Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,4,Mod(16,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.e (of order \(3\), 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: | \(2.65508595026\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(-1.52087 + 2.63422i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.31 |
Dual form | 45.4.e.c.16.2 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.52087 | − | 2.63422i | −0.537709 | − | 0.931339i | −0.999027 | − | 0.0441043i | \(-0.985957\pi\) |
0.461318 | − | 0.887235i | \(-0.347377\pi\) | |||||||
\(3\) | 4.01867 | − | 3.29398i | 0.773393 | − | 0.633927i | ||||
\(4\) | −0.626094 | + | 1.08443i | −0.0782617 | + | 0.135553i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | −14.7890 | − | 5.57636i | −1.00626 | − | 0.379423i | ||||
\(7\) | 6.85611 | + | 11.8751i | 0.370195 | + | 0.641197i | 0.989595 | − | 0.143879i | \(-0.0459575\pi\) |
−0.619400 | + | 0.785075i | \(0.712624\pi\) | |||||||
\(8\) | −20.5251 | −0.907090 | ||||||||
\(9\) | 5.29939 | − | 26.4748i | 0.196274 | − | 0.980549i | ||||
\(10\) | −15.2087 | −0.480941 | ||||||||
\(11\) | −15.9034 | − | 27.5455i | −0.435914 | − | 0.755026i | 0.561455 | − | 0.827507i | \(-0.310242\pi\) |
−0.997370 | + | 0.0724812i | \(0.976908\pi\) | |||||||
\(12\) | 1.05602 | + | 6.42029i | 0.0254038 | + | 0.154448i | ||||
\(13\) | −29.1216 | + | 50.4401i | −0.621298 | + | 1.07612i | 0.367946 | + | 0.929847i | \(0.380061\pi\) |
−0.989244 | + | 0.146272i | \(0.953272\pi\) | |||||||
\(14\) | 20.8545 | − | 36.1211i | 0.398115 | − | 0.689555i | ||||
\(15\) | −4.21668 | − | 25.6363i | −0.0725828 | − | 0.441284i | ||||
\(16\) | 36.2248 | + | 62.7431i | 0.566012 | + | 0.980361i | ||||
\(17\) | 109.055 | 1.55586 | 0.777932 | − | 0.628348i | \(-0.216269\pi\) | ||||
0.777932 | + | 0.628348i | \(0.216269\pi\) | |||||||
\(18\) | −77.8003 | + | 26.3050i | −1.01876 | + | 0.344453i | ||||
\(19\) | 129.695 | 1.56601 | 0.783004 | − | 0.622017i | \(-0.213687\pi\) | ||||
0.783004 | + | 0.622017i | \(0.213687\pi\) | |||||||
\(20\) | 3.13047 | + | 5.42213i | 0.0349997 | + | 0.0606213i | ||||
\(21\) | 66.6689 | + | 25.1383i | 0.692778 | + | 0.261221i | ||||
\(22\) | −48.3740 | + | 83.7863i | −0.468790 | + | 0.811968i | ||||
\(23\) | −39.8342 | + | 68.9949i | −0.361131 | + | 0.625497i | −0.988147 | − | 0.153509i | \(-0.950943\pi\) |
0.627017 | + | 0.779006i | \(0.284276\pi\) | |||||||
\(24\) | −82.4836 | + | 67.6093i | −0.701537 | + | 0.575028i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 177.161 | 1.33631 | ||||||||
\(27\) | −65.9111 | − | 123.850i | −0.469800 | − | 0.882773i | ||||
\(28\) | −17.1703 | −0.115888 | ||||||||
\(29\) | −4.51769 | − | 7.82486i | −0.0289280 | − | 0.0501048i | 0.851199 | − | 0.524843i | \(-0.175876\pi\) |
−0.880127 | + | 0.474738i | \(0.842543\pi\) | |||||||
\(30\) | −61.1187 | + | 50.0972i | −0.371957 | + | 0.304882i | ||||
\(31\) | 16.6904 | − | 28.9087i | 0.0966998 | − | 0.167489i | −0.813617 | − | 0.581401i | \(-0.802505\pi\) |
0.910317 | + | 0.413912i | \(0.135838\pi\) | |||||||
\(32\) | 28.0860 | − | 48.6463i | 0.155154 | − | 0.268735i | ||||
\(33\) | −154.645 | − | 58.3108i | −0.815764 | − | 0.307594i | ||||
\(34\) | −165.858 | − | 287.275i | −0.836602 | − | 1.44904i | ||||
\(35\) | 68.5611 | 0.331113 | ||||||||
\(36\) | 25.3921 | + | 22.3225i | 0.117556 | + | 0.103345i | ||||
\(37\) | −22.1645 | −0.0984817 | −0.0492408 | − | 0.998787i | \(-0.515680\pi\) | ||||
−0.0492408 | + | 0.998787i | \(0.515680\pi\) | |||||||
\(38\) | −197.250 | − | 341.647i | −0.842056 | − | 1.45848i | ||||
\(39\) | 49.1186 | + | 298.628i | 0.201673 | + | 1.22612i | ||||
\(40\) | −51.3127 | + | 88.8763i | −0.202831 | + | 0.351314i | ||||
\(41\) | −60.8698 | + | 105.430i | −0.231860 | + | 0.401593i | −0.958356 | − | 0.285578i | \(-0.907814\pi\) |
0.726495 | + | 0.687171i | \(0.241148\pi\) | |||||||
\(42\) | −35.1747 | − | 213.853i | −0.129228 | − | 0.785672i | ||||
\(43\) | −5.07086 | − | 8.78298i | −0.0179837 | − | 0.0311487i | 0.856894 | − | 0.515493i | \(-0.172391\pi\) |
−0.874877 | + | 0.484345i | \(0.839058\pi\) | |||||||
\(44\) | 39.8281 | 0.136462 | ||||||||
\(45\) | −101.391 | − | 89.1341i | −0.335877 | − | 0.295274i | ||||
\(46\) | 242.331 | 0.776733 | ||||||||
\(47\) | 220.746 | + | 382.343i | 0.685088 | + | 1.18661i | 0.973409 | + | 0.229073i | \(0.0735695\pi\) |
−0.288321 | + | 0.957534i | \(0.593097\pi\) | |||||||
\(48\) | 352.250 | + | 132.820i | 1.05923 | + | 0.399395i | ||||
\(49\) | 77.4875 | − | 134.212i | 0.225911 | − | 0.391289i | ||||
\(50\) | −38.0218 | + | 65.8556i | −0.107542 | + | 0.186268i | ||||
\(51\) | 438.255 | − | 359.225i | 1.20329 | − | 0.986304i | ||||
\(52\) | −36.4657 | − | 63.1604i | −0.0972477 | − | 0.168438i | ||||
\(53\) | −593.610 | −1.53846 | −0.769232 | − | 0.638969i | \(-0.779361\pi\) | ||||
−0.769232 | + | 0.638969i | \(0.779361\pi\) | |||||||
\(54\) | −226.006 | + | 361.984i | −0.569546 | + | 0.912218i | ||||
\(55\) | −159.034 | −0.389894 | ||||||||
\(56\) | −140.722 | − | 243.738i | −0.335800 | − | 0.581623i | ||||
\(57\) | 521.202 | − | 427.214i | 1.21114 | − | 0.992734i | ||||
\(58\) | −13.7416 | + | 23.8012i | −0.0311097 | + | 0.0538836i | ||||
\(59\) | −221.230 | + | 383.182i | −0.488164 | + | 0.845525i | −0.999907 | − | 0.0136133i | \(-0.995667\pi\) |
0.511743 | + | 0.859139i | \(0.329000\pi\) | |||||||
\(60\) | 30.4407 | + | 11.4780i | 0.0654980 | + | 0.0246968i | ||||
\(61\) | −72.2881 | − | 125.207i | −0.151730 | − | 0.262804i | 0.780133 | − | 0.625613i | \(-0.215151\pi\) |
−0.931864 | + | 0.362809i | \(0.881818\pi\) | |||||||
\(62\) | −101.536 | −0.207985 | ||||||||
\(63\) | 350.725 | − | 118.583i | 0.701385 | − | 0.237145i | ||||
\(64\) | 408.736 | 0.798312 | ||||||||
\(65\) | 145.608 | + | 252.200i | 0.277853 | + | 0.481255i | ||||
\(66\) | 81.5912 | + | 496.052i | 0.152169 | + | 0.925149i | ||||
\(67\) | −431.360 | + | 747.138i | −0.786553 | + | 1.36235i | 0.141514 | + | 0.989936i | \(0.454803\pi\) |
−0.928067 | + | 0.372414i | \(0.878530\pi\) | |||||||
\(68\) | −68.2786 | + | 118.262i | −0.121765 | + | 0.210902i | ||||
\(69\) | 67.1873 | + | 408.481i | 0.117223 | + | 0.712685i | ||||
\(70\) | −104.273 | − | 180.605i | −0.178042 | − | 0.308378i | ||||
\(71\) | −818.541 | −1.36821 | −0.684105 | − | 0.729384i | \(-0.739807\pi\) | ||||
−0.684105 | + | 0.729384i | \(0.739807\pi\) | |||||||
\(72\) | −108.771 | + | 543.398i | −0.178038 | + | 0.889446i | ||||
\(73\) | 495.052 | 0.793719 | 0.396859 | − | 0.917879i | \(-0.370100\pi\) | ||||
0.396859 | + | 0.917879i | \(0.370100\pi\) | |||||||
\(74\) | 33.7093 | + | 58.3863i | 0.0529545 | + | 0.0917198i | ||||
\(75\) | −121.550 | − | 45.8320i | −0.187139 | − | 0.0705629i | ||||
\(76\) | −81.2014 | + | 140.645i | −0.122558 | + | 0.212277i | ||||
\(77\) | 218.071 | − | 377.710i | 0.322747 | − | 0.559014i | ||||
\(78\) | 711.950 | − | 583.563i | 1.03349 | − | 0.847122i | ||||
\(79\) | −585.263 | − | 1013.71i | −0.833510 | − | 1.44368i | −0.895238 | − | 0.445588i | \(-0.852995\pi\) |
0.0617284 | − | 0.998093i | \(-0.480339\pi\) | |||||||
\(80\) | 362.248 | 0.506256 | ||||||||
\(81\) | −672.833 | − | 280.601i | −0.922953 | − | 0.384912i | ||||
\(82\) | 370.300 | 0.498693 | ||||||||
\(83\) | 212.022 | + | 367.232i | 0.280390 | + | 0.485651i | 0.971481 | − | 0.237118i | \(-0.0762027\pi\) |
−0.691090 | + | 0.722768i | \(0.742869\pi\) | |||||||
\(84\) | −69.0017 | + | 56.5586i | −0.0896273 | + | 0.0734648i | ||||
\(85\) | 272.637 | − | 472.221i | 0.347902 | − | 0.602584i | ||||
\(86\) | −15.4242 | + | 26.7156i | −0.0193400 | + | 0.0334978i | ||||
\(87\) | −43.9300 | − | 16.5644i | −0.0541355 | − | 0.0204125i | ||||
\(88\) | 326.419 | + | 565.374i | 0.395413 | + | 0.684876i | ||||
\(89\) | 1031.37 | 1.22837 | 0.614183 | − | 0.789163i | \(-0.289486\pi\) | ||||
0.614183 | + | 0.789163i | \(0.289486\pi\) | |||||||
\(90\) | −80.5969 | + | 402.648i | −0.0943962 | + | 0.471587i | ||||
\(91\) | −798.643 | −0.920006 | ||||||||
\(92\) | −49.8799 | − | 86.3945i | −0.0565254 | − | 0.0979049i | ||||
\(93\) | −28.1513 | − | 171.152i | −0.0313888 | − | 0.190835i | ||||
\(94\) | 671.452 | − | 1162.99i | 0.736756 | − | 1.27610i | ||||
\(95\) | 324.238 | − | 561.597i | 0.350170 | − | 0.606512i | ||||
\(96\) | −47.3718 | − | 288.008i | −0.0503632 | − | 0.306195i | ||||
\(97\) | −799.356 | − | 1384.53i | −0.836725 | − | 1.44925i | −0.892618 | − | 0.450814i | \(-0.851134\pi\) |
0.0558930 | − | 0.998437i | \(-0.482199\pi\) | |||||||
\(98\) | −471.394 | −0.485897 | ||||||||
\(99\) | −813.541 | + | 275.066i | −0.825898 | + | 0.279244i | ||||
\(100\) | 31.3047 | 0.0313047 | ||||||||
\(101\) | 107.000 | + | 185.330i | 0.105415 | + | 0.182584i | 0.913908 | − | 0.405922i | \(-0.133050\pi\) |
−0.808493 | + | 0.588506i | \(0.799716\pi\) | |||||||
\(102\) | −1612.81 | − | 608.129i | −1.56561 | − | 0.590331i | ||||
\(103\) | −836.160 | + | 1448.27i | −0.799897 | + | 1.38546i | 0.119786 | + | 0.992800i | \(0.461779\pi\) |
−0.919683 | + | 0.392662i | \(0.871554\pi\) | |||||||
\(104\) | 597.723 | − | 1035.29i | 0.563573 | − | 0.976137i | ||||
\(105\) | 275.524 | − | 225.839i | 0.256080 | − | 0.209901i | ||||
\(106\) | 902.804 | + | 1563.70i | 0.827246 | + | 1.43283i | ||||
\(107\) | −600.699 | −0.542727 | −0.271363 | − | 0.962477i | \(-0.587475\pi\) | ||||
−0.271363 | + | 0.962477i | \(0.587475\pi\) | |||||||
\(108\) | 175.572 | + | 6.06581i | 0.156430 | + | 0.00540447i | ||||
\(109\) | −771.570 | −0.678009 | −0.339005 | − | 0.940785i | \(-0.610090\pi\) | ||||
−0.339005 | + | 0.940785i | \(0.610090\pi\) | |||||||
\(110\) | 241.870 | + | 418.931i | 0.209649 | + | 0.363123i | ||||
\(111\) | −89.0718 | + | 73.0094i | −0.0761650 | + | 0.0624302i | ||||
\(112\) | −496.722 | + | 860.348i | −0.419070 | + | 0.725850i | ||||
\(113\) | 583.338 | − | 1010.37i | 0.485627 | − | 0.841131i | −0.514237 | − | 0.857648i | \(-0.671925\pi\) |
0.999864 | + | 0.0165177i | \(0.00525800\pi\) | |||||||
\(114\) | −1918.06 | − | 723.228i | −1.57581 | − | 0.594180i | ||||
\(115\) | 199.171 | + | 344.974i | 0.161503 | + | 0.279731i | ||||
\(116\) | 11.3140 | 0.00905583 | ||||||||
\(117\) | 1181.06 | + | 1038.29i | 0.933244 | + | 0.820427i | ||||
\(118\) | 1345.85 | 1.04996 | ||||||||
\(119\) | 747.692 | + | 1295.04i | 0.575973 | + | 0.997615i | ||||
\(120\) | 86.5478 | + | 526.187i | 0.0658391 | + | 0.400284i | ||||
\(121\) | 159.663 | − | 276.545i | 0.119957 | − | 0.207772i | ||||
\(122\) | −219.882 | + | 380.846i | −0.163173 | + | 0.282624i | ||||
\(123\) | 102.667 | + | 624.190i | 0.0752618 | + | 0.457572i | ||||
\(124\) | 20.8996 | + | 36.1991i | 0.0151358 | + | 0.0262159i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −845.783 | − | 743.539i | −0.598003 | − | 0.525712i | ||||
\(127\) | 1630.10 | 1.13896 | 0.569479 | − | 0.822006i | \(-0.307145\pi\) | ||||
0.569479 | + | 0.822006i | \(0.307145\pi\) | |||||||
\(128\) | −846.322 | − | 1465.87i | −0.584414 | − | 1.01223i | ||||
\(129\) | −49.3091 | − | 18.5926i | −0.0336544 | − | 0.0126898i | ||||
\(130\) | 442.901 | − | 767.128i | 0.298808 | − | 0.517550i | ||||
\(131\) | −129.412 | + | 224.149i | −0.0863115 | + | 0.149496i | −0.905949 | − | 0.423386i | \(-0.860841\pi\) |
0.819638 | + | 0.572882i | \(0.194175\pi\) | |||||||
\(132\) | 160.056 | − | 131.193i | 0.105538 | − | 0.0865067i | ||||
\(133\) | 889.206 | + | 1540.15i | 0.579729 | + | 1.00412i | ||||
\(134\) | 2624.17 | 1.69175 | ||||||||
\(135\) | −701.062 | − | 24.2208i | −0.446947 | − | 0.0154415i | ||||
\(136\) | −2238.36 | −1.41131 | ||||||||
\(137\) | −526.385 | − | 911.726i | −0.328264 | − | 0.568569i | 0.653904 | − | 0.756578i | \(-0.273130\pi\) |
−0.982167 | + | 0.188009i | \(0.939797\pi\) | |||||||
\(138\) | 973.847 | − | 798.232i | 0.600720 | − | 0.492392i | ||||
\(139\) | −1192.25 | + | 2065.03i | −0.727519 | + | 1.26010i | 0.230410 | + | 0.973094i | \(0.425993\pi\) |
−0.957929 | + | 0.287006i | \(0.907340\pi\) | |||||||
\(140\) | −42.9257 | + | 74.3495i | −0.0259135 | + | 0.0448834i | ||||
\(141\) | 2146.54 | + | 809.378i | 1.28206 | + | 0.483418i | ||||
\(142\) | 1244.89 | + | 2156.22i | 0.735699 | + | 1.27427i | ||||
\(143\) | 1852.53 | 1.08333 | ||||||||
\(144\) | 1853.08 | − | 626.544i | 1.07239 | − | 0.362583i | ||||
\(145\) | −45.1769 | −0.0258740 | ||||||||
\(146\) | −752.910 | − | 1304.08i | −0.426790 | − | 0.739221i | ||||
\(147\) | −130.696 | − | 794.597i | −0.0733308 | − | 0.445831i | ||||
\(148\) | 13.8771 | − | 24.0358i | 0.00770735 | − | 0.0133495i | ||||
\(149\) | −573.144 | + | 992.715i | −0.315126 | + | 0.545815i | −0.979464 | − | 0.201617i | \(-0.935380\pi\) |
0.664338 | + | 0.747432i | \(0.268714\pi\) | |||||||
\(150\) | 64.1303 | + | 389.895i | 0.0349081 | + | 0.212232i | ||||
\(151\) | 583.058 | + | 1009.89i | 0.314229 | + | 0.544261i | 0.979273 | − | 0.202543i | \(-0.0649207\pi\) |
−0.665044 | + | 0.746804i | \(0.731587\pi\) | |||||||
\(152\) | −2662.01 | −1.42051 | ||||||||
\(153\) | 577.924 | − | 2887.21i | 0.305375 | − | 1.52560i | ||||
\(154\) | −1326.63 | −0.694175 | ||||||||
\(155\) | −83.4522 | − | 144.544i | −0.0432454 | − | 0.0749033i | ||||
\(156\) | −354.593 | − | 133.704i | −0.181988 | − | 0.0686208i | ||||
\(157\) | 1737.81 | − | 3009.97i | 0.883390 | − | 1.53008i | 0.0358423 | − | 0.999357i | \(-0.488589\pi\) |
0.847548 | − | 0.530719i | \(-0.178078\pi\) | |||||||
\(158\) | −1780.22 | + | 3083.43i | −0.896371 | + | 1.55256i | ||||
\(159\) | −2385.52 | + | 1955.34i | −1.18984 | + | 0.975274i | ||||
\(160\) | −140.430 | − | 243.232i | −0.0693872 | − | 0.120182i | ||||
\(161\) | −1092.43 | −0.534755 | ||||||||
\(162\) | 284.126 | + | 2199.15i | 0.137796 | + | 1.06655i | ||||
\(163\) | −2223.32 | −1.06837 | −0.534183 | − | 0.845369i | \(-0.679381\pi\) | ||||
−0.534183 | + | 0.845369i | \(0.679381\pi\) | |||||||
\(164\) | −76.2204 | − | 132.018i | −0.0362915 | − | 0.0628588i | ||||
\(165\) | −639.105 | + | 523.855i | −0.301541 | + | 0.247164i | ||||
\(166\) | 644.915 | − | 1117.03i | 0.301537 | − | 0.522277i | ||||
\(167\) | 793.991 | − | 1375.23i | 0.367909 | − | 0.637238i | −0.621329 | − | 0.783550i | \(-0.713407\pi\) |
0.989239 | + | 0.146312i | \(0.0467403\pi\) | |||||||
\(168\) | −1368.39 | − | 515.967i | −0.628412 | − | 0.236951i | ||||
\(169\) | −597.632 | − | 1035.13i | −0.272022 | − | 0.471156i | ||||
\(170\) | −1658.58 | −0.748280 | ||||||||
\(171\) | 687.306 | − | 3433.66i | 0.307366 | − | 1.53555i | ||||
\(172\) | 12.6993 | 0.00562974 | ||||||||
\(173\) | −753.898 | − | 1305.79i | −0.331317 | − | 0.573857i | 0.651454 | − | 0.758689i | \(-0.274160\pi\) |
−0.982770 | + | 0.184831i | \(0.940826\pi\) | |||||||
\(174\) | 23.1776 | + | 140.914i | 0.0100982 | + | 0.0613945i | ||||
\(175\) | 171.403 | − | 296.878i | 0.0740390 | − | 0.128239i | ||||
\(176\) | 1152.19 | − | 1995.66i | 0.493465 | − | 0.854707i | ||||
\(177\) | 373.143 | + | 2268.61i | 0.158458 | + | 0.963384i | ||||
\(178\) | −1568.58 | − | 2716.85i | −0.660504 | − | 1.14403i | ||||
\(179\) | 1572.66 | 0.656683 | 0.328341 | − | 0.944559i | \(-0.393510\pi\) | ||||
0.328341 | + | 0.944559i | \(0.393510\pi\) | |||||||
\(180\) | 160.140 | − | 54.1446i | 0.0663117 | − | 0.0224206i | ||||
\(181\) | 1984.41 | 0.814918 | 0.407459 | − | 0.913223i | \(-0.366415\pi\) | ||||
0.407459 | + | 0.913223i | \(0.366415\pi\) | |||||||
\(182\) | 1214.63 | + | 2103.81i | 0.494695 | + | 0.856838i | ||||
\(183\) | −702.930 | − | 265.048i | −0.283946 | − | 0.107065i | ||||
\(184\) | 817.601 | − | 1416.13i | 0.327578 | − | 0.567382i | ||||
\(185\) | −55.4113 | + | 95.9751i | −0.0220212 | + | 0.0381418i | ||||
\(186\) | −408.040 | + | 334.458i | −0.160854 | + | 0.131847i | ||||
\(187\) | −1734.34 | − | 3003.97i | −0.678223 | − | 1.17472i | ||||
\(188\) | −552.831 | −0.214465 | ||||||||
\(189\) | 1018.84 | − | 1631.83i | 0.392114 | − | 0.628032i | ||||
\(190\) | −1972.50 | −0.753158 | ||||||||
\(191\) | 1174.18 | + | 2033.73i | 0.444819 | + | 0.770450i | 0.998040 | − | 0.0625853i | \(-0.0199345\pi\) |
−0.553220 | + | 0.833035i | \(0.686601\pi\) | |||||||
\(192\) | 1642.57 | − | 1346.37i | 0.617409 | − | 0.506071i | ||||
\(193\) | 117.085 | − | 202.797i | 0.0436681 | − | 0.0756354i | −0.843365 | − | 0.537341i | \(-0.819429\pi\) |
0.887033 | + | 0.461705i | \(0.152762\pi\) | |||||||
\(194\) | −2431.43 | + | 4211.37i | −0.899829 | + | 1.55855i | ||||
\(195\) | 1415.89 | + | 533.880i | 0.519970 | + | 0.196061i | ||||
\(196\) | 97.0288 | + | 168.059i | 0.0353604 | + | 0.0612460i | ||||
\(197\) | −717.846 | −0.259616 | −0.129808 | − | 0.991539i | \(-0.541436\pi\) | ||||
−0.129808 | + | 0.991539i | \(0.541436\pi\) | |||||||
\(198\) | 1961.87 | + | 1724.71i | 0.704163 | + | 0.619040i | ||||
\(199\) | 1701.45 | 0.606094 | 0.303047 | − | 0.952976i | \(-0.401996\pi\) | ||||
0.303047 | + | 0.952976i | \(0.401996\pi\) | |||||||
\(200\) | 256.564 | + | 444.381i | 0.0907090 | + | 0.157113i | ||||
\(201\) | 727.564 | + | 4423.39i | 0.255315 | + | 1.55225i | ||||
\(202\) | 325.467 | − | 563.725i | 0.113365 | − | 0.196354i | ||||
\(203\) | 61.9475 | − | 107.296i | 0.0214180 | − | 0.0370971i | ||||
\(204\) | 115.164 | + | 700.164i | 0.0395248 | + | 0.240300i | ||||
\(205\) | 304.349 | + | 527.148i | 0.103691 | + | 0.179598i | ||||
\(206\) | 5086.77 | 1.72045 | ||||||||
\(207\) | 1615.53 | + | 1420.23i | 0.542450 | + | 0.476875i | ||||
\(208\) | −4219.69 | −1.40665 | ||||||||
\(209\) | −2062.60 | − | 3572.52i | −0.682645 | − | 1.18238i | ||||
\(210\) | −1013.95 | − | 382.321i | −0.333186 | − | 0.125632i | ||||
\(211\) | 2469.33 | − | 4277.01i | 0.805667 | − | 1.39546i | −0.110172 | − | 0.993912i | \(-0.535140\pi\) |
0.915840 | − | 0.401544i | \(-0.131526\pi\) | |||||||
\(212\) | 371.656 | − | 643.727i | 0.120403 | − | 0.208544i | ||||
\(213\) | −3289.44 | + | 2696.26i | −1.05816 | + | 0.867345i | ||||
\(214\) | 913.585 | + | 1582.38i | 0.291829 | + | 0.505463i | ||||
\(215\) | −50.7086 | −0.0160851 | ||||||||
\(216\) | 1352.83 | + | 2542.03i | 0.426150 | + | 0.800754i | ||||
\(217\) | 457.726 | 0.143191 | ||||||||
\(218\) | 1173.46 | + | 2032.49i | 0.364572 | + | 0.631456i | ||||
\(219\) | 1989.45 | − | 1630.69i | 0.613857 | − | 0.503160i | ||||
\(220\) | 99.5703 | − | 172.461i | 0.0305137 | − | 0.0528514i | ||||
\(221\) | −3175.85 | + | 5500.73i | −0.966655 | + | 1.67430i | ||||
\(222\) | 327.790 | + | 123.597i | 0.0990983 | + | 0.0373662i | ||||
\(223\) | 1526.57 | + | 2644.10i | 0.458416 | + | 0.794001i | 0.998877 | − | 0.0473684i | \(-0.0150835\pi\) |
−0.540461 | + | 0.841369i | \(0.681750\pi\) | |||||||
\(224\) | 770.242 | 0.229750 | ||||||||
\(225\) | −639.439 | + | 216.200i | −0.189463 | + | 0.0640593i | ||||
\(226\) | −3548.73 | −1.04450 | ||||||||
\(227\) | 419.976 | + | 727.420i | 0.122797 | + | 0.212690i | 0.920869 | − | 0.389871i | \(-0.127480\pi\) |
−0.798073 | + | 0.602561i | \(0.794147\pi\) | |||||||
\(228\) | 136.960 | + | 832.682i | 0.0397825 | + | 0.241867i | ||||
\(229\) | −700.753 | + | 1213.74i | −0.202214 | + | 0.350245i | −0.949242 | − | 0.314548i | \(-0.898147\pi\) |
0.747027 | + | 0.664793i | \(0.231480\pi\) | |||||||
\(230\) | 605.827 | − | 1049.32i | 0.173683 | − | 0.300827i | ||||
\(231\) | −367.814 | − | 2236.21i | −0.104764 | − | 0.636935i | ||||
\(232\) | 92.7259 | + | 160.606i | 0.0262403 | + | 0.0454496i | ||||
\(233\) | −2856.99 | −0.803295 | −0.401647 | − | 0.915794i | \(-0.631562\pi\) | ||||
−0.401647 | + | 0.915794i | \(0.631562\pi\) | |||||||
\(234\) | 938.843 | − | 4690.30i | 0.262282 | − | 1.31032i | ||||
\(235\) | 2207.46 | 0.612761 | ||||||||
\(236\) | −277.021 | − | 479.815i | −0.0764092 | − | 0.132345i | ||||
\(237\) | −5691.11 | − | 2145.90i | −1.55982 | − | 0.588149i | ||||
\(238\) | 2274.29 | − | 3939.18i | 0.619412 | − | 1.07285i | ||||
\(239\) | 854.917 | − | 1480.76i | 0.231381 | − | 0.400763i | −0.726834 | − | 0.686813i | \(-0.759009\pi\) |
0.958215 | + | 0.286050i | \(0.0923424\pi\) | |||||||
\(240\) | 1455.75 | − | 1193.24i | 0.391535 | − | 0.320930i | ||||
\(241\) | 2166.23 | + | 3752.02i | 0.579000 | + | 1.00286i | 0.995594 | + | 0.0937648i | \(0.0298902\pi\) |
−0.416594 | + | 0.909092i | \(0.636776\pi\) | |||||||
\(242\) | −971.309 | −0.258009 | ||||||||
\(243\) | −3628.19 | + | 1088.66i | −0.957812 | + | 0.287396i | ||||
\(244\) | 181.036 | 0.0474987 | ||||||||
\(245\) | −387.437 | − | 671.061i | −0.101030 | − | 0.174990i | ||||
\(246\) | 1488.11 | − | 1219.76i | 0.385686 | − | 0.316135i | ||||
\(247\) | −3776.93 | + | 6541.84i | −0.972957 | + | 1.68521i | ||||
\(248\) | −342.573 | + | 593.354i | −0.0877154 | + | 0.151927i | ||||
\(249\) | 2061.70 | + | 777.390i | 0.524719 | + | 0.197852i | ||||
\(250\) | 190.109 | + | 329.278i | 0.0480941 | + | 0.0833015i | ||||
\(251\) | −1724.73 | −0.433722 | −0.216861 | − | 0.976202i | \(-0.569582\pi\) | ||||
−0.216861 | + | 0.976202i | \(0.569582\pi\) | |||||||
\(252\) | −90.9920 | + | 454.580i | −0.0227459 | + | 0.113634i | ||||
\(253\) | 2534.00 | 0.629688 | ||||||||
\(254\) | −2479.16 | − | 4294.04i | −0.612428 | − | 1.06076i | ||||
\(255\) | −459.850 | − | 2795.76i | −0.112929 | − | 0.686578i | ||||
\(256\) | −939.349 | + | 1627.00i | −0.229333 | + | 0.397217i | ||||
\(257\) | 2926.63 | − | 5069.07i | 0.710342 | − | 1.23035i | −0.254386 | − | 0.967103i | \(-0.581873\pi\) |
0.964729 | − | 0.263246i | \(-0.0847932\pi\) | |||||||
\(258\) | 26.0156 | + | 158.168i | 0.00627776 | + | 0.0381671i | ||||
\(259\) | −151.962 | − | 263.206i | −0.0364574 | − | 0.0631462i | ||||
\(260\) | −364.657 | −0.0869810 | ||||||||
\(261\) | −231.103 | + | 78.1380i | −0.0548081 | + | 0.0185311i | ||||
\(262\) | 787.277 | 0.185642 | ||||||||
\(263\) | −196.180 | − | 339.794i | −0.0459962 | − | 0.0796677i | 0.842111 | − | 0.539305i | \(-0.181313\pi\) |
−0.888107 | + | 0.459637i | \(0.847980\pi\) | |||||||
\(264\) | 3174.10 | + | 1196.83i | 0.739971 | + | 0.279015i | ||||
\(265\) | −1484.03 | + | 2570.41i | −0.344011 | + | 0.595845i | ||||
\(266\) | 2704.73 | − | 4684.73i | 0.623450 | − | 1.07985i | ||||
\(267\) | 4144.72 | − | 3397.30i | 0.950010 | − | 0.778695i | ||||
\(268\) | −540.144 | − | 935.557i | −0.123114 | − | 0.213240i | ||||
\(269\) | −4610.33 | −1.04497 | −0.522485 | − | 0.852648i | \(-0.674995\pi\) | ||||
−0.522485 | + | 0.852648i | \(0.674995\pi\) | |||||||
\(270\) | 1002.42 | + | 1883.59i | 0.225946 | + | 0.424562i | ||||
\(271\) | −1155.72 | −0.259058 | −0.129529 | − | 0.991576i | \(-0.541347\pi\) | ||||
−0.129529 | + | 0.991576i | \(0.541347\pi\) | |||||||
\(272\) | 3950.49 | + | 6842.44i | 0.880638 | + | 1.52531i | ||||
\(273\) | −3209.48 | + | 2630.71i | −0.711526 | + | 0.583216i | ||||
\(274\) | −1601.13 | + | 2773.23i | −0.353020 | + | 0.611449i | ||||
\(275\) | −397.585 | + | 688.638i | −0.0871829 | + | 0.151005i | ||||
\(276\) | −485.033 | − | 182.888i | −0.105781 | − | 0.0398860i | ||||
\(277\) | 304.205 | + | 526.898i | 0.0659852 | + | 0.114290i | 0.897131 | − | 0.441765i | \(-0.145648\pi\) |
−0.831145 | + | 0.556055i | \(0.812314\pi\) | |||||||
\(278\) | 7253.02 | 1.56477 | ||||||||
\(279\) | −676.904 | − | 595.075i | −0.145251 | − | 0.127693i | ||||
\(280\) | −1407.22 | −0.300349 | ||||||||
\(281\) | −1374.62 | − | 2380.91i | −0.291825 | − | 0.505456i | 0.682416 | − | 0.730964i | \(-0.260929\pi\) |
−0.974241 | + | 0.225508i | \(0.927596\pi\) | |||||||
\(282\) | −1132.52 | − | 6885.42i | −0.239151 | − | 1.45397i | ||||
\(283\) | −510.780 | + | 884.697i | −0.107289 | + | 0.185830i | −0.914671 | − | 0.404199i | \(-0.867550\pi\) |
0.807382 | + | 0.590029i | \(0.200884\pi\) | |||||||
\(284\) | 512.483 | − | 887.647i | 0.107078 | − | 0.185465i | ||||
\(285\) | −546.884 | − | 3324.91i | −0.113665 | − | 0.691054i | ||||
\(286\) | −2817.46 | − | 4879.98i | −0.582516 | − | 1.00895i | ||||
\(287\) | −1669.32 | −0.343334 | ||||||||
\(288\) | −1139.06 | − | 1001.37i | −0.233056 | − | 0.204882i | ||||
\(289\) | 6979.96 | 1.42071 | ||||||||
\(290\) | 68.7082 | + | 119.006i | 0.0139127 | + | 0.0240975i | ||||
\(291\) | −7772.95 | − | 2930.89i | −1.56584 | − | 0.590418i | ||||
\(292\) | −309.949 | + | 536.848i | −0.0621178 | + | 0.107591i | ||||
\(293\) | 2616.25 | − | 4531.47i | 0.521648 | − | 0.903521i | −0.478035 | − | 0.878341i | \(-0.658651\pi\) |
0.999683 | − | 0.0251800i | \(-0.00801588\pi\) | |||||||
\(294\) | −1894.37 | + | 1552.76i | −0.375790 | + | 0.308023i | ||||
\(295\) | 1106.15 | + | 1915.91i | 0.218314 | + | 0.378130i | ||||
\(296\) | 454.929 | 0.0893317 | ||||||||
\(297\) | −2363.29 | + | 3785.18i | −0.461724 | + | 0.739524i | ||||
\(298\) | 3486.71 | 0.677785 | ||||||||
\(299\) | −2320.07 | − | 4018.48i | −0.448739 | − | 0.777240i | ||||
\(300\) | 125.803 | − | 103.117i | 0.0242108 | − | 0.0198449i | ||||
\(301\) | 69.5327 | − | 120.434i | 0.0133149 | − | 0.0230622i | ||||
\(302\) | 1773.51 | − | 3071.81i | 0.337927 | − | 0.585307i | ||||
\(303\) | 1040.47 | + | 392.322i | 0.197272 | + | 0.0743839i | ||||
\(304\) | 4698.18 | + | 8137.49i | 0.886379 | + | 1.53525i | ||||
\(305\) | −722.881 | −0.135712 | ||||||||
\(306\) | −8484.50 | + | 2868.69i | −1.58506 | + | 0.535921i | ||||
\(307\) | −4912.68 | −0.913296 | −0.456648 | − | 0.889648i | \(-0.650950\pi\) | ||||
−0.456648 | + | 0.889648i | \(0.650950\pi\) | |||||||
\(308\) | 273.066 | + | 472.964i | 0.0505174 | + | 0.0874988i | ||||
\(309\) | 1410.33 | + | 8574.42i | 0.259647 | + | 1.57858i | ||||
\(310\) | −253.840 | + | 439.664i | −0.0465069 | + | 0.0805524i | ||||
\(311\) | 414.430 | − | 717.813i | 0.0755632 | − | 0.130879i | −0.825768 | − | 0.564010i | \(-0.809258\pi\) |
0.901331 | + | 0.433131i | \(0.142591\pi\) | |||||||
\(312\) | −1008.16 | − | 6129.36i | −0.182936 | − | 1.11220i | ||||
\(313\) | −4618.60 | − | 7999.66i | −0.834054 | − | 1.44462i | −0.894798 | − | 0.446471i | \(-0.852681\pi\) |
0.0607442 | − | 0.998153i | \(-0.480653\pi\) | |||||||
\(314\) | −10571.9 | −1.90003 | ||||||||
\(315\) | 363.332 | − | 1815.14i | 0.0649887 | − | 0.324672i | ||||
\(316\) | 1465.72 | 0.260928 | ||||||||
\(317\) | 4549.20 | + | 7879.45i | 0.806021 | + | 1.39607i | 0.915599 | + | 0.402091i | \(0.131717\pi\) |
−0.109578 | + | 0.993978i | \(0.534950\pi\) | |||||||
\(318\) | 8778.88 | + | 3310.18i | 1.54810 | + | 0.583729i | ||||
\(319\) | −143.693 | + | 248.884i | −0.0252203 | + | 0.0436828i | ||||
\(320\) | 1021.84 | − | 1769.88i | 0.178508 | − | 0.309185i | ||||
\(321\) | −2414.01 | + | 1978.69i | −0.419741 | + | 0.344049i | ||||
\(322\) | 1661.45 | + | 2877.71i | 0.287543 | + | 0.498039i | ||||
\(323\) | 14143.9 | 2.43649 | ||||||||
\(324\) | 725.548 | − | 553.955i | 0.124408 | − | 0.0949855i | ||||
\(325\) | 1456.08 | 0.248519 | ||||||||
\(326\) | 3381.38 | + | 5856.72i | 0.574470 | + | 0.995011i | ||||
\(327\) | −3100.68 | + | 2541.54i | −0.524368 | + | 0.429808i | ||||
\(328\) | 1249.36 | − | 2163.95i | 0.210318 | − | 0.364281i | ||||
\(329\) | −3026.92 | + | 5242.78i | −0.507233 | + | 0.878553i | ||||
\(330\) | 2351.95 | + | 886.831i | 0.392335 | + | 0.147935i | ||||
\(331\) | −2981.73 | − | 5164.50i | −0.495137 | − | 0.857603i | 0.504847 | − | 0.863209i | \(-0.331549\pi\) |
−0.999984 | + | 0.00560570i | \(0.998216\pi\) | |||||||
\(332\) | −530.982 | −0.0877754 | ||||||||
\(333\) | −117.458 | + | 586.801i | −0.0193294 | + | 0.0965661i | ||||
\(334\) | −4830.23 | −0.791313 | ||||||||
\(335\) | 2156.80 | + | 3735.69i | 0.351757 | + | 0.609261i | ||||
\(336\) | 837.807 | + | 5093.65i | 0.136030 | + | 0.827027i | ||||
\(337\) | −298.427 | + | 516.890i | −0.0482384 | + | 0.0835514i | −0.889136 | − | 0.457642i | \(-0.848694\pi\) |
0.840898 | + | 0.541194i | \(0.182027\pi\) | |||||||
\(338\) | −1817.84 | + | 3148.60i | −0.292537 | + | 0.506690i | ||||
\(339\) | −983.901 | − | 5981.85i | −0.157635 | − | 0.958377i | ||||
\(340\) | 341.393 | + | 591.310i | 0.0544548 | + | 0.0943185i | ||||
\(341\) | −1061.74 | −0.168611 | ||||||||
\(342\) | −10090.3 | + | 3411.63i | −1.59539 | + | 0.539415i | ||||
\(343\) | 6828.34 | 1.07492 | ||||||||
\(344\) | 104.080 | + | 180.272i | 0.0163128 | + | 0.0282546i | ||||
\(345\) | 1936.74 | + | 730.272i | 0.302234 | + | 0.113961i | ||||
\(346\) | −2293.16 | + | 3971.87i | −0.356304 | + | 0.617137i | ||||
\(347\) | 2281.05 | − | 3950.90i | 0.352891 | − | 0.611226i | −0.633863 | − | 0.773445i | \(-0.718532\pi\) |
0.986755 | + | 0.162219i | \(0.0518652\pi\) | |||||||
\(348\) | 45.4671 | − | 37.2680i | 0.00700372 | − | 0.00574074i | ||||
\(349\) | −337.633 | − | 584.798i | −0.0517854 | − | 0.0896949i | 0.838971 | − | 0.544177i | \(-0.183158\pi\) |
−0.890756 | + | 0.454482i | \(0.849825\pi\) | |||||||
\(350\) | −1042.73 | −0.159246 | ||||||||
\(351\) | 8166.42 | + | 282.140i | 1.24185 | + | 0.0429046i | ||||
\(352\) | −1786.65 | −0.270536 | ||||||||
\(353\) | 1680.91 | + | 2911.43i | 0.253445 | + | 0.438979i | 0.964472 | − | 0.264185i | \(-0.0851030\pi\) |
−0.711027 | + | 0.703165i | \(0.751770\pi\) | |||||||
\(354\) | 5408.52 | − | 4433.20i | 0.812033 | − | 0.665598i | ||||
\(355\) | −2046.35 | + | 3544.38i | −0.305941 | + | 0.529905i | ||||
\(356\) | −645.732 | + | 1118.44i | −0.0961341 | + | 0.166509i | ||||
\(357\) | 7270.57 | + | 2741.46i | 1.07787 | + | 0.406424i | ||||
\(358\) | −2391.81 | − | 4142.74i | −0.353104 | − | 0.611594i | ||||
\(359\) | 7701.61 | 1.13224 | 0.566122 | − | 0.824322i | \(-0.308443\pi\) | ||||
0.566122 | + | 0.824322i | \(0.308443\pi\) | |||||||
\(360\) | 2081.06 | + | 1829.49i | 0.304670 | + | 0.267840i | ||||
\(361\) | 9961.87 | 1.45238 | ||||||||
\(362\) | −3018.03 | − | 5227.39i | −0.438189 | − | 0.758965i | ||||
\(363\) | −269.300 | − | 1637.27i | −0.0389382 | − | 0.236734i | ||||
\(364\) | 500.026 | − | 866.070i | 0.0720013 | − | 0.124710i | ||||
\(365\) | 1237.63 | − | 2143.64i | 0.177481 | − | 0.307406i | ||||
\(366\) | 370.868 | + | 2254.78i | 0.0529661 | + | 0.322020i | ||||
\(367\) | −2954.75 | − | 5117.77i | −0.420263 | − | 0.727917i | 0.575702 | − | 0.817660i | \(-0.304729\pi\) |
−0.995965 | + | 0.0897425i | \(0.971396\pi\) | |||||||
\(368\) | −5771.94 | −0.817617 | ||||||||
\(369\) | 2468.66 | + | 2170.23i | 0.348274 | + | 0.306172i | ||||
\(370\) | 337.093 | 0.0473639 | ||||||||
\(371\) | −4069.86 | − | 7049.20i | −0.569532 | − | 0.986459i | ||||
\(372\) | 203.228 | + | 76.6295i | 0.0283249 | + | 0.0106803i | ||||
\(373\) | 4212.19 | − | 7295.73i | 0.584716 | − | 1.01276i | −0.410195 | − | 0.911998i | \(-0.634539\pi\) |
0.994911 | − | 0.100760i | \(-0.0321273\pi\) | |||||||
\(374\) | −5275.42 | + | 9137.30i | −0.729374 | + | 1.26331i | ||||
\(375\) | −502.334 | + | 411.748i | −0.0691744 | + | 0.0567001i | ||||
\(376\) | −4530.84 | − | 7847.64i | −0.621436 | − | 1.07636i | ||||
\(377\) | 526.249 | 0.0718917 | ||||||||
\(378\) | −5848.13 | − | 202.046i | −0.795754 | − | 0.0274923i | ||||
\(379\) | −3510.24 | −0.475749 | −0.237875 | − | 0.971296i | \(-0.576451\pi\) | ||||
−0.237875 | + | 0.971296i | \(0.576451\pi\) | |||||||
\(380\) | 406.007 | + | 703.225i | 0.0548098 | + | 0.0949334i | ||||
\(381\) | 6550.81 | − | 5369.50i | 0.880862 | − | 0.722016i | ||||
\(382\) | 3571.54 | − | 6186.09i | 0.478367 | − | 0.828555i | ||||
\(383\) | −2866.01 | + | 4964.08i | −0.382367 | + | 0.662279i | −0.991400 | − | 0.130866i | \(-0.958224\pi\) |
0.609033 | + | 0.793145i | \(0.291558\pi\) | |||||||
\(384\) | −8229.64 | − | 3103.09i | −1.09366 | − | 0.412380i | ||||
\(385\) | −1090.36 | − | 1888.55i | −0.144337 | − | 0.249999i | ||||
\(386\) | −712.283 | −0.0939229 | ||||||||
\(387\) | −259.400 | + | 87.7056i | −0.0340725 | + | 0.0115202i | ||||
\(388\) | 2001.89 | 0.261934 | ||||||||
\(389\) | −7183.60 | − | 12442.4i | −0.936306 | − | 1.62173i | −0.772288 | − | 0.635273i | \(-0.780888\pi\) |
−0.164019 | − | 0.986457i | \(-0.552446\pi\) | |||||||
\(390\) | −747.030 | − | 4541.74i | −0.0969931 | − | 0.589692i | ||||
\(391\) | −4344.11 | + | 7524.23i | −0.561870 | + | 0.973188i | ||||
\(392\) | −1590.44 | + | 2754.72i | −0.204922 | + | 0.354934i | ||||
\(393\) | 218.276 | + | 1327.06i | 0.0280167 | + | 0.170334i | ||||
\(394\) | 1091.75 | + | 1890.97i | 0.139598 | + | 0.241791i | ||||
\(395\) | −5852.63 | −0.745514 | ||||||||
\(396\) | 211.065 | − | 1054.44i | 0.0267838 | − | 0.133807i | ||||
\(397\) | −9014.42 | −1.13960 | −0.569800 | − | 0.821784i | \(-0.692979\pi\) | ||||
−0.569800 | + | 0.821784i | \(0.692979\pi\) | |||||||
\(398\) | −2587.69 | − | 4482.01i | −0.325902 | − | 0.564479i | ||||
\(399\) | 8646.64 | + | 3260.32i | 1.08490 | + | 0.409073i | ||||
\(400\) | 905.619 | − | 1568.58i | 0.113202 | − | 0.196072i | ||||
\(401\) | −5255.55 | + | 9102.87i | −0.654487 | + | 1.13361i | 0.327535 | + | 0.944839i | \(0.393782\pi\) |
−0.982022 | + | 0.188766i | \(0.939551\pi\) | |||||||
\(402\) | 10545.7 | − | 8643.97i | 1.30839 | − | 1.07244i | ||||
\(403\) | 972.104 | + | 1683.73i | 0.120159 | + | 0.208121i | ||||
\(404\) | −267.969 | −0.0329998 | ||||||||
\(405\) | −2897.12 | + | 2211.95i | −0.355454 | + | 0.271389i | ||||
\(406\) | −376.857 | −0.0460667 | ||||||||
\(407\) | 352.491 | + | 610.533i | 0.0429296 | + | 0.0743562i | ||||
\(408\) | −8995.23 | + | 7373.12i | −1.09150 | + | 0.894666i | ||||
\(409\) | −1659.10 | + | 2873.65i | −0.200580 | + | 0.347415i | −0.948715 | − | 0.316131i | \(-0.897616\pi\) |
0.748135 | + | 0.663546i | \(0.230949\pi\) | |||||||
\(410\) | 925.751 | − | 1603.45i | 0.111511 | − | 0.193143i | ||||
\(411\) | −5118.57 | − | 1930.02i | −0.614308 | − | 0.231632i | ||||
\(412\) | −1047.03 | − | 1813.51i | −0.125203 | − | 0.216857i | ||||
\(413\) | −6067.11 | −0.722864 | ||||||||
\(414\) | 1284.20 | − | 6415.66i | 0.152452 | − | 0.761625i | ||||
\(415\) | 2120.22 | 0.250789 | ||||||||
\(416\) | 1635.81 | + | 2833.31i | 0.192794 | + | 0.333929i | ||||
\(417\) | 2010.93 | + | 12225.9i | 0.236153 | + | 1.43575i | ||||
\(418\) | −6273.89 | + | 10866.7i | −0.734129 | + | 1.27155i | ||||
\(419\) | 243.069 | − | 421.008i | 0.0283406 | − | 0.0490873i | −0.851507 | − | 0.524343i | \(-0.824311\pi\) |
0.879848 | + | 0.475255i | \(0.157644\pi\) | |||||||
\(420\) | 72.4016 | + | 440.182i | 0.00841151 | + | 0.0511398i | ||||
\(421\) | −2525.96 | − | 4375.10i | −0.292418 | − | 0.506482i | 0.681963 | − | 0.731387i | \(-0.261126\pi\) |
−0.974381 | + | 0.224904i | \(0.927793\pi\) | |||||||
\(422\) | −15022.1 | −1.73286 | ||||||||
\(423\) | 11292.3 | − | 3818.03i | 1.29799 | − | 0.438863i | ||||
\(424\) | 12183.9 | 1.39553 | ||||||||
\(425\) | −1363.19 | − | 2361.11i | −0.155586 | − | 0.269484i | ||||
\(426\) | 12105.4 | + | 4564.48i | 1.37678 | + | 0.519130i | ||||
\(427\) | 991.230 | − | 1716.86i | 0.112340 | − | 0.194578i | ||||
\(428\) | 376.094 | − | 651.414i | 0.0424747 | − | 0.0735684i | ||||
\(429\) | 7444.70 | − | 6102.19i | 0.837840 | − | 0.686752i | ||||
\(430\) | 77.1212 | + | 133.578i | 0.00864910 | + | 0.0149807i | ||||
\(431\) | 6944.24 | 0.776084 | 0.388042 | − | 0.921642i | \(-0.373152\pi\) | ||||
0.388042 | + | 0.921642i | \(0.373152\pi\) | |||||||
\(432\) | 5383.10 | − | 8621.89i | 0.599525 | − | 0.960234i | ||||
\(433\) | −13738.3 | −1.52476 | −0.762378 | − | 0.647131i | \(-0.775968\pi\) | ||||
−0.762378 | + | 0.647131i | \(0.775968\pi\) | |||||||
\(434\) | −696.142 | − | 1205.75i | −0.0769952 | − | 0.133360i | ||||
\(435\) | −181.551 | + | 148.812i | −0.0200108 | + | 0.0164022i | ||||
\(436\) | 483.075 | − | 836.711i | 0.0530622 | − | 0.0919064i | ||||
\(437\) | −5166.31 | + | 8948.31i | −0.565533 | + | 0.979533i | ||||
\(438\) | −7321.31 | − | 2760.59i | −0.798688 | − | 0.301155i | ||||
\(439\) | −4240.92 | − | 7345.48i | −0.461066 | − | 0.798589i | 0.537949 | − | 0.842978i | \(-0.319199\pi\) |
−0.999014 | + | 0.0443883i | \(0.985866\pi\) | |||||||
\(440\) | 3264.19 | 0.353668 | ||||||||
\(441\) | −3142.61 | − | 2762.71i | −0.339338 | − | 0.298317i | ||||
\(442\) | 19320.2 | 2.07912 | ||||||||
\(443\) | 279.098 | + | 483.411i | 0.0299330 | + | 0.0518455i | 0.880604 | − | 0.473853i | \(-0.157137\pi\) |
−0.850671 | + | 0.525699i | \(0.823804\pi\) | |||||||
\(444\) | −23.4061 | − | 142.303i | −0.00250181 | − | 0.0152103i | ||||
\(445\) | 2578.42 | − | 4465.95i | 0.274671 | − | 0.475744i | ||||
\(446\) | 4643.44 | − | 8042.67i | 0.492989 | − | 0.853882i | ||||
\(447\) | 966.707 | + | 5877.32i | 0.102290 | + | 0.621896i | ||||
\(448\) | 2802.34 | + | 4853.79i | 0.295531 | + | 0.511875i | ||||
\(449\) | 14775.0 | 1.55295 | 0.776476 | − | 0.630147i | \(-0.217005\pi\) | ||||
0.776476 | + | 0.630147i | \(0.217005\pi\) | |||||||
\(450\) | 1542.02 | + | 1355.61i | 0.161537 | + | 0.142009i | ||||
\(451\) | 3872.15 | 0.404285 | ||||||||
\(452\) | 730.449 | + | 1265.17i | 0.0760120 | + | 0.131657i | ||||
\(453\) | 5669.66 | + | 2137.82i | 0.588044 | + | 0.221729i | ||||
\(454\) | 1277.46 | − | 2212.62i | 0.132058 | − | 0.228730i | ||||
\(455\) | −1996.61 | + | 3458.23i | −0.205720 | + | 0.356317i | ||||
\(456\) | −10697.7 | + | 8768.60i | −1.09861 | + | 0.900499i | ||||
\(457\) | 7103.97 | + | 12304.4i | 0.727154 | + | 1.25947i | 0.958081 | + | 0.286497i | \(0.0924909\pi\) |
−0.230927 | + | 0.972971i | \(0.574176\pi\) | |||||||
\(458\) | 4263.02 | 0.434930 | ||||||||
\(459\) | −7187.92 | − | 13506.4i | −0.730944 | − | 1.37347i | ||||
\(460\) | −498.799 | −0.0505579 | ||||||||
\(461\) | 3851.26 | + | 6670.57i | 0.389091 | + | 0.673925i | 0.992328 | − | 0.123637i | \(-0.0394558\pi\) |
−0.603237 | + | 0.797562i | \(0.706123\pi\) | |||||||
\(462\) | −5331.29 | + | 4369.90i | −0.536870 | + | 0.440056i | ||||
\(463\) | −3954.53 | + | 6849.45i | −0.396939 | + | 0.687518i | −0.993347 | − | 0.115163i | \(-0.963261\pi\) |
0.596408 | + | 0.802682i | \(0.296594\pi\) | |||||||
\(464\) | 327.304 | − | 566.908i | 0.0327472 | − | 0.0567199i | ||||
\(465\) | −811.490 | − | 305.982i | −0.0809289 | − | 0.0305153i | ||||
\(466\) | 4345.11 | + | 7525.96i | 0.431939 | + | 0.748140i | ||||
\(467\) | 11639.8 | 1.15337 | 0.576685 | − | 0.816967i | \(-0.304346\pi\) | ||||
0.576685 | + | 0.816967i | \(0.304346\pi\) | |||||||
\(468\) | −1865.41 | + | 630.711i | −0.184249 | + | 0.0622962i | ||||
\(469\) | −11829.8 | −1.16471 | ||||||||
\(470\) | −3357.26 | − | 5814.95i | −0.329487 | − | 0.570688i | ||||
\(471\) | −2931.11 | − | 17820.4i | −0.286749 | − | 1.74336i | ||||
\(472\) | 4540.77 | − | 7864.84i | 0.442809 | − | 0.766967i | ||||
\(473\) | −161.288 | + | 279.359i | −0.0156787 | + | 0.0271563i | ||||
\(474\) | 3002.65 | + | 18255.3i | 0.290962 | + | 1.76897i | ||||
\(475\) | −1621.19 | − | 2807.99i | −0.156601 | − | 0.271240i | ||||
\(476\) | −1872.50 | −0.180307 | ||||||||
\(477\) | −3145.77 | + | 15715.7i | −0.301960 | + | 1.50854i | ||||
\(478\) | −5200.87 | −0.497662 | ||||||||
\(479\) | 9347.93 | + | 16191.1i | 0.891687 | + | 1.54445i | 0.837853 | + | 0.545897i | \(0.183811\pi\) |
0.0538341 | + | 0.998550i | \(0.482856\pi\) | |||||||
\(480\) | −1365.54 | − | 514.894i | −0.129850 | − | 0.0489616i | ||||
\(481\) | 645.465 | − | 1117.98i | 0.0611865 | − | 0.105978i | ||||
\(482\) | 6589.10 | − | 11412.7i | 0.622667 | − | 1.07849i | ||||
\(483\) | −4390.12 | + | 3598.45i | −0.413576 | + | 0.338996i | ||||
\(484\) | 199.928 | + | 346.286i | 0.0187761 | + | 0.0325212i | ||||
\(485\) | −7993.56 | −0.748390 | ||||||||
\(486\) | 8385.77 | + | 7901.75i | 0.782687 | + | 0.737512i | ||||
\(487\) | −2249.54 | −0.209315 | −0.104658 | − | 0.994508i | \(-0.533375\pi\) | ||||
−0.104658 | + | 0.994508i | \(0.533375\pi\) | |||||||
\(488\) | 1483.72 | + | 2569.88i | 0.137633 | + | 0.238387i | ||||
\(489\) | −8934.78 | + | 7323.57i | −0.826267 | + | 0.677266i | ||||
\(490\) | −1178.48 | + | 2041.19i | −0.108650 | + | 0.188187i | ||||
\(491\) | −994.175 | + | 1721.96i | −0.0913778 | + | 0.158271i | −0.908091 | − | 0.418773i | \(-0.862460\pi\) |
0.816713 | + | 0.577044i | \(0.195794\pi\) | |||||||
\(492\) | −741.168 | − | 279.466i | −0.0679155 | − | 0.0256084i | ||||
\(493\) | −492.676 | − | 853.339i | −0.0450081 | − | 0.0779563i | ||||
\(494\) | 22976.9 | 2.09267 | ||||||||
\(495\) | −842.784 | + | 4210.40i | −0.0765259 | + | 0.382310i | ||||
\(496\) | 2418.43 | 0.218933 | ||||||||
\(497\) | −5612.01 | − | 9720.28i | −0.506505 | − | 0.877292i | ||||
\(498\) | −1087.76 | − | 6613.29i | −0.0978790 | − | 0.595078i | ||||
\(499\) | −1206.95 | + | 2090.50i | −0.108278 | + | 0.187543i | −0.915073 | − | 0.403289i | \(-0.867867\pi\) |
0.806795 | + | 0.590832i | \(0.201200\pi\) | |||||||
\(500\) | 78.2617 | − | 135.553i | 0.00699994 | − | 0.0121243i | ||||
\(501\) | −1339.20 | − | 8142.00i | −0.119423 | − | 0.726063i | ||||
\(502\) | 2623.10 | + | 4543.34i | 0.233216 | + | 0.403942i | ||||
\(503\) | −8758.56 | −0.776391 | −0.388196 | − | 0.921577i | \(-0.626902\pi\) | ||||
−0.388196 | + | 0.921577i | \(0.626902\pi\) | |||||||
\(504\) | −7198.67 | + | 2433.94i | −0.636219 | + | 0.215111i | ||||
\(505\) | 1070.00 | 0.0942860 | ||||||||
\(506\) | −3853.88 | − | 6675.12i | −0.338589 | − | 0.586453i | ||||
\(507\) | −5811.38 | − | 2191.25i | −0.509058 | − | 0.191947i | ||||
\(508\) | −1020.59 | + | 1767.72i | −0.0891368 | + | 0.154389i | ||||
\(509\) | 5924.01 | − | 10260.7i | 0.515869 | − | 0.893511i | −0.483961 | − | 0.875089i | \(-0.660802\pi\) |
0.999830 | − | 0.0184220i | \(-0.00586422\pi\) | |||||||
\(510\) | −6665.30 | + | 5463.34i | −0.578714 | + | 0.474354i | ||||
\(511\) | 3394.13 | + | 5878.81i | 0.293831 | + | 0.508930i | ||||
\(512\) | −7826.64 | −0.675570 | ||||||||
\(513\) | −8548.36 | − | 16062.7i | −0.735710 | − | 1.38243i | ||||
\(514\) | −17804.1 | −1.52783 | ||||||||
\(515\) | 4180.80 | + | 7241.36i | 0.357725 | + | 0.619597i | ||||
\(516\) | 51.0344 | − | 41.8313i | 0.00435400 | − | 0.00356884i | ||||
\(517\) | 7021.23 | − | 12161.1i | 0.597279 | − | 1.03452i | ||||
\(518\) | −462.230 | + | 800.606i | −0.0392070 | + | 0.0679085i | ||||
\(519\) | −7330.91 | − | 2764.21i | −0.620022 | − | 0.233787i | ||||
\(520\) | −2988.62 | − | 5176.43i | −0.252037 | − | 0.436542i | ||||
\(521\) | 3816.55 | 0.320933 | 0.160466 | − | 0.987041i | \(-0.448700\pi\) | ||||
0.160466 | + | 0.987041i | \(0.448700\pi\) | |||||||
\(522\) | 557.310 | + | 489.939i | 0.0467295 | + | 0.0410806i | ||||
\(523\) | −12158.9 | −1.01658 | −0.508288 | − | 0.861187i | \(-0.669722\pi\) | ||||
−0.508288 | + | 0.861187i | \(0.669722\pi\) | |||||||
\(524\) | −162.049 | − | 280.676i | −0.0135098 | − | 0.0233996i | ||||
\(525\) | −289.100 | − | 1757.65i | −0.0240331 | − | 0.146115i | ||||
\(526\) | −596.729 | + | 1033.57i | −0.0494651 | + | 0.0856761i | ||||
\(527\) | 1820.17 | − | 3152.63i | 0.150452 | − | 0.260590i | ||||
\(528\) | −1943.37 | − | 11815.2i | −0.160179 | − | 0.973846i | ||||
\(529\) | 2909.97 | + | 5040.22i | 0.239169 | + | 0.414253i | ||||
\(530\) | 9028.04 | 0.739911 | ||||||||
\(531\) | 8972.28 | + | 7887.65i | 0.733265 | + | 0.644623i | ||||
\(532\) | −2226.90 | −0.181482 | ||||||||
\(533\) | −3545.25 | − | 6140.55i | −0.288108 | − | 0.499018i | ||||
\(534\) | −15252.8 | − | 5751.27i | −1.23606 | − | 0.466071i | ||||
\(535\) | −1501.75 | + | 2601.10i | −0.121357 | + | 0.210197i | ||||
\(536\) | 8853.71 | − | 15335.1i | 0.713474 | − | 1.23577i | ||||
\(537\) | 6320.00 | − | 5180.31i | 0.507874 | − | 0.416289i | ||||
\(538\) | 7011.72 | + | 12144.7i | 0.561890 | + | 0.973222i | ||||
\(539\) | −4929.26 | −0.393911 | ||||||||
\(540\) | 465.197 | − | 745.086i | 0.0370720 | − | 0.0593767i | ||||
\(541\) | 14919.8 | 1.18568 | 0.592840 | − | 0.805321i | \(-0.298007\pi\) | ||||
0.592840 | + | 0.805321i | \(0.298007\pi\) | |||||||
\(542\) | 1757.69 | + | 3044.42i | 0.139298 | + | 0.241271i | ||||
\(543\) | 7974.69 | − | 6536.61i | 0.630252 | − | 0.516598i | ||||
\(544\) | 3062.91 | − | 5305.12i | 0.241399 | − | 0.418116i | ||||
\(545\) | −1928.92 | + | 3341.00i | −0.151607 | + | 0.262592i | ||||
\(546\) | 11811.1 | + | 4453.52i | 0.925766 | + | 0.349072i | ||||
\(547\) | 513.578 | + | 889.543i | 0.0401444 | + | 0.0695322i | 0.885400 | − | 0.464831i | \(-0.153885\pi\) |
−0.845255 | + | 0.534363i | \(0.820552\pi\) | |||||||
\(548\) | 1318.27 | 0.102762 | ||||||||
\(549\) | −3697.91 | + | 1250.30i | −0.287473 | + | 0.0971973i | ||||
\(550\) | 2418.70 | 0.187516 | ||||||||
\(551\) | −585.923 | − | 1014.85i | −0.0453015 | − | 0.0784646i | ||||
\(552\) | −1379.02 | − | 8384.10i | −0.106332 | − | 0.646469i | ||||
\(553\) | 8025.26 | − | 13900.2i | 0.617123 | − | 1.06889i | ||||
\(554\) | 925.313 | − | 1602.69i | 0.0709617 | − | 0.122909i | ||||
\(555\) | 93.4606 | + | 568.216i | 0.00714808 | + | 0.0434584i | ||||
\(556\) | −1492.92 | − | 2585.81i | −0.113874 | − | 0.197235i | ||||
\(557\) | −10590.8 | −0.805648 | −0.402824 | − | 0.915277i | \(-0.631971\pi\) | ||||
−0.402824 | + | 0.915277i | \(0.631971\pi\) | |||||||
\(558\) | −538.079 | + | 2688.15i | −0.0408220 | + | 0.203940i | ||||
\(559\) | 590.685 | 0.0446929 | ||||||||
\(560\) | 2483.61 | + | 4301.74i | 0.187414 | + | 0.324610i | ||||
\(561\) | −16864.8 | − | 6359.07i | −1.26922 | − | 0.478574i | ||||
\(562\) | −4181.23 | + | 7242.11i | −0.313834 | + | 0.543576i | ||||
\(563\) | 1096.03 | − | 1898.38i | 0.0820467 | − | 0.142109i | −0.822082 | − | 0.569369i | \(-0.807188\pi\) |
0.904129 | + | 0.427260i | \(0.140521\pi\) | |||||||
\(564\) | −2221.64 | + | 1821.01i | −0.165865 | + | 0.135955i | ||||
\(565\) | −2916.69 | − | 5051.86i | −0.217179 | − | 0.376165i | ||||
\(566\) | 3107.32 | 0.230761 | ||||||||
\(567\) | −1280.84 | − | 9913.81i | −0.0948684 | − | 0.734287i | ||||
\(568\) | 16800.6 | 1.24109 | ||||||||
\(569\) | 8284.89 | + | 14349.8i | 0.610405 | + | 1.05725i | 0.991172 | + | 0.132582i | \(0.0423267\pi\) |
−0.380767 | + | 0.924671i | \(0.624340\pi\) | |||||||
\(570\) | −7926.81 | + | 6497.37i | −0.582487 | + | 0.477447i | ||||
\(571\) | −3639.66 | + | 6304.08i | −0.266752 | + | 0.462027i | −0.968021 | − | 0.250869i | \(-0.919284\pi\) |
0.701269 | + | 0.712896i | \(0.252617\pi\) | |||||||
\(572\) | −1159.86 | + | 2008.93i | −0.0847833 | + | 0.146849i | ||||
\(573\) | 11417.7 | + | 4305.19i | 0.832429 | + | 0.313878i | ||||
\(574\) | 2538.82 | + | 4397.36i | 0.184614 | + | 0.319760i | ||||
\(575\) | 1991.71 | 0.144452 | ||||||||
\(576\) | 2166.05 | − | 10821.2i | 0.156688 | − | 0.782784i | ||||
\(577\) | −17938.0 | −1.29422 | −0.647112 | − | 0.762395i | \(-0.724024\pi\) | ||||
−0.647112 | + | 0.762395i | \(0.724024\pi\) | |||||||
\(578\) | −10615.6 | − | 18386.8i | −0.763930 | − | 1.32317i | ||||
\(579\) | −197.484 | − | 1200.65i | −0.0141747 | − | 0.0861782i | ||||
\(580\) | 28.2850 | − | 48.9910i | 0.00202495 | − | 0.00350731i | ||||
\(581\) | −2907.29 | + | 5035.57i | −0.207598 | + | 0.359571i | ||||
\(582\) | 4101.03 | + | 24933.2i | 0.292085 | + | 1.77580i | ||||
\(583\) | 9440.42 | + | 16351.3i | 0.670639 | + | 1.16158i | ||||
\(584\) | −10161.0 | −0.719974 | ||||||||
\(585\) | 7448.59 | − | 2518.44i | 0.526430 | − | 0.177991i | ||||
\(586\) | −15915.9 | −1.12198 | ||||||||
\(587\) | −5754.83 | − | 9967.67i | −0.404646 | − | 0.700868i | 0.589634 | − | 0.807671i | \(-0.299272\pi\) |
−0.994280 | + | 0.106803i | \(0.965939\pi\) | |||||||
\(588\) | 943.509 | + | 355.762i | 0.0661729 | + | 0.0249513i | ||||
\(589\) | 2164.67 | − | 3749.32i | 0.151433 | − | 0.262289i | ||||
\(590\) | 3364.62 | − | 5827.70i | 0.234778 | − | 0.406648i | ||||
\(591\) | −2884.79 | + | 2364.57i | −0.200785 | + | 0.164578i | ||||
\(592\) | −802.904 | − | 1390.67i | −0.0557418 | − | 0.0965476i | ||||
\(593\) | −9612.80 | −0.665684 | −0.332842 | − | 0.942983i | \(-0.608008\pi\) | ||||
−0.332842 | + | 0.942983i | \(0.608008\pi\) | |||||||
\(594\) | 13565.3 | + | 468.664i | 0.937021 | + | 0.0323729i | ||||
\(595\) | 7476.92 | 0.515166 | ||||||||
\(596\) | −717.684 | − | 1243.07i | −0.0493247 | − | 0.0854328i | ||||
\(597\) | 6837.57 | − | 5604.55i | 0.468749 | − | 0.384219i | ||||
\(598\) | −7057.05 | + | 12223.2i | −0.482582 | + | 0.835857i | ||||
\(599\) | −3686.00 | + | 6384.33i | −0.251429 | + | 0.435487i | −0.963919 | − | 0.266194i | \(-0.914234\pi\) |
0.712491 | + | 0.701681i | \(0.247567\pi\) | |||||||
\(600\) | 2494.83 | + | 940.706i | 0.169752 | + | 0.0640069i | ||||
\(601\) | 12095.3 | + | 20949.7i | 0.820927 | + | 1.42189i | 0.904993 | + | 0.425427i | \(0.139876\pi\) |
−0.0840654 | + | 0.996460i | \(0.526790\pi\) | |||||||
\(602\) | −423.001 | −0.0286383 | ||||||||
\(603\) | 17494.4 | + | 15379.6i | 1.18147 | + | 1.03865i | ||||
\(604\) | −1460.20 | −0.0983684 | ||||||||
\(605\) | −798.317 | − | 1382.72i | −0.0536466 | − | 0.0929186i | ||||
\(606\) | −548.956 | − | 3337.50i | −0.0367984 | − | 0.223724i | ||||
\(607\) | 658.866 | − | 1141.19i | 0.0440569 | − | 0.0763088i | −0.843156 | − | 0.537669i | \(-0.819305\pi\) |
0.887213 | + | 0.461360i | \(0.152638\pi\) | |||||||
\(608\) | 3642.62 | − | 6309.20i | 0.242973 | − | 0.420842i | ||||
\(609\) | −104.485 | − | 635.242i | −0.00695230 | − | 0.0422681i | ||||
\(610\) | 1099.41 | + | 1904.23i | 0.0729733 | + | 0.126393i | ||||
\(611\) | −25713.9 | −1.70257 | ||||||||
\(612\) | 2769.13 | + | 2434.38i | 0.182901 | + | 0.160791i | ||||
\(613\) | −4137.52 | −0.272615 | −0.136307 | − | 0.990667i | \(-0.543523\pi\) | ||||
−0.136307 | + | 0.990667i | \(0.543523\pi\) | |||||||
\(614\) | 7471.56 | + | 12941.1i | 0.491087 | + | 0.850588i | ||||
\(615\) | 2959.49 | + | 1115.91i | 0.194046 | + | 0.0731674i | ||||
\(616\) | −4475.93 | + | 7752.54i | −0.292760 | + | 0.507076i | ||||
\(617\) | 3895.81 | − | 6747.74i | 0.254197 | − | 0.440281i | −0.710480 | − | 0.703717i | \(-0.751522\pi\) |
0.964677 | + | 0.263436i | \(0.0848557\pi\) | |||||||
\(618\) | 20442.0 | − | 16755.7i | 1.33058 | − | 1.09064i | ||||
\(619\) | −10978.2 | − | 19014.8i | −0.712844 | − | 1.23468i | −0.963785 | − | 0.266680i | \(-0.914073\pi\) |
0.250941 | − | 0.968002i | \(-0.419260\pi\) | |||||||
\(620\) | 208.996 | 0.0135379 | ||||||||
\(621\) | 11170.5 | + | 385.927i | 0.721831 | + | 0.0249384i | ||||
\(622\) | −2521.18 | −0.162524 | ||||||||
\(623\) | 7071.17 | + | 12247.6i | 0.454736 | + | 0.787625i | ||||
\(624\) | −16957.5 | + | 13899.6i | −1.08789 | + | 0.891712i | ||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −14048.6 | + | 24332.9i | −0.896957 | + | 1.55357i | ||||
\(627\) | −20056.7 | − | 7562.63i | −1.27749 | − | 0.481694i | ||||
\(628\) | 2176.06 | + | 3769.05i | 0.138271 | + | 0.239493i | ||||
\(629\) | −2417.15 | −0.153224 | ||||||||
\(630\) | −5334.08 | + | 1803.50i | −0.337325 | + | 0.114053i | ||||
\(631\) | −11152.7 | −0.703618 | −0.351809 | − | 0.936072i | \(-0.614433\pi\) | ||||
−0.351809 | + | 0.936072i | \(0.614433\pi\) | |||||||
\(632\) | 12012.6 | + | 20806.4i | 0.756068 | + | 1.30955i | ||||
\(633\) | −4164.95 | − | 25321.8i | −0.261520 | − | 1.58997i | ||||
\(634\) | 13837.5 | − | 23967.2i | 0.866810 | − | 1.50136i | ||||
\(635\) | 4075.24 | − | 7058.52i | 0.254679 | − | 0.441116i | ||||
\(636\) | −626.861 | − | 3811.15i | −0.0390828 | − | 0.237613i | ||||
\(637\) | 4513.11 | + | 7816.94i | 0.280716 | + | 0.486214i | ||||
\(638\) | 874.155 | 0.0542447 | ||||||||
\(639\) | −4337.77 | + | 21670.7i | −0.268544 | + | 1.34160i | ||||
\(640\) | −8463.22 | −0.522716 | ||||||||
\(641\) | −2404.72 | − | 4165.10i | −0.148176 | − | 0.256648i | 0.782377 | − | 0.622805i | \(-0.214007\pi\) |
−0.930553 | + | 0.366156i | \(0.880674\pi\) | |||||||
\(642\) | 8883.71 | + | 3349.71i | 0.546125 | + | 0.205923i | ||||
\(643\) | 1276.51 | − | 2210.98i | 0.0782904 | − | 0.135603i | −0.824222 | − | 0.566267i | \(-0.808387\pi\) |
0.902512 | + | 0.430664i | \(0.141721\pi\) | |||||||
\(644\) | 683.964 | − | 1184.66i | 0.0418509 | − | 0.0724879i | ||||
\(645\) | −203.781 | + | 167.033i | −0.0124401 | + | 0.0101968i | ||||
\(646\) | −21511.0 | − | 37258.2i | −1.31013 | − | 2.26920i | ||||
\(647\) | 8446.00 | 0.513210 | 0.256605 | − | 0.966516i | \(-0.417396\pi\) | ||||
0.256605 | + | 0.966516i | \(0.417396\pi\) | |||||||
\(648\) | 13810.0 | + | 5759.36i | 0.837201 | + | 0.349150i | ||||
\(649\) | 14073.2 | 0.851191 | ||||||||
\(650\) | −2214.51 | − | 3835.64i | −0.133631 | − | 0.231456i | ||||
\(651\) | 1839.45 | − | 1507.74i | 0.110743 | − | 0.0907727i | ||||
\(652\) | 1392.01 | − | 2411.02i | 0.0836122 | − | 0.144821i | ||||
\(653\) | −4047.44 | + | 7010.37i | −0.242555 | + | 0.420118i | −0.961441 | − | 0.275010i | \(-0.911319\pi\) |
0.718886 | + | 0.695128i | \(0.244652\pi\) | |||||||
\(654\) | 11410.7 | + | 4302.55i | 0.682254 | + | 0.257252i | ||||
\(655\) | 647.062 | + | 1120.74i | 0.0385997 | + | 0.0668566i | ||||
\(656\) | −8819.97 | −0.524942 | ||||||||
\(657\) | 2623.47 | − | 13106.4i | 0.155786 | − | 0.778280i | ||||
\(658\) | 18414.2 | 1.09097 | ||||||||
\(659\) | −1087.67 | − | 1883.89i | −0.0642936 | − | 0.111360i | 0.832087 | − | 0.554645i | \(-0.187146\pi\) |
−0.896380 | + | 0.443286i | \(0.853813\pi\) | |||||||
\(660\) | −167.942 | − | 1021.04i | −0.00990477 | − | 0.0602184i | ||||
\(661\) | 4438.47 | − | 7687.66i | 0.261175 | − | 0.452368i | −0.705379 | − | 0.708830i | \(-0.749223\pi\) |
0.966554 | + | 0.256462i | \(0.0825567\pi\) | |||||||
\(662\) | −9069.64 | + | 15709.1i | −0.532480 | + | 0.922282i | ||||
\(663\) | 5356.62 | + | 32566.8i | 0.313776 | + | 1.90768i | ||||
\(664\) | −4351.77 | − | 7537.48i | −0.254339 | − | 0.440529i | ||||
\(665\) | 8892.06 | 0.518525 | ||||||||
\(666\) | 1724.41 | − | 583.037i | 0.100329 | − | 0.0339223i | ||||
\(667\) | 719.834 | 0.0417872 | ||||||||
\(668\) | 994.226 | + | 1722.05i | 0.0575865 | + | 0.0997427i | ||||
\(669\) | 14844.4 | + | 5597.27i | 0.857874 | + | 0.323472i | ||||
\(670\) | 6560.43 | − | 11363.0i | 0.378286 | − | 0.655211i | ||||
\(671\) | −2299.25 | + | 3982.42i | −0.132283 | + | 0.229120i | ||||
\(672\) | 3095.35 | − | 2537.16i | 0.177687 | − | 0.145645i | ||||
\(673\) | 4583.96 | + | 7939.65i | 0.262554 | + | 0.454757i | 0.966920 | − | 0.255080i | \(-0.0821019\pi\) |
−0.704366 | + | 0.709837i | \(0.748769\pi\) | |||||||
\(674\) | 1815.47 | 0.103753 | ||||||||
\(675\) | −1857.54 | + | 2975.14i | −0.105921 | + | 0.169649i | ||||
\(676\) | 1496.70 | 0.0851557 | ||||||||
\(677\) | 9438.93 | + | 16348.7i | 0.535846 | + | 0.928112i | 0.999122 | + | 0.0418983i | \(0.0133405\pi\) |
−0.463276 | + | 0.886214i | \(0.653326\pi\) | |||||||
\(678\) | −14261.2 | + | 11689.4i | −0.807812 | + | 0.662139i | ||||
\(679\) | 10961.0 | − | 18984.9i | 0.619503 | − | 1.07301i | ||||
\(680\) | −5595.90 | + | 9692.39i | −0.315578 | + | 0.546597i | ||||
\(681\) | 4083.85 | + | 1539.87i | 0.229800 | + | 0.0866488i | ||||
\(682\) | 1614.77 | + | 2796.86i | 0.0906638 | + | 0.157034i | ||||
\(683\) | −27207.5 | −1.52426 | −0.762128 | − | 0.647426i | \(-0.775845\pi\) | ||||
−0.762128 | + | 0.647426i | \(0.775845\pi\) | |||||||
\(684\) | 3293.23 | + | 2895.13i | 0.184094 | + | 0.161839i | ||||
\(685\) | −5263.85 | −0.293608 | ||||||||
\(686\) | −10385.0 | − | 17987.4i | −0.577991 | − | 1.00111i | ||||
\(687\) | 1181.94 | + | 7185.89i | 0.0656388 | + | 0.399067i | ||||
\(688\) | 367.381 | − | 636.323i | 0.0203580 | − | 0.0352610i | ||||
\(689\) | 17286.9 | − | 29941.7i | 0.955845 | − | 1.65557i | ||||
\(690\) | −1021.83 | − | 6212.46i | −0.0563775 | − | 0.342760i | ||||
\(691\) | 8703.62 | + | 15075.1i | 0.479162 | + | 0.829934i | 0.999714 | − | 0.0238963i | \(-0.00760715\pi\) |
−0.520552 | + | 0.853830i | \(0.674274\pi\) | |||||||
\(692\) | 1888.04 | 0.103718 | ||||||||
\(693\) | −8844.17 | − | 7775.03i | −0.484794 | − | 0.426189i | ||||
\(694\) | −13876.7 | −0.759011 | ||||||||
\(695\) | 5961.24 | + | 10325.2i | 0.325356 | + | 0.563534i | ||||
\(696\) | 901.668 | + | 339.985i | 0.0491058 | + | 0.0185159i | ||||
\(697\) | −6638.15 | + | 11497.6i | −0.360743 | + | 0.624825i | ||||
\(698\) | −1026.99 | + | 1778.80i | −0.0556909 | + | 0.0964595i | ||||
\(699\) | −11481.3 | + | 9410.87i | −0.621263 | + | 0.509230i | ||||
\(700\) | 214.628 | + | 371.747i | 0.0115888 | + | 0.0200725i | ||||
\(701\) | 18543.0 | 0.999086 | 0.499543 | − | 0.866289i | \(-0.333501\pi\) | ||||
0.499543 | + | 0.866289i | \(0.333501\pi\) | |||||||
\(702\) | −11676.8 | − | 21941.3i | −0.627798 | − | 1.17966i | ||||
\(703\) | −2874.63 | −0.154223 | ||||||||
\(704\) | −6500.29 | − | 11258.8i | −0.347996 | − | 0.602746i | ||||
\(705\) | 8871.05 | − | 7271.33i | 0.473905 | − | 0.388446i | ||||
\(706\) | 5112.91 | − | 8855.81i | 0.272559 | − | 0.472086i | ||||
\(707\) | −1467.21 | + | 2541.28i | −0.0780482 | + | 0.135184i | ||||
\(708\) | −2693.76 | − | 1015.72i | −0.142991 | − | 0.0539165i | ||||
\(709\) | −13116.9 | − | 22719.1i | −0.694803 | − | 1.20343i | −0.970247 | − | 0.242117i | \(-0.922158\pi\) |
0.275444 | − | 0.961317i | \(-0.411175\pi\) | |||||||
\(710\) | 12448.9 | 0.658029 | ||||||||
\(711\) | −29939.2 | + | 10122.7i | −1.57920 | + | 0.533941i | ||||
\(712\) | −21168.9 | −1.11424 | ||||||||
\(713\) | 1329.70 | + | 2303.11i | 0.0698425 | + | 0.120971i | ||||
\(714\) | −3835.98 | − | 23321.7i | −0.201061 | − | 1.22240i | ||||
\(715\) | 4631.32 | − | 8021.69i | 0.242240 | − | 0.419572i | ||||
\(716\) | −984.633 | + | 1705.43i | −0.0513931 | + | 0.0890155i | ||||
\(717\) | −1441.96 | − | 8766.76i | −0.0751062 | − | 0.456626i | ||||
\(718\) | −11713.2 | − | 20287.8i | −0.608817 | − | 1.05450i | ||||
\(719\) | −3043.06 | −0.157840 | −0.0789199 | − | 0.996881i | \(-0.525147\pi\) | ||||
−0.0789199 | + | 0.996881i | \(0.525147\pi\) | |||||||
\(720\) | 1919.69 | − | 9590.44i | 0.0993648 | − | 0.496409i | ||||
\(721\) | −22931.2 | −1.18447 | ||||||||
\(722\) | −15150.7 | − | 26241.8i | −0.780958 | − | 1.35266i | ||||
\(723\) | 21064.4 | + | 7942.60i | 1.08353 | + | 0.408559i | ||||
\(724\) | −1242.43 | + | 2151.95i | −0.0637769 | + | 0.110465i | ||||
\(725\) | −112.942 | + | 195.622i | −0.00578561 | + | 0.0100210i | ||||
\(726\) | −3903.37 | + | 3199.47i | −0.199542 | + | 0.163559i | ||||
\(727\) | −10971.2 | − | 19002.7i | −0.559698 | − | 0.969426i | −0.997521 | − | 0.0703647i | \(-0.977584\pi\) |
0.437823 | − | 0.899061i | \(-0.355750\pi\) | |||||||
\(728\) | 16392.2 | 0.834528 | ||||||||
\(729\) | −10994.5 | + | 16326.1i | −0.558577 | + | 0.829453i | ||||
\(730\) | −7529.10 | −0.381732 | ||||||||
\(731\) | −553.002 | − | 957.827i | −0.0279802 | − | 0.0484631i | ||||
\(732\) | 727.525 | − | 596.330i | 0.0367351 | − | 0.0301107i | ||||
\(733\) | 13288.4 | − | 23016.2i | 0.669604 | − | 1.15979i | −0.308411 | − | 0.951253i | \(-0.599797\pi\) |
0.978015 | − | 0.208535i | \(-0.0668694\pi\) | |||||||
\(734\) | −8987.58 | + | 15566.9i | −0.451959 | + | 0.782815i | ||||
\(735\) | −3767.44 | − | 1420.56i | −0.189067 | − | 0.0712901i | ||||
\(736\) | 2237.56 | + | 3875.57i | 0.112062 | + | 0.194097i | ||||
\(737\) | 27440.4 | 1.37148 | ||||||||
\(738\) | 1962.37 | − | 9803.63i | 0.0978803 | − | 0.488993i | ||||
\(739\) | 28787.7 | 1.43298 | 0.716489 | − | 0.697598i | \(-0.245748\pi\) | ||||
0.716489 | + | 0.697598i | \(0.245748\pi\) | |||||||
\(740\) | −69.3853 | − | 120.179i | −0.00344683 | − | 0.00597008i | ||||
\(741\) | 6370.45 | + | 38730.6i | 0.315822 | + | 1.92011i | ||||
\(742\) | −12379.5 | + | 21441.8i | −0.612485 | + | 1.06086i | ||||
\(743\) | 2251.51 | − | 3899.73i | 0.111171 | − | 0.192553i | −0.805072 | − | 0.593177i | \(-0.797873\pi\) |
0.916243 | + | 0.400624i | \(0.131207\pi\) | |||||||
\(744\) | 577.808 | + | 3512.92i | 0.0284724 | + | 0.173105i | ||||
\(745\) | 2865.72 | + | 4963.58i | 0.140929 | + | 0.244096i | ||||
\(746\) | −25624.8 | −1.25763 | ||||||||
\(747\) | 10846.0 | − | 3667.13i | 0.531238 | − | 0.179616i | ||||
\(748\) | 4343.45 | 0.212316 | ||||||||
\(749\) | −4118.46 | − | 7133.38i | −0.200915 | − | 0.347995i | ||||
\(750\) | 1848.62 | + | 697.045i | 0.0900027 | + | 0.0339366i | ||||
\(751\) | −2852.83 | + | 4941.24i | −0.138617 | + | 0.240091i | −0.926973 | − | 0.375128i | \(-0.877599\pi\) |
0.788357 | + | 0.615219i | \(0.210932\pi\) | |||||||
\(752\) | −15993.0 | + | 27700.6i | −0.775536 | + | 1.34327i | ||||
\(753\) | −6931.13 | + | 5681.24i | −0.335438 | + | 0.274948i | ||||
\(754\) | −800.356 | − | 1386.26i | −0.0386568 | − | 0.0669556i | ||||
\(755\) | 5830.58 | 0.281055 | ||||||||
\(756\) | 1131.71 | + | 2126.53i | 0.0544444 | + | 0.102303i | ||||
\(757\) | 17397.6 | 0.835305 | 0.417652 | − | 0.908607i | \(-0.362853\pi\) | ||||
0.417652 | + | 0.908607i | \(0.362853\pi\) | |||||||
\(758\) | 5338.62 | + | 9246.77i | 0.255815 | + | 0.443084i | ||||
\(759\) | 10183.3 | − | 8346.94i | 0.486996 | − | 0.399176i | ||||
\(760\) | −6655.02 | + | 11526.8i | −0.317636 | + | 0.550161i | ||||
\(761\) | 17757.2 | − | 30756.3i | 0.845857 | − | 1.46507i | −0.0390179 | − | 0.999239i | \(-0.512423\pi\) |
0.884875 | − | 0.465829i | \(-0.154244\pi\) | |||||||
\(762\) | −24107.4 | − | 9090.00i | −1.14609 | − | 0.432147i | ||||
\(763\) | −5289.97 | − | 9162.50i | −0.250996 | − | 0.434737i | ||||
\(764\) | −2940.58 | −0.139249 | ||||||||
\(765\) | −11057.2 | − | 9720.51i | −0.522579 | − | 0.459406i | ||||
\(766\) | 17435.3 | 0.822408 | ||||||||
\(767\) | −12885.1 | − | 22317.7i | −0.606591 | − | 1.05065i | ||||
\(768\) | 1584.37 | + | 9632.57i | 0.0744416 | + | 0.452585i | ||||
\(769\) | −15631.8 | + | 27075.1i | −0.733027 | + | 1.26964i | 0.222556 | + | 0.974920i | \(0.428560\pi\) |
−0.955583 | + | 0.294721i | \(0.904773\pi\) | |||||||
\(770\) | −3316.58 | + | 5744.48i | −0.155222 | + | 0.268853i | ||||
\(771\) | −4936.26 | − | 30011.2i | −0.230577 | − | 1.40185i | ||||
\(772\) | 146.612 | + | 253.940i | 0.00683508 | + | 0.0118387i | ||||
\(773\) | −6676.47 | −0.310654 | −0.155327 | − | 0.987863i | \(-0.549643\pi\) | ||||
−0.155327 | + | 0.987863i | \(0.549643\pi\) | |||||||
\(774\) | 625.551 | + | 549.930i | 0.0290503 | + | 0.0255385i | ||||
\(775\) | −834.522 | −0.0386799 | ||||||||
\(776\) | 16406.9 | + | 28417.5i | 0.758985 | + | 1.31460i | ||||
\(777\) | −1477.68 | − | 557.179i | −0.0682260 | − | 0.0257254i | ||||
\(778\) | −21850.7 | + | 37846.5i | −1.00692 | + | 1.74404i | ||||
\(779\) | −7894.53 | + | 13673.7i | −0.363095 | + | 0.628898i | ||||
\(780\) | −1465.43 | + | 1201.17i | −0.0672705 | + | 0.0551396i | ||||
\(781\) | 13017.6 | + | 22547.1i | 0.596422 | + | 1.03303i | ||||
\(782\) | 26427.3 | 1.20849 | ||||||||
\(783\) | −671.341 | + | 1075.26i | −0.0306408 | + | 0.0490761i | ||||
\(784\) | 11227.9 | 0.511473 | ||||||||
\(785\) | −8689.04 | − | 15049.9i | −0.395064 | − | 0.684271i | ||||
\(786\) | 3163.81 | − | 2593.28i | 0.143574 | − | 0.117683i | ||||
\(787\) | −4716.91 | + | 8169.93i | −0.213646 | + | 0.370047i | −0.952853 | − | 0.303432i | \(-0.901867\pi\) |
0.739207 | + | 0.673479i | \(0.235201\pi\) | |||||||
\(788\) | 449.439 | − | 778.451i | 0.0203180 | − | 0.0351919i | ||||
\(789\) | −1907.66 | − | 719.306i | −0.0860766 | − | 0.0324562i | ||||
\(790\) | 8901.10 | + | 15417.2i | 0.400869 | + | 0.694326i | ||||
\(791\) | 15997.7 | 0.719107 | ||||||||
\(792\) | 16698.0 | − | 5645.75i | 0.749164 | − | 0.253299i | ||||
\(793\) | 8420.57 | 0.377078 | ||||||||
\(794\) | 13709.8 | + | 23746.0i | 0.612773 | + | 1.06135i | ||||
\(795\) | 2503.06 | + | 15218.0i | 0.111666 | + | 0.678900i | ||||
\(796\) | −1065.27 | + | 1845.10i | −0.0474340 | + | 0.0821580i | ||||
\(797\) | 11738.1 | − | 20331.1i | 0.521689 | − | 0.903592i | −0.477992 | − | 0.878364i | \(-0.658635\pi\) |
0.999682 | − | 0.0252283i | \(-0.00803128\pi\) | |||||||
\(798\) | −4562.00 | − | 27735.7i | −0.202372 | − | 1.23037i | ||||
\(799\) | 24073.4 | + | 41696.4i | 1.06590 | + | 1.84620i | ||||
\(800\) | −1404.30 | −0.0620618 | ||||||||
\(801\) | 5465.61 | − | 27305.3i | 0.241096 | − | 1.20447i | ||||
\(802\) | 31972.0 | 1.40769 | ||||||||
\(803\) | −7873.02 | − | 13636.5i | −0.345993 | − | 0.599278i | ||||
\(804\) | −5252.37 | − | 1980.47i | −0.230394 | − | 0.0868729i | ||||
\(805\) | −2731.08 | + | 4730.37i | −0.119575 | + | 0.207110i | ||||
\(806\) | 2956.89 | − | 5121.48i | 0.129221 | − | 0.223817i | ||||
\(807\) | −18527.4 | + | 15186.3i | −0.808173 | + | 0.662435i | ||||
\(808\) | −2196.19 | − | 3803.91i | −0.0956208 | − | 0.165620i | ||||
\(809\) | −33269.8 | −1.44586 | −0.722932 | − | 0.690919i | \(-0.757206\pi\) | ||||
−0.722932 | + | 0.690919i | \(0.757206\pi\) | |||||||
\(810\) | 10232.9 | + | 4267.58i | 0.443886 | + | 0.185120i | ||||
\(811\) | 27892.8 | 1.20771 | 0.603853 | − | 0.797096i | \(-0.293631\pi\) | ||||
0.603853 | + | 0.797096i | \(0.293631\pi\) | |||||||
\(812\) | 77.5699 | + | 134.355i | 0.00335243 | + | 0.00580657i | ||||
\(813\) | −4644.44 | + | 3806.91i | −0.200354 | + | 0.164224i | ||||
\(814\) | 1072.19 | − | 1857.08i | 0.0461672 | − | 0.0799640i | ||||
\(815\) | −5558.30 | + | 9627.25i | −0.238894 | + | 0.413777i | ||||
\(816\) | 38414.6 | + | 14484.7i | 1.64801 | + | 0.621404i | ||||
\(817\) | −657.666 | − | 1139.11i | −0.0281626 | − | 0.0487790i | ||||
\(818\) | 10093.1 | 0.431415 | ||||||||
\(819\) | −4232.32 | + | 21143.9i | −0.180573 | + | 0.902111i | ||||
\(820\) | −762.204 | −0.0324601 | ||||||||
\(821\) | 1848.66 | + | 3201.98i | 0.0785856 | + | 0.136114i | 0.902640 | − | 0.430397i | \(-0.141626\pi\) |
−0.824054 | + | 0.566511i | \(0.808293\pi\) | |||||||
\(822\) | 2700.58 | + | 16418.8i | 0.114591 | + | 0.696680i | ||||
\(823\) | −3572.25 | + | 6187.32i | −0.151301 | + | 0.262061i | −0.931706 | − | 0.363213i | \(-0.881680\pi\) |
0.780405 | + | 0.625275i | \(0.215013\pi\) | |||||||
\(824\) | 17162.3 | − | 29725.9i | 0.725578 | − | 1.25674i | ||||
\(825\) | 670.596 | + | 4077.04i | 0.0282996 | + | 0.172054i | ||||
\(826\) | 9227.29 | + | 15982.1i | 0.388691 | + | 0.673232i | ||||
\(827\) | 19866.9 | 0.835357 | 0.417679 | − | 0.908595i | \(-0.362844\pi\) | ||||
0.417679 | + | 0.908595i | \(0.362844\pi\) | |||||||
\(828\) | −2551.61 | + | 862.723i | −0.107095 | + | 0.0362098i | ||||
\(829\) | −36736.5 | −1.53910 | −0.769548 | − | 0.638589i | \(-0.779518\pi\) | ||||
−0.769548 | + | 0.638589i | \(0.779518\pi\) | |||||||
\(830\) | −3224.58 | − | 5585.13i | −0.134851 | − | 0.233569i | ||||
\(831\) | 2958.09 | + | 1115.39i | 0.123484 | + | 0.0465611i | ||||
\(832\) | −11903.0 | + | 20616.7i | −0.495990 | + | 0.859079i | ||||
\(833\) | 8450.38 | − | 14636.5i | 0.351487 | − | 0.608793i | ||||
\(834\) | 29147.5 | − | 23891.3i | 1.21018 | − | 0.991952i | ||||
\(835\) | −3969.96 | − | 6876.16i | −0.164534 | − | 0.284981i | ||||
\(836\) | 5165.52 | 0.213700 | ||||||||
\(837\) | −4680.42 | − | 161.703i | −0.193284 | − | 0.00667773i | ||||
\(838\) | −1478.71 | −0.0609560 | ||||||||
\(839\) | −15006.1 | − | 25991.4i | −0.617485 | − | 1.06951i | −0.989943 | − | 0.141466i | \(-0.954818\pi\) |
0.372458 | − | 0.928049i | \(-0.378515\pi\) | |||||||
\(840\) | −5655.16 | + | 4635.37i | −0.232288 | + | 0.190399i | ||||
\(841\) | 12153.7 | − | 21050.8i | 0.498326 | − | 0.863127i | ||||
\(842\) | −7683.32 | + | 13307.9i | −0.314471 | + | 0.544680i | ||||
\(843\) | −13366.8 | − | 5040.12i | −0.546117 | − | 0.205920i | ||||
\(844\) | 3092.07 | + | 5355.62i | 0.126106 | + | 0.218422i | ||||
\(845\) | −5976.32 | −0.243304 | ||||||||
\(846\) | −27231.7 | − | 23939.7i | −1.10667 | − | 0.972890i | ||||
\(847\) | 4378.68 | 0.177631 | ||||||||
\(848\) | −21503.4 | − | 37245.0i | −0.870789 | − | 1.50825i | ||||
\(849\) | 861.519 | + | 5237.80i | 0.0348260 | + | 0.211733i | ||||
\(850\) | −4146.46 | + | 7181.88i | −0.167320 | + | 0.289807i | ||||
\(851\) | 882.905 | − | 1529.24i | 0.0355648 | − | 0.0616000i | ||||
\(852\) | −864.391 | − | 5255.27i | −0.0347577 | − | 0.211318i | ||||
\(853\) | 2690.51 | + | 4660.10i | 0.107997 | + | 0.187056i | 0.914959 | − | 0.403548i | \(-0.132223\pi\) |
−0.806962 | + | 0.590604i | \(0.798890\pi\) | |||||||
\(854\) | −6030.13 | −0.241624 | ||||||||
\(855\) | −13149.9 | − | 11560.3i | −0.525986 | − | 0.462401i | ||||
\(856\) | 12329.4 | 0.492302 | ||||||||
\(857\) | −7319.88 | − | 12678.4i | −0.291765 | − | 0.505352i | 0.682462 | − | 0.730921i | \(-0.260909\pi\) |
−0.974227 | + | 0.225569i | \(0.927576\pi\) | |||||||
\(858\) | −27397.0 | − | 10330.4i | −1.09011 | − | 0.411041i | ||||
\(859\) | −14770.0 | + | 25582.4i | −0.586667 | + | 1.01614i | 0.407999 | + | 0.912983i | \(0.366227\pi\) |
−0.994665 | + | 0.103154i | \(0.967107\pi\) | |||||||
\(860\) | 31.7483 | − | 54.9897i | 0.00125885 | − | 0.00218039i | ||||
\(861\) | −6708.44 | + | 5498.71i | −0.265532 | + | 0.217649i | ||||
\(862\) | −10561.3 | − | 18292.7i | −0.417307 | − | 0.722797i | ||||
\(863\) | 3387.63 | 0.133622 | 0.0668112 | − | 0.997766i | \(-0.478717\pi\) | ||||
0.0668112 | + | 0.997766i | \(0.478717\pi\) | |||||||
\(864\) | −7876.00 | − | 272.106i | −0.310124 | − | 0.0107144i | ||||
\(865\) | −7538.98 | −0.296339 | ||||||||
\(866\) | 20894.1 | + | 36189.7i | 0.819875 | + | 1.42007i | ||||
\(867\) | 28050.2 | − | 22991.9i | 1.09877 | − | 0.900628i | ||||
\(868\) | −286.580 | + | 496.370i | −0.0112064 | + | 0.0194100i | ||||
\(869\) | −18615.4 | + | 32242.8i | −0.726678 | + | 1.25864i | ||||
\(870\) | 668.119 | + | 251.922i | 0.0260360 | + | 0.00981721i | ||||
\(871\) | −25123.8 | − | 43515.7i | −0.977368 | − | 1.69285i | ||||
\(872\) | 15836.5 | 0.615015 | ||||||||
\(873\) | −40891.2 | + | 13825.7i | −1.58529 | + | 0.536000i | ||||
\(874\) | 31429.2 | 1.21637 | ||||||||
\(875\) | −857.014 | − | 1484.39i | −0.0331113 | − | 0.0573504i | ||||
\(876\) | 522.783 | + | 3178.38i | 0.0201635 | + | 0.122588i | ||||
\(877\) | 122.052 | − | 211.400i | 0.00469944 | − | 0.00813967i | −0.863666 | − | 0.504064i | \(-0.831837\pi\) |
0.868366 | + | 0.495925i | \(0.165171\pi\) | |||||||
\(878\) | −12899.8 | + | 22343.1i | −0.495838 | + | 0.858817i | ||||
\(879\) | −4412.75 | − | 26828.4i | −0.169327 | − | 1.02946i | ||||
\(880\) | −5760.97 | − | 9978.30i | −0.220684 | − | 0.382237i | ||||
\(881\) | 13910.2 | 0.531948 | 0.265974 | − | 0.963980i | \(-0.414307\pi\) | ||||
0.265974 | + | 0.963980i | \(0.414307\pi\) | |||||||
\(882\) | −2498.10 | + | 12480.1i | −0.0953689 | + | 0.476446i | ||||
\(883\) | −8805.87 | −0.335607 | −0.167803 | − | 0.985820i | \(-0.553667\pi\) | ||||
−0.167803 | + | 0.985820i | \(0.553667\pi\) | |||||||
\(884\) | −3976.76 | − | 6887.95i | −0.151304 | − | 0.262067i | ||||
\(885\) | 10756.2 | + | 4055.76i | 0.408549 | + | 0.154049i | ||||
\(886\) | 848.943 | − | 1470.41i | 0.0321905 | − | 0.0557556i | ||||
\(887\) | −6640.41 | + | 11501.5i | −0.251368 | + | 0.435381i | −0.963903 | − | 0.266255i | \(-0.914214\pi\) |
0.712535 | + | 0.701637i | \(0.247547\pi\) | |||||||
\(888\) | 1828.21 | − | 1498.53i | 0.0690885 | − | 0.0566298i | ||||
\(889\) | 11176.1 | + | 19357.6i | 0.421637 | + | 0.730296i | ||||
\(890\) | −15685.8 | −0.590773 | ||||||||
\(891\) | 2971.04 | + | 22996.0i | 0.111710 | + | 0.864642i | ||||
\(892\) | −3823.11 | −0.143506 | ||||||||
\(893\) | 28629.7 | + | 49588.2i | 1.07285 | + | 1.85824i | ||||
\(894\) | 14011.9 | − | 11485.2i | 0.524194 | − | 0.429666i | ||||
\(895\) | 3931.65 | − | 6809.82i | 0.146839 | − | 0.254332i | ||||
\(896\) | 11605.0 | − | 20100.4i | 0.432695 | − | 0.749449i | ||||
\(897\) | −22560.4 | − | 8506.67i | −0.839765 | − | 0.316644i | ||||
\(898\) | −22470.9 | − | 38920.7i | −0.835036 | − | 1.44633i | ||||
\(899\) | −301.609 | −0.0111893 | ||||||||
\(900\) | 165.896 | − | 828.786i | 0.00614429 | − | 0.0306958i | ||||
\(901\) | −64736.1 | −2.39364 | ||||||||
\(902\) | −5889.04 | − | 10200.1i | −0.217387 | − | 0.376526i | ||||
\(903\) | −117.279 | − | 713.025i | −0.00432204 | − | 0.0262768i | ||||
\(904\) | −11973.1 | + | 20738.0i | −0.440507 | + | 0.762981i | ||||
\(905\) | 4961.03 | − | 8592.76i | 0.182221 | − | 0.315616i | ||||
\(906\) | −2991.33 | − | 18186.5i | −0.109691 | − | 0.666894i | ||||
\(907\) | 542.122 | + | 938.982i | 0.0198466 | + | 0.0343753i | 0.875778 | − | 0.482714i | \(-0.160349\pi\) |
−0.855932 | + | 0.517089i | \(0.827016\pi\) | |||||||
\(908\) | −1051.78 | −0.0384411 | ||||||||
\(909\) | 5473.61 | − | 1850.68i | 0.199723 | − | 0.0675281i | ||||
\(910\) | 12146.3 | 0.442469 | ||||||||
\(911\) | −25094.4 | − | 43464.7i | −0.912638 | − | 1.58073i | −0.810324 | − | 0.585983i | \(-0.800709\pi\) |
−0.102314 | − | 0.994752i | \(-0.532625\pi\) | |||||||
\(912\) | 45685.2 | + | 17226.2i | 1.65876 | + | 0.625455i | ||||
\(913\) | 6743.74 | − | 11680.5i | 0.244452 | − | 0.423404i | ||||
\(914\) | 21608.4 | − | 37426.9i | 0.781995 | − | 1.35445i | ||||
\(915\) | −2905.02 | + | 2381.15i | −0.104958 | + | 0.0860312i | ||||
\(916\) | −877.475 | − | 1519.83i | −0.0316513 | − | 0.0548216i | ||||
\(917\) | −3549.06 | −0.127808 | ||||||||
\(918\) | −24647.0 | + | 39476.1i | −0.886136 | + | 1.41929i | ||||
\(919\) | 30376.1 | 1.09033 | 0.545166 | − | 0.838328i | \(-0.316467\pi\) | ||||
0.545166 | + | 0.838328i | \(0.316467\pi\) | |||||||
\(920\) | −4088.00 | − | 7080.63i | −0.146497 | − | 0.253741i | ||||
\(921\) | −19742.5 | + | 16182.3i | −0.706336 | + | 0.578962i | ||||
\(922\) | 11714.5 | − | 20290.2i | 0.418435 | − | 0.724751i | ||||
\(923\) | 23837.2 | − | 41287.2i | 0.850066 | − | 1.47236i | ||||
\(924\) | 2655.30 | + | 1001.21i | 0.0945377 | + | 0.0356466i | ||||
\(925\) | 277.056 | + | 479.876i | 0.00984817 | + | 0.0170575i | ||||
\(926\) | 24057.3 | 0.853750 | ||||||||
\(927\) | 33911.6 | + | 29812.2i | 1.20151 | + | 1.05627i | ||||
\(928\) | −507.534 | −0.0179533 | ||||||||
\(929\) | 23098.8 | + | 40008.3i | 0.815766 | + | 1.41295i | 0.908776 | + | 0.417283i | \(0.137018\pi\) |
−0.0930102 | + | 0.995665i | \(0.529649\pi\) | |||||||
\(930\) | 428.145 | + | 2603.01i | 0.0150962 | + | 0.0917806i | ||||
\(931\) | 10049.8 | − | 17406.7i | 0.353778 | − | 0.612762i | ||||
\(932\) | 1788.74 | − | 3098.20i | 0.0628672 | − | 0.108889i | ||||
\(933\) | −699.007 | − | 4249.78i | −0.0245278 | − | 0.149123i | ||||
\(934\) | −17702.6 | − | 30661.7i | −0.620177 | − | 1.07418i | ||||
\(935\) | −17343.4 | −0.606621 | ||||||||
\(936\) | −24241.5 | − | 21311.0i | −0.846536 | − | 0.744201i | ||||
\(937\) | 37004.7 | 1.29017 | 0.645085 | − | 0.764111i | \(-0.276822\pi\) | ||||
0.645085 | + | 0.764111i | \(0.276822\pi\) | |||||||
\(938\) | 17991.6 | + | 31162.4i | 0.626277 | + | 1.08474i | ||||
\(939\) | −44911.3 | − | 16934.4i | −1.56084 | − | 0.588533i | ||||
\(940\) | −1382.08 | + | 2393.83i | −0.0479558 | + | 0.0830618i | ||||
\(941\) | −21907.2 | + | 37944.4i | −0.758932 | + | 1.31451i | 0.184464 | + | 0.982839i | \(0.440945\pi\) |
−0.943396 | + | 0.331669i | \(0.892388\pi\) | |||||||
\(942\) | −42485.1 | + | 34823.7i | −1.46947 | + | 1.20448i | ||||
\(943\) | −4849.40 | − | 8399.41i | −0.167464 | − | 0.290055i | ||||
\(944\) | −32056.0 | −1.10523 | ||||||||
\(945\) | −4518.94 | − | 8491.27i | −0.155557 | − | 0.292297i | ||||
\(946\) | 981.191 | 0.0337223 | ||||||||
\(947\) | −2304.86 | − | 3992.14i | −0.0790898 | − | 0.136988i | 0.823768 | − | 0.566928i | \(-0.191868\pi\) |
−0.902857 | + | 0.429940i | \(0.858535\pi\) | |||||||
\(948\) | 5890.24 | − | 4828.05i | 0.201800 | − | 0.165409i | ||||
\(949\) | −14416.7 | + | 24970.5i | −0.493136 | + | 0.854136i | ||||
\(950\) | −4931.24 | + | 8541.17i | −0.168411 | + | 0.291697i | ||||
\(951\) | 44236.5 | + | 16679.9i | 1.50838 | + | 0.568752i | ||||
\(952\) | −15346.5 | − | 26580.8i | −0.522460 | − | 0.904927i | ||||
\(953\) | 4281.80 | 0.145542 | 0.0727708 | − | 0.997349i | \(-0.476816\pi\) | ||||
0.0727708 | + | 0.997349i | \(0.476816\pi\) | |||||||
\(954\) | 46183.1 | − | 15614.9i | 1.56733 | − | 0.529928i | ||||
\(955\) | 11741.8 | 0.397859 | ||||||||
\(956\) | 1070.52 | + | 1854.19i | 0.0362165 | + | 0.0627288i | ||||
\(957\) | 242.363 | + | 1473.50i | 0.00818651 | + | 0.0497718i | ||||
\(958\) | 28434.0 | − | 49249.1i | 0.958936 | − | 1.66093i | ||||
\(959\) | 7217.91 | − | 12501.8i | 0.243043 | − | 0.420963i | ||||
\(960\) | −1723.51 | − | 10478.5i | −0.0579437 | − | 0.352283i | ||||
\(961\) | 14338.4 | + | 24834.8i | 0.481298 | + | 0.833633i | ||||
\(962\) | −3926.68 | −0.131602 | ||||||||
\(963\) | −3183.34 | + | 15903.4i | −0.106523 | + | 0.532170i | ||||
\(964\) | −5425.05 | −0.181254 | ||||||||
\(965\) | −585.424 | − | 1013.98i | −0.0195290 | − | 0.0338252i | ||||
\(966\) | 16155.9 | + | 6091.79i | 0.538104 | + | 0.202899i | ||||
\(967\) | 18114.9 | − | 31375.9i | 0.602416 | − | 1.04341i | −0.390038 | − | 0.920799i | \(-0.627538\pi\) |
0.992454 | − | 0.122616i | \(-0.0391284\pi\) | |||||||
\(968\) | −3277.10 | + | 5676.11i | −0.108812 | + | 0.188468i | ||||
\(969\) | 56839.7 | − | 46589.7i | 1.88437 | − | 1.54456i | ||||
\(970\) | 12157.2 | + | 21056.8i | 0.402416 | + | 0.697005i | ||||
\(971\) | 844.928 | 0.0279249 | 0.0139624 | − | 0.999903i | \(-0.495555\pi\) | ||||
0.0139624 | + | 0.999903i | \(0.495555\pi\) | |||||||
\(972\) | 1091.02 | − | 4616.10i | 0.0360025 | − | 0.152327i | ||||
\(973\) | −32696.7 | −1.07730 | ||||||||
\(974\) | 3421.26 | + | 5925.80i | 0.112551 | + | 0.194943i | ||||
\(975\) | 5851.50 | − | 4796.29i | 0.192203 | − | 0.157543i | ||||
\(976\) | 5237.24 | − | 9071.16i | 0.171762 | − | 0.297501i | ||||
\(977\) | −22922.5 | + | 39702.9i | −0.750619 | + | 1.30011i | 0.196904 | + | 0.980423i | \(0.436911\pi\) |
−0.947523 | + | 0.319687i | \(0.896422\pi\) | |||||||
\(978\) | 32880.6 | + | 12398.0i | 1.07506 | + | 0.405363i | ||||
\(979\) | −16402.2 | − | 28409.5i | −0.535463 | − | 0.927449i | ||||
\(980\) | 970.288 | 0.0316273 | ||||||||
\(981\) | −4088.85 | + | 20427.2i | −0.133075 | + | 0.664821i | ||||
\(982\) | 6048.05 | 0.196539 | ||||||||
\(983\) | 20101.0 | + | 34815.9i | 0.652210 | + | 1.12966i | 0.982586 | + | 0.185811i | \(0.0594911\pi\) |
−0.330376 | + | 0.943849i | \(0.607176\pi\) | |||||||
\(984\) | −2107.26 | − | 12811.6i | −0.0682692 | − | 0.415059i | ||||
\(985\) | −1794.62 | + | 3108.37i | −0.0580520 | + | 0.100549i | ||||
\(986\) | −1498.59 | + | 2595.64i | −0.0484025 | + | 0.0838356i | ||||
\(987\) | 5105.42 | + | 31039.6i | 0.164648 | + | 1.00101i | ||||
\(988\) | −4729.43 | − | 8191.61i | −0.152291 | − | 0.263775i | ||||
\(989\) | 807.974 | 0.0259778 | ||||||||
\(990\) | 12372.9 | − | 4183.39i | 0.397209 | − | 0.134300i | ||||
\(991\) | 1797.91 | 0.0576313 | 0.0288157 | − | 0.999585i | \(-0.490826\pi\) | ||||
0.0288157 | + | 0.999585i | \(0.490826\pi\) | |||||||
\(992\) | −937.534 | − | 1623.86i | −0.0300068 | − | 0.0519733i | ||||
\(993\) | −28994.3 | − | 10932.7i | −0.926594 | − | 0.349384i | ||||
\(994\) | −17070.3 | + | 29566.6i | −0.544704 | + | 0.943455i | ||||
\(995\) | 4253.63 | − | 7367.50i | 0.135527 | − | 0.234739i | ||||
\(996\) | −2133.84 | + | 1749.04i | −0.0678849 | + | 0.0556432i | ||||
\(997\) | −4566.04 | − | 7908.61i | −0.145043 | − | 0.251222i | 0.784346 | − | 0.620324i | \(-0.212999\pi\) |
−0.929389 | + | 0.369102i | \(0.879665\pi\) | |||||||
\(998\) | 7342.47 | 0.232888 | ||||||||
\(999\) | 1460.89 | + | 2745.07i | 0.0462667 | + | 0.0869370i |
(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 | 45.4.e.c.31.2 | yes | 14 | |
3.2 | odd | 2 | 135.4.e.c.91.6 | 14 | |||
5.2 | odd | 4 | 225.4.k.d.49.11 | 28 | |||
5.3 | odd | 4 | 225.4.k.d.49.4 | 28 | |||
5.4 | even | 2 | 225.4.e.d.76.6 | 14 | |||
9.2 | odd | 6 | 135.4.e.c.46.6 | 14 | |||
9.4 | even | 3 | 405.4.a.m.1.6 | 7 | |||
9.5 | odd | 6 | 405.4.a.n.1.2 | 7 | |||
9.7 | even | 3 | inner | 45.4.e.c.16.2 | ✓ | 14 | |
45.4 | even | 6 | 2025.4.a.bb.1.2 | 7 | |||
45.7 | odd | 12 | 225.4.k.d.124.4 | 28 | |||
45.14 | odd | 6 | 2025.4.a.ba.1.6 | 7 | |||
45.34 | even | 6 | 225.4.e.d.151.6 | 14 | |||
45.43 | odd | 12 | 225.4.k.d.124.11 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.2 | ✓ | 14 | 9.7 | even | 3 | inner | |
45.4.e.c.31.2 | yes | 14 | 1.1 | even | 1 | trivial | |
135.4.e.c.46.6 | 14 | 9.2 | odd | 6 | |||
135.4.e.c.91.6 | 14 | 3.2 | odd | 2 | |||
225.4.e.d.76.6 | 14 | 5.4 | even | 2 | |||
225.4.e.d.151.6 | 14 | 45.34 | even | 6 | |||
225.4.k.d.49.4 | 28 | 5.3 | odd | 4 | |||
225.4.k.d.49.11 | 28 | 5.2 | odd | 4 | |||
225.4.k.d.124.4 | 28 | 45.7 | odd | 12 | |||
225.4.k.d.124.11 | 28 | 45.43 | odd | 12 | |||
405.4.a.m.1.6 | 7 | 9.4 | even | 3 | |||
405.4.a.n.1.2 | 7 | 9.5 | odd | 6 | |||
2025.4.a.ba.1.6 | 7 | 45.14 | odd | 6 | |||
2025.4.a.bb.1.2 | 7 | 45.4 | even | 6 |