Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 33.5 | ||
Character | \(\chi\) | \(=\) | 76.33 |
Dual form | 76.7.j.a.53.5 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{7}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.55244 | + | 0.626392i | 0.131572 | + | 0.0231997i | 0.239046 | − | 0.971008i | \(-0.423165\pi\) |
−0.107474 | + | 0.994208i | \(0.534276\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.1242 | − | 8.49522i | −0.0809937 | − | 0.0679618i | 0.601392 | − | 0.798954i | \(-0.294613\pi\) |
−0.682386 | + | 0.730992i | \(0.739057\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 110.999 | + | 192.257i | 0.323614 | + | 0.560515i | 0.981231 | − | 0.192837i | \(-0.0617689\pi\) |
−0.657617 | + | 0.753352i | \(0.728436\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −672.808 | − | 244.882i | −0.922920 | − | 0.335915i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −245.534 | + | 425.277i | −0.184473 | + | 0.319517i | −0.943399 | − | 0.331660i | \(-0.892391\pi\) |
0.758926 | + | 0.651177i | \(0.225725\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1550.95 | − | 273.474i | 0.705939 | − | 0.124476i | 0.190858 | − | 0.981618i | \(-0.438873\pi\) |
0.515081 | + | 0.857142i | \(0.327762\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −30.6444 | − | 36.5205i | −0.00907981 | − | 0.0108209i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7565.82 | + | 2753.73i | −1.53996 | + | 0.560499i | −0.966036 | − | 0.258409i | \(-0.916802\pi\) |
−0.573924 | + | 0.818909i | \(0.694580\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 305.082 | + | 6852.21i | 0.0444791 | + | 0.999010i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 273.891 | + | 752.510i | 0.0295747 | + | 0.0812558i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4764.38 | + | 3997.79i | −0.391582 | + | 0.328576i | −0.817229 | − | 0.576313i | \(-0.804491\pi\) |
0.425647 | + | 0.904889i | \(0.360046\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2682.92 | − | 15215.6i | −0.171707 | − | 0.973799i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4514.09 | − | 2606.21i | −0.229340 | − | 0.132409i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −12693.0 | + | 34873.8i | −0.520440 | + | 1.42990i | 0.349592 | + | 0.936902i | \(0.386320\pi\) |
−0.870032 | + | 0.492996i | \(0.835902\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −35759.6 | + | 20645.8i | −1.20035 | + | 0.693022i | −0.960633 | − | 0.277821i | \(-0.910388\pi\) |
−0.239717 | + | 0.970843i | \(0.577055\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1138.63 | + | 1356.97i | −0.0316842 | + | 0.0377597i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 509.481 | − | 2889.41i | 0.0118829 | − | 0.0673916i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 73991.1i | 1.46074i | 0.683050 | + | 0.730372i | \(0.260653\pi\) | ||||
−0.683050 | + | 0.730372i | \(0.739347\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5680.96 | 0.0957696 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −64009.4 | − | 11286.6i | −0.928736 | − | 0.163761i | −0.311236 | − | 0.950333i | \(-0.600743\pi\) |
−0.617499 | + | 0.786571i | \(0.711854\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −57910.4 | − | 48592.6i | −0.728369 | − | 0.611174i | 0.201318 | − | 0.979526i | \(-0.435478\pi\) |
−0.929686 | + | 0.368352i | \(0.879922\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4731.33 | + | 8194.90i | 0.0519213 | + | 0.0899303i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 80803.1 | + | 29409.9i | 0.778277 | + | 0.283270i | 0.700454 | − | 0.713697i | \(-0.252981\pi\) |
0.0778231 | + | 0.996967i | \(0.475203\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 34182.7 | − | 59206.2i | 0.290548 | − | 0.503245i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −28602.1 | + | 5043.32i | −0.215619 | + | 0.0380194i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1911.87 | − | 2278.48i | −0.0128420 | − | 0.0153045i | 0.759585 | − | 0.650408i | \(-0.225402\pi\) |
−0.772427 | + | 0.635103i | \(0.780958\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6098.65 | − | 2219.73i | 0.0366561 | − | 0.0133417i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3208.38 | + | 24533.2i | −0.0173245 | + | 0.132474i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 66931.9 | + | 183894.i | 0.325894 | + | 0.895388i | 0.989139 | + | 0.146985i | \(0.0469568\pi\) |
−0.663244 | + | 0.748403i | \(0.730821\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 255234. | − | 214167.i | 1.12447 | − | 0.943544i | 0.125650 | − | 0.992075i | \(-0.459898\pi\) |
0.998822 | + | 0.0485305i | \(0.0154538\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −27601.1 | − | 156534.i | −0.110384 | − | 0.626017i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −18025.3 | − | 10406.9i | −0.0656362 | − | 0.0378951i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 115279. | − | 316726.i | 0.383288 | − | 1.05308i | −0.586674 | − | 0.809823i | \(-0.699563\pi\) |
0.969963 | − | 0.243253i | \(-0.0782147\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −19429.4 | + | 11217.5i | −0.0591441 | + | 0.0341468i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 416036. | − | 495812.i | 1.16240 | − | 1.38529i | 0.253994 | − | 0.967206i | \(-0.418256\pi\) |
0.908406 | − | 0.418089i | \(-0.137300\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −65628.3 | + | 372197.i | −0.168703 | + | 0.956762i | 0.776461 | + | 0.630165i | \(0.217013\pi\) |
−0.945164 | + | 0.326596i | \(0.894098\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 55733.1i | − | 0.132108i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −109016. | −0.238792 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 303328. | + | 53484.9i | 0.615220 | + | 0.108480i | 0.472570 | − | 0.881293i | \(-0.343326\pi\) |
0.142651 | + | 0.989773i | \(0.454438\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 385437. | + | 323420.i | 0.725268 | + | 0.608572i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −391211. | − | 677597.i | −0.684190 | − | 1.18505i | −0.973691 | − | 0.227874i | \(-0.926823\pi\) |
0.289501 | − | 0.957178i | \(-0.406511\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 99991.6 | + | 36394.0i | 0.162820 | + | 0.0592615i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −66935.9 | + | 115936.i | −0.101649 | + | 0.176060i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −103944. | + | 18328.2i | −0.147445 | + | 0.0259986i | −0.246884 | − | 0.969045i | \(-0.579407\pi\) |
0.0994382 | + | 0.995044i | \(0.468295\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 224732. | + | 267825.i | 0.298222 | + | 0.355407i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −139966. | + | 50943.6i | −0.174010 | + | 0.0633346i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 55122.3 | − | 71965.0i | 0.0642920 | − | 0.0839364i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −164328. | − | 451487.i | −0.180051 | − | 0.494687i | 0.816530 | − | 0.577303i | \(-0.195895\pi\) |
−0.996581 | + | 0.0826159i | \(0.973673\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 269340. | − | 226003.i | 0.277584 | − | 0.232921i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 159947. | + | 907103.i | 0.155243 | + | 0.880425i | 0.958564 | + | 0.284879i | \(0.0919533\pi\) |
−0.803321 | + | 0.595547i | \(0.796936\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −950614. | − | 548837.i | −0.869947 | − | 0.502264i | −0.00261628 | − | 0.999997i | \(-0.500833\pi\) |
−0.867331 | + | 0.497733i | \(0.834166\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3619.81 | − | 9945.34i | 0.00312693 | − | 0.00859116i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −359996. | + | 207844.i | −0.293864 | + | 0.169663i | −0.639683 | − | 0.768639i | \(-0.720934\pi\) |
0.345819 | + | 0.938301i | \(0.387601\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.09863e6 | + | 1.30930e6i | −0.848348 | + | 1.01102i | 0.151398 | + | 0.988473i | \(0.451622\pi\) |
−0.999746 | + | 0.0225485i | \(0.992822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −46347.4 | + | 262849.i | −0.0338888 | + | 0.192193i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.52260e6i | 1.05524i | 0.849481 | + | 0.527619i | \(0.176915\pi\) | ||||
−0.849481 | + | 0.527619i | \(0.823085\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 82197.6 | 0.0540463 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.11046e6 | − | 195804.i | −0.693338 | − | 0.122254i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.36923e6 | − | 1.14892e6i | −0.812520 | − | 0.681785i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 765207. | + | 1.32538e6i | 0.431939 | + | 0.748141i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −220320. | − | 80189.9i | −0.118396 | − | 0.0430928i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −205349. | + | 355675.i | −0.105139 | + | 0.182106i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.63595e6 | − | 288461.i | 0.798652 | − | 0.140824i | 0.240594 | − | 0.970626i | \(-0.422658\pi\) |
0.558058 | + | 0.829802i | \(0.311547\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −175285. | − | 208897.i | −0.0816539 | − | 0.0973113i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21290.1 | − | 7748.95i | 0.00947028 | − | 0.00344690i | −0.337281 | − | 0.941404i | \(-0.609507\pi\) |
0.346751 | + | 0.937957i | \(0.387285\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.28352e6 | + | 819246.i | −0.545566 | + | 0.348225i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 23561.3 | + | 64734.1i | 0.00957630 | + | 0.0263107i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.33810e6 | + | 2.80100e6i | −1.29819 | + | 1.08931i | −0.307731 | + | 0.951473i | \(0.599570\pi\) |
−0.990455 | + | 0.137835i | \(0.955986\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −210259. | − | 1.19244e6i | −0.0782907 | − | 0.444009i | −0.998604 | − | 0.0528259i | \(-0.983177\pi\) |
0.920313 | − | 0.391183i | \(-0.127934\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 268626. | + | 155091.i | 0.0958277 | + | 0.0553261i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −264508. | + | 726729.i | −0.0904545 | + | 0.248522i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 424767. | − | 245240.i | 0.139331 | − | 0.0804427i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 158519. | − | 188915.i | 0.0499032 | − | 0.0594723i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 389070. | − | 2.20653e6i | 0.117617 | − | 0.667038i | −0.867804 | − | 0.496906i | \(-0.834469\pi\) |
0.985421 | − | 0.170132i | \(-0.0544195\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.78577e6i | − | 1.09957i | −0.835306 | − | 0.549785i | \(-0.814710\pi\) | ||
0.835306 | − | 0.549785i | \(-0.185290\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.76469e6 | 1.60954 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 537429. | + | 94763.2i | 0.144320 | + | 0.0254475i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.82569e6 | + | 2.37103e6i | 0.730172 | + | 0.612687i | 0.930179 | − | 0.367107i | \(-0.119652\pi\) |
−0.200006 | + | 0.979795i | \(0.564096\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5364.60 | − | 9291.76i | −0.00133458 | − | 0.00231157i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.29744e6 | − | 472231.i | −0.310893 | − | 0.113156i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.39955e6 | − | 2.42409e6i | 0.323166 | − | 0.559741i | −0.657973 | − | 0.753041i | \(-0.728586\pi\) |
0.981140 | + | 0.193301i | \(0.0619193\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 23055.5 | − | 4065.31i | 0.00513244 | − | 0.000904987i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 254695. | + | 303534.i | 0.0546853 | + | 0.0651714i | 0.792694 | − | 0.609620i | \(-0.208678\pi\) |
−0.738008 | + | 0.674792i | \(0.764234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.20506e6 | + | 802578.i | −0.456837 | + | 0.166275i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.47272e6 | − | 4.68494e6i | 0.294532 | − | 0.936947i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.13559e6 | − | 3.12001e6i | −0.219323 | − | 0.602584i | 0.780420 | − | 0.625255i | \(-0.215005\pi\) |
−0.999743 | + | 0.0226712i | \(0.992783\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.62750e6 | − | 2.20473e6i | 0.490262 | − | 0.411379i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 122582. | + | 695198.i | 0.0221059 | + | 0.125369i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.62765e6 | + | 4.40383e6i | 1.32994 | + | 0.767841i | 0.985290 | − | 0.170891i | \(-0.0546646\pi\) |
0.344649 | + | 0.938732i | \(0.387998\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.36553e6 | − | 3.75175e6i | 0.230284 | − | 0.632700i | −0.769700 | − | 0.638406i | \(-0.779594\pi\) |
0.999984 | + | 0.00570578i | \(0.00181622\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.04086e6 | − | 600938.i | 0.169839 | − | 0.0980566i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 628571. | − | 749101.i | 0.0992748 | − | 0.118311i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 686565. | − | 3.89370e6i | 0.104992 | − | 0.595440i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.15715e6i | − | 0.171398i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.27729e7 | −1.83311 | −0.916554 | − | 0.399911i | \(-0.869041\pi\) | ||||
−0.916554 | + | 0.399911i | \(0.869041\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.43536e6 | + | 1.48738e6i | 1.17336 | + | 0.206895i | 0.726152 | − | 0.687534i | \(-0.241307\pi\) |
0.447209 | + | 0.894429i | \(0.352418\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −57515.2 | − | 48261.0i | −0.00775673 | − | 0.00650867i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.69481e6 | + | 2.93549e6i | 0.221677 | + | 0.383956i | 0.955317 | − | 0.295582i | \(-0.0955135\pi\) |
−0.733640 | + | 0.679538i | \(0.762180\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.85541e6 | + | 1.40326e6i | 0.489229 | + | 0.178065i | 0.574843 | − | 0.818264i | \(-0.305063\pi\) |
−0.0856145 | + | 0.996328i | \(0.527285\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 607917. | − | 1.05294e6i | 0.0748611 | − | 0.129663i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.11364e6 | + | 1.43065e6i | −0.969901 | + | 0.171020i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 552163. | + | 658042.i | 0.0640922 | + | 0.0763822i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.18450e6 | − | 1.52303e6i | 0.471772 | − | 0.171711i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.98899e6 | − | 1.55270e6i | −0.327406 | − | 0.170079i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.00360e6 | + | 8.25231e6i | 0.319738 | + | 0.878473i | 0.990588 | + | 0.136879i | \(0.0437073\pi\) |
−0.670850 | + | 0.741593i | \(0.734070\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.78852e6 | − | 1.50074e6i | 0.185078 | − | 0.155299i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 173492. | + | 983924.i | 0.0174568 | + | 0.0990025i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.93859e6 | − | 4.58335e6i | −0.776899 | − | 0.448543i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −466282. | + | 1.28110e6i | −0.0443931 | + | 0.121969i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.09811e7 | + | 6.33995e6i | −1.01735 | + | 0.587367i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.84800e6 | + | 4.58587e6i | −0.346993 | + | 0.413530i | −0.911109 | − | 0.412166i | \(-0.864773\pi\) |
0.564116 | + | 0.825695i | \(0.309217\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.92094e6 | + | 1.08942e7i | −0.168642 | + | 0.956417i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.57369e6i | − | 0.561994i | −0.959709 | − | 0.280997i | \(-0.909335\pi\) | ||
0.959709 | − | 0.280997i | \(-0.0906650\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 277192. | 0.0230821 | 0.0115410 | − | 0.999933i | \(-0.496326\pi\) | ||||
0.0115410 | + | 0.999933i | \(0.496326\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −387275. | − | 68287.0i | −0.0314183 | − | 0.00553990i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.81884e6 | − | 7.39989e6i | −0.697178 | − | 0.585002i | 0.223791 | − | 0.974637i | \(-0.428157\pi\) |
−0.920969 | + | 0.389635i | \(0.872601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −568224. | − | 984192.i | −0.0437840 | − | 0.0758362i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.04405e6 | + | 380004.i | 0.0784291 | + | 0.0285458i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.07572e6 | + | 3.59525e6i | −0.152046 | + | 0.263351i | −0.931979 | − | 0.362511i | \(-0.881919\pi\) |
0.779934 | + | 0.625862i | \(0.215253\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.59558e6 | − | 986651.i | 0.399755 | − | 0.0704876i | 0.0298434 | − | 0.999555i | \(-0.490499\pi\) |
0.369911 | + | 0.929067i | \(0.379388\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.60916e6 | + | 4.30123e6i | 0.251528 | + | 0.299760i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −849044. | + | 309027.i | −0.0577340 | + | 0.0210135i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.34707e6 | + | 1.05440e7i | 0.155752 | + | 0.699704i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −965313. | − | 2.65218e6i | −0.0625274 | − | 0.171793i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.15904e7 | + | 1.81165e7i | −1.36534 | + | 1.14565i | −0.391045 | + | 0.920372i | \(0.627886\pi\) |
−0.974293 | + | 0.225283i | \(0.927669\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −530351. | − | 3.00777e6i | −0.0327493 | − | 0.185730i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 332418. | + | 191921.i | 0.0200476 | + | 0.0115745i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.68345e6 | + | 1.01202e7i | −0.216998 | + | 0.596197i | −0.999655 | − | 0.0262557i | \(-0.991642\pi\) |
0.782657 | + | 0.622453i | \(0.213864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.42253e7 | + | 8.21297e6i | −0.818769 | + | 0.472717i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.70799e7 | − | 2.03551e7i | 0.960649 | − | 1.14486i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.84522e6 | + | 1.61360e7i | −0.156404 | + | 0.887012i | 0.801087 | + | 0.598549i | \(0.204256\pi\) |
−0.957491 | + | 0.288464i | \(0.906855\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 39309.6i | 0.00211233i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −380737. | −0.0200028 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.27929e7 | − | 4.01900e6i | −1.17096 | − | 0.206472i | −0.445853 | − | 0.895106i | \(-0.647099\pi\) |
−0.725109 | + | 0.688634i | \(0.758211\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.17676e6 | − | 4.34381e6i | −0.260106 | − | 0.218255i | 0.503404 | − | 0.864051i | \(-0.332081\pi\) |
−0.763509 | + | 0.645797i | \(0.776525\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 630583. | + | 1.09220e6i | 0.0309923 | + | 0.0536803i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.12959e6 | + | 2.59496e6i | 0.342820 | + | 0.124776i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.73007e6 | − | 1.68530e7i | 0.457801 | − | 0.792934i | −0.541044 | − | 0.840995i | \(-0.681971\pi\) |
0.998844 | + | 0.0480601i | \(0.0153039\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.91152e7 | − | 5.13379e6i | 1.34062 | − | 0.236388i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.31255e7 | + | 1.56424e7i | 0.591558 | + | 0.704992i | 0.975905 | − | 0.218197i | \(-0.0700176\pi\) |
−0.384346 | + | 0.923189i | \(0.625573\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.14851e7 | + | 4.18023e6i | −0.506728 | + | 0.184434i | −0.582718 | − | 0.812675i | \(-0.698011\pi\) |
0.0759894 | + | 0.997109i | \(0.475788\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 240897. | − | 221123.i | 0.0104063 | − | 0.00955213i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.93509e6 | − | 1.35590e7i | −0.208761 | − | 0.573566i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.11682e7 | − | 2.61532e7i | 1.29127 | − | 1.08351i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −300958. | − | 1.70682e6i | −0.0122131 | − | 0.0692641i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.90286e7 | − | 1.67597e7i | −1.15405 | − | 0.666289i | −0.204176 | − | 0.978934i | \(-0.565452\pi\) |
−0.949870 | + | 0.312645i | \(0.898785\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 884587. | − | 2.43038e6i | 0.0344567 | − | 0.0946691i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.21672e6 | − | 1.27983e6i | 0.0846140 | − | 0.0488519i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.29601e6 | + | 7.50329e6i | −0.235533 | + | 0.280697i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.91423e6 | − | 1.65274e7i | 0.106862 | − | 0.606046i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.32262e6i | 0.119441i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.40343e6 | −0.155200 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.91685e7 | + | 8.66974e6i | 1.69931 | + | 0.299634i | 0.937453 | − | 0.348113i | \(-0.113177\pi\) |
0.761856 | + | 0.647747i | \(0.224288\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.03322e6 | − | 2.54517e6i | −0.102808 | − | 0.0862664i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.35355e7 | + | 2.34441e7i | 0.449979 | + | 0.779386i | 0.998384 | − | 0.0568267i | \(-0.0180982\pi\) |
−0.548405 | + | 0.836213i | \(0.684765\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.36900e7 | + | 1.59019e7i | 1.42478 | + | 0.518579i | 0.935432 | − | 0.353508i | \(-0.115011\pi\) |
0.489352 | + | 0.872086i | \(0.337233\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.05035e6 | + | 1.81926e6i | −0.0336049 | + | 0.0582053i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.85635e6 | − | 679978.i | 0.121059 | − | 0.0213460i | −0.112790 | − | 0.993619i | \(-0.535979\pi\) |
0.233850 | + | 0.972273i | \(0.424868\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.17144e7 | − | 1.39607e7i | −0.360869 | − | 0.430067i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.40906e6 | + | 512855.i | −0.0426004 | + | 0.0155053i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.11774e7 | − | 5.10025e7i | −0.628441 | − | 1.51350i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.32215e6 | − | 2.28649e7i | −0.242429 | − | 0.666069i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.72297e6 | + | 3.96305e6i | −0.135074 | + | 0.113341i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.31484e6 | + | 1.87994e7i | 0.0930841 | + | 0.527906i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.57682e7 | + | 9.10376e6i | 0.434808 | + | 0.251037i | 0.701393 | − | 0.712775i | \(-0.252562\pi\) |
−0.266585 | + | 0.963811i | \(0.585895\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.81191e7 | − | 4.97818e7i | 0.490686 | − | 1.34815i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.85777e6 | + | 2.22728e6i | −0.102613 | + | 0.0592436i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.11531e7 | − | 1.32918e7i | 0.291412 | − | 0.347291i | −0.600398 | − | 0.799701i | \(-0.704991\pi\) |
0.891810 | + | 0.452410i | \(0.149436\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −953743. | + | 5.40895e6i | −0.0244812 | + | 0.138840i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.02770e7i | − | 0.511376i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.12950e7 | 1.02333 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 292002. | + | 51487.9i | 0.00711098 | + | 0.00125386i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.92198e7 | + | 1.61273e7i | 0.460003 | + | 0.385989i | 0.843132 | − | 0.537706i | \(-0.180709\pi\) |
−0.383129 | + | 0.923695i | \(0.625153\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.12064e6 | − | 8.86921e6i | −0.120461 | − | 0.208645i | 0.799488 | − | 0.600682i | \(-0.205104\pi\) |
−0.919950 | + | 0.392036i | \(0.871771\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.71386e6 | − | 2.80761e6i | −0.178382 | − | 0.0649256i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.30444e6 | + | 3.99141e6i | −0.0523892 | + | 0.0907408i | −0.891031 | − | 0.453943i | \(-0.850017\pi\) |
0.838642 | + | 0.544684i | \(0.183350\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.42407e6 | + | 1.48539e6i | −0.188294 | + | 0.0332013i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.14443e6 | − | 4.93913e6i | −0.0910877 | − | 0.108554i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.11571e7 | + | 2.22593e7i | −1.32179 | + | 0.481093i | −0.904032 | − | 0.427464i | \(-0.859407\pi\) |
−0.417760 | + | 0.908557i | \(0.637185\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.68597e7 | + | 4.18098e6i | −0.996043 | + | 0.0888702i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.88815e6 | + | 5.18765e6i | 0.0394745 | + | 0.108455i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.82633e6 | − | 3.21067e6i | 0.0786871 | − | 0.0660263i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.34590e7 | + | 7.63297e7i | 0.272279 | + | 1.54417i | 0.747475 | + | 0.664290i | \(0.231266\pi\) |
−0.475196 | + | 0.879880i | \(0.657623\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.03022e7 | + | 2.32685e7i | 0.802139 | + | 0.463115i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 225837. | − | 620481.i | 0.00442255 | − | 0.0121509i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.68390e7 | + | 3.85895e7i | −1.28796 | + | 0.743605i | −0.978291 | − | 0.207238i | \(-0.933553\pi\) |
−0.309672 | + | 0.950843i | \(0.600219\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −952284. | + | 1.13489e6i | −0.0180581 | + | 0.0215208i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.01491e7 | + | 5.75586e7i | −0.189411 | + | 1.07420i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.13267e7i | − | 1.67757i | −0.544464 | − | 0.838784i | \(-0.683267\pi\) | ||
0.544464 | − | 0.838784i | \(-0.316733\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.99229e6 | 0.108347 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.35265e7 | − | 7.67490e6i | −0.774743 | − | 0.136608i | −0.227721 | − | 0.973726i | \(-0.573127\pi\) |
−0.547022 | + | 0.837118i | \(0.684239\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.10371e6 | + | 926119.i | 0.0193406 | + | 0.0162287i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.70631e7 | + | 4.68747e7i | 0.466923 | + | 0.808734i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.47665e7 | + | 5.37458e6i | 0.250859 | + | 0.0913052i | 0.464389 | − | 0.885631i | \(-0.346274\pi\) |
−0.213530 | + | 0.976936i | \(0.568496\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.50376e7 | − | 4.33664e7i | 0.418853 | − | 0.725475i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 80485.6 | − | 14191.8i | 0.00132599 | − | 0.000233808i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.61659e6 | − | 3.11833e6i | −0.0424565 | − | 0.0505977i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.52133e7 | + | 2.00960e7i | −0.882414 | + | 0.321172i | −0.743183 | − | 0.669088i | \(-0.766685\pi\) |
−0.139230 | + | 0.990260i | \(0.544463\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.07280e6 | + | 2.10634e6i | −0.0798600 | + | 0.0331596i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.51186e6 | − | 2.33861e7i | −0.132005 | − | 0.362682i | 0.856026 | − | 0.516932i | \(-0.172926\pi\) |
−0.988032 | + | 0.154250i | \(0.950704\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.98152e7 | + | 4.17999e7i | −0.761109 | + | 0.638646i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.15472e6 | − | 6.54875e6i | −0.0173825 | − | 0.0985810i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.14667e7 | − | 1.81673e7i | −0.466732 | − | 0.269468i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.02283e7 | + | 2.81021e7i | −0.149498 | + | 0.410742i | −0.991725 | − | 0.128381i | \(-0.959022\pi\) |
0.842227 | + | 0.539123i | \(0.181244\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.36129e7 | + | 7.85942e6i | −0.196077 | + | 0.113205i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.79254e7 | + | 3.32802e7i | −0.396415 | + | 0.472428i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.79564e6 | + | 1.01836e7i | −0.0251232 | + | 0.142480i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 4.36777e6i | − | 0.0602354i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.15655e8 | −1.57225 | −0.786126 | − | 0.618066i | \(-0.787916\pi\) | ||||
−0.786126 | + | 0.618066i | \(0.787916\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.23326e7 | + | 3.93784e6i | 0.299291 | + | 0.0527730i | 0.321277 | − | 0.946985i | \(-0.395888\pi\) |
−0.0219864 | + | 0.999758i | \(0.506999\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.71630e7 | − | 3.95745e7i | −0.623133 | − | 0.522870i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.21982e7 | + | 1.07731e8i | 0.810236 | + | 1.40337i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.95058e7 | + | 2.52980e7i | 0.892765 | + | 0.324940i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.39487e6 | + | 2.41598e6i | −0.0176669 | + | 0.0306000i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.28628e8 | − | 2.26806e7i | 1.60658 | − | 0.283284i | 0.702837 | − | 0.711351i | \(-0.251916\pi\) |
0.903747 | + | 0.428067i | \(0.140805\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.94573e7 | + | 8.27760e7i | 0.855568 | + | 1.01963i | 0.999549 | + | 0.0300453i | \(0.00956516\pi\) |
−0.143981 | + | 0.989580i | \(0.545990\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.66258e6 | − | 605129.i | 0.0201983 | − | 0.00735157i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.88472e7 | − | 3.14269e7i | −0.345668 | − | 0.376579i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.65750e7 | − | 1.27964e8i | −0.550502 | − | 1.51249i | −0.833027 | − | 0.553232i | \(-0.813394\pi\) |
0.282525 | − | 0.959260i | \(-0.408828\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.74970e7 | + | 3.14637e7i | −0.437201 | + | 0.366855i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.78118e6 | − | 3.84580e7i | −0.0779999 | − | 0.442359i | −0.998649 | − | 0.0519677i | \(-0.983451\pi\) |
0.920649 | − | 0.390392i | \(-0.127660\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.20806e6 | + | 697472.i | 0.0137091 | + | 0.00791493i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.76430e6 | − | 7.59486e6i | 0.0309502 | − | 0.0850349i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.02605e8 | + | 5.92389e7i | −1.13352 | + | 0.654437i | −0.944817 | − | 0.327597i | \(-0.893761\pi\) |
−0.188701 | + | 0.982035i | \(0.560428\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.05164e7 | − | 2.44505e7i | 0.223651 | − | 0.266537i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.37137e6 | − | 1.34487e7i | 0.0255097 | − | 0.144673i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 4.62066e6i | − | 0.0490535i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.94324e7 | 0.203600 | 0.101800 | − | 0.994805i | \(-0.467540\pi\) | ||||
0.101800 | + | 0.994805i | \(0.467540\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.13296e7 | + | 7.28753e6i | 0.427389 | + | 0.0753603i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.72179e7 | − | 6.47935e7i | −0.788162 | − | 0.661346i | 0.157128 | − | 0.987578i | \(-0.449777\pi\) |
−0.945290 | + | 0.326232i | \(0.894221\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.70251e7 | + | 2.94883e7i | 0.171532 | + | 0.297103i | 0.938956 | − | 0.344038i | \(-0.111795\pi\) |
−0.767423 | + | 0.641141i | \(0.778462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.84983e6 | + | 673282.i | 0.0183981 | + | 0.00669635i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.75086e7 | − | 1.34249e8i | 0.761026 | − | 1.31814i | −0.181296 | − | 0.983429i | \(-0.558029\pi\) |
0.942322 | − | 0.334707i | \(-0.108637\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.36887e7 | − | 1.29933e7i | 0.714303 | − | 0.125951i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.55290e6 | + | 1.01930e7i | 0.0818561 | + | 0.0975523i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.48843e7 | − | 1.26968e7i | 0.329645 | − | 0.119981i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.03442e8 | − | 2.30260e7i | 0.965198 | − | 0.214851i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 728365. | + | 2.00117e6i | 0.00671110 | + | 0.0184386i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.95642e7 | − | 8.35443e7i | 0.905934 | − | 0.760169i | −0.0654069 | − | 0.997859i | \(-0.520835\pi\) |
0.971341 | + | 0.237690i | \(0.0763901\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.02346e7 | + | 1.14756e8i | 0.181828 | + | 1.03120i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.31330e6 | − | 2.49028e6i | −0.0382796 | − | 0.0221008i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.17179e6 | + | 5.96696e6i | −0.0190368 | + | 0.0523031i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.66544e8 | + | 9.61541e7i | −1.44192 | + | 0.832494i | −0.997978 | − | 0.0635607i | \(-0.979754\pi\) |
−0.443944 | + | 0.896055i | \(0.646421\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.49026e6 | − | 7.73479e6i | 0.0555055 | − | 0.0661488i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.14352e7 | + | 6.48521e7i | −0.0966047 | + | 0.547873i | 0.897639 | + | 0.440731i | \(0.145281\pi\) |
−0.994244 | + | 0.107141i | \(0.965830\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.98802e8i | − | 2.49369i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.64680e6 | −0.0383123 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.41503e8 | + | 2.49508e7i | 1.15265 | + | 0.203243i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.21017e8 | − | 1.01546e8i | −0.973972 | − | 0.817259i | 0.00919739 | − | 0.999958i | \(-0.497072\pi\) |
−0.983169 | + | 0.182698i | \(0.941517\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 714658. | + | 1.23782e6i | 0.00568310 | + | 0.00984342i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.36136e8 | + | 8.59465e7i | 1.85549 | + | 0.675343i | 0.982112 | + | 0.188299i | \(0.0602974\pi\) |
0.873378 | + | 0.487044i | \(0.161925\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.08671e6 | − | 1.05425e7i | 0.0472616 | − | 0.0818595i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.33610e6 | + | 1.46988e6i | −0.0639645 | + | 0.0112787i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.30870e7 | + | 2.75140e7i | 0.175071 | + | 0.208641i | 0.846443 | − | 0.532479i | \(-0.178739\pi\) |
−0.671373 | + | 0.741120i | \(0.734295\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.88420e7 | + | 2.86961e7i | −0.590874 | + | 0.215061i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.64812e7 | − | 3.17266e7i | 0.122077 | − | 0.235002i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.96173e6 | + | 1.36322e7i | 0.0363255 | + | 0.0998034i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.23472e7 | + | 2.71425e7i | −0.234081 | + | 0.196417i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.07977e6 | − | 1.17950e7i | −0.0148770 | − | 0.0843714i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.00335e7 | + | 2.88868e7i | 0.353792 | + | 0.204262i | 0.666354 | − | 0.745636i | \(-0.267854\pi\) |
−0.312562 | + | 0.949897i | \(0.601187\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.67288e7 | − | 1.00912e8i | 0.256745 | − | 0.705401i | −0.742618 | − | 0.669715i | \(-0.766416\pi\) |
0.999363 | − | 0.0356856i | \(-0.0113615\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.07151e7 | − | 6.18635e6i | 0.0740486 | − | 0.0427520i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.13698e8 | − | 2.54675e8i | 1.46005 | − | 1.74002i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.89892e7 | + | 1.07693e8i | −0.128274 | + | 0.727479i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.40116e8i | − | 0.935844i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.02362e8 | −0.676015 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.41036e6 | + | 953993.i | 0.0353317 | + | 0.00622994i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.43383e7 | + | 2.04222e7i | 0.157169 | + | 0.131880i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.67860e7 | + | 2.90742e7i | 0.107197 | + | 0.185670i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.67571e6 | + | 1.33785e6i | 0.0232140 | + | 0.00844919i | 0.353601 | − | 0.935396i | \(-0.384957\pi\) |
−0.330387 | + | 0.943846i | \(0.607179\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.20102e6 | − | 1.24725e7i | 0.0449774 | − | 0.0779031i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.22456e7 | − | 3.92250e6i | 0.137422 | − | 0.0242311i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.02447e8 | + | 1.22092e8i | 0.625948 | + | 0.745976i | 0.982081 | − | 0.188459i | \(-0.0603494\pi\) |
−0.356133 | + | 0.934435i | \(0.615905\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.24169e8 | + | 8.15909e7i | −1.35475 | + | 0.493088i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.42835e8 | − | 7.63359e7i | −1.45163 | − | 0.456325i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.33864e7 | + | 6.42536e7i | 0.138289 | + | 0.379946i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.70219e6 | − | 2.26741e6i | 0.0158066 | − | 0.0132633i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.28092e7 | + | 2.42783e8i | 0.247726 | + | 1.40492i | 0.814075 | + | 0.580759i | \(0.197244\pi\) |
−0.566349 | + | 0.824165i | \(0.691645\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.03105e8 | − | 5.95276e7i | −0.590260 | − | 0.340787i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.87796e6 | − | 1.34021e7i | 0.0276280 | − | 0.0759074i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.25335e8 | + | 7.23624e7i | −0.702342 | + | 0.405497i | −0.808219 | − | 0.588882i | \(-0.799568\pi\) |
0.105877 | + | 0.994379i | \(0.466235\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.29348e7 | − | 1.54151e7i | 0.0717158 | − | 0.0854676i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.93964e7 | + | 1.10002e8i | −0.106407 | + | 0.603466i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.41826e8i | − | 0.769873i | −0.922943 | − | 0.384936i | \(-0.874223\pi\) | ||
0.922943 | − | 0.384936i | \(-0.125777\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.41023e8 | −0.757500 | −0.378750 | − | 0.925499i | \(-0.623646\pi\) | ||||
−0.378750 | + | 0.925499i | \(0.623646\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.53749e7 | − | 8.00081e6i | −0.241186 | − | 0.0425275i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.36112e7 | + | 6.17671e7i | 0.387204 | + | 0.324903i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.77807e8 | + | 3.07971e8i | 0.925596 | + | 1.60318i | 0.790600 | + | 0.612333i | \(0.209769\pi\) |
0.134996 | + | 0.990846i | \(0.456898\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.90345e7 | + | 1.05677e7i | 0.149582 | + | 0.0544432i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.68484e7 | − | 1.50426e8i | 0.442826 | − | 0.766998i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.43841e6 | − | 253631.i | 0.00725903 | − | 0.00127996i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.57913e6 | + | 1.14160e7i | 0.0478474 | + | 0.0570223i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.43344e8 | + | 5.21729e7i | −0.708704 | + | 0.257947i | −0.671122 | − | 0.741347i | \(-0.734188\pi\) |
−0.0375812 | + | 0.999294i | \(0.511965\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.52379e8 | − | 2.38734e8i | −0.745727 | − | 1.16834i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.18194e6 | + | 1.14898e7i | 0.0202589 | + | 0.0556607i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.95521e7 | + | 8.35342e7i | −0.477405 | + | 0.400590i | −0.849487 | − | 0.527610i | \(-0.823088\pi\) |
0.372082 | + | 0.928200i | \(0.378644\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.10203e6 | + | 2.32638e7i | 0.0194737 | + | 0.110441i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.28172e7 | + | 7.39999e6i | 0.0602377 | + | 0.0347783i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.20947e6 | + | 1.43129e7i | −0.0242389 | + | 0.0665959i | −0.951222 | − | 0.308507i | \(-0.900171\pi\) |
0.926983 | + | 0.375103i | \(0.122393\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.23384e8 | + | 1.28971e8i | −1.02903 | + | 0.594112i | −0.916707 | − | 0.399559i | \(-0.869163\pi\) |
−0.112325 | + | 0.993671i | \(0.535830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.55121e8 | + | 1.84866e8i | −0.707489 | + | 0.843152i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.51226e6 | − | 1.99190e7i | 0.0158606 | − | 0.0899501i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.13026e8i | 0.952505i | 0.879309 | + | 0.476252i | \(0.158005\pi\) | ||||
−0.879309 | + | 0.476252i | \(0.841995\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.97194e7 | −0.131579 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.33364e8 | + | 2.35157e7i | 0.584677 | + | 0.103094i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.80944e8 | − | 1.51830e8i | −0.785528 | − | 0.659136i | 0.159106 | − | 0.987261i | \(-0.449139\pi\) |
−0.944634 | + | 0.328125i | \(0.893583\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.54933e6 | + | 2.68353e6i | 0.00666070 | + | 0.0115367i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.04199e8 | + | 1.47117e8i | 1.72084 | + | 0.626334i | 0.997912 | − | 0.0645904i | \(-0.0205741\pi\) |
0.722927 | + | 0.690925i | \(0.242796\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.54619e7 | + | 1.30704e8i | −0.318168 | + | 0.551082i | −0.980106 | − | 0.198476i | \(-0.936401\pi\) |
0.661938 | + | 0.749558i | \(0.269734\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.19259e7 | − | 5.62940e6i | 0.133312 | − | 0.0235065i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.50615e7 | − | 1.79496e7i | −0.0622879 | − | 0.0742319i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.21752e8 | + | 8.07111e7i | −0.908296 | + | 0.330593i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.64563e6 | − | 7.38817e6i | −0.0391316 | − | 0.0299733i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.03752e8 | − | 5.59803e8i | −0.818746 | − | 2.24949i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.10002e7 | − | 2.60123e7i | 0.123389 | − | 0.103536i | −0.579005 | − | 0.815324i | \(-0.696559\pi\) |
0.702394 | + | 0.711788i | \(0.252114\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.50092e6 | + | 3.11973e7i | 0.0216883 | + | 0.123000i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.90132e7 | − | 1.09773e7i | −0.0742564 | − | 0.0428720i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.68243e7 | − | 1.01174e8i | 0.142468 | − | 0.391426i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.01328e8 | + | 2.31707e8i | −1.53814 | + | 0.888048i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.33042e7 | − | 2.77729e7i | 0.0884832 | − | 0.105450i | −0.719986 | − | 0.693988i | \(-0.755852\pi\) |
0.808469 | + | 0.588538i | \(0.200296\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.06300e7 | + | 2.30424e8i | −0.152832 | + | 0.866752i | 0.807910 | + | 0.589306i | \(0.200599\pi\) |
−0.960741 | + | 0.277446i | \(0.910512\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.60401e6i | 0.0134309i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.73795e8 | 1.74936 | 0.874678 | − | 0.484705i | \(-0.161073\pi\) | ||||
0.874678 | + | 0.484705i | \(0.161073\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.46398e7 | − | 1.66875e7i | −0.346210 | − | 0.0610462i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.53304e7 | − | 2.12548e7i | −0.0918121 | − | 0.0770395i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.53796e7 | + | 1.13241e8i | 0.234802 | + | 0.406690i | 0.959215 | − | 0.282677i | \(-0.0912224\pi\) |
−0.724413 | + | 0.689366i | \(0.757889\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −281374. | − | 102412.i | −0.00100129 | − | 0.000364440i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.35300e8 | − | 2.34346e8i | 0.477090 | − | 0.826344i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.17209e8 | − | 9.11979e7i | 1.80721 | − | 0.318661i | 0.834560 | − | 0.550917i | \(-0.185722\pi\) |
0.972655 | + | 0.232256i | \(0.0746108\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 327961. | + | 390849.i | 0.00113558 | + | 0.00135333i | 0.766612 | − | 0.642111i | \(-0.221941\pi\) |
−0.765476 | + | 0.643464i | \(0.777497\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.29811e7 | + | 1.56438e7i | −0.147481 | + | 0.0536788i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.99543e7 | + | 2.60957e6i | 0.0678534 | + | 0.00887367i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.89436e7 | − | 2.16896e8i | −0.266035 | − | 0.730926i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.65423e7 | + | 1.38807e7i | −0.0552483 | + | 0.0463588i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.84116e7 | + | 1.61130e8i | 0.0940433 | + | 0.533346i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.32803e6 | + | 2.49879e6i | 0.0141986 | + | 0.00819756i | 0.507082 | − | 0.861898i | \(-0.330724\pi\) |
−0.492884 | + | 0.870095i | \(0.664057\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.75442e7 | + | 7.56769e7i | −0.0895608 | + | 0.246066i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.83889e7 | + | 2.79373e7i | −0.155948 | + | 0.0900365i | −0.575943 | − | 0.817490i | \(-0.695365\pi\) |
0.419995 | + | 0.907526i | \(0.362032\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.85612e7 | − | 8.17080e7i | 0.219012 | − | 0.261009i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.11770e6 | − | 2.33526e7i | 0.0130381 | − | 0.0739426i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 6.36127e8i | − | 1.99656i | −0.0586497 | − | 0.998279i | \(-0.518680\pi\) | ||
0.0586497 | − | 0.998279i | \(-0.481320\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.75907e7 | 0.179176 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 984711. | + | 173631.i | 0.00303696 | + | 0.000535497i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.58832e6 | − | 3.01096e6i | −0.0109707 | − | 0.00920550i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.45296e8 | + | 4.24866e8i | 0.743459 | + | 1.28771i | 0.950911 | + | 0.309463i | \(0.100149\pi\) |
−0.207453 | + | 0.978245i | \(0.566517\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.33472e7 | + | 2.66962e7i | 0.220386 | + | 0.0802139i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.00132e6 | + | 1.38587e7i | −0.0238346 | + | 0.0412827i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.15364e8 | − | 9.08726e7i | 1.52200 | − | 0.268370i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.66932e7 | − | 3.18117e7i | −0.0781573 | − | 0.0931442i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.46423e8 | − | 5.32937e7i | 0.425065 | − | 0.154711i | −0.120625 | − | 0.992698i | \(-0.538490\pi\) |
0.545690 | + | 0.837987i | \(0.316268\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.07002e8 | + | 2.25734e7i | −1.45930 | + | 0.0649726i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.40209e6 | − | 3.85222e6i | −0.00400138 | − | 0.0109937i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.56643e8 | + | 1.31439e8i | −0.443253 | + | 0.371933i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.61310e7 | − | 3.18335e8i | −0.157494 | − | 0.893193i | −0.956470 | − | 0.291830i | \(-0.905736\pi\) |
0.798976 | − | 0.601363i | \(-0.205375\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.90984e8 | − | 1.10265e8i | −0.531359 | − | 0.306780i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.78346e7 | − | 2.41324e8i | 0.242324 | − | 0.665781i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.85166e6 | − | 5.11051e6i | 0.0242162 | − | 0.0139812i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.62589e6 | + | 1.14717e7i | −0.0261146 | + | 0.0311222i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.28045e7 | − | 1.29331e8i | 0.0613528 | − | 0.347949i | −0.938643 | − | 0.344892i | \(-0.887916\pi\) |
0.999995 | − | 0.00305749i | \(-0.000973231\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 2.43683e8i | − | 0.650158i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.04960e7 | 0.0542318 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.64680e8 | + | 9.95683e7i | 1.48180 | + | 0.261281i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.56144e8 | + | 1.31020e8i | 0.406370 | + | 0.340985i | 0.822950 | − | 0.568114i | \(-0.192327\pi\) |
−0.416579 | + | 0.909099i | \(0.636771\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.73272e8 | − | 3.00116e8i | −0.447245 | − | 0.774652i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.71951e8 | + | 2.08173e8i | 1.46422 | + | 0.532933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.54135e8 | − | 6.13380e8i | 0.899202 | − | 1.55746i | 0.0706857 | − | 0.997499i | \(-0.477481\pi\) |
0.828516 | − | 0.559965i | \(-0.189185\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.20975e6 | + | 565966.i | −0.00808368 | + | 0.00142537i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.06392e8 | + | 1.26792e8i | 0.265769 | + | 0.316731i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.67304e8 | + | 6.08938e7i | −0.414547 | + | 0.150883i | −0.540870 | − | 0.841106i | \(-0.681905\pi\) |
0.126323 | + | 0.991989i | \(0.459683\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.73316e6 | + | 3.89271e7i | 0.00425975 | + | 0.0956748i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.78472e7 | − | 1.58934e8i | −0.141031 | − | 0.387480i | 0.848988 | − | 0.528412i | \(-0.177212\pi\) |
−0.990019 | + | 0.140932i | \(0.954990\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.26840e7 | + | 1.90341e7i | −0.0548593 | + | 0.0460324i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.72785e7 | + | 5.51694e8i | 0.233375 | + | 1.32354i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.99188e7 | − | 4.61412e7i | −0.190197 | − | 0.109810i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.70297e8 | − | 4.67888e8i | 0.402057 | − | 1.10464i | −0.559210 | − | 0.829026i | \(-0.688896\pi\) |
0.961268 | − | 0.275617i | \(-0.0888822\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.80468e7 | + | 5.08339e7i | −0.206219 | + | 0.119061i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.21609e7 | + | 3.83279e7i | −0.0747288 | + | 0.0890583i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.93862e7 | + | 5.06934e8i | −0.206055 | + | 1.16860i | 0.689716 | + | 0.724080i | \(0.257735\pi\) |
−0.895771 | + | 0.444516i | \(0.853376\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.10171e7i | − | 0.0251967i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.75349e8 | −1.07860 | −0.539298 | − | 0.842115i | \(-0.681310\pi\) | ||||
−0.539298 | + | 0.842115i | \(0.681310\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.73670e8 | − | 6.58881e7i | −0.841230 | − | 0.148331i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.83629e7 | − | 4.89723e7i | −0.130363 | − | 0.109387i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.54098e8 | + | 2.66906e8i | 0.341516 | + | 0.591523i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.51595e8 | − | 5.51762e7i | −0.333355 | − | 0.121331i | 0.169919 | − | 0.985458i | \(-0.445649\pi\) |
−0.503274 | + | 0.864127i | \(0.667871\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.94245e7 | + | 3.36442e7i | −0.0423825 | + | 0.0734086i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.86435e8 | + | 6.81389e7i | −0.836638 | + | 0.147522i | −0.575523 | − | 0.817786i | \(-0.695201\pi\) |
−0.261115 | + | 0.965308i | \(0.584090\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.10079e8 | + | 4.88713e8i | 0.880972 | + | 1.04990i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.56790e7 | + | 2.02655e7i | −0.118694 | + | 0.0432011i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.78099e7 | − | 4.42049e8i | 0.122290 | − | 0.935101i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.08707e8 | + | 2.98669e8i | 0.228193 | + | 0.626956i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.48186e8 | − | 1.24343e8i | 0.308689 | − | 0.259021i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.46541e6 | − | 4.80097e7i | −0.0175000 | − | 0.0992476i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.89964e8 | + | 1.67411e8i | 0.594868 | + | 0.343447i | 0.767020 | − | 0.641623i | \(-0.221739\pi\) |
−0.172152 | + | 0.985070i | \(0.555072\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.02150e7 | + | 5.55401e7i | −0.0411568 | + | 0.113077i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.92730e8 | + | 1.69008e8i | −0.591477 | + | 0.341489i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.37285e8 | − | 4.01961e8i | 0.676360 | − | 0.806054i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24623.2 | + | 139645.i | −4.90054e−5 | + | 0.000277923i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.89140e8i | − | 0.571127i | −0.958360 | − | 0.285563i | \(-0.907819\pi\) | ||
0.958360 | − | 0.285563i | \(-0.0921807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.92329e8 | −1.35729 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.44229e7 | + | 1.31228e7i | 0.144814 | + | 0.0255345i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.42173e8 | − | 1.19297e8i | −0.274580 | − | 0.230400i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.12389e6 | + | 1.58030e7i | 0.0174901 | + | 0.0302938i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.84530e7 | − | 2.85546e7i | −0.149276 | − | 0.0543319i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.16516e8 | + | 3.75017e8i | −0.408926 | + | 0.708280i | −0.994770 | − | 0.102144i | \(-0.967430\pi\) |
0.585844 | + | 0.810424i | \(0.300763\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.92109e8 | + | 6.91395e7i | −0.735097 | + | 0.129617i | −0.528650 | − | 0.848840i | \(-0.677301\pi\) |
−0.206448 | + | 0.978458i | \(0.566190\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.56692e7 | − | 1.86738e7i | −0.0291592 | − | 0.0347506i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.47626e7 | + | 1.26525e7i | −0.0642154 | + | 0.0233725i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.15299e8 | − | 4.11639e8i | 0.578172 | − | 0.754832i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.56158e7 | − | 2.35227e8i | −0.155848 | − | 0.428190i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.68012e7 | + | 3.08799e7i | −0.0665017 | + | 0.0558015i | −0.675433 | − | 0.737422i | \(-0.736043\pi\) |
0.608931 | + | 0.793223i | \(0.291599\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.35848e7 | + | 5.30746e8i | 0.167883 | + | 0.952110i | 0.946042 | + | 0.324043i | \(0.105042\pi\) |
−0.778160 | + | 0.628067i | \(0.783847\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.37020e7 | + | 1.36844e7i | 0.0422108 | + | 0.0243704i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.30362e8 | + | 6.32914e8i | −0.407281 | + | 1.11900i | 0.551333 | + | 0.834286i | \(0.314120\pi\) |
−0.958614 | + | 0.284710i | \(0.908103\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.20283e8 | + | 4.73590e8i | −1.43979 | + | 0.831265i | −0.997835 | − | 0.0657714i | \(-0.979049\pi\) |
−0.441958 | + | 0.897036i | \(0.645716\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.51221e7 | − | 5.37744e7i | 0.0786296 | − | 0.0937071i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.55823e7 | + | 5.42074e8i | −0.165365 | + | 0.937829i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 5.23673e6i | − | 0.00899499i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.15230e8 | 0.367050 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.61530e8 | + | 1.16646e8i | 1.12012 | + | 0.197507i | 0.702892 | − | 0.711296i | \(-0.251892\pi\) |
0.417225 | + | 0.908803i | \(0.363003\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.99407e8 | − | 5.02962e8i | −1.00771 | − | 0.845565i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.68294e7 | + | 6.37904e7i | 0.0614769 | + | 0.106481i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.91426e7 | + | 1.06070e7i | 0.0483013 | + | 0.0175802i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.69875e8 | + | 2.94232e8i | −0.279563 | + | 0.484217i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.34186e7 | + | 7.65587e6i | −0.0709501 | + | 0.0125104i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.95800e8 | − | 3.52521e8i | −0.479966 | − | 0.572001i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.54576e8 | + | 1.65452e8i | −0.732419 | + | 0.266579i | −0.681188 | − | 0.732108i | \(-0.738537\pi\) |
−0.0512306 | + | 0.998687i | \(0.516314\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.47097e7 | + | 3.49202e7i | −0.0875319 | + | 0.0558699i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.59194e8 | + | 7.12129e8i | 0.411796 | + | 1.13140i | 0.956235 | + | 0.292600i | \(0.0945203\pi\) |
−0.544439 | + | 0.838800i | \(0.683257\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.55332e8 | + | 2.14249e8i | −0.402834 | + | 0.338017i | −0.821588 | − | 0.570082i | \(-0.806911\pi\) |
0.418754 | + | 0.908100i | \(0.362467\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.03835e6 | − | 5.12590e7i | −0.0141605 | − | 0.0803084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.20580e8 | − | 6.96168e7i | −0.187604 | − | 0.108313i | 0.403256 | − | 0.915087i | \(-0.367878\pi\) |
−0.590860 | + | 0.806774i | \(0.701212\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.50082e7 | + | 4.12347e7i | −0.0231889 | + | 0.0637111i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.27105e8 | − | 7.33842e7i | 0.195032 | − | 0.112602i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.72230e7 | + | 1.15866e8i | −0.148153 | + | 0.176562i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.21753e7 | − | 5.22752e8i | 0.139495 | − | 0.791118i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.44006e8i | 0.517038i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.11746e7 | −0.136097 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.93530e7 | + | 1.57553e7i | 0.132468 | + | 0.0233576i | 0.239489 | − | 0.970899i | \(-0.423020\pi\) |
−0.107021 | + | 0.994257i | \(0.534131\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.26243e7 | − | 7.77210e7i | −0.136382 | − | 0.114438i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.73752e8 | + | 3.00947e8i | 0.254099 | + | 0.440112i | 0.964650 | − | 0.263533i | \(-0.0848879\pi\) |
−0.710552 | + | 0.703645i | \(0.751555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.17941e8 | + | 1.15721e8i | 0.461812 | + | 0.168086i | 0.562440 | − | 0.826838i | \(-0.309863\pi\) |
−0.100628 | + | 0.994924i | \(0.532085\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.66481e6 | − | 8.07970e6i | 0.00672984 | − | 0.0116564i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.54467e8 | + | 2.72367e7i | −0.221343 | + | 0.0390287i | −0.283220 | − | 0.959055i | \(-0.591402\pi\) |
0.0618769 | + | 0.998084i | \(0.480291\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.37048e8 | + | 2.82502e8i | 0.337389 | + | 0.402084i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.32181e8 | + | 8.45069e7i | −0.328241 | + | 0.119470i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.76871e8 | + | 5.62652e8i | −0.248372 | + | 0.790106i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.98125e7 | − | 1.09384e8i | −0.0555329 | − | 0.152575i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.70662e7 | + | 2.27112e7i | −0.0375016 | + | 0.0314676i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.66100e8 | − | 1.50913e9i | −0.366241 | − | 2.07705i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.07392e7 | + | 1.19738e7i | 0.0283543 | + | 0.0163703i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.07053e7 | − | 5.68873e7i | 0.0281201 | − | 0.0772595i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.56968e7 | + | 2.63831e7i | −0.0616510 | + | 0.0355942i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.11594e8 | − | 1.32992e8i | 0.149561 | − | 0.178240i | −0.686062 | − | 0.727543i | \(-0.740662\pi\) |
0.835623 | + | 0.549303i | \(0.185107\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.14520e8 | − | 6.49475e8i | 0.152472 | − | 0.864710i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.03648e9i | − | 1.37091i | −0.728117 | − | 0.685453i | \(-0.759604\pi\) | ||
0.728117 | − | 0.685453i | \(-0.240396\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.84222e8 | 0.504858 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.56429e7 | − | 2.75827e6i | −0.0204200 | − | 0.00360059i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.85297e6 | + | 3.23303e6i | 0.00499675 | + | 0.00419277i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.07678e7 | − | 1.22573e8i | −0.0911778 | − | 0.157925i | 0.816829 | − | 0.576880i | \(-0.195730\pi\) |
−0.908007 | + | 0.418955i | \(0.862396\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.69238e8 | + | 6.15975e7i | 0.216630 | + | 0.0788469i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.09658e8 | − | 8.82754e8i | 0.648148 | − | 1.12262i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.12582e9 | − | 1.98512e8i | 1.42247 | − | 0.250820i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.05181e8 | + | 6.02051e8i | 0.634173 | + | 0.755778i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.39692e8 | + | 1.23638e8i | −0.423680 | + | 0.154207i | −0.545056 | − | 0.838400i | \(-0.683492\pi\) |
0.121376 | + | 0.992607i | \(0.461269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.16122e8 | + | 2.16165e8i | 0.515670 | + | 0.267877i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.33988e7 | + | 9.17624e7i | 0.0411231 | + | 0.112985i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.00288e7 | + | 3.35881e7i | −0.0489709 | + | 0.0410914i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.28327e7 | + | 4.13055e8i | 0.0885335 | + | 0.502098i | 0.996538 | + | 0.0831380i | \(0.0264942\pi\) |
−0.908005 | + | 0.418960i | \(0.862395\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.45245e8 | + | 8.38575e7i | 0.175431 | + | 0.101285i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.51052e8 | + | 4.15013e8i | −0.181284 | + | 0.498073i | −0.996734 | − | 0.0807540i | \(-0.974267\pi\) |
0.815450 | + | 0.578827i | \(0.196489\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.50086e8 | − | 2.02122e8i | 0.417484 | − | 0.241035i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.83027e6 | + | 1.17153e7i | −0.0116485 | + | 0.0138821i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.33011e7 | − | 7.54342e7i | 0.0156616 | − | 0.0888216i | −0.975975 | − | 0.217882i | \(-0.930085\pi\) |
0.991637 | + | 0.129061i | \(0.0411962\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.95205e8i | 0.696415i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.41254e7 | 0.0164232 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.28182e9 | − | 2.26020e8i | −1.48098 | − | 0.261136i | −0.626009 | − | 0.779816i | \(-0.715313\pi\) |
−0.854969 | + | 0.518679i | \(0.826424\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.29315e8 | + | 1.08508e8i | 0.148470 | + | 0.124581i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.28700e7 | − | 5.69325e7i | −0.0375028 | − | 0.0649568i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.09037e8 | − | 3.30862e8i | −1.03068 | − | 0.375138i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.08748e8 | − | 7.07972e8i | 0.460559 | − | 0.797712i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.93106e8 | − | 5.16825e7i | 0.328205 | − | 0.0578715i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.27658e7 | − | 8.67189e7i | −0.0809739 | − | 0.0965009i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.59375e9 | − | 5.80079e8i | 1.76255 | − | 0.641516i | 0.762565 | − | 0.646912i | \(-0.223940\pi\) |
0.999985 | + | 0.00539588i | \(0.00171757\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.32839e7 | − | 1.94449e8i | −0.0475724 | − | 0.213714i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.09518e8 | + | 3.00899e8i | 0.119627 | + | 0.328673i | 0.985025 | − | 0.172413i | \(-0.0551564\pi\) |
−0.865398 | + | 0.501086i | \(0.832934\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.05916e8 | − | 1.72784e8i | 0.223538 | − | 0.187570i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.52416e7 | − | 8.64392e7i | −0.0164443 | − | 0.0932603i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.11787e8 | − | 6.45403e7i | −0.119869 | − | 0.0692066i | 0.438867 | − | 0.898552i | \(-0.355380\pi\) |
−0.558736 | + | 0.829346i | \(0.688713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.77273e7 | − | 4.87053e7i | 0.0188927 | − | 0.0519073i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.05980e9 | − | 6.11873e8i | 1.12257 | − | 0.648119i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.11750e8 | − | 3.71529e8i | 0.328205 | − | 0.391140i | −0.576557 | − | 0.817057i | \(-0.695604\pi\) |
0.904762 | + | 0.425917i | \(0.140048\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.77907e6 | − | 4.41173e7i | 0.00813989 | − | 0.0461636i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.88603e7i | 0.0716172i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.70170e8 | 0.486033 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.75131e8 | + | 3.08803e7i | 0.179946 | + | 0.0317293i | 0.262895 | − | 0.964825i | \(-0.415323\pi\) |
−0.0829492 | + | 0.996554i | \(0.526434\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.03131e7 | + | 4.22177e7i | 0.0513846 | + | 0.0431168i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.71121e7 | − | 4.69595e7i | −0.0275228 | − | 0.0476710i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.22672e8 | + | 3.35825e8i | 0.931026 | + | 0.338866i | 0.762616 | − | 0.646851i | \(-0.223915\pi\) |
0.168410 | + | 0.985717i | \(0.446137\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.92836e8 | − | 3.34003e8i | 0.193416 | − | 0.335007i |
(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 | 76.7.j.a.33.5 | ✓ | 60 | |
19.15 | odd | 18 | inner | 76.7.j.a.53.5 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.j.a.33.5 | ✓ | 60 | 1.1 | even | 1 | trivial | |
76.7.j.a.53.5 | yes | 60 | 19.15 | odd | 18 | inner |