Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(49,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 124.11 | ||
Character | \(\chi\) | \(=\) | 225.124 |
Dual form | 225.4.k.d.49.11 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.63422 | + | 1.52087i | 0.931339 | + | 0.537709i | 0.887235 | − | 0.461318i | \(-0.152623\pi\) |
0.0441043 | + | 0.999027i | \(0.485957\pi\) | |||||||
\(3\) | −3.29398 | + | 4.01867i | −0.633927 | + | 0.773393i | ||||
\(4\) | 0.626094 | + | 1.08443i | 0.0782617 | + | 0.135553i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −14.7890 | + | 5.57636i | −1.00626 | + | 0.379423i | ||||
\(7\) | −11.8751 | − | 6.85611i | −0.641197 | − | 0.370195i | 0.143879 | − | 0.989595i | \(-0.454043\pi\) |
−0.785075 | + | 0.619400i | \(0.787376\pi\) | |||||||
\(8\) | − | 20.5251i | − | 0.907090i | ||||||
\(9\) | −5.29939 | − | 26.4748i | −0.196274 | − | 0.980549i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.9034 | + | 27.5455i | −0.435914 | + | 0.755026i | −0.997370 | − | 0.0724812i | \(-0.976908\pi\) |
0.561455 | + | 0.827507i | \(0.310242\pi\) | |||||||
\(12\) | −6.42029 | − | 1.05602i | −0.154448 | − | 0.0254038i | ||||
\(13\) | 50.4401 | − | 29.1216i | 1.07612 | − | 0.621298i | 0.146272 | − | 0.989244i | \(-0.453272\pi\) |
0.929847 | + | 0.367946i | \(0.119939\pi\) | |||||||
\(14\) | −20.8545 | − | 36.1211i | −0.398115 | − | 0.689555i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 36.2248 | − | 62.7431i | 0.566012 | − | 0.980361i | ||||
\(17\) | − | 109.055i | − | 1.55586i | −0.628348 | − | 0.777932i | \(-0.716269\pi\) | ||
0.628348 | − | 0.777932i | \(-0.283731\pi\) | |||||||
\(18\) | 26.3050 | − | 77.8003i | 0.344453 | − | 1.01876i | ||||
\(19\) | −129.695 | −1.56601 | −0.783004 | − | 0.622017i | \(-0.786313\pi\) | ||||
−0.783004 | + | 0.622017i | \(0.786313\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 66.6689 | − | 25.1383i | 0.692778 | − | 0.261221i | ||||
\(22\) | −83.7863 | + | 48.3740i | −0.811968 | + | 0.468790i | ||||
\(23\) | 68.9949 | − | 39.8342i | 0.625497 | − | 0.361131i | −0.153509 | − | 0.988147i | \(-0.549057\pi\) |
0.779006 | + | 0.627017i | \(0.215724\pi\) | |||||||
\(24\) | 82.4836 | + | 67.6093i | 0.701537 | + | 0.575028i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 177.161 | 1.33631 | ||||||||
\(27\) | 123.850 | + | 65.9111i | 0.882773 | + | 0.469800i | ||||
\(28\) | − | 17.1703i | − | 0.115888i | ||||||
\(29\) | 4.51769 | − | 7.82486i | 0.0289280 | − | 0.0501048i | −0.851199 | − | 0.524843i | \(-0.824124\pi\) |
0.880127 | + | 0.474738i | \(0.157457\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.6904 | + | 28.9087i | 0.0966998 | + | 0.167489i | 0.910317 | − | 0.413912i | \(-0.135838\pi\) |
−0.813617 | + | 0.581401i | \(0.802505\pi\) | |||||||
\(32\) | 48.6463 | − | 28.0860i | 0.268735 | − | 0.155154i | ||||
\(33\) | −58.3108 | − | 154.645i | −0.307594 | − | 0.815764i | ||||
\(34\) | 165.858 | − | 287.275i | 0.836602 | − | 1.44904i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 25.3921 | − | 22.3225i | 0.117556 | − | 0.103345i | ||||
\(37\) | 22.1645i | 0.0984817i | 0.998787 | + | 0.0492408i | \(0.0156802\pi\) | ||||
−0.998787 | + | 0.0492408i | \(0.984320\pi\) | |||||||
\(38\) | −341.647 | − | 197.250i | −1.45848 | − | 0.842056i | ||||
\(39\) | −49.1186 | + | 298.628i | −0.201673 | + | 1.22612i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −60.8698 | − | 105.430i | −0.231860 | − | 0.401593i | 0.726495 | − | 0.687171i | \(-0.241148\pi\) |
−0.958356 | + | 0.285578i | \(0.907814\pi\) | |||||||
\(42\) | 213.853 | + | 35.1747i | 0.785672 | + | 0.129228i | ||||
\(43\) | −8.78298 | − | 5.07086i | −0.0311487 | − | 0.0179837i | 0.484345 | − | 0.874877i | \(-0.339058\pi\) |
−0.515493 | + | 0.856894i | \(0.672391\pi\) | |||||||
\(44\) | −39.8281 | −0.136462 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 242.331 | 0.776733 | ||||||||
\(47\) | −382.343 | − | 220.746i | −1.18661 | − | 0.685088i | −0.229073 | − | 0.973409i | \(-0.573570\pi\) |
−0.957534 | + | 0.288321i | \(0.906903\pi\) | |||||||
\(48\) | 132.820 | + | 352.250i | 0.399395 | + | 1.05923i | ||||
\(49\) | −77.4875 | − | 134.212i | −0.225911 | − | 0.391289i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 438.255 | + | 359.225i | 1.20329 | + | 0.986304i | ||||
\(52\) | 63.1604 | + | 36.4657i | 0.168438 | + | 0.0972477i | ||||
\(53\) | − | 593.610i | − | 1.53846i | −0.638969 | − | 0.769232i | \(-0.720639\pi\) | ||
0.638969 | − | 0.769232i | \(-0.279361\pi\) | |||||||
\(54\) | 226.006 | + | 361.984i | 0.569546 | + | 0.912218i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −140.722 | + | 243.738i | −0.335800 | + | 0.581623i | ||||
\(57\) | 427.214 | − | 521.202i | 0.992734 | − | 1.21114i | ||||
\(58\) | 23.8012 | − | 13.7416i | 0.0538836 | − | 0.0311097i | ||||
\(59\) | 221.230 | + | 383.182i | 0.488164 | + | 0.845525i | 0.999907 | − | 0.0136133i | \(-0.00433337\pi\) |
−0.511743 | + | 0.859139i | \(0.671000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −72.2881 | + | 125.207i | −0.151730 | + | 0.262804i | −0.931864 | − | 0.362809i | \(-0.881818\pi\) |
0.780133 | + | 0.625613i | \(0.215151\pi\) | |||||||
\(62\) | 101.536i | 0.207985i | ||||||||
\(63\) | −118.583 | + | 350.725i | −0.237145 | + | 0.701385i | ||||
\(64\) | −408.736 | −0.798312 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 81.5912 | − | 496.052i | 0.152169 | − | 0.925149i | ||||
\(67\) | −747.138 | + | 431.360i | −1.36235 | + | 0.786553i | −0.989936 | − | 0.141514i | \(-0.954803\pi\) |
−0.372414 | + | 0.928067i | \(0.621470\pi\) | |||||||
\(68\) | 118.262 | − | 68.2786i | 0.210902 | − | 0.121765i | ||||
\(69\) | −67.1873 | + | 408.481i | −0.117223 | + | 0.712685i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −818.541 | −1.36821 | −0.684105 | − | 0.729384i | \(-0.739807\pi\) | ||||
−0.684105 | + | 0.729384i | \(0.739807\pi\) | |||||||
\(72\) | −543.398 | + | 108.771i | −0.889446 | + | 0.178038i | ||||
\(73\) | 495.052i | 0.793719i | 0.917879 | + | 0.396859i | \(0.129900\pi\) | ||||
−0.917879 | + | 0.396859i | \(0.870100\pi\) | |||||||
\(74\) | −33.7093 | + | 58.3863i | −0.0529545 | + | 0.0917198i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −81.2014 | − | 140.645i | −0.122558 | − | 0.212277i | ||||
\(77\) | 377.710 | − | 218.071i | 0.559014 | − | 0.322747i | ||||
\(78\) | −583.563 | + | 711.950i | −0.847122 | + | 1.03349i | ||||
\(79\) | 585.263 | − | 1013.71i | 0.833510 | − | 1.44368i | −0.0617284 | − | 0.998093i | \(-0.519661\pi\) |
0.895238 | − | 0.445588i | \(-0.147005\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −672.833 | + | 280.601i | −0.922953 | + | 0.384912i | ||||
\(82\) | − | 370.300i | − | 0.498693i | ||||||
\(83\) | 367.232 | + | 212.022i | 0.485651 | + | 0.280390i | 0.722768 | − | 0.691090i | \(-0.242869\pi\) |
−0.237118 | + | 0.971481i | \(0.576203\pi\) | |||||||
\(84\) | 69.0017 | + | 56.5586i | 0.0896273 | + | 0.0734648i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −15.4242 | − | 26.7156i | −0.0193400 | − | 0.0334978i | ||||
\(87\) | 16.5644 | + | 43.9300i | 0.0204125 | + | 0.0541355i | ||||
\(88\) | 565.374 | + | 326.419i | 0.684876 | + | 0.395413i | ||||
\(89\) | −1031.37 | −1.22837 | −0.614183 | − | 0.789163i | \(-0.710514\pi\) | ||||
−0.614183 | + | 0.789163i | \(0.710514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −798.643 | −0.920006 | ||||||||
\(92\) | 86.3945 | + | 49.8799i | 0.0979049 | + | 0.0565254i | ||||
\(93\) | −171.152 | − | 28.1513i | −0.190835 | − | 0.0313888i | ||||
\(94\) | −671.452 | − | 1162.99i | −0.736756 | − | 1.27610i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −47.3718 | + | 288.008i | −0.0503632 | + | 0.306195i | ||||
\(97\) | 1384.53 | + | 799.356i | 1.44925 | + | 0.836725i | 0.998437 | − | 0.0558930i | \(-0.0178006\pi\) |
0.450814 | + | 0.892618i | \(0.351134\pi\) | |||||||
\(98\) | − | 471.394i | − | 0.485897i | ||||||
\(99\) | 813.541 | + | 275.066i | 0.825898 | + | 0.279244i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 107.000 | − | 185.330i | 0.105415 | − | 0.182584i | −0.808493 | − | 0.588506i | \(-0.799716\pi\) |
0.913908 | + | 0.405922i | \(0.133050\pi\) | |||||||
\(102\) | 608.129 | + | 1612.81i | 0.590331 | + | 1.56561i | ||||
\(103\) | 1448.27 | − | 836.160i | 1.38546 | − | 0.799897i | 0.392662 | − | 0.919683i | \(-0.371554\pi\) |
0.992800 | + | 0.119786i | \(0.0382210\pi\) | |||||||
\(104\) | −597.723 | − | 1035.29i | −0.563573 | − | 0.976137i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 902.804 | − | 1563.70i | 0.827246 | − | 1.43283i | ||||
\(107\) | 600.699i | 0.542727i | 0.962477 | + | 0.271363i | \(0.0874745\pi\) | ||||
−0.962477 | + | 0.271363i | \(0.912525\pi\) | |||||||
\(108\) | 6.06581 | + | 175.572i | 0.00540447 | + | 0.156430i | ||||
\(109\) | 771.570 | 0.678009 | 0.339005 | − | 0.940785i | \(-0.389910\pi\) | ||||
0.339005 | + | 0.940785i | \(0.389910\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −89.0718 | − | 73.0094i | −0.0761650 | − | 0.0624302i | ||||
\(112\) | −860.348 | + | 496.722i | −0.725850 | + | 0.419070i | ||||
\(113\) | −1010.37 | + | 583.338i | −0.841131 | + | 0.485627i | −0.857648 | − | 0.514237i | \(-0.828075\pi\) |
0.0165177 | + | 0.999864i | \(0.494742\pi\) | |||||||
\(114\) | 1918.06 | − | 723.228i | 1.57581 | − | 0.594180i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11.3140 | 0.00905583 | ||||||||
\(117\) | −1038.29 | − | 1181.06i | −0.820427 | − | 0.933244i | ||||
\(118\) | 1345.85i | 1.04996i | ||||||||
\(119\) | −747.692 | + | 1295.04i | −0.575973 | + | 0.997615i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 159.663 | + | 276.545i | 0.119957 | + | 0.207772i | ||||
\(122\) | −380.846 | + | 219.882i | −0.282624 | + | 0.163173i | ||||
\(123\) | 624.190 | + | 102.667i | 0.457572 | + | 0.0752618i | ||||
\(124\) | −20.8996 | + | 36.1991i | −0.0151358 | + | 0.0262159i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −845.783 | + | 743.539i | −0.598003 | + | 0.525712i | ||||
\(127\) | − | 1630.10i | − | 1.13896i | −0.822006 | − | 0.569479i | \(-0.807145\pi\) | ||
0.822006 | − | 0.569479i | \(-0.192855\pi\) | |||||||
\(128\) | −1465.87 | − | 846.322i | −1.01223 | − | 0.584414i | ||||
\(129\) | 49.3091 | − | 18.5926i | 0.0336544 | − | 0.0126898i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −129.412 | − | 224.149i | −0.0863115 | − | 0.149496i | 0.819638 | − | 0.572882i | \(-0.194175\pi\) |
−0.905949 | + | 0.423386i | \(0.860841\pi\) | |||||||
\(132\) | 131.193 | − | 160.056i | 0.0865067 | − | 0.105538i | ||||
\(133\) | 1540.15 | + | 889.206i | 1.00412 | + | 0.579729i | ||||
\(134\) | −2624.17 | −1.69175 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2238.36 | −1.41131 | ||||||||
\(137\) | 911.726 | + | 526.385i | 0.568569 | + | 0.328264i | 0.756578 | − | 0.653904i | \(-0.226870\pi\) |
−0.188009 | + | 0.982167i | \(0.560203\pi\) | |||||||
\(138\) | −798.232 | + | 973.847i | −0.492392 | + | 0.600720i | ||||
\(139\) | 1192.25 | + | 2065.03i | 0.727519 | + | 1.26010i | 0.957929 | + | 0.287006i | \(0.0926599\pi\) |
−0.230410 | + | 0.973094i | \(0.574007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2146.54 | − | 809.378i | 1.28206 | − | 0.483418i | ||||
\(142\) | −2156.22 | − | 1244.89i | −1.27427 | − | 0.735699i | ||||
\(143\) | 1852.53i | 1.08333i | ||||||||
\(144\) | −1853.08 | − | 626.544i | −1.07239 | − | 0.362583i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −752.910 | + | 1304.08i | −0.426790 | + | 0.739221i | ||||
\(147\) | 794.597 | + | 130.696i | 0.445831 | + | 0.0733308i | ||||
\(148\) | −24.0358 | + | 13.8771i | −0.0133495 | + | 0.00770735i | ||||
\(149\) | 573.144 | + | 992.715i | 0.315126 | + | 0.545815i | 0.979464 | − | 0.201617i | \(-0.0646198\pi\) |
−0.664338 | + | 0.747432i | \(0.731286\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 583.058 | − | 1009.89i | 0.314229 | − | 0.544261i | −0.665044 | − | 0.746804i | \(-0.731587\pi\) |
0.979273 | + | 0.202543i | \(0.0649207\pi\) | |||||||
\(152\) | 2662.01i | 1.42051i | ||||||||
\(153\) | −2887.21 | + | 577.924i | −1.52560 | + | 0.305375i | ||||
\(154\) | 1326.63 | 0.694175 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −354.593 | + | 133.704i | −0.181988 | + | 0.0686208i | ||||
\(157\) | 3009.97 | − | 1737.81i | 1.53008 | − | 0.883390i | 0.530719 | − | 0.847548i | \(-0.321922\pi\) |
0.999357 | − | 0.0358423i | \(-0.0114114\pi\) | |||||||
\(158\) | 3083.43 | − | 1780.22i | 1.55256 | − | 0.896371i | ||||
\(159\) | 2385.52 | + | 1955.34i | 1.18984 | + | 0.975274i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1092.43 | −0.534755 | ||||||||
\(162\) | −2199.15 | − | 284.126i | −1.06655 | − | 0.137796i | ||||
\(163\) | − | 2223.32i | − | 1.06837i | −0.845369 | − | 0.534183i | \(-0.820619\pi\) | ||
0.845369 | − | 0.534183i | \(-0.179381\pi\) | |||||||
\(164\) | 76.2204 | − | 132.018i | 0.0362915 | − | 0.0628588i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 644.915 | + | 1117.03i | 0.301537 | + | 0.522277i | ||||
\(167\) | 1375.23 | − | 793.991i | 0.637238 | − | 0.367909i | −0.146312 | − | 0.989239i | \(-0.546740\pi\) |
0.783550 | + | 0.621329i | \(0.213407\pi\) | |||||||
\(168\) | −515.967 | − | 1368.39i | −0.236951 | − | 0.628412i | ||||
\(169\) | 597.632 | − | 1035.13i | 0.272022 | − | 0.471156i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 687.306 | + | 3433.66i | 0.307366 | + | 1.53555i | ||||
\(172\) | − | 12.6993i | − | 0.00562974i | ||||||
\(173\) | −1305.79 | − | 753.898i | −0.573857 | − | 0.331317i | 0.184831 | − | 0.982770i | \(-0.440826\pi\) |
−0.758689 | + | 0.651454i | \(0.774160\pi\) | |||||||
\(174\) | −23.1776 | + | 140.914i | −0.0100982 | + | 0.0613945i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1152.19 | + | 1995.66i | 0.493465 | + | 0.854707i | ||||
\(177\) | −2268.61 | − | 373.143i | −0.963384 | − | 0.158458i | ||||
\(178\) | −2716.85 | − | 1568.58i | −1.14403 | − | 0.660504i | ||||
\(179\) | −1572.66 | −0.656683 | −0.328341 | − | 0.944559i | \(-0.606490\pi\) | ||||
−0.328341 | + | 0.944559i | \(0.606490\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1984.41 | 0.814918 | 0.407459 | − | 0.913223i | \(-0.366415\pi\) | ||||
0.407459 | + | 0.913223i | \(0.366415\pi\) | |||||||
\(182\) | −2103.81 | − | 1214.63i | −0.856838 | − | 0.494695i | ||||
\(183\) | −265.048 | − | 702.930i | −0.107065 | − | 0.283946i | ||||
\(184\) | −817.601 | − | 1416.13i | −0.327578 | − | 0.567382i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −408.040 | − | 334.458i | −0.160854 | − | 0.131847i | ||||
\(187\) | 3003.97 | + | 1734.34i | 1.17472 | + | 0.678223i | ||||
\(188\) | − | 552.831i | − | 0.214465i | ||||||
\(189\) | −1018.84 | − | 1631.83i | −0.392114 | − | 0.628032i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1174.18 | − | 2033.73i | 0.444819 | − | 0.770450i | −0.553220 | − | 0.833035i | \(-0.686601\pi\) |
0.998040 | + | 0.0625853i | \(0.0199345\pi\) | |||||||
\(192\) | 1346.37 | − | 1642.57i | 0.506071 | − | 0.617409i | ||||
\(193\) | −202.797 | + | 117.085i | −0.0756354 | + | 0.0436681i | −0.537341 | − | 0.843365i | \(-0.680571\pi\) |
0.461705 | + | 0.887033i | \(0.347238\pi\) | |||||||
\(194\) | 2431.43 | + | 4211.37i | 0.899829 | + | 1.55855i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 97.0288 | − | 168.059i | 0.0353604 | − | 0.0612460i | ||||
\(197\) | 717.846i | 0.259616i | 0.991539 | + | 0.129808i | \(0.0414362\pi\) | ||||
−0.991539 | + | 0.129808i | \(0.958564\pi\) | |||||||
\(198\) | 1724.71 | + | 1961.87i | 0.619040 | + | 0.704163i | ||||
\(199\) | −1701.45 | −0.606094 | −0.303047 | − | 0.952976i | \(-0.598004\pi\) | ||||
−0.303047 | + | 0.952976i | \(0.598004\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 727.564 | − | 4423.39i | 0.255315 | − | 1.55225i | ||||
\(202\) | 563.725 | − | 325.467i | 0.196354 | − | 0.113365i | ||||
\(203\) | −107.296 | + | 61.9475i | −0.0370971 | + | 0.0214180i | ||||
\(204\) | −115.164 | + | 700.164i | −0.0395248 | + | 0.240300i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5086.77 | 1.72045 | ||||||||
\(207\) | −1420.23 | − | 1615.53i | −0.476875 | − | 0.542450i | ||||
\(208\) | − | 4219.69i | − | 1.40665i | ||||||
\(209\) | 2062.60 | − | 3572.52i | 0.682645 | − | 1.18238i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2469.33 | + | 4277.01i | 0.805667 | + | 1.39546i | 0.915840 | + | 0.401544i | \(0.131526\pi\) |
−0.110172 | + | 0.993912i | \(0.535140\pi\) | |||||||
\(212\) | 643.727 | − | 371.656i | 0.208544 | − | 0.120403i | ||||
\(213\) | 2696.26 | − | 3289.44i | 0.867345 | − | 1.05816i | ||||
\(214\) | −913.585 | + | 1582.38i | −0.291829 | + | 0.505463i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1352.83 | − | 2542.03i | 0.426150 | − | 0.800754i | ||||
\(217\) | − | 457.726i | − | 0.143191i | ||||||
\(218\) | 2032.49 | + | 1173.46i | 0.631456 | + | 0.364572i | ||||
\(219\) | −1989.45 | − | 1630.69i | −0.613857 | − | 0.503160i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3175.85 | − | 5500.73i | −0.966655 | − | 1.67430i | ||||
\(222\) | −123.597 | − | 327.790i | −0.0373662 | − | 0.0990983i | ||||
\(223\) | 2644.10 | + | 1526.57i | 0.794001 | + | 0.458416i | 0.841369 | − | 0.540461i | \(-0.181750\pi\) |
−0.0473684 | + | 0.998877i | \(0.515083\pi\) | |||||||
\(224\) | −770.242 | −0.229750 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3548.73 | −1.04450 | ||||||||
\(227\) | −727.420 | − | 419.976i | −0.212690 | − | 0.122797i | 0.389871 | − | 0.920869i | \(-0.372520\pi\) |
−0.602561 | + | 0.798073i | \(0.705853\pi\) | |||||||
\(228\) | 832.682 | + | 136.960i | 0.241867 | + | 0.0397825i | ||||
\(229\) | 700.753 | + | 1213.74i | 0.202214 | + | 0.350245i | 0.949242 | − | 0.314548i | \(-0.101853\pi\) |
−0.747027 | + | 0.664793i | \(0.768520\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −367.814 | + | 2236.21i | −0.104764 | + | 0.636935i | ||||
\(232\) | −160.606 | − | 92.7259i | −0.0454496 | − | 0.0262403i | ||||
\(233\) | − | 2856.99i | − | 0.803295i | −0.915794 | − | 0.401647i | \(-0.868438\pi\) | ||
0.915794 | − | 0.401647i | \(-0.131562\pi\) | |||||||
\(234\) | −938.843 | − | 4690.30i | −0.262282 | − | 1.31032i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −277.021 | + | 479.815i | −0.0764092 | + | 0.132345i | ||||
\(237\) | 2145.90 | + | 5691.11i | 0.588149 | + | 1.55982i | ||||
\(238\) | −3939.18 | + | 2274.29i | −1.07285 | + | 0.619412i | ||||
\(239\) | −854.917 | − | 1480.76i | −0.231381 | − | 0.400763i | 0.726834 | − | 0.686813i | \(-0.240991\pi\) |
−0.958215 | + | 0.286050i | \(0.907658\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2166.23 | − | 3752.02i | 0.579000 | − | 1.00286i | −0.416594 | − | 0.909092i | \(-0.636776\pi\) |
0.995594 | − | 0.0937648i | \(-0.0298902\pi\) | |||||||
\(242\) | 971.309i | 0.258009i | ||||||||
\(243\) | 1088.66 | − | 3628.19i | 0.287396 | − | 0.957812i | ||||
\(244\) | −181.036 | −0.0474987 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1488.11 | + | 1219.76i | 0.385686 | + | 0.316135i | ||||
\(247\) | −6541.84 | + | 3776.93i | −1.68521 | + | 0.972957i | ||||
\(248\) | 593.354 | − | 342.573i | 0.151927 | − | 0.0877154i | ||||
\(249\) | −2061.70 | + | 777.390i | −0.524719 | + | 0.197852i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1724.73 | −0.433722 | −0.216861 | − | 0.976202i | \(-0.569582\pi\) | ||||
−0.216861 | + | 0.976202i | \(0.569582\pi\) | |||||||
\(252\) | −454.580 | + | 90.9920i | −0.113634 | + | 0.0227459i | ||||
\(253\) | 2534.00i | 0.629688i | ||||||||
\(254\) | 2479.16 | − | 4294.04i | 0.612428 | − | 1.06076i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −939.349 | − | 1627.00i | −0.229333 | − | 0.397217i | ||||
\(257\) | 5069.07 | − | 2926.63i | 1.23035 | − | 0.710342i | 0.263246 | − | 0.964729i | \(-0.415207\pi\) |
0.967103 | + | 0.254386i | \(0.0818734\pi\) | |||||||
\(258\) | 158.168 | + | 26.0156i | 0.0381671 | + | 0.00627776i | ||||
\(259\) | 151.962 | − | 263.206i | 0.0364574 | − | 0.0631462i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −231.103 | − | 78.1380i | −0.0548081 | − | 0.0185311i | ||||
\(262\) | − | 787.277i | − | 0.185642i | ||||||
\(263\) | −339.794 | − | 196.180i | −0.0796677 | − | 0.0459962i | 0.459637 | − | 0.888107i | \(-0.347980\pi\) |
−0.539305 | + | 0.842111i | \(0.681313\pi\) | |||||||
\(264\) | −3174.10 | + | 1196.83i | −0.739971 | + | 0.279015i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2704.73 | + | 4684.73i | 0.623450 | + | 1.07985i | ||||
\(267\) | 3397.30 | − | 4144.72i | 0.778695 | − | 0.950010i | ||||
\(268\) | −935.557 | − | 540.144i | −0.213240 | − | 0.123114i | ||||
\(269\) | 4610.33 | 1.04497 | 0.522485 | − | 0.852648i | \(-0.325005\pi\) | ||||
0.522485 | + | 0.852648i | \(0.325005\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1155.72 | −0.259058 | −0.129529 | − | 0.991576i | \(-0.541347\pi\) | ||||
−0.129529 | + | 0.991576i | \(0.541347\pi\) | |||||||
\(272\) | −6842.44 | − | 3950.49i | −1.52531 | − | 0.880638i | ||||
\(273\) | 2630.71 | − | 3209.48i | 0.583216 | − | 0.711526i | ||||
\(274\) | 1601.13 | + | 2773.23i | 0.353020 | + | 0.611449i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −485.033 | + | 182.888i | −0.105781 | + | 0.0398860i | ||||
\(277\) | −526.898 | − | 304.205i | −0.114290 | − | 0.0659852i | 0.441765 | − | 0.897131i | \(-0.354352\pi\) |
−0.556055 | + | 0.831145i | \(0.687686\pi\) | |||||||
\(278\) | 7253.02i | 1.56477i | ||||||||
\(279\) | 676.904 | − | 595.075i | 0.145251 | − | 0.127693i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1374.62 | + | 2380.91i | −0.291825 | + | 0.505456i | −0.974241 | − | 0.225508i | \(-0.927596\pi\) |
0.682416 | + | 0.730964i | \(0.260929\pi\) | |||||||
\(282\) | 6885.42 | + | 1132.52i | 1.45397 | + | 0.239151i | ||||
\(283\) | 884.697 | − | 510.780i | 0.185830 | − | 0.107289i | −0.404199 | − | 0.914671i | \(-0.632450\pi\) |
0.590029 | + | 0.807382i | \(0.299116\pi\) | |||||||
\(284\) | −512.483 | − | 887.647i | −0.107078 | − | 0.185465i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2817.46 | + | 4879.98i | −0.582516 | + | 1.00895i | ||||
\(287\) | 1669.32i | 0.343334i | ||||||||
\(288\) | −1001.37 | − | 1139.06i | −0.204882 | − | 0.233056i | ||||
\(289\) | −6979.96 | −1.42071 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7772.95 | + | 2930.89i | −1.56584 | + | 0.590418i | ||||
\(292\) | −536.848 | + | 309.949i | −0.107591 | + | 0.0621178i | ||||
\(293\) | −4531.47 | + | 2616.25i | −0.903521 | + | 0.521648i | −0.878341 | − | 0.478035i | \(-0.841349\pi\) |
−0.0251800 | + | 0.999683i | \(0.508016\pi\) | |||||||
\(294\) | 1894.37 | + | 1552.76i | 0.375790 | + | 0.308023i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 454.929 | 0.0893317 | ||||||||
\(297\) | −3785.18 | + | 2363.29i | −0.739524 | + | 0.461724i | ||||
\(298\) | 3486.71i | 0.677785i | ||||||||
\(299\) | 2320.07 | − | 4018.48i | 0.448739 | − | 0.777240i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 69.5327 | + | 120.434i | 0.0133149 | + | 0.0230622i | ||||
\(302\) | 3071.81 | − | 1773.51i | 0.585307 | − | 0.337927i | ||||
\(303\) | 392.322 | + | 1040.47i | 0.0743839 | + | 0.197272i | ||||
\(304\) | −4698.18 | + | 8137.49i | −0.886379 | + | 1.53525i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8484.50 | − | 2868.69i | −1.58506 | − | 0.535921i | ||||
\(307\) | 4912.68i | 0.913296i | 0.889648 | + | 0.456648i | \(0.150950\pi\) | ||||
−0.889648 | + | 0.456648i | \(0.849050\pi\) | |||||||
\(308\) | 472.964 | + | 273.066i | 0.0874988 | + | 0.0505174i | ||||
\(309\) | −1410.33 | + | 8574.42i | −0.259647 | + | 1.57858i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 414.430 | + | 717.813i | 0.0755632 | + | 0.130879i | 0.901331 | − | 0.433131i | \(-0.142591\pi\) |
−0.825768 | + | 0.564010i | \(0.809258\pi\) | |||||||
\(312\) | 6129.36 | + | 1008.16i | 1.11220 | + | 0.182936i | ||||
\(313\) | −7999.66 | − | 4618.60i | −1.44462 | − | 0.834054i | −0.446471 | − | 0.894798i | \(-0.647319\pi\) |
−0.998153 | + | 0.0607442i | \(0.980653\pi\) | |||||||
\(314\) | 10571.9 | 1.90003 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1465.72 | 0.260928 | ||||||||
\(317\) | −7879.45 | − | 4549.20i | −1.39607 | − | 0.806021i | −0.402091 | − | 0.915599i | \(-0.631717\pi\) |
−0.993978 | + | 0.109578i | \(0.965050\pi\) | |||||||
\(318\) | 3310.18 | + | 8778.88i | 0.583729 | + | 1.54810i | ||||
\(319\) | 143.693 | + | 248.884i | 0.0252203 | + | 0.0436828i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2414.01 | − | 1978.69i | −0.419741 | − | 0.344049i | ||||
\(322\) | −2877.71 | − | 1661.45i | −0.498039 | − | 0.287543i | ||||
\(323\) | 14143.9i | 2.43649i | ||||||||
\(324\) | −725.548 | − | 553.955i | −0.124408 | − | 0.0949855i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3381.38 | − | 5856.72i | 0.574470 | − | 0.995011i | ||||
\(327\) | −2541.54 | + | 3100.68i | −0.429808 | + | 0.524368i | ||||
\(328\) | −2163.95 | + | 1249.36i | −0.364281 | + | 0.210318i | ||||
\(329\) | 3026.92 | + | 5242.78i | 0.507233 | + | 0.878553i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2981.73 | + | 5164.50i | −0.495137 | + | 0.857603i | −0.999984 | − | 0.00560570i | \(-0.998216\pi\) |
0.504847 | + | 0.863209i | \(0.331549\pi\) | |||||||
\(332\) | 530.982i | 0.0877754i | ||||||||
\(333\) | 586.801 | − | 117.458i | 0.0965661 | − | 0.0193294i | ||||
\(334\) | 4830.23 | 0.791313 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 837.807 | − | 5093.65i | 0.136030 | − | 0.827027i | ||||
\(337\) | −516.890 | + | 298.427i | −0.0835514 | + | 0.0482384i | −0.541194 | − | 0.840898i | \(-0.682027\pi\) |
0.457642 | + | 0.889136i | \(0.348694\pi\) | |||||||
\(338\) | 3148.60 | − | 1817.84i | 0.506690 | − | 0.292537i | ||||
\(339\) | 983.901 | − | 5981.85i | 0.157635 | − | 0.958377i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1061.74 | −0.168611 | ||||||||
\(342\) | −3411.63 | + | 10090.3i | −0.539415 | + | 1.59539i | ||||
\(343\) | 6828.34i | 1.07492i | ||||||||
\(344\) | −104.080 | + | 180.272i | −0.0163128 | + | 0.0282546i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2293.16 | − | 3971.87i | −0.356304 | − | 0.617137i | ||||
\(347\) | 3950.90 | − | 2281.05i | 0.611226 | − | 0.352891i | −0.162219 | − | 0.986755i | \(-0.551865\pi\) |
0.773445 | + | 0.633863i | \(0.218532\pi\) | |||||||
\(348\) | −37.2680 | + | 45.4671i | −0.00574074 | + | 0.00700372i | ||||
\(349\) | 337.633 | − | 584.798i | 0.0517854 | − | 0.0896949i | −0.838971 | − | 0.544177i | \(-0.816842\pi\) |
0.890756 | + | 0.454482i | \(0.150175\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8166.42 | − | 282.140i | 1.24185 | − | 0.0429046i | ||||
\(352\) | 1786.65i | 0.270536i | ||||||||
\(353\) | 2911.43 | + | 1680.91i | 0.438979 | + | 0.253445i | 0.703165 | − | 0.711027i | \(-0.251770\pi\) |
−0.264185 | + | 0.964472i | \(0.585103\pi\) | |||||||
\(354\) | −5408.52 | − | 4433.20i | −0.812033 | − | 0.665598i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −645.732 | − | 1118.44i | −0.0961341 | − | 0.166509i | ||||
\(357\) | −2741.46 | − | 7270.57i | −0.406424 | − | 1.07787i | ||||
\(358\) | −4142.74 | − | 2391.81i | −0.611594 | − | 0.353104i | ||||
\(359\) | −7701.61 | −1.13224 | −0.566122 | − | 0.824322i | \(-0.691557\pi\) | ||||
−0.566122 | + | 0.824322i | \(0.691557\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9961.87 | 1.45238 | ||||||||
\(362\) | 5227.39 | + | 3018.03i | 0.758965 | + | 0.438189i | ||||
\(363\) | −1637.27 | − | 269.300i | −0.236734 | − | 0.0389382i | ||||
\(364\) | −500.026 | − | 866.070i | −0.0720013 | − | 0.124710i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 370.868 | − | 2254.78i | 0.0529661 | − | 0.322020i | ||||
\(367\) | 5117.77 | + | 2954.75i | 0.727917 | + | 0.420263i | 0.817660 | − | 0.575702i | \(-0.195271\pi\) |
−0.0897425 | + | 0.995965i | \(0.528604\pi\) | |||||||
\(368\) | − | 5771.94i | − | 0.817617i | ||||||
\(369\) | −2468.66 | + | 2170.23i | −0.348274 | + | 0.306172i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4069.86 | + | 7049.20i | −0.569532 | + | 0.986459i | ||||
\(372\) | −76.6295 | − | 203.228i | −0.0106803 | − | 0.0283249i | ||||
\(373\) | −7295.73 | + | 4212.19i | −1.01276 | + | 0.584716i | −0.911998 | − | 0.410195i | \(-0.865461\pi\) |
−0.100760 | + | 0.994911i | \(0.532127\pi\) | |||||||
\(374\) | 5275.42 | + | 9137.30i | 0.729374 | + | 1.26331i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4530.84 | + | 7847.64i | −0.621436 | + | 1.07636i | ||||
\(377\) | − | 526.249i | − | 0.0718917i | ||||||
\(378\) | −202.046 | − | 5848.13i | −0.0274923 | − | 0.795754i | ||||
\(379\) | 3510.24 | 0.475749 | 0.237875 | − | 0.971296i | \(-0.423549\pi\) | ||||
0.237875 | + | 0.971296i | \(0.423549\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6550.81 | + | 5369.50i | 0.880862 | + | 0.722016i | ||||
\(382\) | 6186.09 | − | 3571.54i | 0.828555 | − | 0.478367i | ||||
\(383\) | 4964.08 | − | 2866.01i | 0.662279 | − | 0.382367i | −0.130866 | − | 0.991400i | \(-0.541776\pi\) |
0.793145 | + | 0.609033i | \(0.208442\pi\) | |||||||
\(384\) | 8229.64 | − | 3103.09i | 1.09366 | − | 0.412380i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −712.283 | −0.0939229 | ||||||||
\(387\) | −87.7056 | + | 259.400i | −0.0115202 | + | 0.0340725i | ||||
\(388\) | 2001.89i | 0.261934i | ||||||||
\(389\) | 7183.60 | − | 12442.4i | 0.936306 | − | 1.62173i | 0.164019 | − | 0.986457i | \(-0.447554\pi\) |
0.772288 | − | 0.635273i | \(-0.219112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4344.11 | − | 7524.23i | −0.561870 | − | 0.973188i | ||||
\(392\) | −2754.72 | + | 1590.44i | −0.354934 | + | 0.204922i | ||||
\(393\) | 1327.06 | + | 218.276i | 0.170334 | + | 0.0280167i | ||||
\(394\) | −1091.75 | + | 1890.97i | −0.139598 | + | 0.241791i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 211.065 | + | 1054.44i | 0.0267838 | + | 0.133807i | ||||
\(397\) | 9014.42i | 1.13960i | 0.821784 | + | 0.569800i | \(0.192979\pi\) | ||||
−0.821784 | + | 0.569800i | \(0.807021\pi\) | |||||||
\(398\) | −4482.01 | − | 2587.69i | −0.564479 | − | 0.325902i | ||||
\(399\) | −8646.64 | + | 3260.32i | −1.08490 | + | 0.409073i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5255.55 | − | 9102.87i | −0.654487 | − | 1.13361i | −0.982022 | − | 0.188766i | \(-0.939551\pi\) |
0.327535 | − | 0.944839i | \(-0.393782\pi\) | |||||||
\(402\) | 8643.97 | − | 10545.7i | 1.07244 | − | 1.30839i | ||||
\(403\) | 1683.73 | + | 972.104i | 0.208121 | + | 0.120159i | ||||
\(404\) | 267.969 | 0.0329998 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −376.857 | −0.0460667 | ||||||||
\(407\) | −610.533 | − | 352.491i | −0.0743562 | − | 0.0429296i | ||||
\(408\) | 7373.12 | − | 8995.23i | 0.894666 | − | 1.09150i | ||||
\(409\) | 1659.10 | + | 2873.65i | 0.200580 | + | 0.347415i | 0.948715 | − | 0.316131i | \(-0.102384\pi\) |
−0.748135 | + | 0.663546i | \(0.769051\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5118.57 | + | 1930.02i | −0.614308 | + | 0.231632i | ||||
\(412\) | 1813.51 | + | 1047.03i | 0.216857 | + | 0.125203i | ||||
\(413\) | − | 6067.11i | − | 0.722864i | ||||||
\(414\) | −1284.20 | − | 6415.66i | −0.152452 | − | 0.761625i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1635.81 | − | 2833.31i | 0.192794 | − | 0.333929i | ||||
\(417\) | −12225.9 | − | 2010.93i | −1.43575 | − | 0.236153i | ||||
\(418\) | 10866.7 | − | 6273.89i | 1.27155 | − | 0.734129i | ||||
\(419\) | −243.069 | − | 421.008i | −0.0283406 | − | 0.0490873i | 0.851507 | − | 0.524343i | \(-0.175689\pi\) |
−0.879848 | + | 0.475255i | \(0.842356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2525.96 | + | 4375.10i | −0.292418 | + | 0.506482i | −0.974381 | − | 0.224904i | \(-0.927793\pi\) |
0.681963 | + | 0.731387i | \(0.261126\pi\) | |||||||
\(422\) | 15022.1i | 1.73286i | ||||||||
\(423\) | −3818.03 | + | 11292.3i | −0.438863 | + | 1.29799i | ||||
\(424\) | −12183.9 | −1.39553 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12105.4 | − | 4564.48i | 1.37678 | − | 0.519130i | ||||
\(427\) | 1716.86 | − | 991.230i | 0.194578 | − | 0.112340i | ||||
\(428\) | −651.414 | + | 376.094i | −0.0735684 | + | 0.0424747i | ||||
\(429\) | −7444.70 | − | 6102.19i | −0.837840 | − | 0.686752i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6944.24 | 0.776084 | 0.388042 | − | 0.921642i | \(-0.373152\pi\) | ||||
0.388042 | + | 0.921642i | \(0.373152\pi\) | |||||||
\(432\) | 8621.89 | − | 5383.10i | 0.960234 | − | 0.599525i | ||||
\(433\) | − | 13738.3i | − | 1.52476i | −0.647131 | − | 0.762378i | \(-0.724032\pi\) | ||
0.647131 | − | 0.762378i | \(-0.275968\pi\) | |||||||
\(434\) | 696.142 | − | 1205.75i | 0.0769952 | − | 0.133360i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 483.075 | + | 836.711i | 0.0530622 | + | 0.0919064i | ||||
\(437\) | −8948.31 | + | 5166.31i | −0.979533 | + | 0.565533i | ||||
\(438\) | −2760.59 | − | 7321.31i | −0.301155 | − | 0.798688i | ||||
\(439\) | 4240.92 | − | 7345.48i | 0.461066 | − | 0.798589i | −0.537949 | − | 0.842978i | \(-0.680801\pi\) |
0.999014 | + | 0.0443883i | \(0.0141339\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3142.61 | + | 2762.71i | −0.339338 | + | 0.298317i | ||||
\(442\) | − | 19320.2i | − | 2.07912i | ||||||
\(443\) | 483.411 | + | 279.098i | 0.0518455 | + | 0.0299330i | 0.525699 | − | 0.850671i | \(-0.323804\pi\) |
−0.473853 | + | 0.880604i | \(0.657137\pi\) | |||||||
\(444\) | 23.4061 | − | 142.303i | 0.00250181 | − | 0.0152103i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4643.44 | + | 8042.67i | 0.492989 | + | 0.853882i | ||||
\(447\) | −5877.32 | − | 966.707i | −0.621896 | − | 0.102290i | ||||
\(448\) | 4853.79 | + | 2802.34i | 0.511875 | + | 0.295531i | ||||
\(449\) | −14775.0 | −1.55295 | −0.776476 | − | 0.630147i | \(-0.782995\pi\) | ||||
−0.776476 | + | 0.630147i | \(0.782995\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3872.15 | 0.404285 | ||||||||
\(452\) | −1265.17 | − | 730.449i | −0.131657 | − | 0.0760120i | ||||
\(453\) | 2137.82 | + | 5669.66i | 0.221729 | + | 0.588044i | ||||
\(454\) | −1277.46 | − | 2212.62i | −0.132058 | − | 0.228730i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10697.7 | − | 8768.60i | −1.09861 | − | 0.900499i | ||||
\(457\) | −12304.4 | − | 7103.97i | −1.25947 | − | 0.727154i | −0.286497 | − | 0.958081i | \(-0.592491\pi\) |
−0.972971 | + | 0.230927i | \(0.925824\pi\) | |||||||
\(458\) | 4263.02i | 0.434930i | ||||||||
\(459\) | 7187.92 | − | 13506.4i | 0.730944 | − | 1.37347i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3851.26 | − | 6670.57i | 0.389091 | − | 0.673925i | −0.603237 | − | 0.797562i | \(-0.706123\pi\) |
0.992328 | + | 0.123637i | \(0.0394558\pi\) | |||||||
\(462\) | −4369.90 | + | 5331.29i | −0.440056 | + | 0.536870i | ||||
\(463\) | 6849.45 | − | 3954.53i | 0.687518 | − | 0.396939i | −0.115163 | − | 0.993347i | \(-0.536739\pi\) |
0.802682 | + | 0.596408i | \(0.203406\pi\) | |||||||
\(464\) | −327.304 | − | 566.908i | −0.0327472 | − | 0.0567199i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4345.11 | − | 7525.96i | 0.431939 | − | 0.748140i | ||||
\(467\) | − | 11639.8i | − | 1.15337i | −0.816967 | − | 0.576685i | \(-0.804346\pi\) | ||
0.816967 | − | 0.576685i | \(-0.195654\pi\) | |||||||
\(468\) | 630.711 | − | 1865.41i | 0.0622962 | − | 0.184249i | ||||
\(469\) | 11829.8 | 1.16471 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2931.11 | + | 17820.4i | −0.286749 | + | 1.74336i | ||||
\(472\) | 7864.84 | − | 4540.77i | 0.766967 | − | 0.442809i | ||||
\(473\) | 279.359 | − | 161.288i | 0.0271563 | − | 0.0156787i | ||||
\(474\) | −3002.65 | + | 18255.3i | −0.290962 | + | 1.76897i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1872.50 | −0.180307 | ||||||||
\(477\) | −15715.7 | + | 3145.77i | −1.50854 | + | 0.301960i | ||||
\(478\) | − | 5200.87i | − | 0.497662i | ||||||
\(479\) | −9347.93 | + | 16191.1i | −0.891687 | + | 1.54445i | −0.0538341 | + | 0.998550i | \(0.517144\pi\) |
−0.837853 | + | 0.545897i | \(0.816189\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 645.465 | + | 1117.98i | 0.0611865 | + | 0.105978i | ||||
\(482\) | 11412.7 | − | 6589.10i | 1.07849 | − | 0.622667i | ||||
\(483\) | 3598.45 | − | 4390.12i | 0.338996 | − | 0.413576i | ||||
\(484\) | −199.928 | + | 346.286i | −0.0187761 | + | 0.0325212i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8385.77 | − | 7901.75i | 0.782687 | − | 0.737512i | ||||
\(487\) | 2249.54i | 0.209315i | 0.994508 | + | 0.104658i | \(0.0333747\pi\) | ||||
−0.994508 | + | 0.104658i | \(0.966625\pi\) | |||||||
\(488\) | 2569.88 | + | 1483.72i | 0.238387 | + | 0.137633i | ||||
\(489\) | 8934.78 | + | 7323.57i | 0.826267 | + | 0.677266i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −994.175 | − | 1721.96i | −0.0913778 | − | 0.158271i | 0.816713 | − | 0.577044i | \(-0.195794\pi\) |
−0.908091 | + | 0.418773i | \(0.862460\pi\) | |||||||
\(492\) | 279.466 | + | 741.168i | 0.0256084 | + | 0.0679155i | ||||
\(493\) | −853.339 | − | 492.676i | −0.0779563 | − | 0.0450081i | ||||
\(494\) | −22976.9 | −2.09267 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2418.43 | 0.218933 | ||||||||
\(497\) | 9720.28 | + | 5612.01i | 0.877292 | + | 0.506505i | ||||
\(498\) | −6613.29 | − | 1087.76i | −0.595078 | − | 0.0978790i | ||||
\(499\) | 1206.95 | + | 2090.50i | 0.108278 | + | 0.187543i | 0.915073 | − | 0.403289i | \(-0.132133\pi\) |
−0.806795 | + | 0.590832i | \(0.798800\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1339.20 | + | 8142.00i | −0.119423 | + | 0.726063i | ||||
\(502\) | −4543.34 | − | 2623.10i | −0.403942 | − | 0.233216i | ||||
\(503\) | − | 8758.56i | − | 0.776391i | −0.921577 | − | 0.388196i | \(-0.873098\pi\) | ||
0.921577 | − | 0.388196i | \(-0.126902\pi\) | |||||||
\(504\) | 7198.67 | + | 2433.94i | 0.636219 | + | 0.215111i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3853.88 | + | 6675.12i | −0.338589 | + | 0.586453i | ||||
\(507\) | 2191.25 | + | 5811.38i | 0.191947 | + | 0.509058i | ||||
\(508\) | 1767.72 | − | 1020.59i | 0.154389 | − | 0.0891368i | ||||
\(509\) | −5924.01 | − | 10260.7i | −0.515869 | − | 0.893511i | −0.999830 | − | 0.0184220i | \(-0.994136\pi\) |
0.483961 | − | 0.875089i | \(-0.339198\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3394.13 | − | 5878.81i | 0.293831 | − | 0.508930i | ||||
\(512\) | 7826.64i | 0.675570i | ||||||||
\(513\) | −16062.7 | − | 8548.36i | −1.38243 | − | 0.735710i | ||||
\(514\) | 17804.1 | 1.52783 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 51.0344 | + | 41.8313i | 0.00435400 | + | 0.00356884i | ||||
\(517\) | 12161.1 | − | 7021.23i | 1.03452 | − | 0.597279i | ||||
\(518\) | 800.606 | − | 462.230i | 0.0679085 | − | 0.0392070i | ||||
\(519\) | 7330.91 | − | 2764.21i | 0.620022 | − | 0.233787i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3816.55 | 0.320933 | 0.160466 | − | 0.987041i | \(-0.448700\pi\) | ||||
0.160466 | + | 0.987041i | \(0.448700\pi\) | |||||||
\(522\) | −489.939 | − | 557.310i | −0.0410806 | − | 0.0467295i | ||||
\(523\) | − | 12158.9i | − | 1.01658i | −0.861187 | − | 0.508288i | \(-0.830278\pi\) | ||
0.861187 | − | 0.508288i | \(-0.169722\pi\) | |||||||
\(524\) | 162.049 | − | 280.676i | 0.0135098 | − | 0.0233996i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −596.729 | − | 1033.57i | −0.0494651 | − | 0.0856761i | ||||
\(527\) | 3152.63 | − | 1820.17i | 0.260590 | − | 0.150452i | ||||
\(528\) | −11815.2 | − | 1943.37i | −0.973846 | − | 0.160179i | ||||
\(529\) | −2909.97 | + | 5040.22i | −0.239169 | + | 0.414253i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8972.28 | − | 7887.65i | 0.733265 | − | 0.644623i | ||||
\(532\) | 2226.90i | 0.181482i | ||||||||
\(533\) | −6140.55 | − | 3545.25i | −0.499018 | − | 0.288108i | ||||
\(534\) | 15252.8 | − | 5751.27i | 1.23606 | − | 0.466071i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8853.71 | + | 15335.1i | 0.713474 | + | 1.23577i | ||||
\(537\) | 5180.31 | − | 6320.00i | 0.416289 | − | 0.507874i | ||||
\(538\) | 12144.7 | + | 7011.72i | 0.973222 | + | 0.561890i | ||||
\(539\) | 4929.26 | 0.393911 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14919.8 | 1.18568 | 0.592840 | − | 0.805321i | \(-0.298007\pi\) | ||||
0.592840 | + | 0.805321i | \(0.298007\pi\) | |||||||
\(542\) | −3044.42 | − | 1757.69i | −0.241271 | − | 0.139298i | ||||
\(543\) | −6536.61 | + | 7974.69i | −0.516598 | + | 0.630252i | ||||
\(544\) | −3062.91 | − | 5305.12i | −0.241399 | − | 0.418116i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11811.1 | − | 4453.52i | 0.925766 | − | 0.349072i | ||||
\(547\) | −889.543 | − | 513.578i | −0.0695322 | − | 0.0401444i | 0.464831 | − | 0.885400i | \(-0.346115\pi\) |
−0.534363 | + | 0.845255i | \(0.679448\pi\) | |||||||
\(548\) | 1318.27i | 0.102762i | ||||||||
\(549\) | 3697.91 | + | 1250.30i | 0.287473 | + | 0.0971973i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −585.923 | + | 1014.85i | −0.0453015 | + | 0.0784646i | ||||
\(552\) | 8384.10 | + | 1379.02i | 0.646469 | + | 0.106332i | ||||
\(553\) | −13900.2 | + | 8025.26i | −1.06889 | + | 0.617123i | ||||
\(554\) | −925.313 | − | 1602.69i | −0.0709617 | − | 0.122909i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1492.92 | + | 2585.81i | −0.113874 | + | 0.197235i | ||||
\(557\) | 10590.8i | 0.805648i | 0.915277 | + | 0.402824i | \(0.131971\pi\) | ||||
−0.915277 | + | 0.402824i | \(0.868029\pi\) | |||||||
\(558\) | 2688.15 | − | 538.079i | 0.203940 | − | 0.0408220i | ||||
\(559\) | −590.685 | −0.0446929 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16864.8 | + | 6359.07i | −1.26922 | + | 0.478574i | ||||
\(562\) | −7242.11 | + | 4181.23i | −0.543576 | + | 0.313834i | ||||
\(563\) | −1898.38 | + | 1096.03i | −0.142109 | + | 0.0820467i | −0.569369 | − | 0.822082i | \(-0.692812\pi\) |
0.427260 | + | 0.904129i | \(0.359479\pi\) | |||||||
\(564\) | 2221.64 | + | 1821.01i | 0.165865 | + | 0.135955i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3107.32 | 0.230761 | ||||||||
\(567\) | 9913.81 | + | 1280.84i | 0.734287 | + | 0.0948684i | ||||
\(568\) | 16800.6i | 1.24109i | ||||||||
\(569\) | −8284.89 | + | 14349.8i | −0.610405 | + | 1.05725i | 0.380767 | + | 0.924671i | \(0.375660\pi\) |
−0.991172 | + | 0.132582i | \(0.957673\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3639.66 | − | 6304.08i | −0.266752 | − | 0.462027i | 0.701269 | − | 0.712896i | \(-0.252617\pi\) |
−0.968021 | + | 0.250869i | \(0.919284\pi\) | |||||||
\(572\) | −2008.93 | + | 1159.86i | −0.146849 | + | 0.0847833i | ||||
\(573\) | 4305.19 | + | 11417.7i | 0.313878 | + | 0.832429i | ||||
\(574\) | −2538.82 | + | 4397.36i | −0.184614 | + | 0.319760i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2166.05 | + | 10821.2i | 0.156688 | + | 0.782784i | ||||
\(577\) | 17938.0i | 1.29422i | 0.762395 | + | 0.647112i | \(0.224024\pi\) | ||||
−0.762395 | + | 0.647112i | \(0.775976\pi\) | |||||||
\(578\) | −18386.8 | − | 10615.6i | −1.32317 | − | 0.763930i | ||||
\(579\) | 197.484 | − | 1200.65i | 0.0141747 | − | 0.0861782i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2907.29 | − | 5035.57i | −0.207598 | − | 0.359571i | ||||
\(582\) | −24933.2 | − | 4101.03i | −1.77580 | − | 0.292085i | ||||
\(583\) | 16351.3 | + | 9440.42i | 1.16158 | + | 0.670639i | ||||
\(584\) | 10161.0 | 0.719974 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15915.9 | −1.12198 | ||||||||
\(587\) | 9967.67 | + | 5754.83i | 0.700868 | + | 0.404646i | 0.807671 | − | 0.589634i | \(-0.200728\pi\) |
−0.106803 | + | 0.994280i | \(0.534061\pi\) | |||||||
\(588\) | 355.762 | + | 943.509i | 0.0249513 | + | 0.0661729i | ||||
\(589\) | −2164.67 | − | 3749.32i | −0.151433 | − | 0.262289i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2884.79 | − | 2364.57i | −0.200785 | − | 0.164578i | ||||
\(592\) | 1390.67 | + | 802.904i | 0.0965476 | + | 0.0557418i | ||||
\(593\) | − | 9612.80i | − | 0.665684i | −0.942983 | − | 0.332842i | \(-0.891992\pi\) | ||
0.942983 | − | 0.332842i | \(-0.108008\pi\) | |||||||
\(594\) | −13565.3 | + | 468.664i | −0.937021 | + | 0.0323729i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −717.684 | + | 1243.07i | −0.0493247 | + | 0.0854328i | ||||
\(597\) | 5604.55 | − | 6837.57i | 0.384219 | − | 0.468749i | ||||
\(598\) | 12223.2 | − | 7057.05i | 0.835857 | − | 0.482582i | ||||
\(599\) | 3686.00 | + | 6384.33i | 0.251429 | + | 0.435487i | 0.963919 | − | 0.266194i | \(-0.0857663\pi\) |
−0.712491 | + | 0.701681i | \(0.752433\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12095.3 | − | 20949.7i | 0.820927 | − | 1.42189i | −0.0840654 | − | 0.996460i | \(-0.526790\pi\) |
0.904993 | − | 0.425427i | \(-0.139876\pi\) | |||||||
\(602\) | 423.001i | 0.0286383i | ||||||||
\(603\) | 15379.6 | + | 17494.4i | 1.03865 | + | 1.18147i | ||||
\(604\) | 1460.20 | 0.0983684 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −548.956 | + | 3337.50i | −0.0367984 | + | 0.223724i | ||||
\(607\) | 1141.19 | − | 658.866i | 0.0763088 | − | 0.0440569i | −0.461360 | − | 0.887213i | \(-0.652638\pi\) |
0.537669 | + | 0.843156i | \(0.319305\pi\) | |||||||
\(608\) | −6309.20 | + | 3642.62i | −0.420842 | + | 0.242973i | ||||
\(609\) | 104.485 | − | 635.242i | 0.00695230 | − | 0.0422681i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25713.9 | −1.70257 | ||||||||
\(612\) | −2434.38 | − | 2769.13i | −0.160791 | − | 0.182901i | ||||
\(613\) | − | 4137.52i | − | 0.272615i | −0.990667 | − | 0.136307i | \(-0.956477\pi\) | ||
0.990667 | − | 0.136307i | \(-0.0435235\pi\) | |||||||
\(614\) | −7471.56 | + | 12941.1i | −0.491087 | + | 0.850588i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4475.93 | − | 7752.54i | −0.292760 | − | 0.507076i | ||||
\(617\) | 6747.74 | − | 3895.81i | 0.440281 | − | 0.254197i | −0.263436 | − | 0.964677i | \(-0.584856\pi\) |
0.703717 | + | 0.710480i | \(0.251522\pi\) | |||||||
\(618\) | −16755.7 | + | 20442.0i | −1.09064 | + | 1.33058i | ||||
\(619\) | 10978.2 | − | 19014.8i | 0.712844 | − | 1.23468i | −0.250941 | − | 0.968002i | \(-0.580740\pi\) |
0.963785 | − | 0.266680i | \(-0.0859268\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11170.5 | − | 385.927i | 0.721831 | − | 0.0249384i | ||||
\(622\) | 2521.18i | 0.162524i | ||||||||
\(623\) | 12247.6 | + | 7071.17i | 0.787625 | + | 0.454736i | ||||
\(624\) | 16957.5 | + | 13899.6i | 1.08789 | + | 0.891712i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14048.6 | − | 24332.9i | −0.896957 | − | 1.55357i | ||||
\(627\) | 7562.63 | + | 20056.7i | 0.481694 | + | 1.27749i | ||||
\(628\) | 3769.05 | + | 2176.06i | 0.239493 | + | 0.138271i | ||||
\(629\) | 2417.15 | 0.153224 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11152.7 | −0.703618 | −0.351809 | − | 0.936072i | \(-0.614433\pi\) | ||||
−0.351809 | + | 0.936072i | \(0.614433\pi\) | |||||||
\(632\) | −20806.4 | − | 12012.6i | −1.30955 | − | 0.756068i | ||||
\(633\) | −25321.8 | − | 4164.95i | −1.58997 | − | 0.261520i | ||||
\(634\) | −13837.5 | − | 23967.2i | −0.866810 | − | 1.50136i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −626.861 | + | 3811.15i | −0.0390828 | + | 0.237613i | ||||
\(637\) | −7816.94 | − | 4513.11i | −0.486214 | − | 0.280716i | ||||
\(638\) | 874.155i | 0.0542447i | ||||||||
\(639\) | 4337.77 | + | 21670.7i | 0.268544 | + | 1.34160i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2404.72 | + | 4165.10i | −0.148176 | + | 0.256648i | −0.930553 | − | 0.366156i | \(-0.880674\pi\) |
0.782377 | + | 0.622805i | \(0.214007\pi\) | |||||||
\(642\) | −3349.71 | − | 8883.71i | −0.205923 | − | 0.546125i | ||||
\(643\) | −2210.98 | + | 1276.51i | −0.135603 | + | 0.0782904i | −0.566267 | − | 0.824222i | \(-0.691613\pi\) |
0.430664 | + | 0.902512i | \(0.358279\pi\) | |||||||
\(644\) | −683.964 | − | 1184.66i | −0.0418509 | − | 0.0724879i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21511.0 | + | 37258.2i | −1.31013 | + | 2.26920i | ||||
\(647\) | − | 8446.00i | − | 0.513210i | −0.966516 | − | 0.256605i | \(-0.917396\pi\) | ||
0.966516 | − | 0.256605i | \(-0.0826039\pi\) | |||||||
\(648\) | 5759.36 | + | 13810.0i | 0.349150 | + | 0.837201i | ||||
\(649\) | −14073.2 | −0.851191 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1839.45 | + | 1507.74i | 0.110743 | + | 0.0907727i | ||||
\(652\) | 2411.02 | − | 1392.01i | 0.144821 | − | 0.0836122i | ||||
\(653\) | 7010.37 | − | 4047.44i | 0.420118 | − | 0.242555i | −0.275010 | − | 0.961441i | \(-0.588681\pi\) |
0.695128 | + | 0.718886i | \(0.255348\pi\) | |||||||
\(654\) | −11410.7 | + | 4302.55i | −0.682254 | + | 0.257252i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8819.97 | −0.524942 | ||||||||
\(657\) | 13106.4 | − | 2623.47i | 0.778280 | − | 0.155786i | ||||
\(658\) | 18414.2i | 1.09097i | ||||||||
\(659\) | 1087.67 | − | 1883.89i | 0.0642936 | − | 0.111360i | −0.832087 | − | 0.554645i | \(-0.812854\pi\) |
0.896380 | + | 0.443286i | \(0.146187\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4438.47 | + | 7687.66i | 0.261175 | + | 0.452368i | 0.966554 | − | 0.256462i | \(-0.0825567\pi\) |
−0.705379 | + | 0.708830i | \(0.749223\pi\) | |||||||
\(662\) | −15709.1 | + | 9069.64i | −0.922282 | + | 0.532480i | ||||
\(663\) | 32566.8 | + | 5356.62i | 1.90768 | + | 0.313776i | ||||
\(664\) | 4351.77 | − | 7537.48i | 0.254339 | − | 0.440529i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1724.41 | + | 583.037i | 0.100329 | + | 0.0339223i | ||||
\(667\) | − | 719.834i | − | 0.0417872i | ||||||
\(668\) | 1722.05 | + | 994.226i | 0.0997427 | + | 0.0575865i | ||||
\(669\) | −14844.4 | + | 5597.27i | −0.857874 | + | 0.323472i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2299.25 | − | 3982.42i | −0.132283 | − | 0.229120i | ||||
\(672\) | 2537.16 | − | 3095.35i | 0.145645 | − | 0.177687i | ||||
\(673\) | 7939.65 | + | 4583.96i | 0.454757 | + | 0.262554i | 0.709837 | − | 0.704366i | \(-0.248769\pi\) |
−0.255080 | + | 0.966920i | \(0.582102\pi\) | |||||||
\(674\) | −1815.47 | −0.103753 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1496.70 | 0.0851557 | ||||||||
\(677\) | −16348.7 | − | 9438.93i | −0.928112 | − | 0.535846i | −0.0418983 | − | 0.999122i | \(-0.513341\pi\) |
−0.886214 | + | 0.463276i | \(0.846674\pi\) | |||||||
\(678\) | 11689.4 | − | 14261.2i | 0.662139 | − | 0.807812i | ||||
\(679\) | −10961.0 | − | 18984.9i | −0.619503 | − | 1.07301i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4083.85 | − | 1539.87i | 0.229800 | − | 0.0866488i | ||||
\(682\) | −2796.86 | − | 1614.77i | −0.157034 | − | 0.0906638i | ||||
\(683\) | − | 27207.5i | − | 1.52426i | −0.647426 | − | 0.762128i | \(-0.724155\pi\) | ||
0.647426 | − | 0.762128i | \(-0.275845\pi\) | |||||||
\(684\) | −3293.23 | + | 2895.13i | −0.184094 | + | 0.161839i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10385.0 | + | 17987.4i | −0.577991 | + | 1.00111i | ||||
\(687\) | −7185.89 | − | 1181.94i | −0.399067 | − | 0.0656388i | ||||
\(688\) | −636.323 | + | 367.381i | −0.0352610 | + | 0.0203580i | ||||
\(689\) | −17286.9 | − | 29941.7i | −0.955845 | − | 1.65557i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8703.62 | − | 15075.1i | 0.479162 | − | 0.829934i | −0.520552 | − | 0.853830i | \(-0.674274\pi\) |
0.999714 | + | 0.0238963i | \(0.00760715\pi\) | |||||||
\(692\) | − | 1888.04i | − | 0.103718i | ||||||
\(693\) | −7775.03 | − | 8844.17i | −0.426189 | − | 0.484794i | ||||
\(694\) | 13876.7 | 0.759011 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 901.668 | − | 339.985i | 0.0491058 | − | 0.0185159i | ||||
\(697\) | −11497.6 | + | 6638.15i | −0.624825 | + | 0.360743i | ||||
\(698\) | 1778.80 | − | 1026.99i | 0.0964595 | − | 0.0556909i | ||||
\(699\) | 11481.3 | + | 9410.87i | 0.621263 | + | 0.509230i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18543.0 | 0.999086 | 0.499543 | − | 0.866289i | \(-0.333501\pi\) | ||||
0.499543 | + | 0.866289i | \(0.333501\pi\) | |||||||
\(702\) | 21941.3 | + | 11676.8i | 1.17966 | + | 0.627798i | ||||
\(703\) | − | 2874.63i | − | 0.154223i | ||||||
\(704\) | 6500.29 | − | 11258.8i | 0.347996 | − | 0.602746i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5112.91 | + | 8855.81i | 0.272559 | + | 0.472086i | ||||
\(707\) | −2541.28 | + | 1467.21i | −0.135184 | + | 0.0780482i | ||||
\(708\) | −1015.72 | − | 2693.76i | −0.0539165 | − | 0.142991i | ||||
\(709\) | 13116.9 | − | 22719.1i | 0.694803 | − | 1.20343i | −0.275444 | − | 0.961317i | \(-0.588825\pi\) |
0.970247 | − | 0.242117i | \(-0.0778417\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29939.2 | − | 10122.7i | −1.57920 | − | 0.533941i | ||||
\(712\) | 21168.9i | 1.11424i | ||||||||
\(713\) | 2303.11 | + | 1329.70i | 0.120971 | + | 0.0698425i | ||||
\(714\) | 3835.98 | − | 23321.7i | 0.201061 | − | 1.22240i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −984.633 | − | 1705.43i | −0.0513931 | − | 0.0890155i | ||||
\(717\) | 8766.76 | + | 1441.96i | 0.456626 | + | 0.0751062i | ||||
\(718\) | −20287.8 | − | 11713.2i | −1.05450 | − | 0.608817i | ||||
\(719\) | 3043.06 | 0.157840 | 0.0789199 | − | 0.996881i | \(-0.474853\pi\) | ||||
0.0789199 | + | 0.996881i | \(0.474853\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22931.2 | −1.18447 | ||||||||
\(722\) | 26241.8 | + | 15150.7i | 1.35266 | + | 0.780958i | ||||
\(723\) | 7942.60 | + | 21064.4i | 0.408559 | + | 1.08353i | ||||
\(724\) | 1242.43 | + | 2151.95i | 0.0637769 | + | 0.110465i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3903.37 | − | 3199.47i | −0.199542 | − | 0.163559i | ||||
\(727\) | 19002.7 | + | 10971.2i | 0.969426 | + | 0.559698i | 0.899061 | − | 0.437823i | \(-0.144250\pi\) |
0.0703647 | + | 0.997521i | \(0.477584\pi\) | |||||||
\(728\) | 16392.2i | 0.834528i | ||||||||
\(729\) | 10994.5 | + | 16326.1i | 0.558577 | + | 0.829453i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −553.002 | + | 957.827i | −0.0279802 | + | 0.0484631i | ||||
\(732\) | 596.330 | − | 727.525i | 0.0301107 | − | 0.0367351i | ||||
\(733\) | −23016.2 | + | 13288.4i | −1.15979 | + | 0.669604i | −0.951253 | − | 0.308411i | \(-0.900203\pi\) |
−0.208535 | + | 0.978015i | \(0.566869\pi\) | |||||||
\(734\) | 8987.58 | + | 15566.9i | 0.451959 | + | 0.782815i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2237.56 | − | 3875.57i | 0.112062 | − | 0.194097i | ||||
\(737\) | − | 27440.4i | − | 1.37148i | ||||||
\(738\) | −9803.63 | + | 1962.37i | −0.488993 | + | 0.0978803i | ||||
\(739\) | −28787.7 | −1.43298 | −0.716489 | − | 0.697598i | \(-0.754252\pi\) | ||||
−0.716489 | + | 0.697598i | \(0.754252\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6370.45 | − | 38730.6i | 0.315822 | − | 1.92011i | ||||
\(742\) | −21441.8 | + | 12379.5i | −1.06086 | + | 0.612485i | ||||
\(743\) | −3899.73 | + | 2251.51i | −0.192553 | + | 0.111171i | −0.593177 | − | 0.805072i | \(-0.702127\pi\) |
0.400624 | + | 0.916243i | \(0.368793\pi\) | |||||||
\(744\) | −577.808 | + | 3512.92i | −0.0284724 | + | 0.173105i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −25624.8 | −1.25763 | ||||||||
\(747\) | 3667.13 | − | 10846.0i | 0.179616 | − | 0.531238i | ||||
\(748\) | 4343.45i | 0.212316i | ||||||||
\(749\) | 4118.46 | − | 7133.38i | 0.200915 | − | 0.347995i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2852.83 | − | 4941.24i | −0.138617 | − | 0.240091i | 0.788357 | − | 0.615219i | \(-0.210932\pi\) |
−0.926973 | + | 0.375128i | \(0.877599\pi\) | |||||||
\(752\) | −27700.6 | + | 15993.0i | −1.34327 | + | 0.775536i | ||||
\(753\) | 5681.24 | − | 6931.13i | 0.274948 | − | 0.335438i | ||||
\(754\) | 800.356 | − | 1386.26i | 0.0386568 | − | 0.0669556i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1131.71 | − | 2126.53i | 0.0544444 | − | 0.102303i | ||||
\(757\) | − | 17397.6i | − | 0.835305i | −0.908607 | − | 0.417652i | \(-0.862853\pi\) | ||
0.908607 | − | 0.417652i | \(-0.137147\pi\) | |||||||
\(758\) | 9246.77 | + | 5338.62i | 0.443084 | + | 0.255815i | ||||
\(759\) | −10183.3 | − | 8346.94i | −0.486996 | − | 0.399176i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17757.2 | + | 30756.3i | 0.845857 | + | 1.46507i | 0.884875 | + | 0.465829i | \(0.154244\pi\) |
−0.0390179 | + | 0.999239i | \(0.512423\pi\) | |||||||
\(762\) | 9090.00 | + | 24107.4i | 0.432147 | + | 1.14609i | ||||
\(763\) | −9162.50 | − | 5289.97i | −0.434737 | − | 0.250996i | ||||
\(764\) | 2940.58 | 0.139249 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17435.3 | 0.822408 | ||||||||
\(767\) | 22317.7 | + | 12885.1i | 1.05065 | + | 0.606591i | ||||
\(768\) | 9632.57 | + | 1584.37i | 0.452585 | + | 0.0744416i | ||||
\(769\) | 15631.8 | + | 27075.1i | 0.733027 | + | 1.26964i | 0.955583 | + | 0.294721i | \(0.0952266\pi\) |
−0.222556 | + | 0.974920i | \(0.571440\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4936.26 | + | 30011.2i | −0.230577 | + | 1.40185i | ||||
\(772\) | −253.940 | − | 146.612i | −0.0118387 | − | 0.00683508i | ||||
\(773\) | − | 6676.47i | − | 0.310654i | −0.987863 | − | 0.155327i | \(-0.950357\pi\) | ||
0.987863 | − | 0.155327i | \(-0.0496432\pi\) | |||||||
\(774\) | −625.551 | + | 549.930i | −0.0290503 | + | 0.0255385i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16406.9 | − | 28417.5i | 0.758985 | − | 1.31460i | ||||
\(777\) | 557.179 | + | 1477.68i | 0.0257254 | + | 0.0682260i | ||||
\(778\) | 37846.5 | − | 21850.7i | 1.74404 | − | 1.00692i | ||||
\(779\) | 7894.53 | + | 13673.7i | 0.363095 | + | 0.628898i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13017.6 | − | 22547.1i | 0.596422 | − | 1.03303i | ||||
\(782\) | − | 26427.3i | − | 1.20849i | ||||||
\(783\) | 1075.26 | − | 671.341i | 0.0490761 | − | 0.0306408i | ||||
\(784\) | −11227.9 | −0.511473 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3163.81 | + | 2593.28i | 0.143574 | + | 0.117683i | ||||
\(787\) | −8169.93 | + | 4716.91i | −0.370047 | + | 0.213646i | −0.673479 | − | 0.739207i | \(-0.735201\pi\) |
0.303432 | + | 0.952853i | \(0.401867\pi\) | |||||||
\(788\) | −778.451 | + | 449.439i | −0.0351919 | + | 0.0203180i | ||||
\(789\) | 1907.66 | − | 719.306i | 0.0860766 | − | 0.0324562i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15997.7 | 0.719107 | ||||||||
\(792\) | 5645.75 | − | 16698.0i | 0.253299 | − | 0.749164i | ||||
\(793\) | 8420.57i | 0.377078i | ||||||||
\(794\) | −13709.8 | + | 23746.0i | −0.612773 | + | 1.06135i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1065.27 | − | 1845.10i | −0.0474340 | − | 0.0821580i | ||||
\(797\) | 20331.1 | − | 11738.1i | 0.903592 | − | 0.521689i | 0.0252283 | − | 0.999682i | \(-0.491969\pi\) |
0.878364 | + | 0.477992i | \(0.158635\pi\) | |||||||
\(798\) | −27735.7 | − | 4562.00i | −1.23037 | − | 0.202372i | ||||
\(799\) | −24073.4 | + | 41696.4i | −1.06590 | + | 1.84620i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5465.61 | + | 27305.3i | 0.241096 | + | 1.20447i | ||||
\(802\) | − | 31972.0i | − | 1.40769i | ||||||
\(803\) | −13636.5 | − | 7873.02i | −0.599278 | − | 0.345993i | ||||
\(804\) | 5252.37 | − | 1980.47i | 0.230394 | − | 0.0868729i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2956.89 | + | 5121.48i | 0.129221 | + | 0.223817i | ||||
\(807\) | −15186.3 | + | 18527.4i | −0.662435 | + | 0.808173i | ||||
\(808\) | −3803.91 | − | 2196.19i | −0.165620 | − | 0.0956208i | ||||
\(809\) | 33269.8 | 1.44586 | 0.722932 | − | 0.690919i | \(-0.242794\pi\) | ||||
0.722932 | + | 0.690919i | \(0.242794\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27892.8 | 1.20771 | 0.603853 | − | 0.797096i | \(-0.293631\pi\) | ||||
0.603853 | + | 0.797096i | \(0.293631\pi\) | |||||||
\(812\) | −134.355 | − | 77.5699i | −0.00580657 | − | 0.00335243i | ||||
\(813\) | 3806.91 | − | 4644.44i | 0.164224 | − | 0.200354i | ||||
\(814\) | −1072.19 | − | 1857.08i | −0.0461672 | − | 0.0799640i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 38414.6 | − | 14484.7i | 1.64801 | − | 0.621404i | ||||
\(817\) | 1139.11 | + | 657.666i | 0.0487790 | + | 0.0281626i | ||||
\(818\) | 10093.1i | 0.431415i | ||||||||
\(819\) | 4232.32 | + | 21143.9i | 0.180573 | + | 0.902111i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1848.66 | − | 3201.98i | 0.0785856 | − | 0.136114i | −0.824054 | − | 0.566511i | \(-0.808293\pi\) |
0.902640 | + | 0.430397i | \(0.141626\pi\) | |||||||
\(822\) | −16418.8 | − | 2700.58i | −0.696680 | − | 0.114591i | ||||
\(823\) | 6187.32 | − | 3572.25i | 0.262061 | − | 0.151301i | −0.363213 | − | 0.931706i | \(-0.618320\pi\) |
0.625275 | + | 0.780405i | \(0.284987\pi\) | |||||||
\(824\) | −17162.3 | − | 29725.9i | −0.725578 | − | 1.25674i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9227.29 | − | 15982.1i | 0.388691 | − | 0.673232i | ||||
\(827\) | − | 19866.9i | − | 0.835357i | −0.908595 | − | 0.417679i | \(-0.862844\pi\) | ||
0.908595 | − | 0.417679i | \(-0.137156\pi\) | |||||||
\(828\) | 862.723 | − | 2551.61i | 0.0362098 | − | 0.107095i | ||||
\(829\) | 36736.5 | 1.53910 | 0.769548 | − | 0.638589i | \(-0.220482\pi\) | ||||
0.769548 | + | 0.638589i | \(0.220482\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2958.09 | − | 1115.39i | 0.123484 | − | 0.0465611i | ||||
\(832\) | −20616.7 | + | 11903.0i | −0.859079 | + | 0.495990i | ||||
\(833\) | −14636.5 | + | 8450.38i | −0.608793 | + | 0.351487i | ||||
\(834\) | −29147.5 | − | 23891.3i | −1.21018 | − | 0.991952i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5165.52 | 0.213700 | ||||||||
\(837\) | 161.703 | + | 4680.42i | 0.00667773 | + | 0.193284i | ||||
\(838\) | − | 1478.71i | − | 0.0609560i | ||||||
\(839\) | 15006.1 | − | 25991.4i | 0.617485 | − | 1.06951i | −0.372458 | − | 0.928049i | \(-0.621485\pi\) |
0.989943 | − | 0.141466i | \(-0.0451816\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12153.7 | + | 21050.8i | 0.498326 | + | 0.863127i | ||||
\(842\) | −13307.9 | + | 7683.32i | −0.544680 | + | 0.314471i | ||||
\(843\) | −5040.12 | − | 13366.8i | −0.205920 | − | 0.546117i | ||||
\(844\) | −3092.07 | + | 5355.62i | −0.126106 | + | 0.218422i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −27231.7 | + | 23939.7i | −1.10667 | + | 0.972890i | ||||
\(847\) | − | 4378.68i | − | 0.177631i | ||||||
\(848\) | −37245.0 | − | 21503.4i | −1.50825 | − | 0.870789i | ||||
\(849\) | −861.519 | + | 5237.80i | −0.0348260 | + | 0.211733i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 882.905 | + | 1529.24i | 0.0355648 | + | 0.0616000i | ||||
\(852\) | 5255.27 | + | 864.391i | 0.211318 | + | 0.0347577i | ||||
\(853\) | 4660.10 | + | 2690.51i | 0.187056 | + | 0.107997i | 0.590604 | − | 0.806962i | \(-0.298890\pi\) |
−0.403548 | + | 0.914959i | \(0.632223\pi\) | |||||||
\(854\) | 6030.13 | 0.241624 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12329.4 | 0.492302 | ||||||||
\(857\) | 12678.4 | + | 7319.88i | 0.505352 | + | 0.291765i | 0.730921 | − | 0.682462i | \(-0.239091\pi\) |
−0.225569 | + | 0.974227i | \(0.572424\pi\) | |||||||
\(858\) | −10330.4 | − | 27397.0i | −0.411041 | − | 1.09011i | ||||
\(859\) | 14770.0 | + | 25582.4i | 0.586667 | + | 1.01614i | 0.994665 | + | 0.103154i | \(0.0328935\pi\) |
−0.407999 | + | 0.912983i | \(0.633773\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6708.44 | − | 5498.71i | −0.265532 | − | 0.217649i | ||||
\(862\) | 18292.7 | + | 10561.3i | 0.722797 | + | 0.417307i | ||||
\(863\) | 3387.63i | 0.133622i | 0.997766 | + | 0.0668112i | \(0.0212825\pi\) | ||||
−0.997766 | + | 0.0668112i | \(0.978717\pi\) | |||||||
\(864\) | 7876.00 | − | 272.106i | 0.310124 | − | 0.0107144i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20894.1 | − | 36189.7i | 0.819875 | − | 1.42007i | ||||
\(867\) | 22991.9 | − | 28050.2i | 0.900628 | − | 1.09877i | ||||
\(868\) | 496.370 | − | 286.580i | 0.0194100 | − | 0.0112064i | ||||
\(869\) | 18615.4 | + | 32242.8i | 0.726678 | + | 1.25864i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25123.8 | + | 43515.7i | −0.977368 | + | 1.69285i | ||||
\(872\) | − | 15836.5i | − | 0.615015i | ||||||
\(873\) | 13825.7 | − | 40891.2i | 0.536000 | − | 1.58529i | ||||
\(874\) | −31429.2 | −1.21637 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 522.783 | − | 3178.38i | 0.0201635 | − | 0.122588i | ||||
\(877\) | 211.400 | − | 122.052i | 0.00813967 | − | 0.00469944i | −0.495925 | − | 0.868366i | \(-0.665171\pi\) |
0.504064 | + | 0.863666i | \(0.331837\pi\) | |||||||
\(878\) | 22343.1 | − | 12899.8i | 0.858817 | − | 0.495838i | ||||
\(879\) | 4412.75 | − | 26828.4i | 0.169327 | − | 1.02946i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13910.2 | 0.531948 | 0.265974 | − | 0.963980i | \(-0.414307\pi\) | ||||
0.265974 | + | 0.963980i | \(0.414307\pi\) | |||||||
\(882\) | −12480.1 | + | 2498.10i | −0.476446 | + | 0.0953689i | ||||
\(883\) | − | 8805.87i | − | 0.335607i | −0.985820 | − | 0.167803i | \(-0.946333\pi\) | ||
0.985820 | − | 0.167803i | \(-0.0536674\pi\) | |||||||
\(884\) | 3976.76 | − | 6887.95i | 0.151304 | − | 0.262067i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 848.943 | + | 1470.41i | 0.0321905 | + | 0.0557556i | ||||
\(887\) | −11501.5 | + | 6640.41i | −0.435381 | + | 0.251368i | −0.701637 | − | 0.712535i | \(-0.747547\pi\) |
0.266255 | + | 0.963903i | \(0.414214\pi\) | |||||||
\(888\) | −1498.53 | + | 1828.21i | −0.0566298 | + | 0.0690885i | ||||
\(889\) | −11176.1 | + | 19357.6i | −0.421637 | + | 0.730296i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2971.04 | − | 22996.0i | 0.111710 | − | 0.864642i | ||||
\(892\) | 3823.11i | 0.143506i | ||||||||
\(893\) | 49588.2 | + | 28629.7i | 1.85824 | + | 1.07285i | ||||
\(894\) | −14011.9 | − | 11485.2i | −0.524194 | − | 0.429666i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11605.0 | + | 20100.4i | 0.432695 | + | 0.749449i | ||||
\(897\) | 8506.67 | + | 22560.4i | 0.316644 | + | 0.839765i | ||||
\(898\) | −38920.7 | − | 22470.9i | −1.44633 | − | 0.835036i | ||||
\(899\) | 301.609 | 0.0111893 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −64736.1 | −2.39364 | ||||||||
\(902\) | 10200.1 | + | 5889.04i | 0.376526 | + | 0.217387i | ||||
\(903\) | −713.025 | − | 117.279i | −0.0262768 | − | 0.00432204i | ||||
\(904\) | 11973.1 | + | 20738.0i | 0.440507 | + | 0.762981i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2991.33 | + | 18186.5i | −0.109691 | + | 0.666894i | ||||
\(907\) | −938.982 | − | 542.122i | −0.0343753 | − | 0.0198466i | 0.482714 | − | 0.875778i | \(-0.339651\pi\) |
−0.517089 | + | 0.855932i | \(0.672984\pi\) | |||||||
\(908\) | − | 1051.78i | − | 0.0384411i | ||||||
\(909\) | −5473.61 | − | 1850.68i | −0.199723 | − | 0.0675281i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25094.4 | + | 43464.7i | −0.912638 | + | 1.58073i | −0.102314 | + | 0.994752i | \(0.532625\pi\) |
−0.810324 | + | 0.585983i | \(0.800709\pi\) | |||||||
\(912\) | −17226.2 | − | 45685.2i | −0.625455 | − | 1.65876i | ||||
\(913\) | −11680.5 | + | 6743.74i | −0.423404 | + | 0.244452i | ||||
\(914\) | −21608.4 | − | 37426.9i | −0.781995 | − | 1.35445i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −877.475 | + | 1519.83i | −0.0316513 | + | 0.0548216i | ||||
\(917\) | 3549.06i | 0.127808i | ||||||||
\(918\) | 39476.1 | − | 24647.0i | 1.41929 | − | 0.886136i | ||||
\(919\) | −30376.1 | −1.09033 | −0.545166 | − | 0.838328i | \(-0.683533\pi\) | ||||
−0.545166 | + | 0.838328i | \(0.683533\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19742.5 | − | 16182.3i | −0.706336 | − | 0.578962i | ||||
\(922\) | 20290.2 | − | 11714.5i | 0.724751 | − | 0.418435i | ||||
\(923\) | −41287.2 | + | 23837.2i | −1.47236 | + | 0.850066i | ||||
\(924\) | −2655.30 | + | 1001.21i | −0.0945377 | + | 0.0356466i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 24057.3 | 0.853750 | ||||||||
\(927\) | −29812.2 | − | 33911.6i | −1.05627 | − | 1.20151i | ||||
\(928\) | − | 507.534i | − | 0.0179533i | ||||||
\(929\) | −23098.8 | + | 40008.3i | −0.815766 | + | 1.41295i | 0.0930102 | + | 0.995665i | \(0.470351\pi\) |
−0.908776 | + | 0.417283i | \(0.862982\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10049.8 | + | 17406.7i | 0.353778 | + | 0.612762i | ||||
\(932\) | 3098.20 | − | 1788.74i | 0.108889 | − | 0.0628672i | ||||
\(933\) | −4249.78 | − | 699.007i | −0.149123 | − | 0.0245278i | ||||
\(934\) | 17702.6 | − | 30661.7i | 0.620177 | − | 1.07418i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −24241.5 | + | 21311.0i | −0.846536 | + | 0.744201i | ||||
\(937\) | − | 37004.7i | − | 1.29017i | −0.764111 | − | 0.645085i | \(-0.776822\pi\) | ||
0.764111 | − | 0.645085i | \(-0.223178\pi\) | |||||||
\(938\) | 31162.4 | + | 17991.6i | 1.08474 | + | 0.626277i | ||||
\(939\) | 44911.3 | − | 16934.4i | 1.56084 | − | 0.588533i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21907.2 | − | 37944.4i | −0.758932 | − | 1.31451i | −0.943396 | − | 0.331669i | \(-0.892388\pi\) |
0.184464 | − | 0.982839i | \(-0.440945\pi\) | |||||||
\(942\) | −34823.7 | + | 42485.1i | −1.20448 | + | 1.46947i | ||||
\(943\) | −8399.41 | − | 4849.40i | −0.290055 | − | 0.167464i | ||||
\(944\) | 32056.0 | 1.10523 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 981.191 | 0.0337223 | ||||||||
\(947\) | 3992.14 | + | 2304.86i | 0.136988 | + | 0.0790898i | 0.566928 | − | 0.823768i | \(-0.308132\pi\) |
−0.429940 | + | 0.902857i | \(0.641465\pi\) | |||||||
\(948\) | −4828.05 | + | 5890.24i | −0.165409 | + | 0.201800i | ||||
\(949\) | 14416.7 | + | 24970.5i | 0.493136 | + | 0.854136i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 44236.5 | − | 16679.9i | 1.50838 | − | 0.568752i | ||||
\(952\) | 26580.8 | + | 15346.5i | 0.904927 | + | 0.522460i | ||||
\(953\) | 4281.80i | 0.145542i | 0.997349 | + | 0.0727708i | \(0.0231841\pi\) | ||||
−0.997349 | + | 0.0727708i | \(0.976816\pi\) | |||||||
\(954\) | −46183.1 | − | 15614.9i | −1.56733 | − | 0.529928i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1070.52 | − | 1854.19i | 0.0362165 | − | 0.0627288i | ||||
\(957\) | −1473.50 | − | 242.363i | −0.0497718 | − | 0.00818651i | ||||
\(958\) | −49249.1 | + | 28434.0i | −1.66093 | + | 0.958936i | ||||
\(959\) | −7217.91 | − | 12501.8i | −0.243043 | − | 0.420963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14338.4 | − | 24834.8i | 0.481298 | − | 0.833633i | ||||
\(962\) | 3926.68i | 0.131602i | ||||||||
\(963\) | 15903.4 | − | 3183.34i | 0.532170 | − | 0.106523i | ||||
\(964\) | 5425.05 | 0.181254 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16155.9 | − | 6091.79i | 0.538104 | − | 0.202899i | ||||
\(967\) | 31375.9 | − | 18114.9i | 1.04341 | − | 0.602416i | 0.122616 | − | 0.992454i | \(-0.460872\pi\) |
0.920799 | + | 0.390038i | \(0.127538\pi\) | |||||||
\(968\) | 5676.11 | − | 3277.10i | 0.188468 | − | 0.108812i | ||||
\(969\) | −56839.7 | − | 46589.7i | −1.88437 | − | 1.54456i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 844.928 | 0.0279249 | 0.0139624 | − | 0.999903i | \(-0.495555\pi\) | ||||
0.0139624 | + | 0.999903i | \(0.495555\pi\) | |||||||
\(972\) | 4616.10 | − | 1091.02i | 0.152327 | − | 0.0360025i | ||||
\(973\) | − | 32696.7i | − | 1.07730i | ||||||
\(974\) | −3421.26 | + | 5925.80i | −0.112551 | + | 0.194943i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5237.24 | + | 9071.16i | 0.171762 | + | 0.297501i | ||||
\(977\) | −39702.9 | + | 22922.5i | −1.30011 | + | 0.750619i | −0.980423 | − | 0.196904i | \(-0.936911\pi\) |
−0.319687 | + | 0.947523i | \(0.603578\pi\) | |||||||
\(978\) | 12398.0 | + | 32880.6i | 0.405363 | + | 1.07506i | ||||
\(979\) | 16402.2 | − | 28409.5i | 0.535463 | − | 0.927449i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4088.85 | − | 20427.2i | −0.133075 | − | 0.664821i | ||||
\(982\) | − | 6048.05i | − | 0.196539i | ||||||
\(983\) | 34815.9 | + | 20101.0i | 1.12966 | + | 0.652210i | 0.943849 | − | 0.330376i | \(-0.107176\pi\) |
0.185811 | + | 0.982586i | \(0.440509\pi\) | |||||||
\(984\) | 2107.26 | − | 12811.6i | 0.0682692 | − | 0.415059i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1498.59 | − | 2595.64i | −0.0484025 | − | 0.0838356i | ||||
\(987\) | −31039.6 | − | 5105.42i | −1.00101 | − | 0.164648i | ||||
\(988\) | −8191.61 | − | 4729.43i | −0.263775 | − | 0.152291i | ||||
\(989\) | −807.974 | −0.0259778 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1797.91 | 0.0576313 | 0.0288157 | − | 0.999585i | \(-0.490826\pi\) | ||||
0.0288157 | + | 0.999585i | \(0.490826\pi\) | |||||||
\(992\) | 1623.86 | + | 937.534i | 0.0519733 | + | 0.0300068i | ||||
\(993\) | −10932.7 | − | 28994.3i | −0.349384 | − | 0.926594i | ||||
\(994\) | 17070.3 | + | 29566.6i | 0.544704 | + | 0.943455i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2133.84 | − | 1749.04i | −0.0678849 | − | 0.0556432i | ||||
\(997\) | 7908.61 | + | 4566.04i | 0.251222 | + | 0.145043i | 0.620324 | − | 0.784346i | \(-0.287001\pi\) |
−0.369102 | + | 0.929389i | \(0.620335\pi\) | |||||||
\(998\) | 7342.47i | 0.232888i | ||||||||
\(999\) | −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 | 225.4.k.d.124.11 | 28 | ||
5.2 | odd | 4 | 45.4.e.c.16.2 | ✓ | 14 | ||
5.3 | odd | 4 | 225.4.e.d.151.6 | 14 | |||
5.4 | even | 2 | inner | 225.4.k.d.124.4 | 28 | ||
9.4 | even | 3 | inner | 225.4.k.d.49.4 | 28 | ||
15.2 | even | 4 | 135.4.e.c.46.6 | 14 | |||
45.2 | even | 12 | 405.4.a.n.1.2 | 7 | |||
45.4 | even | 6 | inner | 225.4.k.d.49.11 | 28 | ||
45.7 | odd | 12 | 405.4.a.m.1.6 | 7 | |||
45.13 | odd | 12 | 225.4.e.d.76.6 | 14 | |||
45.22 | odd | 12 | 45.4.e.c.31.2 | yes | 14 | ||
45.32 | even | 12 | 135.4.e.c.91.6 | 14 | |||
45.38 | even | 12 | 2025.4.a.ba.1.6 | 7 | |||
45.43 | odd | 12 | 2025.4.a.bb.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.2 | ✓ | 14 | 5.2 | odd | 4 | ||
45.4.e.c.31.2 | yes | 14 | 45.22 | odd | 12 | ||
135.4.e.c.46.6 | 14 | 15.2 | even | 4 | |||
135.4.e.c.91.6 | 14 | 45.32 | even | 12 | |||
225.4.e.d.76.6 | 14 | 45.13 | odd | 12 | |||
225.4.e.d.151.6 | 14 | 5.3 | odd | 4 | |||
225.4.k.d.49.4 | 28 | 9.4 | even | 3 | inner | ||
225.4.k.d.49.11 | 28 | 45.4 | even | 6 | inner | ||
225.4.k.d.124.4 | 28 | 5.4 | even | 2 | inner | ||
225.4.k.d.124.11 | 28 | 1.1 | even | 1 | trivial | ||
405.4.a.m.1.6 | 7 | 45.7 | odd | 12 | |||
405.4.a.n.1.2 | 7 | 45.2 | even | 12 | |||
2025.4.a.ba.1.6 | 7 | 45.38 | even | 12 | |||
2025.4.a.bb.1.2 | 7 | 45.43 | odd | 12 |