Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,4,Mod(4,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.e (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.94706303019\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.682515625.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 16.1 | ||
Root | \(2.51217 - 1.82520i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.16 |
Dual form | 33.4.e.b.31.1 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.45957 | − | 4.49208i | −0.516034 | − | 1.58819i | −0.781392 | − | 0.624040i | \(-0.785490\pi\) |
0.265358 | − | 0.964150i | \(-0.414510\pi\) | |||||||
\(3\) | −2.42705 | − | 1.76336i | −0.467086 | − | 0.339358i | ||||
\(4\) | −11.5763 | + | 8.41069i | −1.44704 | + | 1.05134i | ||||
\(5\) | 1.86000 | − | 5.72450i | 0.166364 | − | 0.512014i | −0.832771 | − | 0.553618i | \(-0.813247\pi\) |
0.999134 | + | 0.0416038i | \(0.0132467\pi\) | |||||||
\(6\) | −4.37870 | + | 13.4762i | −0.297933 | + | 0.916942i | ||||
\(7\) | −8.05785 | + | 5.85437i | −0.435083 | + | 0.316106i | −0.783678 | − | 0.621167i | \(-0.786659\pi\) |
0.348595 | + | 0.937273i | \(0.386659\pi\) | |||||||
\(8\) | 24.1083 | + | 17.5157i | 1.06545 | + | 0.774094i | ||||
\(9\) | 2.78115 | + | 8.55951i | 0.103006 | + | 0.317019i | ||||
\(10\) | −28.4297 | −0.899026 | ||||||||
\(11\) | 8.30870 | − | 35.5242i | 0.227743 | − | 0.973721i | ||||
\(12\) | 42.9273 | 1.03267 | ||||||||
\(13\) | −27.8826 | − | 85.8139i | −0.594865 | − | 1.83081i | −0.555396 | − | 0.831586i | \(-0.687433\pi\) |
−0.0394690 | − | 0.999221i | \(-0.512567\pi\) | |||||||
\(14\) | 38.0593 | + | 27.6517i | 0.726555 | + | 0.527873i | ||||
\(15\) | −14.6086 | + | 10.6138i | −0.251462 | + | 0.182698i | ||||
\(16\) | 8.12031 | − | 24.9917i | 0.126880 | − | 0.390496i | ||||
\(17\) | 13.8539 | − | 42.6379i | 0.197651 | − | 0.608306i | −0.802285 | − | 0.596941i | \(-0.796382\pi\) |
0.999935 | − | 0.0113645i | \(-0.00361750\pi\) | |||||||
\(18\) | 34.3907 | − | 24.9863i | 0.450332 | − | 0.327185i | ||||
\(19\) | 110.890 | + | 80.5660i | 1.33894 | + | 0.972795i | 0.999482 | + | 0.0321734i | \(0.0102429\pi\) |
0.339456 | + | 0.940622i | \(0.389757\pi\) | |||||||
\(20\) | 26.6150 | + | 81.9125i | 0.297564 | + | 0.915809i | ||||
\(21\) | 29.8801 | 0.310494 | ||||||||
\(22\) | −171.704 | + | 14.5265i | −1.66398 | + | 0.140775i | ||||
\(23\) | −71.4719 | −0.647953 | −0.323977 | − | 0.946065i | \(-0.605020\pi\) | ||||
−0.323977 | + | 0.946065i | \(0.605020\pi\) | |||||||
\(24\) | −27.6257 | − | 85.0232i | −0.234961 | − | 0.723137i | ||||
\(25\) | 71.8169 | + | 52.1780i | 0.574535 | + | 0.417424i | ||||
\(26\) | −344.786 | + | 250.502i | −2.60070 | + | 1.88952i | ||||
\(27\) | 8.34346 | − | 25.6785i | 0.0594703 | − | 0.183031i | ||||
\(28\) | 44.0409 | − | 135.544i | 0.297248 | − | 0.914837i | ||||
\(29\) | 119.601 | − | 86.8950i | 0.765838 | − | 0.556414i | −0.134857 | − | 0.990865i | \(-0.543058\pi\) |
0.900695 | + | 0.434451i | \(0.143058\pi\) | |||||||
\(30\) | 69.0003 | + | 50.1317i | 0.419922 | + | 0.305092i | ||||
\(31\) | 2.38514 | + | 7.34071i | 0.0138188 | + | 0.0425300i | 0.957728 | − | 0.287675i | \(-0.0928822\pi\) |
−0.943909 | + | 0.330205i | \(0.892882\pi\) | |||||||
\(32\) | 114.279 | 0.631310 | ||||||||
\(33\) | −82.8074 | + | 71.5677i | −0.436815 | + | 0.377526i | ||||
\(34\) | −211.753 | −1.06810 | ||||||||
\(35\) | 18.5257 | + | 57.0163i | 0.0894690 | + | 0.275357i | ||||
\(36\) | −104.187 | − | 75.6962i | −0.482347 | − | 0.350445i | ||||
\(37\) | −8.18776 | + | 5.94875i | −0.0363800 | + | 0.0264316i | −0.605827 | − | 0.795597i | \(-0.707158\pi\) |
0.569447 | + | 0.822028i | \(0.307158\pi\) | |||||||
\(38\) | 200.058 | − | 615.716i | 0.854046 | − | 2.62848i | ||||
\(39\) | −83.6479 | + | 257.442i | −0.343446 | + | 1.05702i | ||||
\(40\) | 145.110 | − | 105.429i | 0.573599 | − | 0.416744i | ||||
\(41\) | −305.780 | − | 222.162i | −1.16475 | − | 0.846242i | −0.174381 | − | 0.984678i | \(-0.555793\pi\) |
−0.990371 | + | 0.138436i | \(0.955793\pi\) | |||||||
\(42\) | −43.6120 | − | 134.224i | −0.160226 | − | 0.493124i | ||||
\(43\) | 276.048 | 0.979000 | 0.489500 | − | 0.872003i | \(-0.337179\pi\) | ||||
0.489500 | + | 0.872003i | \(0.337179\pi\) | |||||||
\(44\) | 202.598 | + | 481.121i | 0.694156 | + | 1.64845i | ||||
\(45\) | 54.1718 | 0.179455 | ||||||||
\(46\) | 104.318 | + | 321.057i | 0.334366 | + | 1.02907i | ||||
\(47\) | 191.854 | + | 139.390i | 0.595421 | + | 0.432599i | 0.844251 | − | 0.535949i | \(-0.180046\pi\) |
−0.248830 | + | 0.968547i | \(0.580046\pi\) | |||||||
\(48\) | −63.7778 | + | 46.3373i | −0.191782 | + | 0.139338i | ||||
\(49\) | −75.3376 | + | 231.865i | −0.219643 | + | 0.675992i | ||||
\(50\) | 129.566 | − | 398.764i | 0.366469 | − | 1.12788i | ||||
\(51\) | −108.810 | + | 79.0549i | −0.298753 | + | 0.217057i | ||||
\(52\) | 1044.53 | + | 758.897i | 2.78559 | + | 2.02385i | ||||
\(53\) | −68.6297 | − | 211.221i | −0.177868 | − | 0.547422i | 0.821885 | − | 0.569654i | \(-0.192923\pi\) |
−0.999753 | + | 0.0222318i | \(0.992923\pi\) | |||||||
\(54\) | −127.528 | −0.321377 | ||||||||
\(55\) | −187.904 | − | 113.638i | −0.460671 | − | 0.278599i | ||||
\(56\) | −296.805 | −0.708254 | ||||||||
\(57\) | −127.068 | − | 391.076i | −0.295274 | − | 0.908759i | ||||
\(58\) | −564.905 | − | 410.427i | −1.27889 | − | 0.929168i | ||||
\(59\) | −136.832 | + | 99.4144i | −0.301933 | + | 0.219367i | −0.728427 | − | 0.685123i | \(-0.759748\pi\) |
0.426494 | + | 0.904490i | \(0.359748\pi\) | |||||||
\(60\) | 79.8449 | − | 245.737i | 0.171799 | − | 0.528743i | ||||
\(61\) | 70.1651 | − | 215.946i | 0.147274 | − | 0.453263i | −0.850022 | − | 0.526747i | \(-0.823412\pi\) |
0.997296 | + | 0.0734835i | \(0.0234116\pi\) | |||||||
\(62\) | 29.4938 | − | 21.4285i | 0.0604147 | − | 0.0438939i | ||||
\(63\) | −72.5206 | − | 52.6893i | −0.145028 | − | 0.105369i | ||||
\(64\) | −231.761 | − | 713.286i | −0.452658 | − | 1.39314i | ||||
\(65\) | −543.103 | −1.03636 | ||||||||
\(66\) | 442.351 | + | 267.520i | 0.824994 | + | 0.498930i | ||||
\(67\) | −362.669 | −0.661300 | −0.330650 | − | 0.943753i | \(-0.607268\pi\) | ||||
−0.330650 | + | 0.943753i | \(0.607268\pi\) | |||||||
\(68\) | 198.237 | + | 610.110i | 0.353526 | + | 1.08804i | ||||
\(69\) | 173.466 | + | 126.030i | 0.302650 | + | 0.219888i | ||||
\(70\) | 229.082 | − | 166.438i | 0.391151 | − | 0.284188i | ||||
\(71\) | −219.919 | + | 676.841i | −0.367600 | + | 1.13136i | 0.580737 | + | 0.814091i | \(0.302764\pi\) |
−0.948337 | + | 0.317265i | \(0.897236\pi\) | |||||||
\(72\) | −82.8771 | + | 255.070i | −0.135655 | + | 0.417503i | ||||
\(73\) | 845.463 | − | 614.265i | 1.35553 | − | 0.984853i | 0.356820 | − | 0.934173i | \(-0.383861\pi\) |
0.998715 | − | 0.0506801i | \(-0.0161389\pi\) | |||||||
\(74\) | 38.6729 | + | 28.0975i | 0.0607517 | + | 0.0441387i | ||||
\(75\) | −82.2948 | − | 253.277i | −0.126701 | − | 0.389946i | ||||
\(76\) | −1961.31 | −2.96023 | ||||||||
\(77\) | 141.021 | + | 334.890i | 0.208713 | + | 0.495640i | ||||
\(78\) | 1278.54 | 1.85597 | ||||||||
\(79\) | 15.6957 | + | 48.3063i | 0.0223532 | + | 0.0687959i | 0.961611 | − | 0.274417i | \(-0.0884848\pi\) |
−0.939258 | + | 0.343213i | \(0.888485\pi\) | |||||||
\(80\) | −127.961 | − | 92.9694i | −0.178831 | − | 0.129929i | ||||
\(81\) | −65.5304 | + | 47.6106i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | −551.665 | + | 1697.85i | −0.742942 | + | 2.28654i | ||||
\(83\) | −378.188 | + | 1163.94i | −0.500139 | + | 1.53927i | 0.308653 | + | 0.951175i | \(0.400122\pi\) |
−0.808792 | + | 0.588095i | \(0.799878\pi\) | |||||||
\(84\) | −345.902 | + | 251.313i | −0.449298 | + | 0.326434i | ||||
\(85\) | −218.312 | − | 158.613i | −0.278580 | − | 0.202400i | ||||
\(86\) | −402.911 | − | 1240.03i | −0.505197 | − | 1.55484i | ||||
\(87\) | −443.504 | −0.546536 | ||||||||
\(88\) | 822.541 | − | 710.895i | 0.996399 | − | 0.861156i | ||||
\(89\) | 964.845 | 1.14914 | 0.574569 | − | 0.818456i | \(-0.305170\pi\) | ||||
0.574569 | + | 0.818456i | \(0.305170\pi\) | |||||||
\(90\) | −79.0673 | − | 243.344i | −0.0926047 | − | 0.285008i | ||||
\(91\) | 727.060 | + | 528.240i | 0.837545 | + | 0.608512i | ||||
\(92\) | 827.381 | − | 601.128i | 0.937614 | − | 0.681216i | ||||
\(93\) | 7.15542 | − | 22.0221i | 0.00797831 | − | 0.0245547i | ||||
\(94\) | 346.128 | − | 1065.27i | 0.379791 | − | 1.16888i | ||||
\(95\) | 667.455 | − | 484.934i | 0.720836 | − | 0.523718i | ||||
\(96\) | −277.362 | − | 201.515i | −0.294876 | − | 0.214240i | ||||
\(97\) | 78.8462 | + | 242.664i | 0.0825321 | + | 0.254008i | 0.983804 | − | 0.179245i | \(-0.0573656\pi\) |
−0.901272 | + | 0.433253i | \(0.857366\pi\) | |||||||
\(98\) | 1151.52 | 1.18695 | ||||||||
\(99\) | 327.177 | − | 27.6797i | 0.332147 | − | 0.0281002i | ||||
\(100\) | −1270.23 | −1.27023 | ||||||||
\(101\) | 41.9267 | + | 129.037i | 0.0413055 | + | 0.127125i | 0.969583 | − | 0.244763i | \(-0.0787103\pi\) |
−0.928277 | + | 0.371889i | \(0.878710\pi\) | |||||||
\(102\) | 513.936 | + | 373.396i | 0.498895 | + | 0.362468i | ||||
\(103\) | 557.554 | − | 405.087i | 0.533373 | − | 0.387518i | −0.288245 | − | 0.957557i | \(-0.593072\pi\) |
0.821618 | + | 0.570039i | \(0.193072\pi\) | |||||||
\(104\) | 830.890 | − | 2557.21i | 0.783418 | − | 2.41111i | ||||
\(105\) | 55.5771 | − | 171.049i | 0.0516550 | − | 0.158978i | ||||
\(106\) | −848.650 | + | 616.581i | −0.777625 | + | 0.564977i | ||||
\(107\) | −784.130 | − | 569.704i | −0.708455 | − | 0.514723i | 0.174220 | − | 0.984707i | \(-0.444260\pi\) |
−0.882675 | + | 0.469984i | \(0.844260\pi\) | |||||||
\(108\) | 119.388 | + | 367.437i | 0.106371 | + | 0.327376i | ||||
\(109\) | −235.888 | −0.207284 | −0.103642 | − | 0.994615i | \(-0.533050\pi\) | ||||
−0.103642 | + | 0.994615i | \(0.533050\pi\) | |||||||
\(110\) | −236.214 | + | 1009.94i | −0.204746 | + | 0.875400i | ||||
\(111\) | 30.3619 | 0.0259624 | ||||||||
\(112\) | 80.8787 | + | 248.919i | 0.0682350 | + | 0.210006i | ||||
\(113\) | −416.768 | − | 302.800i | −0.346958 | − | 0.252080i | 0.400634 | − | 0.916238i | \(-0.368790\pi\) |
−0.747592 | + | 0.664159i | \(0.768790\pi\) | |||||||
\(114\) | −1571.28 | + | 1141.60i | −1.29091 | + | 0.937901i | ||||
\(115\) | −132.938 | + | 409.141i | −0.107796 | + | 0.331761i | ||||
\(116\) | −653.689 | + | 2011.85i | −0.523220 | + | 1.61031i | ||||
\(117\) | 656.979 | − | 477.323i | 0.519126 | − | 0.377167i | ||||
\(118\) | 646.293 | + | 469.559i | 0.504204 | + | 0.366326i | ||||
\(119\) | 137.985 | + | 424.675i | 0.106295 | + | 0.327142i | ||||
\(120\) | −538.099 | −0.409345 | ||||||||
\(121\) | −1192.93 | − | 590.319i | −0.896267 | − | 0.443515i | ||||
\(122\) | −1072.46 | −0.795867 | ||||||||
\(123\) | 350.393 | + | 1078.40i | 0.256861 | + | 0.790536i | ||||
\(124\) | −89.3515 | − | 64.9177i | −0.0647097 | − | 0.0470144i | ||||
\(125\) | 1040.97 | − | 756.306i | 0.744854 | − | 0.541168i | ||||
\(126\) | −130.836 | + | 402.672i | −0.0925064 | + | 0.284705i | ||||
\(127\) | 319.132 | − | 982.188i | 0.222980 | − | 0.686261i | −0.775511 | − | 0.631334i | \(-0.782508\pi\) |
0.998490 | − | 0.0549264i | \(-0.0174924\pi\) | |||||||
\(128\) | −2126.24 | + | 1544.80i | −1.46824 | + | 1.06674i | ||||
\(129\) | −669.983 | − | 486.771i | −0.457277 | − | 0.332231i | ||||
\(130\) | 792.694 | + | 2439.66i | 0.534799 | + | 1.64594i | ||||
\(131\) | 1366.16 | 0.911157 | 0.455578 | − | 0.890196i | \(-0.349432\pi\) | ||||
0.455578 | + | 0.890196i | \(0.349432\pi\) | |||||||
\(132\) | 356.670 | − | 1524.96i | 0.235183 | − | 1.00553i | ||||
\(133\) | −1365.19 | −0.890056 | ||||||||
\(134\) | 529.339 | + | 1629.14i | 0.341253 | + | 1.05027i | ||||
\(135\) | −131.478 | − | 95.5242i | −0.0838208 | − | 0.0608994i | ||||
\(136\) | 1080.83 | − | 785.267i | 0.681472 | − | 0.495118i | ||||
\(137\) | 467.210 | − | 1437.92i | 0.291361 | − | 0.896716i | −0.693059 | − | 0.720881i | \(-0.743737\pi\) |
0.984420 | − | 0.175835i | \(-0.0562625\pi\) | |||||||
\(138\) | 312.954 | − | 963.172i | 0.193046 | − | 0.594135i | ||||
\(139\) | 848.109 | − | 616.187i | 0.517523 | − | 0.376002i | −0.298147 | − | 0.954520i | \(-0.596369\pi\) |
0.815670 | + | 0.578518i | \(0.196369\pi\) | |||||||
\(140\) | −694.005 | − | 504.224i | −0.418958 | − | 0.304391i | ||||
\(141\) | −219.845 | − | 676.614i | −0.131307 | − | 0.404122i | ||||
\(142\) | 3361.41 | 1.98650 | ||||||||
\(143\) | −3280.13 | + | 277.505i | −1.91817 | + | 0.162280i | ||||
\(144\) | 236.501 | 0.136864 | ||||||||
\(145\) | −274.973 | − | 846.279i | −0.157484 | − | 0.484687i | ||||
\(146\) | −3993.34 | − | 2901.33i | −2.26364 | − | 1.64463i | ||||
\(147\) | 591.709 | − | 429.902i | 0.331995 | − | 0.241209i | ||||
\(148\) | 44.7510 | − | 137.729i | 0.0248548 | − | 0.0764952i | ||||
\(149\) | −119.658 | + | 368.270i | −0.0657905 | + | 0.202482i | −0.978548 | − | 0.206020i | \(-0.933949\pi\) |
0.912757 | + | 0.408502i | \(0.133949\pi\) | |||||||
\(150\) | −1017.63 | + | 739.350i | −0.553926 | + | 0.402451i | ||||
\(151\) | −549.139 | − | 398.973i | −0.295949 | − | 0.215019i | 0.429895 | − | 0.902879i | \(-0.358551\pi\) |
−0.725844 | + | 0.687859i | \(0.758551\pi\) | |||||||
\(152\) | 1262.19 | + | 3884.63i | 0.673535 | + | 2.07293i | ||||
\(153\) | 403.489 | 0.213204 | ||||||||
\(154\) | 1298.53 | − | 1122.27i | 0.679468 | − | 0.587243i | ||||
\(155\) | 46.4582 | 0.0240749 | ||||||||
\(156\) | −1196.93 | − | 3683.76i | −0.614300 | − | 1.89062i | ||||
\(157\) | 2919.99 | + | 2121.50i | 1.48434 | + | 1.07843i | 0.976127 | + | 0.217200i | \(0.0696925\pi\) |
0.508210 | + | 0.861233i | \(0.330308\pi\) | |||||||
\(158\) | 194.087 | − | 141.012i | 0.0977260 | − | 0.0710021i | ||||
\(159\) | −205.889 | + | 633.662i | −0.102692 | + | 0.316054i | ||||
\(160\) | 212.560 | − | 654.192i | 0.105027 | − | 0.323240i | ||||
\(161\) | 575.910 | − | 418.423i | 0.281913 | − | 0.204822i | ||||
\(162\) | 309.517 | + | 224.877i | 0.150111 | + | 0.109062i | ||||
\(163\) | 284.219 | + | 874.736i | 0.136575 | + | 0.420335i | 0.995832 | − | 0.0912099i | \(-0.0290734\pi\) |
−0.859257 | + | 0.511545i | \(0.829073\pi\) | |||||||
\(164\) | 5408.35 | 2.57513 | ||||||||
\(165\) | 255.667 | + | 607.146i | 0.120628 | + | 0.286462i | ||||
\(166\) | 5780.52 | 2.70274 | ||||||||
\(167\) | −713.424 | − | 2195.69i | −0.330577 | − | 1.01741i | −0.968860 | − | 0.247610i | \(-0.920355\pi\) |
0.638282 | − | 0.769802i | \(-0.279645\pi\) | |||||||
\(168\) | 720.361 | + | 523.373i | 0.330816 | + | 0.240352i | ||||
\(169\) | −4809.17 | + | 3494.07i | −2.18897 | + | 1.59038i | ||||
\(170\) | −393.861 | + | 1212.18i | −0.177693 | + | 0.546883i | ||||
\(171\) | −381.205 | + | 1173.23i | −0.170476 | + | 0.524672i | ||||
\(172\) | −3195.62 | + | 2321.76i | −1.41665 | + | 1.02926i | ||||
\(173\) | 370.871 | + | 269.454i | 0.162987 | + | 0.118417i | 0.666289 | − | 0.745693i | \(-0.267882\pi\) |
−0.503302 | + | 0.864111i | \(0.667882\pi\) | |||||||
\(174\) | 647.323 | + | 1992.26i | 0.282031 | + | 0.868003i | ||||
\(175\) | −884.159 | −0.381921 | ||||||||
\(176\) | −820.342 | − | 496.116i | −0.351338 | − | 0.212478i | ||||
\(177\) | 507.402 | 0.215473 | ||||||||
\(178\) | −1408.25 | − | 4334.16i | −0.592995 | − | 1.82505i | ||||
\(179\) | 2880.70 | + | 2092.95i | 1.20287 | + | 0.873935i | 0.994564 | − | 0.104129i | \(-0.0332056\pi\) |
0.208304 | + | 0.978064i | \(0.433206\pi\) | |||||||
\(180\) | −627.110 | + | 455.622i | −0.259678 | + | 0.188667i | ||||
\(181\) | 248.804 | − | 765.741i | 0.102174 | − | 0.314459i | −0.886883 | − | 0.461994i | \(-0.847134\pi\) |
0.989057 | + | 0.147535i | \(0.0471340\pi\) | |||||||
\(182\) | 1311.71 | − | 4037.01i | 0.534231 | − | 1.64419i | ||||
\(183\) | −551.084 | + | 400.386i | −0.222608 | + | 0.161734i | ||||
\(184\) | −1723.07 | − | 1251.88i | −0.690360 | − | 0.501576i | ||||
\(185\) | 18.8244 | + | 57.9355i | 0.00748106 | + | 0.0230243i | ||||
\(186\) | −109.369 | −0.0431146 | ||||||||
\(187\) | −1399.57 | − | 846.413i | −0.547307 | − | 0.330994i | ||||
\(188\) | −3393.33 | −1.31640 | ||||||||
\(189\) | 83.1013 | + | 255.759i | 0.0319827 | + | 0.0984326i | ||||
\(190\) | −3152.56 | − | 2290.47i | −1.20374 | − | 0.874568i | ||||
\(191\) | 1836.35 | − | 1334.19i | 0.695674 | − | 0.505437i | −0.182847 | − | 0.983141i | \(-0.558531\pi\) |
0.878520 | + | 0.477705i | \(0.158531\pi\) | |||||||
\(192\) | −695.282 | + | 2139.86i | −0.261342 | + | 0.804328i | ||||
\(193\) | −1477.59 | + | 4547.55i | −0.551083 | + | 1.69606i | 0.154986 | + | 0.987917i | \(0.450467\pi\) |
−0.706069 | + | 0.708143i | \(0.749533\pi\) | |||||||
\(194\) | 974.983 | − | 708.367i | 0.360823 | − | 0.262153i | ||||
\(195\) | 1318.14 | + | 957.684i | 0.484071 | + | 0.351698i | ||||
\(196\) | −1078.01 | − | 3317.79i | −0.392862 | − | 1.20911i | ||||
\(197\) | −2009.15 | −0.726630 | −0.363315 | − | 0.931666i | \(-0.618355\pi\) | ||||
−0.363315 | + | 0.931666i | \(0.618355\pi\) | |||||||
\(198\) | −601.876 | − | 1429.31i | −0.216028 | − | 0.513012i | ||||
\(199\) | 3250.22 | 1.15780 | 0.578900 | − | 0.815398i | \(-0.303482\pi\) | ||||
0.578900 | + | 0.815398i | \(0.303482\pi\) | |||||||
\(200\) | 817.450 | + | 2515.85i | 0.289012 | + | 0.889488i | ||||
\(201\) | 880.217 | + | 639.515i | 0.308884 | + | 0.224417i | ||||
\(202\) | 518.450 | − | 376.676i | 0.180584 | − | 0.131202i | ||||
\(203\) | −455.009 | + | 1400.37i | −0.157317 | + | 0.484172i | ||||
\(204\) | 594.710 | − | 1830.33i | 0.204108 | − | 0.628180i | ||||
\(205\) | −1840.52 | + | 1337.22i | −0.627061 | + | 0.455586i | ||||
\(206\) | −2633.47 | − | 1913.33i | −0.890691 | − | 0.647125i | ||||
\(207\) | −198.774 | − | 611.764i | −0.0667428 | − | 0.205413i | ||||
\(208\) | −2371.05 | −0.790399 | ||||||||
\(209\) | 3783.39 | − | 3269.86i | 1.25216 | − | 1.08221i | ||||
\(210\) | −849.483 | −0.279142 | ||||||||
\(211\) | −95.3371 | − | 293.417i | −0.0311056 | − | 0.0957331i | 0.934298 | − | 0.356492i | \(-0.116027\pi\) |
−0.965404 | + | 0.260759i | \(0.916027\pi\) | |||||||
\(212\) | 2570.99 | + | 1867.93i | 0.832907 | + | 0.605143i | ||||
\(213\) | 1727.27 | − | 1254.93i | 0.555635 | − | 0.403693i | ||||
\(214\) | −1414.67 | + | 4353.89i | −0.451890 | + | 1.39078i | ||||
\(215\) | 513.450 | − | 1580.24i | 0.162870 | − | 0.501262i | ||||
\(216\) | 650.925 | − | 472.925i | 0.205046 | − | 0.148974i | ||||
\(217\) | −62.1943 | − | 45.1868i | −0.0194563 | − | 0.0141359i | ||||
\(218\) | 344.294 | + | 1059.63i | 0.106966 | + | 0.329207i | ||||
\(219\) | −3135.15 | −0.967369 | ||||||||
\(220\) | 3131.01 | − | 264.888i | 0.959511 | − | 0.0811762i | ||||
\(221\) | −4045.20 | −1.23127 | ||||||||
\(222\) | −44.3151 | − | 136.388i | −0.0133975 | − | 0.0412332i | ||||
\(223\) | −3744.98 | − | 2720.89i | −1.12458 | − | 0.817058i | −0.139687 | − | 0.990196i | \(-0.544610\pi\) |
−0.984898 | + | 0.173137i | \(0.944610\pi\) | |||||||
\(224\) | −920.846 | + | 669.033i | −0.274672 | + | 0.199561i | ||||
\(225\) | −246.884 | + | 759.832i | −0.0731510 | + | 0.225135i | ||||
\(226\) | −751.901 | + | 2314.11i | −0.221308 | + | 0.681117i | ||||
\(227\) | −2093.34 | + | 1520.90i | −0.612070 | + | 0.444695i | −0.850142 | − | 0.526553i | \(-0.823484\pi\) |
0.238073 | + | 0.971247i | \(0.423484\pi\) | |||||||
\(228\) | 4760.20 | + | 3458.49i | 1.38268 | + | 1.00458i | ||||
\(229\) | 675.764 | + | 2079.79i | 0.195003 | + | 0.600158i | 0.999977 | + | 0.00684712i | \(0.00217952\pi\) |
−0.804973 | + | 0.593311i | \(0.797820\pi\) | |||||||
\(230\) | 2031.92 | 0.582526 | ||||||||
\(231\) | 248.265 | − | 1061.47i | 0.0707128 | − | 0.302335i | ||||
\(232\) | 4405.41 | 1.24668 | ||||||||
\(233\) | 2059.58 | + | 6338.75i | 0.579090 | + | 1.78225i | 0.621810 | + | 0.783168i | \(0.286397\pi\) |
−0.0427208 | + | 0.999087i | \(0.513603\pi\) | |||||||
\(234\) | −3103.08 | − | 2254.52i | −0.866899 | − | 0.629839i | ||||
\(235\) | 1154.79 | − | 839.002i | 0.320553 | − | 0.232895i | ||||
\(236\) | 747.869 | − | 2301.71i | 0.206280 | − | 0.634866i | ||||
\(237\) | 47.0870 | − | 144.919i | 0.0129056 | − | 0.0397194i | ||||
\(238\) | 1706.28 | − | 1239.68i | 0.464712 | − | 0.337633i | ||||
\(239\) | −1800.04 | − | 1307.80i | −0.487174 | − | 0.353953i | 0.316922 | − | 0.948451i | \(-0.397350\pi\) |
−0.804097 | + | 0.594499i | \(0.797350\pi\) | |||||||
\(240\) | 146.631 | + | 451.283i | 0.0394374 | + | 0.121376i | ||||
\(241\) | 745.650 | 0.199301 | 0.0996505 | − | 0.995023i | \(-0.468228\pi\) | ||||
0.0996505 | + | 0.995023i | \(0.468228\pi\) | |||||||
\(242\) | −910.600 | + | 6220.35i | −0.241883 | + | 1.65231i | ||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1004.00 | + | 3090.00i | 0.263420 | + | 0.810724i | ||||
\(245\) | 1187.18 | + | 862.539i | 0.309577 | + | 0.224921i | ||||
\(246\) | 4332.83 | − | 3147.99i | 1.12297 | − | 0.815888i | ||||
\(247\) | 3821.79 | − | 11762.3i | 0.984513 | − | 3.03002i | ||||
\(248\) | −71.0761 | + | 218.750i | −0.0181989 | + | 0.0560106i | ||||
\(249\) | 2970.33 | − | 2158.07i | 0.755972 | − | 0.549246i | ||||
\(250\) | −4916.74 | − | 3572.22i | −1.24385 | − | 0.903709i | ||||
\(251\) | −546.697 | − | 1682.56i | −0.137479 | − | 0.423116i | 0.858489 | − | 0.512833i | \(-0.171404\pi\) |
−0.995967 | + | 0.0897164i | \(0.971404\pi\) | |||||||
\(252\) | 1282.68 | 0.320639 | ||||||||
\(253\) | −593.839 | + | 2538.98i | −0.147566 | + | 0.630926i | ||||
\(254\) | −4877.86 | −1.20498 | ||||||||
\(255\) | 250.163 | + | 769.923i | 0.0614346 | + | 0.189076i | ||||
\(256\) | 5188.69 | + | 3769.81i | 1.26677 | + | 0.920363i | ||||
\(257\) | 1942.61 | − | 1411.39i | 0.471505 | − | 0.342569i | −0.326522 | − | 0.945189i | \(-0.605877\pi\) |
0.798028 | + | 0.602621i | \(0.205877\pi\) | |||||||
\(258\) | −1208.73 | + | 3720.09i | −0.291676 | + | 0.897686i | ||||
\(259\) | 31.1495 | − | 95.8683i | 0.00747311 | − | 0.0229999i | ||||
\(260\) | 6287.13 | − | 4567.87i | 1.49966 | − | 1.08957i | ||||
\(261\) | 1076.41 | + | 782.055i | 0.255279 | + | 0.185471i | ||||
\(262\) | −1993.99 | − | 6136.88i | −0.470188 | − | 1.44709i | ||||
\(263\) | −5999.10 | −1.40654 | −0.703270 | − | 0.710923i | \(-0.748278\pi\) | ||||
−0.703270 | + | 0.710923i | \(0.748278\pi\) | |||||||
\(264\) | −3249.91 | + | 274.948i | −0.757644 | + | 0.0640979i | ||||
\(265\) | −1336.78 | −0.309879 | ||||||||
\(266\) | 1992.59 | + | 6132.57i | 0.459299 | + | 1.41358i | ||||
\(267\) | −2341.73 | − | 1701.36i | −0.536747 | − | 0.389969i | ||||
\(268\) | 4198.37 | − | 3050.30i | 0.956927 | − | 0.695248i | ||||
\(269\) | 241.484 | − | 743.212i | 0.0547344 | − | 0.168455i | −0.919952 | − | 0.392030i | \(-0.871773\pi\) |
0.974687 | + | 0.223575i | \(0.0717728\pi\) | |||||||
\(270\) | −237.202 | + | 730.032i | −0.0534654 | + | 0.164549i | ||||
\(271\) | −363.969 | + | 264.439i | −0.0815851 | + | 0.0592751i | −0.627830 | − | 0.778350i | \(-0.716057\pi\) |
0.546245 | + | 0.837625i | \(0.316057\pi\) | |||||||
\(272\) | −953.097 | − | 692.465i | −0.212463 | − | 0.154364i | ||||
\(273\) | −833.137 | − | 2564.13i | −0.184702 | − | 0.568455i | ||||
\(274\) | −7141.19 | −1.57451 | ||||||||
\(275\) | 2450.28 | − | 2117.70i | 0.537301 | − | 0.464372i | ||||
\(276\) | −3068.10 | −0.669123 | ||||||||
\(277\) | −1303.43 | − | 4011.55i | −0.282728 | − | 0.870147i | −0.987070 | − | 0.160287i | \(-0.948758\pi\) |
0.704342 | − | 0.709860i | \(-0.251242\pi\) | |||||||
\(278\) | −4005.83 | − | 2910.41i | −0.864223 | − | 0.627895i | ||||
\(279\) | −56.1994 | + | 40.8313i | −0.0120594 | + | 0.00876166i | ||||
\(280\) | −552.058 | + | 1699.06i | −0.117828 | + | 0.362636i | ||||
\(281\) | −945.957 | + | 2911.36i | −0.200822 | + | 0.618068i | 0.799037 | + | 0.601282i | \(0.205343\pi\) |
−0.999859 | + | 0.0167855i | \(0.994657\pi\) | |||||||
\(282\) | −2718.53 | + | 1975.12i | −0.574063 | + | 0.417081i | ||||
\(283\) | 4714.18 | + | 3425.05i | 0.990208 | + | 0.719428i | 0.959967 | − | 0.280115i | \(-0.0903725\pi\) |
0.0302411 | + | 0.999543i | \(0.490372\pi\) | |||||||
\(284\) | −3146.85 | − | 9685.00i | −0.657504 | − | 2.02359i | ||||
\(285\) | −2475.06 | −0.514420 | ||||||||
\(286\) | 6034.14 | + | 14329.6i | 1.24757 | + | 2.96268i | ||||
\(287\) | 3764.55 | 0.774267 | ||||||||
\(288\) | 317.828 | + | 978.175i | 0.0650285 | + | 0.200137i | ||||
\(289\) | 2348.64 | + | 1706.39i | 0.478047 | + | 0.347321i | ||||
\(290\) | −3400.21 | + | 2470.40i | −0.688508 | + | 0.500230i | ||||
\(291\) | 236.539 | − | 727.991i | 0.0476499 | − | 0.146651i | ||||
\(292\) | −4620.96 | + | 14221.9i | −0.926100 | + | 2.85024i | ||||
\(293\) | 370.485 | − | 269.173i | 0.0738703 | − | 0.0536699i | −0.550237 | − | 0.835008i | \(-0.685463\pi\) |
0.624108 | + | 0.781338i | \(0.285463\pi\) | |||||||
\(294\) | −2794.79 | − | 2030.53i | −0.554406 | − | 0.402800i | ||||
\(295\) | 314.589 | + | 968.206i | 0.0620885 | + | 0.191089i | ||||
\(296\) | −301.590 | −0.0592215 | ||||||||
\(297\) | −842.885 | − | 509.750i | −0.164677 | − | 0.0995915i | ||||
\(298\) | 1828.95 | 0.355531 | ||||||||
\(299\) | 1992.82 | + | 6133.28i | 0.385445 | + | 1.18628i | ||||
\(300\) | 3082.91 | + | 2239.86i | 0.593306 | + | 0.431062i | ||||
\(301\) | −2224.36 | + | 1616.09i | −0.425946 | + | 0.309468i | ||||
\(302\) | −990.713 | + | 3049.10i | −0.188772 | + | 0.580980i | ||||
\(303\) | 125.780 | − | 387.111i | 0.0238478 | − | 0.0733959i | ||||
\(304\) | 2913.94 | − | 2117.10i | 0.549757 | − | 0.399422i | ||||
\(305\) | −1105.67 | − | 803.320i | −0.207576 | − | 0.150813i | ||||
\(306\) | −588.918 | − | 1812.50i | −0.110020 | − | 0.338608i | ||||
\(307\) | 3941.62 | 0.732769 | 0.366385 | − | 0.930463i | \(-0.380595\pi\) | ||||
0.366385 | + | 0.930463i | \(0.380595\pi\) | |||||||
\(308\) | −4449.17 | − | 2690.71i | −0.823100 | − | 0.497784i | ||||
\(309\) | −2067.52 | −0.380638 | ||||||||
\(310\) | −67.8088 | − | 208.694i | −0.0124235 | − | 0.0382356i | ||||
\(311\) | −2220.01 | − | 1612.93i | −0.404776 | − | 0.294087i | 0.366708 | − | 0.930336i | \(-0.380485\pi\) |
−0.771483 | + | 0.636249i | \(0.780485\pi\) | |||||||
\(312\) | −6525.89 | + | 4741.34i | −1.18415 | + | 0.860338i | ||||
\(313\) | −607.584 | + | 1869.95i | −0.109721 | + | 0.337687i | −0.990809 | − | 0.135265i | \(-0.956811\pi\) |
0.881088 | + | 0.472952i | \(0.156811\pi\) | |||||||
\(314\) | 5268.02 | − | 16213.3i | 0.946789 | − | 2.91392i | ||||
\(315\) | −436.508 | + | 317.142i | −0.0780776 | + | 0.0567267i | ||||
\(316\) | −587.987 | − | 427.197i | −0.104674 | − | 0.0760498i | ||||
\(317\) | 1972.03 | + | 6069.28i | 0.349401 | + | 1.07535i | 0.959185 | + | 0.282778i | \(0.0912561\pi\) |
−0.609784 | + | 0.792568i | \(0.708744\pi\) | |||||||
\(318\) | 3146.97 | 0.554947 | ||||||||
\(319\) | −2093.15 | − | 4970.70i | −0.367378 | − | 0.872432i | ||||
\(320\) | −4514.28 | −0.788612 | ||||||||
\(321\) | 898.533 | + | 2765.40i | 0.156234 | + | 0.480840i | ||||
\(322\) | −2720.17 | − | 1976.32i | −0.470773 | − | 0.342037i | ||||
\(323\) | 4971.41 | − | 3611.94i | 0.856399 | − | 0.622210i | ||||
\(324\) | 358.163 | − | 1102.31i | 0.0614133 | − | 0.189011i | ||||
\(325\) | 2475.16 | − | 7617.74i | 0.422452 | − | 1.30017i | ||||
\(326\) | 3514.55 | − | 2553.47i | 0.597094 | − | 0.433814i | ||||
\(327\) | 572.513 | + | 415.955i | 0.0968197 | + | 0.0703436i | ||||
\(328\) | −3480.52 | − | 10711.9i | −0.585913 | − | 1.80326i | ||||
\(329\) | −2361.97 | −0.395805 | ||||||||
\(330\) | 2354.19 | − | 2034.65i | 0.392708 | − | 0.339405i | ||||
\(331\) | 3351.60 | 0.556557 | 0.278279 | − | 0.960500i | \(-0.410236\pi\) | ||||
0.278279 | + | 0.960500i | \(0.410236\pi\) | |||||||
\(332\) | −5411.54 | − | 16655.0i | −0.894569 | − | 2.75320i | ||||
\(333\) | −73.6898 | − | 53.5388i | −0.0121267 | − | 0.00881053i | ||||
\(334\) | −8821.95 | + | 6409.52i | −1.44526 | + | 1.05004i | ||||
\(335\) | −674.565 | + | 2076.10i | −0.110016 | + | 0.338595i | ||||
\(336\) | 242.636 | − | 746.757i | 0.0393955 | − | 0.121247i | ||||
\(337\) | 2127.64 | − | 1545.82i | 0.343916 | − | 0.249870i | −0.402396 | − | 0.915466i | \(-0.631823\pi\) |
0.746312 | + | 0.665596i | \(0.231823\pi\) | |||||||
\(338\) | 22714.9 | + | 16503.4i | 3.65541 | + | 2.65581i | ||||
\(339\) | 477.574 | + | 1469.82i | 0.0765140 | + | 0.235486i | ||||
\(340\) | 3861.29 | 0.615906 | ||||||||
\(341\) | 280.590 | − | 23.7383i | 0.0445595 | − | 0.00376981i | ||||
\(342\) | 5826.62 | 0.921251 | ||||||||
\(343\) | −1806.06 | − | 5558.48i | −0.284309 | − | 0.875014i | ||||
\(344\) | 6655.07 | + | 4835.19i | 1.04307 | + | 0.757837i | ||||
\(345\) | 1044.11 | − | 758.588i | 0.162936 | − | 0.118380i | ||||
\(346\) | 669.097 | − | 2059.27i | 0.103962 | − | 0.319962i | ||||
\(347\) | −2710.55 | + | 8342.20i | −0.419336 | + | 1.29058i | 0.488978 | + | 0.872296i | \(0.337370\pi\) |
−0.908314 | + | 0.418288i | \(0.862630\pi\) | |||||||
\(348\) | 5134.14 | − | 3730.17i | 0.790859 | − | 0.574593i | ||||
\(349\) | 5365.95 | + | 3898.59i | 0.823017 | + | 0.597957i | 0.917575 | − | 0.397563i | \(-0.130144\pi\) |
−0.0945581 | + | 0.995519i | \(0.530144\pi\) | |||||||
\(350\) | 1290.49 | + | 3971.71i | 0.197084 | + | 0.606563i | ||||
\(351\) | −2436.21 | −0.370471 | ||||||||
\(352\) | 949.513 | − | 4059.68i | 0.143776 | − | 0.614720i | ||||
\(353\) | 722.467 | 0.108932 | 0.0544661 | − | 0.998516i | \(-0.482654\pi\) | ||||
0.0544661 | + | 0.998516i | \(0.482654\pi\) | |||||||
\(354\) | −740.586 | − | 2279.29i | −0.111191 | − | 0.342211i | ||||
\(355\) | 3465.52 | + | 2517.85i | 0.518115 | + | 0.376433i | ||||
\(356\) | −11169.4 | + | 8115.01i | −1.66285 | + | 1.20813i | ||||
\(357\) | 413.956 | − | 1274.03i | 0.0613694 | − | 0.188876i | ||||
\(358\) | 5197.13 | − | 15995.1i | 0.767254 | − | 2.36136i | ||||
\(359\) | −6597.95 | + | 4793.69i | −0.969990 | + | 0.704739i | −0.955449 | − | 0.295155i | \(-0.904629\pi\) |
−0.0145406 | + | 0.999894i | \(0.504629\pi\) | |||||||
\(360\) | 1305.99 | + | 948.859i | 0.191200 | + | 0.138915i | ||||
\(361\) | 3686.08 | + | 11344.6i | 0.537407 | + | 1.65397i | ||||
\(362\) | −3802.92 | −0.552146 | ||||||||
\(363\) | 1854.36 | + | 3536.30i | 0.268123 | + | 0.511315i | ||||
\(364\) | −12859.5 | −1.85171 | ||||||||
\(365\) | −1943.79 | − | 5982.39i | −0.278748 | − | 0.857897i | ||||
\(366\) | 2602.91 | + | 1891.12i | 0.371738 | + | 0.270084i | ||||
\(367\) | −9647.07 | + | 7009.00i | −1.37213 | + | 0.996913i | −0.374566 | + | 0.927200i | \(0.622208\pi\) |
−0.997567 | + | 0.0697126i | \(0.977792\pi\) | |||||||
\(368\) | −580.374 | + | 1786.21i | −0.0822122 | + | 0.253023i | ||||
\(369\) | 1051.18 | − | 3235.20i | 0.148299 | − | 0.456416i | ||||
\(370\) | 232.775 | − | 169.121i | 0.0327065 | − | 0.0237627i | ||||
\(371\) | 1789.57 | + | 1300.20i | 0.250431 | + | 0.181949i | ||||
\(372\) | 102.388 | + | 315.117i | 0.0142703 | + | 0.0439195i | ||||
\(373\) | −5520.95 | −0.766391 | −0.383195 | − | 0.923667i | \(-0.625176\pi\) | ||||
−0.383195 | + | 0.923667i | \(0.625176\pi\) | |||||||
\(374\) | −1759.39 | + | 7522.36i | −0.243252 | + | 1.04003i | ||||
\(375\) | −3860.11 | −0.531561 | ||||||||
\(376\) | 2183.76 | + | 6720.93i | 0.299518 | + | 0.921823i | ||||
\(377\) | −10791.6 | − | 7840.54i | −1.47426 | − | 1.07111i | ||||
\(378\) | 1027.60 | − | 746.595i | 0.139825 | − | 0.101589i | ||||
\(379\) | 2086.95 | − | 6422.98i | 0.282848 | − | 0.870518i | −0.704187 | − | 0.710015i | \(-0.748688\pi\) |
0.987035 | − | 0.160503i | \(-0.0513117\pi\) | |||||||
\(380\) | −3648.04 | + | 11227.5i | −0.492475 | + | 1.51568i | ||||
\(381\) | −2506.50 | + | 1821.08i | −0.337039 | + | 0.244873i | ||||
\(382\) | −8673.55 | − | 6301.70i | −1.16172 | − | 0.844040i | ||||
\(383\) | −1642.23 | − | 5054.26i | −0.219097 | − | 0.674310i | −0.998837 | − | 0.0482074i | \(-0.984649\pi\) |
0.779741 | − | 0.626102i | \(-0.215351\pi\) | |||||||
\(384\) | 7884.52 | 1.04780 | ||||||||
\(385\) | 2179.38 | − | 184.379i | 0.288497 | − | 0.0244073i | ||||
\(386\) | 22584.6 | 2.97804 | ||||||||
\(387\) | 767.733 | + | 2362.84i | 0.100843 | + | 0.310361i | ||||
\(388\) | −2953.72 | − | 2146.00i | −0.386475 | − | 0.280790i | ||||
\(389\) | 92.0601 | − | 66.8856i | 0.0119991 | − | 0.00871783i | −0.581770 | − | 0.813354i | \(-0.697639\pi\) |
0.593769 | + | 0.804636i | \(0.297639\pi\) | |||||||
\(390\) | 2378.08 | − | 7318.98i | 0.308766 | − | 0.950285i | ||||
\(391\) | −990.163 | + | 3047.41i | −0.128068 | + | 0.394154i | ||||
\(392\) | −5877.55 | + | 4270.29i | −0.757299 | + | 0.550210i | ||||
\(393\) | −3315.73 | − | 2409.02i | −0.425589 | − | 0.309208i | ||||
\(394\) | 2932.49 | + | 9025.27i | 0.374966 | + | 1.15403i | ||||
\(395\) | 305.723 | 0.0389433 | ||||||||
\(396\) | −3554.70 | + | 3072.21i | −0.451087 | + | 0.389860i | ||||
\(397\) | −4034.28 | −0.510012 | −0.255006 | − | 0.966940i | \(-0.582077\pi\) | ||||
−0.255006 | + | 0.966940i | \(0.582077\pi\) | |||||||
\(398\) | −4743.91 | − | 14600.3i | −0.597465 | − | 1.83881i | ||||
\(399\) | 3313.40 | + | 2407.32i | 0.415733 | + | 0.302048i | ||||
\(400\) | 1887.20 | − | 1371.13i | 0.235899 | − | 0.171391i | ||||
\(401\) | 3098.74 | − | 9536.93i | 0.385894 | − | 1.18766i | −0.549936 | − | 0.835207i | \(-0.685348\pi\) |
0.935830 | − | 0.352452i | \(-0.114652\pi\) | |||||||
\(402\) | 1588.02 | − | 4887.42i | 0.197023 | − | 0.606374i | ||||
\(403\) | 563.430 | − | 409.356i | 0.0696438 | − | 0.0505992i | ||||
\(404\) | −1570.65 | − | 1141.14i | −0.193422 | − | 0.140529i | ||||
\(405\) | 150.660 | + | 463.684i | 0.0184848 | + | 0.0568905i | ||||
\(406\) | 6954.71 | 0.850139 | ||||||||
\(407\) | 143.295 | + | 340.290i | 0.0174517 | + | 0.0414436i | ||||
\(408\) | −4007.93 | −0.486329 | ||||||||
\(409\) | 91.0554 | + | 280.240i | 0.0110083 | + | 0.0338801i | 0.956410 | − | 0.292028i | \(-0.0943300\pi\) |
−0.945401 | + | 0.325908i | \(0.894330\pi\) | |||||||
\(410\) | 8693.24 | + | 6316.01i | 1.04714 | + | 0.760794i | ||||
\(411\) | −3669.51 | + | 2666.06i | −0.440398 | + | 0.319968i | ||||
\(412\) | −3047.36 | + | 9378.82i | −0.364400 | + | 1.12151i | ||||
\(413\) | 520.564 | − | 1602.13i | 0.0620225 | − | 0.190886i | ||||
\(414\) | −2457.97 | + | 1785.82i | −0.291794 | + | 0.212001i | ||||
\(415\) | 5959.56 | + | 4329.87i | 0.704924 | + | 0.512157i | ||||
\(416\) | −3186.41 | − | 9806.75i | −0.375544 | − | 1.15581i | ||||
\(417\) | −3144.96 | −0.369327 | ||||||||
\(418\) | −20210.6 | − | 12222.7i | −2.36491 | − | 1.43022i | ||||
\(419\) | −1094.76 | −0.127643 | −0.0638215 | − | 0.997961i | \(-0.520329\pi\) | ||||
−0.0638215 | + | 0.997961i | \(0.520329\pi\) | |||||||
\(420\) | 795.259 | + | 2447.56i | 0.0923921 | + | 0.284354i | ||||
\(421\) | −10574.2 | − | 7682.63i | −1.22412 | − | 0.889379i | −0.227689 | − | 0.973734i | \(-0.573117\pi\) |
−0.996436 | + | 0.0843554i | \(0.973117\pi\) | |||||||
\(422\) | −1178.90 | + | 856.524i | −0.135991 | + | 0.0988031i | ||||
\(423\) | −659.535 | + | 2029.84i | −0.0758102 | + | 0.233320i | ||||
\(424\) | 2045.14 | − | 6294.28i | 0.234247 | − | 0.720937i | ||||
\(425\) | 3219.70 | − | 2339.25i | 0.367479 | − | 0.266989i | ||||
\(426\) | −8158.32 | − | 5927.36i | −0.927868 | − | 0.674136i | ||||
\(427\) | 698.848 | + | 2150.83i | 0.0792029 | + | 0.243761i | ||||
\(428\) | 13868.9 | 1.56631 | ||||||||
\(429\) | 8450.39 | + | 5110.52i | 0.951023 | + | 0.575148i | ||||
\(430\) | −7847.97 | −0.880146 | ||||||||
\(431\) | −455.301 | − | 1401.27i | −0.0508842 | − | 0.156605i | 0.922386 | − | 0.386271i | \(-0.126237\pi\) |
−0.973270 | + | 0.229665i | \(0.926237\pi\) | |||||||
\(432\) | −574.000 | − | 417.035i | −0.0639273 | − | 0.0464459i | ||||
\(433\) | 3285.04 | − | 2386.72i | 0.364594 | − | 0.264893i | −0.390372 | − | 0.920657i | \(-0.627654\pi\) |
0.754966 | + | 0.655764i | \(0.227654\pi\) | |||||||
\(434\) | −112.206 | + | 345.335i | −0.0124103 | + | 0.0381949i | ||||
\(435\) | −824.918 | + | 2538.84i | −0.0909237 | + | 0.279834i | ||||
\(436\) | 2730.72 | − | 1983.98i | 0.299949 | − | 0.217926i | ||||
\(437\) | −7925.49 | − | 5758.21i | −0.867569 | − | 0.630326i | ||||
\(438\) | 4575.96 | + | 14083.3i | 0.499196 | + | 1.53637i | ||||
\(439\) | 11732.1 | 1.27550 | 0.637749 | − | 0.770244i | \(-0.279866\pi\) | ||||
0.637749 | + | 0.770244i | \(0.279866\pi\) | |||||||
\(440\) | −2539.59 | − | 6030.90i | −0.275160 | − | 0.653436i | ||||
\(441\) | −2194.18 | −0.236927 | ||||||||
\(442\) | 5904.24 | + | 18171.4i | 0.635375 | + | 1.95548i | ||||
\(443\) | 738.883 | + | 536.830i | 0.0792447 | + | 0.0575747i | 0.626702 | − | 0.779259i | \(-0.284404\pi\) |
−0.547458 | + | 0.836833i | \(0.684404\pi\) | |||||||
\(444\) | −351.479 | + | 255.364i | −0.0375686 | + | 0.0272952i | ||||
\(445\) | 1794.61 | − | 5523.25i | 0.191175 | − | 0.588376i | ||||
\(446\) | −6756.40 | + | 20794.1i | −0.717320 | + | 2.20768i | ||||
\(447\) | 939.808 | − | 682.810i | 0.0994438 | − | 0.0722502i | ||||
\(448\) | 6043.33 | + | 4390.74i | 0.637323 | + | 0.463042i | ||||
\(449\) | 4495.39 | + | 13835.4i | 0.472495 | + | 1.45419i | 0.849306 | + | 0.527901i | \(0.177021\pi\) |
−0.376810 | + | 0.926290i | \(0.622979\pi\) | |||||||
\(450\) | 3773.57 | 0.395306 | ||||||||
\(451\) | −10432.8 | + | 9016.71i | −1.08927 | + | 0.941419i | ||||
\(452\) | 7371.40 | 0.767083 | ||||||||
\(453\) | 629.257 | + | 1936.65i | 0.0652650 | + | 0.200865i | ||||
\(454\) | 9887.37 | + | 7183.59i | 1.02211 | + | 0.742605i | ||||
\(455\) | 4376.24 | − | 3179.52i | 0.450904 | − | 0.327601i | ||||
\(456\) | 3786.58 | − | 11653.9i | 0.388865 | − | 1.19680i | ||||
\(457\) | 559.410 | − | 1721.69i | 0.0572606 | − | 0.176230i | −0.918335 | − | 0.395803i | \(-0.870466\pi\) |
0.975596 | + | 0.219573i | \(0.0704663\pi\) | |||||||
\(458\) | 8356.25 | − | 6071.17i | 0.852537 | − | 0.619404i | ||||
\(459\) | −979.288 | − | 711.494i | −0.0995844 | − | 0.0723523i | ||||
\(460\) | −1902.22 | − | 5854.44i | −0.192808 | − | 0.593401i | ||||
\(461\) | 15271.1 | 1.54284 | 0.771419 | − | 0.636328i | \(-0.219547\pi\) | ||||
0.771419 | + | 0.636328i | \(0.219547\pi\) | |||||||
\(462\) | −5130.55 | + | 434.053i | −0.516656 | + | 0.0437099i | ||||
\(463\) | −12919.4 | −1.29679 | −0.648397 | − | 0.761302i | \(-0.724560\pi\) | ||||
−0.648397 | + | 0.761302i | \(0.724560\pi\) | |||||||
\(464\) | −1200.46 | − | 3694.65i | −0.120108 | − | 0.369654i | ||||
\(465\) | −112.756 | − | 81.9223i | −0.0112451 | − | 0.00817002i | ||||
\(466\) | 25468.1 | − | 18503.6i | 2.53173 | − | 1.83941i | ||||
\(467\) | −1120.49 | + | 3448.51i | −0.111028 | + | 0.341709i | −0.991098 | − | 0.133135i | \(-0.957496\pi\) |
0.880070 | + | 0.474844i | \(0.157496\pi\) | |||||||
\(468\) | −3590.78 | + | 11051.3i | −0.354666 | + | 1.09155i | ||||
\(469\) | 2922.33 | − | 2123.20i | 0.287720 | − | 0.209041i | ||||
\(470\) | −5454.35 | − | 3962.82i | −0.535299 | − | 0.388917i | ||||
\(471\) | −3346.01 | − | 10298.0i | −0.327338 | − | 1.00744i | ||||
\(472\) | −5040.11 | −0.491504 | ||||||||
\(473\) | 2293.60 | − | 9806.38i | 0.222960 | − | 0.953273i | ||||
\(474\) | −719.713 | −0.0697416 | ||||||||
\(475\) | 3759.97 | + | 11572.0i | 0.363199 | + | 1.11781i | ||||
\(476\) | −5169.17 | − | 3755.62i | −0.497749 | − | 0.361636i | ||||
\(477\) | 1617.07 | − | 1174.87i | 0.155222 | − | 0.112775i | ||||
\(478\) | −3247.48 | + | 9994.73i | −0.310746 | + | 0.956377i | ||||
\(479\) | 2325.95 | − | 7158.52i | 0.221869 | − | 0.682842i | −0.776726 | − | 0.629839i | \(-0.783121\pi\) |
0.998594 | − | 0.0530027i | \(-0.0168792\pi\) | |||||||
\(480\) | −1669.47 | + | 1212.94i | −0.158751 | + | 0.115339i | ||||
\(481\) | 738.782 | + | 536.756i | 0.0700323 | + | 0.0508815i | ||||
\(482\) | −1088.32 | − | 3349.52i | −0.102846 | − | 0.316528i | ||||
\(483\) | −2135.59 | −0.201186 | ||||||||
\(484\) | 18774.7 | − | 3199.65i | 1.76322 | − | 0.300493i | ||||
\(485\) | 1535.78 | 0.143786 | ||||||||
\(486\) | −354.674 | − | 1091.58i | −0.0331036 | − | 0.101882i | ||||
\(487\) | 8956.17 | + | 6507.04i | 0.833353 | + | 0.605466i | 0.920506 | − | 0.390729i | \(-0.127777\pi\) |
−0.0871530 | + | 0.996195i | \(0.527777\pi\) | |||||||
\(488\) | 5474.02 | − | 3977.11i | 0.507781 | − | 0.368925i | ||||
\(489\) | 852.657 | − | 2624.21i | 0.0788517 | − | 0.242680i | ||||
\(490\) | 2141.82 | − | 6591.85i | 0.197465 | − | 0.607734i | ||||
\(491\) | −12589.0 | + | 9146.43i | −1.15709 | + | 0.840678i | −0.989408 | − | 0.145163i | \(-0.953629\pi\) |
−0.167686 | + | 0.985840i | \(0.553629\pi\) | |||||||
\(492\) | −13126.3 | − | 9536.84i | −1.20281 | − | 0.873890i | ||||
\(493\) | −2048.08 | − | 6303.35i | −0.187102 | − | 0.575839i | ||||
\(494\) | −58415.2 | −5.32029 | ||||||||
\(495\) | 450.097 | − | 1924.41i | 0.0408694 | − | 0.174739i | ||||
\(496\) | 202.825 | 0.0183611 | ||||||||
\(497\) | −2190.40 | − | 6741.37i | −0.197692 | − | 0.608434i | ||||
\(498\) | −14029.6 | − | 10193.1i | −1.26241 | − | 0.917197i | ||||
\(499\) | 6505.61 | − | 4726.61i | 0.583630 | − | 0.424032i | −0.256401 | − | 0.966570i | \(-0.582537\pi\) |
0.840031 | + | 0.542539i | \(0.182537\pi\) | |||||||
\(500\) | −5689.50 | + | 17510.5i | −0.508884 | + | 1.56618i | ||||
\(501\) | −2140.27 | + | 6587.08i | −0.190859 | + | 0.587404i | ||||
\(502\) | −6760.25 | + | 4911.61i | −0.601045 | + | 0.436685i | ||||
\(503\) | −2493.19 | − | 1811.41i | −0.221005 | − | 0.160570i | 0.471774 | − | 0.881720i | \(-0.343614\pi\) |
−0.692779 | + | 0.721150i | \(0.743614\pi\) | |||||||
\(504\) | −825.460 | − | 2540.50i | −0.0729542 | − | 0.224530i | ||||
\(505\) | 816.656 | 0.0719618 | ||||||||
\(506\) | 12272.0 | − | 1038.23i | 1.07818 | − | 0.0912157i | ||||
\(507\) | 17833.4 | 1.56215 | ||||||||
\(508\) | 4566.50 | + | 14054.2i | 0.398830 | + | 1.22747i | ||||
\(509\) | 9792.05 | + | 7114.34i | 0.852701 | + | 0.619524i | 0.925890 | − | 0.377794i | \(-0.123317\pi\) |
−0.0731882 | + | 0.997318i | \(0.523317\pi\) | |||||||
\(510\) | 3093.43 | − | 2247.51i | 0.268587 | − | 0.195140i | ||||
\(511\) | −3216.48 | + | 9899.31i | −0.278452 | + | 0.856986i | ||||
\(512\) | 2863.84 | − | 8813.98i | 0.247197 | − | 0.760794i | ||||
\(513\) | 2994.02 | − | 2175.28i | 0.257679 | − | 0.187215i | ||||
\(514\) | −9175.45 | − | 6666.36i | −0.787377 | − | 0.572063i | ||||
\(515\) | −1281.87 | − | 3945.18i | −0.109681 | − | 0.337563i | ||||
\(516\) | 11850.0 | 1.01098 | ||||||||
\(517\) | 6545.77 | − | 5657.30i | 0.556833 | − | 0.481253i | ||||
\(518\) | −476.113 | −0.0403846 | ||||||||
\(519\) | −424.980 | − | 1307.95i | −0.0359433 | − | 0.110622i | ||||
\(520\) | −13093.3 | − | 9512.85i | −1.10419 | − | 0.802242i | ||||
\(521\) | 723.094 | − | 525.359i | 0.0608048 | − | 0.0441773i | −0.556968 | − | 0.830534i | \(-0.688035\pi\) |
0.617772 | + | 0.786357i | \(0.288035\pi\) | |||||||
\(522\) | 1941.97 | − | 5976.77i | 0.162831 | − | 0.501142i | ||||
\(523\) | 1461.97 | − | 4499.48i | 0.122232 | − | 0.376193i | −0.871154 | − | 0.491009i | \(-0.836628\pi\) |
0.993387 | + | 0.114817i | \(0.0366281\pi\) | |||||||
\(524\) | −15815.0 | + | 11490.3i | −1.31848 | + | 0.957932i | ||||
\(525\) | 2145.90 | + | 1559.09i | 0.178390 | + | 0.129608i | ||||
\(526\) | 8756.07 | + | 26948.4i | 0.725823 | + | 2.23385i | ||||
\(527\) | 346.035 | 0.0286025 | ||||||||
\(528\) | 1116.18 | + | 2650.65i | 0.0919992 | + | 0.218475i | ||||
\(529\) | −7058.77 | −0.580157 | ||||||||
\(530\) | 1951.12 | + | 6004.94i | 0.159908 | + | 0.492147i | ||||
\(531\) | −1231.49 | − | 894.730i | −0.100644 | − | 0.0731223i | ||||
\(532\) | 15803.9 | − | 11482.2i | 1.28795 | − | 0.935748i | ||||
\(533\) | −10538.7 | + | 32434.7i | −0.856435 | + | 2.63584i | ||||
\(534\) | −4224.76 | + | 13002.5i | −0.342366 | + | 1.05369i | ||||
\(535\) | −4719.75 | + | 3429.10i | −0.381406 | + | 0.277108i | ||||
\(536\) | −8743.35 | − | 6352.42i | −0.704581 | − | 0.511908i | ||||
\(537\) | −3300.98 | − | 10159.4i | −0.265266 | − | 0.816406i | ||||
\(538\) | −3691.03 | −0.295783 | ||||||||
\(539\) | 7610.86 | + | 4602.80i | 0.608205 | + | 0.367823i | ||||
\(540\) | 2325.45 | 0.185318 | ||||||||
\(541\) | −5944.61 | − | 18295.6i | −0.472419 | − | 1.45396i | −0.849407 | − | 0.527739i | \(-0.823040\pi\) |
0.376987 | − | 0.926219i | \(-0.376960\pi\) | |||||||
\(542\) | 1719.12 | + | 1249.01i | 0.136241 | + | 0.0989847i | ||||
\(543\) | −1954.13 | + | 1419.76i | −0.154438 | + | 0.112206i | ||||
\(544\) | 1583.21 | − | 4872.63i | 0.124779 | − | 0.384030i | ||||
\(545\) | −438.753 | + | 1350.34i | −0.0344846 | + | 0.106133i | ||||
\(546\) | −10302.3 | + | 7485.03i | −0.807502 | + | 0.586685i | ||||
\(547\) | −1572.62 | − | 1142.57i | −0.122925 | − | 0.0893105i | 0.524624 | − | 0.851334i | \(-0.324206\pi\) |
−0.647549 | + | 0.762024i | \(0.724206\pi\) | |||||||
\(548\) | 6685.36 | + | 20575.4i | 0.521139 | + | 1.60390i | ||||
\(549\) | 2043.53 | 0.158863 | ||||||||
\(550\) | −13089.2 | − | 7915.95i | −1.01478 | − | 0.613704i | ||||
\(551\) | 20263.3 | 1.56669 | ||||||||
\(552\) | 1974.46 | + | 6076.77i | 0.152244 | + | 0.468559i | ||||
\(553\) | −409.276 | − | 297.356i | −0.0314723 | − | 0.0228660i | ||||
\(554\) | −16117.8 | + | 11710.2i | −1.23606 | + | 0.898052i | ||||
\(555\) | 56.4731 | − | 173.806i | 0.00431919 | − | 0.0132931i | ||||
\(556\) | −4635.42 | + | 14266.4i | −0.353571 | + | 1.08818i | ||||
\(557\) | 11344.0 | − | 8241.91i | 0.862947 | − | 0.626967i | −0.0657384 | − | 0.997837i | \(-0.520940\pi\) |
0.928685 | + | 0.370869i | \(0.120940\pi\) | |||||||
\(558\) | 265.444 | + | 192.856i | 0.0201382 | + | 0.0146313i | ||||
\(559\) | −7696.95 | − | 23688.8i | −0.582373 | − | 1.79236i | ||||
\(560\) | 1575.37 | 0.118878 | ||||||||
\(561\) | 1904.29 | + | 4522.22i | 0.143314 | + | 0.340336i | ||||
\(562\) | 14458.7 | 1.08524 | ||||||||
\(563\) | 2766.65 | + | 8514.86i | 0.207105 | + | 0.637404i | 0.999620 | + | 0.0275520i | \(0.00877120\pi\) |
−0.792515 | + | 0.609852i | \(0.791229\pi\) | |||||||
\(564\) | 8235.79 | + | 5983.65i | 0.614874 | + | 0.446732i | ||||
\(565\) | −2508.57 | + | 1822.58i | −0.186790 | + | 0.135711i | ||||
\(566\) | 8504.95 | − | 26175.6i | 0.631607 | − | 1.94389i | ||||
\(567\) | 249.304 | − | 767.278i | 0.0184652 | − | 0.0568301i | ||||
\(568\) | −17157.3 | + | 12465.5i | −1.26743 | + | 0.920845i | ||||
\(569\) | −14526.8 | − | 10554.4i | −1.07029 | − | 0.777612i | −0.0943269 | − | 0.995541i | \(-0.530070\pi\) |
−0.975965 | + | 0.217929i | \(0.930070\pi\) | |||||||
\(570\) | 3612.51 | + | 11118.2i | 0.265458 | + | 0.816997i | ||||
\(571\) | −10089.5 | −0.739464 | −0.369732 | − | 0.929138i | \(-0.620551\pi\) | ||||
−0.369732 | + | 0.929138i | \(0.620551\pi\) | |||||||
\(572\) | 35637.9 | − | 30800.7i | 2.60506 | − | 2.25147i | ||||
\(573\) | −6809.57 | −0.496464 | ||||||||
\(574\) | −5494.61 | − | 16910.7i | −0.399548 | − | 1.22968i | ||||
\(575\) | −5132.89 | − | 3729.26i | −0.372272 | − | 0.270471i | ||||
\(576\) | 5460.82 | − | 3967.51i | 0.395024 | − | 0.287002i | ||||
\(577\) | −6570.03 | + | 20220.5i | −0.474027 | + | 1.45891i | 0.373238 | + | 0.927736i | \(0.378248\pi\) |
−0.847265 | + | 0.531170i | \(0.821752\pi\) | |||||||
\(578\) | 4237.24 | − | 13040.9i | 0.304924 | − | 0.938459i | ||||
\(579\) | 11605.1 | − | 8431.61i | 0.832975 | − | 0.605192i | ||||
\(580\) | 10301.0 | + | 7484.08i | 0.737455 | + | 0.535793i | ||||
\(581\) | −3766.77 | − | 11592.9i | −0.268971 | − | 0.827807i | ||||
\(582\) | −3615.44 | −0.257499 | ||||||||
\(583\) | −8073.66 | + | 683.044i | −0.573545 | + | 0.0485228i | ||||
\(584\) | 31142.0 | 2.20662 | ||||||||
\(585\) | −1510.45 | − | 4648.69i | −0.106751 | − | 0.328547i | ||||
\(586\) | −1749.90 | − | 1271.37i | −0.123358 | − | 0.0896245i | ||||
\(587\) | −6016.43 | + | 4371.19i | −0.423040 | + | 0.307357i | −0.778860 | − | 0.627198i | \(-0.784202\pi\) |
0.355820 | + | 0.934555i | \(0.384202\pi\) | |||||||
\(588\) | −3234.04 | + | 9953.36i | −0.226819 | + | 0.698077i | ||||
\(589\) | −326.924 | + | 1006.17i | −0.0228704 | + | 0.0703879i | ||||
\(590\) | 3890.10 | − | 2826.32i | 0.271445 | − | 0.197217i | ||||
\(591\) | 4876.31 | + | 3542.85i | 0.339399 | + | 0.246588i | ||||
\(592\) | 82.1826 | + | 252.932i | 0.00570555 | + | 0.0175599i | ||||
\(593\) | 1727.95 | 0.119660 | 0.0598301 | − | 0.998209i | \(-0.480944\pi\) | ||||
0.0598301 | + | 0.998209i | \(0.480944\pi\) | |||||||
\(594\) | −1059.59 | + | 4530.32i | −0.0731911 | + | 0.312931i | ||||
\(595\) | 2687.70 | 0.185185 | ||||||||
\(596\) | −1712.20 | − | 5269.62i | −0.117675 | − | 0.362168i | ||||
\(597\) | −7888.46 | − | 5731.30i | −0.540793 | − | 0.392909i | ||||
\(598\) | 24642.5 | − | 17903.8i | 1.68513 | − | 1.22432i | ||||
\(599\) | 854.645 | − | 2630.33i | 0.0582969 | − | 0.179419i | −0.917668 | − | 0.397349i | \(-0.869930\pi\) |
0.975965 | + | 0.217929i | \(0.0699303\pi\) | |||||||
\(600\) | 2452.35 | − | 7547.55i | 0.166861 | − | 0.513546i | ||||
\(601\) | 9978.89 | − | 7250.09i | 0.677283 | − | 0.492075i | −0.195172 | − | 0.980769i | \(-0.562527\pi\) |
0.872455 | + | 0.488694i | \(0.162527\pi\) | |||||||
\(602\) | 10506.2 | + | 7633.20i | 0.711297 | + | 0.516787i | ||||
\(603\) | −1008.64 | − | 3104.27i | −0.0681176 | − | 0.209645i | ||||
\(604\) | 9712.64 | 0.654307 | ||||||||
\(605\) | −5598.13 | + | 5730.93i | −0.376192 | + | 0.385117i | ||||
\(606\) | −1922.52 | −0.128873 | ||||||||
\(607\) | 2570.13 | + | 7910.05i | 0.171859 | + | 0.528928i | 0.999476 | − | 0.0323655i | \(-0.0103041\pi\) |
−0.827617 | + | 0.561293i | \(0.810304\pi\) | |||||||
\(608\) | 12672.4 | + | 9207.03i | 0.845285 | + | 0.614136i | ||||
\(609\) | 3573.69 | − | 2596.44i | 0.237788 | − | 0.172763i | ||||
\(610\) | −1994.77 | + | 6139.28i | −0.132403 | + | 0.407495i | ||||
\(611\) | 6612.21 | − | 20350.3i | 0.437809 | − | 1.34744i | ||||
\(612\) | −4670.92 | + | 3393.62i | −0.308514 | + | 0.224149i | ||||
\(613\) | 1049.66 | + | 762.620i | 0.0691602 | + | 0.0502478i | 0.621828 | − | 0.783154i | \(-0.286390\pi\) |
−0.552668 | + | 0.833402i | \(0.686390\pi\) | |||||||
\(614\) | −5753.05 | − | 17706.1i | −0.378134 | − | 1.16378i | ||||
\(615\) | 6825.02 | 0.447498 | ||||||||
\(616\) | −2466.06 | + | 10543.7i | −0.161300 | + | 0.689642i | ||||
\(617\) | −13415.2 | −0.875328 | −0.437664 | − | 0.899139i | \(-0.644194\pi\) | ||||
−0.437664 | + | 0.899139i | \(0.644194\pi\) | |||||||
\(618\) | 3017.69 | + | 9287.48i | 0.196422 | + | 0.604526i | ||||
\(619\) | −11943.5 | − | 8677.44i | −0.775523 | − | 0.563450i | 0.128109 | − | 0.991760i | \(-0.459109\pi\) |
−0.903632 | + | 0.428310i | \(0.859109\pi\) | |||||||
\(620\) | −537.815 | + | 390.745i | −0.0348374 | + | 0.0253108i | ||||
\(621\) | −596.323 | + | 1835.29i | −0.0385340 | + | 0.118595i | ||||
\(622\) | −4005.17 | + | 12326.6i | −0.258188 | + | 0.794620i | ||||
\(623\) | −7774.57 | + | 5648.56i | −0.499971 | + | 0.363250i | ||||
\(624\) | 5754.67 | + | 4181.01i | 0.369185 | + | 0.268228i | ||||
\(625\) | 1035.68 | + | 3187.49i | 0.0662835 | + | 0.204000i | ||||
\(626\) | 9286.78 | 0.592930 | ||||||||
\(627\) | −14948.4 | + | 1264.66i | −0.952124 | + | 0.0805512i | ||||
\(628\) | −51646.0 | −3.28169 | ||||||||
\(629\) | 140.210 | + | 431.522i | 0.00888797 | + | 0.0273544i | ||||
\(630\) | 2061.74 | + | 1497.94i | 0.130384 | + | 0.0947292i | ||||
\(631\) | −20996.8 | + | 15255.1i | −1.32467 | + | 0.962432i | −0.324813 | + | 0.945778i | \(0.605301\pi\) |
−0.999861 | + | 0.0166535i | \(0.994699\pi\) | |||||||
\(632\) | −467.723 | + | 1439.50i | −0.0294384 | + | 0.0906019i | ||||
\(633\) | −286.011 | + | 880.252i | −0.0179588 | + | 0.0552715i | ||||
\(634\) | 24385.4 | − | 17717.0i | 1.52755 | − | 1.10983i | ||||
\(635\) | −5028.95 | − | 3653.74i | −0.314280 | − | 0.228338i | ||||
\(636\) | −2946.09 | − | 9067.14i | −0.183680 | − | 0.565307i | ||||
\(637\) | 21997.9 | 1.36827 | ||||||||
\(638\) | −19273.7 | + | 16657.6i | −1.19601 | + | 1.03367i | ||||
\(639\) | −6405.06 | −0.396526 | ||||||||
\(640\) | 4888.41 | + | 15045.0i | 0.301924 | + | 0.929226i | ||||
\(641\) | 16063.7 | + | 11671.0i | 0.989827 | + | 0.719152i | 0.959883 | − | 0.280400i | \(-0.0904671\pi\) |
0.0299440 | + | 0.999552i | \(0.490467\pi\) | |||||||
\(642\) | 11110.9 | − | 8072.56i | 0.683043 | − | 0.496259i | ||||
\(643\) | −4581.91 | + | 14101.7i | −0.281015 | + | 0.864877i | 0.706549 | + | 0.707664i | \(0.250251\pi\) |
−0.987565 | + | 0.157213i | \(0.949749\pi\) | |||||||
\(644\) | −3147.69 | + | 9687.59i | −0.192603 | + | 0.592771i | ||||
\(645\) | −4032.69 | + | 2929.92i | −0.246181 | + | 0.178861i | ||||
\(646\) | −23481.2 | − | 17060.1i | −1.43012 | − | 1.03904i | ||||
\(647\) | 9349.60 | + | 28775.1i | 0.568115 | + | 1.74848i | 0.658509 | + | 0.752573i | \(0.271188\pi\) |
−0.0903934 | + | 0.995906i | \(0.528812\pi\) | |||||||
\(648\) | −2413.76 | −0.146330 | ||||||||
\(649\) | 2394.71 | + | 5686.85i | 0.144839 | + | 0.343958i | ||||
\(650\) | −37832.2 | −2.28292 | ||||||||
\(651\) | 71.2683 | + | 219.341i | 0.00429067 | + | 0.0132053i | ||||
\(652\) | −10647.3 | − | 7735.74i | −0.639543 | − | 0.464655i | ||||
\(653\) | 7520.52 | − | 5463.98i | 0.450690 | − | 0.327446i | −0.339178 | − | 0.940722i | \(-0.610149\pi\) |
0.789868 | + | 0.613277i | \(0.210149\pi\) | |||||||
\(654\) | 1032.88 | − | 3178.89i | 0.0617568 | − | 0.190068i | ||||
\(655\) | 2541.05 | − | 7820.55i | 0.151583 | − | 0.466525i | ||||
\(656\) | −8035.26 | + | 5837.96i | −0.478238 | + | 0.347460i | ||||
\(657\) | 7609.17 | + | 5528.39i | 0.451845 | + | 0.328284i | ||||
\(658\) | 3447.45 | + | 10610.2i | 0.204249 | + | 0.628613i | ||||
\(659\) | 15034.4 | 0.888705 | 0.444353 | − | 0.895852i | \(-0.353434\pi\) | ||||
0.444353 | + | 0.895852i | \(0.353434\pi\) | |||||||
\(660\) | −8066.21 | − | 4878.18i | −0.475722 | − | 0.287701i | ||||
\(661\) | 18459.0 | 1.08619 | 0.543095 | − | 0.839671i | \(-0.317252\pi\) | ||||
0.543095 | + | 0.839671i | \(0.317252\pi\) | |||||||
\(662\) | −4891.88 | − | 15055.6i | −0.287203 | − | 0.883919i | ||||
\(663\) | 9817.91 | + | 7133.13i | 0.575107 | + | 0.417840i | ||||
\(664\) | −29504.8 | + | 21436.5i | −1.72441 | + | 1.25286i | ||||
\(665\) | −2539.26 | + | 7815.05i | −0.148073 | + | 0.455721i | ||||
\(666\) | −132.945 | + | 409.164i | −0.00773503 | + | 0.0238060i | ||||
\(667\) | −8548.09 | + | 6210.55i | −0.496227 | + | 0.360530i | ||||
\(668\) | 26726.1 | + | 19417.7i | 1.54800 | + | 1.12469i | ||||
\(669\) | 4291.36 | + | 13207.5i | 0.248003 | + | 0.763273i | ||||
\(670\) | 10310.6 | 0.594525 | ||||||||
\(671\) | −7088.32 | − | 4286.79i | −0.407811 | − | 0.246631i | ||||
\(672\) | 3414.68 | 0.196018 | ||||||||
\(673\) | −4568.65 | − | 14060.8i | −0.261677 | − | 0.805358i | −0.992440 | − | 0.122727i | \(-0.960836\pi\) |
0.730764 | − | 0.682630i | \(-0.239164\pi\) | |||||||
\(674\) | −10049.4 | − | 7301.29i | −0.574313 | − | 0.417263i | ||||
\(675\) | 1939.06 | − | 1408.81i | 0.110569 | − | 0.0803333i | ||||
\(676\) | 26285.0 | − | 80896.9i | 1.49550 | − | 4.60269i | ||||
\(677\) | −9528.48 | + | 29325.6i | −0.540929 | + | 1.66481i | 0.189547 | + | 0.981872i | \(0.439298\pi\) |
−0.730476 | + | 0.682938i | \(0.760702\pi\) | |||||||
\(678\) | 5905.50 | − | 4290.60i | 0.334513 | − | 0.243038i | ||||
\(679\) | −2055.97 | − | 1493.75i | −0.116202 | − | 0.0844255i | ||||
\(680\) | −2484.92 | − | 7647.79i | −0.140136 | − | 0.431293i | ||||
\(681\) | 7762.53 | 0.436800 | ||||||||
\(682\) | −516.174 | − | 1225.78i | −0.0289814 | − | 0.0688236i | ||||
\(683\) | 7599.08 | 0.425726 | 0.212863 | − | 0.977082i | \(-0.431721\pi\) | ||||
0.212863 | + | 0.977082i | \(0.431721\pi\) | |||||||
\(684\) | −5454.70 | − | 16787.8i | −0.304921 | − | 0.938449i | ||||
\(685\) | −7362.37 | − | 5349.08i | −0.410660 | − | 0.298362i | ||||
\(686\) | −22333.1 | + | 16225.9i | −1.24297 | + | 0.903074i | ||||
\(687\) | 2027.29 | − | 6239.36i | 0.112585 | − | 0.346501i | ||||
\(688\) | 2241.60 | − | 6898.93i | 0.124215 | − | 0.382296i | ||||
\(689\) | −16212.1 | + | 11778.8i | −0.896417 | + | 0.651285i | ||||
\(690\) | −4931.58 | − | 3583.00i | −0.272090 | − | 0.197685i | ||||
\(691\) | −795.657 | − | 2448.78i | −0.0438035 | − | 0.134813i | 0.926763 | − | 0.375647i | \(-0.122579\pi\) |
−0.970567 | + | 0.240833i | \(0.922579\pi\) | |||||||
\(692\) | −6559.61 | −0.360345 | ||||||||
\(693\) | −2474.30 | + | 2138.45i | −0.135629 | + | 0.117220i | ||||
\(694\) | 41430.1 | 2.26609 | ||||||||
\(695\) | −1949.88 | − | 6001.11i | −0.106422 | − | 0.327532i | ||||
\(696\) | −10692.1 | − | 7768.30i | −0.582306 | − | 0.423070i | ||||
\(697\) | −13708.8 | + | 9960.01i | −0.744988 | + | 0.541266i | ||||
\(698\) | 9680.84 | − | 29794.5i | 0.524964 | − | 1.61567i | ||||
\(699\) | 6178.75 | − | 19016.3i | 0.334338 | − | 1.02899i | ||||
\(700\) | 10235.3 | − | 7436.38i | 0.552655 | − | 0.401527i | ||||
\(701\) | −15435.4 | − | 11214.5i | −0.831652 | − | 0.604231i | 0.0883741 | − | 0.996087i | \(-0.471833\pi\) |
−0.920026 | + | 0.391857i | \(0.871833\pi\) | |||||||
\(702\) | 3555.81 | + | 10943.7i | 0.191176 | + | 0.588379i | ||||
\(703\) | −1387.20 | −0.0744231 | ||||||||
\(704\) | −27264.5 | + | 2306.62i | −1.45962 | + | 0.123486i | ||||
\(705\) | −4282.19 | −0.228761 | ||||||||
\(706\) | −1054.49 | − | 3245.38i | −0.0562127 | − | 0.173005i | ||||
\(707\) | −1093.27 | − | 794.307i | −0.0581565 | − | 0.0422531i | ||||
\(708\) | −5873.84 | + | 4267.60i | −0.311797 | + | 0.226534i | ||||
\(709\) | 4345.14 | − | 13373.0i | 0.230162 | − | 0.708367i | −0.767564 | − | 0.640972i | \(-0.778531\pi\) |
0.997726 | − | 0.0673949i | \(-0.0214687\pi\) | |||||||
\(710\) | 6252.23 | − | 19242.4i | 0.330482 | − | 1.01712i | ||||
\(711\) | −369.826 | + | 268.694i | −0.0195071 | + | 0.0141727i | ||||
\(712\) | 23260.8 | + | 16900.0i | 1.22435 | + | 0.889541i | ||||
\(713\) | −170.470 | − | 524.654i | −0.00895395 | − | 0.0275574i | ||||
\(714\) | −6327.22 | −0.331639 | ||||||||
\(715\) | −4512.48 | + | 19293.3i | −0.236024 | + | 1.00913i | ||||
\(716\) | −50951.0 | −2.65940 | ||||||||
\(717\) | 2062.66 | + | 6348.20i | 0.107436 | + | 0.330653i | ||||
\(718\) | 31163.8 | + | 22641.8i | 1.61981 | + | 1.17686i | ||||
\(719\) | 9313.93 | − | 6766.96i | 0.483103 | − | 0.350995i | −0.319423 | − | 0.947612i | \(-0.603489\pi\) |
0.802526 | + | 0.596618i | \(0.203489\pi\) | |||||||
\(720\) | 439.892 | − | 1353.85i | 0.0227692 | − | 0.0700763i | ||||
\(721\) | −2121.16 | + | 6528.25i | −0.109565 | + | 0.337205i | ||||
\(722\) | 45580.7 | − | 33116.3i | 2.34950 | − | 1.70701i | ||||
\(723\) | −1809.73 | − | 1314.85i | −0.0930907 | − | 0.0676344i | ||||
\(724\) | 3560.17 | + | 10957.1i | 0.182752 | + | 0.562454i | ||||
\(725\) | 13123.4 | 0.672261 | ||||||||
\(726\) | 13178.8 | − | 13491.4i | 0.673705 | − | 0.689687i | ||||
\(727\) | 23297.3 | 1.18851 | 0.594257 | − | 0.804275i | \(-0.297446\pi\) | ||||
0.594257 | + | 0.804275i | \(0.297446\pi\) | |||||||
\(728\) | 8275.70 | + | 25470.0i | 0.421316 | + | 1.29668i | ||||
\(729\) | −589.773 | − | 428.495i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | −24036.3 | + | 17463.4i | −1.21866 | + | 0.885408i | ||||
\(731\) | 3824.34 | − | 11770.1i | 0.193500 | − | 0.595531i | ||||
\(732\) | 3012.00 | − | 9269.99i | 0.152086 | − | 0.468072i | ||||
\(733\) | 10078.1 | − | 7322.20i | 0.507837 | − | 0.368965i | −0.304165 | − | 0.952619i | \(-0.598377\pi\) |
0.812003 | + | 0.583654i | \(0.198377\pi\) | |||||||
\(734\) | 45565.5 | + | 33105.3i | 2.29136 | + | 1.66477i | ||||
\(735\) | −1360.39 | − | 4186.85i | −0.0682704 | − | 0.210115i | ||||
\(736\) | −8167.76 | −0.409059 | ||||||||
\(737\) | −3013.31 | + | 12883.5i | −0.150606 | + | 0.643922i | ||||
\(738\) | −16067.0 | −0.801403 | ||||||||
\(739\) | 6903.68 | + | 21247.4i | 0.343648 | + | 1.05764i | 0.962303 | + | 0.271978i | \(0.0876778\pi\) |
−0.618655 | + | 0.785663i | \(0.712322\pi\) | |||||||
\(740\) | −705.194 | − | 512.354i | −0.0350317 | − | 0.0254520i | ||||
\(741\) | −30016.7 | + | 21808.4i | −1.48811 | + | 1.08118i | ||||
\(742\) | 3228.61 | − | 9936.63i | 0.159738 | − | 0.491624i | ||||
\(743\) | 10596.5 | − | 32612.5i | 0.523212 | − | 1.61028i | −0.244614 | − | 0.969621i | \(-0.578661\pi\) |
0.767825 | − | 0.640659i | \(-0.221339\pi\) | |||||||
\(744\) | 558.239 | − | 405.584i | 0.0275081 | − | 0.0199858i | ||||
\(745\) | 1885.60 | + | 1369.97i | 0.0927287 | + | 0.0673714i | ||||
\(746\) | 8058.18 | + | 24800.5i | 0.395484 | + | 1.21717i | ||||
\(747\) | −11014.6 | −0.539495 | ||||||||
\(748\) | 23320.7 | − | 1972.97i | 1.13996 | − | 0.0964425i | ||||
\(749\) | 9653.65 | 0.470944 | ||||||||
\(750\) | 5634.09 | + | 17339.9i | 0.274304 | + | 0.844220i | ||||
\(751\) | 15565.4 | + | 11308.9i | 0.756312 | + | 0.549493i | 0.897777 | − | 0.440450i | \(-0.145181\pi\) |
−0.141465 | + | 0.989943i | \(0.545181\pi\) | |||||||
\(752\) | 5041.52 | − | 3662.88i | 0.244475 | − | 0.177622i | ||||
\(753\) | −1640.09 | + | 5047.68i | −0.0793734 | + | 0.244286i | ||||
\(754\) | −19469.3 | + | 59920.4i | −0.940360 | + | 2.89413i | ||||
\(755\) | −3305.31 | + | 2401.45i | −0.159328 | + | 0.115759i | ||||
\(756\) | −3113.12 | − | 2261.81i | −0.149766 | − | 0.108811i | ||||
\(757\) | −4457.45 | − | 13718.6i | −0.214014 | − | 0.658668i | −0.999222 | − | 0.0394359i | \(-0.987444\pi\) |
0.785208 | − | 0.619232i | \(-0.212556\pi\) | |||||||
\(758\) | −31898.6 | −1.52851 | ||||||||
\(759\) | 5918.40 | − | 5115.08i | 0.283036 | − | 0.244619i | ||||
\(760\) | 24585.2 | 1.17342 | ||||||||
\(761\) | −7973.32 | − | 24539.4i | −0.379806 | − | 1.16892i | −0.940178 | − | 0.340683i | \(-0.889342\pi\) |
0.560372 | − | 0.828241i | \(-0.310658\pi\) | |||||||
\(762\) | 11838.8 | + | 8601.41i | 0.562828 | + | 0.408919i | ||||
\(763\) | 1900.75 | − | 1380.98i | 0.0901859 | − | 0.0655239i | ||||
\(764\) | −10036.8 | + | 30890.0i | −0.475284 | + | 1.46277i | ||||
\(765\) | 750.490 | − | 2309.77i | 0.0354693 | − | 0.109163i | ||||
\(766\) | −20307.2 | + | 14754.1i | −0.957871 | + | 0.695934i | ||||
\(767\) | 12346.4 | + | 8970.17i | 0.581228 | + | 0.422287i | ||||
\(768\) | −5945.71 | − | 18299.0i | −0.279359 | − | 0.859778i | ||||
\(769\) | −1832.44 | −0.0859291 | −0.0429646 | − | 0.999077i | \(-0.513680\pi\) | ||||
−0.0429646 | + | 0.999077i | \(0.513680\pi\) | |||||||
\(770\) | −4009.19 | − | 9520.83i | −0.187638 | − | 0.445593i | ||||
\(771\) | −7203.60 | −0.336487 | ||||||||
\(772\) | −21143.0 | − | 65071.4i | −0.985689 | − | 3.03364i | ||||
\(773\) | −30476.8 | − | 22142.7i | −1.41808 | − | 1.03030i | −0.992085 | − | 0.125570i | \(-0.959924\pi\) |
−0.425995 | − | 0.904725i | \(-0.640076\pi\) | |||||||
\(774\) | 9493.50 | − | 6897.43i | 0.440875 | − | 0.320314i | ||||
\(775\) | −211.730 | + | 651.638i | −0.00981364 | + | 0.0302033i | ||||
\(776\) | −2349.58 | + | 7231.27i | −0.108692 | + | 0.334520i | ||||
\(777\) | −244.651 | + | 177.750i | −0.0112958 | + | 0.00820686i | ||||
\(778\) | −434.823 | − | 315.918i | −0.0200375 | − | 0.0145581i | ||||
\(779\) | −16009.1 | − | 49271.0i | −0.736311 | − | 2.26613i | ||||
\(780\) | −23314.0 | −1.07022 | ||||||||
\(781\) | 22217.0 | + | 13436.1i | 1.01791 | + | 0.615598i | ||||
\(782\) | 15134.4 | 0.692079 | ||||||||
\(783\) | −1233.45 | − | 3796.18i | −0.0562963 | − | 0.173262i | ||||
\(784\) | 5182.95 | + | 3765.63i | 0.236104 | + | 0.171539i | ||||
\(785\) | 17575.7 | − | 12769.5i | 0.799113 | − | 0.580590i | ||||
\(786\) | −5981.98 | + | 18410.6i | −0.271463 | + | 0.835478i | ||||
\(787\) | 9808.52 | − | 30187.5i | 0.444264 | − | 1.36730i | −0.439024 | − | 0.898475i | \(-0.644676\pi\) |
0.883289 | − | 0.468830i | \(-0.155324\pi\) | |||||||
\(788\) | 23258.6 | − | 16898.3i | 1.05146 | − | 0.763932i | ||||
\(789\) | 14560.1 | + | 10578.5i | 0.656976 | + | 0.477321i | ||||
\(790\) | −446.223 | − | 1373.33i | −0.0200961 | − | 0.0618493i | ||||
\(791\) | 5130.96 | 0.230639 | ||||||||
\(792\) | 8372.53 | + | 5063.44i | 0.375637 | + | 0.227173i | ||||
\(793\) | −20487.6 | −0.917446 | ||||||||
\(794\) | 5888.29 | + | 18122.3i | 0.263184 | + | 0.809996i | ||||
\(795\) | 3244.44 | + | 2357.22i | 0.144740 | + | 0.105160i | ||||
\(796\) | −37625.6 | + | 27336.6i | −1.67538 | + | 1.21724i | ||||
\(797\) | −9351.45 | + | 28780.8i | −0.415615 | + | 1.27913i | 0.496084 | + | 0.868275i | \(0.334771\pi\) |
−0.911699 | + | 0.410858i | \(0.865229\pi\) | |||||||
\(798\) | 5977.77 | − | 18397.7i | 0.265177 | − | 0.816130i | ||||
\(799\) | 8601.22 | − | 6249.15i | 0.380838 | − | 0.276695i | ||||
\(800\) | 8207.19 | + | 5962.87i | 0.362710 | + | 0.263524i | ||||
\(801\) | 2683.38 | + | 8258.60i | 0.118368 | + | 0.364299i | ||||
\(802\) | −47363.4 | −2.08536 | ||||||||
\(803\) | −14796.5 | − | 35138.1i | −0.650260 | − | 1.54421i | ||||
\(804\) | −15568.4 | −0.682906 | ||||||||
\(805\) | −1324.07 | − | 4075.06i | −0.0579717 | − | 0.178419i | ||||
\(806\) | −2661.22 | − | 1933.49i | −0.116300 | − | 0.0844967i | ||||
\(807\) | −1896.64 | + | 1377.99i | −0.0827322 | + | 0.0601085i | ||||
\(808\) | −1249.40 | + | 3845.25i | −0.0543980 | + | 0.167420i | ||||
\(809\) | −2434.74 | + | 7493.36i | −0.105811 | + | 0.325652i | −0.989920 | − | 0.141628i | \(-0.954766\pi\) |
0.884109 | + | 0.467281i | \(0.154766\pi\) | |||||||
\(810\) | 1863.01 | − | 1353.55i | 0.0808141 | − | 0.0587149i | ||||
\(811\) | −33536.1 | − | 24365.4i | −1.45205 | − | 1.05498i | −0.985347 | − | 0.170564i | \(-0.945441\pi\) |
−0.466704 | − | 0.884413i | \(-0.654559\pi\) | |||||||
\(812\) | −6510.78 | − | 20038.1i | −0.281384 | − | 0.866010i | ||||
\(813\) | 1349.67 | 0.0582227 | ||||||||
\(814\) | 1319.46 | − | 1140.37i | 0.0568146 | − | 0.0491030i | ||||
\(815\) | 5536.07 | 0.237939 | ||||||||
\(816\) | 1092.15 | + | 3361.30i | 0.0468541 | + | 0.144202i | ||||
\(817\) | 30610.9 | + | 22240.1i | 1.31082 | + | 0.952366i | ||||
\(818\) | 1125.96 | − | 818.056i | 0.0481274 | − | 0.0349666i | ||||
\(819\) | −2499.41 | + | 7692.39i | −0.106638 | + | 0.328198i | ||||
\(820\) | 10059.5 | − | 30960.1i | 0.428408 | − | 1.31850i | ||||
\(821\) | 14844.6 | − | 10785.2i | 0.631034 | − | 0.458473i | −0.225724 | − | 0.974191i | \(-0.572475\pi\) |
0.856758 | + | 0.515718i | \(0.172475\pi\) | |||||||
\(822\) | 17332.0 | + | 12592.5i | 0.735431 | + | 0.534322i | ||||
\(823\) | −8201.31 | − | 25241.0i | −0.347363 | − | 1.06907i | −0.960307 | − | 0.278946i | \(-0.910015\pi\) |
0.612944 | − | 0.790126i | \(-0.289985\pi\) | |||||||
\(824\) | 20537.1 | 0.868256 | ||||||||
\(825\) | −9681.23 | + | 819.048i | −0.408554 | + | 0.0345643i | ||||
\(826\) | −7956.70 | −0.335168 | ||||||||
\(827\) | −2363.74 | − | 7274.85i | −0.0993898 | − | 0.305890i | 0.888983 | − | 0.457940i | \(-0.151413\pi\) |
−0.988373 | + | 0.152050i | \(0.951413\pi\) | |||||||
\(828\) | 7446.43 | + | 5410.15i | 0.312538 | + | 0.227072i | ||||
\(829\) | 23147.8 | − | 16817.9i | 0.969791 | − | 0.704595i | 0.0143874 | − | 0.999896i | \(-0.495420\pi\) |
0.955404 | + | 0.295302i | \(0.0954202\pi\) | |||||||
\(830\) | 10751.8 | − | 33090.6i | 0.449638 | − | 1.38384i | ||||
\(831\) | −3910.30 | + | 12034.7i | −0.163233 | + | 0.502380i | ||||
\(832\) | −54747.7 | + | 39776.6i | −2.28129 | + | 1.65746i | ||||
\(833\) | 8842.52 | + | 6424.46i | 0.367797 | + | 0.267220i | ||||
\(834\) | 4590.28 | + | 14127.4i | 0.190585 | + | 0.586562i | ||||
\(835\) | −13896.2 | −0.575926 | ||||||||
\(836\) | −16295.9 | + | 69673.8i | −0.674171 | + | 2.88244i | ||||
\(837\) | 208.399 | 0.00860611 | ||||||||
\(838\) | 1597.87 | + | 4917.74i | 0.0658682 | + | 0.202721i | ||||
\(839\) | −10416.9 | − | 7568.35i | −0.428644 | − | 0.311428i | 0.352462 | − | 0.935826i | \(-0.385344\pi\) |
−0.781107 | + | 0.624398i | \(0.785344\pi\) | |||||||
\(840\) | 4335.92 | − | 3150.23i | 0.178099 | − | 0.129397i | ||||
\(841\) | −783.022 | + | 2409.89i | −0.0321055 | + | 0.0988107i | ||||
\(842\) | −19077.2 | + | 58713.6i | −0.780812 | + | 2.40309i | ||||
\(843\) | 7429.64 | − | 5397.95i | 0.303548 | − | 0.220540i | ||||
\(844\) | 3571.49 | + | 2594.84i | 0.145659 | + | 0.105827i | ||||
\(845\) | 11056.7 | + | 34029.0i | 0.450133 | + | 1.38537i | ||||
\(846\) | 10080.8 | 0.409677 | ||||||||
\(847\) | 13068.4 | − | 2227.16i | 0.530148 | − | 0.0903495i | ||||
\(848\) | −5836.07 | −0.236334 | ||||||||
\(849\) | −5401.97 | − | 16625.5i | −0.218369 | − | 0.672070i | ||||
\(850\) | −15207.5 | − | 11048.9i | −0.613661 | − | 0.445851i | ||||
\(851\) | 585.195 | − | 425.169i | 0.0235725 | − | 0.0171264i | ||||
\(852\) | −9440.54 | + | 29055.0i | −0.379610 | + | 1.16832i | ||||
\(853\) | −196.513 | + | 604.804i | −0.00788800 | + | 0.0242768i | −0.954923 | − | 0.296853i | \(-0.904063\pi\) |
0.947035 | + | 0.321130i | \(0.104063\pi\) | |||||||
\(854\) | 8641.70 | − | 6278.56i | 0.346268 | − | 0.251578i | ||||
\(855\) | 6007.09 | + | 4364.41i | 0.240279 | + | 0.174573i | ||||
\(856\) | −8925.29 | − | 27469.2i | −0.356379 | − | 1.09682i | ||||
\(857\) | −7820.86 | −0.311733 | −0.155867 | − | 0.987778i | \(-0.549817\pi\) | ||||
−0.155867 | + | 0.987778i | \(0.549817\pi\) | |||||||
\(858\) | 10623.0 | − | 45419.0i | 0.422684 | − | 1.80720i | ||||
\(859\) | 119.816 | 0.00475910 | 0.00237955 | − | 0.999997i | \(-0.499243\pi\) | ||||
0.00237955 | + | 0.999997i | \(0.499243\pi\) | |||||||
\(860\) | 7347.02 | + | 22611.8i | 0.291315 | + | 0.896577i | ||||
\(861\) | −9136.76 | − | 6638.24i | −0.361649 | − | 0.262754i | ||||
\(862\) | −5630.09 | + | 4090.50i | −0.222461 | + | 0.161628i | ||||
\(863\) | −9940.00 | + | 30592.2i | −0.392076 | + | 1.20669i | 0.539139 | + | 0.842217i | \(0.318750\pi\) |
−0.931215 | + | 0.364469i | \(0.881250\pi\) | |||||||
\(864\) | 953.485 | − | 2934.52i | 0.0375442 | − | 0.115549i | ||||
\(865\) | 2232.31 | − | 1621.87i | 0.0877465 | − | 0.0637515i | ||||
\(866\) | −15516.1 | − | 11273.1i | −0.608843 | − | 0.442351i | ||||
\(867\) | −2691.31 | − | 8282.99i | −0.105423 | − | 0.324458i | ||||
\(868\) | 1100.03 | 0.0430156 | ||||||||
\(869\) | 1846.45 | − | 156.213i | 0.0720788 | − | 0.00609799i | ||||
\(870\) | 12608.7 | 0.491350 | ||||||||
\(871\) | 10112.2 | + | 31122.0i | 0.393384 | + | 1.21071i | ||||
\(872\) | −5686.88 | − | 4131.76i | −0.220851 | − | 0.160458i | ||||
\(873\) | −1857.80 | + | 1349.77i | −0.0720240 | + | 0.0523285i | ||||
\(874\) | −14298.6 | + | 44006.4i | −0.553382 | + | 1.70313i | ||||
\(875\) | −3960.25 | + | 12188.4i | −0.153007 | + | 0.470906i | ||||
\(876\) | 36293.5 | − | 26368.8i | 1.39982 | − | 1.01703i | ||||
\(877\) | −6320.86 | − | 4592.37i | −0.243375 | − | 0.176822i | 0.459410 | − | 0.888224i | \(-0.348061\pi\) |
−0.702786 | + | 0.711402i | \(0.748061\pi\) | |||||||
\(878\) | −17123.8 | − | 52701.6i | −0.658201 | − | 2.02573i | ||||
\(879\) | −1373.84 | −0.0527171 | ||||||||
\(880\) | −4365.85 | + | 3773.26i | −0.167242 | + | 0.144542i | ||||
\(881\) | −11759.7 | −0.449709 | −0.224855 | − | 0.974392i | \(-0.572191\pi\) | ||||
−0.224855 | + | 0.974392i | \(0.572191\pi\) | |||||||
\(882\) | 3202.54 | + | 9856.42i | 0.122262 | + | 0.376284i | ||||
\(883\) | 7639.22 | + | 5550.22i | 0.291144 | + | 0.211529i | 0.723764 | − | 0.690048i | \(-0.242411\pi\) |
−0.432619 | + | 0.901577i | \(0.642411\pi\) | |||||||
\(884\) | 46828.5 | − | 34022.9i | 1.78169 | − | 1.29447i | ||||
\(885\) | 943.768 | − | 2904.62i | 0.0358468 | − | 0.110325i | ||||
\(886\) | 1333.04 | − | 4102.66i | 0.0505465 | − | 0.155566i | ||||
\(887\) | −30976.4 | + | 22505.6i | −1.17259 | + | 0.851934i | −0.991316 | − | 0.131499i | \(-0.958021\pi\) |
−0.181270 | + | 0.983433i | \(0.558021\pi\) | |||||||
\(888\) | 731.975 | + | 531.811i | 0.0276616 | + | 0.0200973i | ||||
\(889\) | 3178.57 | + | 9782.64i | 0.119917 | + | 0.369066i | ||||
\(890\) | −27430.2 | −1.03311 | ||||||||
\(891\) | 1146.85 | + | 2723.49i | 0.0431213 | + | 0.102402i | ||||
\(892\) | 66237.6 | 2.48632 | ||||||||
\(893\) | 10044.5 | + | 30913.8i | 0.376402 | + | 1.15845i | ||||
\(894\) | −4438.95 | − | 3225.09i | −0.166063 | − | 0.120652i | ||||
\(895\) | 17339.2 | − | 12597.6i | 0.647581 | − | 0.470495i | ||||
\(896\) | 8089.05 | − | 24895.5i | 0.301603 | − | 0.928239i | ||||
\(897\) | 5978.47 | − | 18399.8i | 0.222537 | − | 0.684897i | ||||
\(898\) | 55588.3 | − | 40387.3i | 2.06571 | − | 1.50083i | ||||
\(899\) | 923.135 | + | 670.697i | 0.0342473 | + | 0.0248821i | ||||
\(900\) | −3532.70 | − | 10872.5i | −0.130841 | − | 0.402686i | ||||
\(901\) | −9956.78 | −0.368156 | ||||||||
\(902\) | 55731.1 | + | 33704.4i | 2.05725 | + | 1.24416i | ||||
\(903\) | 8248.37 | 0.303974 | ||||||||
\(904\) | −4743.83 | − | 14600.0i | −0.174533 | − | 0.537156i | ||||
\(905\) | −3920.70 | − | 2848.56i | −0.144010 | − | 0.104629i | ||||
\(906\) | 7781.16 | − | 5653.34i | 0.285333 | − | 0.207307i | ||||
\(907\) | 12422.6 | − | 38232.9i | 0.454782 | − | 1.39967i | −0.416610 | − | 0.909085i | \(-0.636782\pi\) |
0.871391 | − | 0.490588i | \(-0.163218\pi\) | |||||||
\(908\) | 11441.3 | − | 35212.8i | 0.418166 | − | 1.28698i | ||||
\(909\) | −987.889 | + | 717.743i | −0.0360464 | + | 0.0261893i | ||||
\(910\) | −20670.1 | − | 15017.7i | −0.752974 | − | 0.547068i | ||||
\(911\) | 6470.55 | + | 19914.3i | 0.235323 | + | 0.724249i | 0.997078 | + | 0.0763845i | \(0.0243376\pi\) |
−0.761756 | + | 0.647864i | \(0.775662\pi\) | |||||||
\(912\) | −10805.5 | −0.392331 | ||||||||
\(913\) | 38205.9 | + | 23105.7i | 1.38492 | + | 0.837553i | ||||
\(914\) | −8550.45 | −0.309435 | ||||||||
\(915\) | 1266.99 | + | 3899.40i | 0.0457764 | + | 0.140885i | ||||
\(916\) | −25315.3 | − | 18392.6i | −0.913145 | − | 0.663439i | ||||
\(917\) | −11008.3 | + | 7997.98i | −0.396429 | + | 0.288022i | ||||
\(918\) | −1766.76 | + | 5437.51i | −0.0635203 | + | 0.195495i | ||||
\(919\) | −14412.6 | + | 44357.6i | −0.517333 | + | 1.59219i | 0.261663 | + | 0.965159i | \(0.415729\pi\) |
−0.778996 | + | 0.627029i | \(0.784271\pi\) | |||||||
\(920\) | −10371.3 | + | 7535.20i | −0.371665 | + | 0.270031i | ||||
\(921\) | −9566.51 | − | 6950.48i | −0.342266 | − | 0.248671i | ||||
\(922\) | −22289.2 | − | 68599.2i | −0.796157 | − | 2.45032i | ||||
\(923\) | 64214.3 | 2.28997 | ||||||||
\(924\) | 6053.67 | + | 14376.0i | 0.215531 | + | 0.511834i | ||||
\(925\) | −898.413 | −0.0319348 | ||||||||
\(926\) | 18856.7 | + | 58035.0i | 0.669190 | + | 2.05956i | ||||
\(927\) | 5017.98 | + | 3645.78i | 0.177791 | + | 0.129173i | ||||
\(928\) | 13667.9 | − | 9930.31i | 0.483481 | − | 0.351270i | ||||
\(929\) | 15712.4 | − | 48357.8i | 0.554906 | − | 1.70782i | −0.141286 | − | 0.989969i | \(-0.545124\pi\) |
0.696192 | − | 0.717856i | \(-0.254876\pi\) | |||||||
\(930\) | −203.426 | + | 626.082i | −0.00717270 | + | 0.0220753i | ||||
\(931\) | −27034.6 | + | 19641.8i | −0.951690 | + | 0.691443i | ||||
\(932\) | −77155.7 | − | 56056.9i | −2.71171 | − | 1.97018i | ||||
\(933\) | 2543.91 | + | 7829.34i | 0.0892645 | + | 0.274728i | ||||
\(934\) | 17126.4 | 0.599993 | ||||||||
\(935\) | −7448.48 | + | 6437.48i | −0.260525 | + | 0.225164i | ||||
\(936\) | 24199.3 | 0.845064 | ||||||||
\(937\) | 5230.89 | + | 16099.0i | 0.182375 | + | 0.561293i | 0.999893 | − | 0.0146096i | \(-0.00465055\pi\) |
−0.817518 | + | 0.575903i | \(0.804651\pi\) | |||||||
\(938\) | −13802.9 | − | 10028.4i | −0.480470 | − | 0.349082i | ||||
\(939\) | 4772.03 | − | 3467.08i | 0.165846 | − | 0.120494i | ||||
\(940\) | −6311.60 | + | 19425.1i | −0.219002 | + | 0.674018i | ||||
\(941\) | −6371.09 | + | 19608.2i | −0.220714 | + | 0.679287i | 0.777985 | + | 0.628283i | \(0.216242\pi\) |
−0.998698 | + | 0.0510038i | \(0.983758\pi\) | |||||||
\(942\) | −41375.6 | + | 30061.1i | −1.43109 | + | 1.03975i | ||||
\(943\) | 21854.7 | + | 15878.4i | 0.754705 | + | 0.548325i | ||||
\(944\) | 1373.42 | + | 4226.95i | 0.0473528 | + | 0.145737i | ||||
\(945\) | 1618.66 | 0.0557197 | ||||||||
\(946\) | −47398.7 | + | 4010.01i | −1.62903 | + | 0.137819i | ||||
\(947\) | −46642.8 | −1.60052 | −0.800258 | − | 0.599656i | \(-0.795304\pi\) | ||||
−0.800258 | + | 0.599656i | \(0.795304\pi\) | |||||||
\(948\) | 673.773 | + | 2073.66i | 0.0230835 | + | 0.0710436i | ||||
\(949\) | −76286.2 | − | 55425.2i | −2.60944 | − | 1.89587i | ||||
\(950\) | 46494.4 | − | 33780.2i | 1.58787 | − | 1.15366i | ||||
\(951\) | 5916.09 | − | 18207.8i | 0.201727 | − | 0.620851i | ||||
\(952\) | −4111.90 | + | 12655.1i | −0.139987 | + | 0.430835i | ||||
\(953\) | 12290.8 | − | 8929.79i | 0.417773 | − | 0.303530i | −0.358968 | − | 0.933350i | \(-0.616871\pi\) |
0.776741 | + | 0.629820i | \(0.216871\pi\) | |||||||
\(954\) | −7637.85 | − | 5549.23i | −0.259208 | − | 0.188326i | ||||
\(955\) | −4221.93 | − | 12993.8i | −0.143056 | − | 0.440281i | ||||
\(956\) | 31837.3 | 1.07708 | ||||||||
\(957\) | −3684.94 | + | 15755.1i | −0.124469 | + | 0.532174i | ||||
\(958\) | −35551.5 | −1.19897 | ||||||||
\(959\) | 4653.43 | + | 14321.8i | 0.156691 | + | 0.482247i | ||||
\(960\) | 10956.4 | + | 7960.28i | 0.368350 | + | 0.267622i | ||||
\(961\) | 24053.2 | − | 17475.7i | 0.807399 | − | 0.586610i | ||||
\(962\) | 1332.85 | − | 4102.10i | 0.0446704 | − | 0.137481i | ||||
\(963\) | 2695.60 | − | 8296.20i | 0.0902019 | − | 0.277613i | ||||
\(964\) | −8631.88 | + | 6271.43i | −0.288396 | + | 0.209532i | ||||
\(965\) | 23284.1 | + | 16916.9i | 0.776727 | + | 0.564325i | ||||
\(966\) | 3117.03 | + | 9593.24i | 0.103819 | + | 0.319521i | ||||
\(967\) | −31663.0 | −1.05296 | −0.526481 | − | 0.850187i | \(-0.676489\pi\) | ||||
−0.526481 | + | 0.850187i | \(0.676489\pi\) | |||||||
\(968\) | −18419.7 | − | 35126.7i | −0.611603 | − | 1.16634i | ||||
\(969\) | −18435.0 | −0.611164 | ||||||||
\(970\) | −2241.57 | − | 6898.85i | −0.0741985 | − | 0.228359i | ||||
\(971\) | 18374.8 | + | 13350.1i | 0.607287 | + | 0.441220i | 0.848458 | − | 0.529263i | \(-0.177531\pi\) |
−0.241171 | + | 0.970483i | \(0.577531\pi\) | |||||||
\(972\) | −2813.05 | + | 2043.80i | −0.0928276 | + | 0.0674432i | ||||
\(973\) | −3226.55 | + | 9930.29i | −0.106309 | + | 0.327184i | ||||
\(974\) | 16158.0 | − | 49729.3i | 0.531557 | − | 1.63596i | ||||
\(975\) | −19440.1 | + | 14124.1i | −0.638546 | + | 0.463931i | ||||
\(976\) | −4827.11 | − | 3507.10i | −0.158311 | − | 0.115020i | ||||
\(977\) | 17034.6 | + | 52427.1i | 0.557815 | + | 1.71678i | 0.688390 | + | 0.725340i | \(0.258318\pi\) |
−0.130575 | + | 0.991438i | \(0.541682\pi\) | |||||||
\(978\) | −13032.7 | −0.426113 | ||||||||
\(979\) | 8016.61 | − | 34275.3i | 0.261708 | − | 1.11894i | ||||
\(980\) | −20997.8 | −0.684437 | ||||||||
\(981\) | −656.042 | − | 2019.09i | −0.0213515 | − | 0.0657131i | ||||
\(982\) | 59461.0 | + | 43200.9i | 1.93226 | + | 1.40387i | ||||
\(983\) | −41726.4 | + | 30316.0i | −1.35388 | + | 0.983653i | −0.355075 | + | 0.934838i | \(0.615545\pi\) |
−0.998808 | + | 0.0488155i | \(0.984455\pi\) | |||||||
\(984\) | −10441.6 | + | 32135.8i | −0.338277 | + | 1.04111i | ||||
\(985\) | −3737.03 | + | 11501.4i | −0.120885 | + | 0.372045i | ||||
\(986\) | −25325.9 | + | 18400.3i | −0.817991 | + | 0.594306i | ||||
\(987\) | 5732.63 | + | 4165.00i | 0.184875 | + | 0.134319i | ||||
\(988\) | 54686.4 | + | 168308.i | 1.76094 | + | 5.41961i | ||||
\(989\) | −19729.7 | −0.634346 | ||||||||
\(990\) | −9301.54 | + | 786.925i | −0.298608 | + | 0.0252628i | ||||
\(991\) | 8219.68 | 0.263478 | 0.131739 | − | 0.991284i | \(-0.457944\pi\) | ||||
0.131739 | + | 0.991284i | \(0.457944\pi\) | |||||||
\(992\) | 272.572 | + | 838.891i | 0.00872397 | + | 0.0268496i | ||||
\(993\) | −8134.50 | − | 5910.06i | −0.259960 | − | 0.188872i | ||||
\(994\) | −27085.7 | + | 19678.9i | −0.864293 | + | 0.627946i | ||||
\(995\) | 6045.42 | − | 18605.9i | 0.192616 | − | 0.592811i | ||||
\(996\) | −16234.6 | + | 49965.0i | −0.516479 | + | 1.58956i | ||||
\(997\) | 22916.4 | − | 16649.7i | 0.727952 | − | 0.528888i | −0.160963 | − | 0.986960i | \(-0.551460\pi\) |
0.888915 | + | 0.458072i | \(0.151460\pi\) | |||||||
\(998\) | −30727.7 | − | 22325.0i | −0.974616 | − | 0.708100i | ||||
\(999\) | 84.4410 | + | 259.883i | 0.00267427 | + | 0.00823056i |
(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 | 33.4.e.b.16.1 | ✓ | 8 | |
3.2 | odd | 2 | 99.4.f.b.82.2 | 8 | |||
11.3 | even | 5 | 363.4.a.p.1.1 | 4 | |||
11.8 | odd | 10 | 363.4.a.t.1.4 | 4 | |||
11.9 | even | 5 | inner | 33.4.e.b.31.1 | yes | 8 | |
33.8 | even | 10 | 1089.4.a.z.1.1 | 4 | |||
33.14 | odd | 10 | 1089.4.a.bg.1.4 | 4 | |||
33.20 | odd | 10 | 99.4.f.b.64.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.4.e.b.16.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
33.4.e.b.31.1 | yes | 8 | 11.9 | even | 5 | inner | |
99.4.f.b.64.2 | 8 | 33.20 | odd | 10 | |||
99.4.f.b.82.2 | 8 | 3.2 | odd | 2 | |||
363.4.a.p.1.1 | 4 | 11.3 | even | 5 | |||
363.4.a.t.1.4 | 4 | 11.8 | odd | 10 | |||
1089.4.a.z.1.1 | 4 | 33.8 | even | 10 | |||
1089.4.a.bg.1.4 | 4 | 33.14 | odd | 10 |