Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,3,Mod(3,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.3");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.f (of order \(20\), degree \(8\), 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: | \(1.36240132180\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{20})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 17.2 | ||
Character | \(\chi\) | \(=\) | 50.17 |
Dual form | 50.3.f.b.3.2 |
$q$-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 \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).
\(n\) | \(27\) |
\(\chi(n)\) | \(e\left(\frac{13}{20}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.642040 | − | 1.26007i | 0.321020 | − | 0.630037i | ||||
\(3\) | 0.304004 | − | 1.91941i | 0.101335 | − | 0.639802i | −0.883780 | − | 0.467903i | \(-0.845010\pi\) |
0.985115 | − | 0.171899i | \(-0.0549903\pi\) | |||||||
\(4\) | −1.17557 | − | 1.61803i | −0.293893 | − | 0.404508i | ||||
\(5\) | −3.29532 | − | 3.76044i | −0.659063 | − | 0.752088i | ||||
\(6\) | −2.22341 | − | 1.61540i | −0.370568 | − | 0.269234i | ||||
\(7\) | 6.96775 | + | 6.96775i | 0.995393 | + | 0.995393i | 0.999989 | − | 0.00459653i | \(-0.00146312\pi\) |
−0.00459653 | + | 0.999989i | \(0.501463\pi\) | |||||||
\(8\) | −2.79360 | + | 0.442463i | −0.349201 | + | 0.0553079i | ||||
\(9\) | 4.96781 | + | 1.61414i | 0.551979 | + | 0.179349i | ||||
\(10\) | −6.85415 | + | 1.73799i | −0.685415 | + | 0.173799i | ||||
\(11\) | −2.27872 | − | 7.01318i | −0.207157 | − | 0.637562i | −0.999618 | − | 0.0276401i | \(-0.991201\pi\) |
0.792461 | − | 0.609922i | \(-0.208799\pi\) | |||||||
\(12\) | −3.46304 | + | 1.76451i | −0.288587 | + | 0.147042i | ||||
\(13\) | 2.19652 | + | 4.31091i | 0.168963 | + | 0.331608i | 0.959925 | − | 0.280257i | \(-0.0904196\pi\) |
−0.790962 | + | 0.611865i | \(0.790420\pi\) | |||||||
\(14\) | 13.2534 | − | 4.30631i | 0.946675 | − | 0.307593i | ||||
\(15\) | −8.21960 | + | 5.18186i | −0.547973 | + | 0.345457i | ||||
\(16\) | −1.23607 | + | 3.80423i | −0.0772542 | + | 0.237764i | ||||
\(17\) | 4.91496 | + | 31.0318i | 0.289115 | + | 1.82540i | 0.522056 | + | 0.852911i | \(0.325165\pi\) |
−0.232940 | + | 0.972491i | \(0.574835\pi\) | |||||||
\(18\) | 5.22346 | − | 5.22346i | 0.290192 | − | 0.290192i | ||||
\(19\) | 2.91847 | − | 4.01693i | 0.153604 | − | 0.211417i | −0.725279 | − | 0.688455i | \(-0.758289\pi\) |
0.878883 | + | 0.477038i | \(0.158289\pi\) | |||||||
\(20\) | −2.21064 | + | 9.75259i | −0.110532 | + | 0.487630i | ||||
\(21\) | 15.4922 | − | 11.2557i | 0.737722 | − | 0.535987i | ||||
\(22\) | −10.3002 | − | 1.63138i | −0.468189 | − | 0.0741538i | ||||
\(23\) | −30.5816 | − | 15.5821i | −1.32963 | − | 0.677482i | −0.362556 | − | 0.931962i | \(-0.618096\pi\) |
−0.967078 | + | 0.254480i | \(0.918096\pi\) | |||||||
\(24\) | 5.49657i | 0.229024i | ||||||||
\(25\) | −3.28179 | + | 24.7837i | −0.131272 | + | 0.991346i | ||||
\(26\) | 6.84231 | 0.263166 | ||||||||
\(27\) | 12.5487 | − | 24.6282i | 0.464767 | − | 0.912157i | ||||
\(28\) | 3.08298 | − | 19.4651i | 0.110106 | − | 0.695184i | ||||
\(29\) | −7.51040 | − | 10.3372i | −0.258979 | − | 0.356455i | 0.659651 | − | 0.751572i | \(-0.270704\pi\) |
−0.918631 | + | 0.395117i | \(0.870704\pi\) | |||||||
\(30\) | 1.25222 | + | 13.6843i | 0.0417406 | + | 0.456142i | ||||
\(31\) | −8.48508 | − | 6.16477i | −0.273712 | − | 0.198864i | 0.442458 | − | 0.896789i | \(-0.354107\pi\) |
−0.716170 | + | 0.697926i | \(0.754107\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | −14.1539 | + | 2.24176i | −0.428906 | + | 0.0679320i | ||||
\(34\) | 42.2580 | + | 13.7305i | 1.24288 | + | 0.403837i | ||||
\(35\) | 3.24086 | − | 49.1627i | 0.0925959 | − | 1.40465i | ||||
\(36\) | −3.22828 | − | 9.93561i | −0.0896743 | − | 0.275989i | ||||
\(37\) | −36.3060 | + | 18.4988i | −0.981243 | + | 0.499968i | −0.869587 | − | 0.493779i | \(-0.835615\pi\) |
−0.111655 | + | 0.993747i | \(0.535615\pi\) | |||||||
\(38\) | −3.18785 | − | 6.25651i | −0.0838908 | − | 0.164645i | ||||
\(39\) | 8.94214 | − | 2.90548i | 0.229286 | − | 0.0744994i | ||||
\(40\) | 10.8697 | + | 9.04712i | 0.271742 | + | 0.226178i | ||||
\(41\) | 15.0755 | − | 46.3975i | 0.367694 | − | 1.13165i | −0.580583 | − | 0.814201i | \(-0.697175\pi\) |
0.948277 | − | 0.317445i | \(-0.102825\pi\) | |||||||
\(42\) | −4.23645 | − | 26.7479i | −0.100868 | − | 0.636854i | ||||
\(43\) | −8.60508 | + | 8.60508i | −0.200118 | + | 0.200118i | −0.800051 | − | 0.599932i | \(-0.795194\pi\) |
0.599932 | + | 0.800051i | \(0.295194\pi\) | |||||||
\(44\) | −8.66877 | + | 11.9315i | −0.197018 | + | 0.271171i | ||||
\(45\) | −10.3006 | − | 24.0002i | −0.228903 | − | 0.533338i | ||||
\(46\) | −39.2692 | + | 28.5307i | −0.853678 | + | 0.620233i | ||||
\(47\) | 48.5171 | + | 7.68435i | 1.03228 | + | 0.163497i | 0.649514 | − | 0.760349i | \(-0.274972\pi\) |
0.382764 | + | 0.923846i | \(0.374972\pi\) | |||||||
\(48\) | 6.92609 | + | 3.52902i | 0.144293 | + | 0.0735212i | ||||
\(49\) | 48.0991i | 0.981614i | ||||||||
\(50\) | 29.1222 | + | 20.0474i | 0.582444 | + | 0.400948i | ||||
\(51\) | 61.0569 | 1.19719 | ||||||||
\(52\) | 4.39304 | − | 8.62182i | 0.0844814 | − | 0.165804i | ||||
\(53\) | −7.71392 | + | 48.7038i | −0.145546 | + | 0.918939i | 0.801536 | + | 0.597946i | \(0.204016\pi\) |
−0.947082 | + | 0.320993i | \(0.895984\pi\) | |||||||
\(54\) | −22.9766 | − | 31.6246i | −0.425493 | − | 0.585641i | ||||
\(55\) | −18.8635 | + | 31.6796i | −0.342973 | + | 0.575994i | ||||
\(56\) | −22.5481 | − | 16.3822i | −0.402645 | − | 0.292539i | ||||
\(57\) | −6.82289 | − | 6.82289i | −0.119700 | − | 0.119700i | ||||
\(58\) | −17.8476 | + | 2.82678i | −0.307717 | + | 0.0487376i | ||||
\(59\) | −66.1155 | − | 21.4822i | −1.12060 | − | 0.364106i | −0.310604 | − | 0.950539i | \(-0.600531\pi\) |
−0.809997 | + | 0.586434i | \(0.800531\pi\) | |||||||
\(60\) | 18.0471 | + | 7.20795i | 0.300786 | + | 0.120132i | ||||
\(61\) | 23.3342 | + | 71.8153i | 0.382528 | + | 1.17730i | 0.938258 | + | 0.345937i | \(0.112439\pi\) |
−0.555730 | + | 0.831363i | \(0.687561\pi\) | |||||||
\(62\) | −13.2158 | + | 6.73380i | −0.213158 | + | 0.108610i | ||||
\(63\) | 23.3675 | + | 45.8613i | 0.370913 | + | 0.727958i | ||||
\(64\) | 7.60845 | − | 2.47214i | 0.118882 | − | 0.0386271i | ||||
\(65\) | 8.97269 | − | 22.4657i | 0.138041 | − | 0.345626i | ||||
\(66\) | −6.26258 | + | 19.2742i | −0.0948876 | + | 0.292034i | ||||
\(67\) | −0.769216 | − | 4.85664i | −0.0114808 | − | 0.0724872i | 0.981283 | − | 0.192573i | \(-0.0616831\pi\) |
−0.992764 | + | 0.120086i | \(0.961683\pi\) | |||||||
\(68\) | 44.4327 | − | 44.4327i | 0.653422 | − | 0.653422i | ||||
\(69\) | −39.2053 | + | 53.9615i | −0.568193 | + | 0.782050i | ||||
\(70\) | −59.8679 | − | 35.6481i | −0.855256 | − | 0.509259i | ||||
\(71\) | −46.2320 | + | 33.5895i | −0.651155 | + | 0.473092i | −0.863665 | − | 0.504067i | \(-0.831836\pi\) |
0.212509 | + | 0.977159i | \(0.431836\pi\) | |||||||
\(72\) | −14.5923 | − | 2.31119i | −0.202671 | − | 0.0320999i | ||||
\(73\) | 50.0339 | + | 25.4935i | 0.685395 | + | 0.349226i | 0.761765 | − | 0.647853i | \(-0.224333\pi\) |
−0.0763699 | + | 0.997080i | \(0.524333\pi\) | |||||||
\(74\) | 57.6252i | 0.778719i | ||||||||
\(75\) | 46.5722 | + | 13.8334i | 0.620963 | + | 0.184446i | ||||
\(76\) | −9.93039 | −0.130663 | ||||||||
\(77\) | 32.9886 | − | 64.7437i | 0.428423 | − | 0.840827i | ||||
\(78\) | 2.08009 | − | 13.1332i | 0.0266678 | − | 0.168374i | ||||
\(79\) | −89.5179 | − | 123.211i | −1.13314 | − | 1.55963i | −0.781968 | − | 0.623319i | \(-0.785784\pi\) |
−0.351170 | − | 0.936312i | \(-0.614216\pi\) | |||||||
\(80\) | 18.3788 | − | 7.88797i | 0.229735 | − | 0.0985996i | ||||
\(81\) | −5.42390 | − | 3.94069i | −0.0669617 | − | 0.0486505i | ||||
\(82\) | −48.7852 | − | 48.7852i | −0.594941 | − | 0.594941i | ||||
\(83\) | 107.353 | − | 17.0030i | 1.29341 | − | 0.204856i | 0.528466 | − | 0.848955i | \(-0.322767\pi\) |
0.764942 | + | 0.644099i | \(0.222767\pi\) | |||||||
\(84\) | −36.4243 | − | 11.8350i | −0.433622 | − | 0.140892i | ||||
\(85\) | 100.497 | − | 120.742i | 1.18232 | − | 1.42050i | ||||
\(86\) | 5.31823 | + | 16.3678i | 0.0618399 | + | 0.190324i | ||||
\(87\) | −22.1244 | + | 11.2730i | −0.254304 | + | 0.129574i | ||||
\(88\) | 9.46892 | + | 18.5838i | 0.107601 | + | 0.211180i | ||||
\(89\) | 125.692 | − | 40.8397i | 1.41227 | − | 0.458873i | 0.499130 | − | 0.866527i | \(-0.333653\pi\) |
0.913136 | + | 0.407654i | \(0.133653\pi\) | |||||||
\(90\) | −36.8555 | − | 2.42955i | −0.409505 | − | 0.0269950i | ||||
\(91\) | −14.7325 | + | 45.3421i | −0.161896 | + | 0.498265i | ||||
\(92\) | 10.7384 | + | 67.7999i | 0.116722 | + | 0.736955i | ||||
\(93\) | −14.4122 | + | 14.4122i | −0.154970 | + | 0.154970i | ||||
\(94\) | 40.8327 | − | 56.2014i | 0.434391 | − | 0.597888i | ||||
\(95\) | −24.7227 | + | 2.26232i | −0.260239 | + | 0.0238139i | ||||
\(96\) | 8.89364 | − | 6.46161i | 0.0926421 | − | 0.0673084i | ||||
\(97\) | −54.9088 | − | 8.69669i | −0.566070 | − | 0.0896566i | −0.133161 | − | 0.991094i | \(-0.542513\pi\) |
−0.432909 | + | 0.901438i | \(0.642513\pi\) | |||||||
\(98\) | 60.6084 | + | 30.8815i | 0.618453 | + | 0.315118i | ||||
\(99\) | − | 38.5183i | − | 0.389074i | ||||||
\(100\) | 43.9588 | − | 23.8249i | 0.439588 | − | 0.238249i | ||||
\(101\) | −182.579 | −1.80771 | −0.903855 | − | 0.427839i | \(-0.859275\pi\) | ||||
−0.903855 | + | 0.427839i | \(0.859275\pi\) | |||||||
\(102\) | 39.2009 | − | 76.9362i | 0.384323 | − | 0.754276i | ||||
\(103\) | 3.02075 | − | 19.0722i | 0.0293276 | − | 0.185167i | −0.968676 | − | 0.248329i | \(-0.920118\pi\) |
0.998003 | + | 0.0631620i | \(0.0201185\pi\) | |||||||
\(104\) | −8.04362 | − | 11.0711i | −0.0773425 | − | 0.106453i | ||||
\(105\) | −93.3780 | − | 21.1662i | −0.889314 | − | 0.201583i | ||||
\(106\) | 56.4177 | + | 40.9899i | 0.532242 | + | 0.386697i | ||||
\(107\) | −2.49555 | − | 2.49555i | −0.0233229 | − | 0.0233229i | 0.695349 | − | 0.718672i | \(-0.255250\pi\) |
−0.718672 | + | 0.695349i | \(0.755250\pi\) | |||||||
\(108\) | −54.6012 | + | 8.64798i | −0.505567 | + | 0.0800739i | ||||
\(109\) | 19.1934 | + | 6.23632i | 0.176086 | + | 0.0572139i | 0.395733 | − | 0.918366i | \(-0.370491\pi\) |
−0.219647 | + | 0.975579i | \(0.570491\pi\) | |||||||
\(110\) | 27.8075 | + | 44.1090i | 0.252796 | + | 0.400991i | ||||
\(111\) | 24.4696 | + | 75.3096i | 0.220447 | + | 0.678465i | ||||
\(112\) | −35.1195 | + | 17.8943i | −0.313567 | + | 0.159770i | ||||
\(113\) | −54.5747 | − | 107.109i | −0.482962 | − | 0.947866i | −0.995988 | − | 0.0894924i | \(-0.971476\pi\) |
0.513026 | − | 0.858373i | \(-0.328524\pi\) | |||||||
\(114\) | −12.9779 | + | 4.21678i | −0.113841 | + | 0.0369893i | ||||
\(115\) | 42.1805 | + | 166.348i | 0.366787 | + | 1.44650i | ||||
\(116\) | −7.89691 | + | 24.3042i | −0.0680768 | + | 0.209519i | ||||
\(117\) | 3.95347 | + | 24.9612i | 0.0337904 | + | 0.213344i | ||||
\(118\) | −69.5179 | + | 69.5179i | −0.589135 | + | 0.589135i | ||||
\(119\) | −181.976 | + | 250.468i | −1.52921 | + | 2.10478i | ||||
\(120\) | 20.6695 | − | 18.1129i | 0.172246 | − | 0.150941i | ||||
\(121\) | 53.8989 | − | 39.1598i | 0.445445 | − | 0.323635i | ||||
\(122\) | 105.474 | + | 16.7054i | 0.864541 | + | 0.136930i | ||||
\(123\) | −84.4726 | − | 43.0409i | −0.686769 | − | 0.349926i | ||||
\(124\) | 20.9763i | 0.169163i | ||||||||
\(125\) | 104.012 | − | 69.3290i | 0.832096 | − | 0.554632i | ||||
\(126\) | 72.7915 | 0.577711 | ||||||||
\(127\) | 43.6037 | − | 85.5772i | 0.343337 | − | 0.673836i | −0.653183 | − | 0.757201i | \(-0.726567\pi\) |
0.996519 | + | 0.0833645i | \(0.0265666\pi\) | |||||||
\(128\) | 1.76985 | − | 11.1744i | 0.0138270 | − | 0.0873001i | ||||
\(129\) | 13.9007 | + | 19.1326i | 0.107757 | + | 0.148315i | ||||
\(130\) | −22.5476 | − | 25.7301i | −0.173443 | − | 0.197924i | ||||
\(131\) | 18.7606 | + | 13.6303i | 0.143210 | + | 0.104048i | 0.657084 | − | 0.753818i | \(-0.271790\pi\) |
−0.513873 | + | 0.857866i | \(0.671790\pi\) | |||||||
\(132\) | 20.2661 | + | 20.2661i | 0.153531 | + | 0.153531i | ||||
\(133\) | 48.3241 | − | 7.65378i | 0.363339 | − | 0.0575472i | ||||
\(134\) | −6.61359 | − | 2.14889i | −0.0493552 | − | 0.0160365i | ||||
\(135\) | −133.965 | + | 33.9691i | −0.992332 | + | 0.251623i | ||||
\(136\) | −27.4609 | − | 84.5160i | −0.201918 | − | 0.621441i | ||||
\(137\) | −121.194 | + | 61.7516i | −0.884630 | + | 0.450741i | −0.836416 | − | 0.548096i | \(-0.815353\pi\) |
−0.0482140 | + | 0.998837i | \(0.515353\pi\) | |||||||
\(138\) | 42.8241 | + | 84.0469i | 0.310319 | + | 0.609036i | ||||
\(139\) | 248.403 | − | 80.7112i | 1.78707 | − | 0.580656i | 0.787702 | − | 0.616057i | \(-0.211271\pi\) |
0.999373 | + | 0.0354010i | \(0.0112708\pi\) | |||||||
\(140\) | −83.3568 | + | 52.5504i | −0.595406 | + | 0.375360i | ||||
\(141\) | 29.4988 | − | 90.7879i | 0.209211 | − | 0.643886i | ||||
\(142\) | 12.6425 | + | 79.8216i | 0.0890316 | + | 0.562124i | ||||
\(143\) | 25.2279 | − | 25.2279i | 0.176419 | − | 0.176419i | ||||
\(144\) | −12.2811 | + | 16.9035i | −0.0852854 | + | 0.117385i | ||||
\(145\) | −14.1232 | + | 62.3067i | −0.0974013 | + | 0.429701i | ||||
\(146\) | 64.2474 | − | 46.6785i | 0.440051 | − | 0.319716i | ||||
\(147\) | 92.3217 | + | 14.6223i | 0.628039 | + | 0.0994716i | ||||
\(148\) | 72.6120 | + | 36.9976i | 0.490621 | + | 0.249984i | ||||
\(149\) | 63.1967i | 0.424139i | 0.977255 | + | 0.212069i | \(0.0680203\pi\) | ||||
−0.977255 | + | 0.212069i | \(0.931980\pi\) | |||||||
\(150\) | 47.3323 | − | 49.8028i | 0.315549 | − | 0.332019i | ||||
\(151\) | 71.0637 | 0.470621 | 0.235310 | − | 0.971920i | \(-0.424389\pi\) | ||||
0.235310 | + | 0.971920i | \(0.424389\pi\) | |||||||
\(152\) | −6.37570 | + | 12.5130i | −0.0419454 | + | 0.0823225i | ||||
\(153\) | −25.6731 | + | 162.094i | −0.167798 | + | 1.05944i | ||||
\(154\) | −60.4018 | − | 83.1360i | −0.392220 | − | 0.539844i | ||||
\(155\) | 4.77877 | + | 52.2225i | 0.0308308 | + | 0.336919i | ||||
\(156\) | −15.2133 | − | 11.0531i | −0.0975210 | − | 0.0708531i | ||||
\(157\) | −150.002 | − | 150.002i | −0.955427 | − | 0.955427i | 0.0436208 | − | 0.999048i | \(-0.486111\pi\) |
−0.999048 | + | 0.0436208i | \(0.986111\pi\) | |||||||
\(158\) | −212.729 | + | 33.6929i | −1.34638 | + | 0.213246i | ||||
\(159\) | 91.1373 | + | 29.6123i | 0.573190 | + | 0.186241i | ||||
\(160\) | 1.86049 | − | 28.2230i | 0.0116281 | − | 0.176394i | ||||
\(161\) | −104.513 | − | 321.657i | −0.649147 | − | 1.99787i | ||||
\(162\) | −8.44792 | + | 4.30443i | −0.0521477 | + | 0.0265706i | ||||
\(163\) | −125.792 | − | 246.881i | −0.771730 | − | 1.51461i | −0.855317 | − | 0.518105i | \(-0.826638\pi\) |
0.0835873 | − | 0.996500i | \(-0.473362\pi\) | |||||||
\(164\) | −92.7949 | + | 30.1509i | −0.565823 | + | 0.183847i | ||||
\(165\) | 55.0715 | + | 45.8375i | 0.333767 | + | 0.277803i | ||||
\(166\) | 47.4997 | − | 146.189i | 0.286143 | − | 0.880657i | ||||
\(167\) | 28.4957 | + | 179.915i | 0.170633 | + | 1.07734i | 0.913184 | + | 0.407546i | \(0.133616\pi\) |
−0.742551 | + | 0.669789i | \(0.766384\pi\) | |||||||
\(168\) | −38.2987 | + | 38.2987i | −0.227969 | + | 0.227969i | ||||
\(169\) | 85.5765 | − | 117.786i | 0.506370 | − | 0.696958i | ||||
\(170\) | −87.6209 | − | 204.155i | −0.515417 | − | 1.20091i | ||||
\(171\) | 20.9823 | − | 15.2445i | 0.122703 | − | 0.0891491i | ||||
\(172\) | 24.0392 | + | 3.80744i | 0.139763 | + | 0.0221363i | ||||
\(173\) | −70.6137 | − | 35.9795i | −0.408171 | − | 0.207974i | 0.237835 | − | 0.971306i | \(-0.423562\pi\) |
−0.646007 | + | 0.763332i | \(0.723562\pi\) | |||||||
\(174\) | 35.1161i | 0.201817i | ||||||||
\(175\) | −195.553 | + | 149.820i | −1.11745 | + | 0.856112i | ||||
\(176\) | 29.4964 | 0.167593 | ||||||||
\(177\) | −61.3325 | + | 120.372i | −0.346511 | + | 0.680067i | ||||
\(178\) | 29.2380 | − | 184.601i | 0.164258 | − | 1.03709i | ||||
\(179\) | 0.398502 | + | 0.548491i | 0.00222627 | + | 0.00306420i | 0.810129 | − | 0.586252i | \(-0.199397\pi\) |
−0.807902 | + | 0.589316i | \(0.799397\pi\) | |||||||
\(180\) | −26.7241 | + | 44.8807i | −0.148467 | + | 0.249337i | ||||
\(181\) | 37.0773 | + | 26.9382i | 0.204847 | + | 0.148830i | 0.685479 | − | 0.728092i | \(-0.259593\pi\) |
−0.480632 | + | 0.876922i | \(0.659593\pi\) | |||||||
\(182\) | 47.6755 | + | 47.6755i | 0.261953 | + | 0.261953i | ||||
\(183\) | 144.936 | − | 22.9557i | 0.792002 | − | 0.125441i | ||||
\(184\) | 92.3274 | + | 29.9990i | 0.501779 | + | 0.163038i | ||||
\(185\) | 189.203 | + | 75.5669i | 1.02272 | + | 0.408470i | ||||
\(186\) | 8.90723 | + | 27.4136i | 0.0478883 | + | 0.147385i | ||||
\(187\) | 206.432 | − | 105.182i | 1.10392 | − | 0.562473i | ||||
\(188\) | −44.6017 | − | 87.5358i | −0.237243 | − | 0.465616i | ||||
\(189\) | 259.040 | − | 84.1671i | 1.37058 | − | 0.445328i | ||||
\(190\) | −13.0222 | + | 32.6049i | −0.0685381 | + | 0.171605i | ||||
\(191\) | −60.9194 | + | 187.491i | −0.318950 | + | 0.981627i | 0.655148 | + | 0.755501i | \(0.272606\pi\) |
−0.974098 | + | 0.226126i | \(0.927394\pi\) | |||||||
\(192\) | −2.43203 | − | 15.3553i | −0.0126668 | − | 0.0799753i | ||||
\(193\) | −74.7620 | + | 74.7620i | −0.387368 | + | 0.387368i | −0.873748 | − | 0.486380i | \(-0.838317\pi\) |
0.486380 | + | 0.873748i | \(0.338317\pi\) | |||||||
\(194\) | −46.2121 | + | 63.6054i | −0.238206 | + | 0.327863i | ||||
\(195\) | −40.3930 | − | 24.0519i | −0.207144 | − | 0.123343i | ||||
\(196\) | 77.8260 | − | 56.5439i | 0.397071 | − | 0.288489i | ||||
\(197\) | 175.706 | + | 27.8291i | 0.891908 | + | 0.141264i | 0.585535 | − | 0.810647i | \(-0.300885\pi\) |
0.306373 | + | 0.951912i | \(0.400885\pi\) | |||||||
\(198\) | −48.5359 | − | 24.7303i | −0.245131 | − | 0.124900i | ||||
\(199\) | 14.6408i | 0.0735720i | 0.999323 | + | 0.0367860i | \(0.0117120\pi\) | ||||
−0.999323 | + | 0.0367860i | \(0.988288\pi\) | |||||||
\(200\) | −1.79784 | − | 70.6878i | −0.00898921 | − | 0.353439i | ||||
\(201\) | −9.55571 | −0.0475409 | ||||||||
\(202\) | −117.223 | + | 230.063i | −0.580311 | + | 1.13892i | ||||
\(203\) | 19.6963 | − | 124.358i | 0.0970261 | − | 0.612599i | ||||
\(204\) | −71.7767 | − | 98.7921i | −0.351846 | − | 0.484275i | ||||
\(205\) | −224.153 | + | 96.2040i | −1.09343 | + | 0.469288i | ||||
\(206\) | −22.0930 | − | 16.0515i | −0.107247 | − | 0.0779198i | ||||
\(207\) | −126.772 | − | 126.772i | −0.612424 | − | 0.612424i | ||||
\(208\) | −19.1147 | + | 3.02747i | −0.0918977 | + | 0.0145552i | ||||
\(209\) | −34.8218 | − | 11.3143i | −0.166612 | − | 0.0541354i | ||||
\(210\) | −86.6233 | + | 104.074i | −0.412492 | + | 0.495589i | ||||
\(211\) | 50.9278 | + | 156.740i | 0.241364 | + | 0.742842i | 0.996213 | + | 0.0869438i | \(0.0277100\pi\) |
−0.754849 | + | 0.655898i | \(0.772290\pi\) | |||||||
\(212\) | 87.8726 | − | 44.7733i | 0.414493 | − | 0.211195i | ||||
\(213\) | 50.4172 | + | 98.9494i | 0.236701 | + | 0.464551i | ||||
\(214\) | −4.74682 | + | 1.54234i | −0.0221814 | + | 0.00720718i | ||||
\(215\) | 60.7154 | + | 4.00242i | 0.282397 | + | 0.0186159i | ||||
\(216\) | −24.1590 | + | 74.3539i | −0.111847 | + | 0.344231i | ||||
\(217\) | −16.1673 | − | 102.077i | −0.0745038 | − | 0.470399i | ||||
\(218\) | 20.1812 | − | 20.1812i | 0.0925741 | − | 0.0925741i | ||||
\(219\) | 64.1429 | − | 88.2852i | 0.292890 | − | 0.403129i | ||||
\(220\) | 73.4342 | − | 6.71981i | 0.333792 | − | 0.0305446i | ||||
\(221\) | −122.980 | + | 89.3499i | −0.556469 | + | 0.404298i | ||||
\(222\) | 110.606 | + | 17.5183i | 0.498226 | + | 0.0789112i | ||||
\(223\) | −107.607 | − | 54.8286i | −0.482543 | − | 0.245868i | 0.195758 | − | 0.980652i | \(-0.437283\pi\) |
−0.678301 | + | 0.734784i | \(0.737283\pi\) | |||||||
\(224\) | 55.7420i | 0.248848i | ||||||||
\(225\) | −56.3076 | + | 117.823i | −0.250256 | + | 0.523659i | ||||
\(226\) | −170.004 | −0.752230 | ||||||||
\(227\) | −145.398 | + | 285.359i | −0.640519 | + | 1.25709i | 0.311266 | + | 0.950323i | \(0.399247\pi\) |
−0.951785 | + | 0.306766i | \(0.900753\pi\) | |||||||
\(228\) | −3.01888 | + | 19.0604i | −0.0132407 | + | 0.0835984i | ||||
\(229\) | 155.195 | + | 213.607i | 0.677706 | + | 0.932782i | 0.999904 | − | 0.0138901i | \(-0.00442151\pi\) |
−0.322197 | + | 0.946672i | \(0.604422\pi\) | |||||||
\(230\) | 236.692 | + | 53.6515i | 1.02910 | + | 0.233268i | ||||
\(231\) | −114.241 | − | 83.0008i | −0.494549 | − | 0.359311i | ||||
\(232\) | 25.5549 | + | 25.5549i | 0.110151 | + | 0.110151i | ||||
\(233\) | 144.484 | − | 22.8840i | 0.620102 | − | 0.0982145i | 0.161524 | − | 0.986869i | \(-0.448359\pi\) |
0.458578 | + | 0.888654i | \(0.348359\pi\) | |||||||
\(234\) | 33.9913 | + | 11.0444i | 0.145262 | + | 0.0471985i | ||||
\(235\) | −130.983 | − | 207.768i | −0.557373 | − | 0.884119i | ||||
\(236\) | 42.9644 | + | 132.231i | 0.182053 | + | 0.560301i | ||||
\(237\) | −263.705 | + | 134.365i | −1.11268 | + | 0.566939i | ||||
\(238\) | 198.773 | + | 390.114i | 0.835180 | + | 1.63913i | ||||
\(239\) | −161.553 | + | 52.4917i | −0.675953 | + | 0.219630i | −0.626823 | − | 0.779162i | \(-0.715645\pi\) |
−0.0491301 | + | 0.998792i | \(0.515645\pi\) | |||||||
\(240\) | −9.55299 | − | 37.6743i | −0.0398041 | − | 0.156976i | ||||
\(241\) | −29.0163 | + | 89.3031i | −0.120400 | + | 0.370552i | −0.993035 | − | 0.117820i | \(-0.962409\pi\) |
0.872635 | + | 0.488373i | \(0.162409\pi\) | |||||||
\(242\) | −14.7391 | − | 93.0587i | −0.0609052 | − | 0.384540i | ||||
\(243\) | 166.693 | − | 166.693i | 0.685979 | − | 0.685979i | ||||
\(244\) | 88.7686 | − | 122.179i | 0.363806 | − | 0.500735i | ||||
\(245\) | 180.874 | − | 158.502i | 0.738260 | − | 0.646946i | ||||
\(246\) | −108.470 | + | 78.8077i | −0.440933 | + | 0.320357i | ||||
\(247\) | 23.7271 | + | 3.75800i | 0.0960610 | + | 0.0152146i | ||||
\(248\) | 26.4316 | + | 13.4676i | 0.106579 | + | 0.0543048i | ||||
\(249\) | − | 211.223i | − | 0.848284i | ||||||
\(250\) | −20.5799 | − | 175.575i | −0.0823195 | − | 0.702299i | ||||
\(251\) | 123.629 | 0.492545 | 0.246272 | − | 0.969201i | \(-0.420794\pi\) | ||||
0.246272 | + | 0.969201i | \(0.420794\pi\) | |||||||
\(252\) | 46.7350 | − | 91.7227i | 0.185457 | − | 0.363979i | ||||
\(253\) | −39.5932 | + | 249.982i | −0.156495 | + | 0.988069i | ||||
\(254\) | −79.8382 | − | 109.888i | −0.314324 | − | 0.432629i | ||||
\(255\) | −201.202 | − | 229.601i | −0.789026 | − | 0.900395i | ||||
\(256\) | −12.9443 | − | 9.40456i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 45.6784 | + | 45.6784i | 0.177737 | + | 0.177737i | 0.790369 | − | 0.612632i | \(-0.209889\pi\) |
−0.612632 | + | 0.790369i | \(0.709889\pi\) | |||||||
\(258\) | 33.0333 | − | 5.23196i | 0.128036 | − | 0.0202789i | ||||
\(259\) | −381.866 | − | 124.076i | −1.47439 | − | 0.479057i | ||||
\(260\) | −46.8982 | + | 11.8919i | −0.180378 | + | 0.0457380i | ||||
\(261\) | −20.6246 | − | 63.4760i | −0.0790214 | − | 0.243203i | ||||
\(262\) | 29.2202 | − | 14.8885i | 0.111528 | − | 0.0568262i | ||||
\(263\) | −17.2068 | − | 33.7702i | −0.0654249 | − | 0.128404i | 0.855978 | − | 0.517012i | \(-0.172956\pi\) |
−0.921403 | + | 0.388609i | \(0.872956\pi\) | |||||||
\(264\) | 38.5485 | − | 12.5252i | 0.146017 | − | 0.0474438i | ||||
\(265\) | 208.567 | − | 131.487i | 0.787046 | − | 0.496176i | ||||
\(266\) | 21.3816 | − | 65.8059i | 0.0803821 | − | 0.247391i | ||||
\(267\) | −40.1772 | − | 253.669i | −0.150476 | − | 0.950071i | ||||
\(268\) | −6.95394 | + | 6.95394i | −0.0259475 | + | 0.0259475i | ||||
\(269\) | −64.8044 | + | 89.1956i | −0.240908 | + | 0.331582i | −0.912301 | − | 0.409520i | \(-0.865696\pi\) |
0.671393 | + | 0.741102i | \(0.265696\pi\) | |||||||
\(270\) | −43.2071 | + | 190.615i | −0.160026 | + | 0.705982i | ||||
\(271\) | 146.860 | − | 106.700i | 0.541918 | − | 0.393727i | −0.282879 | − | 0.959156i | \(-0.591289\pi\) |
0.824797 | + | 0.565429i | \(0.191289\pi\) | |||||||
\(272\) | −124.127 | − | 19.6598i | −0.456351 | − | 0.0722788i | ||||
\(273\) | 82.5512 | + | 42.0619i | 0.302385 | + | 0.154073i | ||||
\(274\) | 192.361i | 0.702046i | ||||||||
\(275\) | 181.291 | − | 33.4593i | 0.659239 | − | 0.121670i | ||||
\(276\) | 133.400 | 0.483334 | ||||||||
\(277\) | 145.052 | − | 284.680i | 0.523652 | − | 1.02772i | −0.466074 | − | 0.884746i | \(-0.654332\pi\) |
0.989726 | − | 0.142979i | \(-0.0456681\pi\) | |||||||
\(278\) | 57.7828 | − | 364.826i | 0.207852 | − | 1.31232i | ||||
\(279\) | −32.2014 | − | 44.3215i | −0.115417 | − | 0.158858i | ||||
\(280\) | 12.6990 | + | 138.775i | 0.0453537 | + | 0.495626i | ||||
\(281\) | 21.3424 | + | 15.5062i | 0.0759516 | + | 0.0551821i | 0.625113 | − | 0.780534i | \(-0.285053\pi\) |
−0.549162 | + | 0.835716i | \(0.685053\pi\) | |||||||
\(282\) | −95.4601 | − | 95.4601i | −0.338511 | − | 0.338511i | ||||
\(283\) | −66.9720 | + | 10.6073i | −0.236650 | + | 0.0374817i | −0.273633 | − | 0.961834i | \(-0.588225\pi\) |
0.0369828 | + | 0.999316i | \(0.488225\pi\) | |||||||
\(284\) | 108.698 | + | 35.3181i | 0.382739 | + | 0.124360i | ||||
\(285\) | −3.17348 | + | 48.1406i | −0.0111350 | + | 0.168914i | ||||
\(286\) | −15.5917 | − | 47.9864i | −0.0545165 | − | 0.167785i | ||||
\(287\) | 428.328 | − | 218.244i | 1.49243 | − | 0.760432i | ||||
\(288\) | 13.4147 | + | 26.3278i | 0.0465787 | + | 0.0914159i | ||||
\(289\) | −663.963 | + | 215.735i | −2.29745 | + | 0.746487i | ||||
\(290\) | 69.4434 | + | 57.7996i | 0.239460 | + | 0.199309i | ||||
\(291\) | −33.3850 | + | 102.748i | −0.114725 | + | 0.353087i | ||||
\(292\) | −17.5689 | − | 110.926i | −0.0601676 | − | 0.379883i | ||||
\(293\) | 0.372340 | − | 0.372340i | 0.00127079 | − | 0.00127079i | −0.706471 | − | 0.707742i | \(-0.749714\pi\) |
0.707742 | + | 0.706471i | \(0.249714\pi\) | |||||||
\(294\) | 77.6994 | − | 106.944i | 0.264284 | − | 0.363755i | ||||
\(295\) | 137.089 | + | 319.414i | 0.464708 | + | 1.08276i | ||||
\(296\) | 93.2395 | − | 67.7425i | 0.314998 | − | 0.228860i | ||||
\(297\) | −201.317 | − | 31.8855i | −0.677836 | − | 0.107359i | ||||
\(298\) | 79.6325 | + | 40.5748i | 0.267223 | + | 0.136157i | ||||
\(299\) | − | 166.061i | − | 0.555387i | ||||||
\(300\) | −32.3660 | − | 91.6176i | −0.107887 | − | 0.305392i | ||||
\(301\) | −119.916 | −0.398393 | ||||||||
\(302\) | 45.6257 | − | 89.5455i | 0.151079 | − | 0.296508i | ||||
\(303\) | −55.5047 | + | 350.443i | −0.183184 | + | 1.15658i | ||||
\(304\) | 11.6739 | + | 16.0677i | 0.0384009 | + | 0.0528543i | ||||
\(305\) | 193.163 | − | 324.401i | 0.633322 | − | 1.06361i | ||||
\(306\) | 187.767 | + | 136.421i | 0.613617 | + | 0.445819i | ||||
\(307\) | 72.1739 | + | 72.1739i | 0.235094 | + | 0.235094i | 0.814815 | − | 0.579721i | \(-0.196838\pi\) |
−0.579721 | + | 0.814815i | \(0.696838\pi\) | |||||||
\(308\) | −143.538 | + | 22.7342i | −0.466032 | + | 0.0738122i | ||||
\(309\) | −35.6890 | − | 11.5961i | −0.115499 | − | 0.0375277i | ||||
\(310\) | 68.8723 | + | 27.5073i | 0.222169 | + | 0.0887332i | ||||
\(311\) | −76.9184 | − | 236.730i | −0.247326 | − | 0.761191i | −0.995245 | − | 0.0974014i | \(-0.968947\pi\) |
0.747919 | − | 0.663790i | \(-0.231053\pi\) | |||||||
\(312\) | −23.6952 | + | 12.0733i | −0.0759462 | + | 0.0386965i | ||||
\(313\) | 155.789 | + | 305.754i | 0.497729 | + | 0.976849i | 0.994072 | + | 0.108722i | \(0.0346759\pi\) |
−0.496343 | + | 0.868127i | \(0.665324\pi\) | |||||||
\(314\) | −285.321 | + | 92.7064i | −0.908665 | + | 0.295243i | ||||
\(315\) | 95.4554 | − | 239.000i | 0.303033 | − | 0.758729i | ||||
\(316\) | −94.1247 | + | 289.686i | −0.297863 | + | 0.916728i | ||||
\(317\) | 24.4560 | + | 154.409i | 0.0771483 | + | 0.487095i | 0.995764 | + | 0.0919436i | \(0.0293079\pi\) |
−0.918616 | + | 0.395152i | \(0.870692\pi\) | |||||||
\(318\) | 95.8274 | − | 95.8274i | 0.301344 | − | 0.301344i | ||||
\(319\) | −55.3825 | + | 76.2274i | −0.173613 | + | 0.238957i | ||||
\(320\) | −34.3686 | − | 20.4646i | −0.107402 | − | 0.0639520i | ||||
\(321\) | −5.54863 | + | 4.03132i | −0.0172855 | + | 0.0125586i | ||||
\(322\) | −472.413 | − | 74.8228i | −1.46712 | − | 0.232369i | ||||
\(323\) | 138.997 | + | 70.8224i | 0.430330 | + | 0.219264i | ||||
\(324\) | 13.4086i | 0.0413846i | ||||||||
\(325\) | −114.049 | + | 40.2902i | −0.350919 | + | 0.123970i | ||||
\(326\) | −391.851 | −1.20200 | ||||||||
\(327\) | 17.8049 | − | 34.9441i | 0.0544493 | − | 0.106863i | ||||
\(328\) | −21.5857 | + | 136.287i | −0.0658100 | + | 0.415508i | ||||
\(329\) | 284.512 | + | 391.598i | 0.864779 | + | 1.19027i | ||||
\(330\) | 93.1168 | − | 39.9647i | 0.282172 | − | 0.121105i | ||||
\(331\) | 402.818 | + | 292.664i | 1.21697 | + | 0.884182i | 0.995845 | − | 0.0910633i | \(-0.0290266\pi\) |
0.221127 | + | 0.975245i | \(0.429027\pi\) | |||||||
\(332\) | −153.712 | − | 153.712i | −0.462989 | − | 0.462989i | ||||
\(333\) | −210.221 | + | 33.2957i | −0.631293 | + | 0.0999871i | ||||
\(334\) | 245.002 | + | 79.6058i | 0.733538 | + | 0.238341i | ||||
\(335\) | −15.7283 | + | 18.8968i | −0.0469501 | + | 0.0564082i | ||||
\(336\) | 23.6699 | + | 72.8485i | 0.0704462 | + | 0.216811i | ||||
\(337\) | −22.6810 | + | 11.5565i | −0.0673026 | + | 0.0342924i | −0.487318 | − | 0.873225i | \(-0.662025\pi\) |
0.420015 | + | 0.907517i | \(0.362025\pi\) | |||||||
\(338\) | −93.4754 | − | 183.456i | −0.276554 | − | 0.542769i | ||||
\(339\) | −222.176 | + | 72.1894i | −0.655387 | + | 0.212948i | ||||
\(340\) | −313.506 | − | 20.6666i | −0.922077 | − | 0.0607843i | ||||
\(341\) | −23.8995 | + | 73.5552i | −0.0700866 | + | 0.215704i | ||||
\(342\) | −5.73775 | − | 36.2268i | −0.0167771 | − | 0.105926i | ||||
\(343\) | 6.27731 | − | 6.27731i | 0.0183012 | − | 0.0183012i | ||||
\(344\) | 20.2318 | − | 27.8466i | 0.0588133 | − | 0.0809495i | ||||
\(345\) | 332.113 | − | 30.3910i | 0.962645 | − | 0.0880897i | ||||
\(346\) | −90.6735 | + | 65.8782i | −0.262062 | + | 0.190399i | ||||
\(347\) | −427.376 | − | 67.6897i | −1.23163 | − | 0.195071i | −0.493510 | − | 0.869740i | \(-0.664286\pi\) |
−0.738121 | + | 0.674669i | \(0.764286\pi\) | |||||||
\(348\) | 44.2489 | + | 22.5459i | 0.127152 | + | 0.0647872i | ||||
\(349\) | 16.9445i | 0.0485515i | 0.999705 | + | 0.0242757i | \(0.00772796\pi\) | ||||
−0.999705 | + | 0.0242757i | \(0.992272\pi\) | |||||||
\(350\) | 63.2310 | + | 342.601i | 0.180660 | + | 0.978861i | ||||
\(351\) | 133.733 | 0.381007 | ||||||||
\(352\) | 18.9378 | − | 37.1676i | 0.0538007 | − | 0.105590i | ||||
\(353\) | −25.5006 | + | 161.004i | −0.0722396 | + | 0.456103i | 0.924880 | + | 0.380259i | \(0.124165\pi\) |
−0.997120 | + | 0.0758440i | \(0.975835\pi\) | |||||||
\(354\) | 112.299 | + | 154.567i | 0.317230 | + | 0.436630i | ||||
\(355\) | 278.660 | + | 63.1646i | 0.784959 | + | 0.177928i | ||||
\(356\) | −213.839 | − | 155.363i | −0.600673 | − | 0.436414i | ||||
\(357\) | 425.429 | + | 425.429i | 1.19168 | + | 1.19168i | ||||
\(358\) | 0.946994 | − | 0.149989i | 0.00264523 | − | 0.000418964i | ||||
\(359\) | 35.6372 | + | 11.5792i | 0.0992679 | + | 0.0322541i | 0.358230 | − | 0.933633i | \(-0.383380\pi\) |
−0.258962 | + | 0.965888i | \(0.583380\pi\) | |||||||
\(360\) | 39.3951 | + | 62.4895i | 0.109431 | + | 0.173582i | ||||
\(361\) | 103.937 | + | 319.885i | 0.287914 | + | 0.886108i | ||||
\(362\) | 57.7492 | − | 29.4247i | 0.159528 | − | 0.0812837i | ||||
\(363\) | −58.7781 | − | 115.359i | −0.161923 | − | 0.317792i | ||||
\(364\) | 90.6842 | − | 29.4651i | 0.249133 | − | 0.0809481i | ||||
\(365\) | −69.0105 | − | 272.158i | −0.189070 | − | 0.745640i | ||||
\(366\) | 64.1291 | − | 197.369i | 0.175216 | − | 0.539259i | ||||
\(367\) | 1.52982 | + | 9.65893i | 0.00416846 | + | 0.0263186i | 0.989685 | − | 0.143261i | \(-0.0457589\pi\) |
−0.985516 | + | 0.169580i | \(0.945759\pi\) | |||||||
\(368\) | 97.0787 | − | 97.0787i | 0.263801 | − | 0.263801i | ||||
\(369\) | 149.784 | − | 206.160i | 0.405918 | − | 0.558699i | ||||
\(370\) | 216.696 | − | 189.893i | 0.585665 | − | 0.513225i | ||||
\(371\) | −393.104 | + | 285.607i | −1.05958 | + | 0.769830i | ||||
\(372\) | 40.2620 | + | 6.37687i | 0.108231 | + | 0.0171421i | ||||
\(373\) | −407.559 | − | 207.662i | −1.09265 | − | 0.556734i | −0.187691 | − | 0.982228i | \(-0.560100\pi\) |
−0.904961 | + | 0.425494i | \(0.860100\pi\) | |||||||
\(374\) | − | 327.651i | − | 0.876072i | ||||||
\(375\) | −101.450 | − | 220.718i | −0.270535 | − | 0.588580i | ||||
\(376\) | −138.938 | −0.369515 | ||||||||
\(377\) | 28.0659 | − | 55.0825i | 0.0744454 | − | 0.146107i | ||||
\(378\) | 60.2570 | − | 380.448i | 0.159410 | − | 1.00647i | ||||
\(379\) | −97.0905 | − | 133.634i | −0.256176 | − | 0.352595i | 0.661487 | − | 0.749957i | \(-0.269926\pi\) |
−0.917662 | + | 0.397362i | \(0.869926\pi\) | |||||||
\(380\) | 32.7238 | + | 37.3426i | 0.0861151 | + | 0.0982700i | ||||
\(381\) | −151.002 | − | 109.709i | −0.396330 | − | 0.287950i | ||||
\(382\) | 197.139 | + | 197.139i | 0.516072 | + | 0.516072i | ||||
\(383\) | 250.949 | − | 39.7465i | 0.655220 | − | 0.103777i | 0.180032 | − | 0.983661i | \(-0.442380\pi\) |
0.475188 | + | 0.879884i | \(0.342380\pi\) | |||||||
\(384\) | −20.9102 | − | 6.79414i | −0.0544537 | − | 0.0176931i | ||||
\(385\) | −352.172 | + | 89.2994i | −0.914733 | + | 0.231947i | ||||
\(386\) | 46.2055 | + | 142.206i | 0.119703 | + | 0.368409i | ||||
\(387\) | −56.6382 | + | 28.8586i | −0.146352 | + | 0.0745700i | ||||
\(388\) | 50.4776 | + | 99.0678i | 0.130097 | + | 0.255329i | ||||
\(389\) | 323.557 | − | 105.130i | 0.831766 | − | 0.270257i | 0.137977 | − | 0.990435i | \(-0.455940\pi\) |
0.693789 | + | 0.720178i | \(0.255940\pi\) | |||||||
\(390\) | −56.2411 | + | 35.4559i | −0.144208 | + | 0.0909126i | ||||
\(391\) | 333.234 | − | 1025.59i | 0.852260 | − | 2.62299i | ||||
\(392\) | −21.2821 | − | 134.370i | −0.0542910 | − | 0.342780i | ||||
\(393\) | 31.8654 | − | 31.8654i | 0.0810826 | − | 0.0810826i | ||||
\(394\) | 147.877 | − | 203.535i | 0.375322 | − | 0.516586i | ||||
\(395\) | −168.337 | + | 742.645i | −0.426169 | + | 1.88011i | ||||
\(396\) | −62.3239 | + | 45.2810i | −0.157384 | + | 0.114346i | ||||
\(397\) | 131.048 | + | 20.7559i | 0.330095 | + | 0.0522819i | 0.319282 | − | 0.947660i | \(-0.396558\pi\) |
0.0108126 | + | 0.999942i | \(0.496558\pi\) | |||||||
\(398\) | 18.4485 | + | 9.39999i | 0.0463531 | + | 0.0236181i | ||||
\(399\) | − | 95.0803i | − | 0.238297i | ||||||
\(400\) | −90.2261 | − | 43.1190i | −0.225565 | − | 0.107797i | ||||
\(401\) | 391.076 | 0.975253 | 0.487626 | − | 0.873052i | \(-0.337863\pi\) | ||||
0.487626 | + | 0.873052i | \(0.337863\pi\) | |||||||
\(402\) | −6.13514 | + | 12.0409i | −0.0152616 | + | 0.0299525i | ||||
\(403\) | 7.93814 | − | 50.1194i | 0.0196976 | − | 0.124366i | ||||
\(404\) | 214.634 | + | 295.419i | 0.531273 | + | 0.731234i | ||||
\(405\) | 3.05473 | + | 33.3821i | 0.00754253 | + | 0.0824248i | ||||
\(406\) | −144.054 | − | 104.661i | −0.354812 | − | 0.257786i | ||||
\(407\) | 212.467 | + | 212.467i | 0.522032 | + | 0.522032i | ||||
\(408\) | −170.569 | + | 27.0154i | −0.418061 | + | 0.0662143i | ||||
\(409\) | −176.459 | − | 57.3352i | −0.431441 | − | 0.140184i | 0.0852422 | − | 0.996360i | \(-0.472834\pi\) |
−0.516683 | + | 0.856176i | \(0.672834\pi\) | |||||||
\(410\) | −22.6911 | + | 344.216i | −0.0553441 | + | 0.839552i | ||||
\(411\) | 81.6828 | + | 251.394i | 0.198742 | + | 0.611664i | ||||
\(412\) | −34.4106 | + | 17.5331i | −0.0835209 | + | 0.0425560i | ||||
\(413\) | −310.993 | − | 610.359i | −0.753011 | − | 1.47787i | ||||
\(414\) | −241.134 | + | 78.3492i | −0.582450 | + | 0.189249i | ||||
\(415\) | −417.700 | − | 347.664i | −1.00651 | − | 0.837743i | ||||
\(416\) | −8.45756 | + | 26.0297i | −0.0203307 | + | 0.0625714i | ||||
\(417\) | −79.4019 | − | 501.324i | −0.190412 | − | 1.20221i | ||||
\(418\) | −36.6138 | + | 36.6138i | −0.0875929 | + | 0.0875929i | ||||
\(419\) | 125.580 | − | 172.846i | 0.299714 | − | 0.412521i | −0.632425 | − | 0.774622i | \(-0.717940\pi\) |
0.932139 | + | 0.362101i | \(0.117940\pi\) | |||||||
\(420\) | 75.5248 | + | 175.971i | 0.179821 | + | 0.418979i | ||||
\(421\) | 582.175 | − | 422.975i | 1.38284 | − | 1.00469i | 0.386229 | − | 0.922403i | \(-0.373777\pi\) |
0.996609 | − | 0.0822874i | \(-0.0262226\pi\) | |||||||
\(422\) | 230.201 | + | 36.4603i | 0.545501 | + | 0.0863988i | ||||
\(423\) | 228.620 | + | 116.488i | 0.540473 | + | 0.275385i | ||||
\(424\) | − | 139.472i | − | 0.328944i | ||||||
\(425\) | −785.212 | + | 19.9707i | −1.84756 | + | 0.0469900i | ||||
\(426\) | 157.053 | 0.368670 | ||||||||
\(427\) | −337.804 | + | 662.978i | −0.791110 | + | 1.55264i | ||||
\(428\) | −1.10419 | + | 6.97158i | −0.00257988 | + | 0.0162887i | ||||
\(429\) | −40.7533 | − | 56.0921i | −0.0949960 | − | 0.130751i | ||||
\(430\) | 44.0250 | − | 73.9361i | 0.102384 | − | 0.171944i | ||||
\(431\) | −364.855 | − | 265.083i | −0.846531 | − | 0.615041i | 0.0776561 | − | 0.996980i | \(-0.475256\pi\) |
−0.924187 | + | 0.381939i | \(0.875256\pi\) | |||||||
\(432\) | 78.1803 | + | 78.1803i | 0.180973 | + | 0.180973i | ||||
\(433\) | 283.110 | − | 44.8402i | 0.653834 | − | 0.103557i | 0.179300 | − | 0.983794i | \(-0.442617\pi\) |
0.474534 | + | 0.880237i | \(0.342617\pi\) | |||||||
\(434\) | −139.004 | − | 45.1651i | −0.320286 | − | 0.104067i | ||||
\(435\) | 115.298 | + | 46.0496i | 0.265054 | + | 0.105861i | ||||
\(436\) | −12.4726 | − | 38.3868i | −0.0286070 | − | 0.0880432i | ||||
\(437\) | −151.843 | + | 77.3681i | −0.347468 | + | 0.177044i | ||||
\(438\) | −70.0635 | − | 137.507i | −0.159962 | − | 0.313944i | ||||
\(439\) | −109.894 | + | 35.7066i | −0.250327 | + | 0.0813362i | −0.431493 | − | 0.902116i | \(-0.642013\pi\) |
0.181166 | + | 0.983453i | \(0.442013\pi\) | |||||||
\(440\) | 38.6802 | − | 96.8468i | 0.0879095 | − | 0.220106i | ||||
\(441\) | −77.6386 | + | 238.947i | −0.176051 | + | 0.541830i | ||||
\(442\) | 33.6297 | + | 212.330i | 0.0760853 | + | 0.480384i | ||||
\(443\) | −516.584 | + | 516.584i | −1.16610 | + | 1.16610i | −0.182988 | + | 0.983115i | \(0.558577\pi\) |
−0.983115 | + | 0.182988i | \(0.941423\pi\) | |||||||
\(444\) | 93.0878 | − | 128.124i | 0.209657 | − | 0.288568i | ||||
\(445\) | −567.769 | − | 338.076i | −1.27589 | − | 0.759722i | ||||
\(446\) | −138.176 | + | 100.391i | −0.309812 | + | 0.225091i | ||||
\(447\) | 121.300 | + | 19.2121i | 0.271365 | + | 0.0429800i | ||||
\(448\) | 70.2390 | + | 35.7886i | 0.156784 | + | 0.0798852i | ||||
\(449\) | − | 611.042i | − | 1.36090i | −0.732796 | − | 0.680448i | \(-0.761785\pi\) | ||
0.732796 | − | 0.680448i | \(-0.238215\pi\) | |||||||
\(450\) | 112.314 | + | 146.599i | 0.249587 | + | 0.325775i | ||||
\(451\) | −359.747 | −0.797665 | ||||||||
\(452\) | −109.149 | + | 214.218i | −0.241481 | + | 0.473933i | ||||
\(453\) | 21.6037 | − | 136.400i | 0.0476902 | − | 0.301104i | ||||
\(454\) | 266.222 | + | 366.424i | 0.586393 | + | 0.807101i | ||||
\(455\) | 219.055 | − | 94.0158i | 0.481439 | − | 0.206628i | ||||
\(456\) | 22.0793 | + | 16.0416i | 0.0484196 | + | 0.0351789i | ||||
\(457\) | 445.089 | + | 445.089i | 0.973936 | + | 0.973936i | 0.999669 | − | 0.0257328i | \(-0.00819192\pi\) |
−0.0257328 | + | 0.999669i | \(0.508192\pi\) | |||||||
\(458\) | 368.802 | − | 58.4125i | 0.805244 | − | 0.127538i | ||||
\(459\) | 825.936 | + | 268.363i | 1.79942 | + | 0.584668i | ||||
\(460\) | 219.571 | − | 263.803i | 0.477328 | − | 0.573485i | ||||
\(461\) | −129.655 | − | 399.038i | −0.281248 | − | 0.865592i | −0.987498 | − | 0.157630i | \(-0.949615\pi\) |
0.706251 | − | 0.707962i | \(-0.250385\pi\) | |||||||
\(462\) | −177.934 | + | 90.6620i | −0.385139 | + | 0.196238i | ||||
\(463\) | 132.982 | + | 260.991i | 0.287218 | + | 0.563696i | 0.988863 | − | 0.148830i | \(-0.0475508\pi\) |
−0.701645 | + | 0.712526i | \(0.747551\pi\) | |||||||
\(464\) | 48.6084 | − | 15.7938i | 0.104759 | − | 0.0340384i | ||||
\(465\) | 101.689 | + | 6.70344i | 0.218686 | + | 0.0144160i | ||||
\(466\) | 63.9288 | − | 196.752i | 0.137186 | − | 0.422216i | ||||
\(467\) | 45.6149 | + | 288.001i | 0.0976765 | + | 0.616705i | 0.987160 | + | 0.159737i | \(0.0510647\pi\) |
−0.889483 | + | 0.456968i | \(0.848935\pi\) | |||||||
\(468\) | 35.7406 | − | 35.7406i | 0.0763687 | − | 0.0763687i | ||||
\(469\) | 28.4802 | − | 39.1996i | 0.0607253 | − | 0.0835812i | ||||
\(470\) | −345.899 | + | 31.6525i | −0.735955 | + | 0.0673457i | ||||
\(471\) | −333.516 | + | 242.314i | −0.708102 | + | 0.514466i | ||||
\(472\) | 194.206 | + | 30.7591i | 0.411453 | + | 0.0651677i | ||||
\(473\) | 79.9576 | + | 40.7404i | 0.169044 | + | 0.0861320i | ||||
\(474\) | 418.556i | 0.883029i | ||||||||
\(475\) | 89.9763 | + | 85.5130i | 0.189424 | + | 0.180027i | ||||
\(476\) | 619.192 | 1.30082 | ||||||||
\(477\) | −116.936 | + | 229.500i | −0.245149 | + | 0.481131i | ||||
\(478\) | −37.5799 | + | 237.270i | −0.0786190 | + | 0.496381i | ||||
\(479\) | 492.895 | + | 678.412i | 1.02901 | + | 1.41631i | 0.905690 | + | 0.423941i | \(0.139354\pi\) |
0.123319 | + | 0.992367i | \(0.460646\pi\) | |||||||
\(480\) | −53.6058 | − | 12.1509i | −0.111679 | − | 0.0253145i | ||||
\(481\) | −159.493 | − | 115.879i | −0.331587 | − | 0.240912i | ||||
\(482\) | 93.8989 | + | 93.8989i | 0.194811 | + | 0.194811i | ||||
\(483\) | −649.163 | + | 102.817i | −1.34402 | + | 0.212872i | ||||
\(484\) | −126.724 | − | 41.1751i | −0.261826 | − | 0.0850725i | ||||
\(485\) | 148.238 | + | 235.139i | 0.305646 | + | 0.484823i | ||||
\(486\) | −103.022 | − | 317.069i | −0.211979 | − | 0.652405i | ||||
\(487\) | 756.556 | − | 385.485i | 1.55350 | − | 0.791549i | 0.554334 | − | 0.832294i | \(-0.312973\pi\) |
0.999170 | + | 0.0407450i | \(0.0129731\pi\) | |||||||
\(488\) | −96.9621 | − | 190.299i | −0.198693 | − | 0.389957i | ||||
\(489\) | −512.106 | + | 166.393i | −1.04725 | + | 0.340272i | ||||
\(490\) | −83.5957 | − | 329.678i | −0.170604 | − | 0.672813i | ||||
\(491\) | 1.50701 | − | 4.63810i | 0.00306926 | − | 0.00944622i | −0.949510 | − | 0.313736i | \(-0.898419\pi\) |
0.952579 | + | 0.304290i | \(0.0984192\pi\) | |||||||
\(492\) | 29.6618 | + | 187.277i | 0.0602882 | + | 0.380645i | ||||
\(493\) | 283.868 | − | 283.868i | 0.575798 | − | 0.575798i | ||||
\(494\) | 19.9691 | − | 27.4851i | 0.0404232 | − | 0.0556378i | ||||
\(495\) | −144.846 | + | 126.930i | −0.292618 | + | 0.256424i | ||||
\(496\) | 33.9403 | − | 24.6591i | 0.0684281 | − | 0.0497159i | ||||
\(497\) | −556.177 | − | 88.0897i | −1.11907 | − | 0.177243i | ||||
\(498\) | −266.156 | − | 135.613i | −0.534450 | − | 0.272316i | ||||
\(499\) | − | 363.411i | − | 0.728279i | −0.931344 | − | 0.364139i | \(-0.881363\pi\) | ||
0.931344 | − | 0.364139i | \(-0.118637\pi\) | |||||||
\(500\) | −234.450 | − | 86.7937i | −0.468900 | − | 0.173587i | ||||
\(501\) | 353.993 | 0.706573 | ||||||||
\(502\) | 79.3745 | − | 155.781i | 0.158117 | − | 0.310321i | ||||
\(503\) | −33.2643 | + | 210.023i | −0.0661318 | + | 0.417540i | 0.932306 | + | 0.361670i | \(0.117793\pi\) |
−0.998438 | + | 0.0558701i | \(0.982207\pi\) | |||||||
\(504\) | −85.5716 | − | 117.779i | −0.169785 | − | 0.233689i | ||||
\(505\) | 601.654 | + | 686.576i | 1.19139 | + | 1.35956i | ||||
\(506\) | 289.575 | + | 210.388i | 0.572282 | + | 0.415787i | ||||
\(507\) | −200.063 | − | 200.063i | −0.394602 | − | 0.394602i | ||||
\(508\) | −189.726 | + | 30.0497i | −0.373477 | + | 0.0591529i | ||||
\(509\) | −340.104 | − | 110.506i | −0.668180 | − | 0.217105i | −0.0447671 | − | 0.998997i | \(-0.514255\pi\) |
−0.623413 | + | 0.781892i | \(0.714255\pi\) | |||||||
\(510\) | −418.493 | + | 106.116i | −0.820575 | + | 0.208071i | ||||
\(511\) | 170.991 | + | 526.256i | 0.334620 | + | 1.02986i | ||||
\(512\) | −20.1612 | + | 10.2726i | −0.0393773 | + | 0.0200637i | ||||
\(513\) | −62.3068 | − | 122.284i | −0.121456 | − | 0.238370i | ||||
\(514\) | 86.8854 | − | 28.2308i | 0.169038 | − | 0.0549237i | ||||
\(515\) | −81.6743 | + | 51.4897i | −0.158591 | + | 0.0999800i | ||||
\(516\) | 14.6160 | − | 44.9835i | 0.0283256 | − | 0.0871774i | ||||
\(517\) | −56.6652 | − | 357.770i | −0.109604 | − | 0.692011i | ||||
\(518\) | −401.518 | + | 401.518i | −0.775131 | + | 0.775131i | ||||
\(519\) | −90.5260 | + | 124.598i | −0.174424 | + | 0.240074i | ||||
\(520\) | −15.1259 | + | 66.7303i | −0.0290883 | + | 0.128327i | ||||
\(521\) | 261.371 | − | 189.897i | 0.501671 | − | 0.364485i | −0.307984 | − | 0.951392i | \(-0.599654\pi\) |
0.809655 | + | 0.586906i | \(0.199654\pi\) | |||||||
\(522\) | −93.2262 | − | 14.7656i | −0.178594 | − | 0.0282865i | ||||
\(523\) | −545.090 | − | 277.737i | −1.04224 | − | 0.531046i | −0.152872 | − | 0.988246i | \(-0.548852\pi\) |
−0.889364 | + | 0.457200i | \(0.848852\pi\) | |||||||
\(524\) | − | 46.3786i | − | 0.0885089i | ||||||
\(525\) | 228.116 | + | 420.892i | 0.434506 | + | 0.801698i | ||||
\(526\) | −53.6003 | −0.101902 | ||||||||
\(527\) | 149.600 | − | 293.607i | 0.283872 | − | 0.557129i | ||||
\(528\) | 8.96702 | − | 56.6156i | 0.0169830 | − | 0.107226i | ||||
\(529\) | 381.493 | + | 525.080i | 0.721159 | + | 0.992590i | ||||
\(530\) | −31.7743 | − | 347.230i | −0.0599515 | − | 0.655150i | ||||
\(531\) | −293.774 | − | 213.439i | −0.553246 | − | 0.401957i | ||||
\(532\) | −69.1925 | − | 69.1925i | −0.130061 | − | 0.130061i | ||||
\(533\) | 233.129 | − | 36.9240i | 0.437390 | − | 0.0692757i | ||||
\(534\) | −345.437 | − | 112.239i | −0.646885 | − | 0.210186i | ||||
\(535\) | −1.16074 | + | 17.6080i | −0.00216960 | + | 0.0329121i | ||||
\(536\) | 4.29777 | + | 13.2272i | 0.00801823 | + | 0.0246776i | ||||
\(537\) | 1.17392 | − | 0.598144i | 0.00218608 | − | 0.00111386i | ||||
\(538\) | 70.7860 | + | 138.925i | 0.131573 | + | 0.258226i | ||||
\(539\) | 337.328 | − | 109.604i | 0.625840 | − | 0.203348i | ||||
\(540\) | 212.448 | + | 176.827i | 0.393423 | + | 0.327457i | ||||
\(541\) | −140.029 | + | 430.965i | −0.258834 | + | 0.796609i | 0.734216 | + | 0.678916i | \(0.237550\pi\) |
−0.993050 | + | 0.117693i | \(0.962450\pi\) | |||||||
\(542\) | −40.1599 | − | 253.560i | −0.0740958 | − | 0.467823i | ||||
\(543\) | 62.9770 | − | 62.9770i | 0.115980 | − | 0.115980i | ||||
\(544\) | −104.468 | + | 143.787i | −0.192036 | + | 0.264315i | ||||
\(545\) | −39.7971 | − | 92.7263i | −0.0730221 | − | 0.170140i | ||||
\(546\) | 106.002 | − | 77.0152i | 0.194143 | − | 0.141053i | ||||
\(547\) | −445.065 | − | 70.4914i | −0.813648 | − | 0.128869i | −0.264276 | − | 0.964447i | \(-0.585133\pi\) |
−0.549372 | + | 0.835578i | \(0.685133\pi\) | |||||||
\(548\) | 242.389 | + | 123.503i | 0.442315 | + | 0.225371i | ||||
\(549\) | 394.429i | 0.718450i | ||||||||
\(550\) | 74.2346 | − | 249.922i | 0.134972 | − | 0.454403i | ||||
\(551\) | −63.4426 | −0.115141 | ||||||||
\(552\) | 85.6481 | − | 168.094i | 0.155160 | − | 0.304518i | ||||
\(553\) | 234.764 | − | 1482.24i | 0.424528 | − | 2.68036i | ||||
\(554\) | −265.589 | − | 365.551i | −0.479402 | − | 0.659840i | ||||
\(555\) | 202.562 | − | 340.185i | 0.364977 | − | 0.612947i | ||||
\(556\) | −422.609 | − | 307.044i | −0.760088 | − | 0.552237i | ||||
\(557\) | −37.6917 | − | 37.6917i | −0.0676692 | − | 0.0676692i | 0.672462 | − | 0.740131i | \(-0.265237\pi\) |
−0.740131 | + | 0.672462i | \(0.765237\pi\) | |||||||
\(558\) | −76.5229 | + | 12.1200i | −0.137138 | + | 0.0217205i | ||||
\(559\) | −55.9970 | − | 18.1945i | −0.100173 | − | 0.0325483i | ||||
\(560\) | 183.020 | + | 73.0974i | 0.326822 | + | 0.130531i | ||||
\(561\) | −139.132 | − | 428.203i | −0.248006 | − | 0.763285i | ||||
\(562\) | 33.2416 | − | 16.9374i | 0.0591487 | − | 0.0301378i | ||||
\(563\) | −11.5693 | − | 22.7061i | −0.0205494 | − | 0.0403305i | 0.880504 | − | 0.474039i | \(-0.157205\pi\) |
−0.901053 | + | 0.433709i | \(0.857205\pi\) | |||||||
\(564\) | −181.576 | + | 58.9976i | −0.321943 | + | 0.104606i | ||||
\(565\) | −222.935 | + | 558.182i | −0.394576 | + | 0.987933i | ||||
\(566\) | −29.6327 | + | 91.1999i | −0.0523545 | + | 0.161131i | ||||
\(567\) | −10.3346 | − | 65.2501i | −0.0182268 | − | 0.115080i | ||||
\(568\) | 114.292 | − | 114.292i | 0.201218 | − | 0.201218i | ||||
\(569\) | 328.912 | − | 452.709i | 0.578053 | − | 0.795622i | −0.415427 | − | 0.909627i | \(-0.636368\pi\) |
0.993480 | + | 0.114004i | \(0.0363678\pi\) | |||||||
\(570\) | 58.6232 | + | 34.9070i | 0.102848 | + | 0.0612403i | ||||
\(571\) | −98.3806 | + | 71.4777i | −0.172295 | + | 0.125180i | −0.670591 | − | 0.741827i | \(-0.733959\pi\) |
0.498296 | + | 0.867007i | \(0.333959\pi\) | |||||||
\(572\) | −70.4769 | − | 11.1624i | −0.123211 | − | 0.0195148i | ||||
\(573\) | 341.351 | + | 173.927i | 0.595726 | + | 0.303538i | ||||
\(574\) | − | 679.846i | − | 1.18440i | ||||||
\(575\) | 486.544 | − | 706.786i | 0.846163 | − | 1.22919i | ||||
\(576\) | 41.7877 | 0.0725481 | ||||||||
\(577\) | 277.724 | − | 545.065i | 0.481325 | − | 0.944653i | −0.514851 | − | 0.857280i | \(-0.672153\pi\) |
0.996176 | − | 0.0873732i | \(-0.0278472\pi\) | |||||||
\(578\) | −154.449 | + | 975.152i | −0.267213 | + | 1.68711i | ||||
\(579\) | 120.771 | + | 166.227i | 0.208585 | + | 0.287093i | ||||
\(580\) | 117.417 | − | 50.3941i | 0.202443 | − | 0.0868864i | ||||
\(581\) | 866.481 | + | 629.535i | 1.49136 | + | 1.08354i | ||||
\(582\) | 108.036 | + | 108.036i | 0.185629 | + | 0.185629i | ||||
\(583\) | 359.146 | − | 56.8832i | 0.616032 | − | 0.0975698i | ||||
\(584\) | −151.055 | − | 49.0807i | −0.258655 | − | 0.0840422i | ||||
\(585\) | 80.8373 | − | 97.1220i | 0.138183 | − | 0.166020i | ||||
\(586\) | −0.230119 | − | 0.708233i | −0.000392695 | − | 0.00120859i | ||||
\(587\) | −678.013 | + | 345.465i | −1.15505 | + | 0.588526i | −0.923235 | − | 0.384235i | \(-0.874465\pi\) |
−0.231812 | + | 0.972761i | \(0.574465\pi\) | |||||||
\(588\) | −84.8713 | − | 166.569i | −0.144339 | − | 0.283281i | ||||
\(589\) | −49.5269 | + | 16.0923i | −0.0840863 | + | 0.0273213i | ||||
\(590\) | 490.501 | + | 32.3344i | 0.831358 | + | 0.0548040i | ||||
\(591\) | 106.831 | − | 328.791i | 0.180762 | − | 0.556329i | ||||
\(592\) | −25.4970 | − | 160.982i | −0.0430693 | − | 0.271929i | ||||
\(593\) | −362.694 | + | 362.694i | −0.611625 | + | 0.611625i | −0.943369 | − | 0.331744i | \(-0.892363\pi\) |
0.331744 | + | 0.943369i | \(0.392363\pi\) | |||||||
\(594\) | −169.432 | + | 233.203i | −0.285239 | + | 0.392597i | ||||
\(595\) | 1541.54 | − | 141.063i | 2.59082 | − | 0.237081i | ||||
\(596\) | 102.254 | − | 74.2922i | 0.171568 | − | 0.124651i | ||||
\(597\) | 28.1017 | + | 4.45087i | 0.0470715 | + | 0.00745540i | ||||
\(598\) | −209.249 | − | 106.618i | −0.349914 | − | 0.178290i | ||||
\(599\) | 654.617i | 1.09285i | 0.837508 | + | 0.546425i | \(0.184012\pi\) | ||||
−0.837508 | + | 0.546425i | \(0.815988\pi\) | |||||||
\(600\) | −136.225 | − | 18.0386i | −0.227042 | − | 0.0300643i | ||||
\(601\) | −911.373 | −1.51643 | −0.758213 | − | 0.652006i | \(-0.773928\pi\) | ||||
−0.758213 | + | 0.652006i | \(0.773928\pi\) | |||||||
\(602\) | −76.9909 | + | 151.103i | −0.127892 | + | 0.251002i | ||||
\(603\) | 4.01797 | − | 25.3685i | 0.00666330 | − | 0.0420704i | ||||
\(604\) | −83.5404 | − | 114.984i | −0.138312 | − | 0.190370i | ||||
\(605\) | −324.872 | − | 73.6394i | −0.536978 | − | 0.121718i | ||||
\(606\) | 405.947 | + | 294.938i | 0.669880 | + | 0.486696i | ||||
\(607\) | −656.124 | − | 656.124i | −1.08093 | − | 1.08093i | −0.996423 | − | 0.0845069i | \(-0.973068\pi\) |
−0.0845069 | − | 0.996423i | \(-0.526932\pi\) | |||||||
\(608\) | 27.7416 | − | 4.39383i | 0.0456276 | − | 0.00722670i | ||||
\(609\) | −232.705 | − | 75.6104i | −0.382110 | − | 0.124155i | ||||
\(610\) | −284.750 | − | 451.678i | −0.466804 | − | 0.740456i | ||||
\(611\) | 73.4421 | + | 226.032i | 0.120200 | + | 0.369937i | ||||
\(612\) | 292.454 | − | 149.013i | 0.477865 | − | 0.243484i | ||||
\(613\) | 344.538 | + | 676.194i | 0.562052 | + | 1.10309i | 0.980805 | + | 0.194989i | \(0.0624672\pi\) |
−0.418753 | + | 0.908100i | \(0.637533\pi\) | |||||||
\(614\) | 137.283 | − | 44.6059i | 0.223588 | − | 0.0726481i | ||||
\(615\) | 116.511 | + | 459.487i | 0.189449 | + | 0.747134i | ||||
\(616\) | −63.5103 | + | 195.464i | −0.103101 | + | 0.317312i | ||||
\(617\) | −27.9487 | − | 176.461i | −0.0452977 | − | 0.285998i | 0.954633 | − | 0.297785i | \(-0.0962480\pi\) |
−0.999931 | + | 0.0117871i | \(0.996248\pi\) | |||||||
\(618\) | −37.5257 | + | 37.5257i | −0.0607212 | + | 0.0607212i | ||||
\(619\) | −28.4751 | + | 39.1926i | −0.0460017 | + | 0.0633159i | −0.831398 | − | 0.555677i | \(-0.812459\pi\) |
0.785396 | + | 0.618993i | \(0.212459\pi\) | |||||||
\(620\) | 78.8800 | − | 69.1234i | 0.127226 | − | 0.111489i | ||||
\(621\) | −767.519 | + | 557.635i | −1.23594 | + | 0.897963i | ||||
\(622\) | −347.682 | − | 55.0675i | −0.558975 | − | 0.0885329i | ||||
\(623\) | 1160.35 | + | 591.227i | 1.86252 | + | 0.949001i | ||||
\(624\) | 37.6093i | 0.0602713i | ||||||||
\(625\) | −603.460 | − | 162.670i | −0.965536 | − | 0.260271i | ||||
\(626\) | 485.295 | 0.775232 | ||||||||
\(627\) | −32.3027 | + | 63.3976i | −0.0515195 | + | 0.101113i | ||||
\(628\) | −66.3704 | + | 419.047i | −0.105685 | + | 0.667272i | ||||
\(629\) | −752.495 | − | 1035.72i | −1.19634 | − | 1.64661i | ||||
\(630\) | −239.871 | − | 273.728i | −0.380748 | − | 0.434489i | ||||
\(631\) | −456.354 | − | 331.561i | −0.723224 | − | 0.525453i | 0.164189 | − | 0.986429i | \(-0.447499\pi\) |
−0.887412 | + | 0.460976i | \(0.847499\pi\) | |||||||
\(632\) | 304.594 | + | 304.594i | 0.481952 | + | 0.481952i | ||||
\(633\) | 316.329 | − | 50.1017i | 0.499731 | − | 0.0791495i | ||||
\(634\) | 210.269 | + | 68.3204i | 0.331654 | + | 0.107761i | ||||
\(635\) | −465.496 | + | 118.035i | −0.733064 | + | 0.185881i | ||||
\(636\) | −59.2246 | − | 182.275i | −0.0931204 | − | 0.286595i | ||||
\(637\) | −207.351 | + | 105.650i | −0.325511 | + | 0.165856i | ||||
\(638\) | 60.4944 | + | 118.727i | 0.0948188 | + | 0.186092i | ||||
\(639\) | −283.890 | + | 92.2414i | −0.444272 | + | 0.144353i | ||||
\(640\) | −47.8529 | + | 30.1678i | −0.0747702 | + | 0.0471372i | ||||
\(641\) | −360.242 | + | 1108.71i | −0.562000 | + | 1.72966i | 0.114701 | + | 0.993400i | \(0.463409\pi\) |
−0.676701 | + | 0.736258i | \(0.736591\pi\) | |||||||
\(642\) | 1.51732 | + | 9.57995i | 0.00236342 | + | 0.0149220i | ||||
\(643\) | 286.144 | − | 286.144i | 0.445014 | − | 0.445014i | −0.448679 | − | 0.893693i | \(-0.648105\pi\) |
0.893693 | + | 0.448679i | \(0.148105\pi\) | |||||||
\(644\) | −397.590 | + | 547.236i | −0.617376 | + | 0.849745i | ||||
\(645\) | 26.1400 | − | 115.321i | 0.0405271 | − | 0.178792i | ||||
\(646\) | 178.483 | − | 129.675i | 0.276289 | − | 0.200736i | ||||
\(647\) | −254.625 | − | 40.3286i | −0.393547 | − | 0.0623317i | −0.0434750 | − | 0.999055i | \(-0.513843\pi\) |
−0.350072 | + | 0.936723i | \(0.613843\pi\) | |||||||
\(648\) | 16.8958 | + | 8.60886i | 0.0260738 | + | 0.0132853i | ||||
\(649\) | 512.632i | 0.789880i | ||||||||
\(650\) | −22.4550 | + | 169.578i | −0.0345462 | + | 0.260889i | ||||
\(651\) | −200.841 | −0.308512 | ||||||||
\(652\) | −251.584 | + | 493.761i | −0.385865 | + | 0.757303i | ||||
\(653\) | −12.6590 | + | 79.9258i | −0.0193859 | + | 0.122398i | −0.995483 | − | 0.0949350i | \(-0.969736\pi\) |
0.976098 | + | 0.217333i | \(0.0697357\pi\) | |||||||
\(654\) | −32.6007 | − | 44.8710i | −0.0498481 | − | 0.0686101i | ||||
\(655\) | −10.5659 | − | 115.464i | −0.0161311 | − | 0.176281i | ||||
\(656\) | 157.872 | + | 114.701i | 0.240659 | + | 0.174849i | ||||
\(657\) | 207.408 | + | 207.408i | 0.315690 | + | 0.315690i | ||||
\(658\) | 676.110 | − | 107.085i | 1.02752 | − | 0.162744i | ||||
\(659\) | −155.596 | − | 50.5561i | −0.236109 | − | 0.0767164i | 0.188573 | − | 0.982059i | \(-0.439614\pi\) |
−0.424681 | + | 0.905343i | \(0.639614\pi\) | |||||||
\(660\) | 9.42624 | − | 142.993i | 0.0142822 | − | 0.216656i | ||||
\(661\) | 167.623 | + | 515.891i | 0.253590 | + | 0.780470i | 0.994104 | + | 0.108429i | \(0.0345821\pi\) |
−0.740514 | + | 0.672041i | \(0.765418\pi\) | |||||||
\(662\) | 627.403 | − | 319.678i | 0.947739 | − | 0.482897i | ||||
\(663\) | 134.113 | + | 263.211i | 0.202281 | + | 0.396999i | ||||
\(664\) | −292.378 | + | 94.9995i | −0.440329 | + | 0.143071i | ||||
\(665\) | −188.025 | − | 156.498i | −0.282744 | − | 0.235335i | ||||
\(666\) | −93.0150 | + | 286.271i | −0.139662 | + | 0.429836i | ||||
\(667\) | 68.6051 | + | 433.155i | 0.102856 | + | 0.649408i | ||||
\(668\) | 257.610 | − | 257.610i | 0.385644 | − | 0.385644i | ||||
\(669\) | −137.951 | + | 189.874i | −0.206205 | + | 0.283817i | ||||
\(670\) | 13.7131 | + | 31.9513i | 0.0204673 | + | 0.0476884i | ||||
\(671\) | 450.482 | − | 327.294i | 0.671358 | − | 0.487770i | ||||
\(672\) | 106.992 | + | 16.9458i | 0.159214 | + | 0.0252170i | ||||
\(673\) | −847.508 | − | 431.827i | −1.25930 | − | 0.641645i | −0.308432 | − | 0.951246i | \(-0.599804\pi\) |
−0.950866 | + | 0.309602i | \(0.899804\pi\) | |||||||
\(674\) | 35.9995i | 0.0534116i | ||||||||
\(675\) | 569.195 | + | 391.828i | 0.843252 | + | 0.580485i | ||||
\(676\) | −291.183 | −0.430744 | ||||||||
\(677\) | 498.680 | − | 978.716i | 0.736603 | − | 1.44567i | −0.152664 | − | 0.988278i | \(-0.548785\pi\) |
0.889268 | − | 0.457387i | \(-0.151215\pi\) | |||||||
\(678\) | −51.6819 | + | 326.307i | −0.0762270 | + | 0.481279i | ||||
\(679\) | −321.994 | − | 443.187i | −0.474218 | − | 0.652705i | ||||
\(680\) | −227.325 | + | 381.772i | −0.334301 | + | 0.561429i | ||||
\(681\) | 503.519 | + | 365.828i | 0.739381 | + | 0.537192i | ||||
\(682\) | 77.3405 | + | 77.3405i | 0.113403 | + | 0.113403i | ||||
\(683\) | −707.782 | + | 112.102i | −1.03628 | + | 0.164131i | −0.651322 | − | 0.758801i | \(-0.725785\pi\) |
−0.384962 | + | 0.922933i | \(0.625785\pi\) | |||||||
\(684\) | −49.3322 | − | 16.0290i | −0.0721232 | − | 0.0234342i | ||||
\(685\) | 631.586 | + | 252.253i | 0.922024 | + | 0.368252i | ||||
\(686\) | −3.87959 | − | 11.9402i | −0.00565538 | − | 0.0174055i | ||||
\(687\) | 457.179 | − | 232.944i | 0.665471 | − | 0.339075i | ||||
\(688\) | −22.0992 | − | 43.3722i | −0.0321210 | − | 0.0630409i | ||||
\(689\) | −226.901 | + | 73.7247i | −0.329320 | + | 0.107002i | ||||
\(690\) | 174.935 | − | 437.998i | 0.253528 | − | 0.634780i | ||||
\(691\) | −24.3198 | + | 74.8487i | −0.0351951 | + | 0.108319i | −0.967111 | − | 0.254356i | \(-0.918137\pi\) |
0.931916 | + | 0.362675i | \(0.118137\pi\) | |||||||
\(692\) | 24.7954 | + | 156.552i | 0.0358314 | + | 0.226231i | ||||
\(693\) | 268.386 | − | 268.386i | 0.387281 | − | 0.387281i | ||||
\(694\) | −359.686 | + | 495.066i | −0.518280 | + | 0.713351i | ||||
\(695\) | −1122.08 | − | 668.137i | −1.61450 | − | 0.961348i | ||||
\(696\) | 56.8191 | − | 41.2815i | 0.0816366 | − | 0.0593125i | ||||
\(697\) | 1513.89 | + | 239.777i | 2.17201 | + | 0.344013i | ||||
\(698\) | 21.3513 | + | 10.8790i | 0.0305892 | + | 0.0155860i | ||||
\(699\) | − | 284.280i | − | 0.406695i | ||||||
\(700\) | 472.300 | + | 140.288i | 0.674714 | + | 0.200411i | ||||
\(701\) | −484.373 | −0.690974 | −0.345487 | − | 0.938424i | \(-0.612286\pi\) | ||||
−0.345487 | + | 0.938424i | \(0.612286\pi\) | |||||||
\(702\) | 85.8622 | − | 168.514i | 0.122311 | − | 0.240048i | ||||
\(703\) | −31.6494 | + | 199.827i | −0.0450205 | + | 0.284248i | ||||
\(704\) | −34.6751 | − | 47.7262i | −0.0492544 | − | 0.0677928i | ||||
\(705\) | −438.610 | + | 188.247i | −0.622142 | + | 0.267016i | ||||
\(706\) | 186.505 | + | 135.504i | 0.264171 | + | 0.191932i | ||||
\(707\) | −1272.16 | − | 1272.16i | −1.79938 | − | 1.79938i | ||||
\(708\) | 266.866 | − | 42.2675i | 0.376930 | − | 0.0596998i | ||||
\(709\) | 448.636 | + | 145.771i | 0.632773 | + | 0.205600i | 0.607803 | − | 0.794088i | \(-0.292051\pi\) |
0.0249697 | + | 0.999688i | \(0.492051\pi\) | |||||||
\(710\) | 258.503 | − | 310.579i | 0.364089 | − | 0.437435i | ||||
\(711\) | −245.828 | − | 756.582i | −0.345750 | − | 1.06411i | ||||
\(712\) | −333.063 | + | 169.704i | −0.467785 | + | 0.238348i | ||||
\(713\) | 163.427 | + | 320.744i | 0.229211 | + | 0.449851i | ||||
\(714\) | 809.214 | − | 262.930i | 1.13335 | − | 0.368249i | ||||
\(715\) | −178.002 | − | 11.7341i | −0.248954 | − | 0.0164113i | ||||
\(716\) | 0.419010 | − | 1.28958i | 0.000585210 | − | 0.00180109i | ||||
\(717\) | 51.6401 | + | 326.043i | 0.0720225 | + | 0.454732i | ||||
\(718\) | 37.4711 | − | 37.4711i | 0.0521882 | − | 0.0521882i | ||||
\(719\) | 552.973 | − | 761.102i | 0.769086 | − | 1.05856i | −0.227317 | − | 0.973821i | \(-0.572995\pi\) |
0.996403 | − | 0.0847357i | \(-0.0270046\pi\) | |||||||
\(720\) | 104.035 | − | 9.51999i | 0.144492 | − | 0.0132222i | ||||
\(721\) | 153.938 | − | 111.843i | 0.213507 | − | 0.155122i | ||||
\(722\) | 469.810 | + | 74.4106i | 0.650706 | + | 0.103062i | ||||
\(723\) | 162.588 | + | 82.8427i | 0.224880 | + | 0.114582i | ||||
\(724\) | − | 91.6601i | − | 0.126602i | ||||||
\(725\) | 280.841 | − | 152.211i | 0.387367 | − | 0.209946i | ||||
\(726\) | −183.098 | −0.252201 | ||||||||
\(727\) | −460.348 | + | 903.484i | −0.633216 | + | 1.24276i | 0.321969 | + | 0.946750i | \(0.395655\pi\) |
−0.955186 | + | 0.296007i | \(0.904345\pi\) | |||||||
\(728\) | 21.0947 | − | 133.187i | 0.0289762 | − | 0.182949i | ||||
\(729\) | −304.742 | − | 419.442i | −0.418028 | − | 0.575366i | ||||
\(730\) | −387.247 | − | 87.7781i | −0.530476 | − | 0.120244i | ||||
\(731\) | −309.325 | − | 224.738i | −0.423154 | − | 0.307439i | ||||
\(732\) | −207.526 | − | 207.526i | −0.283505 | − | 0.283505i | ||||
\(733\) | −459.050 | + | 72.7064i | −0.626262 | + | 0.0991902i | −0.461496 | − | 0.887142i | \(-0.652687\pi\) |
−0.164766 | + | 0.986333i | \(0.552687\pi\) | |||||||
\(734\) | 13.1532 | + | 4.27373i | 0.0179199 | + | 0.00582251i | ||||
\(735\) | −249.243 | − | 395.355i | −0.339106 | − | 0.537898i | ||||
\(736\) | −59.9980 | − | 184.655i | −0.0815190 | − | 0.250890i | ||||
\(737\) | −32.3077 | + | 16.4616i | −0.0438368 | + | 0.0223359i | ||||
\(738\) | −163.609 | − | 321.101i | −0.221693 | − | 0.435097i | ||||
\(739\) | 548.414 | − | 178.190i | 0.742103 | − | 0.241124i | 0.0865231 | − | 0.996250i | \(-0.472424\pi\) |
0.655580 | + | 0.755126i | \(0.272424\pi\) | |||||||
\(740\) | −100.152 | − | 394.972i | −0.135340 | − | 0.533745i | ||||
\(741\) | 14.4262 | − | 44.3994i | 0.0194686 | − | 0.0599183i | ||||
\(742\) | 107.497 | + | 678.711i | 0.144875 | + | 0.914705i | ||||
\(743\) | 406.087 | − | 406.087i | 0.546550 | − | 0.546550i | −0.378891 | − | 0.925441i | \(-0.623695\pi\) |
0.925441 | + | 0.378891i | \(0.123695\pi\) | |||||||
\(744\) | 33.8851 | − | 46.6389i | 0.0455445 | − | 0.0626866i | ||||
\(745\) | 237.647 | − | 208.253i | 0.318990 | − | 0.279534i | ||||
\(746\) | −523.338 | + | 380.227i | −0.701526 | + | 0.509688i | ||||
\(747\) | 560.754 | + | 88.8146i | 0.750674 | + | 0.118895i | ||||
\(748\) | −412.864 | − | 210.365i | −0.551958 | − | 0.281236i | ||||
\(749\) | − | 34.7768i | − | 0.0464309i | ||||||
\(750\) | −343.256 | − | 13.8743i | −0.457674 | − | 0.0184991i | ||||
\(751\) | 183.361 | 0.244156 | 0.122078 | − | 0.992520i | \(-0.461044\pi\) | ||||
0.122078 | + | 0.992520i | \(0.461044\pi\) | |||||||
\(752\) | −89.2034 | + | 175.072i | −0.118622 | + | 0.232808i | ||||
\(753\) | 37.5836 | − | 237.294i | 0.0499119 | − | 0.315131i | ||||
\(754\) | −51.3885 | − | 70.7302i | −0.0681545 | − | 0.0938067i | ||||
\(755\) | −234.177 | − | 267.231i | −0.310169 | − | 0.353948i | ||||
\(756\) | −440.705 | − | 320.191i | −0.582942 | − | 0.423532i | ||||
\(757\) | −145.626 | − | 145.626i | −0.192373 | − | 0.192373i | 0.604348 | − | 0.796721i | \(-0.293434\pi\) |
−0.796721 | + | 0.604348i | \(0.793434\pi\) | |||||||
\(758\) | −230.724 | + | 36.5431i | −0.304385 | + | 0.0482099i | ||||
\(759\) | 467.780 | + | 151.991i | 0.616310 | + | 0.200251i | ||||
\(760\) | 68.0644 | − | 17.2589i | 0.0895584 | − | 0.0227091i | ||||
\(761\) | 41.7820 | + | 128.592i | 0.0549041 | + | 0.168978i | 0.974748 | − | 0.223306i | \(-0.0716851\pi\) |
−0.919844 | + | 0.392284i | \(0.871685\pi\) | |||||||
\(762\) | −235.191 | + | 119.836i | −0.308649 | + | 0.157265i | ||||
\(763\) | 90.2818 | + | 177.188i | 0.118325 | + | 0.232225i | ||||
\(764\) | 374.981 | − | 121.839i | 0.490813 | − | 0.159475i | ||||
\(765\) | 694.144 | − | 437.607i | 0.907378 | − | 0.572036i | ||||
\(766\) | 111.036 | − | 341.733i | 0.144956 | − | 0.446127i | ||||
\(767\) | −52.6159 | − | 332.204i | −0.0685996 | − | 0.433121i | ||||
\(768\) | −21.9863 | + | 21.9863i | −0.0286280 | + | 0.0286280i | ||||
\(769\) | −257.147 | + | 353.933i | −0.334392 | + | 0.460251i | −0.942793 | − | 0.333379i | \(-0.891811\pi\) |
0.608401 | + | 0.793630i | \(0.291811\pi\) | |||||||
\(770\) | −113.585 | + | 501.097i | −0.147513 | + | 0.650775i | ||||
\(771\) | 101.562 | − | 73.7889i | 0.131727 | − | 0.0957055i | ||||
\(772\) | 208.856 | + | 33.0795i | 0.270538 | + | 0.0428491i | ||||
\(773\) | 692.294 | + | 352.742i | 0.895594 | + | 0.456328i | 0.840287 | − | 0.542141i | \(-0.182386\pi\) |
0.0553069 | + | 0.998469i | \(0.482386\pi\) | |||||||
\(774\) | 89.8966i | 0.116146i | ||||||||
\(775\) | 180.632 | − | 190.060i | 0.233073 | − | 0.245239i | ||||
\(776\) | 157.241 | 0.202631 | ||||||||
\(777\) | −354.241 | + | 695.237i | −0.455908 | + | 0.894771i | ||||
\(778\) | 75.2648 | − | 475.203i | 0.0967413 | − | 0.610801i | ||||
\(779\) | −142.378 | − | 195.966i | −0.182770 | − | 0.251562i | ||||
\(780\) | 8.56807 | + | 93.6320i | 0.0109847 | + | 0.120041i | ||||
\(781\) | 340.919 | + | 247.693i | 0.436517 | + | 0.317148i | ||||
\(782\) | −1078.37 | − | 1078.37i | −1.37899 | − | 1.37899i | ||||
\(783\) | −348.832 | + | 55.2496i | −0.445508 | + | 0.0705615i | ||||
\(784\) | −182.980 | − | 59.4537i | −0.233393 | − | 0.0758339i | ||||
\(785\) | −69.7694 | + | 1058.38i | −0.0888782 | + | 1.34825i | ||||
\(786\) | −19.6939 | − | 60.6117i | −0.0250559 | − | 0.0771141i | ||||
\(787\) | −863.979 | + | 440.219i | −1.09781 | + | 0.559364i | −0.906517 | − | 0.422169i | \(-0.861269\pi\) |
−0.191296 | + | 0.981532i | \(0.561269\pi\) | |||||||
\(788\) | −161.526 | − | 317.013i | −0.204983 | − | 0.402301i | ||||
\(789\) | −70.0496 | + | 22.7605i | −0.0887828 | + | 0.0288473i | ||||
\(790\) | 827.708 | + | 688.924i | 1.04773 | + | 0.872056i | ||||
\(791\) | 366.045 | − | 1126.57i | 0.462762 | − | 1.42424i | ||||
\(792\) | 17.0429 | + | 107.605i | 0.0215189 | + | 0.135865i | ||||
\(793\) | −258.335 | + | 258.335i | −0.325769 | + | 0.325769i | ||||
\(794\) | 110.292 | − | 151.804i | 0.138907 | − | 0.191188i | ||||
\(795\) | −188.971 | − | 440.298i | −0.237699 | − | 0.553834i | ||||
\(796\) | 23.6894 | − | 17.2113i | 0.0297605 | − | 0.0216223i | ||||
\(797\) | 416.756 | + | 66.0077i | 0.522906 | + | 0.0828202i | 0.412307 | − | 0.911045i | \(-0.364723\pi\) |
0.110599 | + | 0.993865i | \(0.464723\pi\) | |||||||
\(798\) | −119.808 | − | 61.0453i | −0.150136 | − | 0.0764979i | ||||
\(799\) | 1543.34i | 1.93159i | ||||||||
\(800\) | −112.262 | + | 86.0075i | −0.140327 | + | 0.107509i | ||||
\(801\) | 690.333 | 0.861839 | ||||||||
\(802\) | 251.086 | − | 492.785i | 0.313075 | − | 0.614445i | ||||
\(803\) | 64.7775 | − | 408.989i | 0.0806694 | − | 0.509327i | ||||
\(804\) | 11.2334 | + | 15.4615i | 0.0139719 | + | 0.0192307i | ||||
\(805\) | −865.169 | + | 1452.97i | −1.07474 | + | 1.80494i | ||||
\(806\) | −58.0576 | − | 42.1813i | −0.0720317 | − | 0.0523341i | ||||
\(807\) | 151.502 | + | 151.502i | 0.187735 | + | 0.187735i | ||||
\(808\) | 510.053 | − | 80.7844i | 0.631253 | − | 0.0999807i | ||||
\(809\) | 1217.64 | + | 395.634i | 1.50511 | + | 0.489041i | 0.941505 | − | 0.337000i | \(-0.109412\pi\) |
0.563610 | + | 0.826041i | \(0.309412\pi\) | |||||||
\(810\) | 44.0251 | + | 17.5834i | 0.0543520 | + | 0.0217079i | ||||
\(811\) | 343.527 | + | 1057.27i | 0.423585 | + | 1.30366i | 0.904343 | + | 0.426807i | \(0.140362\pi\) |
−0.480758 | + | 0.876853i | \(0.659638\pi\) | |||||||
\(812\) | −224.369 | + | 114.322i | −0.276317 | + | 0.140790i | ||||
\(813\) | −160.155 | − | 314.321i | −0.196992 | − | 0.386619i | ||||
\(814\) | 404.136 | − | 131.312i | 0.496481 | − | 0.161317i | ||||
\(815\) | −513.855 | + | 1286.58i | −0.630497 | + | 1.57863i | ||||
\(816\) | −75.4705 | + | 232.274i | −0.0924883 | + | 0.284650i | ||||
\(817\) | 9.45233 | + | 59.6796i | 0.0115696 | + | 0.0730473i | ||||
\(818\) | −185.540 | + | 185.540i | −0.226822 | + | 0.226822i | ||||
\(819\) | −146.377 | + | 201.471i | −0.178726 | + | 0.245996i | ||||
\(820\) | 419.169 | + | 249.593i | 0.511182 | + | 0.304382i | ||||
\(821\) | 736.621 | − | 535.186i | 0.897224 | − | 0.651871i | −0.0405274 | − | 0.999178i | \(-0.512904\pi\) |
0.937751 | + | 0.347307i | \(0.112904\pi\) | |||||||
\(822\) | 369.218 | + | 58.4784i | 0.449171 | + | 0.0711416i | ||||
\(823\) | −977.955 | − | 498.293i | −1.18828 | − | 0.605459i | −0.255818 | − | 0.966725i | \(-0.582345\pi\) |
−0.932463 | + | 0.361266i | \(0.882345\pi\) | |||||||
\(824\) | 54.6168i | 0.0662826i | ||||||||
\(825\) | −9.10882 | − | 358.142i | −0.0110410 | − | 0.434112i | ||||
\(826\) | −968.767 | −1.17284 | ||||||||
\(827\) | −324.913 | + | 637.677i | −0.392881 | + | 0.771073i | −0.999718 | − | 0.0237538i | \(-0.992438\pi\) |
0.606837 | + | 0.794827i | \(0.292438\pi\) | |||||||
\(828\) | −56.0919 | + | 354.150i | −0.0677438 | + | 0.427717i | ||||
\(829\) | −836.025 | − | 1150.69i | −1.00847 | − | 1.38805i | −0.919978 | − | 0.391969i | \(-0.871794\pi\) |
−0.0884961 | − | 0.996077i | \(-0.528206\pi\) | |||||||
\(830\) | −706.262 | + | 303.120i | −0.850918 | + | 0.365204i | ||||
\(831\) | −502.320 | − | 364.957i | −0.604476 | − | 0.439178i | ||||
\(832\) | 27.3693 | + | 27.3693i | 0.0328957 | + | 0.0328957i | ||||
\(833\) | −1492.60 | + | 236.405i | −1.79184 | + | 0.283800i | ||||
\(834\) | −682.684 | − | 221.817i | −0.818566 | − | 0.265968i | ||||
\(835\) | 582.657 | − | 700.033i | 0.697793 | − | 0.838363i | ||||
\(836\) | 22.6286 | + | 69.6436i | 0.0270677 | + | 0.0833058i | ||||
\(837\) | −258.304 | + | 131.613i | −0.308607 | + | 0.157243i | ||||
\(838\) | −137.172 | − | 269.214i | −0.163689 | − | 0.321258i | ||||
\(839\) | 549.819 | − | 178.647i | 0.655327 | − | 0.212928i | 0.0375652 | − | 0.999294i | \(-0.488040\pi\) |
0.617761 | + | 0.786366i | \(0.288040\pi\) | |||||||
\(840\) | 270.227 | + | 17.8136i | 0.321698 | + | 0.0212067i | ||||
\(841\) | 209.432 | − | 644.566i | 0.249027 | − | 0.766428i | ||||
\(842\) | −159.200 | − | 1005.15i | −0.189074 | − | 1.19376i | ||||
\(843\) | 36.2508 | − | 36.2508i | 0.0430021 | − | 0.0430021i | ||||
\(844\) | 193.741 | − | 266.662i | 0.229551 | − | 0.315950i | ||||
\(845\) | −724.928 | + | 66.3367i | −0.857903 | + | 0.0785050i | ||||
\(846\) | 293.566 | − | 213.288i | 0.347005 | − | 0.252114i | ||||
\(847\) | 648.410 | + | 102.698i | 0.765537 | + | 0.121249i | ||||
\(848\) | −175.745 | − | 89.5467i | −0.207247 | − | 0.105597i | ||||
\(849\) | 131.771i | 0.155207i | ||||||||
\(850\) | −478.973 | + | 1002.25i | −0.563497 | + | 1.17911i | ||||
\(851\) | 1398.54 | 1.64341 | ||||||||
\(852\) | 100.834 | − | 197.899i | 0.118350 | − | 0.232276i | ||||
\(853\) | 54.9523 | − | 346.955i | 0.0644224 | − | 0.406747i | −0.934312 | − | 0.356456i | \(-0.883985\pi\) |
0.998735 | − | 0.0502913i | \(-0.0160150\pi\) | |||||||
\(854\) | 618.517 | + | 851.316i | 0.724259 | + | 0.996857i | ||||
\(855\) | −126.469 | − | 28.6670i | −0.147917 | − | 0.0335287i | ||||
\(856\) | 8.07577 | + | 5.86739i | 0.00943431 | + | 0.00685443i | ||||
\(857\) | 942.292 | + | 942.292i | 1.09952 | + | 1.09952i | 0.994466 | + | 0.105058i | \(0.0335029\pi\) |
0.105058 | + | 0.994466i | \(0.466497\pi\) | |||||||
\(858\) | −96.8453 | + | 15.3388i | −0.112873 | + | 0.0178774i | ||||
\(859\) | 540.757 | + | 175.703i | 0.629519 | + | 0.204543i | 0.606362 | − | 0.795189i | \(-0.292628\pi\) |
0.0231569 | + | 0.999732i | \(0.492628\pi\) | |||||||
\(860\) | −64.8991 | − | 102.945i | −0.0754641 | − | 0.119703i | ||||
\(861\) | −288.685 | − | 888.483i | −0.335291 | − | 1.03192i | ||||
\(862\) | −568.275 | + | 289.551i | −0.659252 | + | 0.335906i | ||||
\(863\) | 415.861 | + | 816.174i | 0.481879 | + | 0.945740i | 0.996113 | + | 0.0880901i | \(0.0280764\pi\) |
−0.514234 | + | 0.857650i | \(0.671924\pi\) | |||||||
\(864\) | 148.708 | − | 48.3181i | 0.172115 | − | 0.0559237i | ||||
\(865\) | 97.3958 | + | 384.102i | 0.112596 | + | 0.444048i | ||||
\(866\) | 125.266 | − | 385.529i | 0.144649 | − | 0.445183i | ||||
\(867\) | 212.235 | + | 1340.00i | 0.244792 | + | 1.54556i | ||||
\(868\) | −146.157 | + | 146.157i | −0.168384 | + | 0.168384i | ||||
\(869\) | −660.114 | + | 908.569i | −0.759625 | + | 1.04553i | ||||
\(870\) | 132.052 | − | 115.719i | 0.151784 | − | 0.133010i | ||||
\(871\) | 19.2469 | − | 13.9837i | 0.0220975 | − | 0.0160548i | ||||
\(872\) | −56.3782 | − | 8.92942i | −0.0646538 | − | 0.0102402i | ||||
\(873\) | −258.738 | − | 131.834i | −0.296378 | − | 0.151012i | ||||
\(874\) | 241.007i | 0.275752i | ||||||||
\(875\) | 1207.80 | + | 241.662i | 1.38034 | + | 0.276185i | ||||
\(876\) | −218.253 | −0.249147 | ||||||||
\(877\) | 361.033 | − | 708.567i | 0.411668 | − | 0.807944i | −0.588332 | − | 0.808620i | \(-0.700215\pi\) |
1.00000 | 0.000675700i | \(0.000215082\pi\) | ||||||||
\(878\) | −25.5631 | + | 161.399i | −0.0291152 | + | 0.183826i | ||||
\(879\) | −0.601479 | − | 0.827865i | −0.000684277 | − | 0.000941826i | ||||
\(880\) | −97.1999 | − | 110.919i | −0.110454 | − | 0.126045i | ||||
\(881\) | 422.550 | + | 307.001i | 0.479626 | + | 0.348468i | 0.801181 | − | 0.598423i | \(-0.204206\pi\) |
−0.321555 | + | 0.946891i | \(0.604206\pi\) | |||||||
\(882\) | 251.244 | + | 251.244i | 0.284857 | + | 0.284857i | ||||
\(883\) | −401.805 | + | 63.6396i | −0.455045 | + | 0.0720721i | −0.379750 | − | 0.925089i | \(-0.623990\pi\) |
−0.0752953 | + | 0.997161i | \(0.523990\pi\) | |||||||
\(884\) | 289.142 | + | 93.9481i | 0.327084 | + | 0.106276i | ||||
\(885\) | 654.761 | − | 166.026i | 0.739843 | − | 0.187600i | ||||
\(886\) | 319.266 | + | 982.601i | 0.360346 | + | 1.10903i | ||||
\(887\) | 1105.57 | − | 563.317i | 1.24642 | − | 0.635081i | 0.298746 | − | 0.954333i | \(-0.403432\pi\) |
0.947670 | + | 0.319252i | \(0.103432\pi\) | |||||||
\(888\) | −101.680 | − | 199.558i | −0.114505 | − | 0.224728i | ||||
\(889\) | 900.100 | − | 292.460i | 1.01249 | − | 0.328977i | ||||
\(890\) | −790.531 | + | 498.372i | −0.888237 | + | 0.559969i | ||||
\(891\) | −15.2772 | + | 47.0185i | −0.0171462 | + | 0.0527705i | ||||
\(892\) | 37.7853 | + | 238.567i | 0.0423602 | + | 0.267452i | ||||
\(893\) | 172.463 | − | 172.463i | 0.193128 | − | 0.193128i | ||||
\(894\) | 102.088 | − | 140.512i | 0.114192 | − | 0.157172i | ||||
\(895\) | 0.749377 | − | 3.30600i | 0.000837293 | − | 0.00369385i | ||||
\(896\) | 90.1925 | − | 65.5287i | 0.100661 | − | 0.0731347i | ||||
\(897\) | −318.738 | − | 50.4831i | −0.355338 | − | 0.0562800i | ||||
\(898\) | −769.958 | − | 392.313i | −0.857415 | − | 0.436875i | ||||
\(899\) | 134.012i | 0.149068i | ||||||||
\(900\) | 256.835 | − | 47.4019i | 0.285373 | − | 0.0526688i | ||||
\(901\) | −1549.28 | −1.71951 | ||||||||
\(902\) | −230.972 | + | 453.307i | −0.256066 | + | 0.502558i | ||||
\(903\) | −36.4550 | + | 230.168i | −0.0403710 | + | 0.254892i | ||||
\(904\) | 199.852 | + | 275.072i | 0.221075 | + | 0.304284i | ||||
\(905\) | −20.8818 | − | 228.197i | −0.0230738 | − | 0.252151i | ||||
\(906\) | −158.004 | − | 114.796i | −0.174397 | − | 0.126707i | ||||
\(907\) | −334.245 | − | 334.245i | −0.368517 | − | 0.368517i | 0.498419 | − | 0.866936i | \(-0.333914\pi\) |
−0.866936 | + | 0.498419i | \(0.833914\pi\) | |||||||
\(908\) | 632.646 | − | 100.201i | 0.696747 | − | 0.110354i | ||||
\(909\) | −907.016 | − | 294.707i | −0.997817 | − | 0.324210i | ||||
\(910\) | 22.1750 | − | 336.387i | 0.0243681 | − | 0.369656i | ||||
\(911\) | −483.718 | − | 1488.73i | −0.530975 | − | 1.63417i | −0.752189 | − | 0.658948i | \(-0.771002\pi\) |
0.221213 | − | 0.975225i | \(-0.428998\pi\) | |||||||
\(912\) | 34.3894 | − | 17.5223i | 0.0377076 | − | 0.0192130i | ||||
\(913\) | −363.873 | − | 714.140i | −0.398546 | − | 0.782191i | ||||
\(914\) | 846.609 | − | 275.080i | 0.926268 | − | 0.300963i | ||||
\(915\) | −563.934 | − | 469.378i | −0.616322 | − | 0.512982i | ||||
\(916\) | 163.181 | − | 502.221i | 0.178146 | − | 0.548276i | ||||
\(917\) | 35.7461 | + | 225.692i | 0.0389815 | + | 0.246120i | ||||
\(918\) | 868.440 | − | 868.440i | 0.946013 | − | 0.946013i | ||||
\(919\) | −418.432 | + | 575.923i | −0.455313 | + | 0.626684i | −0.973528 | − | 0.228566i | \(-0.926596\pi\) |
0.518216 | + | 0.855250i | \(0.326596\pi\) | |||||||
\(920\) | −191.438 | − | 446.047i | −0.208085 | − | 0.484834i | ||||
\(921\) | 160.472 | − | 116.590i | 0.174237 | − | 0.126591i | ||||
\(922\) | −586.061 | − | 92.8229i | −0.635641 | − | 0.100676i | ||||
\(923\) | −246.351 | − | 125.522i | −0.266902 | − | 0.135994i | ||||
\(924\) | 282.419i | 0.305648i | ||||||||
\(925\) | −339.320 | − | 960.504i | −0.366832 | − | 1.03838i | ||||
\(926\) | 414.248 | 0.447352 | ||||||||
\(927\) | 45.7917 | − | 89.8713i | 0.0493977 | − | 0.0969485i | ||||
\(928\) | 11.3071 | − | 71.3903i | 0.0121844 | − | 0.0769293i | ||||
\(929\) | −720.018 | − | 991.019i | −0.775046 | − | 1.06676i | −0.995811 | − | 0.0914321i | \(-0.970856\pi\) |
0.220765 | − | 0.975327i | \(-0.429144\pi\) | |||||||
\(930\) | 73.7351 | − | 123.832i | 0.0792851 | − | 0.133152i | ||||
\(931\) | 193.210 | + | 140.376i | 0.207530 | + | 0.150779i | ||||
\(932\) | −206.878 | − | 206.878i | −0.221972 | − | 0.221972i | ||||
\(933\) | −477.765 | + | 75.6706i | −0.512074 | + | 0.0811046i | ||||
\(934\) | 392.190 | + | 127.430i | 0.419903 | + | 0.136435i | ||||
\(935\) | −1075.79 | − | 429.666i | −1.15058 | − | 0.459536i | ||||
\(936\) | −22.0889 | − | 67.9826i | −0.0235992 | − | 0.0726310i | ||||
\(937\) | −104.962 | + | 53.4806i | −0.112019 | + | 0.0570764i | −0.509102 | − | 0.860706i | \(-0.670022\pi\) |
0.397083 | + | 0.917783i | \(0.370022\pi\) | |||||||
\(938\) | −31.1090 | − | 61.0548i | −0.0331652 | − | 0.0650904i | ||||
\(939\) | 634.226 | − | 206.073i | 0.675427 | − | 0.219460i | ||||
\(940\) | −182.196 | + | 456.180i | −0.193826 | + | 0.485298i | ||||
\(941\) | 20.7873 | − | 63.9766i | 0.0220906 | − | 0.0679879i | −0.939403 | − | 0.342813i | \(-0.888620\pi\) |
0.961494 | + | 0.274826i | \(0.0886201\pi\) | |||||||
\(942\) | 91.2025 | + | 575.830i | 0.0968179 | + | 0.611284i | ||||
\(943\) | −1184.00 | + | 1184.00i | −1.25557 | + | 1.25557i | ||||
\(944\) | 163.446 | − | 224.965i | 0.173142 | − | 0.238310i | ||||
\(945\) | −1170.12 | − | 696.745i | −1.23822 | − | 0.737297i | ||||
\(946\) | 102.672 | − | 74.5955i | 0.108533 | − | 0.0788536i | ||||
\(947\) | −42.5385 | − | 6.73744i | −0.0449193 | − | 0.00711451i | 0.133934 | − | 0.990990i | \(-0.457239\pi\) |
−0.178854 | + | 0.983876i | \(0.557239\pi\) | |||||||
\(948\) | 527.411 | + | 268.729i | 0.556341 | + | 0.283470i | ||||
\(949\) | 271.688i | 0.286289i | ||||||||
\(950\) | 165.521 | − | 58.4741i | 0.174233 | − | 0.0615516i | ||||
\(951\) | 303.809 | 0.319462 | ||||||||
\(952\) | 397.546 | − | 780.227i | 0.417590 | − | 0.819566i | ||||
\(953\) | −175.898 | + | 1110.58i | −0.184573 | + | 1.16535i | 0.705221 | + | 0.708988i | \(0.250848\pi\) |
−0.889794 | + | 0.456363i | \(0.849152\pi\) | |||||||
\(954\) | 214.109 | + | 294.696i | 0.224433 | + | 0.308905i | ||||
\(955\) | 905.796 | − | 388.757i | 0.948478 | − | 0.407076i | ||||
\(956\) | 274.850 | + | 199.690i | 0.287500 | + | 0.208881i | ||||
\(957\) | 129.475 | + | 129.475i | 0.135292 | + | 0.135292i | ||||
\(958\) | 1171.31 | − | 185.517i | 1.22266 | − | 0.193650i | ||||
\(959\) | −1274.72 | − | 414.182i | −1.32922 | − | 0.431889i | ||||
\(960\) | −49.7282 | + | 59.7459i | −0.0518002 | + | 0.0622353i | ||||
\(961\) | −262.973 | − | 809.348i | −0.273645 | − | 0.842194i | ||||
\(962\) | −248.417 | + | 126.575i | −0.258230 | + | 0.131575i | ||||
\(963\) | −8.36925 | − | 16.4256i | −0.00869081 | − | 0.0170567i | ||||
\(964\) | 178.606 | − | 58.0327i | 0.185276 | − | 0.0601999i | ||||
\(965\) | 527.502 | + | 34.7735i | 0.546635 | + | 0.0360347i | ||||
\(966\) | −287.231 | + | 884.005i | −0.297340 | + | 0.915120i | ||||
\(967\) | 210.501 | + | 1329.05i | 0.217685 | + | 1.37441i | 0.818264 | + | 0.574842i | \(0.194937\pi\) |
−0.600580 | + | 0.799565i | \(0.705063\pi\) | |||||||
\(968\) | −133.245 | + | 133.245i | −0.137650 | + | 0.137650i | ||||
\(969\) | 178.193 | − | 245.261i | 0.183893 | − | 0.253107i | ||||
\(970\) | 391.468 | − | 35.8224i | 0.403575 | − | 0.0369303i | ||||
\(971\) | −642.430 | + | 466.753i | −0.661617 | + | 0.480693i | −0.867209 | − | 0.497945i | \(-0.834088\pi\) |
0.205592 | + | 0.978638i | \(0.434088\pi\) | |||||||
\(972\) | −465.674 | − | 73.7556i | −0.479089 | − | 0.0758802i | ||||
\(973\) | 2293.19 | + | 1168.44i | 2.35682 | + | 1.20086i | ||||
\(974\) | − | 1200.81i | − | 1.23287i | ||||||
\(975\) | 42.6621 | + | 231.154i | 0.0437560 | + | 0.237081i | ||||
\(976\) | −302.044 | −0.309471 | ||||||||
\(977\) | 517.073 | − | 1014.81i | 0.529245 | − | 1.03870i | −0.459371 | − | 0.888244i | \(-0.651925\pi\) |
0.988616 | − | 0.150458i | \(-0.0480748\pi\) | |||||||
\(978\) | −119.124 | + | 752.122i | −0.121804 | + | 0.769040i | ||||
\(979\) | −572.833 | − | 788.437i | −0.585120 | − | 0.805349i | ||||
\(980\) | −469.091 | − | 106.330i | −0.478664 | − | 0.108500i | ||||
\(981\) | 85.2829 | + | 61.9616i | 0.0869346 | + | 0.0631617i | ||||
\(982\) | −4.87678 | − | 4.87678i | −0.00496617 | − | 0.00496617i | ||||
\(983\) | 325.742 | − | 51.5924i | 0.331375 | − | 0.0524847i | 0.0114699 | − | 0.999934i | \(-0.496349\pi\) |
0.319905 | + | 0.947450i | \(0.396349\pi\) | |||||||
\(984\) | 255.027 | + | 82.8633i | 0.259174 | + | 0.0842107i | ||||
\(985\) | −474.357 | − | 752.436i | −0.481580 | − | 0.763895i | ||||
\(986\) | −175.440 | − | 539.950i | −0.177931 | − | 0.547617i | ||||
\(987\) | 838.128 | − | 427.047i | 0.849167 | − | 0.432672i | ||||
\(988\) | −21.8123 | − | 42.8090i | −0.0220772 | − | 0.0433289i | ||||
\(989\) | 397.242 | − | 129.072i | 0.401661 | − | 0.130507i | ||||
\(990\) | 66.9444 | + | 264.010i | 0.0676206 | + | 0.266677i | ||||
\(991\) | −377.775 | + | 1162.67i | −0.381206 | + | 1.17323i | 0.557989 | + | 0.829848i | \(0.311573\pi\) |
−0.939195 | + | 0.343383i | \(0.888427\pi\) | |||||||
\(992\) | −9.28123 | − | 58.5994i | −0.00935608 | − | 0.0590720i | ||||
\(993\) | 684.200 | − | 684.200i | 0.689023 | − | 0.689023i | ||||
\(994\) | −468.087 | + | 644.266i | −0.470912 | + | 0.648155i | ||||
\(995\) | 55.0559 | − | 48.2461i | 0.0553326 | − | 0.0484886i | ||||
\(996\) | −341.766 | + | 248.307i | −0.343138 | + | 0.249304i | ||||
\(997\) | −651.668 | − | 103.214i | −0.653629 | − | 0.103525i | −0.179192 | − | 0.983814i | \(-0.557348\pi\) |
−0.474437 | + | 0.880289i | \(0.657348\pi\) | |||||||
\(998\) | −457.925 | − | 233.324i | −0.458843 | − | 0.233792i | ||||
\(999\) | 1126.29i | 1.12742i |
(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 | 50.3.f.b.17.2 | yes | 24 | |
4.3 | odd | 2 | 400.3.bg.b.17.2 | 24 | |||
5.2 | odd | 4 | 250.3.f.d.143.2 | 24 | |||
5.3 | odd | 4 | 250.3.f.f.143.2 | 24 | |||
5.4 | even | 2 | 250.3.f.e.107.2 | 24 | |||
25.3 | odd | 20 | inner | 50.3.f.b.3.2 | ✓ | 24 | |
25.4 | even | 10 | 250.3.f.d.7.2 | 24 | |||
25.21 | even | 5 | 250.3.f.f.7.2 | 24 | |||
25.22 | odd | 20 | 250.3.f.e.243.2 | 24 | |||
100.3 | even | 20 | 400.3.bg.b.353.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.3.f.b.3.2 | ✓ | 24 | 25.3 | odd | 20 | inner | |
50.3.f.b.17.2 | yes | 24 | 1.1 | even | 1 | trivial | |
250.3.f.d.7.2 | 24 | 25.4 | even | 10 | |||
250.3.f.d.143.2 | 24 | 5.2 | odd | 4 | |||
250.3.f.e.107.2 | 24 | 5.4 | even | 2 | |||
250.3.f.e.243.2 | 24 | 25.22 | odd | 20 | |||
250.3.f.f.7.2 | 24 | 25.21 | even | 5 | |||
250.3.f.f.143.2 | 24 | 5.3 | odd | 4 | |||
400.3.bg.b.17.2 | 24 | 4.3 | odd | 2 | |||
400.3.bg.b.353.2 | 24 | 100.3 | even | 20 |