Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,4,Mod(62,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.62");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.o (of order \(6\), 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: | \(11.1513609911\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 62.10 | ||
Character | \(\chi\) | \(=\) | 189.62 |
Dual form | 189.4.o.a.125.10 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.628557 | − | 0.362898i | −0.222229 | − | 0.128304i | 0.384753 | − | 0.923019i | \(-0.374287\pi\) |
−0.606982 | + | 0.794716i | \(0.707620\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.73661 | − | 6.47200i | −0.467076 | − | 0.809000i | ||||
\(5\) | 5.53318 | + | 9.58374i | 0.494902 | + | 0.857196i | 0.999983 | − | 0.00587635i | \(-0.00187051\pi\) |
−0.505080 | + | 0.863072i | \(0.668537\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.3114 | − | 12.8765i | 0.718750 | − | 0.695268i | ||||
\(8\) | 11.2304i | 0.496318i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 8.03191i | − | 0.253991i | ||||||
\(11\) | −0.219645 | − | 0.126812i | −0.00602049 | − | 0.00347593i | 0.496987 | − | 0.867758i | \(-0.334440\pi\) |
−0.503007 | + | 0.864282i | \(0.667773\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.3956 | + | 7.15663i | −0.264456 | + | 0.152684i | −0.626366 | − | 0.779529i | \(-0.715458\pi\) |
0.361909 | + | 0.932213i | \(0.382125\pi\) | |||||||
\(14\) | −13.0399 | + | 3.26296i | −0.248932 | + | 0.0622901i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −25.8174 | + | 44.7170i | −0.403397 | + | 0.698704i | ||||
\(17\) | 92.5854 | 1.32090 | 0.660449 | − | 0.750871i | \(-0.270366\pi\) | ||||
0.660449 | + | 0.750871i | \(0.270366\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 130.104i | − | 1.57094i | −0.618899 | − | 0.785470i | \(-0.712421\pi\) | ||
0.618899 | − | 0.785470i | \(-0.287579\pi\) | |||||||
\(20\) | 41.3506 | − | 71.6214i | 0.462314 | − | 0.800752i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0920395 | + | 0.159417i | 0.000891950 | + | 0.00154490i | ||||
\(23\) | 102.797 | − | 59.3500i | 0.931944 | − | 0.538058i | 0.0445181 | − | 0.999009i | \(-0.485825\pi\) |
0.887426 | + | 0.460951i | \(0.152491\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.26793 | − | 2.19612i | 0.0101434 | − | 0.0175689i | ||||
\(26\) | 10.3885 | 0.0783597 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −133.077 | − | 38.0370i | −0.898183 | − | 0.256726i | ||||
\(29\) | −248.320 | − | 143.368i | −1.59007 | − | 0.918025i | −0.993294 | − | 0.115615i | \(-0.963116\pi\) |
−0.596772 | − | 0.802411i | \(-0.703550\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 214.225 | − | 123.683i | 1.24116 | − | 0.716582i | 0.271827 | − | 0.962346i | \(-0.412372\pi\) |
0.969330 | + | 0.245764i | \(0.0790388\pi\) | |||||||
\(32\) | 110.262 | − | 63.6597i | 0.609117 | − | 0.351674i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −58.1952 | − | 33.5990i | −0.293541 | − | 0.169476i | ||||
\(35\) | 197.060 | + | 56.3252i | 0.951692 | + | 0.272020i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 188.615 | 0.838058 | 0.419029 | − | 0.907973i | \(-0.362371\pi\) | ||||
0.419029 | + | 0.907973i | \(0.362371\pi\) | |||||||
\(38\) | −47.2144 | + | 81.7777i | −0.201558 | + | 0.349108i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −107.629 | + | 62.1397i | −0.425442 | + | 0.245629i | ||||
\(41\) | −53.2437 | − | 92.2207i | −0.202811 | − | 0.351279i | 0.746622 | − | 0.665249i | \(-0.231674\pi\) |
−0.949433 | + | 0.313969i | \(0.898341\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21.5586 | + | 37.3406i | −0.0764572 | + | 0.132428i | −0.901719 | − | 0.432323i | \(-0.857694\pi\) |
0.825262 | + | 0.564750i | \(0.191028\pi\) | |||||||
\(44\) | 1.89539i | 0.00649410i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −86.1520 | −0.276139 | ||||||||
\(47\) | 68.8818 | − | 119.307i | 0.213776 | − | 0.370270i | −0.739118 | − | 0.673576i | \(-0.764757\pi\) |
0.952893 | + | 0.303306i | \(0.0980906\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.3890 | − | 342.811i | 0.0332041 | − | 0.999449i | ||||
\(50\) | −1.59393 | + | 0.920258i | −0.00450832 | + | 0.00260288i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 92.6354 | + | 53.4830i | 0.247043 | + | 0.142630i | ||||
\(53\) | 419.280i | 1.08665i | 0.839522 | + | 0.543325i | \(0.182835\pi\) | ||||
−0.839522 | + | 0.543325i | \(0.817165\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.80669i | − | 0.00688098i | ||||||
\(56\) | 144.609 | + | 149.493i | 0.345074 | + | 0.356729i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 104.056 | + | 180.230i | 0.235572 | + | 0.408023i | ||||
\(59\) | 217.560 | + | 376.825i | 0.480066 | + | 0.831498i | 0.999739 | − | 0.0228670i | \(-0.00727943\pi\) |
−0.519673 | + | 0.854365i | \(0.673946\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −163.504 | − | 94.3989i | −0.343189 | − | 0.198140i | 0.318493 | − | 0.947925i | \(-0.396823\pi\) |
−0.661681 | + | 0.749785i | \(0.730157\pi\) | |||||||
\(62\) | −179.537 | −0.367761 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 320.670 | 0.626310 | ||||||||
\(65\) | −137.175 | − | 79.1977i | −0.261760 | − | 0.151127i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −185.350 | − | 321.035i | −0.337971 | − | 0.585383i | 0.646080 | − | 0.763270i | \(-0.276407\pi\) |
−0.984051 | + | 0.177887i | \(0.943074\pi\) | |||||||
\(68\) | −345.956 | − | 599.213i | −0.616960 | − | 1.06861i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −103.423 | − | 106.916i | −0.176592 | − | 0.182556i | ||||
\(71\) | 26.1630i | 0.0437321i | 0.999761 | + | 0.0218661i | \(0.00696074\pi\) | ||||
−0.999761 | + | 0.0218661i | \(0.993039\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 728.545i | 1.16808i | 0.811725 | + | 0.584039i | \(0.198529\pi\) | ||||
−0.811725 | + | 0.584039i | \(0.801471\pi\) | |||||||
\(74\) | −118.555 | − | 68.4480i | −0.186240 | − | 0.107526i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −842.032 | + | 486.147i | −1.27089 | + | 0.733749i | ||||
\(77\) | −4.55669 | + | 1.14022i | −0.00674393 | + | 0.00168753i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −48.6779 | + | 84.3125i | −0.0693251 | + | 0.120075i | −0.898604 | − | 0.438760i | \(-0.855418\pi\) |
0.829279 | + | 0.558834i | \(0.188751\pi\) | |||||||
\(80\) | −571.409 | −0.798568 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 77.2880i | 0.104086i | ||||||||
\(83\) | −401.359 | + | 695.174i | −0.530781 | + | 0.919340i | 0.468573 | + | 0.883425i | \(0.344768\pi\) |
−0.999355 | + | 0.0359157i | \(0.988565\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 512.291 | + | 887.315i | 0.653715 | + | 1.13227i | ||||
\(86\) | 27.1017 | − | 15.6471i | 0.0339819 | − | 0.0196195i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.42415 | − | 2.46670i | 0.00172517 | − | 0.00298808i | ||||
\(89\) | −236.618 | −0.281814 | −0.140907 | − | 0.990023i | \(-0.545002\pi\) | ||||
−0.140907 | + | 0.990023i | \(0.545002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −72.8512 | + | 254.878i | −0.0839218 | + | 0.293610i | ||||
\(92\) | −768.227 | − | 443.536i | −0.870578 | − | 0.502628i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −86.5924 | + | 49.9941i | −0.0950141 | + | 0.0548564i | ||||
\(95\) | 1246.88 | − | 719.887i | 1.34660 | − | 0.777462i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1268.09 | + | 732.133i | 1.32737 | + | 0.766360i | 0.984893 | − | 0.173165i | \(-0.0553995\pi\) |
0.342481 | + | 0.939525i | \(0.388733\pi\) | |||||||
\(98\) | −131.564 | + | 211.343i | −0.135612 | + | 0.217846i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.9510 | −0.0189510 | ||||||||
\(101\) | −783.722 | + | 1357.45i | −0.772112 | + | 1.33734i | 0.164292 | + | 0.986412i | \(0.447466\pi\) |
−0.936404 | + | 0.350925i | \(0.885867\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −86.8588 | + | 50.1479i | −0.0830918 | + | 0.0479730i | −0.540970 | − | 0.841042i | \(-0.681943\pi\) |
0.457878 | + | 0.889015i | \(0.348609\pi\) | |||||||
\(104\) | −80.3717 | − | 139.208i | −0.0757798 | − | 0.131254i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 152.156 | − | 263.541i | 0.139421 | − | 0.241485i | ||||
\(107\) | 553.381i | 0.499976i | 0.968249 | + | 0.249988i | \(0.0804266\pi\) | ||||
−0.968249 | + | 0.249988i | \(0.919573\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −400.600 | −0.352023 | −0.176012 | − | 0.984388i | \(-0.556320\pi\) | ||||
−0.176012 | + | 0.984388i | \(0.556320\pi\) | |||||||
\(110\) | −1.01854 | + | 1.76417i | −0.000882856 | + | 0.00152915i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 232.134 | + | 927.687i | 0.195845 | + | 0.782663i | ||||
\(113\) | 617.417 | − | 356.466i | 0.513997 | − | 0.296756i | −0.220478 | − | 0.975392i | \(-0.570762\pi\) |
0.734475 | + | 0.678635i | \(0.237428\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1137.59 | + | 656.788i | 0.922442 | + | 0.532572i | ||||
\(116\) | 2142.84i | 1.71515i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 315.808i | − | 0.246377i | ||||||
\(119\) | 1232.45 | − | 1192.18i | 0.949396 | − | 0.918378i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −665.468 | − | 1152.62i | −0.499976 | − | 0.865984i | ||||
\(122\) | 68.5143 | + | 118.670i | 0.0508442 | + | 0.0880648i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1600.95 | − | 924.307i | −1.15943 | − | 0.669397i | ||||
\(125\) | 1411.36 | 1.00988 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 102.170 | 0.0713865 | 0.0356932 | − | 0.999363i | \(-0.488636\pi\) | ||||
0.0356932 | + | 0.999363i | \(0.488636\pi\) | |||||||
\(128\) | −1083.65 | − | 625.648i | −0.748300 | − | 0.432031i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 57.4814 | + | 99.5606i | 0.0387804 | + | 0.0671696i | ||||
\(131\) | −236.423 | − | 409.496i | −0.157682 | − | 0.273113i | 0.776350 | − | 0.630302i | \(-0.217069\pi\) |
−0.934032 | + | 0.357188i | \(0.883735\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1675.29 | − | 1731.87i | −1.09222 | − | 1.12911i | ||||
\(134\) | 269.052i | 0.173452i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1039.77i | 0.655585i | ||||||||
\(137\) | −2268.47 | − | 1309.70i | −1.41466 | − | 0.816756i | −0.418840 | − | 0.908060i | \(-0.637563\pi\) |
−0.995823 | + | 0.0913039i | \(0.970897\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1075.92 | − | 621.185i | 0.656537 | − | 0.379052i | −0.134419 | − | 0.990925i | \(-0.542917\pi\) |
0.790956 | + | 0.611873i | \(0.209583\pi\) | |||||||
\(140\) | −371.800 | − | 1485.84i | −0.224449 | − | 0.896973i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.49451 | − | 16.4450i | 0.00561100 | − | 0.00971853i | ||||
\(143\) | 3.63018 | 0.00212287 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3173.12i | − | 1.81733i | ||||||
\(146\) | 264.387 | − | 457.932i | 0.149869 | − | 0.259581i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −704.781 | − | 1220.72i | −0.391437 | − | 0.677989i | ||||
\(149\) | −973.891 | + | 562.276i | −0.535465 | + | 0.309151i | −0.743239 | − | 0.669026i | \(-0.766711\pi\) |
0.207774 | + | 0.978177i | \(0.433378\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 237.798 | − | 411.879i | 0.128157 | − | 0.221975i | −0.794805 | − | 0.606864i | \(-0.792427\pi\) |
0.922963 | + | 0.384889i | \(0.125760\pi\) | |||||||
\(152\) | 1461.12 | 0.779686 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.27792 | + | 0.936921i | 0.00171521 | + | 0.000490255i | ||||
\(155\) | 2370.68 | + | 1368.71i | 1.22850 | + | 0.709276i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1674.30 | − | 966.660i | 0.851108 | − | 0.491388i | −0.00991644 | − | 0.999951i | \(-0.503157\pi\) |
0.861025 | + | 0.508563i | \(0.169823\pi\) | |||||||
\(158\) | 61.1936 | − | 35.3302i | 0.0308121 | − | 0.0177893i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1220.20 | + | 704.481i | 0.602906 | + | 0.348088i | ||||
\(161\) | 604.156 | − | 2113.71i | 0.295740 | − | 1.03468i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −743.323 | −0.357187 | −0.178594 | − | 0.983923i | \(-0.557155\pi\) | ||||
−0.178594 | + | 0.983923i | \(0.557155\pi\) | |||||||
\(164\) | −397.902 | + | 689.186i | −0.189457 | + | 0.328149i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 504.554 | − | 291.304i | 0.235910 | − | 0.136202i | ||||
\(167\) | 1811.60 | + | 3137.78i | 0.839435 | + | 1.45394i | 0.890368 | + | 0.455242i | \(0.150447\pi\) |
−0.0509327 | + | 0.998702i | \(0.516219\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −996.065 | + | 1725.24i | −0.453375 | + | 0.785269i | ||||
\(170\) | − | 743.638i | − | 0.335496i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 322.225 | 0.142845 | ||||||||
\(173\) | 1648.50 | − | 2855.29i | 0.724470 | − | 1.25482i | −0.234722 | − | 0.972063i | \(-0.575418\pi\) |
0.959192 | − | 0.282756i | \(-0.0912488\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.4005 | − | 45.5601i | −0.00492453 | − | 0.0196801i | ||||
\(176\) | 11.3413 | − | 6.54791i | 0.00485729 | − | 0.00280436i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 148.728 | + | 85.8680i | 0.0626270 | + | 0.0361577i | ||||
\(179\) | − | 2746.77i | − | 1.14695i | −0.819225 | − | 0.573473i | \(-0.805596\pi\) | ||
0.819225 | − | 0.573473i | \(-0.194404\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 738.434i | − | 0.303245i | −0.988438 | − | 0.151622i | \(-0.951550\pi\) | ||
0.988438 | − | 0.151622i | \(-0.0484498\pi\) | |||||||
\(182\) | 138.286 | − | 133.768i | 0.0563210 | − | 0.0544810i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 666.524 | + | 1154.45i | 0.267048 | + | 0.462541i | ||||
\(185\) | 1043.64 | + | 1807.64i | 0.414757 | + | 0.718380i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.3359 | − | 11.7409i | −0.00795245 | − | 0.00459135i | ||||
\(188\) | −1029.54 | −0.399398 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1044.98 | −0.399005 | ||||||||
\(191\) | 2879.69 | + | 1662.59i | 1.09093 | + | 0.629848i | 0.933823 | − | 0.357734i | \(-0.116451\pi\) |
0.157105 | + | 0.987582i | \(0.449784\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1660.75 | + | 2876.50i | 0.619394 | + | 1.07282i | 0.989596 | + | 0.143871i | \(0.0459550\pi\) |
−0.370202 | + | 0.928951i | \(0.620712\pi\) | |||||||
\(194\) | −531.379 | − | 920.376i | −0.196654 | − | 0.340614i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2261.23 | + | 1207.24i | −0.824063 | + | 0.439957i | ||||
\(197\) | − | 501.482i | − | 0.181366i | −0.995880 | − | 0.0906830i | \(-0.971095\pi\) | ||
0.995880 | − | 0.0906830i | \(-0.0289050\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4067.59i | 1.44896i | 0.689294 | + | 0.724482i | \(0.257921\pi\) | ||||
−0.689294 | + | 0.724482i | \(0.742079\pi\) | |||||||
\(200\) | 24.6633 | + | 14.2393i | 0.00871978 | + | 0.00503437i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 985.229 | − | 568.822i | 0.343171 | − | 0.198130i | ||||
\(203\) | −5151.58 | + | 1289.08i | −1.78113 | + | 0.445692i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 589.213 | − | 1020.55i | 0.200744 | − | 0.347698i | ||||
\(206\) | 72.7943 | 0.0246205 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 739.062i | − | 0.246369i | ||||||
\(209\) | −16.4987 | + | 28.5766i | −0.00546048 | + | 0.00945783i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2456.95 | − | 4255.56i | −0.801628 | − | 1.38846i | −0.918544 | − | 0.395319i | \(-0.870634\pi\) |
0.116916 | − | 0.993142i | \(-0.462699\pi\) | |||||||
\(212\) | 2713.58 | − | 1566.68i | 0.879100 | − | 0.507549i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 200.821 | − | 347.832i | 0.0641487 | − | 0.111109i | ||||
\(215\) | −477.150 | −0.151355 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1259.03 | − | 4404.87i | 0.393865 | − | 1.37798i | ||||
\(218\) | 251.800 | + | 145.377i | 0.0782296 | + | 0.0451659i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −18.1649 | + | 10.4875i | −0.00556672 | + | 0.00321394i | ||||
\(221\) | −1147.66 | + | 662.599i | −0.349320 | + | 0.201680i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1033.31 | − | 596.580i | −0.310293 | − | 0.179148i | 0.336765 | − | 0.941589i | \(-0.390667\pi\) |
−0.647058 | + | 0.762441i | \(0.724001\pi\) | |||||||
\(224\) | 648.027 | − | 2267.20i | 0.193295 | − | 0.676265i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −517.443 | −0.152300 | ||||||||
\(227\) | −2804.31 | + | 4857.22i | −0.819951 | + | 1.42020i | 0.0857665 | + | 0.996315i | \(0.472666\pi\) |
−0.905718 | + | 0.423882i | \(0.860667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4618.56 | + | 2666.53i | −1.33276 | + | 0.769472i | −0.985722 | − | 0.168378i | \(-0.946147\pi\) |
−0.347042 | + | 0.937850i | \(0.612814\pi\) | |||||||
\(230\) | −476.694 | − | 825.658i | −0.136662 | − | 0.236706i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1610.08 | − | 2788.73i | 0.455632 | − | 0.789179i | ||||
\(233\) | 111.828i | 0.0314424i | 0.999876 | + | 0.0157212i | \(0.00500442\pi\) | ||||
−0.999876 | + | 0.0157212i | \(0.994996\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1524.54 | 0.423192 | ||||||||
\(236\) | 1625.87 | − | 2816.09i | 0.448455 | − | 0.776746i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1207.30 | + | 302.102i | −0.328814 | + | 0.0822789i | ||||
\(239\) | −4132.66 | + | 2385.99i | −1.11849 | + | 0.645762i | −0.941016 | − | 0.338363i | \(-0.890127\pi\) |
−0.177477 | + | 0.984125i | \(0.556794\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4621.37 | + | 2668.15i | 1.23522 | + | 0.713156i | 0.968114 | − | 0.250510i | \(-0.0805984\pi\) |
0.267109 | + | 0.963666i | \(0.413932\pi\) | |||||||
\(242\) | 965.987i | 0.256595i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1410.93i | 0.370186i | ||||||||
\(245\) | 3348.43 | − | 1787.68i | 0.873156 | − | 0.466167i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 931.104 | + | 1612.72i | 0.239857 | + | 0.415445i | ||||
\(248\) | 1389.00 | + | 2405.83i | 0.355653 | + | 0.616008i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −887.119 | − | 512.178i | −0.224425 | − | 0.129572i | ||||
\(251\) | −3081.73 | −0.774970 | −0.387485 | − | 0.921876i | \(-0.626656\pi\) | ||||
−0.387485 | + | 0.921876i | \(0.626656\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.1052 | −0.00748101 | ||||||||
\(254\) | −64.2194 | − | 37.0771i | −0.0158641 | − | 0.00915915i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −828.589 | − | 1435.16i | −0.202292 | − | 0.350381i | ||||
\(257\) | −1067.55 | − | 1849.05i | −0.259113 | − | 0.448797i | 0.706892 | − | 0.707322i | \(-0.250097\pi\) |
−0.966005 | + | 0.258525i | \(0.916764\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2510.74 | − | 2428.71i | 0.602354 | − | 0.582675i | ||||
\(260\) | 1183.72i | 0.282352i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 343.189i | 0.0809248i | ||||||||
\(263\) | 1429.14 | + | 825.115i | 0.335075 | + | 0.193455i | 0.658092 | − | 0.752938i | \(-0.271364\pi\) |
−0.323017 | + | 0.946393i | \(0.604697\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4018.27 | + | 2319.95i | −0.931473 | + | 0.537786i | ||||
\(266\) | 424.523 | + | 1696.54i | 0.0978541 | + | 0.391058i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1385.16 | + | 2399.16i | −0.315716 | + | 0.546837i | ||||
\(269\) | −5477.73 | −1.24157 | −0.620787 | − | 0.783979i | \(-0.713187\pi\) | ||||
−0.620787 | + | 0.783979i | \(0.713187\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3607.16i | 0.808558i | 0.914636 | + | 0.404279i | \(0.132477\pi\) | ||||
−0.914636 | + | 0.404279i | \(0.867523\pi\) | |||||||
\(272\) | −2390.31 | + | 4140.15i | −0.532846 | + | 0.922916i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 950.577 | + | 1646.45i | 0.209586 | + | 0.363013i | ||||
\(275\) | −0.556988 | + | 0.321577i | −0.000122137 | + | 7.05158e-5i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1488.99 | + | 2579.00i | −0.322977 | + | 0.559413i | −0.981101 | − | 0.193497i | \(-0.938017\pi\) |
0.658124 | + | 0.752910i | \(0.271350\pi\) | |||||||
\(278\) | −901.707 | −0.194535 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −632.554 | + | 2213.06i | −0.135008 | + | 0.472342i | ||||
\(281\) | 4936.36 | + | 2850.01i | 1.04797 | + | 0.605043i | 0.922079 | − | 0.387002i | \(-0.126489\pi\) |
0.125886 | + | 0.992045i | \(0.459823\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 476.719 | − | 275.234i | 0.100134 | − | 0.0578125i | −0.449097 | − | 0.893483i | \(-0.648254\pi\) |
0.549231 | + | 0.835671i | \(0.314921\pi\) | |||||||
\(284\) | 169.327 | − | 97.7611i | 0.0353793 | − | 0.0204262i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.28178 | − | 1.31739i | −0.000471763 | − | 0.000272373i | ||||
\(287\) | −1896.23 | − | 541.996i | −0.390004 | − | 0.111474i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3659.06 | 0.744771 | ||||||||
\(290\) | −1151.52 | + | 1994.49i | −0.233170 | + | 0.403863i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4715.14 | − | 2722.29i | 0.944976 | − | 0.545582i | ||||
\(293\) | −3915.00 | − | 6780.98i | −0.780603 | − | 1.35204i | −0.931591 | − | 0.363508i | \(-0.881579\pi\) |
0.150988 | − | 0.988536i | \(-0.451754\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2407.59 | + | 4170.08i | −0.475171 | + | 0.823021i | ||||
\(296\) | 2118.22i | 0.415943i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 816.195 | 0.158661 | ||||||||
\(299\) | −849.492 | + | 1471.36i | −0.164306 | + | 0.284586i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 193.842 | + | 774.658i | 0.0371192 | + | 0.148341i | ||||
\(302\) | −298.940 | + | 172.593i | −0.0569604 | + | 0.0328861i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5817.86 | + | 3358.94i | 1.09762 | + | 0.633712i | ||||
\(305\) | − | 2089.30i | − | 0.392240i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5845.06i | 1.08663i | 0.839529 | + | 0.543315i | \(0.182831\pi\) | ||||
−0.839529 | + | 0.543315i | \(0.817169\pi\) | |||||||
\(308\) | 24.4060 | + | 25.2303i | 0.00451514 | + | 0.00466764i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −993.407 | − | 1720.63i | −0.182006 | − | 0.315243i | ||||
\(311\) | 2909.85 | + | 5040.01i | 0.530554 | + | 0.918947i | 0.999364 | + | 0.0356482i | \(0.0113496\pi\) |
−0.468810 | + | 0.883299i | \(0.655317\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5754.23 | − | 3322.21i | −1.03913 | − | 0.599943i | −0.119545 | − | 0.992829i | \(-0.538143\pi\) |
−0.919587 | + | 0.392886i | \(0.871477\pi\) | |||||||
\(314\) | −1403.19 | −0.252187 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 727.561 | 0.129521 | ||||||||
\(317\) | −5206.82 | − | 3006.16i | −0.922536 | − | 0.532626i | −0.0380927 | − | 0.999274i | \(-0.512128\pi\) |
−0.884443 | + | 0.466648i | \(0.845462\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.3615 | + | 62.9800i | 0.00638198 | + | 0.0110539i | ||||
\(320\) | 1774.33 | + | 3073.22i | 0.309962 | + | 0.536870i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1146.81 | + | 1109.34i | −0.198475 | + | 0.191991i | ||||
\(323\) | − | 12045.7i | − | 2.07505i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 36.2964i | 0.00619496i | ||||||||
\(326\) | 467.221 | + | 269.750i | 0.0793772 | + | 0.0458285i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1035.68 | − | 597.947i | 0.174346 | − | 0.100659i | ||||
\(329\) | −619.344 | − | 2475.11i | −0.103786 | − | 0.414763i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1371.24 | − | 2375.06i | 0.227705 | − | 0.394397i | −0.729422 | − | 0.684064i | \(-0.760211\pi\) |
0.957128 | + | 0.289667i | \(0.0935444\pi\) | |||||||
\(332\) | 5998.89 | 0.991662 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 2629.70i | − | 0.430811i | ||||||
\(335\) | 2051.14 | − | 3552.68i | 0.334525 | − | 0.579414i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1953.27 | + | 3383.16i | 0.315731 | + | 0.546862i | 0.979593 | − | 0.200993i | \(-0.0644169\pi\) |
−0.663862 | + | 0.747856i | \(0.731084\pi\) | |||||||
\(338\) | 1252.17 | − | 722.940i | 0.201506 | − | 0.116339i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3828.47 | − | 6631.10i | 0.610670 | − | 1.05771i | ||||
\(341\) | −62.7377 | −0.00996316 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4262.62 | − | 4709.96i | −0.671019 | − | 0.741440i | ||||
\(344\) | −419.350 | − | 242.112i | −0.0657262 | − | 0.0379471i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2072.36 | + | 1196.48i | −0.321996 | + | 0.185904i | ||||
\(347\) | 509.871 | − | 294.374i | 0.0788799 | − | 0.0455413i | −0.460041 | − | 0.887898i | \(-0.652165\pi\) |
0.538921 | + | 0.842356i | \(0.318832\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6360.33 | − | 3672.14i | −0.975532 | − | 0.563224i | −0.0746138 | − | 0.997213i | \(-0.523772\pi\) |
−0.900918 | + | 0.433989i | \(0.857106\pi\) | |||||||
\(350\) | −9.36780 | + | 32.7743i | −0.00143066 | + | 0.00500532i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −32.2913 | −0.00488957 | ||||||||
\(353\) | 4370.77 | − | 7570.40i | 0.659016 | − | 1.14145i | −0.321855 | − | 0.946789i | \(-0.604306\pi\) |
0.980871 | − | 0.194660i | \(-0.0623604\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −250.740 | + | 144.765i | −0.0374870 | + | 0.0216431i | ||||
\(356\) | 884.148 | + | 1531.39i | 0.131628 | + | 0.227987i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −996.797 | + | 1726.50i | −0.147157 | + | 0.254884i | ||||
\(359\) | 7817.81i | 1.14933i | 0.818390 | + | 0.574663i | \(0.194867\pi\) | ||||
−0.818390 | + | 0.574663i | \(0.805133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10068.0 | −1.46785 | ||||||||
\(362\) | −267.976 | + | 464.148i | −0.0389075 | + | 0.0673897i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1921.79 | − | 480.887i | 0.276728 | − | 0.0692454i | ||||
\(365\) | −6982.19 | + | 4031.17i | −1.00127 | + | 0.578085i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2084.12 | − | 1203.27i | −0.296431 | − | 0.171145i | 0.344407 | − | 0.938820i | \(-0.388080\pi\) |
−0.640839 | + | 0.767676i | \(0.721413\pi\) | |||||||
\(368\) | 6129.05i | 0.868204i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 1514.94i | − | 0.212859i | ||||||
\(371\) | 5398.87 | + | 5581.22i | 0.755514 | + | 0.781031i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2185.08 | − | 3784.67i | −0.303322 | − | 0.525370i | 0.673564 | − | 0.739129i | \(-0.264763\pi\) |
−0.976886 | + | 0.213759i | \(0.931429\pi\) | |||||||
\(374\) | 8.52152 | + | 14.7597i | 0.00117817 | + | 0.00204066i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1339.86 | + | 773.570i | 0.183772 | + | 0.106101i | ||||
\(377\) | 4104.12 | 0.560671 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11260.9 | 1.52620 | 0.763102 | − | 0.646278i | \(-0.223675\pi\) | ||||
0.763102 | + | 0.646278i | \(0.223675\pi\) | |||||||
\(380\) | −9318.22 | − | 5379.88i | −1.25793 | − | 0.726268i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1206.70 | − | 2090.07i | −0.161624 | − | 0.279940i | ||||
\(383\) | −1486.57 | − | 2574.82i | −0.198330 | − | 0.343517i | 0.749657 | − | 0.661826i | \(-0.230218\pi\) |
−0.947987 | + | 0.318309i | \(0.896885\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −36.1405 | − | 37.3611i | −0.00478413 | − | 0.00494571i | ||||
\(386\) | − | 2410.72i | − | 0.317882i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 10942.8i | − | 1.43179i | ||||||
\(389\) | 5714.27 | + | 3299.13i | 0.744794 | + | 0.430007i | 0.823810 | − | 0.566866i | \(-0.191844\pi\) |
−0.0790159 | + | 0.996873i | \(0.525178\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9517.53 | − | 5494.95i | 1.23100 | − | 0.710720i | ||||
\(392\) | 3849.90 | + | 127.903i | 0.496044 | + | 0.0164798i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −181.987 | + | 315.210i | −0.0232699 | + | 0.0403047i | ||||
\(395\) | −1077.37 | −0.137237 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5908.48i | 0.746947i | 0.927641 | + | 0.373474i | \(0.121833\pi\) | ||||
−0.927641 | + | 0.373474i | \(0.878167\pi\) | |||||||
\(398\) | 1476.12 | − | 2556.71i | 0.185907 | − | 0.322001i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 65.4693 | + | 113.396i | 0.00818366 | + | 0.0141745i | ||||
\(401\) | 4847.53 | − | 2798.72i | 0.603676 | − | 0.348532i | −0.166811 | − | 0.985989i | \(-0.553347\pi\) |
0.770486 | + | 0.637457i | \(0.220014\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1770.30 | + | 3066.25i | −0.218821 | + | 0.379009i | ||||
\(404\) | 11713.9 | 1.44254 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3705.87 | + | 1059.24i | 0.453003 | + | 0.129481i | ||||
\(407\) | −41.4283 | − | 23.9187i | −0.00504552 | − | 0.00291303i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −948.568 | + | 547.656i | −0.114679 | + | 0.0662099i | −0.556242 | − | 0.831020i | \(-0.687757\pi\) |
0.441563 | + | 0.897230i | \(0.354424\pi\) | |||||||
\(410\) | −740.708 | + | 427.648i | −0.0892219 | + | 0.0515123i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 649.115 | + | 374.767i | 0.0776204 | + | 0.0448141i | ||||
\(413\) | 7748.24 | + | 2214.66i | 0.923162 | + | 0.263865i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8883.16 | −1.05074 | ||||||||
\(416\) | −911.178 | + | 1578.21i | −0.107390 | + | 0.186005i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 20.7408 | − | 11.9747i | 0.00242695 | − | 0.00140120i | ||||
\(419\) | 6796.78 | + | 11772.4i | 0.792468 | + | 1.37260i | 0.924434 | + | 0.381341i | \(0.124538\pi\) |
−0.131966 | + | 0.991254i | \(0.542129\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2842.13 | − | 4922.72i | 0.329019 | − | 0.569878i | −0.653298 | − | 0.757101i | \(-0.726615\pi\) |
0.982318 | + | 0.187222i | \(0.0599485\pi\) | |||||||
\(422\) | 3566.49i | 0.411407i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4708.68 | −0.539324 | ||||||||
\(425\) | 117.392 | − | 203.329i | 0.0133984 | − | 0.0232068i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3392.00 | + | 848.778i | −0.384427 | + | 0.0961949i | ||||
\(428\) | 3581.48 | − | 2067.77i | 0.404480 | − | 0.233527i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 299.916 | + | 173.157i | 0.0336355 | + | 0.0194194i | ||||
\(431\) | − | 4806.22i | − | 0.537140i | −0.963260 | − | 0.268570i | \(-0.913449\pi\) | ||
0.963260 | − | 0.268570i | \(-0.0865511\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9621.49i | − | 1.06785i | −0.845532 | − | 0.533925i | \(-0.820716\pi\) | ||
0.845532 | − | 0.533925i | \(-0.179284\pi\) | |||||||
\(434\) | −2389.89 | + | 2311.81i | −0.264328 | + | 0.255692i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1496.89 | + | 2592.68i | 0.164422 | + | 0.284787i | ||||
\(437\) | −7721.67 | − | 13374.3i | −0.845257 | − | 1.46403i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11200.0 | + | 6466.31i | 1.21764 | + | 0.703007i | 0.964413 | − | 0.264399i | \(-0.0851737\pi\) |
0.253230 | + | 0.967406i | \(0.418507\pi\) | |||||||
\(440\) | 31.5202 | 0.00341516 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 961.823 | 0.103505 | ||||||||
\(443\) | −11401.0 | − | 6582.35i | −1.22275 | − | 0.705953i | −0.257244 | − | 0.966347i | \(-0.582814\pi\) |
−0.965502 | + | 0.260394i | \(0.916148\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1309.25 | − | 2267.68i | −0.139470 | − | 0.241569i | ||||
\(446\) | 432.995 | + | 749.969i | 0.0459706 | + | 0.0796235i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4268.59 | − | 4129.13i | 0.450160 | − | 0.435453i | ||||
\(449\) | − | 7787.86i | − | 0.818557i | −0.912410 | − | 0.409278i | \(-0.865781\pi\) | ||
0.912410 | − | 0.409278i | \(-0.134219\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.0077i | 0.00281983i | ||||||||
\(452\) | −4614.09 | − | 2663.95i | −0.480152 | − | 0.277216i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3525.34 | − | 2035.36i | 0.364433 | − | 0.210406i | ||||
\(455\) | −2845.78 | + | 712.098i | −0.293214 | + | 0.0733707i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2408.56 | + | 4171.76i | −0.246538 | + | 0.427017i | −0.962563 | − | 0.271058i | \(-0.912626\pi\) |
0.716025 | + | 0.698075i | \(0.245960\pi\) | |||||||
\(458\) | 3870.71 | 0.394904 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 9816.65i | − | 0.995008i | ||||||
\(461\) | 25.6446 | − | 44.4177i | 0.00259086 | − | 0.00448750i | −0.864727 | − | 0.502242i | \(-0.832509\pi\) |
0.867318 | + | 0.497755i | \(0.165842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4787.43 | + | 8292.07i | 0.480542 | + | 0.832322i | 0.999751 | − | 0.0223247i | \(-0.00710677\pi\) |
−0.519209 | + | 0.854647i | \(0.673773\pi\) | |||||||
\(464\) | 12822.0 | − | 7402.77i | 1.28286 | − | 0.740657i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 40.5820 | − | 70.2901i | 0.00403418 | − | 0.00698740i | ||||
\(467\) | −12806.5 | −1.26898 | −0.634492 | − | 0.772929i | \(-0.718791\pi\) | ||||
−0.634492 | + | 0.772929i | \(0.718791\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6601.09 | − | 1886.77i | −0.649915 | − | 0.185764i | ||||
\(470\) | −958.262 | − | 553.253i | −0.0940453 | − | 0.0542971i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4231.89 | + | 2443.28i | −0.412688 | + | 0.238265i | ||||
\(473\) | 9.47047 | − | 5.46778i | 0.000920619 | − | 0.000531520i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −285.723 | − | 164.962i | −0.0275998 | − | 0.0159347i | ||||
\(476\) | −12321.0 | − | 3521.67i | −1.18641 | − | 0.339108i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3463.49 | 0.331415 | ||||||||
\(479\) | 2542.79 | − | 4404.24i | 0.242553 | − | 0.420114i | −0.718888 | − | 0.695126i | \(-0.755348\pi\) |
0.961441 | + | 0.275012i | \(0.0886818\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2338.01 | + | 1349.85i | −0.221630 | + | 0.127958i | ||||
\(482\) | −1936.53 | − | 3354.17i | −0.183001 | − | 0.316967i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4973.19 | + | 8613.81i | −0.467054 | + | 0.808961i | ||||
\(485\) | 16204.1i | 1.51709i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16991.3 | 1.58100 | 0.790501 | − | 0.612461i | \(-0.209820\pi\) | ||||
0.790501 | + | 0.612461i | \(0.209820\pi\) | |||||||
\(488\) | 1060.14 | − | 1836.21i | 0.0983405 | − | 0.170331i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2753.43 | − | 91.4755i | −0.253851 | − | 0.00843355i | ||||
\(491\) | −8055.59 | + | 4650.90i | −0.740415 | + | 0.427479i | −0.822220 | − | 0.569170i | \(-0.807265\pi\) |
0.0818052 | + | 0.996648i | \(0.473931\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22990.8 | − | 13273.8i | −2.10032 | − | 1.21262i | ||||
\(494\) | − | 1351.58i | − | 0.123098i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12772.6i | 1.15627i | ||||||||
\(497\) | 336.890 | + | 348.268i | 0.0304056 | + | 0.0314325i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 250.332 | + | 433.588i | 0.0224577 | + | 0.0388979i | 0.877036 | − | 0.480425i | \(-0.159518\pi\) |
−0.854578 | + | 0.519323i | \(0.826184\pi\) | |||||||
\(500\) | −5273.69 | − | 9134.30i | −0.471693 | − | 0.816997i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1937.05 | + | 1118.35i | 0.172220 | + | 0.0994315i | ||||
\(503\) | 3581.09 | 0.317441 | 0.158721 | − | 0.987324i | \(-0.449263\pi\) | ||||
0.158721 | + | 0.987324i | \(0.449263\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17345.9 | −1.52848 | ||||||||
\(506\) | 18.9228 | + | 10.9251i | 0.00166249 | + | 0.000959842i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −381.768 | − | 661.241i | −0.0333429 | − | 0.0577516i | ||||
\(509\) | 5085.37 | + | 8808.13i | 0.442839 | + | 0.767020i | 0.997899 | − | 0.0647904i | \(-0.0206379\pi\) |
−0.555060 | + | 0.831811i | \(0.687305\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9381.15 | + | 9697.99i | 0.812128 | + | 0.839557i | ||||
\(512\) | 11213.1i | 0.967882i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1549.65i | 0.132981i | ||||||||
\(515\) | −961.210 | − | 554.955i | −0.0822446 | − | 0.0474839i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.2591 | + | 17.4701i | −0.00257407 | + | 0.00148614i | ||||
\(518\) | −2459.52 | + | 615.443i | −0.208620 | + | 0.0522027i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 889.422 | − | 1540.52i | 0.0750072 | − | 0.129916i | ||||
\(521\) | 389.899 | 0.0327865 | 0.0163933 | − | 0.999866i | \(-0.494782\pi\) | ||||
0.0163933 | + | 0.999866i | \(0.494782\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14306.4i | 1.19613i | 0.801448 | + | 0.598065i | \(0.204063\pi\) | ||||
−0.801448 | + | 0.598065i | \(0.795937\pi\) | |||||||
\(524\) | −1766.84 | + | 3060.25i | −0.147299 | + | 0.255130i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −598.865 | − | 1037.26i | −0.0496421 | − | 0.0859827i | ||||
\(527\) | 19834.1 | − | 11451.2i | 1.63944 | − | 0.946532i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 961.351 | − | 1665.11i | 0.0790130 | − | 0.136854i | ||||
\(530\) | 3367.62 | 0.276000 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4948.76 | + | 17313.8i | −0.403301 | + | 1.41099i | ||||
\(533\) | 1319.98 | + | 762.090i | 0.107269 | + | 0.0619320i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5303.46 | + | 3061.96i | −0.428577 | + | 0.247439i | ||||
\(536\) | 3605.35 | − | 2081.55i | 0.290536 | − | 0.167741i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3443.07 | + | 1987.86i | 0.275913 | + | 0.159299i | ||||
\(539\) | −45.9740 | + | 73.8523i | −0.00367392 | + | 0.00590175i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21775.6 | 1.73051 | 0.865257 | − | 0.501328i | \(-0.167155\pi\) | ||||
0.865257 | + | 0.501328i | \(0.167155\pi\) | |||||||
\(542\) | 1309.03 | − | 2267.30i | 0.103741 | − | 0.179685i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10208.6 | − | 5893.96i | 0.804581 | − | 0.464525i | ||||
\(545\) | −2216.59 | − | 3839.25i | −0.174217 | − | 0.301753i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8960.85 | − | 15520.7i | 0.700436 | − | 1.21319i | −0.267878 | − | 0.963453i | \(-0.586322\pi\) |
0.968314 | − | 0.249738i | \(-0.0803444\pi\) | |||||||
\(548\) | 19575.4i | 1.52595i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.466799 | 3.61897e−5 | ||||||||
\(551\) | −18652.7 | + | 32307.4i | −1.44216 | + | 2.49790i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 437.682 | + | 1749.12i | 0.0336566 | + | 0.134503i | ||||
\(554\) | 1871.83 | − | 1080.70i | 0.143550 | − | 0.0828783i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8040.62 | − | 4642.25i | −0.613306 | − | 0.354092i | ||||
\(557\) | 19309.8i | 1.46891i | 0.678657 | + | 0.734455i | \(0.262562\pi\) | ||||
−0.678657 | + | 0.734455i | \(0.737438\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 617.148i | − | 0.0466951i | ||||||
\(560\) | −7606.28 | + | 7357.77i | −0.573971 | + | 0.555219i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2068.52 | − | 3582.78i | −0.155259 | − | 0.268916i | ||||
\(563\) | −3232.24 | − | 5598.41i | −0.241959 | − | 0.419085i | 0.719313 | − | 0.694686i | \(-0.244457\pi\) |
−0.961272 | + | 0.275601i | \(0.911123\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6832.55 | + | 3944.78i | 0.508757 | + | 0.293731i | ||||
\(566\) | −399.527 | −0.0296702 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −293.821 | −0.0217050 | ||||||||
\(569\) | −17286.9 | − | 9980.61i | −1.27365 | − | 0.735341i | −0.297975 | − | 0.954574i | \(-0.596311\pi\) |
−0.975673 | + | 0.219233i | \(0.929645\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6257.56 | + | 10838.4i | 0.458617 | + | 0.794349i | 0.998888 | − | 0.0471426i | \(-0.0150115\pi\) |
−0.540271 | + | 0.841491i | \(0.681678\pi\) | |||||||
\(572\) | −13.5646 | − | 23.4945i | −0.000991545 | − | 0.00171741i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 995.203 | + | 1028.82i | 0.0723675 | + | 0.0748117i | ||||
\(575\) | − | 301.007i | − | 0.0218310i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 547.118i | − | 0.0394746i | −0.999805 | − | 0.0197373i | \(-0.993717\pi\) | ||
0.999805 | − | 0.0197373i | \(-0.00628298\pi\) | |||||||
\(578\) | −2299.93 | − | 1327.87i | −0.165509 | − | 0.0955569i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20536.4 | + | 11856.7i | −1.47022 | + | 0.848832i | ||||
\(581\) | 3608.77 | + | 14421.9i | 0.257689 | + | 1.02981i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 53.1697 | − | 92.0926i | 0.00377712 | − | 0.00654217i | ||||
\(584\) | −8181.85 | −0.579739 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5682.98i | 0.400617i | ||||||||
\(587\) | −902.414 | + | 1563.03i | −0.0634525 | + | 0.109903i | −0.896006 | − | 0.444041i | \(-0.853544\pi\) |
0.832554 | + | 0.553944i | \(0.186878\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16091.6 | − | 27871.4i | −1.12571 | − | 1.94978i | ||||
\(590\) | 3026.62 | − | 1747.42i | 0.211193 | − | 0.121933i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4869.55 | + | 8434.31i | −0.338070 | + | 0.585554i | ||||
\(593\) | −20359.7 | −1.40990 | −0.704951 | − | 0.709256i | \(-0.749031\pi\) | ||||
−0.704951 | + | 0.709256i | \(0.749031\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18244.9 | + | 5214.89i | 1.25709 | + | 0.359311i | ||||
\(596\) | 7278.10 | + | 4202.01i | 0.500206 | + | 0.288794i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1067.91 | − | 616.557i | 0.0730268 | − | 0.0421620i | ||||
\(599\) | 3739.33 | − | 2158.90i | 0.255067 | − | 0.147263i | −0.367015 | − | 0.930215i | \(-0.619620\pi\) |
0.622082 | + | 0.782952i | \(0.286287\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6928.17 | + | 3999.98i | 0.470227 | + | 0.271485i | 0.716335 | − | 0.697757i | \(-0.245818\pi\) |
−0.246108 | + | 0.969242i | \(0.579152\pi\) | |||||||
\(602\) | 159.281 | − | 557.262i | 0.0107837 | − | 0.0377281i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3554.24 | −0.239437 | ||||||||
\(605\) | 7364.30 | − | 12755.3i | 0.494878 | − | 0.857154i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3079.67 | + | 1778.05i | −0.205931 | + | 0.118894i | −0.599419 | − | 0.800435i | \(-0.704602\pi\) |
0.393488 | + | 0.919330i | \(0.371268\pi\) | |||||||
\(608\) | −8282.37 | − | 14345.5i | −0.552458 | − | 0.956886i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −758.204 | + | 1313.25i | −0.0503258 | + | 0.0871669i | ||||
\(611\) | 1971.85i | 0.130560i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7113.75 | −0.468714 | −0.234357 | − | 0.972151i | \(-0.575298\pi\) | ||||
−0.234357 | + | 0.972151i | \(0.575298\pi\) | |||||||
\(614\) | 2121.16 | − | 3673.96i | 0.139419 | − | 0.241480i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.8051 | − | 51.1734i | −0.000837551 | − | 0.00334714i | ||||
\(617\) | −790.942 | + | 456.650i | −0.0516080 | + | 0.0297959i | −0.525582 | − | 0.850743i | \(-0.676152\pi\) |
0.473974 | + | 0.880539i | \(0.342819\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −819.836 | − | 473.333i | −0.0532342 | − | 0.0307348i | 0.473147 | − | 0.880984i | \(-0.343118\pi\) |
−0.526381 | + | 0.850249i | \(0.676451\pi\) | |||||||
\(620\) | − | 20457.4i | − | 1.32514i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 4223.91i | − | 0.272288i | ||||||
\(623\) | −3149.72 | + | 3046.82i | −0.202554 | + | 0.195936i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7650.79 | + | 13251.6i | 0.489651 | + | 0.848100i | ||||
\(626\) | 2411.24 | + | 4176.39i | 0.153950 | + | 0.266649i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12512.4 | − | 7224.06i | −0.795065 | − | 0.459031i | ||||
\(629\) | 17463.0 | 1.10699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3209.46 | 0.202482 | 0.101241 | − | 0.994862i | \(-0.467719\pi\) | ||||
0.101241 | + | 0.994862i | \(0.467719\pi\) | |||||||
\(632\) | −946.863 | − | 546.671i | −0.0595952 | − | 0.0344073i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2181.85 | + | 3779.08i | 0.136676 | + | 0.236730i | ||||
\(635\) | 565.322 | + | 979.167i | 0.0353293 | + | 0.0611922i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2312.20 | + | 4330.87i | 0.143819 | + | 0.269380i | ||||
\(638\) | − | 52.7820i | − | 0.00327533i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 13847.3i | − | 0.855253i | ||||||
\(641\) | −12387.1 | − | 7151.71i | −0.763279 | − | 0.440679i | 0.0671928 | − | 0.997740i | \(-0.478596\pi\) |
−0.830472 | + | 0.557061i | \(0.811929\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −844.276 | + | 487.443i | −0.0517807 | + | 0.0298956i | −0.525667 | − | 0.850691i | \(-0.676184\pi\) |
0.473886 | + | 0.880586i | \(0.342851\pi\) | |||||||
\(644\) | −15937.4 | + | 3988.01i | −0.975190 | + | 0.244021i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4371.36 | + | 7571.43i | −0.266237 | + | 0.461136i | ||||
\(647\) | 12668.5 | 0.769783 | 0.384891 | − | 0.922962i | \(-0.374239\pi\) | ||||
0.384891 | + | 0.922962i | \(0.374239\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 110.357i | − | 0.00667470i | ||||||
\(650\) | 13.1719 | − | 22.8144i | 0.000794836 | − | 0.00137670i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2777.51 | + | 4810.78i | 0.166834 | + | 0.288964i | ||||
\(653\) | 13746.7 | − | 7936.65i | 0.823812 | − | 0.475628i | −0.0279172 | − | 0.999610i | \(-0.508887\pi\) |
0.851729 | + | 0.523982i | \(0.175554\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2616.34 | − | 4531.63i | 0.156074 | − | 0.270329i | ||||
\(656\) | 5498.45 | 0.327254 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −508.918 | + | 1780.50i | −0.0301515 | + | 0.105488i | ||||
\(659\) | 26410.9 | + | 15248.4i | 1.56119 | + | 0.901353i | 0.997137 | + | 0.0756145i | \(0.0240918\pi\) |
0.564053 | + | 0.825739i | \(0.309241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14464.7 | − | 8351.23i | 0.851155 | − | 0.491415i | −0.00988528 | − | 0.999951i | \(-0.503147\pi\) |
0.861040 | + | 0.508536i | \(0.169813\pi\) | |||||||
\(662\) | −1723.81 | + | 995.243i | −0.101205 | + | 0.0584308i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7807.08 | − | 4507.42i | −0.456285 | − | 0.263436i | ||||
\(665\) | 7328.13 | − | 25638.3i | 0.427327 | − | 1.49505i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34035.5 | −1.97580 | ||||||||
\(668\) | 13538.5 | − | 23449.3i | 0.784160 | − | 1.35821i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2578.52 | + | 1488.71i | −0.148682 | + | 0.0858416i | ||||
\(671\) | 23.9418 | + | 41.4685i | 0.00137744 | + | 0.00238580i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12445.2 | + | 21555.7i | −0.712820 | + | 1.23464i | 0.250975 | + | 0.967994i | \(0.419249\pi\) |
−0.963794 | + | 0.266646i | \(0.914084\pi\) | |||||||
\(674\) | − | 2835.35i | − | 0.162038i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14887.6 | 0.847043 | ||||||||
\(677\) | 756.276 | − | 1309.91i | 0.0429336 | − | 0.0743632i | −0.843760 | − | 0.536721i | \(-0.819663\pi\) |
0.886694 | + | 0.462357i | \(0.152996\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26307.5 | − | 6582.90i | 1.48688 | − | 0.372060i | ||||
\(680\) | −9964.90 | + | 5753.23i | −0.561965 | + | 0.324451i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 39.4342 | + | 22.7674i | 0.00221410 | + | 0.00127831i | ||||
\(683\) | − | 2180.44i | − | 0.122156i | −0.998133 | − | 0.0610778i | \(-0.980546\pi\) | ||
0.998133 | − | 0.0610778i | \(-0.0194538\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 28987.3i | − | 1.61686i | ||||||
\(686\) | 970.066 | + | 4507.37i | 0.0539902 | + | 0.250863i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1113.17 | − | 1928.08i | −0.0616852 | − | 0.106842i | ||||
\(689\) | −3000.63 | − | 5197.24i | −0.165914 | − | 0.287372i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24166.2 | + | 13952.4i | 1.33043 | + | 0.768124i | 0.985365 | − | 0.170455i | \(-0.0545237\pi\) |
0.345064 | + | 0.938579i | \(0.387857\pi\) | |||||||
\(692\) | −24639.2 | −1.35353 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −427.311 | −0.0233725 | ||||||||
\(695\) | 11906.6 | + | 6874.25i | 0.649844 | + | 0.375187i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4929.59 | − | 8538.30i | −0.267893 | − | 0.464004i | ||||
\(698\) | 2665.22 | + | 4616.30i | 0.144527 | + | 0.250329i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −252.266 | + | 244.024i | −0.0136211 | + | 0.0131761i | ||||
\(701\) | − | 15696.6i | − | 0.845722i | −0.906195 | − | 0.422861i | \(-0.861026\pi\) | ||
0.906195 | − | 0.422861i | \(-0.138974\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 24539.6i | − | 1.31654i | ||||||
\(704\) | −70.4336 | − | 40.6648i | −0.00377069 | − | 0.00217701i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5494.56 | + | 3172.29i | −0.292904 | + | 0.169108i | ||||
\(707\) | 7046.76 | + | 28161.2i | 0.374852 | + | 1.49804i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9253.46 | − | 16027.5i | 0.490157 | − | 0.848976i | −0.509779 | − | 0.860305i | \(-0.670273\pi\) |
0.999936 | + | 0.0113291i | \(0.00360624\pi\) | |||||||
\(710\) | 210.139 | 0.0111076 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 2657.31i | − | 0.139869i | ||||||
\(713\) | 14681.1 | − | 25428.5i | 0.771126 | − | 1.33563i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.0864 | + | 34.7907i | 0.00105062 | + | 0.00181972i | ||||
\(716\) | −17777.1 | + | 10263.6i | −0.927879 | + | 0.535711i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2837.06 | − | 4913.94i | 0.147463 | − | 0.255413i | ||||
\(719\) | 12998.8 | 0.674232 | 0.337116 | − | 0.941463i | \(-0.390549\pi\) | ||||
0.337116 | + | 0.941463i | \(0.390549\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −510.483 | + | 1785.98i | −0.0263681 | + | 0.0922517i | ||||
\(722\) | 6328.32 | + | 3653.66i | 0.326199 | + | 0.188331i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4779.14 | + | 2759.24i | −0.245325 | + | 0.141639i | ||||
\(725\) | −629.705 | + | 363.561i | −0.0322575 | + | 0.0186239i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1646.14 | − | 950.399i | −0.0839779 | − | 0.0484846i | 0.457423 | − | 0.889249i | \(-0.348773\pi\) |
−0.541401 | + | 0.840765i | \(0.682106\pi\) | |||||||
\(728\) | −2862.38 | − | 818.148i | −0.145724 | − | 0.0416519i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5851.61 | 0.296682 | ||||||||
\(731\) | −1996.01 | + | 3457.20i | −0.100992 | + | 0.174923i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4804.26 | + | 2773.74i | −0.242087 | + | 0.139769i | −0.616135 | − | 0.787640i | \(-0.711303\pi\) |
0.374049 | + | 0.927409i | \(0.377969\pi\) | |||||||
\(734\) | 873.327 | + | 1512.65i | 0.0439170 | + | 0.0760665i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7556.41 | − | 13088.1i | 0.378442 | − | 0.655480i | ||||
\(737\) | 94.0181i | 0.00469905i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15681.5 | −0.780586 | −0.390293 | − | 0.920691i | \(-0.627626\pi\) | ||||
−0.390293 | + | 0.920691i | \(0.627626\pi\) | |||||||
\(740\) | 7799.36 | − | 13508.9i | 0.387446 | − | 0.671076i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1368.09 | − | 5467.35i | −0.0676876 | − | 0.270503i | ||||
\(743\) | −15659.4 | + | 9040.97i | −0.773201 | + | 0.446408i | −0.834015 | − | 0.551741i | \(-0.813964\pi\) |
0.0608145 | + | 0.998149i | \(0.480630\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10777.4 | − | 6222.35i | −0.530006 | − | 0.305999i | ||||
\(746\) | 3171.84i | 0.155669i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 175.485i | 0.00857804i | ||||||||
\(749\) | 7125.64 | + | 7366.30i | 0.347617 | + | 0.359358i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11091.4 | − | 19210.8i | −0.538921 | − | 0.933438i | −0.998962 | − | 0.0455407i | \(-0.985499\pi\) |
0.460042 | − | 0.887897i | \(-0.347834\pi\) | |||||||
\(752\) | 3556.70 | + | 6160.39i | 0.172473 | + | 0.298732i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2579.67 | − | 1489.38i | −0.124597 | − | 0.0719361i | ||||
\(755\) | 5263.12 | 0.253701 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2531.12 | −0.121526 | −0.0607630 | − | 0.998152i | \(-0.519353\pi\) | ||||
−0.0607630 | + | 0.998152i | \(0.519353\pi\) | |||||||
\(758\) | −7078.10 | − | 4086.54i | −0.339166 | − | 0.195818i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8084.62 | + | 14003.0i | 0.385868 | + | 0.668344i | ||||
\(761\) | 1897.02 | + | 3285.73i | 0.0903637 | + | 0.156514i | 0.907664 | − | 0.419697i | \(-0.137864\pi\) |
−0.817301 | + | 0.576212i | \(0.804530\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5332.57 | + | 5158.35i | −0.253017 | + | 0.244751i | ||||
\(764\) | − | 24849.8i | − | 1.17675i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2157.89i | 0.101786i | ||||||||
\(767\) | −5393.59 | − | 3113.99i | −0.253913 | − | 0.146597i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5524.12 | + | 3189.35i | −0.259044 | + | 0.149559i | −0.623898 | − | 0.781506i | \(-0.714452\pi\) |
0.364854 | + | 0.931065i | \(0.381119\pi\) | |||||||
\(770\) | 9.15811 | + | 36.5989i | 0.000428617 | + | 0.00171290i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12411.1 | − | 21496.7i | 0.578609 | − | 1.00218i | ||||
\(773\) | 29728.9 | 1.38328 | 0.691638 | − | 0.722244i | \(-0.256889\pi\) | ||||
0.691638 | + | 0.722244i | \(0.256889\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 627.283i | − | 0.0290744i | ||||||
\(776\) | −8222.15 | + | 14241.2i | −0.380358 | + | 0.658799i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2394.50 | − | 4147.39i | −0.110343 | − | 0.191120i | ||||
\(779\) | −11998.3 | + | 6927.20i | −0.551839 | + | 0.318604i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.31779 | − | 5.74657i | 0.000152010 | − | 0.000263289i | ||||
\(782\) | −7976.42 | −0.364752 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 15035.5 | + | 9359.77i | 0.684924 | + | 0.426374i | ||||
\(785\) | 18528.4 | + | 10697.4i | 0.842431 | + | 0.486378i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3237.27 | − | 1869.04i | 0.146628 | − | 0.0846556i | −0.424891 | − | 0.905244i | \(-0.639688\pi\) |
0.571519 | + | 0.820589i | \(0.306354\pi\) | |||||||
\(788\) | −3245.59 | + | 1873.84i | −0.146725 | + | 0.0847117i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 677.190 | + | 390.976i | 0.0304979 | + | 0.0176080i | ||||
\(791\) | 3628.66 | − | 12695.3i | 0.163110 | − | 0.570660i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2702.31 | 0.121011 | ||||||||
\(794\) | 2144.17 | − | 3713.82i | 0.0958361 | − | 0.165993i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26325.4 | − | 15199.0i | 1.17221 | − | 0.676776i | ||||
\(797\) | 5377.39 | + | 9313.91i | 0.238992 | + | 0.413947i | 0.960425 | − | 0.278537i | \(-0.0898496\pi\) |
−0.721433 | + | 0.692484i | \(0.756516\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6377.45 | − | 11046.1i | 0.282376 | − | 0.489089i | ||||
\(800\) | − | 322.864i | − | 0.0142687i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4062.60 | −0.178872 | ||||||||
\(803\) | 92.3882 | − | 160.021i | 0.00406016 | − | 0.00703241i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23600.1 | − | 5905.44i | 1.03329 | − | 0.258558i | ||||
\(806\) | 2225.47 | − | 1284.88i | 0.0972566 | − | 0.0561511i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15244.7 | − | 8801.51i | −0.663744 | − | 0.383213i | ||||
\(809\) | 31037.7i | 1.34886i | 0.738340 | + | 0.674429i | \(0.235610\pi\) | ||||
−0.738340 | + | 0.674429i | \(0.764390\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3943.22i | 0.170734i | 0.996350 | + | 0.0853669i | \(0.0272062\pi\) | ||||
−0.996350 | + | 0.0853669i | \(0.972794\pi\) | |||||||
\(812\) | 27592.4 | + | 28524.3i | 1.19249 | + | 1.23277i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 17.3601 | + | 30.0685i | 0.000747506 | + | 0.00129472i | ||||
\(815\) | −4112.93 | − | 7123.81i | −0.176773 | − | 0.306179i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4858.16 | + | 2804.86i | 0.208036 | + | 0.120110i | ||||
\(818\) | 794.973 | 0.0339799 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8806.64 | −0.375050 | ||||||||
\(821\) | −25087.6 | − | 14484.3i | −1.06646 | − | 0.615720i | −0.139247 | − | 0.990258i | \(-0.544468\pi\) |
−0.927212 | + | 0.374537i | \(0.877802\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18643.1 | − | 32290.8i | −0.789622 | − | 1.36766i | −0.926199 | − | 0.377035i | \(-0.876944\pi\) |
0.136577 | − | 0.990629i | \(-0.456390\pi\) | |||||||
\(824\) | −563.181 | − | 975.458i | −0.0238099 | − | 0.0412399i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4066.52 | − | 4203.86i | −0.171298 | − | 0.177084i | ||||
\(827\) | − | 13151.6i | − | 0.552992i | −0.961015 | − | 0.276496i | \(-0.910827\pi\) | ||
0.961015 | − | 0.276496i | \(-0.0891732\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27671.1i | 1.15929i | 0.814867 | + | 0.579647i | \(0.196810\pi\) | ||||
−0.814867 | + | 0.579647i | \(0.803190\pi\) | |||||||
\(830\) | 5583.57 | + | 3223.68i | 0.233504 | + | 0.134814i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3974.92 | + | 2294.92i | −0.165632 | + | 0.0956274i | ||||
\(833\) | 1054.46 | − | 31739.3i | 0.0438592 | − | 1.32017i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20047.8 | + | 34723.8i | −0.830877 | + | 1.43912i | ||||
\(836\) | 246.597 | 0.0102018 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 9866.14i | − | 0.406707i | ||||||
\(839\) | 8498.72 | − | 14720.2i | 0.349712 | − | 0.605719i | −0.636486 | − | 0.771288i | \(-0.719613\pi\) |
0.986198 | + | 0.165569i | \(0.0529461\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28914.2 | + | 50080.8i | 1.18554 | + | 2.05342i | ||||
\(842\) | −3572.89 | + | 2062.81i | −0.146235 | + | 0.0844288i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18361.3 | + | 31802.8i | −0.748843 | + | 1.29703i | ||||
\(845\) | −22045.6 | −0.897506 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23700.2 | − | 6774.16i | −0.961449 | − | 0.274809i | ||||
\(848\) | −18748.9 | − | 10824.7i | −0.759247 | − | 0.438351i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −147.575 | + | 85.2024i | −0.00595503 | + | 0.00343814i | ||||
\(851\) | 19389.1 | − | 11194.3i | 0.781023 | − | 0.450924i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13130.3 | − | 7580.75i | −0.527047 | − | 0.304291i | 0.212766 | − | 0.977103i | \(-0.431753\pi\) |
−0.739813 | + | 0.672812i | \(0.765086\pi\) | |||||||
\(854\) | 2440.09 | + | 697.445i | 0.0977729 | + | 0.0279462i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6214.69 | −0.248147 | ||||||||
\(857\) | −14186.9 | + | 24572.4i | −0.565477 | + | 0.979436i | 0.431528 | + | 0.902100i | \(0.357975\pi\) |
−0.997005 | + | 0.0773360i | \(0.975359\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33411.7 | + | 19290.2i | −1.32712 | + | 0.766210i | −0.984853 | − | 0.173394i | \(-0.944527\pi\) |
−0.342263 | + | 0.939604i | \(0.611193\pi\) | |||||||
\(860\) | 1782.93 | + | 3088.12i | 0.0706945 | + | 0.122446i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1744.17 | + | 3020.98i | −0.0689171 | + | 0.119368i | ||||
\(863\) | 112.649i | 0.00444337i | 0.999998 | + | 0.00222168i | \(0.000707185\pi\) | ||||
−0.999998 | + | 0.00222168i | \(0.999293\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36485.8 | 1.43417 | ||||||||
\(866\) | −3491.62 | + | 6047.66i | −0.137009 | + | 0.237307i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −33212.8 | + | 8310.81i | −1.29875 | + | 0.324985i | ||||
\(869\) | 21.3837 | − | 12.3459i | 0.000834742 | − | 0.000481939i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4595.05 | + | 2652.95i | 0.178757 | + | 0.103205i | ||||
\(872\) | − | 4498.90i | − | 0.174716i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11208.7i | 0.433799i | ||||||||
\(875\) | 18787.2 | − | 18173.4i | 0.725855 | − | 0.702141i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10379.3 | + | 17977.5i | 0.399639 | + | 0.692196i | 0.993681 | − | 0.112238i | \(-0.0358020\pi\) |
−0.594042 | + | 0.804434i | \(0.702469\pi\) | |||||||
\(878\) | −4693.22 | − | 8128.89i | −0.180397 | − | 0.312456i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 125.507 | + | 72.4615i | 0.00480777 | + | 0.00277577i | ||||
\(881\) | −18603.4 | −0.711425 | −0.355712 | − | 0.934595i | \(-0.615762\pi\) | ||||
−0.355712 | + | 0.934595i | \(0.615762\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17188.8 | 0.655096 | 0.327548 | − | 0.944835i | \(-0.393778\pi\) | ||||
0.327548 | + | 0.944835i | \(0.393778\pi\) | |||||||
\(884\) | 8576.68 | + | 4951.75i | 0.326318 | + | 0.188400i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4777.44 | + | 8274.77i | 0.181153 | + | 0.313766i | ||||
\(887\) | 6615.31 | + | 11458.1i | 0.250417 | + | 0.433736i | 0.963641 | − | 0.267201i | \(-0.0860988\pi\) |
−0.713223 | + | 0.700937i | \(0.752765\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1360.02 | − | 1315.59i | 0.0513090 | − | 0.0496327i | ||||
\(890\) | 1900.49i | 0.0715782i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8916.74i | 0.334703i | ||||||||
\(893\) | −15522.3 | − | 8961.79i | −0.581672 | − | 0.335829i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26324.3 | − | 15198.4i | 0.983157 | − | 0.567626i | ||||
\(896\) | −22481.2 | + | 5625.45i | −0.838219 | + | 0.209747i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2826.20 | + | 4895.12i | −0.105024 | + | 0.181907i | ||||
\(899\) | −70928.4 | −2.63136 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38819.2i | 1.43535i | ||||||||
\(902\) | 9.80104 | − | 16.9759i | 0.000361795 | − | 0.000626647i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4003.25 | + | 6933.83i | 0.147286 | + | 0.255106i | ||||
\(905\) | 7076.96 | − | 4085.88i | 0.259940 | − | 0.150077i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21753.0 | − | 37677.2i | 0.796356 | − | 1.37933i | −0.125618 | − | 0.992079i | \(-0.540091\pi\) |
0.921975 | − | 0.387251i | \(-0.126575\pi\) | |||||||
\(908\) | 41914.5 | 1.53192 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2047.16 | + | 585.134i | 0.0745743 | + | 0.0213154i | ||||
\(911\) | −14899.7 | − | 8602.33i | −0.541875 | − | 0.312852i | 0.203964 | − | 0.978978i | \(-0.434618\pi\) |
−0.745838 | + | 0.666127i | \(0.767951\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 176.313 | − | 101.794i | 0.00639113 | − | 0.00368992i | ||||
\(914\) | 3027.84 | − | 1748.13i | 0.109576 | − | 0.0632635i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 34515.5 | + | 19927.5i | 1.24500 | + | 0.718804i | ||||
\(917\) | −8420.02 | − | 2406.68i | −0.303221 | − | 0.0866690i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18441.8 | 0.661956 | 0.330978 | − | 0.943639i | \(-0.392621\pi\) | ||||
0.330978 | + | 0.943639i | \(0.392621\pi\) | |||||||
\(920\) | −7375.99 | + | 12775.6i | −0.264325 | + | 0.457825i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −32.2382 | + | 18.6127i | −0.00115153 | + | 0.000664834i | ||||
\(923\) | −187.239 | − | 324.308i | −0.00667719 | − | 0.0115652i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 239.151 | − | 414.221i | 0.00850079 | − | 0.0147238i | ||||
\(926\) | − | 6949.39i | − | 0.246621i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −36507.0 | −1.29138 | ||||||||
\(929\) | −17234.7 | + | 29851.4i | −0.608668 | + | 1.05424i | 0.382792 | + | 0.923835i | \(0.374963\pi\) |
−0.991460 | + | 0.130410i | \(0.958371\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44601.0 | − | 1481.75i | −1.57007 | − | 0.0521617i | ||||
\(932\) | 723.749 | − | 417.857i | 0.0254369 | − | 0.0146860i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8049.64 | + | 4647.46i | 0.282005 | + | 0.162815i | ||||
\(935\) | − | 259.859i | − | 0.00908908i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8204.91i | 0.286065i | 0.989718 | + | 0.143032i | \(0.0456853\pi\) | ||||
−0.989718 | + | 0.143032i | \(0.954315\pi\) | |||||||
\(938\) | 3464.46 | + | 3581.47i | 0.120595 | + | 0.124668i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5696.62 | − | 9866.83i | −0.197663 | − | 0.342362i | ||||
\(941\) | 11955.6 | + | 20707.8i | 0.414179 | + | 0.717380i | 0.995342 | − | 0.0964079i | \(-0.0307353\pi\) |
−0.581163 | + | 0.813787i | \(0.697402\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10946.6 | − | 6320.03i | −0.378017 | − | 0.218249i | ||||
\(944\) | −22467.3 | −0.774628 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.93698 | −0.000272784 | ||||||||
\(947\) | 34519.4 | + | 19929.8i | 1.18451 | + | 0.683877i | 0.957054 | − | 0.289911i | \(-0.0936257\pi\) |
0.227456 | + | 0.973788i | \(0.426959\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5213.93 | − | 9030.78i | −0.178347 | − | 0.308906i | ||||
\(950\) | 119.729 | + | 207.377i | 0.00408897 | + | 0.00708231i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13388.7 | + | 13840.8i | 0.455808 | + | 0.471202i | ||||
\(953\) | 10983.4i | 0.373334i | 0.982423 | + | 0.186667i | \(0.0597685\pi\) | ||||
−0.982423 | + | 0.186667i | \(0.940232\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36797.6i | 1.24685i | ||||||||
\(956\) | 30884.3 | + | 17831.1i | 1.04484 | + | 0.603240i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3196.58 | + | 1845.54i | −0.107804 | + | 0.0622409i | ||||
\(959\) | −47061.1 | + | 11776.1i | −1.58465 | + | 0.396527i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15699.3 | − | 27191.9i | 0.526980 | − | 0.912756i | ||||
\(962\) | 1959.43 | 0.0656699 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 39879.3i | − | 1.33239i | ||||||
\(965\) | −18378.4 | + | 31832.3i | −0.613079 | + | 1.06188i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7413.81 | − | 12841.1i | −0.246548 | − | 0.427034i | 0.716018 | − | 0.698082i | \(-0.245963\pi\) |
−0.962566 | + | 0.271048i | \(0.912630\pi\) | |||||||
\(968\) | 12944.4 | − | 7473.47i | 0.429803 | − | 0.248147i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5880.43 | − | 10185.2i | 0.194649 | − | 0.337141i | ||||
\(971\) | −8249.56 | −0.272648 | −0.136324 | − | 0.990664i | \(-0.543529\pi\) | ||||
−0.136324 | + | 0.990664i | \(0.543529\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6323.38 | − | 22123.1i | 0.208344 | − | 0.728913i | ||||
\(974\) | −10680.0 | − | 6166.09i | −0.351344 | − | 0.202848i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8442.48 | − | 4874.27i | 0.276882 | − | 0.159858i | ||||
\(977\) | −4134.88 | + | 2387.28i | −0.135401 | + | 0.0781737i | −0.566170 | − | 0.824288i | \(-0.691576\pi\) |
0.430769 | + | 0.902462i | \(0.358242\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 51.9718 | + | 30.0059i | 0.00169666 | + | 0.000979564i | ||||
\(980\) | −24081.7 | − | 14991.1i | −0.784960 | − | 0.488648i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6751.20 | 0.219389 | ||||||||
\(983\) | 8970.02 | − | 15536.5i | 0.291047 | − | 0.504108i | −0.683011 | − | 0.730409i | \(-0.739330\pi\) |
0.974058 | + | 0.226300i | \(0.0726630\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4806.07 | − | 2774.79i | 0.155466 | − | 0.0897584i | ||||
\(986\) | 9634.04 | + | 16686.6i | 0.311167 | + | 0.538957i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6958.35 | − | 12052.2i | 0.224063 | − | 0.388089i | ||||
\(989\) | 5118.02i | 0.164554i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1714.50 | 0.0549574 | 0.0274787 | − | 0.999622i | \(-0.491252\pi\) | ||||
0.0274787 | + | 0.999622i | \(0.491252\pi\) | |||||||
\(992\) | 15747.2 | − | 27274.9i | 0.504006 | − | 0.872964i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −85.3688 | − | 341.163i | −0.00272408 | − | 0.0108863i | ||||
\(995\) | −38982.7 | + | 22506.7i | −1.24205 | + | 0.717095i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29996.8 | + | 17318.7i | 0.952867 | + | 0.550138i | 0.893970 | − | 0.448126i | \(-0.147908\pi\) |
0.0588968 | + | 0.998264i | \(0.481242\pi\) | |||||||
\(998\) | − | 363.380i | − | 0.0115256i | ||||||
\(999\) | 0 | 0 |
(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 | 189.4.o.a.62.10 | 44 | ||
3.2 | odd | 2 | 63.4.o.a.20.13 | ✓ | 44 | ||
7.6 | odd | 2 | inner | 189.4.o.a.62.9 | 44 | ||
9.2 | odd | 6 | 567.4.c.c.566.11 | 44 | |||
9.4 | even | 3 | 63.4.o.a.41.14 | yes | 44 | ||
9.5 | odd | 6 | inner | 189.4.o.a.125.9 | 44 | ||
9.7 | even | 3 | 567.4.c.c.566.34 | 44 | |||
21.20 | even | 2 | 63.4.o.a.20.14 | yes | 44 | ||
63.13 | odd | 6 | 63.4.o.a.41.13 | yes | 44 | ||
63.20 | even | 6 | 567.4.c.c.566.33 | 44 | |||
63.34 | odd | 6 | 567.4.c.c.566.12 | 44 | |||
63.41 | even | 6 | inner | 189.4.o.a.125.10 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.o.a.20.13 | ✓ | 44 | 3.2 | odd | 2 | ||
63.4.o.a.20.14 | yes | 44 | 21.20 | even | 2 | ||
63.4.o.a.41.13 | yes | 44 | 63.13 | odd | 6 | ||
63.4.o.a.41.14 | yes | 44 | 9.4 | even | 3 | ||
189.4.o.a.62.9 | 44 | 7.6 | odd | 2 | inner | ||
189.4.o.a.62.10 | 44 | 1.1 | even | 1 | trivial | ||
189.4.o.a.125.9 | 44 | 9.5 | odd | 6 | inner | ||
189.4.o.a.125.10 | 44 | 63.41 | even | 6 | inner | ||
567.4.c.c.566.11 | 44 | 9.2 | odd | 6 | |||
567.4.c.c.566.12 | 44 | 63.34 | odd | 6 | |||
567.4.c.c.566.33 | 44 | 63.20 | even | 6 | |||
567.4.c.c.566.34 | 44 | 9.7 | even | 3 |