Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,3,Mod(269,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("810.269");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.j (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: | \(22.0709014132\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.81622204416.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 14x^{6} + 165x^{4} - 434x^{2} + 961 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.2 | ||
Root | \(-1.43806 + 0.830265i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 810.269 |
Dual form | 810.3.j.a.539.2 |
$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(731\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 1.22474i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.173381 | − | 4.99699i | −0.0346763 | − | 0.999399i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.8534 | + | 6.84358i | 1.69335 | + | 0.977654i | 0.951784 | + | 0.306769i | \(0.0992479\pi\) |
0.741562 | + | 0.670885i | \(0.234085\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.24264 | + | 3.32106i | 0.624264 | + | 0.332106i | ||||
\(11\) | 10.6621 | + | 6.15576i | 0.969281 | + | 0.559615i | 0.899017 | − | 0.437914i | \(-0.144282\pi\) |
0.0702641 | + | 0.997528i | \(0.477616\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.7295 | − | 8.50411i | 1.13304 | − | 0.654162i | 0.188344 | − | 0.982103i | \(-0.439688\pi\) |
0.944698 | + | 0.327941i | \(0.106355\pi\) | |||||||
\(14\) | −16.7633 | + | 9.67828i | −1.19738 | + | 0.691306i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 6.89949 | 0.405853 | 0.202926 | − | 0.979194i | \(-0.434955\pi\) | ||||
0.202926 | + | 0.979194i | \(0.434955\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.24264 | −0.381192 | −0.190596 | − | 0.981669i | \(-0.561042\pi\) | ||||
−0.190596 | + | 0.981669i | \(0.561042\pi\) | |||||||
\(20\) | −8.48166 | + | 5.29730i | −0.424083 | + | 0.264865i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −15.0785 | + | 8.70556i | −0.685385 | + | 0.395707i | ||||
\(23\) | −17.3995 | − | 30.1368i | −0.756500 | − | 1.31030i | −0.944625 | − | 0.328151i | \(-0.893574\pi\) |
0.188125 | − | 0.982145i | \(-0.439759\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.9399 | + | 1.73277i | −0.997595 | + | 0.0693108i | ||||
\(26\) | 24.0532i | 0.925125i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 27.3743i | − | 0.977654i | ||||||
\(29\) | −18.3035 | − | 10.5675i | −0.631156 | − | 0.364398i | 0.150044 | − | 0.988679i | \(-0.452059\pi\) |
−0.781200 | + | 0.624281i | \(0.785392\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.1066 | + | 33.0936i | 0.616342 | + | 1.06754i | 0.990147 | + | 0.140029i | \(0.0447194\pi\) |
−0.373805 | + | 0.927507i | \(0.621947\pi\) | |||||||
\(32\) | −2.82843 | − | 4.89898i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.87868 | + | 8.45012i | −0.143491 | + | 0.248533i | ||||
\(35\) | 32.1421 | − | 60.4180i | 0.918347 | − | 1.72623i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 21.5380i | 0.582108i | 0.956707 | + | 0.291054i | \(0.0940060\pi\) | ||||
−0.956707 | + | 0.291054i | \(0.905994\pi\) | |||||||
\(38\) | 5.12132 | − | 8.87039i | 0.134772 | − | 0.233431i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.490397 | − | 14.1336i | −0.0122599 | − | 0.353341i | ||||
\(41\) | −31.4928 | + | 18.1824i | −0.768117 | + | 0.443473i | −0.832203 | − | 0.554472i | \(-0.812920\pi\) |
0.0640853 | + | 0.997944i | \(0.479587\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.40331 | + | 3.11960i | 0.125658 | + | 0.0725489i | 0.561512 | − | 0.827469i | \(-0.310220\pi\) |
−0.435853 | + | 0.900018i | \(0.643553\pi\) | |||||||
\(44\) | − | 24.6230i | − | 0.559615i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 49.2132 | 1.06985 | ||||||||
\(47\) | 20.1005 | − | 34.8151i | 0.427670 | − | 0.740747i | −0.568995 | − | 0.822341i | \(-0.692668\pi\) |
0.996666 | + | 0.0815940i | \(0.0260011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 69.1690 | + | 119.804i | 1.41161 | + | 2.44499i | ||||
\(50\) | 15.5130 | − | 31.7702i | 0.310259 | − | 0.635405i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −29.4591 | − | 17.0082i | −0.566521 | − | 0.327081i | ||||
\(53\) | 38.2721 | 0.722115 | 0.361057 | − | 0.932544i | \(-0.382416\pi\) | ||||
0.361057 | + | 0.932544i | \(0.382416\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 28.9117 | − | 54.3457i | 0.525667 | − | 0.988103i | ||||
\(56\) | 33.5265 | + | 19.3566i | 0.598688 | + | 0.345653i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 25.8851 | − | 14.9448i | 0.446295 | − | 0.257668i | ||||
\(59\) | 36.0537 | − | 20.8156i | 0.611080 | − | 0.352807i | −0.162308 | − | 0.986740i | \(-0.551894\pi\) |
0.773388 | + | 0.633933i | \(0.218560\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.52944 | − | 13.0414i | 0.123433 | − | 0.213793i | −0.797686 | − | 0.603073i | \(-0.793943\pi\) |
0.921119 | + | 0.389280i | \(0.127276\pi\) | |||||||
\(62\) | −54.0416 | −0.871639 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −45.0488 | − | 72.1290i | −0.693058 | − | 1.10968i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 111.386 | − | 64.3089i | 1.66248 | − | 0.959834i | 0.690956 | − | 0.722897i | \(-0.257190\pi\) |
0.971525 | − | 0.236937i | \(-0.0761435\pi\) | |||||||
\(68\) | −6.89949 | − | 11.9503i | −0.101463 | − | 0.175739i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 51.2687 | + | 82.0879i | 0.732410 | + | 1.17268i | ||||
\(71\) | 104.967i | 1.47841i | 0.673478 | + | 0.739207i | \(0.264800\pi\) | ||||
−0.673478 | + | 0.739207i | \(0.735200\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.11232i | − | 0.0289359i | −0.999895 | − | 0.0144680i | \(-0.995395\pi\) | ||
0.999895 | − | 0.0144680i | \(-0.00460546\pi\) | |||||||
\(74\) | −26.3786 | − | 15.2297i | −0.356467 | − | 0.205806i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.24264 | + | 12.5446i | 0.0952979 | + | 0.165061i | ||||
\(77\) | 84.2548 | + | 145.934i | 1.09422 | + | 1.89524i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 22.0477 | − | 38.1878i | 0.279085 | − | 0.483390i | −0.692072 | − | 0.721828i | \(-0.743302\pi\) |
0.971158 | + | 0.238438i | \(0.0766355\pi\) | |||||||
\(80\) | 17.6569 | + | 9.39338i | 0.220711 | + | 0.117417i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 51.4275i | − | 0.627165i | ||||||
\(83\) | 27.5122 | − | 47.6525i | 0.331472 | − | 0.574127i | −0.651329 | − | 0.758796i | \(-0.725788\pi\) |
0.982801 | + | 0.184669i | \(0.0591214\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.19624 | − | 34.4767i | −0.0140735 | − | 0.405609i | ||||
\(86\) | −7.64144 | + | 4.41179i | −0.0888539 | + | 0.0512998i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 30.1569 | + | 17.4111i | 0.342693 | + | 0.197854i | ||||
\(89\) | − | 68.1020i | − | 0.765191i | −0.923916 | − | 0.382595i | \(-0.875030\pi\) | ||
0.923916 | − | 0.382595i | \(-0.124970\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 232.794 | 2.55818 | ||||||||
\(92\) | −34.7990 | + | 60.2736i | −0.378250 | + | 0.655148i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 28.4264 | + | 49.2360i | 0.302409 | + | 0.523787i | ||||
\(95\) | 1.25574 | + | 36.1914i | 0.0132183 | + | 0.380962i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 87.6794 | + | 50.6217i | 0.903911 | + | 0.521873i | 0.878467 | − | 0.477803i | \(-0.158567\pi\) |
0.0254441 | + | 0.999676i | \(0.491900\pi\) | |||||||
\(98\) | −195.640 | −1.99632 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 27.9411 | + | 41.4644i | 0.279411 | + | 0.414644i | ||||
\(101\) | −13.1893 | − | 7.61484i | −0.130587 | − | 0.0753944i | 0.433283 | − | 0.901258i | \(-0.357355\pi\) |
−0.563870 | + | 0.825863i | \(0.690688\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −66.7640 | + | 38.5462i | −0.648194 | + | 0.374235i | −0.787764 | − | 0.615977i | \(-0.788761\pi\) |
0.139570 | + | 0.990212i | \(0.455428\pi\) | |||||||
\(104\) | 41.6614 | − | 24.0532i | 0.400591 | − | 0.231281i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −27.0624 | + | 46.8735i | −0.255306 | + | 0.442203i | ||||
\(107\) | −78.4264 | −0.732957 | −0.366479 | − | 0.930427i | \(-0.619437\pi\) | ||||
−0.366479 | + | 0.930427i | \(0.619437\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −146.279 | −1.34201 | −0.671006 | − | 0.741452i | \(-0.734137\pi\) | ||||
−0.671006 | + | 0.741452i | \(0.734137\pi\) | |||||||
\(110\) | 46.1160 | + | 73.8376i | 0.419236 | + | 0.671251i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −47.4137 | + | 27.3743i | −0.423336 | + | 0.244413i | ||||
\(113\) | −27.2132 | − | 47.1347i | −0.240825 | − | 0.417121i | 0.720125 | − | 0.693845i | \(-0.244085\pi\) |
−0.960949 | + | 0.276724i | \(0.910751\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −147.577 | + | 92.1703i | −1.28328 | + | 0.801481i | ||||
\(116\) | 42.2702i | 0.364398i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 58.8755i | 0.498945i | ||||||||
\(119\) | 81.7826 | + | 47.2172i | 0.687249 | + | 0.396783i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2868 | + | 26.4775i | 0.126337 | + | 0.218822i | ||||
\(122\) | 10.6482 | + | 18.4433i | 0.0872806 | + | 0.151174i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 38.2132 | − | 66.1872i | 0.308171 | − | 0.533768i | ||||
\(125\) | 12.9828 | + | 124.324i | 0.103862 | + | 0.994592i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 159.215i | − | 1.25366i | −0.779154 | − | 0.626832i | \(-0.784351\pi\) | ||
0.779154 | − | 0.626832i | \(-0.215649\pi\) | |||||||
\(128\) | −5.65685 | + | 9.79796i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 120.194 | − | 4.17038i | 0.924568 | − | 0.0320799i | ||||
\(131\) | 95.5252 | − | 55.1515i | 0.729200 | − | 0.421004i | −0.0889293 | − | 0.996038i | \(-0.528345\pi\) |
0.818130 | + | 0.575034i | \(0.195011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −85.8501 | − | 49.5656i | −0.645489 | − | 0.372673i | ||||
\(134\) | 181.893i | 1.35741i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 19.5147 | 0.143491 | ||||||||
\(137\) | −108.959 | + | 188.723i | −0.795324 | + | 1.37754i | 0.127309 | + | 0.991863i | \(0.459366\pi\) |
−0.922633 | + | 0.385679i | \(0.873967\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 53.1249 | + | 92.0150i | 0.382193 | + | 0.661979i | 0.991376 | − | 0.131052i | \(-0.0418355\pi\) |
−0.609182 | + | 0.793030i | \(0.708502\pi\) | |||||||
\(140\) | −136.789 | + | 4.74619i | −0.977066 | + | 0.0339014i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −128.558 | − | 74.2232i | −0.905340 | − | 0.522698i | ||||
\(143\) | 209.397 | 1.46431 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −49.6325 | + | 93.2948i | −0.342293 | + | 0.643413i | ||||
\(146\) | 2.58706 | + | 1.49364i | 0.0177196 | + | 0.0102304i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 37.3049 | − | 21.5380i | 0.252060 | − | 0.145527i | ||||
\(149\) | 12.2622 | − | 7.07960i | 0.0822968 | − | 0.0475141i | −0.458287 | − | 0.888804i | \(-0.651537\pi\) |
0.540584 | + | 0.841290i | \(0.318203\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −36.6690 | + | 63.5127i | −0.242841 | + | 0.420614i | −0.961522 | − | 0.274726i | \(-0.911413\pi\) |
0.718681 | + | 0.695340i | \(0.244746\pi\) | |||||||
\(152\) | −20.4853 | −0.134772 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −238.309 | −1.54746 | ||||||||
\(155\) | 162.056 | − | 101.213i | 1.04552 | − | 0.652989i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −60.7475 | + | 35.0726i | −0.386927 | + | 0.223392i | −0.680828 | − | 0.732444i | \(-0.738380\pi\) |
0.293901 | + | 0.955836i | \(0.405046\pi\) | |||||||
\(158\) | 31.1802 | + | 54.0057i | 0.197343 | + | 0.341808i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −23.9898 | + | 14.9830i | −0.149936 | + | 0.0936439i | ||||
\(161\) | − | 476.299i | − | 2.95838i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 9.05959i | − | 0.0555803i | −0.999614 | − | 0.0277902i | \(-0.991153\pi\) | ||
0.999614 | − | 0.0277902i | \(-0.00884702\pi\) | |||||||
\(164\) | 62.9856 | + | 36.3648i | 0.384059 | + | 0.221736i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 38.9081 | + | 67.3908i | 0.234386 | + | 0.405969i | ||||
\(167\) | 31.9264 | + | 55.2982i | 0.191176 | + | 0.331127i | 0.945640 | − | 0.325215i | \(-0.105437\pi\) |
−0.754464 | + | 0.656341i | \(0.772103\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 60.1396 | − | 104.165i | 0.355856 | − | 0.616360i | ||||
\(170\) | 43.0711 | + | 22.9136i | 0.253359 | + | 0.134786i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 12.4784i | − | 0.0725489i | ||||||
\(173\) | −13.9939 | + | 24.2382i | −0.0808896 | + | 0.140105i | −0.903632 | − | 0.428309i | \(-0.859109\pi\) |
0.822743 | + | 0.568414i | \(0.192443\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −307.481 | − | 150.139i | −1.75704 | − | 0.857935i | ||||
\(176\) | −42.6484 | + | 24.6230i | −0.242320 | + | 0.139904i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 83.4075 | + | 48.1554i | 0.468582 | + | 0.270536i | ||||
\(179\) | − | 21.0660i | − | 0.117687i | −0.998267 | − | 0.0588435i | \(-0.981259\pi\) | ||
0.998267 | − | 0.0588435i | \(-0.0187413\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 53.6030 | 0.296149 | 0.148075 | − | 0.988976i | \(-0.452692\pi\) | ||||
0.148075 | + | 0.988976i | \(0.452692\pi\) | |||||||
\(182\) | −164.610 | + | 285.113i | −0.904452 | + | 1.56656i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −49.2132 | − | 85.2398i | −0.267463 | − | 0.463260i | ||||
\(185\) | 107.625 | − | 3.73429i | 0.581758 | − | 0.0201853i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 73.5630 | + | 42.4716i | 0.393385 | + | 0.227121i | ||||
\(188\) | −80.4020 | −0.427670 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −45.2132 | − | 24.0532i | −0.237964 | − | 0.126596i | ||||
\(191\) | −193.144 | − | 111.512i | −1.01123 | − | 0.583831i | −0.0996752 | − | 0.995020i | \(-0.531780\pi\) |
−0.911550 | + | 0.411189i | \(0.865114\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 152.614 | − | 88.1118i | 0.790746 | − | 0.456538i | −0.0494788 | − | 0.998775i | \(-0.515756\pi\) |
0.840225 | + | 0.542237i | \(0.182423\pi\) | |||||||
\(194\) | −123.997 | + | 71.5899i | −0.639162 | + | 0.369020i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 138.338 | − | 239.609i | 0.705807 | − | 1.22249i | ||||
\(197\) | 277.586 | 1.40906 | 0.704532 | − | 0.709672i | \(-0.251157\pi\) | ||||
0.704532 | + | 0.709672i | \(0.251157\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 71.5736 | 0.359666 | 0.179833 | − | 0.983697i | \(-0.442444\pi\) | ||||
0.179833 | + | 0.983697i | \(0.442444\pi\) | |||||||
\(200\) | −70.5406 | + | 4.90102i | −0.352703 | + | 0.0245051i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18.6525 | − | 10.7690i | 0.0923389 | − | 0.0533119i | ||||
\(203\) | −144.640 | − | 250.523i | −0.712510 | − | 1.23410i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 96.3175 | + | 154.217i | 0.469841 | + | 0.752277i | ||||
\(206\) | − | 109.025i | − | 0.529248i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 68.0328i | 0.327081i | ||||||||
\(209\) | −77.2217 | − | 44.5840i | −0.369482 | − | 0.213320i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −159.746 | − | 276.689i | −0.757091 | − | 1.31132i | −0.944328 | − | 0.329005i | \(-0.893287\pi\) |
0.187237 | − | 0.982315i | \(-0.440047\pi\) | |||||||
\(212\) | −38.2721 | − | 66.2892i | −0.180529 | − | 0.312685i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 55.4558 | − | 96.0523i | 0.259139 | − | 0.448843i | ||||
\(215\) | 14.6518 | − | 27.5412i | 0.0681479 | − | 0.128099i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 523.030i | 2.41028i | ||||||||
\(218\) | 103.435 | − | 179.155i | 0.474473 | − | 0.821811i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −123.041 | + | 4.26918i | −0.559278 | + | 0.0194054i | ||||
\(221\) | 101.626 | − | 58.6740i | 0.459848 | − | 0.265493i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 140.676 | + | 81.2193i | 0.630834 | + | 0.364212i | 0.781075 | − | 0.624437i | \(-0.214672\pi\) |
−0.150241 | + | 0.988649i | \(0.548005\pi\) | |||||||
\(224\) | − | 77.4262i | − | 0.345653i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 76.9706 | 0.340578 | ||||||||
\(227\) | −120.549 | + | 208.797i | −0.531052 | + | 0.919809i | 0.468291 | + | 0.883574i | \(0.344870\pi\) |
−0.999343 | + | 0.0362347i | \(0.988464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −51.1102 | − | 88.5254i | −0.223189 | − | 0.386574i | 0.732586 | − | 0.680675i | \(-0.238313\pi\) |
−0.955774 | + | 0.294101i | \(0.904980\pi\) | |||||||
\(230\) | −8.53265 | − | 245.918i | −0.0370985 | − | 1.06921i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −51.7702 | − | 29.8895i | −0.223147 | − | 0.128834i | ||||
\(233\) | 241.966 | 1.03848 | 0.519239 | − | 0.854629i | \(-0.326215\pi\) | ||||
0.519239 | + | 0.854629i | \(0.326215\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −177.456 | − | 94.4058i | −0.755131 | − | 0.401727i | ||||
\(236\) | −72.1075 | − | 41.6313i | −0.305540 | − | 0.176404i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −115.658 | + | 66.7752i | −0.485958 | + | 0.280568i | ||||
\(239\) | −325.157 | + | 187.729i | −1.36049 | + | 0.785478i | −0.989689 | − | 0.143235i | \(-0.954250\pi\) |
−0.370799 | + | 0.928713i | \(0.620916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 159.140 | − | 275.638i | 0.660330 | − | 1.14373i | −0.320198 | − | 0.947350i | \(-0.603750\pi\) |
0.980529 | − | 0.196375i | \(-0.0629171\pi\) | |||||||
\(242\) | −43.2376 | −0.178668 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −30.1177 | −0.123433 | ||||||||
\(245\) | 586.669 | − | 366.409i | 2.39457 | − | 1.49555i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −106.681 | + | 61.5922i | −0.431906 | + | 0.249361i | ||||
\(248\) | 54.0416 | + | 93.6028i | 0.217910 | + | 0.377431i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −161.445 | − | 72.0098i | −0.645781 | − | 0.288039i | ||||
\(251\) | 85.5417i | 0.340804i | 0.985375 | + | 0.170402i | \(0.0545066\pi\) | ||||
−0.985375 | + | 0.170402i | \(0.945493\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 428.429i | − | 1.69339i | ||||||
\(254\) | 194.998 | + | 112.582i | 0.767709 | + | 0.443237i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 107.114 | + | 185.526i | 0.416785 | + | 0.721893i | 0.995614 | − | 0.0935562i | \(-0.0298235\pi\) |
−0.578829 | + | 0.815449i | \(0.696490\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −147.397 | + | 255.299i | −0.569100 | + | 0.985711i | ||||
\(260\) | −79.8823 | + | 150.156i | −0.307239 | + | 0.577522i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 155.992i | 0.595389i | ||||||||
\(263\) | 53.4386 | − | 92.5584i | 0.203189 | − | 0.351933i | −0.746365 | − | 0.665536i | \(-0.768203\pi\) |
0.949554 | + | 0.313603i | \(0.101536\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.63567 | − | 191.245i | −0.0250402 | − | 0.721680i | ||||
\(266\) | 121.410 | − | 70.0963i | 0.456430 | − | 0.263520i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −222.772 | − | 128.618i | −0.831241 | − | 0.479917i | ||||
\(269\) | 365.927i | 1.36032i | 0.733062 | + | 0.680161i | \(0.238090\pi\) | ||||
−0.733062 | + | 0.680161i | \(0.761910\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −92.8894 | −0.342765 | −0.171383 | − | 0.985205i | \(-0.554823\pi\) | ||||
−0.171383 | + | 0.985205i | \(0.554823\pi\) | |||||||
\(272\) | −13.7990 | + | 23.9006i | −0.0507316 | + | 0.0878697i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −154.092 | − | 266.895i | −0.562379 | − | 0.974069i | ||||
\(275\) | −276.578 | − | 135.049i | −1.00574 | − | 0.491087i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −195.841 | − | 113.069i | −0.707006 | − | 0.408190i | 0.102946 | − | 0.994687i | \(-0.467173\pi\) |
−0.809951 | + | 0.586497i | \(0.800507\pi\) | |||||||
\(278\) | −150.260 | −0.540503 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 90.9117 | − | 170.888i | 0.324685 | − | 0.610314i | ||||
\(281\) | 54.9106 | + | 31.7026i | 0.195411 | + | 0.112821i | 0.594513 | − | 0.804086i | \(-0.297345\pi\) |
−0.399102 | + | 0.916907i | \(0.630678\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −314.459 | + | 181.553i | −1.11116 | + | 0.641531i | −0.939131 | − | 0.343560i | \(-0.888367\pi\) |
−0.172033 | + | 0.985091i | \(0.555034\pi\) | |||||||
\(284\) | 181.809 | − | 104.967i | 0.640172 | − | 0.369604i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −148.066 | + | 256.458i | −0.517713 | + | 0.896706i | ||||
\(287\) | −497.730 | −1.73425 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −241.397 | −0.835284 | ||||||||
\(290\) | −79.1669 | − | 126.757i | −0.272989 | − | 0.437091i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.65865 | + | 2.11232i | −0.0125296 | + | 0.00723398i | ||||
\(293\) | 113.717 | + | 196.963i | 0.388112 | + | 0.672229i | 0.992196 | − | 0.124691i | \(-0.0397941\pi\) |
−0.604084 | + | 0.796921i | \(0.706461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −110.267 | − | 176.551i | −0.373785 | − | 0.598479i | ||||
\(296\) | 60.9187i | 0.205806i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 20.0241i | 0.0671950i | ||||||||
\(299\) | −512.573 | − | 295.934i | −1.71429 | − | 0.989747i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.6985 | + | 73.9559i | 0.141855 | + | 0.245701i | ||||
\(302\) | −51.8579 | − | 89.8205i | −0.171715 | − | 0.297419i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.4853 | − | 25.0892i | 0.0476490 | − | 0.0825304i | ||||
\(305\) | −66.4731 | − | 35.3634i | −0.217945 | − | 0.115946i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 340.164i | − | 1.10803i | −0.832508 | − | 0.554013i | \(-0.813096\pi\) | ||
0.832508 | − | 0.554013i | \(-0.186904\pi\) | |||||||
\(308\) | 168.510 | − | 291.867i | 0.547109 | − | 0.947621i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.36981 | + | 270.046i | 0.0302252 | + | 0.871115i | ||||
\(311\) | −334.951 | + | 193.384i | −1.07701 | + | 0.621815i | −0.930089 | − | 0.367333i | \(-0.880271\pi\) |
−0.146925 | + | 0.989148i | \(0.546938\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −325.974 | − | 188.201i | −1.04145 | − | 0.601282i | −0.121207 | − | 0.992627i | \(-0.538677\pi\) |
−0.920244 | + | 0.391345i | \(0.872010\pi\) | |||||||
\(314\) | − | 99.2002i | − | 0.315924i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −88.1909 | −0.279085 | ||||||||
\(317\) | −177.700 | + | 307.785i | −0.560566 | + | 0.970929i | 0.436881 | + | 0.899519i | \(0.356083\pi\) |
−0.997447 | + | 0.0714099i | \(0.977250\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −130.103 | − | 225.344i | −0.407845 | − | 0.706408i | ||||
\(320\) | −1.38705 | − | 39.9759i | −0.00433453 | − | 0.124925i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 583.345 | + | 336.794i | 1.81163 | + | 1.04594i | ||||
\(323\) | −49.9706 | −0.154708 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −352.617 | + | 237.614i | −1.08498 | + | 0.731121i | ||||
\(326\) | 11.0957 | + | 6.40610i | 0.0340359 | + | 0.0196506i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −89.0751 | + | 51.4275i | −0.271570 | + | 0.156791i | ||||
\(329\) | 476.519 | − | 275.119i | 1.44839 | − | 0.836227i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 222.095 | − | 384.681i | 0.670983 | − | 1.16218i | −0.306642 | − | 0.951825i | \(-0.599206\pi\) |
0.977626 | − | 0.210352i | \(-0.0674611\pi\) | |||||||
\(332\) | −110.049 | −0.331472 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −90.3015 | −0.270364 | ||||||||
\(335\) | −340.663 | − | 545.446i | −1.01691 | − | 1.62820i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −352.547 | + | 203.543i | −1.04613 | + | 0.603985i | −0.921564 | − | 0.388226i | \(-0.873088\pi\) |
−0.124569 | + | 0.992211i | \(0.539755\pi\) | |||||||
\(338\) | 85.0503 | + | 147.311i | 0.251628 | + | 0.435832i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −58.5192 | + | 36.5487i | −0.172115 | + | 0.107496i | ||||
\(341\) | 470.463i | 1.37966i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1222.78i | 3.56497i | ||||||||
\(344\) | 15.2829 | + | 8.82357i | 0.0444270 | + | 0.0256499i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.7904 | − | 34.2779i | −0.0571976 | − | 0.0990691i | ||||
\(347\) | 244.706 | + | 423.843i | 0.705204 | + | 1.22145i | 0.966618 | + | 0.256222i | \(0.0824777\pi\) |
−0.261414 | + | 0.965227i | \(0.584189\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −40.8970 | + | 70.8356i | −0.117183 | + | 0.202967i | −0.918650 | − | 0.395071i | \(-0.870720\pi\) |
0.801467 | + | 0.598039i | \(0.204053\pi\) | |||||||
\(350\) | 401.304 | − | 270.422i | 1.14658 | − | 0.772634i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 69.6445i | − | 0.197854i | ||||||
\(353\) | 125.693 | − | 217.707i | 0.356072 | − | 0.616735i | −0.631229 | − | 0.775597i | \(-0.717449\pi\) |
0.987301 | + | 0.158862i | \(0.0507824\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 524.521 | − | 18.1994i | 1.47753 | − | 0.0512659i | ||||
\(356\) | −117.956 | + | 68.1020i | −0.331337 | + | 0.191298i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25.8004 | + | 14.8959i | 0.0720682 | + | 0.0416086i | ||||
\(359\) | − | 518.500i | − | 1.44429i | −0.691742 | − | 0.722145i | \(-0.743156\pi\) | ||
0.691742 | − | 0.722145i | \(-0.256844\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −308.544 | −0.854693 | ||||||||
\(362\) | −37.9031 | + | 65.6500i | −0.104705 | + | 0.181354i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −232.794 | − | 403.211i | −0.639544 | − | 1.10772i | ||||
\(365\) | −10.5553 | + | 0.366238i | −0.0289185 | + | 0.00100339i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −296.166 | − | 170.992i | −0.806992 | − | 0.465917i | 0.0389180 | − | 0.999242i | \(-0.487609\pi\) |
−0.845910 | + | 0.533325i | \(0.820942\pi\) | |||||||
\(368\) | 139.196 | 0.378250 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −71.5290 | + | 134.454i | −0.193322 | + | 0.363389i | ||||
\(371\) | 453.655 | + | 261.918i | 1.22279 | + | 0.705978i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 95.5252 | − | 55.1515i | 0.256100 | − | 0.147859i | −0.366454 | − | 0.930436i | \(-0.619428\pi\) |
0.622554 | + | 0.782577i | \(0.286095\pi\) | |||||||
\(374\) | −104.034 | + | 60.0640i | −0.278165 | + | 0.160599i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 56.8528 | − | 98.4720i | 0.151204 | − | 0.261894i | ||||
\(377\) | −359.470 | −0.953502 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 324.345 | 0.855792 | 0.427896 | − | 0.903828i | \(-0.359255\pi\) | ||||
0.427896 | + | 0.903828i | \(0.359255\pi\) | |||||||
\(380\) | 61.4296 | − | 38.3664i | 0.161657 | − | 0.100964i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 273.147 | − | 157.701i | 0.715044 | − | 0.412831i | ||||
\(383\) | −286.240 | − | 495.782i | −0.747363 | − | 1.29447i | −0.949082 | − | 0.315028i | \(-0.897986\pi\) |
0.201719 | − | 0.979443i | \(-0.435347\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 714.621 | − | 446.323i | 1.85616 | − | 1.15928i | ||||
\(386\) | 249.218i | 0.645642i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 202.487i | − | 0.521873i | ||||||
\(389\) | 624.981 | + | 360.833i | 1.60664 | + | 0.927592i | 0.990116 | + | 0.140253i | \(0.0447915\pi\) |
0.616520 | + | 0.787339i | \(0.288542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −120.048 | − | 207.929i | −0.307027 | − | 0.531787i | ||||
\(392\) | 195.640 | + | 338.858i | 0.499081 | + | 0.864433i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −196.283 | + | 339.972i | −0.498180 | + | 0.862873i | ||||
\(395\) | −194.647 | − | 103.551i | −0.492777 | − | 0.262155i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 379.321i | − | 0.955468i | −0.878505 | − | 0.477734i | \(-0.841458\pi\) | ||
0.878505 | − | 0.477734i | \(-0.158542\pi\) | |||||||
\(398\) | −50.6102 | + | 87.6594i | −0.127161 | + | 0.220250i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 43.8773 | − | 89.8598i | 0.109693 | − | 0.224650i | ||||
\(401\) | 303.952 | − | 175.487i | 0.757985 | − | 0.437623i | −0.0705866 | − | 0.997506i | \(-0.522487\pi\) |
0.828572 | + | 0.559883i | \(0.189154\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 562.863 | + | 324.969i | 1.39668 | + | 0.806375i | ||||
\(404\) | 30.4593i | 0.0753944i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 409.103 | 1.00764 | ||||||||
\(407\) | −132.583 | + | 229.640i | −0.325756 | + | 0.564227i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 266.713 | + | 461.961i | 0.652111 | + | 1.12949i | 0.982610 | + | 0.185682i | \(0.0594495\pi\) |
−0.330499 | + | 0.943806i | \(0.607217\pi\) | |||||||
\(410\) | −256.983 | + | 8.91658i | −0.626788 | + | 0.0217478i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 133.528 | + | 77.0924i | 0.324097 | + | 0.187118i | ||||
\(413\) | 569.813 | 1.37969 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −242.889 | − | 129.216i | −0.585276 | − | 0.311364i | ||||
\(416\) | −83.3229 | − | 48.1065i | −0.200295 | − | 0.115641i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 109.208 | − | 63.0513i | 0.261263 | − | 0.150840i | ||||
\(419\) | 207.634 | − | 119.878i | 0.495547 | − | 0.286104i | −0.231326 | − | 0.972876i | \(-0.574306\pi\) |
0.726873 | + | 0.686772i | \(0.240973\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −212.471 | + | 368.010i | −0.504681 | + | 0.874133i | 0.495305 | + | 0.868719i | \(0.335056\pi\) |
−0.999985 | + | 0.00541323i | \(0.998277\pi\) | |||||||
\(422\) | 451.831 | 1.07069 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 108.250 | 0.255306 | ||||||||
\(425\) | −172.073 | + | 11.9552i | −0.404877 | + | 0.0281300i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 178.499 | − | 103.057i | 0.418031 | − | 0.241350i | ||||
\(428\) | 78.4264 | + | 135.839i | 0.183239 | + | 0.317380i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 23.3705 | + | 37.4193i | 0.0543501 | + | 0.0870216i | ||||
\(431\) | 544.039i | 1.26227i | 0.775673 | + | 0.631135i | \(0.217411\pi\) | ||||
−0.775673 | + | 0.631135i | \(0.782589\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 602.735i | − | 1.39200i | −0.718043 | − | 0.695999i | \(-0.754962\pi\) | ||
0.718043 | − | 0.695999i | \(-0.245038\pi\) | |||||||
\(434\) | −640.578 | − | 369.838i | −1.47599 | − | 0.852161i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 146.279 | + | 253.363i | 0.335503 | + | 0.581108i | ||||
\(437\) | 126.018 | + | 218.270i | 0.288371 | + | 0.499474i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −201.143 | + | 348.390i | −0.458185 | + | 0.793600i | −0.998865 | − | 0.0476287i | \(-0.984834\pi\) |
0.540680 | + | 0.841228i | \(0.318167\pi\) | |||||||
\(440\) | 81.7746 | − | 153.713i | 0.185851 | − | 0.349347i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 165.955i | 0.375464i | ||||||||
\(443\) | −219.257 | + | 379.765i | −0.494938 | + | 0.857257i | −0.999983 | − | 0.00583572i | \(-0.998142\pi\) |
0.505045 | + | 0.863093i | \(0.331476\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −340.305 | + | 11.8076i | −0.764730 | + | 0.0265340i | ||||
\(446\) | −198.946 | + | 114.861i | −0.446067 | + | 0.257537i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 94.8274 | + | 54.7486i | 0.211668 | + | 0.122207i | ||||
\(449\) | − | 670.866i | − | 1.49413i | −0.664749 | − | 0.747067i | \(-0.731462\pi\) | ||
0.664749 | − | 0.747067i | \(-0.268538\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −447.706 | −0.992695 | ||||||||
\(452\) | −54.4264 | + | 94.2693i | −0.120412 | + | 0.208560i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −170.482 | − | 295.283i | −0.375510 | − | 0.650403i | ||||
\(455\) | −40.3621 | − | 1163.27i | −0.0887080 | − | 2.55664i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −601.913 | − | 347.514i | −1.31710 | − | 0.760425i | −0.333835 | − | 0.942632i | \(-0.608343\pi\) |
−0.983260 | + | 0.182206i | \(0.941676\pi\) | |||||||
\(458\) | 144.561 | 0.315636 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 307.220 | + | 163.440i | 0.667870 | + | 0.355304i | ||||
\(461\) | 11.3352 | + | 6.54436i | 0.0245882 | + | 0.0141960i | 0.512244 | − | 0.858840i | \(-0.328814\pi\) |
−0.487656 | + | 0.873036i | \(0.662148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 202.894 | − | 117.141i | 0.438215 | − | 0.253004i | −0.264625 | − | 0.964351i | \(-0.585248\pi\) |
0.702840 | + | 0.711348i | \(0.251915\pi\) | |||||||
\(464\) | 73.2141 | − | 42.2702i | 0.157789 | − | 0.0910995i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −171.095 | + | 296.346i | −0.367158 | + | 0.635936i | ||||
\(467\) | −742.882 | −1.59075 | −0.795377 | − | 0.606115i | \(-0.792727\pi\) | ||||
−0.795377 | + | 0.606115i | \(0.792727\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1760.41 | 3.75354 | ||||||||
\(470\) | 241.103 | − | 150.583i | 0.512986 | − | 0.320390i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 101.975 | − | 58.8755i | 0.216049 | − | 0.124736i | ||||
\(473\) | 38.4071 | + | 66.5230i | 0.0811989 | + | 0.140641i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 180.631 | − | 12.5498i | 0.380275 | − | 0.0264207i | ||||
\(476\) | − | 188.869i | − | 0.396783i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 530.978i | − | 1.11083i | ||||||
\(479\) | 387.469 | + | 223.705i | 0.808913 | + | 0.467026i | 0.846578 | − | 0.532264i | \(-0.178659\pi\) |
−0.0376655 | + | 0.999290i | \(0.511992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 183.161 | + | 317.245i | 0.380793 | + | 0.659553i | ||||
\(482\) | 225.057 | + | 389.811i | 0.466924 | + | 0.808736i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 30.5736 | − | 52.9550i | 0.0631686 | − | 0.109411i | ||||
\(485\) | 237.754 | − | 446.910i | 0.490215 | − | 0.921464i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 50.3166i | − | 0.103319i | −0.998665 | − | 0.0516597i | \(-0.983549\pi\) | ||
0.998665 | − | 0.0516597i | \(-0.0164511\pi\) | |||||||
\(488\) | 21.2965 | − | 36.8866i | 0.0436403 | − | 0.0755872i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 33.9203 | + | 977.610i | 0.0692250 | + | 1.99512i | ||||
\(491\) | −684.707 | + | 395.316i | −1.39452 | + | 0.805124i | −0.993811 | − | 0.111084i | \(-0.964568\pi\) |
−0.400704 | + | 0.916208i | \(0.631234\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −126.285 | − | 72.9107i | −0.256156 | − | 0.147892i | ||||
\(494\) | − | 174.209i | − | 0.352650i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −152.853 | −0.308171 | ||||||||
\(497\) | −718.352 | + | 1244.22i | −1.44538 | + | 2.50347i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 300.195 | + | 519.953i | 0.601593 | + | 1.04199i | 0.992580 | + | 0.121593i | \(0.0388004\pi\) |
−0.390987 | + | 0.920396i | \(0.627866\pi\) | |||||||
\(500\) | 202.353 | − | 146.811i | 0.404705 | − | 0.293622i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −104.767 | − | 60.4871i | −0.208699 | − | 0.120492i | ||||
\(503\) | −433.368 | −0.861566 | −0.430783 | − | 0.902456i | \(-0.641763\pi\) | ||||
−0.430783 | + | 0.902456i | \(0.641763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.7645 | + | 67.2270i | −0.0708208 | + | 0.133123i | ||||
\(506\) | 524.716 | + | 302.945i | 1.03699 | + | 0.598705i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −275.769 | + | 159.215i | −0.542852 | + | 0.313416i | ||||
\(509\) | −832.870 | + | 480.857i | −1.63629 | + | 0.944710i | −0.654190 | + | 0.756331i | \(0.726990\pi\) |
−0.982096 | + | 0.188380i | \(0.939676\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.4558 | − | 25.0383i | 0.0282893 | − | 0.0489985i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −302.963 | −0.589423 | ||||||||
\(515\) | 204.191 | + | 326.936i | 0.396487 | + | 0.634827i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 428.627 | − | 247.468i | 0.829065 | − | 0.478661i | ||||
\(518\) | −208.451 | − | 361.047i | −0.402415 | − | 0.697003i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −127.417 | − | 204.012i | −0.245033 | − | 0.392330i | ||||
\(521\) | − | 5.90542i | − | 0.0113348i | −0.999984 | − | 0.00566739i | \(-0.998196\pi\) | ||
0.999984 | − | 0.00566739i | \(-0.00180400\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 165.846i | − | 0.317104i | −0.987351 | − | 0.158552i | \(-0.949317\pi\) | ||
0.987351 | − | 0.158552i | \(-0.0506826\pi\) | |||||||
\(524\) | −191.050 | − | 110.303i | −0.364600 | − | 0.210502i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 75.5736 | + | 130.897i | 0.143676 | + | 0.248854i | ||||
\(527\) | 131.826 | + | 228.329i | 0.250144 | + | 0.433262i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −340.985 | + | 590.603i | −0.644584 | + | 1.11645i | ||||
\(530\) | 238.919 | + | 127.104i | 0.450790 | + | 0.239819i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 198.262i | 0.372673i | ||||||||
\(533\) | −309.250 | + | 535.636i | −0.580206 | + | 1.00495i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.5977 | + | 391.896i | 0.0254162 | + | 0.732516i | ||||
\(536\) | 315.048 | − | 181.893i | 0.587776 | − | 0.339353i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −448.167 | − | 258.749i | −0.833024 | − | 0.480947i | ||||
\(539\) | 1703.15i | 3.15984i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 216.985 | 0.401081 | 0.200541 | − | 0.979685i | \(-0.435730\pi\) | ||||
0.200541 | + | 0.979685i | \(0.435730\pi\) | |||||||
\(542\) | 65.6827 | − | 113.766i | 0.121186 | − | 0.209900i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −19.5147 | − | 33.8005i | −0.0358726 | − | 0.0621332i | ||||
\(545\) | 25.3621 | + | 730.956i | 0.0465360 | + | 1.34120i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 87.1611 | + | 50.3225i | 0.159344 | + | 0.0919973i | 0.577552 | − | 0.816354i | \(-0.304008\pi\) |
−0.418208 | + | 0.908351i | \(0.637342\pi\) | |||||||
\(548\) | 435.838 | 0.795324 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 360.971 | − | 243.243i | 0.656310 | − | 0.442260i | ||||
\(551\) | 132.566 | + | 76.5369i | 0.240591 | + | 0.138906i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 522.682 | − | 301.771i | 0.945175 | − | 0.545697i | ||||
\(554\) | 276.960 | − | 159.903i | 0.499928 | − | 0.288634i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 106.250 | − | 184.030i | 0.191097 | − | 0.330989i | ||||
\(557\) | 116.662 | 0.209447 | 0.104723 | − | 0.994501i | \(-0.466604\pi\) | ||||
0.104723 | + | 0.994501i | \(0.466604\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 106.118 | 0.189835 | ||||||||
\(560\) | 145.010 | + | 232.180i | 0.258946 | + | 0.414606i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −77.6553 | + | 44.8343i | −0.138177 | + | 0.0797763i | ||||
\(563\) | −266.953 | − | 462.377i | −0.474162 | − | 0.821273i | 0.525400 | − | 0.850855i | \(-0.323916\pi\) |
−0.999562 | + | 0.0295822i | \(0.990582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −230.813 | + | 144.156i | −0.408519 | + | 0.255144i | ||||
\(566\) | − | 513.510i | − | 0.907262i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 296.893i | 0.522698i | ||||||||
\(569\) | −97.5590 | − | 56.3257i | −0.171457 | − | 0.0989907i | 0.411816 | − | 0.911267i | \(-0.364895\pi\) |
−0.583273 | + | 0.812276i | \(0.698228\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 430.768 | + | 746.111i | 0.754409 | + | 1.30668i | 0.945668 | + | 0.325135i | \(0.105410\pi\) |
−0.191258 | + | 0.981540i | \(0.561257\pi\) | |||||||
\(572\) | −209.397 | − | 362.686i | −0.366079 | − | 0.634067i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 351.948 | − | 609.592i | 0.613150 | − | 1.06201i | ||||
\(575\) | 486.161 | + | 721.459i | 0.845498 | + | 1.25471i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 37.3256i | − | 0.0646891i | −0.999477 | − | 0.0323446i | \(-0.989703\pi\) | ||
0.999477 | − | 0.0323446i | \(-0.0102974\pi\) | |||||||
\(578\) | 170.693 | − | 295.650i | 0.295317 | − | 0.511505i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 211.224 | − | 7.32886i | 0.364179 | − | 0.0126360i | ||||
\(581\) | 652.227 | − | 376.564i | 1.12259 | − | 0.648130i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 408.060 | + | 235.594i | 0.699932 | + | 0.404106i | ||||
\(584\) | − | 5.97455i | − | 0.0102304i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −321.640 | −0.548873 | ||||||||
\(587\) | 269.051 | − | 466.011i | 0.458350 | − | 0.793885i | −0.540524 | − | 0.841328i | \(-0.681774\pi\) |
0.998874 | + | 0.0474434i | \(0.0151074\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −138.382 | − | 239.685i | −0.234944 | − | 0.406936i | ||||
\(590\) | 294.200 | − | 10.2079i | 0.498645 | − | 0.0173015i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −74.6098 | − | 43.0760i | −0.126030 | − | 0.0727635i | ||||
\(593\) | −884.169 | −1.49101 | −0.745505 | − | 0.666500i | \(-0.767792\pi\) | ||||
−0.745505 | + | 0.666500i | \(0.767792\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 221.765 | − | 416.854i | 0.372713 | − | 0.700595i | ||||
\(596\) | −24.5244 | − | 14.1592i | −0.0411484 | − | 0.0237570i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 724.888 | − | 418.514i | 1.21219 | − | 0.699857i | ||||
\(599\) | 38.7750 | − | 22.3868i | 0.0647330 | − | 0.0373736i | −0.467284 | − | 0.884107i | \(-0.654768\pi\) |
0.532017 | + | 0.846734i | \(0.321434\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −197.287 | + | 341.711i | −0.328264 | + | 0.568570i | −0.982168 | − | 0.188008i | \(-0.939797\pi\) |
0.653903 | + | 0.756578i | \(0.273130\pi\) | |||||||
\(602\) | −120.770 | −0.200614 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 146.676 | 0.242841 | ||||||||
\(605\) | 129.657 | − | 80.9787i | 0.214310 | − | 0.133849i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −186.345 | + | 107.586i | −0.306993 | + | 0.177243i | −0.645580 | − | 0.763692i | \(-0.723384\pi\) |
0.338587 | + | 0.940935i | \(0.390051\pi\) | |||||||
\(608\) | 20.4853 | + | 35.4815i | 0.0336929 | + | 0.0583578i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 90.3147 | − | 56.4069i | 0.148057 | − | 0.0924703i | ||||
\(611\) | − | 683.747i | − | 1.11906i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 333.937i | − | 0.544758i | −0.962190 | − | 0.272379i | \(-0.912189\pi\) | ||
0.962190 | − | 0.272379i | \(-0.0878105\pi\) | |||||||
\(614\) | 416.614 | + | 240.532i | 0.678525 | + | 0.391747i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 238.309 | + | 412.763i | 0.386865 | + | 0.670069i | ||||
\(617\) | 32.7117 | + | 56.6584i | 0.0530174 | + | 0.0918288i | 0.891316 | − | 0.453382i | \(-0.149783\pi\) |
−0.838299 | + | 0.545211i | \(0.816449\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.96342 | − | 17.2571i | 0.0160960 | − | 0.0278791i | −0.857865 | − | 0.513875i | \(-0.828210\pi\) |
0.873961 | + | 0.485996i | \(0.161543\pi\) | |||||||
\(620\) | −337.362 | − | 179.475i | −0.544133 | − | 0.289477i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 546.973i | − | 0.879379i | ||||||
\(623\) | 466.061 | − | 807.241i | 0.748091 | − | 1.29573i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 618.995 | − | 86.4302i | 0.990392 | − | 0.138288i | ||||
\(626\) | 460.997 | − | 266.157i | 0.736417 | − | 0.425171i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 121.495 | + | 70.1452i | 0.193463 | + | 0.111696i | ||||
\(629\) | 148.601i | 0.236250i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −210.625 | −0.333796 | −0.166898 | − | 0.985974i | \(-0.553375\pi\) | ||||
−0.166898 | + | 0.985974i | \(0.553375\pi\) | |||||||
\(632\) | 62.3604 | − | 108.011i | 0.0986715 | − | 0.170904i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −251.305 | − | 435.273i | −0.396380 | − | 0.686551i | ||||
\(635\) | −795.598 | + | 27.6050i | −1.25291 | + | 0.0434724i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2037.66 | + | 1176.44i | 3.19883 | + | 1.84685i | ||||
\(638\) | 367.986 | 0.576780 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 49.9411 | + | 26.5685i | 0.0780330 | + | 0.0415132i | ||||
\(641\) | −1019.97 | − | 588.881i | −1.59122 | − | 0.918692i | −0.993098 | − | 0.117287i | \(-0.962580\pi\) |
−0.598122 | − | 0.801405i | \(-0.704086\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.5995 | − | 18.8213i | 0.0506990 | − | 0.0292711i | −0.474436 | − | 0.880290i | \(-0.657348\pi\) |
0.525135 | + | 0.851019i | \(0.324015\pi\) | |||||||
\(644\) | −824.974 | + | 476.299i | −1.28102 | + | 0.739595i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 35.3345 | − | 61.2012i | 0.0546974 | − | 0.0947387i | ||||
\(647\) | −695.382 | −1.07478 | −0.537389 | − | 0.843334i | \(-0.680589\pi\) | ||||
−0.537389 | + | 0.843334i | \(0.680589\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 512.544 | 0.789744 | ||||||||
\(650\) | −41.6788 | − | 599.885i | −0.0641212 | − | 0.922900i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.6917 | + | 9.05959i | −0.0240670 | + | 0.0138951i | ||||
\(653\) | 462.148 | + | 800.464i | 0.707731 | + | 1.22583i | 0.965697 | + | 0.259672i | \(0.0836144\pi\) |
−0.257966 | + | 0.966154i | \(0.583052\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −292.154 | − | 467.777i | −0.446037 | − | 0.714163i | ||||
\(656\) | − | 145.459i | − | 0.221736i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 778.153i | 1.18260i | ||||||||
\(659\) | 58.6043 | + | 33.8352i | 0.0889291 | + | 0.0513433i | 0.543805 | − | 0.839212i | \(-0.316983\pi\) |
−0.454876 | + | 0.890555i | \(0.650316\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −516.434 | − | 894.489i | −0.781291 | − | 1.35324i | −0.931190 | − | 0.364535i | \(-0.881228\pi\) |
0.149898 | − | 0.988701i | \(-0.452105\pi\) | |||||||
\(662\) | 314.090 | + | 544.021i | 0.474457 | + | 0.821783i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 77.8162 | − | 134.782i | 0.117193 | − | 0.202984i | ||||
\(665\) | −232.794 | + | 437.586i | −0.350066 | + | 0.658024i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 735.480i | 1.10267i | ||||||||
\(668\) | 63.8528 | − | 110.596i | 0.0955880 | − | 0.165563i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 908.918 | − | 31.5369i | 1.35659 | − | 0.0470699i | ||||
\(671\) | 160.559 | − | 92.6988i | 0.239283 | − | 0.138150i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.80797 | + | 5.08528i | 0.0130876 | + | 0.00755614i | 0.506530 | − | 0.862223i | \(-0.330928\pi\) |
−0.493442 | + | 0.869779i | \(0.664261\pi\) | |||||||
\(674\) | − | 575.707i | − | 0.854164i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −240.558 | −0.355856 | ||||||||
\(677\) | −288.468 | + | 499.641i | −0.426098 | + | 0.738023i | −0.996522 | − | 0.0833273i | \(-0.973445\pi\) |
0.570425 | + | 0.821350i | \(0.306779\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 692.867 | + | 1200.08i | 1.02042 | + | 1.76742i | ||||
\(680\) | −3.38349 | − | 97.5149i | −0.00497572 | − | 0.143404i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −576.197 | − | 332.667i | −0.844863 | − | 0.487782i | ||||
\(683\) | −526.009 | −0.770145 | −0.385073 | − | 0.922886i | \(-0.625824\pi\) | ||||
−0.385073 | + | 0.922886i | \(0.625824\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 961.940 | + | 511.748i | 1.40429 | + | 0.747078i | ||||
\(686\) | −1497.60 | − | 864.639i | −2.18309 | − | 1.26041i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −21.6132 | + | 12.4784i | −0.0314146 | + | 0.0181372i | ||||
\(689\) | 563.730 | − | 325.470i | 0.818186 | − | 0.472380i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −211.452 | + | 366.245i | −0.306008 | + | 0.530022i | −0.977485 | − | 0.211003i | \(-0.932327\pi\) |
0.671477 | + | 0.741025i | \(0.265660\pi\) | |||||||
\(692\) | 55.9756 | 0.0808896 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −692.132 | −0.997308 | ||||||||
\(695\) | 450.587 | − | 281.418i | 0.648327 | − | 0.404919i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −217.284 | + | 125.449i | −0.311742 | + | 0.179985i | ||||
\(698\) | −57.8370 | − | 100.177i | −0.0828611 | − | 0.143520i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 47.4334 | + | 682.712i | 0.0677620 | + | 0.975302i | ||||
\(701\) | − | 881.146i | − | 1.25698i | −0.777816 | − | 0.628492i | \(-0.783672\pi\) | ||
0.777816 | − | 0.628492i | \(-0.216328\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 155.992i | − | 0.221895i | ||||||
\(704\) | 85.2967 | + | 49.2461i | 0.121160 | + | 0.0699518i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 177.757 | + | 307.885i | 0.251781 | + | 0.436097i | ||||
\(707\) | −104.225 | − | 180.524i | −0.147419 | − | 0.255338i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −50.7136 | + | 87.8386i | −0.0715284 | + | 0.123891i | −0.899571 | − | 0.436774i | \(-0.856121\pi\) |
0.828043 | + | 0.560665i | \(0.189454\pi\) | |||||||
\(710\) | −348.603 | + | 655.274i | −0.490990 | + | 0.922921i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 192.621i | − | 0.270536i | ||||||
\(713\) | 664.890 | − | 1151.62i | 0.932525 | − | 1.61518i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.3055 | − | 1046.36i | −0.0507770 | − | 1.46343i | ||||
\(716\) | −36.4873 | + | 21.0660i | −0.0509599 | + | 0.0294217i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 635.030 | + | 366.635i | 0.884443 | + | 0.510634i | ||||
\(719\) | − | 36.2956i | − | 0.0504807i | −0.999681 | − | 0.0252404i | \(-0.991965\pi\) | ||
0.999681 | − | 0.0252404i | \(-0.00803511\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1055.18 | −1.46349 | ||||||||
\(722\) | 218.174 | − | 377.888i | 0.302180 | − | 0.523390i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −53.6030 | − | 92.8432i | −0.0740373 | − | 0.128236i | ||||
\(725\) | 474.799 | + | 231.838i | 0.654895 | + | 0.319776i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −457.049 | − | 263.878i | −0.628679 | − | 0.362968i | 0.151561 | − | 0.988448i | \(-0.451570\pi\) |
−0.780240 | + | 0.625480i | \(0.784903\pi\) | |||||||
\(728\) | 658.441 | 0.904452 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.01515 | − | 13.1865i | 0.00960980 | − | 0.0180637i | ||||
\(731\) | 37.2801 | + | 21.5237i | 0.0509988 | + | 0.0294442i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1130.97 | + | 652.966i | −1.54293 | + | 0.890813i | −0.544282 | + | 0.838902i | \(0.683198\pi\) |
−0.998652 | + | 0.0519106i | \(0.983469\pi\) | |||||||
\(734\) | 418.842 | − | 241.819i | 0.570630 | − | 0.329453i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −98.4264 | + | 170.480i | −0.133732 | + | 0.231630i | ||||
\(737\) | 1583.48 | 2.14855 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 754.875 | 1.02148 | 0.510741 | − | 0.859735i | \(-0.329371\pi\) | ||||
0.510741 | + | 0.859735i | \(0.329371\pi\) | |||||||
\(740\) | −114.093 | − | 182.678i | −0.154180 | − | 0.246862i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −641.565 | + | 370.408i | −0.864643 | + | 0.499202i | ||||
\(743\) | −656.294 | − | 1136.73i | −0.883302 | − | 1.52992i | −0.847647 | − | 0.530560i | \(-0.821982\pi\) |
−0.0356548 | − | 0.999364i | \(-0.511352\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.5027 | − | 60.0468i | −0.0503392 | − | 0.0805997i | ||||
\(746\) | 155.992i | 0.209105i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 169.887i | − | 0.227121i | ||||||
\(749\) | −929.621 | − | 536.717i | −1.24115 | − | 0.716578i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −616.216 | − | 1067.32i | −0.820528 | − | 1.42120i | −0.905290 | − | 0.424795i | \(-0.860346\pi\) |
0.0847620 | − | 0.996401i | \(-0.472987\pi\) | |||||||
\(752\) | 80.4020 | + | 139.260i | 0.106918 | + | 0.185187i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 254.184 | − | 440.259i | 0.337114 | − | 0.583898i | ||||
\(755\) | 323.730 | + | 172.223i | 0.428781 | + | 0.228110i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 401.164i | − | 0.529939i | −0.964257 | − | 0.264970i | \(-0.914638\pi\) | ||
0.964257 | − | 0.264970i | \(-0.0853619\pi\) | |||||||
\(758\) | −229.347 | + | 397.240i | −0.302568 | + | 0.524064i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.55177 | + | 102.365i | 0.00467338 | + | 0.134691i | ||||
\(761\) | −454.776 | + | 262.565i | −0.597603 | + | 0.345027i | −0.768098 | − | 0.640332i | \(-0.778797\pi\) |
0.170495 | + | 0.985359i | \(0.445463\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1733.91 | − | 1001.07i | −2.27249 | − | 1.31202i | ||||
\(764\) | 446.047i | 0.583831i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 809.609 | 1.05693 | ||||||||
\(767\) | 354.037 | − | 613.209i | 0.461586 | − | 0.799491i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 271.375 | + | 470.035i | 0.352894 | + | 0.611229i | 0.986755 | − | 0.162217i | \(-0.0518645\pi\) |
−0.633862 | + | 0.773446i | \(0.718531\pi\) | |||||||
\(770\) | 41.3183 | + | 1190.83i | 0.0536601 | + | 1.54653i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −305.228 | − | 176.224i | −0.395373 | − | 0.228269i | ||||
\(773\) | −522.640 | −0.676119 | −0.338059 | − | 0.941125i | \(-0.609770\pi\) | ||||
−0.338059 | + | 0.941125i | \(0.609770\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −533.860 | − | 792.243i | −0.688852 | − | 1.02225i | ||||
\(776\) | 247.995 | + | 143.180i | 0.319581 | + | 0.184510i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −883.857 | + | 510.295i | −1.13606 | + | 0.655906i | ||||
\(779\) | 228.091 | − | 131.688i | 0.292800 | − | 0.169048i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −646.154 | + | 1119.17i | −0.827342 | + | 1.43300i | ||||
\(782\) | 339.546 | 0.434202 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −553.352 | −0.705807 | ||||||||
\(785\) | 185.790 | + | 297.474i | 0.236675 | + | 0.378948i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 717.835 | − | 414.442i | 0.912116 | − | 0.526610i | 0.0310043 | − | 0.999519i | \(-0.490129\pi\) |
0.881111 | + | 0.472909i | \(0.156796\pi\) | |||||||
\(788\) | −277.586 | − | 480.793i | −0.352266 | − | 0.610143i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 264.460 | − | 165.171i | 0.334759 | − | 0.209077i | ||||
\(791\) | − | 744.942i | − | 0.941773i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 256.125i | − | 0.322982i | ||||||
\(794\) | 464.571 | + | 268.220i | 0.585102 | + | 0.337809i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −71.5736 | − | 123.969i | −0.0899166 | − | 0.155740i | ||||
\(797\) | −306.803 | − | 531.398i | −0.384947 | − | 0.666748i | 0.606815 | − | 0.794843i | \(-0.292447\pi\) |
−0.991762 | + | 0.128095i | \(0.959114\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 138.683 | − | 240.207i | 0.173571 | − | 0.300634i | ||||
\(800\) | 79.0294 | + | 117.279i | 0.0987868 | + | 0.146599i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 496.352i | 0.618892i | ||||||||
\(803\) | 13.0030 | − | 22.5218i | 0.0161930 | − | 0.0280471i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2380.06 | + | 82.5814i | −2.95660 | + | 0.102586i | ||||
\(806\) | −796.008 | + | 459.576i | −0.987604 | + | 0.570193i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −37.3049 | − | 21.5380i | −0.0461695 | − | 0.0266559i | ||||
\(809\) | − | 545.471i | − | 0.674254i | −0.941459 | − | 0.337127i | \(-0.890545\pi\) | ||
0.941459 | − | 0.337127i | \(-0.109455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −293.192 | −0.361519 | −0.180759 | − | 0.983527i | \(-0.557856\pi\) | ||||
−0.180759 | + | 0.983527i | \(0.557856\pi\) | |||||||
\(812\) | −289.279 | + | 501.046i | −0.356255 | + | 0.617052i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −187.500 | − | 324.760i | −0.230345 | − | 0.398968i | ||||
\(815\) | −45.2707 | + | 1.57076i | −0.0555469 | + | 0.00192732i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −39.1342 | − | 22.5942i | −0.0478999 | − | 0.0276550i | ||||
\(818\) | −754.379 | −0.922224 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 170.794 | − | 321.044i | 0.208285 | − | 0.391517i | ||||
\(821\) | 739.318 | + | 426.846i | 0.900509 | + | 0.519909i | 0.877365 | − | 0.479823i | \(-0.159299\pi\) |
0.0231439 | + | 0.999732i | \(0.492632\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −175.349 | + | 101.238i | −0.213060 | + | 0.123010i | −0.602733 | − | 0.797943i | \(-0.705921\pi\) |
0.389673 | + | 0.920953i | \(0.372588\pi\) | |||||||
\(824\) | −188.837 | + | 109.025i | −0.229171 | + | 0.132312i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −402.919 | + | 697.876i | −0.487795 | + | 0.844886i | ||||
\(827\) | −15.3734 | −0.0185894 | −0.00929471 | − | 0.999957i | \(-0.502959\pi\) | ||||
−0.00929471 | + | 0.999957i | \(0.502959\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1135.22 | −1.36938 | −0.684692 | − | 0.728833i | \(-0.740063\pi\) | ||||
−0.684692 | + | 0.728833i | \(0.740063\pi\) | |||||||
\(830\) | 330.006 | − | 206.108i | 0.397597 | − | 0.248323i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 117.836 | − | 68.0328i | 0.141630 | − | 0.0817702i | ||||
\(833\) | 477.231 | + | 826.589i | 0.572907 | + | 0.992304i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 270.789 | − | 169.124i | 0.324298 | − | 0.202543i | ||||
\(836\) | 178.336i | 0.213320i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 339.065i | 0.404612i | ||||||||
\(839\) | 215.216 | + | 124.255i | 0.256515 | + | 0.148099i | 0.622744 | − | 0.782426i | \(-0.286018\pi\) |
−0.366229 | + | 0.930525i | \(0.619351\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −197.154 | − | 341.481i | −0.234428 | − | 0.406041i | ||||
\(842\) | −300.479 | − | 520.444i | −0.356863 | − | 0.618105i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −319.492 | + | 553.377i | −0.378546 | + | 0.655660i | ||||
\(845\) | −530.938 | − | 282.457i | −0.628329 | − | 0.334269i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 418.465i | 0.494056i | ||||||||
\(848\) | −76.5442 | + | 132.578i | −0.0902643 | + | 0.156342i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 107.032 | − | 219.199i | 0.125919 | − | 0.257881i | ||||
\(851\) | 649.087 | − | 374.750i | 0.762734 | − | 0.440365i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.4261 | − | 10.0609i | −0.0204291 | − | 0.0117948i | 0.489751 | − | 0.871863i | \(-0.337088\pi\) |
−0.510180 | + | 0.860068i | \(0.670421\pi\) | |||||||
\(854\) | 291.488i | 0.341321i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −221.823 | −0.259139 | ||||||||
\(857\) | −92.7837 | + | 160.706i | −0.108266 | + | 0.187522i | −0.915068 | − | 0.403300i | \(-0.867863\pi\) |
0.806802 | + | 0.590822i | \(0.201196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 549.239 | + | 951.309i | 0.639393 | + | 1.10746i | 0.985566 | + | 0.169291i | \(0.0541476\pi\) |
−0.346173 | + | 0.938171i | \(0.612519\pi\) | |||||||
\(860\) | −62.3545 | + | 2.16352i | −0.0725053 | + | 0.00251573i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −666.308 | − | 384.693i | −0.772980 | − | 0.446280i | ||||
\(863\) | 32.5736 | 0.0377446 | 0.0188723 | − | 0.999822i | \(-0.493992\pi\) | ||||
0.0188723 | + | 0.999822i | \(0.493992\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 123.544 | + | 65.7250i | 0.142826 | + | 0.0759827i | ||||
\(866\) | 738.197 | + | 426.198i | 0.852421 | + | 0.492146i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 905.914 | − | 523.030i | 1.04368 | − | 0.602569i | ||||
\(869\) | 470.150 | − | 271.441i | 0.541024 | − | 0.312360i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1093.78 | − | 1894.48i | 1.25577 | − | 2.17506i | ||||
\(872\) | −413.740 | −0.474473 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −356.434 | −0.407819 | ||||||||
\(875\) | −696.930 | + | 1562.51i | −0.796492 | + | 1.78573i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 867.139 | − | 500.643i | 0.988756 | − | 0.570859i | 0.0838540 | − | 0.996478i | \(-0.473277\pi\) |
0.904902 | + | 0.425619i | \(0.139944\pi\) | |||||||
\(878\) | −284.459 | − | 492.698i | −0.323986 | − | 0.561160i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 130.436 | + | 208.844i | 0.148222 | + | 0.237323i | ||||
\(881\) | 1664.18i | 1.88897i | 0.328559 | + | 0.944483i | \(0.393437\pi\) | ||||
−0.328559 | + | 0.944483i | \(0.606563\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 221.400i | 0.250736i | 0.992110 | + | 0.125368i | \(0.0400112\pi\) | ||||
−0.992110 | + | 0.125368i | \(0.959989\pi\) | |||||||
\(884\) | −203.253 | − | 117.348i | −0.229924 | − | 0.132747i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −310.077 | − | 537.069i | −0.349974 | − | 0.606172i | ||||
\(887\) | −829.771 | − | 1437.21i | −0.935481 | − | 1.62030i | −0.773775 | − | 0.633461i | \(-0.781634\pi\) |
−0.161706 | − | 0.986839i | \(-0.551700\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1089.60 | − | 1887.25i | 1.22565 | − | 2.12289i | ||||
\(890\) | 226.171 | − | 425.136i | 0.254124 | − | 0.477681i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 324.877i | − | 0.364212i | ||||||
\(893\) | −145.581 | + | 252.153i | −0.163024 | + | 0.282366i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −105.266 | + | 3.65245i | −0.117616 | + | 0.00408095i | ||||
\(896\) | −134.106 | + | 77.4262i | −0.149672 | + | 0.0864132i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 821.640 | + | 474.374i | 0.914966 | + | 0.528256i | ||||
\(899\) | − | 807.640i | − | 0.898376i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 264.058 | 0.293072 | ||||||||
\(902\) | 316.576 | − | 548.325i | 0.350971 | − | 0.607899i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −76.9706 | − | 133.317i | −0.0851444 | − | 0.147474i | ||||
\(905\) | −9.29377 | − | 267.854i | −0.0102694 | − | 0.295971i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −145.920 | − | 84.2471i | −0.160882 | − | 0.0928854i | 0.417397 | − | 0.908724i | \(-0.362942\pi\) |
−0.578280 | + | 0.815839i | \(0.696276\pi\) | |||||||
\(908\) | 482.195 | 0.531052 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1453.25 | + | 773.123i | 1.59698 | + | 0.849585i | ||||
\(911\) | −1252.73 | − | 723.264i | −1.37511 | − | 0.793923i | −0.383548 | − | 0.923521i | \(-0.625298\pi\) |
−0.991567 | + | 0.129598i | \(0.958631\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 586.675 | − | 338.717i | 0.642579 | − | 0.370993i | ||||
\(914\) | 851.233 | − | 491.460i | 0.931327 | − | 0.537702i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −102.220 | + | 177.051i | −0.111594 | + | 0.193287i | ||||
\(917\) | 1509.73 | 1.64638 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1279.60 | −1.39239 | −0.696193 | − | 0.717855i | \(-0.745124\pi\) | ||||
−0.696193 | + | 0.717855i | \(0.745124\pi\) | |||||||
\(920\) | −417.410 | + | 260.697i | −0.453706 | + | 0.283366i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.0303 | + | 9.25512i | −0.0173865 | + | 0.0100381i | ||||
\(923\) | 892.654 | + | 1546.12i | 0.967122 | + | 1.67510i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −37.3204 | − | 537.155i | −0.0403464 | − | 0.580708i | ||||
\(926\) | 331.324i | 0.357801i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 119.558i | 0.128834i | ||||||||
\(929\) | 851.532 | + | 491.632i | 0.916612 | + | 0.529206i | 0.882553 | − | 0.470214i | \(-0.155823\pi\) |
0.0340592 | + | 0.999420i | \(0.489157\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −500.967 | − | 867.700i | −0.538095 | − | 0.932008i | ||||
\(932\) | −241.966 | − | 419.097i | −0.259620 | − | 0.449674i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 525.297 | − | 909.841i | 0.562417 | − | 0.974134i | ||||
\(935\) | 199.476 | − | 374.958i | 0.213343 | − | 0.401024i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 964.938i | 1.02982i | 0.857245 | + | 0.514908i | \(0.172174\pi\) | ||||
−0.857245 | + | 0.514908i | \(0.827826\pi\) | |||||||
\(938\) | −1244.80 | + | 2156.05i | −1.32708 | + | 2.29856i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.9402 | + | 401.768i | 0.0148300 | + | 0.427413i | ||||
\(941\) | −891.907 | + | 514.943i | −0.947829 | + | 0.547230i | −0.892406 | − | 0.451233i | \(-0.850984\pi\) |
−0.0554234 | + | 0.998463i | \(0.517651\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1095.92 | + | 632.729i | 1.16216 | + | 0.670974i | ||||
\(944\) | 166.525i | 0.176404i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −108.632 | −0.114833 | ||||||||
\(947\) | −93.4340 | + | 161.832i | −0.0986631 | + | 0.170890i | −0.911132 | − | 0.412116i | \(-0.864790\pi\) |
0.812468 | + | 0.583005i | \(0.198123\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.9634 | − | 31.1136i | −0.0189288 | − | 0.0327856i | ||||
\(950\) | −112.355 | + | 230.100i | −0.118268 | + | 0.242211i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 231.316 | + | 133.550i | 0.242979 | + | 0.140284i | ||||
\(953\) | 857.170 | 0.899444 | 0.449722 | − | 0.893169i | \(-0.351523\pi\) | ||||
0.449722 | + | 0.893169i | \(0.351523\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −523.736 | + | 984.474i | −0.548415 | + | 1.03086i | ||||
\(956\) | 650.313 | + | 375.458i | 0.680244 | + | 0.392739i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −547.964 | + | 316.367i | −0.571988 | + | 0.330237i | ||||
\(959\) | −2583.08 | + | 1491.34i | −2.69352 | + | 1.55510i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −249.624 | + | 432.362i | −0.259755 | + | 0.449909i | ||||
\(962\) | −518.059 | −0.538523 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −636.558 | −0.660330 | ||||||||
\(965\) | −466.754 | − | 747.334i | −0.483683 | − | 0.774440i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1068.71 | + | 617.021i | −1.10518 | + | 0.638077i | −0.937577 | − | 0.347777i | \(-0.886937\pi\) |
−0.167605 | + | 0.985854i | \(0.553603\pi\) | |||||||
\(968\) | 43.2376 | + | 74.8897i | 0.0446669 | + | 0.0773654i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 379.233 | + | 607.202i | 0.390962 | + | 0.625981i | ||||
\(971\) | 1313.38i | 1.35261i | 0.736624 | + | 0.676303i | \(0.236419\pi\) | ||||
−0.736624 | + | 0.676303i | \(0.763581\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1454.26i | 1.49461i | ||||||||
\(974\) | 61.6250 | + | 35.5792i | 0.0632700 | + | 0.0365289i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.1177 | + | 52.1655i | 0.0308583 | + | 0.0534482i | ||||
\(977\) | 54.7431 | + | 94.8178i | 0.0560318 | + | 0.0970499i | 0.892681 | − | 0.450690i | \(-0.148822\pi\) |
−0.836649 | + | 0.547739i | \(0.815489\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 419.219 | − | 726.109i | 0.428212 | − | 0.741685i | ||||
\(980\) | −1221.31 | − | 649.731i | −1.24623 | − | 0.662991i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 1118.12i | − | 1.13862i | ||||||
\(983\) | −170.997 | + | 296.176i | −0.173955 | + | 0.301298i | −0.939799 | − | 0.341728i | \(-0.888988\pi\) |
0.765844 | + | 0.643026i | \(0.222321\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −48.1282 | − | 1387.09i | −0.0488611 | − | 1.40822i | ||||
\(986\) | 178.594 | − | 103.111i | 0.181130 | − | 0.104575i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 213.362 | + | 123.184i | 0.215953 | + | 0.124681i | ||||
\(989\) | − | 217.118i | − | 0.219533i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 140.258 | 0.141532 | 0.0707658 | − | 0.997493i | \(-0.477456\pi\) | ||||
0.0707658 | + | 0.997493i | \(0.477456\pi\) | |||||||
\(992\) | 108.083 | − | 187.206i | 0.108955 | − | 0.188715i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1015.90 | − | 1759.60i | −1.02204 | − | 1.77022i | ||||
\(995\) | −12.4095 | − | 357.653i | −0.0124719 | − | 0.359450i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −536.619 | − | 309.817i | −0.538233 | − | 0.310749i | 0.206129 | − | 0.978525i | \(-0.433913\pi\) |
−0.744363 | + | 0.667776i | \(0.767247\pi\) | |||||||
\(998\) | −849.079 | −0.850781 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 810.3.j.a.269.2 | 8 | ||
3.2 | odd | 2 | 810.3.j.f.269.3 | 8 | |||
5.4 | even | 2 | 810.3.j.f.269.4 | 8 | |||
9.2 | odd | 6 | 270.3.b.a.269.1 | ✓ | 4 | ||
9.4 | even | 3 | inner | 810.3.j.a.539.1 | 8 | ||
9.5 | odd | 6 | 810.3.j.f.539.4 | 8 | |||
9.7 | even | 3 | 270.3.b.d.269.4 | yes | 4 | ||
15.14 | odd | 2 | inner | 810.3.j.a.269.1 | 8 | ||
36.7 | odd | 6 | 2160.3.c.m.1889.4 | 4 | |||
36.11 | even | 6 | 2160.3.c.g.1889.1 | 4 | |||
45.2 | even | 12 | 1350.3.d.o.701.4 | 8 | |||
45.4 | even | 6 | 810.3.j.f.539.3 | 8 | |||
45.7 | odd | 12 | 1350.3.d.o.701.8 | 8 | |||
45.14 | odd | 6 | inner | 810.3.j.a.539.2 | 8 | ||
45.29 | odd | 6 | 270.3.b.d.269.3 | yes | 4 | ||
45.34 | even | 6 | 270.3.b.a.269.2 | yes | 4 | ||
45.38 | even | 12 | 1350.3.d.o.701.5 | 8 | |||
45.43 | odd | 12 | 1350.3.d.o.701.1 | 8 | |||
180.79 | odd | 6 | 2160.3.c.g.1889.2 | 4 | |||
180.119 | even | 6 | 2160.3.c.m.1889.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.3.b.a.269.1 | ✓ | 4 | 9.2 | odd | 6 | ||
270.3.b.a.269.2 | yes | 4 | 45.34 | even | 6 | ||
270.3.b.d.269.3 | yes | 4 | 45.29 | odd | 6 | ||
270.3.b.d.269.4 | yes | 4 | 9.7 | even | 3 | ||
810.3.j.a.269.1 | 8 | 15.14 | odd | 2 | inner | ||
810.3.j.a.269.2 | 8 | 1.1 | even | 1 | trivial | ||
810.3.j.a.539.1 | 8 | 9.4 | even | 3 | inner | ||
810.3.j.a.539.2 | 8 | 45.14 | odd | 6 | inner | ||
810.3.j.f.269.3 | 8 | 3.2 | odd | 2 | |||
810.3.j.f.269.4 | 8 | 5.4 | even | 2 | |||
810.3.j.f.539.3 | 8 | 45.4 | even | 6 | |||
810.3.j.f.539.4 | 8 | 9.5 | odd | 6 | |||
1350.3.d.o.701.1 | 8 | 45.43 | odd | 12 | |||
1350.3.d.o.701.4 | 8 | 45.2 | even | 12 | |||
1350.3.d.o.701.5 | 8 | 45.38 | even | 12 | |||
1350.3.d.o.701.8 | 8 | 45.7 | odd | 12 | |||
2160.3.c.g.1889.1 | 4 | 36.11 | even | 6 | |||
2160.3.c.g.1889.2 | 4 | 180.79 | odd | 6 | |||
2160.3.c.m.1889.3 | 4 | 180.119 | even | 6 | |||
2160.3.c.m.1889.4 | 4 | 36.7 | odd | 6 |