Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(116,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, 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("245.116");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 116.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.116 |
Dual form | 245.4.e.i.226.2 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.29289 | − | 2.23936i | −0.457107 | − | 0.791732i | 0.541700 | − | 0.840572i | \(-0.317781\pi\) |
−0.998807 | + | 0.0488398i | \(0.984448\pi\) | |||||||
\(3\) | 3.32843 | − | 5.76500i | 0.640556 | − | 1.10948i | −0.344753 | − | 0.938694i | \(-0.612037\pi\) |
0.985309 | − | 0.170782i | \(-0.0546294\pi\) | |||||||
\(4\) | 0.656854 | − | 1.13770i | 0.0821068 | − | 0.142213i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | −17.2132 | −1.17121 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −24.0833 | −1.06434 | ||||||||
\(9\) | −8.65685 | − | 14.9941i | −0.320624 | − | 0.555337i | ||||
\(10\) | −6.46447 | + | 11.1968i | −0.204424 | + | 0.354073i | ||||
\(11\) | −19.1274 | + | 33.1297i | −0.524285 | + | 0.908088i | 0.475315 | + | 0.879815i | \(0.342334\pi\) |
−0.999600 | + | 0.0282725i | \(0.990999\pi\) | |||||||
\(12\) | −4.37258 | − | 7.57354i | −0.105188 | − | 0.182191i | ||||
\(13\) | −19.3431 | −0.412679 | −0.206339 | − | 0.978480i | \(-0.566155\pi\) | ||||
−0.206339 | + | 0.978480i | \(0.566155\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −33.2843 | −0.572931 | ||||||||
\(16\) | 25.8823 | + | 44.8294i | 0.404410 | + | 0.700459i | ||||
\(17\) | −43.6127 | + | 75.5394i | −0.622214 | + | 1.07771i | 0.366859 | + | 0.930277i | \(0.380433\pi\) |
−0.989073 | + | 0.147429i | \(0.952900\pi\) | |||||||
\(18\) | −22.3848 | + | 38.7716i | −0.293119 | + | 0.507697i | ||||
\(19\) | −22.1127 | − | 38.3003i | −0.267000 | − | 0.462458i | 0.701086 | − | 0.713077i | \(-0.252699\pi\) |
−0.968086 | + | 0.250619i | \(0.919366\pi\) | |||||||
\(20\) | −6.56854 | −0.0734385 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 98.9188 | 0.958617 | ||||||||
\(23\) | −109.083 | − | 188.938i | −0.988932 | − | 1.71288i | −0.622959 | − | 0.782255i | \(-0.714069\pi\) |
−0.365973 | − | 0.930625i | \(-0.619264\pi\) | |||||||
\(24\) | −80.1594 | + | 138.840i | −0.681769 | + | 1.18086i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 25.0086 | + | 43.3162i | 0.188638 | + | 0.326731i | ||||
\(27\) | 64.4802 | 0.459601 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −46.9411 | −0.300578 | −0.150289 | − | 0.988642i | \(-0.548020\pi\) | ||||
−0.150289 | + | 0.988642i | \(0.548020\pi\) | |||||||
\(30\) | 43.0330 | + | 74.5354i | 0.261891 | + | 0.453608i | ||||
\(31\) | 97.2792 | − | 168.493i | 0.563609 | − | 0.976199i | −0.433569 | − | 0.901120i | \(-0.642746\pi\) |
0.997178 | − | 0.0750783i | \(-0.0239207\pi\) | |||||||
\(32\) | −29.4071 | + | 50.9345i | −0.162453 | + | 0.281376i | ||||
\(33\) | 127.328 | + | 220.539i | 0.671668 | + | 1.16336i | ||||
\(34\) | 225.546 | 1.13767 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −22.7452 | −0.105302 | ||||||||
\(37\) | −183.426 | − | 317.704i | −0.815003 | − | 1.41163i | −0.909326 | − | 0.416085i | \(-0.863402\pi\) |
0.0943225 | − | 0.995542i | \(-0.469932\pi\) | |||||||
\(38\) | −57.1787 | + | 99.0364i | −0.244095 | + | 0.422785i | ||||
\(39\) | −64.3823 | + | 111.513i | −0.264344 | + | 0.457857i | ||||
\(40\) | 60.2082 | + | 104.284i | 0.237994 | + | 0.412217i | ||||
\(41\) | 339.362 | 1.29267 | 0.646336 | − | 0.763053i | \(-0.276301\pi\) | ||||
0.646336 | + | 0.763053i | \(0.276301\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −226.167 | −0.802095 | −0.401047 | − | 0.916057i | \(-0.631354\pi\) | ||||
−0.401047 | + | 0.916057i | \(0.631354\pi\) | |||||||
\(44\) | 25.1279 | + | 43.5227i | 0.0860947 | + | 0.149120i | ||||
\(45\) | −43.2843 | + | 74.9706i | −0.143388 | + | 0.248354i | ||||
\(46\) | −282.066 | + | 488.553i | −0.904095 | + | 1.56594i | ||||
\(47\) | 5.83810 | + | 10.1119i | 0.0181186 | + | 0.0313823i | 0.874943 | − | 0.484227i | \(-0.160899\pi\) |
−0.856824 | + | 0.515609i | \(0.827566\pi\) | |||||||
\(48\) | 344.589 | 1.03619 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 64.6447 | 0.182843 | ||||||||
\(51\) | 290.323 | + | 502.855i | 0.797126 | + | 1.38066i | ||||
\(52\) | −12.7056 | + | 22.0068i | −0.0338837 | + | 0.0586883i | ||||
\(53\) | 104.510 | − | 181.016i | 0.270859 | − | 0.469141i | −0.698223 | − | 0.715880i | \(-0.746026\pi\) |
0.969082 | + | 0.246739i | \(0.0793591\pi\) | |||||||
\(54\) | −83.3661 | − | 144.394i | −0.210087 | − | 0.363881i | ||||
\(55\) | 191.274 | 0.468935 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −294.402 | −0.684114 | ||||||||
\(58\) | 60.6899 | + | 105.118i | 0.137396 | + | 0.237977i | ||||
\(59\) | −308.000 | + | 533.472i | −0.679630 | + | 1.17715i | 0.295462 | + | 0.955354i | \(0.404526\pi\) |
−0.975092 | + | 0.221800i | \(0.928807\pi\) | |||||||
\(60\) | −21.8629 | + | 37.8677i | −0.0470415 | + | 0.0814783i | ||||
\(61\) | 160.368 | + | 277.765i | 0.336606 | + | 0.583018i | 0.983792 | − | 0.179314i | \(-0.0573877\pi\) |
−0.647186 | + | 0.762332i | \(0.724054\pi\) | |||||||
\(62\) | −503.087 | −1.03052 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 566.197 | 1.10585 | ||||||||
\(65\) | 48.3579 | + | 83.7583i | 0.0922778 | + | 0.159830i | ||||
\(66\) | 329.244 | − | 570.268i | 0.614048 | − | 1.06356i | ||||
\(67\) | −7.25483 | + | 12.5657i | −0.0132286 | + | 0.0229127i | −0.872564 | − | 0.488500i | \(-0.837544\pi\) |
0.859335 | + | 0.511413i | \(0.170878\pi\) | |||||||
\(68\) | 57.2944 | + | 99.2368i | 0.102176 | + | 0.176974i | ||||
\(69\) | −1452.30 | −2.53387 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −952.000 | −1.59129 | −0.795645 | − | 0.605763i | \(-0.792868\pi\) | ||||
−0.795645 | + | 0.605763i | \(0.792868\pi\) | |||||||
\(72\) | 208.485 | + | 361.107i | 0.341253 | + | 0.591068i | ||||
\(73\) | 412.245 | − | 714.029i | 0.660953 | − | 1.14480i | −0.319412 | − | 0.947616i | \(-0.603485\pi\) |
0.980366 | − | 0.197189i | \(-0.0631812\pi\) | |||||||
\(74\) | −474.302 | + | 821.514i | −0.745087 | + | 1.29053i | ||||
\(75\) | 83.2107 | + | 144.125i | 0.128111 | + | 0.221895i | ||||
\(76\) | −58.0993 | −0.0876901 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 332.958 | 0.483334 | ||||||||
\(79\) | −78.1375 | − | 135.338i | −0.111280 | − | 0.192743i | 0.805006 | − | 0.593266i | \(-0.202162\pi\) |
−0.916287 | + | 0.400523i | \(0.868829\pi\) | |||||||
\(80\) | 129.411 | − | 224.147i | 0.180858 | − | 0.313255i | ||||
\(81\) | 448.353 | − | 776.570i | 0.615024 | − | 1.06525i | ||||
\(82\) | −438.759 | − | 759.954i | −0.590889 | − | 1.02345i | ||||
\(83\) | 1036.53 | 1.37077 | 0.685384 | − | 0.728182i | \(-0.259634\pi\) | ||||
0.685384 | + | 0.728182i | \(0.259634\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 436.127 | 0.556525 | ||||||||
\(86\) | 292.409 | + | 506.468i | 0.366643 | + | 0.635044i | ||||
\(87\) | −156.240 | + | 270.616i | −0.192537 | + | 0.333483i | ||||
\(88\) | 460.651 | − | 797.870i | 0.558017 | − | 0.966514i | ||||
\(89\) | −85.1127 | − | 147.420i | −0.101370 | − | 0.175578i | 0.810879 | − | 0.585213i | \(-0.198989\pi\) |
−0.912249 | + | 0.409635i | \(0.865656\pi\) | |||||||
\(90\) | 223.848 | 0.262174 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −286.607 | −0.324792 | ||||||||
\(93\) | −647.574 | − | 1121.63i | −0.722046 | − | 1.25062i | ||||
\(94\) | 15.0961 | − | 26.1472i | 0.0165643 | − | 0.0286901i | ||||
\(95\) | −110.563 | + | 191.502i | −0.119406 | + | 0.206817i | ||||
\(96\) | 195.759 | + | 339.064i | 0.208120 | + | 0.360475i | ||||
\(97\) | −1059.87 | −1.10942 | −0.554710 | − | 0.832044i | \(-0.687171\pi\) | ||||
−0.554710 | + | 0.832044i | \(0.687171\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 662.333 | 0.672394 | ||||||||
\(100\) | 16.4214 | + | 28.4426i | 0.0164214 | + | 0.0284426i | ||||
\(101\) | −120.917 | + | 209.434i | −0.119125 | + | 0.206331i | −0.919421 | − | 0.393274i | \(-0.871342\pi\) |
0.800296 | + | 0.599605i | \(0.204676\pi\) | |||||||
\(102\) | 750.714 | − | 1300.28i | 0.728743 | − | 1.26222i | ||||
\(103\) | −839.788 | − | 1454.56i | −0.803367 | − | 1.39147i | −0.917388 | − | 0.397994i | \(-0.869706\pi\) |
0.114021 | − | 0.993478i | \(-0.463627\pi\) | |||||||
\(104\) | 465.846 | 0.439230 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −540.479 | −0.495245 | ||||||||
\(107\) | −753.441 | − | 1305.00i | −0.680728 | − | 1.17905i | −0.974759 | − | 0.223259i | \(-0.928330\pi\) |
0.294031 | − | 0.955796i | \(-0.405003\pi\) | |||||||
\(108\) | 42.3541 | − | 73.3595i | 0.0377364 | − | 0.0653613i | ||||
\(109\) | 626.205 | − | 1084.62i | 0.550271 | − | 0.953097i | −0.447984 | − | 0.894042i | \(-0.647858\pi\) |
0.998255 | − | 0.0590556i | \(-0.0188089\pi\) | |||||||
\(110\) | −247.297 | − | 428.331i | −0.214353 | − | 0.371271i | ||||
\(111\) | −2442.09 | −2.08822 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1370.20 | 1.14069 | 0.570345 | − | 0.821405i | \(-0.306810\pi\) | ||||
0.570345 | + | 0.821405i | \(0.306810\pi\) | |||||||
\(114\) | 380.630 | + | 659.271i | 0.312713 | + | 0.541635i | ||||
\(115\) | −545.416 | + | 944.689i | −0.442264 | + | 0.766023i | ||||
\(116\) | −30.8335 | + | 53.4052i | −0.0246795 | + | 0.0427461i | ||||
\(117\) | 167.451 | + | 290.033i | 0.132315 | + | 0.229176i | ||||
\(118\) | 1592.84 | 1.24265 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 801.594 | 0.609793 | ||||||||
\(121\) | −66.2162 | − | 114.690i | −0.0497492 | − | 0.0861681i | ||||
\(122\) | 414.676 | − | 718.240i | 0.307730 | − | 0.533003i | ||||
\(123\) | 1129.54 | − | 1956.43i | 0.828028 | − | 1.43419i | ||||
\(124\) | −127.797 | − | 221.350i | −0.0925522 | − | 0.160305i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1213.49 | 0.847873 | 0.423936 | − | 0.905692i | \(-0.360648\pi\) | ||||
0.423936 | + | 0.905692i | \(0.360648\pi\) | |||||||
\(128\) | −496.775 | − | 860.440i | −0.343040 | − | 0.594163i | ||||
\(129\) | −752.779 | + | 1303.85i | −0.513787 | + | 0.889905i | ||||
\(130\) | 125.043 | − | 216.581i | 0.0843616 | − | 0.146119i | ||||
\(131\) | −991.209 | − | 1716.83i | −0.661087 | − | 1.14504i | −0.980330 | − | 0.197363i | \(-0.936762\pi\) |
0.319244 | − | 0.947673i | \(-0.396571\pi\) | |||||||
\(132\) | 334.545 | 0.220594 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 37.5189 | 0.0241876 | ||||||||
\(135\) | −161.201 | − | 279.208i | −0.102770 | − | 0.178003i | ||||
\(136\) | 1050.34 | − | 1819.24i | 0.662247 | − | 1.14705i | ||||
\(137\) | −1105.47 | + | 1914.74i | −0.689394 | + | 1.19407i | 0.282640 | + | 0.959226i | \(0.408790\pi\) |
−0.972034 | + | 0.234840i | \(0.924543\pi\) | |||||||
\(138\) | 1877.67 | + | 3252.22i | 1.15825 | + | 2.00614i | ||||
\(139\) | −528.039 | −0.322213 | −0.161107 | − | 0.986937i | \(-0.551506\pi\) | ||||
−0.161107 | + | 0.986937i | \(0.551506\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 77.7267 | 0.0464239 | ||||||||
\(142\) | 1230.83 | + | 2131.87i | 0.727390 | + | 1.25988i | ||||
\(143\) | 369.984 | − | 640.832i | 0.216361 | − | 0.374749i | ||||
\(144\) | 448.118 | − | 776.163i | 0.259327 | − | 0.449168i | ||||
\(145\) | 117.353 | + | 203.261i | 0.0672112 | + | 0.116413i | ||||
\(146\) | −2131.95 | −1.20851 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −481.938 | −0.267669 | ||||||||
\(149\) | 164.186 | + | 284.378i | 0.0902727 | + | 0.156357i | 0.907626 | − | 0.419780i | \(-0.137893\pi\) |
−0.817353 | + | 0.576137i | \(0.804559\pi\) | |||||||
\(150\) | 215.165 | − | 372.677i | 0.117121 | − | 0.202860i | ||||
\(151\) | −514.714 | + | 891.512i | −0.277396 | + | 0.480465i | −0.970737 | − | 0.240145i | \(-0.922805\pi\) |
0.693340 | + | 0.720610i | \(0.256138\pi\) | |||||||
\(152\) | 532.546 | + | 922.397i | 0.284179 | + | 0.492212i | ||||
\(153\) | 1510.20 | 0.797987 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −972.792 | −0.504107 | ||||||||
\(156\) | 84.5795 | + | 146.496i | 0.0434088 | + | 0.0751863i | ||||
\(157\) | 262.549 | − | 454.749i | 0.133463 | − | 0.231165i | −0.791546 | − | 0.611109i | \(-0.790724\pi\) |
0.925009 | + | 0.379944i | \(0.124057\pi\) | |||||||
\(158\) | −202.047 | + | 349.956i | −0.101734 | + | 0.176209i | ||||
\(159\) | −695.706 | − | 1205.00i | −0.347000 | − | 0.601022i | ||||
\(160\) | 294.071 | 0.145302 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2318.69 | −1.12453 | ||||||||
\(163\) | −501.313 | − | 868.299i | −0.240895 | − | 0.417242i | 0.720075 | − | 0.693897i | \(-0.244108\pi\) |
−0.960969 | + | 0.276655i | \(0.910774\pi\) | |||||||
\(164\) | 222.912 | − | 386.094i | 0.106137 | − | 0.183835i | ||||
\(165\) | 636.642 | − | 1102.70i | 0.300379 | − | 0.520272i | ||||
\(166\) | −1340.12 | − | 2321.16i | −0.626587 | − | 1.08528i | ||||
\(167\) | 359.422 | 0.166544 | 0.0832722 | − | 0.996527i | \(-0.473463\pi\) | ||||
0.0832722 | + | 0.996527i | \(0.473463\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1822.84 | −0.829696 | ||||||||
\(170\) | −563.866 | − | 976.644i | −0.254391 | − | 0.440619i | ||||
\(171\) | −382.853 | + | 663.121i | −0.171213 | + | 0.296550i | ||||
\(172\) | −148.558 | + | 257.311i | −0.0658574 | + | 0.114068i | ||||
\(173\) | 1646.83 | + | 2852.39i | 0.723733 | + | 1.25354i | 0.959493 | + | 0.281732i | \(0.0909088\pi\) |
−0.235760 | + | 0.971811i | \(0.575758\pi\) | |||||||
\(174\) | 808.007 | 0.352039 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1980.24 | −0.848104 | ||||||||
\(177\) | 2050.31 | + | 3551.24i | 0.870683 | + | 1.50807i | ||||
\(178\) | −220.083 | + | 381.195i | −0.0926738 | + | 0.160516i | ||||
\(179\) | −1489.41 | + | 2579.74i | −0.621921 | + | 1.07720i | 0.367207 | + | 0.930139i | \(0.380314\pi\) |
−0.989128 | + | 0.147059i | \(0.953019\pi\) | |||||||
\(180\) | 56.8629 | + | 98.4895i | 0.0235462 | + | 0.0407832i | ||||
\(181\) | −1462.31 | −0.600514 | −0.300257 | − | 0.953858i | \(-0.597072\pi\) | ||||
−0.300257 | + | 0.953858i | \(0.597072\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2135.09 | 0.862460 | ||||||||
\(184\) | 2627.08 | + | 4550.24i | 1.05256 | + | 1.82309i | ||||
\(185\) | −917.132 | + | 1588.52i | −0.364480 | + | 0.631299i | ||||
\(186\) | −1674.49 | + | 2900.30i | −0.660104 | + | 1.14333i | ||||
\(187\) | −1668.40 | − | 2889.75i | −0.652434 | − | 1.13005i | ||||
\(188\) | 15.3391 | 0.00595064 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 571.787 | 0.218325 | ||||||||
\(191\) | 187.461 | + | 324.693i | 0.0710169 | + | 0.123005i | 0.899347 | − | 0.437235i | \(-0.144042\pi\) |
−0.828330 | + | 0.560240i | \(0.810709\pi\) | |||||||
\(192\) | 1884.54 | − | 3264.13i | 0.708361 | − | 1.22692i | ||||
\(193\) | −366.514 | + | 634.821i | −0.136696 | + | 0.236764i | −0.926244 | − | 0.376925i | \(-0.876982\pi\) |
0.789548 | + | 0.613688i | \(0.210315\pi\) | |||||||
\(194\) | 1370.30 | + | 2373.43i | 0.507124 | + | 0.878364i | ||||
\(195\) | 643.823 | 0.236436 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2093.24 | −0.757043 | −0.378521 | − | 0.925593i | \(-0.623567\pi\) | ||||
−0.378521 | + | 0.925593i | \(0.623567\pi\) | |||||||
\(198\) | −856.326 | − | 1483.20i | −0.307356 | − | 0.532356i | ||||
\(199\) | 1432.52 | − | 2481.20i | 0.510295 | − | 0.883856i | −0.489634 | − | 0.871928i | \(-0.662870\pi\) |
0.999929 | − | 0.0119283i | \(-0.00379699\pi\) | |||||||
\(200\) | 301.041 | − | 521.418i | 0.106434 | − | 0.184349i | ||||
\(201\) | 48.2944 | + | 83.6483i | 0.0169474 | + | 0.0293537i | ||||
\(202\) | 625.330 | 0.217812 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 762.801 | 0.261798 | ||||||||
\(205\) | −848.406 | − | 1469.48i | −0.289050 | − | 0.500649i | ||||
\(206\) | −2171.51 | + | 3761.17i | −0.734449 | + | 1.27210i | ||||
\(207\) | −1888.64 | + | 3271.21i | −0.634151 | + | 1.09838i | ||||
\(208\) | −500.644 | − | 867.141i | −0.166891 | − | 0.289065i | ||||
\(209\) | 1691.84 | 0.559936 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5643.65 | 1.84135 | 0.920674 | − | 0.390331i | \(-0.127640\pi\) | ||||
0.920674 | + | 0.390331i | \(0.127640\pi\) | |||||||
\(212\) | −137.295 | − | 237.802i | −0.0444787 | − | 0.0770393i | ||||
\(213\) | −3168.66 | + | 5488.28i | −1.01931 | + | 1.76550i | ||||
\(214\) | −1948.24 | + | 3374.44i | −0.622330 | + | 1.07791i | ||||
\(215\) | 565.416 | + | 979.330i | 0.179354 | + | 0.310650i | ||||
\(216\) | −1552.89 | −0.489172 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3238.46 | −1.00613 | ||||||||
\(219\) | −2744.25 | − | 4753.19i | −0.846755 | − | 1.46662i | ||||
\(220\) | 125.639 | − | 217.614i | 0.0385027 | − | 0.0666887i | ||||
\(221\) | 843.607 | − | 1461.17i | 0.256774 | − | 0.444746i | ||||
\(222\) | 3157.36 | + | 5468.70i | 0.954540 | + | 1.65331i | ||||
\(223\) | 6369.16 | 1.91260 | 0.956302 | − | 0.292381i | \(-0.0944477\pi\) | ||||
0.956302 | + | 0.292381i | \(0.0944477\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 432.843 | 0.128250 | ||||||||
\(226\) | −1771.53 | − | 3068.37i | −0.521417 | − | 0.903120i | ||||
\(227\) | −507.837 | + | 879.600i | −0.148486 | + | 0.257185i | −0.930668 | − | 0.365865i | \(-0.880773\pi\) |
0.782182 | + | 0.623050i | \(0.214107\pi\) | |||||||
\(228\) | −193.379 | + | 334.943i | −0.0561704 | + | 0.0972900i | ||||
\(229\) | 2054.18 | + | 3557.94i | 0.592768 | + | 1.02670i | 0.993858 | + | 0.110665i | \(0.0352982\pi\) |
−0.401090 | + | 0.916039i | \(0.631368\pi\) | |||||||
\(230\) | 2820.66 | 0.808647 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1130.50 | 0.319917 | ||||||||
\(233\) | −304.215 | − | 526.916i | −0.0855357 | − | 0.148152i | 0.820084 | − | 0.572244i | \(-0.193927\pi\) |
−0.905619 | + | 0.424092i | \(0.860593\pi\) | |||||||
\(234\) | 432.992 | − | 749.964i | 0.120964 | − | 0.209516i | ||||
\(235\) | 29.1905 | − | 50.5594i | 0.00810288 | − | 0.0140346i | ||||
\(236\) | 404.622 | + | 700.826i | 0.111605 | + | 0.193305i | ||||
\(237\) | −1040.30 | −0.285126 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5054.44 | −1.36797 | −0.683985 | − | 0.729496i | \(-0.739755\pi\) | ||||
−0.683985 | + | 0.729496i | \(0.739755\pi\) | |||||||
\(240\) | −861.472 | − | 1492.11i | −0.231699 | − | 0.401315i | ||||
\(241\) | 2.43391 | − | 4.21565i | 0.000650547 | − | 0.00112678i | −0.865700 | − | 0.500563i | \(-0.833126\pi\) |
0.866350 | + | 0.499437i | \(0.166460\pi\) | |||||||
\(242\) | −171.221 | + | 296.563i | −0.0454814 | + | 0.0787761i | ||||
\(243\) | −2114.14 | − | 3661.79i | −0.558115 | − | 0.966683i | ||||
\(244\) | 421.352 | 0.110551 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5841.52 | −1.51399 | ||||||||
\(247\) | 427.729 | + | 740.849i | 0.110185 | + | 0.190846i | ||||
\(248\) | −2342.80 | + | 4057.85i | −0.599871 | + | 1.03901i | ||||
\(249\) | 3450.01 | − | 5975.59i | 0.878054 | − | 1.52083i | ||||
\(250\) | −161.612 | − | 279.920i | −0.0408849 | − | 0.0708147i | ||||
\(251\) | 547.921 | 0.137787 | 0.0688934 | − | 0.997624i | \(-0.478053\pi\) | ||||
0.0688934 | + | 0.997624i | \(0.478053\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8345.92 | 2.07393 | ||||||||
\(254\) | −1568.91 | − | 2717.44i | −0.387568 | − | 0.671288i | ||||
\(255\) | 1451.62 | − | 2514.27i | 0.356485 | − | 0.617451i | ||||
\(256\) | 980.232 | − | 1697.81i | 0.239314 | − | 0.414505i | ||||
\(257\) | −887.306 | − | 1536.86i | −0.215364 | − | 0.373022i | 0.738021 | − | 0.674778i | \(-0.235761\pi\) |
−0.953385 | + | 0.301756i | \(0.902427\pi\) | |||||||
\(258\) | 3893.05 | 0.939421 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 127.056 | 0.0303065 | ||||||||
\(261\) | 406.362 | + | 703.840i | 0.0963724 | + | 0.166922i | ||||
\(262\) | −2563.06 | + | 4439.34i | −0.604374 | + | 1.04681i | ||||
\(263\) | 599.547 | − | 1038.45i | 0.140569 | − | 0.243473i | −0.787142 | − | 0.616772i | \(-0.788440\pi\) |
0.927711 | + | 0.373299i | \(0.121774\pi\) | |||||||
\(264\) | −3066.48 | − | 5311.31i | −0.714883 | − | 1.23821i | ||||
\(265\) | −1045.10 | −0.242263 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1133.17 | −0.259733 | ||||||||
\(268\) | 9.53074 | + | 16.5077i | 0.00217232 | + | 0.00376257i | ||||
\(269\) | 1625.15 | − | 2814.84i | 0.368353 | − | 0.638006i | −0.620955 | − | 0.783846i | \(-0.713255\pi\) |
0.989308 | + | 0.145840i | \(0.0465885\pi\) | |||||||
\(270\) | −416.830 | + | 721.971i | −0.0939536 | + | 0.162732i | ||||
\(271\) | −448.071 | − | 776.082i | −0.100437 | − | 0.173962i | 0.811428 | − | 0.584453i | \(-0.198691\pi\) |
−0.911865 | + | 0.410491i | \(0.865357\pi\) | |||||||
\(272\) | −4515.18 | −1.00652 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5717.04 | 1.26051 | ||||||||
\(275\) | −478.185 | − | 828.241i | −0.104857 | − | 0.181618i | ||||
\(276\) | −953.951 | + | 1652.29i | −0.208048 | + | 0.360349i | ||||
\(277\) | 193.281 | − | 334.772i | 0.0419246 | − | 0.0726156i | −0.844302 | − | 0.535868i | \(-0.819984\pi\) |
0.886226 | + | 0.463253i | \(0.153318\pi\) | |||||||
\(278\) | 682.698 | + | 1182.47i | 0.147286 | + | 0.255107i | ||||
\(279\) | −3368.53 | −0.722826 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3335.10 | −0.708025 | −0.354013 | − | 0.935241i | \(-0.615183\pi\) | ||||
−0.354013 | + | 0.935241i | \(0.615183\pi\) | |||||||
\(282\) | −100.492 | − | 174.058i | −0.0212207 | − | 0.0367553i | ||||
\(283\) | 2706.13 | − | 4687.15i | 0.568419 | − | 0.984531i | −0.428303 | − | 0.903635i | \(-0.640889\pi\) |
0.996723 | − | 0.0808959i | \(-0.0257781\pi\) | |||||||
\(284\) | −625.325 | + | 1083.10i | −0.130656 | + | 0.226302i | ||||
\(285\) | 736.005 | + | 1274.80i | 0.152973 | + | 0.264956i | ||||
\(286\) | −1913.40 | −0.395601 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1018.29 | 0.208345 | ||||||||
\(289\) | −1347.63 | − | 2334.17i | −0.274300 | − | 0.475101i | ||||
\(290\) | 303.449 | − | 525.590i | 0.0614454 | − | 0.106427i | ||||
\(291\) | −3527.71 | + | 6110.17i | −0.710646 | + | 1.23088i | ||||
\(292\) | −541.569 | − | 938.026i | −0.108538 | − | 0.187992i | ||||
\(293\) | −282.211 | −0.0562695 | −0.0281347 | − | 0.999604i | \(-0.508957\pi\) | ||||
−0.0281347 | + | 0.999604i | \(0.508957\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3080.00 | 0.607880 | ||||||||
\(296\) | 4417.51 | + | 7651.34i | 0.867440 | + | 1.50245i | ||||
\(297\) | −1233.34 | + | 2136.21i | −0.240962 | + | 0.417358i | ||||
\(298\) | 424.550 | − | 735.341i | 0.0825285 | − | 0.142944i | ||||
\(299\) | 2110.01 | + | 3654.65i | 0.408111 | + | 0.706869i | ||||
\(300\) | 218.629 | 0.0420752 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2661.88 | 0.507199 | ||||||||
\(303\) | 804.925 | + | 1394.17i | 0.152613 | + | 0.264333i | ||||
\(304\) | 1144.65 | − | 1982.60i | 0.215955 | − | 0.374045i | ||||
\(305\) | 801.838 | − | 1388.82i | 0.150535 | − | 0.260734i | ||||
\(306\) | −1952.52 | − | 3381.87i | −0.364765 | − | 0.631792i | ||||
\(307\) | −1919.67 | −0.356878 | −0.178439 | − | 0.983951i | \(-0.557105\pi\) | ||||
−0.178439 | + | 0.983951i | \(0.557105\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11180.7 | −2.05841 | ||||||||
\(310\) | 1257.72 | + | 2178.43i | 0.230431 | + | 0.399118i | ||||
\(311\) | 606.654 | − | 1050.76i | 0.110612 | − | 0.191585i | −0.805405 | − | 0.592724i | \(-0.798052\pi\) |
0.916017 | + | 0.401139i | \(0.131386\pi\) | |||||||
\(312\) | 1550.53 | − | 2685.60i | 0.281352 | − | 0.487315i | ||||
\(313\) | −717.001 | − | 1241.88i | −0.129480 | − | 0.224266i | 0.793995 | − | 0.607924i | \(-0.207998\pi\) |
−0.923475 | + | 0.383658i | \(0.874664\pi\) | |||||||
\(314\) | −1357.79 | −0.244028 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −205.300 | −0.0365475 | ||||||||
\(317\) | −3248.48 | − | 5626.52i | −0.575560 | − | 0.996899i | −0.995981 | − | 0.0895699i | \(-0.971451\pi\) |
0.420420 | − | 0.907329i | \(-0.361883\pi\) | |||||||
\(318\) | −1798.95 | + | 3115.87i | −0.317232 | + | 0.549463i | ||||
\(319\) | 897.862 | − | 1555.14i | 0.157588 | − | 0.272951i | ||||
\(320\) | −1415.49 | − | 2451.70i | −0.247276 | − | 0.428295i | ||||
\(321\) | −10031.1 | −1.74418 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3857.58 | 0.664524 | ||||||||
\(324\) | −589.005 | − | 1020.19i | −0.100995 | − | 0.174929i | ||||
\(325\) | 241.789 | − | 418.791i | 0.0412679 | − | 0.0714781i | ||||
\(326\) | −1296.29 | + | 2245.24i | −0.220229 | + | 0.381448i | ||||
\(327\) | −4168.55 | − | 7220.15i | −0.704959 | − | 1.22102i | ||||
\(328\) | −8172.96 | −1.37584 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3292.44 | −0.549221 | ||||||||
\(331\) | 4841.94 | + | 8386.49i | 0.804039 | + | 1.39264i | 0.916938 | + | 0.399031i | \(0.130653\pi\) |
−0.112898 | + | 0.993607i | \(0.536013\pi\) | |||||||
\(332\) | 680.848 | − | 1179.26i | 0.112549 | − | 0.194941i | ||||
\(333\) | −3175.79 | + | 5500.63i | −0.522619 | + | 0.905204i | ||||
\(334\) | −464.695 | − | 804.875i | −0.0761286 | − | 0.131859i | ||||
\(335\) | 72.5483 | 0.0118321 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.1319 | 0.00470895 | 0.00235447 | − | 0.999997i | \(-0.499251\pi\) | ||||
0.00235447 | + | 0.999997i | \(0.499251\pi\) | |||||||
\(338\) | 2356.74 | + | 4082.00i | 0.379260 | + | 0.656897i | ||||
\(339\) | 4560.62 | − | 7899.23i | 0.730676 | − | 1.26557i | ||||
\(340\) | 286.472 | − | 496.184i | 0.0456945 | − | 0.0791451i | ||||
\(341\) | 3721.40 | + | 6445.65i | 0.590983 | + | 1.02361i | ||||
\(342\) | 1979.95 | 0.313051 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5446.83 | 0.853701 | ||||||||
\(345\) | 3630.76 | + | 6288.66i | 0.566590 | + | 0.981362i | ||||
\(346\) | 4258.34 | − | 7375.66i | 0.661647 | − | 1.14601i | ||||
\(347\) | 3924.29 | − | 6797.07i | 0.607110 | − | 1.05154i | −0.384605 | − | 0.923081i | \(-0.625662\pi\) |
0.991714 | − | 0.128463i | \(-0.0410045\pi\) | |||||||
\(348\) | 205.254 | + | 355.510i | 0.0316171 | + | 0.0547625i | ||||
\(349\) | 10269.6 | 1.57513 | 0.787567 | − | 0.616229i | \(-0.211341\pi\) | ||||
0.787567 | + | 0.616229i | \(0.211341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1247.25 | −0.189668 | ||||||||
\(352\) | −1124.96 | − | 1948.49i | −0.170343 | − | 0.295043i | ||||
\(353\) | 1399.97 | − | 2424.81i | 0.211084 | − | 0.365609i | −0.740970 | − | 0.671538i | \(-0.765634\pi\) |
0.952054 | + | 0.305930i | \(0.0989672\pi\) | |||||||
\(354\) | 5301.67 | − | 9182.76i | 0.795990 | − | 1.37869i | ||||
\(355\) | 2380.00 | + | 4122.28i | 0.355823 | + | 0.616304i | ||||
\(356\) | −223.627 | −0.0332927 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7702.60 | 1.13714 | ||||||||
\(359\) | 1581.65 | + | 2739.49i | 0.232524 | + | 0.402743i | 0.958550 | − | 0.284924i | \(-0.0919683\pi\) |
−0.726026 | + | 0.687667i | \(0.758635\pi\) | |||||||
\(360\) | 1042.43 | − | 1805.54i | 0.152613 | − | 0.264334i | ||||
\(361\) | 2451.56 | − | 4246.22i | 0.357422 | − | 0.619073i | ||||
\(362\) | 1890.62 | + | 3274.64i | 0.274499 | + | 0.475446i | ||||
\(363\) | −881.583 | −0.127469 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4122.45 | −0.591175 | ||||||||
\(366\) | −2760.44 | − | 4781.22i | −0.394236 | − | 0.682837i | ||||
\(367\) | 1591.42 | − | 2756.42i | 0.226353 | − | 0.392055i | −0.730371 | − | 0.683050i | \(-0.760653\pi\) |
0.956725 | + | 0.290995i | \(0.0939864\pi\) | |||||||
\(368\) | 5646.64 | − | 9780.27i | 0.799868 | − | 1.38541i | ||||
\(369\) | −2937.81 | − | 5088.44i | −0.414462 | − | 0.717869i | ||||
\(370\) | 4743.02 | 0.666426 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1701.45 | −0.237139 | ||||||||
\(373\) | 1307.57 | + | 2264.78i | 0.181510 | + | 0.314385i | 0.942395 | − | 0.334502i | \(-0.108568\pi\) |
−0.760885 | + | 0.648887i | \(0.775235\pi\) | |||||||
\(374\) | −4314.12 | + | 7472.27i | −0.596464 | + | 1.03311i | ||||
\(375\) | 416.053 | − | 720.626i | 0.0572931 | − | 0.0992345i | ||||
\(376\) | −140.600 | − | 243.527i | −0.0192843 | − | 0.0334015i | ||||
\(377\) | 907.989 | 0.124042 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −672.434 | −0.0911362 | −0.0455681 | − | 0.998961i | \(-0.514510\pi\) | ||||
−0.0455681 | + | 0.998961i | \(0.514510\pi\) | |||||||
\(380\) | 145.248 | + | 251.577i | 0.0196081 | + | 0.0339622i | ||||
\(381\) | 4039.01 | − | 6995.78i | 0.543110 | − | 0.940694i | ||||
\(382\) | 484.735 | − | 839.586i | 0.0649246 | − | 0.112453i | ||||
\(383\) | 584.928 | + | 1013.13i | 0.0780377 | + | 0.135165i | 0.902403 | − | 0.430893i | \(-0.141801\pi\) |
−0.824366 | + | 0.566058i | \(0.808468\pi\) | |||||||
\(384\) | −6613.92 | −0.878946 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1895.45 | 0.249938 | ||||||||
\(387\) | 1957.89 | + | 3391.17i | 0.257171 | + | 0.445433i | ||||
\(388\) | −696.182 | + | 1205.82i | −0.0910910 | + | 0.157774i | ||||
\(389\) | 561.110 | − | 971.871i | 0.0731347 | − | 0.126673i | −0.827139 | − | 0.561998i | \(-0.810033\pi\) |
0.900274 | + | 0.435325i | \(0.143366\pi\) | |||||||
\(390\) | −832.394 | − | 1441.75i | −0.108077 | − | 0.187194i | ||||
\(391\) | 19029.7 | 2.46131 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13196.7 | −1.69385 | ||||||||
\(394\) | 2706.34 | + | 4687.52i | 0.346049 | + | 0.599375i | ||||
\(395\) | −390.688 | + | 676.691i | −0.0497661 | + | 0.0861975i | ||||
\(396\) | 435.056 | − | 753.540i | 0.0552081 | − | 0.0956232i | ||||
\(397\) | −992.963 | − | 1719.86i | −0.125530 | − | 0.217424i | 0.796410 | − | 0.604757i | \(-0.206730\pi\) |
−0.921940 | + | 0.387333i | \(0.873396\pi\) | |||||||
\(398\) | −7408.38 | −0.933037 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1294.11 | −0.161764 | ||||||||
\(401\) | 2086.19 | + | 3613.38i | 0.259799 | + | 0.449984i | 0.966188 | − | 0.257839i | \(-0.0830105\pi\) |
−0.706389 | + | 0.707824i | \(0.749677\pi\) | |||||||
\(402\) | 124.879 | − | 216.297i | 0.0154935 | − | 0.0268356i | ||||
\(403\) | −1881.69 | + | 3259.18i | −0.232589 | + | 0.402856i | ||||
\(404\) | 158.849 | + | 275.135i | 0.0195620 | + | 0.0338824i | ||||
\(405\) | −4483.53 | −0.550095 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14033.9 | 1.70918 | ||||||||
\(408\) | −6991.93 | − | 12110.4i | −0.848412 | − | 1.46949i | ||||
\(409\) | −5850.40 | + | 10133.2i | −0.707295 | + | 1.22507i | 0.258562 | + | 0.965995i | \(0.416751\pi\) |
−0.965857 | + | 0.259076i | \(0.916582\pi\) | |||||||
\(410\) | −2193.80 | + | 3799.77i | −0.264253 | + | 0.457700i | ||||
\(411\) | 7358.98 | + | 12746.1i | 0.883192 | + | 1.52973i | ||||
\(412\) | −2206.47 | −0.263848 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9767.22 | 1.15950 | ||||||||
\(415\) | −2591.32 | − | 4488.30i | −0.306513 | − | 0.530896i | ||||
\(416\) | 568.825 | − | 985.234i | 0.0670408 | − | 0.116118i | ||||
\(417\) | −1757.54 | + | 3044.15i | −0.206396 | + | 0.357488i | ||||
\(418\) | −2187.36 | − | 3788.62i | −0.255951 | − | 0.443320i | ||||
\(419\) | −2733.20 | −0.318677 | −0.159339 | − | 0.987224i | \(-0.550936\pi\) | ||||
−0.159339 | + | 0.987224i | \(0.550936\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13549.4 | 1.56854 | 0.784272 | − | 0.620417i | \(-0.213037\pi\) | ||||
0.784272 | + | 0.620417i | \(0.213037\pi\) | |||||||
\(422\) | −7296.63 | − | 12638.1i | −0.841693 | − | 1.45786i | ||||
\(423\) | 101.079 | − | 175.074i | 0.0116185 | − | 0.0201239i | ||||
\(424\) | −2516.93 | + | 4359.46i | −0.288286 | + | 0.499325i | ||||
\(425\) | −1090.32 | − | 1888.49i | −0.124443 | − | 0.215541i | ||||
\(426\) | 16387.0 | 1.86374 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1979.60 | −0.223569 | ||||||||
\(429\) | −2462.93 | − | 4265.92i | −0.277183 | − | 0.480095i | ||||
\(430\) | 1462.05 | − | 2532.34i | 0.163968 | − | 0.284000i | ||||
\(431\) | 3214.63 | − | 5567.90i | 0.359265 | − | 0.622265i | −0.628573 | − | 0.777750i | \(-0.716361\pi\) |
0.987838 | + | 0.155485i | \(0.0496942\pi\) | |||||||
\(432\) | 1668.89 | + | 2890.61i | 0.185867 | + | 0.321932i | ||||
\(433\) | −8022.03 | −0.890333 | −0.445166 | − | 0.895448i | \(-0.646855\pi\) | ||||
−0.445166 | + | 0.895448i | \(0.646855\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1562.40 | 0.172210 | ||||||||
\(436\) | −822.651 | − | 1424.87i | −0.0903620 | − | 0.156512i | ||||
\(437\) | −4824.25 | + | 8355.85i | −0.528090 | + | 0.914678i | ||||
\(438\) | −7096.05 | + | 12290.7i | −0.774115 | + | 1.34081i | ||||
\(439\) | −2784.94 | − | 4823.66i | −0.302774 | − | 0.524421i | 0.673989 | − | 0.738741i | \(-0.264580\pi\) |
−0.976763 | + | 0.214321i | \(0.931246\pi\) | |||||||
\(440\) | −4606.51 | −0.499106 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4362.77 | −0.469493 | ||||||||
\(443\) | 2743.11 | + | 4751.20i | 0.294196 | + | 0.509563i | 0.974798 | − | 0.223091i | \(-0.0716148\pi\) |
−0.680601 | + | 0.732654i | \(0.738281\pi\) | |||||||
\(444\) | −1604.09 | + | 2778.37i | −0.171457 | + | 0.296972i | ||||
\(445\) | −425.563 | + | 737.098i | −0.0453340 | + | 0.0785208i | ||||
\(446\) | −8234.65 | − | 14262.8i | −0.874264 | − | 1.51427i | ||||
\(447\) | 2185.92 | 0.231299 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7232.67 | −0.760203 | −0.380101 | − | 0.924945i | \(-0.624111\pi\) | ||||
−0.380101 | + | 0.924945i | \(0.624111\pi\) | |||||||
\(450\) | −559.619 | − | 969.289i | −0.0586238 | − | 0.101539i | ||||
\(451\) | −6491.13 | + | 11243.0i | −0.677728 | + | 1.17386i | ||||
\(452\) | 900.024 | − | 1558.89i | 0.0936583 | − | 0.162221i | ||||
\(453\) | 3426.38 | + | 5934.66i | 0.355376 | + | 0.615529i | ||||
\(454\) | 2626.32 | 0.271496 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7090.16 | 0.728130 | ||||||||
\(457\) | 1450.25 | + | 2511.91i | 0.148446 | + | 0.257117i | 0.930653 | − | 0.365902i | \(-0.119239\pi\) |
−0.782207 | + | 0.623019i | \(0.785906\pi\) | |||||||
\(458\) | 5311.66 | − | 9200.07i | 0.541916 | − | 0.938627i | ||||
\(459\) | −2812.16 | + | 4870.80i | −0.285970 | + | 0.495315i | ||||
\(460\) | 716.518 | + | 1241.05i | 0.0726257 | + | 0.125791i | ||||
\(461\) | −6073.57 | −0.613611 | −0.306805 | − | 0.951772i | \(-0.599260\pi\) | ||||
−0.306805 | + | 0.951772i | \(0.599260\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18922.8 | −1.89939 | −0.949693 | − | 0.313183i | \(-0.898605\pi\) | ||||
−0.949693 | + | 0.313183i | \(0.898605\pi\) | |||||||
\(464\) | −1214.94 | − | 2104.34i | −0.121557 | − | 0.210542i | ||||
\(465\) | −3237.87 | + | 5608.15i | −0.322909 | + | 0.559294i | ||||
\(466\) | −786.636 | + | 1362.49i | −0.0781979 | + | 0.135443i | ||||
\(467\) | −3388.35 | − | 5868.80i | −0.335748 | − | 0.581532i | 0.647880 | − | 0.761742i | \(-0.275656\pi\) |
−0.983628 | + | 0.180210i | \(0.942322\pi\) | |||||||
\(468\) | 439.963 | 0.0434558 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −150.961 | −0.0148155 | ||||||||
\(471\) | −1747.75 | − | 3027.19i | −0.170981 | − | 0.296148i | ||||
\(472\) | 7417.64 | − | 12847.7i | 0.723358 | − | 1.25289i | ||||
\(473\) | 4325.98 | − | 7492.82i | 0.420526 | − | 0.728373i | ||||
\(474\) | 1345.00 | + | 2329.60i | 0.130333 | + | 0.225743i | ||||
\(475\) | 1105.63 | 0.106800 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3618.90 | −0.347375 | ||||||||
\(478\) | 6534.86 | + | 11318.7i | 0.625308 | + | 1.08307i | ||||
\(479\) | 1198.66 | − | 2076.14i | 0.114338 | − | 0.198040i | −0.803177 | − | 0.595741i | \(-0.796859\pi\) |
0.917515 | + | 0.397701i | \(0.130192\pi\) | |||||||
\(480\) | 978.793 | − | 1695.32i | 0.0930741 | − | 0.161209i | ||||
\(481\) | 3548.04 | + | 6145.39i | 0.336334 | + | 0.582548i | ||||
\(482\) | −12.5871 | −0.00118948 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −173.977 | −0.0163390 | ||||||||
\(485\) | 2649.68 | + | 4589.38i | 0.248074 | + | 0.429677i | ||||
\(486\) | −5466.70 | + | 9468.61i | −0.510236 | + | 0.883755i | ||||
\(487\) | −2793.08 | + | 4837.76i | −0.259890 | + | 0.450143i | −0.966212 | − | 0.257747i | \(-0.917020\pi\) |
0.706322 | + | 0.707891i | \(0.250353\pi\) | |||||||
\(488\) | −3862.17 | − | 6689.48i | −0.358263 | − | 0.620530i | ||||
\(489\) | −6674.33 | −0.617227 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 537.392 | 0.0493934 | 0.0246967 | − | 0.999695i | \(-0.492138\pi\) | ||||
0.0246967 | + | 0.999695i | \(0.492138\pi\) | |||||||
\(492\) | −1483.89 | − | 2570.17i | −0.135973 | − | 0.235513i | ||||
\(493\) | 2047.23 | − | 3545.90i | 0.187023 | − | 0.323934i | ||||
\(494\) | 1106.02 | − | 1915.68i | 0.100733 | − | 0.174474i | ||||
\(495\) | −1655.83 | − | 2867.99i | −0.150352 | − | 0.260417i | ||||
\(496\) | 10071.2 | 0.911716 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −17842.0 | −1.60546 | ||||||||
\(499\) | −299.482 | − | 518.719i | −0.0268671 | − | 0.0465351i | 0.852279 | − | 0.523087i | \(-0.175220\pi\) |
−0.879146 | + | 0.476552i | \(0.841886\pi\) | |||||||
\(500\) | 82.1068 | − | 142.213i | 0.00734385 | − | 0.0127199i | ||||
\(501\) | 1196.31 | − | 2072.07i | 0.106681 | − | 0.184777i | ||||
\(502\) | −708.403 | − | 1226.99i | −0.0629832 | − | 0.109090i | ||||
\(503\) | −4426.76 | −0.392405 | −0.196202 | − | 0.980563i | \(-0.562861\pi\) | ||||
−0.196202 | + | 0.980563i | \(0.562861\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1209.17 | 0.106549 | ||||||||
\(506\) | −10790.4 | − | 18689.5i | −0.948006 | − | 1.64200i | ||||
\(507\) | −6067.20 | + | 10508.7i | −0.531467 | + | 0.920528i | ||||
\(508\) | 797.086 | − | 1380.59i | 0.0696161 | − | 0.120579i | ||||
\(509\) | 8863.84 | + | 15352.6i | 0.771872 | + | 1.33692i | 0.936536 | + | 0.350571i | \(0.114013\pi\) |
−0.164665 | + | 0.986350i | \(0.552654\pi\) | |||||||
\(510\) | −7507.14 | −0.651808 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −13017.7 | −1.12365 | ||||||||
\(513\) | −1425.83 | − | 2469.61i | −0.122713 | − | 0.212546i | ||||
\(514\) | −2294.38 | + | 3973.99i | −0.196889 | + | 0.341022i | ||||
\(515\) | −4198.94 | + | 7272.78i | −0.359277 | + | 0.622286i | ||||
\(516\) | 988.932 | + | 1712.88i | 0.0843707 | + | 0.146134i | ||||
\(517\) | −446.671 | −0.0379972 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21925.4 | 1.85437 | ||||||||
\(520\) | −1164.62 | − | 2017.17i | −0.0982149 | − | 0.170113i | ||||
\(521\) | 4331.40 | − | 7502.20i | 0.364226 | − | 0.630858i | −0.624425 | − | 0.781084i | \(-0.714667\pi\) |
0.988652 | + | 0.150226i | \(0.0480001\pi\) | |||||||
\(522\) | 1050.77 | − | 1819.98i | 0.0881050 | − | 0.152602i | ||||
\(523\) | −3885.20 | − | 6729.36i | −0.324833 | − | 0.562628i | 0.656645 | − | 0.754200i | \(-0.271975\pi\) |
−0.981479 | + | 0.191572i | \(0.938642\pi\) | |||||||
\(524\) | −2604.32 | −0.217119 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3100.60 | −0.257020 | ||||||||
\(527\) | 8485.22 | + | 14696.8i | 0.701370 | + | 1.21481i | ||||
\(528\) | −6591.09 | + | 11416.1i | −0.543259 | + | 0.940951i | ||||
\(529\) | −17714.8 | + | 30683.0i | −1.45597 | + | 2.52182i | ||||
\(530\) | 1351.20 | + | 2340.34i | 0.110740 | + | 0.191808i | ||||
\(531\) | 10665.2 | 0.871624 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6564.34 | −0.533458 | ||||||||
\(534\) | 1465.06 | + | 2537.56i | 0.118726 | + | 0.205639i | ||||
\(535\) | −3767.20 | + | 6524.99i | −0.304431 | + | 0.527289i | ||||
\(536\) | 174.720 | − | 302.624i | 0.0140798 | − | 0.0243869i | ||||
\(537\) | 9914.79 | + | 17172.9i | 0.796750 | + | 1.38001i | ||||
\(538\) | −8404.56 | −0.673506 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −423.541 | −0.0337524 | ||||||||
\(541\) | −10820.5 | − | 18741.6i | −0.859906 | − | 1.48940i | −0.872018 | − | 0.489474i | \(-0.837189\pi\) |
0.0121123 | − | 0.999927i | \(-0.496144\pi\) | |||||||
\(542\) | −1158.62 | + | 2006.78i | −0.0918208 | + | 0.159038i | ||||
\(543\) | −4867.21 | + | 8430.25i | −0.384663 | + | 0.666255i | ||||
\(544\) | −2565.04 | − | 4442.79i | −0.202161 | − | 0.350152i | ||||
\(545\) | −6262.05 | −0.492177 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7489.29 | 0.585409 | 0.292705 | − | 0.956203i | \(-0.405445\pi\) | ||||
0.292705 | + | 0.956203i | \(0.405445\pi\) | |||||||
\(548\) | 1452.27 | + | 2515.41i | 0.113208 | + | 0.196082i | ||||
\(549\) | 2776.56 | − | 4809.14i | 0.215848 | − | 0.373860i | ||||
\(550\) | −1236.49 | + | 2141.66i | −0.0958617 | + | 0.166037i | ||||
\(551\) | 1037.99 | + | 1797.86i | 0.0802542 | + | 0.139004i | ||||
\(552\) | 34976.2 | 2.69689 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −999.566 | −0.0766561 | ||||||||
\(555\) | 6105.21 | + | 10574.5i | 0.466940 | + | 0.808764i | ||||
\(556\) | −346.844 | + | 600.752i | −0.0264559 | + | 0.0458230i | ||||
\(557\) | −12648.9 | + | 21908.6i | −0.962214 | + | 1.66660i | −0.245293 | + | 0.969449i | \(0.578884\pi\) |
−0.716921 | + | 0.697154i | \(0.754449\pi\) | |||||||
\(558\) | 4355.15 | + | 7543.34i | 0.330409 | + | 0.572285i | ||||
\(559\) | 4374.77 | 0.331007 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22212.5 | −1.67168 | ||||||||
\(562\) | 4311.92 | + | 7468.47i | 0.323643 | + | 0.560566i | ||||
\(563\) | 7830.65 | − | 13563.1i | 0.586186 | − | 1.01530i | −0.408541 | − | 0.912740i | \(-0.633962\pi\) |
0.994726 | − | 0.102563i | \(-0.0327044\pi\) | |||||||
\(564\) | 51.0551 | − | 88.4300i | 0.00381172 | − | 0.00660209i | ||||
\(565\) | −3425.51 | − | 5933.16i | −0.255066 | − | 0.441787i | ||||
\(566\) | −13994.9 | −1.03931 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 22927.3 | 1.69367 | ||||||||
\(569\) | 4991.37 | + | 8645.31i | 0.367749 | + | 0.636960i | 0.989213 | − | 0.146482i | \(-0.0467952\pi\) |
−0.621464 | + | 0.783443i | \(0.713462\pi\) | |||||||
\(570\) | 1903.15 | − | 3296.36i | 0.139850 | − | 0.242227i | ||||
\(571\) | 5791.81 | − | 10031.7i | 0.424483 | − | 0.735226i | −0.571889 | − | 0.820331i | \(-0.693789\pi\) |
0.996372 | + | 0.0851049i | \(0.0271226\pi\) | |||||||
\(572\) | −486.052 | − | 841.866i | −0.0355294 | − | 0.0615388i | ||||
\(573\) | 2495.81 | 0.181961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5454.16 | 0.395573 | ||||||||
\(576\) | −4901.48 | − | 8489.62i | −0.354563 | − | 0.614122i | ||||
\(577\) | −297.689 | + | 515.613i | −0.0214783 | + | 0.0372015i | −0.876565 | − | 0.481284i | \(-0.840171\pi\) |
0.855086 | + | 0.518485i | \(0.173504\pi\) | |||||||
\(578\) | −3484.70 | + | 6035.67i | −0.250769 | + | 0.434344i | ||||
\(579\) | 2439.83 | + | 4225.91i | 0.175122 | + | 0.303321i | ||||
\(580\) | 308.335 | 0.0220740 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 18243.8 | 1.29936 | ||||||||
\(583\) | 3998.00 | + | 6924.74i | 0.284014 | + | 0.491927i | ||||
\(584\) | −9928.20 | + | 17196.1i | −0.703479 | + | 1.21846i | ||||
\(585\) | 837.254 | − | 1450.17i | 0.0591730 | − | 0.102491i | ||||
\(586\) | 364.869 | + | 631.972i | 0.0257212 | + | 0.0445504i | ||||
\(587\) | 15750.3 | 1.10747 | 0.553736 | − | 0.832693i | \(-0.313202\pi\) | ||||
0.553736 | + | 0.832693i | \(0.313202\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8604.42 | −0.601934 | ||||||||
\(590\) | −3982.11 | − | 6897.22i | −0.277866 | − | 0.481278i | ||||
\(591\) | −6967.21 | + | 12067.6i | −0.484928 | + | 0.839920i | ||||
\(592\) | 9494.98 | − | 16445.8i | 0.659191 | − | 1.14175i | ||||
\(593\) | −208.939 | − | 361.893i | −0.0144690 | − | 0.0250610i | 0.858700 | − | 0.512478i | \(-0.171272\pi\) |
−0.873169 | + | 0.487417i | \(0.837939\pi\) | |||||||
\(594\) | 6378.31 | 0.440581 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 431.385 | 0.0296480 | ||||||||
\(597\) | −9536.08 | − | 16517.0i | −0.653745 | − | 1.13232i | ||||
\(598\) | 5456.04 | − | 9450.15i | 0.373101 | − | 0.646229i | ||||
\(599\) | 9998.67 | − | 17318.2i | 0.682028 | − | 1.18131i | −0.292333 | − | 0.956316i | \(-0.594432\pi\) |
0.974361 | − | 0.224990i | \(-0.0722350\pi\) | |||||||
\(600\) | −2003.98 | − | 3471.00i | −0.136354 | − | 0.236172i | ||||
\(601\) | 15992.6 | 1.08545 | 0.542723 | − | 0.839912i | \(-0.317393\pi\) | ||||
0.542723 | + | 0.839912i | \(0.317393\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 251.216 | 0.0169657 | ||||||||
\(604\) | 676.185 | + | 1171.19i | 0.0455523 | + | 0.0788988i | ||||
\(605\) | −331.081 | + | 573.449i | −0.0222485 | + | 0.0385356i | ||||
\(606\) | 2081.36 | − | 3605.03i | 0.139521 | − | 0.241657i | ||||
\(607\) | 7079.59 | + | 12262.2i | 0.473396 | + | 0.819947i | 0.999536 | − | 0.0304515i | \(-0.00969450\pi\) |
−0.526140 | + | 0.850398i | \(0.676361\pi\) | |||||||
\(608\) | 2601.08 | 0.173499 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4146.76 | −0.275242 | ||||||||
\(611\) | −112.927 | − | 195.596i | −0.00747716 | − | 0.0129508i | ||||
\(612\) | 991.978 | − | 1718.16i | 0.0655202 | − | 0.113484i | ||||
\(613\) | 2314.70 | − | 4009.18i | 0.152512 | − | 0.264159i | −0.779638 | − | 0.626230i | \(-0.784597\pi\) |
0.932150 | + | 0.362071i | \(0.117930\pi\) | |||||||
\(614\) | 2481.93 | + | 4298.84i | 0.163131 | + | 0.282552i | ||||
\(615\) | −11295.4 | −0.740611 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23165.3 | −1.51151 | −0.755753 | − | 0.654857i | \(-0.772729\pi\) | ||||
−0.755753 | + | 0.654857i | \(0.772729\pi\) | |||||||
\(618\) | 14455.4 | + | 25037.6i | 0.940912 | + | 1.62971i | ||||
\(619\) | 6185.30 | − | 10713.3i | 0.401629 | − | 0.695641i | −0.592294 | − | 0.805722i | \(-0.701778\pi\) |
0.993923 | + | 0.110081i | \(0.0351109\pi\) | |||||||
\(620\) | −638.983 | + | 1106.75i | −0.0413906 | + | 0.0716906i | ||||
\(621\) | −7033.71 | − | 12182.7i | −0.454514 | − | 0.787241i | ||||
\(622\) | −3137.36 | −0.202245 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6665.43 | −0.427613 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −1854.01 | + | 3211.24i | −0.118373 | + | 0.205027i | ||||
\(627\) | 5631.15 | − | 9753.44i | 0.358671 | − | 0.621236i | ||||
\(628\) | −344.913 | − | 597.407i | −0.0219165 | − | 0.0379604i | ||||
\(629\) | 31998.9 | 2.02842 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13980.2 | 0.882002 | 0.441001 | − | 0.897507i | \(-0.354623\pi\) | ||||
0.441001 | + | 0.897507i | \(0.354623\pi\) | |||||||
\(632\) | 1881.81 | + | 3259.38i | 0.118440 | + | 0.205145i | ||||
\(633\) | 18784.5 | − | 32535.6i | 1.17949 | − | 2.04293i | ||||
\(634\) | −8399.86 | + | 14549.0i | −0.526185 | + | 0.911379i | ||||
\(635\) | −3033.73 | − | 5254.57i | −0.189590 | − | 0.328380i | ||||
\(636\) | −1827.91 | −0.113964 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4643.36 | −0.288139 | ||||||||
\(639\) | 8241.33 | + | 14274.4i | 0.510206 | + | 0.883703i | ||||
\(640\) | −2483.88 | + | 4302.20i | −0.153412 | + | 0.265718i | ||||
\(641\) | 8030.47 | − | 13909.2i | 0.494828 | − | 0.857067i | −0.505155 | − | 0.863029i | \(-0.668564\pi\) |
0.999982 | + | 0.00596217i | \(0.00189783\pi\) | |||||||
\(642\) | 12969.1 | + | 22463.2i | 0.797275 | + | 1.38092i | ||||
\(643\) | 4502.17 | 0.276125 | 0.138063 | − | 0.990424i | \(-0.455913\pi\) | ||||
0.138063 | + | 0.990424i | \(0.455913\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7527.79 | 0.459545 | ||||||||
\(646\) | −4987.44 | − | 8638.49i | −0.303759 | − | 0.526125i | ||||
\(647\) | 14707.4 | − | 25474.0i | 0.893675 | − | 1.54789i | 0.0582393 | − | 0.998303i | \(-0.481451\pi\) |
0.835436 | − | 0.549588i | \(-0.185215\pi\) | |||||||
\(648\) | −10797.8 | + | 18702.3i | −0.654595 | + | 1.13379i | ||||
\(649\) | −11782.5 | − | 20407.9i | −0.712640 | − | 1.23433i | ||||
\(650\) | −1250.43 | −0.0754553 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1317.16 | −0.0791164 | ||||||||
\(653\) | −6506.82 | − | 11270.1i | −0.389941 | − | 0.675398i | 0.602500 | − | 0.798119i | \(-0.294171\pi\) |
−0.992441 | + | 0.122721i | \(0.960838\pi\) | |||||||
\(654\) | −10779.0 | + | 18669.8i | −0.644483 | + | 1.11628i | ||||
\(655\) | −4956.05 | + | 8584.13i | −0.295647 | + | 0.512076i | ||||
\(656\) | 8783.46 | + | 15213.4i | 0.522769 | + | 0.905463i | ||||
\(657\) | −14275.0 | −0.847671 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23474.2 | 1.38759 | 0.693797 | − | 0.720171i | \(-0.255937\pi\) | ||||
0.693797 | + | 0.720171i | \(0.255937\pi\) | |||||||
\(660\) | −836.362 | − | 1448.62i | −0.0493263 | − | 0.0854356i | ||||
\(661\) | −4633.18 | + | 8024.91i | −0.272632 | + | 0.472213i | −0.969535 | − | 0.244953i | \(-0.921228\pi\) |
0.696903 | + | 0.717166i | \(0.254561\pi\) | |||||||
\(662\) | 12520.2 | − | 21685.7i | 0.735064 | − | 1.27317i | ||||
\(663\) | −5615.77 | − | 9726.79i | −0.328957 | − | 0.569770i | ||||
\(664\) | −24963.0 | −1.45896 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16423.8 | 0.955572 | ||||||||
\(667\) | 5120.49 | + | 8868.95i | 0.297251 | + | 0.514853i | ||||
\(668\) | 236.088 | − | 408.916i | 0.0136744 | − | 0.0236848i | ||||
\(669\) | 21199.3 | − | 36718.2i | 1.22513 | − | 2.12199i | ||||
\(670\) | −93.7973 | − | 162.462i | −0.00540851 | − | 0.00936782i | ||||
\(671\) | −12269.7 | −0.705909 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25067.2 | −1.43576 | −0.717882 | − | 0.696164i | \(-0.754888\pi\) | ||||
−0.717882 | + | 0.696164i | \(0.754888\pi\) | |||||||
\(674\) | −37.6644 | − | 65.2367i | −0.00215249 | − | 0.00372822i | ||||
\(675\) | −806.003 | + | 1396.04i | −0.0459601 | + | 0.0796052i | ||||
\(676\) | −1197.34 | + | 2073.86i | −0.0681237 | + | 0.117994i | ||||
\(677\) | −11204.8 | − | 19407.3i | −0.636093 | − | 1.10174i | −0.986283 | − | 0.165066i | \(-0.947216\pi\) |
0.350190 | − | 0.936679i | \(-0.386117\pi\) | |||||||
\(678\) | −23585.6 | −1.33599 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −10503.4 | −0.592332 | ||||||||
\(681\) | 3380.60 | + | 5855.37i | 0.190227 | + | 0.329483i | ||||
\(682\) | 9622.75 | − | 16667.1i | 0.540284 | − | 0.935800i | ||||
\(683\) | 4378.77 | − | 7584.24i | 0.245313 | − | 0.424895i | −0.716907 | − | 0.697169i | \(-0.754443\pi\) |
0.962220 | + | 0.272275i | \(0.0877759\pi\) | |||||||
\(684\) | 502.957 | + | 871.147i | 0.0281156 | + | 0.0486976i | ||||
\(685\) | 11054.7 | 0.616613 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27348.7 | 1.51880 | ||||||||
\(688\) | −5853.70 | − | 10138.9i | −0.324375 | − | 0.561834i | ||||
\(689\) | −2021.55 | + | 3501.42i | −0.111778 | + | 0.193604i | ||||
\(690\) | 9388.36 | − | 16261.1i | 0.517984 | − | 0.897174i | ||||
\(691\) | 4234.21 | + | 7333.87i | 0.233107 | + | 0.403753i | 0.958721 | − | 0.284349i | \(-0.0917774\pi\) |
−0.725614 | + | 0.688102i | \(0.758444\pi\) | |||||||
\(692\) | 4326.90 | 0.237694 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20294.8 | −1.11006 | ||||||||
\(695\) | 1320.10 | + | 2286.47i | 0.0720491 | + | 0.124793i | ||||
\(696\) | 3762.77 | − | 6517.31i | 0.204925 | − | 0.354940i | ||||
\(697\) | −14800.5 | + | 25635.2i | −0.804318 | + | 1.39312i | ||||
\(698\) | −13277.6 | − | 22997.4i | −0.720004 | − | 1.24708i | ||||
\(699\) | −4050.23 | −0.219162 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15996.9 | 0.861906 | 0.430953 | − | 0.902374i | \(-0.358177\pi\) | ||||
0.430953 | + | 0.902374i | \(0.358177\pi\) | |||||||
\(702\) | 1612.56 | + | 2793.04i | 0.0866983 | + | 0.150166i | ||||
\(703\) | −8112.11 | + | 14050.6i | −0.435212 | + | 0.753809i | ||||
\(704\) | −10829.9 | + | 18757.9i | −0.579782 | + | 1.00421i | ||||
\(705\) | −194.317 | − | 336.566i | −0.0103807 | − | 0.0179799i | ||||
\(706\) | −7240.03 | −0.385952 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5387.02 | 0.285956 | ||||||||
\(709\) | −9951.48 | − | 17236.5i | −0.527131 | − | 0.913017i | −0.999500 | − | 0.0316164i | \(-0.989935\pi\) |
0.472369 | − | 0.881401i | \(-0.343399\pi\) | |||||||
\(710\) | 6154.17 | − | 10659.3i | 0.325299 | − | 0.563434i | ||||
\(711\) | −1352.85 | + | 2343.21i | −0.0713584 | + | 0.123596i | ||||
\(712\) | 2049.79 | + | 3550.34i | 0.107892 | + | 0.186875i | ||||
\(713\) | −42446.1 | −2.22948 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3699.84 | −0.193519 | ||||||||
\(716\) | 1956.65 | + | 3389.02i | 0.102128 | + | 0.176891i | ||||
\(717\) | −16823.3 | + | 29138.9i | −0.876261 | + | 1.51773i | ||||
\(718\) | 4089.80 | − | 7083.73i | 0.212576 | − | 0.368193i | ||||
\(719\) | −5536.53 | − | 9589.56i | −0.287174 | − | 0.497399i | 0.685960 | − | 0.727639i | \(-0.259382\pi\) |
−0.973134 | + | 0.230240i | \(0.926049\pi\) | |||||||
\(720\) | −4481.18 | −0.231949 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12678.4 | −0.653520 | ||||||||
\(723\) | −16.2022 | − | 28.0630i | −0.000833424 | − | 0.00144353i | ||||
\(724\) | −960.528 | + | 1663.68i | −0.0493062 | + | 0.0854009i | ||||
\(725\) | 586.764 | − | 1016.31i | 0.0300578 | − | 0.0520616i | ||||
\(726\) | 1139.79 | + | 1974.18i | 0.0582667 | + | 0.100921i | ||||
\(727\) | −31652.7 | −1.61476 | −0.807382 | − | 0.590029i | \(-0.799116\pi\) | ||||
−0.807382 | + | 0.590029i | \(0.799116\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3935.94 | −0.199967 | ||||||||
\(730\) | 5329.88 | + | 9231.63i | 0.270230 | + | 0.468052i | ||||
\(731\) | 9863.73 | − | 17084.5i | 0.499074 | − | 0.864422i | ||||
\(732\) | 1402.44 | − | 2429.10i | 0.0708138 | − | 0.122653i | ||||
\(733\) | 8479.15 | + | 14686.3i | 0.427264 | + | 0.740043i | 0.996629 | − | 0.0820419i | \(-0.0261441\pi\) |
−0.569365 | + | 0.822085i | \(0.692811\pi\) | |||||||
\(734\) | −8230.16 | −0.413870 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12831.3 | 0.642618 | ||||||||
\(737\) | −277.532 | − | 480.700i | −0.0138712 | − | 0.0240255i | ||||
\(738\) | −7596.55 | + | 13157.6i | −0.378906 | + | 0.656285i | ||||
\(739\) | 5808.30 | − | 10060.3i | 0.289123 | − | 0.500775i | −0.684478 | − | 0.729034i | \(-0.739970\pi\) |
0.973601 | + | 0.228258i | \(0.0733031\pi\) | |||||||
\(740\) | 1204.84 | + | 2086.85i | 0.0598526 | + | 0.103668i | ||||
\(741\) | 5694.66 | 0.282319 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15928.0 | 0.786464 | 0.393232 | − | 0.919439i | \(-0.371357\pi\) | ||||
0.393232 | + | 0.919439i | \(0.371357\pi\) | |||||||
\(744\) | 15595.7 | + | 27012.5i | 0.768502 | + | 1.33108i | ||||
\(745\) | 820.929 | − | 1421.89i | 0.0403712 | − | 0.0699249i | ||||
\(746\) | 3381.10 | − | 5856.23i | 0.165939 | − | 0.287415i | ||||
\(747\) | −8973.07 | − | 15541.8i | −0.439501 | − | 0.761239i | ||||
\(748\) | −4383.57 | −0.214277 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2151.65 | −0.104756 | ||||||||
\(751\) | −12786.0 | − | 22145.9i | −0.621260 | − | 1.07605i | −0.989251 | − | 0.146225i | \(-0.953288\pi\) |
0.367991 | − | 0.929829i | \(-0.380046\pi\) | |||||||
\(752\) | −302.206 | + | 523.436i | −0.0146547 | + | 0.0253827i | ||||
\(753\) | 1823.71 | − | 3158.77i | 0.0882601 | − | 0.152871i | ||||
\(754\) | −1173.93 | − | 2033.31i | −0.0567004 | − | 0.0982080i | ||||
\(755\) | 5147.14 | 0.248111 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6202.41 | 0.297794 | 0.148897 | − | 0.988853i | \(-0.452428\pi\) | ||||
0.148897 | + | 0.988853i | \(0.452428\pi\) | |||||||
\(758\) | 869.385 | + | 1505.82i | 0.0416590 | + | 0.0721555i | ||||
\(759\) | 27778.8 | − | 48114.3i | 1.32847 | − | 2.30097i | ||||
\(760\) | 2662.73 | − | 4611.98i | 0.127089 | − | 0.220124i | ||||
\(761\) | −14599.5 | − | 25287.1i | −0.695444 | − | 1.20454i | −0.970031 | − | 0.242982i | \(-0.921874\pi\) |
0.274587 | − | 0.961562i | \(-0.411459\pi\) | |||||||
\(762\) | −20888.1 | −0.993037 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 492.539 | 0.0233239 | ||||||||
\(765\) | −3775.49 | − | 6539.34i | −0.178435 | − | 0.309059i | ||||
\(766\) | 1512.50 | − | 2619.73i | 0.0713431 | − | 0.123570i | ||||
\(767\) | 5957.69 | − | 10319.0i | 0.280469 | − | 0.485786i | ||||
\(768\) | −6525.26 | − | 11302.1i | −0.306589 | − | 0.531027i | ||||
\(769\) | −21838.2 | −1.02407 | −0.512033 | − | 0.858966i | \(-0.671108\pi\) | ||||
−0.512033 | + | 0.858966i | \(0.671108\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11813.3 | −0.551812 | ||||||||
\(772\) | 481.492 | + | 833.969i | 0.0224473 | + | 0.0388798i | ||||
\(773\) | −12772.4 | + | 22122.4i | −0.594296 | + | 1.02935i | 0.399349 | + | 0.916799i | \(0.369236\pi\) |
−0.993646 | + | 0.112553i | \(0.964097\pi\) | |||||||
\(774\) | 5062.69 | − | 8768.83i | 0.235109 | − | 0.407221i | ||||
\(775\) | 2431.98 | + | 4212.31i | 0.112722 | + | 0.195240i | ||||
\(776\) | 25525.2 | 1.18080 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2901.82 | −0.133721 | ||||||||
\(779\) | −7504.22 | − | 12997.7i | −0.345143 | − | 0.597806i | ||||
\(780\) | 422.898 | − | 732.480i | 0.0194130 | − | 0.0336243i | ||||
\(781\) | 18209.3 | − | 31539.4i | 0.834289 | − | 1.44503i | ||||
\(782\) | −24603.3 | − | 42614.2i | −1.12508 | − | 1.94870i | ||||
\(783\) | −3026.77 | −0.138146 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2625.49 | −0.119373 | ||||||||
\(786\) | 17061.9 | + | 29552.1i | 0.774272 | + | 1.34108i | ||||
\(787\) | −18611.6 | + | 32236.2i | −0.842989 | + | 1.46010i | 0.0443677 | + | 0.999015i | \(0.485873\pi\) |
−0.887356 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(788\) | −1374.96 | + | 2381.49i | −0.0621583 | + | 0.107661i | ||||
\(789\) | −3991.09 | − | 6912.78i | −0.180085 | − | 0.311916i | ||||
\(790\) | 2020.47 | 0.0909938 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −15951.1 | −0.715655 | ||||||||
\(793\) | −3102.01 | − | 5372.84i | −0.138910 | − | 0.240599i | ||||
\(794\) | −2567.59 | + | 4447.20i | −0.114761 | + | 0.198772i | ||||
\(795\) | −3478.53 | + | 6024.99i | −0.155183 | + | 0.268785i | ||||
\(796\) | −1881.91 | − | 3259.57i | −0.0837973 | − | 0.145141i | ||||
\(797\) | 40384.6 | 1.79485 | 0.897425 | − | 0.441168i | \(-0.145436\pi\) | ||||
0.897425 | + | 0.441168i | \(0.145436\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1018.46 | −0.0450945 | ||||||||
\(800\) | −735.177 | − | 1273.36i | −0.0324905 | − | 0.0562752i | ||||
\(801\) | −1473.62 | + | 2552.38i | −0.0650033 | + | 0.112589i | ||||
\(802\) | 5394.44 | − | 9343.44i | 0.237511 | − | 0.411382i | ||||
\(803\) | 15770.4 | + | 27315.1i | 0.693056 | + | 1.20041i | ||||
\(804\) | 126.889 | 0.00556598 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9731.28 | 0.425272 | ||||||||
\(807\) | −10818.4 | − | 18738.0i | −0.471901 | − | 0.817357i | ||||
\(808\) | 2912.07 | − | 5043.85i | 0.126790 | − | 0.219607i | ||||
\(809\) | 977.879 | − | 1693.74i | 0.0424974 | − | 0.0736076i | −0.843994 | − | 0.536352i | \(-0.819802\pi\) |
0.886492 | + | 0.462744i | \(0.153135\pi\) | |||||||
\(810\) | 5796.72 | + | 10040.2i | 0.251452 | + | 0.435528i | ||||
\(811\) | 34301.8 | 1.48520 | 0.742600 | − | 0.669735i | \(-0.233592\pi\) | ||||
0.742600 | + | 0.669735i | \(0.233592\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5965.49 | −0.257342 | ||||||||
\(814\) | −18144.3 | − | 31426.9i | −0.781276 | − | 1.35321i | ||||
\(815\) | −2506.56 | + | 4341.50i | −0.107731 | + | 0.186596i | ||||
\(816\) | −15028.4 | + | 26030.0i | −0.644731 | + | 1.11671i | ||||
\(817\) | 5001.15 | + | 8662.25i | 0.214159 | + | 0.370935i | ||||
\(818\) | 30255.8 | 1.29324 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2229.12 | −0.0949319 | ||||||||
\(821\) | 6832.81 | + | 11834.8i | 0.290459 | + | 0.503090i | 0.973918 | − | 0.226899i | \(-0.0728587\pi\) |
−0.683459 | + | 0.729989i | \(0.739525\pi\) | |||||||
\(822\) | 19028.8 | − | 32958.8i | 0.807426 | − | 1.39850i | ||||
\(823\) | 10759.7 | − | 18636.4i | 0.455724 | − | 0.789338i | −0.543005 | − | 0.839729i | \(-0.682714\pi\) |
0.998730 | + | 0.0503916i | \(0.0160469\pi\) | |||||||
\(824\) | 20224.8 | + | 35030.5i | 0.855056 | + | 1.48100i | ||||
\(825\) | −6366.42 | −0.268667 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35220.6 | 1.48094 | 0.740471 | − | 0.672088i | \(-0.234602\pi\) | ||||
0.740471 | + | 0.672088i | \(0.234602\pi\) | |||||||
\(828\) | 2481.12 | + | 4297.42i | 0.104136 | + | 0.180369i | ||||
\(829\) | 15682.8 | − | 27163.3i | 0.657039 | − | 1.13802i | −0.324340 | − | 0.945941i | \(-0.605142\pi\) |
0.981379 | − | 0.192084i | \(-0.0615245\pi\) | |||||||
\(830\) | −6700.60 | + | 11605.8i | −0.280218 | + | 0.485352i | ||||
\(831\) | −1286.64 | − | 2228.53i | −0.0537101 | − | 0.0930287i | ||||
\(832\) | −10952.0 | −0.456362 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 9089.24 | 0.377380 | ||||||||
\(835\) | −898.556 | − | 1556.34i | −0.0372405 | − | 0.0645024i | ||||
\(836\) | 1111.29 | − | 1924.81i | 0.0459746 | − | 0.0796303i | ||||
\(837\) | 6272.59 | − | 10864.4i | 0.259035 | − | 0.448662i | ||||
\(838\) | 3533.74 | + | 6120.62i | 0.145670 | + | 0.252307i | ||||
\(839\) | 28287.1 | 1.16398 | 0.581990 | − | 0.813196i | \(-0.302274\pi\) | ||||
0.581990 | + | 0.813196i | \(0.302274\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22185.5 | −0.909653 | ||||||||
\(842\) | −17517.9 | − | 30341.9i | −0.716992 | − | 1.24187i | ||||
\(843\) | −11100.6 | + | 19226.8i | −0.453530 | + | 0.785537i | ||||
\(844\) | 3707.05 | − | 6420.80i | 0.151187 | − | 0.261864i | ||||
\(845\) | 4557.11 | + | 7893.14i | 0.185526 | + | 0.321340i | ||||
\(846\) | −522.738 | −0.0212436 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10819.8 | 0.438152 | ||||||||
\(849\) | −18014.3 | − | 31201.7i | −0.728209 | − | 1.26129i | ||||
\(850\) | −2819.33 | + | 4883.22i | −0.113767 | + | 0.197051i | ||||
\(851\) | −40017.5 | + | 69312.3i | −1.61197 | + | 2.79201i | ||||
\(852\) | 4162.70 | + | 7210.01i | 0.167385 | + | 0.289919i | ||||
\(853\) | −9405.41 | −0.377533 | −0.188766 | − | 0.982022i | \(-0.560449\pi\) | ||||
−0.188766 | + | 0.982022i | \(0.560449\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3828.53 | 0.153138 | ||||||||
\(856\) | 18145.3 | + | 31428.6i | 0.724526 | + | 1.25492i | ||||
\(857\) | −13983.4 | + | 24220.0i | −0.557369 | + | 0.965391i | 0.440346 | + | 0.897828i | \(0.354856\pi\) |
−0.997715 | + | 0.0675629i | \(0.978478\pi\) | |||||||
\(858\) | −6368.62 | + | 11030.8i | −0.253404 | + | 0.438909i | ||||
\(859\) | 3140.55 | + | 5439.60i | 0.124743 | + | 0.216061i | 0.921632 | − | 0.388064i | \(-0.126856\pi\) |
−0.796889 | + | 0.604125i | \(0.793523\pi\) | |||||||
\(860\) | 1485.58 | 0.0589047 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16624.7 | −0.656890 | ||||||||
\(863\) | 2378.57 | + | 4119.80i | 0.0938208 | + | 0.162502i | 0.909116 | − | 0.416543i | \(-0.136759\pi\) |
−0.815295 | + | 0.579046i | \(0.803425\pi\) | |||||||
\(864\) | −1896.17 | + | 3284.27i | −0.0746634 | + | 0.129321i | ||||
\(865\) | 8234.13 | − | 14261.9i | 0.323663 | − | 0.560601i | ||||
\(866\) | 10371.6 | + | 17964.2i | 0.406977 | + | 0.704905i | ||||
\(867\) | −17942.0 | −0.702818 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5978.28 | 0.233371 | ||||||||
\(870\) | −2020.02 | − | 3498.77i | −0.0787184 | − | 0.136344i | ||||
\(871\) | 140.331 | − | 243.061i | 0.00545918 | − | 0.00945558i | ||||
\(872\) | −15081.1 | + | 26121.1i | −0.585675 | + | 1.01442i | ||||
\(873\) | 9175.17 | + | 15891.9i | 0.355707 | + | 0.616103i | ||||
\(874\) | 24949.0 | 0.965574 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7210.30 | −0.278097 | ||||||||
\(877\) | 15120.3 | + | 26189.1i | 0.582184 | + | 1.00837i | 0.995220 | + | 0.0976572i | \(0.0311349\pi\) |
−0.413036 | + | 0.910715i | \(0.635532\pi\) | |||||||
\(878\) | −7201.26 | + | 12473.0i | −0.276801 | + | 0.479433i | ||||
\(879\) | −939.320 | + | 1626.95i | −0.0360438 | + | 0.0624296i | ||||
\(880\) | 4950.61 | + | 8574.70i | 0.189642 | + | 0.328469i | ||||
\(881\) | −44875.5 | −1.71611 | −0.858056 | − | 0.513556i | \(-0.828328\pi\) | ||||
−0.858056 | + | 0.513556i | \(0.828328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4892.13 | 0.186448 | 0.0932238 | − | 0.995645i | \(-0.470283\pi\) | ||||
0.0932238 | + | 0.995645i | \(0.470283\pi\) | |||||||
\(884\) | −1108.25 | − | 1919.55i | −0.0421658 | − | 0.0730334i | ||||
\(885\) | 10251.6 | − | 17756.2i | 0.389381 | − | 0.674428i | ||||
\(886\) | 7093.08 | − | 12285.6i | 0.268958 | − | 0.465849i | ||||
\(887\) | 880.700 | + | 1525.42i | 0.0333382 | + | 0.0577435i | 0.882213 | − | 0.470850i | \(-0.156053\pi\) |
−0.848875 | + | 0.528594i | \(0.822719\pi\) | |||||||
\(888\) | 58813.4 | 2.22258 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2200.83 | 0.0828900 | ||||||||
\(891\) | 17151.7 | + | 29707.6i | 0.644896 | + | 1.11699i | ||||
\(892\) | 4183.61 | − | 7246.23i | 0.157038 | − | 0.271997i | ||||
\(893\) | 258.192 | − | 447.202i | 0.00967533 | − | 0.0167582i | ||||
\(894\) | −2826.16 | − | 4895.06i | −0.105728 | − | 0.183127i | ||||
\(895\) | 14894.1 | 0.556263 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28092.1 | 1.04567 | ||||||||
\(898\) | 9351.08 | + | 16196.5i | 0.347494 | + | 0.601877i | ||||
\(899\) | −4566.40 | + | 7909.23i | −0.169408 | + | 0.293423i | ||||
\(900\) | 284.315 | − | 492.447i | 0.0105302 | − | 0.0182388i | ||||
\(901\) | 9115.90 | + | 15789.2i | 0.337064 | + | 0.583812i | ||||
\(902\) | 33569.3 | 1.23918 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32999.0 | −1.21408 | ||||||||
\(905\) | 3655.79 | + | 6332.01i | 0.134279 | + | 0.232578i | ||||
\(906\) | 8859.88 | − | 15345.8i | 0.324890 | − | 0.562725i | ||||
\(907\) | −11844.6 | + | 20515.4i | −0.433619 | + | 0.751050i | −0.997182 | − | 0.0750229i | \(-0.976097\pi\) |
0.563563 | + | 0.826073i | \(0.309430\pi\) | |||||||
\(908\) | 667.150 | + | 1155.54i | 0.0243834 | + | 0.0422333i | ||||
\(909\) | 4187.03 | 0.152778 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13877.3 | −0.504692 | −0.252346 | − | 0.967637i | \(-0.581202\pi\) | ||||
−0.252346 | + | 0.967637i | \(0.581202\pi\) | |||||||
\(912\) | −7619.79 | − | 13197.9i | −0.276663 | − | 0.479194i | ||||
\(913\) | −19826.1 | + | 34339.8i | −0.718673 | + | 1.24478i | ||||
\(914\) | 3750.04 | − | 6495.27i | 0.135712 | − | 0.235059i | ||||
\(915\) | −5337.72 | − | 9245.20i | −0.192852 | − | 0.334029i | ||||
\(916\) | 5397.18 | 0.194681 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 14543.3 | 0.522875 | ||||||||
\(919\) | −7165.82 | − | 12411.6i | −0.257213 | − | 0.445506i | 0.708281 | − | 0.705930i | \(-0.249471\pi\) |
−0.965494 | + | 0.260425i | \(0.916137\pi\) | |||||||
\(920\) | 13135.4 | − | 22751.2i | 0.470719 | − | 0.815309i | ||||
\(921\) | −6389.50 | + | 11066.9i | −0.228601 | + | 0.395948i | ||||
\(922\) | 7852.48 | + | 13600.9i | 0.280486 | + | 0.485815i | ||||
\(923\) | 18414.7 | 0.656692 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9171.32 | 0.326001 | ||||||||
\(926\) | 24465.1 | + | 42374.8i | 0.868222 | + | 1.50380i | ||||
\(927\) | −14539.9 | + | 25183.8i | −0.515158 | + | 0.892280i | ||||
\(928\) | 1380.40 | − | 2390.92i | 0.0488296 | − | 0.0845754i | ||||
\(929\) | 8334.21 | + | 14435.3i | 0.294334 | + | 0.509802i | 0.974830 | − | 0.222950i | \(-0.0715688\pi\) |
−0.680496 | + | 0.732752i | \(0.738235\pi\) | |||||||
\(930\) | 16744.9 | 0.590415 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −799.300 | −0.0280922 | ||||||||
\(933\) | −4038.41 | − | 6994.73i | −0.141706 | − | 0.245442i | ||||
\(934\) | −8761.56 | + | 15175.5i | −0.306945 | + | 0.531645i | ||||
\(935\) | −8341.98 | + | 14448.7i | −0.291778 | + | 0.505374i | ||||
\(936\) | −4032.76 | − | 6984.95i | −0.140828 | − | 0.243921i | ||||
\(937\) | −30384.9 | −1.05937 | −0.529685 | − | 0.848194i | \(-0.677690\pi\) | ||||
−0.529685 | + | 0.848194i | \(0.677690\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9545.94 | −0.331757 | ||||||||
\(940\) | −38.3478 | − | 66.4203i | −0.00133060 | − | 0.00230467i | ||||
\(941\) | −598.176 | + | 1036.07i | −0.0207226 | + | 0.0358926i | −0.876201 | − | 0.481946i | \(-0.839930\pi\) |
0.855478 | + | 0.517839i | \(0.173263\pi\) | |||||||
\(942\) | −4519.31 | + | 7827.68i | −0.156313 | + | 0.270743i | ||||
\(943\) | −37018.8 | − | 64118.4i | −1.27836 | − | 2.21419i | ||||
\(944\) | −31886.9 | −1.09940 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22372.1 | −0.768901 | ||||||||
\(947\) | −894.206 | − | 1548.81i | −0.0306840 | − | 0.0531463i | 0.850276 | − | 0.526338i | \(-0.176435\pi\) |
−0.880960 | + | 0.473191i | \(0.843102\pi\) | |||||||
\(948\) | −683.326 | + | 1183.55i | −0.0234107 | + | 0.0405486i | ||||
\(949\) | −7974.11 | + | 13811.6i | −0.272761 | + | 0.472437i | ||||
\(950\) | −1429.47 | − | 2475.91i | −0.0488190 | − | 0.0845570i | ||||
\(951\) | −43249.2 | −1.47471 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8578.60 | 0.291593 | 0.145796 | − | 0.989315i | \(-0.453426\pi\) | ||||
0.145796 | + | 0.989315i | \(0.453426\pi\) | |||||||
\(954\) | 4678.85 | + | 8104.01i | 0.158788 | + | 0.275028i | ||||
\(955\) | 937.307 | − | 1623.46i | 0.0317597 | − | 0.0550094i | ||||
\(956\) | −3320.03 | + | 5750.46i | −0.112320 | + | 0.194543i | ||||
\(957\) | −5976.94 | − | 10352.4i | −0.201888 | − | 0.349681i | ||||
\(958\) | −6198.95 | −0.209059 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −18845.4 | −0.633577 | ||||||||
\(961\) | −4030.99 | − | 6981.89i | −0.135309 | − | 0.234362i | ||||
\(962\) | 9174.48 | − | 15890.7i | 0.307482 | − | 0.532574i | ||||
\(963\) | −13044.9 | + | 22594.3i | −0.436516 | + | 0.756067i | ||||
\(964\) | −3.19745 | − | 5.53814i | −0.000106829 | − | 0.000185033i | ||||
\(965\) | 3665.14 | 0.122264 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55459.3 | −1.84431 | −0.922156 | − | 0.386818i | \(-0.873574\pi\) | ||||
−0.922156 | + | 0.386818i | \(0.873574\pi\) | |||||||
\(968\) | 1594.70 | + | 2762.10i | 0.0529500 | + | 0.0917122i | ||||
\(969\) | 12839.7 | − | 22239.0i | 0.425665 | − | 0.737274i | ||||
\(970\) | 6851.51 | − | 11867.2i | 0.226793 | − | 0.392816i | ||||
\(971\) | 11023.6 | + | 19093.5i | 0.364331 | + | 0.631039i | 0.988669 | − | 0.150115i | \(-0.0479644\pi\) |
−0.624338 | + | 0.781155i | \(0.714631\pi\) | |||||||
\(972\) | −5554.72 | −0.183300 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 14444.6 | 0.475191 | ||||||||
\(975\) | −1609.56 | − | 2787.83i | −0.0528688 | − | 0.0915714i | ||||
\(976\) | −8301.35 | + | 14378.4i | −0.272254 | + | 0.471557i | ||||
\(977\) | −7201.14 | + | 12472.7i | −0.235809 | + | 0.408432i | −0.959507 | − | 0.281684i | \(-0.909107\pi\) |
0.723699 | + | 0.690116i | \(0.242440\pi\) | |||||||
\(978\) | 8629.20 | + | 14946.2i | 0.282138 | + | 0.488678i | ||||
\(979\) | 6511.94 | 0.212587 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21683.9 | −0.705721 | ||||||||
\(982\) | −694.790 | − | 1203.41i | −0.0225781 | − | 0.0391063i | ||||
\(983\) | 3908.55 | − | 6769.81i | 0.126819 | − | 0.219658i | −0.795623 | − | 0.605792i | \(-0.792856\pi\) |
0.922443 | + | 0.386134i | \(0.126190\pi\) | |||||||
\(984\) | −27203.1 | + | 47117.1i | −0.881304 | + | 1.52646i | ||||
\(985\) | 5233.11 | + | 9064.01i | 0.169280 | + | 0.293201i | ||||
\(986\) | −10587.4 | −0.341959 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1123.82 | 0.0361878 | ||||||||
\(989\) | 24671.0 | + | 42731.4i | 0.793217 | + | 1.37389i | ||||
\(990\) | −4281.63 | + | 7416.00i | −0.137454 | + | 0.238077i | ||||
\(991\) | −12250.8 | + | 21219.0i | −0.392693 | + | 0.680164i | −0.992804 | − | 0.119753i | \(-0.961790\pi\) |
0.600111 | + | 0.799917i | \(0.295123\pi\) | |||||||
\(992\) | 5721.39 | + | 9909.74i | 0.183119 | + | 0.317172i | ||||
\(993\) | 64464.2 | 2.06013 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14325.2 | −0.456421 | ||||||||
\(996\) | −4532.31 | − | 7850.18i | −0.144188 | − | 0.249742i | ||||
\(997\) | −25348.0 | + | 43904.0i | −0.805195 | + | 1.39464i | 0.110964 | + | 0.993824i | \(0.464606\pi\) |
−0.916159 | + | 0.400815i | \(0.868727\pi\) | |||||||
\(998\) | −774.398 | + | 1341.30i | −0.0245622 | + | 0.0425431i | ||||
\(999\) | −11827.4 | − | 20485.6i | −0.374576 | − | 0.648785i |
(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 | 245.4.e.i.116.2 | 4 | ||
7.2 | even | 3 | inner | 245.4.e.i.226.2 | 4 | ||
7.3 | odd | 6 | 35.4.a.b.1.1 | ✓ | 2 | ||
7.4 | even | 3 | 245.4.a.k.1.1 | 2 | |||
7.5 | odd | 6 | 245.4.e.h.226.2 | 4 | |||
7.6 | odd | 2 | 245.4.e.h.116.2 | 4 | |||
21.11 | odd | 6 | 2205.4.a.u.1.2 | 2 | |||
21.17 | even | 6 | 315.4.a.f.1.2 | 2 | |||
28.3 | even | 6 | 560.4.a.r.1.1 | 2 | |||
35.3 | even | 12 | 175.4.b.c.99.2 | 4 | |||
35.4 | even | 6 | 1225.4.a.m.1.2 | 2 | |||
35.17 | even | 12 | 175.4.b.c.99.3 | 4 | |||
35.24 | odd | 6 | 175.4.a.c.1.2 | 2 | |||
56.3 | even | 6 | 2240.4.a.bo.1.2 | 2 | |||
56.45 | odd | 6 | 2240.4.a.bn.1.1 | 2 | |||
105.59 | even | 6 | 1575.4.a.z.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.a.b.1.1 | ✓ | 2 | 7.3 | odd | 6 | ||
175.4.a.c.1.2 | 2 | 35.24 | odd | 6 | |||
175.4.b.c.99.2 | 4 | 35.3 | even | 12 | |||
175.4.b.c.99.3 | 4 | 35.17 | even | 12 | |||
245.4.a.k.1.1 | 2 | 7.4 | even | 3 | |||
245.4.e.h.116.2 | 4 | 7.6 | odd | 2 | |||
245.4.e.h.226.2 | 4 | 7.5 | odd | 6 | |||
245.4.e.i.116.2 | 4 | 1.1 | even | 1 | trivial | ||
245.4.e.i.226.2 | 4 | 7.2 | even | 3 | inner | ||
315.4.a.f.1.2 | 2 | 21.17 | even | 6 | |||
560.4.a.r.1.1 | 2 | 28.3 | even | 6 | |||
1225.4.a.m.1.2 | 2 | 35.4 | even | 6 | |||
1575.4.a.z.1.1 | 2 | 105.59 | even | 6 | |||
2205.4.a.u.1.2 | 2 | 21.11 | odd | 6 | |||
2240.4.a.bn.1.1 | 2 | 56.45 | odd | 6 | |||
2240.4.a.bo.1.2 | 2 | 56.3 | even | 6 |