Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [42,4,Mod(25,42)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(42, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("42.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 42 = 2 \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 42.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.47808022024\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{1345})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 337x^{2} + 336x + 112896 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(9.41856 - 16.3134i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 42.37 |
Dual form | 42.4.e.c.25.2 |
$q$-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 \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.353553 | + | 0.612372i | ||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 7.91856 | − | 13.7153i | 0.708258 | − | 1.22674i | −0.257245 | − | 0.966346i | \(-0.582815\pi\) |
0.965503 | − | 0.260392i | \(-0.0838518\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 18.3371 | + | 2.59808i | 0.990111 | + | 0.140283i | ||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 15.8371 | + | 27.4307i | 0.500814 | + | 0.867435i | ||||
\(11\) | −25.9186 | − | 44.8923i | −0.710431 | − | 1.23050i | −0.964696 | − | 0.263368i | \(-0.915167\pi\) |
0.254265 | − | 0.967135i | \(-0.418167\pi\) | |||||||
\(12\) | −6.00000 | + | 10.3923i | −0.144338 | + | 0.250000i | ||||
\(13\) | 38.8371 | 0.828575 | 0.414288 | − | 0.910146i | \(-0.364031\pi\) | ||||
0.414288 | + | 0.910146i | \(0.364031\pi\) | |||||||
\(14\) | −22.8371 | + | 29.1627i | −0.435963 | + | 0.556719i | ||||
\(15\) | −47.5114 | −0.817825 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −13.6742 | − | 23.6845i | −0.195088 | − | 0.337902i | 0.751842 | − | 0.659344i | \(-0.229166\pi\) |
−0.946929 | + | 0.321442i | \(0.895832\pi\) | |||||||
\(18\) | −9.00000 | − | 15.5885i | −0.117851 | − | 0.204124i | ||||
\(19\) | −38.2557 | + | 66.2608i | −0.461919 | + | 0.800067i | −0.999057 | − | 0.0434278i | \(-0.986172\pi\) |
0.537138 | + | 0.843494i | \(0.319505\pi\) | |||||||
\(20\) | −63.3485 | −0.708258 | ||||||||
\(21\) | −20.7557 | − | 51.5384i | −0.215679 | − | 0.535552i | ||||
\(22\) | 103.674 | 1.00470 | ||||||||
\(23\) | −73.6742 | + | 127.608i | −0.667919 | + | 1.15687i | 0.310566 | + | 0.950552i | \(0.399481\pi\) |
−0.978485 | + | 0.206318i | \(0.933852\pi\) | |||||||
\(24\) | −12.0000 | − | 20.7846i | −0.102062 | − | 0.176777i | ||||
\(25\) | −62.9072 | − | 108.958i | −0.503258 | − | 0.871668i | ||||
\(26\) | −38.8371 | + | 67.2679i | −0.292946 | + | 0.507397i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −27.6742 | − | 68.7178i | −0.186784 | − | 0.463802i | ||||
\(29\) | 240.208 | 1.53812 | 0.769061 | − | 0.639175i | \(-0.220724\pi\) | ||||
0.769061 | + | 0.639175i | \(0.220724\pi\) | |||||||
\(30\) | 47.5114 | − | 82.2921i | 0.289145 | − | 0.500814i | ||||
\(31\) | 148.337 | + | 256.927i | 0.859424 | + | 1.48857i | 0.872480 | + | 0.488651i | \(0.162511\pi\) |
−0.0130559 | + | 0.999915i | \(0.504156\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −77.7557 | + | 134.677i | −0.410167 | + | 0.710431i | ||||
\(34\) | 54.6970 | 0.275896 | ||||||||
\(35\) | 180.837 | − | 230.927i | 0.873344 | − | 1.11525i | ||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 80.7670 | − | 139.893i | 0.358865 | − | 0.621573i | −0.628906 | − | 0.777481i | \(-0.716497\pi\) |
0.987772 | + | 0.155908i | \(0.0498304\pi\) | |||||||
\(38\) | −76.5114 | − | 132.522i | −0.326626 | − | 0.565733i | ||||
\(39\) | −58.2557 | − | 100.902i | −0.239189 | − | 0.414288i | ||||
\(40\) | 63.3485 | − | 109.723i | 0.250407 | − | 0.433717i | ||||
\(41\) | −102.977 | −0.392252 | −0.196126 | − | 0.980579i | \(-0.562836\pi\) | ||||
−0.196126 | + | 0.980579i | \(0.562836\pi\) | |||||||
\(42\) | 110.023 | + | 15.5885i | 0.404211 | + | 0.0572703i | ||||
\(43\) | −328.557 | −1.16522 | −0.582610 | − | 0.812752i | \(-0.697968\pi\) | ||||
−0.582610 | + | 0.812752i | \(0.697968\pi\) | |||||||
\(44\) | −103.674 | + | 179.569i | −0.355215 | + | 0.615251i | ||||
\(45\) | 71.2670 | + | 123.438i | 0.236086 | + | 0.408913i | ||||
\(46\) | −147.348 | − | 255.215i | −0.472290 | − | 0.818031i | ||||
\(47\) | −33.9773 | + | 58.8504i | −0.105449 | + | 0.182643i | −0.913921 | − | 0.405891i | \(-0.866961\pi\) |
0.808473 | + | 0.588534i | \(0.200295\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 329.500 | + | 95.2825i | 0.960641 | + | 0.277791i | ||||
\(50\) | 251.629 | 0.711714 | ||||||||
\(51\) | −41.0227 | + | 71.0534i | −0.112634 | + | 0.195088i | ||||
\(52\) | −77.6742 | − | 134.536i | −0.207144 | − | 0.358784i | ||||
\(53\) | 33.2443 | + | 57.5808i | 0.0861596 | + | 0.149233i | 0.905885 | − | 0.423524i | \(-0.139207\pi\) |
−0.819725 | + | 0.572757i | \(0.805874\pi\) | |||||||
\(54\) | −27.0000 | + | 46.7654i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −820.951 | −2.01267 | ||||||||
\(56\) | 146.697 | + | 20.7846i | 0.350057 | + | 0.0495975i | ||||
\(57\) | 229.534 | 0.533378 | ||||||||
\(58\) | −240.208 | + | 416.053i | −0.543809 | + | 0.941904i | ||||
\(59\) | 230.964 | + | 400.041i | 0.509643 | + | 0.882728i | 0.999938 | + | 0.0111711i | \(0.00355595\pi\) |
−0.490294 | + | 0.871557i | \(0.663111\pi\) | |||||||
\(60\) | 95.0227 | + | 164.584i | 0.204456 | + | 0.354129i | ||||
\(61\) | −92.6742 | + | 160.516i | −0.194520 | + | 0.336919i | −0.946743 | − | 0.321990i | \(-0.895648\pi\) |
0.752223 | + | 0.658909i | \(0.228982\pi\) | |||||||
\(62\) | −593.348 | −1.21541 | ||||||||
\(63\) | −102.767 | + | 131.232i | −0.205515 | + | 0.262440i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 307.534 | − | 532.665i | 0.586845 | − | 1.01644i | ||||
\(66\) | −155.511 | − | 269.354i | −0.290032 | − | 0.502351i | ||||
\(67\) | −272.604 | − | 472.164i | −0.497073 | − | 0.860956i | 0.502921 | − | 0.864332i | \(-0.332259\pi\) |
−0.999994 | + | 0.00337637i | \(0.998925\pi\) | |||||||
\(68\) | −54.6970 | + | 94.7379i | −0.0975438 | + | 0.168951i | ||||
\(69\) | 442.045 | 0.771247 | ||||||||
\(70\) | 219.140 | + | 544.146i | 0.374175 | + | 0.929113i | ||||
\(71\) | −130.742 | −0.218539 | −0.109270 | − | 0.994012i | \(-0.534851\pi\) | ||||
−0.109270 | + | 0.994012i | \(0.534851\pi\) | |||||||
\(72\) | −36.0000 | + | 62.3538i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −90.6496 | − | 157.010i | −0.145339 | − | 0.251734i | 0.784160 | − | 0.620558i | \(-0.213094\pi\) |
−0.929499 | + | 0.368824i | \(0.879761\pi\) | |||||||
\(74\) | 161.534 | + | 279.785i | 0.253756 | + | 0.439519i | ||||
\(75\) | −188.722 | + | 326.875i | −0.290556 | + | 0.503258i | ||||
\(76\) | 306.045 | 0.461919 | ||||||||
\(77\) | −358.638 | − | 890.533i | −0.530787 | − | 1.31800i | ||||
\(78\) | 233.023 | 0.338264 | ||||||||
\(79\) | 204.848 | − | 354.808i | 0.291737 | − | 0.505304i | −0.682483 | − | 0.730901i | \(-0.739100\pi\) |
0.974221 | + | 0.225597i | \(0.0724333\pi\) | |||||||
\(80\) | 126.697 | + | 219.446i | 0.177064 | + | 0.306685i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 102.977 | − | 178.362i | 0.138682 | − | 0.240205i | ||||
\(83\) | 347.928 | 0.460121 | 0.230061 | − | 0.973176i | \(-0.426108\pi\) | ||||
0.230061 | + | 0.973176i | \(0.426108\pi\) | |||||||
\(84\) | −137.023 | + | 174.976i | −0.177981 | + | 0.227280i | ||||
\(85\) | −433.121 | −0.552689 | ||||||||
\(86\) | 328.557 | − | 569.077i | 0.411967 | − | 0.713548i | ||||
\(87\) | −360.312 | − | 624.080i | −0.444018 | − | 0.769061i | ||||
\(88\) | −207.348 | − | 359.138i | −0.251175 | − | 0.435048i | ||||
\(89\) | −578.580 | + | 1002.13i | −0.689093 | + | 1.19354i | 0.283038 | + | 0.959109i | \(0.408658\pi\) |
−0.972132 | + | 0.234436i | \(0.924676\pi\) | |||||||
\(90\) | −285.068 | −0.333876 | ||||||||
\(91\) | 712.161 | + | 100.902i | 0.820382 | + | 0.116235i | ||||
\(92\) | 589.394 | 0.667919 | ||||||||
\(93\) | 445.011 | − | 770.782i | 0.496188 | − | 0.859424i | ||||
\(94\) | −67.9546 | − | 117.701i | −0.0745636 | − | 0.129148i | ||||
\(95\) | 605.860 | + | 1049.38i | 0.654315 | + | 1.13331i | ||||
\(96\) | −48.0000 | + | 83.1384i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 1618.30 | 1.69395 | 0.846976 | − | 0.531631i | \(-0.178421\pi\) | ||||
0.846976 | + | 0.531631i | \(0.178421\pi\) | |||||||
\(98\) | −494.534 | + | 475.428i | −0.509750 | + | 0.490056i | ||||
\(99\) | 466.534 | 0.473621 | ||||||||
\(100\) | −251.629 | + | 435.834i | −0.251629 | + | 0.435834i | ||||
\(101\) | −359.371 | − | 622.449i | −0.354047 | − | 0.613228i | 0.632907 | − | 0.774228i | \(-0.281861\pi\) |
−0.986954 | + | 0.161000i | \(0.948528\pi\) | |||||||
\(102\) | −82.0454 | − | 142.107i | −0.0796442 | − | 0.137948i | ||||
\(103\) | 805.790 | − | 1395.67i | 0.770843 | − | 1.33514i | −0.166259 | − | 0.986082i | \(-0.553169\pi\) |
0.937102 | − | 0.349057i | \(-0.113498\pi\) | |||||||
\(104\) | 310.697 | 0.292946 | ||||||||
\(105\) | −871.222 | − | 123.438i | −0.809738 | − | 0.114727i | ||||
\(106\) | −132.977 | −0.121848 | ||||||||
\(107\) | −467.335 | + | 809.448i | −0.422234 | + | 0.731330i | −0.996158 | − | 0.0875784i | \(-0.972087\pi\) |
0.573924 | + | 0.818909i | \(0.305420\pi\) | |||||||
\(108\) | −54.0000 | − | 93.5307i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 598.509 | + | 1036.65i | 0.525934 | + | 0.910944i | 0.999544 | + | 0.0302095i | \(0.00961746\pi\) |
−0.473610 | + | 0.880735i | \(0.657049\pi\) | |||||||
\(110\) | 820.951 | − | 1421.93i | 0.711587 | − | 1.23251i | ||||
\(111\) | −484.602 | −0.414382 | ||||||||
\(112\) | −182.697 | + | 233.302i | −0.154136 | + | 0.196830i | ||||
\(113\) | −2384.64 | −1.98521 | −0.992604 | − | 0.121400i | \(-0.961262\pi\) | ||||
−0.992604 | + | 0.121400i | \(0.961262\pi\) | |||||||
\(114\) | −229.534 | + | 397.565i | −0.188578 | + | 0.326626i | ||||
\(115\) | 1166.79 | + | 2020.94i | 0.946118 | + | 1.63872i | ||||
\(116\) | −480.417 | − | 832.106i | −0.384531 | − | 0.666027i | ||||
\(117\) | −174.767 | + | 302.705i | −0.138096 | + | 0.239189i | ||||
\(118\) | −923.856 | −0.720744 | ||||||||
\(119\) | −189.212 | − | 469.832i | −0.145757 | − | 0.361928i | ||||
\(120\) | −380.091 | −0.289145 | ||||||||
\(121\) | −678.044 | + | 1174.41i | −0.509424 | + | 0.882349i | ||||
\(122\) | −185.348 | − | 321.033i | −0.137546 | − | 0.238237i | ||||
\(123\) | 154.466 | + | 267.543i | 0.113234 | + | 0.196126i | ||||
\(124\) | 593.348 | − | 1027.71i | 0.429712 | − | 0.744283i | ||||
\(125\) | −12.8977 | −0.00922883 | ||||||||
\(126\) | −124.534 | − | 309.230i | −0.0880506 | − | 0.218638i | ||||
\(127\) | −2673.92 | −1.86829 | −0.934143 | − | 0.356898i | \(-0.883834\pi\) | ||||
−0.934143 | + | 0.356898i | \(0.883834\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 492.835 | + | 853.616i | 0.336370 | + | 0.582610i | ||||
\(130\) | 615.068 | + | 1065.33i | 0.414962 | + | 0.718735i | ||||
\(131\) | 19.4299 | − | 33.6536i | 0.0129588 | − | 0.0224453i | −0.859473 | − | 0.511181i | \(-0.829208\pi\) |
0.872432 | + | 0.488735i | \(0.162542\pi\) | |||||||
\(132\) | 622.045 | 0.410167 | ||||||||
\(133\) | −873.650 | + | 1115.64i | −0.569587 | + | 0.727356i | ||||
\(134\) | 1090.42 | 0.702968 | ||||||||
\(135\) | 213.801 | − | 370.314i | 0.136304 | − | 0.236086i | ||||
\(136\) | −109.394 | − | 189.476i | −0.0689739 | − | 0.119466i | ||||
\(137\) | 384.072 | + | 665.232i | 0.239514 | + | 0.414851i | 0.960575 | − | 0.278021i | \(-0.0896784\pi\) |
−0.721061 | + | 0.692872i | \(0.756345\pi\) | |||||||
\(138\) | −442.045 | + | 765.645i | −0.272677 | + | 0.472290i | ||||
\(139\) | 1052.55 | 0.642274 | 0.321137 | − | 0.947033i | \(-0.395935\pi\) | ||||
0.321137 | + | 0.947033i | \(0.395935\pi\) | |||||||
\(140\) | −1161.63 | − | 164.584i | −0.701254 | − | 0.0993564i | ||||
\(141\) | 203.864 | 0.121762 | ||||||||
\(142\) | 130.742 | − | 226.453i | 0.0772652 | − | 0.133827i | ||||
\(143\) | −1006.60 | − | 1743.49i | −0.588646 | − | 1.01956i | ||||
\(144\) | −72.0000 | − | 124.708i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 1902.10 | − | 3294.54i | 1.08939 | − | 1.88687i | ||||
\(146\) | 362.598 | 0.205540 | ||||||||
\(147\) | −246.699 | − | 998.990i | −0.138418 | − | 0.560512i | ||||
\(148\) | −646.136 | −0.358865 | ||||||||
\(149\) | −180.489 | + | 312.615i | −0.0992363 | + | 0.171882i | −0.911369 | − | 0.411591i | \(-0.864973\pi\) |
0.812132 | + | 0.583473i | \(0.198307\pi\) | |||||||
\(150\) | −377.443 | − | 653.751i | −0.205454 | − | 0.355857i | ||||
\(151\) | −774.195 | − | 1340.95i | −0.417239 | − | 0.722679i | 0.578422 | − | 0.815738i | \(-0.303669\pi\) |
−0.995661 | + | 0.0930587i | \(0.970336\pi\) | |||||||
\(152\) | −306.045 | + | 530.086i | −0.163313 | + | 0.282866i | ||||
\(153\) | 246.136 | 0.130058 | ||||||||
\(154\) | 1901.09 | + | 269.354i | 0.994766 | + | 0.140942i | ||||
\(155\) | 4698.47 | 2.43477 | ||||||||
\(156\) | −233.023 | + | 403.607i | −0.119595 | + | 0.207144i | ||||
\(157\) | 483.534 | + | 837.506i | 0.245798 | + | 0.425734i | 0.962356 | − | 0.271794i | \(-0.0876168\pi\) |
−0.716558 | + | 0.697528i | \(0.754283\pi\) | |||||||
\(158\) | 409.697 | + | 709.616i | 0.206289 | + | 0.357304i | ||||
\(159\) | 99.7330 | − | 172.743i | 0.0497443 | − | 0.0861596i | ||||
\(160\) | −506.788 | −0.250407 | ||||||||
\(161\) | −1682.51 | + | 2148.54i | −0.823604 | + | 1.05173i | ||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 663.250 | − | 1148.78i | 0.318710 | − | 0.552022i | −0.661509 | − | 0.749937i | \(-0.730084\pi\) |
0.980219 | + | 0.197915i | \(0.0634170\pi\) | |||||||
\(164\) | 205.955 | + | 356.724i | 0.0980631 | + | 0.169850i | ||||
\(165\) | 1231.43 | + | 2132.89i | 0.581008 | + | 1.00634i | ||||
\(166\) | −347.928 | + | 602.629i | −0.162677 | + | 0.281766i | ||||
\(167\) | 1416.70 | 0.656451 | 0.328225 | − | 0.944599i | \(-0.393549\pi\) | ||||
0.328225 | + | 0.944599i | \(0.393549\pi\) | |||||||
\(168\) | −166.045 | − | 412.307i | −0.0762541 | − | 0.189346i | ||||
\(169\) | −688.678 | −0.313463 | ||||||||
\(170\) | 433.121 | − | 750.188i | 0.195405 | − | 0.338452i | ||||
\(171\) | −344.301 | − | 596.347i | −0.153973 | − | 0.266689i | ||||
\(172\) | 657.114 | + | 1138.15i | 0.291305 | + | 0.504555i | ||||
\(173\) | 518.299 | − | 897.721i | 0.227778 | − | 0.394523i | −0.729371 | − | 0.684118i | \(-0.760187\pi\) |
0.957149 | + | 0.289595i | \(0.0935207\pi\) | |||||||
\(174\) | 1441.25 | 0.627936 | ||||||||
\(175\) | −870.454 | − | 2161.42i | −0.376001 | − | 0.933647i | ||||
\(176\) | 829.394 | 0.355215 | ||||||||
\(177\) | 692.892 | − | 1200.12i | 0.294243 | − | 0.509643i | ||||
\(178\) | −1157.16 | − | 2004.26i | −0.487263 | − | 0.843964i | ||||
\(179\) | 383.716 | + | 664.615i | 0.160225 | + | 0.277518i | 0.934949 | − | 0.354781i | \(-0.115445\pi\) |
−0.774724 | + | 0.632299i | \(0.782111\pi\) | |||||||
\(180\) | 285.068 | − | 493.753i | 0.118043 | − | 0.204456i | ||||
\(181\) | −3957.71 | −1.62527 | −0.812636 | − | 0.582772i | \(-0.801968\pi\) | ||||
−0.812636 | + | 0.582772i | \(0.801968\pi\) | |||||||
\(182\) | −886.928 | + | 1132.60i | −0.361228 | + | 0.461284i | ||||
\(183\) | 556.045 | 0.224612 | ||||||||
\(184\) | −589.394 | + | 1020.86i | −0.236145 | + | 0.409015i | ||||
\(185\) | −1279.12 | − | 2215.50i | −0.508338 | − | 0.880468i | ||||
\(186\) | 890.023 | + | 1541.56i | 0.350858 | + | 0.607704i | ||||
\(187\) | −708.833 | + | 1227.74i | −0.277193 | + | 0.480112i | ||||
\(188\) | 271.818 | 0.105449 | ||||||||
\(189\) | 495.102 | + | 70.1481i | 0.190547 | + | 0.0269975i | ||||
\(190\) | −2423.44 | −0.925341 | ||||||||
\(191\) | 902.648 | − | 1563.43i | 0.341954 | − | 0.592282i | −0.642841 | − | 0.765999i | \(-0.722244\pi\) |
0.984796 | + | 0.173717i | \(0.0555778\pi\) | |||||||
\(192\) | −96.0000 | − | 166.277i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −1685.42 | − | 2919.23i | −0.628597 | − | 1.08876i | −0.987833 | − | 0.155515i | \(-0.950296\pi\) |
0.359237 | − | 0.933247i | \(-0.383037\pi\) | |||||||
\(194\) | −1618.30 | + | 2802.98i | −0.598903 | + | 1.03733i | ||||
\(195\) | −1845.20 | −0.677630 | ||||||||
\(196\) | −328.932 | − | 1331.99i | −0.119873 | − | 0.485418i | ||||
\(197\) | −4612.31 | −1.66809 | −0.834044 | − | 0.551697i | \(-0.813980\pi\) | ||||
−0.834044 | + | 0.551697i | \(0.813980\pi\) | |||||||
\(198\) | −466.534 | + | 808.061i | −0.167450 | + | 0.290032i | ||||
\(199\) | 1114.93 | + | 1931.12i | 0.397163 | + | 0.687906i | 0.993375 | − | 0.114921i | \(-0.0366615\pi\) |
−0.596212 | + | 0.802827i | \(0.703328\pi\) | |||||||
\(200\) | −503.258 | − | 871.668i | −0.177928 | − | 0.308181i | ||||
\(201\) | −817.812 | + | 1416.49i | −0.286985 | + | 0.497073i | ||||
\(202\) | 1437.48 | 0.500698 | ||||||||
\(203\) | 4404.73 | + | 624.080i | 1.52291 | + | 0.215772i | ||||
\(204\) | 328.182 | 0.112634 | ||||||||
\(205\) | −815.432 | + | 1412.37i | −0.277816 | + | 0.481191i | ||||
\(206\) | 1611.58 | + | 2791.34i | 0.545068 | + | 0.944086i | ||||
\(207\) | −663.068 | − | 1148.47i | −0.222640 | − | 0.385623i | ||||
\(208\) | −310.697 | + | 538.143i | −0.103572 | + | 0.179392i | ||||
\(209\) | 3966.13 | 1.31265 | ||||||||
\(210\) | 1085.02 | − | 1385.56i | 0.356541 | − | 0.455299i | ||||
\(211\) | 912.614 | 0.297758 | 0.148879 | − | 0.988855i | \(-0.452434\pi\) | ||||
0.148879 | + | 0.988855i | \(0.452434\pi\) | |||||||
\(212\) | 132.977 | − | 230.323i | 0.0430798 | − | 0.0746164i | ||||
\(213\) | 196.114 | + | 339.679i | 0.0630868 | + | 0.109270i | ||||
\(214\) | −934.670 | − | 1618.90i | −0.298564 | − | 0.517129i | ||||
\(215\) | −2601.70 | + | 4506.27i | −0.825276 | + | 1.42942i | ||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 2052.56 | + | 5096.70i | 0.642105 | + | 1.59441i | ||||
\(218\) | −2394.04 | −0.743783 | ||||||||
\(219\) | −271.949 | + | 471.029i | −0.0839114 | + | 0.145339i | ||||
\(220\) | 1641.90 | + | 2843.86i | 0.503168 | + | 0.871513i | ||||
\(221\) | −531.068 | − | 919.837i | −0.161645 | − | 0.279977i | ||||
\(222\) | 484.602 | − | 839.356i | 0.146506 | − | 0.253756i | ||||
\(223\) | −4319.47 | −1.29710 | −0.648549 | − | 0.761173i | \(-0.724624\pi\) | ||||
−0.648549 | + | 0.761173i | \(0.724624\pi\) | |||||||
\(224\) | −221.394 | − | 549.742i | −0.0660380 | − | 0.163979i | ||||
\(225\) | 1132.33 | 0.335505 | ||||||||
\(226\) | 2384.64 | − | 4130.32i | 0.701877 | − | 1.21569i | ||||
\(227\) | −1030.64 | − | 1785.12i | −0.301349 | − | 0.521951i | 0.675093 | − | 0.737733i | \(-0.264103\pi\) |
−0.976442 | + | 0.215782i | \(0.930770\pi\) | |||||||
\(228\) | −459.068 | − | 795.129i | −0.133344 | − | 0.230959i | ||||
\(229\) | 1737.32 | − | 3009.12i | 0.501332 | − | 0.868333i | −0.498667 | − | 0.866794i | \(-0.666177\pi\) |
0.999999 | − | 0.00153905i | \(-0.000489896\pi\) | |||||||
\(230\) | −4667.15 | −1.33801 | ||||||||
\(231\) | −1775.72 | + | 2267.57i | −0.505773 | + | 0.645866i | ||||
\(232\) | 1921.67 | 0.543809 | ||||||||
\(233\) | −388.049 | + | 672.121i | −0.109107 | + | 0.188979i | −0.915409 | − | 0.402525i | \(-0.868132\pi\) |
0.806302 | + | 0.591505i | \(0.201466\pi\) | |||||||
\(234\) | −349.534 | − | 605.411i | −0.0976485 | − | 0.169132i | ||||
\(235\) | 538.102 | + | 932.020i | 0.149370 | + | 0.258716i | ||||
\(236\) | 923.856 | − | 1600.17i | 0.254822 | − | 0.441364i | ||||
\(237\) | −1229.09 | −0.336869 | ||||||||
\(238\) | 1002.98 | + | 142.107i | 0.273167 | + | 0.0387035i | ||||
\(239\) | 2006.80 | 0.543133 | 0.271567 | − | 0.962420i | \(-0.412458\pi\) | ||||
0.271567 | + | 0.962420i | \(0.412458\pi\) | |||||||
\(240\) | 380.091 | − | 658.337i | 0.102228 | − | 0.177064i | ||||
\(241\) | −402.824 | − | 697.711i | −0.107669 | − | 0.186488i | 0.807157 | − | 0.590337i | \(-0.201005\pi\) |
−0.914825 | + | 0.403850i | \(0.867672\pi\) | |||||||
\(242\) | −1356.09 | − | 2348.81i | −0.360217 | − | 0.623915i | ||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 741.394 | 0.194520 | ||||||||
\(245\) | 3916.00 | − | 3764.71i | 1.02116 | − | 0.981707i | ||||
\(246\) | −617.864 | −0.160136 | ||||||||
\(247\) | −1485.74 | + | 2573.38i | −0.382734 | + | 0.662915i | ||||
\(248\) | 1186.70 | + | 2055.42i | 0.303852 | + | 0.526287i | ||||
\(249\) | −521.892 | − | 903.944i | −0.132826 | − | 0.230061i | ||||
\(250\) | 12.8977 | − | 22.3394i | 0.00326289 | − | 0.00565148i | ||||
\(251\) | 1421.78 | 0.357539 | 0.178769 | − | 0.983891i | \(-0.442788\pi\) | ||||
0.178769 | + | 0.983891i | \(0.442788\pi\) | |||||||
\(252\) | 660.136 | + | 93.5307i | 0.165019 | + | 0.0233805i | ||||
\(253\) | 7638.12 | 1.89804 | ||||||||
\(254\) | 2673.92 | − | 4631.37i | 0.660539 | − | 1.14409i | ||||
\(255\) | 649.682 | + | 1125.28i | 0.159548 | + | 0.276345i | ||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 732.909 | − | 1269.44i | 0.177890 | − | 0.308114i | −0.763268 | − | 0.646082i | \(-0.776406\pi\) |
0.941157 | + | 0.337968i | \(0.109740\pi\) | |||||||
\(258\) | −1971.34 | −0.475699 | ||||||||
\(259\) | 1844.49 | − | 2355.39i | 0.442513 | − | 0.565084i | ||||
\(260\) | −2460.27 | −0.586845 | ||||||||
\(261\) | −1080.94 | + | 1872.24i | −0.256354 | + | 0.444018i | ||||
\(262\) | 38.8598 | + | 67.3072i | 0.00916324 | + | 0.0158712i | ||||
\(263\) | −3495.69 | − | 6054.72i | −0.819596 | − | 1.41958i | −0.905980 | − | 0.423320i | \(-0.860865\pi\) |
0.0863847 | − | 0.996262i | \(-0.472469\pi\) | |||||||
\(264\) | −622.045 | + | 1077.41i | −0.145016 | + | 0.251175i | ||||
\(265\) | 1052.99 | 0.244093 | ||||||||
\(266\) | −1058.70 | − | 2628.85i | −0.244033 | − | 0.605958i | ||||
\(267\) | 3471.48 | 0.795696 | ||||||||
\(268\) | −1090.42 | + | 1888.66i | −0.248537 | + | 0.430478i | ||||
\(269\) | −404.479 | − | 700.578i | −0.0916786 | − | 0.158792i | 0.816539 | − | 0.577290i | \(-0.195890\pi\) |
−0.908218 | + | 0.418498i | \(0.862557\pi\) | |||||||
\(270\) | 427.602 | + | 740.629i | 0.0963816 | + | 0.166938i | ||||
\(271\) | −3330.88 | + | 5769.26i | −0.746630 | + | 1.29320i | 0.202799 | + | 0.979220i | \(0.434996\pi\) |
−0.949429 | + | 0.313981i | \(0.898337\pi\) | |||||||
\(272\) | 437.576 | 0.0975438 | ||||||||
\(273\) | −806.091 | − | 2001.60i | −0.178706 | − | 0.443745i | ||||
\(274\) | −1536.29 | −0.338725 | ||||||||
\(275\) | −3260.93 | + | 5648.09i | −0.715059 | + | 1.23852i | ||||
\(276\) | −884.091 | − | 1531.29i | −0.192812 | − | 0.333960i | ||||
\(277\) | 3765.73 | + | 6522.44i | 0.816827 | + | 1.41479i | 0.908009 | + | 0.418951i | \(0.137602\pi\) |
−0.0911823 | + | 0.995834i | \(0.529065\pi\) | |||||||
\(278\) | −1052.55 | + | 1823.07i | −0.227078 | + | 0.393311i | ||||
\(279\) | −2670.07 | −0.572949 | ||||||||
\(280\) | 1446.70 | − | 1847.42i | 0.308774 | − | 0.394301i | ||||
\(281\) | 1690.19 | 0.358819 | 0.179410 | − | 0.983774i | \(-0.442581\pi\) | ||||
0.179410 | + | 0.983774i | \(0.442581\pi\) | |||||||
\(282\) | −203.864 | + | 353.102i | −0.0430493 | + | 0.0745636i | ||||
\(283\) | −1589.12 | − | 2752.43i | −0.333792 | − | 0.578145i | 0.649460 | − | 0.760396i | \(-0.274995\pi\) |
−0.983252 | + | 0.182251i | \(0.941662\pi\) | |||||||
\(284\) | 261.485 | + | 452.905i | 0.0546348 | + | 0.0946302i | ||||
\(285\) | 1817.58 | − | 3148.14i | 0.377769 | − | 0.654315i | ||||
\(286\) | 4026.41 | 0.832470 | ||||||||
\(287\) | −1888.31 | − | 267.543i | −0.388374 | − | 0.0550263i | ||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | 2082.53 | − | 3607.05i | 0.423882 | − | 0.734184i | ||||
\(290\) | 3804.21 | + | 6589.08i | 0.770313 | + | 1.33422i | ||||
\(291\) | −2427.45 | − | 4204.46i | −0.489002 | − | 0.846976i | ||||
\(292\) | −362.598 | + | 628.039i | −0.0726694 | + | 0.125867i | ||||
\(293\) | −2176.53 | −0.433974 | −0.216987 | − | 0.976174i | \(-0.569623\pi\) | ||||
−0.216987 | + | 0.976174i | \(0.569623\pi\) | |||||||
\(294\) | 1977.00 | + | 571.695i | 0.392180 | + | 0.113408i | ||||
\(295\) | 7315.61 | 1.44383 | ||||||||
\(296\) | 646.136 | − | 1119.14i | 0.126878 | − | 0.219759i | ||||
\(297\) | −699.801 | − | 1212.09i | −0.136722 | − | 0.236810i | ||||
\(298\) | −360.977 | − | 625.231i | −0.0701706 | − | 0.121539i | ||||
\(299\) | −2861.30 | + | 4955.91i | −0.553421 | + | 0.958554i | ||||
\(300\) | 1509.77 | 0.290556 | ||||||||
\(301\) | −6024.79 | − | 853.616i | −1.15370 | − | 0.163460i | ||||
\(302\) | 3096.78 | 0.590065 | ||||||||
\(303\) | −1078.11 | + | 1867.35i | −0.204409 | + | 0.354047i | ||||
\(304\) | −612.091 | − | 1060.17i | −0.115480 | − | 0.200017i | ||||
\(305\) | 1467.69 | + | 2542.12i | 0.275541 | + | 0.477250i | ||||
\(306\) | −246.136 | + | 426.321i | −0.0459826 | + | 0.0796442i | ||||
\(307\) | 623.504 | 0.115913 | 0.0579564 | − | 0.998319i | \(-0.481542\pi\) | ||||
0.0579564 | + | 0.998319i | \(0.481542\pi\) | |||||||
\(308\) | −2367.62 | + | 3023.43i | −0.438012 | + | 0.559337i | ||||
\(309\) | −4834.74 | −0.890093 | ||||||||
\(310\) | −4698.47 | + | 8137.98i | −0.860822 | + | 1.49099i | ||||
\(311\) | −233.996 | − | 405.293i | −0.0426647 | − | 0.0738973i | 0.843905 | − | 0.536493i | \(-0.180251\pi\) |
−0.886569 | + | 0.462596i | \(0.846918\pi\) | |||||||
\(312\) | −466.045 | − | 807.214i | −0.0845661 | − | 0.146473i | ||||
\(313\) | −1806.41 | + | 3128.79i | −0.326211 | + | 0.565014i | −0.981757 | − | 0.190141i | \(-0.939105\pi\) |
0.655546 | + | 0.755156i | \(0.272439\pi\) | |||||||
\(314\) | −1934.14 | −0.347610 | ||||||||
\(315\) | 986.131 | + | 2448.66i | 0.176388 | + | 0.437988i | ||||
\(316\) | −1638.79 | −0.291737 | ||||||||
\(317\) | −2265.87 | + | 3924.60i | −0.401463 | + | 0.695355i | −0.993903 | − | 0.110260i | \(-0.964832\pi\) |
0.592439 | + | 0.805615i | \(0.298165\pi\) | |||||||
\(318\) | 199.466 | + | 345.485i | 0.0351745 | + | 0.0609240i | ||||
\(319\) | −6225.85 | − | 10783.5i | −1.09273 | − | 1.89266i | ||||
\(320\) | 506.788 | − | 877.782i | 0.0885322 | − | 0.153342i | ||||
\(321\) | 2804.01 | 0.487553 | ||||||||
\(322\) | −2038.88 | − | 5062.73i | −0.352864 | − | 0.876196i | ||||
\(323\) | 2092.47 | 0.360459 | ||||||||
\(324\) | −162.000 | + | 280.592i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −2443.13 | − | 4231.63i | −0.416987 | − | 0.722242i | ||||
\(326\) | 1326.50 | + | 2297.57i | 0.225362 | + | 0.390339i | ||||
\(327\) | 1795.53 | − | 3109.95i | 0.303648 | − | 0.525934i | ||||
\(328\) | −823.818 | −0.138682 | ||||||||
\(329\) | −775.943 | + | 990.871i | −0.130028 | + | 0.166044i | ||||
\(330\) | −4925.70 | −0.821670 | ||||||||
\(331\) | 618.528 | − | 1071.32i | 0.102711 | − | 0.177901i | −0.810090 | − | 0.586306i | \(-0.800582\pi\) |
0.912801 | + | 0.408405i | \(0.133915\pi\) | |||||||
\(332\) | −695.856 | − | 1205.26i | −0.115030 | − | 0.199238i | ||||
\(333\) | 726.903 | + | 1259.03i | 0.119622 | + | 0.207191i | ||||
\(334\) | −1416.70 | + | 2453.79i | −0.232090 | + | 0.401992i | ||||
\(335\) | −8634.53 | −1.40822 | ||||||||
\(336\) | 880.182 | + | 124.708i | 0.142910 | + | 0.0202481i | ||||
\(337\) | −1867.83 | −0.301921 | −0.150960 | − | 0.988540i | \(-0.548237\pi\) | ||||
−0.150960 | + | 0.988540i | \(0.548237\pi\) | |||||||
\(338\) | 688.678 | − | 1192.83i | 0.110826 | − | 0.191956i | ||||
\(339\) | 3576.97 | + | 6195.49i | 0.573080 | + | 0.992604i | ||||
\(340\) | 866.242 | + | 1500.38i | 0.138172 | + | 0.239322i | ||||
\(341\) | 7689.37 | − | 13318.4i | 1.22112 | − | 2.11505i | ||||
\(342\) | 1377.20 | 0.217751 | ||||||||
\(343\) | 5794.53 | + | 2603.27i | 0.912173 | + | 0.409806i | ||||
\(344\) | −2628.45 | −0.411967 | ||||||||
\(345\) | 3500.36 | − | 6062.81i | 0.546241 | − | 0.946118i | ||||
\(346\) | 1036.60 | + | 1795.44i | 0.161063 | + | 0.278970i | ||||
\(347\) | 31.6819 | + | 54.8746i | 0.00490136 | + | 0.00848940i | 0.868466 | − | 0.495749i | \(-0.165107\pi\) |
−0.863564 | + | 0.504239i | \(0.831773\pi\) | |||||||
\(348\) | −1441.25 | + | 2496.32i | −0.222009 | + | 0.384531i | ||||
\(349\) | 1223.79 | 0.187702 | 0.0938508 | − | 0.995586i | \(-0.470082\pi\) | ||||
0.0938508 | + | 0.995586i | \(0.470082\pi\) | |||||||
\(350\) | 4614.15 | + | 653.751i | 0.704676 | + | 0.0998413i | ||||
\(351\) | 1048.60 | 0.159459 | ||||||||
\(352\) | −829.394 | + | 1436.55i | −0.125588 | + | 0.217524i | ||||
\(353\) | 2257.81 | + | 3910.64i | 0.340428 | + | 0.589638i | 0.984512 | − | 0.175316i | \(-0.0560949\pi\) |
−0.644085 | + | 0.764954i | \(0.722762\pi\) | |||||||
\(354\) | 1385.78 | + | 2400.25i | 0.208061 | + | 0.360372i | ||||
\(355\) | −1035.29 | + | 1793.18i | −0.154782 | + | 0.268090i | ||||
\(356\) | 4628.64 | 0.689093 | ||||||||
\(357\) | −936.841 | + | 1196.34i | −0.138888 | + | 0.177358i | ||||
\(358\) | −1534.86 | −0.226592 | ||||||||
\(359\) | −1114.25 | + | 1929.93i | −0.163810 | + | 0.283727i | −0.936232 | − | 0.351383i | \(-0.885712\pi\) |
0.772422 | + | 0.635109i | \(0.219045\pi\) | |||||||
\(360\) | 570.136 | + | 987.505i | 0.0834690 | + | 0.144572i | ||||
\(361\) | 502.506 | + | 870.365i | 0.0732622 | + | 0.126894i | ||||
\(362\) | 3957.71 | − | 6854.95i | 0.574620 | − | 0.995271i | ||||
\(363\) | 4068.26 | 0.588232 | ||||||||
\(364\) | −1074.79 | − | 2668.80i | −0.154764 | − | 0.384295i | ||||
\(365\) | −2871.26 | −0.411749 | ||||||||
\(366\) | −556.045 | + | 963.099i | −0.0794125 | + | 0.137546i | ||||
\(367\) | 718.670 | + | 1244.77i | 0.102219 | + | 0.177048i | 0.912598 | − | 0.408857i | \(-0.134072\pi\) |
−0.810380 | + | 0.585905i | \(0.800739\pi\) | |||||||
\(368\) | −1178.79 | − | 2041.72i | −0.166980 | − | 0.289217i | ||||
\(369\) | 463.398 | − | 802.628i | 0.0653754 | − | 0.113234i | ||||
\(370\) | 5116.47 | 0.718899 | ||||||||
\(371\) | 460.006 | + | 1142.24i | 0.0643728 | + | 0.159844i | ||||
\(372\) | −3560.09 | −0.496188 | ||||||||
\(373\) | 6118.71 | − | 10597.9i | 0.849370 | − | 1.47115i | −0.0324014 | − | 0.999475i | \(-0.510315\pi\) |
0.881771 | − | 0.471677i | \(-0.156351\pi\) | |||||||
\(374\) | −1417.67 | − | 2455.47i | −0.196005 | − | 0.339490i | ||||
\(375\) | 19.3465 | + | 33.5092i | 0.00266413 | + | 0.00461442i | ||||
\(376\) | −271.818 | + | 470.803i | −0.0372818 | + | 0.0645740i | ||||
\(377\) | 9329.00 | 1.27445 | ||||||||
\(378\) | −616.602 | + | 787.394i | −0.0839011 | + | 0.107141i | ||||
\(379\) | −10647.0 | −1.44301 | −0.721503 | − | 0.692411i | \(-0.756549\pi\) | ||||
−0.721503 | + | 0.692411i | \(0.756549\pi\) | |||||||
\(380\) | 2423.44 | − | 4197.52i | 0.327157 | − | 0.566653i | ||||
\(381\) | 4010.89 | + | 6947.06i | 0.539328 | + | 0.934143i | ||||
\(382\) | 1805.30 | + | 3126.86i | 0.241798 | + | 0.418807i | ||||
\(383\) | 3357.41 | − | 5815.20i | 0.447925 | − | 0.775829i | −0.550326 | − | 0.834950i | \(-0.685496\pi\) |
0.998251 | + | 0.0591208i | \(0.0188297\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | −15053.9 | − | 2132.89i | −1.99277 | − | 0.282344i | ||||
\(386\) | 6741.68 | 0.888970 | ||||||||
\(387\) | 1478.51 | − | 2560.85i | 0.194203 | − | 0.336370i | ||||
\(388\) | −3236.60 | − | 5605.95i | −0.423488 | − | 0.733503i | ||||
\(389\) | 5326.54 | + | 9225.83i | 0.694258 | + | 1.20249i | 0.970430 | + | 0.241381i | \(0.0776005\pi\) |
−0.276173 | + | 0.961108i | \(0.589066\pi\) | |||||||
\(390\) | 1845.20 | − | 3195.99i | 0.239578 | − | 0.414962i | ||||
\(391\) | 4029.76 | 0.521211 | ||||||||
\(392\) | 2636.00 | + | 762.260i | 0.339638 | + | 0.0982141i | ||||
\(393\) | −116.580 | −0.0149635 | ||||||||
\(394\) | 4612.31 | − | 7988.76i | 0.589758 | − | 1.02149i | ||||
\(395\) | −3244.21 | − | 5619.14i | −0.413250 | − | 0.715771i | ||||
\(396\) | −933.068 | − | 1616.12i | −0.118405 | − | 0.205084i | ||||
\(397\) | −1610.52 | + | 2789.50i | −0.203601 | + | 0.352648i | −0.949686 | − | 0.313203i | \(-0.898598\pi\) |
0.746085 | + | 0.665851i | \(0.231931\pi\) | |||||||
\(398\) | −4459.73 | −0.561673 | ||||||||
\(399\) | 4208.99 | + | 596.347i | 0.528103 | + | 0.0748238i | ||||
\(400\) | 2013.03 | 0.251629 | ||||||||
\(401\) | −6242.50 | + | 10812.3i | −0.777395 | + | 1.34649i | 0.156043 | + | 0.987750i | \(0.450126\pi\) |
−0.933438 | + | 0.358738i | \(0.883207\pi\) | |||||||
\(402\) | −1635.62 | − | 2832.99i | −0.202929 | − | 0.351484i | ||||
\(403\) | 5760.99 | + | 9978.32i | 0.712097 | + | 1.23339i | ||||
\(404\) | −1437.48 | + | 2489.80i | −0.177024 | + | 0.306614i | ||||
\(405\) | −1282.81 | −0.157391 | ||||||||
\(406\) | −5485.67 | + | 7005.14i | −0.670564 | + | 0.856303i | ||||
\(407\) | −8373.46 | −1.01980 | ||||||||
\(408\) | −328.182 | + | 568.428i | −0.0398221 | + | 0.0689739i | ||||
\(409\) | −3518.69 | − | 6094.56i | −0.425399 | − | 0.736813i | 0.571059 | − | 0.820909i | \(-0.306533\pi\) |
−0.996458 | + | 0.0840967i | \(0.973200\pi\) | |||||||
\(410\) | −1630.86 | − | 2824.74i | −0.196445 | − | 0.340253i | ||||
\(411\) | 1152.22 | − | 1995.70i | 0.138284 | − | 0.239514i | ||||
\(412\) | −6446.32 | −0.770843 | ||||||||
\(413\) | 3195.88 | + | 7935.67i | 0.380772 | + | 0.945493i | ||||
\(414\) | 2652.27 | 0.314860 | ||||||||
\(415\) | 2755.09 | − | 4771.95i | 0.325884 | − | 0.564448i | ||||
\(416\) | −621.394 | − | 1076.29i | −0.0732364 | − | 0.126849i | ||||
\(417\) | −1578.82 | − | 2734.60i | −0.185408 | − | 0.321137i | ||||
\(418\) | −3966.13 | + | 6869.54i | −0.464090 | + | 0.803828i | ||||
\(419\) | −1549.66 | −0.180682 | −0.0903410 | − | 0.995911i | \(-0.528796\pi\) | ||||
−0.0903410 | + | 0.995911i | \(0.528796\pi\) | |||||||
\(420\) | 1314.84 | + | 3264.88i | 0.152756 | + | 0.379309i | ||||
\(421\) | 5531.63 | 0.640369 | 0.320184 | − | 0.947355i | \(-0.396255\pi\) | ||||
0.320184 | + | 0.947355i | \(0.396255\pi\) | |||||||
\(422\) | −912.614 | + | 1580.69i | −0.105273 | + | 0.182339i | ||||
\(423\) | −305.795 | − | 529.653i | −0.0351496 | − | 0.0608809i | ||||
\(424\) | 265.955 | + | 460.647i | 0.0304620 | + | 0.0527618i | ||||
\(425\) | −1720.42 | + | 2979.85i | −0.196359 | + | 0.340103i | ||||
\(426\) | −784.454 | −0.0892182 | ||||||||
\(427\) | −2116.41 | + | 2702.64i | −0.239860 | + | 0.306299i | ||||
\(428\) | 3738.68 | 0.422234 | ||||||||
\(429\) | −3019.81 | + | 5230.46i | −0.339855 | + | 0.588646i | ||||
\(430\) | −5203.39 | − | 9012.54i | −0.583558 | − | 1.01075i | ||||
\(431\) | 1014.97 | + | 1757.97i | 0.113432 | + | 0.196470i | 0.917152 | − | 0.398538i | \(-0.130482\pi\) |
−0.803720 | + | 0.595008i | \(0.797149\pi\) | |||||||
\(432\) | −216.000 | + | 374.123i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −327.739 | −0.0363744 | −0.0181872 | − | 0.999835i | \(-0.505789\pi\) | ||||
−0.0181872 | + | 0.999835i | \(0.505789\pi\) | |||||||
\(434\) | −10880.3 | − | 1541.56i | −1.20339 | − | 0.170501i | ||||
\(435\) | −11412.6 | −1.25792 | ||||||||
\(436\) | 2394.04 | − | 4146.60i | 0.262967 | − | 0.455472i | ||||
\(437\) | −5636.92 | − | 9763.43i | −0.617049 | − | 1.06876i | ||||
\(438\) | −543.898 | − | 942.058i | −0.0593343 | − | 0.102770i | ||||
\(439\) | −3954.34 | + | 6849.12i | −0.429910 | + | 0.744625i | −0.996865 | − | 0.0791234i | \(-0.974788\pi\) |
0.566955 | + | 0.823749i | \(0.308121\pi\) | |||||||
\(440\) | −6567.61 | −0.711587 | ||||||||
\(441\) | −2225.40 | + | 2139.43i | −0.240298 | + | 0.231015i | ||||
\(442\) | 2124.27 | 0.228600 | ||||||||
\(443\) | 1460.41 | − | 2529.51i | 0.156628 | − | 0.271288i | −0.777023 | − | 0.629473i | \(-0.783271\pi\) |
0.933651 | + | 0.358185i | \(0.116604\pi\) | |||||||
\(444\) | 969.205 | + | 1678.71i | 0.103596 | + | 0.179433i | ||||
\(445\) | 9163.03 | + | 15870.8i | 0.976111 | + | 1.69067i | ||||
\(446\) | 4319.47 | − | 7481.53i | 0.458593 | − | 0.794307i | ||||
\(447\) | 1082.93 | 0.114588 | ||||||||
\(448\) | 1173.58 | + | 166.277i | 0.123764 | + | 0.0175354i | ||||
\(449\) | −10240.2 | −1.07631 | −0.538156 | − | 0.842845i | \(-0.680879\pi\) | ||||
−0.538156 | + | 0.842845i | \(0.680879\pi\) | |||||||
\(450\) | −1132.33 | + | 1961.25i | −0.118619 | + | 0.205454i | ||||
\(451\) | 2669.02 | + | 4622.88i | 0.278668 | + | 0.482668i | ||||
\(452\) | 4769.29 | + | 8260.65i | 0.496302 | + | 0.859620i | ||||
\(453\) | −2322.59 | + | 4022.84i | −0.240893 | + | 0.417239i | ||||
\(454\) | 4122.57 | 0.426171 | ||||||||
\(455\) | 7023.19 | − | 8968.54i | 0.723632 | − | 0.924069i | ||||
\(456\) | 1836.27 | 0.188578 | ||||||||
\(457\) | −2946.31 | + | 5103.17i | −0.301582 | + | 0.522355i | −0.976494 | − | 0.215543i | \(-0.930848\pi\) |
0.674913 | + | 0.737897i | \(0.264181\pi\) | |||||||
\(458\) | 3474.63 | + | 6018.24i | 0.354495 | + | 0.614004i | ||||
\(459\) | −369.205 | − | 639.481i | −0.0375446 | − | 0.0650292i | ||||
\(460\) | 4667.15 | − | 8083.74i | 0.473059 | − | 0.819362i | ||||
\(461\) | −12643.4 | −1.27735 | −0.638677 | − | 0.769475i | \(-0.720518\pi\) | ||||
−0.638677 | + | 0.769475i | \(0.720518\pi\) | |||||||
\(462\) | −2151.83 | − | 5343.20i | −0.216693 | − | 0.538070i | ||||
\(463\) | 15093.2 | 1.51499 | 0.757494 | − | 0.652842i | \(-0.226423\pi\) | ||||
0.757494 | + | 0.652842i | \(0.226423\pi\) | |||||||
\(464\) | −1921.67 | + | 3328.42i | −0.192265 | + | 0.333013i | ||||
\(465\) | −7047.70 | − | 12207.0i | −0.702858 | − | 1.21739i | ||||
\(466\) | −776.099 | − | 1344.24i | −0.0771504 | − | 0.133628i | ||||
\(467\) | 1410.12 | − | 2442.39i | 0.139727 | − | 0.242014i | −0.787666 | − | 0.616102i | \(-0.788711\pi\) |
0.927393 | + | 0.374088i | \(0.122044\pi\) | |||||||
\(468\) | 1398.14 | 0.138096 | ||||||||
\(469\) | −3772.06 | − | 9366.38i | −0.371380 | − | 0.922173i | ||||
\(470\) | −2152.41 | −0.211241 | ||||||||
\(471\) | 1450.60 | − | 2512.52i | 0.141911 | − | 0.245798i | ||||
\(472\) | 1847.71 | + | 3200.33i | 0.180186 | + | 0.312091i | ||||
\(473\) | 8515.72 | + | 14749.7i | 0.827808 | + | 1.43381i | ||||
\(474\) | 1229.09 | − | 2128.85i | 0.119101 | − | 0.206289i | ||||
\(475\) | 9626.23 | 0.929856 | ||||||||
\(476\) | −1249.12 | + | 1595.11i | −0.120280 | + | 0.153596i | ||||
\(477\) | −598.398 | −0.0574397 | ||||||||
\(478\) | −2006.80 | + | 3475.87i | −0.192027 | + | 0.332600i | ||||
\(479\) | 8224.25 | + | 14244.8i | 0.784500 | + | 1.35879i | 0.929297 | + | 0.369332i | \(0.120414\pi\) |
−0.144798 | + | 0.989461i | \(0.546253\pi\) | |||||||
\(480\) | 760.182 | + | 1316.67i | 0.0722862 | + | 0.125203i | ||||
\(481\) | 3136.76 | − | 5433.03i | 0.297347 | − | 0.515020i | ||||
\(482\) | 1611.30 | 0.152267 | ||||||||
\(483\) | 8105.84 | + | 1148.47i | 0.763620 | + | 0.108193i | ||||
\(484\) | 5424.35 | 0.509424 | ||||||||
\(485\) | 12814.6 | − | 22195.5i | 1.19975 | − | 2.07804i | ||||
\(486\) | −243.000 | − | 420.888i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −3165.53 | − | 5482.87i | −0.294546 | − | 0.510169i | 0.680333 | − | 0.732903i | \(-0.261835\pi\) |
−0.974879 | + | 0.222734i | \(0.928502\pi\) | |||||||
\(488\) | −741.394 | + | 1284.13i | −0.0687732 | + | 0.119119i | ||||
\(489\) | −3979.50 | −0.368015 | ||||||||
\(490\) | 2604.67 | + | 10547.4i | 0.240136 | + | 0.972416i | ||||
\(491\) | −9286.90 | −0.853588 | −0.426794 | − | 0.904349i | \(-0.640357\pi\) | ||||
−0.426794 | + | 0.904349i | \(0.640357\pi\) | |||||||
\(492\) | 617.864 | − | 1070.17i | 0.0566168 | − | 0.0980631i | ||||
\(493\) | −3284.67 | − | 5689.21i | −0.300069 | − | 0.519735i | ||||
\(494\) | −2971.48 | − | 5146.76i | −0.270634 | − | 0.468752i | ||||
\(495\) | 3694.28 | − | 6398.68i | 0.335445 | − | 0.581008i | ||||
\(496\) | −4746.79 | −0.429712 | ||||||||
\(497\) | −2397.44 | − | 339.679i | −0.216378 | − | 0.0306573i | ||||
\(498\) | 2087.57 | 0.187844 | ||||||||
\(499\) | 121.725 | − | 210.835i | 0.0109202 | − | 0.0189143i | −0.860514 | − | 0.509427i | \(-0.829857\pi\) |
0.871434 | + | 0.490513i | \(0.163191\pi\) | |||||||
\(500\) | 25.7954 | + | 44.6789i | 0.00230721 | + | 0.00399620i | ||||
\(501\) | −2125.05 | − | 3680.69i | −0.189501 | − | 0.328225i | ||||
\(502\) | −1421.78 | + | 2462.60i | −0.126409 | + | 0.218947i | ||||
\(503\) | 8499.30 | 0.753409 | 0.376705 | − | 0.926333i | \(-0.377057\pi\) | ||||
0.376705 | + | 0.926333i | \(0.377057\pi\) | |||||||
\(504\) | −822.136 | + | 1049.86i | −0.0726604 | + | 0.0927866i | ||||
\(505\) | −11382.8 | −1.00303 | ||||||||
\(506\) | −7638.12 | + | 13229.6i | −0.671059 | + | 1.16231i | ||||
\(507\) | 1033.02 | + | 1789.24i | 0.0904890 | + | 0.156731i | ||||
\(508\) | 5347.85 | + | 9262.75i | 0.467072 | + | 0.808992i | ||||
\(509\) | 3841.55 | − | 6653.76i | 0.334526 | − | 0.579416i | −0.648868 | − | 0.760901i | \(-0.724757\pi\) |
0.983394 | + | 0.181485i | \(0.0580904\pi\) | |||||||
\(510\) | −2598.73 | −0.225634 | ||||||||
\(511\) | −1254.33 | − | 3114.62i | −0.108588 | − | 0.269634i | ||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −1032.90 | + | 1789.04i | −0.0888963 | + | 0.153973i | ||||
\(514\) | 1465.82 | + | 2538.87i | 0.125787 | + | 0.217869i | ||||
\(515\) | −12761.4 | − | 22103.4i | −1.09191 | − | 1.89124i | ||||
\(516\) | 1971.34 | − | 3414.46i | 0.168185 | − | 0.291305i | ||||
\(517\) | 3522.57 | 0.299656 | ||||||||
\(518\) | 2235.17 | + | 5550.13i | 0.189590 | + | 0.470770i | ||||
\(519\) | −3109.80 | −0.263015 | ||||||||
\(520\) | 2460.27 | − | 4261.32i | 0.207481 | − | 0.359368i | ||||
\(521\) | 10765.3 | + | 18646.1i | 0.905253 | + | 1.56794i | 0.820578 | + | 0.571535i | \(0.193652\pi\) |
0.0846750 | + | 0.996409i | \(0.473015\pi\) | |||||||
\(522\) | −2161.87 | − | 3744.48i | −0.181270 | − | 0.313968i | ||||
\(523\) | 8423.53 | − | 14590.0i | 0.704274 | − | 1.21984i | −0.262679 | − | 0.964883i | \(-0.584606\pi\) |
0.966953 | − | 0.254955i | \(-0.0820606\pi\) | |||||||
\(524\) | −155.439 | −0.0129588 | ||||||||
\(525\) | −4309.86 | + | 5503.64i | −0.358281 | + | 0.457521i | ||||
\(526\) | 13982.8 | 1.15908 | ||||||||
\(527\) | 4056.80 | − | 7026.58i | 0.335326 | − | 0.580802i | ||||
\(528\) | −1244.09 | − | 2154.83i | −0.102542 | − | 0.177608i | ||||
\(529\) | −4772.29 | − | 8265.84i | −0.392232 | − | 0.679366i | ||||
\(530\) | −1052.99 | + | 1823.83i | −0.0862998 | + | 0.149476i | ||||
\(531\) | −4157.35 | −0.339762 | ||||||||
\(532\) | 5611.99 | + | 795.129i | 0.457351 | + | 0.0647993i | ||||
\(533\) | −3999.34 | −0.325011 | ||||||||
\(534\) | −3471.48 | + | 6012.77i | −0.281321 | + | 0.487263i | ||||
\(535\) | 7401.24 | + | 12819.3i | 0.598100 | + | 1.03594i | ||||
\(536\) | −2180.83 | − | 3777.31i | −0.175742 | − | 0.304394i | ||||
\(537\) | 1151.15 | − | 1993.85i | 0.0925059 | − | 0.160225i | ||||
\(538\) | 1617.92 | 0.129653 | ||||||||
\(539\) | −4262.72 | − | 17261.6i | −0.340646 | − | 1.37942i | ||||
\(540\) | −1710.41 | −0.136304 | ||||||||
\(541\) | −8720.02 | + | 15103.5i | −0.692981 | + | 1.20028i | 0.277875 | + | 0.960617i | \(0.410370\pi\) |
−0.970856 | + | 0.239662i | \(0.922963\pi\) | |||||||
\(542\) | −6661.77 | − | 11538.5i | −0.527947 | − | 0.914432i | ||||
\(543\) | 5936.56 | + | 10282.4i | 0.469175 | + | 0.812636i | ||||
\(544\) | −437.576 | + | 757.903i | −0.0344870 | + | 0.0597332i | ||||
\(545\) | 18957.3 | 1.48999 | ||||||||
\(546\) | 4272.97 | + | 605.411i | 0.334920 | + | 0.0474527i | ||||
\(547\) | 11520.7 | 0.900530 | 0.450265 | − | 0.892895i | \(-0.351329\pi\) | ||||
0.450265 | + | 0.892895i | \(0.351329\pi\) | |||||||
\(548\) | 1536.29 | − | 2660.93i | 0.119757 | − | 0.207426i | ||||
\(549\) | −834.068 | − | 1444.65i | −0.0648400 | − | 0.112306i | ||||
\(550\) | −6521.86 | − | 11296.2i | −0.505623 | − | 0.875765i | ||||
\(551\) | −9189.33 | + | 15916.4i | −0.710488 | + | 1.23060i | ||||
\(552\) | 3536.36 | 0.272677 | ||||||||
\(553\) | 4678.15 | − | 5973.94i | 0.359738 | − | 0.459382i | ||||
\(554\) | −15062.9 | −1.15517 | ||||||||
\(555\) | −3837.35 | + | 6646.49i | −0.293489 | + | 0.508338i | ||||
\(556\) | −2105.10 | − | 3646.14i | −0.160568 | − | 0.278113i | ||||
\(557\) | −5746.51 | − | 9953.25i | −0.437141 | − | 0.757151i | 0.560327 | − | 0.828272i | \(-0.310676\pi\) |
−0.997468 | + | 0.0711212i | \(0.977342\pi\) | |||||||
\(558\) | 2670.07 | − | 4624.69i | 0.202568 | − | 0.350858i | ||||
\(559\) | −12760.2 | −0.965472 | ||||||||
\(560\) | 1753.12 | + | 4353.17i | 0.132291 | + | 0.328491i | ||||
\(561\) | 4253.00 | 0.320075 | ||||||||
\(562\) | −1690.19 | + | 2927.49i | −0.126862 | + | 0.219731i | ||||
\(563\) | −9055.65 | − | 15684.8i | −0.677886 | − | 1.17413i | −0.975616 | − | 0.219483i | \(-0.929563\pi\) |
0.297730 | − | 0.954650i | \(-0.403770\pi\) | |||||||
\(564\) | −407.727 | − | 706.204i | −0.0304405 | − | 0.0527244i | ||||
\(565\) | −18882.9 | + | 32706.2i | −1.40604 | + | 2.43533i | ||||
\(566\) | 6356.46 | 0.472053 | ||||||||
\(567\) | −560.403 | − | 1391.54i | −0.0415075 | − | 0.103067i | ||||
\(568\) | −1045.94 | −0.0772652 | ||||||||
\(569\) | −2208.81 | + | 3825.77i | −0.162738 | + | 0.281871i | −0.935850 | − | 0.352399i | \(-0.885366\pi\) |
0.773112 | + | 0.634270i | \(0.218699\pi\) | |||||||
\(570\) | 3635.16 | + | 6296.28i | 0.267123 | + | 0.462670i | ||||
\(571\) | −6609.87 | − | 11448.6i | −0.484439 | − | 0.839073i | 0.515401 | − | 0.856949i | \(-0.327643\pi\) |
−0.999840 | + | 0.0178762i | \(0.994310\pi\) | |||||||
\(572\) | −4026.41 | + | 6973.95i | −0.294323 | + | 0.509782i | ||||
\(573\) | −5415.89 | −0.394855 | ||||||||
\(574\) | 2351.70 | − | 3003.10i | 0.171007 | − | 0.218375i | ||||
\(575\) | 18538.6 | 1.34454 | ||||||||
\(576\) | −288.000 | + | 498.831i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 8748.20 | + | 15152.3i | 0.631182 | + | 1.09324i | 0.987310 | + | 0.158803i | \(0.0507634\pi\) |
−0.356128 | + | 0.934437i | \(0.615903\pi\) | |||||||
\(578\) | 4165.06 | + | 7214.10i | 0.299730 | + | 0.519147i | ||||
\(579\) | −5056.26 | + | 8757.70i | −0.362921 | + | 0.628597i | ||||
\(580\) | −15216.8 | −1.08939 | ||||||||
\(581\) | 6380.00 | + | 903.944i | 0.455571 | + | 0.0645472i | ||||
\(582\) | 9709.80 | 0.691553 | ||||||||
\(583\) | 1723.29 | − | 2984.83i | 0.122421 | − | 0.212039i | ||||
\(584\) | −725.197 | − | 1256.08i | −0.0513850 | − | 0.0890015i | ||||
\(585\) | 2767.81 | + | 4793.98i | 0.195615 | + | 0.338815i | ||||
\(586\) | 2176.53 | − | 3769.87i | 0.153433 | − | 0.265754i | ||||
\(587\) | −4280.53 | −0.300982 | −0.150491 | − | 0.988611i | \(-0.548085\pi\) | ||||
−0.150491 | + | 0.988611i | \(0.548085\pi\) | |||||||
\(588\) | −2967.20 | + | 2852.57i | −0.208105 | + | 0.200065i | ||||
\(589\) | −22699.0 | −1.58794 | ||||||||
\(590\) | −7315.61 | + | 12671.0i | −0.510473 | + | 0.884165i | ||||
\(591\) | 6918.47 | + | 11983.1i | 0.481536 | + | 0.834044i | ||||
\(592\) | 1292.27 | + | 2238.28i | 0.0897164 | + | 0.155393i | ||||
\(593\) | 795.466 | − | 1377.79i | 0.0550858 | − | 0.0954114i | −0.837168 | − | 0.546946i | \(-0.815790\pi\) |
0.892253 | + | 0.451535i | \(0.149123\pi\) | |||||||
\(594\) | 2799.20 | 0.193355 | ||||||||
\(595\) | −7942.20 | − | 1125.28i | −0.547224 | − | 0.0775329i | ||||
\(596\) | 1443.91 | 0.0992363 | ||||||||
\(597\) | 3344.80 | − | 5793.36i | 0.229302 | − | 0.397163i | ||||
\(598\) | −5722.59 | − | 9911.82i | −0.391328 | − | 0.677800i | ||||
\(599\) | 6961.42 | + | 12057.5i | 0.474851 | + | 0.822467i | 0.999585 | − | 0.0287997i | \(-0.00916851\pi\) |
−0.524734 | + | 0.851266i | \(0.675835\pi\) | |||||||
\(600\) | −1509.77 | + | 2615.00i | −0.102727 | + | 0.177928i | ||||
\(601\) | 12559.7 | 0.852446 | 0.426223 | − | 0.904618i | \(-0.359844\pi\) | ||||
0.426223 | + | 0.904618i | \(0.359844\pi\) | |||||||
\(602\) | 7503.29 | − | 9581.62i | 0.507992 | − | 0.648700i | ||||
\(603\) | 4906.87 | 0.331382 | ||||||||
\(604\) | −3096.78 | + | 5363.78i | −0.208620 | + | 0.361340i | ||||
\(605\) | 10738.3 | + | 18599.2i | 0.721607 | + | 1.24986i | ||||
\(606\) | −2156.23 | − | 3734.70i | −0.144539 | − | 0.250349i | ||||
\(607\) | −3839.19 | + | 6649.66i | −0.256718 | + | 0.444648i | −0.965361 | − | 0.260919i | \(-0.915974\pi\) |
0.708643 | + | 0.705567i | \(0.249308\pi\) | |||||||
\(608\) | 2448.36 | 0.163313 | ||||||||
\(609\) | −4985.69 | − | 12379.9i | −0.331741 | − | 0.823745i | ||||
\(610\) | −5870.77 | −0.389673 | ||||||||
\(611\) | −1319.58 | + | 2285.58i | −0.0873723 | + | 0.151333i | ||||
\(612\) | −492.273 | − | 852.641i | −0.0325146 | − | 0.0563170i | ||||
\(613\) | −3079.19 | − | 5333.31i | −0.202883 | − | 0.351403i | 0.746573 | − | 0.665303i | \(-0.231698\pi\) |
−0.949456 | + | 0.313900i | \(0.898364\pi\) | |||||||
\(614\) | −623.504 | + | 1079.94i | −0.0409814 | + | 0.0709818i | ||||
\(615\) | 4892.59 | 0.320794 | ||||||||
\(616\) | −2869.11 | − | 7124.27i | −0.187662 | − | 0.465982i | ||||
\(617\) | 8813.12 | 0.575045 | 0.287523 | − | 0.957774i | \(-0.407168\pi\) | ||||
0.287523 | + | 0.957774i | \(0.407168\pi\) | |||||||
\(618\) | 4834.74 | − | 8374.01i | 0.314695 | − | 0.545068i | ||||
\(619\) | −11595.0 | − | 20083.1i | −0.752894 | − | 1.30405i | −0.946415 | − | 0.322954i | \(-0.895324\pi\) |
0.193521 | − | 0.981096i | \(-0.438009\pi\) | |||||||
\(620\) | −9396.93 | − | 16276.0i | −0.608693 | − | 1.05429i | ||||
\(621\) | −1989.20 | + | 3445.40i | −0.128541 | + | 0.222640i | ||||
\(622\) | 935.985 | 0.0603369 | ||||||||
\(623\) | −13213.1 | + | 16873.0i | −0.849713 | + | 1.08507i | ||||
\(624\) | 1864.18 | 0.119595 | ||||||||
\(625\) | 7761.27 | − | 13442.9i | 0.496721 | − | 0.860346i | ||||
\(626\) | −3612.81 | − | 6257.57i | −0.230666 | − | 0.399525i | ||||
\(627\) | −5949.19 | − | 10304.3i | −0.378928 | − | 0.656323i | ||||
\(628\) | 1934.14 | − | 3350.02i | 0.122899 | − | 0.212867i | ||||
\(629\) | −4417.71 | −0.280041 | ||||||||
\(630\) | −5227.33 | − | 740.629i | −0.330574 | − | 0.0468371i | ||||
\(631\) | 7936.94 | 0.500736 | 0.250368 | − | 0.968151i | \(-0.419448\pi\) | ||||
0.250368 | + | 0.968151i | \(0.419448\pi\) | |||||||
\(632\) | 1638.79 | − | 2838.46i | 0.103145 | − | 0.178652i | ||||
\(633\) | −1368.92 | − | 2371.04i | −0.0859553 | − | 0.148879i | ||||
\(634\) | −4531.74 | − | 7849.20i | −0.283877 | − | 0.491690i | ||||
\(635\) | −21173.6 | + | 36673.8i | −1.32323 | + | 2.29190i | ||||
\(636\) | −797.864 | −0.0497443 | ||||||||
\(637\) | 12796.8 | + | 3700.50i | 0.795964 | + | 0.230171i | ||||
\(638\) | 24903.4 | 1.54535 | ||||||||
\(639\) | 588.341 | − | 1019.04i | 0.0364232 | − | 0.0630868i | ||||
\(640\) | 1013.58 | + | 1755.56i | 0.0626017 | + | 0.108429i | ||||
\(641\) | −16057.3 | − | 27812.1i | −0.989432 | − | 1.71375i | −0.620286 | − | 0.784376i | \(-0.712984\pi\) |
−0.369146 | − | 0.929371i | \(-0.620350\pi\) | |||||||
\(642\) | −2804.01 | + | 4856.69i | −0.172376 | + | 0.298564i | ||||
\(643\) | −24786.7 | −1.52021 | −0.760104 | − | 0.649802i | \(-0.774852\pi\) | ||||
−0.760104 | + | 0.649802i | \(0.774852\pi\) | |||||||
\(644\) | 10807.8 | + | 1531.29i | 0.661314 | + | 0.0936977i | ||||
\(645\) | 15610.2 | 0.952946 | ||||||||
\(646\) | −2092.47 | + | 3624.26i | −0.127441 | + | 0.220735i | ||||
\(647\) | −3772.80 | − | 6534.67i | −0.229249 | − | 0.397070i | 0.728337 | − | 0.685219i | \(-0.240294\pi\) |
−0.957586 | + | 0.288149i | \(0.906960\pi\) | |||||||
\(648\) | −324.000 | − | 561.184i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 11972.5 | − | 20737.0i | 0.724133 | − | 1.25423i | ||||
\(650\) | 9772.54 | 0.589708 | ||||||||
\(651\) | 10162.8 | − | 12977.8i | 0.611844 | − | 0.781318i | ||||
\(652\) | −5306.00 | −0.318710 | ||||||||
\(653\) | 2444.49 | − | 4233.99i | 0.146494 | − | 0.253735i | −0.783435 | − | 0.621473i | \(-0.786534\pi\) |
0.929929 | + | 0.367738i | \(0.119868\pi\) | |||||||
\(654\) | 3591.06 | + | 6219.89i | 0.214712 | + | 0.371892i | ||||
\(655\) | −307.714 | − | 532.976i | −0.0183563 | − | 0.0317941i | ||||
\(656\) | 823.818 | − | 1426.89i | 0.0490316 | − | 0.0849251i | ||||
\(657\) | 1631.69 | 0.0968926 | ||||||||
\(658\) | −940.295 | − | 2334.84i | −0.0557090 | − | 0.138331i | ||||
\(659\) | 25895.9 | 1.53075 | 0.765374 | − | 0.643586i | \(-0.222554\pi\) | ||||
0.765374 | + | 0.643586i | \(0.222554\pi\) | |||||||
\(660\) | 4925.70 | − | 8531.57i | 0.290504 | − | 0.503168i | ||||
\(661\) | −4091.68 | − | 7087.00i | −0.240769 | − | 0.417023i | 0.720165 | − | 0.693803i | \(-0.244066\pi\) |
−0.960933 | + | 0.276780i | \(0.910733\pi\) | |||||||
\(662\) | 1237.06 | + | 2142.65i | 0.0726278 | + | 0.125795i | ||||
\(663\) | −1593.20 | + | 2759.51i | −0.0933257 | + | 0.161645i | ||||
\(664\) | 2783.42 | 0.162677 | ||||||||
\(665\) | 8383.36 | + | 20816.7i | 0.488861 | + | 1.21389i | ||||
\(666\) | −2907.61 | −0.169171 | ||||||||
\(667\) | −17697.2 | + | 30652.4i | −1.02734 | + | 1.77941i | ||||
\(668\) | −2833.39 | − | 4907.58i | −0.164113 | − | 0.284252i | ||||
\(669\) | 6479.20 | + | 11222.3i | 0.374440 | + | 0.648549i | ||||
\(670\) | 8634.53 | − | 14955.4i | 0.497882 | − | 0.862357i | ||||
\(671\) | 9607.93 | 0.552772 | ||||||||
\(672\) | −1096.18 | + | 1399.81i | −0.0629258 | + | 0.0803555i | ||||
\(673\) | −4635.02 | −0.265478 | −0.132739 | − | 0.991151i | \(-0.542377\pi\) | ||||
−0.132739 | + | 0.991151i | \(0.542377\pi\) | |||||||
\(674\) | 1867.83 | − | 3235.18i | 0.106745 | − | 0.184888i | ||||
\(675\) | −1698.49 | − | 2941.88i | −0.0968520 | − | 0.167753i | ||||
\(676\) | 1377.36 | + | 2385.65i | 0.0783657 | + | 0.135733i | ||||
\(677\) | 12192.9 | − | 21118.7i | 0.692187 | − | 1.19890i | −0.278932 | − | 0.960311i | \(-0.589980\pi\) |
0.971120 | − | 0.238593i | \(-0.0766862\pi\) | |||||||
\(678\) | −14307.9 | −0.810458 | ||||||||
\(679\) | 29674.9 | + | 4204.46i | 1.67720 | + | 0.237633i | ||||
\(680\) | −3464.97 | −0.195405 | ||||||||
\(681\) | −3091.93 | + | 5355.37i | −0.173984 | + | 0.301349i | ||||
\(682\) | 15378.7 | + | 26636.8i | 0.863464 | + | 1.49556i | ||||
\(683\) | 9196.71 | + | 15929.2i | 0.515230 | + | 0.892405i | 0.999844 | + | 0.0176767i | \(0.00562697\pi\) |
−0.484613 | + | 0.874728i | \(0.661040\pi\) | |||||||
\(684\) | −1377.20 | + | 2385.39i | −0.0769864 | + | 0.133344i | ||||
\(685\) | 12165.2 | 0.678552 | ||||||||
\(686\) | −10303.5 | + | 7433.15i | −0.573456 | + | 0.413701i | ||||
\(687\) | −10423.9 | −0.578889 | ||||||||
\(688\) | 2628.45 | − | 4552.62i | 0.145652 | − | 0.252277i | ||||
\(689\) | 1291.11 | + | 2236.27i | 0.0713897 | + | 0.123651i | ||||
\(690\) | 7000.73 | + | 12125.6i | 0.386251 | + | 0.669006i | ||||
\(691\) | 7449.44 | − | 12902.8i | 0.410116 | − | 0.710341i | −0.584786 | − | 0.811187i | \(-0.698822\pi\) |
0.994902 | + | 0.100846i | \(0.0321550\pi\) | |||||||
\(692\) | −4146.39 | −0.227778 | ||||||||
\(693\) | 8554.89 | + | 1212.09i | 0.468937 | + | 0.0664409i | ||||
\(694\) | −126.727 | −0.00693157 | ||||||||
\(695\) | 8334.67 | − | 14436.1i | 0.454895 | − | 0.787902i | ||||
\(696\) | −2882.50 | − | 4992.64i | −0.156984 | − | 0.271904i | ||||
\(697\) | 1408.14 | + | 2438.96i | 0.0765236 | + | 0.132543i | ||||
\(698\) | −1223.79 | + | 2119.66i | −0.0663625 | + | 0.114943i | ||||
\(699\) | 2328.30 | 0.125986 | ||||||||
\(700\) | −5746.48 | + | 7338.19i | −0.310281 | + | 0.396225i | ||||
\(701\) | −5725.70 | −0.308497 | −0.154249 | − | 0.988032i | \(-0.549296\pi\) | ||||
−0.154249 | + | 0.988032i | \(0.549296\pi\) | |||||||
\(702\) | −1048.60 | + | 1816.23i | −0.0563774 | + | 0.0976485i | ||||
\(703\) | 6179.60 | + | 10703.4i | 0.331533 | + | 0.574232i | ||||
\(704\) | −1658.79 | − | 2873.10i | −0.0888039 | − | 0.153813i | ||||
\(705\) | 1614.31 | − | 2796.06i | 0.0862387 | − | 0.149370i | ||||
\(706\) | −9031.23 | −0.481437 | ||||||||
\(707\) | −4972.66 | − | 12347.6i | −0.264521 | − | 0.656831i | ||||
\(708\) | −5543.14 | −0.294243 | ||||||||
\(709\) | 11728.4 | − | 20314.2i | 0.621255 | − | 1.07604i | −0.367998 | − | 0.929827i | \(-0.619957\pi\) |
0.989252 | − | 0.146218i | \(-0.0467101\pi\) | |||||||
\(710\) | −2070.58 | − | 3586.36i | −0.109447 | − | 0.189568i | ||||
\(711\) | 1843.64 | + | 3193.27i | 0.0972458 | + | 0.168435i | ||||
\(712\) | −4628.64 | + | 8017.03i | −0.243631 | + | 0.421982i | ||||
\(713\) | −43714.5 | −2.29610 | ||||||||
\(714\) | −1135.27 | − | 2818.99i | −0.0595049 | − | 0.147756i | ||||
\(715\) | −31883.4 | −1.66765 | ||||||||
\(716\) | 1534.86 | − | 2658.46i | 0.0801125 | − | 0.138759i | ||||
\(717\) | −3010.19 | − | 5213.81i | −0.156789 | − | 0.271567i | ||||
\(718\) | −2228.49 | − | 3859.86i | −0.115831 | − | 0.200625i | ||||
\(719\) | 4229.50 | − | 7325.71i | 0.219379 | − | 0.379976i | −0.735239 | − | 0.677808i | \(-0.762930\pi\) |
0.954618 | + | 0.297832i | \(0.0962634\pi\) | |||||||
\(720\) | −2280.55 | −0.118043 | ||||||||
\(721\) | 18401.9 | − | 23499.0i | 0.950518 | − | 1.21380i | ||||
\(722\) | −2010.02 | −0.103608 | ||||||||
\(723\) | −1208.47 | + | 2093.13i | −0.0621626 | + | 0.107669i | ||||
\(724\) | 7915.42 | + | 13709.9i | 0.406318 | + | 0.703763i | ||||
\(725\) | −15110.8 | − | 26172.7i | −0.774072 | − | 1.34073i | ||||
\(726\) | −4068.26 | + | 7046.44i | −0.207972 | + | 0.360217i | ||||
\(727\) | −11822.2 | −0.603111 | −0.301555 | − | 0.953449i | \(-0.597506\pi\) | ||||
−0.301555 | + | 0.953449i | \(0.597506\pi\) | |||||||
\(728\) | 5697.29 | + | 807.214i | 0.290049 | + | 0.0410953i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 2871.26 | − | 4973.16i | 0.145575 | − | 0.252144i | ||||
\(731\) | 4492.77 | + | 7781.70i | 0.227320 | + | 0.393730i | ||||
\(732\) | −1112.09 | − | 1926.20i | −0.0561531 | − | 0.0972600i | ||||
\(733\) | −2514.48 | + | 4355.20i | −0.126704 | + | 0.219458i | −0.922398 | − | 0.386241i | \(-0.873773\pi\) |
0.795694 | + | 0.605699i | \(0.207107\pi\) | |||||||
\(734\) | −2874.68 | −0.144559 | ||||||||
\(735\) | −15655.0 | − | 4527.00i | −0.785637 | − | 0.227185i | ||||
\(736\) | 4715.15 | 0.236145 | ||||||||
\(737\) | −14131.0 | + | 24475.6i | −0.706272 | + | 1.22330i | ||||
\(738\) | 926.795 | + | 1605.26i | 0.0462274 | + | 0.0800682i | ||||
\(739\) | 8871.95 | + | 15366.7i | 0.441624 | + | 0.764914i | 0.997810 | − | 0.0661431i | \(-0.0210694\pi\) |
−0.556187 | + | 0.831057i | \(0.687736\pi\) | |||||||
\(740\) | −5116.47 | + | 8861.99i | −0.254169 | + | 0.440234i | ||||
\(741\) | 8914.44 | 0.441944 | ||||||||
\(742\) | −2438.42 | − | 345.485i | −0.120643 | − | 0.0170932i | ||||
\(743\) | −13202.3 | −0.651877 | −0.325938 | − | 0.945391i | \(-0.605680\pi\) | ||||
−0.325938 | + | 0.945391i | \(0.605680\pi\) | |||||||
\(744\) | 3560.09 | − | 6166.26i | 0.175429 | − | 0.303852i | ||||
\(745\) | 2858.42 | + | 4950.93i | 0.140570 | + | 0.243474i | ||||
\(746\) | 12237.4 | + | 21195.8i | 0.600595 | + | 1.04026i | ||||
\(747\) | −1565.68 | + | 2711.83i | −0.0766869 | + | 0.132826i | ||||
\(748\) | 5670.67 | 0.277193 | ||||||||
\(749\) | −10672.6 | + | 13628.8i | −0.520652 | + | 0.664866i | ||||
\(750\) | −77.3861 | −0.00376766 | ||||||||
\(751\) | −7800.49 | + | 13510.8i | −0.379020 | + | 0.656482i | −0.990920 | − | 0.134453i | \(-0.957072\pi\) |
0.611900 | + | 0.790935i | \(0.290406\pi\) | |||||||
\(752\) | −543.636 | − | 941.606i | −0.0263622 | − | 0.0456607i | ||||
\(753\) | −2132.68 | − | 3693.90i | −0.103213 | − | 0.178769i | ||||
\(754\) | −9329.00 | + | 16158.3i | −0.450586 | + | 0.780439i | ||||
\(755\) | −24522.0 | −1.18205 | ||||||||
\(756\) | −747.205 | − | 1855.38i | −0.0359465 | − | 0.0892587i | ||||
\(757\) | 2948.08 | 0.141545 | 0.0707725 | − | 0.997492i | \(-0.477454\pi\) | ||||
0.0707725 | + | 0.997492i | \(0.477454\pi\) | |||||||
\(758\) | 10647.0 | − | 18441.1i | 0.510180 | − | 0.883657i | ||||
\(759\) | −11457.2 | − | 19844.4i | −0.547917 | − | 0.949021i | ||||
\(760\) | 4846.88 | + | 8395.04i | 0.231335 | + | 0.400684i | ||||
\(761\) | −848.515 | + | 1469.67i | −0.0404187 | + | 0.0700073i | −0.885527 | − | 0.464588i | \(-0.846203\pi\) |
0.845108 | + | 0.534595i | \(0.179536\pi\) | |||||||
\(762\) | −16043.5 | −0.762725 | ||||||||
\(763\) | 8281.65 | + | 20564.1i | 0.392943 | + | 0.975716i | ||||
\(764\) | −7221.18 | −0.341954 | ||||||||
\(765\) | 1949.05 | − | 3375.85i | 0.0921149 | − | 0.159548i | ||||
\(766\) | 6714.81 | + | 11630.4i | 0.316731 | + | 0.548594i | ||||
\(767\) | 8969.98 | + | 15536.5i | 0.422278 | + | 0.731407i | ||||
\(768\) | −384.000 | + | 665.108i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | −96.7799 | −0.00453833 | −0.00226916 | − | 0.999997i | \(-0.500722\pi\) | ||||
−0.00226916 | + | 0.999997i | \(0.500722\pi\) | |||||||
\(770\) | 18748.2 | − | 23941.2i | 0.877450 | − | 1.12049i | ||||
\(771\) | −4397.45 | −0.205409 | ||||||||
\(772\) | −6741.68 | + | 11676.9i | −0.314298 | + | 0.544381i | ||||
\(773\) | −18163.4 | − | 31459.9i | −0.845138 | − | 1.46382i | −0.885501 | − | 0.464637i | \(-0.846185\pi\) |
0.0403629 | − | 0.999185i | \(-0.487149\pi\) | |||||||
\(774\) | 2957.01 | + | 5121.69i | 0.137322 | + | 0.237849i | ||||
\(775\) | 18662.9 | − | 32325.2i | 0.865023 | − | 1.49826i | ||||
\(776\) | 12946.4 | 0.598903 | ||||||||
\(777\) | −8886.21 | − | 1259.03i | −0.410284 | − | 0.0581307i | ||||
\(778\) | −21306.2 | −0.981828 | ||||||||
\(779\) | 3939.47 | − | 6823.35i | 0.181189 | − | 0.313828i | ||||
\(780\) | 3690.41 | + | 6391.98i | 0.169407 | + | 0.293422i | ||||
\(781\) | 3388.66 | + | 5869.32i | 0.155257 | + | 0.268913i | ||||
\(782\) | −4029.76 | + | 6979.74i | −0.184276 | + | 0.319175i | ||||
\(783\) | 6485.62 | 0.296012 | ||||||||
\(784\) | −3956.27 | + | 3803.43i | −0.180224 | + | 0.173261i | ||||
\(785\) | 15315.6 | 0.696352 | ||||||||
\(786\) | 116.580 | − | 201.922i | 0.00529040 | − | 0.00916324i | ||||
\(787\) | −3548.23 | − | 6145.72i | −0.160713 | − | 0.278362i | 0.774412 | − | 0.632682i | \(-0.218046\pi\) |
−0.935124 | + | 0.354319i | \(0.884713\pi\) | |||||||
\(788\) | 9224.62 | + | 15977.5i | 0.417022 | + | 0.722304i | ||||
\(789\) | −10487.1 | + | 18164.2i | −0.473194 | + | 0.819596i | ||||
\(790\) | 12976.8 | 0.584424 | ||||||||
\(791\) | −43727.5 | − | 6195.49i | −1.96558 | − | 0.278491i | ||||
\(792\) | 3732.27 | 0.167450 | ||||||||
\(793\) | −3599.20 | + | 6234.00i | −0.161174 | + | 0.279162i | ||||
\(794\) | −3221.04 | − | 5579.01i | −0.143968 | − | 0.249360i | ||||
\(795\) | −1579.48 | − | 2735.74i | −0.0704635 | − | 0.122046i | ||||
\(796\) | 4459.73 | − | 7724.47i | 0.198581 | − | 0.343953i | ||||
\(797\) | 40289.6 | 1.79063 | 0.895314 | − | 0.445436i | \(-0.146951\pi\) | ||||
0.895314 | + | 0.445436i | \(0.146951\pi\) | |||||||
\(798\) | −5241.90 | + | 6693.84i | −0.232533 | + | 0.296942i | ||||
\(799\) | 1858.45 | 0.0822871 | ||||||||
\(800\) | −2013.03 | + | 3486.67i | −0.0889642 | + | 0.154091i | ||||
\(801\) | −5207.22 | − | 9019.16i | −0.229698 | − | 0.397848i | ||||
\(802\) | −12485.0 | − | 21624.7i | −0.549702 | − | 0.952111i | ||||
\(803\) | −4699.02 | + | 8138.93i | −0.206506 | + | 0.357680i | ||||
\(804\) | 6542.50 | 0.286985 | ||||||||
\(805\) | 16145.0 | + | 40089.5i | 0.706877 | + | 1.75524i | ||||
\(806\) | −23043.9 | −1.00706 | ||||||||
\(807\) | −1213.44 | + | 2101.74i | −0.0529306 | + | 0.0916786i | ||||
\(808\) | −2874.97 | − | 4979.59i | −0.125175 | − | 0.216809i | ||||
\(809\) | 5782.98 | + | 10016.4i | 0.251321 | + | 0.435301i | 0.963890 | − | 0.266301i | \(-0.0858017\pi\) |
−0.712569 | + | 0.701602i | \(0.752468\pi\) | |||||||
\(810\) | 1282.81 | − | 2221.89i | 0.0556460 | − | 0.0963816i | ||||
\(811\) | 18014.2 | 0.779981 | 0.389991 | − | 0.920819i | \(-0.372478\pi\) | ||||
0.389991 | + | 0.920819i | \(0.372478\pi\) | |||||||
\(812\) | −6647.58 | − | 16506.6i | −0.287296 | − | 0.713384i | ||||
\(813\) | 19985.3 | 0.862134 | ||||||||
\(814\) | 8373.46 | − | 14503.3i | 0.360552 | − | 0.624495i | ||||
\(815\) | −10504.0 | − | 18193.4i | −0.451458 | − | 0.781948i | ||||
\(816\) | −656.364 | − | 1136.86i | −0.0281585 | − | 0.0487719i | ||||
\(817\) | 12569.2 | − | 21770.4i | 0.538237 | − | 0.932253i | ||||
\(818\) | 14074.8 | 0.601605 | ||||||||
\(819\) | −3991.18 | + | 5096.69i | −0.170284 | + | 0.217451i | ||||
\(820\) | 6523.45 | 0.277816 | ||||||||
\(821\) | 8396.22 | − | 14542.7i | 0.356918 | − | 0.618201i | −0.630526 | − | 0.776168i | \(-0.717161\pi\) |
0.987444 | + | 0.157967i | \(0.0504941\pi\) | |||||||
\(822\) | 2304.43 | + | 3991.39i | 0.0977814 | + | 0.169362i | ||||
\(823\) | 4409.52 | + | 7637.50i | 0.186763 | + | 0.323483i | 0.944169 | − | 0.329461i | \(-0.106867\pi\) |
−0.757406 | + | 0.652944i | \(0.773534\pi\) | |||||||
\(824\) | 6446.32 | − | 11165.4i | 0.272534 | − | 0.472043i | ||||
\(825\) | 19565.6 | 0.825680 | ||||||||
\(826\) | −16940.9 | − | 2400.25i | −0.713617 | − | 0.101108i | ||||
\(827\) | 8250.13 | 0.346898 | 0.173449 | − | 0.984843i | \(-0.444509\pi\) | ||||
0.173449 | + | 0.984843i | \(0.444509\pi\) | |||||||
\(828\) | −2652.27 | + | 4593.87i | −0.111320 | + | 0.192812i | ||||
\(829\) | 10775.2 | + | 18663.3i | 0.451435 | + | 0.781909i | 0.998475 | − | 0.0551975i | \(-0.0175789\pi\) |
−0.547040 | + | 0.837106i | \(0.684246\pi\) | |||||||
\(830\) | 5510.18 | + | 9543.91i | 0.230435 | + | 0.399125i | ||||
\(831\) | 11297.2 | − | 19567.3i | 0.471595 | − | 0.816827i | ||||
\(832\) | 2485.58 | 0.103572 | ||||||||
\(833\) | −2248.95 | − | 9106.95i | −0.0935431 | − | 0.378796i | ||||
\(834\) | 6315.30 | 0.262207 | ||||||||
\(835\) | 11218.2 | − | 19430.5i | 0.464936 | − | 0.805293i | ||||
\(836\) | −7932.26 | − | 13739.1i | −0.328161 | − | 0.568392i | ||||
\(837\) | 4005.10 | + | 6937.04i | 0.165396 | + | 0.286475i | ||||
\(838\) | 1549.66 | − | 2684.09i | 0.0638808 | − | 0.110645i | ||||
\(839\) | 30130.4 | 1.23983 | 0.619916 | − | 0.784669i | \(-0.287167\pi\) | ||||
0.619916 | + | 0.784669i | \(0.287167\pi\) | |||||||
\(840\) | −6969.77 | − | 987.505i | −0.286286 | − | 0.0405621i | ||||
\(841\) | 33311.0 | 1.36582 | ||||||||
\(842\) | −5531.63 | + | 9581.07i | −0.226405 | + | 0.392144i | ||||
\(843\) | −2535.28 | − | 4391.24i | −0.103582 | − | 0.179410i | ||||
\(844\) | −1825.23 | − | 3161.39i | −0.0744395 | − | 0.128933i | ||||
\(845\) | −5453.34 | + | 9445.46i | −0.222012 | + | 0.384537i | ||||
\(846\) | 1223.18 | 0.0497091 | ||||||||
\(847\) | −15484.6 | + | 19773.6i | −0.628165 | + | 0.802160i | ||||
\(848\) | −1063.82 | −0.0430798 | ||||||||
\(849\) | −4767.35 | + | 8257.29i | −0.192715 | + | 0.333792i | ||||
\(850\) | −3440.83 | − | 5959.70i | −0.138847 | − | 0.240489i | ||||
\(851\) | 11900.9 | + | 20613.0i | 0.479386 | + | 0.830321i | ||||
\(852\) | 784.454 | − | 1358.72i | 0.0315434 | − | 0.0546348i | ||||
\(853\) | −40738.6 | −1.63525 | −0.817623 | − | 0.575754i | \(-0.804709\pi\) | ||||
−0.817623 | + | 0.575754i | \(0.804709\pi\) | |||||||
\(854\) | −2564.69 | − | 6368.37i | −0.102766 | − | 0.255177i | ||||
\(855\) | −10905.5 | −0.436210 | ||||||||
\(856\) | −3738.68 | + | 6475.59i | −0.149282 | + | 0.258564i | ||||
\(857\) | 18254.1 | + | 31617.0i | 0.727594 | + | 1.26023i | 0.957897 | + | 0.287111i | \(0.0926949\pi\) |
−0.230303 | + | 0.973119i | \(0.573972\pi\) | |||||||
\(858\) | −6039.61 | − | 10460.9i | −0.240314 | − | 0.416235i | ||||
\(859\) | 10990.4 | − | 19036.0i | 0.436541 | − | 0.756110i | −0.560879 | − | 0.827897i | \(-0.689537\pi\) |
0.997420 | + | 0.0717871i | \(0.0228702\pi\) | |||||||
\(860\) | 20813.6 | 0.825276 | ||||||||
\(861\) | 2137.36 | + | 5307.28i | 0.0846006 | + | 0.210072i | ||||
\(862\) | −4059.86 | −0.160417 | ||||||||
\(863\) | 11713.0 | − | 20287.6i | 0.462012 | − | 0.800228i | −0.537049 | − | 0.843551i | \(-0.680461\pi\) |
0.999061 | + | 0.0433226i | \(0.0137943\pi\) | |||||||
\(864\) | −432.000 | − | 748.246i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −8208.37 | − | 14217.3i | −0.322651 | − | 0.558847i | ||||
\(866\) | 327.739 | − | 567.660i | 0.0128603 | − | 0.0222747i | ||||
\(867\) | −12495.2 | −0.489456 | ||||||||
\(868\) | 13550.4 | − | 17303.7i | 0.529873 | − | 0.676642i | ||||
\(869\) | −21237.5 | −0.829037 | ||||||||
\(870\) | 11412.6 | − | 19767.2i | 0.444740 | − | 0.770313i | ||||
\(871\) | −10587.2 | − | 18337.5i | −0.411863 | − | 0.713367i | ||||
\(872\) | 4788.08 | + | 8293.19i | 0.185946 | + | 0.322068i | ||||
\(873\) | −7282.35 | + | 12613.4i | −0.282325 | + | 0.489002i | ||||
\(874\) | 22547.7 | 0.872639 | ||||||||
\(875\) | −236.506 | − | 33.5092i | −0.00913757 | − | 0.00129465i | ||||
\(876\) | 2175.59 | 0.0839114 | ||||||||
\(877\) | −153.701 | + | 266.217i | −0.00591802 | + | 0.0102503i | −0.868969 | − | 0.494866i | \(-0.835217\pi\) |
0.863051 | + | 0.505116i | \(0.168550\pi\) | |||||||
\(878\) | −7908.68 | − | 13698.2i | −0.303992 | − | 0.526530i | ||||
\(879\) | 3264.80 | + | 5654.80i | 0.125278 | + | 0.216987i | ||||
\(880\) | 6567.61 | − | 11375.4i | 0.251584 | − | 0.435756i | ||||
\(881\) | −19941.7 | −0.762605 | −0.381302 | − | 0.924450i | \(-0.624524\pi\) | ||||
−0.381302 | + | 0.924450i | \(0.624524\pi\) | |||||||
\(882\) | −1480.19 | − | 5993.94i | −0.0565087 | − | 0.228828i | ||||
\(883\) | −37524.1 | −1.43011 | −0.715056 | − | 0.699068i | \(-0.753599\pi\) | ||||
−0.715056 | + | 0.699068i | \(0.753599\pi\) | |||||||
\(884\) | −2124.27 | + | 3679.35i | −0.0808224 | + | 0.139989i | ||||
\(885\) | −10973.4 | − | 19006.5i | −0.416799 | − | 0.721917i | ||||
\(886\) | 2920.82 | + | 5059.01i | 0.110753 | + | 0.191829i | ||||
\(887\) | 1440.10 | − | 2494.33i | 0.0545140 | − | 0.0944210i | −0.837481 | − | 0.546467i | \(-0.815972\pi\) |
0.891995 | + | 0.452046i | \(0.149306\pi\) | |||||||
\(888\) | −3876.82 | −0.146506 | ||||||||
\(889\) | −49032.1 | − | 6947.06i | −1.84981 | − | 0.262089i | ||||
\(890\) | −36652.1 | −1.38043 | ||||||||
\(891\) | −2099.40 | + | 3636.27i | −0.0789368 | + | 0.136722i | ||||
\(892\) | 8638.93 | + | 14963.1i | 0.324274 | + | 0.561660i | ||||
\(893\) | −2599.65 | − | 4502.72i | −0.0974176 | − | 0.168732i | ||||
\(894\) | −1082.93 | + | 1875.69i | −0.0405130 | + | 0.0701706i | ||||
\(895\) | 12153.9 | 0.453922 | ||||||||
\(896\) | −1461.58 | + | 1866.42i | −0.0544953 | + | 0.0695899i | ||||
\(897\) | 17167.8 | 0.639036 | ||||||||
\(898\) | 10240.2 | − | 17736.5i | 0.380534 | − | 0.659104i | ||||
\(899\) | 35631.8 | + | 61716.1i | 1.32190 | + | 2.28960i | ||||
\(900\) | −2264.66 | − | 3922.50i | −0.0838763 | − | 0.145278i | ||||
\(901\) | 909.182 | − | 1574.75i | 0.0336174 | − | 0.0582270i | ||||
\(902\) | −10676.1 | −0.394096 | ||||||||
\(903\) | 6819.42 | + | 16933.3i | 0.251314 | + | 0.624036i | ||||
\(904\) | −19077.2 | −0.701877 | ||||||||
\(905\) | −31339.4 | + | 54281.4i | −1.15111 | + | 1.99378i | ||||
\(906\) | −4645.17 | − | 8045.67i | −0.170337 | − | 0.295033i | ||||
\(907\) | −9159.62 | − | 15864.9i | −0.335326 | − | 0.580801i | 0.648222 | − | 0.761452i | \(-0.275513\pi\) |
−0.983547 | + | 0.180651i | \(0.942180\pi\) | |||||||
\(908\) | −4122.57 | + | 7140.50i | −0.150674 | + | 0.260975i | ||||
\(909\) | 6468.68 | 0.236031 | ||||||||
\(910\) | 8510.77 | + | 21133.1i | 0.310032 | + | 0.769840i | ||||
\(911\) | 46150.7 | 1.67842 | 0.839210 | − | 0.543807i | \(-0.183018\pi\) | ||||
0.839210 | + | 0.543807i | \(0.183018\pi\) | |||||||
\(912\) | −1836.27 | + | 3180.52i | −0.0666722 | + | 0.115480i | ||||
\(913\) | −9017.79 | − | 15619.3i | −0.326884 | − | 0.566180i | ||||
\(914\) | −5892.63 | − | 10206.3i | −0.213250 | − | 0.369360i | ||||
\(915\) | 4403.08 | − | 7626.36i | 0.159083 | − | 0.275541i | ||||
\(916\) | −13898.5 | −0.501332 | ||||||||
\(917\) | 443.723 | − | 566.630i | 0.0159793 | − | 0.0204054i | ||||
\(918\) | 1476.82 | 0.0530961 | ||||||||
\(919\) | −23632.1 | + | 40932.1i | −0.848261 | + | 1.46923i | 0.0344969 | + | 0.999405i | \(0.489017\pi\) |
−0.882758 | + | 0.469827i | \(0.844316\pi\) | |||||||
\(920\) | 9334.30 | + | 16167.5i | 0.334503 | + | 0.579376i | ||||
\(921\) | −935.256 | − | 1619.91i | −0.0334612 | − | 0.0579564i | ||||
\(922\) | 12643.4 | − | 21899.0i | 0.451613 | − | 0.782217i | ||||
\(923\) | −5077.66 | −0.181076 | ||||||||
\(924\) | 11406.5 | + | 1616.12i | 0.406112 | + | 0.0575395i | ||||
\(925\) | −20323.3 | −0.722407 | ||||||||
\(926\) | −15093.2 | + | 26142.2i | −0.535629 | + | 0.927737i | ||||
\(927\) | 7252.11 | + | 12561.0i | 0.256948 | + | 0.445046i | ||||
\(928\) | −3843.33 | − | 6656.85i | −0.135952 | − | 0.235476i | ||||
\(929\) | 26635.7 | − | 46134.4i | 0.940678 | − | 1.62930i | 0.176496 | − | 0.984301i | \(-0.443524\pi\) |
0.764182 | − | 0.645001i | \(-0.223143\pi\) | |||||||
\(930\) | 28190.8 | 0.993992 | ||||||||
\(931\) | −18918.7 | + | 18187.8i | −0.665990 | + | 0.640260i | ||||
\(932\) | 3104.39 | 0.109107 | ||||||||
\(933\) | −701.989 | + | 1215.88i | −0.0246324 | + | 0.0426647i | ||||
\(934\) | 2820.23 | + | 4884.79i | 0.0988018 | + | 0.171130i | ||||
\(935\) | 11225.9 | + | 19443.8i | 0.392648 | + | 0.680086i | ||||
\(936\) | −1398.14 | + | 2421.64i | −0.0488243 | + | 0.0845661i | ||||
\(937\) | 17197.8 | 0.599602 | 0.299801 | − | 0.954002i | \(-0.403080\pi\) | ||||
0.299801 | + | 0.954002i | \(0.403080\pi\) | |||||||
\(938\) | 19995.1 | + | 2832.99i | 0.696016 | + | 0.0986143i | ||||
\(939\) | 10838.4 | 0.376676 | ||||||||
\(940\) | 2152.41 | − | 3728.08i | 0.0746849 | − | 0.129358i | ||||
\(941\) | −14417.4 | − | 24971.7i | −0.499463 | − | 0.865096i | 0.500537 | − | 0.865715i | \(-0.333136\pi\) |
−1.00000 | 0.000619696i | \(0.999803\pi\) | ||||||||
\(942\) | 2901.20 | + | 5025.03i | 0.100346 | + | 0.173805i | ||||
\(943\) | 7586.77 | − | 13140.7i | 0.261993 | − | 0.453785i | ||||
\(944\) | −7390.85 | −0.254822 | ||||||||
\(945\) | 4882.60 | − | 6235.03i | 0.168075 | − | 0.214630i | ||||
\(946\) | −34062.9 | −1.17070 | ||||||||
\(947\) | 25920.6 | − | 44895.8i | 0.889448 | − | 1.54057i | 0.0489180 | − | 0.998803i | \(-0.484423\pi\) |
0.840530 | − | 0.541766i | \(-0.182244\pi\) | |||||||
\(948\) | 2458.18 | + | 4257.70i | 0.0842173 | + | 0.145869i | ||||
\(949\) | −3520.57 | − | 6097.81i | −0.120424 | − | 0.208581i | ||||
\(950\) | −9626.23 | + | 16673.1i | −0.328754 | + | 0.569418i | ||||
\(951\) | 13595.2 | 0.463570 | ||||||||
\(952\) | −1513.70 | − | 3758.66i | −0.0515328 | − | 0.127961i | ||||
\(953\) | −5887.31 | −0.200114 | −0.100057 | − | 0.994982i | \(-0.531903\pi\) | ||||
−0.100057 | + | 0.994982i | \(0.531903\pi\) | |||||||
\(954\) | 598.398 | − | 1036.46i | 0.0203080 | − | 0.0351745i | ||||
\(955\) | −14295.3 | − | 24760.3i | −0.484384 | − | 0.838977i | ||||
\(956\) | −4013.59 | − | 6951.74i | −0.135783 | − | 0.235184i | ||||
\(957\) | −18677.6 | + | 32350.5i | −0.630888 | + | 1.09273i | ||||
\(958\) | −32897.0 | −1.10945 | ||||||||
\(959\) | 5314.45 | + | 13196.3i | 0.178949 | + | 0.444349i | ||||
\(960\) | −3040.73 | −0.102228 | ||||||||
\(961\) | −29112.3 | + | 50424.0i | −0.977218 | + | 1.69259i | ||||
\(962\) | 6273.52 | + | 10866.1i | 0.210256 | + | 0.364174i | ||||
\(963\) | −4206.02 | − | 7285.04i | −0.140745 | − | 0.243777i | ||||
\(964\) | −1611.30 | + | 2790.85i | −0.0538344 | + | 0.0932439i | ||||
\(965\) | −53384.4 | −1.78083 | ||||||||
\(966\) | −10095.0 | + | 12891.3i | −0.336235 | + | 0.429368i | ||||
\(967\) | −36620.0 | −1.21781 | −0.608904 | − | 0.793244i | \(-0.708391\pi\) | ||||
−0.608904 | + | 0.793244i | \(0.708391\pi\) | |||||||
\(968\) | −5424.35 | + | 9395.25i | −0.180109 | + | 0.311957i | ||||
\(969\) | −3138.70 | − | 5436.40i | −0.104055 | − | 0.180229i | ||||
\(970\) | 25629.2 | + | 44391.1i | 0.848355 | + | 1.46939i | ||||
\(971\) | 21182.4 | − | 36689.1i | 0.700079 | − | 1.21257i | −0.268359 | − | 0.963319i | \(-0.586481\pi\) |
0.968438 | − | 0.249254i | \(-0.0801853\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 19300.7 | + | 2734.60i | 0.635923 | + | 0.0901001i | ||||
\(974\) | 12662.1 | 0.416551 | ||||||||
\(975\) | −7329.40 | + | 12694.9i | −0.240747 | + | 0.416987i | ||||
\(976\) | −1482.79 | − | 2568.26i | −0.0486300 | − | 0.0842296i | ||||
\(977\) | −2511.16 | − | 4349.46i | −0.0822304 | − | 0.142427i | 0.821977 | − | 0.569520i | \(-0.192871\pi\) |
−0.904208 | + | 0.427093i | \(0.859538\pi\) | |||||||
\(978\) | 3979.50 | − | 6892.70i | 0.130113 | − | 0.225362i | ||||
\(979\) | 59983.8 | 1.95821 | ||||||||
\(980\) | −20873.3 | − | 6036.00i | −0.680382 | − | 0.196748i | ||||
\(981\) | −10773.2 | −0.350623 | ||||||||
\(982\) | 9286.90 | − | 16085.4i | 0.301789 | − | 0.522714i | ||||
\(983\) | −14146.4 | − | 24502.3i | −0.459003 | − | 0.795016i | 0.539906 | − | 0.841725i | \(-0.318460\pi\) |
−0.998909 | + | 0.0467095i | \(0.985127\pi\) | |||||||
\(984\) | 1235.73 | + | 2140.34i | 0.0400341 | + | 0.0693411i | ||||
\(985\) | −36522.9 | + | 63259.4i | −1.18144 | + | 2.04631i | ||||
\(986\) | 13138.7 | 0.424361 | ||||||||
\(987\) | 3738.27 | + | 529.653i | 0.120558 | + | 0.0170811i | ||||
\(988\) | 11885.9 | 0.382734 | ||||||||
\(989\) | 24206.2 | − | 41926.3i | 0.778273 | − | 1.34801i | ||||
\(990\) | 7388.56 | + | 12797.4i | 0.237196 | + | 0.410835i | ||||
\(991\) | −18200.5 | − | 31524.2i | −0.583410 | − | 1.01050i | −0.995072 | − | 0.0991586i | \(-0.968385\pi\) |
0.411662 | − | 0.911337i | \(-0.364948\pi\) | |||||||
\(992\) | 4746.79 | − | 8221.68i | 0.151926 | − | 0.263144i | ||||
\(993\) | −3711.17 | −0.118601 | ||||||||
\(994\) | 2985.78 | − | 3812.81i | 0.0952749 | − | 0.121665i | ||||
\(995\) | 35314.6 | 1.12517 | ||||||||
\(996\) | −2087.57 | + | 3615.77i | −0.0664128 | + | 0.115030i | ||||
\(997\) | 1178.60 | + | 2041.39i | 0.0374389 | + | 0.0648460i | 0.884138 | − | 0.467226i | \(-0.154747\pi\) |
−0.846699 | + | 0.532072i | \(0.821413\pi\) | |||||||
\(998\) | 243.451 | + | 421.669i | 0.00772174 | + | 0.0133745i | ||||
\(999\) | 2180.71 | − | 3777.10i | 0.0690637 | − | 0.119622i |
(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 | 42.4.e.c.37.2 | yes | 4 | |
3.2 | odd | 2 | 126.4.g.g.37.1 | 4 | |||
4.3 | odd | 2 | 336.4.q.j.289.2 | 4 | |||
7.2 | even | 3 | 294.4.a.n.1.1 | 2 | |||
7.3 | odd | 6 | 294.4.e.l.67.1 | 4 | |||
7.4 | even | 3 | inner | 42.4.e.c.25.2 | ✓ | 4 | |
7.5 | odd | 6 | 294.4.a.m.1.2 | 2 | |||
7.6 | odd | 2 | 294.4.e.l.79.1 | 4 | |||
21.2 | odd | 6 | 882.4.a.v.1.2 | 2 | |||
21.5 | even | 6 | 882.4.a.z.1.1 | 2 | |||
21.11 | odd | 6 | 126.4.g.g.109.1 | 4 | |||
21.17 | even | 6 | 882.4.g.bf.361.2 | 4 | |||
21.20 | even | 2 | 882.4.g.bf.667.2 | 4 | |||
28.11 | odd | 6 | 336.4.q.j.193.2 | 4 | |||
28.19 | even | 6 | 2352.4.a.ca.1.2 | 2 | |||
28.23 | odd | 6 | 2352.4.a.bq.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.e.c.25.2 | ✓ | 4 | 7.4 | even | 3 | inner | |
42.4.e.c.37.2 | yes | 4 | 1.1 | even | 1 | trivial | |
126.4.g.g.37.1 | 4 | 3.2 | odd | 2 | |||
126.4.g.g.109.1 | 4 | 21.11 | odd | 6 | |||
294.4.a.m.1.2 | 2 | 7.5 | odd | 6 | |||
294.4.a.n.1.1 | 2 | 7.2 | even | 3 | |||
294.4.e.l.67.1 | 4 | 7.3 | odd | 6 | |||
294.4.e.l.79.1 | 4 | 7.6 | odd | 2 | |||
336.4.q.j.193.2 | 4 | 28.11 | odd | 6 | |||
336.4.q.j.289.2 | 4 | 4.3 | odd | 2 | |||
882.4.a.v.1.2 | 2 | 21.2 | odd | 6 | |||
882.4.a.z.1.1 | 2 | 21.5 | even | 6 | |||
882.4.g.bf.361.2 | 4 | 21.17 | even | 6 | |||
882.4.g.bf.667.2 | 4 | 21.20 | even | 2 | |||
2352.4.a.bq.1.1 | 2 | 28.23 | odd | 6 | |||
2352.4.a.ca.1.2 | 2 | 28.19 | even | 6 |