794i | ||||
\(685\) | −11.2748 | − | 34.7004i | −0.430789 | − | 1.32583i | ||||
\(686\) | −0.711597 | + | 2.19007i | −0.0271689 | + | 0.0836173i | ||||
\(687\) | −4.85410 | − | 3.52671i | −0.185196 | − | 0.134552i | ||||
\(688\) | 0.415736 | + | 0.302050i | 0.0158498 | + | 0.0115155i | ||||
\(689\) | 26.3488 | − | 81.0934i | 1.00381 | − | 3.08941i | ||||
\(690\) | −15.9358 | − | 49.0454i | −0.606666 | − | 1.86713i | ||||
\(691\) | 13.7757 | − | 10.0087i | 0.524054 | − | 0.380748i | −0.294075 | − | 0.955782i | \(-0.595012\pi\) |
0.818129 | + | 0.575035i | \(0.195012\pi\) | |||||||
\(692\) | 4.30278 | 0.163567 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.1194 | 0.839642 | ||||||||
\(695\) | 63.0224 | − | 45.7884i | 2.39057 | − | 1.73685i | ||||
\(696\) | −10.0276 | − | 30.8617i | −0.380095 | − | 1.16981i | ||||
\(697\) | 5.83442 | − | 17.9565i | 0.220994 | − | 0.680151i | ||||
\(698\) | 8.75086 | + | 6.35787i | 0.331225 | + | 0.240649i | ||||
\(699\) | −33.5337 | − | 24.3637i | −1.26836 | − | 0.921519i | ||||
\(700\) | 8.16491 | − | 25.1290i | 0.308605 | − | 0.949787i | ||||
\(701\) | 9.61643 | + | 29.5963i | 0.363208 | + | 1.11784i | 0.951096 | + | 0.308896i | \(0.0999595\pi\) |
−0.587888 | + | 0.808942i | \(0.700040\pi\) | |||||||
\(702\) | −19.7580 | + | 14.3550i | −0.745717 | + | 0.541795i | ||||
\(703\) | −15.6333 | −0.589621 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.8444 | 0.596735 | ||||||||
\(706\) | 9.48571 | − | 6.89177i | 0.356999 | − | 0.259375i | ||||
\(707\) | 1.63865 | + | 5.04324i | 0.0616277 | + | 0.189671i | ||||
\(708\) | −15.7401 | + | 48.4431i | −0.591550 | + | 1.82060i | ||||
\(709\) | −20.4928 | − | 14.8889i | −0.769624 | − | 0.559165i | 0.132223 | − | 0.991220i | \(-0.457789\pi\) |
−0.901847 | + | 0.432055i | \(0.857789\pi\) | |||||||
\(710\) | −28.9021 | − | 20.9986i | −1.08468 | − | 0.788064i | ||||
\(711\) | 5.90823 | − | 18.1837i | 0.221576 | − | 0.681940i | ||||
\(712\) | 13.6508 | + | 42.0129i | 0.511586 | + | 1.57450i | ||||
\(713\) | 2.18210 | − | 1.58539i | 0.0817203 | − | 0.0593733i | ||||
\(714\) | −14.3028 | −0.535268 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −21.1194 | −0.789270 | ||||||||
\(717\) | −49.0534 | + | 35.6394i | −1.83193 | + | 1.33098i | ||||
\(718\) | −24.1488 | − | 74.3224i | −0.901226 | − | 2.77369i | ||||
\(719\) | 6.56317 | − | 20.1994i | 0.244765 | − | 0.753309i | −0.750910 | − | 0.660404i | \(-0.770385\pi\) |
0.995675 | − | 0.0929045i | \(-0.0296151\pi\) | |||||||
\(720\) | −2.03377 | − | 1.47762i | −0.0757941 | − | 0.0550677i | ||||
\(721\) | 11.5712 | + | 8.40696i | 0.430934 | + | 0.313092i | ||||
\(722\) | 7.11597 | − | 21.9007i | 0.264829 | − | 0.815060i | ||||
\(723\) | 0.345923 | + | 1.06464i | 0.0128650 | + | 0.0395944i | ||||
\(724\) | 67.3641 | − | 48.9429i | 2.50357 | − | 1.81895i | ||||
\(725\) | −37.5778 | −1.39560 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.1194 | 0.894540 | 0.447270 | − | 0.894399i | \(-0.352396\pi\) | ||||
0.447270 | + | 0.894399i | \(0.352396\pi\) | |||||||
\(728\) | −16.0320 | + | 11.6479i | −0.594186 | + | 0.431701i | ||||
\(729\) | −4.11936 | − | 12.6781i | −0.152569 | − | 0.469559i | ||||
\(730\) | −12.8285 | + | 39.4820i | −0.474804 | + | 1.46130i | ||||
\(731\) | −3.70351 | − | 2.69076i | −0.136979 | − | 0.0995214i | ||||
\(732\) | 26.4751 | + | 19.2353i | 0.978547 | + | 0.710956i | ||||
\(733\) | 2.09788 | − | 6.45663i | 0.0774871 | − | 0.238481i | −0.904808 | − | 0.425819i | \(-0.859986\pi\) |
0.982295 | + | 0.187338i | \(0.0599860\pi\) | |||||||
\(734\) | 12.5478 | + | 38.6182i | 0.463148 | + | 1.42542i | ||||
\(735\) | 6.71709 | − | 4.88025i | 0.247763 | − | 0.180011i | ||||
\(736\) | −14.3028 | −0.527207 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 37.1194 | 1.36639 | ||||||||
\(739\) | −34.8844 | + | 25.3450i | −1.28324 | + | 0.932330i | −0.999646 | − | 0.0266143i | \(-0.991527\pi\) |
−0.283596 | + | 0.958944i | \(0.591527\pi\) | |||||||
\(740\) | −19.1762 | − | 59.0183i | −0.704931 | − | 2.16956i | ||||
\(741\) | 14.1015 | − | 43.3999i | 0.518030 | − | 1.59433i | ||||
\(742\) | −24.0480 | − | 17.4719i | −0.882830 | − | 0.641414i | ||||
\(743\) | 36.3541 | + | 26.4128i | 1.33370 | + | 0.968990i | 0.999651 | + | 0.0264352i | \(0.00841558\pi\) |
0.334050 | + | 0.942555i | \(0.391584\pi\) | |||||||
\(744\) | 2.13479 | − | 6.57021i | 0.0782652 | − | 0.240876i | ||||
\(745\) | 5.46874 | + | 16.8311i | 0.200359 | + | 0.616642i | ||||
\(746\) | 37.4822 | − | 27.2324i | 1.37232 | − | 0.997049i | ||||
\(747\) | −6.90833 | −0.252762 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.3944 | −0.452883 | ||||||||
\(750\) | −46.4038 | + | 33.7144i | −1.69443 | + | 1.23107i | ||||
\(751\) | 2.35882 | + | 7.25971i | 0.0860746 | + | 0.264910i | 0.984825 | − | 0.173550i | \(-0.0555239\pi\) |
−0.898750 | + | 0.438461i | \(0.855524\pi\) | |||||||
\(752\) | −0.178548 | + | 0.549516i | −0.00651099 | + | 0.0200388i | ||||
\(753\) | 8.18679 | + | 5.94805i | 0.298343 | + | 0.216759i | ||||
\(754\) | 57.8042 | + | 41.9972i | 2.10511 | + | 1.52945i | ||||
\(755\) | 0.235206 | − | 0.723888i | 0.00856001 | − | 0.0263450i | ||||
\(756\) | 1.63865 | + | 5.04324i | 0.0595970 | + | 0.183421i | ||||
\(757\) | 19.2681 | − | 13.9991i | 0.700310 | − | 0.508805i | −0.179723 | − | 0.983717i | \(-0.557520\pi\) |
0.880033 | + | 0.474912i | \(0.157520\pi\) | |||||||
\(758\) | 36.4222 | 1.32291 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −32.4500 | −1.17708 | ||||||||
\(761\) | 33.9787 | − | 24.6870i | 1.23173 | − | 0.894902i | 0.234709 | − | 0.972066i | \(-0.424586\pi\) |
0.997018 | + | 0.0771633i | \(0.0245863\pi\) | |||||||
\(762\) | −3.27730 | − | 10.0865i | −0.118724 | − | 0.365395i | ||||
\(763\) | 2.47214 | − | 7.60845i | 0.0894973 | − | 0.275444i | ||||
\(764\) | 71.6541 | + | 52.0598i | 2.59236 | + | 1.88346i | ||||
\(765\) | 18.1175 | + | 13.1631i | 0.655039 | + | 0.475914i | ||||
\(766\) | −27.4913 | + | 84.6096i | −0.993302 | + | 3.05707i | ||||
\(767\) | −13.6706 | − | 42.0737i | −0.493615 | − | 1.51919i | ||||
\(768\) | −33.3629 | + | 24.2396i | −1.20388 | + | 0.874671i | ||||
\(769\) | 39.3305 | 1.41830 | 0.709148 | − | 0.705060i | \(-0.249080\pi\) | ||||
0.709148 | + | 0.705060i | \(0.249080\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.9361 | −0.537910 | ||||||||
\(772\) | −5.66312 | + | 4.11450i | −0.203820 | + | 0.148084i | ||||
\(773\) | 9.46621 | + | 29.1340i | 0.340476 | + | 1.04788i | 0.963961 | + | 0.266042i | \(0.0857161\pi\) |
−0.623485 | + | 0.781835i | \(0.714284\pi\) | |||||||
\(774\) | 2.78115 | − | 8.55951i | 0.0999665 | − | 0.307665i | ||||
\(775\) | −6.47214 | − | 4.70228i | −0.232486 | − | 0.168911i | ||||
\(776\) | −8.75086 | − | 6.35787i | −0.314137 | − | 0.228234i | ||||
\(777\) | 3.70820 | − | 11.4127i | 0.133031 | − | 0.409428i | ||||
\(778\) | 5.56231 | + | 17.1190i | 0.199418 | + | 0.613747i | ||||
\(779\) | 16.9894 | − | 12.3435i | 0.608707 | − | 0.442251i | ||||
\(780\) | 181.139 | 6.48581 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −16.7527 | −0.599077 | ||||||||
\(783\) | 6.10131 | − | 4.43286i | 0.218043 | − | 0.158418i | ||||
\(784\) | 0.0935628 | + | 0.287957i | 0.00334153 | + | 0.0102842i | ||||
\(785\) | 8.03444 | − | 24.7275i | 0.286762 | − | 0.882561i | ||||
\(786\) | −25.7402 | − | 18.7014i | −0.918123 | − | 0.667055i | ||||
\(787\) | −18.1917 | − | 13.2170i | −0.648462 | − | 0.471136i | 0.214285 | − | 0.976771i | \(-0.431258\pi\) |
−0.862747 | + | 0.505636i | \(0.831258\pi\) | |||||||
\(788\) | 10.8242 | − | 33.3134i | 0.385595 | − | 1.18674i | ||||
\(789\) | 14.4019 | + | 44.3245i | 0.512721 | + | 1.57799i | ||||
\(790\) | 55.7705 | − | 40.5196i | 1.98422 | − | 1.44162i | ||||
\(791\) | −10.6972 | −0.380350 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.4222 | −1.00930 | ||||||||
\(794\) | 56.2828 | − | 40.8919i | 1.99740 | − | 1.45120i | ||||
\(795\) | 33.1189 | + | 101.929i | 1.17461 | + | 3.61506i | ||||
\(796\) | 19.8226 | − | 61.0076i | 0.702592 | − | 2.16236i | ||||
\(797\) | 23.1648 | + | 16.8302i | 0.820540 | + | 0.596158i | 0.916867 | − | 0.399192i | \(-0.130709\pi\) |
−0.0963268 | + | 0.995350i | \(0.530709\pi\) | |||||||
\(798\) | −12.8701 | − | 9.35068i | −0.455597 | − | 0.331010i | ||||
\(799\) | 1.59057 | − | 4.89526i | 0.0562702 | − | 0.173182i | ||||
\(800\) | 13.1092 | + | 40.3459i | 0.463480 | + | 1.42644i | ||||
\(801\) | 27.4324 | − | 19.9308i | 0.969277 | − | 0.704221i | ||||
\(802\) | 48.8444 | 1.72476 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −64.7527 | −2.28365 | ||||||||
\(805\) | 7.86767 | − | 5.71620i | 0.277299 | − | 0.201470i | ||||
\(806\) | 4.70049 | + | 14.4666i | 0.165568 | + | 0.509565i | ||||
\(807\) | −11.4705 | + | 35.3027i | −0.403782 | + | 1.24271i | ||||
\(808\) | 12.8701 | + | 9.35068i | 0.452769 | + | 0.328956i | ||||
\(809\) | 6.54630 | + | 4.75617i | 0.230156 | + | 0.167218i | 0.696886 | − | 0.717182i | \(-0.254568\pi\) |
−0.466731 | + | 0.884400i | \(0.654568\pi\) | |||||||
\(810\) | 27.2106 | − | 83.7458i | 0.956085 | − | 2.94253i | ||||
\(811\) | 12.6216 | + | 38.8453i | 0.443205 | + | 1.36404i | 0.884440 | + | 0.466653i | \(0.154540\pi\) |
−0.441236 | + | 0.897391i | \(0.645460\pi\) | |||||||
\(812\) | 12.5510 | − | 9.11883i | 0.440453 | − | 0.320008i | ||||
\(813\) | −65.6611 | −2.30283 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.1556 | 0.355735 | ||||||||
\(816\) | −1.52141 | + | 1.10537i | −0.0532601 | + | 0.0386957i | ||||
\(817\) | −1.57341 | − | 4.84247i | −0.0550468 | − | 0.169417i | ||||
\(818\) | 14.6628 | − | 45.1276i | 0.512674 | − | 1.57785i | ||||
\(819\) | 12.3060 | + | 8.94086i | 0.430008 | + | 0.312419i | ||||
\(820\) | 67.4383 | + | 48.9968i | 2.35505 | + | 1.71104i | ||||
\(821\) | 8.47393 | − | 26.0801i | 0.295742 | − | 0.910201i | −0.687229 | − | 0.726441i | \(-0.741173\pi\) |
0.982971 | − | 0.183760i | \(-0.0588269\pi\) | |||||||
\(822\) | −16.5822 | − | 51.0347i | −0.578370 | − | 1.78004i | ||||
\(823\) | −28.4864 | + | 20.6966i | −0.992973 | + | 0.721437i | −0.960570 | − | 0.278038i | \(-0.910316\pi\) |
−0.0324027 | + | 0.999475i | \(0.510316\pi\) | |||||||
\(824\) | 42.9083 | 1.49478 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.4222 | −0.536607 | ||||||||
\(827\) | −11.4746 | + | 8.33676i | −0.399010 | + | 0.289898i | −0.769138 | − | 0.639083i | \(-0.779314\pi\) |
0.370128 | + | 0.928981i | \(0.379314\pi\) | |||||||
\(828\) | −6.33914 | − | 19.5099i | −0.220300 | − | 0.678014i | ||||
\(829\) | 4.10221 | − | 12.6253i | 0.142476 | − | 0.438495i | −0.854202 | − | 0.519941i | \(-0.825954\pi\) |
0.996678 | + | 0.0814464i | \(0.0259539\pi\) | |||||||
\(830\) | −20.1513 | − | 14.6407i | −0.699460 | − | 0.508188i | ||||
\(831\) | −55.7705 | − | 40.5196i | −1.93466 | − | 1.40561i | ||||
\(832\) | 26.1617 | − | 80.5175i | 0.906994 | − | 2.79144i | ||||
\(833\) | −0.833488 | − | 2.56521i | −0.0288787 | − | 0.0888794i | ||||
\(834\) | 92.6886 | − | 67.3422i | 3.20954 | − | 2.33187i | ||||
\(835\) | 18.7889 | 0.650217 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.60555 | 0.0554960 | ||||||||
\(838\) | −71.5800 | + | 52.0059i | −2.47269 | + | 1.79651i | ||||
\(839\) | 13.0439 | + | 40.1451i | 0.450327 | + | 1.38596i | 0.876535 | + | 0.481339i | \(0.159849\pi\) |
−0.426208 | + | 0.904625i | \(0.640151\pi\) | |||||||
\(840\) | 7.69710 | − | 23.6892i | 0.265575 | − | 0.817356i | ||||
\(841\) | 5.61141 | + | 4.07693i | 0.193497 | + | 0.140584i | ||||
\(842\) | −40.6441 | − | 29.5297i | −1.40069 | − | 1.01766i | ||||
\(843\) | 4.55027 | − | 14.0043i | 0.156720 | − | 0.482333i | ||||
\(844\) | −15.8337 | − | 48.7311i | −0.545018 | − | 1.67739i | ||||
\(845\) | −89.3559 | + | 64.9209i | −3.07394 | + | 2.23335i | ||||
\(846\) | 10.1194 | 0.347913 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.90833 | −0.134212 | ||||||||
\(849\) | −8.18679 | + | 5.94805i | −0.280970 | + | 0.204137i | ||||
\(850\) | 15.3547 | + | 47.2569i | 0.526662 | + | 1.62090i | ||||
\(851\) | 4.34339 | − | 13.3676i | 0.148890 | − | 0.458235i | ||||
\(852\) | −26.4751 | − | 19.2353i | −0.907021 | − | 0.658989i | ||||
\(853\) | −36.9923 | − | 26.8765i | −1.26659 | − | 0.920233i | −0.267530 | − | 0.963549i | \(-0.586208\pi\) |
−0.999061 | + | 0.0433166i | \(0.986208\pi\) | |||||||
\(854\) | −3.06184 | + | 9.42338i | −0.104774 | + | 0.322461i | ||||
\(855\) | 7.69710 | + | 23.6892i | 0.263235 | + | 0.810154i | ||||
\(856\) | −30.0820 | + | 21.8558i | −1.02818 | + | 0.747017i | ||||
\(857\) | −35.3583 | −1.20782 | −0.603908 | − | 0.797054i | \(-0.706391\pi\) | ||||
−0.603908 | + | 0.797054i | \(0.706391\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.3028 | −0.863320 | −0.431660 | − | 0.902036i | \(-0.642072\pi\) | ||||
−0.431660 | + | 0.902036i | \(0.642072\pi\) | |||||||
\(860\) | 16.3511 | − | 11.8798i | 0.557569 | − | 0.405097i | ||||
\(861\) | 4.98118 | + | 15.3305i | 0.169758 | + | 0.522462i | ||||
\(862\) | −2.21978 | + | 6.83177i | −0.0756059 | + | 0.232691i | ||||
\(863\) | −25.4211 | − | 18.4695i | −0.865344 | − | 0.628709i | 0.0639894 | − | 0.997951i | \(-0.479618\pi\) |
−0.929334 | + | 0.369241i | \(0.879618\pi\) | |||||||
\(864\) | −6.88787 | − | 5.00433i | −0.234330 | − | 0.170251i | ||||
\(865\) | 1.45152 | − | 4.46733i | 0.0493532 | − | 0.151894i | ||||
\(866\) | −20.7410 | − | 63.8344i | −0.704809 | − | 2.16918i | ||||
\(867\) | −18.1175 | + | 13.1631i | −0.615302 | + | 0.447043i | ||||
\(868\) | 3.30278 | 0.112104 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −89.8082 | −3.04478 | ||||||||
\(871\) | 45.4982 | − | 33.0564i | 1.54165 | − | 1.12007i | ||||
\(872\) | −7.41641 | − | 22.8254i | −0.251151 | − | 0.772964i | ||||
\(873\) | −2.56570 | + | 7.89641i | −0.0868357 | + | 0.267253i | ||||
\(874\) | −15.0747 | − | 10.9524i | −0.509908 | − | 0.370470i | ||||
\(875\) | −8.75086 | − | 6.35787i | −0.295833 | − | 0.214935i | ||||
\(876\) | −11.7512 | + | 36.1665i | −0.397037 | + | 1.22195i | ||||
\(877\) | −14.5410 | − | 44.7525i | −0.491013 | − | 1.51118i | −0.823079 | − | 0.567927i | \(-0.807746\pi\) |
0.332066 | − | 0.943256i | \(-0.392254\pi\) | |||||||
\(878\) | −51.6512 | + | 37.5268i | −1.74314 | + | 1.26647i | ||||
\(879\) | 11.0917 | 0.374113 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.3305 | 1.15663 | 0.578313 | − | 0.815815i | \(-0.303711\pi\) | ||||
0.578313 | + | 0.815815i | \(0.303711\pi\) | |||||||
\(882\) | 4.29004 | − | 3.11689i | 0.144453 | − | 0.104951i | ||||
\(883\) | −2.38715 | − | 7.34689i | −0.0803340 | − | 0.247243i | 0.902821 | − | 0.430017i | \(-0.141492\pi\) |
−0.983155 | + | 0.182774i | \(0.941492\pi\) | |||||||
\(884\) | 18.1839 | − | 55.9644i | 0.611592 | − | 1.88229i | ||||
\(885\) | 44.9858 | + | 32.6841i | 1.51218 | + | 1.09866i | ||||
\(886\) | 50.1815 | + | 36.4590i | 1.68588 | + | 1.22486i | ||||
\(887\) | −13.6337 | + | 41.9601i | −0.457773 | + | 1.40888i | 0.410075 | + | 0.912052i | \(0.365503\pi\) |
−0.867848 | + | 0.496829i | \(0.834497\pi\) | |||||||
\(888\) | −11.1246 | − | 34.2380i | −0.373318 | − | 1.14895i | ||||
\(889\) | 1.61803 | − | 1.17557i | 0.0542671 | − | 0.0394274i | ||||
\(890\) | 122.258 | 4.09810 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 45.9361 | 1.53805 | ||||||||
\(893\) | 4.63161 | − | 3.36506i | 0.154991 | − | 0.112607i | ||||
\(894\) | 8.04302 | + | 24.7539i | 0.268999 | + | 0.827893i | ||||
\(895\) | −7.12455 | + | 21.9271i | −0.238147 | + | 0.732942i | ||||
\(896\) | −15.2972 | − | 11.1140i | −0.511042 | − | 0.371294i | ||||
\(897\) | 33.1922 | + | 24.1155i | 1.10825 | + | 0.805193i | ||||
\(898\) | −28.6991 | + | 88.3267i | −0.957701 | + | 2.94750i | ||||
\(899\) | −1.45152 | − | 4.46733i | −0.0484110 | − | 0.148994i | ||||
\(900\) | −49.2242 | + | 35.7634i | −1.64081 | + | 1.19211i | ||||
\(901\) | 34.8167 | 1.15991 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.90833 | 0.130061 | ||||||||
\(904\) | −25.9627 | + | 18.8630i | −0.863507 | + | 0.627374i | ||||
\(905\) | −28.0896 | − | 86.4510i | −0.933731 | − | 2.87373i | ||||
\(906\) | 0.345923 | − | 1.06464i | 0.0114925 | − | 0.0353703i | ||||
\(907\) | −0.319116 | − | 0.231851i | −0.0105961 | − | 0.00769849i | 0.582475 | − | 0.812849i | \(-0.302085\pi\) |
−0.593071 | + | 0.805150i | \(0.702085\pi\) | |||||||
\(908\) | 17.4051 | + | 12.6455i | 0.577608 | + | 0.419657i | ||||
\(909\) | 3.77344 | − | 11.6134i | 0.125157 | − | 0.385194i | ||||
\(910\) | 16.9479 | + | 52.1601i | 0.561816 | + | 1.72909i | ||||
\(911\) | 40.8149 | − | 29.6537i | 1.35226 | − | 0.982472i | 0.353362 | − | 0.935487i | \(-0.385039\pi\) |
0.998896 | − | 0.0469855i | \(-0.0149615\pi\) | |||||||
\(912\) | −2.09167 | −0.0692622 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 48.6333 | 1.60865 | ||||||||
\(915\) | 28.9021 | − | 20.9986i | 0.955474 | − | 0.694193i | ||||
\(916\) | −2.65926 | − | 8.18437i | −0.0878645 | − | 0.270419i | ||||
\(917\) | 1.85410 | − | 5.70634i | 0.0612278 | − | 0.188440i | ||||
\(918\) | −8.06771 | − | 5.86154i | −0.266274 | − | 0.193460i | ||||
\(919\) | 44.8824 | + | 32.6090i | 1.48053 | + | 1.07567i | 0.977384 | + | 0.211472i | \(0.0678258\pi\) |
0.503150 | + | 0.864199i | \(0.332174\pi\) | |||||||
\(920\) | 9.01555 | − | 27.7470i | 0.297234 | − | 0.914792i | ||||
\(921\) | −11.8362 | − | 36.4281i | −0.390016 | − | 1.20035i | ||||
\(922\) | −15.0747 | + | 10.9524i | −0.496458 | + | 0.360698i | ||||
\(923\) | 28.4222 | 0.935528 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.6888 | −1.37072 | ||||||||
\(926\) | −57.4110 | + | 41.7115i | −1.88664 | + | 1.37072i | ||||
\(927\) | −10.1778 | − | 31.3241i | −0.334283 | − | 1.02882i | ||||
\(928\) | −7.69710 | + | 23.6892i | −0.252670 | + | 0.777637i | ||||
\(929\) | 22.3558 | + | 16.2425i | 0.733471 | + | 0.532898i | 0.890659 | − | 0.454671i | \(-0.150243\pi\) |
−0.157189 | + | 0.987569i | \(0.550243\pi\) | |||||||
\(930\) | −15.4679 | − | 11.2381i | −0.507214 | − | 0.368512i | ||||
\(931\) | 0.927051 | − | 2.85317i | 0.0303829 | − | 0.0935089i | ||||
\(932\) | −18.3710 | − | 56.5403i | −0.601764 | − | 1.85204i | ||||
\(933\) | 11.9128 | − | 8.65513i | 0.390006 | − | 0.283356i | ||||
\(934\) | 31.1833 | 1.02035 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 45.6333 | 1.49157 | ||||||||
\(937\) | 25.5694 | − | 18.5773i | 0.835317 | − | 0.606893i | −0.0857417 | − | 0.996317i | \(-0.527326\pi\) |
0.921059 | + | 0.389424i | \(0.127326\pi\) | |||||||
\(938\) | −6.05845 | − | 18.6460i | −0.197815 | − | 0.608813i | ||||
\(939\) | −10.8894 | + | 33.5141i | −0.355362 | + | 1.09369i | ||||
\(940\) | 18.3849 | + | 13.3574i | 0.599649 | + | 0.435671i | ||||
\(941\) | 30.2752 | + | 21.9962i | 0.986943 | + | 0.717056i | 0.959250 | − | 0.282560i | \(-0.0911837\pi\) |
0.0276937 | + | 0.999616i | \(0.491184\pi\) | |||||||
\(942\) | 11.8165 | − | 36.3673i | 0.385001 | − | 1.18491i | ||||
\(943\) | 5.83442 | + | 17.9565i | 0.189995 | + | 0.584744i | ||||
\(944\) | −1.64049 | + | 1.19189i | −0.0533934 | + | 0.0387926i | ||||
\(945\) | 5.78890 | 0.188313 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.6611 | 1.51628 | 0.758140 | − | 0.652091i | \(-0.226108\pi\) | ||||
0.758140 | + | 0.652091i | \(0.226108\pi\) | |||||||
\(948\) | 51.0871 | − | 37.1170i | 1.65923 | − | 1.20550i | ||||
\(949\) | −10.2061 | − | 31.4113i | −0.331305 | − | 1.01965i | ||||
\(950\) | −17.0783 | + | 52.5617i | −0.554094 | + | 1.70533i | ||||
\(951\) | 32.2348 | + | 23.4200i | 1.04529 | + | 0.759444i | ||||
\(952\) | −6.54630 | − | 4.75617i | −0.212167 | − | 0.154148i | ||||
\(953\) | 1.86268 | − | 5.73274i | 0.0603381 | − | 0.185702i | −0.916344 | − | 0.400392i | \(-0.868874\pi\) |
0.976682 | + | 0.214690i | \(0.0688741\pi\) | |||||||
\(954\) | 21.1522 | + | 65.0998i | 0.684828 | + | 2.10768i | ||||
\(955\) | 78.2229 | − | 56.8323i | 2.53123 | − | 1.83905i | ||||
\(956\) | −86.9638 | −2.81261 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −65.9361 | −2.13030 | ||||||||
\(959\) | 8.18679 | − | 5.94805i | 0.264365 | − | 0.192073i | ||||
\(960\) | 32.8837 | + | 101.206i | 1.06132 | + | 3.26639i | ||||
\(961\) | −9.27051 | + | 28.5317i | −0.299049 | + | 0.920377i | ||||
\(962\) | 64.1280 | + | 46.5917i | 2.06757 | + | 1.50218i | ||||
\(963\) | 23.0907 | + | 16.7764i | 0.744086 | + | 0.540610i | ||||
\(964\) | −0.496143 | + | 1.52697i | −0.0159797 | + | 0.0491804i | ||||
\(965\) | 2.36142 | + | 7.26770i | 0.0760168 | + | 0.233956i | ||||
\(966\) | 11.5712 | − | 8.40696i | 0.372297 | − | 0.270490i | ||||
\(967\) | −40.5139 | −1.30284 | −0.651419 | − | 0.758718i | \(-0.725826\pi\) | ||||
−0.651419 | + | 0.758718i | \(0.725826\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.6333 | 0.598588 | ||||||||
\(970\) | −24.2188 | + | 17.5960i | −0.777619 | + | 0.564973i | ||||
\(971\) | −1.96742 | − | 6.05508i | −0.0631374 | − | 0.194317i | 0.914512 | − | 0.404559i | \(-0.132575\pi\) |
−0.977649 | + | 0.210242i | \(0.932575\pi\) | |||||||
\(972\) | 20.0097 | − | 61.5835i | 0.641811 | − | 1.97529i | ||||
\(973\) | 17.4793 | + | 12.6994i | 0.560359 | + | 0.407125i | ||||
\(974\) | −5.24738 | − | 3.81245i | −0.168137 | − | 0.122159i | ||||
\(975\) | 37.6039 | − | 115.733i | 1.20429 | − | 3.70642i | ||||
\(976\) | 0.402580 | + | 1.23901i | 0.0128863 | + | 0.0396598i | ||||
\(977\) | −32.3831 | + | 23.5277i | −1.03603 | + | 0.752719i | −0.969506 | − | 0.245066i | \(-0.921190\pi\) |
−0.0665220 | + | 0.997785i | \(0.521190\pi\) | |||||||
\(978\) | 14.9361 | 0.477603 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 11.9083 | 0.380398 | ||||||||
\(981\) | −14.9039 | + | 10.8283i | −0.475844 | + | 0.345721i | ||||
\(982\) | −9.03530 | − | 27.8078i | −0.288328 | − | 0.887383i | ||||
\(983\) | −2.86614 | + | 8.82107i | −0.0914156 | + | 0.281348i | −0.986303 | − | 0.164944i | \(-0.947256\pi\) |
0.894887 | + | 0.446292i | \(0.147256\pi\) | |||||||
\(984\) | 39.1227 | + | 28.4243i | 1.24719 | + | 0.906133i | ||||
\(985\) | −30.9359 | − | 22.4762i | −0.985699 | − | 0.716152i | ||||
\(986\) | −9.01555 | + | 27.7470i | −0.287114 | + | 0.883645i | ||||
\(987\) | 1.35796 | + | 4.17937i | 0.0432243 | + | 0.133031i | ||||
\(988\) | 52.9501 | − | 38.4705i | 1.68457 | − | 1.22391i | ||||
\(989\) | 4.57779 | 0.145565 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.7250 | −1.38897 | −0.694485 | − | 0.719507i | \(-0.744368\pi\) | ||||
−0.694485 | + | 0.719507i | \(0.744368\pi\) | |||||||
\(992\) | −4.29004 | + | 3.11689i | −0.136209 | + | 0.0989615i | ||||
\(993\) | −16.9479 | − | 52.1601i | −0.537824 | − | 1.65525i | ||||
\(994\) | 3.06184 | − | 9.42338i | 0.0971157 | − | 0.298891i | ||||
\(995\) | −56.6536 | − | 41.1613i | −1.79604 | − | 1.30490i | ||||
\(996\) | −18.4591 | − | 13.4113i | −0.584898 | − | 0.424953i | ||||
\(997\) | −14.1212 | + | 43.4606i | −0.447223 | + | 1.37641i | 0.432803 | + | 0.901488i | \(0.357524\pi\) |
−0.880027 | + | 0.474924i | \(0.842476\pi\) | |||||||
\(998\) | −2.06956 | − | 6.36944i | −0.0655107 | − | 0.201621i | ||||
\(999\) | 6.76880 | − | 4.91782i | 0.214155 | − | 0.155593i |
(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 | 847.2.f.r.729.2 | 8 | ||
11.2 | odd | 10 | 847.2.a.g.1.2 | yes | 2 | ||
11.3 | even | 5 | inner | 847.2.f.r.148.1 | 8 | ||
11.4 | even | 5 | inner | 847.2.f.r.323.2 | 8 | ||
11.5 | even | 5 | inner | 847.2.f.r.372.1 | 8 | ||
11.6 | odd | 10 | 847.2.f.o.372.2 | 8 | |||
11.7 | odd | 10 | 847.2.f.o.323.1 | 8 | |||
11.8 | odd | 10 | 847.2.f.o.148.2 | 8 | |||
11.9 | even | 5 | 847.2.a.e.1.1 | ✓ | 2 | ||
11.10 | odd | 2 | 847.2.f.o.729.1 | 8 | |||
33.2 | even | 10 | 7623.2.a.bc.1.1 | 2 | |||
33.20 | odd | 10 | 7623.2.a.bs.1.2 | 2 | |||
77.13 | even | 10 | 5929.2.a.p.1.2 | 2 | |||
77.20 | odd | 10 | 5929.2.a.k.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.e.1.1 | ✓ | 2 | 11.9 | even | 5 | ||
847.2.a.g.1.2 | yes | 2 | 11.2 | odd | 10 | ||
847.2.f.o.148.2 | 8 | 11.8 | odd | 10 | |||
847.2.f.o.323.1 | 8 | 11.7 | odd | 10 | |||
847.2.f.o.372.2 | 8 | 11.6 | odd | 10 | |||
847.2.f.o.729.1 | 8 | 11.10 | odd | 2 | |||
847.2.f.r.148.1 | 8 | 11.3 | even | 5 | inner | ||
847.2.f.r.323.2 | 8 | 11.4 | even | 5 | inner | ||
847.2.f.r.372.1 | 8 | 11.5 | even | 5 | inner | ||
847.2.f.r.729.2 | 8 | 1.1 | even | 1 | trivial | ||
5929.2.a.k.1.1 | 2 | 77.20 | odd | 10 | |||
5929.2.a.p.1.2 | 2 | 77.13 | even | 10 | |||
7623.2.a.bc.1.1 | 2 | 33.2 | even | 10 | |||
7623.2.a.bs.1.2 | 2 | 33.20 | odd | 10 |