Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(26,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.26");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.s (of order \(6\), degree \(2\), 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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 26.14 | ||
Character | \(\chi\) | \(=\) | 105.26 |
Dual form | 105.4.s.b.101.14 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.31734 | + | 1.91526i | 1.17286 | + | 0.677148i | 0.954351 | − | 0.298688i | \(-0.0965489\pi\) |
0.218504 | + | 0.975836i | \(0.429882\pi\) | |||||||
\(3\) | −0.144315 | − | 5.19415i | −0.0277734 | − | 0.999614i | ||||
\(4\) | 3.33648 | + | 5.77895i | 0.417060 | + | 0.722368i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 9.46943 | − | 17.5071i | 0.644313 | − | 1.19121i | ||||
\(7\) | 8.94735 | − | 16.2156i | 0.483112 | − | 0.875559i | ||||
\(8\) | − | 5.08329i | − | 0.224652i | ||||||
\(9\) | −26.9583 | + | 1.49918i | −0.998457 | + | 0.0555253i | ||||
\(10\) | 16.5867 | − | 9.57632i | 0.524517 | − | 0.302830i | ||||
\(11\) | 12.9526 | − | 7.47816i | 0.355031 | − | 0.204977i | −0.311868 | − | 0.950126i | \(-0.600955\pi\) |
0.666899 | + | 0.745148i | \(0.267621\pi\) | |||||||
\(12\) | 29.5352 | − | 18.1641i | 0.710507 | − | 0.436961i | ||||
\(13\) | 63.8636i | 1.36251i | 0.732048 | + | 0.681253i | \(0.238564\pi\) | ||||
−0.732048 | + | 0.681253i | \(0.761436\pi\) | |||||||
\(14\) | 60.7385 | − | 36.6560i | 1.15950 | − | 0.699765i | ||||
\(15\) | −22.8521 | − | 12.3605i | −0.393359 | − | 0.212764i | ||||
\(16\) | 36.4277 | − | 63.0946i | 0.569182 | − | 0.985852i | ||||
\(17\) | 11.0025 | + | 19.0569i | 0.156970 | + | 0.271881i | 0.933775 | − | 0.357861i | \(-0.116494\pi\) |
−0.776804 | + | 0.629742i | \(0.783161\pi\) | |||||||
\(18\) | −92.3012 | − | 46.6591i | −1.20864 | − | 0.610980i | ||||
\(19\) | 137.229 | + | 79.2293i | 1.65697 | + | 0.956655i | 0.974099 | + | 0.226120i | \(0.0726041\pi\) |
0.682875 | + | 0.730535i | \(0.260729\pi\) | |||||||
\(20\) | 33.3648 | 0.373029 | ||||||||
\(21\) | −85.5173 | − | 44.1337i | −0.888639 | − | 0.458608i | ||||
\(22\) | 57.2906 | 0.555200 | ||||||||
\(23\) | −162.564 | − | 93.8566i | −1.47378 | − | 0.850889i | −0.474219 | − | 0.880407i | \(-0.657270\pi\) |
−0.999564 | + | 0.0295172i | \(0.990603\pi\) | |||||||
\(24\) | −26.4033 | + | 0.733593i | −0.224565 | + | 0.00623934i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | −122.316 | + | 211.857i | −0.922618 | + | 1.59802i | ||||
\(27\) | 11.6775 | + | 139.809i | 0.0832344 | + | 0.996530i | ||||
\(28\) | 123.562 | − | 2.39660i | 0.833962 | − | 0.0161755i | ||||
\(29\) | 179.589i | 1.14996i | 0.818167 | + | 0.574980i | \(0.194990\pi\) | ||||
−0.818167 | + | 0.574980i | \(0.805010\pi\) | |||||||
\(30\) | −52.1345 | − | 84.7717i | −0.317281 | − | 0.515904i | ||||
\(31\) | 64.0984 | − | 37.0072i | 0.371368 | − | 0.214410i | −0.302688 | − | 0.953090i | \(-0.597884\pi\) |
0.674056 | + | 0.738680i | \(0.264551\pi\) | |||||||
\(32\) | 206.467 | − | 119.204i | 1.14058 | − | 0.658516i | ||||
\(33\) | −40.7119 | − | 66.1983i | −0.214759 | − | 0.349201i | ||||
\(34\) | 84.2908i | 0.425169i | ||||||||
\(35\) | −47.8471 | − | 79.2821i | −0.231075 | − | 0.382889i | ||||
\(36\) | −98.6096 | − | 150.789i | −0.456526 | − | 0.698097i | ||||
\(37\) | −182.983 | + | 316.935i | −0.813031 | + | 1.40821i | 0.0977017 | + | 0.995216i | \(0.468851\pi\) |
−0.910733 | + | 0.412996i | \(0.864482\pi\) | |||||||
\(38\) | 303.490 | + | 525.660i | 1.29559 | + | 2.24404i | ||||
\(39\) | 331.717 | − | 9.21645i | 1.36198 | − | 0.0378414i | ||||
\(40\) | −22.0113 | − | 12.7082i | −0.0870072 | − | 0.0502336i | ||||
\(41\) | −168.976 | −0.643650 | −0.321825 | − | 0.946799i | \(-0.604296\pi\) | ||||
−0.321825 | + | 0.946799i | \(0.604296\pi\) | |||||||
\(42\) | −199.162 | − | 310.195i | −0.731699 | − | 1.13962i | ||||
\(43\) | −60.4265 | −0.214301 | −0.107151 | − | 0.994243i | \(-0.534173\pi\) | ||||
−0.107151 | + | 0.994243i | \(0.534173\pi\) | |||||||
\(44\) | 86.4318 | + | 49.9014i | 0.296138 | + | 0.170976i | ||||
\(45\) | −60.9042 | + | 120.481i | −0.201757 | + | 0.399117i | ||||
\(46\) | −359.521 | − | 622.708i | −1.15236 | − | 1.99594i | ||||
\(47\) | 5.05040 | − | 8.74755i | 0.0156740 | − | 0.0271481i | −0.858082 | − | 0.513513i | \(-0.828344\pi\) |
0.873756 | + | 0.486365i | \(0.161677\pi\) | |||||||
\(48\) | −332.979 | − | 180.105i | −1.00128 | − | 0.541582i | ||||
\(49\) | −182.890 | − | 290.173i | −0.533206 | − | 0.845985i | ||||
\(50\) | − | 95.7632i | − | 0.270859i | ||||||
\(51\) | 97.3965 | − | 59.8988i | 0.267416 | − | 0.164461i | ||||
\(52\) | −369.064 | + | 213.079i | −0.984231 | + | 0.568246i | ||||
\(53\) | 467.597 | − | 269.967i | 1.21188 | − | 0.699676i | 0.248708 | − | 0.968579i | \(-0.419994\pi\) |
0.963168 | + | 0.268902i | \(0.0866608\pi\) | |||||||
\(54\) | −229.034 | + | 486.160i | −0.577177 | + | 1.22515i | ||||
\(55\) | − | 74.7816i | − | 0.183337i | ||||||
\(56\) | −82.4284 | − | 45.4820i | −0.196696 | − | 0.108532i | ||||
\(57\) | 391.724 | − | 724.222i | 0.910266 | − | 1.68291i | ||||
\(58\) | −343.961 | + | 595.757i | −0.778694 | + | 1.34874i | ||||
\(59\) | 165.592 | + | 286.813i | 0.365393 | + | 0.632879i | 0.988839 | − | 0.148987i | \(-0.0476013\pi\) |
−0.623446 | + | 0.781866i | \(0.714268\pi\) | |||||||
\(60\) | −4.81503 | − | 173.302i | −0.0103603 | − | 0.372886i | ||||
\(61\) | −15.5603 | − | 8.98375i | −0.0326606 | − | 0.0188566i | 0.483581 | − | 0.875300i | \(-0.339336\pi\) |
−0.516241 | + | 0.856443i | \(0.672669\pi\) | |||||||
\(62\) | 283.515 | 0.580748 | ||||||||
\(63\) | −216.896 | + | 450.559i | −0.433751 | + | 0.901033i | ||||
\(64\) | 330.387 | 0.645287 | ||||||||
\(65\) | 276.537 | + | 159.659i | 0.527696 | + | 0.304665i | ||||
\(66\) | −8.26788 | − | 297.576i | −0.0154198 | − | 0.554986i | ||||
\(67\) | −111.665 | − | 193.410i | −0.203613 | − | 0.352668i | 0.746077 | − | 0.665860i | \(-0.231935\pi\) |
−0.949690 | + | 0.313192i | \(0.898602\pi\) | |||||||
\(68\) | −73.4192 | + | 127.166i | −0.130932 | + | 0.226781i | ||||
\(69\) | −464.045 | + | 857.929i | −0.809629 | + | 1.49685i | ||||
\(70\) | −6.87870 | − | 354.645i | −0.0117452 | − | 0.605546i | ||||
\(71\) | 563.097i | 0.941230i | 0.882339 | + | 0.470615i | \(0.155968\pi\) | ||||
−0.882339 | + | 0.470615i | \(0.844032\pi\) | |||||||
\(72\) | 7.62078 | + | 137.037i | 0.0124739 | + | 0.224305i | ||||
\(73\) | 525.173 | − | 303.209i | 0.842012 | − | 0.486136i | −0.0159358 | − | 0.999873i | \(-0.505073\pi\) |
0.857948 | + | 0.513737i | \(0.171739\pi\) | |||||||
\(74\) | −1214.03 | + | 700.920i | −1.90714 | + | 1.10109i | ||||
\(75\) | −110.653 | + | 68.0514i | −0.170361 | + | 0.104772i | ||||
\(76\) | 1057.39i | 1.59593i | ||||||||
\(77\) | −5.37159 | − | 276.943i | −0.00794999 | − | 0.409878i | ||||
\(78\) | 1118.07 | + | 604.751i | 1.62303 | + | 0.877880i | ||||
\(79\) | 88.0028 | − | 152.425i | 0.125330 | − | 0.217078i | −0.796532 | − | 0.604597i | \(-0.793334\pi\) |
0.921862 | + | 0.387518i | \(0.126668\pi\) | |||||||
\(80\) | −182.138 | − | 315.473i | −0.254546 | − | 0.440887i | ||||
\(81\) | 724.505 | − | 80.8310i | 0.993834 | − | 0.110879i | ||||
\(82\) | −560.551 | − | 323.634i | −0.754908 | − | 0.435847i | ||||
\(83\) | 635.008 | 0.839773 | 0.419887 | − | 0.907577i | \(-0.362070\pi\) | ||||
0.419887 | + | 0.907577i | \(0.362070\pi\) | |||||||
\(84\) | −30.2801 | − | 641.451i | −0.0393312 | − | 0.833191i | ||||
\(85\) | 110.025 | 0.140399 | ||||||||
\(86\) | −200.455 | − | 115.733i | −0.251344 | − | 0.145114i | ||||
\(87\) | 932.812 | − | 25.9173i | 1.14952 | − | 0.0319383i | ||||
\(88\) | −38.0136 | − | 65.8416i | −0.0460485 | − | 0.0797583i | ||||
\(89\) | −388.869 | + | 673.540i | −0.463146 | + | 0.802193i | −0.999116 | − | 0.0420446i | \(-0.986613\pi\) |
0.535970 | + | 0.844237i | \(0.319946\pi\) | |||||||
\(90\) | −432.793 | + | 283.028i | −0.506893 | + | 0.331487i | ||||
\(91\) | 1035.58 | + | 571.410i | 1.19295 | + | 0.658242i | ||||
\(92\) | − | 1252.60i | − | 1.41949i | ||||||
\(93\) | −201.471 | − | 327.596i | −0.224641 | − | 0.365270i | ||||
\(94\) | 33.5077 | − | 19.3457i | 0.0367666 | − | 0.0212272i | ||||
\(95\) | 686.146 | − | 396.146i | 0.741022 | − | 0.427829i | ||||
\(96\) | −648.960 | − | 1055.22i | −0.689939 | − | 1.12185i | ||||
\(97\) | − | 1032.16i | − | 1.08041i | −0.841533 | − | 0.540206i | \(-0.818346\pi\) | ||
0.841533 | − | 0.540206i | \(-0.181654\pi\) | |||||||
\(98\) | −50.9485 | − | 1312.88i | −0.0525161 | − | 1.35328i | ||||
\(99\) | −337.968 | + | 221.017i | −0.343102 | + | 0.224374i | ||||
\(100\) | 83.4119 | − | 144.474i | 0.0834119 | − | 0.144474i | ||||
\(101\) | −16.5291 | − | 28.6292i | −0.0162842 | − | 0.0282050i | 0.857768 | − | 0.514036i | \(-0.171850\pi\) |
−0.874053 | + | 0.485831i | \(0.838517\pi\) | |||||||
\(102\) | 437.819 | − | 12.1644i | 0.425005 | − | 0.0118084i | ||||
\(103\) | −814.812 | − | 470.432i | −0.779474 | − | 0.450030i | 0.0567697 | − | 0.998387i | \(-0.481920\pi\) |
−0.836244 | + | 0.548358i | \(0.815253\pi\) | |||||||
\(104\) | 324.637 | 0.306089 | ||||||||
\(105\) | −404.898 | + | 259.967i | −0.376324 | + | 0.241620i | ||||
\(106\) | 2068.23 | 1.89514 | ||||||||
\(107\) | −374.880 | − | 216.437i | −0.338701 | − | 0.195549i | 0.320997 | − | 0.947080i | \(-0.395982\pi\) |
−0.659697 | + | 0.751531i | \(0.729316\pi\) | |||||||
\(108\) | −768.989 | + | 533.954i | −0.685148 | + | 0.475738i | ||||
\(109\) | −389.652 | − | 674.896i | −0.342402 | − | 0.593058i | 0.642476 | − | 0.766306i | \(-0.277907\pi\) |
−0.984878 | + | 0.173248i | \(0.944574\pi\) | |||||||
\(110\) | 143.227 | − | 248.076i | 0.124147 | − | 0.215028i | ||||
\(111\) | 1672.62 | + | 904.700i | 1.43025 | + | 0.773607i | ||||
\(112\) | −697.183 | − | 1155.22i | −0.588193 | − | 0.974629i | ||||
\(113\) | − | 489.634i | − | 0.407619i | −0.979011 | − | 0.203809i | \(-0.934668\pi\) | ||
0.979011 | − | 0.203809i | \(-0.0653323\pi\) | |||||||
\(114\) | 2686.56 | − | 1652.23i | 2.20719 | − | 1.35742i | ||||
\(115\) | −812.822 | + | 469.283i | −0.659096 | + | 0.380529i | ||||
\(116\) | −1037.84 | + | 599.195i | −0.830695 | + | 0.479602i | ||||
\(117\) | −95.7432 | − | 1721.66i | −0.0756535 | − | 1.36040i | ||||
\(118\) | 1268.61i | 0.989701i | ||||||||
\(119\) | 407.462 | − | 7.90313i | 0.313882 | − | 0.00608805i | ||||
\(120\) | −62.8318 | + | 116.164i | −0.0477978 | + | 0.0883688i | ||||
\(121\) | −553.654 | + | 958.957i | −0.415969 | + | 0.720479i | ||||
\(122\) | −34.4125 | − | 59.6042i | −0.0255374 | − | 0.0442321i | ||||
\(123\) | 24.3858 | + | 877.688i | 0.0178763 | + | 0.643402i | ||||
\(124\) | 427.726 | + | 246.948i | 0.309765 | + | 0.178843i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −1582.46 | + | 1079.24i | −1.11886 | + | 0.763068i | ||||
\(127\) | 435.222 | 0.304092 | 0.152046 | − | 0.988373i | \(-0.451414\pi\) | ||||
0.152046 | + | 0.988373i | \(0.451414\pi\) | |||||||
\(128\) | −555.736 | − | 320.854i | −0.383755 | − | 0.221561i | ||||
\(129\) | 8.72043 | + | 313.864i | 0.00595187 | + | 0.214219i | ||||
\(130\) | 611.578 | + | 1059.28i | 0.412607 | + | 0.714657i | ||||
\(131\) | −16.9758 | + | 29.4029i | −0.0113220 | + | 0.0196103i | −0.871631 | − | 0.490163i | \(-0.836937\pi\) |
0.860309 | + | 0.509773i | \(0.170271\pi\) | |||||||
\(132\) | 246.722 | − | 456.141i | 0.162685 | − | 0.300773i | ||||
\(133\) | 2512.59 | − | 1516.36i | 1.63811 | − | 0.988608i | ||||
\(134\) | − | 855.474i | − | 0.551505i | ||||||
\(135\) | 634.586 | + | 298.958i | 0.404566 | + | 0.190594i | ||||
\(136\) | 96.8716 | − | 55.9289i | 0.0610785 | − | 0.0352637i | ||||
\(137\) | −2721.27 | + | 1571.13i | −1.69704 | + | 0.979784i | −0.748488 | + | 0.663149i | \(0.769220\pi\) |
−0.948547 | + | 0.316635i | \(0.897447\pi\) | |||||||
\(138\) | −3182.55 | + | 1957.27i | −1.96317 | + | 1.20735i | ||||
\(139\) | 2399.79i | 1.46437i | 0.681106 | + | 0.732185i | \(0.261499\pi\) | ||||
−0.681106 | + | 0.732185i | \(0.738501\pi\) | |||||||
\(140\) | 298.526 | − | 541.029i | 0.180215 | − | 0.326609i | ||||
\(141\) | −46.1649 | − | 24.9701i | −0.0275730 | − | 0.0149139i | ||||
\(142\) | −1078.48 | + | 1867.98i | −0.637352 | + | 1.10393i | ||||
\(143\) | 477.582 | + | 827.196i | 0.279283 | + | 0.483732i | ||||
\(144\) | −887.439 | + | 1755.54i | −0.513564 | + | 1.01594i | ||||
\(145\) | 777.643 | + | 448.973i | 0.445378 | + | 0.257139i | ||||
\(146\) | 2322.90 | 1.31674 | ||||||||
\(147\) | −1480.81 | + | 991.832i | −0.830850 | + | 0.556496i | ||||
\(148\) | −2442.07 | −1.35633 | ||||||||
\(149\) | −687.647 | − | 397.013i | −0.378082 | − | 0.218286i | 0.298901 | − | 0.954284i | \(-0.403380\pi\) |
−0.676984 | + | 0.735998i | \(0.736713\pi\) | |||||||
\(150\) | −497.408 | + | 13.8200i | −0.270755 | + | 0.00752268i | ||||
\(151\) | −288.851 | − | 500.304i | −0.155671 | − | 0.269630i | 0.777632 | − | 0.628720i | \(-0.216421\pi\) |
−0.933303 | + | 0.359089i | \(0.883087\pi\) | |||||||
\(152\) | 402.745 | − | 697.575i | 0.214914 | − | 0.372242i | ||||
\(153\) | −325.179 | − | 497.247i | −0.171825 | − | 0.262746i | ||||
\(154\) | 512.600 | − | 929.000i | 0.268224 | − | 0.486110i | ||||
\(155\) | − | 370.072i | − | 0.191774i | ||||||
\(156\) | 1160.03 | + | 1886.22i | 0.595362 | + | 0.968069i | ||||
\(157\) | −1228.62 | + | 709.343i | −0.624550 | + | 0.360584i | −0.778638 | − | 0.627473i | \(-0.784089\pi\) |
0.154088 | + | 0.988057i | \(0.450756\pi\) | |||||||
\(158\) | 583.870 | − | 337.097i | 0.293989 | − | 0.169734i | ||||
\(159\) | −1469.73 | − | 2389.81i | −0.733064 | − | 1.19198i | ||||
\(160\) | − | 1192.04i | − | 0.588994i | ||||||
\(161\) | −2976.46 | + | 1796.31i | −1.45701 | + | 0.879310i | ||||
\(162\) | 2558.24 | + | 1119.47i | 1.24071 | + | 0.542928i | ||||
\(163\) | 1060.60 | − | 1837.02i | 0.509649 | − | 0.882737i | −0.490289 | − | 0.871560i | \(-0.663109\pi\) |
0.999938 | − | 0.0111775i | \(-0.00355797\pi\) | |||||||
\(164\) | −563.785 | − | 976.505i | −0.268440 | − | 0.464953i | ||||
\(165\) | −388.427 | + | 10.7921i | −0.183267 | + | 0.00509190i | ||||
\(166\) | 2106.53 | + | 1216.21i | 0.984932 | + | 0.568651i | ||||
\(167\) | −2298.28 | −1.06495 | −0.532473 | − | 0.846447i | \(-0.678737\pi\) | ||||
−0.532473 | + | 0.846447i | \(0.678737\pi\) | |||||||
\(168\) | −224.344 | + | 434.709i | −0.103027 | + | 0.199634i | ||||
\(169\) | −1881.56 | −0.856421 | ||||||||
\(170\) | 364.990 | + | 210.727i | 0.164667 | + | 0.0950707i | ||||
\(171\) | −3818.25 | − | 1930.16i | −1.70754 | − | 0.863175i | ||||
\(172\) | −201.612 | − | 349.202i | −0.0893764 | − | 0.154804i | ||||
\(173\) | 602.351 | − | 1043.30i | 0.264716 | − | 0.458502i | −0.702773 | − | 0.711414i | \(-0.748055\pi\) |
0.967489 | + | 0.252912i | \(0.0813884\pi\) | |||||||
\(174\) | 3144.09 | + | 1700.61i | 1.36984 | + | 0.740934i | ||||
\(175\) | −462.919 | + | 8.97879i | −0.199962 | + | 0.00387847i | ||||
\(176\) | − | 1089.65i | − | 0.466678i | ||||||
\(177\) | 1465.85 | − | 901.498i | 0.622487 | − | 0.382829i | ||||
\(178\) | −2580.02 | + | 1489.57i | −1.08641 | + | 0.627237i | ||||
\(179\) | −956.963 | + | 552.503i | −0.399591 | + | 0.230704i | −0.686308 | − | 0.727311i | \(-0.740770\pi\) |
0.286716 | + | 0.958015i | \(0.407436\pi\) | |||||||
\(180\) | −899.459 | + | 50.0199i | −0.372454 | + | 0.0207126i | ||||
\(181\) | − | 2923.49i | − | 1.20056i | −0.799789 | − | 0.600281i | \(-0.795056\pi\) | ||
0.799789 | − | 0.600281i | \(-0.204944\pi\) | |||||||
\(182\) | 2340.98 | + | 3878.98i | 0.953434 | + | 1.57983i | ||||
\(183\) | −44.4173 | + | 82.1191i | −0.0179422 | + | 0.0331717i | ||||
\(184\) | −477.100 | + | 826.362i | −0.191154 | + | 0.331088i | ||||
\(185\) | 914.913 | + | 1584.68i | 0.363599 | + | 0.629771i | ||||
\(186\) | −40.9153 | − | 1472.62i | −0.0161293 | − | 0.580524i | ||||
\(187\) | 285.021 | + | 164.557i | 0.111459 | + | 0.0643508i | ||||
\(188\) | 67.4022 | 0.0261479 | ||||||||
\(189\) | 2371.57 | + | 1061.57i | 0.912732 | + | 0.408559i | ||||
\(190\) | 3034.90 | 1.15881 | ||||||||
\(191\) | −832.436 | − | 480.607i | −0.315356 | − | 0.182071i | 0.333965 | − | 0.942586i | \(-0.391613\pi\) |
−0.649321 | + | 0.760515i | \(0.724947\pi\) | |||||||
\(192\) | −47.6797 | − | 1716.08i | −0.0179218 | − | 0.645038i | ||||
\(193\) | −590.830 | − | 1023.35i | −0.220357 | − | 0.381669i | 0.734560 | − | 0.678544i | \(-0.237389\pi\) |
−0.954916 | + | 0.296875i | \(0.904055\pi\) | |||||||
\(194\) | 1976.86 | − | 3424.02i | 0.731599 | − | 1.26717i | ||||
\(195\) | 789.384 | − | 1459.42i | 0.289892 | − | 0.535954i | ||||
\(196\) | 1066.69 | − | 2025.07i | 0.388734 | − | 0.737998i | ||||
\(197\) | − | 3727.40i | − | 1.34805i | −0.738708 | − | 0.674025i | \(-0.764564\pi\) | ||
0.738708 | − | 0.674025i | \(-0.235436\pi\) | |||||||
\(198\) | −1544.46 | + | 85.8892i | −0.554344 | + | 0.0308277i | ||||
\(199\) | −2229.58 | + | 1287.25i | −0.794225 | + | 0.458546i | −0.841448 | − | 0.540339i | \(-0.818296\pi\) |
0.0472231 | + | 0.998884i | \(0.484963\pi\) | |||||||
\(200\) | −110.056 | + | 63.5411i | −0.0389108 | + | 0.0224652i | ||||
\(201\) | −988.484 | + | 607.917i | −0.346877 | + | 0.213329i | ||||
\(202\) | − | 126.630i | − | 0.0441072i | ||||||
\(203\) | 2912.14 | + | 1606.85i | 1.00686 | + | 0.555559i | ||||
\(204\) | 671.113 | + | 362.998i | 0.230330 | + | 0.124583i | ||||
\(205\) | −422.441 | + | 731.689i | −0.143925 | + | 0.249285i | ||||
\(206\) | −1802.00 | − | 3121.16i | −0.609474 | − | 1.05564i | ||||
\(207\) | 4523.18 | + | 2286.51i | 1.51876 | + | 0.767744i | ||||
\(208\) | 4029.44 | + | 2326.40i | 1.34323 | + | 0.775514i | ||||
\(209\) | 2369.96 | 0.784370 | ||||||||
\(210\) | −1841.09 | + | 86.9095i | −0.604986 | + | 0.0285587i | ||||
\(211\) | −1310.06 | −0.427434 | −0.213717 | − | 0.976896i | \(-0.568557\pi\) | ||||
−0.213717 | + | 0.976896i | \(0.568557\pi\) | |||||||
\(212\) | 3120.25 | + | 1801.48i | 1.01085 | + | 0.583614i | ||||
\(213\) | 2924.81 | − | 81.2631i | 0.940866 | − | 0.0261411i | ||||
\(214\) | −829.068 | − | 1435.99i | −0.264831 | − | 0.458701i | ||||
\(215\) | −151.066 | + | 261.654i | −0.0479192 | + | 0.0829985i | ||||
\(216\) | 710.691 | − | 59.3599i | 0.223872 | − | 0.0186988i | ||||
\(217\) | −26.5824 | − | 1370.51i | −0.00831581 | − | 0.428738i | ||||
\(218\) | − | 2985.14i | − | 0.927429i | ||||||
\(219\) | −1650.70 | − | 2684.07i | −0.509334 | − | 0.828185i | ||||
\(220\) | 432.159 | − | 249.507i | 0.132437 | − | 0.0764626i | ||||
\(221\) | −1217.04 | + | 702.659i | −0.370439 | + | 0.213873i | ||||
\(222\) | 3815.89 | + | 6204.70i | 1.15363 | + | 1.87582i | ||||
\(223\) | − | 1484.59i | − | 0.445809i | −0.974840 | − | 0.222904i | \(-0.928446\pi\) | ||
0.974840 | − | 0.222904i | \(-0.0715538\pi\) | |||||||
\(224\) | −85.6246 | − | 4414.55i | −0.0255403 | − | 1.31678i | ||||
\(225\) | 369.438 | + | 564.926i | 0.109463 | + | 0.167385i | ||||
\(226\) | 937.779 | − | 1624.28i | 0.276018 | − | 0.478078i | ||||
\(227\) | 1387.78 | + | 2403.71i | 0.405773 | + | 0.702819i | 0.994411 | − | 0.105577i | \(-0.0336691\pi\) |
−0.588638 | + | 0.808397i | \(0.700336\pi\) | |||||||
\(228\) | 5492.22 | − | 152.596i | 1.59531 | − | 0.0443243i | ||||
\(229\) | −3258.94 | − | 1881.55i | −0.940422 | − | 0.542953i | −0.0503294 | − | 0.998733i | \(-0.516027\pi\) |
−0.890093 | + | 0.455780i | \(0.849360\pi\) | |||||||
\(230\) | −3595.21 | −1.03070 | ||||||||
\(231\) | −1437.71 | + | 67.8677i | −0.409499 | + | 0.0193306i | ||||
\(232\) | 912.903 | 0.258341 | ||||||||
\(233\) | −3132.07 | − | 1808.30i | −0.880640 | − | 0.508438i | −0.00977035 | − | 0.999952i | \(-0.503110\pi\) |
−0.870869 | + | 0.491515i | \(0.836443\pi\) | |||||||
\(234\) | 2979.82 | − | 5894.69i | 0.832464 | − | 1.64678i | ||||
\(235\) | −25.2520 | − | 43.7378i | −0.00700961 | − | 0.0121410i | ||||
\(236\) | −1104.98 | + | 1913.89i | −0.304781 | + | 0.527897i | ||||
\(237\) | −804.420 | − | 435.103i | −0.220476 | − | 0.119253i | ||||
\(238\) | 1366.82 | + | 754.179i | 0.372261 | + | 0.205404i | ||||
\(239\) | 4715.60i | 1.27626i | 0.769928 | + | 0.638131i | \(0.220292\pi\) | ||||
−0.769928 | + | 0.638131i | \(0.779708\pi\) | |||||||
\(240\) | −1612.33 | + | 991.581i | −0.433647 | + | 0.266693i | ||||
\(241\) | 6330.88 | − | 3655.14i | 1.69215 | − | 0.976963i | 0.739369 | − | 0.673300i | \(-0.235124\pi\) |
0.952780 | − | 0.303662i | \(-0.0982095\pi\) | |||||||
\(242\) | −3673.31 | + | 2120.79i | −0.975742 | + | 0.563345i | ||||
\(243\) | −524.405 | − | 3751.52i | −0.138439 | − | 0.990371i | ||||
\(244\) | − | 119.896i | − | 0.0314573i | ||||||
\(245\) | −1713.71 | + | 66.5033i | −0.446877 | + | 0.0173418i | ||||
\(246\) | −1600.11 | + | 2958.29i | −0.414712 | + | 0.766722i | ||||
\(247\) | −5059.86 | + | 8763.94i | −1.30345 | + | 2.25764i | ||||
\(248\) | −188.118 | − | 325.831i | −0.0481675 | − | 0.0834285i | ||||
\(249\) | −91.6410 | − | 3298.32i | −0.0233233 | − | 0.839449i | ||||
\(250\) | −414.667 | − | 239.408i | −0.104903 | − | 0.0605660i | ||||
\(251\) | −2817.02 | −0.708402 | −0.354201 | − | 0.935169i | \(-0.615247\pi\) | ||||
−0.354201 | + | 0.935169i | \(0.615247\pi\) | |||||||
\(252\) | −3327.42 | + | 249.850i | −0.831778 | + | 0.0624566i | ||||
\(253\) | −2807.50 | −0.697652 | ||||||||
\(254\) | 1443.78 | + | 833.565i | 0.356656 | + | 0.205916i | ||||
\(255\) | −15.8782 | − | 571.486i | −0.00389934 | − | 0.140344i | ||||
\(256\) | −2550.59 | − | 4417.75i | −0.622702 | − | 1.07855i | ||||
\(257\) | −1583.48 | + | 2742.67i | −0.384338 | + | 0.665693i | −0.991677 | − | 0.128750i | \(-0.958904\pi\) |
0.607339 | + | 0.794443i | \(0.292237\pi\) | |||||||
\(258\) | −572.204 | + | 1057.89i | −0.138077 | + | 0.255278i | ||||
\(259\) | 3502.08 | + | 5802.90i | 0.840187 | + | 1.39218i | ||||
\(260\) | 2130.79i | 0.508255i | ||||||||
\(261\) | −269.237 | − | 4841.42i | −0.0638519 | − | 1.14819i | ||||
\(262\) | −112.629 | + | 65.0263i | −0.0265581 | + | 0.0153333i | ||||
\(263\) | 4281.12 | − | 2471.71i | 1.00375 | − | 0.579513i | 0.0943917 | − | 0.995535i | \(-0.469909\pi\) |
0.909355 | + | 0.416022i | \(0.136576\pi\) | |||||||
\(264\) | −336.505 | + | 206.950i | −0.0784487 | + | 0.0482459i | ||||
\(265\) | − | 2699.67i | − | 0.625810i | ||||||
\(266\) | 11239.3 | − | 217.998i | 2.59070 | − | 0.0502493i | ||||
\(267\) | 3554.59 | + | 1922.64i | 0.814746 | + | 0.440688i | ||||
\(268\) | 745.137 | − | 1290.61i | 0.169838 | − | 0.294167i | ||||
\(269\) | 2686.98 | + | 4653.99i | 0.609026 | + | 1.05486i | 0.991401 | + | 0.130857i | \(0.0417730\pi\) |
−0.382375 | + | 0.924007i | \(0.624894\pi\) | |||||||
\(270\) | 1532.55 | + | 2207.14i | 0.345437 | + | 0.497491i | ||||
\(271\) | 3808.34 | + | 2198.74i | 0.853653 | + | 0.492857i | 0.861882 | − | 0.507109i | \(-0.169286\pi\) |
−0.00822876 | + | 0.999966i | \(0.502619\pi\) | |||||||
\(272\) | 1603.18 | 0.357379 | ||||||||
\(273\) | 2818.54 | − | 5461.44i | 0.624856 | − | 1.21077i | ||||
\(274\) | −12036.5 | −2.65384 | ||||||||
\(275\) | −323.814 | − | 186.954i | −0.0710062 | − | 0.0409955i | ||||
\(276\) | −6506.20 | + | 180.769i | −1.41894 | + | 0.0394239i | ||||
\(277\) | 1386.56 | + | 2401.60i | 0.300760 | + | 0.520931i | 0.976308 | − | 0.216384i | \(-0.0694264\pi\) |
−0.675548 | + | 0.737316i | \(0.736093\pi\) | |||||||
\(278\) | −4596.23 | + | 7960.90i | −0.991596 | + | 1.71749i | ||||
\(279\) | −1672.51 | + | 1093.75i | −0.358890 | + | 0.234699i | ||||
\(280\) | −403.014 | + | 243.221i | −0.0860167 | + | 0.0519115i | ||||
\(281\) | − | 2638.82i | − | 0.560208i | −0.959970 | − | 0.280104i | \(-0.909631\pi\) | ||
0.959970 | − | 0.280104i | \(-0.0903690\pi\) | |||||||
\(282\) | −105.320 | − | 171.252i | −0.0222402 | − | 0.0361629i | ||||
\(283\) | −6563.91 | + | 3789.67i | −1.37874 | + | 0.796017i | −0.992008 | − | 0.126175i | \(-0.959730\pi\) |
−0.386733 | + | 0.922192i | \(0.626397\pi\) | |||||||
\(284\) | −3254.11 | + | 1878.76i | −0.679915 | + | 0.392549i | ||||
\(285\) | −2156.66 | − | 3506.77i | −0.448245 | − | 0.728854i | ||||
\(286\) | 3658.78i | 0.756463i | ||||||||
\(287\) | −1511.89 | + | 2740.05i | −0.310955 | + | 0.563553i | ||||
\(288\) | −5387.31 | + | 3523.08i | −1.10226 | + | 0.720831i | ||||
\(289\) | 2214.39 | − | 3835.44i | 0.450721 | − | 0.780671i | ||||
\(290\) | 1719.80 | + | 2978.79i | 0.348242 | + | 0.603174i | ||||
\(291\) | −5361.19 | + | 148.956i | −1.08000 | + | 0.0300067i | ||||
\(292\) | 3504.46 | + | 2023.30i | 0.702338 | + | 0.405495i | ||||
\(293\) | 116.449 | 0.0232186 | 0.0116093 | − | 0.999933i | \(-0.496305\pi\) | ||||
0.0116093 | + | 0.999933i | \(0.496305\pi\) | |||||||
\(294\) | −6811.96 | + | 454.103i | −1.35130 | + | 0.0900810i | ||||
\(295\) | 1655.92 | 0.326817 | ||||||||
\(296\) | 1611.07 | + | 930.153i | 0.316357 | + | 0.182649i | ||||
\(297\) | 1196.77 | + | 1723.56i | 0.233817 | + | 0.336738i | ||||
\(298\) | −1520.77 | − | 2634.05i | −0.295624 | − | 0.512036i | ||||
\(299\) | 5994.02 | − | 10381.9i | 1.15934 | − | 2.00804i | ||||
\(300\) | −762.455 | − | 412.404i | −0.146735 | − | 0.0793672i | ||||
\(301\) | −540.657 | + | 979.850i | −0.103531 | + | 0.187633i | ||||
\(302\) | − | 2212.90i | − | 0.421650i | ||||||
\(303\) | −146.319 | + | 89.9860i | −0.0277419 | + | 0.0170612i | ||||
\(304\) | 9997.87 | − | 5772.27i | 1.88624 | − | 1.08902i | ||||
\(305\) | −77.8016 | + | 44.9188i | −0.0146062 | + | 0.00843292i | ||||
\(306\) | −126.367 | − | 2272.34i | −0.0236077 | − | 0.424513i | ||||
\(307\) | − | 7885.43i | − | 1.46595i | −0.680258 | − | 0.732973i | \(-0.738132\pi\) | ||
0.680258 | − | 0.732973i | \(-0.261868\pi\) | |||||||
\(308\) | 1582.52 | − | 955.056i | 0.292767 | − | 0.176686i | ||||
\(309\) | −2325.90 | + | 4300.15i | −0.428207 | + | 0.791672i | ||||
\(310\) | 708.787 | − | 1227.65i | 0.129859 | − | 0.224923i | ||||
\(311\) | 4926.79 | + | 8533.45i | 0.898304 | + | 1.55591i | 0.829662 | + | 0.558266i | \(0.188533\pi\) |
0.0686420 | + | 0.997641i | \(0.478133\pi\) | |||||||
\(312\) | −46.8499 | − | 1686.21i | −0.00850113 | − | 0.305971i | ||||
\(313\) | 4182.59 | + | 2414.82i | 0.755316 | + | 0.436082i | 0.827612 | − | 0.561301i | \(-0.189699\pi\) |
−0.0722952 | + | 0.997383i | \(0.523032\pi\) | |||||||
\(314\) | −5434.32 | −0.976676 | ||||||||
\(315\) | 1408.74 | + | 2065.58i | 0.251979 | + | 0.369468i | ||||
\(316\) | 1174.48 | 0.209081 | ||||||||
\(317\) | 1492.49 | + | 861.692i | 0.264438 | + | 0.152673i | 0.626357 | − | 0.779536i | \(-0.284545\pi\) |
−0.361919 | + | 0.932209i | \(0.617878\pi\) | |||||||
\(318\) | −298.477 | − | 10742.7i | −0.0526344 | − | 1.89441i | ||||
\(319\) | 1343.00 | + | 2326.14i | 0.235716 | + | 0.408272i | ||||
\(320\) | 825.967 | − | 1430.62i | 0.144290 | − | 0.249918i | ||||
\(321\) | −1070.10 | + | 1978.42i | −0.186067 | + | 0.344001i | ||||
\(322\) | −13314.3 | + | 258.245i | −2.30428 | + | 0.0446938i | ||||
\(323\) | 3486.88i | 0.600666i | ||||||||
\(324\) | 2884.41 | + | 3917.19i | 0.494584 | + | 0.671671i | ||||
\(325\) | 1382.69 | − | 798.295i | 0.235993 | − | 0.136251i | ||||
\(326\) | 7036.74 | − | 4062.67i | 1.19549 | − | 0.690216i | ||||
\(327\) | −3449.28 | + | 2121.31i | −0.583320 | + | 0.358741i | ||||
\(328\) | 858.955i | 0.144597i | ||||||||
\(329\) | −96.6588 | − | 160.163i | −0.0161975 | − | 0.0268391i | ||||
\(330\) | −1309.21 | − | 708.139i | −0.218393 | − | 0.118127i | ||||
\(331\) | −2957.83 | + | 5123.10i | −0.491168 | + | 0.850729i | −0.999948 | − | 0.0101679i | \(-0.996763\pi\) |
0.508780 | + | 0.860897i | \(0.330097\pi\) | |||||||
\(332\) | 2118.69 | + | 3669.68i | 0.350235 | + | 0.606626i | ||||
\(333\) | 4457.76 | − | 8818.37i | 0.733586 | − | 1.45118i | ||||
\(334\) | −7624.15 | − | 4401.81i | −1.24903 | − | 0.721126i | ||||
\(335\) | −1116.65 | −0.182117 | ||||||||
\(336\) | −5899.79 | + | 3787.99i | −0.957917 | + | 0.615035i | ||||
\(337\) | 10105.7 | 1.63350 | 0.816752 | − | 0.576989i | \(-0.195773\pi\) | ||||
0.816752 | + | 0.576989i | \(0.195773\pi\) | |||||||
\(338\) | −6241.75 | − | 3603.68i | −1.00446 | − | 0.579924i | ||||
\(339\) | −2543.23 | + | 70.6614i | −0.407461 | + | 0.0113209i | ||||
\(340\) | 367.096 | + | 635.829i | 0.0585546 | + | 0.101420i | ||||
\(341\) | 553.492 | − | 958.677i | 0.0878982 | − | 0.152244i | ||||
\(342\) | −8969.65 | − | 13715.9i | −1.41820 | − | 2.16864i | ||||
\(343\) | −6341.70 | + | 369.382i | −0.998308 | + | 0.0581479i | ||||
\(344\) | 307.165i | 0.0481431i | ||||||||
\(345\) | 2554.83 | + | 4154.19i | 0.398688 | + | 0.648273i | ||||
\(346\) | 3996.40 | − | 2307.32i | 0.620947 | − | 0.358504i | ||||
\(347\) | 7526.30 | − | 4345.31i | 1.16436 | − | 0.672244i | 0.212015 | − | 0.977266i | \(-0.431997\pi\) |
0.952345 | + | 0.305023i | \(0.0986640\pi\) | |||||||
\(348\) | 3262.08 | + | 5304.20i | 0.502488 | + | 0.817054i | ||||
\(349\) | 1429.22i | 0.219210i | 0.993975 | + | 0.109605i | \(0.0349586\pi\) | ||||
−0.993975 | + | 0.109605i | \(0.965041\pi\) | |||||||
\(350\) | −1552.86 | − | 856.828i | −0.237153 | − | 0.130855i | ||||
\(351\) | −8928.72 | + | 745.765i | −1.35778 | + | 0.113407i | ||||
\(352\) | 1782.85 | − | 3087.99i | 0.269962 | − | 0.467587i | ||||
\(353\) | 4132.48 | + | 7157.66i | 0.623087 | + | 1.07922i | 0.988907 | + | 0.148533i | \(0.0474551\pi\) |
−0.365821 | + | 0.930685i | \(0.619212\pi\) | |||||||
\(354\) | 6589.33 | − | 183.079i | 0.989319 | − | 0.0274873i | ||||
\(355\) | 2438.28 | + | 1407.74i | 0.364537 | + | 0.210465i | ||||
\(356\) | −5189.81 | −0.772638 | ||||||||
\(357\) | −99.8527 | − | 2115.28i | −0.0148033 | − | 0.313592i | ||||
\(358\) | −4232.76 | −0.624883 | ||||||||
\(359\) | −256.265 | − | 147.955i | −0.0376745 | − | 0.0217514i | 0.481044 | − | 0.876696i | \(-0.340258\pi\) |
−0.518719 | + | 0.854945i | \(0.673591\pi\) | |||||||
\(360\) | 612.440 | + | 309.594i | 0.0896622 | + | 0.0453250i | ||||
\(361\) | 9125.06 | + | 15805.1i | 1.33038 | + | 2.30428i | ||||
\(362\) | 5599.26 | − | 9698.21i | 0.812958 | − | 1.40808i | ||||
\(363\) | 5060.87 | + | 2737.37i | 0.731754 | + | 0.395798i | ||||
\(364\) | 153.056 | + | 7891.09i | 0.0220393 | + | 1.13628i | ||||
\(365\) | − | 3032.09i | − | 0.434813i | ||||||
\(366\) | −304.627 | + | 187.345i | −0.0435058 | + | 0.0267560i | ||||
\(367\) | −2372.36 | + | 1369.68i | −0.337428 | + | 0.194814i | −0.659134 | − | 0.752025i | \(-0.729077\pi\) |
0.321706 | + | 0.946840i | \(0.395744\pi\) | |||||||
\(368\) | −11843.7 | + | 6837.95i | −1.67770 | + | 0.968622i | ||||
\(369\) | 4555.32 | − | 253.326i | 0.642657 | − | 0.0357389i | ||||
\(370\) | 7009.20i | 0.984841i | ||||||||
\(371\) | −193.918 | − | 9997.85i | −0.0271368 | − | 1.39909i | ||||
\(372\) | 1220.96 | − | 2257.31i | 0.170171 | − | 0.314613i | ||||
\(373\) | 3659.18 | − | 6337.88i | 0.507949 | − | 0.879793i | −0.492009 | − | 0.870590i | \(-0.663737\pi\) |
0.999958 | − | 0.00920295i | \(-0.00292943\pi\) | |||||||
\(374\) | 630.340 | + | 1091.78i | 0.0871500 | + | 0.150948i | ||||
\(375\) | 18.0393 | + | 649.268i | 0.00248413 | + | 0.0894082i | ||||
\(376\) | −44.4663 | − | 25.6726i | −0.00609887 | − | 0.00352118i | ||||
\(377\) | −11469.2 | −1.56683 | ||||||||
\(378\) | 5834.11 | + | 8063.76i | 0.793848 | + | 1.09724i | ||||
\(379\) | 6215.46 | 0.842392 | 0.421196 | − | 0.906970i | \(-0.361610\pi\) | ||||
0.421196 | + | 0.906970i | \(0.361610\pi\) | |||||||
\(380\) | 4578.62 | + | 2643.47i | 0.618100 | + | 0.356860i | ||||
\(381\) | −62.8089 | − | 2260.61i | −0.00844567 | − | 0.303975i | ||||
\(382\) | −1840.98 | − | 3188.67i | −0.246578 | − | 0.427085i | ||||
\(383\) | −3384.88 | + | 5862.78i | −0.451590 | + | 0.782177i | −0.998485 | − | 0.0550240i | \(-0.982476\pi\) |
0.546895 | + | 0.837201i | \(0.315810\pi\) | |||||||
\(384\) | −1586.36 | + | 2932.88i | −0.210817 | + | 0.389760i | ||||
\(385\) | −1212.63 | − | 669.098i | −0.160523 | − | 0.0885724i | ||||
\(386\) | − | 4526.38i | − | 0.596857i | ||||||
\(387\) | 1629.00 | − | 90.5904i | 0.213971 | − | 0.0118991i | ||||
\(388\) | 5964.80 | − | 3443.78i | 0.780456 | − | 0.450596i | ||||
\(389\) | −6822.93 | + | 3939.22i | −0.889297 | + | 0.513436i | −0.873712 | − | 0.486443i | \(-0.838294\pi\) |
−0.0155842 | + | 0.999879i | \(0.504961\pi\) | |||||||
\(390\) | 5413.82 | − | 3329.50i | 0.702922 | − | 0.432297i | ||||
\(391\) | − | 4130.63i | − | 0.534258i | ||||||
\(392\) | −1475.03 | + | 929.681i | −0.190052 | + | 0.119786i | ||||
\(393\) | 155.173 | + | 83.9315i | 0.0199172 | + | 0.0107730i | ||||
\(394\) | 7138.95 | − | 12365.0i | 0.912830 | − | 1.58107i | ||||
\(395\) | −440.014 | − | 762.127i | −0.0560494 | − | 0.0970804i | ||||
\(396\) | −2404.87 | − | 1215.68i | −0.305175 | − | 0.154269i | ||||
\(397\) | −6608.87 | − | 3815.63i | −0.835490 | − | 0.482370i | 0.0202386 | − | 0.999795i | \(-0.493557\pi\) |
−0.855729 | + | 0.517425i | \(0.826891\pi\) | |||||||
\(398\) | −9861.68 | −1.24201 | ||||||||
\(399\) | −8238.78 | − | 12831.9i | −1.03372 | − | 1.61002i | ||||
\(400\) | −1821.38 | −0.227673 | ||||||||
\(401\) | −13358.9 | − | 7712.79i | −1.66363 | − | 0.960495i | −0.970962 | − | 0.239234i | \(-0.923104\pi\) |
−0.692664 | − | 0.721261i | \(-0.743563\pi\) | |||||||
\(402\) | −4443.46 | + | 123.457i | −0.551292 | + | 0.0153172i | ||||
\(403\) | 2363.41 | + | 4093.55i | 0.292134 | + | 0.505991i | ||||
\(404\) | 110.298 | − | 191.041i | 0.0135829 | − | 0.0235264i | ||||
\(405\) | 1461.25 | − | 3339.28i | 0.179285 | − | 0.409704i | ||||
\(406\) | 6583.01 | + | 10908.0i | 0.804702 | + | 1.33338i | ||||
\(407\) | 5473.49i | 0.666612i | ||||||||
\(408\) | −304.483 | − | 495.094i | −0.0369464 | − | 0.0600755i | ||||
\(409\) | 157.429 | − | 90.8918i | 0.0190327 | − | 0.0109885i | −0.490453 | − | 0.871467i | \(-0.663169\pi\) |
0.509486 | + | 0.860479i | \(0.329836\pi\) | |||||||
\(410\) | −2802.75 | + | 1618.17i | −0.337605 | + | 0.194917i | ||||
\(411\) | 8553.38 | + | 13907.9i | 1.02654 | + | 1.66917i | ||||
\(412\) | − | 6278.34i | − | 0.750757i | ||||||
\(413\) | 6132.44 | − | 118.945i | 0.730649 | − | 0.0141717i | ||||
\(414\) | 10625.6 | + | 16248.2i | 1.26140 | + | 1.92888i | ||||
\(415\) | 1587.52 | − | 2749.66i | 0.187779 | − | 0.325243i | ||||
\(416\) | 7612.80 | + | 13185.8i | 0.897231 | + | 1.55405i | ||||
\(417\) | 12464.9 | − | 346.325i | 1.46381 | − | 0.0406705i | ||||
\(418\) | 7861.94 | + | 4539.10i | 0.919953 | + | 0.531135i | ||||
\(419\) | 7479.61 | 0.872084 | 0.436042 | − | 0.899926i | \(-0.356380\pi\) | ||||
0.436042 | + | 0.899926i | \(0.356380\pi\) | |||||||
\(420\) | −2853.27 | − | 1472.51i | −0.331488 | − | 0.171074i | ||||
\(421\) | −9069.56 | −1.04994 | −0.524968 | − | 0.851122i | \(-0.675923\pi\) | ||||
−0.524968 | + | 0.851122i | \(0.675923\pi\) | |||||||
\(422\) | −4345.92 | − | 2509.12i | −0.501318 | − | 0.289436i | ||||
\(423\) | −123.036 | + | 243.391i | −0.0141424 | + | 0.0279765i | ||||
\(424\) | −1372.32 | − | 2376.93i | −0.157184 | − | 0.272250i | ||||
\(425\) | 275.062 | − | 476.422i | 0.0313941 | − | 0.0543762i | ||||
\(426\) | 9858.21 | + | 5332.20i | 1.12120 | + | 0.606446i | ||||
\(427\) | −284.900 | + | 171.939i | −0.0322887 | + | 0.0194864i | ||||
\(428\) | − | 2888.55i | − | 0.326222i | ||||||
\(429\) | 4227.66 | − | 2600.01i | 0.475789 | − | 0.292610i | ||||
\(430\) | −1002.27 | + | 578.664i | −0.112405 | + | 0.0648968i | ||||
\(431\) | 7258.46 | − | 4190.67i | 0.811201 | − | 0.468347i | −0.0361715 | − | 0.999346i | \(-0.511516\pi\) |
0.847373 | + | 0.530998i | \(0.178183\pi\) | |||||||
\(432\) | 9246.59 | + | 4356.14i | 1.02981 | + | 0.485150i | ||||
\(433\) | − | 5640.66i | − | 0.626034i | −0.949747 | − | 0.313017i | \(-0.898660\pi\) | ||
0.949747 | − | 0.313017i | \(-0.101340\pi\) | |||||||
\(434\) | 2536.71 | − | 4597.35i | 0.280566 | − | 0.508479i | ||||
\(435\) | 2219.80 | − | 4103.99i | 0.244670 | − | 0.452348i | ||||
\(436\) | 2600.13 | − | 4503.55i | 0.285604 | − | 0.494681i | ||||
\(437\) | −14872.4 | − | 25759.7i | −1.62802 | − | 2.81980i | ||||
\(438\) | −335.229 | − | 12065.5i | −0.0365704 | − | 1.31624i | ||||
\(439\) | 1828.10 | + | 1055.45i | 0.198748 | + | 0.114747i | 0.596071 | − | 0.802931i | \(-0.296727\pi\) |
−0.397323 | + | 0.917679i | \(0.630061\pi\) | |||||||
\(440\) | −380.136 | −0.0411870 | ||||||||
\(441\) | 5365.43 | + | 7548.40i | 0.579357 | + | 0.815074i | ||||
\(442\) | −5383.11 | −0.579295 | ||||||||
\(443\) | −825.998 | − | 476.890i | −0.0885877 | − | 0.0511462i | 0.455052 | − | 0.890465i | \(-0.349621\pi\) |
−0.543639 | + | 0.839319i | \(0.682954\pi\) | |||||||
\(444\) | 352.426 | + | 12684.5i | 0.0376699 | + | 1.35581i | ||||
\(445\) | 1944.34 | + | 3367.70i | 0.207125 | + | 0.358751i | ||||
\(446\) | 2843.38 | − | 4924.88i | 0.301879 | − | 0.522869i | ||||
\(447\) | −1962.91 | + | 3629.04i | −0.207701 | + | 0.383999i | ||||
\(448\) | 2956.09 | − | 5357.41i | 0.311745 | − | 0.564986i | ||||
\(449\) | 3666.11i | 0.385332i | 0.981264 | + | 0.192666i | \(0.0617135\pi\) | ||||
−0.981264 | + | 0.192666i | \(0.938287\pi\) | |||||||
\(450\) | 143.567 | + | 2581.62i | 0.0150396 | + | 0.270441i | ||||
\(451\) | −2188.67 | + | 1263.63i | −0.228516 | + | 0.131934i | ||||
\(452\) | 2829.57 | − | 1633.65i | 0.294451 | − | 0.170001i | ||||
\(453\) | −2556.97 | + | 1572.53i | −0.265203 | + | 0.163100i | ||||
\(454\) | 10631.9i | 1.09907i | ||||||||
\(455\) | 5063.24 | − | 3055.69i | 0.521689 | − | 0.314841i | ||||
\(456\) | −3681.43 | − | 1991.25i | −0.378068 | − | 0.204493i | ||||
\(457\) | −4313.23 | + | 7470.73i | −0.441497 | + | 0.764696i | −0.997801 | − | 0.0662833i | \(-0.978886\pi\) |
0.556303 | + | 0.830979i | \(0.312219\pi\) | |||||||
\(458\) | −7207.33 | − | 12483.5i | −0.735319 | − | 1.27361i | ||||
\(459\) | −2535.85 | + | 1760.79i | −0.257872 | + | 0.179056i | ||||
\(460\) | −5423.92 | − | 3131.50i | −0.549765 | − | 0.317407i | ||||
\(461\) | 7189.28 | 0.726330 | 0.363165 | − | 0.931725i | \(-0.381696\pi\) | ||||
0.363165 | + | 0.931725i | \(0.381696\pi\) | |||||||
\(462\) | −4899.34 | − | 2528.45i | −0.493372 | − | 0.254619i | ||||
\(463\) | −2282.41 | −0.229099 | −0.114549 | − | 0.993418i | \(-0.536542\pi\) | ||||
−0.114549 | + | 0.993418i | \(0.536542\pi\) | |||||||
\(464\) | 11331.1 | + | 6542.01i | 1.13369 | + | 0.654537i | ||||
\(465\) | −1922.21 | + | 53.4069i | −0.191700 | + | 0.00532620i | ||||
\(466\) | −6926.76 | − | 11997.5i | −0.688575 | − | 1.19265i | ||||
\(467\) | 3228.56 | − | 5592.04i | 0.319915 | − | 0.554108i | −0.660555 | − | 0.750777i | \(-0.729679\pi\) |
0.980470 | + | 0.196669i | \(0.0630125\pi\) | |||||||
\(468\) | 9629.92 | − | 6297.56i | 0.951160 | − | 0.622019i | ||||
\(469\) | −4135.36 | + | 80.2094i | −0.407150 | + | 0.00789707i | ||||
\(470\) | − | 193.457i | − | 0.0189862i | ||||||
\(471\) | 3861.74 | + | 6279.25i | 0.377791 | + | 0.614294i | ||||
\(472\) | 1457.95 | − | 841.750i | 0.142177 | − | 0.0820862i | ||||
\(473\) | −782.677 | + | 451.879i | −0.0760836 | + | 0.0439269i | ||||
\(474\) | −1835.20 | − | 2984.06i | −0.177834 | − | 0.289161i | ||||
\(475\) | − | 3961.46i | − | 0.382662i | ||||||
\(476\) | 1405.16 | + | 2328.33i | 0.135305 | + | 0.224199i | ||||
\(477\) | −12200.9 | + | 7978.88i | −1.17116 | + | 0.765887i | ||||
\(478\) | −9031.62 | + | 15643.2i | −0.864219 | + | 1.49687i | ||||
\(479\) | −6881.73 | − | 11919.5i | −0.656439 | − | 1.13699i | −0.981531 | − | 0.191303i | \(-0.938729\pi\) |
0.325092 | − | 0.945682i | \(-0.394605\pi\) | |||||||
\(480\) | −6191.64 | + | 172.029i | −0.588767 | + | 0.0163584i | ||||
\(481\) | −20240.6 | − | 11685.9i | −1.91870 | − | 1.10776i | ||||
\(482\) | 28002.2 | 2.64619 | ||||||||
\(483\) | 9759.83 | + | 15200.9i | 0.919436 | + | 1.43202i | ||||
\(484\) | −7389.02 | −0.693935 | ||||||||
\(485\) | −4469.38 | − | 2580.40i | −0.418442 | − | 0.241587i | ||||
\(486\) | 5445.53 | − | 13449.4i | 0.508260 | − | 1.25531i | ||||
\(487\) | −3315.76 | − | 5743.07i | −0.308525 | − | 0.534380i | 0.669515 | − | 0.742798i | \(-0.266502\pi\) |
−0.978040 | + | 0.208418i | \(0.933169\pi\) | |||||||
\(488\) | −45.6670 | + | 79.0975i | −0.00423616 | + | 0.00733725i | ||||
\(489\) | −9694.79 | − | 5243.81i | −0.896552 | − | 0.484936i | ||||
\(490\) | −5812.32 | − | 3061.59i | −0.535865 | − | 0.282263i | ||||
\(491\) | 1848.57i | 0.169908i | 0.996385 | + | 0.0849540i | \(0.0270743\pi\) | ||||
−0.996385 | + | 0.0849540i | \(0.972926\pi\) | |||||||
\(492\) | −4990.75 | + | 3069.31i | −0.457318 | + | 0.281250i | ||||
\(493\) | −3422.41 | + | 1975.93i | −0.312652 | + | 0.180510i | ||||
\(494\) | −33570.5 | + | 19382.0i | −3.05751 | + | 1.76525i | ||||
\(495\) | 112.111 | + | 2015.99i | 0.0101799 | + | 0.183054i | ||||
\(496\) | − | 5392.35i | − | 0.488152i | ||||||
\(497\) | 9130.94 | + | 5038.23i | 0.824102 | + | 0.454719i | ||||
\(498\) | 6013.16 | − | 11117.2i | 0.541077 | − | 1.00035i | ||||
\(499\) | 6454.39 | − | 11179.3i | 0.579034 | − | 1.00292i | −0.416556 | − | 0.909110i | \(-0.636763\pi\) |
0.995590 | − | 0.0938066i | \(-0.0299035\pi\) | |||||||
\(500\) | −417.060 | − | 722.368i | −0.0373029 | − | 0.0646106i | ||||
\(501\) | 331.675 | + | 11937.6i | 0.0295771 | + | 1.06453i | ||||
\(502\) | −9345.00 | − | 5395.34i | −0.830853 | − | 0.479693i | ||||
\(503\) | 16082.5 | 1.42562 | 0.712808 | − | 0.701359i | \(-0.247423\pi\) | ||||
0.712808 | + | 0.701359i | \(0.247423\pi\) | |||||||
\(504\) | 2290.32 | + | 1102.54i | 0.202419 | + | 0.0974428i | ||||
\(505\) | −165.291 | −0.0145650 | ||||||||
\(506\) | −9313.42 | − | 5377.10i | −0.818245 | − | 0.472414i | ||||
\(507\) | 271.536 | + | 9773.08i | 0.0237857 | + | 0.856090i | ||||
\(508\) | 1452.11 | + | 2515.13i | 0.126825 | + | 0.219667i | ||||
\(509\) | −4553.38 | + | 7886.69i | −0.396513 | + | 0.686781i | −0.993293 | − | 0.115624i | \(-0.963113\pi\) |
0.596780 | + | 0.802405i | \(0.296446\pi\) | |||||||
\(510\) | 1041.87 | − | 1926.22i | 0.0904607 | − | 0.167244i | ||||
\(511\) | −217.796 | − | 11228.9i | −0.0188546 | − | 0.972089i | ||||
\(512\) | − | 14406.5i | − | 1.24353i | ||||||
\(513\) | −9474.50 | + | 20111.1i | −0.815418 | + | 1.73085i | ||||
\(514\) | −10505.9 | + | 6065.57i | −0.901545 | + | 0.520507i | ||||
\(515\) | −4074.06 | + | 2352.16i | −0.348591 | + | 0.201259i | ||||
\(516\) | −1784.71 | + | 1097.60i | −0.152262 | + | 0.0936414i | ||||
\(517\) | − | 151.071i | − | 0.0128512i | ||||||
\(518\) | 503.473 | + | 25957.6i | 0.0427053 | + | 2.20176i | ||||
\(519\) | −5505.99 | − | 2978.14i | −0.465677 | − | 0.251880i | ||||
\(520\) | 811.592 | − | 1405.72i | 0.0684436 | − | 0.118548i | ||||
\(521\) | 2366.98 | + | 4099.73i | 0.199039 | + | 0.344745i | 0.948217 | − | 0.317623i | \(-0.102885\pi\) |
−0.749178 | + | 0.662368i | \(0.769551\pi\) | |||||||
\(522\) | 8379.46 | − | 16576.3i | 0.702603 | − | 1.38989i | ||||
\(523\) | −1342.45 | − | 775.065i | −0.112240 | − | 0.0648016i | 0.442829 | − | 0.896606i | \(-0.353975\pi\) |
−0.555069 | + | 0.831804i | \(0.687308\pi\) | |||||||
\(524\) | −226.557 | −0.0188878 | ||||||||
\(525\) | 113.443 | + | 2403.18i | 0.00943061 | + | 0.199778i | ||||
\(526\) | 18935.9 | 1.56967 | ||||||||
\(527\) | 1410.49 | + | 814.344i | 0.116588 | + | 0.0673119i | ||||
\(528\) | −5659.79 | + | 157.252i | −0.466498 | + | 0.0129612i | ||||
\(529\) | 11534.6 | + | 19978.6i | 0.948026 | + | 1.64203i | ||||
\(530\) | 5170.59 | − | 8955.72i | 0.423766 | − | 0.733984i | ||||
\(531\) | −4894.06 | − | 7483.75i | −0.399970 | − | 0.611614i | ||||
\(532\) | 17146.1 | + | 9460.81i | 1.39733 | + | 0.771012i | ||||
\(533\) | − | 10791.4i | − | 0.876977i | ||||||
\(534\) | 8109.40 | + | 13186.0i | 0.657168 | + | 1.06857i | ||||
\(535\) | −1874.40 | + | 1082.18i | −0.151472 | + | 0.0874522i | ||||
\(536\) | −983.158 | + | 567.626i | −0.0792275 | + | 0.0457420i | ||||
\(537\) | 3007.89 | + | 4890.88i | 0.241713 | + | 0.393030i | ||||
\(538\) | 20585.1i | 1.64960i | ||||||||
\(539\) | −4538.85 | − | 2390.80i | −0.362713 | − | 0.191056i | ||||
\(540\) | 389.616 | + | 4664.70i | 0.0310489 | + | 0.371735i | ||||
\(541\) | −4421.27 | + | 7657.86i | −0.351359 | + | 0.608571i | −0.986488 | − | 0.163835i | \(-0.947614\pi\) |
0.635129 | + | 0.772406i | \(0.280947\pi\) | |||||||
\(542\) | 8422.35 | + | 14587.9i | 0.667474 | + | 1.15610i | ||||
\(543\) | −15185.1 | + | 421.903i | −1.20010 | + | 0.0333436i | ||||
\(544\) | 4543.32 | + | 2623.08i | 0.358076 | + | 0.206735i | ||||
\(545\) | −3896.52 | −0.306254 | ||||||||
\(546\) | 19810.1 | − | 12719.2i | 1.55274 | − | 0.996943i | ||||
\(547\) | 14918.7 | 1.16614 | 0.583068 | − | 0.812423i | \(-0.301852\pi\) | ||||
0.583068 | + | 0.812423i | \(0.301852\pi\) | |||||||
\(548\) | −18158.9 | − | 10484.1i | −1.41553 | − | 0.817256i | ||||
\(549\) | 432.949 | + | 218.859i | 0.0336572 | + | 0.0170140i | ||||
\(550\) | −716.133 | − | 1240.38i | −0.0555200 | − | 0.0961635i | ||||
\(551\) | −14228.7 | + | 24644.8i | −1.10012 | + | 1.90546i | ||||
\(552\) | 4361.10 | + | 2358.87i | 0.336269 | + | 0.181885i | ||||
\(553\) | −1684.27 | − | 2790.82i | −0.129516 | − | 0.214607i | ||||
\(554\) | 10622.5i | 0.814636i | ||||||||
\(555\) | 8099.01 | − | 4980.89i | 0.619430 | − | 0.380949i | ||||
\(556\) | −13868.3 | + | 8006.84i | −1.05781 | + | 0.610730i | ||||
\(557\) | −15459.3 | + | 8925.46i | −1.17600 | + | 0.678966i | −0.955087 | − | 0.296327i | \(-0.904238\pi\) |
−0.220916 | + | 0.975293i | \(0.570905\pi\) | |||||||
\(558\) | −7643.08 | + | 425.040i | −0.579852 | + | 0.0322462i | ||||
\(559\) | − | 3859.05i | − | 0.291987i | ||||||
\(560\) | −6745.23 | + | 130.830i | −0.508996 | + | 0.00987249i | ||||
\(561\) | 813.600 | − | 1504.19i | 0.0612304 | − | 0.113203i | ||||
\(562\) | 5054.03 | − | 8753.84i | 0.379344 | − | 0.657043i | ||||
\(563\) | −2584.61 | − | 4476.68i | −0.193478 | − | 0.335114i | 0.752922 | − | 0.658109i | \(-0.228644\pi\) |
−0.946401 | + | 0.322995i | \(0.895310\pi\) | |||||||
\(564\) | −9.72713 | − | 350.097i | −0.000726216 | − | 0.0261378i | ||||
\(565\) | −2120.18 | − | 1224.09i | −0.157870 | − | 0.0911463i | ||||
\(566\) | −29032.9 | −2.15609 | ||||||||
\(567\) | 5171.68 | − | 12471.5i | 0.383051 | − | 0.923727i | ||||
\(568\) | 2862.38 | 0.211449 | ||||||||
\(569\) | 16171.2 | + | 9336.43i | 1.19144 | + | 0.687880i | 0.958634 | − | 0.284643i | \(-0.0918749\pi\) |
0.232809 | + | 0.972522i | \(0.425208\pi\) | |||||||
\(570\) | −437.981 | − | 15763.7i | −0.0321842 | − | 1.15837i | ||||
\(571\) | 1206.49 | + | 2089.71i | 0.0884242 | + | 0.153155i | 0.906845 | − | 0.421464i | \(-0.138484\pi\) |
−0.818421 | + | 0.574619i | \(0.805150\pi\) | |||||||
\(572\) | −3186.88 | + | 5519.84i | −0.232955 | + | 0.403490i | ||||
\(573\) | −2376.21 | + | 4393.15i | −0.173242 | + | 0.320291i | ||||
\(574\) | −10263.4 | + | 6193.99i | −0.746314 | + | 0.450404i | ||||
\(575\) | 4692.83i | 0.340356i | ||||||||
\(576\) | −8906.68 | + | 495.310i | −0.644291 | + | 0.0358297i | ||||
\(577\) | −13459.4 | + | 7770.80i | −0.971097 | + | 0.560663i | −0.899570 | − | 0.436776i | \(-0.856120\pi\) |
−0.0715262 | + | 0.997439i | \(0.522787\pi\) | |||||||
\(578\) | 14691.7 | − | 8482.29i | 1.05726 | − | 0.610409i | ||||
\(579\) | −5230.15 | + | 3216.54i | −0.375402 | + | 0.230872i | ||||
\(580\) | 5991.95i | 0.428969i | ||||||||
\(581\) | 5681.64 | − | 10297.0i | 0.405704 | − | 0.735271i | ||||
\(582\) | −18070.2 | − | 9773.97i | −1.28700 | − | 0.696124i | ||||
\(583\) | 4037.72 | − | 6993.53i | 0.286836 | − | 0.496814i | ||||
\(584\) | −1541.30 | − | 2669.61i | −0.109211 | − | 0.189159i | ||||
\(585\) | −7694.35 | − | 3889.56i | −0.543799 | − | 0.274895i | ||||
\(586\) | 386.302 | + | 223.032i | 0.0272321 | + | 0.0157224i | ||||
\(587\) | 998.851 | 0.0702334 | 0.0351167 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351167 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(588\) | −10672.4 | − | 5248.28i | −0.748509 | − | 0.368088i | ||||
\(589\) | 11728.2 | 0.820464 | ||||||||
\(590\) | 5493.23 | + | 3171.52i | 0.383310 | + | 0.221304i | ||||
\(591\) | −19360.6 | + | 537.918i | −1.34753 | + | 0.0374399i | ||||
\(592\) | 13331.3 | + | 23090.4i | 0.925526 | + | 1.60306i | ||||
\(593\) | 1608.16 | − | 2785.42i | 0.111365 | − | 0.192889i | −0.804956 | − | 0.593334i | \(-0.797811\pi\) |
0.916321 | + | 0.400445i | \(0.131145\pi\) | |||||||
\(594\) | 669.010 | + | 8009.76i | 0.0462118 | + | 0.553274i | ||||
\(595\) | 984.433 | − | 1784.12i | 0.0678282 | − | 0.122927i | ||||
\(596\) | − | 5298.50i | − | 0.364153i | ||||||
\(597\) | 7007.92 | + | 11395.0i | 0.480427 | + | 0.781183i | ||||
\(598\) | 39768.3 | − | 22960.3i | 2.71948 | − | 1.57009i | ||||
\(599\) | 14726.7 | − | 8502.49i | 1.00454 | − | 0.579970i | 0.0949504 | − | 0.995482i | \(-0.469731\pi\) |
0.909588 | + | 0.415512i | \(0.136397\pi\) | |||||||
\(600\) | 345.925 | + | 562.479i | 0.0235372 | + | 0.0382719i | ||||
\(601\) | − | 19431.1i | − | 1.31882i | −0.751782 | − | 0.659412i | \(-0.770805\pi\) | ||
0.751782 | − | 0.659412i | \(-0.229195\pi\) | |||||||
\(602\) | −3670.21 | + | 2214.99i | −0.248483 | + | 0.149961i | ||||
\(603\) | 3300.27 | + | 5046.60i | 0.222881 | + | 0.340818i | ||||
\(604\) | 1927.49 | − | 3338.51i | 0.129848 | − | 0.224904i | ||||
\(605\) | 2768.27 | + | 4794.79i | 0.186027 | + | 0.322208i | ||||
\(606\) | −657.735 | + | 18.2746i | −0.0440902 | + | 0.00122501i | ||||
\(607\) | −6767.31 | − | 3907.11i | −0.452515 | − | 0.261260i | 0.256377 | − | 0.966577i | \(-0.417471\pi\) |
−0.708892 | + | 0.705317i | \(0.750805\pi\) | |||||||
\(608\) | 37777.8 | 2.51989 | ||||||||
\(609\) | 7925.94 | − | 15358.0i | 0.527381 | − | 1.02190i | ||||
\(610\) | −344.125 | −0.0228413 | ||||||||
\(611\) | 558.650 | + | 322.537i | 0.0369894 | + | 0.0213559i | ||||
\(612\) | 1788.61 | − | 3538.25i | 0.118138 | − | 0.233701i | ||||
\(613\) | −9304.17 | − | 16115.3i | −0.613038 | − | 1.06181i | −0.990725 | − | 0.135879i | \(-0.956614\pi\) |
0.377688 | − | 0.925933i | \(-0.376719\pi\) | |||||||
\(614\) | 15102.7 | − | 26158.6i | 0.992663 | − | 1.71934i | ||||
\(615\) | 3861.46 | + | 2088.63i | 0.253186 | + | 0.136946i | ||||
\(616\) | −1407.78 | + | 27.3053i | −0.0920797 | + | 0.00178598i | ||||
\(617\) | − | 25699.5i | − | 1.67686i | −0.545011 | − | 0.838429i | \(-0.683475\pi\) | ||
0.545011 | − | 0.838429i | \(-0.316525\pi\) | |||||||
\(618\) | −15951.7 | + | 9810.30i | −1.03830 | + | 0.638557i | ||||
\(619\) | 2647.00 | − | 1528.25i | 0.171877 | − | 0.0992334i | −0.411593 | − | 0.911368i | \(-0.635028\pi\) |
0.583471 | + | 0.812134i | \(0.301694\pi\) | |||||||
\(620\) | 2138.63 | − | 1234.74i | 0.138531 | − | 0.0799811i | ||||
\(621\) | 11223.7 | − | 23824.0i | 0.725267 | − | 1.53949i | ||||
\(622\) | 37744.4i | 2.43314i | ||||||||
\(623\) | 7442.50 | + | 12332.1i | 0.478615 | + | 0.793060i | ||||
\(624\) | 11502.2 | − | 21265.3i | 0.737909 | − | 1.36425i | ||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 9250.04 | + | 16021.5i | 0.590585 | + | 1.02292i | ||||
\(627\) | −342.020 | − | 12309.9i | −0.0217846 | − | 0.784068i | ||||
\(628\) | −8198.51 | − | 4733.41i | −0.520949 | − | 0.300770i | ||||
\(629\) | −8053.06 | −0.510488 | ||||||||
\(630\) | 717.117 | + | 9550.34i | 0.0453502 | + | 0.603960i | ||||
\(631\) | 4012.52 | 0.253147 | 0.126574 | − | 0.991957i | \(-0.459602\pi\) | ||||
0.126574 | + | 0.991957i | \(0.459602\pi\) | |||||||
\(632\) | −774.822 | − | 447.344i | −0.0487670 | − | 0.0281557i | ||||
\(633\) | 189.061 | + | 6804.67i | 0.0118713 | + | 0.427269i | ||||
\(634\) | 3300.74 | + | 5717.04i | 0.206765 | + | 0.358127i | ||||
\(635\) | 1088.06 | − | 1884.57i | 0.0679971 | − | 0.117774i | ||||
\(636\) | 8906.85 | − | 16467.0i | 0.555314 | − | 1.02667i | ||||
\(637\) | 18531.5 | − | 11680.0i | 1.15266 | − | 0.726496i | ||||
\(638\) | 10288.8i | 0.638458i | ||||||||
\(639\) | −844.186 | − | 15180.2i | −0.0522621 | − | 0.939778i | ||||
\(640\) | −2778.68 | + | 1604.27i | −0.171620 | + | 0.0990850i | ||||
\(641\) | 15938.5 | − | 9202.09i | 0.982110 | − | 0.567021i | 0.0792033 | − | 0.996858i | \(-0.474762\pi\) |
0.902906 | + | 0.429837i | \(0.141429\pi\) | |||||||
\(642\) | −7339.09 | + | 4513.54i | −0.451169 | + | 0.277469i | ||||
\(643\) | − | 18685.2i | − | 1.14599i | −0.819558 | − | 0.572996i | \(-0.805781\pi\) | ||
0.819558 | − | 0.572996i | \(-0.194219\pi\) | |||||||
\(644\) | −20311.7 | − | 11207.5i | −1.24284 | − | 0.685771i | ||||
\(645\) | 1380.87 | + | 746.900i | 0.0842974 | + | 0.0455956i | ||||
\(646\) | −6678.30 | + | 11567.2i | −0.406740 | + | 0.704495i | ||||
\(647\) | 106.007 | + | 183.609i | 0.00644134 | + | 0.0111567i | 0.869228 | − | 0.494411i | \(-0.164616\pi\) |
−0.862787 | + | 0.505568i | \(0.831283\pi\) | |||||||
\(648\) | −410.887 | − | 3682.87i | −0.0249092 | − | 0.223266i | ||||
\(649\) | 4289.67 | + | 2476.64i | 0.259452 | + | 0.149795i | ||||
\(650\) | 6115.78 | 0.369047 | ||||||||
\(651\) | −7114.79 | + | 335.858i | −0.428342 | + | 0.0202201i | ||||
\(652\) | 14154.7 | 0.850216 | ||||||||
\(653\) | 888.276 | + | 512.847i | 0.0532327 | + | 0.0307339i | 0.526380 | − | 0.850249i | \(-0.323549\pi\) |
−0.473147 | + | 0.880983i | \(0.656882\pi\) | |||||||
\(654\) | −15505.3 | + | 430.800i | −0.927071 | + | 0.0257578i | ||||
\(655\) | 84.8790 | + | 147.015i | 0.00506335 | + | 0.00876998i | ||||
\(656\) | −6155.41 | + | 10661.5i | −0.366354 | + | 0.634544i | ||||
\(657\) | −13703.2 | + | 8961.34i | −0.813720 | + | 0.532139i | ||||
\(658\) | −13.8961 | − | 716.440i | −0.000823291 | − | 0.0424464i | ||||
\(659\) | − | 16866.8i | − | 0.997024i | −0.866883 | − | 0.498512i | \(-0.833880\pi\) | ||
0.866883 | − | 0.498512i | \(-0.166120\pi\) | |||||||
\(660\) | −1358.34 | − | 2208.69i | −0.0801113 | − | 0.130262i | ||||
\(661\) | 1890.14 | − | 1091.27i | 0.111222 | − | 0.0642141i | −0.443357 | − | 0.896345i | \(-0.646213\pi\) |
0.554579 | + | 0.832131i | \(0.312879\pi\) | |||||||
\(662\) | −19624.2 | + | 11330.0i | −1.15214 | + | 0.665188i | ||||
\(663\) | 3825.35 | + | 6220.09i | 0.224079 | + | 0.364356i | ||||
\(664\) | − | 3227.93i | − | 0.188656i | ||||||
\(665\) | −284.553 | − | 14670.7i | −0.0165932 | − | 0.855497i | ||||
\(666\) | 31677.4 | − | 20715.7i | 1.84306 | − | 1.20528i | ||||
\(667\) | 16855.6 | − | 29194.8i | 0.978489 | − | 1.69479i | ||||
\(668\) | −7668.14 | − | 13281.6i | −0.444146 | − | 0.769283i | ||||
\(669\) | −7711.17 | + | 214.248i | −0.445637 | + | 0.0123816i | ||||
\(670\) | −3704.31 | − | 2138.68i | −0.213597 | − | 0.123320i | ||||
\(671\) | −268.728 | −0.0154607 | ||||||||
\(672\) | −22917.5 | + | 1081.83i | −1.31557 | + | 0.0621020i | ||||
\(673\) | 15734.2 | 0.901203 | 0.450601 | − | 0.892725i | \(-0.351210\pi\) | ||||
0.450601 | + | 0.892725i | \(0.351210\pi\) | |||||||
\(674\) | 33523.9 | + | 19355.0i | 1.91586 | + | 1.10612i | ||||
\(675\) | 2880.99 | − | 2000.44i | 0.164281 | − | 0.114070i | ||||
\(676\) | −6277.77 | − | 10873.4i | −0.357178 | − | 0.618651i | ||||
\(677\) | −12363.2 | + | 21413.8i | −0.701858 | + | 1.21565i | 0.265955 | + | 0.963985i | \(0.414313\pi\) |
−0.967813 | + | 0.251669i | \(0.919021\pi\) | |||||||
\(678\) | −8572.09 | − | 4636.56i | −0.485559 | − | 0.262634i | ||||
\(679\) | −16737.1 | − | 9235.10i | −0.945964 | − | 0.521960i | ||||
\(680\) | − | 559.289i | − | 0.0315408i | ||||||
\(681\) | 12285.0 | − | 7555.24i | 0.691278 | − | 0.425136i | ||||
\(682\) | 3672.24 | − | 2120.17i | 0.206184 | − | 0.119040i | ||||
\(683\) | 561.677 | − | 324.284i | 0.0314670 | − | 0.0181675i | −0.484184 | − | 0.874966i | \(-0.660883\pi\) |
0.515651 | + | 0.856799i | \(0.327550\pi\) | |||||||
\(684\) | −1585.22 | − | 28505.4i | −0.0886144 | − | 1.59347i | ||||
\(685\) | 15711.3i | 0.876345i | ||||||||
\(686\) | −21745.0 | − | 10920.7i | −1.21025 | − | 0.607803i | ||||
\(687\) | −9302.73 | + | 17198.9i | −0.516625 | + | 0.955139i | ||||
\(688\) | −2201.20 | + | 3812.58i | −0.121976 | + | 0.211269i | ||||
\(689\) | 17241.1 | + | 29862.4i | 0.953313 | + | 1.65119i | ||||
\(690\) | 518.841 | + | 18674.0i | 0.0286260 | + | 1.03030i | ||||
\(691\) | 5917.06 | + | 3416.22i | 0.325754 | + | 0.188074i | 0.653954 | − | 0.756534i | \(-0.273109\pi\) |
−0.328201 | + | 0.944608i | \(0.606442\pi\) | |||||||
\(692\) | 8038.92 | 0.441610 | ||||||||
\(693\) | 559.997 | + | 7457.87i | 0.0306963 | + | 0.408804i | ||||
\(694\) | 33289.7 | 1.82084 | ||||||||
\(695\) | 10391.4 | + | 5999.47i | 0.567148 | + | 0.327443i | ||||
\(696\) | −131.745 | − | 4741.75i | −0.00717499 | − | 0.258241i | ||||
\(697\) | −1859.16 | − | 3220.16i | −0.101034 | − | 0.174996i | ||||
\(698\) | −2737.33 | + | 4741.20i | −0.148438 | + | 0.257102i | ||||
\(699\) | −8940.59 | + | 16529.4i | −0.483783 | + | 0.894421i | ||||
\(700\) | −1596.41 | − | 2645.23i | −0.0861979 | − | 0.142829i | ||||
\(701\) | 18697.9i | 1.00743i | 0.863869 | + | 0.503717i | \(0.168035\pi\) | ||||
−0.863869 | + | 0.503717i | \(0.831965\pi\) | |||||||
\(702\) | −31047.9 | − | 14626.9i | −1.66927 | − | 0.786406i | ||||
\(703\) | −50221.1 | + | 28995.2i | −2.69434 | + | 1.55558i | ||||
\(704\) | 4279.35 | − | 2470.69i | 0.229097 | − | 0.132269i | ||||
\(705\) | −223.536 | + | 137.475i | −0.0119416 | + | 0.00734411i | ||||
\(706\) | 31659.2i | 1.68769i | ||||||||
\(707\) | −612.130 | + | 11.8729i | −0.0325622 | + | 0.000631577i | ||||
\(708\) | 10100.5 | + | 5463.25i | 0.536158 | + | 0.290002i | ||||
\(709\) | −6566.08 | + | 11372.8i | −0.347806 | + | 0.602417i | −0.985859 | − | 0.167575i | \(-0.946406\pi\) |
0.638054 | + | 0.769992i | \(0.279740\pi\) | |||||||
\(710\) | 5392.40 | + | 9339.91i | 0.285032 | + | 0.493691i | ||||
\(711\) | −2143.90 | + | 4241.07i | −0.113084 | + | 0.223703i | ||||
\(712\) | 3423.80 | + | 1976.73i | 0.180214 | + | 0.104047i | ||||
\(713\) | −13893.5 | −0.729755 | ||||||||
\(714\) | 3720.07 | − | 7208.32i | 0.194986 | − | 0.377822i | ||||
\(715\) | 4775.82 | 0.249798 | ||||||||
\(716\) | −6385.77 | − | 3686.83i | −0.333307 | − | 0.192435i | ||||
\(717\) | 24493.5 | − | 680.530i | 1.27577 | − | 0.0354461i | ||||
\(718\) | −566.745 | − | 981.631i | −0.0294578 | − | 0.0510225i | ||||
\(719\) | 9575.52 | − | 16585.3i | 0.496671 | − | 0.860259i | −0.503322 | − | 0.864099i | \(-0.667889\pi\) |
0.999993 | + | 0.00383968i | \(0.00122221\pi\) | |||||||
\(720\) | 5383.10 | + | 8231.57i | 0.278634 | + | 0.426073i | ||||
\(721\) | −14918.7 | + | 9003.53i | −0.770600 | + | 0.465061i | ||||
\(722\) | 69907.6i | 3.60345i | ||||||||
\(723\) | −19899.0 | − | 32356.0i | −1.02358 | − | 1.66436i | ||||
\(724\) | 16894.7 | − | 9754.17i | 0.867248 | − | 0.500706i | ||||
\(725\) | 3888.22 | − | 2244.86i | 0.199179 | − | 0.114996i | ||||
\(726\) | 11545.8 | + | 18773.7i | 0.590227 | + | 0.959720i | ||||
\(727\) | 21313.6i | 1.08731i | 0.839307 | + | 0.543657i | \(0.182961\pi\) | ||||
−0.839307 | + | 0.543657i | \(0.817039\pi\) | |||||||
\(728\) | 2904.64 | − | 5264.17i | 0.147875 | − | 0.267999i | ||||
\(729\) | −19410.3 | + | 3265.24i | −0.986144 | + | 0.165891i | ||||
\(730\) | 5807.25 | − | 10058.5i | 0.294433 | − | 0.509973i | ||||
\(731\) | −664.842 | − | 1151.54i | −0.0336390 | − | 0.0582644i | ||||
\(732\) | −622.759 | + | 17.3028i | −0.0314451 | + | 0.000873675i | ||||
\(733\) | 15935.6 | + | 9200.45i | 0.802996 | + | 0.463610i | 0.844518 | − | 0.535528i | \(-0.179887\pi\) |
−0.0415215 | + | 0.999138i | \(0.513221\pi\) | |||||||
\(734\) | −10493.2 | −0.527672 | ||||||||
\(735\) | 592.741 | + | 8891.67i | 0.0297464 | + | 0.446223i | ||||
\(736\) | −44752.4 | −2.24130 | ||||||||
\(737\) | −2892.70 | − | 1670.10i | −0.144578 | − | 0.0834721i | ||||
\(738\) | 15596.7 | + | 7884.27i | 0.777944 | + | 0.393258i | ||||
\(739\) | 1609.97 | + | 2788.55i | 0.0801404 | + | 0.138807i | 0.903310 | − | 0.428988i | \(-0.141130\pi\) |
−0.823170 | + | 0.567795i | \(0.807796\pi\) | |||||||
\(740\) | −6105.17 | + | 10574.5i | −0.303285 | + | 0.525304i | ||||
\(741\) | 46251.4 | + | 25016.9i | 2.29297 | + | 1.24024i | ||||
\(742\) | 18505.2 | − | 33537.6i | 0.915564 | − | 1.65931i | ||||
\(743\) | − | 36940.2i | − | 1.82396i | −0.410229 | − | 0.911982i | \(-0.634551\pi\) | ||
0.410229 | − | 0.911982i | \(-0.365449\pi\) | |||||||
\(744\) | −1665.26 | + | 1024.14i | −0.0820585 | + | 0.0504660i | ||||
\(745\) | −3438.24 | + | 1985.07i | −0.169084 | + | 0.0976204i | ||||
\(746\) | 24277.4 | − | 14016.6i | 1.19150 | − | 0.687913i | ||||
\(747\) | −17118.8 | + | 951.993i | −0.838478 | + | 0.0466287i | ||||
\(748\) | 2196.16i | 0.107352i | ||||||||
\(749\) | −6863.83 | + | 4142.35i | −0.334845 | + | 0.202080i | ||||
\(750\) | −1183.68 | + | 2188.39i | −0.0576291 | + | 0.106545i | ||||
\(751\) | 568.670 | − | 984.966i | 0.0276313 | − | 0.0478587i | −0.851879 | − | 0.523738i | \(-0.824537\pi\) |
0.879510 | + | 0.475880i | \(0.157870\pi\) | |||||||
\(752\) | −367.949 | − | 637.306i | −0.0178427 | − | 0.0309044i | ||||
\(753\) | 406.538 | + | 14632.0i | 0.0196747 | + | 0.708128i | ||||
\(754\) | −38047.2 | − | 21966.6i | −1.83766 | − | 1.06097i | ||||
\(755\) | −2888.51 | −0.139236 | ||||||||
\(756\) | 1777.95 | + | 17247.1i | 0.0855338 | + | 0.829722i | ||||
\(757\) | −24998.2 | −1.20023 | −0.600117 | − | 0.799912i | \(-0.704879\pi\) | ||||
−0.600117 | + | 0.799912i | \(0.704879\pi\) | |||||||
\(758\) | 20618.8 | + | 11904.2i | 0.988004 | + | 0.570424i | ||||
\(759\) | 405.163 | + | 14582.6i | 0.0193762 | + | 0.697383i | ||||
\(760\) | −2013.73 | − | 3487.88i | −0.0961125 | − | 0.166472i | ||||
\(761\) | −16387.5 | + | 28383.9i | −0.780611 | + | 1.35206i | 0.150976 | + | 0.988537i | \(0.451758\pi\) |
−0.931586 | + | 0.363520i | \(0.881575\pi\) | |||||||
\(762\) | 4121.30 | − | 7619.49i | 0.195931 | − | 0.362238i | ||||
\(763\) | −14430.2 | + | 279.888i | −0.684676 | + | 0.0132800i | ||||
\(764\) | − | 6414.14i | − | 0.303737i | ||||||
\(765\) | −2966.09 | + | 164.948i | −0.140182 | + | 0.00779568i | ||||
\(766\) | −22457.5 | + | 12965.9i | −1.05930 | + | 0.611587i | ||||
\(767\) | −18316.9 | + | 10575.3i | −0.862301 | + | 0.497850i | ||||
\(768\) | −22578.4 | + | 13885.7i | −1.06084 | + | 0.652417i | ||||
\(769\) | − | 15999.0i | − | 0.750244i | −0.926976 | − | 0.375122i | \(-0.877601\pi\) | ||
0.926976 | − | 0.375122i | \(-0.122399\pi\) | |||||||
\(770\) | −2741.19 | − | 4542.12i | −0.128293 | − | 0.212580i | ||||
\(771\) | 14474.3 | + | 7829.03i | 0.676110 | + | 0.365701i | ||||
\(772\) | 3942.58 | − | 6828.75i | 0.183804 | − | 0.318357i | ||||
\(773\) | 2048.20 | + | 3547.59i | 0.0953024 | + | 0.165069i | 0.909735 | − | 0.415190i | \(-0.136285\pi\) |
−0.814432 | + | 0.580259i | \(0.802952\pi\) | |||||||
\(774\) | 5577.44 | + | 2819.44i | 0.259014 | + | 0.130934i | ||||
\(775\) | −1602.46 | − | 925.181i | −0.0742736 | − | 0.0428819i | ||||
\(776\) | −5246.77 | −0.242716 | ||||||||
\(777\) | 29635.7 | − | 19027.7i | 1.36831 | − | 0.878528i | ||||
\(778\) | −30178.6 | −1.39069 | ||||||||
\(779\) | −23188.5 | − | 13387.9i | −1.06651 | − | 0.615751i | ||||
\(780\) | 11067.7 | − | 307.505i | 0.508059 | − | 0.0141159i | ||||
\(781\) | 4210.93 | + | 7293.54i | 0.192931 | + | 0.334166i | ||||
\(782\) | 7911.25 | − | 13702.7i | 0.361772 | − | 0.626607i | ||||
\(783\) | −25108.2 | + | 2097.15i | −1.14597 | + | 0.0957163i | ||||
\(784\) | −24970.6 | + | 969.023i | −1.13751 | + | 0.0441428i | ||||
\(785\) | 7093.43i | 0.322516i | ||||||||
\(786\) | 354.010 | + | 575.626i | 0.0160650 | + | 0.0261220i | ||||
\(787\) | 36383.7 | − | 21006.2i | 1.64795 | − | 0.951447i | 0.670071 | − | 0.742297i | \(-0.266264\pi\) |
0.977884 | − | 0.209149i | \(-0.0670695\pi\) | |||||||
\(788\) | 21540.4 | − | 12436.4i | 0.973789 | − | 0.562218i | ||||
\(789\) | −13456.2 | − | 21880.1i | −0.607167 | − | 0.987264i | ||||
\(790\) | − | 3370.97i | − | 0.151815i | ||||||
\(791\) | −7939.70 | − | 4380.93i | −0.356894 | − | 0.196925i | ||||
\(792\) | 1123.49 | + | 1717.99i | 0.0504061 | + | 0.0770784i | ||||
\(793\) | 573.734 | − | 993.737i | 0.0256922 | − | 0.0445002i | ||||
\(794\) | −14615.9 | − | 25315.5i | −0.653273 | − | 1.13150i | ||||
\(795\) | −14022.5 | + | 389.602i | −0.625568 | + | 0.0173808i | ||||
\(796\) | −14877.9 | − | 8589.75i | −0.662478 | − | 0.382482i | ||||
\(797\) | 5478.00 | 0.243464 | 0.121732 | − | 0.992563i | \(-0.461155\pi\) | ||||
0.121732 | + | 0.992563i | \(0.461155\pi\) | |||||||
\(798\) | −2754.31 | − | 58347.2i | −0.122182 | − | 2.58831i | ||||
\(799\) | 222.268 | 0.00984140 | ||||||||
\(800\) | −5161.69 | − | 2980.10i | −0.228116 | − | 0.131703i | ||||
\(801\) | 9473.50 | − | 18740.5i | 0.417890 | − | 0.826671i | ||||
\(802\) | −29544.1 | − | 51171.8i | −1.30079 | − | 2.25304i | ||||
\(803\) | 4534.89 | − | 7854.66i | 0.199294 | − | 0.345187i | ||||
\(804\) | −6811.18 | − | 3684.10i | −0.298771 | − | 0.161602i | ||||
\(805\) | 337.087 | + | 17379.2i | 0.0147587 | + | 0.760916i | ||||
\(806\) | 18106.3i | 0.791273i | ||||||||
\(807\) | 23785.7 | − | 14628.2i | 1.03754 | − | 0.638089i | ||||
\(808\) | −145.530 | + | 84.0219i | −0.00633631 | + | 0.00365827i | ||||
\(809\) | 6862.81 | − | 3962.25i | 0.298249 | − | 0.172194i | −0.343407 | − | 0.939187i | \(-0.611581\pi\) |
0.641656 | + | 0.766992i | \(0.278248\pi\) | |||||||
\(810\) | 11243.1 | − | 8278.81i | 0.487705 | − | 0.359121i | ||||
\(811\) | 17180.9i | 0.743899i | 0.928253 | + | 0.371949i | \(0.121311\pi\) | ||||
−0.928253 | + | 0.371949i | \(0.878689\pi\) | |||||||
\(812\) | 430.403 | + | 22190.3i | 0.0186012 | + | 0.959024i | ||||
\(813\) | 10871.0 | − | 20098.4i | 0.468958 | − | 0.867012i | ||||
\(814\) | −10483.2 | + | 18157.4i | −0.451395 | + | 0.781839i | ||||
\(815\) | −5303.01 | − | 9185.08i | −0.227922 | − | 0.394772i | ||||
\(816\) | −231.363 | − | 8327.16i | −0.00992563 | − | 0.357241i | ||||
\(817\) | −8292.27 | − | 4787.55i | −0.355092 | − | 0.205012i | ||||
\(818\) | 696.327 | 0.0297635 | ||||||||
\(819\) | −28774.3 | − | 13851.7i | −1.22766 | − | 0.590988i | ||||
\(820\) | −5637.85 | −0.240100 | ||||||||
\(821\) | 14693.9 | + | 8483.55i | 0.624631 | + | 0.360631i | 0.778670 | − | 0.627434i | \(-0.215895\pi\) |
−0.154039 | + | 0.988065i | \(0.549228\pi\) | |||||||
\(822\) | 1737.04 | + | 62519.3i | 0.0737060 | + | 2.65281i | ||||
\(823\) | −12711.3 | − | 22016.6i | −0.538381 | − | 0.932504i | −0.998991 | − | 0.0449014i | \(-0.985703\pi\) |
0.460610 | − | 0.887603i | \(-0.347631\pi\) | |||||||
\(824\) | −2391.34 | + | 4141.93i | −0.101100 | + | 0.175110i | ||||
\(825\) | −924.336 | + | 1708.92i | −0.0390076 | + | 0.0721174i | ||||
\(826\) | 20571.2 | + | 11350.7i | 0.866541 | + | 0.478136i | ||||
\(827\) | 1688.52i | 0.0709984i | 0.999370 | + | 0.0354992i | \(0.0113021\pi\) | ||||
−0.999370 | + | 0.0354992i | \(0.988698\pi\) | |||||||
\(828\) | 1877.88 | + | 33768.1i | 0.0788175 | + | 1.41730i | ||||
\(829\) | 2085.14 | − | 1203.86i | 0.0873582 | − | 0.0504363i | −0.455685 | − | 0.890141i | \(-0.650605\pi\) |
0.543043 | + | 0.839705i | \(0.317272\pi\) | |||||||
\(830\) | 10532.7 | − | 6081.04i | 0.440475 | − | 0.254308i | ||||
\(831\) | 12274.1 | − | 7548.60i | 0.512377 | − | 0.315112i | ||||
\(832\) | 21099.7i | 0.879206i | ||||||||
\(833\) | 3517.55 | − | 6677.94i | 0.146310 | − | 0.277763i | ||||
\(834\) | 42013.4 | + | 22724.6i | 1.74437 | + | 0.943513i | ||||
\(835\) | −5745.69 | + | 9951.83i | −0.238129 | + | 0.412452i | ||||
\(836\) | 7907.31 | + | 13695.9i | 0.327129 | + | 0.566604i | ||||
\(837\) | 5922.46 | + | 8529.40i | 0.244576 | + | 0.352233i | ||||
\(838\) | 24812.4 | + | 14325.4i | 1.02283 | + | 0.590530i | ||||
\(839\) | −12915.1 | −0.531442 | −0.265721 | − | 0.964050i | \(-0.585610\pi\) | ||||
−0.265721 | + | 0.964050i | \(0.585610\pi\) | |||||||
\(840\) | 1321.48 | + | 2058.21i | 0.0542804 | + | 0.0845418i | ||||
\(841\) | −7863.23 | −0.322409 | ||||||||
\(842\) | −30086.8 | − | 17370.6i | −1.23142 | − | 0.710962i | ||||
\(843\) | −13706.4 | + | 380.820i | −0.559992 | + | 0.0155589i | ||||
\(844\) | −4371.00 | − | 7570.79i | −0.178265 | − | 0.308765i | ||||
\(845\) | −4703.89 | + | 8147.38i | −0.191501 | + | 0.331690i | ||||
\(846\) | −874.311 | + | 571.763i | −0.0355312 | + | 0.0232359i | ||||
\(847\) | 10596.3 | + | 17558.0i | 0.429862 | + | 0.712277i | ||||
\(848\) | − | 39337.1i | − | 1.59297i | ||||||
\(849\) | 20631.4 | + | 33547.0i | 0.834002 | + | 1.35610i | ||||
\(850\) | 1824.95 | − | 1053.63i | 0.0736415 | − | 0.0425169i | ||||
\(851\) | 59492.9 | − | 34348.3i | 2.39646 | − | 1.38360i | ||||
\(852\) | 10228.2 | + | 16631.2i | 0.411281 | + | 0.668750i | ||||
\(853\) | 16815.4i | 0.674968i | 0.941331 | + | 0.337484i | \(0.109576\pi\) | ||||
−0.941331 | + | 0.337484i | \(0.890424\pi\) | |||||||
\(854\) | −1274.42 | + | 24.7186i | −0.0510652 | + | 0.000990461i | ||||
\(855\) | −17903.5 | + | 11708.1i | −0.716123 | + | 0.468315i | ||||
\(856\) | −1100.21 | + | 1905.62i | −0.0439304 | + | 0.0760897i | ||||
\(857\) | −11067.3 | − | 19169.2i | −0.441135 | − | 0.764069i | 0.556639 | − | 0.830755i | \(-0.312091\pi\) |
−0.997774 | + | 0.0666857i | \(0.978758\pi\) | |||||||
\(858\) | 19004.3 | − | 528.016i | 0.756171 | − | 0.0210095i | ||||
\(859\) | 27724.8 | + | 16006.9i | 1.10123 | + | 0.635798i | 0.936545 | − | 0.350548i | \(-0.114005\pi\) |
0.164689 | + | 0.986346i | \(0.447338\pi\) | |||||||
\(860\) | −2016.12 | −0.0799407 | ||||||||
\(861\) | 14450.4 | + | 7457.55i | 0.571972 | + | 0.295183i | ||||
\(862\) | 32105.0 | 1.26856 | ||||||||
\(863\) | 3035.49 | + | 1752.54i | 0.119733 | + | 0.0691277i | 0.558670 | − | 0.829390i | \(-0.311312\pi\) |
−0.438938 | + | 0.898518i | \(0.644645\pi\) | |||||||
\(864\) | 19076.9 | + | 27474.1i | 0.751166 | + | 1.08181i | ||||
\(865\) | −3011.75 | − | 5216.51i | −0.118385 | − | 0.205048i | ||||
\(866\) | 10803.4 | − | 18712.0i | 0.423918 | − | 0.734248i | ||||
\(867\) | −20241.4 | − | 10948.4i | −0.792888 | − | 0.428865i | ||||
\(868\) | 7831.41 | − | 4726.29i | 0.306239 | − | 0.184817i | ||||
\(869\) | − | 2632.40i | − | 0.102759i | ||||||
\(870\) | 15224.1 | − | 9362.79i | 0.593269 | − | 0.364860i | ||||
\(871\) | 12351.8 | − | 7131.34i | 0.480512 | − | 0.277424i | ||||
\(872\) | −3430.69 | + | 1980.71i | −0.133232 | + | 0.0769213i | ||||
\(873\) | 1547.40 | + | 27825.3i | 0.0599902 | + | 1.07875i | ||||
\(874\) | − | 113938.i | − | 4.40963i | ||||||
\(875\) | −1118.42 | + | 2026.95i | −0.0432108 | + | 0.0783124i | ||||
\(876\) | 10003.6 | − | 18494.7i | 0.385832 | − | 0.713329i | ||||
\(877\) | −22418.6 | + | 38830.1i | −0.863194 | + | 1.49510i | 0.00563608 | + | 0.999984i | \(0.498206\pi\) |
−0.868830 | + | 0.495111i | \(0.835127\pi\) | |||||||
\(878\) | 4042.95 | + | 7002.59i | 0.155402 | + | 0.269164i | ||||
\(879\) | −16.8054 | − | 604.856i | −0.000644859 | − | 0.0232096i | ||||
\(880\) | −4718.31 | − | 2724.12i | −0.180744 | − | 0.104352i | ||||
\(881\) | −34786.1 | −1.33028 | −0.665138 | − | 0.746720i | \(-0.731627\pi\) | ||||
−0.665138 | + | 0.746720i | \(0.731627\pi\) | |||||||
\(882\) | 3341.74 | + | 35316.8i | 0.127576 | + | 1.34827i | ||||
\(883\) | 41449.1 | 1.57970 | 0.789848 | − | 0.613302i | \(-0.210159\pi\) | ||||
0.789848 | + | 0.613302i | \(0.210159\pi\) | |||||||
\(884\) | −8121.26 | − | 4688.81i | −0.308990 | − | 0.178396i | ||||
\(885\) | −238.973 | − | 8601.07i | −0.00907682 | − | 0.326691i | ||||
\(886\) | −1826.74 | − | 3164.01i | −0.0692671 | − | 0.119974i | ||||
\(887\) | −5361.62 | + | 9286.60i | −0.202960 | + | 0.351537i | −0.949481 | − | 0.313825i | \(-0.898389\pi\) |
0.746521 | + | 0.665362i | \(0.231723\pi\) | |||||||
\(888\) | 4598.85 | − | 8502.39i | 0.173792 | − | 0.321308i | ||||
\(889\) | 3894.09 | − | 7057.37i | 0.146910 | − | 0.266251i | ||||
\(890\) | 14895.7i | 0.561018i | ||||||||
\(891\) | 8779.72 | − | 6464.93i | 0.330114 | − | 0.243079i | ||||
\(892\) | 8579.35 | − | 4953.29i | 0.322038 | − | 0.185929i | ||||
\(893\) | 1386.12 | − | 800.279i | 0.0519428 | − | 0.0299892i | ||||
\(894\) | −13462.2 | + | 8279.24i | −0.503628 | + | 0.309731i | ||||
\(895\) | 5525.03i | 0.206348i | ||||||||
\(896\) | −10175.2 | + | 6140.78i | −0.379386 | + | 0.228961i | ||||
\(897\) | −54790.4 | − | 29635.6i | −2.03946 | − | 1.10312i | ||||
\(898\) | −7021.56 | + | 12161.7i | −0.260927 | + | 0.451939i | ||||
\(899\) | 6646.09 | + | 11511.4i | 0.246562 | + | 0.427059i | ||||
\(900\) | −2032.06 | + | 4019.82i | −0.0752613 | + | 0.148882i | ||||
\(901\) | 10289.5 | + | 5940.63i | 0.380457 | + | 0.219657i | ||||
\(902\) | −9680.76 | −0.357355 | ||||||||
\(903\) | 5167.51 | + | 2666.85i | 0.190436 | + | 0.0982803i | ||||
\(904\) | −2488.95 | −0.0915722 | ||||||||
\(905\) | −12659.1 | − | 7308.74i | −0.464975 | − | 0.268454i | ||||
\(906\) | −11494.1 | + | 319.354i | −0.421487 | + | 0.0117106i | ||||
\(907\) | 18339.4 | + | 31764.8i | 0.671389 | + | 1.16288i | 0.977510 | + | 0.210887i | \(0.0676353\pi\) |
−0.306122 | + | 0.951992i | \(0.599031\pi\) | |||||||
\(908\) | −9260.61 | + | 16039.9i | −0.338463 | + | 0.586235i | ||||
\(909\) | 488.516 | + | 747.015i | 0.0178252 | + | 0.0272573i | ||||
\(910\) | 22648.9 | − | 439.298i | 0.825060 | − | 0.0160029i | ||||
\(911\) | − | 13062.2i | − | 0.475051i | −0.971381 | − | 0.237525i | \(-0.923664\pi\) | ||
0.971381 | − | 0.237525i | \(-0.0763363\pi\) | |||||||
\(912\) | −31424.9 | − | 51097.4i | −1.14099 | − | 1.85527i | ||||
\(913\) | 8224.97 | − | 4748.69i | 0.298146 | − | 0.172134i | ||||
\(914\) | −28616.9 | + | 16521.9i | −1.03563 | + | 0.597918i | ||||
\(915\) | 244.543 | + | 397.630i | 0.00883533 | + | 0.0143664i | ||||
\(916\) | − | 25111.0i | − | 0.905775i | ||||||
\(917\) | 324.897 | + | 538.351i | 0.0117002 | + | 0.0193870i | ||||
\(918\) | −11784.6 | + | 984.303i | −0.423694 | + | 0.0353887i | ||||
\(919\) | −19593.8 | + | 33937.5i | −0.703309 | + | 1.21817i | 0.263990 | + | 0.964525i | \(0.414961\pi\) |
−0.967299 | + | 0.253641i | \(0.918372\pi\) | |||||||
\(920\) | 2385.50 | + | 4131.81i | 0.0854866 | + | 0.148067i | ||||
\(921\) | −40958.1 | + | 1137.98i | −1.46538 | + | 0.0407143i | ||||
\(922\) | 23849.3 | + | 13769.4i | 0.851880 | + | 0.491833i | ||||
\(923\) | −35961.4 | −1.28243 | ||||||||
\(924\) | −5189.08 | − | 8082.00i | −0.184749 | − | 0.287747i | ||||
\(925\) | 9149.13 | 0.325213 | ||||||||
\(926\) | −7571.52 | − | 4371.42i | −0.268699 | − | 0.155134i | ||||
\(927\) | 22671.3 | + | 11460.5i | 0.803260 | + | 0.406055i | ||||
\(928\) | 21407.7 | + | 37079.3i | 0.757267 | + | 1.31162i | ||||
\(929\) | 15873.1 | − | 27493.1i | 0.560582 | − | 0.970956i | −0.436864 | − | 0.899528i | \(-0.643911\pi\) |
0.997446 | − | 0.0714285i | \(-0.0227558\pi\) | |||||||
\(930\) | −6478.91 | − | 3504.37i | −0.228443 | − | 0.123562i | ||||
\(931\) | −2107.60 | − | 54310.4i | −0.0741932 | − | 1.91187i | ||||
\(932\) | − | 24133.5i | − | 0.848195i | ||||||
\(933\) | 43613.0 | − | 26822.0i | 1.53036 | − | 0.941170i | ||||
\(934\) | 21420.5 | − | 12367.1i | 0.750427 | − | 0.433259i | ||||
\(935\) | 1425.10 | − | 822.785i | 0.0498459 | − | 0.0287785i | ||||
\(936\) | −8751.67 | + | 486.690i | −0.305617 | + | 0.0169957i | ||||
\(937\) | 16884.3i | 0.588674i | 0.955702 | + | 0.294337i | \(0.0950988\pi\) | ||||
−0.955702 | + | 0.294337i | \(0.904901\pi\) | |||||||
\(938\) | −13872.0 | − | 7654.23i | −0.482875 | − | 0.266439i | ||||
\(939\) | 11939.3 | − | 22073.5i | 0.414936 | − | 0.767137i | ||||
\(940\) | 168.505 | − | 291.860i | 0.00584685 | − | 0.0101270i | ||||
\(941\) | −22301.8 | − | 38627.9i | −0.772603 | − | 1.33819i | −0.936132 | − | 0.351649i | \(-0.885621\pi\) |
0.163529 | − | 0.986539i | \(-0.447712\pi\) | |||||||
\(942\) | 784.252 | + | 28226.6i | 0.0271256 | + | 0.976299i | ||||
\(943\) | 27469.5 | + | 15859.5i | 0.948601 | + | 0.547675i | ||||
\(944\) | 24128.5 | 0.831901 | ||||||||
\(945\) | 10525.6 | − | 7615.29i | 0.362327 | − | 0.262143i | ||||
\(946\) | −3461.87 | −0.118980 | ||||||||
\(947\) | 47658.4 | + | 27515.6i | 1.63537 | + | 0.944179i | 0.982400 | + | 0.186791i | \(0.0598088\pi\) |
0.652966 | + | 0.757387i | \(0.273524\pi\) | |||||||
\(948\) | −169.494 | − | 6100.41i | −0.00580688 | − | 0.209000i | ||||
\(949\) | 19364.0 | + | 33539.4i | 0.662362 | + | 1.14725i | ||||
\(950\) | 7587.25 | − | 13141.5i | 0.259119 | − | 0.448807i | ||||
\(951\) | 4260.37 | − | 7876.59i | 0.145270 | − | 0.268576i | ||||
\(952\) | −40.1739 | − | 2071.24i | −0.00136769 | − | 0.0705141i | ||||
\(953\) | 44397.5i | 1.50910i | 0.656240 | + | 0.754552i | \(0.272146\pi\) | ||||
−0.656240 | + | 0.754552i | \(0.727854\pi\) | |||||||
\(954\) | −55756.2 | + | 3100.66i | −1.89222 | + | 0.105228i | ||||
\(955\) | −4162.18 | + | 2403.03i | −0.141031 | + | 0.0814245i | ||||
\(956\) | −27251.2 | + | 15733.5i | −0.921932 | + | 0.532278i | ||||
\(957\) | 11888.5 | − | 7311.42i | 0.401568 | − | 0.246964i | ||||
\(958\) | − | 52721.3i | − | 1.77803i | ||||||
\(959\) | 1128.54 | + | 58184.4i | 0.0380006 | + | 1.95920i | ||||
\(960\) | −7550.03 | − | 4083.73i | −0.253829 | − | 0.137294i | ||||
\(961\) | −12156.4 | + | 21055.6i | −0.408057 | + | 0.706776i | ||||
\(962\) | −44763.3 | − | 77532.3i | −1.50023 | − | 2.59848i | ||||
\(963\) | 10430.6 | + | 5272.77i | 0.349036 | + | 0.176441i | ||||
\(964\) | 42245.7 | + | 24390.6i | 1.41145 | + | 0.814903i | ||||
\(965\) | −5908.30 | −0.197093 | ||||||||
\(966\) | 3262.81 | + | 69119.3i | 0.108674 | + | 2.30215i | ||||
\(967\) | −42649.0 | −1.41830 | −0.709151 | − | 0.705057i | \(-0.750922\pi\) | ||||
−0.709151 | + | 0.705057i | \(0.750922\pi\) | |||||||
\(968\) | 4874.66 | + | 2814.38i | 0.161857 | + | 0.0934481i | ||||
\(969\) | 18111.4 | − | 503.208i | 0.600435 | − | 0.0166825i | ||||
\(970\) | −9884.30 | − | 17120.1i | −0.327181 | − | 0.566694i | ||||
\(971\) | 6546.89 | − | 11339.6i | 0.216375 | − | 0.374772i | −0.737322 | − | 0.675541i | \(-0.763910\pi\) |
0.953697 | + | 0.300769i | \(0.0972434\pi\) | |||||||
\(972\) | 19930.2 | − | 15547.4i | 0.657676 | − | 0.513048i | ||||
\(973\) | 38914.0 | + | 21471.8i | 1.28214 | + | 0.707454i | ||||
\(974\) | − | 25402.2i | − | 0.835668i | ||||||
\(975\) | −4346.00 | − | 7066.67i | −0.142752 | − | 0.232118i | ||||
\(976\) | −1133.65 | + | 654.514i | −0.0371796 | + | 0.0214657i | ||||
\(977\) | 13101.1 | − | 7563.95i | 0.429010 | − | 0.247689i | −0.269915 | − | 0.962884i | \(-0.586996\pi\) |
0.698925 | + | 0.715195i | \(0.253662\pi\) | |||||||
\(978\) | −22117.6 | − | 35963.6i | −0.723152 | − | 1.17586i | ||||
\(979\) | 11632.1i | 0.379738i | ||||||||
\(980\) | −6102.07 | − | 9681.55i | −0.198902 | − | 0.315577i | ||||
\(981\) | 11516.2 | + | 17609.9i | 0.374804 | + | 0.573131i | ||||
\(982\) | −3540.50 | + | 6132.33i | −0.115053 | + | 0.199277i | ||||
\(983\) | −9102.04 | − | 15765.2i | −0.295330 | − | 0.511527i | 0.679731 | − | 0.733461i | \(-0.262096\pi\) |
−0.975062 | + | 0.221934i | \(0.928763\pi\) | |||||||
\(984\) | 4461.54 | − | 123.960i | 0.144541 | − | 0.00401595i | ||||
\(985\) | −16140.1 | − | 9318.49i | −0.522098 | − | 0.301433i | ||||
\(986\) | −15137.7 | −0.488928 | ||||||||
\(987\) | −817.959 | + | 525.174i | −0.0263788 | + | 0.0169367i | ||||
\(988\) | −67528.5 | −2.17446 | ||||||||
\(989\) | 9823.20 | + | 5671.43i | 0.315834 | + | 0.182347i | ||||
\(990\) | −3489.24 | + | 6902.43i | −0.112016 | + | 0.221590i | ||||
\(991\) | −22984.4 | − | 39810.1i | −0.736754 | − | 1.27610i | −0.953950 | − | 0.299967i | \(-0.903024\pi\) |
0.217196 | − | 0.976128i | \(-0.430309\pi\) | |||||||
\(992\) | 8822.83 | − | 15281.6i | 0.282384 | − | 0.489104i | ||||
\(993\) | 27037.0 | + | 14624.0i | 0.864042 | + | 0.467351i | ||||
\(994\) | 20640.9 | + | 34201.7i | 0.658640 | + | 1.09136i | ||||
\(995\) | 12872.5i | 0.410136i | ||||||||
\(996\) | 18755.1 | − | 11534.4i | 0.596664 | − | 0.366948i | ||||
\(997\) | 23332.0 | − | 13470.8i | 0.741156 | − | 0.427907i | −0.0813334 | − | 0.996687i | \(-0.525918\pi\) |
0.822490 | + | 0.568780i | \(0.192585\pi\) | |||||||
\(998\) | 42822.7 | − | 24723.7i | 1.35825 | − | 0.784184i | ||||
\(999\) | −46447.3 | − | 21881.7i | −1.47100 | − | 0.692998i |
(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 | 105.4.s.b.26.14 | yes | 32 | |
3.2 | odd | 2 | 105.4.s.a.26.3 | ✓ | 32 | ||
7.3 | odd | 6 | 105.4.s.a.101.3 | yes | 32 | ||
21.17 | even | 6 | inner | 105.4.s.b.101.14 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.s.a.26.3 | ✓ | 32 | 3.2 | odd | 2 | ||
105.4.s.a.101.3 | yes | 32 | 7.3 | odd | 6 | ||
105.4.s.b.26.14 | yes | 32 | 1.1 | even | 1 | trivial | |
105.4.s.b.101.14 | yes | 32 | 21.17 | even | 6 | inner |