Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,6,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (of order \(2\), degree \(1\), 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: | \(3.36806021607\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 484x^{10} + 194194x^{8} - 39867800x^{6} + 5398720873x^{4} - 310089434788x^{2} + 9371104623076 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.1 | ||
Root | \(-13.7499 + 10.2458i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.6.c.a.20.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 10.2458i | − | 1.81122i | −0.424114 | − | 0.905609i | \(-0.639414\pi\) | ||
0.424114 | − | 0.905609i | \(-0.360586\pi\) | |||||||
\(3\) | −4.60012 | + | 14.8943i | −0.295098 | + | 0.955467i | ||||
\(4\) | −72.9763 | −2.28051 | ||||||||
\(5\) | −73.2992 | −1.31122 | −0.655608 | − | 0.755101i | \(-0.727588\pi\) | ||||
−0.655608 | + | 0.755101i | \(0.727588\pi\) | |||||||
\(6\) | 152.604 | + | 47.1319i | 1.73056 | + | 0.534487i | ||||
\(7\) | 55.7250 | − | 117.054i | 0.429838 | − | 0.902906i | ||||
\(8\) | 419.835i | 2.31928i | ||||||||
\(9\) | −200.678 | − | 137.031i | −0.825834 | − | 0.563913i | ||||
\(10\) | 751.009i | 2.37490i | ||||||||
\(11\) | − | 237.986i | − | 0.593020i | −0.955030 | − | 0.296510i | \(-0.904177\pi\) | ||
0.955030 | − | 0.296510i | \(-0.0958228\pi\) | |||||||
\(12\) | 335.700 | − | 1086.93i | 0.672974 | − | 2.17895i | ||||
\(13\) | − | 63.3779i | − | 0.104011i | −0.998647 | − | 0.0520055i | \(-0.983439\pi\) | ||
0.998647 | − | 0.0520055i | \(-0.0165613\pi\) | |||||||
\(14\) | −1199.31 | − | 570.947i | −1.63536 | − | 0.778531i | ||||
\(15\) | 337.186 | − | 1091.74i | 0.386937 | − | 1.25282i | ||||
\(16\) | 1966.30 | 1.92022 | ||||||||
\(17\) | −814.556 | −0.683595 | −0.341797 | − | 0.939774i | \(-0.611036\pi\) | ||||
−0.341797 | + | 0.939774i | \(0.611036\pi\) | |||||||
\(18\) | −1403.99 | + | 2056.10i | −1.02137 | + | 1.49577i | ||||
\(19\) | 64.1691i | 0.0407795i | 0.999792 | + | 0.0203898i | \(0.00649071\pi\) | ||||
−0.999792 | + | 0.0203898i | \(0.993509\pi\) | |||||||
\(20\) | 5349.11 | 2.99024 | ||||||||
\(21\) | 1487.10 | + | 1368.45i | 0.735852 | + | 0.677142i | ||||
\(22\) | −2438.35 | −1.07409 | ||||||||
\(23\) | 988.504i | 0.389636i | 0.980839 | + | 0.194818i | \(0.0624116\pi\) | ||||
−0.980839 | + | 0.194818i | \(0.937588\pi\) | |||||||
\(24\) | −6253.13 | − | 1931.29i | −2.21600 | − | 0.684416i | ||||
\(25\) | 2247.78 | 0.719289 | ||||||||
\(26\) | −649.357 | −0.188387 | ||||||||
\(27\) | 2964.11 | − | 2358.59i | 0.782502 | − | 0.622648i | ||||
\(28\) | −4066.61 | + | 8542.20i | −0.980251 | + | 2.05909i | ||||
\(29\) | − | 1569.70i | − | 0.346594i | −0.984870 | − | 0.173297i | \(-0.944558\pi\) | ||
0.984870 | − | 0.173297i | \(-0.0554420\pi\) | |||||||
\(30\) | −11185.7 | − | 3454.73i | −2.26914 | − | 0.700828i | ||||
\(31\) | − | 5256.16i | − | 0.982346i | −0.871062 | − | 0.491173i | \(-0.836568\pi\) | ||
0.871062 | − | 0.491173i | \(-0.163432\pi\) | |||||||
\(32\) | − | 6711.62i | − | 1.15865i | ||||||
\(33\) | 3544.62 | + | 1094.76i | 0.566611 | + | 0.174999i | ||||
\(34\) | 8345.77i | 1.23814i | ||||||||
\(35\) | −4084.60 | + | 8579.99i | −0.563611 | + | 1.18390i | ||||
\(36\) | 14644.7 | + | 10000.0i | 1.88332 | + | 1.28601i | ||||
\(37\) | 11308.5 | 1.35800 | 0.678999 | − | 0.734139i | \(-0.262414\pi\) | ||||
0.678999 | + | 0.734139i | \(0.262414\pi\) | |||||||
\(38\) | 657.464 | 0.0738606 | ||||||||
\(39\) | 943.966 | + | 291.546i | 0.0993791 | + | 0.0306935i | ||||
\(40\) | − | 30773.6i | − | 3.04108i | ||||||
\(41\) | −3795.80 | −0.352650 | −0.176325 | − | 0.984332i | \(-0.556421\pi\) | ||||
−0.176325 | + | 0.984332i | \(0.556421\pi\) | |||||||
\(42\) | 14020.8 | − | 15236.5i | 1.22645 | − | 1.33279i | ||||
\(43\) | −15837.6 | −1.30622 | −0.653111 | − | 0.757262i | \(-0.726536\pi\) | ||||
−0.653111 | + | 0.757262i | \(0.726536\pi\) | |||||||
\(44\) | 17367.3i | 1.35239i | ||||||||
\(45\) | 14709.5 | + | 10044.3i | 1.08285 | + | 0.739412i | ||||
\(46\) | 10128.0 | 0.705715 | ||||||||
\(47\) | −23236.9 | −1.53438 | −0.767192 | − | 0.641418i | \(-0.778346\pi\) | ||||
−0.767192 | + | 0.641418i | \(0.778346\pi\) | |||||||
\(48\) | −9045.24 | + | 29286.6i | −0.566653 | + | 1.83471i | ||||
\(49\) | −10596.4 | − | 13045.7i | −0.630478 | − | 0.776207i | ||||
\(50\) | − | 23030.3i | − | 1.30279i | ||||||
\(51\) | 3747.06 | − | 12132.2i | 0.201727 | − | 0.653152i | ||||
\(52\) | 4625.09i | 0.237198i | ||||||||
\(53\) | − | 19952.5i | − | 0.975681i | −0.872933 | − | 0.487840i | \(-0.837785\pi\) | ||
0.872933 | − | 0.487840i | \(-0.162215\pi\) | |||||||
\(54\) | −24165.6 | − | 30369.7i | −1.12775 | − | 1.41728i | ||||
\(55\) | 17444.2i | 0.777577i | ||||||||
\(56\) | 49143.5 | + | 23395.3i | 2.09409 | + | 0.996917i | ||||
\(57\) | −955.751 | − | 295.186i | −0.0389635 | − | 0.0120340i | ||||
\(58\) | −16082.8 | −0.627757 | ||||||||
\(59\) | 34515.5 | 1.29087 | 0.645437 | − | 0.763814i | \(-0.276675\pi\) | ||||
0.645437 | + | 0.763814i | \(0.276675\pi\) | |||||||
\(60\) | −24606.6 | + | 79671.0i | −0.882415 | + | 2.85708i | ||||
\(61\) | 12095.9i | 0.416212i | 0.978106 | + | 0.208106i | \(0.0667299\pi\) | ||||
−0.978106 | + | 0.208106i | \(0.933270\pi\) | |||||||
\(62\) | −53853.6 | −1.77924 | ||||||||
\(63\) | −27222.8 | + | 15854.2i | −0.864136 | + | 0.503259i | ||||
\(64\) | −5844.15 | −0.178349 | ||||||||
\(65\) | 4645.55i | 0.136381i | ||||||||
\(66\) | 11216.7 | − | 36317.5i | 0.316961 | − | 1.02626i | ||||
\(67\) | −29255.2 | −0.796189 | −0.398094 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398094 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(68\) | 59443.3 | 1.55894 | ||||||||
\(69\) | −14723.0 | − | 4547.24i | −0.372284 | − | 0.114981i | ||||
\(70\) | 87908.9 | + | 41850.0i | 2.14431 | + | 1.02082i | ||||
\(71\) | 54089.1i | 1.27340i | 0.771113 | + | 0.636699i | \(0.219701\pi\) | ||||
−0.771113 | + | 0.636699i | \(0.780299\pi\) | |||||||
\(72\) | 57530.4 | − | 84251.6i | 1.30787 | − | 1.91534i | ||||
\(73\) | − | 73706.7i | − | 1.61883i | −0.587240 | − | 0.809413i | \(-0.699786\pi\) | ||
0.587240 | − | 0.809413i | \(-0.300214\pi\) | |||||||
\(74\) | − | 115864.i | − | 2.45963i | ||||||
\(75\) | −10340.1 | + | 33479.0i | −0.212261 | + | 0.687257i | ||||
\(76\) | − | 4682.83i | − | 0.0929981i | ||||||
\(77\) | −27857.3 | − | 13261.8i | −0.535441 | − | 0.254903i | ||||
\(78\) | 2987.12 | − | 9671.69i | 0.0555925 | − | 0.179997i | ||||
\(79\) | −49241.9 | −0.887701 | −0.443851 | − | 0.896101i | \(-0.646388\pi\) | ||||
−0.443851 | + | 0.896101i | \(0.646388\pi\) | |||||||
\(80\) | −144129. | −2.51782 | ||||||||
\(81\) | 21494.1 | + | 54998.1i | 0.364004 | + | 0.931397i | ||||
\(82\) | 38891.0i | 0.638725i | ||||||||
\(83\) | 112435. | 1.79146 | 0.895732 | − | 0.444595i | \(-0.146652\pi\) | ||||
0.895732 | + | 0.444595i | \(0.146652\pi\) | |||||||
\(84\) | −108523. | − | 99864.3i | −1.67812 | − | 1.54423i | ||||
\(85\) | 59706.3 | 0.896340 | ||||||||
\(86\) | 162268.i | 2.36585i | ||||||||
\(87\) | 23379.5 | + | 7220.80i | 0.331159 | + | 0.102279i | ||||
\(88\) | 99914.8 | 1.37538 | ||||||||
\(89\) | −71787.2 | −0.960665 | −0.480332 | − | 0.877087i | \(-0.659484\pi\) | ||||
−0.480332 | + | 0.877087i | \(0.659484\pi\) | |||||||
\(90\) | 102911. | − | 150711.i | 1.33924 | − | 1.96127i | ||||
\(91\) | −7418.66 | − | 3531.74i | −0.0939122 | − | 0.0447079i | ||||
\(92\) | − | 72137.4i | − | 0.888568i | ||||||
\(93\) | 78286.6 | + | 24179.0i | 0.938599 | + | 0.289888i | ||||
\(94\) | 238081.i | 2.77910i | ||||||||
\(95\) | − | 4703.55i | − | 0.0534708i | ||||||
\(96\) | 99964.5 | + | 30874.3i | 1.10705 | + | 0.341915i | ||||
\(97\) | − | 18031.4i | − | 0.194581i | −0.995256 | − | 0.0972905i | \(-0.968982\pi\) | ||
0.995256 | − | 0.0972905i | \(-0.0310176\pi\) | |||||||
\(98\) | −133664. | + | 108569.i | −1.40588 | + | 1.14193i | ||||
\(99\) | −32611.4 | + | 47758.4i | −0.334412 | + | 0.489736i | ||||
\(100\) | −164035. | −1.64035 | ||||||||
\(101\) | 113298. | 1.10515 | 0.552574 | − | 0.833464i | \(-0.313646\pi\) | ||||
0.552574 | + | 0.833464i | \(0.313646\pi\) | |||||||
\(102\) | −124304. | − | 38391.6i | −1.18300 | − | 0.365372i | ||||
\(103\) | − | 28838.5i | − | 0.267842i | −0.990992 | − | 0.133921i | \(-0.957243\pi\) | ||
0.990992 | − | 0.133921i | \(-0.0427569\pi\) | |||||||
\(104\) | 26608.3 | 0.241231 | ||||||||
\(105\) | −109003. | − | 100306.i | −0.964862 | − | 0.887880i | ||||
\(106\) | −204429. | −1.76717 | ||||||||
\(107\) | − | 163105.i | − | 1.37724i | −0.725125 | − | 0.688618i | \(-0.758218\pi\) | ||
0.725125 | − | 0.688618i | \(-0.241782\pi\) | |||||||
\(108\) | −216310. | + | 172121.i | −1.78450 | + | 1.41995i | ||||
\(109\) | 80804.9 | 0.651436 | 0.325718 | − | 0.945467i | \(-0.394394\pi\) | ||||
0.325718 | + | 0.945467i | \(0.394394\pi\) | |||||||
\(110\) | 178729. | 1.40836 | ||||||||
\(111\) | −52020.3 | + | 168431.i | −0.400742 | + | 1.29752i | ||||
\(112\) | 109572. | − | 230164.i | 0.825384 | − | 1.73378i | ||||
\(113\) | − | 166803.i | − | 1.22887i | −0.788966 | − | 0.614437i | \(-0.789383\pi\) | ||
0.788966 | − | 0.614437i | \(-0.210617\pi\) | |||||||
\(114\) | −3024.42 | + | 9792.43i | −0.0217961 | + | 0.0705714i | ||||
\(115\) | − | 72456.6i | − | 0.510897i | ||||||
\(116\) | 114551.i | 0.790411i | ||||||||
\(117\) | −8684.73 | + | 12718.5i | −0.0586532 | + | 0.0858959i | ||||
\(118\) | − | 353638.i | − | 2.33805i | ||||||
\(119\) | −45391.2 | + | 95347.3i | −0.293835 | + | 0.617222i | ||||
\(120\) | 458350. | + | 141562.i | 2.90565 | + | 0.897418i | ||||
\(121\) | 104414. | 0.648328 | ||||||||
\(122\) | 123932. | 0.753851 | ||||||||
\(123\) | 17461.1 | − | 56535.6i | 0.104066 | − | 0.336945i | ||||
\(124\) | 383575.i | 2.24025i | ||||||||
\(125\) | 64299.8 | 0.368073 | ||||||||
\(126\) | 162438. | + | 278920.i | 0.911512 | + | 1.56514i | ||||
\(127\) | −134331. | −0.739040 | −0.369520 | − | 0.929223i | \(-0.620478\pi\) | ||||
−0.369520 | + | 0.929223i | \(0.620478\pi\) | |||||||
\(128\) | − | 154894.i | − | 0.835620i | ||||||
\(129\) | 72854.7 | − | 235889.i | 0.385464 | − | 1.24805i | ||||
\(130\) | 47597.4 | 0.247016 | ||||||||
\(131\) | −206373. | −1.05069 | −0.525346 | − | 0.850889i | \(-0.676064\pi\) | ||||
−0.525346 | + | 0.850889i | \(0.676064\pi\) | |||||||
\(132\) | −258673. | − | 79891.9i | −1.29216 | − | 0.399087i | ||||
\(133\) | 7511.28 | + | 3575.83i | 0.0368201 | + | 0.0175286i | ||||
\(134\) | 299743.i | 1.44207i | ||||||||
\(135\) | −217267. | + | 172883.i | −1.02603 | + | 0.816426i | ||||
\(136\) | − | 341979.i | − | 1.58545i | ||||||
\(137\) | 104556.i | 0.475936i | 0.971273 | + | 0.237968i | \(0.0764813\pi\) | ||||
−0.971273 | + | 0.237968i | \(0.923519\pi\) | |||||||
\(138\) | −46590.1 | + | 150849.i | −0.208255 | + | 0.674287i | ||||
\(139\) | 106570.i | 0.467842i | 0.972256 | + | 0.233921i | \(0.0751558\pi\) | ||||
−0.972256 | + | 0.233921i | \(0.924844\pi\) | |||||||
\(140\) | 298079. | − | 626137.i | 1.28532 | − | 2.69991i | ||||
\(141\) | 106893. | − | 346097.i | 0.452794 | − | 1.46605i | ||||
\(142\) | 554186. | 2.30640 | ||||||||
\(143\) | −15083.0 | −0.0616806 | ||||||||
\(144\) | −394593. | − | 269444.i | −1.58578 | − | 1.08284i | ||||
\(145\) | 115058.i | 0.454460i | ||||||||
\(146\) | −755184. | −2.93205 | ||||||||
\(147\) | 243051. | − | 97814.2i | 0.927693 | − | 0.373343i | ||||
\(148\) | −825250. | −3.09693 | ||||||||
\(149\) | 234489.i | 0.865279i | 0.901567 | + | 0.432640i | \(0.142418\pi\) | ||||
−0.901567 | + | 0.432640i | \(0.857582\pi\) | |||||||
\(150\) | 343019. | + | 105942.i | 1.24477 | + | 0.384450i | ||||
\(151\) | −82844.4 | −0.295679 | −0.147840 | − | 0.989011i | \(-0.547232\pi\) | ||||
−0.147840 | + | 0.989011i | \(0.547232\pi\) | |||||||
\(152\) | −26940.5 | −0.0945793 | ||||||||
\(153\) | 163463. | + | 111619.i | 0.564536 | + | 0.385488i | ||||
\(154\) | −135877. | + | 285420.i | −0.461684 | + | 0.969800i | ||||
\(155\) | 385273.i | 1.28807i | ||||||||
\(156\) | −68887.2 | − | 21276.0i | −0.226635 | − | 0.0699968i | ||||
\(157\) | 65986.0i | 0.213650i | 0.994278 | + | 0.106825i | \(0.0340684\pi\) | ||||
−0.994278 | + | 0.106825i | \(0.965932\pi\) | |||||||
\(158\) | 504522.i | 1.60782i | ||||||||
\(159\) | 297178. | + | 91784.0i | 0.932231 | + | 0.287922i | ||||
\(160\) | 491956.i | 1.51924i | ||||||||
\(161\) | 115709. | + | 55084.4i | 0.351804 | + | 0.167480i | ||||
\(162\) | 563499. | − | 220224.i | 1.68696 | − | 0.659291i | ||||
\(163\) | −327678. | −0.966001 | −0.483001 | − | 0.875620i | \(-0.660453\pi\) | ||||
−0.483001 | + | 0.875620i | \(0.660453\pi\) | |||||||
\(164\) | 277003. | 0.804221 | ||||||||
\(165\) | −259818. | − | 80245.3i | −0.742949 | − | 0.229462i | ||||
\(166\) | − | 1.15199e6i | − | 3.24473i | ||||||
\(167\) | −96558.3 | −0.267916 | −0.133958 | − | 0.990987i | \(-0.542769\pi\) | ||||
−0.133958 | + | 0.990987i | \(0.542769\pi\) | |||||||
\(168\) | −574522. | + | 624335.i | −1.57049 | + | 1.70665i | ||||
\(169\) | 367276. | 0.989182 | ||||||||
\(170\) | − | 611739.i | − | 1.62347i | ||||||
\(171\) | 8793.15 | − | 12877.3i | 0.0229961 | − | 0.0336771i | ||||
\(172\) | 1.15577e6 | 2.97885 | ||||||||
\(173\) | 137087. | 0.348243 | 0.174121 | − | 0.984724i | \(-0.444291\pi\) | ||||
0.174121 | + | 0.984724i | \(0.444291\pi\) | |||||||
\(174\) | 73982.8 | − | 239541.i | 0.185250 | − | 0.599801i | ||||
\(175\) | 125257. | − | 263112.i | 0.309178 | − | 0.649450i | ||||
\(176\) | − | 467952.i | − | 1.13873i | ||||||
\(177\) | −158775. | + | 514082.i | −0.380934 | + | 1.23339i | ||||
\(178\) | 735517.i | 1.73997i | ||||||||
\(179\) | − | 203680.i | − | 0.475135i | −0.971371 | − | 0.237567i | \(-0.923650\pi\) | ||
0.971371 | − | 0.237567i | \(-0.0763500\pi\) | |||||||
\(180\) | −1.07345e6 | − | 732993.i | −2.46945 | − | 1.68624i | ||||
\(181\) | 733278.i | 1.66369i | 0.555009 | + | 0.831845i | \(0.312715\pi\) | ||||
−0.555009 | + | 0.831845i | \(0.687285\pi\) | |||||||
\(182\) | −36185.4 | + | 76010.1i | −0.0809758 | + | 0.170095i | ||||
\(183\) | −180160. | − | 55642.8i | −0.397677 | − | 0.122823i | ||||
\(184\) | −415009. | −0.903676 | ||||||||
\(185\) | −828901. | −1.78063 | ||||||||
\(186\) | 247733. | − | 802109.i | 0.525051 | − | 1.70001i | ||||
\(187\) | 193853.i | 0.405385i | ||||||||
\(188\) | 1.69574e6 | 3.49918 | ||||||||
\(189\) | −110907. | − | 478395.i | −0.225843 | − | 0.974164i | ||||
\(190\) | −48191.6 | −0.0968473 | ||||||||
\(191\) | − | 768632.i | − | 1.52453i | −0.647267 | − | 0.762263i | \(-0.724088\pi\) | ||
0.647267 | − | 0.762263i | \(-0.275912\pi\) | |||||||
\(192\) | 26883.8 | − | 87044.2i | 0.0526305 | − | 0.170407i | ||||
\(193\) | −278059. | −0.537334 | −0.268667 | − | 0.963233i | \(-0.586583\pi\) | ||||
−0.268667 | + | 0.963233i | \(0.586583\pi\) | |||||||
\(194\) | −184746. | −0.352428 | ||||||||
\(195\) | −69192.0 | − | 21370.1i | −0.130308 | − | 0.0402458i | ||||
\(196\) | 773289. | + | 952029.i | 1.43781 | + | 1.77015i | ||||
\(197\) | 224299.i | 0.411776i | 0.978576 | + | 0.205888i | \(0.0660082\pi\) | ||||
−0.978576 | + | 0.205888i | \(0.933992\pi\) | |||||||
\(198\) | 489323. | + | 334130.i | 0.887019 | + | 0.605692i | ||||
\(199\) | − | 283632.i | − | 0.507718i | −0.967241 | − | 0.253859i | \(-0.918300\pi\) | ||
0.967241 | − | 0.253859i | \(-0.0817000\pi\) | |||||||
\(200\) | 943696.i | 1.66823i | ||||||||
\(201\) | 134578. | − | 435734.i | 0.234954 | − | 0.760732i | ||||
\(202\) | − | 1.16083e6i | − | 2.00166i | ||||||
\(203\) | −183740. | − | 87471.4i | −0.312942 | − | 0.148979i | ||||
\(204\) | −273447. | + | 885364.i | −0.460042 | + | 1.48952i | ||||
\(205\) | 278229. | 0.462400 | ||||||||
\(206\) | −295473. | −0.485121 | ||||||||
\(207\) | 135455. | − | 198371.i | 0.219721 | − | 0.321774i | ||||
\(208\) | − | 124620.i | − | 0.199724i | ||||||
\(209\) | 15271.3 | 0.0241831 | ||||||||
\(210\) | −1.02772e6 | + | 1.11682e6i | −1.60814 | + | 1.74757i | ||||
\(211\) | 96651.9 | 0.149453 | 0.0747264 | − | 0.997204i | \(-0.476192\pi\) | ||||
0.0747264 | + | 0.997204i | \(0.476192\pi\) | |||||||
\(212\) | 1.45606e6i | 2.22505i | ||||||||
\(213\) | −805617. | − | 248817.i | −1.21669 | − | 0.375777i | ||||
\(214\) | −1.67114e6 | −2.49447 | ||||||||
\(215\) | 1.16088e6 | 1.71274 | ||||||||
\(216\) | 990218. | + | 1.24444e6i | 1.44410 | + | 1.81485i | ||||
\(217\) | −615257. | − | 292900.i | −0.886966 | − | 0.422250i | ||||
\(218\) | − | 827911.i | − | 1.17989i | ||||||
\(219\) | 1.09781e6 | + | 339060.i | 1.54673 | + | 0.477712i | ||||
\(220\) | − | 1.27301e6i | − | 1.77327i | ||||||
\(221\) | 51624.8i | 0.0711014i | ||||||||
\(222\) | 1.72571e6 | + | 532989.i | 2.35009 | + | 0.725832i | ||||
\(223\) | 438734.i | 0.590798i | 0.955374 | + | 0.295399i | \(0.0954526\pi\) | ||||
−0.955374 | + | 0.295399i | \(0.904547\pi\) | |||||||
\(224\) | −785624. | − | 374005.i | −1.04615 | − | 0.498032i | ||||
\(225\) | −451079. | − | 308015.i | −0.594013 | − | 0.405616i | ||||
\(226\) | −1.70903e6 | −2.22576 | ||||||||
\(227\) | −702045. | −0.904275 | −0.452137 | − | 0.891948i | \(-0.649338\pi\) | ||||
−0.452137 | + | 0.891948i | \(0.649338\pi\) | |||||||
\(228\) | 69747.2 | + | 21541.6i | 0.0888567 | + | 0.0274436i | ||||
\(229\) | 418280.i | 0.527082i | 0.964648 | + | 0.263541i | \(0.0848904\pi\) | ||||
−0.964648 | + | 0.263541i | \(0.915110\pi\) | |||||||
\(230\) | −742375. | −0.925345 | ||||||||
\(231\) | 325671. | − | 353907.i | 0.401559 | − | 0.436375i | ||||
\(232\) | 659014. | 0.803849 | ||||||||
\(233\) | − | 1.19771e6i | − | 1.44531i | −0.691208 | − | 0.722656i | \(-0.742921\pi\) | ||
0.691208 | − | 0.722656i | \(-0.257079\pi\) | |||||||
\(234\) | 130311. | + | 88981.9i | 0.155576 | + | 0.106234i | ||||
\(235\) | 1.70325e6 | 2.01191 | ||||||||
\(236\) | −2.51881e6 | −2.94385 | ||||||||
\(237\) | 226519. | − | 733421.i | 0.261959 | − | 0.848169i | ||||
\(238\) | 976909. | + | 465069.i | 1.11792 | + | 0.532200i | ||||
\(239\) | 1.24466e6i | 1.40947i | 0.709470 | + | 0.704736i | \(0.248935\pi\) | ||||
−0.709470 | + | 0.704736i | \(0.751065\pi\) | |||||||
\(240\) | 663009. | − | 2.14669e6i | 0.743004 | − | 2.40570i | ||||
\(241\) | − | 23511.7i | − | 0.0260760i | −0.999915 | − | 0.0130380i | \(-0.995850\pi\) | ||
0.999915 | − | 0.0130380i | \(-0.00415024\pi\) | |||||||
\(242\) | − | 1.06980e6i | − | 1.17426i | ||||||
\(243\) | −918031. | + | 67140.6i | −0.997336 | + | 0.0729406i | ||||
\(244\) | − | 882716.i | − | 0.949176i | ||||||
\(245\) | 776711. | + | 956241.i | 0.826693 | + | 1.01778i | ||||
\(246\) | −579252. | − | 178903.i | −0.610281 | − | 0.188487i | ||||
\(247\) | 4066.90 | 0.00424152 | ||||||||
\(248\) | 2.20672e6 | 2.27834 | ||||||||
\(249\) | −517217. | + | 1.67464e6i | −0.528658 | + | 1.71168i | ||||
\(250\) | − | 658802.i | − | 0.666661i | ||||||
\(251\) | 483287. | 0.484195 | 0.242098 | − | 0.970252i | \(-0.422165\pi\) | ||||
0.242098 | + | 0.970252i | \(0.422165\pi\) | |||||||
\(252\) | 1.98662e6 | − | 1.15698e6i | 1.97067 | − | 1.14769i | ||||
\(253\) | 235250. | 0.231062 | ||||||||
\(254\) | 1.37633e6i | 1.33856i | ||||||||
\(255\) | −274656. | + | 889281.i | −0.264508 | + | 0.856424i | ||||
\(256\) | −1.77402e6 | −1.69184 | ||||||||
\(257\) | 697129. | 0.658386 | 0.329193 | − | 0.944263i | \(-0.393223\pi\) | ||||
0.329193 | + | 0.944263i | \(0.393223\pi\) | |||||||
\(258\) | −2.41687e6 | − | 746454.i | −2.26049 | − | 0.698159i | ||||
\(259\) | 630164. | − | 1.32370e6i | 0.583720 | − | 1.22614i | ||||
\(260\) | − | 339015.i | − | 0.311018i | ||||||
\(261\) | −215097. | + | 315003.i | −0.195449 | + | 0.286229i | ||||
\(262\) | 2.11446e6i | 1.90303i | ||||||||
\(263\) | − | 454708.i | − | 0.405363i | −0.979245 | − | 0.202681i | \(-0.935034\pi\) | ||
0.979245 | − | 0.202681i | \(-0.0649655\pi\) | |||||||
\(264\) | −459620. | + | 1.48816e6i | −0.405872 | + | 1.31413i | ||||
\(265\) | 1.46250e6i | 1.27933i | ||||||||
\(266\) | 36637.2 | − | 76959.0i | 0.0317481 | − | 0.0666892i | ||||
\(267\) | 330230. | − | 1.06922e6i | 0.283490 | − | 0.917883i | ||||
\(268\) | 2.13494e6 | 1.81572 | ||||||||
\(269\) | 1.26132e6 | 1.06278 | 0.531392 | − | 0.847126i | \(-0.321669\pi\) | ||||
0.531392 | + | 0.847126i | \(0.321669\pi\) | |||||||
\(270\) | 1.77132e6 | + | 2.22608e6i | 1.47873 | + | 1.85836i | ||||
\(271\) | − | 1.75801e6i | − | 1.45411i | −0.686577 | − | 0.727057i | \(-0.740888\pi\) | ||
0.686577 | − | 0.727057i | \(-0.259112\pi\) | |||||||
\(272\) | −1.60166e6 | −1.31265 | ||||||||
\(273\) | 86729.3 | − | 94249.0i | 0.0704303 | − | 0.0765367i | ||||
\(274\) | 1.07126e6 | 0.862024 | ||||||||
\(275\) | − | 534939.i | − | 0.426552i | ||||||
\(276\) | 1.07443e6 | + | 331841.i | 0.848998 | + | 0.262215i | ||||
\(277\) | −579921. | −0.454119 | −0.227059 | − | 0.973881i | \(-0.572911\pi\) | ||||
−0.227059 | + | 0.973881i | \(0.572911\pi\) | |||||||
\(278\) | 1.09190e6 | 0.847365 | ||||||||
\(279\) | −720256. | + | 1.05479e6i | −0.553958 | + | 0.811255i | ||||
\(280\) | −3.60218e6 | − | 1.71486e6i | −2.74581 | − | 1.30717i | ||||
\(281\) | − | 887445.i | − | 0.670464i | −0.942136 | − | 0.335232i | \(-0.891185\pi\) | ||
0.942136 | − | 0.335232i | \(-0.108815\pi\) | |||||||
\(282\) | −3.54603e6 | − | 1.09520e6i | −2.65534 | − | 0.820108i | ||||
\(283\) | − | 695661.i | − | 0.516335i | −0.966100 | − | 0.258167i | \(-0.916881\pi\) | ||
0.966100 | − | 0.258167i | \(-0.0831186\pi\) | |||||||
\(284\) | − | 3.94723e6i | − | 2.90400i | ||||||
\(285\) | 70055.8 | + | 21636.9i | 0.0510896 | + | 0.0157791i | ||||
\(286\) | 154538.i | 0.111717i | ||||||||
\(287\) | −211521. | + | 444314.i | −0.151582 | + | 0.318409i | ||||
\(288\) | −919699. | + | 1.34687e6i | −0.653378 | + | 0.956853i | ||||
\(289\) | −756356. | −0.532698 | ||||||||
\(290\) | 1.17886e6 | 0.823125 | ||||||||
\(291\) | 268564. | + | 82946.7i | 0.185916 | + | 0.0574205i | ||||
\(292\) | 5.37885e6i | 3.69175i | ||||||||
\(293\) | −2.41780e6 | −1.64533 | −0.822663 | − | 0.568530i | \(-0.807513\pi\) | ||||
−0.822663 | + | 0.568530i | \(0.807513\pi\) | |||||||
\(294\) | −1.00218e6 | − | 2.49025e6i | −0.676206 | − | 1.68025i | ||||
\(295\) | −2.52996e6 | −1.69261 | ||||||||
\(296\) | 4.74769e6i | 3.14958i | ||||||||
\(297\) | −561310. | − | 705417.i | −0.369242 | − | 0.464039i | ||||
\(298\) | 2.40252e6 | 1.56721 | ||||||||
\(299\) | 62649.3 | 0.0405264 | ||||||||
\(300\) | 754579. | − | 2.44317e6i | 0.484063 | − | 1.56730i | ||||
\(301\) | −882548. | + | 1.85385e6i | −0.561464 | + | 1.17940i | ||||
\(302\) | 848807.i | 0.535539i | ||||||||
\(303\) | −521187. | + | 1.68750e6i | −0.326127 | + | 1.05593i | ||||
\(304\) | 126176.i | 0.0783056i | ||||||||
\(305\) | − | 886622.i | − | 0.545744i | ||||||
\(306\) | 1.14363e6 | − | 1.67481e6i | 0.698202 | − | 1.02250i | ||||
\(307\) | − | 2.10484e6i | − | 1.27460i | −0.770617 | − | 0.637298i | \(-0.780052\pi\) | ||
0.770617 | − | 0.637298i | \(-0.219948\pi\) | |||||||
\(308\) | 2.03292e6 | + | 967795.i | 1.22108 | + | 0.581308i | ||||
\(309\) | 429528. | + | 132661.i | 0.255914 | + | 0.0790397i | ||||
\(310\) | 3.94742e6 | 2.33297 | ||||||||
\(311\) | −1.33156e6 | −0.780657 | −0.390328 | − | 0.920676i | \(-0.627639\pi\) | ||||
−0.390328 | + | 0.920676i | \(0.627639\pi\) | |||||||
\(312\) | −122401. | + | 396310.i | −0.0711868 | + | 0.230488i | ||||
\(313\) | 2.68703e6i | 1.55028i | 0.631788 | + | 0.775142i | \(0.282322\pi\) | ||||
−0.631788 | + | 0.775142i | \(0.717678\pi\) | |||||||
\(314\) | 676079. | 0.386967 | ||||||||
\(315\) | 1.99541e6 | − | 1.16210e6i | 1.13307 | − | 0.659882i | ||||
\(316\) | 3.59349e6 | 2.02441 | ||||||||
\(317\) | − | 1.36978e6i | − | 0.765602i | −0.923831 | − | 0.382801i | \(-0.874959\pi\) | ||
0.923831 | − | 0.382801i | \(-0.125041\pi\) | |||||||
\(318\) | 940400. | − | 3.04482e6i | 0.521489 | − | 1.68847i | ||||
\(319\) | −373565. | −0.205537 | ||||||||
\(320\) | 428372. | 0.233854 | ||||||||
\(321\) | 2.42933e6 | + | 750304.i | 1.31590 | + | 0.406419i | ||||
\(322\) | 564384. | − | 1.18553e6i | 0.303343 | − | 0.637194i | ||||
\(323\) | − | 52269.3i | − | 0.0278767i | ||||||
\(324\) | −1.56856e6 | − | 4.01356e6i | −0.830116 | − | 2.12406i | ||||
\(325\) | − | 142459.i | − | 0.0748140i | ||||||
\(326\) | 3.35732e6i | 1.74964i | ||||||||
\(327\) | −371713. | + | 1.20353e6i | −0.192237 | + | 0.622425i | ||||
\(328\) | − | 1.59361e6i | − | 0.817894i | ||||||
\(329\) | −1.29488e6 | + | 2.71998e6i | −0.659537 | + | 1.38540i | ||||
\(330\) | −822177. | + | 2.66204e6i | −0.415605 | + | 1.34564i | ||||
\(331\) | 675406. | 0.338840 | 0.169420 | − | 0.985544i | \(-0.445811\pi\) | ||||
0.169420 | + | 0.985544i | \(0.445811\pi\) | |||||||
\(332\) | −8.20513e6 | −4.08545 | ||||||||
\(333\) | −2.26936e6 | − | 1.54961e6i | −1.12148 | − | 0.765792i | ||||
\(334\) | 989317.i | 0.485254i | ||||||||
\(335\) | 2.14438e6 | 1.04398 | ||||||||
\(336\) | 2.92408e6 | + | 2.69078e6i | 1.41300 | + | 1.30026i | ||||
\(337\) | 1.11714e6 | 0.535838 | 0.267919 | − | 0.963442i | \(-0.413664\pi\) | ||||
0.267919 | + | 0.963442i | \(0.413664\pi\) | |||||||
\(338\) | − | 3.76304e6i | − | 1.79162i | ||||||
\(339\) | 2.48440e6 | + | 767314.i | 1.17415 | + | 0.362638i | ||||
\(340\) | −4.35715e6 | −2.04411 | ||||||||
\(341\) | −1.25089e6 | −0.582551 | ||||||||
\(342\) | −131938. | − | 90092.8i | −0.0609966 | − | 0.0416510i | ||||
\(343\) | −2.11754e6 | + | 513386.i | −0.971846 | + | 0.235618i | ||||
\(344\) | − | 6.64916e6i | − | 3.02950i | ||||||
\(345\) | 1.07919e6 | + | 333309.i | 0.488145 | + | 0.150765i | ||||
\(346\) | − | 1.40457e6i | − | 0.630744i | ||||||
\(347\) | − | 805408.i | − | 0.359081i | −0.983751 | − | 0.179540i | \(-0.942539\pi\) | ||
0.983751 | − | 0.179540i | \(-0.0574611\pi\) | |||||||
\(348\) | −1.70615e6 | − | 526948.i | −0.755211 | − | 0.233249i | ||||
\(349\) | − | 3.67675e6i | − | 1.61585i | −0.589287 | − | 0.807924i | \(-0.700591\pi\) | ||
0.589287 | − | 0.807924i | \(-0.299409\pi\) | |||||||
\(350\) | −2.69579e6 | − | 1.28336e6i | −1.17630 | − | 0.559989i | ||||
\(351\) | −149482. | − | 187859.i | −0.0647622 | − | 0.0813889i | ||||
\(352\) | −1.59727e6 | −0.687102 | ||||||||
\(353\) | 2.54872e6 | 1.08864 | 0.544321 | − | 0.838877i | \(-0.316787\pi\) | ||||
0.544321 | + | 0.838877i | \(0.316787\pi\) | |||||||
\(354\) | 5.26718e6 | + | 1.62678e6i | 2.23393 | + | 0.689955i | ||||
\(355\) | − | 3.96469e6i | − | 1.66970i | ||||||
\(356\) | 5.23877e6 | 2.19081 | ||||||||
\(357\) | −1.21132e6 | − | 1.11468e6i | −0.503025 | − | 0.462891i | ||||
\(358\) | −2.08687e6 | −0.860572 | ||||||||
\(359\) | 2.74337e6i | 1.12344i | 0.827329 | + | 0.561718i | \(0.189859\pi\) | ||||
−0.827329 | + | 0.561718i | \(0.810141\pi\) | |||||||
\(360\) | −4.21693e6 | + | 6.17558e6i | −1.71491 | + | 2.51143i | ||||
\(361\) | 2.47198e6 | 0.998337 | ||||||||
\(362\) | 7.51302e6 | 3.01330 | ||||||||
\(363\) | −480316. | + | 1.55517e6i | −0.191320 | + | 0.619456i | ||||
\(364\) | 541386. | + | 257733.i | 0.214168 | + | 0.101957i | ||||
\(365\) | 5.40265e6i | 2.12263i | ||||||||
\(366\) | −570104. | + | 1.84588e6i | −0.222460 | + | 0.720279i | ||||
\(367\) | 3.04407e6i | 1.17975i | 0.807495 | + | 0.589874i | \(0.200823\pi\) | ||||
−0.807495 | + | 0.589874i | \(0.799177\pi\) | |||||||
\(368\) | 1.94370e6i | 0.748185i | ||||||||
\(369\) | 761732. | + | 520141.i | 0.291230 | + | 0.198864i | ||||
\(370\) | 8.49275e6i | 3.22511i | ||||||||
\(371\) | −2.33553e6 | − | 1.11185e6i | −0.880948 | − | 0.419385i | ||||
\(372\) | −5.71307e6 | − | 1.76449e6i | −2.14049 | − | 0.661094i | ||||
\(373\) | −1.13635e6 | −0.422902 | −0.211451 | − | 0.977389i | \(-0.567819\pi\) | ||||
−0.211451 | + | 0.977389i | \(0.567819\pi\) | |||||||
\(374\) | 1.98618e6 | 0.734241 | ||||||||
\(375\) | −295787. | + | 957697.i | −0.108618 | + | 0.351682i | ||||
\(376\) | − | 9.75568e6i | − | 3.55867i | ||||||
\(377\) | −99484.1 | −0.0360496 | ||||||||
\(378\) | −4.90154e6 | + | 1.13633e6i | −1.76442 | + | 0.409050i | ||||
\(379\) | 2.11965e6 | 0.757995 | 0.378998 | − | 0.925398i | \(-0.376269\pi\) | ||||
0.378998 | + | 0.925398i | \(0.376269\pi\) | |||||||
\(380\) | 343248.i | 0.121941i | ||||||||
\(381\) | 617941. | − | 2.00077e6i | 0.218089 | − | 0.706129i | ||||
\(382\) | −7.87525e6 | −2.76125 | ||||||||
\(383\) | −4.43402e6 | −1.54455 | −0.772273 | − | 0.635291i | \(-0.780880\pi\) | ||||
−0.772273 | + | 0.635291i | \(0.780880\pi\) | |||||||
\(384\) | 2.30703e6 | + | 712531.i | 0.798408 | + | 0.246590i | ||||
\(385\) | 2.04192e6 | + | 972077.i | 0.702079 | + | 0.334233i | ||||
\(386\) | 2.84894e6i | 0.973229i | ||||||||
\(387\) | 3.17824e6 | + | 2.17023e6i | 1.07872 | + | 0.736595i | ||||
\(388\) | 1.31587e6i | 0.443744i | ||||||||
\(389\) | 495729.i | 0.166100i | 0.996545 | + | 0.0830502i | \(0.0264662\pi\) | ||||
−0.996545 | + | 0.0830502i | \(0.973534\pi\) | |||||||
\(390\) | −218954. | + | 708927.i | −0.0728939 | + | 0.236015i | ||||
\(391\) | − | 805192.i | − | 0.266353i | ||||||
\(392\) | 5.47705e6 | − | 4.44876e6i | 1.80025 | − | 1.46226i | ||||
\(393\) | 949343. | − | 3.07378e6i | 0.310057 | − | 1.00390i | ||||
\(394\) | 2.29812e6 | 0.745816 | ||||||||
\(395\) | 3.60939e6 | 1.16397 | ||||||||
\(396\) | 2.37986e6 | − | 3.48524e6i | 0.762629 | − | 1.11685i | ||||
\(397\) | − | 19953.4i | − | 0.00635392i | −0.999995 | − | 0.00317696i | \(-0.998989\pi\) | ||
0.999995 | − | 0.00317696i | \(-0.00101126\pi\) | |||||||
\(398\) | −2.90604e6 | −0.919588 | ||||||||
\(399\) | −87812.1 | + | 95425.6i | −0.0276135 | + | 0.0300077i | ||||
\(400\) | 4.41981e6 | 1.38119 | ||||||||
\(401\) | − | 3.27975e6i | − | 1.01854i | −0.860606 | − | 0.509272i | \(-0.829915\pi\) | ||
0.860606 | − | 0.509272i | \(-0.170085\pi\) | |||||||
\(402\) | −4.46445e6 | − | 1.37885e6i | −1.37785 | − | 0.425552i | ||||
\(403\) | −333124. | −0.102175 | ||||||||
\(404\) | −8.26810e6 | −2.52030 | ||||||||
\(405\) | −1.57550e6 | − | 4.03132e6i | −0.477289 | − | 1.22126i | ||||
\(406\) | −896214. | + | 1.88256e6i | −0.269834 | + | 0.566805i | ||||
\(407\) | − | 2.69125e6i | − | 0.805319i | ||||||
\(408\) | 5.09353e6 | + | 1.57315e6i | 1.51485 | + | 0.467863i | ||||
\(409\) | − | 1.89585e6i | − | 0.560396i | −0.959942 | − | 0.280198i | \(-0.909600\pi\) | ||
0.959942 | − | 0.280198i | \(-0.0904001\pi\) | |||||||
\(410\) | − | 2.85068e6i | − | 0.837507i | ||||||
\(411\) | −1.55729e6 | − | 480972.i | −0.454741 | − | 0.140448i | ||||
\(412\) | 2.10453e6i | 0.610817i | ||||||||
\(413\) | 1.92338e6 | − | 4.04019e6i | 0.554867 | − | 1.16554i | ||||
\(414\) | −2.03247e6 | − | 1.38785e6i | −0.582804 | − | 0.397962i | ||||
\(415\) | −8.24143e6 | −2.34900 | ||||||||
\(416\) | −425368. | −0.120512 | ||||||||
\(417\) | −1.58729e6 | − | 490237.i | −0.447008 | − | 0.138059i | ||||
\(418\) | − | 156467.i | − | 0.0438008i | ||||||
\(419\) | −151699. | −0.0422130 | −0.0211065 | − | 0.999777i | \(-0.506719\pi\) | ||||
−0.0211065 | + | 0.999777i | \(0.506719\pi\) | |||||||
\(420\) | 7.95464e6 | + | 7.31998e6i | 2.20038 | + | 2.02482i | ||||
\(421\) | 4.56414e6 | 1.25503 | 0.627514 | − | 0.778605i | \(-0.284072\pi\) | ||||
0.627514 | + | 0.778605i | \(0.284072\pi\) | |||||||
\(422\) | − | 990276.i | − | 0.270692i | ||||||
\(423\) | 4.66313e6 | + | 3.18417e6i | 1.26715 | + | 0.865258i | ||||
\(424\) | 8.37677e6 | 2.26288 | ||||||||
\(425\) | −1.83094e6 | −0.491702 | ||||||||
\(426\) | −2.54932e6 | + | 8.25419e6i | −0.680614 | + | 2.20369i | ||||
\(427\) | 1.41588e6 | + | 674046.i | 0.375800 | + | 0.178904i | ||||
\(428\) | 1.19028e7i | 3.14080i | ||||||||
\(429\) | 69383.8 | − | 224651.i | 0.0182018 | − | 0.0589338i | ||||
\(430\) | − | 1.18941e7i | − | 3.10214i | ||||||
\(431\) | 2.09819e6i | 0.544065i | 0.962288 | + | 0.272033i | \(0.0876959\pi\) | ||||
−0.962288 | + | 0.272033i | \(0.912304\pi\) | |||||||
\(432\) | 5.82835e6 | − | 4.63770e6i | 1.50258 | − | 1.19562i | ||||
\(433\) | − | 1.90211e6i | − | 0.487545i | −0.969832 | − | 0.243773i | \(-0.921615\pi\) | ||
0.969832 | − | 0.243773i | \(-0.0783850\pi\) | |||||||
\(434\) | −3.00099e6 | + | 6.30379e6i | −0.764787 | + | 1.60649i | ||||
\(435\) | −1.71370e6 | − | 529279.i | −0.434221 | − | 0.134110i | ||||
\(436\) | −5.89685e6 | −1.48561 | ||||||||
\(437\) | −63431.4 | −0.0158892 | ||||||||
\(438\) | 3.47394e6 | − | 1.12479e7i | 0.865241 | − | 2.80147i | ||||
\(439\) | 5.44478e6i | 1.34840i | 0.738548 | + | 0.674200i | \(0.235512\pi\) | ||||
−0.738548 | + | 0.674200i | \(0.764488\pi\) | |||||||
\(440\) | −7.32368e6 | −1.80342 | ||||||||
\(441\) | 338804. | + | 4.07002e6i | 0.0829568 | + | 0.996553i | ||||
\(442\) | 528938. | 0.128780 | ||||||||
\(443\) | − | 3.14646e6i | − | 0.761750i | −0.924626 | − | 0.380875i | \(-0.875623\pi\) | ||
0.924626 | − | 0.380875i | \(-0.124377\pi\) | |||||||
\(444\) | 3.79625e6 | − | 1.22915e7i | 0.913898 | − | 2.95901i | ||||
\(445\) | 5.26194e6 | 1.25964 | ||||||||
\(446\) | 4.49518e6 | 1.07006 | ||||||||
\(447\) | −3.49253e6 | − | 1.07868e6i | −0.826746 | − | 0.255342i | ||||
\(448\) | −325665. | + | 684083.i | −0.0766614 | + | 0.161033i | ||||
\(449\) | − | 3.39222e6i | − | 0.794086i | −0.917800 | − | 0.397043i | \(-0.870036\pi\) | ||
0.917800 | − | 0.397043i | \(-0.129964\pi\) | |||||||
\(450\) | −3.15586e6 | + | 4.62166e6i | −0.734659 | + | 1.07589i | ||||
\(451\) | 903345.i | 0.209128i | ||||||||
\(452\) | 1.21727e7i | 2.80246i | ||||||||
\(453\) | 381094. | − | 1.23391e6i | 0.0872543 | − | 0.282512i | ||||
\(454\) | 7.19301e6i | 1.63784i | ||||||||
\(455\) | 543782. | + | 258873.i | 0.123139 | + | 0.0586218i | ||||
\(456\) | 123929. | − | 401258.i | 0.0279102 | − | 0.0903674i | ||||
\(457\) | 1.15372e6 | 0.258411 | 0.129206 | − | 0.991618i | \(-0.458757\pi\) | ||||
0.129206 | + | 0.991618i | \(0.458757\pi\) | |||||||
\(458\) | 4.28561e6 | 0.954660 | ||||||||
\(459\) | −2.41444e6 | + | 1.92120e6i | −0.534914 | + | 0.425639i | ||||
\(460\) | 5.28761e6i | 1.16511i | ||||||||
\(461\) | −1.23356e6 | −0.270339 | −0.135170 | − | 0.990822i | \(-0.543158\pi\) | ||||
−0.135170 | + | 0.990822i | \(0.543158\pi\) | |||||||
\(462\) | −3.62606e6 | − | 3.33676e6i | −0.790370 | − | 0.727310i | ||||
\(463\) | −3.22552e6 | −0.699274 | −0.349637 | − | 0.936885i | \(-0.613695\pi\) | ||||
−0.349637 | + | 0.936885i | \(0.613695\pi\) | |||||||
\(464\) | − | 3.08650e6i | − | 0.665536i | ||||||
\(465\) | −5.73835e6 | − | 1.77230e6i | −1.23071 | − | 0.380106i | ||||
\(466\) | −1.22715e7 | −2.61777 | ||||||||
\(467\) | 2.58165e6 | 0.547780 | 0.273890 | − | 0.961761i | \(-0.411690\pi\) | ||||
0.273890 | + | 0.961761i | \(0.411690\pi\) | |||||||
\(468\) | 633779. | − | 928152.i | 0.133759 | − | 0.195886i | ||||
\(469\) | −1.63025e6 | + | 3.42445e6i | −0.342232 | + | 0.718883i | ||||
\(470\) | − | 1.74511e7i | − | 3.64400i | ||||||
\(471\) | −982813. | − | 303544.i | −0.204135 | − | 0.0630477i | ||||
\(472\) | 1.44908e7i | 2.99390i | ||||||||
\(473\) | 3.76911e6i | 0.774615i | ||||||||
\(474\) | −7.51448e6 | − | 2.32087e6i | −1.53622 | − | 0.474465i | ||||
\(475\) | 144238.i | 0.0293323i | ||||||||
\(476\) | 3.31248e6 | − | 6.95810e6i | 0.670094 | − | 1.40758i | ||||
\(477\) | −2.73411e6 | + | 4.00402e6i | −0.550199 | + | 0.805751i | ||||
\(478\) | 1.27525e7 | 2.55286 | ||||||||
\(479\) | 2.84704e6 | 0.566962 | 0.283481 | − | 0.958978i | \(-0.408511\pi\) | ||||
0.283481 | + | 0.958978i | \(0.408511\pi\) | |||||||
\(480\) | −7.32732e6 | − | 2.26306e6i | −1.45158 | − | 0.448325i | ||||
\(481\) | − | 716706.i | − | 0.141247i | ||||||
\(482\) | −240896. | −0.0472293 | ||||||||
\(483\) | −1.35272e6 | + | 1.47000e6i | −0.263839 | + | 0.286714i | ||||
\(484\) | −7.61974e6 | −1.47852 | ||||||||
\(485\) | 1.32169e6i | 0.255138i | ||||||||
\(486\) | 687909. | + | 9.40596e6i | 0.132111 | + | 1.80639i | ||||
\(487\) | 5382.73 | 0.00102844 | 0.000514221 | − | 1.00000i | \(-0.499836\pi\) | ||||
0.000514221 | 1.00000i | \(0.499836\pi\) | ||||||||
\(488\) | −5.07830e6 | −0.965314 | ||||||||
\(489\) | 1.50736e6 | − | 4.88051e6i | 0.285065 | − | 0.922982i | ||||
\(490\) | 9.79745e6 | − | 7.95802e6i | 1.84341 | − | 1.49732i | ||||
\(491\) | 623789.i | 0.116771i | 0.998294 | + | 0.0583853i | \(0.0185952\pi\) | ||||
−0.998294 | + | 0.0583853i | \(0.981405\pi\) | |||||||
\(492\) | −1.27425e6 | + | 4.12576e6i | −0.237324 | + | 0.768407i | ||||
\(493\) | 1.27861e6i | 0.236930i | ||||||||
\(494\) | − | 41668.7i | − | 0.00768232i | ||||||
\(495\) | 2.39039e6 | − | 3.50066e6i | 0.438486 | − | 0.642150i | ||||
\(496\) | − | 1.03352e7i | − | 1.88632i | ||||||
\(497\) | 6.33137e6 | + | 3.01412e6i | 1.14976 | + | 0.547355i | ||||
\(498\) | 1.71580e7 | + | 5.29930e6i | 3.10023 | + | 0.957514i | ||||
\(499\) | 5.48238e6 | 0.985640 | 0.492820 | − | 0.870131i | \(-0.335966\pi\) | ||||
0.492820 | + | 0.870131i | \(0.335966\pi\) | |||||||
\(500\) | −4.69236e6 | −0.839395 | ||||||||
\(501\) | 444180. | − | 1.43816e6i | 0.0790615 | − | 0.255985i | ||||
\(502\) | − | 4.95166e6i | − | 0.876983i | ||||||
\(503\) | 7.04138e6 | 1.24090 | 0.620452 | − | 0.784245i | \(-0.286949\pi\) | ||||
0.620452 | + | 0.784245i | \(0.286949\pi\) | |||||||
\(504\) | −6.65613e6 | − | 1.14291e7i | −1.16720 | − | 2.00418i | ||||
\(505\) | −8.30469e6 | −1.44909 | ||||||||
\(506\) | − | 2.41032e6i | − | 0.418503i | ||||||
\(507\) | −1.68952e6 | + | 5.47031e6i | −0.291906 | + | 0.945130i | ||||
\(508\) | 9.80301e6 | 1.68539 | ||||||||
\(509\) | 1.23522e6 | 0.211325 | 0.105663 | − | 0.994402i | \(-0.466304\pi\) | ||||
0.105663 | + | 0.994402i | \(0.466304\pi\) | |||||||
\(510\) | 9.11139e6 | + | 2.81407e6i | 1.55117 | + | 0.479082i | ||||
\(511\) | −8.62769e6 | − | 4.10731e6i | −1.46165 | − | 0.695833i | ||||
\(512\) | 1.32197e7i | 2.22867i | ||||||||
\(513\) | 151348. | + | 190205.i | 0.0253913 | + | 0.0319101i | ||||
\(514\) | − | 7.14265e6i | − | 1.19248i | ||||||
\(515\) | 2.11384e6i | 0.351199i | ||||||||
\(516\) | −5.31667e6 | + | 1.72143e7i | −0.879054 | + | 2.84620i | ||||
\(517\) | 5.53005e6i | 0.909920i | ||||||||
\(518\) | −1.35624e7 | − | 6.45653e6i | −2.22081 | − | 1.05724i | ||||
\(519\) | −630619. | + | 2.04181e6i | −0.102766 | + | 0.332735i | ||||
\(520\) | −1.95037e6 | −0.316306 | ||||||||
\(521\) | −2.65806e6 | −0.429013 | −0.214506 | − | 0.976723i | \(-0.568814\pi\) | ||||
−0.214506 | + | 0.976723i | \(0.568814\pi\) | |||||||
\(522\) | 3.22746e6 | + | 2.20384e6i | 0.518423 | + | 0.354000i | ||||
\(523\) | − | 8.11005e6i | − | 1.29649i | −0.761432 | − | 0.648245i | \(-0.775503\pi\) | ||
0.761432 | − | 0.648245i | \(-0.224497\pi\) | |||||||
\(524\) | 1.50604e7 | 2.39611 | ||||||||
\(525\) | 3.34266e6 | + | 3.07597e6i | 0.529290 | + | 0.487061i | ||||
\(526\) | −4.65885e6 | −0.734200 | ||||||||
\(527\) | 4.28144e6i | 0.671526i | ||||||||
\(528\) | 6.96980e6 | + | 2.15264e6i | 1.08802 | + | 0.336036i | ||||
\(529\) | 5.45920e6 | 0.848184 | ||||||||
\(530\) | 1.49845e7 | 2.31714 | ||||||||
\(531\) | −6.92649e6 | − | 4.72968e6i | −1.06605 | − | 0.727940i | ||||
\(532\) | −548145. | − | 260951.i | −0.0839686 | − | 0.0399742i | ||||
\(533\) | 240570.i | 0.0366794i | ||||||||
\(534\) | −1.09550e7 | − | 3.38347e6i | −1.66249 | − | 0.513463i | ||||
\(535\) | 1.19555e7i | 1.80585i | ||||||||
\(536\) | − | 1.22824e7i | − | 1.84659i | ||||||
\(537\) | 3.03367e6 | + | 936955.i | 0.453975 | + | 0.140211i | ||||
\(538\) | − | 1.29232e7i | − | 1.92493i | ||||||
\(539\) | −3.10469e6 | + | 2.52180e6i | −0.460306 | + | 0.373886i | ||||
\(540\) | 1.58554e7 | − | 1.26163e7i | 2.33987 | − | 1.86187i | ||||
\(541\) | 4.11443e6 | 0.604389 | 0.302194 | − | 0.953246i | \(-0.402281\pi\) | ||||
0.302194 | + | 0.953246i | \(0.402281\pi\) | |||||||
\(542\) | −1.80122e7 | −2.63372 | ||||||||
\(543\) | −1.09216e7 | − | 3.37317e6i | −1.58960 | − | 0.490951i | ||||
\(544\) | 5.46699e6i | 0.792047i | ||||||||
\(545\) | −5.92294e6 | −0.854173 | ||||||||
\(546\) | −965656. | − | 888611.i | −0.138625 | − | 0.127565i | ||||
\(547\) | 8.29884e6 | 1.18590 | 0.592952 | − | 0.805238i | \(-0.297963\pi\) | ||||
0.592952 | + | 0.805238i | \(0.297963\pi\) | |||||||
\(548\) | − | 7.63013e6i | − | 1.08538i | ||||||
\(549\) | 1.65752e6 | − | 2.42738e6i | 0.234707 | − | 0.343722i | ||||
\(550\) | −5.48087e6 | −0.772579 | ||||||||
\(551\) | 100726. | 0.0141339 | ||||||||
\(552\) | 1.90909e6 | − | 6.18125e6i | 0.266673 | − | 0.863432i | ||||
\(553\) | −2.74401e6 | + | 5.76398e6i | −0.381568 | + | 0.801511i | ||||
\(554\) | 5.94175e6i | 0.822508i | ||||||||
\(555\) | 3.81305e6 | − | 1.23459e7i | 0.525460 | − | 1.70133i | ||||
\(556\) | − | 7.77712e6i | − | 1.06692i | ||||||
\(557\) | − | 1.30905e7i | − | 1.78780i | −0.448269 | − | 0.893899i | \(-0.647959\pi\) | ||
0.448269 | − | 0.893899i | \(-0.352041\pi\) | |||||||
\(558\) | 1.08072e7 | + | 7.37960e6i | 1.46936 | + | 1.00334i | ||||
\(559\) | 1.00375e6i | 0.135861i | ||||||||
\(560\) | −8.03157e6 | + | 1.68709e7i | −1.08226 | + | 2.27336i | ||||
\(561\) | −2.88729e6 | − | 891746.i | −0.387332 | − | 0.119628i | ||||
\(562\) | −9.09258e6 | −1.21436 | ||||||||
\(563\) | −1.39979e7 | −1.86119 | −0.930595 | − | 0.366051i | \(-0.880710\pi\) | ||||
−0.930595 | + | 0.366051i | \(0.880710\pi\) | |||||||
\(564\) | −7.80064e6 | + | 2.52569e7i | −1.03260 | + | 3.34335i | ||||
\(565\) | 1.22265e7i | 1.61132i | ||||||||
\(566\) | −7.12760e6 | −0.935195 | ||||||||
\(567\) | 7.63552e6 | + | 548793.i | 0.997427 | + | 0.0716887i | ||||
\(568\) | −2.27085e7 | −2.95337 | ||||||||
\(569\) | 7.90475e6i | 1.02355i | 0.859121 | + | 0.511773i | \(0.171011\pi\) | ||||
−0.859121 | + | 0.511773i | \(0.828989\pi\) | |||||||
\(570\) | 221687. | − | 717778.i | 0.0285794 | − | 0.0925343i | ||||
\(571\) | 2.34007e6 | 0.300358 | 0.150179 | − | 0.988659i | \(-0.452015\pi\) | ||||
0.150179 | + | 0.988659i | \(0.452015\pi\) | |||||||
\(572\) | 1.10070e6 | 0.140663 | ||||||||
\(573\) | 1.14482e7 | + | 3.53580e6i | 1.45664 | + | 0.449885i | ||||
\(574\) | 4.55236e6 | + | 2.16720e6i | 0.576709 | + | 0.274549i | ||||
\(575\) | 2.22194e6i | 0.280261i | ||||||||
\(576\) | 1.17279e6 | + | 800829.i | 0.147287 | + | 0.100573i | ||||
\(577\) | − | 1.34986e7i | − | 1.68791i | −0.536417 | − | 0.843953i | \(-0.680223\pi\) | ||
0.536417 | − | 0.843953i | \(-0.319777\pi\) | |||||||
\(578\) | 7.74947e6i | 0.964833i | ||||||||
\(579\) | 1.27911e6 | − | 4.14149e6i | 0.158566 | − | 0.513405i | ||||
\(580\) | − | 8.39648e6i | − | 1.03640i | ||||||
\(581\) | 6.26547e6 | − | 1.31611e7i | 0.770040 | − | 1.61752i | ||||
\(582\) | 849855. | − | 2.75166e6i | 0.104001 | − | 0.336734i | ||||
\(583\) | −4.74841e6 | −0.578598 | ||||||||
\(584\) | 3.09447e7 | 3.75452 | ||||||||
\(585\) | 636584. | − | 932258.i | 0.0769070 | − | 0.112628i | ||||
\(586\) | 2.47723e7i | 2.98004i | ||||||||
\(587\) | −3.29677e6 | −0.394906 | −0.197453 | − | 0.980312i | \(-0.563267\pi\) | ||||
−0.197453 | + | 0.980312i | \(0.563267\pi\) | |||||||
\(588\) | −1.77370e7 | + | 7.13812e6i | −2.11561 | + | 0.851414i | ||||
\(589\) | 337283. | 0.0400596 | ||||||||
\(590\) | 2.59214e7i | 3.06569i | ||||||||
\(591\) | −3.34076e6 | − | 1.03180e6i | −0.393438 | − | 0.121514i | ||||
\(592\) | 2.22359e7 | 2.60765 | ||||||||
\(593\) | −142588. | −0.0166512 | −0.00832562 | − | 0.999965i | \(-0.502650\pi\) | ||||
−0.00832562 | + | 0.999965i | \(0.502650\pi\) | |||||||
\(594\) | −7.22756e6 | + | 5.75107e6i | −0.840476 | + | 0.668778i | ||||
\(595\) | 3.32714e6 | − | 6.98888e6i | 0.385282 | − | 0.809311i | ||||
\(596\) | − | 1.71121e7i | − | 1.97328i | ||||||
\(597\) | 4.22449e6 | + | 1.30474e6i | 0.485108 | + | 0.149827i | ||||
\(598\) | − | 641892.i | − | 0.0734022i | ||||||
\(599\) | − | 7.94570e6i | − | 0.904826i | −0.891808 | − | 0.452413i | \(-0.850563\pi\) | ||
0.891808 | − | 0.452413i | \(-0.149437\pi\) | |||||||
\(600\) | −1.40557e7 | − | 4.34112e6i | −1.59394 | − | 0.492293i | ||||
\(601\) | − | 9.95474e6i | − | 1.12420i | −0.827069 | − | 0.562100i | \(-0.809994\pi\) | ||
0.827069 | − | 0.562100i | \(-0.190006\pi\) | |||||||
\(602\) | 1.89942e7 | + | 9.04241e6i | 2.13614 | + | 1.01693i | ||||
\(603\) | 5.87087e6 | + | 4.00886e6i | 0.657520 | + | 0.448981i | ||||
\(604\) | 6.04568e6 | 0.674299 | ||||||||
\(605\) | −7.65345e6 | −0.850098 | ||||||||
\(606\) | 1.72897e7 | + | 5.33997e6i | 1.91252 | + | 0.590687i | ||||
\(607\) | − | 1.09452e7i | − | 1.20574i | −0.797841 | − | 0.602868i | \(-0.794025\pi\) | ||
0.797841 | − | 0.602868i | \(-0.205975\pi\) | |||||||
\(608\) | 430679. | 0.0472492 | ||||||||
\(609\) | 2.14805e6 | − | 2.33429e6i | 0.234693 | − | 0.255042i | ||||
\(610\) | −9.08415e6 | −0.988461 | ||||||||
\(611\) | 1.47271e6i | 0.159593i | ||||||||
\(612\) | −1.19289e7 | − | 8.14557e6i | −1.28743 | − | 0.879109i | ||||
\(613\) | −4.24023e6 | −0.455762 | −0.227881 | − | 0.973689i | \(-0.573180\pi\) | ||||
−0.227881 | + | 0.973689i | \(0.573180\pi\) | |||||||
\(614\) | −2.15657e7 | −2.30857 | ||||||||
\(615\) | −1.27989e6 | + | 4.14401e6i | −0.136453 | + | 0.441808i | ||||
\(616\) | 5.56776e6 | − | 1.16955e7i | 0.591192 | − | 1.24184i | ||||
\(617\) | − | 7.07280e6i | − | 0.747961i | −0.927437 | − | 0.373980i | \(-0.877993\pi\) | ||
0.927437 | − | 0.373980i | \(-0.122007\pi\) | |||||||
\(618\) | 1.35921e6 | − | 4.40085e6i | 0.143158 | − | 0.463517i | ||||
\(619\) | 1.48040e7i | 1.55293i | 0.630158 | + | 0.776467i | \(0.282990\pi\) | ||||
−0.630158 | + | 0.776467i | \(0.717010\pi\) | |||||||
\(620\) | − | 2.81158e7i | − | 2.93745i | ||||||
\(621\) | 2.33147e6 | + | 2.93004e6i | 0.242606 | + | 0.304891i | ||||
\(622\) | 1.36429e7i | 1.41394i | ||||||||
\(623\) | −4.00034e6 | + | 8.40300e6i | −0.412931 | + | 0.867390i | ||||
\(624\) | 1.85612e6 | + | 573268.i | 0.190830 | + | 0.0589381i | ||||
\(625\) | −1.17374e7 | −1.20191 | ||||||||
\(626\) | 2.75307e7 | 2.80790 | ||||||||
\(627\) | −70250.0 | + | 227455.i | −0.00713638 | + | 0.0231061i | ||||
\(628\) | − | 4.81542e6i | − | 0.487231i | ||||||
\(629\) | −9.21137e6 | −0.928320 | ||||||||
\(630\) | −1.19066e7 | − | 2.04446e7i | −1.19519 | − | 2.05223i | ||||
\(631\) | 1.72214e7 | 1.72184 | 0.860922 | − | 0.508737i | \(-0.169887\pi\) | ||||
0.860922 | + | 0.508737i | \(0.169887\pi\) | |||||||
\(632\) | − | 2.06735e7i | − | 2.05883i | ||||||
\(633\) | −444611. | + | 1.43956e6i | −0.0441033 | + | 0.142797i | ||||
\(634\) | −1.40345e7 | −1.38667 | ||||||||
\(635\) | 9.84639e6 | 0.969042 | ||||||||
\(636\) | −2.16869e7 | − | 6.69806e6i | −2.12596 | − | 0.656608i | ||||
\(637\) | −826810. | + | 671580.i | −0.0807341 | + | 0.0655766i | ||||
\(638\) | 3.82748e6i | 0.372272i | ||||||||
\(639\) | 7.41188e6 | − | 1.08545e7i | 0.718085 | − | 1.05162i | ||||
\(640\) | 1.13536e7i | 1.09568i | ||||||||
\(641\) | 1.86269e7i | 1.79059i | 0.445476 | + | 0.895294i | \(0.353035\pi\) | ||||
−0.445476 | + | 0.895294i | \(0.646965\pi\) | |||||||
\(642\) | 7.68746e6 | − | 2.48904e7i | 0.736114 | − | 2.38339i | ||||
\(643\) | 5.13948e6i | 0.490221i | 0.969495 | + | 0.245111i | \(0.0788243\pi\) | ||||
−0.969495 | + | 0.245111i | \(0.921176\pi\) | |||||||
\(644\) | −8.44399e6 | − | 4.01986e6i | −0.802293 | − | 0.381941i | ||||
\(645\) | −5.34019e6 | + | 1.72905e7i | −0.505426 | + | 1.63647i | ||||
\(646\) | −535541. | −0.0504907 | ||||||||
\(647\) | 3.15049e6 | 0.295881 | 0.147940 | − | 0.988996i | \(-0.452736\pi\) | ||||
0.147940 | + | 0.988996i | \(0.452736\pi\) | |||||||
\(648\) | −2.30901e7 | + | 9.02398e6i | −2.16017 | + | 0.844230i | ||||
\(649\) | − | 8.21419e6i | − | 0.765514i | ||||||
\(650\) | −1.45961e6 | −0.135504 | ||||||||
\(651\) | 7.19278e6 | − | 7.81641e6i | 0.665188 | − | 0.722861i | ||||
\(652\) | 2.39127e7 | 2.20298 | ||||||||
\(653\) | 1.93756e7i | 1.77817i | 0.457745 | + | 0.889083i | \(0.348657\pi\) | ||||
−0.457745 | + | 0.889083i | \(0.651343\pi\) | |||||||
\(654\) | 1.23311e7 | + | 3.80849e6i | 1.12735 | + | 0.348184i | ||||
\(655\) | 1.51270e7 | 1.37768 | ||||||||
\(656\) | −7.46369e6 | −0.677164 | ||||||||
\(657\) | −1.01001e7 | + | 1.47913e7i | −0.912877 | + | 1.33688i | ||||
\(658\) | 2.78684e7 | + | 1.32671e7i | 2.50927 | + | 1.19457i | ||||
\(659\) | − | 1.33721e7i | − | 1.19946i | −0.800201 | − | 0.599732i | \(-0.795274\pi\) | ||
0.800201 | − | 0.599732i | \(-0.204726\pi\) | |||||||
\(660\) | 1.89606e7 | + | 5.85601e6i | 1.69430 | + | 0.523290i | ||||
\(661\) | − | 1.20025e7i | − | 1.06848i | −0.845333 | − | 0.534241i | \(-0.820598\pi\) | ||
0.845333 | − | 0.534241i | \(-0.179402\pi\) | |||||||
\(662\) | − | 6.92007e6i | − | 0.613714i | ||||||
\(663\) | −768913. | − | 237481.i | −0.0679350 | − | 0.0209819i | ||||
\(664\) | 4.72044e7i | 4.15491i | ||||||||
\(665\) | −550571. | − | 262105.i | −0.0482791 | − | 0.0229838i | ||||
\(666\) | −1.58770e7 | + | 2.32514e7i | −1.38702 | + | 2.03125i | ||||
\(667\) | 1.55165e6 | 0.135045 | ||||||||
\(668\) | 7.04647e6 | 0.610985 | ||||||||
\(669\) | −6.53462e6 | − | 2.01823e6i | −0.564488 | − | 0.174343i | ||||
\(670\) | − | 2.19709e7i | − | 1.89087i | ||||||
\(671\) | 2.87866e6 | 0.246822 | ||||||||
\(672\) | 9.18450e6 | − | 9.98081e6i | 0.784571 | − | 0.852595i | ||||
\(673\) | −1.60189e7 | −1.36331 | −0.681654 | − | 0.731675i | \(-0.738739\pi\) | ||||
−0.681654 | + | 0.731675i | \(0.738739\pi\) | |||||||
\(674\) | − | 1.14460e7i | − | 0.970519i | ||||||
\(675\) | 6.66267e6 | − | 5.30158e6i | 0.562845 | − | 0.447863i | ||||
\(676\) | −2.68025e7 | −2.25584 | ||||||||
\(677\) | 1.36964e7 | 1.14851 | 0.574257 | − | 0.818675i | \(-0.305291\pi\) | ||||
0.574257 | + | 0.818675i | \(0.305291\pi\) | |||||||
\(678\) | 7.86174e6 | − | 2.54547e7i | 0.656817 | − | 2.12664i | ||||
\(679\) | −2.11065e6 | − | 1.00480e6i | −0.175688 | − | 0.0836384i | ||||
\(680\) | 2.50668e7i | 2.07887i | ||||||||
\(681\) | 3.22949e6 | − | 1.04564e7i | 0.266850 | − | 0.864005i | ||||
\(682\) | 1.28164e7i | 1.05513i | ||||||||
\(683\) | 1.15151e7i | 0.944532i | 0.881456 | + | 0.472266i | \(0.156564\pi\) | ||||
−0.881456 | + | 0.472266i | \(0.843436\pi\) | |||||||
\(684\) | −641692. | + | 939739.i | −0.0524429 | + | 0.0768010i | ||||
\(685\) | − | 7.66389e6i | − | 0.624055i | ||||||
\(686\) | 5.26005e6 | + | 2.16959e7i | 0.426756 | + | 1.76022i | ||||
\(687\) | −6.22996e6 | − | 1.92414e6i | −0.503609 | − | 0.155541i | ||||
\(688\) | −3.11414e7 | −2.50823 | ||||||||
\(689\) | −1.26455e6 | −0.101482 | ||||||||
\(690\) | 3.41502e6 | − | 1.10571e7i | 0.273068 | − | 0.884137i | ||||
\(691\) | 3.17540e6i | 0.252990i | 0.991967 | + | 0.126495i | \(0.0403728\pi\) | ||||
−0.991967 | + | 0.126495i | \(0.959627\pi\) | |||||||
\(692\) | −1.00041e7 | −0.794171 | ||||||||
\(693\) | 3.77306e6 | + | 6.47864e6i | 0.298443 | + | 0.512450i | ||||
\(694\) | −8.25205e6 | −0.650374 | ||||||||
\(695\) | − | 7.81153e6i | − | 0.613443i | ||||||
\(696\) | −3.03155e6 | + | 9.81552e6i | −0.237214 | + | 0.768052i | ||||
\(697\) | 3.09189e6 | 0.241069 | ||||||||
\(698\) | −3.76712e7 | −2.92665 | ||||||||
\(699\) | 1.78390e7 | + | 5.50961e6i | 1.38095 | + | 0.426509i | ||||
\(700\) | −9.14083e6 | + | 1.92010e7i | −0.705084 | + | 1.48108i | ||||
\(701\) | − | 508437.i | − | 0.0390789i | −0.999809 | − | 0.0195394i | \(-0.993780\pi\) | ||
0.999809 | − | 0.0195394i | \(-0.00621999\pi\) | |||||||
\(702\) | −1.92477e6 | + | 1.53156e6i | −0.147413 | + | 0.117299i | ||||
\(703\) | 725654.i | 0.0553785i | ||||||||
\(704\) | 1.39082e6i | 0.105765i | ||||||||
\(705\) | −7.83515e6 | + | 2.53686e7i | −0.593710 | + | 1.92231i | ||||
\(706\) | − | 2.61137e7i | − | 1.97177i | ||||||
\(707\) | 6.31356e6 | − | 1.32621e7i | 0.475035 | − | 0.997845i | ||||
\(708\) | 1.15868e7 | − | 3.75158e7i | 0.868725 | − | 2.81275i | ||||
\(709\) | −1.24662e7 | −0.931366 | −0.465683 | − | 0.884952i | \(-0.654191\pi\) | ||||
−0.465683 | + | 0.884952i | \(0.654191\pi\) | |||||||
\(710\) | −4.06214e7 | −3.02419 | ||||||||
\(711\) | 9.88175e6 | + | 6.74766e6i | 0.733094 | + | 0.500586i | ||||
\(712\) | − | 3.01388e7i | − | 2.22805i | ||||||
\(713\) | 5.19574e6 | 0.382757 | ||||||||
\(714\) | −1.14208e7 | + | 1.24110e7i | −0.838396 | + | 0.911087i | ||||
\(715\) | 1.10557e6 | 0.0808766 | ||||||||
\(716\) | 1.48638e7i | 1.08355i | ||||||||
\(717\) | −1.85383e7 | − | 5.72560e6i | −1.34670 | − | 0.415932i | ||||
\(718\) | 2.81080e7 | 2.03479 | ||||||||
\(719\) | −1.61840e7 | −1.16752 | −0.583760 | − | 0.811926i | \(-0.698419\pi\) | ||||
−0.583760 | + | 0.811926i | \(0.698419\pi\) | |||||||
\(720\) | 2.89234e7 | + | 1.97501e7i | 2.07930 | + | 1.41983i | ||||
\(721\) | −3.37567e6 | − | 1.60702e6i | −0.241836 | − | 0.115129i | ||||
\(722\) | − | 2.53274e7i | − | 1.80821i | ||||||
\(723\) | 350189. | + | 108157.i | 0.0249147 | + | 0.00769498i | ||||
\(724\) | − | 5.35119e7i | − | 3.79406i | ||||||
\(725\) | − | 3.52833e6i | − | 0.249301i | ||||||
\(726\) | 1.59339e7 | + | 4.92122e6i | 1.12197 | + | 0.346523i | ||||
\(727\) | 1.37063e7i | 0.961796i | 0.876776 | + | 0.480898i | \(0.159689\pi\) | ||||
−0.876776 | + | 0.480898i | \(0.840311\pi\) | |||||||
\(728\) | 1.48275e6 | − | 3.11461e6i | 0.103690 | − | 0.217809i | ||||
\(729\) | 3.22305e6 | − | 1.39822e7i | 0.224620 | − | 0.974447i | ||||
\(730\) | 5.53544e7 | 3.84455 | ||||||||
\(731\) | 1.29006e7 | 0.892926 | ||||||||
\(732\) | 1.31474e7 | + | 4.06061e6i | 0.906906 | + | 0.280100i | ||||
\(733\) | 2.11177e7i | 1.45173i | 0.687837 | + | 0.725865i | \(0.258560\pi\) | ||||
−0.687837 | + | 0.725865i | \(0.741440\pi\) | |||||||
\(734\) | 3.11889e7 | 2.13678 | ||||||||
\(735\) | −1.78155e7 | + | 7.16970e6i | −1.21641 | + | 0.489534i | ||||
\(736\) | 6.63446e6 | 0.451451 | ||||||||
\(737\) | 6.96232e6i | 0.472156i | ||||||||
\(738\) | 5.32926e6 | − | 7.80455e6i | 0.360185 | − | 0.527481i | ||||
\(739\) | −2.27372e7 | −1.53153 | −0.765765 | − | 0.643121i | \(-0.777639\pi\) | ||||
−0.765765 | + | 0.643121i | \(0.777639\pi\) | |||||||
\(740\) | 6.04902e7 | 4.06074 | ||||||||
\(741\) | −18708.3 | + | 60573.5i | −0.00125166 | + | 0.00405263i | ||||
\(742\) | −1.13918e7 | + | 2.39293e7i | −0.759598 | + | 1.59559i | ||||
\(743\) | − | 8.15459e6i | − | 0.541914i | −0.962592 | − | 0.270957i | \(-0.912660\pi\) | ||
0.962592 | − | 0.270957i | \(-0.0873400\pi\) | |||||||
\(744\) | −1.01512e7 | + | 3.28675e7i | −0.672334 | + | 2.17688i | ||||
\(745\) | − | 1.71878e7i | − | 1.13457i | ||||||
\(746\) | 1.16428e7i | 0.765967i | ||||||||
\(747\) | −2.25633e7 | − | 1.54071e7i | −1.47945 | − | 1.01023i | ||||
\(748\) | − | 1.41467e7i | − | 0.924485i | ||||||
\(749\) | −1.90922e7 | − | 9.08904e6i | −1.24351 | − | 0.591989i | ||||
\(750\) | 9.81237e6 | + | 3.03057e6i | 0.636973 | + | 0.196730i | ||||
\(751\) | −9.59688e6 | −0.620912 | −0.310456 | − | 0.950588i | \(-0.600482\pi\) | ||||
−0.310456 | + | 0.950588i | \(0.600482\pi\) | |||||||
\(752\) | −4.56908e7 | −2.94635 | ||||||||
\(753\) | −2.22318e6 | + | 7.19820e6i | −0.142885 | + | 0.462633i | ||||
\(754\) | 1.01929e6i | 0.0652936i | ||||||||
\(755\) | 6.07243e6 | 0.387699 | ||||||||
\(756\) | 8.09362e6 | + | 3.49115e7i | 0.515037 | + | 2.22159i | ||||
\(757\) | −1.27794e7 | −0.810535 | −0.405267 | − | 0.914198i | \(-0.632822\pi\) | ||||
−0.405267 | + | 0.914198i | \(0.632822\pi\) | |||||||
\(758\) | − | 2.17175e7i | − | 1.37289i | ||||||
\(759\) | −1.08218e6 | + | 3.50387e6i | −0.0681859 | + | 0.220772i | ||||
\(760\) | 1.97472e6 | 0.124014 | ||||||||
\(761\) | 1.82472e7 | 1.14218 | 0.571091 | − | 0.820886i | \(-0.306520\pi\) | ||||
0.571091 | + | 0.820886i | \(0.306520\pi\) | |||||||
\(762\) | −2.04994e7 | − | 6.33130e6i | −1.27895 | − | 0.395007i | ||||
\(763\) | 4.50286e6 | − | 9.45857e6i | 0.280012 | − | 0.588185i | ||||
\(764\) | 5.60920e7i | 3.47670i | ||||||||
\(765\) | −1.19817e7 | − | 8.18161e6i | −0.740229 | − | 0.505458i | ||||
\(766\) | 4.54301e7i | 2.79751i | ||||||||
\(767\) | − | 2.18752e6i | − | 0.134265i | ||||||
\(768\) | 8.16073e6 | − | 2.64228e7i | 0.499259 | − | 1.61650i | ||||
\(769\) | 1.88190e6i | 0.114757i | 0.998352 | + | 0.0573787i | \(0.0182743\pi\) | ||||
−0.998352 | + | 0.0573787i | \(0.981726\pi\) | |||||||
\(770\) | 9.95970e6 | − | 2.09211e7i | 0.605368 | − | 1.27162i | ||||
\(771\) | −3.20688e6 | + | 1.03832e7i | −0.194288 | + | 0.629066i | ||||
\(772\) | 2.02918e7 | 1.22540 | ||||||||
\(773\) | 1.03151e7 | 0.620903 | 0.310452 | − | 0.950589i | \(-0.399520\pi\) | ||||
0.310452 | + | 0.950589i | \(0.399520\pi\) | |||||||
\(774\) | 2.22358e7 | − | 3.25636e7i | 1.33413 | − | 1.95380i | ||||
\(775\) | − | 1.18147e7i | − | 0.706590i | ||||||
\(776\) | 7.57022e6 | 0.451288 | ||||||||
\(777\) | 1.68168e7 | + | 1.54750e7i | 0.999285 | + | 0.919558i | ||||
\(778\) | 5.07914e6 | 0.300844 | ||||||||
\(779\) | − | 243573.i | − | 0.0143809i | ||||||
\(780\) | 5.04938e6 | + | 1.55951e6i | 0.297168 | + | 0.0917809i | ||||
\(781\) | 1.28724e7 | 0.755150 | ||||||||
\(782\) | −8.24983e6 | −0.482423 | ||||||||
\(783\) | −3.70227e6 | − | 4.65276e6i | −0.215806 | − | 0.271210i | ||||
\(784\) | −2.08358e7 | − | 2.56518e7i | −1.21065 | − | 1.49049i | ||||
\(785\) | − | 4.83672e6i | − | 0.280141i | ||||||
\(786\) | −3.14933e7 | − | 9.72677e6i | −1.81828 | − | 0.561581i | ||||
\(787\) | 3.28643e6i | 0.189142i | 0.995518 | + | 0.0945709i | \(0.0301479\pi\) | ||||
−0.995518 | + | 0.0945709i | \(0.969852\pi\) | |||||||
\(788\) | − | 1.63685e7i | − | 0.939059i | ||||||
\(789\) | 6.77254e6 | + | 2.09171e6i | 0.387311 | + | 0.119622i | ||||
\(790\) | − | 3.69811e7i | − | 2.10820i | ||||||
\(791\) | −1.95250e7 | − | 9.29509e6i | −1.10956 | − | 0.528217i | ||||
\(792\) | −2.00507e7 | − | 1.36914e7i | −1.13584 | − | 0.775595i | ||||
\(793\) | 766614. | 0.0432906 | ||||||||
\(794\) | −204439. | −0.0115083 | ||||||||
\(795\) | −2.17829e7 | − | 6.72770e6i | −1.22236 | − | 0.377527i | ||||
\(796\) | 2.06984e7i | 1.15786i | ||||||||
\(797\) | 2.39117e7 | 1.33341 | 0.666706 | − | 0.745321i | \(-0.267704\pi\) | ||||
0.666706 | + | 0.745321i | \(0.267704\pi\) | |||||||
\(798\) | 977711. | + | 899705.i | 0.0543505 | + | 0.0500141i | ||||
\(799\) | 1.89278e7 | 1.04890 | ||||||||
\(800\) | − | 1.50862e7i | − | 0.833404i | ||||||
\(801\) | 1.44061e7 | + | 9.83706e6i | 0.793350 | + | 0.541731i | ||||
\(802\) | −3.36036e7 | −1.84480 | ||||||||
\(803\) | −1.75411e7 | −0.959995 | ||||||||
\(804\) | −9.82097e6 | + | 3.17983e7i | −0.535814 | + | 1.73486i | ||||
\(805\) | −8.48136e6 | − | 4.03764e6i | −0.461292 | − | 0.219603i | ||||
\(806\) | 3.41313e6i | 0.185061i | ||||||||
\(807\) | −5.80223e6 | + | 1.87864e7i | −0.313625 | + | 1.01545i | ||||
\(808\) | 4.75667e7i | 2.56315i | ||||||||
\(809\) | − | 8.55140e6i | − | 0.459374i | −0.973265 | − | 0.229687i | \(-0.926230\pi\) | ||
0.973265 | − | 0.229687i | \(-0.0737702\pi\) | |||||||
\(810\) | −4.13040e7 | + | 1.61423e7i | −2.21197 | + | 0.864474i | ||||
\(811\) | 1.95536e7i | 1.04394i | 0.852965 | + | 0.521968i | \(0.174802\pi\) | ||||
−0.852965 | + | 0.521968i | \(0.825198\pi\) | |||||||
\(812\) | 1.34087e7 | + | 6.38334e6i | 0.713667 | + | 0.339749i | ||||
\(813\) | 2.61843e7 | + | 8.08707e6i | 1.38936 | + | 0.429106i | ||||
\(814\) | −2.75740e7 | −1.45861 | ||||||||
\(815\) | 2.40185e7 | 1.26664 | ||||||||
\(816\) | 7.36785e6 | − | 2.38556e7i | 0.387361 | − | 1.25419i | ||||
\(817\) | − | 1.01628e6i | − | 0.0532671i | ||||||
\(818\) | −1.94245e7 | −1.01500 | ||||||||
\(819\) | 1.00480e6 | + | 1.72533e6i | 0.0523445 | + | 0.0898796i | ||||
\(820\) | −2.03041e7 | −1.05451 | ||||||||
\(821\) | 3.61123e6i | 0.186981i | 0.995620 | + | 0.0934905i | \(0.0298025\pi\) | ||||
−0.995620 | + | 0.0934905i | \(0.970198\pi\) | |||||||
\(822\) | −4.92794e6 | + | 1.59556e7i | −0.254382 | + | 0.823635i | ||||
\(823\) | 2.73413e7 | 1.40708 | 0.703541 | − | 0.710654i | \(-0.251601\pi\) | ||||
0.703541 | + | 0.710654i | \(0.251601\pi\) | |||||||
\(824\) | 1.21074e7 | 0.621202 | ||||||||
\(825\) | 7.96752e6 | + | 2.46079e6i | 0.407557 | + | 0.125875i | ||||
\(826\) | −4.13949e7 | − | 1.97065e7i | −2.11104 | − | 1.00499i | ||||
\(827\) | 1.08272e7i | 0.550491i | 0.961374 | + | 0.275246i | \(0.0887592\pi\) | ||||
−0.961374 | + | 0.275246i | \(0.911241\pi\) | |||||||
\(828\) | −9.88505e6 | + | 1.44764e7i | −0.501075 | + | 0.733810i | ||||
\(829\) | − | 3.47853e7i | − | 1.75796i | −0.476856 | − | 0.878982i | \(-0.658224\pi\) | ||
0.476856 | − | 0.878982i | \(-0.341776\pi\) | |||||||
\(830\) | 8.44400e7i | 4.25455i | ||||||||
\(831\) | 2.66771e6 | − | 8.63749e6i | 0.134010 | − | 0.433896i | ||||
\(832\) | 370390.i | 0.0185503i | ||||||||
\(833\) | 8.63139e6 | + | 1.06265e7i | 0.430991 | + | 0.530611i | ||||
\(834\) | −5.02287e6 | + | 1.62630e7i | −0.250056 | + | 0.809629i | ||||
\(835\) | 7.07765e6 | 0.351296 | ||||||||
\(836\) | −1.11445e6 | −0.0551497 | ||||||||
\(837\) | −1.23971e7 | − | 1.55799e7i | −0.611655 | − | 0.768688i | ||||
\(838\) | 1.55427e6i | 0.0764570i | ||||||||
\(839\) | −1.55238e7 | −0.761363 | −0.380681 | − | 0.924706i | \(-0.624311\pi\) | ||||
−0.380681 | + | 0.924706i | \(0.624311\pi\) | |||||||
\(840\) | 4.21121e7 | − | 4.57633e7i | 2.05925 | − | 2.23779i | ||||
\(841\) | 1.80472e7 | 0.879873 | ||||||||
\(842\) | − | 4.67632e7i | − | 2.27313i | ||||||
\(843\) | 1.32178e7 | + | 4.08236e6i | 0.640606 | + | 0.197853i | ||||
\(844\) | −7.05330e6 | −0.340829 | ||||||||
\(845\) | −2.69211e7 | −1.29703 | ||||||||
\(846\) | 3.26244e7 | − | 4.77775e7i | 1.56717 | − | 2.29508i | ||||
\(847\) | 5.81846e6 | − | 1.22221e7i | 0.278676 | − | 0.585379i | ||||
\(848\) | − | 3.92327e7i | − | 1.87352i | ||||||
\(849\) | 1.03614e7 | + | 3.20013e6i | 0.493341 | + | 0.152369i | ||||
\(850\) | 1.87594e7i | 0.890579i | ||||||||
\(851\) | 1.11785e7i | 0.529124i | ||||||||
\(852\) | 5.87910e7 | + | 1.81577e7i | 2.77467 | + | 0.856964i | ||||
\(853\) | 2.03197e7i | 0.956189i | 0.878308 | + | 0.478095i | \(0.158672\pi\) | ||||
−0.878308 | + | 0.478095i | \(0.841328\pi\) | |||||||
\(854\) | 6.90614e6 | − | 1.45068e7i | 0.324034 | − | 0.680656i | ||||
\(855\) | −644531. | + | 943897.i | −0.0301529 | + | 0.0441580i | ||||
\(856\) | 6.84773e7 | 3.19420 | ||||||||
\(857\) | 1.04717e6 | 0.0487043 | 0.0243521 | − | 0.999703i | \(-0.492248\pi\) | ||||
0.0243521 | + | 0.999703i | \(0.492248\pi\) | |||||||
\(858\) | −2.30172e6 | − | 710892.i | −0.106742 | − | 0.0329675i | ||||
\(859\) | 1.42509e7i | 0.658958i | 0.944163 | + | 0.329479i | \(0.106873\pi\) | ||||
−0.944163 | + | 0.329479i | \(0.893127\pi\) | |||||||
\(860\) | −8.47168e7 | −3.90592 | ||||||||
\(861\) | −5.64471e6 | − | 5.19435e6i | −0.259498 | − | 0.238794i | ||||
\(862\) | 2.14976e7 | 0.985421 | ||||||||
\(863\) | 3.45867e7i | 1.58082i | 0.612578 | + | 0.790410i | \(0.290132\pi\) | ||||
−0.612578 | + | 0.790410i | \(0.709868\pi\) | |||||||
\(864\) | −1.58299e7 | − | 1.98940e7i | −0.721431 | − | 0.906646i | ||||
\(865\) | −1.00484e7 | −0.456622 | ||||||||
\(866\) | −1.94886e7 | −0.883051 | ||||||||
\(867\) | 3.47933e6 | − | 1.12654e7i | 0.157198 | − | 0.508976i | ||||
\(868\) | 4.48992e7 | + | 2.13748e7i | 2.02274 | + | 0.962946i | ||||
\(869\) | 1.17189e7i | 0.526425i | ||||||||
\(870\) | −5.42289e6 | + | 1.75582e7i | −0.242903 | + | 0.786469i | ||||
\(871\) | 1.85413e6i | 0.0828124i | ||||||||
\(872\) | 3.39248e7i | 1.51086i | ||||||||
\(873\) | −2.47086e6 | + | 3.61850e6i | −0.109727 | + | 0.160692i | ||||
\(874\) | 649905.i | 0.0287787i | ||||||||
\(875\) | 3.58311e6 | − | 7.52657e6i | 0.158212 | − | 0.332336i | ||||
\(876\) | −8.01139e7 | − | 2.47434e7i | −3.52734 | − | 1.08943i | ||||
\(877\) | 3.46186e7 | 1.51988 | 0.759942 | − | 0.649990i | \(-0.225227\pi\) | ||||
0.759942 | + | 0.649990i | \(0.225227\pi\) | |||||||
\(878\) | 5.57861e7 | 2.44225 | ||||||||
\(879\) | 1.11222e7 | − | 3.60114e7i | 0.485532 | − | 1.57205i | ||||
\(880\) | 3.43005e7i | 1.49312i | ||||||||
\(881\) | −1.09303e7 | −0.474451 | −0.237226 | − | 0.971455i | \(-0.576238\pi\) | ||||
−0.237226 | + | 0.971455i | \(0.576238\pi\) | |||||||
\(882\) | 4.17006e7 | − | 3.47132e6i | 1.80497 | − | 0.150253i | ||||
\(883\) | −4.16221e7 | −1.79648 | −0.898240 | − | 0.439505i | \(-0.855154\pi\) | ||||
−0.898240 | + | 0.439505i | \(0.855154\pi\) | |||||||
\(884\) | − | 3.76739e6i | − | 0.162147i | ||||||
\(885\) | 1.16381e7 | − | 3.76818e7i | 0.499487 | − | 1.61724i | ||||
\(886\) | −3.22380e7 | −1.37970 | ||||||||
\(887\) | 1.21043e7 | 0.516572 | 0.258286 | − | 0.966068i | \(-0.416842\pi\) | ||||
0.258286 | + | 0.966068i | \(0.416842\pi\) | |||||||
\(888\) | −7.07133e7 | − | 2.18400e7i | −3.00932 | − | 0.929436i | ||||
\(889\) | −7.48562e6 | + | 1.57241e7i | −0.317668 | + | 0.667284i | ||||
\(890\) | − | 5.39128e7i | − | 2.28148i | ||||||
\(891\) | 1.30888e7 | − | 5.11529e6i | 0.552337 | − | 0.215862i | ||||
\(892\) | − | 3.20172e7i | − | 1.34732i | ||||||
\(893\) | − | 1.49109e6i | − | 0.0625714i | ||||||
\(894\) | −1.10519e7 | + | 3.57838e7i | −0.462480 | + | 1.49742i | ||||
\(895\) | 1.49296e7i | 0.623004i | ||||||||
\(896\) | −1.81310e7 | − | 8.63146e6i | −0.754487 | − | 0.359182i | ||||
\(897\) | −288194. | + | 933114.i | −0.0119593 | + | 0.0387216i | ||||
\(898\) | −3.47560e7 | −1.43826 | ||||||||
\(899\) | −8.25058e6 | −0.340475 | ||||||||
\(900\) | 3.29181e7 | + | 2.24778e7i | 1.35465 | + | 0.925012i | ||||
\(901\) | 1.62524e7i | 0.666970i | ||||||||
\(902\) | 9.25549e6 | 0.378777 | ||||||||
\(903\) | −2.35520e7 | − | 2.16729e7i | −0.961186 | − | 0.884498i | ||||
\(904\) | 7.00297e7 | 2.85011 | ||||||||
\(905\) | − | 5.37487e7i | − | 2.18146i | ||||||
\(906\) | −1.26423e7 | − | 3.90462e6i | −0.511690 | − | 0.158037i | ||||
\(907\) | −1.45100e7 | −0.585664 | −0.292832 | − | 0.956164i | \(-0.594598\pi\) | ||||
−0.292832 | + | 0.956164i | \(0.594598\pi\) | |||||||
\(908\) | 5.12327e7 | 2.06221 | ||||||||
\(909\) | −2.27365e7 | − | 1.55254e7i | −0.912669 | − | 0.623207i | ||||
\(910\) | 2.65236e6 | − | 5.57148e6i | 0.106177 | − | 0.223032i | ||||
\(911\) | − | 4.04836e6i | − | 0.161616i | −0.996730 | − | 0.0808078i | \(-0.974250\pi\) | ||
0.996730 | − | 0.0808078i | \(-0.0257500\pi\) | |||||||
\(912\) | −1.87930e6 | − | 580425.i | −0.0748184 | − | 0.0231078i | ||||
\(913\) | − | 2.67580e7i | − | 1.06237i | ||||||
\(914\) | − | 1.18208e7i | − | 0.468040i | ||||||
\(915\) | 1.32056e7 | + | 4.07857e6i | 0.521440 | + | 0.161048i | ||||
\(916\) | − | 3.05245e7i | − | 1.20202i | ||||||
\(917\) | −1.15002e7 | + | 2.41569e7i | −0.451628 | + | 0.948676i | ||||
\(918\) | 1.96842e7 | + | 2.47378e7i | 0.770924 | + | 0.968846i | ||||
\(919\) | −4.05052e6 | −0.158206 | −0.0791028 | − | 0.996866i | \(-0.525206\pi\) | ||||
−0.0791028 | + | 0.996866i | \(0.525206\pi\) | |||||||
\(920\) | 3.04198e7 | 1.18491 | ||||||||
\(921\) | 3.13500e7 | + | 9.68252e6i | 1.21784 | + | 0.376131i | ||||
\(922\) | 1.26388e7i | 0.489644i | ||||||||
\(923\) | 3.42805e6 | 0.132447 | ||||||||
\(924\) | −2.37663e7 | + | 2.58269e7i | −0.915759 | + | 0.995158i | ||||
\(925\) | 2.54189e7 | 0.976792 | ||||||||
\(926\) | 3.30480e7i | 1.26654i | ||||||||
\(927\) | −3.95176e6 | + | 5.78724e6i | −0.151040 | + | 0.221193i | ||||
\(928\) | −1.05352e7 | −0.401581 | ||||||||
\(929\) | −3.41602e7 | −1.29862 | −0.649308 | − | 0.760525i | \(-0.724941\pi\) | ||||
−0.649308 | + | 0.760525i | \(0.724941\pi\) | |||||||
\(930\) | −1.81586e7 | + | 5.87940e7i | −0.688456 | + | 2.22908i | ||||
\(931\) | 837132. | − | 679964.i | 0.0316534 | − | 0.0257106i | ||||
\(932\) | 8.74044e7i | 3.29605i | ||||||||
\(933\) | 6.12535e6 | − | 1.98326e7i | 0.230370 | − | 0.745892i | ||||
\(934\) | − | 2.64511e7i | − | 0.992148i | ||||||
\(935\) | − | 1.42093e7i | − | 0.531548i | ||||||
\(936\) | −5.33969e6 | − | 3.64615e6i | −0.199217 | − | 0.136033i | ||||
\(937\) | − | 2.79009e7i | − | 1.03817i | −0.854722 | − | 0.519086i | \(-0.826273\pi\) | ||
0.854722 | − | 0.519086i | \(-0.173727\pi\) | |||||||
\(938\) | 3.50862e7 | + | 1.67032e7i | 1.30205 | + | 0.619858i | ||||
\(939\) | −4.00213e7 | − | 1.23607e7i | −1.48124 | − | 0.457486i | ||||
\(940\) | −1.24297e8 | −4.58818 | ||||||||
\(941\) | −3.53618e7 | −1.30185 | −0.650925 | − | 0.759142i | \(-0.725619\pi\) | ||||
−0.650925 | + | 0.759142i | \(0.725619\pi\) | |||||||
\(942\) | −3.11005e6 | + | 1.00697e7i | −0.114193 | + | 0.369734i | ||||
\(943\) | − | 3.75216e6i | − | 0.137405i | ||||||
\(944\) | 6.78679e7 | 2.47876 | ||||||||
\(945\) | 8.12943e6 | + | 3.50660e7i | 0.296129 | + | 1.27734i | ||||
\(946\) | 3.86175e7 | 1.40300 | ||||||||
\(947\) | − | 1.35602e6i | − | 0.0491349i | −0.999698 | − | 0.0245675i | \(-0.992179\pi\) | ||
0.999698 | − | 0.0245675i | \(-0.00782085\pi\) | |||||||
\(948\) | −1.65305e7 | + | 5.35224e7i | −0.597400 | + | 1.93426i | ||||
\(949\) | −4.67138e6 | −0.168376 | ||||||||
\(950\) | 1.47783e6 | 0.0531271 | ||||||||
\(951\) | 2.04019e7 | + | 6.30117e6i | 0.731508 | + | 0.225928i | ||||
\(952\) | −4.00302e7 | − | 1.90568e7i | −1.43151 | − | 0.681487i | ||||
\(953\) | 3.25424e6i | 0.116069i | 0.998315 | + | 0.0580346i | \(0.0184834\pi\) | ||||
−0.998315 | + | 0.0580346i | \(0.981517\pi\) | |||||||
\(954\) | 4.10244e7 | + | 2.80131e7i | 1.45939 | + | 0.996530i | ||||
\(955\) | 5.63401e7i | 1.99898i | ||||||||
\(956\) | − | 9.08308e7i | − | 3.21432i | ||||||
\(957\) | 1.71845e6 | − | 5.56398e6i | 0.0606536 | − | 0.196384i | ||||
\(958\) | − | 2.91702e7i | − | 1.02689i | ||||||
\(959\) | 1.22388e7 | + | 5.82640e6i | 0.429725 | + | 0.204576i | ||||
\(960\) | −1.97056e6 | + | 6.38028e6i | −0.0690100 | + | 0.223440i | ||||
\(961\) | 1.00192e6 | 0.0349963 | ||||||||
\(962\) | −7.34322e6 | −0.255829 | ||||||||
\(963\) | −2.23504e7 | + | 3.27316e7i | −0.776641 | + | 1.13737i | ||||
\(964\) | 1.71580e6i | 0.0594666i | ||||||||
\(965\) | 2.03815e7 | 0.704561 | ||||||||
\(966\) | 1.50613e7 | + | 1.38596e7i | 0.519302 | + | 0.477869i | ||||
\(967\) | −1.93276e7 | −0.664680 | −0.332340 | − | 0.943160i | \(-0.607838\pi\) | ||||
−0.332340 | + | 0.943160i | \(0.607838\pi\) | |||||||
\(968\) | 4.38366e7i | 1.50366i | ||||||||
\(969\) | 778513. | + | 240445.i | 0.0266352 | + | 0.00822635i | ||||
\(970\) | 1.35417e7 | 0.462110 | ||||||||
\(971\) | 603594. | 0.0205446 | 0.0102723 | − | 0.999947i | \(-0.496730\pi\) | ||||
0.0102723 | + | 0.999947i | \(0.496730\pi\) | |||||||
\(972\) | 6.69945e7 | − | 4.89967e6i | 2.27444 | − | 0.166342i | ||||
\(973\) | 1.24745e7 | + | 5.93864e6i | 0.422418 | + | 0.201097i | ||||
\(974\) | − | 55150.3i | − | 0.00186273i | ||||||
\(975\) | 2.12183e6 | + | 655331.i | 0.0714823 | + | 0.0220775i | ||||
\(976\) | 2.37843e7i | 0.799218i | ||||||||
\(977\) | − | 8.97624e6i | − | 0.300856i | −0.988621 | − | 0.150428i | \(-0.951935\pi\) | ||
0.988621 | − | 0.150428i | \(-0.0480651\pi\) | |||||||
\(978\) | −5.00047e7 | − | 1.54441e7i | −1.67172 | − | 0.516315i | ||||
\(979\) | 1.70843e7i | 0.569693i | ||||||||
\(980\) | −5.66815e7 | − | 6.97830e7i | −1.88528 | − | 2.32105i | ||||
\(981\) | −1.62157e7 | − | 1.10728e7i | −0.537978 | − | 0.367353i | ||||
\(982\) | 6.39121e6 | 0.211497 | ||||||||
\(983\) | 6.64620e6 | 0.219376 | 0.109688 | − | 0.993966i | \(-0.465015\pi\) | ||||
0.109688 | + | 0.993966i | \(0.465015\pi\) | |||||||
\(984\) | 2.37356e7 | + | 7.33080e6i | 0.781471 | + | 0.241359i | ||||
\(985\) | − | 1.64409e7i | − | 0.539927i | ||||||
\(986\) | 1.31003e7 | 0.429131 | ||||||||
\(987\) | −3.45555e7 | − | 3.17985e7i | −1.12908 | − | 1.03900i | ||||
\(988\) | −296788. | −0.00967283 | ||||||||
\(989\) | − | 1.56555e7i | − | 0.508951i | ||||||
\(990\) | −3.58670e7 | − | 2.44914e7i | −1.16307 | − | 0.794194i | ||||
\(991\) | 2.63927e7 | 0.853689 | 0.426844 | − | 0.904325i | \(-0.359625\pi\) | ||||
0.426844 | + | 0.904325i | \(0.359625\pi\) | |||||||
\(992\) | −3.52773e7 | −1.13820 | ||||||||
\(993\) | −3.10695e6 | + | 1.00597e7i | −0.0999911 | + | 0.323751i | ||||
\(994\) | 3.08820e7 | − | 6.48699e7i | 0.991380 | − | 2.08246i | ||||
\(995\) | 2.07900e7i | 0.665728i | ||||||||
\(996\) | 3.77446e7 | − | 1.22209e8i | 1.20561 | − | 3.90351i | ||||
\(997\) | 2.42476e7i | 0.772558i | 0.922382 | + | 0.386279i | \(0.126240\pi\) | ||||
−0.922382 | + | 0.386279i | \(0.873760\pi\) | |||||||
\(998\) | − | 5.61714e7i | − | 1.78521i | ||||||
\(999\) | 3.35196e7 | − | 2.66720e7i | 1.06264 | − | 0.845554i |
(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 | 21.6.c.a.20.1 | ✓ | 12 | |
3.2 | odd | 2 | inner | 21.6.c.a.20.12 | yes | 12 | |
4.3 | odd | 2 | 336.6.k.d.209.7 | 12 | |||
7.6 | odd | 2 | inner | 21.6.c.a.20.2 | yes | 12 | |
12.11 | even | 2 | 336.6.k.d.209.5 | 12 | |||
21.20 | even | 2 | inner | 21.6.c.a.20.11 | yes | 12 | |
28.27 | even | 2 | 336.6.k.d.209.6 | 12 | |||
84.83 | odd | 2 | 336.6.k.d.209.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.c.a.20.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
21.6.c.a.20.2 | yes | 12 | 7.6 | odd | 2 | inner | |
21.6.c.a.20.11 | yes | 12 | 21.20 | even | 2 | inner | |
21.6.c.a.20.12 | yes | 12 | 3.2 | odd | 2 | inner | |
336.6.k.d.209.5 | 12 | 12.11 | even | 2 | |||
336.6.k.d.209.6 | 12 | 28.27 | even | 2 | |||
336.6.k.d.209.7 | 12 | 4.3 | odd | 2 | |||
336.6.k.d.209.8 | 12 | 84.83 | odd | 2 |