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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.3 | ||
Root | \(1.26217 - 1.18614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.49 |
Dual form | 225.4.k.a.124.3 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.05446 | − | 1.18614i | 0.726360 | − | 0.419364i | −0.0907292 | − | 0.995876i | \(-0.528920\pi\) |
0.817089 | + | 0.576512i | \(0.195586\pi\) | |||||||
\(3\) | −4.97494 | + | 1.50000i | −0.957427 | + | 0.288675i | ||||
\(4\) | −1.18614 | + | 2.05446i | −0.148268 | + | 0.256807i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −8.44158 | + | 8.98266i | −0.574377 | + | 0.611193i | ||||
\(7\) | 6.38458 | − | 3.68614i | 0.344735 | − | 0.199033i | −0.317629 | − | 0.948215i | \(-0.602887\pi\) |
0.662364 | + | 0.749182i | \(0.269553\pi\) | |||||||
\(8\) | 24.6060i | 1.08744i | ||||||||
\(9\) | 22.5000 | − | 14.9248i | 0.833333 | − | 0.552771i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.06930 | + | 3.58413i | 0.0567197 | + | 0.0982414i | 0.892991 | − | 0.450074i | \(-0.148603\pi\) |
−0.836271 | + | 0.548316i | \(0.815269\pi\) | |||||||
\(12\) | 2.81929 | − | 12.0000i | 0.0678216 | − | 0.288675i | ||||
\(13\) | −68.3972 | − | 39.4891i | −1.45923 | − | 0.842486i | −0.460254 | − | 0.887787i | \(-0.652242\pi\) |
−0.998973 | + | 0.0453014i | \(0.985575\pi\) | |||||||
\(14\) | 8.74456 | − | 15.1460i | 0.166934 | − | 0.289139i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 19.6970 | + | 34.1162i | 0.307766 | + | 0.533066i | ||||
\(17\) | − | 33.3070i | − | 0.475185i | −0.971365 | − | 0.237592i | \(-0.923642\pi\) | ||
0.971365 | − | 0.237592i | \(-0.0763583\pi\) | |||||||
\(18\) | 28.5223 | − | 57.3505i | 0.373488 | − | 0.750981i | ||||
\(19\) | −89.3070 | −1.07834 | −0.539169 | − | 0.842197i | \(-0.681262\pi\) | ||||
−0.539169 | + | 0.842197i | \(0.681262\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −26.2337 | + | 27.9152i | −0.272603 | + | 0.290076i | ||||
\(22\) | 8.50256 | + | 4.90895i | 0.0823978 | + | 0.0475724i | ||||
\(23\) | −172.826 | − | 99.7812i | −1.56682 | − | 0.904601i | −0.996537 | − | 0.0831494i | \(-0.973502\pi\) |
−0.570278 | − | 0.821452i | \(-0.693165\pi\) | |||||||
\(24\) | −36.9090 | − | 122.413i | −0.313917 | − | 1.04114i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −187.359 | −1.41323 | ||||||||
\(27\) | −89.5489 | + | 108.000i | −0.638285 | + | 0.769800i | ||||
\(28\) | 17.4891i | 0.118041i | ||||||||
\(29\) | 25.2405 | + | 43.7179i | 0.161622 | + | 0.279938i | 0.935451 | − | 0.353457i | \(-0.114994\pi\) |
−0.773828 | + | 0.633395i | \(0.781661\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | − | 5.19615i | 0.0173812 | − | 0.0301050i | −0.857204 | − | 0.514977i | \(-0.827800\pi\) |
0.874585 | + | 0.484872i | \(0.161134\pi\) | |||||||
\(32\) | −89.5419 | − | 51.6970i | −0.494654 | − | 0.285588i | ||||
\(33\) | −15.6708 | − | 14.7269i | −0.0826648 | − | 0.0776854i | ||||
\(34\) | −39.5068 | − | 68.4278i | −0.199275 | − | 0.345155i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.97420 | + | 63.9282i | 0.0183991 | + | 0.295964i | ||||
\(37\) | − | 290.277i | − | 1.28976i | −0.764282 | − | 0.644882i | \(-0.776906\pi\) | ||
0.764282 | − | 0.644882i | \(-0.223094\pi\) | |||||||
\(38\) | −183.477 | + | 105.931i | −0.783262 | + | 0.452217i | ||||
\(39\) | 399.505 | + | 93.8602i | 1.64031 | + | 0.385376i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 26.6684 | − | 46.1911i | 0.101583 | − | 0.175947i | −0.810754 | − | 0.585387i | \(-0.800943\pi\) |
0.912337 | + | 0.409440i | \(0.134276\pi\) | |||||||
\(42\) | −20.7846 | + | 88.4674i | −0.0763604 | + | 0.325019i | ||||
\(43\) | 258.412 | − | 149.194i | 0.916453 | − | 0.529114i | 0.0339510 | − | 0.999424i | \(-0.489191\pi\) |
0.882502 | + | 0.470309i | \(0.155858\pi\) | |||||||
\(44\) | −9.81791 | −0.0336388 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −473.418 | −1.51743 | ||||||||
\(47\) | −362.782 | + | 209.452i | −1.12590 | + | 0.650038i | −0.942900 | − | 0.333075i | \(-0.891914\pi\) |
−0.182998 | + | 0.983113i | \(0.558580\pi\) | |||||||
\(48\) | −149.166 | − | 140.181i | −0.448546 | − | 0.421528i | ||||
\(49\) | −144.325 | + | 249.978i | −0.420772 | + | 0.728798i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 49.9605 | + | 165.700i | 0.137174 | + | 0.454955i | ||||
\(52\) | 162.257 | − | 93.6793i | 0.432712 | − | 0.249827i | ||||
\(53\) | − | 399.228i | − | 1.03468i | −0.855779 | − | 0.517342i | \(-0.826922\pi\) | ||
0.855779 | − | 0.517342i | \(-0.173078\pi\) | |||||||
\(54\) | −55.8710 | + | 328.099i | −0.140798 | + | 0.826826i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 90.7011 | + | 157.099i | 0.216436 | + | 0.374879i | ||||
\(57\) | 444.297 | − | 133.961i | 1.03243 | − | 0.311290i | ||||
\(58\) | 103.711 | + | 59.8776i | 0.234792 | + | 0.135557i | ||||
\(59\) | 49.1209 | − | 85.0799i | 0.108390 | − | 0.187737i | −0.806728 | − | 0.590923i | \(-0.798764\pi\) |
0.915118 | + | 0.403186i | \(0.132097\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 341.797 | + | 592.011i | 0.717421 | + | 1.24261i | 0.962018 | + | 0.272985i | \(0.0880109\pi\) |
−0.244597 | + | 0.969625i | \(0.578656\pi\) | |||||||
\(62\) | − | 14.2337i | − | 0.0291561i | ||||||
\(63\) | 88.6382 | − | 178.227i | 0.177260 | − | 0.356420i | ||||
\(64\) | −560.432 | −1.09459 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −49.6631 | − | 11.6679i | −0.0926228 | − | 0.0217609i | ||||
\(67\) | −195.289 | − | 112.750i | −0.356094 | − | 0.205591i | 0.311272 | − | 0.950321i | \(-0.399245\pi\) |
−0.667366 | + | 0.744730i | \(0.732578\pi\) | |||||||
\(68\) | 68.4278 | + | 39.5068i | 0.122031 | + | 0.0704545i | ||||
\(69\) | 1009.47 | + | 237.166i | 1.76125 | + | 0.413789i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 512.951 | 0.857410 | 0.428705 | − | 0.903445i | \(-0.358970\pi\) | ||||
0.428705 | + | 0.903445i | \(0.358970\pi\) | |||||||
\(72\) | 367.239 | + | 553.634i | 0.601105 | + | 0.906200i | ||||
\(73\) | 994.318i | 1.59419i | 0.603852 | + | 0.797096i | \(0.293632\pi\) | ||||
−0.603852 | + | 0.797096i | \(0.706368\pi\) | |||||||
\(74\) | −344.310 | − | 596.362i | −0.540881 | − | 0.936833i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 105.931 | − | 183.477i | 0.159883 | − | 0.276925i | ||||
\(77\) | 26.4232 | + | 15.2554i | 0.0391065 | + | 0.0225782i | ||||
\(78\) | 932.097 | − | 281.038i | 1.35307 | − | 0.407965i | ||||
\(79\) | −100.853 | − | 174.683i | −0.143631 | − | 0.248777i | 0.785230 | − | 0.619204i | \(-0.212545\pi\) |
−0.928862 | + | 0.370427i | \(0.879211\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 283.500 | − | 671.617i | 0.388889 | − | 0.921285i | ||||
\(82\) | − | 126.530i | − | 0.170401i | ||||||
\(83\) | −959.247 | + | 553.822i | −1.26857 | + | 0.732408i | −0.974717 | − | 0.223444i | \(-0.928270\pi\) |
−0.293850 | + | 0.955851i | \(0.594937\pi\) | |||||||
\(84\) | −26.2337 | − | 87.0073i | −0.0340754 | − | 0.113015i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 353.931 | − | 613.026i | 0.443783 | − | 0.768655i | ||||
\(87\) | −191.147 | − | 179.633i | −0.235553 | − | 0.221364i | ||||
\(88\) | −88.1909 | + | 50.9171i | −0.106832 | + | 0.0616793i | ||||
\(89\) | −372.269 | −0.443375 | −0.221688 | − | 0.975118i | \(-0.571157\pi\) | ||||
−0.221688 | + | 0.975118i | \(0.571157\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −582.250 | −0.670729 | ||||||||
\(92\) | 409.992 | − | 236.709i | 0.464616 | − | 0.268246i | ||||
\(93\) | −7.13058 | + | 30.3505i | −0.00795061 | + | 0.0338409i | ||||
\(94\) | −496.880 | + | 860.622i | −0.545205 | + | 0.944323i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 523.011 | + | 122.877i | 0.556037 | + | 0.130636i | ||||
\(97\) | −120.578 | + | 69.6156i | −0.126215 | + | 0.0728700i | −0.561778 | − | 0.827288i | \(-0.689882\pi\) |
0.435563 | + | 0.900158i | \(0.356549\pi\) | |||||||
\(98\) | 684.758i | 0.705826i | ||||||||
\(99\) | 100.052 | + | 49.7590i | 0.101571 | + | 0.0505148i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −985.872 | − | 1707.58i | −0.971267 | − | 1.68228i | −0.691742 | − | 0.722145i | \(-0.743156\pi\) |
−0.279525 | − | 0.960139i | \(-0.590177\pi\) | |||||||
\(102\) | 299.186 | + | 281.164i | 0.290429 | + | 0.272935i | ||||
\(103\) | 1569.85 | + | 906.353i | 1.50177 | + | 0.867045i | 0.999998 | + | 0.00204255i | \(0.000650165\pi\) |
0.501768 | + | 0.865002i | \(0.332683\pi\) | |||||||
\(104\) | 971.668 | − | 1682.98i | 0.916153 | − | 1.58682i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −473.541 | − | 820.197i | −0.433909 | − | 0.751552i | ||||
\(107\) | − | 259.217i | − | 0.234201i | −0.993120 | − | 0.117100i | \(-0.962640\pi\) | ||
0.993120 | − | 0.117100i | \(-0.0373600\pi\) | |||||||
\(108\) | −115.664 | − | 312.077i | −0.103053 | − | 0.278052i | ||||
\(109\) | −775.556 | −0.681512 | −0.340756 | − | 0.940152i | \(-0.610683\pi\) | ||||
−0.340756 | + | 0.940152i | \(0.610683\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 435.416 | + | 1444.11i | 0.372323 | + | 1.23486i | ||||
\(112\) | 251.514 | + | 145.212i | 0.212195 | + | 0.122511i | ||||
\(113\) | −186.417 | − | 107.628i | −0.155191 | − | 0.0895997i | 0.420393 | − | 0.907342i | \(-0.361892\pi\) |
−0.575585 | + | 0.817742i | \(0.695225\pi\) | |||||||
\(114\) | 753.892 | − | 802.215i | 0.619373 | − | 0.659073i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −119.755 | −0.0958534 | ||||||||
\(117\) | −2128.30 | + | 132.310i | −1.68172 | + | 0.104547i | ||||
\(118\) | − | 233.057i | − | 0.181819i | ||||||
\(119\) | −122.774 | − | 212.652i | −0.0945774 | − | 0.163813i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 656.936 | − | 1137.85i | 0.493566 | − | 0.854881i | ||||
\(122\) | 1404.42 | + | 810.840i | 1.04221 | + | 0.601721i | ||||
\(123\) | −63.3872 | + | 269.800i | −0.0464669 | + | 0.197781i | ||||
\(124\) | 7.11684 | + | 12.3267i | 0.00515412 | + | 0.00892721i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −29.2989 | − | 471.297i | −0.0207155 | − | 0.333226i | ||||
\(127\) | 2424.76i | 1.69420i | 0.531436 | + | 0.847098i | \(0.321652\pi\) | ||||
−0.531436 | + | 0.847098i | \(0.678348\pi\) | |||||||
\(128\) | −435.048 | + | 251.175i | −0.300415 | + | 0.173445i | ||||
\(129\) | −1061.79 | + | 1129.85i | −0.724694 | + | 0.771145i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −130.247 | + | 225.595i | −0.0868684 | + | 0.150461i | −0.906186 | − | 0.422880i | \(-0.861019\pi\) |
0.819317 | + | 0.573340i | \(0.194353\pi\) | |||||||
\(132\) | 48.8435 | − | 14.7269i | 0.0322067 | − | 0.00971067i | ||||
\(133\) | −570.188 | + | 329.198i | −0.371741 | + | 0.214625i | ||||
\(134\) | −534.949 | −0.344870 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 819.552 | 0.516735 | ||||||||
\(137\) | −350.427 | + | 202.319i | −0.218533 | + | 0.126170i | −0.605271 | − | 0.796020i | \(-0.706935\pi\) |
0.386738 | + | 0.922190i | \(0.373602\pi\) | |||||||
\(138\) | 2355.23 | − | 710.127i | 1.45283 | − | 0.438044i | ||||
\(139\) | −883.841 | + | 1530.86i | −0.539327 | + | 0.934141i | 0.459614 | + | 0.888119i | \(0.347988\pi\) |
−0.998940 | + | 0.0460221i | \(0.985346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1490.64 | − | 1586.19i | 0.890316 | − | 0.947383i | ||||
\(142\) | 1053.84 | − | 608.432i | 0.622788 | − | 0.359567i | ||||
\(143\) | − | 326.859i | − | 0.191142i | ||||||
\(144\) | 952.361 | + | 473.641i | 0.551135 | + | 0.274098i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1179.40 | + | 2042.78i | 0.668547 | + | 1.15796i | ||||
\(147\) | 343.040 | − | 1460.11i | 0.192472 | − | 0.819237i | ||||
\(148\) | 596.362 | + | 344.310i | 0.331220 | + | 0.191230i | ||||
\(149\) | 960.344 | − | 1663.36i | 0.528016 | − | 0.914551i | −0.471450 | − | 0.881893i | \(-0.656269\pi\) |
0.999467 | − | 0.0326584i | \(-0.0103973\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1262.28 | + | 2186.33i | 0.680284 | + | 1.17829i | 0.974894 | + | 0.222668i | \(0.0714767\pi\) |
−0.294611 | + | 0.955617i | \(0.595190\pi\) | |||||||
\(152\) | − | 2197.49i | − | 1.17263i | ||||||
\(153\) | −497.101 | − | 749.408i | −0.262668 | − | 0.395987i | ||||
\(154\) | 72.3804 | 0.0378739 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −666.701 | + | 709.435i | −0.342172 | + | 0.364104i | ||||
\(157\) | −1682.43 | − | 971.350i | −0.855238 | − | 0.493772i | 0.00717683 | − | 0.999974i | \(-0.497716\pi\) |
−0.862415 | + | 0.506202i | \(0.831049\pi\) | |||||||
\(158\) | −414.397 | − | 239.252i | −0.208656 | − | 0.120468i | ||||
\(159\) | 598.842 | + | 1986.13i | 0.298687 | + | 0.990634i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1471.23 | −0.720181 | ||||||||
\(162\) | −214.193 | − | 1716.08i | −0.103880 | − | 0.832270i | ||||
\(163\) | 1051.21i | 0.505134i | 0.967579 | + | 0.252567i | \(0.0812748\pi\) | ||||
−0.967579 | + | 0.252567i | \(0.918725\pi\) | |||||||
\(164\) | 63.2650 | + | 109.578i | 0.0301230 | + | 0.0521745i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1313.82 | + | 2275.60i | −0.614291 | + | 1.06398i | ||||
\(167\) | 2439.11 | + | 1408.22i | 1.13020 | + | 0.652524i | 0.943986 | − | 0.329985i | \(-0.107044\pi\) |
0.186218 | + | 0.982508i | \(0.440377\pi\) | |||||||
\(168\) | −686.880 | − | 645.505i | −0.315440 | − | 0.296439i | ||||
\(169\) | 2020.28 | + | 3499.23i | 0.919564 | + | 1.59273i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2009.41 | + | 1332.89i | −0.898616 | + | 0.596074i | ||||
\(172\) | 707.861i | 0.313802i | ||||||||
\(173\) | 1249.20 | − | 721.225i | 0.548987 | − | 0.316958i | −0.199726 | − | 0.979852i | \(-0.564005\pi\) |
0.748713 | + | 0.662894i | \(0.230672\pi\) | |||||||
\(174\) | −605.772 | − | 142.321i | −0.263928 | − | 0.0620075i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −81.5179 | + | 141.193i | −0.0349128 | + | 0.0604707i | ||||
\(177\) | −116.754 | + | 496.948i | −0.0495804 | + | 0.211033i | ||||
\(178\) | −764.809 | + | 441.563i | −0.322050 | + | 0.185936i | ||||
\(179\) | −1534.89 | −0.640912 | −0.320456 | − | 0.947263i | \(-0.603836\pi\) | ||||
−0.320456 | + | 0.947263i | \(0.603836\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3650.43 | −1.49908 | −0.749542 | − | 0.661956i | \(-0.769726\pi\) | ||||
−0.749542 | + | 0.661956i | \(0.769726\pi\) | |||||||
\(182\) | −1196.21 | + | 690.630i | −0.487191 | + | 0.281280i | ||||
\(183\) | −2588.44 | − | 2432.52i | −1.04559 | − | 0.982606i | ||||
\(184\) | 2455.21 | − | 4252.56i | 0.983700 | − | 1.70382i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 21.3505 | + | 70.8117i | 0.00841665 | + | 0.0279149i | ||||
\(187\) | 119.377 | − | 68.9221i | 0.0466828 | − | 0.0269523i | ||||
\(188\) | − | 993.760i | − | 0.385518i | ||||||
\(189\) | −173.629 | + | 1019.62i | −0.0668235 | + | 0.392417i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −678.644 | − | 1175.45i | −0.257094 | − | 0.445300i | 0.708368 | − | 0.705843i | \(-0.249432\pi\) |
−0.965462 | + | 0.260543i | \(0.916098\pi\) | |||||||
\(192\) | 2788.11 | − | 840.648i | 1.04799 | − | 0.315982i | ||||
\(193\) | −1561.48 | − | 901.520i | −0.582371 | − | 0.336232i | 0.179704 | − | 0.983721i | \(-0.442486\pi\) |
−0.762075 | + | 0.647488i | \(0.775819\pi\) | |||||||
\(194\) | −165.148 | + | 286.044i | −0.0611181 | + | 0.105860i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −342.379 | − | 593.018i | −0.124774 | − | 0.216114i | ||||
\(197\) | − | 263.403i | − | 0.0952624i | −0.998865 | − | 0.0476312i | \(-0.984833\pi\) | ||
0.998865 | − | 0.0476312i | \(-0.0151672\pi\) | |||||||
\(198\) | 264.573 | − | 16.4476i | 0.0949614 | − | 0.00590344i | ||||
\(199\) | −492.853 | −0.175565 | −0.0877824 | − | 0.996140i | \(-0.527978\pi\) | ||||
−0.0877824 | + | 0.996140i | \(0.527978\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1140.67 | + | 267.991i | 0.400283 | + | 0.0940429i | ||||
\(202\) | −4050.86 | − | 2338.77i | −1.41098 | − | 0.814629i | ||||
\(203\) | 322.300 | + | 186.080i | 0.111434 | + | 0.0643363i | ||||
\(204\) | −399.684 | − | 93.9022i | −0.137174 | − | 0.0322278i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4300.25 | 1.45443 | ||||||||
\(207\) | −5377.80 | + | 334.320i | −1.80572 | + | 0.112255i | ||||
\(208\) | − | 3111.27i | − | 1.03715i | ||||||
\(209\) | −184.803 | − | 320.088i | −0.0611630 | − | 0.105937i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 500.772 | − | 867.362i | 0.163387 | − | 0.282994i | −0.772695 | − | 0.634778i | \(-0.781092\pi\) |
0.936081 | + | 0.351784i | \(0.114425\pi\) | |||||||
\(212\) | 820.197 | + | 473.541i | 0.265714 | + | 0.153410i | ||||
\(213\) | −2551.90 | + | 769.426i | −0.820907 | + | 0.247513i | ||||
\(214\) | −307.468 | − | 532.551i | −0.0982155 | − | 0.170114i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2657.44 | − | 2203.44i | −0.837112 | − | 0.694097i | ||||
\(217\) | − | 44.2337i | − | 0.0138377i | ||||||
\(218\) | −1593.35 | + | 919.919i | −0.495023 | + | 0.285802i | ||||
\(219\) | −1491.48 | − | 4946.67i | −0.460204 | − | 1.52632i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1315.27 | + | 2278.11i | −0.400336 | + | 0.693403i | ||||
\(222\) | 2607.46 | + | 2450.40i | 0.788294 | + | 0.740810i | ||||
\(223\) | −485.969 | + | 280.574i | −0.145932 | + | 0.0842540i | −0.571188 | − | 0.820819i | \(-0.693517\pi\) |
0.425256 | + | 0.905073i | \(0.360184\pi\) | |||||||
\(224\) | −762.250 | −0.227366 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −510.646 | −0.150300 | ||||||||
\(227\) | −3383.09 | + | 1953.23i | −0.989180 | + | 0.571103i | −0.905029 | − | 0.425350i | \(-0.860151\pi\) |
−0.0841506 | + | 0.996453i | \(0.526818\pi\) | |||||||
\(228\) | −251.783 | + | 1071.68i | −0.0731347 | + | 0.311290i | ||||
\(229\) | 1498.45 | − | 2595.40i | 0.432405 | − | 0.748947i | −0.564675 | − | 0.825313i | \(-0.690999\pi\) |
0.997080 | + | 0.0763664i | \(0.0243319\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −154.337 | − | 36.2601i | −0.0439594 | − | 0.0103279i | ||||
\(232\) | −1075.72 | + | 621.067i | −0.304416 | + | 0.175755i | ||||
\(233\) | − | 4194.30i | − | 1.17930i | −0.807658 | − | 0.589651i | \(-0.799265\pi\) | ||
0.807658 | − | 0.589651i | \(-0.200735\pi\) | |||||||
\(234\) | −4215.57 | + | 2796.29i | −1.17769 | + | 0.781194i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 116.529 | + | 201.833i | 0.0321414 | + | 0.0556705i | ||||
\(237\) | 763.763 | + | 717.757i | 0.209332 | + | 0.196723i | ||||
\(238\) | −504.469 | − | 291.255i | −0.137394 | − | 0.0793247i | ||||
\(239\) | −83.2362 | + | 144.169i | −0.0225276 | + | 0.0390190i | −0.877069 | − | 0.480364i | \(-0.840505\pi\) |
0.854542 | + | 0.519383i | \(0.173838\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −307.272 | − | 532.210i | −0.0821291 | − | 0.142252i | 0.822035 | − | 0.569437i | \(-0.192839\pi\) |
−0.904164 | + | 0.427185i | \(0.859505\pi\) | |||||||
\(242\) | − | 3116.87i | − | 0.827935i | ||||||
\(243\) | −402.970 | + | 3766.50i | −0.106381 | + | 0.994325i | ||||
\(244\) | −1621.68 | −0.425481 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 189.795 | + | 629.479i | 0.0491906 | + | 0.163147i | ||||
\(247\) | 6108.35 | + | 3526.66i | 1.57354 | + | 0.908485i | ||||
\(248\) | 127.856 | + | 73.8179i | 0.0327374 | + | 0.0189010i | ||||
\(249\) | 3941.46 | − | 4194.10i | 1.00313 | − | 1.06743i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6136.16 | −1.54307 | −0.771536 | − | 0.636185i | \(-0.780511\pi\) | ||||
−0.771536 | + | 0.636185i | \(0.780511\pi\) | |||||||
\(252\) | 261.022 | + | 393.505i | 0.0652493 | + | 0.0983671i | ||||
\(253\) | − | 825.908i | − | 0.205235i | ||||||
\(254\) | 2876.11 | + | 4981.57i | 0.710485 | + | 1.23060i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1645.87 | − | 2850.73i | 0.401824 | − | 0.695979i | ||||
\(257\) | −4720.19 | − | 2725.20i | −1.14567 | − | 0.661453i | −0.197842 | − | 0.980234i | \(-0.563393\pi\) |
−0.947828 | + | 0.318781i | \(0.896727\pi\) | |||||||
\(258\) | −841.244 | + | 3580.66i | −0.202998 | + | 0.864040i | ||||
\(259\) | −1070.00 | − | 1853.30i | −0.256705 | − | 0.444627i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1220.39 | + | 606.942i | 0.289427 | + | 0.143942i | ||||
\(262\) | 617.967i | 0.145718i | ||||||||
\(263\) | 678.305 | − | 391.620i | 0.159035 | − | 0.0918186i | −0.418371 | − | 0.908276i | \(-0.637399\pi\) |
0.577405 | + | 0.816458i | \(0.304065\pi\) | |||||||
\(264\) | 362.369 | − | 385.596i | 0.0844782 | − | 0.0898930i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −780.951 | + | 1352.65i | −0.180012 | + | 0.311790i | ||||
\(267\) | 1852.01 | − | 558.403i | 0.424499 | − | 0.127991i | ||||
\(268\) | 463.279 | − | 267.474i | 0.105594 | − | 0.0609649i | ||||
\(269\) | −141.019 | −0.0319632 | −0.0159816 | − | 0.999872i | \(-0.505087\pi\) | ||||
−0.0159816 | + | 0.999872i | \(0.505087\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6375.83 | 1.42917 | 0.714583 | − | 0.699551i | \(-0.246616\pi\) | ||||
0.714583 | + | 0.699551i | \(0.246616\pi\) | |||||||
\(272\) | 1136.31 | − | 656.049i | 0.253305 | − | 0.146246i | ||||
\(273\) | 2896.66 | − | 873.375i | 0.642174 | − | 0.193623i | ||||
\(274\) | −479.958 | + | 831.312i | −0.105822 | + | 0.183290i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1684.62 | + | 1792.60i | −0.367400 | + | 0.390949i | ||||
\(277\) | 5909.04 | − | 3411.59i | 1.28173 | − | 0.740008i | 0.304567 | − | 0.952491i | \(-0.401488\pi\) |
0.977165 | + | 0.212482i | \(0.0681548\pi\) | |||||||
\(278\) | 4193.44i | 0.904697i | ||||||||
\(279\) | −10.0516 | − | 161.688i | −0.00215689 | − | 0.0346953i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −294.846 | − | 510.689i | −0.0625945 | − | 0.108417i | 0.833030 | − | 0.553228i | \(-0.186604\pi\) |
−0.895624 | + | 0.444811i | \(0.853271\pi\) | |||||||
\(282\) | 1181.02 | − | 5026.86i | 0.249392 | − | 1.06151i | ||||
\(283\) | −5175.39 | − | 2988.01i | −1.08709 | − | 0.627629i | −0.154286 | − | 0.988026i | \(-0.549308\pi\) |
−0.932799 | + | 0.360397i | \(0.882641\pi\) | |||||||
\(284\) | −608.432 | + | 1053.84i | −0.127126 | + | 0.220189i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −387.701 | − | 671.517i | −0.0801581 | − | 0.138838i | ||||
\(287\) | − | 393.214i | − | 0.0808736i | ||||||
\(288\) | −2786.26 | + | 173.212i | −0.570076 | + | 0.0354397i | ||||
\(289\) | 3803.64 | 0.774199 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 495.443 | − | 527.200i | 0.0998055 | − | 0.106203i | ||||
\(292\) | −2042.78 | − | 1179.40i | −0.409400 | − | 0.236367i | ||||
\(293\) | 6977.99 | + | 4028.74i | 1.39133 | + | 0.803282i | 0.993462 | − | 0.114162i | \(-0.0364184\pi\) |
0.397864 | + | 0.917445i | \(0.369752\pi\) | |||||||
\(294\) | −1027.14 | − | 3406.63i | −0.203755 | − | 0.675777i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7142.55 | 1.40254 | ||||||||
\(297\) | −572.389 | − | 97.4705i | −0.111830 | − | 0.0190431i | ||||
\(298\) | − | 4556.41i | − | 0.885724i | ||||||
\(299\) | 7880.55 | + | 13649.5i | 1.52423 | + | 2.64004i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1099.90 | − | 1905.09i | 0.210622 | − | 0.364808i | ||||
\(302\) | 5186.59 | + | 2994.48i | 0.988261 | + | 0.570573i | ||||
\(303\) | 7466.02 | + | 7016.30i | 1.41555 | + | 1.33028i | ||||
\(304\) | −1759.08 | − | 3046.82i | −0.331876 | − | 0.574826i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1910.18 | − | 949.994i | −0.356855 | − | 0.177476i | ||||
\(307\) | − | 4546.58i | − | 0.845235i | −0.906308 | − | 0.422618i | \(-0.861111\pi\) | ||
0.906308 | − | 0.422618i | \(-0.138889\pi\) | |||||||
\(308\) | −62.6832 | + | 36.1902i | −0.0115965 | + | 0.00669522i | ||||
\(309\) | −9169.43 | − | 2154.28i | −1.68813 | − | 0.396610i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2101.40 | − | 3639.73i | 0.383149 | − | 0.663633i | −0.608362 | − | 0.793660i | \(-0.708173\pi\) |
0.991510 | + | 0.130027i | \(0.0415063\pi\) | |||||||
\(312\) | −2309.52 | + | 9830.22i | −0.419073 | + | 1.78374i | ||||
\(313\) | 6039.04 | − | 3486.64i | 1.09056 | − | 0.629637i | 0.156838 | − | 0.987624i | \(-0.449870\pi\) |
0.933727 | + | 0.357987i | \(0.116537\pi\) | |||||||
\(314\) | −4608.63 | −0.828281 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 478.505 | 0.0851835 | ||||||||
\(317\) | −6373.97 | + | 3680.02i | −1.12933 | + | 0.652020i | −0.943767 | − | 0.330612i | \(-0.892745\pi\) |
−0.185565 | + | 0.982632i | \(0.559411\pi\) | |||||||
\(318\) | 3586.13 | + | 3370.12i | 0.632391 | + | 0.594298i | ||||
\(319\) | −104.460 | + | 180.930i | −0.0183343 | + | 0.0317560i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 388.826 | + | 1289.59i | 0.0676080 | + | 0.224230i | ||||
\(322\) | −3022.58 | + | 1745.09i | −0.523111 | + | 0.302018i | ||||
\(323\) | 2974.55i | 0.512410i | ||||||||
\(324\) | 1043.54 | + | 1379.07i | 0.178933 | + | 0.236466i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1246.88 | + | 2159.66i | 0.211835 | + | 0.366909i | ||||
\(327\) | 3858.34 | − | 1163.33i | 0.652498 | − | 0.196736i | ||||
\(328\) | 1136.58 | + | 656.203i | 0.191332 | + | 0.110466i | ||||
\(329\) | −1544.14 | + | 2674.53i | −0.258758 | + | 0.448182i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3417.06 | + | 5918.52i | 0.567428 | + | 0.982814i | 0.996819 | + | 0.0796957i | \(0.0253949\pi\) |
−0.429391 | + | 0.903119i | \(0.641272\pi\) | |||||||
\(332\) | − | 2627.64i | − | 0.434369i | ||||||
\(333\) | −4332.33 | − | 6531.24i | −0.712944 | − | 1.07480i | ||||
\(334\) | 6681.39 | 1.09458 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1469.09 | − | 345.149i | −0.238528 | − | 0.0560399i | ||||
\(337\) | 6000.24 | + | 3464.24i | 0.969893 | + | 0.559968i | 0.899204 | − | 0.437531i | \(-0.144147\pi\) |
0.0706891 | + | 0.997498i | \(0.477480\pi\) | |||||||
\(338\) | 8301.16 | + | 4792.68i | 1.33587 | + | 0.771264i | ||||
\(339\) | 1088.85 | + | 255.816i | 0.174449 | + | 0.0409853i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.8316 | 0.00394341 | ||||||||
\(342\) | −2547.24 | + | 5121.81i | −0.402746 | + | 0.809812i | ||||
\(343\) | 4656.70i | 0.733055i | ||||||||
\(344\) | 3671.07 | + | 6358.48i | 0.575380 | + | 0.996588i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1710.95 | − | 2963.45i | 0.265842 | − | 0.460451i | ||||
\(347\) | 6530.35 | + | 3770.30i | 1.01028 | + | 0.583286i | 0.911274 | − | 0.411801i | \(-0.135100\pi\) |
0.0990071 | + | 0.995087i | \(0.468433\pi\) | |||||||
\(348\) | 595.775 | − | 179.633i | 0.0917726 | − | 0.0276705i | ||||
\(349\) | −922.084 | − | 1597.10i | −0.141427 | − | 0.244959i | 0.786607 | − | 0.617454i | \(-0.211836\pi\) |
−0.928034 | + | 0.372495i | \(0.878502\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10389.7 | − | 3850.69i | 1.57995 | − | 0.585568i | ||||
\(352\) | − | 427.906i | − | 0.0647939i | ||||||
\(353\) | 6146.61 | − | 3548.74i | 0.926773 | − | 0.535073i | 0.0409833 | − | 0.999160i | \(-0.486951\pi\) |
0.885789 | + | 0.464087i | \(0.153618\pi\) | |||||||
\(354\) | 349.586 | + | 1159.44i | 0.0524866 | + | 0.174079i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 441.563 | − | 764.809i | 0.0657382 | − | 0.113862i | ||||
\(357\) | 929.772 | + | 873.766i | 0.137840 | + | 0.129537i | ||||
\(358\) | −3153.37 | + | 1820.60i | −0.465532 | + | 0.268775i | ||||
\(359\) | −7709.65 | −1.13342 | −0.566712 | − | 0.823916i | \(-0.691785\pi\) | ||||
−0.566712 | + | 0.823916i | \(0.691785\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1116.75 | 0.162815 | ||||||||
\(362\) | −7499.65 | + | 4329.92i | −1.08888 | + | 0.628662i | ||||
\(363\) | −1561.45 | + | 6646.12i | −0.225770 | + | 0.960966i | ||||
\(364\) | 690.630 | − | 1196.21i | 0.0994474 | − | 0.172248i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8203.14 | − | 1927.25i | −1.17154 | − | 0.275244i | ||||
\(367\) | −4552.17 | + | 2628.19i | −0.647469 | + | 0.373816i | −0.787486 | − | 0.616333i | \(-0.788618\pi\) |
0.140017 | + | 0.990149i | \(0.455284\pi\) | |||||||
\(368\) | − | 7861.57i | − | 1.11362i | ||||||
\(369\) | −89.3535 | − | 1437.32i | −0.0126058 | − | 0.202775i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1471.61 | − | 2548.91i | −0.205936 | − | 0.356692i | ||||
\(372\) | −53.8960 | − | 50.6495i | −0.00751176 | − | 0.00705928i | ||||
\(373\) | 862.955 | + | 498.227i | 0.119791 | + | 0.0691615i | 0.558698 | − | 0.829371i | \(-0.311301\pi\) |
−0.438907 | + | 0.898532i | \(0.644634\pi\) | |||||||
\(374\) | 163.503 | − | 283.195i | 0.0226057 | − | 0.0391542i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5153.78 | − | 8926.61i | −0.706878 | − | 1.22435i | ||||
\(377\) | − | 3986.90i | − | 0.544658i | ||||||
\(378\) | 852.705 | + | 2300.72i | 0.116028 | + | 0.313059i | ||||
\(379\) | 2735.20 | 0.370707 | 0.185354 | − | 0.982672i | \(-0.440657\pi\) | ||||
0.185354 | + | 0.982672i | \(0.440657\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3637.14 | − | 12063.0i | −0.489072 | − | 1.62207i | ||||
\(382\) | −2788.49 | − | 1609.93i | −0.373485 | − | 0.215632i | ||||
\(383\) | −7741.80 | − | 4469.73i | −1.03287 | − | 0.596325i | −0.115062 | − | 0.993358i | \(-0.536707\pi\) |
−0.917804 | + | 0.397033i | \(0.870040\pi\) | |||||||
\(384\) | 1787.57 | − | 1902.15i | 0.237557 | − | 0.252783i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4277.32 | −0.564015 | ||||||||
\(387\) | 3587.57 | − | 7213.62i | 0.471232 | − | 0.947517i | ||||
\(388\) | − | 330.295i | − | 0.0432170i | ||||||
\(389\) | −5566.93 | − | 9642.21i | −0.725590 | − | 1.25676i | −0.958731 | − | 0.284316i | \(-0.908233\pi\) |
0.233140 | − | 0.972443i | \(-0.425100\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3323.42 | + | 5756.33i | −0.429853 | + | 0.744527i | ||||
\(392\) | −6150.95 | − | 3551.25i | −0.792525 | − | 0.457564i | ||||
\(393\) | 309.580 | − | 1317.69i | 0.0397360 | − | 0.169132i | ||||
\(394\) | −312.433 | − | 541.150i | −0.0399496 | − | 0.0691948i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −220.903 | + | 146.530i | −0.0280323 | + | 0.0185945i | ||||
\(397\) | − | 9479.40i | − | 1.19838i | −0.800606 | − | 0.599191i | \(-0.795489\pi\) | ||
0.800606 | − | 0.599191i | \(-0.204511\pi\) | |||||||
\(398\) | −1012.54 | + | 584.593i | −0.127523 | + | 0.0736256i | ||||
\(399\) | 2342.85 | − | 2493.02i | 0.293958 | − | 0.312800i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4713.80 | + | 8164.54i | −0.587022 | + | 1.01675i | 0.407598 | + | 0.913162i | \(0.366367\pi\) |
−0.994620 | + | 0.103591i | \(0.966967\pi\) | |||||||
\(402\) | 2661.34 | − | 802.423i | 0.330188 | − | 0.0995553i | ||||
\(403\) | −410.383 | + | 236.935i | −0.0507261 | + | 0.0292868i | ||||
\(404\) | 4677.53 | 0.576029 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 882.869 | 0.107921 | ||||||||
\(407\) | 1040.39 | − | 600.670i | 0.126708 | − | 0.0731550i | ||||
\(408\) | −4077.22 | + | 1229.33i | −0.494736 | + | 0.149169i | ||||
\(409\) | 204.093 | − | 353.500i | 0.0246742 | − | 0.0427370i | −0.853425 | − | 0.521216i | \(-0.825478\pi\) |
0.878099 | + | 0.478479i | \(0.158812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1439.87 | − | 1532.17i | 0.172807 | − | 0.183884i | ||||
\(412\) | −3724.12 | + | 2150.12i | −0.445326 | + | 0.257109i | ||||
\(413\) | − | 724.266i | − | 0.0862925i | ||||||
\(414\) | −10651.9 | + | 7065.68i | −1.26452 | + | 0.838790i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4082.94 | + | 7071.86i | 0.481208 | + | 0.833477i | ||||
\(417\) | 2100.77 | − | 8941.68i | 0.246703 | − | 1.05006i | ||||
\(418\) | −759.338 | − | 438.404i | −0.0888527 | − | 0.0512992i | ||||
\(419\) | 4406.94 | − | 7633.05i | 0.513826 | − | 0.889973i | −0.486045 | − | 0.873934i | \(-0.661561\pi\) |
0.999871 | − | 0.0160393i | \(-0.00510569\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1174.68 | + | 2034.61i | 0.135987 | + | 0.235537i | 0.925974 | − | 0.377587i | \(-0.123246\pi\) |
−0.789987 | + | 0.613124i | \(0.789913\pi\) | |||||||
\(422\) | − | 2375.94i | − | 0.274074i | ||||||
\(423\) | −5036.56 | + | 10127.1i | −0.578927 | + | 1.16406i | ||||
\(424\) | 9823.40 | 1.12516 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4330.12 | + | 4607.66i | −0.492476 | + | 0.524042i | ||||
\(427\) | 4364.47 | + | 2519.83i | 0.494640 | + | 0.285581i | ||||
\(428\) | 532.551 | + | 307.468i | 0.0601444 | + | 0.0347244i | ||||
\(429\) | 490.288 | + | 1626.10i | 0.0551780 | + | 0.183005i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4481.16 | 0.500812 | 0.250406 | − | 0.968141i | \(-0.419436\pi\) | ||||
0.250406 | + | 0.968141i | \(0.419436\pi\) | |||||||
\(432\) | −5448.40 | − | 927.792i | −0.606797 | − | 0.103330i | ||||
\(433\) | − | 3422.69i | − | 0.379871i | −0.981797 | − | 0.189935i | \(-0.939172\pi\) | ||
0.981797 | − | 0.189935i | \(-0.0608279\pi\) | |||||||
\(434\) | −52.4674 | − | 90.8762i | −0.00580303 | − | 0.0100511i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 919.919 | − | 1593.35i | 0.101046 | − | 0.175017i | ||||
\(437\) | 15434.6 | + | 8911.17i | 1.68956 | + | 0.975467i | ||||
\(438\) | −8931.62 | − | 8393.61i | −0.974359 | − | 0.915667i | ||||
\(439\) | −4064.59 | − | 7040.07i | −0.441896 | − | 0.765386i | 0.555934 | − | 0.831226i | \(-0.312361\pi\) |
−0.997830 | + | 0.0658402i | \(0.979027\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 483.565 | + | 7778.52i | 0.0522152 | + | 0.839922i | ||||
\(442\) | 6240.36i | 0.671547i | ||||||||
\(443\) | −2035.83 | + | 1175.39i | −0.218342 | + | 0.126060i | −0.605182 | − | 0.796087i | \(-0.706900\pi\) |
0.386840 | + | 0.922147i | \(0.373566\pi\) | |||||||
\(444\) | −3483.33 | − | 818.376i | −0.372323 | − | 0.0874739i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −665.601 | + | 1152.86i | −0.0706662 | + | 0.122397i | ||||
\(447\) | −2282.60 | + | 9715.65i | −0.241529 | + | 1.02804i | ||||
\(448\) | −3578.12 | + | 2065.83i | −0.377345 | + | 0.217860i | ||||
\(449\) | −4760.99 | −0.500412 | −0.250206 | − | 0.968193i | \(-0.580498\pi\) | ||||
−0.250206 | + | 0.968193i | \(0.580498\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 220.740 | 0.0230471 | ||||||||
\(452\) | 442.233 | − | 255.323i | 0.0460196 | − | 0.0265695i | ||||
\(453\) | −9559.26 | − | 8983.44i | −0.991464 | − | 0.931742i | ||||
\(454\) | −4633.61 | + | 8025.65i | −0.479000 | + | 0.829653i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3296.23 | + | 10932.4i | 0.338509 | + | 1.12271i | ||||
\(457\) | 1930.44 | − | 1114.54i | 0.197598 | − | 0.114083i | −0.397937 | − | 0.917413i | \(-0.630274\pi\) |
0.595535 | + | 0.803330i | \(0.296940\pi\) | |||||||
\(458\) | − | 7109.51i | − | 0.725340i | ||||||
\(459\) | 3597.16 | + | 2982.61i | 0.365797 | + | 0.303303i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2868.31 | − | 4968.06i | −0.289784 | − | 0.501921i | 0.683974 | − | 0.729507i | \(-0.260250\pi\) |
−0.973758 | + | 0.227585i | \(0.926917\pi\) | |||||||
\(462\) | −360.088 | + | 108.571i | −0.0362615 | + | 0.0109332i | ||||
\(463\) | −3121.13 | − | 1801.99i | −0.313286 | − | 0.180876i | 0.335110 | − | 0.942179i | \(-0.391227\pi\) |
−0.648396 | + | 0.761303i | \(0.724560\pi\) | |||||||
\(464\) | −994.326 | + | 1722.22i | −0.0994836 | + | 0.172311i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4975.03 | − | 8617.00i | −0.494557 | − | 0.856598i | ||||
\(467\) | − | 3780.37i | − | 0.374593i | −0.982303 | − | 0.187296i | \(-0.940028\pi\) | ||
0.982303 | − | 0.187296i | \(-0.0599725\pi\) | |||||||
\(468\) | 2252.64 | − | 4529.44i | 0.222497 | − | 0.447380i | ||||
\(469\) | −1662.45 | −0.163677 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9827.00 | + | 2308.76i | 0.961368 | + | 0.225865i | ||||
\(472\) | 2093.47 | + | 1208.67i | 0.204152 | + | 0.117867i | ||||
\(473\) | 1069.46 | + | 617.454i | 0.103962 | + | 0.0600224i | ||||
\(474\) | 2420.48 | + | 568.670i | 0.234549 | + | 0.0551052i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 582.511 | 0.0560911 | ||||||||
\(477\) | −5958.40 | − | 8982.63i | −0.571943 | − | 0.862236i | ||||
\(478\) | 394.920i | 0.0377891i | ||||||||
\(479\) | −7230.58 | − | 12523.7i | −0.689715 | − | 1.19462i | −0.971930 | − | 0.235271i | \(-0.924402\pi\) |
0.282215 | − | 0.959351i | \(-0.408931\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11462.8 | + | 19854.1i | −1.08661 | + | 1.88206i | ||||
\(482\) | −1262.55 | − | 728.935i | −0.119311 | − | 0.0688840i | ||||
\(483\) | 7319.28 | − | 2206.85i | 0.689521 | − | 0.207898i | ||||
\(484\) | 1558.44 | + | 2699.29i | 0.146360 | + | 0.253502i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3639.71 | + | 8216.09i | 0.339714 | + | 0.766850i | ||||
\(487\) | 3581.74i | 0.333273i | 0.986018 | + | 0.166636i | \(0.0532906\pi\) | ||||
−0.986018 | + | 0.166636i | \(0.946709\pi\) | |||||||
\(488\) | −14567.0 | + | 8410.26i | −1.35126 | + | 0.780153i | ||||
\(489\) | −1576.81 | − | 5229.69i | −0.145820 | − | 0.483629i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3507.69 | − | 6075.50i | 0.322403 | − | 0.558419i | −0.658580 | − | 0.752511i | \(-0.728843\pi\) |
0.980983 | + | 0.194092i | \(0.0621760\pi\) | |||||||
\(492\) | −479.107 | − | 450.247i | −0.0439021 | − | 0.0412576i | ||||
\(493\) | 1456.11 | − | 840.687i | 0.133022 | − | 0.0768005i | ||||
\(494\) | 16732.4 | 1.52394 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 236.364 | 0.0213973 | ||||||||
\(497\) | 3274.98 | − | 1890.81i | 0.295579 | − | 0.170653i | ||||
\(498\) | 3122.77 | − | 13291.7i | 0.280993 | − | 1.19602i | ||||
\(499\) | 1259.90 | − | 2182.21i | 0.113028 | − | 0.195769i | −0.803962 | − | 0.594681i | \(-0.797279\pi\) |
0.916990 | + | 0.398911i | \(0.130612\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14246.8 | − | 3347.15i | −1.27046 | − | 0.298482i | ||||
\(502\) | −12606.5 | + | 7278.35i | −1.12083 | + | 0.647109i | ||||
\(503\) | 4989.32i | 0.442272i | 0.975243 | + | 0.221136i | \(0.0709764\pi\) | ||||
−0.975243 | + | 0.221136i | \(0.929024\pi\) | |||||||
\(504\) | 4385.44 | + | 2181.03i | 0.387586 | + | 0.192759i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −979.643 | − | 1696.79i | −0.0860681 | − | 0.149074i | ||||
\(507\) | −15299.6 | − | 14378.0i | −1.34020 | − | 1.25947i | ||||
\(508\) | −4981.57 | − | 2876.11i | −0.435081 | − | 0.251194i | ||||
\(509\) | 2359.76 | − | 4087.22i | 0.205490 | − | 0.355919i | −0.744799 | − | 0.667289i | \(-0.767454\pi\) |
0.950289 | + | 0.311370i | \(0.100788\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3665.19 | + | 6348.30i | 0.317297 | + | 0.549574i | ||||
\(512\) | − | 11827.7i | − | 1.02093i | ||||||
\(513\) | 7997.34 | − | 9645.16i | 0.688287 | − | 0.830106i | ||||
\(514\) | −12929.9 | −1.10956 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1061.79 | − | 3521.57i | −0.0905868 | − | 0.300442i | ||||
\(517\) | −1501.41 | − | 866.839i | −0.127721 | − | 0.0737399i | ||||
\(518\) | −4396.55 | − | 2538.35i | −0.372921 | − | 0.215306i | ||||
\(519\) | −5132.85 | + | 5461.85i | −0.434117 | + | 0.461943i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10711.0 | −0.900682 | −0.450341 | − | 0.892857i | \(-0.648698\pi\) | ||||
−0.450341 | + | 0.892857i | \(0.648698\pi\) | |||||||
\(522\) | 3227.16 | − | 200.622i | 0.270592 | − | 0.0168218i | ||||
\(523\) | 10566.4i | 0.883433i | 0.897155 | + | 0.441717i | \(0.145630\pi\) | ||||
−0.897155 | + | 0.441717i | \(0.854370\pi\) | |||||||
\(524\) | −308.983 | − | 535.175i | −0.0257595 | − | 0.0446168i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 929.032 | − | 1609.13i | 0.0770109 | − | 0.133387i | ||||
\(527\) | −173.068 | − | 99.9211i | −0.0143055 | − | 0.00825926i | ||||
\(528\) | 193.757 | − | 824.704i | 0.0159700 | − | 0.0679747i | ||||
\(529\) | 13829.1 | + | 23952.7i | 1.13661 | + | 1.96866i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −164.581 | − | 2647.42i | −0.0134505 | − | 0.216362i | ||||
\(532\) | − | 1561.90i | − | 0.127288i | ||||||
\(533\) | −3648.09 | + | 2106.23i | −0.296466 | + | 0.171165i | ||||
\(534\) | 3142.53 | − | 3343.96i | 0.254664 | − | 0.270988i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2774.32 | − | 4805.26i | 0.223568 | − | 0.387231i | ||||
\(537\) | 7635.99 | − | 2302.34i | 0.613626 | − | 0.185015i | ||||
\(538\) | −289.718 | + | 167.269i | −0.0232168 | + | 0.0134042i | ||||
\(539\) | −1194.60 | −0.0954642 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6595.81 | −0.524170 | −0.262085 | − | 0.965045i | \(-0.584410\pi\) | ||||
−0.262085 | + | 0.965045i | \(0.584410\pi\) | |||||||
\(542\) | 13098.9 | − | 7562.63i | 1.03809 | − | 0.599341i | ||||
\(543\) | 18160.7 | − | 5475.65i | 1.43526 | − | 0.432749i | ||||
\(544\) | −1721.87 | + | 2982.37i | −0.135707 | + | 0.235052i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4915.11 | − | 5230.15i | 0.385251 | − | 0.409945i | ||||
\(547\) | −5532.85 | + | 3194.39i | −0.432482 | + | 0.249693i | −0.700403 | − | 0.713747i | \(-0.746997\pi\) |
0.267922 | + | 0.963441i | \(0.413663\pi\) | |||||||
\(548\) | − | 959.916i | − | 0.0748277i | ||||||
\(549\) | 16526.1 | + | 8218.97i | 1.28473 | + | 0.638939i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2254.16 | − | 3904.31i | −0.174284 | − | 0.301868i | ||||
\(552\) | −5835.70 | + | 24839.0i | −0.449971 | + | 1.91525i | ||||
\(553\) | −1287.81 | − | 743.519i | −0.0990296 | − | 0.0571748i | ||||
\(554\) | 8093.24 | − | 14017.9i | 0.620666 | − | 1.07502i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2096.72 | − | 3631.62i | −0.159929 | − | 0.277006i | ||||
\(557\) | 15992.4i | 1.21655i | 0.793726 | + | 0.608276i | \(0.208138\pi\) | ||||
−0.793726 | + | 0.608276i | \(0.791862\pi\) | |||||||
\(558\) | −212.435 | − | 320.258i | −0.0161167 | − | 0.0242968i | ||||
\(559\) | −23566.2 | −1.78308 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −490.508 | + | 521.948i | −0.0369149 | + | 0.0392811i | ||||
\(562\) | −1211.50 | − | 699.459i | −0.0909323 | − | 0.0524998i | ||||
\(563\) | −5500.23 | − | 3175.56i | −0.411736 | − | 0.237716i | 0.279800 | − | 0.960058i | \(-0.409732\pi\) |
−0.691535 | + | 0.722343i | \(0.743065\pi\) | |||||||
\(564\) | 1490.64 | + | 4943.89i | 0.111290 | + | 0.369106i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14176.8 | −1.05282 | ||||||||
\(567\) | −665.644 | − | 5333.01i | −0.0493023 | − | 0.395001i | ||||
\(568\) | 12621.7i | 0.932382i | ||||||||
\(569\) | 4810.21 | + | 8331.53i | 0.354402 | + | 0.613842i | 0.987015 | − | 0.160626i | \(-0.0513512\pi\) |
−0.632614 | + | 0.774468i | \(0.718018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2532.30 | − | 4386.08i | 0.185593 | − | 0.321456i | −0.758183 | − | 0.652042i | \(-0.773913\pi\) |
0.943776 | + | 0.330585i | \(0.107246\pi\) | |||||||
\(572\) | 671.517 | + | 387.701i | 0.0490866 | + | 0.0283402i | ||||
\(573\) | 5139.38 | + | 4829.80i | 0.374696 | + | 0.352125i | ||||
\(574\) | −466.408 | − | 807.842i | −0.0339155 | − | 0.0587433i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12609.7 | + | 8364.34i | −0.912161 | + | 0.605059i | ||||
\(577\) | 11355.1i | 0.819273i | 0.912249 | + | 0.409637i | \(0.134345\pi\) | ||||
−0.912249 | + | 0.409637i | \(0.865655\pi\) | |||||||
\(578\) | 7814.41 | − | 4511.65i | 0.562347 | − | 0.324671i | ||||
\(579\) | 9120.54 | + | 2142.79i | 0.654640 | + | 0.153802i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4082.93 | + | 7071.84i | −0.291546 | + | 0.504973i | ||||
\(582\) | 392.533 | − | 1670.77i | 0.0279571 | − | 0.118996i | ||||
\(583\) | 1430.88 | − | 826.121i | 0.101649 | − | 0.0586869i | ||||
\(584\) | −24466.2 | −1.73359 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19114.6 | 1.34747 | ||||||||
\(587\) | −8687.96 | + | 5016.00i | −0.610887 | + | 0.352696i | −0.773312 | − | 0.634025i | \(-0.781402\pi\) |
0.162426 | + | 0.986721i | \(0.448068\pi\) | |||||||
\(588\) | 2592.84 | + | 2436.66i | 0.181848 | + | 0.170895i | ||||
\(589\) | −267.921 | + | 464.053i | −0.0187428 | + | 0.0324634i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 395.105 | + | 1310.41i | 0.0274999 | + | 0.0912068i | ||||
\(592\) | 9903.16 | − | 5717.59i | 0.687530 | − | 0.396945i | ||||
\(593\) | 1325.12i | 0.0917643i | 0.998947 | + | 0.0458821i | \(0.0146099\pi\) | ||||
−0.998947 | + | 0.0458821i | \(0.985390\pi\) | |||||||
\(594\) | −1291.56 | + | 478.685i | −0.0892145 | + | 0.0330651i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2278.21 | + | 3945.97i | 0.156575 | + | 0.271197i | ||||
\(597\) | 2451.91 | − | 739.279i | 0.168091 | − | 0.0506812i | ||||
\(598\) | 32380.5 | + | 18694.9i | 2.21427 | + | 1.27841i | ||||
\(599\) | 8285.78 | − | 14351.4i | 0.565188 | − | 0.978935i | −0.431844 | − | 0.901948i | \(-0.642137\pi\) |
0.997032 | − | 0.0769865i | \(-0.0245298\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8604.49 | − | 14903.4i | −0.584001 | − | 1.01152i | −0.994999 | − | 0.0998833i | \(-0.968153\pi\) |
0.410998 | − | 0.911636i | \(-0.365180\pi\) | |||||||
\(602\) | − | 5218.55i | − | 0.353310i | ||||||
\(603\) | −6076.76 | + | 377.772i | −0.410390 | + | 0.0255126i | ||||
\(604\) | −5988.96 | −0.403456 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 23660.9 | + | 5558.92i | 1.58607 | + | 0.372633i | ||||
\(607\) | −3618.24 | − | 2088.99i | −0.241944 | − | 0.139686i | 0.374126 | − | 0.927378i | \(-0.377943\pi\) |
−0.616070 | + | 0.787692i | \(0.711276\pi\) | |||||||
\(608\) | 7996.72 | + | 4616.91i | 0.533404 | + | 0.307961i | ||||
\(609\) | −1882.54 | − | 442.287i | −0.125262 | − | 0.0294292i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33084.4 | 2.19059 | ||||||||
\(612\) | 2129.26 | − | 132.369i | 0.140638 | − | 0.00874297i | ||||
\(613\) | − | 14944.2i | − | 0.984649i | −0.870412 | − | 0.492324i | \(-0.836147\pi\) | ||
0.870412 | − | 0.492324i | \(-0.163853\pi\) | |||||||
\(614\) | −5392.89 | − | 9340.75i | −0.354461 | − | 0.613945i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −375.375 | + | 650.168i | −0.0245524 | + | 0.0425260i | ||||
\(617\) | −17756.0 | − | 10251.4i | −1.15856 | − | 0.668893i | −0.207600 | − | 0.978214i | \(-0.566565\pi\) |
−0.950958 | + | 0.309320i | \(0.899898\pi\) | |||||||
\(618\) | −21393.5 | + | 6450.37i | −1.39251 | + | 0.419858i | ||||
\(619\) | 1364.26 | + | 2362.97i | 0.0885854 | + | 0.153434i | 0.906913 | − | 0.421317i | \(-0.138432\pi\) |
−0.818328 | + | 0.574751i | \(0.805099\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26252.8 | − | 9729.93i | 1.69644 | − | 0.628742i | ||||
\(622\) | − | 9970.21i | − | 0.642715i | ||||||
\(623\) | −2376.78 | + | 1372.23i | −0.152847 | + | 0.0882463i | ||||
\(624\) | 4666.91 | + | 15478.4i | 0.299400 | + | 0.992999i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8271.29 | − | 14326.3i | 0.528095 | − | 0.914687i | ||||
\(627\) | 1399.51 | + | 1315.21i | 0.0891407 | + | 0.0837712i | ||||
\(628\) | 3991.19 | − | 2304.32i | 0.253608 | − | 0.146421i | ||||
\(629\) | −9668.27 | −0.612876 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3393.08 | −0.214067 | −0.107034 | − | 0.994255i | \(-0.534135\pi\) | ||||
−0.107034 | + | 0.994255i | \(0.534135\pi\) | |||||||
\(632\) | 4298.25 | − | 2481.59i | 0.270530 | − | 0.156191i | ||||
\(633\) | −1190.27 | + | 5066.23i | −0.0747374 | + | 0.318112i | ||||
\(634\) | −8730.03 | + | 15120.9i | −0.546867 | + | 0.947202i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4790.74 | − | 1125.54i | −0.298687 | − | 0.0701739i | ||||
\(637\) | 19742.8 | − | 11398.5i | 1.22800 | − | 0.708988i | ||||
\(638\) | 495.618i | 0.0307550i | ||||||||
\(639\) | 11541.4 | − | 7655.70i | 0.714508 | − | 0.473951i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6780.88 | − | 11744.8i | −0.417830 | − | 0.723702i | 0.577891 | − | 0.816114i | \(-0.303876\pi\) |
−0.995721 | + | 0.0924116i | \(0.970542\pi\) | |||||||
\(642\) | 2328.46 | + | 2188.20i | 0.143142 | + | 0.134520i | ||||
\(643\) | 11229.7 | + | 6483.44i | 0.688731 | + | 0.397639i | 0.803137 | − | 0.595795i | \(-0.203163\pi\) |
−0.114405 | + | 0.993434i | \(0.536496\pi\) | |||||||
\(644\) | 1745.09 | − | 3022.58i | 0.106780 | − | 0.184948i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3528.24 | + | 6111.09i | 0.214886 | + | 0.372194i | ||||
\(647\) | 25837.9i | 1.57000i | 0.619495 | + | 0.785001i | \(0.287337\pi\) | ||||
−0.619495 | + | 0.785001i | \(0.712663\pi\) | |||||||
\(648\) | 16525.8 | + | 6975.79i | 1.00184 | + | 0.422894i | ||||
\(649\) | 406.583 | 0.0245913 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 66.3505 | + | 220.060i | 0.00399460 | + | 0.0132486i | ||||
\(652\) | −2159.66 | − | 1246.88i | −0.129722 | − | 0.0748950i | ||||
\(653\) | −24479.8 | − | 14133.4i | −1.46703 | − | 0.846989i | −0.467709 | − | 0.883883i | \(-0.654920\pi\) |
−0.999319 | + | 0.0368938i | \(0.988254\pi\) | |||||||
\(654\) | 6546.92 | − | 6966.56i | 0.391445 | − | 0.416535i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2101.15 | 0.125055 | ||||||||
\(657\) | 14840.0 | + | 22372.1i | 0.881223 | + | 1.32849i | ||||
\(658\) | 7326.28i | 0.434055i | ||||||||
\(659\) | −7978.92 | − | 13819.9i | −0.471646 | − | 0.816914i | 0.527828 | − | 0.849351i | \(-0.323007\pi\) |
−0.999474 | + | 0.0324369i | \(0.989673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12028.9 | + | 20834.6i | −0.707821 | + | 1.22598i | 0.257843 | + | 0.966187i | \(0.416988\pi\) |
−0.965664 | + | 0.259795i | \(0.916345\pi\) | |||||||
\(662\) | 14040.4 | + | 8106.23i | 0.824314 | + | 0.475918i | ||||
\(663\) | 3126.20 | − | 13306.3i | 0.183125 | − | 0.779450i | ||||
\(664\) | −13627.3 | − | 23603.2i | −0.796450 | − | 1.37949i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16647.6 | − | 8279.38i | −0.968588 | − | 0.481711i | ||||
\(667\) | − | 10074.1i | − | 0.584815i | ||||||
\(668\) | −5786.26 | + | 3340.70i | −0.335145 | + | 0.193496i | ||||
\(669\) | 1996.80 | − | 2124.79i | 0.115397 | − | 0.122794i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1414.56 | + | 2450.09i | −0.0813838 | + | 0.140961i | ||||
\(672\) | 3792.15 | − | 1143.37i | 0.217686 | − | 0.0656349i | ||||
\(673\) | −1085.16 | + | 626.519i | −0.0621545 | + | 0.0358849i | −0.530755 | − | 0.847525i | \(-0.678092\pi\) |
0.468601 | + | 0.883410i | \(0.344758\pi\) | |||||||
\(674\) | 16436.3 | 0.939321 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9585.35 | −0.545366 | ||||||||
\(677\) | 762.733 | − | 440.364i | 0.0433002 | − | 0.0249994i | −0.478194 | − | 0.878254i | \(-0.658708\pi\) |
0.521494 | + | 0.853255i | \(0.325375\pi\) | |||||||
\(678\) | 2540.43 | − | 765.970i | 0.143901 | − | 0.0433877i | ||||
\(679\) | −513.226 | + | 888.933i | −0.0290071 | + | 0.0502417i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13900.8 | − | 14791.8i | 0.782204 | − | 0.832341i | ||||
\(682\) | 51.0153 | − | 29.4537i | 0.00286434 | − | 0.00165373i | ||||
\(683\) | 26686.4i | 1.49506i | 0.664227 | + | 0.747531i | \(0.268761\pi\) | ||||
−0.664227 | + | 0.747531i | \(0.731239\pi\) | |||||||
\(684\) | −354.924 | − | 5709.24i | −0.0198404 | − | 0.319149i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5523.50 | + | 9566.98i | 0.307417 | + | 0.532462i | ||||
\(687\) | −3561.62 | + | 15159.6i | −0.197794 | + | 0.841886i | ||||
\(688\) | 10179.9 | + | 5877.36i | 0.564106 | + | 0.325687i | ||||
\(689\) | −15765.2 | + | 27306.1i | −0.871706 | + | 1.50984i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 85.7060 | + | 148.447i | 0.00471839 | + | 0.00817249i | 0.868375 | − | 0.495908i | \(-0.165165\pi\) |
−0.863657 | + | 0.504081i | \(0.831831\pi\) | |||||||
\(692\) | 3421.90i | 0.187978i | ||||||||
\(693\) | 822.206 | − | 51.1138i | 0.0450693 | − | 0.00280181i | ||||
\(694\) | 17888.4 | 0.978437 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4420.04 | − | 4703.35i | 0.240720 | − | 0.256150i | ||||
\(697\) | −1538.49 | − | 888.247i | −0.0836075 | − | 0.0482708i | ||||
\(698\) | −3788.76 | − | 2187.44i | −0.205454 | − | 0.118619i | ||||
\(699\) | 6291.44 | + | 20866.4i | 0.340435 | + | 1.12910i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14229.6 | −0.766684 | −0.383342 | − | 0.923607i | \(-0.625227\pi\) | ||||
−0.383342 | + | 0.923607i | \(0.625227\pi\) | |||||||
\(702\) | 16777.8 | − | 20234.7i | 0.902045 | − | 1.08791i | ||||
\(703\) | 25923.8i | 1.39080i | ||||||||
\(704\) | −1159.70 | − | 2008.66i | −0.0620850 | − | 0.107534i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8418.62 | − | 14581.5i | 0.448780 | − | 0.777310i | ||||
\(707\) | −12588.8 | − | 7268.13i | −0.669659 | − | 0.386628i | ||||
\(708\) | −882.472 | − | 829.316i | −0.0468437 | − | 0.0440220i | ||||
\(709\) | −3887.04 | − | 6732.55i | −0.205897 | − | 0.356624i | 0.744521 | − | 0.667599i | \(-0.232678\pi\) |
−0.950418 | + | 0.310975i | \(0.899344\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4876.31 | − | 2425.15i | −0.257210 | − | 0.127919i | ||||
\(712\) | − | 9160.03i | − | 0.482144i | ||||||
\(713\) | −1036.96 | + | 598.687i | −0.0544661 | + | 0.0314460i | ||||
\(714\) | 2946.59 | + | 692.274i | 0.154444 | + | 0.0362853i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1820.60 | − | 3153.37i | 0.0950264 | − | 0.164591i | ||||
\(717\) | 197.841 | − | 842.088i | 0.0103047 | − | 0.0438610i | ||||
\(718\) | −15839.1 | + | 9144.72i | −0.823274 | + | 0.475318i | ||||
\(719\) | 22091.8 | 1.14588 | 0.572939 | − | 0.819598i | \(-0.305803\pi\) | ||||
0.572939 | + | 0.819598i | \(0.305803\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13363.8 | 0.690282 | ||||||||
\(722\) | 2294.31 | − | 1324.62i | 0.118262 | − | 0.0682786i | ||||
\(723\) | 2326.97 | + | 2186.81i | 0.119697 | + | 0.112487i | ||||
\(724\) | 4329.92 | − | 7499.65i | 0.222266 | − | 0.384975i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4675.31 | + | 15506.3i | 0.239004 | + | 0.792687i | ||||
\(727\) | 5753.42 | − | 3321.74i | 0.293511 | − | 0.169459i | −0.346013 | − | 0.938230i | \(-0.612465\pi\) |
0.639524 | + | 0.768771i | \(0.279131\pi\) | |||||||
\(728\) | − | 14326.8i | − | 0.729378i | ||||||
\(729\) | −3645.00 | − | 19342.6i | −0.185185 | − | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4969.22 | − | 8606.94i | −0.251427 | − | 0.435484i | ||||
\(732\) | 8067.75 | − | 2432.52i | 0.407367 | − | 0.122826i | ||||
\(733\) | −2704.43 | − | 1561.40i | −0.136276 | − | 0.0786791i | 0.430312 | − | 0.902680i | \(-0.358404\pi\) |
−0.566588 | + | 0.824001i | \(0.691737\pi\) | |||||||
\(734\) | −6234.82 | + | 10799.0i | −0.313530 | + | 0.543050i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10316.8 | + | 17869.2i | 0.516687 | + | 0.894928i | ||||
\(737\) | − | 933.252i | − | 0.0466442i | ||||||
\(738\) | −1888.44 | − | 2846.93i | −0.0941929 | − | 0.142001i | ||||
\(739\) | −19549.5 | −0.973127 | −0.486563 | − | 0.873645i | \(-0.661750\pi\) | ||||
−0.486563 | + | 0.873645i | \(0.661750\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −35678.6 | − | 8382.37i | −1.76881 | − | 0.415566i | ||||
\(742\) | −6046.72 | − | 3491.08i | −0.299167 | − | 0.172724i | ||||
\(743\) | 8133.58 | + | 4695.92i | 0.401604 | + | 0.231866i | 0.687176 | − | 0.726491i | \(-0.258850\pi\) |
−0.285572 | + | 0.958357i | \(0.592183\pi\) | |||||||
\(744\) | −746.804 | − | 175.455i | −0.0368000 | − | 0.00864582i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2363.87 | 0.116015 | ||||||||
\(747\) | −13317.4 | + | 26777.6i | −0.652286 | + | 1.31157i | ||||
\(748\) | 327.005i | 0.0159846i | ||||||||
\(749\) | −955.512 | − | 1655.00i | −0.0466137 | − | 0.0807373i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9136.01 | − | 15824.0i | 0.443912 | − | 0.768878i | −0.554064 | − | 0.832474i | \(-0.686924\pi\) |
0.997976 | + | 0.0635962i | \(0.0202570\pi\) | |||||||
\(752\) | −14291.5 | − | 8251.18i | −0.693026 | − | 0.400119i | ||||
\(753\) | 30527.0 | − | 9204.25i | 1.47738 | − | 0.445447i | ||||
\(754\) | −4729.03 | − | 8190.92i | −0.228410 | − | 0.395618i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1888.83 | − | 1566.13i | −0.0908676 | − | 0.0753434i | ||||
\(757\) | 2016.30i | 0.0968082i | 0.998828 | + | 0.0484041i | \(0.0154135\pi\) | ||||
−0.998828 | + | 0.0484041i | \(0.984586\pi\) | |||||||
\(758\) | 5619.36 | − | 3244.34i | 0.269267 | − | 0.155461i | ||||
\(759\) | 1238.86 | + | 4108.84i | 0.0592462 | + | 0.196497i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8846.39 | − | 15322.4i | 0.421395 | − | 0.729877i | −0.574681 | − | 0.818377i | \(-0.694874\pi\) |
0.996076 | + | 0.0885001i | \(0.0282074\pi\) | |||||||
\(762\) | −21780.8 | − | 20468.8i | −1.03548 | − | 0.973107i | ||||
\(763\) | −4951.60 | + | 2858.81i | −0.234941 | + | 0.135643i | ||||
\(764\) | 3219.87 | 0.152475 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21206.9 | −1.00031 | ||||||||
\(767\) | −6719.46 | + | 3879.48i | −0.316331 | + | 0.182634i | ||||
\(768\) | −3912.00 | + | 16651.0i | −0.183805 | + | 0.782346i | ||||
\(769\) | −4879.86 | + | 8452.16i | −0.228833 | + | 0.396350i | −0.957462 | − | 0.288558i | \(-0.906824\pi\) |
0.728630 | + | 0.684908i | \(0.240157\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27570.4 | + | 6477.43i | 1.28784 | + | 0.302567i | ||||
\(772\) | 3704.27 | − | 2138.66i | 0.172694 | − | 0.0997047i | ||||
\(773\) | 10338.3i | 0.481038i | 0.970644 | + | 0.240519i | \(0.0773177\pi\) | ||||
−0.970644 | + | 0.240519i | \(0.922682\pi\) | |||||||
\(774\) | −1185.86 | − | 19075.4i | −0.0550707 | − | 0.885856i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1712.96 | − | 2966.93i | −0.0792418 | − | 0.137251i | ||||
\(777\) | 8103.14 | + | 7615.04i | 0.374130 | + | 0.351593i | ||||
\(778\) | −22874.0 | − | 13206.3i | −1.05408 | − | 0.608573i | ||||
\(779\) | −2381.68 | + | 4125.19i | −0.109541 | + | 0.189731i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1061.45 | + | 1838.48i | 0.0486320 | + | 0.0842331i | ||||
\(782\) | 15768.2i | 0.721059i | ||||||||
\(783\) | −6981.79 | − | 1188.91i | −0.318657 | − | 0.0542633i | ||||
\(784\) | −11371.1 | −0.517997 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −926.950 | − | 3074.35i | −0.0420652 | − | 0.139514i | ||||
\(787\) | −4093.95 | − | 2363.64i | −0.185430 | − | 0.107058i | 0.404411 | − | 0.914577i | \(-0.367476\pi\) |
−0.589842 | + | 0.807519i | \(0.700810\pi\) | |||||||
\(788\) | 541.150 | + | 312.433i | 0.0244640 | + | 0.0141243i | ||||
\(789\) | −2787.10 | + | 2965.74i | −0.125758 | + | 0.133819i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1586.92 | −0.0713331 | ||||||||
\(792\) | −1224.37 | + | 2461.87i | −0.0549319 | + | 0.110453i | ||||
\(793\) | − | 53989.1i | − | 2.41767i | ||||||
\(794\) | −11243.9 | − | 19475.0i | −0.502558 | − | 0.870456i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 584.593 | − | 1012.54i | 0.0260306 | − | 0.0450863i | ||||
\(797\) | −24420.9 | − | 14099.4i | −1.08536 | − | 0.626634i | −0.153025 | − | 0.988222i | \(-0.548901\pi\) |
−0.932338 | + | 0.361588i | \(0.882235\pi\) | |||||||
\(798\) | 1856.21 | − | 7900.76i | 0.0823423 | − | 0.350481i | ||||
\(799\) | 6976.24 | + | 12083.2i | 0.308888 | + | 0.535010i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8376.04 | + | 5556.04i | −0.369479 | + | 0.245085i | ||||
\(802\) | 22364.9i | 0.984704i | ||||||||
\(803\) | −3563.76 | + | 2057.54i | −0.156616 | + | 0.0904221i | ||||
\(804\) | −1903.57 | + | 2025.59i | −0.0834998 | + | 0.0888519i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −562.076 | + | 973.544i | −0.0245636 | + | 0.0425454i | ||||
\(807\) | 701.562 | − | 211.529i | 0.0306024 | − | 0.00922697i | ||||
\(808\) | 42016.7 | − | 24258.3i | 1.82938 | − | 1.05619i | ||||
\(809\) | 27310.5 | 1.18688 | 0.593439 | − | 0.804879i | \(-0.297770\pi\) | ||||
0.593439 | + | 0.804879i | \(0.297770\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18045.0 | −0.781312 | −0.390656 | − | 0.920537i | \(-0.627752\pi\) | ||||
−0.390656 | + | 0.920537i | \(0.627752\pi\) | |||||||
\(812\) | −764.587 | + | 441.435i | −0.0330440 | + | 0.0190780i | ||||
\(813\) | −31719.3 | + | 9563.74i | −1.36832 | + | 0.412565i | ||||
\(814\) | 1424.96 | − | 2468.10i | 0.0613572 | − | 0.106274i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4669.00 | + | 4968.27i | −0.200304 | + | 0.213142i | ||||
\(817\) | −23078.0 | + | 13324.1i | −0.988246 | + | 0.570564i | ||||
\(818\) | − | 968.333i | − | 0.0413899i | ||||||
\(819\) | −13100.6 | + | 8689.97i | −0.558941 | + | 0.370760i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6288.85 | + | 10892.6i | 0.267335 | + | 0.463038i | 0.968173 | − | 0.250283i | \(-0.0805235\pi\) |
−0.700837 | + | 0.713321i | \(0.747190\pi\) | |||||||
\(822\) | 1140.79 | − | 4855.66i | 0.0484060 | − | 0.206035i | ||||
\(823\) | −30283.6 | − | 17484.2i | −1.28265 | − | 0.740537i | −0.305316 | − | 0.952251i | \(-0.598762\pi\) |
−0.977332 | + | 0.211714i | \(0.932096\pi\) | |||||||
\(824\) | −22301.7 | + | 38627.7i | −0.942860 | + | 1.63308i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −859.081 | − | 1487.97i | −0.0361880 | − | 0.0626794i | ||||
\(827\) | − | 6735.01i | − | 0.283191i | −0.989925 | − | 0.141596i | \(-0.954777\pi\) | ||
0.989925 | − | 0.141596i | \(-0.0452233\pi\) | |||||||
\(828\) | 5691.99 | − | 11445.0i | 0.238901 | − | 0.480364i | ||||
\(829\) | 2867.97 | 0.120155 | 0.0600777 | − | 0.998194i | \(-0.480865\pi\) | ||||
0.0600777 | + | 0.998194i | \(0.480865\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24279.7 | + | 25836.0i | −1.01354 | + | 1.07851i | ||||
\(832\) | 38332.0 | + | 22131.0i | 1.59726 | + | 0.922179i | ||||
\(833\) | 8326.02 | + | 4807.03i | 0.346314 | + | 0.199944i | ||||
\(834\) | −6290.16 | − | 20862.1i | −0.261163 | − | 0.866181i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 876.808 | 0.0362740 | ||||||||
\(837\) | 292.538 | + | 789.310i | 0.0120807 | + | 0.0325956i | ||||
\(838\) | − | 20909.0i | − | 0.861921i | ||||||
\(839\) | 13927.9 | + | 24123.8i | 0.573116 | + | 0.992666i | 0.996244 | + | 0.0865958i | \(0.0275989\pi\) |
−0.423128 | + | 0.906070i | \(0.639068\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10920.3 | − | 18914.6i | 0.447756 | − | 0.775537i | ||||
\(842\) | 4826.67 | + | 2786.68i | 0.197551 | + | 0.114056i | ||||
\(843\) | 2232.88 | + | 2098.38i | 0.0912270 | + | 0.0857318i | ||||
\(844\) | 1187.97 | + | 2057.63i | 0.0484499 | + | 0.0839176i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1664.81 | + | 26779.8i | 0.0676566 | + | 1.08831i | ||||
\(847\) | − | 9686.23i | − | 0.392943i | ||||||
\(848\) | 13620.2 | − | 7863.60i | 0.551554 | − | 0.318440i | ||||
\(849\) | 30229.3 | + | 7102.09i | 1.22199 | + | 0.287094i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28964.2 | + | 50167.5i | −1.16672 | + | 2.02082i | ||||
\(852\) | 1446.16 | − | 6155.41i | 0.0581509 | − | 0.247513i | ||||
\(853\) | −9462.29 | + | 5463.05i | −0.379815 | + | 0.219287i | −0.677738 | − | 0.735304i | \(-0.737040\pi\) |
0.297923 | + | 0.954590i | \(0.403706\pi\) | |||||||
\(854\) | 11955.5 | 0.479049 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6378.30 | 0.254680 | ||||||||
\(857\) | 39117.7 | − | 22584.6i | 1.55920 | − | 0.900206i | 0.561869 | − | 0.827226i | \(-0.310082\pi\) |
0.997333 | − | 0.0729799i | \(-0.0232509\pi\) | |||||||
\(858\) | 2936.06 | + | 2759.20i | 0.116825 | + | 0.109788i | ||||
\(859\) | −3525.95 | + | 6107.12i | −0.140051 | + | 0.242576i | −0.927516 | − | 0.373784i | \(-0.878060\pi\) |
0.787465 | + | 0.616360i | \(0.211393\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 589.822 | + | 1956.22i | 0.0233462 | + | 0.0774306i | ||||
\(862\) | 9206.35 | − | 5315.29i | 0.363770 | − | 0.210022i | ||||
\(863\) | − | 6882.52i | − | 0.271476i | −0.990745 | − | 0.135738i | \(-0.956659\pi\) | ||
0.990745 | − | 0.135738i | \(-0.0433405\pi\) | |||||||
\(864\) | 13601.6 | − | 5041.11i | 0.535576 | − | 0.198498i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4059.80 | − | 7031.77i | −0.159304 | − | 0.275923i | ||||
\(867\) | −18922.9 | + | 5705.46i | −0.741239 | + | 0.223492i | ||||
\(868\) | 90.8762 | + | 52.4674i | 0.00355362 | + | 0.00205168i | ||||
\(869\) | 417.391 | − | 722.942i | 0.0162935 | − | 0.0282211i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8904.79 | + | 15423.5i | 0.346415 | + | 0.600008i | ||||
\(872\) | − | 19083.3i | − | 0.741104i | ||||||
\(873\) | −1674.00 | + | 3365.95i | −0.0648984 | + | 0.130493i | ||||
\(874\) | 42279.6 | 1.63630 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11931.8 | + | 2803.27i | 0.460204 | + | 0.108121i | ||||
\(877\) | −32362.2 | − | 18684.3i | −1.24606 | − | 0.719413i | −0.275738 | − | 0.961233i | \(-0.588922\pi\) |
−0.970321 | + | 0.241820i | \(0.922256\pi\) | |||||||
\(878\) | −16701.0 | − | 9642.35i | −0.641951 | − | 0.370630i | ||||
\(879\) | −40758.2 | − | 9575.76i | −1.56398 | − | 0.367443i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23880.5 | −0.913229 | −0.456614 | − | 0.889665i | \(-0.650938\pi\) | ||||
−0.456614 | + | 0.889665i | \(0.650938\pi\) | |||||||
\(882\) | 10219.9 | + | 15407.0i | 0.390160 | + | 0.588189i | ||||
\(883\) | 33107.0i | 1.26177i | 0.775878 | + | 0.630883i | \(0.217307\pi\) | ||||
−0.775878 | + | 0.630883i | \(0.782693\pi\) | |||||||
\(884\) | −3120.18 | − | 5404.31i | −0.118714 | − | 0.205618i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2788.36 | + | 4829.57i | −0.105730 | + | 0.183129i | ||||
\(887\) | −9787.95 | − | 5651.07i | −0.370515 | − | 0.213917i | 0.303168 | − | 0.952937i | \(-0.401956\pi\) |
−0.673684 | + | 0.739020i | \(0.735289\pi\) | |||||||
\(888\) | −35533.7 | + | 10713.8i | −1.34283 | + | 0.404879i | ||||
\(889\) | 8938.02 | + | 15481.1i | 0.337201 | + | 0.584049i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2993.80 | − | 373.674i | 0.112566 | − | 0.0140500i | ||||
\(892\) | − | 1331.20i | − | 0.0499686i | ||||||
\(893\) | 32399.0 | − | 18705.6i | 1.21410 | − | 0.700961i | ||||
\(894\) | 6834.62 | + | 22667.9i | 0.255687 | + | 0.848016i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1851.73 | + | 3207.30i | −0.0690425 | + | 0.119585i | ||||
\(897\) | −59679.5 | − | 56084.6i | −2.22145 | − | 2.08764i | ||||
\(898\) | −9781.25 | + | 5647.21i | −0.363479 | + | 0.209855i | ||||
\(899\) | 302.886 | 0.0112367 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13297.1 | −0.491666 | ||||||||
\(902\) | 453.500 | − | 261.828i | 0.0167405 | − | 0.00966511i | ||||
\(903\) | −2614.31 | + | 11127.5i | −0.0963443 | + | 0.410079i | ||||
\(904\) | 2648.28 | − | 4586.96i | 0.0974343 | − | 0.168761i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −30294.7 | − | 7117.47i | −1.11090 | − | 0.260996i | ||||
\(907\) | 3431.40 | − | 1981.12i | 0.125620 | − | 0.0725270i | −0.435873 | − | 0.900008i | \(-0.643560\pi\) |
0.561493 | + | 0.827481i | \(0.310227\pi\) | |||||||
\(908\) | − | 9267.22i | − | 0.338704i | ||||||
\(909\) | −47667.4 | − | 23706.6i | −1.73931 | − | 0.865015i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17023.1 | + | 29484.8i | 0.619100 | + | 1.07231i | 0.989650 | + | 0.143500i | \(0.0458356\pi\) |
−0.370551 | + | 0.928812i | \(0.620831\pi\) | |||||||
\(912\) | 13321.6 | + | 12519.1i | 0.483685 | + | 0.454550i | ||||
\(913\) | −3969.93 | − | 2292.04i | −0.143905 | − | 0.0830838i | ||||
\(914\) | 2644.01 | − | 4579.56i | 0.0956849 | − | 0.165731i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3554.76 | + | 6157.02i | 0.128223 | + | 0.222089i | ||||
\(917\) | 1920.44i | 0.0691587i | ||||||||
\(918\) | 10928.0 | + | 1860.90i | 0.392895 | + | 0.0669050i | ||||
\(919\) | 35121.5 | 1.26066 | 0.630332 | − | 0.776326i | \(-0.282919\pi\) | ||||
0.630332 | + | 0.776326i | \(0.282919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6819.87 | + | 22619.0i | 0.243998 | + | 0.809251i | ||||
\(922\) | −11785.6 | − | 6804.44i | −0.420975 | − | 0.243050i | ||||
\(923\) | −35084.4 | − | 20256.0i | −1.25116 | − | 0.722355i | ||||
\(924\) | 257.560 | − | 274.069i | 0.00917002 | − | 0.00975779i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8549.64 | −0.303411 | ||||||||
\(927\) | 48848.8 | − | 3036.76i | 1.73075 | − | 0.107595i | ||||
\(928\) | − | 5219.44i | − | 0.184630i | ||||||
\(929\) | 12228.9 | + | 21181.1i | 0.431881 | + | 0.748039i | 0.997035 | − | 0.0769459i | \(-0.0245169\pi\) |
−0.565155 | + | 0.824985i | \(0.691184\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12889.2 | − | 22324.8i | 0.453735 | − | 0.785891i | ||||
\(932\) | 8617.00 | + | 4975.03i | 0.302853 | + | 0.174852i | ||||
\(933\) | −4994.73 | + | 21259.5i | −0.175263 | + | 0.745986i | ||||
\(934\) | −4484.05 | − | 7766.61i | −0.157091 | − | 0.272089i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3255.61 | − | 52369.0i | −0.113689 | − | 1.82878i | ||||
\(937\) | 41877.5i | 1.46006i | 0.683413 | + | 0.730032i | \(0.260495\pi\) | ||||
−0.683413 | + | 0.730032i | \(0.739505\pi\) | |||||||
\(938\) | −3415.43 | + | 1971.90i | −0.118889 | + | 0.0686404i | ||||
\(939\) | −24813.9 | + | 26404.4i | −0.862375 | + | 0.917651i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4599.48 | − | 7966.54i | 0.159340 | − | 0.275985i | −0.775291 | − | 0.631604i | \(-0.782397\pi\) |
0.934631 | + | 0.355619i | \(0.115730\pi\) | |||||||
\(942\) | 22927.7 | − | 6912.95i | 0.793018 | − | 0.239104i | ||||
\(943\) | −9218.01 | + | 5322.02i | −0.318324 | + | 0.183785i | ||||
\(944\) | 3870.14 | 0.133435 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2929.55 | 0.100685 | ||||||||
\(947\) | 18155.0 | − | 10481.8i | 0.622976 | − | 0.359675i | −0.155051 | − | 0.987906i | \(-0.549554\pi\) |
0.778027 | + | 0.628231i | \(0.216221\pi\) | |||||||
\(948\) | −2380.53 | + | 717.757i | −0.0815570 | + | 0.0245904i | ||||
\(949\) | 39264.7 | − | 68008.5i | 1.34308 | − | 2.32629i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26190.1 | − | 27868.8i | 0.893030 | − | 0.950271i | ||||
\(952\) | 5232.50 | − | 3020.98i | 0.178137 | − | 0.102847i | ||||
\(953\) | 27943.7i | 0.949828i | 0.880032 | + | 0.474914i | \(0.157521\pi\) | ||||
−0.880032 | + | 0.474914i | \(0.842479\pi\) | |||||||
\(954\) | −22895.9 | − | 11386.9i | −0.777027 | − | 0.386441i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −197.460 | − | 342.010i | −0.00668024 | − | 0.0115705i | ||||
\(957\) | 248.287 | − | 1056.81i | 0.00838662 | − | 0.0356967i | ||||
\(958\) | −29709.8 | − | 17153.0i | −1.00196 | − | 0.578484i | ||||
\(959\) | −1491.55 | + | 2583.45i | −0.0502240 | + | 0.0869905i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14877.5 | + | 25768.6i | 0.499396 | + | 0.864979i | ||||
\(962\) | 54385.9i | 1.82274i | ||||||||
\(963\) | −3868.77 | − | 5832.39i | −0.129459 | − | 0.195167i | ||||
\(964\) | 1457.87 | 0.0487084 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 12419.5 | − | 13215.6i | 0.413655 | − | 0.440170i | ||||
\(967\) | −1942.95 | − | 1121.76i | −0.0646132 | − | 0.0373045i | 0.467345 | − | 0.884075i | \(-0.345210\pi\) |
−0.531959 | + | 0.846770i | \(0.678544\pi\) | |||||||
\(968\) | 27997.8 | + | 16164.5i | 0.929632 | + | 0.536723i | ||||
\(969\) | −4461.83 | − | 14798.2i | −0.147920 | − | 0.490595i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57345.0 | 1.89525 | 0.947626 | − | 0.319381i | \(-0.103475\pi\) | ||||
0.947626 | + | 0.319381i | \(0.103475\pi\) | |||||||
\(972\) | −7260.13 | − | 5295.48i | −0.239577 | − | 0.174746i | ||||
\(973\) | 13031.8i | 0.429375i | ||||||||
\(974\) | 4248.44 | + | 7358.52i | 0.139763 | + | 0.242076i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13464.8 | + | 23321.7i | −0.441595 | + | 0.764866i | ||||
\(977\) | −16273.4 | − | 9395.44i | −0.532888 | − | 0.307663i | 0.209304 | − | 0.977851i | \(-0.432880\pi\) |
−0.742192 | + | 0.670188i | \(0.766214\pi\) | |||||||
\(978\) | −9442.63 | − | 8873.84i | −0.308734 | − | 0.290137i | ||||
\(979\) | −770.334 | − | 1334.26i | −0.0251481 | − | 0.0435578i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17450.0 | + | 11575.0i | −0.567927 | + | 0.376720i | ||||
\(982\) | − | 16642.5i | − | 0.540817i | ||||||
\(983\) | 29962.4 | − | 17298.8i | 0.972181 | − | 0.561289i | 0.0722803 | − | 0.997384i | \(-0.476972\pi\) |
0.899900 | + | 0.436096i | \(0.143639\pi\) | |||||||
\(984\) | −6638.70 | − | 1559.70i | −0.215075 | − | 0.0505300i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1994.35 | − | 3454.31i | 0.0644147 | − | 0.111570i | ||||
\(987\) | 3670.21 | − | 15621.8i | 0.118363 | − | 0.503798i | ||||
\(988\) | −14490.7 | + | 8366.22i | −0.466611 | + | 0.269398i | ||||
\(989\) | −59547.1 | −1.91455 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45026.3 | −1.44330 | −0.721649 | − | 0.692259i | \(-0.756616\pi\) | ||||
−0.721649 | + | 0.692259i | \(0.756616\pi\) | |||||||
\(992\) | −537.251 | + | 310.182i | −0.0171953 | + | 0.00992771i | ||||
\(993\) | −25877.5 | − | 24318.7i | −0.826985 | − | 0.777171i | ||||
\(994\) | 4485.53 | − | 7769.17i | 0.143131 | − | 0.247911i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3941.46 | + | 13072.4i | 0.125392 | + | 0.415877i | ||||
\(997\) | −10368.1 | + | 5986.04i | −0.329350 | + | 0.190150i | −0.655552 | − | 0.755150i | \(-0.727564\pi\) |
0.326202 | + | 0.945300i | \(0.394231\pi\) | |||||||
\(998\) | − | 5977.66i | − | 0.189599i | ||||||
\(999\) | 31349.9 | + | 25994.0i | 0.992861 | + | 0.823237i |
(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.a.49.3 | 8 | ||
5.2 | odd | 4 | 225.4.e.a.76.2 | 4 | |||
5.3 | odd | 4 | 45.4.e.a.31.1 | yes | 4 | ||
5.4 | even | 2 | inner | 225.4.k.a.49.2 | 8 | ||
9.7 | even | 3 | inner | 225.4.k.a.124.2 | 8 | ||
15.8 | even | 4 | 135.4.e.a.91.2 | 4 | |||
45.7 | odd | 12 | 225.4.e.a.151.2 | 4 | |||
45.13 | odd | 12 | 405.4.a.d.1.2 | 2 | |||
45.22 | odd | 12 | 2025.4.a.l.1.1 | 2 | |||
45.23 | even | 12 | 405.4.a.e.1.1 | 2 | |||
45.32 | even | 12 | 2025.4.a.j.1.2 | 2 | |||
45.34 | even | 6 | inner | 225.4.k.a.124.3 | 8 | ||
45.38 | even | 12 | 135.4.e.a.46.2 | 4 | |||
45.43 | odd | 12 | 45.4.e.a.16.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.a.16.1 | ✓ | 4 | 45.43 | odd | 12 | ||
45.4.e.a.31.1 | yes | 4 | 5.3 | odd | 4 | ||
135.4.e.a.46.2 | 4 | 45.38 | even | 12 | |||
135.4.e.a.91.2 | 4 | 15.8 | even | 4 | |||
225.4.e.a.76.2 | 4 | 5.2 | odd | 4 | |||
225.4.e.a.151.2 | 4 | 45.7 | odd | 12 | |||
225.4.k.a.49.2 | 8 | 5.4 | even | 2 | inner | ||
225.4.k.a.49.3 | 8 | 1.1 | even | 1 | trivial | ||
225.4.k.a.124.2 | 8 | 9.7 | even | 3 | inner | ||
225.4.k.a.124.3 | 8 | 45.34 | even | 6 | inner | ||
405.4.a.d.1.2 | 2 | 45.13 | odd | 12 | |||
405.4.a.e.1.1 | 2 | 45.23 | even | 12 | |||
2025.4.a.j.1.2 | 2 | 45.32 | even | 12 | |||
2025.4.a.l.1.1 | 2 | 45.22 | odd | 12 |