Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(23,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.23");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.e (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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 147.2 | ||
Root | \(-1.35234 - 0.780776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.147 |
Dual form | 169.4.e.f.23.2 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35234 | − | 0.780776i | −0.478126 | − | 0.276046i | 0.241509 | − | 0.970399i | \(-0.422358\pi\) |
−0.719635 | + | 0.694352i | \(0.755691\pi\) | |||||||
\(3\) | −4.34233 | + | 7.52113i | −0.835682 | + | 1.44744i | 0.0577926 | + | 0.998329i | \(0.481594\pi\) |
−0.893474 | + | 0.449114i | \(0.851740\pi\) | |||||||
\(4\) | −2.78078 | − | 4.81645i | −0.347597 | − | 0.602056i | ||||
\(5\) | 3.56155i | 0.318555i | 0.987234 | + | 0.159277i | \(0.0509165\pi\) | ||||
−0.987234 | + | 0.159277i | \(0.949084\pi\) | |||||||
\(6\) | 11.7446 | − | 6.78078i | 0.799122 | − | 0.461373i | ||||
\(7\) | −23.5360 | + | 13.5885i | −1.27083 | + | 0.733712i | −0.975144 | − | 0.221574i | \(-0.928881\pi\) |
−0.295683 | + | 0.955286i | \(0.595547\pi\) | |||||||
\(8\) | 21.1771i | 0.935904i | ||||||||
\(9\) | −24.2116 | − | 41.9358i | −0.896728 | − | 1.55318i | ||||
\(10\) | 2.78078 | − | 4.81645i | 0.0879359 | − | 0.152309i | ||||
\(11\) | −13.2167 | − | 7.63068i | −0.362272 | − | 0.209158i | 0.307805 | − | 0.951450i | \(-0.400406\pi\) |
−0.670077 | + | 0.742292i | \(0.733739\pi\) | |||||||
\(12\) | 48.3002 | 1.16192 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 42.4384 | 0.810154 | ||||||||
\(15\) | −26.7869 | − | 15.4654i | −0.461090 | − | 0.266211i | ||||
\(16\) | −5.71165 | + | 9.89286i | −0.0892445 | + | 0.154576i | ||||
\(17\) | 22.2732 | + | 38.5783i | 0.317767 | + | 0.550389i | 0.980022 | − | 0.198890i | \(-0.0637336\pi\) |
−0.662255 | + | 0.749279i | \(0.730400\pi\) | |||||||
\(18\) | 75.6155i | 0.990153i | ||||||||
\(19\) | −20.7584 | + | 11.9848i | −0.250647 | + | 0.144711i | −0.620061 | − | 0.784554i | \(-0.712892\pi\) |
0.369413 | + | 0.929265i | \(0.379559\pi\) | |||||||
\(20\) | 17.1540 | − | 9.90388i | 0.191788 | − | 0.110729i | ||||
\(21\) | − | 236.024i | − | 2.45260i | ||||||
\(22\) | 11.9157 | + | 20.6386i | 0.115474 | + | 0.200008i | ||||
\(23\) | 61.3693 | − | 106.295i | 0.556365 | − | 0.963652i | −0.441431 | − | 0.897295i | \(-0.645529\pi\) |
0.997796 | − | 0.0663568i | \(-0.0211376\pi\) | |||||||
\(24\) | −159.276 | − | 91.9579i | −1.35467 | − | 0.782117i | ||||
\(25\) | 112.315 | 0.898523 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 186.054 | 1.32615 | ||||||||
\(28\) | 130.897 | + | 75.5734i | 0.883471 | + | 0.510072i | ||||
\(29\) | 109.955 | − | 190.447i | 0.704071 | − | 1.21949i | −0.262955 | − | 0.964808i | \(-0.584697\pi\) |
0.967026 | − | 0.254678i | \(-0.0819694\pi\) | |||||||
\(30\) | 24.1501 | + | 41.8292i | 0.146973 | + | 0.254564i | ||||
\(31\) | − | 27.0928i | − | 0.156968i | −0.996915 | − | 0.0784840i | \(-0.974992\pi\) | ||
0.996915 | − | 0.0784840i | \(-0.0250080\pi\) | |||||||
\(32\) | 162.167 | − | 93.6274i | 0.895856 | − | 0.517223i | ||||
\(33\) | 114.783 | − | 66.2699i | 0.605488 | − | 0.349579i | ||||
\(34\) | − | 69.5616i | − | 0.350874i | ||||||
\(35\) | −48.3963 | − | 83.8249i | −0.233728 | − | 0.404828i | ||||
\(36\) | −134.654 | + | 233.228i | −0.623400 | + | 1.07976i | ||||
\(37\) | −81.5729 | − | 47.0961i | −0.362446 | − | 0.209258i | 0.307707 | − | 0.951481i | \(-0.400438\pi\) |
−0.670153 | + | 0.742223i | \(0.733772\pi\) | |||||||
\(38\) | 37.4299 | 0.159788 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −75.4233 | −0.298137 | ||||||||
\(41\) | −138.871 | − | 80.1771i | −0.528975 | − | 0.305404i | 0.211624 | − | 0.977351i | \(-0.432125\pi\) |
−0.740599 | + | 0.671947i | \(0.765458\pi\) | |||||||
\(42\) | −184.282 | + | 319.185i | −0.677031 | + | 1.17265i | ||||
\(43\) | −75.6510 | − | 131.031i | −0.268295 | − | 0.464700i | 0.700127 | − | 0.714018i | \(-0.253127\pi\) |
−0.968422 | + | 0.249318i | \(0.919793\pi\) | |||||||
\(44\) | 84.8769i | 0.290811i | ||||||||
\(45\) | 149.357 | − | 86.2311i | 0.494773 | − | 0.285657i | ||||
\(46\) | −165.985 | + | 95.8314i | −0.532025 | + | 0.307165i | ||||
\(47\) | 466.948i | 1.44918i | 0.689181 | + | 0.724589i | \(0.257970\pi\) | ||||
−0.689181 | + | 0.724589i | \(0.742030\pi\) | |||||||
\(48\) | −49.6037 | − | 85.9161i | −0.149160 | − | 0.258353i | ||||
\(49\) | 197.797 | − | 342.594i | 0.576667 | − | 0.998817i | ||||
\(50\) | −151.889 | − | 87.6932i | −0.429607 | − | 0.248034i | ||||
\(51\) | −386.870 | −1.06221 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −120.847 | −0.313199 | −0.156600 | − | 0.987662i | \(-0.550053\pi\) | ||||
−0.156600 | + | 0.987662i | \(0.550053\pi\) | |||||||
\(54\) | −251.609 | − | 145.267i | −0.634068 | − | 0.366079i | ||||
\(55\) | 27.1771 | − | 47.0721i | 0.0666283 | − | 0.115404i | ||||
\(56\) | −287.766 | − | 498.425i | −0.686684 | − | 1.18937i | ||||
\(57\) | − | 208.169i | − | 0.483730i | ||||||
\(58\) | −297.393 | + | 171.700i | −0.673269 | + | 0.388712i | ||||
\(59\) | −380.733 | + | 219.816i | −0.840122 | + | 0.485045i | −0.857306 | − | 0.514808i | \(-0.827863\pi\) |
0.0171836 | + | 0.999852i | \(0.494530\pi\) | |||||||
\(60\) | 172.024i | 0.370136i | ||||||||
\(61\) | 68.6525 | + | 118.910i | 0.144099 | + | 0.249587i | 0.929037 | − | 0.369988i | \(-0.120638\pi\) |
−0.784937 | + | 0.619575i | \(0.787305\pi\) | |||||||
\(62\) | −21.1534 | + | 36.6388i | −0.0433304 | + | 0.0750505i | ||||
\(63\) | 1139.69 | + | 658.002i | 2.27917 | + | 1.31588i | ||||
\(64\) | −201.022 | −0.392621 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −206.968 | −0.386000 | ||||||||
\(67\) | 443.648 | + | 256.140i | 0.808958 | + | 0.467052i | 0.846594 | − | 0.532239i | \(-0.178649\pi\) |
−0.0376358 | + | 0.999292i | \(0.511983\pi\) | |||||||
\(68\) | 123.874 | − | 214.555i | 0.220910 | − | 0.382627i | ||||
\(69\) | 532.972 | + | 923.134i | 0.929887 | + | 1.61061i | ||||
\(70\) | 151.147i | 0.258078i | ||||||||
\(71\) | −355.693 | + | 205.359i | −0.594549 | + | 0.343263i | −0.766894 | − | 0.641774i | \(-0.778199\pi\) |
0.172345 | + | 0.985037i | \(0.444866\pi\) | |||||||
\(72\) | 888.078 | − | 512.732i | 1.45362 | − | 0.839251i | ||||
\(73\) | − | 308.004i | − | 0.493823i | −0.969038 | − | 0.246912i | \(-0.920584\pi\) | ||
0.969038 | − | 0.246912i | \(-0.0794158\pi\) | |||||||
\(74\) | 73.5431 | + | 127.380i | 0.115530 | + | 0.200104i | ||||
\(75\) | −487.710 | + | 844.739i | −0.750879 | + | 1.30056i | ||||
\(76\) | 115.449 | + | 66.6543i | 0.174248 | + | 0.100602i | ||||
\(77\) | 414.759 | 0.613847 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −586.462 | −0.835217 | −0.417608 | − | 0.908627i | \(-0.637132\pi\) | ||||
−0.417608 | + | 0.908627i | \(0.637132\pi\) | |||||||
\(80\) | −35.2339 | − | 20.3423i | −0.0492409 | − | 0.0284293i | ||||
\(81\) | −154.193 | + | 267.070i | −0.211513 | + | 0.366352i | ||||
\(82\) | 125.201 | + | 216.854i | 0.168611 | + | 0.292043i | ||||
\(83\) | − | 1354.20i | − | 1.79088i | −0.445182 | − | 0.895440i | \(-0.646861\pi\) | ||
0.445182 | − | 0.895440i | \(-0.353139\pi\) | |||||||
\(84\) | −1136.80 | + | 656.329i | −1.47660 | + | 0.852516i | ||||
\(85\) | −137.399 | + | 79.3272i | −0.175329 | + | 0.101226i | ||||
\(86\) | 236.266i | 0.296247i | ||||||||
\(87\) | 954.918 | + | 1653.97i | 1.17676 | + | 2.03820i | ||||
\(88\) | 161.596 | − | 279.892i | 0.195752 | − | 0.339052i | ||||
\(89\) | −380.949 | − | 219.941i | −0.453714 | − | 0.261952i | 0.255683 | − | 0.966761i | \(-0.417700\pi\) |
−0.709398 | + | 0.704809i | \(0.751033\pi\) | |||||||
\(90\) | −269.309 | −0.315418 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −682.617 | −0.773563 | ||||||||
\(93\) | 203.769 | + | 117.646i | 0.227202 | + | 0.131175i | ||||
\(94\) | 364.582 | − | 631.474i | 0.400040 | − | 0.692889i | ||||
\(95\) | −42.6847 | − | 73.9320i | −0.0460985 | − | 0.0798449i | ||||
\(96\) | 1626.24i | 1.72894i | ||||||||
\(97\) | 1308.80 | − | 755.634i | 1.36998 | − | 0.790959i | 0.379056 | − | 0.925374i | \(-0.376249\pi\) |
0.990925 | + | 0.134414i | \(0.0429153\pi\) | |||||||
\(98\) | −534.979 | + | 308.870i | −0.551439 | + | 0.318374i | ||||
\(99\) | 739.006i | 0.750231i | ||||||||
\(100\) | −312.324 | − | 540.961i | −0.312324 | − | 0.540961i | ||||
\(101\) | 168.130 | − | 291.209i | 0.165639 | − | 0.286895i | −0.771243 | − | 0.636541i | \(-0.780365\pi\) |
0.936882 | + | 0.349646i | \(0.113698\pi\) | |||||||
\(102\) | 523.182 | + | 302.059i | 0.507870 | + | 0.293219i | ||||
\(103\) | −322.712 | −0.308716 | −0.154358 | − | 0.988015i | \(-0.549331\pi\) | ||||
−0.154358 | + | 0.988015i | \(0.549331\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 840.611 | 0.781288 | ||||||||
\(106\) | 163.426 | + | 94.3542i | 0.149749 | + | 0.0864574i | ||||
\(107\) | −717.309 | + | 1242.42i | −0.648083 | + | 1.12251i | 0.335498 | + | 0.942041i | \(0.391096\pi\) |
−0.983580 | + | 0.180471i | \(0.942238\pi\) | |||||||
\(108\) | −517.375 | − | 896.119i | −0.460967 | − | 0.798417i | ||||
\(109\) | − | 849.147i | − | 0.746179i | −0.927795 | − | 0.373089i | \(-0.878298\pi\) | ||
0.927795 | − | 0.373089i | \(-0.121702\pi\) | |||||||
\(110\) | −73.5055 | + | 42.4384i | −0.0637134 | + | 0.0367850i | ||||
\(111\) | 708.433 | − | 409.014i | 0.605779 | − | 0.349747i | ||||
\(112\) | − | 310.452i | − | 0.261919i | ||||||
\(113\) | −807.263 | − | 1398.22i | −0.672044 | − | 1.16401i | −0.977324 | − | 0.211751i | \(-0.932083\pi\) |
0.305280 | − | 0.952263i | \(-0.401250\pi\) | |||||||
\(114\) | −162.533 | + | 281.516i | −0.133532 | + | 0.231284i | ||||
\(115\) | 378.574 | + | 218.570i | 0.306976 | + | 0.177233i | ||||
\(116\) | −1223.04 | −0.978931 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 686.509 | 0.535579 | ||||||||
\(119\) | −1048.45 | − | 605.321i | −0.807654 | − | 0.466300i | ||||
\(120\) | 327.513 | − | 567.269i | 0.249147 | − | 0.431536i | ||||
\(121\) | −549.045 | − | 950.974i | −0.412506 | − | 0.714481i | ||||
\(122\) | − | 214.409i | − | 0.159112i | ||||||
\(123\) | 1206.05 | − | 696.311i | 0.884109 | − | 0.510441i | ||||
\(124\) | −130.491 | + | 75.3390i | −0.0945035 | + | 0.0545616i | ||||
\(125\) | 845.211i | 0.604784i | ||||||||
\(126\) | −1027.50 | − | 1779.69i | −0.726487 | − | 1.25831i | ||||
\(127\) | 432.587 | − | 749.263i | 0.302251 | − | 0.523514i | −0.674394 | − | 0.738371i | \(-0.735595\pi\) |
0.976646 | + | 0.214857i | \(0.0689285\pi\) | |||||||
\(128\) | −1025.49 | − | 592.066i | −0.708134 | − | 0.408842i | ||||
\(129\) | 1314.01 | 0.896836 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −281.400 | −0.187680 | −0.0938400 | − | 0.995587i | \(-0.529914\pi\) | ||||
−0.0938400 | + | 0.995587i | \(0.529914\pi\) | |||||||
\(132\) | −638.371 | − | 368.563i | −0.420932 | − | 0.243025i | ||||
\(133\) | 325.713 | − | 564.152i | 0.212353 | − | 0.367806i | ||||
\(134\) | −399.976 | − | 692.779i | −0.257856 | − | 0.446620i | ||||
\(135\) | 662.641i | 0.422452i | ||||||||
\(136\) | −816.976 | + | 471.681i | −0.515111 | + | 0.297400i | ||||
\(137\) | −2287.55 | + | 1320.72i | −1.42656 | + | 0.823624i | −0.996847 | − | 0.0793428i | \(-0.974718\pi\) |
−0.429711 | + | 0.902967i | \(0.641384\pi\) | |||||||
\(138\) | − | 1664.53i | − | 1.02677i | ||||||
\(139\) | 999.318 | + | 1730.87i | 0.609791 | + | 1.05619i | 0.991274 | + | 0.131814i | \(0.0420801\pi\) |
−0.381483 | + | 0.924376i | \(0.624587\pi\) | |||||||
\(140\) | −269.159 | + | 466.196i | −0.162486 | + | 0.281434i | ||||
\(141\) | −3511.98 | − | 2027.64i | −2.09760 | − | 1.21105i | ||||
\(142\) | 641.359 | 0.379026 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 553.153 | 0.320112 | ||||||||
\(145\) | 678.286 | + | 391.609i | 0.388473 | + | 0.224285i | ||||
\(146\) | −240.482 | + | 416.527i | −0.136318 | + | 0.236110i | ||||
\(147\) | 1717.80 | + | 2975.31i | 0.963820 | + | 1.66939i | ||||
\(148\) | 523.855i | 0.290950i | ||||||||
\(149\) | 1518.13 | − | 876.491i | 0.834696 | − | 0.481912i | −0.0207617 | − | 0.999784i | \(-0.506609\pi\) |
0.855458 | + | 0.517872i | \(0.173276\pi\) | |||||||
\(150\) | 1319.10 | − | 761.585i | 0.718029 | − | 0.414554i | ||||
\(151\) | − | 2794.64i | − | 1.50613i | −0.657949 | − | 0.753063i | \(-0.728576\pi\) | ||
0.657949 | − | 0.753063i | \(-0.271424\pi\) | |||||||
\(152\) | −253.804 | − | 439.601i | −0.135436 | − | 0.234582i | ||||
\(153\) | 1078.54 | − | 1868.09i | 0.569901 | − | 0.987098i | ||||
\(154\) | −560.898 | − | 323.834i | −0.293496 | − | 0.169450i | ||||
\(155\) | 96.4924 | 0.0500030 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3244.87 | 1.64949 | 0.824743 | − | 0.565508i | \(-0.191320\pi\) | ||||
0.824743 | + | 0.565508i | \(0.191320\pi\) | |||||||
\(158\) | 793.099 | + | 457.896i | 0.399339 | + | 0.230558i | ||||
\(159\) | 524.756 | − | 908.903i | 0.261735 | − | 0.453338i | ||||
\(160\) | 333.459 | + | 577.568i | 0.164764 | + | 0.285380i | ||||
\(161\) | 3335.68i | 1.63285i | ||||||||
\(162\) | 417.045 | − | 240.781i | 0.202260 | − | 0.116775i | ||||
\(163\) | 2841.83 | − | 1640.73i | 1.36558 | − | 0.788418i | 0.375221 | − | 0.926936i | \(-0.377567\pi\) |
0.990360 | + | 0.138517i | \(0.0442336\pi\) | |||||||
\(164\) | 891.818i | 0.424630i | ||||||||
\(165\) | 236.024 | + | 408.805i | 0.111360 | + | 0.192881i | ||||
\(166\) | −1057.33 | + | 1831.35i | −0.494366 | + | 0.856266i | ||||
\(167\) | 2707.65 | + | 1563.26i | 1.25463 | + | 0.724364i | 0.972026 | − | 0.234872i | \(-0.0754671\pi\) |
0.282608 | + | 0.959235i | \(0.408800\pi\) | |||||||
\(168\) | 4998.29 | 2.29540 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 247.747 | 0.111773 | ||||||||
\(171\) | 1005.19 | + | 580.346i | 0.449524 | + | 0.259533i | ||||
\(172\) | −420.737 | + | 728.738i | −0.186517 | + | 0.323057i | ||||
\(173\) | 48.7849 | + | 84.4980i | 0.0214396 | + | 0.0371345i | 0.876546 | − | 0.481318i | \(-0.159842\pi\) |
−0.855107 | + | 0.518452i | \(0.826508\pi\) | |||||||
\(174\) | − | 2982.31i | − | 1.29936i | ||||||
\(175\) | −2643.46 | + | 1526.20i | −1.14187 | + | 0.659257i | ||||
\(176\) | 150.979 | − | 87.1675i | 0.0646616 | − | 0.0373324i | ||||
\(177\) | − | 3818.06i | − | 1.62137i | ||||||
\(178\) | 343.450 | + | 594.873i | 0.144622 | + | 0.250492i | ||||
\(179\) | −17.3575 | + | 30.0640i | −0.00724782 | + | 0.0125536i | −0.869627 | − | 0.493710i | \(-0.835640\pi\) |
0.862379 | + | 0.506264i | \(0.168974\pi\) | |||||||
\(180\) | −830.654 | − | 479.579i | −0.343963 | − | 0.198587i | ||||
\(181\) | 1229.35 | 0.504843 | 0.252422 | − | 0.967617i | \(-0.418773\pi\) | ||||
0.252422 | + | 0.967617i | \(0.418773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1192.45 | −0.481684 | ||||||||
\(184\) | 2251.01 | + | 1299.62i | 0.901885 | + | 0.520704i | ||||
\(185\) | 167.735 | − | 290.526i | 0.0666602 | − | 0.115459i | ||||
\(186\) | −183.710 | − | 318.195i | −0.0724209 | − | 0.125437i | ||||
\(187\) | − | 679.839i | − | 0.265854i | ||||||
\(188\) | 2249.03 | − | 1298.48i | 0.872486 | − | 0.503730i | ||||
\(189\) | −4378.97 | + | 2528.20i | −1.68531 | + | 0.973014i | ||||
\(190\) | 133.309i | 0.0509012i | ||||||||
\(191\) | −2140.40 | − | 3707.28i | −0.810858 | − | 1.40445i | −0.912265 | − | 0.409602i | \(-0.865668\pi\) |
0.101407 | − | 0.994845i | \(-0.467666\pi\) | |||||||
\(192\) | 872.903 | − | 1511.91i | 0.328106 | − | 0.568296i | ||||
\(193\) | −409.041 | − | 236.160i | −0.152557 | − | 0.0880786i | 0.421778 | − | 0.906699i | \(-0.361406\pi\) |
−0.574335 | + | 0.818620i | \(0.694739\pi\) | |||||||
\(194\) | −2359.93 | −0.873365 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2200.12 | −0.801791 | ||||||||
\(197\) | −3883.58 | − | 2242.18i | −1.40453 | − | 0.810908i | −0.409681 | − | 0.912229i | \(-0.634360\pi\) |
−0.994854 | + | 0.101321i | \(0.967693\pi\) | |||||||
\(198\) | 576.998 | − | 999.390i | 0.207098 | − | 0.358705i | ||||
\(199\) | −183.120 | − | 317.173i | −0.0652314 | − | 0.112984i | 0.831565 | − | 0.555427i | \(-0.187445\pi\) |
−0.896797 | + | 0.442443i | \(0.854112\pi\) | |||||||
\(200\) | 2378.51i | 0.840931i | ||||||||
\(201\) | −3852.93 | + | 2224.49i | −1.35206 | + | 0.780614i | ||||
\(202\) | −454.739 | + | 262.543i | −0.158393 | + | 0.0914480i | ||||
\(203\) | 5976.49i | 2.06634i | ||||||||
\(204\) | 1075.80 | + | 1863.34i | 0.369221 | + | 0.639509i | ||||
\(205\) | 285.555 | − | 494.596i | 0.0972879 | − | 0.168508i | ||||
\(206\) | 436.418 | + | 251.966i | 0.147605 | + | 0.0852199i | ||||
\(207\) | −5943.41 | −1.99563 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 365.810 | 0.121070 | ||||||||
\(210\) | −1136.80 | − | 656.329i | −0.373554 | − | 0.215671i | ||||
\(211\) | −1061.28 | + | 1838.19i | −0.346262 | + | 0.599744i | −0.985582 | − | 0.169197i | \(-0.945883\pi\) |
0.639320 | + | 0.768941i | \(0.279216\pi\) | |||||||
\(212\) | 336.047 | + | 582.051i | 0.108867 | + | 0.188563i | ||||
\(213\) | − | 3566.95i | − | 1.14743i | ||||||
\(214\) | 1940.10 | − | 1120.12i | 0.619730 | − | 0.357801i | ||||
\(215\) | 466.675 | − | 269.435i | 0.148033 | − | 0.0854666i | ||||
\(216\) | 3940.08i | 1.24115i | ||||||||
\(217\) | 368.152 | + | 637.657i | 0.115169 | + | 0.199479i | ||||
\(218\) | −662.994 | + | 1148.34i | −0.205980 | + | 0.356768i | ||||
\(219\) | 2316.54 | + | 1337.45i | 0.714781 | + | 0.412679i | ||||
\(220\) | −302.294 | −0.0926392 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1277.39 | −0.386185 | ||||||||
\(223\) | −5132.43 | − | 2963.21i | −1.54122 | − | 0.889826i | −0.998762 | − | 0.0497449i | \(-0.984159\pi\) |
−0.542461 | − | 0.840081i | \(-0.682507\pi\) | |||||||
\(224\) | −2544.52 | + | 4407.24i | −0.758986 | + | 1.31460i | ||||
\(225\) | −2719.34 | − | 4710.03i | −0.805730 | − | 1.39557i | ||||
\(226\) | 2521.17i | 0.742060i | ||||||||
\(227\) | 775.665 | − | 447.830i | 0.226796 | − | 0.130941i | −0.382297 | − | 0.924039i | \(-0.624867\pi\) |
0.609093 | + | 0.793099i | \(0.291534\pi\) | |||||||
\(228\) | −1002.63 | + | 578.870i | −0.291232 | + | 0.168143i | ||||
\(229\) | 627.717i | 0.181138i | 0.995890 | + | 0.0905692i | \(0.0288686\pi\) | ||||
−0.995890 | + | 0.0905692i | \(0.971131\pi\) | |||||||
\(230\) | −341.309 | − | 591.164i | −0.0978488 | − | 0.169479i | ||||
\(231\) | −1801.02 | + | 3119.46i | −0.512981 | + | 0.888509i | ||||
\(232\) | 4033.11 | + | 2328.52i | 1.14132 | + | 0.658942i | ||||
\(233\) | −2303.72 | −0.647734 | −0.323867 | − | 0.946103i | \(-0.604983\pi\) | ||||
−0.323867 | + | 0.946103i | \(0.604983\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1663.06 | −0.461643 | ||||||||
\(236\) | 2117.47 | + | 1222.52i | 0.584048 | + | 0.337200i | ||||
\(237\) | 2546.61 | − | 4410.86i | 0.697976 | − | 1.20893i | ||||
\(238\) | 945.240 | + | 1637.20i | 0.257440 | + | 0.445900i | ||||
\(239\) | − | 544.622i | − | 0.147400i | −0.997280 | − | 0.0737001i | \(-0.976519\pi\) | ||
0.997280 | − | 0.0737001i | \(-0.0234808\pi\) | |||||||
\(240\) | 305.995 | − | 176.666i | 0.0822995 | − | 0.0475156i | ||||
\(241\) | 4699.14 | − | 2713.05i | 1.25601 | − | 0.725157i | 0.283713 | − | 0.958909i | \(-0.408434\pi\) |
0.972296 | + | 0.233752i | \(0.0751005\pi\) | |||||||
\(242\) | 1714.73i | 0.455483i | ||||||||
\(243\) | 1172.61 | + | 2031.03i | 0.309561 | + | 0.536175i | ||||
\(244\) | 381.814 | − | 661.322i | 0.100177 | − | 0.173511i | ||||
\(245\) | 1220.17 | + | 704.464i | 0.318178 | + | 0.183700i | ||||
\(246\) | −2174.65 | −0.563621 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 573.746 | 0.146907 | ||||||||
\(249\) | 10185.1 | + | 5880.39i | 2.59220 | + | 1.49661i | ||||
\(250\) | 659.921 | − | 1143.02i | 0.166948 | − | 0.289163i | ||||
\(251\) | −2610.61 | − | 4521.71i | −0.656494 | − | 1.13708i | −0.981517 | − | 0.191375i | \(-0.938705\pi\) |
0.325022 | − | 0.945706i | \(-0.394628\pi\) | |||||||
\(252\) | − | 7319.02i | − | 1.82958i | ||||||
\(253\) | −1622.20 | + | 936.580i | −0.403111 | + | 0.232736i | ||||
\(254\) | −1170.01 | + | 675.508i | −0.289028 | + | 0.166871i | ||||
\(255\) | − | 1377.86i | − | 0.338372i | ||||||
\(256\) | 1728.63 | + | 2994.07i | 0.422029 | + | 0.730975i | ||||
\(257\) | 329.103 | − | 570.023i | 0.0798789 | − | 0.138354i | −0.823319 | − | 0.567579i | \(-0.807880\pi\) |
0.903198 | + | 0.429225i | \(0.141213\pi\) | |||||||
\(258\) | −1776.99 | − | 1025.95i | −0.428801 | − | 0.247568i | ||||
\(259\) | 2559.87 | 0.614141 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10648.7 | −2.52544 | ||||||||
\(262\) | 380.550 | + | 219.711i | 0.0897346 | + | 0.0518083i | ||||
\(263\) | −1623.23 | + | 2811.51i | −0.380580 | + | 0.659184i | −0.991145 | − | 0.132782i | \(-0.957609\pi\) |
0.610565 | + | 0.791966i | \(0.290942\pi\) | |||||||
\(264\) | 1403.40 | + | 2430.76i | 0.327172 | + | 0.566679i | ||||
\(265\) | − | 430.401i | − | 0.0997711i | ||||||
\(266\) | −880.953 | + | 508.618i | −0.203063 | + | 0.117238i | ||||
\(267\) | 3308.42 | − | 1910.11i | 0.758321 | − | 0.437817i | ||||
\(268\) | − | 2849.07i | − | 0.649384i | ||||||
\(269\) | 1292.90 | + | 2239.37i | 0.293047 | + | 0.507572i | 0.974529 | − | 0.224263i | \(-0.0719976\pi\) |
−0.681482 | + | 0.731835i | \(0.738664\pi\) | |||||||
\(270\) | 517.375 | − | 896.119i | 0.116616 | − | 0.201985i | ||||
\(271\) | −856.441 | − | 494.466i | −0.191974 | − | 0.110836i | 0.400932 | − | 0.916108i | \(-0.368686\pi\) |
−0.592907 | + | 0.805271i | \(0.702020\pi\) | |||||||
\(272\) | −508.867 | −0.113436 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4124.74 | 0.909433 | ||||||||
\(275\) | −1484.44 | − | 857.043i | −0.325510 | − | 0.187933i | ||||
\(276\) | 2964.15 | − | 5134.06i | 0.646452 | − | 1.11969i | ||||
\(277\) | 4071.20 | + | 7051.53i | 0.883086 | + | 1.52955i | 0.847892 | + | 0.530169i | \(0.177872\pi\) |
0.0351939 | + | 0.999381i | \(0.488795\pi\) | |||||||
\(278\) | − | 3120.97i | − | 0.673322i | ||||||
\(279\) | −1136.16 | + | 655.961i | −0.243799 | + | 0.140758i | ||||
\(280\) | 1775.17 | − | 1024.89i | 0.378880 | − | 0.218747i | ||||
\(281\) | 1534.21i | 0.325705i | 0.986650 | + | 0.162853i | \(0.0520695\pi\) | ||||
−0.986650 | + | 0.162853i | \(0.947930\pi\) | |||||||
\(282\) | 3166.27 | + | 5484.14i | 0.668612 | + | 1.15807i | ||||
\(283\) | −3482.50 | + | 6031.87i | −0.731495 | + | 1.26699i | 0.224749 | + | 0.974417i | \(0.427844\pi\) |
−0.956244 | + | 0.292570i | \(0.905490\pi\) | |||||||
\(284\) | 1978.20 | + | 1142.12i | 0.413327 | + | 0.238634i | ||||
\(285\) | 741.403 | 0.154095 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4357.96 | 0.896314 | ||||||||
\(288\) | −7852.68 | − | 4533.75i | −1.60668 | − | 0.927616i | ||||
\(289\) | 1464.31 | − | 2536.26i | 0.298048 | − | 0.516234i | ||||
\(290\) | −611.518 | − | 1059.18i | −0.123826 | − | 0.214473i | ||||
\(291\) | 13124.9i | 2.64396i | ||||||||
\(292\) | −1483.48 | + | 856.490i | −0.297309 | + | 0.171652i | ||||
\(293\) | 554.281 | − | 320.015i | 0.110517 | − | 0.0638070i | −0.443723 | − | 0.896164i | \(-0.646342\pi\) |
0.554240 | + | 0.832357i | \(0.313009\pi\) | |||||||
\(294\) | − | 5364.87i | − | 1.06424i | ||||||
\(295\) | −782.887 | − | 1356.00i | −0.154513 | − | 0.267625i | ||||
\(296\) | 997.358 | − | 1727.48i | 0.195846 | − | 0.339214i | ||||
\(297\) | −2459.03 | − | 1419.72i | −0.480428 | − | 0.277375i | ||||
\(298\) | −2737.37 | −0.532120 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5424.85 | 1.04401 | ||||||||
\(301\) | 3561.05 | + | 2055.97i | 0.681912 | + | 0.393702i | ||||
\(302\) | −2181.99 | + | 3779.32i | −0.415760 | + | 0.720118i | ||||
\(303\) | 1460.15 | + | 2529.05i | 0.276843 | + | 0.479506i | ||||
\(304\) | − | 273.813i | − | 0.0516587i | ||||||
\(305\) | −423.503 | + | 244.509i | −0.0795072 | + | 0.0459035i | ||||
\(306\) | −2917.12 | + | 1684.20i | −0.544969 | + | 0.314638i | ||||
\(307\) | − | 100.406i | − | 0.0186660i | −0.999956 | − | 0.00933299i | \(-0.997029\pi\) | ||
0.999956 | − | 0.00933299i | \(-0.00297083\pi\) | |||||||
\(308\) | −1153.35 | − | 1997.67i | −0.213371 | − | 0.369570i | ||||
\(309\) | 1401.32 | − | 2427.16i | 0.257988 | − | 0.446849i | ||||
\(310\) | −130.491 | − | 75.3390i | −0.0239077 | − | 0.0138031i | ||||
\(311\) | 3878.92 | 0.707245 | 0.353623 | − | 0.935388i | \(-0.384950\pi\) | ||||
0.353623 | + | 0.935388i | \(0.384950\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3789.39 | −0.684311 | −0.342155 | − | 0.939643i | \(-0.611157\pi\) | ||||
−0.342155 | + | 0.939643i | \(0.611157\pi\) | |||||||
\(314\) | −4388.19 | − | 2533.52i | −0.788662 | − | 0.455334i | ||||
\(315\) | −2343.51 | + | 4059.08i | −0.419180 | + | 0.726041i | ||||
\(316\) | 1630.82 | + | 2824.66i | 0.290319 | + | 0.502847i | ||||
\(317\) | − | 4406.81i | − | 0.780791i | −0.920647 | − | 0.390396i | \(-0.872338\pi\) | ||
0.920647 | − | 0.390396i | \(-0.127662\pi\) | |||||||
\(318\) | −1419.30 | + | 819.434i | −0.250284 | + | 0.144502i | ||||
\(319\) | −2906.48 | + | 1678.06i | −0.510130 | + | 0.294524i | ||||
\(320\) | − | 715.950i | − | 0.125071i | ||||||
\(321\) | −6229.58 | − | 10790.0i | −1.08318 | − | 1.87613i | ||||
\(322\) | 2604.42 | − | 4510.99i | 0.450741 | − | 0.780706i | ||||
\(323\) | −924.710 | − | 533.882i | −0.159295 | − | 0.0919690i | ||||
\(324\) | 1715.11 | 0.294086 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5124.19 | −0.870559 | ||||||||
\(327\) | 6386.55 | + | 3687.27i | 1.08005 | + | 0.623568i | ||||
\(328\) | 1697.92 | − | 2940.88i | 0.285829 | − | 0.495070i | ||||
\(329\) | −6345.14 | − | 10990.1i | −1.06328 | − | 1.84165i | ||||
\(330\) | − | 737.127i | − | 0.122962i | ||||||
\(331\) | 3577.98 | − | 2065.75i | 0.594149 | − | 0.343032i | −0.172587 | − | 0.984994i | \(-0.555213\pi\) |
0.766736 | + | 0.641962i | \(0.221879\pi\) | |||||||
\(332\) | −6522.44 | + | 3765.73i | −1.07821 | + | 0.622505i | ||||
\(333\) | 4561.10i | 0.750591i | ||||||||
\(334\) | −2441.11 | − | 4228.13i | −0.399916 | − | 0.692674i | ||||
\(335\) | −912.257 | + | 1580.07i | −0.148782 | + | 0.257698i | ||||
\(336\) | 2334.95 | + | 1348.08i | 0.379113 | + | 0.218881i | ||||
\(337\) | 4560.82 | 0.737221 | 0.368611 | − | 0.929584i | \(-0.379834\pi\) | ||||
0.368611 | + | 0.929584i | \(0.379834\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14021.6 | 2.24646 | ||||||||
\(340\) | 764.150 | + | 441.182i | 0.121888 | + | 0.0703720i | ||||
\(341\) | −206.737 | + | 358.078i | −0.0328311 | + | 0.0568652i | ||||
\(342\) | −906.240 | − | 1569.65i | −0.143286 | − | 0.248179i | ||||
\(343\) | 1429.34i | 0.225007i | ||||||||
\(344\) | 2774.86 | − | 1602.07i | 0.434914 | − | 0.251098i | ||||
\(345\) | −3287.79 | + | 1898.21i | −0.513069 | + | 0.296220i | ||||
\(346\) | − | 152.360i | − | 0.0236733i | ||||||
\(347\) | −5034.70 | − | 8720.36i | −0.778896 | − | 1.34909i | −0.932579 | − | 0.360967i | \(-0.882447\pi\) |
0.153683 | − | 0.988120i | \(-0.450887\pi\) | |||||||
\(348\) | 5310.82 | − | 9198.62i | 0.818075 | − | 1.41695i | ||||
\(349\) | −5091.64 | − | 2939.66i | −0.780944 | − | 0.450878i | 0.0558207 | − | 0.998441i | \(-0.482222\pi\) |
−0.836765 | + | 0.547563i | \(0.815556\pi\) | |||||||
\(350\) | 4766.49 | 0.727942 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2857.76 | −0.432725 | ||||||||
\(353\) | −7917.69 | − | 4571.28i | −1.19381 | − | 0.689249i | −0.234644 | − | 0.972081i | \(-0.575393\pi\) |
−0.959169 | + | 0.282833i | \(0.908726\pi\) | |||||||
\(354\) | −2981.05 | + | 5163.33i | −0.447574 | + | 0.775220i | ||||
\(355\) | −731.398 | − | 1266.82i | −0.109348 | − | 0.189397i | ||||
\(356\) | 2446.43i | 0.364215i | ||||||||
\(357\) | 9105.39 | − | 5257.00i | 1.34988 | − | 0.779356i | ||||
\(358\) | 46.9466 | − | 27.1046i | 0.00693074 | − | 0.00400146i | ||||
\(359\) | − | 2754.32i | − | 0.404924i | −0.979290 | − | 0.202462i | \(-0.935106\pi\) | ||
0.979290 | − | 0.202462i | \(-0.0648942\pi\) | |||||||
\(360\) | 1826.12 | + | 3162.94i | 0.267347 | + | 0.463059i | ||||
\(361\) | −3142.23 | + | 5442.50i | −0.458117 | + | 0.793483i | ||||
\(362\) | −1662.50 | − | 959.845i | −0.241379 | − | 0.139360i | ||||
\(363\) | 9536.54 | 1.37889 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1096.97 | 0.157310 | ||||||||
\(366\) | 1612.60 | + | 931.034i | 0.230306 | + | 0.132967i | ||||
\(367\) | −1520.09 | + | 2632.88i | −0.216208 | + | 0.374483i | −0.953646 | − | 0.300932i | \(-0.902702\pi\) |
0.737438 | + | 0.675415i | \(0.236036\pi\) | |||||||
\(368\) | 701.040 | + | 1214.24i | 0.0993049 | + | 0.172001i | ||||
\(369\) | 7764.88i | 1.09546i | ||||||||
\(370\) | −453.672 | + | 261.928i | −0.0637440 | + | 0.0368026i | ||||
\(371\) | 2844.25 | − | 1642.13i | 0.398022 | − | 0.229798i | ||||
\(372\) | − | 1308.59i | − | 0.182385i | ||||||
\(373\) | 2692.36 | + | 4663.31i | 0.373740 | + | 0.647337i | 0.990138 | − | 0.140098i | \(-0.0447418\pi\) |
−0.616397 | + | 0.787435i | \(0.711408\pi\) | |||||||
\(374\) | −530.802 | + | 919.376i | −0.0733880 | + | 0.127112i | ||||
\(375\) | −6356.95 | − | 3670.18i | −0.875390 | − | 0.505407i | ||||
\(376\) | −9888.59 | −1.35629 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 7895.84 | 1.07439 | ||||||||
\(379\) | −2965.50 | − | 1712.13i | −0.401920 | − | 0.232049i | 0.285392 | − | 0.958411i | \(-0.407876\pi\) |
−0.687312 | + | 0.726362i | \(0.741209\pi\) | |||||||
\(380\) | −237.393 | + | 411.177i | −0.0320474 | + | 0.0555077i | ||||
\(381\) | 3756.87 | + | 6507.09i | 0.505171 | + | 0.874983i | ||||
\(382\) | 6684.69i | 0.895336i | ||||||||
\(383\) | 331.675 | − | 191.493i | 0.0442501 | − | 0.0255478i | −0.477712 | − | 0.878517i | \(-0.658534\pi\) |
0.521962 | + | 0.852969i | \(0.325200\pi\) | |||||||
\(384\) | 8906.01 | − | 5141.89i | 1.18355 | − | 0.683323i | ||||
\(385\) | 1477.19i | 0.195544i | ||||||||
\(386\) | 368.776 | + | 638.739i | 0.0486275 | + | 0.0842253i | ||||
\(387\) | −3663.27 | + | 6344.97i | −0.481175 | + | 0.833419i | ||||
\(388\) | −7278.94 | − | 4202.50i | −0.952403 | − | 0.549870i | ||||
\(389\) | −8588.34 | −1.11940 | −0.559699 | − | 0.828696i | \(-0.689083\pi\) | ||||
−0.559699 | + | 0.828696i | \(0.689083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5467.56 | 0.707178 | ||||||||
\(392\) | 7255.15 | + | 4188.76i | 0.934796 | + | 0.539705i | ||||
\(393\) | 1221.93 | − | 2116.45i | 0.156841 | − | 0.271656i | ||||
\(394\) | 3501.29 | + | 6064.41i | 0.447696 | + | 0.775433i | ||||
\(395\) | − | 2088.72i | − | 0.266063i | ||||||
\(396\) | 3559.38 | − | 2055.01i | 0.451681 | − | 0.260778i | ||||
\(397\) | −6269.30 | + | 3619.58i | −0.792562 | + | 0.457586i | −0.840864 | − | 0.541247i | \(-0.817952\pi\) |
0.0483020 | + | 0.998833i | \(0.484619\pi\) | |||||||
\(398\) | 571.904i | 0.0720275i | ||||||||
\(399\) | 2828.71 | + | 4899.46i | 0.354918 | + | 0.614737i | ||||
\(400\) | −641.505 | + | 1111.12i | −0.0801882 | + | 0.138890i | ||||
\(401\) | −3697.60 | − | 2134.81i | −0.460472 | − | 0.265854i | 0.251770 | − | 0.967787i | \(-0.418987\pi\) |
−0.712243 | + | 0.701933i | \(0.752321\pi\) | |||||||
\(402\) | 6947.32 | 0.861942 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1870.12 | −0.230302 | ||||||||
\(405\) | −951.185 | − | 549.167i | −0.116703 | − | 0.0673786i | ||||
\(406\) | 4666.30 | − | 8082.27i | 0.570405 | − | 0.987971i | ||||
\(407\) | 718.751 | + | 1244.91i | 0.0875360 | + | 0.151617i | ||||
\(408\) | − | 8192.78i | − | 0.994125i | ||||||
\(409\) | −11745.5 | + | 6781.26i | −1.41999 | + | 0.819834i | −0.996298 | − | 0.0859711i | \(-0.972601\pi\) |
−0.423696 | + | 0.905805i | \(0.639267\pi\) | |||||||
\(410\) | −772.337 | + | 445.909i | −0.0930317 | + | 0.0537119i | ||||
\(411\) | − | 22939.9i | − | 2.75315i | ||||||
\(412\) | 897.390 | + | 1554.33i | 0.107309 | + | 0.185864i | ||||
\(413\) | 5973.96 | − | 10347.2i | 0.711767 | − | 1.23282i | ||||
\(414\) | 8037.54 | + | 4640.47i | 0.954163 | + | 0.550886i | ||||
\(415\) | 4823.06 | 0.570494 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17357.5 | −2.03837 | ||||||||
\(418\) | −494.701 | − | 285.616i | −0.0578867 | − | 0.0334209i | ||||
\(419\) | 7288.44 | − | 12624.0i | 0.849794 | − | 1.47189i | −0.0315973 | − | 0.999501i | \(-0.510059\pi\) |
0.881392 | − | 0.472386i | \(-0.156607\pi\) | |||||||
\(420\) | −2337.55 | − | 4048.76i | −0.271573 | − | 0.470379i | ||||
\(421\) | − | 15848.4i | − | 1.83469i | −0.398099 | − | 0.917343i | \(-0.630330\pi\) | ||
0.398099 | − | 0.917343i | \(-0.369670\pi\) | |||||||
\(422\) | 2870.42 | − | 1657.24i | 0.331114 | − | 0.191169i | ||||
\(423\) | 19581.8 | − | 11305.6i | 2.25083 | − | 1.29952i | ||||
\(424\) | − | 2559.18i | − | 0.293124i | ||||||
\(425\) | 2501.62 | + | 4332.94i | 0.285521 | + | 0.494537i | ||||
\(426\) | −2784.99 | + | 4823.75i | −0.316745 | + | 0.548618i | ||||
\(427\) | −3231.62 | − | 1865.77i | −0.366250 | − | 0.211455i | ||||
\(428\) | 7978.70 | 0.901087 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −841.474 | −0.0943709 | ||||||||
\(431\) | 9261.90 | + | 5347.36i | 1.03510 | + | 0.597618i | 0.918443 | − | 0.395554i | \(-0.129447\pi\) |
0.116662 | + | 0.993172i | \(0.462781\pi\) | |||||||
\(432\) | −1062.67 | + | 1840.61i | −0.118352 | + | 0.204991i | ||||
\(433\) | −8039.50 | − | 13924.8i | −0.892272 | − | 1.54546i | −0.837145 | − | 0.546981i | \(-0.815777\pi\) |
−0.0551273 | − | 0.998479i | \(-0.517556\pi\) | |||||||
\(434\) | − | 1149.78i | − | 0.127168i | ||||||
\(435\) | −5890.69 | + | 3400.99i | −0.649280 | + | 0.374862i | ||||
\(436\) | −4089.87 | + | 2361.29i | −0.449241 | + | 0.259370i | ||||
\(437\) | 2942.01i | 0.322049i | ||||||||
\(438\) | −2088.50 | − | 3617.40i | −0.227837 | − | 0.394625i | ||||
\(439\) | 3017.90 | − | 5227.16i | 0.328101 | − | 0.568288i | −0.654034 | − | 0.756465i | \(-0.726925\pi\) |
0.982135 | + | 0.188177i | \(0.0602579\pi\) | |||||||
\(440\) | 996.849 | + | 575.531i | 0.108007 | + | 0.0623577i | ||||
\(441\) | −19156.0 | −2.06845 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10201.3 | 1.09409 | 0.547043 | − | 0.837105i | \(-0.315753\pi\) | ||||
0.547043 | + | 0.837105i | \(0.315753\pi\) | |||||||
\(444\) | −3939.98 | − | 2274.75i | −0.421134 | − | 0.243142i | ||||
\(445\) | 783.332 | − | 1356.77i | 0.0834461 | − | 0.144533i | ||||
\(446\) | 4627.21 | + | 8014.56i | 0.491266 | + | 0.850897i | ||||
\(447\) | 15224.0i | 1.61090i | ||||||||
\(448\) | 4731.26 | − | 2731.59i | 0.498953 | − | 0.288071i | ||||
\(449\) | −5042.47 | + | 2911.27i | −0.529997 | + | 0.305994i | −0.741015 | − | 0.671488i | \(-0.765655\pi\) |
0.211018 | + | 0.977482i | \(0.432322\pi\) | |||||||
\(450\) | 8492.78i | 0.889675i | ||||||||
\(451\) | 1223.61 | + | 2119.36i | 0.127755 | + | 0.221279i | ||||
\(452\) | −4489.64 | + | 7776.28i | −0.467201 | + | 0.809216i | ||||
\(453\) | 21018.9 | + | 12135.3i | 2.18003 | + | 1.25864i | ||||
\(454\) | −1398.62 | −0.144583 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4408.40 | 0.452724 | ||||||||
\(457\) | 4002.42 | + | 2310.80i | 0.409684 | + | 0.236531i | 0.690654 | − | 0.723186i | \(-0.257323\pi\) |
−0.280970 | + | 0.959717i | \(0.590656\pi\) | |||||||
\(458\) | 490.106 | − | 848.889i | 0.0500026 | − | 0.0866070i | ||||
\(459\) | 4144.02 | + | 7177.65i | 0.421408 | + | 0.729900i | ||||
\(460\) | − | 2431.18i | − | 0.246422i | ||||||
\(461\) | −4440.78 | + | 2563.88i | −0.448650 | + | 0.259028i | −0.707260 | − | 0.706954i | \(-0.750069\pi\) |
0.258610 | + | 0.965982i | \(0.416736\pi\) | |||||||
\(462\) | 4871.20 | − | 2812.39i | 0.490539 | − | 0.283213i | ||||
\(463\) | 6486.27i | 0.651064i | 0.945531 | + | 0.325532i | \(0.105543\pi\) | ||||
−0.945531 | + | 0.325532i | \(0.894457\pi\) | |||||||
\(464\) | 1256.04 | + | 2175.53i | 0.125669 | + | 0.217665i | ||||
\(465\) | −419.002 | + | 725.733i | −0.0417866 | + | 0.0723764i | ||||
\(466\) | 3115.43 | + | 1798.69i | 0.309698 | + | 0.178804i | ||||
\(467\) | −12978.0 | −1.28598 | −0.642990 | − | 0.765875i | \(-0.722306\pi\) | ||||
−0.642990 | + | 0.765875i | \(0.722306\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13922.3 | −1.37073 | ||||||||
\(470\) | 2249.03 | + | 1298.48i | 0.220723 | + | 0.127435i | ||||
\(471\) | −14090.3 | + | 24405.1i | −1.37844 | + | 2.38754i | ||||
\(472\) | −4655.07 | − | 8062.81i | −0.453955 | − | 0.786273i | ||||
\(473\) | 2309.08i | 0.224464i | ||||||||
\(474\) | −6887.79 | + | 3976.67i | −0.667440 | + | 0.385347i | ||||
\(475\) | −2331.48 | + | 1346.08i | −0.225212 | + | 0.130026i | ||||
\(476\) | 6733.04i | 0.648337i | ||||||||
\(477\) | 2925.89 | + | 5067.80i | 0.280854 | + | 0.486454i | ||||
\(478\) | −425.228 | + | 736.516i | −0.0406893 | + | 0.0704759i | ||||
\(479\) | 5030.71 | + | 2904.48i | 0.479873 | + | 0.277055i | 0.720363 | − | 0.693597i | \(-0.243975\pi\) |
−0.240491 | + | 0.970651i | \(0.577308\pi\) | |||||||
\(480\) | −5791.95 | −0.550761 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −8473.14 | −0.800707 | ||||||||
\(483\) | −25088.1 | − | 14484.6i | −2.36345 | − | 1.36454i | ||||
\(484\) | −3053.54 | + | 5288.89i | −0.286772 | + | 0.496703i | ||||
\(485\) | 2691.23 | + | 4661.35i | 0.251964 | + | 0.436414i | ||||
\(486\) | − | 3662.20i | − | 0.341812i | ||||||
\(487\) | 4665.40 | − | 2693.57i | 0.434106 | − | 0.250631i | −0.266989 | − | 0.963700i | \(-0.586029\pi\) |
0.701094 | + | 0.713069i | \(0.252695\pi\) | |||||||
\(488\) | −2518.16 | + | 1453.86i | −0.233589 | + | 0.134863i | ||||
\(489\) | 28498.4i | 2.63547i | ||||||||
\(490\) | −1100.06 | − | 1905.36i | −0.101419 | − | 0.175664i | ||||
\(491\) | 7629.53 | − | 13214.7i | 0.701255 | − | 1.21461i | −0.266772 | − | 0.963760i | \(-0.585957\pi\) |
0.968026 | − | 0.250849i | \(-0.0807097\pi\) | |||||||
\(492\) | −6707.48 | − | 3872.57i | −0.614628 | − | 0.354855i | ||||
\(493\) | 9796.16 | 0.894922 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2632.01 | −0.238990 | ||||||||
\(496\) | 268.025 | + | 154.744i | 0.0242635 | + | 0.0140085i | ||||
\(497\) | 5581.07 | − | 9666.69i | 0.503712 | − | 0.872456i | ||||
\(498\) | −9182.55 | − | 15904.6i | −0.826264 | − | 1.43113i | ||||
\(499\) | − | 1856.04i | − | 0.166509i | −0.996528 | − | 0.0832544i | \(-0.973469\pi\) | ||
0.996528 | − | 0.0832544i | \(-0.0265314\pi\) | |||||||
\(500\) | 4070.91 | − | 2350.34i | 0.364114 | − | 0.210221i | ||||
\(501\) | −23515.0 | + | 13576.4i | −2.09695 | + | 1.21067i | ||||
\(502\) | 8153.20i | 0.724891i | ||||||||
\(503\) | −524.732 | − | 908.862i | −0.0465142 | − | 0.0805649i | 0.841831 | − | 0.539741i | \(-0.181478\pi\) |
−0.888345 | + | 0.459176i | \(0.848145\pi\) | |||||||
\(504\) | −13934.6 | + | 24135.4i | −1.23154 | + | 2.13308i | ||||
\(505\) | 1037.16 | + | 598.803i | 0.0913919 | + | 0.0527651i | ||||
\(506\) | 2925.04 | 0.256984 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4811.71 | −0.420246 | ||||||||
\(509\) | −477.272 | − | 275.553i | −0.0415613 | − | 0.0239954i | 0.479075 | − | 0.877774i | \(-0.340972\pi\) |
−0.520637 | + | 0.853778i | \(0.674305\pi\) | |||||||
\(510\) | −1075.80 | + | 1863.34i | −0.0934063 | + | 0.161784i | ||||
\(511\) | 4185.32 | + | 7249.19i | 0.362324 | + | 0.627564i | ||||
\(512\) | 4074.36i | 0.351686i | ||||||||
\(513\) | −3862.18 | + | 2229.83i | −0.332396 | + | 0.191909i | ||||
\(514\) | −890.121 | + | 513.911i | −0.0763843 | + | 0.0441005i | ||||
\(515\) | − | 1149.36i | − | 0.0983431i | ||||||
\(516\) | −3653.96 | − | 6328.84i | −0.311738 | − | 0.539945i | ||||
\(517\) | 3563.13 | − | 6171.52i | 0.303107 | − | 0.524997i | ||||
\(518\) | −3461.83 | − | 1998.69i | −0.293637 | − | 0.169531i | ||||
\(519\) | −847.361 | −0.0716667 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8995.30 | −0.756413 | −0.378206 | − | 0.925721i | \(-0.623459\pi\) | ||||
−0.378206 | + | 0.925721i | \(0.623459\pi\) | |||||||
\(522\) | 14400.7 | + | 8314.27i | 1.20748 | + | 0.697137i | ||||
\(523\) | −1331.96 | + | 2307.02i | −0.111362 | + | 0.192885i | −0.916320 | − | 0.400448i | \(-0.868855\pi\) |
0.804958 | + | 0.593332i | \(0.202188\pi\) | |||||||
\(524\) | 782.512 | + | 1355.35i | 0.0652370 | + | 0.112994i | ||||
\(525\) | − | 26509.1i | − | 2.20372i | ||||||
\(526\) | 4390.32 | − | 2534.76i | 0.363930 | − | 0.210115i | ||||
\(527\) | 1045.19 | − | 603.443i | 0.0863935 | − | 0.0498793i | ||||
\(528\) | 1514.04i | 0.124792i | ||||||||
\(529\) | −1448.89 | − | 2509.54i | −0.119083 | − | 0.206258i | ||||
\(530\) | −336.047 | + | 582.051i | −0.0275414 | + | 0.0477032i | ||||
\(531\) | 18436.3 | + | 10644.2i | 1.50672 | + | 0.869906i | ||||
\(532\) | −3622.94 | −0.295253 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −5965.49 | −0.483431 | ||||||||
\(535\) | −4424.93 | − | 2554.73i | −0.357582 | − | 0.206450i | ||||
\(536\) | −5424.30 | + | 9395.16i | −0.437116 | + | 0.757107i | ||||
\(537\) | −150.744 | − | 261.096i | −0.0121137 | − | 0.0209816i | ||||
\(538\) | − | 4037.86i | − | 0.323577i | ||||||
\(539\) | −5228.46 | + | 3018.65i | −0.417821 | + | 0.241229i | ||||
\(540\) | 3191.57 | − | 1842.66i | 0.254340 | − | 0.146843i | ||||
\(541\) | − | 6169.23i | − | 0.490270i | −0.969489 | − | 0.245135i | \(-0.921168\pi\) | ||
0.969489 | − | 0.245135i | \(-0.0788322\pi\) | |||||||
\(542\) | 772.135 | + | 1337.38i | 0.0611920 | + | 0.105988i | ||||
\(543\) | −5338.23 | + | 9246.08i | −0.421888 | + | 0.730732i | ||||
\(544\) | 7223.97 | + | 4170.76i | 0.569348 | + | 0.328713i | ||||
\(545\) | 3024.28 | 0.237699 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5140.42 | 0.401807 | 0.200904 | − | 0.979611i | \(-0.435612\pi\) | ||||
0.200904 | + | 0.979611i | \(0.435612\pi\) | |||||||
\(548\) | 12722.3 | + | 7345.24i | 0.991735 | + | 0.572578i | ||||
\(549\) | 3324.38 | − | 5757.99i | 0.258435 | − | 0.447623i | ||||
\(550\) | 1338.32 | + | 2318.03i | 0.103756 | + | 0.179711i | ||||
\(551\) | 5271.15i | 0.407547i | ||||||||
\(552\) | −19549.3 | + | 11286.8i | −1.50738 | + | 0.870285i | ||||
\(553\) | 13803.0 | − | 7969.16i | 1.06142 | − | 0.612809i | ||||
\(554\) | − | 12714.8i | − | 0.975090i | ||||||
\(555\) | 1456.72 | + | 2523.12i | 0.111413 | + | 0.192974i | ||||
\(556\) | 5557.76 | − | 9626.32i | 0.423923 | − | 0.734257i | ||||
\(557\) | −2406.30 | − | 1389.28i | −0.183049 | − | 0.105683i | 0.405675 | − | 0.914017i | \(-0.367036\pi\) |
−0.588724 | + | 0.808334i | \(0.700370\pi\) | |||||||
\(558\) | 2048.64 | 0.155422 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1105.69 | 0.0834356 | ||||||||
\(561\) | 5113.16 | + | 2952.08i | 0.384809 | + | 0.222170i | ||||
\(562\) | 1197.87 | − | 2074.78i | 0.0899097 | − | 0.155728i | ||||
\(563\) | 2453.07 | + | 4248.85i | 0.183632 | + | 0.318059i | 0.943115 | − | 0.332468i | \(-0.107881\pi\) |
−0.759483 | + | 0.650527i | \(0.774548\pi\) | |||||||
\(564\) | 22553.7i | 1.68383i | ||||||||
\(565\) | 4979.84 | − | 2875.11i | 0.370802 | − | 0.214083i | ||||
\(566\) | 9419.08 | − | 5438.11i | 0.699494 | − | 0.403853i | ||||
\(567\) | − | 8381.04i | − | 0.620759i | ||||||
\(568\) | −4348.91 | − | 7532.54i | −0.321261 | − | 0.556440i | ||||
\(569\) | −4681.58 | + | 8108.73i | −0.344924 | + | 0.597426i | −0.985340 | − | 0.170602i | \(-0.945429\pi\) |
0.640416 | + | 0.768028i | \(0.278762\pi\) | |||||||
\(570\) | −1002.63 | − | 578.870i | −0.0736766 | − | 0.0425372i | ||||
\(571\) | −7199.32 | −0.527640 | −0.263820 | − | 0.964572i | \(-0.584982\pi\) | ||||
−0.263820 | + | 0.964572i | \(0.584982\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37177.3 | 2.71048 | ||||||||
\(574\) | −5893.46 | − | 3402.59i | −0.428551 | − | 0.247424i | ||||
\(575\) | 6892.72 | − | 11938.5i | 0.499906 | − | 0.865863i | ||||
\(576\) | 4867.07 | + | 8430.01i | 0.352074 | + | 0.609810i | ||||
\(577\) | 11449.6i | 0.826086i | 0.910711 | + | 0.413043i | \(0.135534\pi\) | ||||
−0.910711 | + | 0.413043i | \(0.864466\pi\) | |||||||
\(578\) | −3960.50 | + | 2286.60i | −0.285009 | + | 0.164550i | ||||
\(579\) | 3552.38 | − | 2050.97i | 0.254978 | − | 0.147211i | ||||
\(580\) | − | 4355.91i | − | 0.311843i | ||||||
\(581\) | 18401.6 | + | 31872.6i | 1.31399 | + | 2.27590i | ||||
\(582\) | 10247.6 | − | 17749.3i | 0.729855 | − | 1.26415i | ||||
\(583\) | 1597.20 | + | 922.142i | 0.113463 | + | 0.0655081i | ||||
\(584\) | 6522.62 | 0.462171 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −999.439 | −0.0704547 | ||||||||
\(587\) | −4710.65 | − | 2719.70i | −0.331226 | − | 0.191233i | 0.325160 | − | 0.945659i | \(-0.394582\pi\) |
−0.656385 | + | 0.754426i | \(0.727915\pi\) | |||||||
\(588\) | 9553.63 | − | 16547.4i | 0.670042 | − | 1.16055i | ||||
\(589\) | 324.703 | + | 562.402i | 0.0227150 | + | 0.0393436i | ||||
\(590\) | 2445.04i | 0.170611i | ||||||||
\(591\) | 33727.5 | − | 19472.6i | 2.34749 | − | 1.35532i | ||||
\(592\) | 931.831 | − | 537.993i | 0.0646926 | − | 0.0373503i | ||||
\(593\) | − | 28405.8i | − | 1.96709i | −0.180651 | − | 0.983547i | \(-0.557820\pi\) | ||
0.180651 | − | 0.983547i | \(-0.442180\pi\) | |||||||
\(594\) | 2216.97 | + | 3839.90i | 0.153137 | + | 0.265241i | ||||
\(595\) | 2155.88 | − | 3734.10i | 0.148542 | − | 0.257282i | ||||
\(596\) | −8443.14 | − | 4874.65i | −0.580276 | − | 0.335022i | ||||
\(597\) | 3180.67 | 0.218051 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10482.3 | −0.715020 | −0.357510 | − | 0.933909i | \(-0.616374\pi\) | ||||
−0.357510 | + | 0.933909i | \(0.616374\pi\) | |||||||
\(600\) | −17889.1 | − | 10328.3i | −1.21720 | − | 0.702750i | ||||
\(601\) | −1599.77 | + | 2770.88i | −0.108579 | + | 0.188064i | −0.915195 | − | 0.403012i | \(-0.867963\pi\) |
0.806616 | + | 0.591076i | \(0.201297\pi\) | |||||||
\(602\) | −3210.51 | − | 5560.77i | −0.217360 | − | 0.376479i | ||||
\(603\) | − | 24806.3i | − | 1.67527i | ||||||
\(604\) | −13460.3 | + | 7771.28i | −0.906772 | + | 0.523525i | ||||
\(605\) | 3386.95 | − | 1955.45i | 0.227602 | − | 0.131406i | ||||
\(606\) | − | 4560.20i | − | 0.305686i | ||||||
\(607\) | −5671.40 | − | 9823.15i | −0.379234 | − | 0.656853i | 0.611717 | − | 0.791077i | \(-0.290479\pi\) |
−0.990951 | + | 0.134224i | \(0.957146\pi\) | |||||||
\(608\) | −2244.22 | + | 3887.10i | −0.149696 | + | 0.259281i | ||||
\(609\) | −44950.0 | − | 25951.9i | −2.99091 | − | 1.72680i | ||||
\(610\) | 763.629 | 0.0506859 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −11996.7 | −0.792384 | ||||||||
\(613\) | 12458.1 | + | 7192.70i | 0.820846 | + | 0.473916i | 0.850708 | − | 0.525638i | \(-0.176174\pi\) |
−0.0298622 | + | 0.999554i | \(0.509507\pi\) | |||||||
\(614\) | −78.3944 | + | 135.783i | −0.00515267 | + | 0.00892469i | ||||
\(615\) | 2479.95 | + | 4295.39i | 0.162603 | + | 0.281637i | ||||
\(616\) | 8783.39i | 0.574502i | ||||||||
\(617\) | −19101.7 | + | 11028.4i | −1.24636 | + | 0.719588i | −0.970382 | − | 0.241575i | \(-0.922336\pi\) |
−0.275981 | + | 0.961163i | \(0.589003\pi\) | |||||||
\(618\) | −3790.14 | + | 2188.24i | −0.246702 | + | 0.142433i | ||||
\(619\) | 13621.4i | 0.884477i | 0.896898 | + | 0.442238i | \(0.145815\pi\) | ||||
−0.896898 | + | 0.442238i | \(0.854185\pi\) | |||||||
\(620\) | −268.324 | − | 464.751i | −0.0173809 | − | 0.0301046i | ||||
\(621\) | 11418.0 | − | 19776.6i | 0.737824 | − | 1.27795i | ||||
\(622\) | −5245.63 | − | 3028.57i | −0.338152 | − | 0.195232i | ||||
\(623\) | 11954.7 | 0.768789 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11029.2 | 0.705866 | ||||||||
\(626\) | 5124.57 | + | 2958.67i | 0.327187 | + | 0.188901i | ||||
\(627\) | −1588.47 | + | 2751.31i | −0.101176 | + | 0.175242i | ||||
\(628\) | −9023.27 | − | 15628.8i | −0.573356 | − | 0.993082i | ||||
\(629\) | − | 4195.92i | − | 0.265982i | ||||||
\(630\) | 6338.46 | − | 3659.51i | 0.400842 | − | 0.231426i | ||||
\(631\) | −16227.1 | + | 9368.74i | −1.02376 | + | 0.591068i | −0.915191 | − | 0.403021i | \(-0.867960\pi\) |
−0.108569 | + | 0.994089i | \(0.534627\pi\) | |||||||
\(632\) | − | 12419.6i | − | 0.781683i | ||||||
\(633\) | −9216.83 | − | 15964.0i | −0.578730 | − | 1.00239i | ||||
\(634\) | −3440.73 | + | 5959.52i | −0.215534 | + | 0.373317i | ||||
\(635\) | 2668.54 | + | 1540.68i | 0.166768 | + | 0.0962836i | ||||
\(636\) | −5836.91 | −0.363913 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5240.75 | 0.325209 | ||||||||
\(639\) | 17223.8 | + | 9944.18i | 1.06630 | + | 0.615627i | ||||
\(640\) | 2108.67 | − | 3652.33i | 0.130239 | − | 0.225580i | ||||
\(641\) | 14899.4 | + | 25806.5i | 0.918081 | + | 1.59016i | 0.802327 | + | 0.596884i | \(0.203595\pi\) |
0.115753 | + | 0.993278i | \(0.463072\pi\) | |||||||
\(642\) | 19455.6i | 1.19603i | ||||||||
\(643\) | 19904.3 | − | 11491.8i | 1.22076 | − | 0.704807i | 0.255681 | − | 0.966761i | \(-0.417700\pi\) |
0.965080 | + | 0.261955i | \(0.0843671\pi\) | |||||||
\(644\) | 16066.1 | − | 9275.77i | 0.983064 | − | 0.567573i | ||||
\(645\) | 4679.90i | 0.285692i | ||||||||
\(646\) | 833.684 | + | 1443.98i | 0.0507753 | + | 0.0879455i | ||||
\(647\) | −12452.7 | + | 21568.7i | −0.756672 | + | 1.31059i | 0.187866 | + | 0.982195i | \(0.439843\pi\) |
−0.944539 | + | 0.328400i | \(0.893491\pi\) | |||||||
\(648\) | −5655.77 | − | 3265.36i | −0.342870 | − | 0.197956i | ||||
\(649\) | 6709.39 | 0.405804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6394.54 | −0.384980 | ||||||||
\(652\) | −15805.0 | − | 9125.03i | −0.949344 | − | 0.548104i | ||||
\(653\) | −5038.92 | + | 8727.67i | −0.301973 | + | 0.523033i | −0.976583 | − | 0.215142i | \(-0.930979\pi\) |
0.674610 | + | 0.738175i | \(0.264312\pi\) | |||||||
\(654\) | −5757.87 | − | 9972.93i | −0.344267 | − | 0.596288i | ||||
\(655\) | − | 1002.22i | − | 0.0597864i | ||||||
\(656\) | 1586.36 | − | 915.886i | 0.0944162 | − | 0.0545112i | ||||
\(657\) | −12916.4 | + | 7457.28i | −0.766996 | + | 0.442825i | ||||
\(658\) | 19816.5i | 1.17406i | ||||||||
\(659\) | −6167.30 | − | 10682.1i | −0.364558 | − | 0.631433i | 0.624147 | − | 0.781307i | \(-0.285447\pi\) |
−0.988705 | + | 0.149874i | \(0.952113\pi\) | |||||||
\(660\) | 1312.66 | − | 2273.59i | 0.0774169 | − | 0.134090i | ||||
\(661\) | 11041.1 | + | 6374.56i | 0.649694 | + | 0.375101i | 0.788339 | − | 0.615241i | \(-0.210941\pi\) |
−0.138645 | + | 0.990342i | \(0.544275\pi\) | |||||||
\(662\) | −6451.54 | −0.378771 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28678.1 | 1.67609 | ||||||||
\(665\) | 2009.26 | + | 1160.04i | 0.117166 | + | 0.0676460i | ||||
\(666\) | 3561.20 | − | 6168.18i | 0.207198 | − | 0.358877i | ||||
\(667\) | −13495.7 | − | 23375.2i | −0.783440 | − | 1.35696i | ||||
\(668\) | − | 17388.3i | − | 1.00715i | ||||||
\(669\) | 44573.4 | − | 25734.5i | 2.57594 | − | 1.48722i | ||||
\(670\) | 2467.37 | − | 1424.54i | 0.142273 | − | 0.0821413i | ||||
\(671\) | − | 2095.46i | − | 0.120558i | ||||||
\(672\) | −22098.3 | − | 38275.3i | −1.26854 | − | 2.19718i | ||||
\(673\) | −6809.12 | + | 11793.7i | −0.390004 | + | 0.675506i | −0.992450 | − | 0.122654i | \(-0.960860\pi\) |
0.602446 | + | 0.798160i | \(0.294193\pi\) | |||||||
\(674\) | −6167.80 | − | 3560.98i | −0.352485 | − | 0.203507i | ||||
\(675\) | 20896.7 | 1.19158 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9655.67 | 0.548150 | 0.274075 | − | 0.961708i | \(-0.411628\pi\) | ||||
0.274075 | + | 0.961708i | \(0.411628\pi\) | |||||||
\(678\) | −18962.0 | − | 10947.7i | −1.07409 | − | 0.620126i | ||||
\(679\) | −20535.9 | + | 35569.3i | −1.16067 | + | 2.01034i | ||||
\(680\) | −1679.92 | − | 2909.70i | −0.0947381 | − | 0.164091i | ||||
\(681\) | 7778.51i | 0.437699i | ||||||||
\(682\) | 559.158 | − | 322.830i | 0.0313948 | − | 0.0181258i | ||||
\(683\) | 14130.7 | − | 8158.38i | 0.791650 | − | 0.457060i | −0.0488929 | − | 0.998804i | \(-0.515569\pi\) |
0.840543 | + | 0.541744i | \(0.182236\pi\) | |||||||
\(684\) | − | 6455.25i | − | 0.360852i | ||||||
\(685\) | −4703.80 | − | 8147.23i | −0.262369 | − | 0.454437i | ||||
\(686\) | 1116.00 | − | 1932.97i | 0.0621123 | − | 0.107582i | ||||
\(687\) | −4721.14 | − | 2725.75i | −0.262188 | − | 0.151374i | ||||
\(688\) | 1728.37 | 0.0957753 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 5928.30 | 0.327082 | ||||||||
\(691\) | 2035.89 | + | 1175.42i | 0.112082 | + | 0.0647106i | 0.554993 | − | 0.831855i | \(-0.312721\pi\) |
−0.442911 | + | 0.896566i | \(0.646054\pi\) | |||||||
\(692\) | 271.320 | − | 469.940i | 0.0149047 | − | 0.0258157i | ||||
\(693\) | −10042.0 | − | 17393.3i | −0.550454 | − | 0.953414i | ||||
\(694\) | 15723.9i | 0.860045i | ||||||||
\(695\) | −6164.58 | + | 3559.12i | −0.336455 | + | 0.194252i | ||||
\(696\) | −35026.2 | + | 20222.4i | −1.90756 | + | 1.10133i | ||||
\(697\) | − | 7143.20i | − | 0.388189i | ||||||
\(698\) | 4590.44 | + | 7950.87i | 0.248926 | + | 0.431153i | ||||
\(699\) | 10003.5 | − | 17326.6i | 0.541299 | − | 0.937558i | ||||
\(700\) | 14701.7 | + | 8488.05i | 0.793819 | + | 0.458312i | ||||
\(701\) | 8076.90 | 0.435179 | 0.217589 | − | 0.976040i | \(-0.430181\pi\) | ||||
0.217589 | + | 0.976040i | \(0.430181\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2257.76 | 0.121128 | ||||||||
\(704\) | 2656.85 | + | 1533.93i | 0.142236 | + | 0.0821197i | ||||
\(705\) | 7221.55 | − | 12508.1i | 0.385786 | − | 0.668202i | ||||
\(706\) | 7138.30 | + | 12363.9i | 0.380529 | + | 0.659095i | ||||
\(707\) | 9138.55i | 0.486125i | ||||||||
\(708\) | −18389.5 | + | 10617.2i | −0.976156 | + | 0.563584i | ||||
\(709\) | −11799.5 | + | 6812.44i | −0.625021 | + | 0.360856i | −0.778821 | − | 0.627246i | \(-0.784182\pi\) |
0.153801 | + | 0.988102i | \(0.450849\pi\) | |||||||
\(710\) | 2284.23i | 0.120741i | ||||||||
\(711\) | 14199.2 | + | 24593.8i | 0.748962 | + | 1.29724i | ||||
\(712\) | 4657.71 | − | 8067.40i | 0.245162 | − | 0.424633i | ||||
\(713\) | −2879.82 | − | 1662.67i | −0.151263 | − | 0.0873315i | ||||
\(714\) | −16418.2 | −0.860553 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 193.069 | 0.0100773 | ||||||||
\(717\) | 4096.18 | + | 2364.93i | 0.213354 | + | 0.123180i | ||||
\(718\) | −2150.51 | + | 3724.79i | −0.111778 | + | 0.193605i | ||||
\(719\) | 8117.89 | + | 14060.6i | 0.421066 | + | 0.729307i | 0.996044 | − | 0.0888616i | \(-0.0283229\pi\) |
−0.574978 | + | 0.818169i | \(0.694990\pi\) | |||||||
\(720\) | 1970.09i | 0.101973i | ||||||||
\(721\) | 7595.36 | − | 4385.19i | 0.392325 | − | 0.226509i | ||||
\(722\) | 8498.75 | − | 4906.75i | 0.438076 | − | 0.252923i | ||||
\(723\) | 47123.8i | 2.42400i | ||||||||
\(724\) | −3418.54 | − | 5921.08i | −0.175482 | − | 0.303944i | ||||
\(725\) | 12349.6 | − | 21390.1i | 0.632623 | − | 1.09574i | ||||
\(726\) | −12896.7 | − | 7445.91i | −0.659285 | − | 0.380638i | ||||
\(727\) | −24181.2 | −1.23361 | −0.616803 | − | 0.787118i | \(-0.711572\pi\) | ||||
−0.616803 | + | 0.787118i | \(0.711572\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28693.9 | −1.45780 | ||||||||
\(730\) | −1483.48 | − | 856.490i | −0.0752139 | − | 0.0434248i | ||||
\(731\) | 3369.98 | − | 5836.98i | 0.170511 | − | 0.295333i | ||||
\(732\) | 3315.93 | + | 5743.36i | 0.167432 | + | 0.290001i | ||||
\(733\) | − | 3053.70i | − | 0.153876i | −0.997036 | − | 0.0769379i | \(-0.975486\pi\) | ||
0.997036 | − | 0.0769379i | \(-0.0245143\pi\) | |||||||
\(734\) | 4111.38 | − | 2373.71i | 0.206749 | − | 0.119367i | ||||
\(735\) | −10596.7 | + | 6118.03i | −0.531791 | + | 0.307030i | ||||
\(736\) | − | 22983.4i | − | 1.15106i | ||||||
\(737\) | −3909.05 | − | 6770.67i | −0.195375 | − | 0.338400i | ||||
\(738\) | 6062.63 | − | 10500.8i | 0.302396 | − | 0.523766i | ||||
\(739\) | 6957.32 | + | 4016.81i | 0.346318 | + | 0.199947i | 0.663062 | − | 0.748564i | \(-0.269256\pi\) |
−0.316744 | + | 0.948511i | \(0.602590\pi\) | |||||||
\(740\) | −1865.74 | −0.0926836 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5128.54 | −0.253739 | ||||||||
\(743\) | −13977.3 | − | 8069.81i | −0.690146 | − | 0.398456i | 0.113521 | − | 0.993536i | \(-0.463787\pi\) |
−0.803667 | + | 0.595080i | \(0.797120\pi\) | |||||||
\(744\) | −2491.40 | + | 4315.22i | −0.122767 | + | 0.212639i | ||||
\(745\) | 3121.67 | + | 5406.89i | 0.153515 | + | 0.265897i | ||||
\(746\) | − | 8408.53i | − | 0.412678i | ||||||
\(747\) | −56789.6 | + | 32787.5i | −2.78156 | + | 1.60593i | ||||
\(748\) | −3274.41 | + | 1890.48i | −0.160059 | + | 0.0924102i | ||||
\(749\) | − | 38988.7i | − | 1.90202i | ||||||
\(750\) | 5731.19 | + | 9926.71i | 0.279031 | + | 0.483296i | ||||
\(751\) | −9245.56 | + | 16013.8i | −0.449235 | + | 0.778097i | −0.998336 | − | 0.0576584i | \(-0.981637\pi\) |
0.549102 | + | 0.835755i | \(0.314970\pi\) | |||||||
\(752\) | −4619.45 | − | 2667.04i | −0.224008 | − | 0.129331i | ||||
\(753\) | 45344.5 | 2.19448 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9953.28 | 0.479784 | ||||||||
\(756\) | 24353.9 | + | 14060.7i | 1.17162 | + | 0.676434i | ||||
\(757\) | −80.3149 | + | 139.109i | −0.00385613 | + | 0.00667902i | −0.867947 | − | 0.496657i | \(-0.834561\pi\) |
0.864091 | + | 0.503336i | \(0.167894\pi\) | |||||||
\(758\) | 2673.59 | + | 4630.79i | 0.128112 | + | 0.221897i | ||||
\(759\) | − | 16267.7i | − | 0.777973i | ||||||
\(760\) | 1565.66 | − | 903.936i | 0.0747271 | − | 0.0431437i | ||||
\(761\) | 23208.7 | − | 13399.5i | 1.10554 | − | 0.638282i | 0.167867 | − | 0.985810i | \(-0.446312\pi\) |
0.937670 | + | 0.347528i | \(0.112979\pi\) | |||||||
\(762\) | − | 11733.1i | − | 0.557803i | ||||||
\(763\) | 11538.7 | + | 19985.6i | 0.547481 | + | 0.948264i | ||||
\(764\) | −11903.9 | + | 20618.2i | −0.563703 | + | 0.976363i | ||||
\(765\) | 6653.30 | + | 3841.28i | 0.314445 | + | 0.181545i | ||||
\(766\) | −598.052 | −0.0282095 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −30025.1 | −1.41073 | ||||||||
\(769\) | −4456.41 | − | 2572.91i | −0.208976 | − | 0.120652i | 0.391860 | − | 0.920025i | \(-0.371832\pi\) |
−0.600835 | + | 0.799373i | \(0.705165\pi\) | |||||||
\(770\) | 1153.35 | − | 1997.67i | 0.0539792 | − | 0.0934947i | ||||
\(771\) | 2858.15 | + | 4950.45i | 0.133507 | + | 0.231240i | ||||
\(772\) | 2626.83i | 0.122463i | ||||||||
\(773\) | −11094.3 | + | 6405.28i | −0.516214 | + | 0.298036i | −0.735384 | − | 0.677650i | \(-0.762998\pi\) |
0.219170 | + | 0.975687i | \(0.429665\pi\) | |||||||
\(774\) | 9908.01 | − | 5720.39i | 0.460124 | − | 0.265653i | ||||
\(775\) | − | 3042.94i | − | 0.141039i | ||||||
\(776\) | 16002.1 | + | 27716.5i | 0.740262 | + | 1.28217i | ||||
\(777\) | −11115.8 | + | 19253.1i | −0.513227 | + | 0.888934i | ||||
\(778\) | 11614.4 | + | 6705.57i | 0.535214 | + | 0.309006i | ||||
\(779\) | 3843.64 | 0.176781 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6268.13 | 0.287185 | ||||||||
\(782\) | −7394.03 | − | 4268.94i | −0.338120 | − | 0.195214i | ||||
\(783\) | 20457.5 | − | 35433.4i | 0.933705 | − | 1.61722i | ||||
\(784\) | 2259.49 | + | 3913.55i | 0.102929 | + | 0.178278i | ||||
\(785\) | 11556.8i | 0.525452i | ||||||||
\(786\) | −3304.95 | + | 1908.11i | −0.149979 | + | 0.0865905i | ||||
\(787\) | 24311.9 | − | 14036.5i | 1.10118 | − | 0.635764i | 0.164646 | − | 0.986353i | \(-0.447352\pi\) |
0.936530 | + | 0.350588i | \(0.114018\pi\) | |||||||
\(788\) | 24940.0i | 1.12748i | ||||||||
\(789\) | −14097.2 | − | 24417.0i | −0.636087 | − | 1.10174i | ||||
\(790\) | −1630.82 | + | 2824.66i | −0.0734455 | + | 0.127211i | ||||
\(791\) | 37999.6 | + | 21939.1i | 1.70810 | + | 0.986173i | ||||
\(792\) | −15650.0 | −0.702144 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11304.3 | 0.505259 | ||||||||
\(795\) | 3237.11 | + | 1868.94i | 0.144413 | + | 0.0833769i | ||||
\(796\) | −1018.43 | + | 1763.98i | −0.0453485 | + | 0.0785459i | ||||
\(797\) | 15046.6 | + | 26061.4i | 0.668729 | + | 1.15827i | 0.978260 | + | 0.207383i | \(0.0664945\pi\) |
−0.309531 | + | 0.950889i | \(0.600172\pi\) | |||||||
\(798\) | − | 8834.35i | − | 0.391896i | ||||||
\(799\) | −18014.1 | + | 10400.4i | −0.797612 | + | 0.460501i | ||||
\(800\) | 18213.9 | − | 10515.8i | 0.804947 | − | 0.464737i | ||||
\(801\) | 21300.6i | 0.939598i | ||||||||
\(802\) | 3333.62 | + | 5774.00i | 0.146776 | + | 0.254223i | ||||
\(803\) | −2350.28 | + | 4070.80i | −0.103287 | + | 0.178899i | ||||
\(804\) | 21428.3 | + | 12371.6i | 0.939946 | + | 0.542678i | ||||
\(805\) | −11880.2 | −0.520151 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22456.8 | −0.979575 | ||||||||
\(808\) | 6166.96 | + | 3560.50i | 0.268506 | + | 0.155022i | ||||
\(809\) | 12168.6 | − | 21076.6i | 0.528831 | − | 0.915961i | −0.470604 | − | 0.882344i | \(-0.655964\pi\) |
0.999435 | − | 0.0336170i | \(-0.0107026\pi\) | |||||||
\(810\) | 857.553 | + | 1485.33i | 0.0371992 | + | 0.0644309i | ||||
\(811\) | − | 19078.7i | − | 0.826071i | −0.910715 | − | 0.413035i | \(-0.864469\pi\) | ||
0.910715 | − | 0.413035i | \(-0.135531\pi\) | |||||||
\(812\) | 28785.4 | − | 16619.3i | 1.24405 | − | 0.718254i | ||||
\(813\) | 7437.89 | − | 4294.27i | 0.320859 | − | 0.185248i | ||||
\(814\) | − | 2244.74i | − | 0.0966559i | ||||||
\(815\) | 5843.56 | + | 10121.3i | 0.251155 | + | 0.435013i | ||||
\(816\) | 2209.67 | − | 3827.25i | 0.0947963 | − | 0.164192i | ||||
\(817\) | 3140.78 | + | 1813.33i | 0.134495 | + | 0.0776505i | ||||
\(818\) | 21178.6 | 0.905248 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3176.26 | −0.135268 | ||||||||
\(821\) | 1744.10 | + | 1006.96i | 0.0741408 | + | 0.0428052i | 0.536612 | − | 0.843829i | \(-0.319704\pi\) |
−0.462471 | + | 0.886634i | \(0.653037\pi\) | |||||||
\(822\) | −17911.0 | + | 31022.7i | −0.759996 | + | 1.31635i | ||||
\(823\) | −3846.05 | − | 6661.55i | −0.162898 | − | 0.282147i | 0.773009 | − | 0.634395i | \(-0.218751\pi\) |
−0.935907 | + | 0.352248i | \(0.885417\pi\) | |||||||
\(824\) | − | 6834.10i | − | 0.288929i | ||||||
\(825\) | 12891.9 | − | 7443.12i | 0.544045 | − | 0.314105i | ||||
\(826\) | −16157.7 | + | 9328.66i | −0.680628 | + | 0.392961i | ||||
\(827\) | − | 4762.76i | − | 0.200263i | −0.994974 | − | 0.100131i | \(-0.968074\pi\) | ||
0.994974 | − | 0.100131i | \(-0.0319263\pi\) | |||||||
\(828\) | 16527.3 | + | 28626.1i | 0.693675 | + | 1.20148i | ||||
\(829\) | 9988.83 | − | 17301.2i | 0.418488 | − | 0.724842i | −0.577300 | − | 0.816532i | \(-0.695894\pi\) |
0.995788 | + | 0.0916901i | \(0.0292269\pi\) | |||||||
\(830\) | −6522.44 | − | 3765.73i | −0.272768 | − | 0.157483i | ||||
\(831\) | −70714.0 | −2.95191 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17622.3 | 0.732984 | ||||||||
\(834\) | 23473.3 | + | 13552.3i | 0.974596 | + | 0.562683i | ||||
\(835\) | −5567.63 | + | 9643.43i | −0.230750 | + | 0.399670i | ||||
\(836\) | −1017.24 | − | 1761.91i | −0.0420836 | − | 0.0728909i | ||||
\(837\) | − | 5040.72i | − | 0.208164i | ||||||
\(838\) | −19713.0 | + | 11381.3i | −0.812617 | + | 0.469165i | ||||
\(839\) | −26514.0 | + | 15307.9i | −1.09102 | + | 0.629901i | −0.933848 | − | 0.357670i | \(-0.883571\pi\) |
−0.157172 | + | 0.987571i | \(0.550238\pi\) | |||||||
\(840\) | 17801.7i | 0.731210i | ||||||||
\(841\) | −11985.5 | − | 20759.5i | −0.491431 | − | 0.851183i | ||||
\(842\) | −12374.0 | + | 21432.5i | −0.506458 | + | 0.877211i | ||||
\(843\) | −11539.0 | − | 6662.04i | −0.471440 | − | 0.272186i | ||||
\(844\) | 11804.7 | 0.481439 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −35308.5 | −1.43491 | ||||||||
\(847\) | 25844.7 | + | 14921.4i | 1.04845 | + | 0.605321i | ||||
\(848\) | 690.233 | − | 1195.52i | 0.0279513 | − | 0.0484131i | ||||
\(849\) | −30244.3 | − | 52384.7i | −1.22259 | − | 2.11760i | ||||
\(850\) | − | 7812.83i | − | 0.315268i | ||||||
\(851\) | −10012.1 | + | 5780.51i | −0.403304 | + | 0.232848i | ||||
\(852\) | −17180.0 | + | 9918.89i | −0.690819 | + | 0.398845i | ||||
\(853\) | 5660.88i | 0.227227i | 0.993525 | + | 0.113614i | \(0.0362426\pi\) | ||||
−0.993525 | + | 0.113614i | \(0.963757\pi\) | |||||||
\(854\) | 2913.50 | + | 5046.34i | 0.116742 | + | 0.202204i | ||||
\(855\) | −2066.93 | + | 3580.03i | −0.0826755 | + | 0.143198i | ||||
\(856\) | −26310.7 | − | 15190.5i | −1.05056 | − | 0.606543i | ||||
\(857\) | −41346.1 | −1.64802 | −0.824012 | − | 0.566572i | \(-0.808269\pi\) | ||||
−0.824012 | + | 0.566572i | \(0.808269\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34810.5 | −1.38268 | −0.691339 | − | 0.722530i | \(-0.742979\pi\) | ||||
−0.691339 | + | 0.722530i | \(0.742979\pi\) | |||||||
\(860\) | −2595.44 | − | 1498.48i | −0.102911 | − | 0.0594159i | ||||
\(861\) | −18923.7 | + | 32776.8i | −0.749033 | + | 1.29736i | ||||
\(862\) | −8350.19 | − | 14462.9i | −0.329940 | − | 0.571473i | ||||
\(863\) | 8360.51i | 0.329774i | 0.986312 | + | 0.164887i | \(0.0527260\pi\) | ||||
−0.986312 | + | 0.164887i | \(0.947274\pi\) | |||||||
\(864\) | 30171.9 | − | 17419.7i | 1.18804 | − | 0.685916i | ||||
\(865\) | −300.944 | + | 173.750i | −0.0118294 | + | 0.00682969i | ||||
\(866\) | 25108.2i | 0.985233i | ||||||||
\(867\) | 12717.0 | + | 22026.5i | 0.498146 | + | 0.862815i | ||||
\(868\) | 2047.49 | − | 3546.36i | 0.0800651 | − | 0.138677i | ||||
\(869\) | 7751.11 | + | 4475.11i | 0.302576 | + | 0.174692i | ||||
\(870\) | 10621.6 | 0.413917 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 17982.4 | 0.698352 | ||||||||
\(873\) | −63376.3 | − | 36590.3i | −2.45700 | − | 1.41855i | ||||
\(874\) | 2297.05 | − | 3978.61i | 0.0889003 | − | 0.153980i | ||||
\(875\) | −11485.2 | − | 19892.9i | −0.443737 | − | 0.768576i | ||||
\(876\) | − | 14876.6i | − | 0.573784i | ||||||
\(877\) | 35142.7 | − | 20289.7i | 1.35312 | − | 0.781223i | 0.364434 | − | 0.931229i | \(-0.381263\pi\) |
0.988685 | + | 0.150006i | \(0.0479293\pi\) | |||||||
\(878\) | −8162.48 | + | 4712.61i | −0.313748 | + | 0.181142i | ||||
\(879\) | 5558.43i | 0.213289i | ||||||||
\(880\) | 310.452 | + | 537.718i | 0.0118924 | + | 0.0205983i | ||||
\(881\) | 5222.62 | − | 9045.84i | 0.199721 | − | 0.345927i | −0.748717 | − | 0.662890i | \(-0.769330\pi\) |
0.948438 | + | 0.316963i | \(0.102663\pi\) | |||||||
\(882\) | 25905.4 | + | 14956.5i | 0.988981 | + | 0.570989i | ||||
\(883\) | −18227.6 | −0.694685 | −0.347343 | − | 0.937738i | \(-0.612916\pi\) | ||||
−0.347343 | + | 0.937738i | \(0.612916\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13598.2 | 0.516496 | ||||||||
\(886\) | −13795.7 | − | 7964.96i | −0.523111 | − | 0.302018i | ||||
\(887\) | 11758.8 | − | 20366.9i | 0.445122 | − | 0.770974i | −0.552938 | − | 0.833222i | \(-0.686494\pi\) |
0.998061 | + | 0.0622477i | \(0.0198269\pi\) | |||||||
\(888\) | 8661.72 | + | 15002.5i | 0.327329 | + | 0.566950i | ||||
\(889\) | 23512.9i | 0.887061i | ||||||||
\(890\) | −2118.67 | + | 1223.21i | −0.0797955 | + | 0.0460699i | ||||
\(891\) | 4075.86 | − | 2353.20i | 0.153251 | − | 0.0884794i | ||||
\(892\) | 32960.1i | 1.23720i | ||||||||
\(893\) | −5596.30 | − | 9693.07i | −0.209712 | − | 0.363232i | ||||
\(894\) | 11886.6 | − | 20588.1i | 0.444683 | − | 0.770213i | ||||
\(895\) | −107.075 | − | 61.8196i | −0.00399901 | − | 0.00230883i | ||||
\(896\) | 32181.2 | 1.19989 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9092.21 | 0.337874 | ||||||||
\(899\) | −5159.74 | − | 2978.98i | −0.191420 | − | 0.110517i | ||||
\(900\) | −15123.7 | + | 26195.1i | −0.560139 | + | 0.970189i | ||||
\(901\) | −2691.64 | − | 4662.06i | −0.0995245 | − | 0.172381i | ||||
\(902\) | − | 3821.47i | − | 0.141065i | ||||||
\(903\) | −30926.5 | + | 17855.4i | −1.13972 | + | 0.658019i | ||||
\(904\) | 29610.2 | − | 17095.5i | 1.08940 | − | 0.628968i | ||||
\(905\) | 4378.38i | 0.160820i | ||||||||
\(906\) | −18949.9 | − | 32822.1i | −0.694886 | − | 1.20358i | ||||
\(907\) | −15282.3 | + | 26469.7i | −0.559471 | + | 0.969032i | 0.438070 | + | 0.898941i | \(0.355662\pi\) |
−0.997541 | + | 0.0700908i | \(0.977671\pi\) | |||||||
\(908\) | −4313.90 | − | 2490.63i | −0.157667 | − | 0.0910292i | ||||
\(909\) | −16282.8 | −0.594132 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32766.5 | −1.19166 | −0.595831 | − | 0.803110i | \(-0.703177\pi\) | ||||
−0.595831 | + | 0.803110i | \(0.703177\pi\) | |||||||
\(912\) | 2059.38 | + | 1188.99i | 0.0747730 | + | 0.0431702i | ||||
\(913\) | −10333.5 | + | 17898.1i | −0.374577 | + | 0.648786i | ||||
\(914\) | −3608.44 | − | 6249.99i | −0.130587 | − | 0.226183i | ||||
\(915\) | − | 4246.96i | − | 0.153443i | ||||||
\(916\) | 3023.36 | − | 1745.54i | 0.109055 | − | 0.0629632i | ||||
\(917\) | 6623.05 | − | 3823.82i | 0.238509 | − | 0.137703i | ||||
\(918\) | − | 12942.2i | − | 0.465312i | ||||||
\(919\) | −10343.4 | − | 17915.2i | −0.371269 | − | 0.643057i | 0.618492 | − | 0.785791i | \(-0.287744\pi\) |
−0.989761 | + | 0.142734i | \(0.954411\pi\) | |||||||
\(920\) | −4628.68 | + | 8017.10i | −0.165873 | + | 0.287300i | ||||
\(921\) | 755.165 | + | 435.995i | 0.0270179 | + | 0.0155988i | ||||
\(922\) | 8007.28 | 0.286015 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 20033.0 | 0.713242 | ||||||||
\(925\) | −9161.88 | − | 5289.62i | −0.325666 | − | 0.188023i | ||||
\(926\) | 5064.32 | − | 8771.67i | 0.179724 | − | 0.311290i | ||||
\(927\) | 7813.39 | + | 13533.2i | 0.276834 | + | 0.479491i | ||||
\(928\) | − | 41179.0i | − | 1.45665i | ||||||
\(929\) | −39518.6 | + | 22816.1i | −1.39566 | + | 0.805782i | −0.993934 | − | 0.109979i | \(-0.964922\pi\) |
−0.401722 | + | 0.915762i | \(0.631588\pi\) | |||||||
\(930\) | 1133.27 | − | 654.294i | 0.0399585 | − | 0.0230700i | ||||
\(931\) | 9482.26i | 0.333801i | ||||||||
\(932\) | 6406.14 | + | 11095.8i | 0.225150 | + | 0.389972i | ||||
\(933\) | −16843.5 | + | 29173.9i | −0.591032 | + | 1.02370i | ||||
\(934\) | 17550.8 | + | 10133.0i | 0.614860 | + | 0.354990i | ||||
\(935\) | 2421.28 | 0.0846892 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17761.4 | −0.619253 | −0.309626 | − | 0.950858i | \(-0.600204\pi\) | ||||
−0.309626 | + | 0.950858i | \(0.600204\pi\) | |||||||
\(938\) | 18827.7 | + | 10870.2i | 0.655380 | + | 0.378384i | ||||
\(939\) | 16454.8 | − | 28500.5i | 0.571866 | − | 0.990501i | ||||
\(940\) | 4624.60 | + | 8010.04i | 0.160466 | + | 0.277935i | ||||
\(941\) | 44888.3i | 1.55507i | 0.628841 | + | 0.777534i | \(0.283530\pi\) | ||||
−0.628841 | + | 0.777534i | \(0.716470\pi\) | |||||||
\(942\) | 38109.9 | − | 22002.8i | 1.31814 | − | 0.761029i | ||||
\(943\) | −17044.8 | + | 9840.83i | −0.588606 | + | 0.339832i | ||||
\(944\) | − | 5022.05i | − | 0.173150i | ||||||
\(945\) | −9004.32 | − | 15595.9i | −0.309958 | − | 0.536864i | ||||
\(946\) | 1802.87 | − | 3122.67i | 0.0619624 | − | 0.107322i | ||||
\(947\) | −13916.6 | − | 8034.78i | −0.477540 | − | 0.275708i | 0.241851 | − | 0.970313i | \(-0.422246\pi\) |
−0.719391 | + | 0.694606i | \(0.755579\pi\) | |||||||
\(948\) | −28326.2 | −0.970457 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4203.96 | 0.143573 | ||||||||
\(951\) | 33144.2 | + | 19135.8i | 1.13015 | + | 0.652493i | ||||
\(952\) | 12818.9 | − | 22203.0i | 0.436411 | − | 0.755887i | ||||
\(953\) | 1756.02 | + | 3041.51i | 0.0596883 | + | 0.103383i | 0.894325 | − | 0.447417i | \(-0.147656\pi\) |
−0.834637 | + | 0.550800i | \(0.814323\pi\) | |||||||
\(954\) | − | 9137.88i | − | 0.310115i | ||||||
\(955\) | 13203.7 | − | 7623.14i | 0.447393 | − | 0.258303i | ||||
\(956\) | −2623.14 | + | 1514.47i | −0.0887432 | + | 0.0512359i | ||||
\(957\) | − | 29146.7i | − | 0.984513i | ||||||
\(958\) | −4535.50 | − | 7855.72i | −0.152960 | − | 0.264934i | ||||
\(959\) | 35893.2 | − | 62168.9i | 1.20861 | − | 2.09337i | ||||
\(960\) | 5384.75 | + | 3108.89i | 0.181034 | + | 0.104520i | ||||
\(961\) | 29057.0 | 0.975361 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 69468.9 | 2.32461 | ||||||||
\(964\) | −26134.5 | − | 15088.8i | −0.873170 | − | 0.504125i | ||||
\(965\) | 841.097 | − | 1456.82i | 0.0280579 | − | 0.0485977i | ||||
\(966\) | 22618.5 | + | 39176.4i | 0.753352 | + | 1.30484i | ||||
\(967\) | 37011.9i | 1.23084i | 0.788199 | + | 0.615421i | \(0.211014\pi\) | ||||
−0.788199 | + | 0.615421i | \(0.788986\pi\) | |||||||
\(968\) | 20138.9 | − | 11627.2i | 0.668685 | − | 0.386066i | ||||
\(969\) | 8030.79 | − | 4636.58i | 0.266240 | − | 0.153714i | ||||
\(970\) | − | 8405.00i | − | 0.278215i | ||||||
\(971\) | −9766.15 | − | 16915.5i | −0.322771 | − | 0.559056i | 0.658288 | − | 0.752766i | \(-0.271281\pi\) |
−0.981059 | + | 0.193711i | \(0.937948\pi\) | |||||||
\(972\) | 6521.55 | − | 11295.7i | 0.215205 | − | 0.372745i | ||||
\(973\) | −47040.0 | − | 27158.5i | −1.54988 | − | 0.894823i | ||||
\(974\) | −8412.30 | −0.276743 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1568.47 | −0.0514402 | ||||||||
\(977\) | 26155.0 | + | 15100.6i | 0.856473 | + | 0.494485i | 0.862830 | − | 0.505495i | \(-0.168690\pi\) |
−0.00635674 | + | 0.999980i | \(0.502023\pi\) | |||||||
\(978\) | 22250.9 | − | 38539.7i | 0.727511 | − | 1.26009i | ||||
\(979\) | 3356.60 | + | 5813.81i | 0.109579 | + | 0.189796i | ||||
\(980\) | − | 7835.83i | − | 0.255415i | ||||||
\(981\) | −35609.7 | + | 20559.2i | −1.15895 | + | 0.669119i | ||||
\(982\) | −20635.5 | + | 11913.9i | −0.670576 | + | 0.387157i | ||||
\(983\) | − | 38774.9i | − | 1.25812i | −0.777359 | − | 0.629058i | \(-0.783441\pi\) | ||
0.777359 | − | 0.629058i | \(-0.216559\pi\) | |||||||
\(984\) | 14745.8 | + | 25540.5i | 0.477723 | + | 0.827441i | ||||
\(985\) | 7985.65 | − | 13831.6i | 0.258319 | − | 0.447421i | ||||
\(986\) | −13247.8 | − | 7648.61i | −0.427886 | − | 0.247040i | ||||
\(987\) | 110211. | 3.55425 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18570.6 | −0.597079 | ||||||||
\(990\) | 3559.38 | + | 2055.01i | 0.114267 | + | 0.0659722i | ||||
\(991\) | 13864.5 | − | 24014.0i | 0.444419 | − | 0.769757i | −0.553592 | − | 0.832788i | \(-0.686743\pi\) |
0.998012 | + | 0.0630311i | \(0.0200767\pi\) | |||||||
\(992\) | −2536.63 | − | 4393.57i | −0.0811875 | − | 0.140621i | ||||
\(993\) | 35880.6i | 1.14666i | ||||||||
\(994\) | −15095.1 | + | 8715.13i | −0.481676 | + | 0.278096i | ||||
\(995\) | 1129.63 | − | 652.192i | 0.0359916 | − | 0.0207798i | ||||
\(996\) | − | 65408.2i | − | 2.08086i | ||||||
\(997\) | 24459.1 | + | 42364.4i | 0.776958 | + | 1.34573i | 0.933687 | + | 0.358090i | \(0.116572\pi\) |
−0.156729 | + | 0.987642i | \(0.550095\pi\) | |||||||
\(998\) | −1449.16 | + | 2510.01i | −0.0459641 | + | 0.0796122i | ||||
\(999\) | −15177.0 | − | 8762.42i | −0.480658 | − | 0.277508i |
(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 | 169.4.e.f.147.2 | 8 | ||
13.2 | odd | 12 | 169.4.c.j.146.1 | 4 | |||
13.3 | even | 3 | inner | 169.4.e.f.23.3 | 8 | ||
13.4 | even | 6 | 169.4.b.f.168.2 | 4 | |||
13.5 | odd | 4 | 169.4.c.j.22.1 | 4 | |||
13.6 | odd | 12 | 169.4.a.g.1.2 | 2 | |||
13.7 | odd | 12 | 13.4.a.b.1.1 | ✓ | 2 | ||
13.8 | odd | 4 | 169.4.c.g.22.2 | 4 | |||
13.9 | even | 3 | 169.4.b.f.168.3 | 4 | |||
13.10 | even | 6 | inner | 169.4.e.f.23.2 | 8 | ||
13.11 | odd | 12 | 169.4.c.g.146.2 | 4 | |||
13.12 | even | 2 | inner | 169.4.e.f.147.3 | 8 | ||
39.20 | even | 12 | 117.4.a.d.1.2 | 2 | |||
39.32 | even | 12 | 1521.4.a.r.1.1 | 2 | |||
52.7 | even | 12 | 208.4.a.h.1.1 | 2 | |||
65.7 | even | 12 | 325.4.b.e.274.2 | 4 | |||
65.33 | even | 12 | 325.4.b.e.274.3 | 4 | |||
65.59 | odd | 12 | 325.4.a.f.1.2 | 2 | |||
91.20 | even | 12 | 637.4.a.b.1.1 | 2 | |||
104.59 | even | 12 | 832.4.a.z.1.2 | 2 | |||
104.85 | odd | 12 | 832.4.a.s.1.1 | 2 | |||
143.98 | even | 12 | 1573.4.a.b.1.2 | 2 | |||
156.59 | odd | 12 | 1872.4.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.a.b.1.1 | ✓ | 2 | 13.7 | odd | 12 | ||
117.4.a.d.1.2 | 2 | 39.20 | even | 12 | |||
169.4.a.g.1.2 | 2 | 13.6 | odd | 12 | |||
169.4.b.f.168.2 | 4 | 13.4 | even | 6 | |||
169.4.b.f.168.3 | 4 | 13.9 | even | 3 | |||
169.4.c.g.22.2 | 4 | 13.8 | odd | 4 | |||
169.4.c.g.146.2 | 4 | 13.11 | odd | 12 | |||
169.4.c.j.22.1 | 4 | 13.5 | odd | 4 | |||
169.4.c.j.146.1 | 4 | 13.2 | odd | 12 | |||
169.4.e.f.23.2 | 8 | 13.10 | even | 6 | inner | ||
169.4.e.f.23.3 | 8 | 13.3 | even | 3 | inner | ||
169.4.e.f.147.2 | 8 | 1.1 | even | 1 | trivial | ||
169.4.e.f.147.3 | 8 | 13.12 | even | 2 | inner | ||
208.4.a.h.1.1 | 2 | 52.7 | even | 12 | |||
325.4.a.f.1.2 | 2 | 65.59 | odd | 12 | |||
325.4.b.e.274.2 | 4 | 65.7 | even | 12 | |||
325.4.b.e.274.3 | 4 | 65.33 | even | 12 | |||
637.4.a.b.1.1 | 2 | 91.20 | even | 12 | |||
832.4.a.s.1.1 | 2 | 104.85 | odd | 12 | |||
832.4.a.z.1.2 | 2 | 104.59 | even | 12 | |||
1521.4.a.r.1.1 | 2 | 39.32 | even | 12 | |||
1573.4.a.b.1.2 | 2 | 143.98 | even | 12 | |||
1872.4.a.bb.1.2 | 2 | 156.59 | odd | 12 |