Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,5,Mod(10,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.10");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.f (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17076922476\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.19 |
Dual form | 21.5.f.a.10.1 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.250000 | + | 0.433013i | −0.963525 | − | 0.267617i | \(-0.913764\pi\) |
0.713525 | + | 0.700629i | \(0.247097\pi\) | |||||||
\(3\) | 4.50000 | − | 2.59808i | 0.500000 | − | 0.288675i | ||||
\(4\) | 6.00000 | + | 10.3923i | 0.375000 | + | 0.649519i | ||||
\(5\) | 9.00000 | + | 5.19615i | 0.360000 | + | 0.207846i | 0.669081 | − | 0.743190i | \(-0.266688\pi\) |
−0.309081 | + | 0.951036i | \(0.600021\pi\) | |||||||
\(6\) | 10.3923i | 0.288675i | ||||||||
\(7\) | 38.5000 | + | 30.3109i | 0.785714 | + | 0.618590i | ||||
\(8\) | −56.0000 | −0.875000 | ||||||||
\(9\) | 13.5000 | − | 23.3827i | 0.166667 | − | 0.288675i | ||||
\(10\) | −18.0000 | + | 10.3923i | −0.180000 | + | 0.103923i | ||||
\(11\) | −97.0000 | − | 168.009i | −0.801653 | − | 1.38850i | −0.918528 | − | 0.395357i | \(-0.870621\pi\) |
0.116875 | − | 0.993147i | \(-0.462712\pi\) | |||||||
\(12\) | 54.0000 | + | 31.1769i | 0.375000 | + | 0.216506i | ||||
\(13\) | − | 164.545i | − | 0.973638i | −0.873503 | − | 0.486819i | \(-0.838157\pi\) | ||
0.873503 | − | 0.486819i | \(-0.161843\pi\) | |||||||
\(14\) | −91.0000 | + | 36.3731i | −0.464286 | + | 0.185577i | ||||
\(15\) | 54.0000 | 0.240000 | ||||||||
\(16\) | −40.0000 | + | 69.2820i | −0.156250 | + | 0.270633i | ||||
\(17\) | −210.000 | + | 121.244i | −0.726644 | + | 0.419528i | −0.817193 | − | 0.576364i | \(-0.804471\pi\) |
0.0905494 | + | 0.995892i | \(0.471138\pi\) | |||||||
\(18\) | 27.0000 | + | 46.7654i | 0.0833333 | + | 0.144338i | ||||
\(19\) | 226.500 | + | 130.770i | 0.627424 | + | 0.362243i | 0.779754 | − | 0.626086i | \(-0.215344\pi\) |
−0.152330 | + | 0.988330i | \(0.548678\pi\) | |||||||
\(20\) | 124.708i | 0.311769i | ||||||||
\(21\) | 252.000 | + | 36.3731i | 0.571429 | + | 0.0824786i | ||||
\(22\) | 388.000 | 0.801653 | ||||||||
\(23\) | 56.0000 | − | 96.9948i | 0.105860 | − | 0.183355i | −0.808229 | − | 0.588868i | \(-0.799574\pi\) |
0.914089 | + | 0.405513i | \(0.132907\pi\) | |||||||
\(24\) | −252.000 | + | 145.492i | −0.437500 | + | 0.252591i | ||||
\(25\) | −258.500 | − | 447.735i | −0.413600 | − | 0.716376i | ||||
\(26\) | 285.000 | + | 164.545i | 0.421598 | + | 0.243410i | ||||
\(27\) | − | 140.296i | − | 0.192450i | ||||||
\(28\) | −84.0000 | + | 581.969i | −0.107143 | + | 0.742307i | ||||
\(29\) | 1040.00 | 1.23662 | 0.618312 | − | 0.785933i | \(-0.287817\pi\) | ||||
0.618312 | + | 0.785933i | \(0.287817\pi\) | |||||||
\(30\) | −54.0000 | + | 93.5307i | −0.0600000 | + | 0.103923i | ||||
\(31\) | −1009.50 | + | 582.835i | −1.05047 | + | 0.606488i | −0.922780 | − | 0.385326i | \(-0.874089\pi\) |
−0.127688 | + | 0.991814i | \(0.540756\pi\) | |||||||
\(32\) | −528.000 | − | 914.523i | −0.515625 | − | 0.893089i | ||||
\(33\) | −873.000 | − | 504.027i | −0.801653 | − | 0.462835i | ||||
\(34\) | − | 484.974i | − | 0.419528i | ||||||
\(35\) | 189.000 | + | 472.850i | 0.154286 | + | 0.386000i | ||||
\(36\) | 324.000 | 0.250000 | ||||||||
\(37\) | 537.500 | − | 930.977i | 0.392622 | − | 0.680042i | −0.600172 | − | 0.799871i | \(-0.704901\pi\) |
0.992795 | + | 0.119829i | \(0.0382346\pi\) | |||||||
\(38\) | −453.000 | + | 261.540i | −0.313712 | + | 0.181122i | ||||
\(39\) | −427.500 | − | 740.452i | −0.281065 | − | 0.486819i | ||||
\(40\) | −504.000 | − | 290.985i | −0.315000 | − | 0.181865i | ||||
\(41\) | 1305.97i | 0.776898i | 0.921470 | + | 0.388449i | \(0.126989\pi\) | ||||
−0.921470 | + | 0.388449i | \(0.873011\pi\) | |||||||
\(42\) | −315.000 | + | 400.104i | −0.178571 | + | 0.226816i | ||||
\(43\) | −1087.00 | −0.587885 | −0.293943 | − | 0.955823i | \(-0.594967\pi\) | ||||
−0.293943 | + | 0.955823i | \(0.594967\pi\) | |||||||
\(44\) | 1164.00 | − | 2016.11i | 0.601240 | − | 1.04138i | ||||
\(45\) | 243.000 | − | 140.296i | 0.120000 | − | 0.0692820i | ||||
\(46\) | 112.000 | + | 193.990i | 0.0529301 | + | 0.0916775i | ||||
\(47\) | 1875.00 | + | 1082.53i | 0.848800 | + | 0.490055i | 0.860246 | − | 0.509879i | \(-0.170310\pi\) |
−0.0114455 | + | 0.999934i | \(0.503643\pi\) | |||||||
\(48\) | 415.692i | 0.180422i | ||||||||
\(49\) | 563.500 | + | 2333.94i | 0.234694 | + | 0.972069i | ||||
\(50\) | 1034.00 | 0.413600 | ||||||||
\(51\) | −630.000 | + | 1091.19i | −0.242215 | + | 0.419528i | ||||
\(52\) | 1710.00 | − | 987.269i | 0.632396 | − | 0.365114i | ||||
\(53\) | 1100.00 | + | 1905.26i | 0.391598 | + | 0.678268i | 0.992661 | − | 0.120934i | \(-0.0385889\pi\) |
−0.601062 | + | 0.799202i | \(0.705256\pi\) | |||||||
\(54\) | 243.000 | + | 140.296i | 0.0833333 | + | 0.0481125i | ||||
\(55\) | − | 2016.11i | − | 0.666482i | ||||||
\(56\) | −2156.00 | − | 1697.41i | −0.687500 | − | 0.541266i | ||||
\(57\) | 1359.00 | 0.418283 | ||||||||
\(58\) | −1040.00 | + | 1801.33i | −0.309156 | + | 0.535473i | ||||
\(59\) | −4632.00 | + | 2674.29i | −1.33065 | + | 0.768252i | −0.985400 | − | 0.170257i | \(-0.945540\pi\) |
−0.345253 | + | 0.938510i | \(0.612207\pi\) | |||||||
\(60\) | 324.000 | + | 561.184i | 0.0900000 | + | 0.155885i | ||||
\(61\) | 606.000 | + | 349.874i | 0.162859 | + | 0.0940269i | 0.579215 | − | 0.815175i | \(-0.303359\pi\) |
−0.416355 | + | 0.909202i | \(0.636693\pi\) | |||||||
\(62\) | − | 2331.34i | − | 0.606488i | ||||||
\(63\) | 1228.50 | − | 491.036i | 0.309524 | − | 0.123718i | ||||
\(64\) | 832.000 | 0.203125 | ||||||||
\(65\) | 855.000 | − | 1480.90i | 0.202367 | − | 0.350510i | ||||
\(66\) | 1746.00 | − | 1008.05i | 0.400826 | − | 0.231417i | ||||
\(67\) | −1187.50 | − | 2056.81i | −0.264536 | − | 0.458189i | 0.702906 | − | 0.711282i | \(-0.251885\pi\) |
−0.967442 | + | 0.253093i | \(0.918552\pi\) | |||||||
\(68\) | −2520.00 | − | 1454.92i | −0.544983 | − | 0.314646i | ||||
\(69\) | − | 581.969i | − | 0.122237i | ||||||
\(70\) | −1008.00 | − | 145.492i | −0.205714 | − | 0.0296923i | ||||
\(71\) | −8938.00 | −1.77306 | −0.886530 | − | 0.462670i | \(-0.846891\pi\) | ||||
−0.886530 | + | 0.462670i | \(0.846891\pi\) | |||||||
\(72\) | −756.000 | + | 1309.43i | −0.145833 | + | 0.252591i | ||||
\(73\) | 7903.50 | − | 4563.09i | 1.48311 | − | 0.856275i | 0.483295 | − | 0.875457i | \(-0.339440\pi\) |
0.999816 | + | 0.0191827i | \(0.00610642\pi\) | |||||||
\(74\) | 1075.00 | + | 1861.95i | 0.196311 | + | 0.340021i | ||||
\(75\) | −2326.50 | − | 1343.21i | −0.413600 | − | 0.238792i | ||||
\(76\) | 3138.48i | 0.543365i | ||||||||
\(77\) | 1358.00 | − | 9408.50i | 0.229044 | − | 1.58686i | ||||
\(78\) | 1710.00 | 0.281065 | ||||||||
\(79\) | −4073.50 | + | 7055.51i | −0.652700 | + | 1.13051i | 0.329765 | + | 0.944063i | \(0.393030\pi\) |
−0.982465 | + | 0.186446i | \(0.940303\pi\) | |||||||
\(80\) | −720.000 | + | 415.692i | −0.112500 | + | 0.0649519i | ||||
\(81\) | −364.500 | − | 631.333i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2262.00 | − | 1305.97i | −0.336407 | − | 0.194225i | ||||
\(83\) | 6675.32i | 0.968983i | 0.874796 | + | 0.484491i | \(0.160995\pi\) | ||||
−0.874796 | + | 0.484491i | \(0.839005\pi\) | |||||||
\(84\) | 1134.00 | + | 2837.10i | 0.160714 | + | 0.402083i | ||||
\(85\) | −2520.00 | −0.348789 | ||||||||
\(86\) | 1087.00 | − | 1882.74i | 0.146971 | − | 0.254562i | ||||
\(87\) | 4680.00 | − | 2702.00i | 0.618312 | − | 0.356982i | ||||
\(88\) | 5432.00 | + | 9408.50i | 0.701446 | + | 1.21494i | ||||
\(89\) | 11814.0 | + | 6820.82i | 1.49148 | + | 0.861105i | 0.999952 | − | 0.00975750i | \(-0.00310596\pi\) |
0.491526 | + | 0.870863i | \(0.336439\pi\) | |||||||
\(90\) | 561.184i | 0.0692820i | ||||||||
\(91\) | 4987.50 | − | 6334.98i | 0.602282 | − | 0.765001i | ||||
\(92\) | 1344.00 | 0.158790 | ||||||||
\(93\) | −3028.50 | + | 5245.52i | −0.350156 | + | 0.606488i | ||||
\(94\) | −3750.00 | + | 2165.06i | −0.424400 | + | 0.245028i | ||||
\(95\) | 1359.00 | + | 2353.86i | 0.150582 | + | 0.260815i | ||||
\(96\) | −4752.00 | − | 2743.57i | −0.515625 | − | 0.297696i | ||||
\(97\) | − | 3498.74i | − | 0.371851i | −0.982564 | − | 0.185925i | \(-0.940472\pi\) | ||
0.982564 | − | 0.185925i | \(-0.0595283\pi\) | |||||||
\(98\) | −4606.00 | − | 1357.93i | −0.479592 | − | 0.141392i | ||||
\(99\) | −5238.00 | −0.534435 | ||||||||
\(100\) | 3102.00 | − | 5372.82i | 0.310200 | − | 0.537282i | ||||
\(101\) | 6057.00 | − | 3497.01i | 0.593765 | − | 0.342811i | −0.172820 | − | 0.984953i | \(-0.555288\pi\) |
0.766585 | + | 0.642143i | \(0.221954\pi\) | |||||||
\(102\) | −1260.00 | − | 2182.38i | −0.121107 | − | 0.209764i | ||||
\(103\) | −7906.50 | − | 4564.82i | −0.745263 | − | 0.430278i | 0.0787165 | − | 0.996897i | \(-0.474918\pi\) |
−0.823980 | + | 0.566619i | \(0.808251\pi\) | |||||||
\(104\) | 9214.51i | 0.851933i | ||||||||
\(105\) | 2079.00 | + | 1636.79i | 0.188571 | + | 0.148461i | ||||
\(106\) | −4400.00 | −0.391598 | ||||||||
\(107\) | 5366.00 | − | 9294.18i | 0.468687 | − | 0.811790i | −0.530672 | − | 0.847577i | \(-0.678060\pi\) |
0.999359 | + | 0.0357871i | \(0.0113938\pi\) | |||||||
\(108\) | 1458.00 | − | 841.777i | 0.125000 | − | 0.0721688i | ||||
\(109\) | −3644.50 | − | 6312.46i | −0.306750 | − | 0.531307i | 0.670899 | − | 0.741549i | \(-0.265908\pi\) |
−0.977649 | + | 0.210241i | \(0.932575\pi\) | |||||||
\(110\) | 3492.00 | + | 2016.11i | 0.288595 | + | 0.166620i | ||||
\(111\) | − | 5585.86i | − | 0.453361i | ||||||
\(112\) | −3640.00 | + | 1454.92i | −0.290179 | + | 0.115986i | ||||
\(113\) | −4330.00 | −0.339103 | −0.169551 | − | 0.985521i | \(-0.554232\pi\) | ||||
−0.169551 | + | 0.985521i | \(0.554232\pi\) | |||||||
\(114\) | −1359.00 | + | 2353.86i | −0.104571 | + | 0.181122i | ||||
\(115\) | 1008.00 | − | 581.969i | 0.0762193 | − | 0.0440052i | ||||
\(116\) | 6240.00 | + | 10808.0i | 0.463734 | + | 0.803210i | ||||
\(117\) | −3847.50 | − | 2221.36i | −0.281065 | − | 0.162273i | ||||
\(118\) | − | 10697.1i | − | 0.768252i | ||||||
\(119\) | −11760.0 | − | 1697.41i | −0.830450 | − | 0.119865i | ||||
\(120\) | −3024.00 | −0.210000 | ||||||||
\(121\) | −11497.5 | + | 19914.3i | −0.785295 | + | 1.36017i | ||||
\(122\) | −1212.00 | + | 699.749i | −0.0814297 | + | 0.0470135i | ||||
\(123\) | 3393.00 | + | 5876.85i | 0.224271 | + | 0.388449i | ||||
\(124\) | −12114.0 | − | 6994.02i | −0.787851 | − | 0.454866i | ||||
\(125\) | − | 11868.0i | − | 0.759553i | ||||||
\(126\) | −378.000 | + | 2618.86i | −0.0238095 | + | 0.164957i | ||||
\(127\) | 18899.0 | 1.17174 | 0.585870 | − | 0.810405i | \(-0.300753\pi\) | ||||
0.585870 | + | 0.810405i | \(0.300753\pi\) | |||||||
\(128\) | 7616.00 | − | 13191.3i | 0.464844 | − | 0.805133i | ||||
\(129\) | −4891.50 | + | 2824.11i | −0.293943 | + | 0.169708i | ||||
\(130\) | 1710.00 | + | 2961.81i | 0.101183 | + | 0.175255i | ||||
\(131\) | 18963.0 | + | 10948.3i | 1.10501 | + | 0.637975i | 0.937531 | − | 0.347901i | \(-0.113106\pi\) |
0.167474 | + | 0.985876i | \(0.446439\pi\) | |||||||
\(132\) | − | 12096.6i | − | 0.694252i | ||||||
\(133\) | 4756.50 | + | 11900.1i | 0.268896 | + | 0.672738i | ||||
\(134\) | 4750.00 | 0.264536 | ||||||||
\(135\) | 729.000 | − | 1262.67i | 0.0400000 | − | 0.0692820i | ||||
\(136\) | 11760.0 | − | 6789.64i | 0.635813 | − | 0.367087i | ||||
\(137\) | −10438.0 | − | 18079.1i | −0.556130 | − | 0.963245i | −0.997815 | − | 0.0660748i | \(-0.978952\pi\) |
0.441685 | − | 0.897170i | \(-0.354381\pi\) | |||||||
\(138\) | 1008.00 | + | 581.969i | 0.0529301 | + | 0.0305592i | ||||
\(139\) | 29131.4i | 1.50776i | 0.657014 | + | 0.753878i | \(0.271819\pi\) | ||||
−0.657014 | + | 0.753878i | \(0.728181\pi\) | |||||||
\(140\) | −3780.00 | + | 4801.24i | −0.192857 | + | 0.244961i | ||||
\(141\) | 11250.0 | 0.565867 | ||||||||
\(142\) | 8938.00 | − | 15481.1i | 0.443265 | − | 0.767758i | ||||
\(143\) | −27645.0 | + | 15960.8i | −1.35190 | + | 0.780520i | ||||
\(144\) | 1080.00 | + | 1870.61i | 0.0520833 | + | 0.0902110i | ||||
\(145\) | 9360.00 | + | 5404.00i | 0.445184 | + | 0.257027i | ||||
\(146\) | 18252.4i | 0.856275i | ||||||||
\(147\) | 8599.50 | + | 9038.71i | 0.397959 | + | 0.418284i | ||||
\(148\) | 12900.0 | 0.588934 | ||||||||
\(149\) | −2206.00 | + | 3820.90i | −0.0993649 | + | 0.172105i | −0.911422 | − | 0.411473i | \(-0.865014\pi\) |
0.812057 | + | 0.583578i | \(0.198348\pi\) | |||||||
\(150\) | 4653.00 | − | 2686.41i | 0.206800 | − | 0.119396i | ||||
\(151\) | −10681.0 | − | 18500.0i | −0.468444 | − | 0.811369i | 0.530905 | − | 0.847431i | \(-0.321852\pi\) |
−0.999350 | + | 0.0360618i | \(0.988519\pi\) | |||||||
\(152\) | −12684.0 | − | 7323.11i | −0.548996 | − | 0.316963i | ||||
\(153\) | 6547.15i | 0.279685i | ||||||||
\(154\) | 14938.0 | + | 11760.6i | 0.629870 | + | 0.495894i | ||||
\(155\) | −12114.0 | −0.504225 | ||||||||
\(156\) | 5130.00 | − | 8885.42i | 0.210799 | − | 0.365114i | ||||
\(157\) | −25242.0 | + | 14573.5i | −1.02406 | + | 0.591240i | −0.915277 | − | 0.402826i | \(-0.868028\pi\) |
−0.108781 | + | 0.994066i | \(0.534695\pi\) | |||||||
\(158\) | −8147.00 | − | 14111.0i | −0.326350 | − | 0.565255i | ||||
\(159\) | 9900.00 | + | 5715.77i | 0.391598 | + | 0.226089i | ||||
\(160\) | − | 10974.3i | − | 0.428683i | ||||||
\(161\) | 5096.00 | − | 2036.89i | 0.196597 | − | 0.0785808i | ||||
\(162\) | 1458.00 | 0.0555556 | ||||||||
\(163\) | 6473.00 | − | 11211.6i | 0.243630 | − | 0.421979i | −0.718116 | − | 0.695924i | \(-0.754995\pi\) |
0.961745 | + | 0.273945i | \(0.0883285\pi\) | |||||||
\(164\) | −13572.0 | + | 7835.80i | −0.504610 | + | 0.291337i | ||||
\(165\) | −5238.00 | − | 9072.48i | −0.192397 | − | 0.333241i | ||||
\(166\) | −11562.0 | − | 6675.32i | −0.419582 | − | 0.242246i | ||||
\(167\) | − | 35233.4i | − | 1.26334i | −0.775236 | − | 0.631672i | \(-0.782369\pi\) | ||
0.775236 | − | 0.631672i | \(-0.217631\pi\) | |||||||
\(168\) | −14112.0 | − | 2036.89i | −0.500000 | − | 0.0721688i | ||||
\(169\) | 1486.00 | 0.0520290 | ||||||||
\(170\) | 2520.00 | − | 4364.77i | 0.0871972 | − | 0.151030i | ||||
\(171\) | 6115.50 | − | 3530.79i | 0.209141 | − | 0.120748i | ||||
\(172\) | −6522.00 | − | 11296.4i | −0.220457 | − | 0.381843i | ||||
\(173\) | −4992.00 | − | 2882.13i | −0.166795 | − | 0.0962990i | 0.414279 | − | 0.910150i | \(-0.364034\pi\) |
−0.581074 | + | 0.813851i | \(0.697367\pi\) | |||||||
\(174\) | 10808.0i | 0.356982i | ||||||||
\(175\) | 3619.00 | − | 25073.2i | 0.118171 | − | 0.818716i | ||||
\(176\) | 15520.0 | 0.501033 | ||||||||
\(177\) | −13896.0 | + | 24068.6i | −0.443551 | + | 0.768252i | ||||
\(178\) | −23628.0 | + | 13641.6i | −0.745739 | + | 0.430553i | ||||
\(179\) | −2605.00 | − | 4511.99i | −0.0813021 | − | 0.140819i | 0.822507 | − | 0.568754i | \(-0.192575\pi\) |
−0.903809 | + | 0.427935i | \(0.859241\pi\) | |||||||
\(180\) | 2916.00 | + | 1683.55i | 0.0900000 | + | 0.0519615i | ||||
\(181\) | − | 11426.3i | − | 0.348779i | −0.984677 | − | 0.174389i | \(-0.944205\pi\) | ||
0.984677 | − | 0.174389i | \(-0.0557951\pi\) | |||||||
\(182\) | 5985.00 | + | 14973.6i | 0.180685 | + | 0.452046i | ||||
\(183\) | 3636.00 | 0.108573 | ||||||||
\(184\) | −3136.00 | + | 5431.71i | −0.0926276 | + | 0.160436i | ||||
\(185\) | 9675.00 | − | 5585.86i | 0.282688 | − | 0.163210i | ||||
\(186\) | −6057.00 | − | 10491.0i | −0.175078 | − | 0.303244i | ||||
\(187\) | 40740.0 | + | 23521.2i | 1.16503 | + | 0.672631i | ||||
\(188\) | 25980.8i | 0.735083i | ||||||||
\(189\) | 4252.50 | − | 5401.40i | 0.119048 | − | 0.151211i | ||||
\(190\) | −5436.00 | −0.150582 | ||||||||
\(191\) | −6823.00 | + | 11817.8i | −0.187029 | + | 0.323943i | −0.944258 | − | 0.329205i | \(-0.893219\pi\) |
0.757229 | + | 0.653149i | \(0.226552\pi\) | |||||||
\(192\) | 3744.00 | − | 2161.60i | 0.101562 | − | 0.0586371i | ||||
\(193\) | −698.500 | − | 1209.84i | −0.0187522 | − | 0.0324797i | 0.856497 | − | 0.516152i | \(-0.172636\pi\) |
−0.875249 | + | 0.483672i | \(0.839303\pi\) | |||||||
\(194\) | 6060.00 | + | 3498.74i | 0.161016 | + | 0.0929627i | ||||
\(195\) | − | 8885.42i | − | 0.233673i | ||||||
\(196\) | −20874.0 | + | 19859.7i | −0.543367 | + | 0.516964i | ||||
\(197\) | 25244.0 | 0.650468 | 0.325234 | − | 0.945634i | \(-0.394557\pi\) | ||||
0.325234 | + | 0.945634i | \(0.394557\pi\) | |||||||
\(198\) | 5238.00 | − | 9072.48i | 0.133609 | − | 0.231417i | ||||
\(199\) | 20958.0 | − | 12100.1i | 0.529229 | − | 0.305551i | −0.211473 | − | 0.977384i | \(-0.567826\pi\) |
0.740702 | + | 0.671833i | \(0.234493\pi\) | |||||||
\(200\) | 14476.0 | + | 25073.2i | 0.361900 | + | 0.626829i | ||||
\(201\) | −10687.5 | − | 6170.43i | −0.264536 | − | 0.152730i | ||||
\(202\) | 13988.0i | 0.342811i | ||||||||
\(203\) | 40040.0 | + | 31523.3i | 0.971632 | + | 0.764962i | ||||
\(204\) | −15120.0 | −0.363322 | ||||||||
\(205\) | −6786.00 | + | 11753.7i | −0.161475 | + | 0.279683i | ||||
\(206\) | 15813.0 | − | 9129.64i | 0.372632 | − | 0.215139i | ||||
\(207\) | −1512.00 | − | 2618.86i | −0.0352867 | − | 0.0611184i | ||||
\(208\) | 11400.0 | + | 6581.79i | 0.263499 | + | 0.152131i | ||||
\(209\) | − | 50738.7i | − | 1.16157i | ||||||
\(210\) | −4914.00 | + | 1964.15i | −0.111429 | + | 0.0445384i | ||||
\(211\) | −13366.0 | −0.300218 | −0.150109 | − | 0.988669i | \(-0.547962\pi\) | ||||
−0.150109 | + | 0.988669i | \(0.547962\pi\) | |||||||
\(212\) | −13200.0 | + | 22863.1i | −0.293699 | + | 0.508701i | ||||
\(213\) | −40221.0 | + | 23221.6i | −0.886530 | + | 0.511839i | ||||
\(214\) | 10732.0 | + | 18588.4i | 0.234344 | + | 0.405895i | ||||
\(215\) | −9783.00 | − | 5648.22i | −0.211639 | − | 0.122190i | ||||
\(216\) | 7856.58i | 0.168394i | ||||||||
\(217\) | −56532.0 | − | 8159.69i | −1.20054 | − | 0.173282i | ||||
\(218\) | 14578.0 | 0.306750 | ||||||||
\(219\) | 23710.5 | − | 41067.8i | 0.494370 | − | 0.856275i | ||||
\(220\) | 20952.0 | − | 12096.6i | 0.432893 | − | 0.249931i | ||||
\(221\) | 19950.0 | + | 34554.4i | 0.408468 | + | 0.707488i | ||||
\(222\) | 9675.00 | + | 5585.86i | 0.196311 | + | 0.113340i | ||||
\(223\) | − | 25281.0i | − | 0.508376i | −0.967155 | − | 0.254188i | \(-0.918192\pi\) | ||
0.967155 | − | 0.254188i | \(-0.0818081\pi\) | |||||||
\(224\) | 7392.00 | − | 51213.3i | 0.147321 | − | 1.02067i | ||||
\(225\) | −13959.0 | −0.275733 | ||||||||
\(226\) | 4330.00 | − | 7499.78i | 0.0847756 | − | 0.146836i | ||||
\(227\) | 37881.0 | − | 21870.6i | 0.735139 | − | 0.424433i | −0.0851600 | − | 0.996367i | \(-0.527140\pi\) |
0.820299 | + | 0.571934i | \(0.193807\pi\) | |||||||
\(228\) | 8154.00 | + | 14123.1i | 0.156856 | + | 0.271682i | ||||
\(229\) | −32044.5 | − | 18500.9i | −0.611058 | − | 0.352795i | 0.162321 | − | 0.986738i | \(-0.448102\pi\) |
−0.773379 | + | 0.633943i | \(0.781435\pi\) | |||||||
\(230\) | 2327.88i | 0.0440052i | ||||||||
\(231\) | −18333.0 | − | 45866.4i | −0.343566 | − | 0.859550i | ||||
\(232\) | −58240.0 | −1.08205 | ||||||||
\(233\) | −8599.00 | + | 14893.9i | −0.158393 | + | 0.274345i | −0.934289 | − | 0.356516i | \(-0.883965\pi\) |
0.775896 | + | 0.630860i | \(0.217298\pi\) | |||||||
\(234\) | 7695.00 | − | 4442.71i | 0.140533 | − | 0.0811365i | ||||
\(235\) | 11250.0 | + | 19485.6i | 0.203712 | + | 0.352840i | ||||
\(236\) | −55584.0 | − | 32091.4i | −0.997989 | − | 0.576189i | ||||
\(237\) | 42333.1i | 0.753673i | ||||||||
\(238\) | 14700.0 | − | 18671.5i | 0.259516 | − | 0.329629i | ||||
\(239\) | −66970.0 | −1.17242 | −0.586212 | − | 0.810158i | \(-0.699381\pi\) | ||||
−0.586212 | + | 0.810158i | \(0.699381\pi\) | |||||||
\(240\) | −2160.00 | + | 3741.23i | −0.0375000 | + | 0.0649519i | ||||
\(241\) | 24444.0 | − | 14112.7i | 0.420861 | − | 0.242984i | −0.274585 | − | 0.961563i | \(-0.588540\pi\) |
0.695445 | + | 0.718579i | \(0.255207\pi\) | |||||||
\(242\) | −22995.0 | − | 39828.5i | −0.392647 | − | 0.680085i | ||||
\(243\) | −3280.50 | − | 1894.00i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 8396.98i | 0.141040i | ||||||||
\(245\) | −7056.00 | + | 23933.5i | −0.117551 | + | 0.398725i | ||||
\(246\) | −13572.0 | −0.224271 | ||||||||
\(247\) | 21517.5 | − | 37269.4i | 0.352694 | − | 0.610884i | ||||
\(248\) | 56532.0 | − | 32638.8i | 0.919160 | − | 0.530677i | ||||
\(249\) | 17343.0 | + | 30039.0i | 0.279721 | + | 0.484491i | ||||
\(250\) | 20556.0 | + | 11868.0i | 0.328896 | + | 0.189888i | ||||
\(251\) | 96856.3i | 1.53738i | 0.639623 | + | 0.768688i | \(0.279090\pi\) | ||||
−0.639623 | + | 0.768688i | \(0.720910\pi\) | |||||||
\(252\) | 12474.0 | + | 9820.73i | 0.196429 | + | 0.154647i | ||||
\(253\) | −21728.0 | −0.339452 | ||||||||
\(254\) | −18899.0 | + | 32734.0i | −0.292935 | + | 0.507378i | ||||
\(255\) | −11340.0 | + | 6547.15i | −0.174394 | + | 0.100687i | ||||
\(256\) | 21888.0 | + | 37911.1i | 0.333984 | + | 0.578478i | ||||
\(257\) | −64377.0 | − | 37168.1i | −0.974685 | − | 0.562735i | −0.0740240 | − | 0.997256i | \(-0.523584\pi\) |
−0.900661 | + | 0.434522i | \(0.856917\pi\) | |||||||
\(258\) | − | 11296.4i | − | 0.169708i | ||||||
\(259\) | 48912.5 | − | 19550.5i | 0.729156 | − | 0.291447i | ||||
\(260\) | 20520.0 | 0.303550 | ||||||||
\(261\) | 14040.0 | − | 24318.0i | 0.206104 | − | 0.356982i | ||||
\(262\) | −37926.0 | + | 21896.6i | −0.552503 | + | 0.318988i | ||||
\(263\) | 20396.0 | + | 35326.9i | 0.294872 | + | 0.510733i | 0.974955 | − | 0.222402i | \(-0.0713897\pi\) |
−0.680083 | + | 0.733135i | \(0.738056\pi\) | |||||||
\(264\) | 48888.0 | + | 28225.5i | 0.701446 | + | 0.404980i | ||||
\(265\) | 22863.1i | 0.325569i | ||||||||
\(266\) | −25368.0 | − | 3661.56i | −0.358528 | − | 0.0517490i | ||||
\(267\) | 70884.0 | 0.994319 | ||||||||
\(268\) | 14250.0 | − | 24681.7i | 0.198402 | − | 0.343642i | ||||
\(269\) | 62061.0 | − | 35830.9i | 0.857658 | − | 0.495169i | −0.00556923 | − | 0.999984i | \(-0.501773\pi\) |
0.863227 | + | 0.504815i | \(0.168439\pi\) | |||||||
\(270\) | 1458.00 | + | 2525.33i | 0.0200000 | + | 0.0346410i | ||||
\(271\) | −3306.00 | − | 1908.72i | −0.0450157 | − | 0.0259898i | 0.477323 | − | 0.878728i | \(-0.341607\pi\) |
−0.522339 | + | 0.852738i | \(0.674940\pi\) | |||||||
\(272\) | − | 19399.0i | − | 0.262205i | ||||||
\(273\) | 5985.00 | − | 41465.3i | 0.0803043 | − | 0.556365i | ||||
\(274\) | 41752.0 | 0.556130 | ||||||||
\(275\) | −50149.0 | + | 86860.6i | −0.663127 | + | 1.14857i | ||||
\(276\) | 6048.00 | − | 3491.81i | 0.0793951 | − | 0.0458388i | ||||
\(277\) | 50694.5 | + | 87805.4i | 0.660695 | + | 1.14436i | 0.980433 | + | 0.196852i | \(0.0630718\pi\) |
−0.319738 | + | 0.947506i | \(0.603595\pi\) | |||||||
\(278\) | −50457.0 | − | 29131.4i | −0.652878 | − | 0.376939i | ||||
\(279\) | 31473.1i | 0.404325i | ||||||||
\(280\) | −10584.0 | − | 26479.6i | −0.135000 | − | 0.337750i | ||||
\(281\) | 31916.0 | 0.404200 | 0.202100 | − | 0.979365i | \(-0.435223\pi\) | ||||
0.202100 | + | 0.979365i | \(0.435223\pi\) | |||||||
\(282\) | −11250.0 | + | 19485.6i | −0.141467 | + | 0.245028i | ||||
\(283\) | 16099.5 | − | 9295.05i | 0.201020 | − | 0.116059i | −0.396111 | − | 0.918203i | \(-0.629640\pi\) |
0.597131 | + | 0.802144i | \(0.296307\pi\) | |||||||
\(284\) | −53628.0 | − | 92886.4i | −0.664898 | − | 1.15164i | ||||
\(285\) | 12231.0 | + | 7061.57i | 0.150582 | + | 0.0869384i | ||||
\(286\) | − | 63843.4i | − | 0.780520i | ||||||
\(287\) | −39585.0 | + | 50279.7i | −0.480581 | + | 0.610420i | ||||
\(288\) | −28512.0 | −0.343750 | ||||||||
\(289\) | −12360.5 | + | 21409.0i | −0.147993 | + | 0.256331i | ||||
\(290\) | −18720.0 | + | 10808.0i | −0.222592 | + | 0.128514i | ||||
\(291\) | −9090.00 | − | 15744.3i | −0.107344 | − | 0.185925i | ||||
\(292\) | 94842.0 | + | 54757.1i | 1.11233 | + | 0.642206i | ||||
\(293\) | − | 95934.8i | − | 1.11748i | −0.829342 | − | 0.558742i | \(-0.811284\pi\) | ||
0.829342 | − | 0.558742i | \(-0.188716\pi\) | |||||||
\(294\) | −24255.0 | + | 5856.06i | −0.280612 | + | 0.0677503i | ||||
\(295\) | −55584.0 | −0.638713 | ||||||||
\(296\) | −30100.0 | + | 52134.7i | −0.343545 | + | 0.595037i | ||||
\(297\) | −23571.0 | + | 13608.7i | −0.267218 | + | 0.154278i | ||||
\(298\) | −4412.00 | − | 7641.81i | −0.0496824 | − | 0.0860525i | ||||
\(299\) | −15960.0 | − | 9214.51i | −0.178521 | − | 0.103069i | ||||
\(300\) | − | 32236.9i | − | 0.358188i | ||||||
\(301\) | −41849.5 | − | 32947.9i | −0.461910 | − | 0.363660i | ||||
\(302\) | 42724.0 | 0.468444 | ||||||||
\(303\) | 18171.0 | − | 31473.1i | 0.197922 | − | 0.342811i | ||||
\(304\) | −18120.0 | + | 10461.6i | −0.196070 | + | 0.113201i | ||||
\(305\) | 3636.00 | + | 6297.74i | 0.0390863 | + | 0.0676994i | ||||
\(306\) | −11340.0 | − | 6547.15i | −0.121107 | − | 0.0699213i | ||||
\(307\) | 148241.i | 1.57287i | 0.617676 | + | 0.786433i | \(0.288074\pi\) | ||||
−0.617676 | + | 0.786433i | \(0.711926\pi\) | |||||||
\(308\) | 105924. | − | 42338.2i | 1.11659 | − | 0.446305i | ||||
\(309\) | −47439.0 | −0.496842 | ||||||||
\(310\) | 12114.0 | − | 20982.1i | 0.126056 | − | 0.218336i | ||||
\(311\) | 28785.0 | − | 16619.0i | 0.297609 | − | 0.171824i | −0.343760 | − | 0.939058i | \(-0.611700\pi\) |
0.641368 | + | 0.767233i | \(0.278367\pi\) | |||||||
\(312\) | 23940.0 | + | 41465.3i | 0.245932 | + | 0.425967i | ||||
\(313\) | −23284.5 | − | 13443.3i | −0.237672 | − | 0.137220i | 0.376434 | − | 0.926443i | \(-0.377150\pi\) |
−0.614106 | + | 0.789223i | \(0.710483\pi\) | |||||||
\(314\) | − | 58293.9i | − | 0.591240i | ||||||
\(315\) | 13608.0 | + | 1964.15i | 0.137143 | + | 0.0197949i | ||||
\(316\) | −97764.0 | −0.979050 | ||||||||
\(317\) | 5294.00 | − | 9169.48i | 0.0526824 | − | 0.0912486i | −0.838482 | − | 0.544930i | \(-0.816556\pi\) |
0.891164 | + | 0.453681i | \(0.149890\pi\) | |||||||
\(318\) | −19800.0 | + | 11431.5i | −0.195799 | + | 0.113045i | ||||
\(319\) | −100880. | − | 174729.i | −0.991342 | − | 1.71706i | ||||
\(320\) | 7488.00 | + | 4323.20i | 0.0731250 | + | 0.0422187i | ||||
\(321\) | − | 55765.1i | − | 0.541193i | ||||||
\(322\) | −1568.00 | + | 10863.4i | −0.0151229 | + | 0.104774i | ||||
\(323\) | −63420.0 | −0.607885 | ||||||||
\(324\) | 4374.00 | − | 7575.99i | 0.0416667 | − | 0.0721688i | ||||
\(325\) | −73672.5 | + | 42534.8i | −0.697491 | + | 0.402697i | ||||
\(326\) | 12946.0 | + | 22423.1i | 0.121815 | + | 0.210990i | ||||
\(327\) | −32800.5 | − | 18937.4i | −0.306750 | − | 0.177102i | ||||
\(328\) | − | 73134.1i | − | 0.679786i | ||||||
\(329\) | 39375.0 | + | 98510.4i | 0.363772 | + | 0.910102i | ||||
\(330\) | 20952.0 | 0.192397 | ||||||||
\(331\) | 63663.5 | − | 110268.i | 0.581078 | − | 1.00646i | −0.414274 | − | 0.910152i | \(-0.635964\pi\) |
0.995352 | − | 0.0963045i | \(-0.0307023\pi\) | |||||||
\(332\) | −69372.0 | + | 40051.9i | −0.629373 | + | 0.363369i | ||||
\(333\) | −14512.5 | − | 25136.4i | −0.130874 | − | 0.226681i | ||||
\(334\) | 61026.0 | + | 35233.4i | 0.547044 | + | 0.315836i | ||||
\(335\) | − | 24681.7i | − | 0.219931i | ||||||
\(336\) | −12600.0 | + | 16004.1i | −0.111607 | + | 0.141760i | ||||
\(337\) | 211553. | 1.86277 | 0.931385 | − | 0.364035i | \(-0.118601\pi\) | ||||
0.931385 | + | 0.364035i | \(0.118601\pi\) | |||||||
\(338\) | −1486.00 | + | 2573.83i | −0.0130072 | + | 0.0225292i | ||||
\(339\) | −19485.0 | + | 11249.7i | −0.169551 | + | 0.0978905i | ||||
\(340\) | −15120.0 | − | 26188.6i | −0.130796 | − | 0.226545i | ||||
\(341\) | 195843. | + | 113070.i | 1.68422 | + | 0.972386i | ||||
\(342\) | 14123.1i | 0.120748i | ||||||||
\(343\) | −49049.0 | + | 106937.i | −0.416910 | + | 0.908948i | ||||
\(344\) | 60872.0 | 0.514400 | ||||||||
\(345\) | 3024.00 | − | 5237.72i | 0.0254064 | − | 0.0440052i | ||||
\(346\) | 9984.00 | − | 5764.27i | 0.0833974 | − | 0.0481495i | ||||
\(347\) | 12542.0 | + | 21723.4i | 0.104162 | + | 0.180413i | 0.913395 | − | 0.407074i | \(-0.133451\pi\) |
−0.809234 | + | 0.587487i | \(0.800117\pi\) | |||||||
\(348\) | 56160.0 | + | 32424.0i | 0.463734 | + | 0.267737i | ||||
\(349\) | − | 3831.30i | − | 0.0314554i | −0.999876 | − | 0.0157277i | \(-0.994994\pi\) | ||
0.999876 | − | 0.0157277i | \(-0.00500649\pi\) | |||||||
\(350\) | 39809.0 | + | 31341.5i | 0.324971 | + | 0.255849i | ||||
\(351\) | −23085.0 | −0.187377 | ||||||||
\(352\) | −102432. | + | 177417.i | −0.826705 | + | 1.43189i | ||||
\(353\) | 6327.00 | − | 3652.90i | 0.0507748 | − | 0.0293149i | −0.474398 | − | 0.880311i | \(-0.657334\pi\) |
0.525173 | + | 0.850996i | \(0.324001\pi\) | |||||||
\(354\) | −27792.0 | − | 48137.2i | −0.221775 | − | 0.384126i | ||||
\(355\) | −80442.0 | − | 46443.2i | −0.638302 | − | 0.368524i | ||||
\(356\) | 163700.i | 1.29166i | ||||||||
\(357\) | −57330.0 | + | 22915.0i | −0.449827 | + | 0.179798i | ||||
\(358\) | 10420.0 | 0.0813021 | ||||||||
\(359\) | 117254. | − | 203090.i | 0.909785 | − | 1.57579i | 0.0954228 | − | 0.995437i | \(-0.469580\pi\) |
0.814362 | − | 0.580357i | \(-0.197087\pi\) | |||||||
\(360\) | −13608.0 | + | 7856.58i | −0.105000 | + | 0.0606218i | ||||
\(361\) | −30959.0 | − | 53622.6i | −0.237560 | − | 0.411465i | ||||
\(362\) | 19791.0 | + | 11426.3i | 0.151026 | + | 0.0871947i | ||||
\(363\) | 119486.i | 0.906780i | ||||||||
\(364\) | 95760.0 | + | 13821.8i | 0.722739 | + | 0.104318i | ||||
\(365\) | 94842.0 | 0.711893 | ||||||||
\(366\) | −3636.00 | + | 6297.74i | −0.0271432 | + | 0.0470135i | ||||
\(367\) | −88303.5 | + | 50982.0i | −0.655610 | + | 0.378517i | −0.790602 | − | 0.612330i | \(-0.790232\pi\) |
0.134992 | + | 0.990847i | \(0.456899\pi\) | |||||||
\(368\) | 4480.00 | + | 7759.59i | 0.0330813 | + | 0.0572985i | ||||
\(369\) | 30537.0 | + | 17630.5i | 0.224271 | + | 0.129483i | ||||
\(370\) | 22343.5i | 0.163210i | ||||||||
\(371\) | −15400.0 | + | 106694.i | −0.111885 | + | 0.775164i | ||||
\(372\) | −72684.0 | −0.525234 | ||||||||
\(373\) | 48918.5 | − | 84729.3i | 0.351605 | − | 0.608998i | −0.634926 | − | 0.772573i | \(-0.718969\pi\) |
0.986531 | + | 0.163575i | \(0.0523026\pi\) | |||||||
\(374\) | −81480.0 | + | 47042.5i | −0.582516 | + | 0.336316i | ||||
\(375\) | −30834.0 | − | 53406.1i | −0.219264 | − | 0.379776i | ||||
\(376\) | −105000. | − | 60621.8i | −0.742700 | − | 0.428798i | ||||
\(377\) | − | 171127.i | − | 1.20402i | ||||||
\(378\) | 5103.00 | + | 12766.9i | 0.0357143 | + | 0.0893518i | ||||
\(379\) | 74105.0 | 0.515904 | 0.257952 | − | 0.966158i | \(-0.416952\pi\) | ||||
0.257952 | + | 0.966158i | \(0.416952\pi\) | |||||||
\(380\) | −16308.0 | + | 28246.3i | −0.112936 | + | 0.195611i | ||||
\(381\) | 85045.5 | − | 49101.0i | 0.585870 | − | 0.338252i | ||||
\(382\) | −13646.0 | − | 23635.6i | −0.0935144 | − | 0.161972i | ||||
\(383\) | −223974. | − | 129311.i | −1.52686 | − | 0.881535i | −0.999491 | − | 0.0319002i | \(-0.989844\pi\) |
−0.527372 | − | 0.849635i | \(-0.676823\pi\) | |||||||
\(384\) | − | 79147.8i | − | 0.536755i | ||||||
\(385\) | 61110.0 | − | 77620.1i | 0.412279 | − | 0.523664i | ||||
\(386\) | 2794.00 | 0.0187522 | ||||||||
\(387\) | −14674.5 | + | 25417.0i | −0.0979809 | + | 0.169708i | ||||
\(388\) | 36360.0 | − | 20992.5i | 0.241524 | − | 0.139444i | ||||
\(389\) | −42655.0 | − | 73880.6i | −0.281884 | − | 0.488238i | 0.689965 | − | 0.723843i | \(-0.257626\pi\) |
−0.971849 | + | 0.235605i | \(0.924293\pi\) | |||||||
\(390\) | 15390.0 | + | 8885.42i | 0.101183 | + | 0.0584183i | ||||
\(391\) | 27158.6i | 0.177645i | ||||||||
\(392\) | −31556.0 | − | 130701.i | −0.205357 | − | 0.850561i | ||||
\(393\) | 113778. | 0.736670 | ||||||||
\(394\) | −25244.0 | + | 43723.9i | −0.162617 | + | 0.281661i | ||||
\(395\) | −73323.0 | + | 42333.1i | −0.469944 | + | 0.271322i | ||||
\(396\) | −31428.0 | − | 54434.9i | −0.200413 | − | 0.347126i | ||||
\(397\) | −60775.5 | − | 35088.8i | −0.385609 | − | 0.222632i | 0.294647 | − | 0.955606i | \(-0.404798\pi\) |
−0.680256 | + | 0.732975i | \(0.738131\pi\) | |||||||
\(398\) | 48400.4i | 0.305551i | ||||||||
\(399\) | 52321.5 | + | 41192.5i | 0.328651 | + | 0.258745i | ||||
\(400\) | 41360.0 | 0.258500 | ||||||||
\(401\) | 29852.0 | − | 51705.2i | 0.185646 | − | 0.321548i | −0.758148 | − | 0.652082i | \(-0.773896\pi\) |
0.943794 | + | 0.330535i | \(0.107229\pi\) | |||||||
\(402\) | 21375.0 | − | 12340.9i | 0.132268 | − | 0.0763648i | ||||
\(403\) | 95902.5 | + | 166108.i | 0.590500 | + | 1.02278i | ||||
\(404\) | 72684.0 | + | 41964.1i | 0.445324 | + | 0.257108i | ||||
\(405\) | − | 7575.99i | − | 0.0461880i | ||||||
\(406\) | −94640.0 | + | 37828.0i | −0.574146 | + | 0.229489i | ||||
\(407\) | −208550. | −1.25899 | ||||||||
\(408\) | 35280.0 | − | 61106.8i | 0.211938 | − | 0.367087i | ||||
\(409\) | −30511.5 | + | 17615.8i | −0.182397 | + | 0.105307i | −0.588418 | − | 0.808557i | \(-0.700249\pi\) |
0.406022 | + | 0.913864i | \(0.366916\pi\) | |||||||
\(410\) | −13572.0 | − | 23507.4i | −0.0807377 | − | 0.139842i | ||||
\(411\) | −93942.0 | − | 54237.4i | −0.556130 | − | 0.321082i | ||||
\(412\) | − | 109556.i | − | 0.645417i | ||||||
\(413\) | −259392. | − | 37440.0i | −1.52075 | − | 0.219501i | ||||
\(414\) | 6048.00 | 0.0352867 | ||||||||
\(415\) | −34686.0 | + | 60077.9i | −0.201399 | + | 0.348834i | ||||
\(416\) | −150480. | + | 86879.7i | −0.869545 | + | 0.502032i | ||||
\(417\) | 75685.5 | + | 131091.i | 0.435252 | + | 0.753878i | ||||
\(418\) | 87882.0 | + | 50738.7i | 0.502976 | + | 0.290393i | ||||
\(419\) | − | 9689.09i | − | 0.0551893i | −0.999619 | − | 0.0275947i | \(-0.991215\pi\) | ||
0.999619 | − | 0.0275947i | \(-0.00878477\pi\) | |||||||
\(420\) | −4536.00 | + | 31426.3i | −0.0257143 | + | 0.178154i | ||||
\(421\) | 258923. | 1.46085 | 0.730426 | − | 0.682991i | \(-0.239321\pi\) | ||||
0.730426 | + | 0.682991i | \(0.239321\pi\) | |||||||
\(422\) | 13366.0 | − | 23150.6i | 0.0750545 | − | 0.129998i | ||||
\(423\) | 50625.0 | − | 29228.4i | 0.282933 | − | 0.163352i | ||||
\(424\) | −61600.0 | − | 106694.i | −0.342649 | − | 0.593485i | ||||
\(425\) | 108570. | + | 62682.9i | 0.601080 | + | 0.347033i | ||||
\(426\) | − | 92886.4i | − | 0.511839i | ||||||
\(427\) | 12726.0 | + | 31838.6i | 0.0697969 | + | 0.174621i | ||||
\(428\) | 128784. | 0.703031 | ||||||||
\(429\) | −82935.0 | + | 143648.i | −0.450633 | + | 0.780520i | ||||
\(430\) | 19566.0 | − | 11296.4i | 0.105819 | − | 0.0610948i | ||||
\(431\) | 47525.0 | + | 82315.7i | 0.255839 | + | 0.443127i | 0.965123 | − | 0.261796i | \(-0.0843148\pi\) |
−0.709284 | + | 0.704923i | \(0.750981\pi\) | |||||||
\(432\) | 9720.00 | + | 5611.84i | 0.0520833 | + | 0.0300703i | ||||
\(433\) | 144489.i | 0.770655i | 0.922780 | + | 0.385328i | \(0.125912\pi\) | ||||
−0.922780 | + | 0.385328i | \(0.874088\pi\) | |||||||
\(434\) | 70665.0 | − | 89756.6i | 0.375167 | − | 0.476526i | ||||
\(435\) | 56160.0 | 0.296790 | ||||||||
\(436\) | 43734.0 | − | 75749.5i | 0.230063 | − | 0.398480i | ||||
\(437\) | 25368.0 | − | 14646.2i | 0.132838 | − | 0.0766942i | ||||
\(438\) | 47421.0 | + | 82135.6i | 0.247185 | + | 0.428137i | ||||
\(439\) | 16842.0 | + | 9723.73i | 0.0873906 | + | 0.0504550i | 0.543058 | − | 0.839695i | \(-0.317266\pi\) |
−0.455668 | + | 0.890150i | \(0.650600\pi\) | |||||||
\(440\) | 112902.i | 0.583171i | ||||||||
\(441\) | 62181.0 | + | 18332.0i | 0.319728 | + | 0.0942613i | ||||
\(442\) | −79800.0 | −0.408468 | ||||||||
\(443\) | 59438.0 | − | 102950.i | 0.302870 | − | 0.524587i | −0.673915 | − | 0.738809i | \(-0.735388\pi\) |
0.976785 | + | 0.214222i | \(0.0687218\pi\) | |||||||
\(444\) | 58050.0 | − | 33515.2i | 0.294467 | − | 0.170010i | ||||
\(445\) | 70884.0 | + | 122775.i | 0.357955 | + | 0.619996i | ||||
\(446\) | 43788.0 | + | 25281.0i | 0.220133 | + | 0.127094i | ||||
\(447\) | 22925.4i | 0.114737i | ||||||||
\(448\) | 32032.0 | + | 25218.7i | 0.159598 | + | 0.125651i | ||||
\(449\) | −323110. | −1.60272 | −0.801360 | − | 0.598182i | \(-0.795890\pi\) | ||||
−0.801360 | + | 0.598182i | \(0.795890\pi\) | |||||||
\(450\) | 13959.0 | − | 24177.7i | 0.0689333 | − | 0.119396i | ||||
\(451\) | 219414. | − | 126679.i | 1.07873 | − | 0.622803i | ||||
\(452\) | −25980.0 | − | 44998.7i | −0.127163 | − | 0.220254i | ||||
\(453\) | −96129.0 | − | 55500.1i | −0.468444 | − | 0.270456i | ||||
\(454\) | 87482.4i | 0.424433i | ||||||||
\(455\) | 77805.0 | − | 31099.0i | 0.375824 | − | 0.150218i | ||||
\(456\) | −76104.0 | −0.365997 | ||||||||
\(457\) | −66578.5 | + | 115317.i | −0.318788 | + | 0.552157i | −0.980235 | − | 0.197835i | \(-0.936609\pi\) |
0.661448 | + | 0.749991i | \(0.269942\pi\) | |||||||
\(458\) | 64089.0 | − | 37001.8i | 0.305529 | − | 0.176397i | ||||
\(459\) | 17010.0 | + | 29462.2i | 0.0807382 | + | 0.139843i | ||||
\(460\) | 12096.0 | + | 6983.63i | 0.0571645 | + | 0.0330039i | ||||
\(461\) | 42248.2i | 0.198795i | 0.995048 | + | 0.0993977i | \(0.0316916\pi\) | ||||
−0.995048 | + | 0.0993977i | \(0.968308\pi\) | |||||||
\(462\) | 97776.0 | + | 14112.7i | 0.458087 | + | 0.0661192i | ||||
\(463\) | −412345. | −1.92353 | −0.961765 | − | 0.273878i | \(-0.911694\pi\) | ||||
−0.961765 | + | 0.273878i | \(0.911694\pi\) | |||||||
\(464\) | −41600.0 | + | 72053.3i | −0.193222 | + | 0.334671i | ||||
\(465\) | −54513.0 | + | 31473.1i | −0.252112 | + | 0.145557i | ||||
\(466\) | −17198.0 | − | 29787.8i | −0.0791965 | − | 0.137172i | ||||
\(467\) | 224799. | + | 129788.i | 1.03077 | + | 0.595114i | 0.917204 | − | 0.398417i | \(-0.130440\pi\) |
0.113563 | + | 0.993531i | \(0.463774\pi\) | |||||||
\(468\) | − | 53312.5i | − | 0.243410i | ||||||
\(469\) | 16625.0 | − | 115181.i | 0.0755816 | − | 0.523645i | ||||
\(470\) | −45000.0 | −0.203712 | ||||||||
\(471\) | −75726.0 | + | 131161.i | −0.341353 | + | 0.591240i | ||||
\(472\) | 259392. | − | 149760.i | 1.16432 | − | 0.672221i | ||||
\(473\) | 105439. | + | 182626.i | 0.471280 | + | 0.816281i | ||||
\(474\) | −73323.0 | − | 42333.1i | −0.326350 | − | 0.188418i | ||||
\(475\) | − | 135216.i | − | 0.599295i | ||||||
\(476\) | −52920.0 | − | 132398.i | −0.233564 | − | 0.584342i | ||||
\(477\) | 59400.0 | 0.261066 | ||||||||
\(478\) | 66970.0 | − | 115995.i | 0.293106 | − | 0.507674i | ||||
\(479\) | 193788. | − | 111884.i | 0.844609 | − | 0.487635i | −0.0142190 | − | 0.999899i | \(-0.504526\pi\) |
0.858828 | + | 0.512264i | \(0.171193\pi\) | |||||||
\(480\) | −28512.0 | − | 49384.2i | −0.123750 | − | 0.214341i | ||||
\(481\) | −153188. | − | 88442.8i | −0.662115 | − | 0.382272i | ||||
\(482\) | 56451.0i | 0.242984i | ||||||||
\(483\) | 17640.0 | − | 22405.8i | 0.0756144 | − | 0.0960431i | ||||
\(484\) | −275940. | −1.17794 | ||||||||
\(485\) | 18180.0 | − | 31488.7i | 0.0772877 | − | 0.133866i | ||||
\(486\) | 6561.00 | − | 3788.00i | 0.0277778 | − | 0.0160375i | ||||
\(487\) | −41168.5 | − | 71305.9i | −0.173583 | − | 0.300655i | 0.766087 | − | 0.642737i | \(-0.222201\pi\) |
−0.939670 | + | 0.342082i | \(0.888868\pi\) | |||||||
\(488\) | −33936.0 | − | 19593.0i | −0.142502 | − | 0.0822736i | ||||
\(489\) | − | 67269.4i | − | 0.281319i | ||||||
\(490\) | −34398.0 | − | 36154.8i | −0.143265 | − | 0.150582i | ||||
\(491\) | 812.000 | 0.00336816 | 0.00168408 | − | 0.999999i | \(-0.499464\pi\) | ||||
0.00168408 | + | 0.999999i | \(0.499464\pi\) | |||||||
\(492\) | −40716.0 | + | 70522.2i | −0.168203 | + | 0.291337i | ||||
\(493\) | −218400. | + | 126093.i | −0.898584 | + | 0.518798i | ||||
\(494\) | 43035.0 | + | 74538.8i | 0.176347 | + | 0.305442i | ||||
\(495\) | −47142.0 | − | 27217.4i | −0.192397 | − | 0.111080i | ||||
\(496\) | − | 93253.6i | − | 0.379055i | ||||||
\(497\) | −344113. | − | 270919.i | −1.39312 | − | 1.09680i | ||||
\(498\) | −69372.0 | −0.279721 | ||||||||
\(499\) | −204824. | + | 354766.i | −0.822585 | + | 1.42476i | 0.0811660 | + | 0.996701i | \(0.474136\pi\) |
−0.903751 | + | 0.428059i | \(0.859198\pi\) | |||||||
\(500\) | 123336. | − | 71208.1i | 0.493344 | − | 0.284832i | ||||
\(501\) | −91539.0 | − | 158550.i | −0.364696 | − | 0.631672i | ||||
\(502\) | −167760. | − | 96856.3i | −0.665704 | − | 0.384344i | ||||
\(503\) | 151530.i | 0.598912i | 0.954110 | + | 0.299456i | \(0.0968052\pi\) | ||||
−0.954110 | + | 0.299456i | \(0.903195\pi\) | |||||||
\(504\) | −68796.0 | + | 27498.0i | −0.270833 | + | 0.108253i | ||||
\(505\) | 72684.0 | 0.285007 | ||||||||
\(506\) | 21728.0 | − | 37634.0i | 0.0848631 | − | 0.146987i | ||||
\(507\) | 6687.00 | − | 3860.74i | 0.0260145 | − | 0.0150195i | ||||
\(508\) | 113394. | + | 196404.i | 0.439403 | + | 0.761068i | ||||
\(509\) | 262197. | + | 151380.i | 1.01203 | + | 0.584294i | 0.911785 | − | 0.410669i | \(-0.134705\pi\) |
0.100243 | + | 0.994963i | \(0.468038\pi\) | |||||||
\(510\) | − | 26188.6i | − | 0.100687i | ||||||
\(511\) | 442596. | + | 63883.2i | 1.69498 | + | 0.244650i | ||||
\(512\) | 156160. | 0.595703 | ||||||||
\(513\) | 18346.5 | − | 31777.1i | 0.0697138 | − | 0.120748i | ||||
\(514\) | 128754. | − | 74336.2i | 0.487343 | − | 0.281367i | ||||
\(515\) | −47439.0 | − | 82166.8i | −0.178863 | − | 0.309800i | ||||
\(516\) | −58698.0 | − | 33889.3i | −0.220457 | − | 0.127281i | ||||
\(517\) | − | 420022.i | − | 1.57142i | ||||||
\(518\) | −15050.0 | + | 104269.i | −0.0560889 | + | 0.388595i | ||||
\(519\) | −29952.0 | −0.111196 | ||||||||
\(520\) | −47880.0 | + | 82930.6i | −0.177071 | + | 0.306696i | ||||
\(521\) | −263244. | + | 151984.i | −0.969802 | + | 0.559915i | −0.899176 | − | 0.437587i | \(-0.855833\pi\) |
−0.0706261 | + | 0.997503i | \(0.522500\pi\) | |||||||
\(522\) | 28080.0 | + | 48636.0i | 0.103052 | + | 0.178491i | ||||
\(523\) | −113876. | − | 65746.1i | −0.416320 | − | 0.240362i | 0.277182 | − | 0.960817i | \(-0.410600\pi\) |
−0.693501 | + | 0.720455i | \(0.743933\pi\) | |||||||
\(524\) | 262759.i | 0.956963i | ||||||||
\(525\) | −48856.5 | − | 122232.i | −0.177257 | − | 0.443471i | ||||
\(526\) | −81584.0 | −0.294872 | ||||||||
\(527\) | 141330. | − | 244791.i | 0.508877 | − | 0.881401i | ||||
\(528\) | 69840.0 | − | 40322.1i | 0.250517 | − | 0.144636i | ||||
\(529\) | 133648. | + | 231486.i | 0.477587 | + | 0.827205i | ||||
\(530\) | −39600.0 | − | 22863.1i | −0.140975 | − | 0.0813922i | ||||
\(531\) | 144411.i | 0.512168i | ||||||||
\(532\) | −95130.0 | + | 120831.i | −0.336120 | + | 0.426930i | ||||
\(533\) | 214890. | 0.756418 | ||||||||
\(534\) | −70884.0 | + | 122775.i | −0.248580 | + | 0.430553i | ||||
\(535\) | 96588.0 | − | 55765.1i | 0.337455 | − | 0.194830i | ||||
\(536\) | 66500.0 | + | 115181.i | 0.231469 | + | 0.400915i | ||||
\(537\) | −23445.0 | − | 13536.0i | −0.0813021 | − | 0.0469398i | ||||
\(538\) | 143324.i | 0.495169i | ||||||||
\(539\) | 337463. | − | 321065.i | 1.16158 | − | 1.10514i | ||||
\(540\) | 17496.0 | 0.0600000 | ||||||||
\(541\) | −17651.5 | + | 30573.3i | −0.0603097 | + | 0.104459i | −0.894604 | − | 0.446860i | \(-0.852542\pi\) |
0.834294 | + | 0.551320i | \(0.185875\pi\) | |||||||
\(542\) | 6612.00 | − | 3817.44i | 0.0225079 | − | 0.0129949i | ||||
\(543\) | −29686.5 | − | 51418.5i | −0.100684 | − | 0.174389i | ||||
\(544\) | 221760. | + | 128033.i | 0.749351 | + | 0.432638i | ||||
\(545\) | − | 75749.5i | − | 0.255027i | ||||||
\(546\) | 65835.0 | + | 51831.6i | 0.220837 | + | 0.173864i | ||||
\(547\) | 153398. | 0.512678 | 0.256339 | − | 0.966587i | \(-0.417484\pi\) | ||||
0.256339 | + | 0.966587i | \(0.417484\pi\) | |||||||
\(548\) | 125256. | − | 216950.i | 0.417097 | − | 0.722434i | ||||
\(549\) | 16362.0 | − | 9446.61i | 0.0542865 | − | 0.0313423i | ||||
\(550\) | −100298. | − | 173721.i | −0.331564 | − | 0.574285i | ||||
\(551\) | 235560. | + | 136001.i | 0.775887 | + | 0.447958i | ||||
\(552\) | 32590.3i | 0.106957i | ||||||||
\(553\) | −370688. | + | 148166.i | −1.21216 | + | 0.484504i | ||||
\(554\) | −202778. | −0.660695 | ||||||||
\(555\) | 29025.0 | − | 50272.8i | 0.0942294 | − | 0.163210i | ||||
\(556\) | −302742. | + | 174788.i | −0.979317 | + | 0.565409i | ||||
\(557\) | 48035.0 | + | 83199.1i | 0.154827 | + | 0.268169i | 0.932996 | − | 0.359886i | \(-0.117185\pi\) |
−0.778169 | + | 0.628055i | \(0.783851\pi\) | |||||||
\(558\) | −54513.0 | − | 31473.1i | −0.175078 | − | 0.101081i | ||||
\(559\) | 178860.i | 0.572388i | ||||||||
\(560\) | −40320.0 | − | 5819.69i | −0.128571 | − | 0.0185577i | ||||
\(561\) | 244440. | 0.776688 | ||||||||
\(562\) | −31916.0 | + | 55280.1i | −0.101050 | + | 0.175024i | ||||
\(563\) | −70215.0 | + | 40538.6i | −0.221520 | + | 0.127895i | −0.606654 | − | 0.794966i | \(-0.707489\pi\) |
0.385134 | + | 0.922861i | \(0.374155\pi\) | |||||||
\(564\) | 67500.0 | + | 116913.i | 0.212200 | + | 0.367541i | ||||
\(565\) | −38970.0 | − | 22499.3i | −0.122077 | − | 0.0704811i | ||||
\(566\) | 37180.2i | 0.116059i | ||||||||
\(567\) | 5103.00 | − | 35354.6i | 0.0158730 | − | 0.109971i | ||||
\(568\) | 500528. | 1.55143 | ||||||||
\(569\) | −268885. | + | 465722.i | −0.830505 | + | 1.43848i | 0.0671340 | + | 0.997744i | \(0.478614\pi\) |
−0.897639 | + | 0.440732i | \(0.854719\pi\) | |||||||
\(570\) | −24462.0 | + | 14123.1i | −0.0752909 | + | 0.0434692i | ||||
\(571\) | −90185.5 | − | 156206.i | −0.276608 | − | 0.479099i | 0.693932 | − | 0.720041i | \(-0.255877\pi\) |
−0.970540 | + | 0.240942i | \(0.922544\pi\) | |||||||
\(572\) | −331740. | − | 191530.i | −1.01392 | − | 0.585390i | ||||
\(573\) | 70906.7i | 0.215962i | ||||||||
\(574\) | −47502.0 | − | 118843.i | −0.144174 | − | 0.360703i | ||||
\(575\) | −57904.0 | −0.175135 | ||||||||
\(576\) | 11232.0 | − | 19454.4i | 0.0338542 | − | 0.0586371i | ||||
\(577\) | 479837. | − | 277034.i | 1.44126 | − | 0.832111i | 0.443324 | − | 0.896361i | \(-0.353799\pi\) |
0.997934 | + | 0.0642509i | \(0.0204658\pi\) | |||||||
\(578\) | −24721.0 | − | 42818.0i | −0.0739964 | − | 0.128165i | ||||
\(579\) | −6286.50 | − | 3629.51i | −0.0187522 | − | 0.0108266i | ||||
\(580\) | 129696.i | 0.385541i | ||||||||
\(581\) | −202335. | + | 257000.i | −0.599403 | + | 0.761344i | ||||
\(582\) | 36360.0 | 0.107344 | ||||||||
\(583\) | 213400. | − | 369620.i | 0.627852 | − | 1.08747i | ||||
\(584\) | −442596. | + | 255533.i | −1.29772 | + | 0.749240i | ||||
\(585\) | −23085.0 | − | 39984.4i | −0.0674556 | − | 0.116837i | ||||
\(586\) | 166164. | + | 95934.8i | 0.483884 | + | 0.279371i | ||||
\(587\) | − | 306954.i | − | 0.890835i | −0.895323 | − | 0.445417i | \(-0.853055\pi\) | ||
0.895323 | − | 0.445417i | \(-0.146945\pi\) | |||||||
\(588\) | −42336.0 | + | 143601.i | −0.122449 | + | 0.415339i | ||||
\(589\) | −304869. | −0.878785 | ||||||||
\(590\) | 55584.0 | − | 96274.3i | 0.159678 | − | 0.276571i | ||||
\(591\) | 113598. | − | 65585.8i | 0.325234 | − | 0.187774i | ||||
\(592\) | 43000.0 | + | 74478.2i | 0.122694 | + | 0.212513i | ||||
\(593\) | −277509. | − | 160220.i | −0.789165 | − | 0.455624i | 0.0505037 | − | 0.998724i | \(-0.483917\pi\) |
−0.839668 | + | 0.543099i | \(0.817251\pi\) | |||||||
\(594\) | − | 54434.9i | − | 0.154278i | ||||||
\(595\) | −97020.0 | − | 76383.4i | −0.274048 | − | 0.215757i | ||||
\(596\) | −52944.0 | −0.149047 | ||||||||
\(597\) | 62874.0 | − | 108901.i | 0.176410 | − | 0.305551i | ||||
\(598\) | 31920.0 | − | 18429.0i | 0.0892607 | − | 0.0515347i | ||||
\(599\) | −161986. | − | 280568.i | −0.451465 | − | 0.781960i | 0.547013 | − | 0.837124i | \(-0.315765\pi\) |
−0.998477 | + | 0.0551645i | \(0.982432\pi\) | |||||||
\(600\) | 130284. | + | 75219.5i | 0.361900 | + | 0.208943i | ||||
\(601\) | − | 376993.i | − | 1.04372i | −0.853031 | − | 0.521860i | \(-0.825238\pi\) | ||
0.853031 | − | 0.521860i | \(-0.174762\pi\) | |||||||
\(602\) | 98917.0 | − | 39537.5i | 0.272947 | − | 0.109098i | ||||
\(603\) | −64125.0 | −0.176357 | ||||||||
\(604\) | 128172. | − | 222000.i | 0.351333 | − | 0.608527i | ||||
\(605\) | −206955. | + | 119486.i | −0.565412 | + | 0.326441i | ||||
\(606\) | 36342.0 | + | 62946.2i | 0.0989609 | + | 0.171405i | ||||
\(607\) | 91309.5 | + | 52717.6i | 0.247821 | + | 0.143080i | 0.618766 | − | 0.785575i | \(-0.287633\pi\) |
−0.370945 | + | 0.928655i | \(0.620966\pi\) | |||||||
\(608\) | − | 276186.i | − | 0.747127i | ||||||
\(609\) | 262080. | + | 37828.0i | 0.706642 | + | 0.101995i | ||||
\(610\) | −14544.0 | −0.0390863 | ||||||||
\(611\) | 178125. | − | 308522.i | 0.477136 | − | 0.826424i | ||||
\(612\) | −68040.0 | + | 39282.9i | −0.181661 | + | 0.104882i | ||||
\(613\) | −254635. | − | 441041.i | −0.677637 | − | 1.17370i | −0.975691 | − | 0.219153i | \(-0.929671\pi\) |
0.298054 | − | 0.954549i | \(-0.403663\pi\) | |||||||
\(614\) | −256761. | − | 148241.i | −0.681071 | − | 0.393216i | ||||
\(615\) | 70522.2i | 0.186456i | ||||||||
\(616\) | −76048.0 | + | 526876.i | −0.200413 | + | 1.38850i | ||||
\(617\) | −141154. | −0.370786 | −0.185393 | − | 0.982664i | \(-0.559356\pi\) | ||||
−0.185393 | + | 0.982664i | \(0.559356\pi\) | |||||||
\(618\) | 47439.0 | − | 82166.8i | 0.124211 | − | 0.215139i | ||||
\(619\) | −441005. | + | 254614.i | −1.15096 | + | 0.664509i | −0.949122 | − | 0.314909i | \(-0.898026\pi\) |
−0.201842 | + | 0.979418i | \(0.564693\pi\) | |||||||
\(620\) | −72684.0 | − | 125892.i | −0.189084 | − | 0.327504i | ||||
\(621\) | −13608.0 | − | 7856.58i | −0.0352867 | − | 0.0203728i | ||||
\(622\) | 66476.1i | 0.171824i | ||||||||
\(623\) | 248094. | + | 620694.i | 0.639205 | + | 1.59920i | ||||
\(624\) | 68400.0 | 0.175666 | ||||||||
\(625\) | −99894.5 | + | 173022.i | −0.255730 | + | 0.442937i | ||||
\(626\) | 46569.0 | − | 26886.6i | 0.118836 | − | 0.0686100i | ||||
\(627\) | −131823. | − | 228324.i | −0.335317 | − | 0.580787i | ||||
\(628\) | −302904. | − | 174882.i | −0.768043 | − | 0.443430i | ||||
\(629\) | 260674.i | 0.658864i | ||||||||
\(630\) | −17010.0 | + | 21605.6i | −0.0428571 | + | 0.0544359i | ||||
\(631\) | 135542. | 0.340420 | 0.170210 | − | 0.985408i | \(-0.445555\pi\) | ||||
0.170210 | + | 0.985408i | \(0.445555\pi\) | |||||||
\(632\) | 228116. | − | 395109.i | 0.571112 | − | 0.989196i | ||||
\(633\) | −60147.0 | + | 34725.9i | −0.150109 | + | 0.0866654i | ||||
\(634\) | 10588.0 | + | 18339.0i | 0.0263412 | + | 0.0456243i | ||||
\(635\) | 170091. | + | 98202.1i | 0.421827 | + | 0.243542i | ||||
\(636\) | 137178.i | 0.339134i | ||||||||
\(637\) | 384038. | − | 92721.0i | 0.946444 | − | 0.228507i | ||||
\(638\) | 403520. | 0.991342 | ||||||||
\(639\) | −120663. | + | 208994.i | −0.295510 | + | 0.511839i | ||||
\(640\) | 137088. | − | 79147.8i | 0.334688 | − | 0.193232i | ||||
\(641\) | −29554.0 | − | 51189.0i | −0.0719284 | − | 0.124584i | 0.827818 | − | 0.560997i | \(-0.189582\pi\) |
−0.899746 | + | 0.436413i | \(0.856249\pi\) | |||||||
\(642\) | 96588.0 | + | 55765.1i | 0.234344 | + | 0.135298i | ||||
\(643\) | 520594.i | 1.25915i | 0.776940 | + | 0.629574i | \(0.216771\pi\) | ||||
−0.776940 | + | 0.629574i | \(0.783229\pi\) | |||||||
\(644\) | 51744.0 | + | 40737.8i | 0.124764 | + | 0.0982259i | ||||
\(645\) | −58698.0 | −0.141092 | ||||||||
\(646\) | 63420.0 | − | 109847.i | 0.151971 | − | 0.263222i | ||||
\(647\) | 51207.0 | − | 29564.4i | 0.122327 | − | 0.0706253i | −0.437588 | − | 0.899176i | \(-0.644167\pi\) |
0.559915 | + | 0.828550i | \(0.310834\pi\) | |||||||
\(648\) | 20412.0 | + | 35354.6i | 0.0486111 | + | 0.0841969i | ||||
\(649\) | 898608. | + | 518812.i | 2.13344 | + | 1.23174i | ||||
\(650\) | − | 170139.i | − | 0.402697i | ||||||
\(651\) | −275594. | + | 110156.i | −0.650290 | + | 0.259923i | ||||
\(652\) | 155352. | 0.365445 | ||||||||
\(653\) | −337591. | + | 584725.i | −0.791707 | + | 1.37128i | 0.133202 | + | 0.991089i | \(0.457474\pi\) |
−0.924909 | + | 0.380188i | \(0.875859\pi\) | |||||||
\(654\) | 65601.0 | − | 37874.8i | 0.153375 | − | 0.0885512i | ||||
\(655\) | 113778. | + | 197069.i | 0.265201 | + | 0.459342i | ||||
\(656\) | −90480.0 | − | 52238.7i | −0.210254 | − | 0.121390i | ||||
\(657\) | − | 246407.i | − | 0.570850i | ||||||
\(658\) | −210000. | − | 30310.9i | −0.485029 | − | 0.0700079i | ||||
\(659\) | 74684.0 | 0.171972 | 0.0859858 | − | 0.996296i | \(-0.472596\pi\) | ||||
0.0859858 | + | 0.996296i | \(0.472596\pi\) | |||||||
\(660\) | 62856.0 | − | 108870.i | 0.144298 | − | 0.249931i | ||||
\(661\) | −692030. | + | 399543.i | −1.58388 | + | 0.914452i | −0.589592 | + | 0.807701i | \(0.700711\pi\) |
−0.994286 | + | 0.106751i | \(0.965955\pi\) | |||||||
\(662\) | 127327. | + | 220537.i | 0.290539 | + | 0.503228i | ||||
\(663\) | 179550. | + | 103663.i | 0.408468 | + | 0.235829i | ||||
\(664\) | − | 373818.i | − | 0.847860i | ||||||
\(665\) | −19026.0 | + | 131816.i | −0.0430233 | + | 0.298074i | ||||
\(666\) | 58050.0 | 0.130874 | ||||||||
\(667\) | 58240.0 | − | 100875.i | 0.130909 | − | 0.226741i | ||||
\(668\) | 366156. | − | 211400.i | 0.820565 | − | 0.473754i | ||||
\(669\) | −65682.0 | − | 113765.i | −0.146755 | − | 0.254188i | ||||
\(670\) | 42750.0 | + | 24681.7i | 0.0952328 | + | 0.0549827i | ||||
\(671\) | − | 135751.i | − | 0.301508i | ||||||
\(672\) | −99792.0 | − | 249665.i | −0.220982 | − | 0.552864i | ||||
\(673\) | 155765. | 0.343906 | 0.171953 | − | 0.985105i | \(-0.444992\pi\) | ||||
0.171953 | + | 0.985105i | \(0.444992\pi\) | |||||||
\(674\) | −211553. | + | 366421.i | −0.465693 | + | 0.806603i | ||||
\(675\) | −62815.5 | + | 36266.5i | −0.137867 | + | 0.0795974i | ||||
\(676\) | 8916.00 | + | 15443.0i | 0.0195109 | + | 0.0337938i | ||||
\(677\) | 324858. | + | 187557.i | 0.708788 | + | 0.409219i | 0.810612 | − | 0.585584i | \(-0.199135\pi\) |
−0.101824 | + | 0.994802i | \(0.532468\pi\) | |||||||
\(678\) | − | 44998.7i | − | 0.0978905i | ||||||
\(679\) | 106050. | − | 134702.i | 0.230023 | − | 0.292168i | ||||
\(680\) | 141120. | 0.305190 | ||||||||
\(681\) | 113643. | − | 196835.i | 0.245046 | − | 0.424433i | ||||
\(682\) | −391686. | + | 226140.i | −0.842111 | + | 0.486193i | ||||
\(683\) | −101788. | − | 176302.i | −0.218200 | − | 0.377934i | 0.736058 | − | 0.676919i | \(-0.236685\pi\) |
−0.954258 | + | 0.298985i | \(0.903352\pi\) | |||||||
\(684\) | 73386.0 | + | 42369.4i | 0.156856 | + | 0.0905608i | ||||
\(685\) | − | 216950.i | − | 0.462358i | ||||||
\(686\) | −136171. | − | 191892.i | −0.289359 | − | 0.407764i | ||||
\(687\) | −192267. | −0.407372 | ||||||||
\(688\) | 43480.0 | − | 75309.6i | 0.0918571 | − | 0.159101i | ||||
\(689\) | 313500. | − | 180999.i | 0.660388 | − | 0.381275i | ||||
\(690\) | 6048.00 | + | 10475.4i | 0.0127032 | + | 0.0220026i | ||||
\(691\) | −504128. | − | 291058.i | −1.05581 | − | 0.609570i | −0.131537 | − | 0.991311i | \(-0.541991\pi\) |
−0.924269 | + | 0.381741i | \(0.875325\pi\) | |||||||
\(692\) | − | 69171.2i | − | 0.144448i | ||||||
\(693\) | −201663. | − | 158768.i | −0.419913 | − | 0.330596i | ||||
\(694\) | −50168.0 | −0.104162 | ||||||||
\(695\) | −151371. | + | 262182.i | −0.313381 | + | 0.542792i | ||||
\(696\) | −262080. | + | 151312.i | −0.541023 | + | 0.312360i | ||||
\(697\) | −158340. | − | 274253.i | −0.325931 | − | 0.564528i | ||||
\(698\) | 6636.00 | + | 3831.30i | 0.0136206 | + | 0.00786384i | ||||
\(699\) | 89363.4i | 0.182897i | ||||||||
\(700\) | 282282. | − | 112829.i | 0.576086 | − | 0.230264i | ||||
\(701\) | 372680. | 0.758403 | 0.379202 | − | 0.925314i | \(-0.376199\pi\) | ||||
0.379202 | + | 0.925314i | \(0.376199\pi\) | |||||||
\(702\) | 23085.0 | − | 39984.4i | 0.0468442 | − | 0.0811365i | ||||
\(703\) | 243488. | − | 140578.i | 0.492681 | − | 0.284450i | ||||
\(704\) | −80704.0 | − | 139783.i | −0.162836 | − | 0.282040i | ||||
\(705\) | 101250. | + | 58456.7i | 0.203712 | + | 0.117613i | ||||
\(706\) | 14611.6i | 0.0293149i | ||||||||
\(707\) | 339192. | + | 48958.1i | 0.678589 | + | 0.0979459i | ||||
\(708\) | −333504. | −0.665326 | ||||||||
\(709\) | −56197.0 | + | 97336.1i | −0.111795 | + | 0.193634i | −0.916494 | − | 0.400049i | \(-0.868993\pi\) |
0.804699 | + | 0.593683i | \(0.202327\pi\) | |||||||
\(710\) | 160884. | − | 92886.4i | 0.319151 | − | 0.184262i | ||||
\(711\) | 109984. | + | 190499.i | 0.217567 | + | 0.376836i | ||||
\(712\) | −661584. | − | 381966.i | −1.30504 | − | 0.753467i | ||||
\(713\) | 130555.i | 0.256812i | ||||||||
\(714\) | 17640.0 | − | 122214.i | 0.0346021 | − | 0.239730i | ||||
\(715\) | −331740. | −0.648912 | ||||||||
\(716\) | 31260.0 | − | 54143.9i | 0.0609766 | − | 0.105615i | ||||
\(717\) | −301365. | + | 173993.i | −0.586212 | + | 0.338449i | ||||
\(718\) | 234508. | + | 406180.i | 0.454892 | + | 0.787897i | ||||
\(719\) | 91977.0 | + | 53102.9i | 0.177919 | + | 0.102721i | 0.586314 | − | 0.810084i | \(-0.300578\pi\) |
−0.408396 | + | 0.912805i | \(0.633912\pi\) | |||||||
\(720\) | 22447.4i | 0.0433013i | ||||||||
\(721\) | −166036. | − | 415399.i | −0.319399 | − | 0.799088i | ||||
\(722\) | 123836. | 0.237560 | ||||||||
\(723\) | 73332.0 | − | 127015.i | 0.140287 | − | 0.242984i | ||||
\(724\) | 118746. | − | 68558.0i | 0.226538 | − | 0.130792i | ||||
\(725\) | −268840. | − | 465645.i | −0.511467 | − | 0.885887i | ||||
\(726\) | −206955. | − | 119486.i | −0.392647 | − | 0.226695i | ||||
\(727\) | 662165.i | 1.25284i | 0.779484 | + | 0.626422i | \(0.215481\pi\) | ||||
−0.779484 | + | 0.626422i | \(0.784519\pi\) | |||||||
\(728\) | −279300. | + | 354759.i | −0.526997 | + | 0.669376i | ||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | −94842.0 | + | 164271.i | −0.177973 | + | 0.308259i | ||||
\(731\) | 228270. | − | 131792.i | 0.427183 | − | 0.246634i | ||||
\(732\) | 21816.0 | + | 37786.4i | 0.0407149 | + | 0.0705202i | ||||
\(733\) | 20290.5 | + | 11714.7i | 0.0377646 | + | 0.0218034i | 0.518763 | − | 0.854918i | \(-0.326393\pi\) |
−0.480999 | + | 0.876721i | \(0.659726\pi\) | |||||||
\(734\) | − | 203928.i | − | 0.378517i | ||||||
\(735\) | 30429.0 | + | 126033.i | 0.0563265 | + | 0.233297i | ||||
\(736\) | −118272. | −0.218336 | ||||||||
\(737\) | −230375. | + | 399021.i | −0.424131 | + | 0.734617i | ||||
\(738\) | −61074.0 | + | 35261.1i | −0.112136 | + | 0.0647415i | ||||
\(739\) | −440706. | − | 763324.i | −0.806974 | − | 1.39772i | −0.914950 | − | 0.403567i | \(-0.867770\pi\) |
0.107976 | − | 0.994153i | \(-0.465563\pi\) | |||||||
\(740\) | 116100. | + | 67030.4i | 0.212016 | + | 0.122408i | ||||
\(741\) | − | 223616.i | − | 0.407256i | ||||||
\(742\) | −169400. | − | 133368.i | −0.307684 | − | 0.242239i | ||||
\(743\) | −224686. | −0.407004 | −0.203502 | − | 0.979075i | \(-0.565232\pi\) | ||||
−0.203502 | + | 0.979075i | \(0.565232\pi\) | |||||||
\(744\) | 169596. | − | 293749.i | 0.306387 | − | 0.530677i | ||||
\(745\) | −39708.0 | + | 22925.4i | −0.0715427 | + | 0.0413052i | ||||
\(746\) | 97837.0 | + | 169459.i | 0.175803 | + | 0.304499i | ||||
\(747\) | 156087. | + | 90116.9i | 0.279721 | + | 0.161497i | ||||
\(748\) | 564510.i | 1.00895i | ||||||||
\(749\) | 488306. | − | 195178.i | 0.870419 | − | 0.347910i | ||||
\(750\) | 123336. | 0.219264 | ||||||||
\(751\) | 114430. | − | 198198.i | 0.202889 | − | 0.351414i | −0.746569 | − | 0.665308i | \(-0.768300\pi\) |
0.949458 | + | 0.313894i | \(0.101634\pi\) | |||||||
\(752\) | −150000. | + | 86602.5i | −0.265250 | + | 0.153142i | ||||
\(753\) | 251640. | + | 435853.i | 0.443802 | + | 0.768688i | ||||
\(754\) | 296400. | + | 171127.i | 0.521357 | + | 0.301006i | ||||
\(755\) | − | 222000.i | − | 0.389457i | ||||||
\(756\) | 81648.0 | + | 11784.9i | 0.142857 | + | 0.0206197i | ||||
\(757\) | 95150.0 | 0.166042 | 0.0830208 | − | 0.996548i | \(-0.473543\pi\) | ||||
0.0830208 | + | 0.996548i | \(0.473543\pi\) | |||||||
\(758\) | −74105.0 | + | 128354.i | −0.128976 | + | 0.223393i | ||||
\(759\) | −97776.0 | + | 56451.0i | −0.169726 | + | 0.0979914i | ||||
\(760\) | −76104.0 | − | 131816.i | −0.131759 | − | 0.228213i | ||||
\(761\) | −929034. | − | 536378.i | −1.60421 | − | 0.926193i | −0.990631 | − | 0.136563i | \(-0.956394\pi\) |
−0.613583 | − | 0.789631i | \(-0.710272\pi\) | |||||||
\(762\) | 196404.i | 0.338252i | ||||||||
\(763\) | 51023.0 | − | 353498.i | 0.0876429 | − | 0.607208i | ||||
\(764\) | −163752. | −0.280543 | ||||||||
\(765\) | −34020.0 | + | 58924.4i | −0.0581315 | + | 0.100687i | ||||
\(766\) | 447948. | − | 258623.i | 0.763431 | − | 0.440767i | ||||
\(767\) | 440040. | + | 762172.i | 0.748000 | + | 1.29557i | ||||
\(768\) | 196992. | + | 113733.i | 0.333984 | + | 0.192826i | ||||
\(769\) | − | 279842.i | − | 0.473217i | −0.971605 | − | 0.236609i | \(-0.923964\pi\) | ||
0.971605 | − | 0.236609i | \(-0.0760359\pi\) | |||||||
\(770\) | 73332.0 | + | 183466.i | 0.123684 | + | 0.309438i | ||||
\(771\) | −386262. | −0.649790 | ||||||||
\(772\) | 8382.00 | − | 14518.0i | 0.0140641 | − | 0.0243598i | ||||
\(773\) | 1.01217e6 | − | 584378.i | 1.69393 | − | 0.977992i | 0.742643 | − | 0.669687i | \(-0.233572\pi\) |
0.951288 | − | 0.308305i | \(-0.0997616\pi\) | |||||||
\(774\) | −29349.0 | − | 50834.0i | −0.0489904 | − | 0.0848539i | ||||
\(775\) | 521911. | + | 301326.i | 0.868947 | + | 0.501687i | ||||
\(776\) | 195930.i | 0.325369i | ||||||||
\(777\) | 169312. | − | 215056.i | 0.280445 | − | 0.356212i | ||||
\(778\) | 170620. | 0.281884 | ||||||||
\(779\) | −170781. | + | 295801.i | −0.281426 | + | 0.487445i | ||||
\(780\) | 92340.0 | − | 53312.5i | 0.151775 | − | 0.0876274i | ||||
\(781\) | 866986. | + | 1.50166e6i | 1.42138 | + | 2.46190i | ||||
\(782\) | −47040.0 | − | 27158.6i | −0.0769226 | − | 0.0444113i | ||||
\(783\) | − | 145908.i | − | 0.237988i | ||||||
\(784\) | −184240. | − | 54317.1i | −0.299745 | − | 0.0883699i | ||||
\(785\) | −302904. | −0.491548 | ||||||||
\(786\) | −113778. | + | 197069.i | −0.184168 | + | 0.318988i | ||||
\(787\) | 224040. | − | 129350.i | 0.361723 | − | 0.208841i | −0.308113 | − | 0.951350i | \(-0.599698\pi\) |
0.669836 | + | 0.742509i | \(0.266364\pi\) | |||||||
\(788\) | 151464. | + | 262343.i | 0.243925 | + | 0.422491i | ||||
\(789\) | 183564. | + | 105981.i | 0.294872 | + | 0.170244i | ||||
\(790\) | − | 169332.i | − | 0.271322i | ||||||
\(791\) | −166705. | − | 131246.i | −0.266438 | − | 0.209765i | ||||
\(792\) | 293328. | 0.467631 | ||||||||
\(793\) | 57570.0 | − | 99714.2i | 0.0915482 | − | 0.158566i | ||||
\(794\) | 121551. | − | 70177.5i | 0.192805 | − | 0.111316i | ||||
\(795\) | 59400.0 | + | 102884.i | 0.0939836 | + | 0.162784i | ||||
\(796\) | 251496. | + | 145201.i | 0.396922 | + | 0.229163i | ||||
\(797\) | 243415.i | 0.383205i | 0.981473 | + | 0.191603i | \(0.0613685\pi\) | ||||
−0.981473 | + | 0.191603i | \(0.938632\pi\) | |||||||
\(798\) | −123669. | + | 49431.0i | −0.194203 | + | 0.0776236i | ||||
\(799\) | −525000. | −0.822367 | ||||||||
\(800\) | −272976. | + | 472808.i | −0.426525 | + | 0.738763i | ||||
\(801\) | 318978. | − | 184162.i | 0.497159 | − | 0.287035i | ||||
\(802\) | 59704.0 | + | 103410.i | 0.0928228 | + | 0.160774i | ||||
\(803\) | −1.53328e6 | − | 885239.i | −2.37788 | − | 1.37287i | ||||
\(804\) | − | 148090.i | − | 0.229094i | ||||||
\(805\) | 56448.0 | + | 8147.57i | 0.0871078 | + | 0.0125729i | ||||
\(806\) | −383610. | −0.590500 | ||||||||
\(807\) | 186183. | − | 322478.i | 0.285886 | − | 0.495169i | ||||
\(808\) | −339192. | + | 195833.i | −0.519545 | + | 0.299959i | ||||
\(809\) | −229615. | − | 397705.i | −0.350835 | − | 0.607664i | 0.635561 | − | 0.772051i | \(-0.280769\pi\) |
−0.986396 | + | 0.164386i | \(0.947436\pi\) | |||||||
\(810\) | 13122.0 | + | 7575.99i | 0.0200000 | + | 0.0115470i | ||||
\(811\) | 831509.i | 1.26423i | 0.774876 | + | 0.632114i | \(0.217813\pi\) | ||||
−0.774876 | + | 0.632114i | \(0.782187\pi\) | |||||||
\(812\) | −87360.0 | + | 605248.i | −0.132495 | + | 0.917955i | ||||
\(813\) | −19836.0 | −0.0300105 | ||||||||
\(814\) | 208550. | − | 361219.i | 0.314747 | − | 0.545158i | ||||
\(815\) | 116514. | − | 67269.4i | 0.175413 | − | 0.101275i | ||||
\(816\) | −50400.0 | − | 87295.4i | −0.0756920 | − | 0.131102i | ||||
\(817\) | −246206. | − | 142147.i | −0.368853 | − | 0.212958i | ||||
\(818\) | − | 70463.3i | − | 0.105307i | ||||||
\(819\) | −80797.5 | − | 202143.i | −0.120456 | − | 0.301364i | ||||
\(820\) | −162864. | −0.242213 | ||||||||
\(821\) | 352799. | − | 611066.i | 0.523409 | − | 0.906571i | −0.476220 | − | 0.879326i | \(-0.657993\pi\) |
0.999629 | − | 0.0272445i | \(-0.00867326\pi\) | |||||||
\(822\) | 187884. | − | 108475.i | 0.278065 | − | 0.160541i | ||||
\(823\) | 193193. | + | 334620.i | 0.285228 | + | 0.494029i | 0.972664 | − | 0.232215i | \(-0.0745974\pi\) |
−0.687437 | + | 0.726244i | \(0.741264\pi\) | |||||||
\(824\) | 442764. | + | 255630.i | 0.652106 | + | 0.376493i | ||||
\(825\) | 521164.i | 0.765713i | ||||||||
\(826\) | 324240. | − | 411840.i | 0.475233 | − | 0.603627i | ||||
\(827\) | −842158. | −1.23135 | −0.615676 | − | 0.787999i | \(-0.711117\pi\) | ||||
−0.615676 | + | 0.787999i | \(0.711117\pi\) | |||||||
\(828\) | 18144.0 | − | 31426.3i | 0.0264650 | − | 0.0458388i | ||||
\(829\) | 122446. | − | 70694.5i | 0.178171 | − | 0.102867i | −0.408262 | − | 0.912865i | \(-0.633865\pi\) |
0.586433 | + | 0.809998i | \(0.300532\pi\) | |||||||
\(830\) | −69372.0 | − | 120156.i | −0.100700 | − | 0.174417i | ||||
\(831\) | 456250. | + | 263416.i | 0.660695 | + | 0.381453i | ||||
\(832\) | − | 136901.i | − | 0.197770i | ||||||
\(833\) | −401310. | − | 421806.i | −0.578349 | − | 0.607887i | ||||
\(834\) | −302742. | −0.435252 | ||||||||
\(835\) | 183078. | − | 317100.i | 0.262581 | − | 0.454804i | ||||
\(836\) | 527292. | − | 304432.i | 0.754464 | − | 0.435590i | ||||
\(837\) | 81769.5 | + | 141629.i | 0.116719 | + | 0.202163i | ||||
\(838\) | 16782.0 | + | 9689.09i | 0.0238977 | + | 0.0137973i | ||||
\(839\) | − | 634914.i | − | 0.901968i | −0.892532 | − | 0.450984i | \(-0.851073\pi\) | ||
0.892532 | − | 0.450984i | \(-0.148927\pi\) | |||||||
\(840\) | −116424. | − | 91660.1i | −0.165000 | − | 0.129904i | ||||
\(841\) | 374319. | 0.529237 | ||||||||
\(842\) | −258923. | + | 448468.i | −0.365213 | + | 0.632568i | ||||
\(843\) | 143622. | − | 82920.2i | 0.202100 | − | 0.116682i | ||||
\(844\) | −80196.0 | − | 138904.i | −0.112582 | − | 0.194997i | ||||
\(845\) | 13374.0 | + | 7721.48i | 0.0187304 | + | 0.0108140i | ||||
\(846\) | 116913.i | 0.163352i | ||||||||
\(847\) | −1.04627e6 | + | 418199.i | −1.45840 | + | 0.582930i | ||||
\(848\) | −176000. | −0.244749 | ||||||||
\(849\) | 48298.5 | − | 83655.5i | 0.0670067 | − | 0.116059i | ||||
\(850\) | −217140. | + | 125366.i | −0.300540 | + | 0.173517i | ||||
\(851\) | −60200.0 | − | 104269.i | −0.0831261 | − | 0.143979i | ||||
\(852\) | −482652. | − | 278659.i | −0.664898 | − | 0.383879i | ||||
\(853\) | − | 1.17683e6i | − | 1.61739i | −0.588229 | − | 0.808694i | \(-0.700175\pi\) | ||
0.588229 | − | 0.808694i | \(-0.299825\pi\) | |||||||
\(854\) | −67872.0 | − | 9796.48i | −0.0930625 | − | 0.0134324i | ||||
\(855\) | 73386.0 | 0.100388 | ||||||||
\(856\) | −300496. | + | 520474.i | −0.410101 | + | 0.710316i | ||||
\(857\) | −587808. | + | 339371.i | −0.800339 | + | 0.462076i | −0.843590 | − | 0.536988i | \(-0.819562\pi\) |
0.0432508 | + | 0.999064i | \(0.486229\pi\) | |||||||
\(858\) | −165870. | − | 287295.i | −0.225317 | − | 0.390260i | ||||
\(859\) | 118368. | + | 68339.8i | 0.160416 | + | 0.0926163i | 0.578059 | − | 0.815995i | \(-0.303810\pi\) |
−0.417643 | + | 0.908611i | \(0.637144\pi\) | |||||||
\(860\) | − | 135557.i | − | 0.183285i | ||||||
\(861\) | −47502.0 | + | 329104.i | −0.0640775 | + | 0.443942i | ||||
\(862\) | −190100. | −0.255839 | ||||||||
\(863\) | 80597.0 | − | 139598.i | 0.108217 | − | 0.187438i | −0.806831 | − | 0.590783i | \(-0.798819\pi\) |
0.915048 | + | 0.403345i | \(0.132152\pi\) | |||||||
\(864\) | −128304. | + | 74076.3i | −0.171875 | + | 0.0992321i | ||||
\(865\) | −29952.0 | − | 51878.4i | −0.0400307 | − | 0.0693353i | ||||
\(866\) | −250263. | − | 144489.i | −0.333704 | − | 0.192664i | ||||
\(867\) | 128454.i | 0.170887i | ||||||||
\(868\) | −254394. | − | 636456.i | −0.337651 | − | 0.844751i | ||||
\(869\) | 1.58052e6 | 2.09296 | ||||||||
\(870\) | −56160.0 | + | 97272.0i | −0.0741974 | + | 0.128514i | ||||
\(871\) | −338438. | + | 195397.i | −0.446110 | + | 0.257562i | ||||
\(872\) | 204092. | + | 353498.i | 0.268406 | + | 0.464894i | ||||
\(873\) | −81810.0 | − | 47233.0i | −0.107344 | − | 0.0619751i | ||||
\(874\) | 58584.9i | 0.0766942i | ||||||||
\(875\) | 359730. | − | 456918.i | 0.469851 | − | 0.596791i | ||||
\(876\) | 569052. | 0.741556 | ||||||||
\(877\) | −63415.0 | + | 109838.i | −0.0824504 | + | 0.142808i | −0.904302 | − | 0.426893i | \(-0.859608\pi\) |
0.821852 | + | 0.569702i | \(0.192941\pi\) | |||||||
\(878\) | −33684.0 | + | 19447.5i | −0.0436953 | + | 0.0252275i | ||||
\(879\) | −249246. | − | 431707.i | −0.322590 | − | 0.558742i | ||||
\(880\) | 139680. | + | 80644.3i | 0.180372 | + | 0.104138i | ||||
\(881\) | − | 546926.i | − | 0.704656i | −0.935877 | − | 0.352328i | \(-0.885390\pi\) | ||
0.935877 | − | 0.352328i | \(-0.114610\pi\) | |||||||
\(882\) | −93933.0 | + | 89368.6i | −0.120748 | + | 0.114881i | ||||
\(883\) | 155933. | 0.199994 | 0.0999969 | − | 0.994988i | \(-0.468117\pi\) | ||||
0.0999969 | + | 0.994988i | \(0.468117\pi\) | |||||||
\(884\) | −239400. | + | 414653.i | −0.306351 | + | 0.530616i | ||||
\(885\) | −250128. | + | 144411.i | −0.319357 | + | 0.184381i | ||||
\(886\) | 118876. | + | 205899.i | 0.151435 | + | 0.262293i | ||||
\(887\) | 589707. | + | 340467.i | 0.749530 | + | 0.432741i | 0.825524 | − | 0.564367i | \(-0.190880\pi\) |
−0.0759940 | + | 0.997108i | \(0.524213\pi\) | |||||||
\(888\) | 312808.i | 0.396691i | ||||||||
\(889\) | 727612. | + | 572845.i | 0.920653 | + | 0.724826i | ||||
\(890\) | −283536. | −0.357955 | ||||||||
\(891\) | −70713.0 | + | 122479.i | −0.0890725 | + | 0.154278i | ||||
\(892\) | 262728. | − | 151686.i | 0.330200 | − | 0.190641i | ||||
\(893\) | 283125. | + | 490387.i | 0.355038 | + | 0.614945i | ||||
\(894\) | −39708.0 | − | 22925.4i | −0.0496824 | − | 0.0286842i | ||||
\(895\) | − | 54143.9i | − | 0.0675933i | ||||||
\(896\) | 693056. | − | 277017.i | 0.863281 | − | 0.345057i | ||||
\(897\) | −95760.0 | −0.119014 | ||||||||
\(898\) | 323110. | − | 559643.i | 0.400680 | − | 0.693998i | ||||
\(899\) | −1.04988e6 | + | 606149.i | −1.29903 | + | 0.749997i | ||||
\(900\) | −83754.0 | − | 145066.i | −0.103400 | − | 0.179094i | ||||
\(901\) | −462000. | − | 266736.i | −0.569105 | − | 0.328573i | ||||
\(902\) | 506715.i | 0.622803i | ||||||||
\(903\) | −273924. | − | 39537.5i | −0.335934 | − | 0.0484880i | ||||
\(904\) | 242480. | 0.296715 | ||||||||
\(905\) | 59373.0 | − | 102837.i | 0.0724923 | − | 0.125560i | ||||
\(906\) | 192258. | − | 111000.i | 0.234222 | − | 0.135228i | ||||
\(907\) | −169220. | − | 293099.i | −0.205702 | − | 0.356286i | 0.744654 | − | 0.667450i | \(-0.232614\pi\) |
−0.950356 | + | 0.311164i | \(0.899281\pi\) | |||||||
\(908\) | 454572. | + | 262447.i | 0.551355 | + | 0.318325i | ||||
\(909\) | − | 188839.i | − | 0.228540i | ||||||
\(910\) | −23940.0 | + | 165861.i | −0.0289096 | + | 0.200291i | ||||
\(911\) | 658004. | 0.792851 | 0.396426 | − | 0.918067i | \(-0.370250\pi\) | ||||
0.396426 | + | 0.918067i | \(0.370250\pi\) | |||||||
\(912\) | −54360.0 | + | 94154.3i | −0.0653566 | + | 0.113201i | ||||
\(913\) | 1.12151e6 | − | 647506.i | 1.34544 | − | 0.776788i | ||||
\(914\) | −133157. | − | 230635.i | −0.159394 | − | 0.276078i | ||||
\(915\) | 32724.0 | + | 18893.2i | 0.0390863 | + | 0.0225665i | ||||
\(916\) | − | 444022.i | − | 0.529192i | ||||||
\(917\) | 398223. | + | 996295.i | 0.473574 | + | 1.18481i | ||||
\(918\) | −68040.0 | −0.0807382 | ||||||||
\(919\) | −655904. | + | 1.13606e6i | −0.776622 | + | 1.34515i | 0.157257 | + | 0.987558i | \(0.449735\pi\) |
−0.933878 | + | 0.357591i | \(0.883598\pi\) | |||||||
\(920\) | −56448.0 | + | 32590.3i | −0.0666919 | + | 0.0385046i | ||||
\(921\) | 385142. | + | 667085.i | 0.454047 | + | 0.786433i | ||||
\(922\) | −73176.0 | − | 42248.2i | −0.0860809 | − | 0.0496988i | ||||
\(923\) | 1.47070e6i | 1.72632i | ||||||||
\(924\) | 366660. | − | 465721.i | 0.429457 | − | 0.545484i | ||||
\(925\) | −555775. | −0.649554 | ||||||||
\(926\) | 412345. | − | 714202.i | 0.480882 | − | 0.832913i | ||||
\(927\) | −213476. | + | 123250.i | −0.248421 | + | 0.143426i | ||||
\(928\) | −549120. | − | 951104.i | −0.637634 | − | 1.10441i | ||||
\(929\) | 464583. | + | 268227.i | 0.538309 | + | 0.310793i | 0.744393 | − | 0.667741i | \(-0.232739\pi\) |
−0.206084 | + | 0.978534i | \(0.566072\pi\) | |||||||
\(930\) | − | 125892.i | − | 0.145557i | ||||||
\(931\) | −177576. | + | 602326.i | −0.204873 | + | 0.694916i | ||||
\(932\) | −206376. | −0.237590 | ||||||||
\(933\) | 86355.0 | − | 149571.i | 0.0992029 | − | 0.171824i | ||||
\(934\) | −449598. | + | 259576.i | −0.515384 | + | 0.297557i | ||||
\(935\) | 244440. | + | 423382.i | 0.279608 | + | 0.484295i | ||||
\(936\) | 215460. | + | 124396.i | 0.245932 | + | 0.141989i | ||||
\(937\) | 1.41972e6i | 1.61705i | 0.588463 | + | 0.808524i | \(0.299733\pi\) | ||||
−0.588463 | + | 0.808524i | \(0.700267\pi\) | |||||||
\(938\) | 182875. | + | 143977.i | 0.207849 | + | 0.163639i | ||||
\(939\) | −139707. | −0.158448 | ||||||||
\(940\) | −135000. | + | 233827.i | −0.152784 | + | 0.264630i | ||||
\(941\) | −34458.0 | + | 19894.3i | −0.0389144 | + | 0.0224673i | −0.519331 | − | 0.854573i | \(-0.673819\pi\) |
0.480417 | + | 0.877040i | \(0.340485\pi\) | |||||||
\(942\) | −151452. | − | 262323.i | −0.170676 | − | 0.295620i | ||||
\(943\) | 126672. | + | 73134.1i | 0.142448 | + | 0.0822426i | ||||
\(944\) | − | 427886.i | − | 0.480158i | ||||||
\(945\) | 66339.0 | − | 26516.0i | 0.0742857 | − | 0.0296923i | ||||
\(946\) | −421756. | −0.471280 | ||||||||
\(947\) | 173045. | − | 299723.i | 0.192956 | − | 0.334210i | −0.753272 | − | 0.657709i | \(-0.771526\pi\) |
0.946229 | + | 0.323499i | \(0.104859\pi\) | |||||||
\(948\) | −439938. | + | 253998.i | −0.489525 | + | 0.282627i | ||||
\(949\) | −750832. | − | 1.30048e6i | −0.833702 | − | 1.44401i | ||||
\(950\) | 234201. | + | 135216.i | 0.259502 | + | 0.149824i | ||||
\(951\) | − | 55016.9i | − | 0.0608324i | ||||||
\(952\) | 658560. | + | 95054.9i | 0.726644 | + | 0.104882i | ||||
\(953\) | 806780. | 0.888320 | 0.444160 | − | 0.895948i | \(-0.353502\pi\) | ||||
0.444160 | + | 0.895948i | \(0.353502\pi\) | |||||||
\(954\) | −59400.0 | + | 102884.i | −0.0652664 | + | 0.113045i | ||||
\(955\) | −122814. | + | 70906.7i | −0.134661 | + | 0.0777464i | ||||
\(956\) | −401820. | − | 695973.i | −0.439659 | − | 0.761511i | ||||
\(957\) | −907920. | − | 524188.i | −0.991342 | − | 0.572352i | ||||
\(958\) | 447534.i | 0.487635i | ||||||||
\(959\) | 146132. | − | 1.01243e6i | 0.158894 | − | 1.10085i | ||||
\(960\) | 44928.0 | 0.0487500 | ||||||||
\(961\) | 217633. | − | 376951.i | 0.235656 | − | 0.408168i | ||||
\(962\) | 306375. | − | 176886.i | 0.331057 | − | 0.191136i | ||||
\(963\) | −144882. | − | 250943.i | −0.156229 | − | 0.270597i | ||||
\(964\) | 293328. | + | 169353.i | 0.315645 | + | 0.182238i | ||||
\(965\) | − | 14518.0i | − | 0.0155903i | ||||||
\(966\) | 21168.0 | + | 52959.2i | 0.0226843 | + | 0.0567528i | ||||
\(967\) | 660791. | 0.706661 | 0.353331 | − | 0.935499i | \(-0.385049\pi\) | ||||
0.353331 | + | 0.935499i | \(0.385049\pi\) | |||||||
\(968\) | 643860. | − | 1.11520e6i | 0.687133 | − | 1.19015i | ||||
\(969\) | −285390. | + | 164770.i | −0.303942 | + | 0.175481i | ||||
\(970\) | 36360.0 | + | 62977.4i | 0.0386439 | + | 0.0669331i | ||||
\(971\) | −694758. | − | 401119.i | −0.736877 | − | 0.425436i | 0.0840556 | − | 0.996461i | \(-0.473213\pi\) |
−0.820933 | + | 0.571025i | \(0.806546\pi\) | |||||||
\(972\) | − | 45455.9i | − | 0.0481125i | ||||||
\(973\) | −882998. | + | 1.12156e6i | −0.932682 | + | 1.18467i | ||||
\(974\) | 164674. | 0.173583 | ||||||||
\(975\) | −221018. | + | 382814.i | −0.232497 | + | 0.402697i | ||||
\(976\) | −48480.0 | + | 27989.9i | −0.0508936 | + | 0.0293834i | ||||
\(977\) | −340723. | − | 590150.i | −0.356954 | − | 0.618263i | 0.630496 | − | 0.776192i | \(-0.282851\pi\) |
−0.987450 | + | 0.157930i | \(0.949518\pi\) | |||||||
\(978\) | 116514. | + | 67269.4i | 0.121815 | + | 0.0703299i | ||||
\(979\) | − | 2.64648e6i | − | 2.76123i | ||||||
\(980\) | −291060. | + | 70272.8i | −0.303061 | + | 0.0731703i | ||||
\(981\) | −196803. | −0.204500 | ||||||||
\(982\) | −812.000 | + | 1406.43i | −0.000842041 | + | 0.00145846i | ||||
\(983\) | −1.34161e6 | + | 774580.i | −1.38842 | + | 0.801603i | −0.993137 | − | 0.116958i | \(-0.962686\pi\) |
−0.395280 | + | 0.918561i | \(0.629352\pi\) | |||||||
\(984\) | −190008. | − | 329104.i | −0.196237 | − | 0.339893i | ||||
\(985\) | 227196. | + | 131172.i | 0.234168 | + | 0.135197i | ||||
\(986\) | − | 504373.i | − | 0.518798i | ||||||
\(987\) | 433125. | + | 340998.i | 0.444610 | + | 0.350039i | ||||
\(988\) | 516420. | 0.529041 | ||||||||
\(989\) | −60872.0 | + | 105433.i | −0.0622336 | + | 0.107792i | ||||
\(990\) | 94284.0 | − | 54434.9i | 0.0961983 | − | 0.0555401i | ||||
\(991\) | −39152.5 | − | 67814.1i | −0.0398669 | − | 0.0690515i | 0.845403 | − | 0.534128i | \(-0.179360\pi\) |
−0.885270 | + | 0.465077i | \(0.846027\pi\) | |||||||
\(992\) | 1.06603e6 | + | 615474.i | 1.08330 | + | 0.625441i | ||||
\(993\) | − | 661610.i | − | 0.670971i | ||||||
\(994\) | 813358. | − | 325102.i | 0.823207 | − | 0.329039i | ||||
\(995\) | 251496. | 0.254030 | ||||||||
\(996\) | −208116. | + | 360467.i | −0.209791 | + | 0.363369i | ||||
\(997\) | −1.36361e6 | + | 787282.i | −1.37183 | + | 0.792027i | −0.991159 | − | 0.132683i | \(-0.957641\pi\) |
−0.380673 | + | 0.924710i | \(0.624308\pi\) | |||||||
\(998\) | −409649. | − | 709533.i | −0.411293 | − | 0.712380i | ||||
\(999\) | −130612. | − | 75409.2i | −0.130874 | − | 0.0755602i |
(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 | 21.5.f.a.19.1 | yes | 2 | |
3.2 | odd | 2 | 63.5.m.c.19.1 | 2 | |||
4.3 | odd | 2 | 336.5.bh.b.145.1 | 2 | |||
7.2 | even | 3 | 147.5.d.b.97.2 | 2 | |||
7.3 | odd | 6 | inner | 21.5.f.a.10.1 | ✓ | 2 | |
7.4 | even | 3 | 147.5.f.a.31.1 | 2 | |||
7.5 | odd | 6 | 147.5.d.b.97.1 | 2 | |||
7.6 | odd | 2 | 147.5.f.a.19.1 | 2 | |||
21.2 | odd | 6 | 441.5.d.a.244.2 | 2 | |||
21.5 | even | 6 | 441.5.d.a.244.1 | 2 | |||
21.17 | even | 6 | 63.5.m.c.10.1 | 2 | |||
28.3 | even | 6 | 336.5.bh.b.241.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.5.f.a.10.1 | ✓ | 2 | 7.3 | odd | 6 | inner | |
21.5.f.a.19.1 | yes | 2 | 1.1 | even | 1 | trivial | |
63.5.m.c.10.1 | 2 | 21.17 | even | 6 | |||
63.5.m.c.19.1 | 2 | 3.2 | odd | 2 | |||
147.5.d.b.97.1 | 2 | 7.5 | odd | 6 | |||
147.5.d.b.97.2 | 2 | 7.2 | even | 3 | |||
147.5.f.a.19.1 | 2 | 7.6 | odd | 2 | |||
147.5.f.a.31.1 | 2 | 7.4 | even | 3 | |||
336.5.bh.b.145.1 | 2 | 4.3 | odd | 2 | |||
336.5.bh.b.241.1 | 2 | 28.3 | even | 6 | |||
441.5.d.a.244.1 | 2 | 21.5 | even | 6 | |||
441.5.d.a.244.2 | 2 | 21.2 | odd | 6 |