Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(21,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.21");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.g (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.43727313082\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 21.20 | ||
Character | \(\chi\) | \(=\) | 143.21 |
Dual form | 143.4.g.a.109.20 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.177069 | + | 0.177069i | −0.0626035 | + | 0.0626035i | −0.737715 | − | 0.675112i | \(-0.764095\pi\) |
0.675112 | + | 0.737715i | \(0.264095\pi\) | |||||||
\(3\) | −5.26131 | −1.01254 | −0.506270 | − | 0.862375i | \(-0.668976\pi\) | ||||
−0.506270 | + | 0.862375i | \(0.668976\pi\) | |||||||
\(4\) | 7.93729i | 0.992162i | ||||||||
\(5\) | −2.40696 | − | 2.40696i | −0.215285 | − | 0.215285i | 0.591223 | − | 0.806508i | \(-0.298645\pi\) |
−0.806508 | + | 0.591223i | \(0.798645\pi\) | |||||||
\(6\) | 0.931617 | − | 0.931617i | 0.0633885 | − | 0.0633885i | ||||
\(7\) | −14.4545 | − | 14.4545i | −0.780470 | − | 0.780470i | 0.199440 | − | 0.979910i | \(-0.436088\pi\) |
−0.979910 | + | 0.199440i | \(0.936088\pi\) | |||||||
\(8\) | −2.82201 | − | 2.82201i | −0.124716 | − | 0.124716i | ||||
\(9\) | 0.681391 | 0.0252367 | ||||||||
\(10\) | 0.852396 | 0.0269551 | ||||||||
\(11\) | 36.1216 | − | 5.12149i | 0.990098 | − | 0.140381i | ||||
\(12\) | − | 41.7606i | − | 1.00460i | ||||||
\(13\) | 39.5842 | + | 25.1016i | 0.844514 | + | 0.535533i | ||||
\(14\) | 5.11890 | 0.0977203 | ||||||||
\(15\) | 12.6637 | + | 12.6637i | 0.217984 | + | 0.217984i | ||||
\(16\) | −62.4990 | −0.976546 | ||||||||
\(17\) | 72.8359 | 1.03914 | 0.519568 | − | 0.854429i | \(-0.326093\pi\) | ||||
0.519568 | + | 0.854429i | \(0.326093\pi\) | |||||||
\(18\) | −0.120654 | + | 0.120654i | −0.00157991 | + | 0.00157991i | ||||
\(19\) | 53.3396 | − | 53.3396i | 0.644050 | − | 0.644050i | −0.307499 | − | 0.951548i | \(-0.599492\pi\) |
0.951548 | + | 0.307499i | \(0.0994920\pi\) | |||||||
\(20\) | 19.1047 | − | 19.1047i | 0.213597 | − | 0.213597i | ||||
\(21\) | 76.0497 | + | 76.0497i | 0.790257 | + | 0.790257i | ||||
\(22\) | −5.48917 | + | 7.30289i | −0.0531952 | + | 0.0707718i | ||||
\(23\) | − | 127.048i | − | 1.15180i | −0.817520 | − | 0.575900i | \(-0.804652\pi\) | ||
0.817520 | − | 0.575900i | \(-0.195348\pi\) | |||||||
\(24\) | 14.8474 | + | 14.8474i | 0.126280 | + | 0.126280i | ||||
\(25\) | − | 113.413i | − | 0.907305i | ||||||
\(26\) | −11.4539 | + | 2.56442i | −0.0863957 | + | 0.0193433i | ||||
\(27\) | 138.470 | 0.986987 | ||||||||
\(28\) | 114.730 | − | 114.730i | 0.774353 | − | 0.774353i | ||||
\(29\) | − | 52.5564i | − | 0.336533i | −0.985741 | − | 0.168267i | \(-0.946183\pi\) | ||
0.985741 | − | 0.168267i | \(-0.0538170\pi\) | |||||||
\(30\) | −4.48472 | −0.0272931 | ||||||||
\(31\) | −74.2815 | − | 74.2815i | −0.430366 | − | 0.430366i | 0.458387 | − | 0.888753i | \(-0.348427\pi\) |
−0.888753 | + | 0.458387i | \(0.848427\pi\) | |||||||
\(32\) | 33.6427 | − | 33.6427i | 0.185851 | − | 0.185851i | ||||
\(33\) | −190.047 | + | 26.9457i | −1.00251 | + | 0.142141i | ||||
\(34\) | −12.8970 | + | 12.8970i | −0.0650535 | + | 0.0650535i | ||||
\(35\) | 69.5828i | 0.336047i | ||||||||
\(36\) | 5.40840i | 0.0250389i | ||||||||
\(37\) | −117.423 | + | 117.423i | −0.521735 | + | 0.521735i | −0.918095 | − | 0.396360i | \(-0.870273\pi\) |
0.396360 | + | 0.918095i | \(0.370273\pi\) | |||||||
\(38\) | 18.8896i | 0.0806395i | ||||||||
\(39\) | −208.265 | − | 132.067i | −0.855104 | − | 0.542249i | ||||
\(40\) | 13.5849i | 0.0536990i | ||||||||
\(41\) | −153.677 | + | 153.677i | −0.585375 | + | 0.585375i | −0.936375 | − | 0.351000i | \(-0.885842\pi\) |
0.351000 | + | 0.936375i | \(0.385842\pi\) | |||||||
\(42\) | −26.9321 | −0.0989457 | ||||||||
\(43\) | 341.728 | 1.21193 | 0.605966 | − | 0.795490i | \(-0.292787\pi\) | ||||
0.605966 | + | 0.795490i | \(0.292787\pi\) | |||||||
\(44\) | 40.6507 | + | 286.708i | 0.139280 | + | 0.982337i | ||||
\(45\) | −1.64008 | − | 1.64008i | −0.00543308 | − | 0.00543308i | ||||
\(46\) | 22.4964 | + | 22.4964i | 0.0721067 | + | 0.0721067i | ||||
\(47\) | −82.1608 | + | 82.1608i | −0.254987 | + | 0.254987i | −0.823012 | − | 0.568025i | \(-0.807708\pi\) |
0.568025 | + | 0.823012i | \(0.307708\pi\) | |||||||
\(48\) | 328.826 | 0.988792 | ||||||||
\(49\) | 74.8658i | 0.218268i | ||||||||
\(50\) | 20.0820 | + | 20.0820i | 0.0568004 | + | 0.0568004i | ||||
\(51\) | −383.212 | −1.05217 | ||||||||
\(52\) | −199.239 | + | 314.191i | −0.531336 | + | 0.837895i | ||||
\(53\) | 182.779 | 0.473711 | 0.236855 | − | 0.971545i | \(-0.423883\pi\) | ||||
0.236855 | + | 0.971545i | \(0.423883\pi\) | |||||||
\(54\) | −24.5189 | + | 24.5189i | −0.0617888 | + | 0.0617888i | ||||
\(55\) | −99.2703 | − | 74.6159i | −0.243375 | − | 0.182931i | ||||
\(56\) | 81.5814i | 0.194675i | ||||||||
\(57\) | −280.636 | + | 280.636i | −0.652126 | + | 0.652126i | ||||
\(58\) | 9.30612 | + | 9.30612i | 0.0210682 | + | 0.0210682i | ||||
\(59\) | −60.1255 | + | 60.1255i | −0.132672 | + | 0.132672i | −0.770325 | − | 0.637652i | \(-0.779906\pi\) |
0.637652 | + | 0.770325i | \(0.279906\pi\) | |||||||
\(60\) | −100.516 | + | 100.516i | −0.216276 | + | 0.216276i | ||||
\(61\) | − | 758.712i | − | 1.59251i | −0.604960 | − | 0.796256i | \(-0.706811\pi\) | ||
0.604960 | − | 0.796256i | \(-0.293189\pi\) | |||||||
\(62\) | 26.3059 | 0.0538848 | ||||||||
\(63\) | −9.84918 | − | 9.84918i | −0.0196965 | − | 0.0196965i | ||||
\(64\) | − | 488.078i | − | 0.953276i | ||||||
\(65\) | −34.8590 | − | 155.696i | −0.0665189 | − | 0.297103i | ||||
\(66\) | 28.8802 | − | 38.4228i | 0.0538623 | − | 0.0716593i | ||||
\(67\) | 62.3670 | + | 62.3670i | 0.113722 | + | 0.113722i | 0.761678 | − | 0.647956i | \(-0.224376\pi\) |
−0.647956 | + | 0.761678i | \(0.724376\pi\) | |||||||
\(68\) | 578.120i | 1.03099i | ||||||||
\(69\) | 668.441i | 1.16624i | ||||||||
\(70\) | −12.3210 | − | 12.3210i | −0.0210377 | − | 0.0210377i | ||||
\(71\) | −225.965 | − | 225.965i | −0.377706 | − | 0.377706i | 0.492568 | − | 0.870274i | \(-0.336058\pi\) |
−0.870274 | + | 0.492568i | \(0.836058\pi\) | |||||||
\(72\) | −1.92289 | − | 1.92289i | −0.00314743 | − | 0.00314743i | ||||
\(73\) | −187.376 | − | 187.376i | −0.300421 | − | 0.300421i | 0.540758 | − | 0.841179i | \(-0.318138\pi\) |
−0.841179 | + | 0.540758i | \(0.818138\pi\) | |||||||
\(74\) | − | 41.5840i | − | 0.0653249i | ||||||
\(75\) | 596.702i | 0.918682i | ||||||||
\(76\) | 423.372 | + | 423.372i | 0.639001 | + | 0.639001i | ||||
\(77\) | −596.149 | − | 448.092i | −0.882305 | − | 0.663179i | ||||
\(78\) | 60.2624 | − | 13.4922i | 0.0874791 | − | 0.0195858i | ||||
\(79\) | − | 392.126i | − | 0.558450i | −0.960226 | − | 0.279225i | \(-0.909922\pi\) | ||
0.960226 | − | 0.279225i | \(-0.0900776\pi\) | |||||||
\(80\) | 150.432 | + | 150.432i | 0.210236 | + | 0.210236i | ||||
\(81\) | −746.933 | −1.02460 | ||||||||
\(82\) | − | 54.4231i | − | 0.0732930i | ||||||
\(83\) | 1047.65 | − | 1047.65i | 1.38548 | − | 1.38548i | 0.550916 | − | 0.834561i | \(-0.314278\pi\) |
0.834561 | − | 0.550916i | \(-0.185722\pi\) | |||||||
\(84\) | −603.629 | + | 603.629i | −0.784063 | + | 0.784063i | ||||
\(85\) | −175.313 | − | 175.313i | −0.223710 | − | 0.223710i | ||||
\(86\) | −60.5096 | + | 60.5096i | −0.0758712 | + | 0.0758712i | ||||
\(87\) | 276.515i | 0.340754i | ||||||||
\(88\) | −116.388 | − | 87.4825i | −0.140989 | − | 0.105973i | ||||
\(89\) | −885.585 | + | 885.585i | −1.05474 | + | 1.05474i | −0.0563269 | + | 0.998412i | \(0.517939\pi\) |
−0.998412 | + | 0.0563269i | \(0.982061\pi\) | |||||||
\(90\) | 0.580816 | 0.000680259 | ||||||||
\(91\) | −209.339 | − | 935.002i | −0.241150 | − | 1.07709i | ||||
\(92\) | 1008.42 | 1.14277 | ||||||||
\(93\) | 390.818 | + | 390.818i | 0.435763 | + | 0.435763i | ||||
\(94\) | − | 29.0963i | − | 0.0319261i | ||||||
\(95\) | −256.772 | −0.277308 | ||||||||
\(96\) | −177.005 | + | 177.005i | −0.188182 | + | 0.188182i | ||||
\(97\) | 523.499 | + | 523.499i | 0.547971 | + | 0.547971i | 0.925854 | − | 0.377882i | \(-0.123348\pi\) |
−0.377882 | + | 0.925854i | \(0.623348\pi\) | |||||||
\(98\) | −13.2564 | − | 13.2564i | −0.0136643 | − | 0.0136643i | ||||
\(99\) | 24.6130 | − | 3.48974i | 0.0249868 | − | 0.00354274i | ||||
\(100\) | 900.193 | 0.900193 | ||||||||
\(101\) | −639.965 | −0.630484 | −0.315242 | − | 0.949011i | \(-0.602086\pi\) | ||||
−0.315242 | + | 0.949011i | \(0.602086\pi\) | |||||||
\(102\) | 67.8551 | − | 67.8551i | 0.0658692 | − | 0.0658692i | ||||
\(103\) | − | 1313.12i | − | 1.25617i | −0.778144 | − | 0.628086i | \(-0.783839\pi\) | ||
0.778144 | − | 0.628086i | \(-0.216161\pi\) | |||||||
\(104\) | −40.8700 | − | 182.544i | −0.0385349 | − | 0.172114i | ||||
\(105\) | − | 366.097i | − | 0.340261i | ||||||
\(106\) | −32.3646 | + | 32.3646i | −0.0296559 | + | 0.0296559i | ||||
\(107\) | 1491.01i | 1.34712i | 0.739134 | + | 0.673558i | \(0.235235\pi\) | ||||
−0.739134 | + | 0.673558i | \(0.764765\pi\) | |||||||
\(108\) | 1099.08i | 0.979250i | ||||||||
\(109\) | 342.830 | − | 342.830i | 0.301258 | − | 0.301258i | −0.540248 | − | 0.841506i | \(-0.681669\pi\) |
0.841506 | + | 0.540248i | \(0.181669\pi\) | |||||||
\(110\) | 30.7899 | − | 4.36554i | 0.0266882 | − | 0.00378398i | ||||
\(111\) | 617.798 | − | 617.798i | 0.528278 | − | 0.528278i | ||||
\(112\) | 903.392 | + | 903.392i | 0.762165 | + | 0.762165i | ||||
\(113\) | −513.821 | −0.427754 | −0.213877 | − | 0.976861i | \(-0.568609\pi\) | ||||
−0.213877 | + | 0.976861i | \(0.568609\pi\) | |||||||
\(114\) | − | 99.3841i | − | 0.0816507i | ||||||
\(115\) | −305.800 | + | 305.800i | −0.247965 | + | 0.247965i | ||||
\(116\) | 417.155 | 0.333896 | ||||||||
\(117\) | 26.9723 | + | 17.1040i | 0.0213128 | + | 0.0135151i | ||||
\(118\) | − | 21.2928i | − | 0.0166115i | ||||||
\(119\) | −1052.81 | − | 1052.81i | −0.811014 | − | 0.811014i | ||||
\(120\) | − | 71.4743i | − | 0.0543724i | ||||||
\(121\) | 1278.54 | − | 369.993i | 0.960587 | − | 0.277981i | ||||
\(122\) | 134.345 | + | 134.345i | 0.0996967 | + | 0.0996967i | ||||
\(123\) | 808.545 | − | 808.545i | 0.592716 | − | 0.592716i | ||||
\(124\) | 589.594 | − | 589.594i | 0.426993 | − | 0.426993i | ||||
\(125\) | −573.850 | + | 573.850i | −0.410614 | + | 0.410614i | ||||
\(126\) | 3.48798 | 0.00246614 | ||||||||
\(127\) | 2798.39 | 1.95525 | 0.977624 | − | 0.210359i | \(-0.0674634\pi\) | ||||
0.977624 | + | 0.210359i | \(0.0674634\pi\) | |||||||
\(128\) | 355.565 | + | 355.565i | 0.245530 | + | 0.245530i | ||||
\(129\) | −1797.94 | −1.22713 | ||||||||
\(130\) | 33.7414 | + | 21.3965i | 0.0227640 | + | 0.0144354i | ||||
\(131\) | − | 2160.53i | − | 1.44096i | −0.693474 | − | 0.720482i | \(-0.743921\pi\) | ||
0.693474 | − | 0.720482i | \(-0.256079\pi\) | |||||||
\(132\) | −213.876 | − | 1508.46i | −0.141027 | − | 0.994655i | ||||
\(133\) | −1542.00 | −1.00532 | ||||||||
\(134\) | −22.0866 | −0.0142387 | ||||||||
\(135\) | −333.292 | − | 333.292i | −0.212483 | − | 0.212483i | ||||
\(136\) | −205.543 | − | 205.543i | −0.129597 | − | 0.129597i | ||||
\(137\) | 1860.48 | − | 1860.48i | 1.16023 | − | 1.16023i | 0.175806 | − | 0.984425i | \(-0.443747\pi\) |
0.984425 | − | 0.175806i | \(-0.0562531\pi\) | |||||||
\(138\) | −118.360 | − | 118.360i | −0.0730109 | − | 0.0730109i | ||||
\(139\) | 363.440i | 0.221774i | 0.993833 | + | 0.110887i | \(0.0353691\pi\) | ||||
−0.993833 | + | 0.110887i | \(0.964631\pi\) | |||||||
\(140\) | −552.299 | −0.333413 | ||||||||
\(141\) | 432.274 | − | 432.274i | 0.258184 | − | 0.258184i | ||||
\(142\) | 80.0230 | 0.0472914 | ||||||||
\(143\) | 1558.40 | + | 703.980i | 0.911330 | + | 0.411677i | ||||
\(144\) | −42.5863 | −0.0246448 | ||||||||
\(145\) | −126.501 | + | 126.501i | −0.0724505 | + | 0.0724505i | ||||
\(146\) | 66.3572 | 0.0376148 | ||||||||
\(147\) | − | 393.892i | − | 0.221005i | ||||||
\(148\) | −932.020 | − | 932.020i | −0.517646 | − | 0.517646i | ||||
\(149\) | 322.640 | − | 322.640i | 0.177394 | − | 0.177394i | −0.612825 | − | 0.790219i | \(-0.709967\pi\) |
0.790219 | + | 0.612825i | \(0.209967\pi\) | |||||||
\(150\) | −105.658 | − | 105.658i | −0.0575127 | − | 0.0575127i | ||||
\(151\) | 1774.60 | + | 1774.60i | 0.956388 | + | 0.956388i | 0.999088 | − | 0.0427003i | \(-0.0135961\pi\) |
−0.0427003 | + | 0.999088i | \(0.513596\pi\) | |||||||
\(152\) | −301.049 | −0.160647 | ||||||||
\(153\) | 49.6298 | 0.0262244 | ||||||||
\(154\) | 184.903 | − | 26.2164i | 0.0967526 | − | 0.0137180i | ||||
\(155\) | 357.585i | 0.185302i | ||||||||
\(156\) | 1048.26 | − | 1653.06i | 0.537998 | − | 0.848401i | ||||
\(157\) | 566.438 | 0.287940 | 0.143970 | − | 0.989582i | \(-0.454013\pi\) | ||||
0.143970 | + | 0.989582i | \(0.454013\pi\) | |||||||
\(158\) | 69.4334 | + | 69.4334i | 0.0349609 | + | 0.0349609i | ||||
\(159\) | −961.659 | −0.479651 | ||||||||
\(160\) | −161.953 | −0.0800219 | ||||||||
\(161\) | −1836.42 | + | 1836.42i | −0.898946 | + | 0.898946i | ||||
\(162\) | 132.259 | − | 132.259i | 0.0641435 | − | 0.0641435i | ||||
\(163\) | 1581.77 | − | 1581.77i | 0.760085 | − | 0.760085i | −0.216252 | − | 0.976337i | \(-0.569383\pi\) |
0.976337 | + | 0.216252i | \(0.0693834\pi\) | |||||||
\(164\) | −1219.78 | − | 1219.78i | −0.580787 | − | 0.580787i | ||||
\(165\) | 522.292 | + | 392.578i | 0.246427 | + | 0.185225i | ||||
\(166\) | 371.013i | 0.173471i | ||||||||
\(167\) | −1009.23 | − | 1009.23i | −0.467643 | − | 0.467643i | 0.433507 | − | 0.901150i | \(-0.357276\pi\) |
−0.901150 | + | 0.433507i | \(0.857276\pi\) | |||||||
\(168\) | − | 429.225i | − | 0.197116i | ||||||
\(169\) | 936.819 | + | 1987.25i | 0.426408 | + | 0.904531i | ||||
\(170\) | 62.0850 | 0.0280100 | ||||||||
\(171\) | 36.3452 | − | 36.3452i | 0.0162537 | − | 0.0162537i | ||||
\(172\) | 2712.40i | 1.20243i | ||||||||
\(173\) | −2250.43 | −0.989001 | −0.494500 | − | 0.869177i | \(-0.664649\pi\) | ||||
−0.494500 | + | 0.869177i | \(0.664649\pi\) | |||||||
\(174\) | −48.9624 | − | 48.9624i | −0.0213323 | − | 0.0213323i | ||||
\(175\) | −1639.33 | + | 1639.33i | −0.708125 | + | 0.708125i | ||||
\(176\) | −2257.56 | + | 320.088i | −0.966876 | + | 0.137088i | ||||
\(177\) | 316.339 | − | 316.339i | 0.134336 | − | 0.134336i | ||||
\(178\) | − | 313.620i | − | 0.132061i | ||||||
\(179\) | 4575.49i | 1.91055i | 0.295722 | + | 0.955274i | \(0.404440\pi\) | ||||
−0.295722 | + | 0.955274i | \(0.595560\pi\) | |||||||
\(180\) | 13.0178 | − | 13.0178i | 0.00539049 | − | 0.00539049i | ||||
\(181\) | 2292.82i | 0.941569i | 0.882248 | + | 0.470785i | \(0.156029\pi\) | ||||
−0.882248 | + | 0.470785i | \(0.843971\pi\) | |||||||
\(182\) | 202.628 | + | 128.493i | 0.0825262 | + | 0.0523325i | ||||
\(183\) | 3991.82i | 1.61248i | ||||||||
\(184\) | −358.531 | + | 358.531i | −0.143648 | + | 0.143648i | ||||
\(185\) | 565.264 | 0.224643 | ||||||||
\(186\) | −138.404 | −0.0545605 | ||||||||
\(187\) | 2630.95 | − | 373.028i | 1.02885 | − | 0.145874i | ||||
\(188\) | −652.134 | − | 652.134i | −0.252988 | − | 0.252988i | ||||
\(189\) | −2001.52 | − | 2001.52i | −0.770314 | − | 0.770314i | ||||
\(190\) | 45.4665 | − | 45.4665i | 0.0173605 | − | 0.0173605i | ||||
\(191\) | −394.909 | −0.149605 | −0.0748027 | − | 0.997198i | \(-0.523833\pi\) | ||||
−0.0748027 | + | 0.997198i | \(0.523833\pi\) | |||||||
\(192\) | 2567.93i | 0.965230i | ||||||||
\(193\) | −321.261 | − | 321.261i | −0.119818 | − | 0.119818i | 0.644655 | − | 0.764473i | \(-0.277001\pi\) |
−0.764473 | + | 0.644655i | \(0.777001\pi\) | |||||||
\(194\) | −185.391 | −0.0686098 | ||||||||
\(195\) | 183.404 | + | 819.165i | 0.0673530 | + | 0.300829i | ||||
\(196\) | −594.232 | −0.216557 | ||||||||
\(197\) | −3447.86 | + | 3447.86i | −1.24695 | + | 1.24695i | −0.289896 | + | 0.957058i | \(0.593621\pi\) |
−0.957058 | + | 0.289896i | \(0.906379\pi\) | |||||||
\(198\) | −3.74027 | + | 4.97612i | −0.00134247 | + | 0.00178605i | ||||
\(199\) | − | 4036.98i | − | 1.43806i | −0.694979 | − | 0.719030i | \(-0.744586\pi\) | ||
0.694979 | − | 0.719030i | \(-0.255414\pi\) | |||||||
\(200\) | −320.052 | + | 320.052i | −0.113156 | + | 0.113156i | ||||
\(201\) | −328.132 | − | 328.132i | −0.115148 | − | 0.115148i | ||||
\(202\) | 113.318 | − | 113.318i | 0.0394705 | − | 0.0394705i | ||||
\(203\) | −759.676 | + | 759.676i | −0.262654 | + | 0.262654i | ||||
\(204\) | − | 3041.67i | − | 1.04392i | ||||||
\(205\) | 739.790 | 0.252045 | ||||||||
\(206\) | 232.513 | + | 232.513i | 0.0786407 | + | 0.0786407i | ||||
\(207\) | − | 86.5696i | − | 0.0290677i | ||||||
\(208\) | −2473.97 | − | 1568.82i | −0.824707 | − | 0.522973i | ||||
\(209\) | 1653.53 | − | 2199.89i | 0.547260 | − | 0.728084i | ||||
\(210\) | 64.8245 | + | 64.8245i | 0.0213015 | + | 0.0213015i | ||||
\(211\) | − | 5695.09i | − | 1.85813i | −0.369913 | − | 0.929066i | \(-0.620613\pi\) | ||
0.369913 | − | 0.929066i | \(-0.379387\pi\) | |||||||
\(212\) | 1450.77i | 0.469998i | ||||||||
\(213\) | 1188.87 | + | 1188.87i | 0.382443 | + | 0.382443i | ||||
\(214\) | −264.012 | − | 264.012i | −0.0843341 | − | 0.0843341i | ||||
\(215\) | −822.525 | − | 822.525i | −0.260911 | − | 0.260911i | ||||
\(216\) | −390.764 | − | 390.764i | −0.123093 | − | 0.123093i | ||||
\(217\) | 2147.40i | 0.671776i | ||||||||
\(218\) | 121.409i | 0.0377196i | ||||||||
\(219\) | 985.845 | + | 985.845i | 0.304188 | + | 0.304188i | ||||
\(220\) | 592.249 | − | 787.938i | 0.181497 | − | 0.241467i | ||||
\(221\) | 2883.15 | + | 1828.30i | 0.877564 | + | 0.556491i | ||||
\(222\) | 218.786i | 0.0661440i | ||||||||
\(223\) | −4263.47 | − | 4263.47i | −1.28028 | − | 1.28028i | −0.940507 | − | 0.339775i | \(-0.889649\pi\) |
−0.339775 | − | 0.940507i | \(-0.610351\pi\) | |||||||
\(224\) | −972.577 | −0.290103 | ||||||||
\(225\) | − | 77.2787i | − | 0.0228974i | ||||||
\(226\) | 90.9819 | − | 90.9819i | 0.0267789 | − | 0.0267789i | ||||
\(227\) | −2966.74 | + | 2966.74i | −0.867442 | + | 0.867442i | −0.992189 | − | 0.124746i | \(-0.960188\pi\) |
0.124746 | + | 0.992189i | \(0.460188\pi\) | |||||||
\(228\) | −2227.49 | − | 2227.49i | −0.647014 | − | 0.647014i | ||||
\(229\) | −2387.53 | + | 2387.53i | −0.688962 | + | 0.688962i | −0.962002 | − | 0.273041i | \(-0.911971\pi\) |
0.273041 | + | 0.962002i | \(0.411971\pi\) | |||||||
\(230\) | − | 108.296i | − | 0.0310469i | ||||||
\(231\) | 3136.52 | + | 2357.55i | 0.893368 | + | 0.671495i | ||||
\(232\) | −148.314 | + | 148.314i | −0.0419712 | + | 0.0419712i | ||||
\(233\) | 3968.40 | 1.11579 | 0.557894 | − | 0.829912i | \(-0.311609\pi\) | ||||
0.557894 | + | 0.829912i | \(0.311609\pi\) | |||||||
\(234\) | −7.80457 | + | 1.74738i | −0.00218035 | + | 0.000488161i | ||||
\(235\) | 395.515 | 0.109790 | ||||||||
\(236\) | −477.234 | − | 477.234i | −0.131633 | − | 0.131633i | ||||
\(237\) | 2063.10i | 0.565453i | ||||||||
\(238\) | 372.840 | 0.101545 | ||||||||
\(239\) | −286.400 | + | 286.400i | −0.0775133 | + | 0.0775133i | −0.744800 | − | 0.667287i | \(-0.767455\pi\) |
0.667287 | + | 0.744800i | \(0.267455\pi\) | |||||||
\(240\) | −791.471 | − | 791.471i | −0.212872 | − | 0.212872i | ||||
\(241\) | −1063.69 | − | 1063.69i | −0.284308 | − | 0.284308i | 0.550516 | − | 0.834824i | \(-0.314431\pi\) |
−0.834824 | + | 0.550516i | \(0.814431\pi\) | |||||||
\(242\) | −160.876 | + | 291.905i | −0.0427335 | + | 0.0775386i | ||||
\(243\) | 191.148 | 0.0504615 | ||||||||
\(244\) | 6022.12 | 1.58003 | ||||||||
\(245\) | 180.199 | − | 180.199i | 0.0469897 | − | 0.0469897i | ||||
\(246\) | 286.337i | 0.0742121i | ||||||||
\(247\) | 3450.32 | − | 772.496i | 0.888819 | − | 0.198999i | ||||
\(248\) | 419.245i | 0.107347i | ||||||||
\(249\) | −5512.01 | + | 5512.01i | −1.40285 | + | 1.40285i | ||||
\(250\) | − | 203.222i | − | 0.0514117i | ||||||
\(251\) | − | 1877.54i | − | 0.472147i | −0.971735 | − | 0.236074i | \(-0.924139\pi\) | ||
0.971735 | − | 0.236074i | \(-0.0758607\pi\) | |||||||
\(252\) | 78.1758 | − | 78.1758i | 0.0195421 | − | 0.0195421i | ||||
\(253\) | −650.676 | − | 4589.19i | −0.161690 | − | 1.14039i | ||||
\(254\) | −495.508 | + | 495.508i | −0.122405 | + | 0.122405i | ||||
\(255\) | 922.375 | + | 922.375i | 0.226515 | + | 0.226515i | ||||
\(256\) | 3778.70 | 0.922534 | ||||||||
\(257\) | 1491.33i | 0.361970i | 0.983486 | + | 0.180985i | \(0.0579286\pi\) | ||||
−0.983486 | + | 0.180985i | \(0.942071\pi\) | |||||||
\(258\) | 318.360 | − | 318.360i | 0.0768226 | − | 0.0768226i | ||||
\(259\) | 3394.58 | 0.814398 | ||||||||
\(260\) | 1235.80 | − | 276.686i | 0.294774 | − | 0.0659975i | ||||
\(261\) | − | 35.8115i | − | 0.00849300i | ||||||
\(262\) | 382.563 | + | 382.563i | 0.0902093 | + | 0.0902093i | ||||
\(263\) | 5422.03i | 1.27124i | 0.772001 | + | 0.635621i | \(0.219256\pi\) | ||||
−0.772001 | + | 0.635621i | \(0.780744\pi\) | |||||||
\(264\) | 612.355 | + | 460.273i | 0.142757 | + | 0.107302i | ||||
\(265\) | −439.942 | − | 439.942i | −0.101983 | − | 0.101983i | ||||
\(266\) | 273.040 | − | 273.040i | 0.0629367 | − | 0.0629367i | ||||
\(267\) | 4659.34 | − | 4659.34i | 1.06797 | − | 1.06797i | ||||
\(268\) | −495.025 | + | 495.025i | −0.112830 | + | 0.112830i | ||||
\(269\) | 1301.12 | 0.294909 | 0.147455 | − | 0.989069i | \(-0.452892\pi\) | ||||
0.147455 | + | 0.989069i | \(0.452892\pi\) | |||||||
\(270\) | 118.032 | 0.0266044 | ||||||||
\(271\) | −4550.29 | − | 4550.29i | −1.01996 | − | 1.01996i | −0.999797 | − | 0.0201679i | \(-0.993580\pi\) |
−0.0201679 | − | 0.999797i | \(-0.506420\pi\) | |||||||
\(272\) | −4552.17 | −1.01476 | ||||||||
\(273\) | 1101.40 | + | 4919.33i | 0.244174 | + | 1.09059i | ||||
\(274\) | 658.868i | 0.145269i | ||||||||
\(275\) | −580.844 | − | 4096.66i | −0.127368 | − | 0.898320i | ||||
\(276\) | −5305.61 | −1.15710 | ||||||||
\(277\) | −1207.10 | −0.261833 | −0.130917 | − | 0.991393i | \(-0.541792\pi\) | ||||
−0.130917 | + | 0.991393i | \(0.541792\pi\) | |||||||
\(278\) | −64.3540 | − | 64.3540i | −0.0138838 | − | 0.0138838i | ||||
\(279\) | −50.6148 | − | 50.6148i | −0.0108610 | − | 0.0108610i | ||||
\(280\) | 196.363 | − | 196.363i | 0.0419105 | − | 0.0419105i | ||||
\(281\) | 66.7436 | + | 66.7436i | 0.0141694 | + | 0.0141694i | 0.714156 | − | 0.699987i | \(-0.246811\pi\) |
−0.699987 | + | 0.714156i | \(0.746811\pi\) | |||||||
\(282\) | 153.085i | 0.0323265i | ||||||||
\(283\) | 2264.55 | 0.475665 | 0.237833 | − | 0.971306i | \(-0.423563\pi\) | ||||
0.237833 | + | 0.971306i | \(0.423563\pi\) | |||||||
\(284\) | 1793.55 | − | 1793.55i | 0.374746 | − | 0.374746i | ||||
\(285\) | 1350.96 | 0.280786 | ||||||||
\(286\) | −400.599 | + | 151.292i | −0.0828248 | + | 0.0312800i | ||||
\(287\) | 4442.66 | 0.913736 | ||||||||
\(288\) | 22.9238 | − | 22.9238i | 0.00469028 | − | 0.00469028i | ||||
\(289\) | 392.067 | 0.0798020 | ||||||||
\(290\) | − | 44.7988i | − | 0.00907131i | ||||||
\(291\) | −2754.29 | − | 2754.29i | −0.554843 | − | 0.554843i | ||||
\(292\) | 1487.26 | − | 1487.26i | 0.298066 | − | 0.298066i | ||||
\(293\) | −249.220 | − | 249.220i | −0.0496914 | − | 0.0496914i | 0.681824 | − | 0.731516i | \(-0.261187\pi\) |
−0.731516 | + | 0.681824i | \(0.761187\pi\) | |||||||
\(294\) | 69.7462 | + | 69.7462i | 0.0138357 | + | 0.0138357i | ||||
\(295\) | 289.439 | 0.0571247 | ||||||||
\(296\) | 662.736 | 0.130138 | ||||||||
\(297\) | 5001.77 | − | 709.174i | 0.977213 | − | 0.138554i | ||||
\(298\) | 114.259i | 0.0222110i | ||||||||
\(299\) | 3189.12 | − | 5029.11i | 0.616827 | − | 0.972712i | ||||
\(300\) | −4736.20 | −0.911481 | ||||||||
\(301\) | −4939.52 | − | 4939.52i | −0.945877 | − | 0.945877i | ||||
\(302\) | −628.453 | −0.119746 | ||||||||
\(303\) | 3367.06 | 0.638390 | ||||||||
\(304\) | −3333.67 | + | 3333.67i | −0.628944 | + | 0.628944i | ||||
\(305\) | −1826.19 | + | 1826.19i | −0.342843 | + | 0.342843i | ||||
\(306\) | −8.78791 | + | 8.78791i | −0.00164174 | + | 0.00164174i | ||||
\(307\) | 3033.65 | + | 3033.65i | 0.563973 | + | 0.563973i | 0.930434 | − | 0.366460i | \(-0.119430\pi\) |
−0.366460 | + | 0.930434i | \(0.619430\pi\) | |||||||
\(308\) | 3556.63 | − | 4731.81i | 0.657981 | − | 0.875389i | ||||
\(309\) | 6908.74i | 1.27192i | ||||||||
\(310\) | −63.3173 | − | 63.3173i | −0.0116006 | − | 0.0116006i | ||||
\(311\) | 7291.68i | 1.32950i | 0.747067 | + | 0.664748i | \(0.231461\pi\) | ||||
−0.747067 | + | 0.664748i | \(0.768539\pi\) | |||||||
\(312\) | 215.030 | + | 960.419i | 0.0390181 | + | 0.174273i | ||||
\(313\) | −3893.12 | −0.703043 | −0.351521 | − | 0.936180i | \(-0.614336\pi\) | ||||
−0.351521 | + | 0.936180i | \(0.614336\pi\) | |||||||
\(314\) | −100.299 | + | 100.299i | −0.0180261 | + | 0.0180261i | ||||
\(315\) | 47.4131i | 0.00848072i | ||||||||
\(316\) | 3112.42 | 0.554073 | ||||||||
\(317\) | −3850.14 | − | 3850.14i | −0.682162 | − | 0.682162i | 0.278325 | − | 0.960487i | \(-0.410221\pi\) |
−0.960487 | + | 0.278325i | \(0.910221\pi\) | |||||||
\(318\) | 170.280 | − | 170.280i | 0.0300278 | − | 0.0300278i | ||||
\(319\) | −269.167 | − | 1898.42i | −0.0472428 | − | 0.333201i | ||||
\(320\) | −1174.78 | + | 1174.78i | −0.205226 | + | 0.205226i | ||||
\(321\) | − | 7844.67i | − | 1.36401i | ||||||
\(322\) | − | 650.348i | − | 0.112554i | ||||||
\(323\) | 3885.04 | − | 3885.04i | 0.669255 | − | 0.669255i | ||||
\(324\) | − | 5928.63i | − | 1.01657i | ||||||
\(325\) | 2846.85 | − | 4489.37i | 0.485892 | − | 0.766232i | ||||
\(326\) | 560.166i | 0.0951679i | ||||||||
\(327\) | −1803.74 | + | 1803.74i | −0.305036 | + | 0.305036i | ||||
\(328\) | 867.357 | 0.146012 | ||||||||
\(329\) | 2375.19 | 0.398019 | ||||||||
\(330\) | −161.995 | + | 22.9684i | −0.0270229 | + | 0.00383143i | ||||
\(331\) | −3385.28 | − | 3385.28i | −0.562150 | − | 0.562150i | 0.367768 | − | 0.929918i | \(-0.380122\pi\) |
−0.929918 | + | 0.367768i | \(0.880122\pi\) | |||||||
\(332\) | 8315.51 | + | 8315.51i | 1.37462 | + | 1.37462i | ||||
\(333\) | −80.0109 | + | 80.0109i | −0.0131669 | + | 0.0131669i | ||||
\(334\) | 357.407 | 0.0585522 | ||||||||
\(335\) | − | 300.229i | − | 0.0489650i | ||||||
\(336\) | −4753.03 | − | 4753.03i | −0.771723 | − | 0.771723i | ||||
\(337\) | 2251.11 | 0.363874 | 0.181937 | − | 0.983310i | \(-0.441763\pi\) | ||||
0.181937 | + | 0.983310i | \(0.441763\pi\) | |||||||
\(338\) | −517.764 | − | 186.000i | −0.0833214 | − | 0.0299321i | ||||
\(339\) | 2703.37 | 0.433118 | ||||||||
\(340\) | 1391.51 | − | 1391.51i | 0.221956 | − | 0.221956i | ||||
\(341\) | −3063.60 | − | 2302.73i | −0.486519 | − | 0.365689i | ||||
\(342\) | 12.8712i | 0.00203508i | ||||||||
\(343\) | −3875.75 | + | 3875.75i | −0.610119 | + | 0.610119i | ||||
\(344\) | −964.360 | − | 964.360i | −0.151148 | − | 0.151148i | ||||
\(345\) | 1608.91 | − | 1608.91i | 0.251074 | − | 0.251074i | ||||
\(346\) | 398.482 | − | 398.482i | 0.0619149 | − | 0.0619149i | ||||
\(347\) | − | 1101.36i | − | 0.170387i | −0.996364 | − | 0.0851935i | \(-0.972849\pi\) | ||
0.996364 | − | 0.0851935i | \(-0.0271508\pi\) | |||||||
\(348\) | −2194.78 | −0.338083 | ||||||||
\(349\) | 5053.24 | + | 5053.24i | 0.775054 | + | 0.775054i | 0.978985 | − | 0.203931i | \(-0.0653718\pi\) |
−0.203931 | + | 0.978985i | \(0.565372\pi\) | |||||||
\(350\) | − | 580.551i | − | 0.0886621i | ||||||
\(351\) | 5481.24 | + | 3475.83i | 0.833524 | + | 0.528564i | ||||
\(352\) | 1042.93 | − | 1387.53i | 0.157921 | − | 0.210101i | ||||
\(353\) | 2864.71 | + | 2864.71i | 0.431935 | + | 0.431935i | 0.889286 | − | 0.457351i | \(-0.151202\pi\) |
−0.457351 | + | 0.889286i | \(0.651202\pi\) | |||||||
\(354\) | 112.028i | 0.0168198i | ||||||||
\(355\) | 1087.78i | 0.162629i | ||||||||
\(356\) | −7029.15 | − | 7029.15i | −1.04647 | − | 1.04647i | ||||
\(357\) | 5539.15 | + | 5539.15i | 0.821184 | + | 0.821184i | ||||
\(358\) | −810.179 | − | 810.179i | −0.119607 | − | 0.119607i | ||||
\(359\) | 5297.61 | + | 5297.61i | 0.778822 | + | 0.778822i | 0.979631 | − | 0.200809i | \(-0.0643569\pi\) |
−0.200809 | + | 0.979631i | \(0.564357\pi\) | |||||||
\(360\) | 9.25663i | 0.00135519i | ||||||||
\(361\) | 1168.77i | 0.170400i | ||||||||
\(362\) | −405.988 | − | 405.988i | −0.0589455 | − | 0.0589455i | ||||
\(363\) | −6726.80 | + | 1946.65i | −0.972632 | + | 0.281467i | ||||
\(364\) | 7421.38 | − | 1661.58i | 1.06864 | − | 0.239260i | ||||
\(365\) | 902.013i | 0.129352i | ||||||||
\(366\) | −706.829 | − | 706.829i | −0.100947 | − | 0.100947i | ||||
\(367\) | 8129.45 | 1.15628 | 0.578139 | − | 0.815938i | \(-0.303779\pi\) | ||||
0.578139 | + | 0.815938i | \(0.303779\pi\) | |||||||
\(368\) | 7940.39i | 1.12479i | ||||||||
\(369\) | −104.714 | + | 104.714i | −0.0147730 | + | 0.0147730i | ||||
\(370\) | −100.091 | + | 100.091i | −0.0140634 | + | 0.0140634i | ||||
\(371\) | −2641.99 | − | 2641.99i | −0.369717 | − | 0.369717i | ||||
\(372\) | −3102.04 | + | 3102.04i | −0.432347 | + | 0.432347i | ||||
\(373\) | 2979.05i | 0.413538i | 0.978390 | + | 0.206769i | \(0.0662948\pi\) | ||||
−0.978390 | + | 0.206769i | \(0.933705\pi\) | |||||||
\(374\) | −399.809 | + | 531.912i | −0.0552770 | + | 0.0735415i | ||||
\(375\) | 3019.20 | − | 3019.20i | 0.415763 | − | 0.415763i | ||||
\(376\) | 463.717 | 0.0636020 | ||||||||
\(377\) | 1319.25 | − | 2080.40i | 0.180225 | − | 0.284207i | ||||
\(378\) | 708.816 | 0.0964486 | ||||||||
\(379\) | −5837.73 | − | 5837.73i | −0.791198 | − | 0.791198i | 0.190491 | − | 0.981689i | \(-0.438992\pi\) |
−0.981689 | + | 0.190491i | \(0.938992\pi\) | |||||||
\(380\) | − | 2038.08i | − | 0.275135i | ||||||
\(381\) | −14723.2 | −1.97977 | ||||||||
\(382\) | 69.9263 | − | 69.9263i | 0.00936581 | − | 0.00936581i | ||||
\(383\) | 444.975 | + | 444.975i | 0.0593659 | + | 0.0593659i | 0.736166 | − | 0.676801i | \(-0.236634\pi\) |
−0.676801 | + | 0.736166i | \(0.736634\pi\) | |||||||
\(384\) | −1870.74 | − | 1870.74i | −0.248609 | − | 0.248609i | ||||
\(385\) | 356.367 | + | 2513.44i | 0.0471744 | + | 0.332719i | ||||
\(386\) | 113.771 | 0.0150021 | ||||||||
\(387\) | 232.851 | 0.0305852 | ||||||||
\(388\) | −4155.16 | + | 4155.16i | −0.543676 | + | 0.543676i | ||||
\(389\) | − | 7247.94i | − | 0.944691i | −0.881413 | − | 0.472346i | \(-0.843407\pi\) | ||
0.881413 | − | 0.472346i | \(-0.156593\pi\) | |||||||
\(390\) | −177.524 | − | 112.574i | −0.0230494 | − | 0.0146164i | ||||
\(391\) | − | 9253.68i | − | 1.19688i | ||||||
\(392\) | 211.272 | − | 211.272i | 0.0272215 | − | 0.0272215i | ||||
\(393\) | 11367.2i | 1.45903i | ||||||||
\(394\) | − | 1221.02i | − | 0.156127i | ||||||
\(395\) | −943.829 | + | 943.829i | −0.120226 | + | 0.120226i | ||||
\(396\) | 27.6991 | + | 195.360i | 0.00351498 | + | 0.0247910i | ||||
\(397\) | −4266.33 | + | 4266.33i | −0.539348 | + | 0.539348i | −0.923337 | − | 0.383990i | \(-0.874550\pi\) |
0.383990 | + | 0.923337i | \(0.374550\pi\) | |||||||
\(398\) | 714.826 | + | 714.826i | 0.0900276 | + | 0.0900276i | ||||
\(399\) | 8112.92 | 1.01793 | ||||||||
\(400\) | 7088.20i | 0.886025i | ||||||||
\(401\) | −3334.39 | + | 3334.39i | −0.415240 | + | 0.415240i | −0.883559 | − | 0.468319i | \(-0.844860\pi\) |
0.468319 | + | 0.883559i | \(0.344860\pi\) | |||||||
\(402\) | 116.204 | 0.0144173 | ||||||||
\(403\) | −1075.79 | − | 4804.96i | −0.132975 | − | 0.593925i | ||||
\(404\) | − | 5079.59i | − | 0.625542i | ||||||
\(405\) | 1797.84 | + | 1797.84i | 0.220581 | + | 0.220581i | ||||
\(406\) | − | 269.031i | − | 0.0328861i | ||||||
\(407\) | −3640.12 | + | 4842.88i | −0.443327 | + | 0.589810i | ||||
\(408\) | 1081.43 | + | 1081.43i | 0.131222 | + | 0.131222i | ||||
\(409\) | −9289.12 | + | 9289.12i | −1.12303 | + | 1.12303i | −0.131741 | + | 0.991284i | \(0.542057\pi\) |
−0.991284 | + | 0.131741i | \(0.957943\pi\) | |||||||
\(410\) | −130.994 | + | 130.994i | −0.0157789 | + | 0.0157789i | ||||
\(411\) | −9788.57 | + | 9788.57i | −1.17478 | + | 1.17478i | ||||
\(412\) | 10422.6 | 1.24632 | ||||||||
\(413\) | 1738.17 | 0.207094 | ||||||||
\(414\) | 15.3288 | + | 15.3288i | 0.00181974 | + | 0.00181974i | ||||
\(415\) | −5043.30 | −0.596544 | ||||||||
\(416\) | 2176.20 | − | 487.234i | 0.256484 | − | 0.0574245i | ||||
\(417\) | − | 1912.17i | − | 0.224555i | ||||||
\(418\) | 96.7429 | + | 682.323i | 0.0113202 | + | 0.0798410i | ||||
\(419\) | −12142.9 | −1.41580 | −0.707900 | − | 0.706313i | \(-0.750357\pi\) | ||||
−0.707900 | + | 0.706313i | \(0.750357\pi\) | |||||||
\(420\) | 2905.82 | 0.337593 | ||||||||
\(421\) | 3791.10 | + | 3791.10i | 0.438876 | + | 0.438876i | 0.891634 | − | 0.452757i | \(-0.149560\pi\) |
−0.452757 | + | 0.891634i | \(0.649560\pi\) | |||||||
\(422\) | 1008.43 | + | 1008.43i | 0.116326 | + | 0.116326i | ||||
\(423\) | −55.9837 | + | 55.9837i | −0.00643503 | + | 0.00643503i | ||||
\(424\) | −515.804 | − | 515.804i | −0.0590794 | − | 0.0590794i | ||||
\(425\) | − | 8260.55i | − | 0.942813i | ||||||
\(426\) | −421.026 | −0.0478845 | ||||||||
\(427\) | −10966.8 | + | 10966.8i | −1.24291 | + | 1.24291i | ||||
\(428\) | −11834.6 | −1.33656 | ||||||||
\(429\) | −8199.24 | − | 3703.86i | −0.922758 | − | 0.416839i | ||||
\(430\) | 291.288 | 0.0326678 | ||||||||
\(431\) | −4614.33 | + | 4614.33i | −0.515695 | + | 0.515695i | −0.916266 | − | 0.400571i | \(-0.868812\pi\) |
0.400571 | + | 0.916266i | \(0.368812\pi\) | |||||||
\(432\) | −8654.26 | −0.963838 | ||||||||
\(433\) | 8774.90i | 0.973891i | 0.873432 | + | 0.486945i | \(0.161889\pi\) | ||||
−0.873432 | + | 0.486945i | \(0.838111\pi\) | |||||||
\(434\) | −380.239 | − | 380.239i | −0.0420555 | − | 0.0420555i | ||||
\(435\) | 665.560 | − | 665.560i | 0.0733590 | − | 0.0733590i | ||||
\(436\) | 2721.14 | + | 2721.14i | 0.298897 | + | 0.298897i | ||||
\(437\) | −6776.71 | − | 6776.71i | −0.741817 | − | 0.741817i | ||||
\(438\) | −349.126 | −0.0380865 | ||||||||
\(439\) | 2248.53 | 0.244457 | 0.122228 | − | 0.992502i | \(-0.460996\pi\) | ||||
0.122228 | + | 0.992502i | \(0.460996\pi\) | |||||||
\(440\) | 69.5748 | + | 490.708i | 0.00753829 | + | 0.0531672i | ||||
\(441\) | 51.0129i | 0.00550836i | ||||||||
\(442\) | −834.253 | + | 186.782i | −0.0897769 | + | 0.0201003i | ||||
\(443\) | 3351.20 | 0.359413 | 0.179707 | − | 0.983720i | \(-0.442485\pi\) | ||||
0.179707 | + | 0.983720i | \(0.442485\pi\) | |||||||
\(444\) | 4903.65 | + | 4903.65i | 0.524137 | + | 0.524137i | ||||
\(445\) | 4263.13 | 0.454139 | ||||||||
\(446\) | 1509.86 | 0.160300 | ||||||||
\(447\) | −1697.51 | + | 1697.51i | −0.179619 | + | 0.179619i | ||||
\(448\) | −7054.92 | + | 7054.92i | −0.744004 | + | 0.744004i | ||||
\(449\) | 10506.9 | − | 10506.9i | 1.10434 | − | 1.10434i | 0.110464 | − | 0.993880i | \(-0.464766\pi\) |
0.993880 | − | 0.110464i | \(-0.0352336\pi\) | |||||||
\(450\) | 13.6837 | + | 13.6837i | 0.00143346 | + | 0.00143346i | ||||
\(451\) | −4764.02 | + | 6338.13i | −0.497403 | + | 0.661754i | ||||
\(452\) | − | 4078.34i | − | 0.424401i | ||||||
\(453\) | −9336.70 | − | 9336.70i | −0.968380 | − | 0.968380i | ||||
\(454\) | − | 1050.64i | − | 0.108610i | ||||||
\(455\) | −1746.64 | + | 2754.38i | −0.179964 | + | 0.283796i | ||||
\(456\) | 1583.91 | 0.162661 | ||||||||
\(457\) | −1038.93 | + | 1038.93i | −0.106344 | + | 0.106344i | −0.758277 | − | 0.651933i | \(-0.773958\pi\) |
0.651933 | + | 0.758277i | \(0.273958\pi\) | |||||||
\(458\) | − | 845.516i | − | 0.0862628i | ||||||
\(459\) | 10085.6 | 1.02561 | ||||||||
\(460\) | −2427.22 | − | 2427.22i | −0.246021 | − | 0.246021i | ||||
\(461\) | 10531.6 | − | 10531.6i | 1.06401 | − | 1.06401i | 0.0661994 | − | 0.997806i | \(-0.478913\pi\) |
0.997806 | − | 0.0661994i | \(-0.0210873\pi\) | |||||||
\(462\) | −972.832 | + | 137.933i | −0.0979659 | + | 0.0138900i | ||||
\(463\) | 7606.71 | − | 7606.71i | 0.763528 | − | 0.763528i | −0.213430 | − | 0.976958i | \(-0.568464\pi\) |
0.976958 | + | 0.213430i | \(0.0684635\pi\) | |||||||
\(464\) | 3284.72i | 0.328641i | ||||||||
\(465\) | − | 1881.36i | − | 0.187626i | ||||||
\(466\) | −702.682 | + | 702.682i | −0.0698522 | + | 0.0698522i | ||||
\(467\) | − | 7569.94i | − | 0.750097i | −0.927005 | − | 0.375048i | \(-0.877626\pi\) | ||
0.927005 | − | 0.375048i | \(-0.122374\pi\) | |||||||
\(468\) | −135.760 | + | 214.087i | −0.0134092 | + | 0.0211457i | ||||
\(469\) | − | 1802.97i | − | 0.177513i | ||||||
\(470\) | −70.0336 | + | 70.0336i | −0.00687321 | + | 0.00687321i | ||||
\(471\) | −2980.20 | −0.291551 | ||||||||
\(472\) | 339.349 | 0.0330928 | ||||||||
\(473\) | 12343.8 | − | 1750.16i | 1.19993 | − | 0.170132i | ||||
\(474\) | −365.311 | − | 365.311i | −0.0353993 | − | 0.0353993i | ||||
\(475\) | −6049.41 | − | 6049.41i | −0.584350 | − | 0.584350i | ||||
\(476\) | 8356.44 | − | 8356.44i | 0.804657 | − | 0.804657i | ||||
\(477\) | 124.544 | 0.0119549 | ||||||||
\(478\) | − | 101.425i | − | 0.00970520i | ||||||
\(479\) | 10898.7 | + | 10898.7i | 1.03962 | + | 1.03962i | 0.999182 | + | 0.0404338i | \(0.0128740\pi\) |
0.0404338 | + | 0.999182i | \(0.487126\pi\) | |||||||
\(480\) | 852.085 | 0.0810254 | ||||||||
\(481\) | −7595.59 | + | 1700.59i | −0.720019 | + | 0.161206i | ||||
\(482\) | 376.694 | 0.0355974 | ||||||||
\(483\) | 9661.98 | − | 9661.98i | 0.910218 | − | 0.910218i | ||||
\(484\) | 2936.74 | + | 10148.2i | 0.275802 | + | 0.953057i | ||||
\(485\) | − | 2520.08i | − | 0.235940i | ||||||
\(486\) | −33.8464 | + | 33.8464i | −0.00315906 | + | 0.00315906i | ||||
\(487\) | −3149.01 | − | 3149.01i | −0.293009 | − | 0.293009i | 0.545259 | − | 0.838268i | \(-0.316431\pi\) |
−0.838268 | + | 0.545259i | \(0.816431\pi\) | |||||||
\(488\) | −2141.09 | + | 2141.09i | −0.198612 | + | 0.198612i | ||||
\(489\) | −8322.19 | + | 8322.19i | −0.769616 | + | 0.769616i | ||||
\(490\) | 63.8153i | 0.00588343i | ||||||||
\(491\) | 8514.23 | 0.782570 | 0.391285 | − | 0.920270i | \(-0.372031\pi\) | ||||
0.391285 | + | 0.920270i | \(0.372031\pi\) | |||||||
\(492\) | 6417.66 | + | 6417.66i | 0.588070 | + | 0.588070i | ||||
\(493\) | − | 3827.99i | − | 0.349704i | ||||||
\(494\) | −474.160 | + | 747.731i | −0.0431851 | + | 0.0681012i | ||||
\(495\) | −67.6420 | − | 50.8427i | −0.00614198 | − | 0.00461658i | ||||
\(496\) | 4642.51 | + | 4642.51i | 0.420272 | + | 0.420272i | ||||
\(497\) | 6532.43i | 0.589577i | ||||||||
\(498\) | − | 1952.02i | − | 0.175647i | ||||||
\(499\) | 3839.37 | + | 3839.37i | 0.344437 | + | 0.344437i | 0.858032 | − | 0.513596i | \(-0.171687\pi\) |
−0.513596 | + | 0.858032i | \(0.671687\pi\) | |||||||
\(500\) | −4554.82 | − | 4554.82i | −0.407395 | − | 0.407395i | ||||
\(501\) | 5309.86 | + | 5309.86i | 0.473507 | + | 0.473507i | ||||
\(502\) | 332.454 | + | 332.454i | 0.0295581 | + | 0.0295581i | ||||
\(503\) | 6025.96i | 0.534163i | 0.963674 | + | 0.267082i | \(0.0860593\pi\) | ||||
−0.963674 | + | 0.267082i | \(0.913941\pi\) | |||||||
\(504\) | 55.5889i | 0.00491295i | ||||||||
\(505\) | 1540.37 | + | 1540.37i | 0.135734 | + | 0.135734i | ||||
\(506\) | 927.819 | + | 697.390i | 0.0815150 | + | 0.0612703i | ||||
\(507\) | −4928.90 | − | 10455.6i | −0.431755 | − | 0.915873i | ||||
\(508\) | 22211.6i | 1.93992i | ||||||||
\(509\) | −3343.96 | − | 3343.96i | −0.291196 | − | 0.291196i | 0.546357 | − | 0.837552i | \(-0.316014\pi\) |
−0.837552 | + | 0.546357i | \(0.816014\pi\) | |||||||
\(510\) | −326.649 | −0.0283613 | ||||||||
\(511\) | 5416.86i | 0.468939i | ||||||||
\(512\) | −3513.61 | + | 3513.61i | −0.303284 | + | 0.303284i | ||||
\(513\) | 7385.96 | − | 7385.96i | 0.635668 | − | 0.635668i | ||||
\(514\) | −264.068 | − | 264.068i | −0.0226606 | − | 0.0226606i | ||||
\(515\) | −3160.62 | + | 3160.62i | −0.270435 | + | 0.270435i | ||||
\(516\) | − | 14270.8i | − | 1.21751i | ||||||
\(517\) | −2547.00 | + | 3388.57i | −0.216667 | + | 0.288257i | ||||
\(518\) | −601.076 | + | 601.076i | −0.0509841 | + | 0.0509841i | ||||
\(519\) | 11840.2 | 1.00140 | ||||||||
\(520\) | −341.003 | + | 537.747i | −0.0287576 | + | 0.0453496i | ||||
\(521\) | 4817.90 | 0.405136 | 0.202568 | − | 0.979268i | \(-0.435071\pi\) | ||||
0.202568 | + | 0.979268i | \(0.435071\pi\) | |||||||
\(522\) | 6.34111 | + | 6.34111i | 0.000531691 | + | 0.000531691i | ||||
\(523\) | − | 10322.1i | − | 0.863013i | −0.902110 | − | 0.431506i | \(-0.857982\pi\) | ||
0.902110 | − | 0.431506i | \(-0.142018\pi\) | |||||||
\(524\) | 17148.7 | 1.42967 | ||||||||
\(525\) | 8625.03 | − | 8625.03i | 0.717004 | − | 0.717004i | ||||
\(526\) | −960.076 | − | 960.076i | −0.0795842 | − | 0.0795842i | ||||
\(527\) | −5410.36 | − | 5410.36i | −0.447208 | − | 0.447208i | ||||
\(528\) | 11877.7 | − | 1684.08i | 0.979001 | − | 0.138807i | ||||
\(529\) | −3974.28 | −0.326644 | ||||||||
\(530\) | 155.800 | 0.0127689 | ||||||||
\(531\) | −40.9690 | + | 40.9690i | −0.00334822 | + | 0.00334822i | ||||
\(532\) | − | 12239.3i | − | 0.997443i | ||||||
\(533\) | −9940.75 | + | 2225.65i | −0.807846 | + | 0.180870i | ||||
\(534\) | 1650.05i | 0.133717i | ||||||||
\(535\) | 3588.80 | − | 3588.80i | 0.290014 | − | 0.290014i | ||||
\(536\) | − | 352.000i | − | 0.0283658i | ||||||
\(537\) | − | 24073.1i | − | 1.93451i | ||||||
\(538\) | −230.388 | + | 230.388i | −0.0184623 | + | 0.0184623i | ||||
\(539\) | 383.424 | + | 2704.27i | 0.0306405 | + | 0.216106i | ||||
\(540\) | 2645.44 | − | 2645.44i | 0.210818 | − | 0.210818i | ||||
\(541\) | −14735.7 | − | 14735.7i | −1.17105 | − | 1.17105i | −0.981960 | − | 0.189088i | \(-0.939447\pi\) |
−0.189088 | − | 0.981960i | \(-0.560553\pi\) | |||||||
\(542\) | 1611.43 | 0.127707 | ||||||||
\(543\) | − | 12063.2i | − | 0.953376i | ||||||
\(544\) | 2450.40 | − | 2450.40i | 0.193125 | − | 0.193125i | ||||
\(545\) | −1650.35 | −0.129713 | ||||||||
\(546\) | −1066.09 | − | 676.040i | −0.0835610 | − | 0.0529887i | ||||
\(547\) | − | 14950.4i | − | 1.16862i | −0.811531 | − | 0.584309i | \(-0.801365\pi\) | ||
0.811531 | − | 0.584309i | \(-0.198635\pi\) | |||||||
\(548\) | 14767.2 | + | 14767.2i | 1.15114 | + | 1.15114i | ||||
\(549\) | − | 516.980i | − | 0.0401898i | ||||||
\(550\) | 828.243 | + | 622.544i | 0.0642116 | + | 0.0482643i | ||||
\(551\) | −2803.34 | − | 2803.34i | −0.216744 | − | 0.216744i | ||||
\(552\) | 1886.34 | − | 1886.34i | 0.145449 | − | 0.145449i | ||||
\(553\) | −5667.98 | + | 5667.98i | −0.435854 | + | 0.435854i | ||||
\(554\) | 213.741 | − | 213.741i | 0.0163917 | − | 0.0163917i | ||||
\(555\) | −2974.03 | −0.227460 | ||||||||
\(556\) | −2884.73 | −0.220035 | ||||||||
\(557\) | 3548.72 | + | 3548.72i | 0.269954 | + | 0.269954i | 0.829082 | − | 0.559128i | \(-0.188864\pi\) |
−0.559128 | + | 0.829082i | \(0.688864\pi\) | |||||||
\(558\) | 17.9246 | 0.00135988 | ||||||||
\(559\) | 13527.0 | + | 8577.93i | 1.02349 | + | 0.649030i | ||||
\(560\) | − | 4348.85i | − | 0.328165i | ||||||
\(561\) | −13842.2 | + | 1962.62i | −1.04175 | + | 0.147704i | ||||
\(562\) | −23.6365 | −0.00177410 | ||||||||
\(563\) | −3831.62 | −0.286827 | −0.143413 | − | 0.989663i | \(-0.545808\pi\) | ||||
−0.143413 | + | 0.989663i | \(0.545808\pi\) | |||||||
\(564\) | 3431.08 | + | 3431.08i | 0.256161 | + | 0.256161i | ||||
\(565\) | 1236.74 | + | 1236.74i | 0.0920889 | + | 0.0920889i | ||||
\(566\) | −400.982 | + | 400.982i | −0.0297783 | + | 0.0297783i | ||||
\(567\) | 10796.6 | + | 10796.6i | 0.799670 | + | 0.799670i | ||||
\(568\) | 1275.35i | 0.0942122i | ||||||||
\(569\) | −5696.87 | −0.419728 | −0.209864 | − | 0.977731i | \(-0.567302\pi\) | ||||
−0.209864 | + | 0.977731i | \(0.567302\pi\) | |||||||
\(570\) | −239.213 | + | 239.213i | −0.0175781 | + | 0.0175781i | ||||
\(571\) | −8191.24 | −0.600337 | −0.300169 | − | 0.953886i | \(-0.597043\pi\) | ||||
−0.300169 | + | 0.953886i | \(0.597043\pi\) | |||||||
\(572\) | −5587.70 | + | 12369.5i | −0.408450 | + | 0.904187i | ||||
\(573\) | 2077.74 | 0.151481 | ||||||||
\(574\) | −786.660 | + | 786.660i | −0.0572030 | + | 0.0572030i | ||||
\(575\) | −14408.9 | −1.04503 | ||||||||
\(576\) | − | 332.572i | − | 0.0240576i | ||||||
\(577\) | 9541.10 | + | 9541.10i | 0.688391 | + | 0.688391i | 0.961876 | − | 0.273486i | \(-0.0881766\pi\) |
−0.273486 | + | 0.961876i | \(0.588177\pi\) | |||||||
\(578\) | −69.4231 | + | 69.4231i | −0.00499588 | + | 0.00499588i | ||||
\(579\) | 1690.26 | + | 1690.26i | 0.121321 | + | 0.121321i | ||||
\(580\) | −1004.07 | − | 1004.07i | −0.0718826 | − | 0.0718826i | ||||
\(581\) | −30286.5 | −2.16265 | ||||||||
\(582\) | 975.400 | 0.0694702 | ||||||||
\(583\) | 6602.28 | − | 936.102i | 0.469020 | − | 0.0664998i | ||||
\(584\) | 1057.55i | 0.0749347i | ||||||||
\(585\) | −23.7526 | − | 106.090i | −0.00167872 | − | 0.00749791i | ||||
\(586\) | 88.2584 | 0.00622171 | ||||||||
\(587\) | −11254.8 | − | 11254.8i | −0.791374 | − | 0.791374i | 0.190344 | − | 0.981717i | \(-0.439040\pi\) |
−0.981717 | + | 0.190344i | \(0.939040\pi\) | |||||||
\(588\) | 3126.44 | 0.219272 | ||||||||
\(589\) | −7924.29 | −0.554354 | ||||||||
\(590\) | −51.2508 | + | 51.2508i | −0.00357621 | + | 0.00357621i | ||||
\(591\) | 18140.3 | − | 18140.3i | 1.26259 | − | 1.26259i | ||||
\(592\) | 7338.81 | − | 7338.81i | 0.509499 | − | 0.509499i | ||||
\(593\) | −1020.17 | − | 1020.17i | −0.0706467 | − | 0.0706467i | 0.670901 | − | 0.741547i | \(-0.265908\pi\) |
−0.741547 | + | 0.670901i | \(0.765908\pi\) | |||||||
\(594\) | −760.087 | + | 1011.23i | −0.0525030 | + | 0.0698509i | ||||
\(595\) | 5068.12i | 0.349198i | ||||||||
\(596\) | 2560.89 | + | 2560.89i | 0.176004 | + | 0.176004i | ||||
\(597\) | 21239.8i | 1.45609i | ||||||||
\(598\) | 325.806 | + | 1455.20i | 0.0222796 | + | 0.0995106i | ||||
\(599\) | 19521.6 | 1.33161 | 0.665803 | − | 0.746127i | \(-0.268089\pi\) | ||||
0.665803 | + | 0.746127i | \(0.268089\pi\) | |||||||
\(600\) | 1683.90 | − | 1683.90i | 0.114575 | − | 0.114575i | ||||
\(601\) | − | 13811.4i | − | 0.937405i | −0.883356 | − | 0.468703i | \(-0.844722\pi\) | ||
0.883356 | − | 0.468703i | \(-0.155278\pi\) | |||||||
\(602\) | 1749.27 | 0.118430 | ||||||||
\(603\) | 42.4964 | + | 42.4964i | 0.00286996 | + | 0.00286996i | ||||
\(604\) | −14085.5 | + | 14085.5i | −0.948891 | + | 0.948891i | ||||
\(605\) | −3967.95 | − | 2186.84i | −0.266645 | − | 0.146955i | ||||
\(606\) | −596.202 | + | 596.202i | −0.0399655 | + | 0.0399655i | ||||
\(607\) | − | 3152.31i | − | 0.210788i | −0.994431 | − | 0.105394i | \(-0.966390\pi\) | ||
0.994431 | − | 0.105394i | \(-0.0336104\pi\) | |||||||
\(608\) | − | 3588.98i | − | 0.239395i | ||||||
\(609\) | 3996.89 | − | 3996.89i | 0.265948 | − | 0.265948i | ||||
\(610\) | − | 646.724i | − | 0.0429264i | ||||||
\(611\) | −5314.64 | + | 1189.90i | −0.351894 | + | 0.0787861i | ||||
\(612\) | 393.926i | 0.0260188i | ||||||||
\(613\) | 7095.63 | − | 7095.63i | 0.467520 | − | 0.467520i | −0.433590 | − | 0.901110i | \(-0.642753\pi\) |
0.901110 | + | 0.433590i | \(0.142753\pi\) | |||||||
\(614\) | −1074.33 | −0.0706134 | ||||||||
\(615\) | −3892.26 | −0.255205 | ||||||||
\(616\) | 417.818 | + | 2946.85i | 0.0273285 | + | 0.192747i | ||||
\(617\) | 16049.0 | + | 16049.0i | 1.04718 | + | 1.04718i | 0.998830 | + | 0.0483496i | \(0.0153962\pi\) |
0.0483496 | + | 0.998830i | \(0.484604\pi\) | |||||||
\(618\) | −1223.33 | − | 1223.33i | −0.0796268 | − | 0.0796268i | ||||
\(619\) | 9734.07 | − | 9734.07i | 0.632060 | − | 0.632060i | −0.316524 | − | 0.948584i | \(-0.602516\pi\) |
0.948584 | + | 0.316524i | \(0.102516\pi\) | |||||||
\(620\) | −2838.25 | −0.183850 | ||||||||
\(621\) | − | 17592.4i | − | 1.13681i | ||||||
\(622\) | −1291.13 | − | 1291.13i | −0.0832311 | − | 0.0832311i | ||||
\(623\) | 25601.4 | 1.64639 | ||||||||
\(624\) | 13016.3 | + | 8254.07i | 0.835049 | + | 0.529531i | ||||
\(625\) | −11414.2 | −0.730507 | ||||||||
\(626\) | 689.353 | − | 689.353i | 0.0440129 | − | 0.0440129i | ||||
\(627\) | −8699.76 | + | 11574.3i | −0.554123 | + | 0.737214i | ||||
\(628\) | 4495.98i | 0.285683i | ||||||||
\(629\) | −8552.60 | + | 8552.60i | −0.542153 | + | 0.542153i | ||||
\(630\) | −8.39541 | − | 8.39541i | −0.000530922 | − | 0.000530922i | ||||
\(631\) | −7495.12 | + | 7495.12i | −0.472862 | + | 0.472862i | −0.902840 | − | 0.429977i | \(-0.858522\pi\) |
0.429977 | + | 0.902840i | \(0.358522\pi\) | |||||||
\(632\) | −1106.58 | + | 1106.58i | −0.0696478 | + | 0.0696478i | ||||
\(633\) | 29963.6i | 1.88143i | ||||||||
\(634\) | 1363.48 | 0.0854114 | ||||||||
\(635\) | −6735.59 | − | 6735.59i | −0.420935 | − | 0.420935i | ||||
\(636\) | − | 7632.97i | − | 0.475891i | ||||||
\(637\) | −1879.25 | + | 2963.50i | −0.116890 | + | 0.184330i | ||||
\(638\) | 383.813 | + | 288.491i | 0.0238171 | + | 0.0179020i | ||||
\(639\) | −153.971 | − | 153.971i | −0.00953207 | − | 0.00953207i | ||||
\(640\) | − | 1711.66i | − | 0.105718i | ||||||
\(641\) | − | 8362.09i | − | 0.515261i | −0.966243 | − | 0.257631i | \(-0.917058\pi\) | ||
0.966243 | − | 0.257631i | \(-0.0829418\pi\) | |||||||
\(642\) | 1389.05 | + | 1389.05i | 0.0853917 | + | 0.0853917i | ||||
\(643\) | −16281.7 | − | 16281.7i | −0.998582 | − | 0.998582i | 0.00141660 | − | 0.999999i | \(-0.499549\pi\) |
−0.999999 | + | 0.00141660i | \(0.999549\pi\) | |||||||
\(644\) | −14576.2 | − | 14576.2i | −0.891900 | − | 0.891900i | ||||
\(645\) | 4327.56 | + | 4327.56i | 0.264182 | + | 0.264182i | ||||
\(646\) | 1375.84i | 0.0837953i | ||||||||
\(647\) | − | 6538.20i | − | 0.397285i | −0.980072 | − | 0.198642i | \(-0.936347\pi\) | ||
0.980072 | − | 0.198642i | \(-0.0636532\pi\) | |||||||
\(648\) | 2107.85 | + | 2107.85i | 0.127784 | + | 0.127784i | ||||
\(649\) | −1863.90 | + | 2479.76i | −0.112734 | + | 0.149983i | ||||
\(650\) | 290.839 | + | 1299.02i | 0.0175502 | + | 0.0783873i | ||||
\(651\) | − | 11298.2i | − | 0.680200i | ||||||
\(652\) | 12555.0 | + | 12555.0i | 0.754127 | + | 0.754127i | ||||
\(653\) | 30618.5 | 1.83491 | 0.917455 | − | 0.397839i | \(-0.130240\pi\) | ||||
0.917455 | + | 0.397839i | \(0.130240\pi\) | |||||||
\(654\) | − | 638.773i | − | 0.0381926i | ||||||
\(655\) | −5200.30 | + | 5200.30i | −0.310217 | + | 0.310217i | ||||
\(656\) | 9604.68 | − | 9604.68i | 0.571646 | − | 0.571646i | ||||
\(657\) | −127.677 | − | 127.677i | −0.00758164 | − | 0.00758164i | ||||
\(658\) | −420.573 | + | 420.573i | −0.0249174 | + | 0.0249174i | ||||
\(659\) | 26971.1i | 1.59430i | 0.603782 | + | 0.797149i | \(0.293660\pi\) | ||||
−0.603782 | + | 0.797149i | \(0.706340\pi\) | |||||||
\(660\) | −3116.00 | + | 4145.58i | −0.183773 | + | 0.244495i | ||||
\(661\) | −20378.3 | + | 20378.3i | −1.19913 | + | 1.19913i | −0.224701 | + | 0.974428i | \(0.572141\pi\) |
−0.974428 | + | 0.224701i | \(0.927859\pi\) | |||||||
\(662\) | 1198.86 | 0.0703851 | ||||||||
\(663\) | −15169.2 | − | 9619.24i | −0.888569 | − | 0.563470i | ||||
\(664\) | −5912.95 | −0.345583 | ||||||||
\(665\) | 3711.52 | + | 3711.52i | 0.216431 | + | 0.216431i | ||||
\(666\) | − | 28.3350i | − | 0.00164859i | ||||||
\(667\) | −6677.20 | −0.387619 | ||||||||
\(668\) | 8010.54 | − | 8010.54i | 0.463978 | − | 0.463978i | ||||
\(669\) | 22431.4 | + | 22431.4i | 1.29634 | + | 1.29634i | ||||
\(670\) | 53.1614 | + | 53.1614i | 0.00306538 | + | 0.00306538i | ||||
\(671\) | −3885.74 | − | 27405.9i | −0.223558 | − | 1.57674i | ||||
\(672\) | 5117.03 | 0.293741 | ||||||||
\(673\) | −13616.2 | −0.779889 | −0.389944 | − | 0.920838i | \(-0.627506\pi\) | ||||
−0.389944 | + | 0.920838i | \(0.627506\pi\) | |||||||
\(674\) | −398.602 | + | 398.602i | −0.0227798 | + | 0.0227798i | ||||
\(675\) | − | 15704.4i | − | 0.895498i | ||||||
\(676\) | −15773.4 | + | 7435.81i | −0.897441 | + | 0.423066i | ||||
\(677\) | 25802.6i | 1.46481i | 0.680871 | + | 0.732403i | \(0.261601\pi\) | ||||
−0.680871 | + | 0.732403i | \(0.738399\pi\) | |||||||
\(678\) | −478.684 | + | 478.684i | −0.0271147 | + | 0.0271147i | ||||
\(679\) | − | 15133.8i | − | 0.855351i | ||||||
\(680\) | 989.468i | 0.0558005i | ||||||||
\(681\) | 15608.9 | − | 15608.9i | 0.878320 | − | 0.878320i | ||||
\(682\) | 950.213 | − | 134.725i | 0.0533512 | − | 0.00756438i | ||||
\(683\) | 11929.0 | − | 11929.0i | 0.668300 | − | 0.668300i | −0.289022 | − | 0.957322i | \(-0.593330\pi\) |
0.957322 | + | 0.289022i | \(0.0933302\pi\) | |||||||
\(684\) | 288.482 | + | 288.482i | 0.0161263 | + | 0.0161263i | ||||
\(685\) | −8956.19 | −0.499560 | ||||||||
\(686\) | − | 1372.55i | − | 0.0763911i | ||||||
\(687\) | 12561.5 | − | 12561.5i | 0.697601 | − | 0.697601i | ||||
\(688\) | −21357.7 | −1.18351 | ||||||||
\(689\) | 7235.17 | + | 4588.05i | 0.400055 | + | 0.253688i | ||||
\(690\) | 569.776i | 0.0314363i | ||||||||
\(691\) | 16812.6 | + | 16812.6i | 0.925588 | + | 0.925588i | 0.997417 | − | 0.0718287i | \(-0.0228835\pi\) |
−0.0718287 | + | 0.997417i | \(0.522884\pi\) | |||||||
\(692\) | − | 17862.3i | − | 0.981249i | ||||||
\(693\) | −406.211 | − | 305.326i | −0.0222665 | − | 0.0167365i | ||||
\(694\) | 195.018 | + | 195.018i | 0.0106668 | + | 0.0106668i | ||||
\(695\) | 874.784 | − | 874.784i | 0.0477445 | − | 0.0477445i | ||||
\(696\) | 780.328 | − | 780.328i | 0.0424975 | − | 0.0424975i | ||||
\(697\) | −11193.2 | + | 11193.2i | −0.608284 | + | 0.608284i | ||||
\(698\) | −1789.55 | −0.0970422 | ||||||||
\(699\) | −20879.0 | −1.12978 | ||||||||
\(700\) | −13011.9 | − | 13011.9i | −0.702574 | − | 0.702574i | ||||
\(701\) | −10452.6 | −0.563181 | −0.281591 | − | 0.959535i | \(-0.590862\pi\) | ||||
−0.281591 | + | 0.959535i | \(0.590862\pi\) | |||||||
\(702\) | −1586.02 | + | 355.097i | −0.0852714 | + | 0.0190916i | ||||
\(703\) | 12526.6i | 0.672047i | ||||||||
\(704\) | −2499.68 | − | 17630.1i | −0.133821 | − | 0.943837i | ||||
\(705\) | −2080.93 | −0.111166 | ||||||||
\(706\) | −1014.50 | −0.0540812 | ||||||||
\(707\) | 9250.38 | + | 9250.38i | 0.492074 | + | 0.492074i | ||||
\(708\) | 2510.88 | + | 2510.88i | 0.133283 | + | 0.133283i | ||||
\(709\) | −17085.4 | + | 17085.4i | −0.905016 | + | 0.905016i | −0.995865 | − | 0.0908486i | \(-0.971042\pi\) |
0.0908486 | + | 0.995865i | \(0.471042\pi\) | |||||||
\(710\) | −192.612 | − | 192.612i | −0.0101811 | − | 0.0101811i | ||||
\(711\) | − | 267.191i | − | 0.0140935i | ||||||
\(712\) | 4998.25 | 0.263086 | ||||||||
\(713\) | −9437.34 | + | 9437.34i | −0.495696 | + | 0.495696i | ||||
\(714\) | −1961.63 | −0.102818 | ||||||||
\(715\) | −2056.56 | − | 5445.46i | −0.107568 | − | 0.284823i | ||||
\(716\) | −36317.0 | −1.89557 | ||||||||
\(717\) | 1506.84 | − | 1506.84i | 0.0784853 | − | 0.0784853i | ||||
\(718\) | −1876.09 | −0.0975139 | ||||||||
\(719\) | 18134.0i | 0.940591i | 0.882509 | + | 0.470296i | \(0.155853\pi\) | ||||
−0.882509 | + | 0.470296i | \(0.844147\pi\) | |||||||
\(720\) | 102.503 | + | 102.503i | 0.00530565 | + | 0.00530565i | ||||
\(721\) | −18980.5 | + | 18980.5i | −0.980404 | + | 0.980404i | ||||
\(722\) | −206.954 | − | 206.954i | −0.0106676 | − | 0.0106676i | ||||
\(723\) | 5596.40 | + | 5596.40i | 0.287873 | + | 0.287873i | ||||
\(724\) | −18198.8 | −0.934189 | ||||||||
\(725\) | −5960.58 | −0.305338 | ||||||||
\(726\) | 846.419 | − | 1535.80i | 0.0432693 | − | 0.0785109i | ||||
\(727\) | 30588.7i | 1.56049i | 0.625477 | + | 0.780243i | \(0.284904\pi\) | ||||
−0.625477 | + | 0.780243i | \(0.715096\pi\) | |||||||
\(728\) | −2047.82 | + | 3229.34i | −0.104255 | + | 0.164405i | ||||
\(729\) | 19161.5 | 0.973506 | ||||||||
\(730\) | −159.719 | − | 159.719i | −0.00809789 | − | 0.00809789i | ||||
\(731\) | 24890.1 | 1.25936 | ||||||||
\(732\) | −31684.3 | −1.59984 | ||||||||
\(733\) | 21298.7 | − | 21298.7i | 1.07324 | − | 1.07324i | 0.0761425 | − | 0.997097i | \(-0.475740\pi\) |
0.997097 | − | 0.0761425i | \(-0.0242604\pi\) | |||||||
\(734\) | −1439.48 | + | 1439.48i | −0.0723870 | + | 0.0723870i | ||||
\(735\) | −948.081 | + | 948.081i | −0.0475789 | + | 0.0475789i | ||||
\(736\) | −4274.25 | − | 4274.25i | −0.214064 | − | 0.214064i | ||||
\(737\) | 2572.21 | + | 1933.39i | 0.128560 | + | 0.0966312i | ||||
\(738\) | − | 37.0834i | − | 0.00184968i | ||||||
\(739\) | −4160.87 | − | 4160.87i | −0.207118 | − | 0.207118i | 0.595924 | − | 0.803041i | \(-0.296786\pi\) |
−0.803041 | + | 0.595924i | \(0.796786\pi\) | |||||||
\(740\) | 4486.66i | 0.222882i | ||||||||
\(741\) | −18153.2 | + | 4064.34i | −0.899965 | + | 0.201494i | ||||
\(742\) | 935.629 | 0.0462911 | ||||||||
\(743\) | −13009.5 | + | 13009.5i | −0.642359 | + | 0.642359i | −0.951135 | − | 0.308776i | \(-0.900081\pi\) |
0.308776 | + | 0.951135i | \(0.400081\pi\) | |||||||
\(744\) | − | 2205.78i | − | 0.108693i | ||||||
\(745\) | −1553.16 | −0.0763805 | ||||||||
\(746\) | −527.499 | − | 527.499i | −0.0258889 | − | 0.0258889i | ||||
\(747\) | 713.860 | − | 713.860i | 0.0349649 | − | 0.0349649i | ||||
\(748\) | 2960.83 | + | 20882.6i | 0.144731 | + | 1.02078i | ||||
\(749\) | 21551.8 | − | 21551.8i | 1.05138 | − | 1.05138i | ||||
\(750\) | 1069.22i | 0.0520564i | ||||||||
\(751\) | 6031.00i | 0.293042i | 0.989208 | + | 0.146521i | \(0.0468076\pi\) | ||||
−0.989208 | + | 0.146521i | \(0.953192\pi\) | |||||||
\(752\) | 5134.97 | − | 5134.97i | 0.249007 | − | 0.249007i | ||||
\(753\) | 9878.30i | 0.478068i | ||||||||
\(754\) | 134.777 | + | 601.974i | 0.00650966 | + | 0.0290751i | ||||
\(755\) | − | 8542.75i | − | 0.411791i | ||||||
\(756\) | 15886.7 | − | 15886.7i | 0.764276 | − | 0.764276i | ||||
\(757\) | 38206.2 | 1.83438 | 0.917191 | − | 0.398448i | \(-0.130451\pi\) | ||||
0.917191 | + | 0.398448i | \(0.130451\pi\) | |||||||
\(758\) | 2067.37 | 0.0990635 | ||||||||
\(759\) | 3423.41 | + | 24145.2i | 0.163718 | + | 1.15469i | ||||
\(760\) | 724.613 | + | 724.613i | 0.0345848 | + | 0.0345848i | ||||
\(761\) | 22425.6 | + | 22425.6i | 1.06823 | + | 1.06823i | 0.997495 | + | 0.0707400i | \(0.0225361\pi\) |
0.0707400 | + | 0.997495i | \(0.477464\pi\) | |||||||
\(762\) | 2607.02 | − | 2607.02i | 0.123940 | − | 0.123940i | ||||
\(763\) | −9910.88 | −0.470247 | ||||||||
\(764\) | − | 3134.51i | − | 0.148433i | ||||||
\(765\) | −119.457 | − | 119.457i | −0.00564571 | − | 0.00564571i | ||||
\(766\) | −157.583 | −0.00743302 | ||||||||
\(767\) | −3889.27 | + | 870.774i | −0.183094 | + | 0.0409933i | ||||
\(768\) | −19880.9 | −0.934103 | ||||||||
\(769\) | −15337.9 | + | 15337.9i | −0.719246 | + | 0.719246i | −0.968451 | − | 0.249205i | \(-0.919831\pi\) |
0.249205 | + | 0.968451i | \(0.419831\pi\) | |||||||
\(770\) | −508.155 | − | 381.952i | −0.0237826 | − | 0.0178761i | ||||
\(771\) | − | 7846.33i | − | 0.366509i | ||||||
\(772\) | 2549.95 | − | 2549.95i | 0.118879 | − | 0.118879i | ||||
\(773\) | −22491.0 | − | 22491.0i | −1.04650 | − | 1.04650i | −0.998865 | − | 0.0476356i | \(-0.984831\pi\) |
−0.0476356 | − | 0.998865i | \(-0.515169\pi\) | |||||||
\(774\) | −41.2307 | + | 41.2307i | −0.00191474 | + | 0.00191474i | ||||
\(775\) | −8424.49 | + | 8424.49i | −0.390473 | + | 0.390473i | ||||
\(776\) | − | 2954.63i | − | 0.136682i | ||||||
\(777\) | −17859.9 | −0.824610 | ||||||||
\(778\) | 1283.39 | + | 1283.39i | 0.0591409 | + | 0.0591409i | ||||
\(779\) | 16394.2i | 0.754022i | ||||||||
\(780\) | −6501.95 | + | 1455.73i | −0.298471 | + | 0.0668251i | ||||
\(781\) | −9319.51 | − | 7004.95i | −0.426989 | − | 0.320943i | ||||
\(782\) | 1638.54 | + | 1638.54i | 0.0749286 | + | 0.0749286i | ||||
\(783\) | − | 7277.50i | − | 0.332154i | ||||||
\(784\) | − | 4679.03i | − | 0.213148i | ||||||
\(785\) | −1363.39 | − | 1363.39i | −0.0619892 | − | 0.0619892i | ||||
\(786\) | −2012.78 | − | 2012.78i | −0.0913405 | − | 0.0913405i | ||||
\(787\) | 25040.8 | + | 25040.8i | 1.13419 | + | 1.13419i | 0.989473 | + | 0.144715i | \(0.0462266\pi\) |
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(788\) | −27366.7 | − | 27366.7i | −1.23718 | − | 1.23718i | ||||
\(789\) | − | 28527.0i | − | 1.28718i | ||||||
\(790\) | − | 334.246i | − | 0.0150531i | ||||||
\(791\) | 7427.03 | + | 7427.03i | 0.333849 | + | 0.333849i | ||||
\(792\) | −79.3060 | − | 59.6098i | −0.00355810 | − | 0.00267442i | ||||
\(793\) | 19044.9 | − | 30033.0i | 0.852843 | − | 1.34490i | ||||
\(794\) | − | 1510.87i | − | 0.0675301i | ||||||
\(795\) | 2314.67 | + | 2314.67i | 0.103262 | + | 0.103262i | ||||
\(796\) | 32042.7 | 1.42679 | ||||||||
\(797\) | 2596.99i | 0.115421i | 0.998333 | + | 0.0577103i | \(0.0183800\pi\) | ||||
−0.998333 | + | 0.0577103i | \(0.981620\pi\) | |||||||
\(798\) | −1436.55 | + | 1436.55i | −0.0637259 | + | 0.0637259i | ||||
\(799\) | −5984.26 | + | 5984.26i | −0.264966 | + | 0.264966i | ||||
\(800\) | −3815.52 | − | 3815.52i | −0.168624 | − | 0.168624i | ||||
\(801\) | −603.430 | + | 603.430i | −0.0266182 | + | 0.0266182i | ||||
\(802\) | − | 1180.83i | − | 0.0519909i | ||||||
\(803\) | −7727.98 | − | 5808.69i | −0.339619 | − | 0.255273i | ||||
\(804\) | 2604.48 | − | 2604.48i | 0.114245 | − | 0.114245i | ||||
\(805\) | 8840.37 | 0.387059 | ||||||||
\(806\) | 1041.30 | + | 660.321i | 0.0455065 | + | 0.0288571i | ||||
\(807\) | −6845.58 | −0.298607 | ||||||||
\(808\) | 1805.99 | + | 1805.99i | 0.0786316 | + | 0.0786316i | ||||
\(809\) | 15527.0i | 0.674783i | 0.941365 | + | 0.337391i | \(0.109545\pi\) | ||||
−0.941365 | + | 0.337391i | \(0.890455\pi\) | |||||||
\(810\) | −636.683 | −0.0276182 | ||||||||
\(811\) | 3027.82 | − | 3027.82i | 0.131099 | − | 0.131099i | −0.638513 | − | 0.769611i | \(-0.720450\pi\) |
0.769611 | + | 0.638513i | \(0.220450\pi\) | |||||||
\(812\) | −6029.77 | − | 6029.77i | −0.260596 | − | 0.260596i | ||||
\(813\) | 23940.5 | + | 23940.5i | 1.03275 | + | 1.03275i | ||||
\(814\) | −212.972 | − | 1502.08i | −0.00917034 | − | 0.0646780i | ||||
\(815\) | −7614.51 | −0.327269 | ||||||||
\(816\) | 23950.4 | 1.02749 | ||||||||
\(817\) | 18227.7 | − | 18227.7i | 0.780545 | − | 0.780545i | ||||
\(818\) | − | 3289.64i | − | 0.140611i | ||||||
\(819\) | −142.642 | − | 637.102i | −0.00608585 | − | 0.0271821i | ||||
\(820\) | 5871.93i | 0.250069i | ||||||||
\(821\) | 25255.1 | − | 25255.1i | 1.07358 | − | 1.07358i | 0.0765134 | − | 0.997069i | \(-0.475621\pi\) |
0.997069 | − | 0.0765134i | \(-0.0243788\pi\) | |||||||
\(822\) | − | 3466.51i | − | 0.147091i | ||||||
\(823\) | − | 38094.1i | − | 1.61346i | −0.590919 | − | 0.806731i | \(-0.701235\pi\) | ||
0.590919 | − | 0.806731i | \(-0.298765\pi\) | |||||||
\(824\) | −3705.63 | + | 3705.63i | −0.156665 | + | 0.156665i | ||||
\(825\) | 3056.00 | + | 21553.8i | 0.128965 | + | 0.909585i | ||||
\(826\) | −307.777 | + | 307.777i | −0.0129648 | + | 0.0129648i | ||||
\(827\) | 16275.7 | + | 16275.7i | 0.684356 | + | 0.684356i | 0.960979 | − | 0.276623i | \(-0.0892152\pi\) |
−0.276623 | + | 0.960979i | \(0.589215\pi\) | |||||||
\(828\) | 687.129 | 0.0288398 | ||||||||
\(829\) | − | 25965.8i | − | 1.08785i | −0.839134 | − | 0.543925i | \(-0.816937\pi\) | ||
0.839134 | − | 0.543925i | \(-0.183063\pi\) | |||||||
\(830\) | 893.013 | − | 893.013i | 0.0373457 | − | 0.0373457i | ||||
\(831\) | 6350.95 | 0.265117 | ||||||||
\(832\) | 12251.5 | − | 19320.2i | 0.510511 | − | 0.805055i | ||||
\(833\) | 5452.92i | 0.226810i | ||||||||
\(834\) | 338.587 | + | 338.587i | 0.0140579 | + | 0.0140579i | ||||
\(835\) | 4858.34i | 0.201353i | ||||||||
\(836\) | 17461.2 | + | 13124.6i | 0.722377 | + | 0.542970i | ||||
\(837\) | −10285.8 | − | 10285.8i | −0.424765 | − | 0.424765i | ||||
\(838\) | 2150.14 | − | 2150.14i | 0.0886340 | − | 0.0886340i | ||||
\(839\) | −12381.7 | + | 12381.7i | −0.509493 | + | 0.509493i | −0.914371 | − | 0.404878i | \(-0.867314\pi\) |
0.404878 | + | 0.914371i | \(0.367314\pi\) | |||||||
\(840\) | −1033.13 | + | 1033.13i | −0.0424360 | + | 0.0424360i | ||||
\(841\) | 21626.8 | 0.886745 | ||||||||
\(842\) | −1342.58 | −0.0549504 | ||||||||
\(843\) | −351.159 | − | 351.159i | −0.0143470 | − | 0.0143470i | ||||
\(844\) | 45203.6 | 1.84357 | ||||||||
\(845\) | 2528.35 | − | 7038.12i | 0.102932 | − | 0.286531i | ||||
\(846\) | − | 19.8260i | − | 0.000805711i | ||||||
\(847\) | −23828.7 | − | 13132.6i | −0.966665 | − | 0.532753i | ||||
\(848\) | −11423.5 | −0.462600 | ||||||||
\(849\) | −11914.5 | −0.481630 | ||||||||
\(850\) | 1462.69 | + | 1462.69i | 0.0590233 | + | 0.0590233i | ||||
\(851\) | 14918.4 | + | 14918.4i | 0.600935 | + | 0.600935i | ||||
\(852\) | −9436.44 | + | 9436.44i | −0.379445 | + | 0.379445i | ||||
\(853\) | 2285.54 | + | 2285.54i | 0.0917414 | + | 0.0917414i | 0.751488 | − | 0.659747i | \(-0.229336\pi\) |
−0.659747 | + | 0.751488i | \(0.729336\pi\) | |||||||
\(854\) | − | 3883.77i | − | 0.155621i | ||||||
\(855\) | −174.962 | −0.00699835 | ||||||||
\(856\) | 4207.64 | − | 4207.64i | 0.168007 | − | 0.168007i | ||||
\(857\) | 46269.3 | 1.84426 | 0.922130 | − | 0.386880i | \(-0.126447\pi\) | ||||
0.922130 | + | 0.386880i | \(0.126447\pi\) | |||||||
\(858\) | 2107.67 | − | 795.994i | 0.0838634 | − | 0.0316723i | ||||
\(859\) | −22798.6 | −0.905564 | −0.452782 | − | 0.891621i | \(-0.649568\pi\) | ||||
−0.452782 | + | 0.891621i | \(0.649568\pi\) | |||||||
\(860\) | 6528.63 | − | 6528.63i | 0.258865 | − | 0.258865i | ||||
\(861\) | −23374.2 | −0.925194 | ||||||||
\(862\) | − | 1634.11i | − | 0.0645686i | ||||||
\(863\) | −16723.7 | − | 16723.7i | −0.659654 | − | 0.659654i | 0.295644 | − | 0.955298i | \(-0.404466\pi\) |
−0.955298 | + | 0.295644i | \(0.904466\pi\) | |||||||
\(864\) | 4658.52 | − | 4658.52i | 0.183433 | − | 0.183433i | ||||
\(865\) | 5416.69 | + | 5416.69i | 0.212917 | + | 0.212917i | ||||
\(866\) | −1553.77 | − | 1553.77i | −0.0609689 | − | 0.0609689i | ||||
\(867\) | −2062.79 | −0.0808027 | ||||||||
\(868\) | −17044.6 | −0.666510 | ||||||||
\(869\) | −2008.27 | − | 14164.2i | −0.0783956 | − | 0.552920i | ||||
\(870\) | 235.701i | 0.00918506i | ||||||||
\(871\) | 903.237 | + | 4034.26i | 0.0351378 | + | 0.156941i | ||||
\(872\) | −1934.94 | −0.0751436 | ||||||||
\(873\) | 356.707 | + | 356.707i | 0.0138290 | + | 0.0138290i | ||||
\(874\) | 2399.89 | 0.0928806 | ||||||||
\(875\) | 16589.4 | 0.640943 | ||||||||
\(876\) | −7824.94 | + | 7824.94i | −0.301804 | + | 0.301804i | ||||
\(877\) | 22320.7 | − | 22320.7i | 0.859427 | − | 0.859427i | −0.131843 | − | 0.991271i | \(-0.542090\pi\) |
0.991271 | + | 0.131843i | \(0.0420896\pi\) | |||||||
\(878\) | −398.145 | + | 398.145i | −0.0153038 | + | 0.0153038i | ||||
\(879\) | 1311.22 | + | 1311.22i | 0.0503145 | + | 0.0503145i | ||||
\(880\) | 6204.29 | + | 4663.42i | 0.237667 | + | 0.178641i | ||||
\(881\) | − | 27135.6i | − | 1.03771i | −0.854863 | − | 0.518855i | \(-0.826359\pi\) | ||
0.854863 | − | 0.518855i | \(-0.173641\pi\) | |||||||
\(882\) | −9.03282 | − | 9.03282i | −0.000344842 | − | 0.000344842i | ||||
\(883\) | 45709.7i | 1.74208i | 0.491216 | + | 0.871038i | \(0.336552\pi\) | ||||
−0.491216 | + | 0.871038i | \(0.663448\pi\) | |||||||
\(884\) | −14511.7 | + | 22884.4i | −0.552129 | + | 0.870686i | ||||
\(885\) | −1522.83 | −0.0578411 | ||||||||
\(886\) | −593.394 | + | 593.394i | −0.0225005 | + | 0.0225005i | ||||
\(887\) | − | 14520.5i | − | 0.549663i | −0.961492 | − | 0.274831i | \(-0.911378\pi\) | ||
0.961492 | − | 0.274831i | \(-0.0886221\pi\) | |||||||
\(888\) | −3486.86 | −0.131770 | ||||||||
\(889\) | −40449.3 | − | 40449.3i | −1.52601 | − | 1.52601i | ||||
\(890\) | −754.869 | + | 754.869i | −0.0284306 | + | 0.0284306i | ||||
\(891\) | −26980.4 | + | 3825.41i | −1.01445 | + | 0.143834i | ||||
\(892\) | 33840.4 | − | 33840.4i | 1.27025 | − | 1.27025i | ||||
\(893\) | 8764.85i | 0.328449i | ||||||||
\(894\) | − | 601.154i | − | 0.0224895i | ||||||
\(895\) | 11013.0 | − | 11013.0i | 0.411312 | − | 0.411312i | ||||
\(896\) | − | 10279.0i | − | 0.383257i | ||||||
\(897\) | −16778.9 | + | 26459.7i | −0.624562 | + | 0.984909i | ||||
\(898\) | 3720.89i | 0.138271i | ||||||||
\(899\) | −3903.96 | + | 3903.96i | −0.144833 | + | 0.144833i | ||||
\(900\) | 613.384 | 0.0227179 | ||||||||
\(901\) | 13312.9 | 0.492249 | ||||||||
\(902\) | −278.727 | − | 1965.85i | −0.0102889 | − | 0.0725672i | ||||
\(903\) | 25988.3 | + | 25988.3i | 0.957738 | + | 0.957738i | ||||
\(904\) | 1450.00 | + | 1450.00i | 0.0533478 | + | 0.0533478i | ||||
\(905\) | 5518.72 | − | 5518.72i | 0.202705 | − | 0.202705i | ||||
\(906\) | 3306.49 | 0.121248 | ||||||||
\(907\) | − | 19337.2i | − | 0.707916i | −0.935261 | − | 0.353958i | \(-0.884836\pi\) | ||
0.935261 | − | 0.353958i | \(-0.115164\pi\) | |||||||
\(908\) | −23547.9 | − | 23547.9i | −0.860643 | − | 0.860643i | ||||
\(909\) | −436.067 | −0.0159114 | ||||||||
\(910\) | −178.440 | − | 796.992i | −0.00650024 | − | 0.0290330i | ||||
\(911\) | 16029.7 | 0.582971 | 0.291485 | − | 0.956575i | \(-0.405851\pi\) | ||||
0.291485 | + | 0.956575i | \(0.405851\pi\) | |||||||
\(912\) | 17539.5 | − | 17539.5i | 0.636831 | − | 0.636831i | ||||
\(913\) | 32477.3 | − | 43208.3i | 1.17726 | − | 1.56625i | ||||
\(914\) | − | 367.925i | − | 0.0133149i | ||||||
\(915\) | 9608.14 | − | 9608.14i | 0.347143 | − | 0.347143i | ||||
\(916\) | −18950.5 | − | 18950.5i | −0.683561 | − | 0.683561i | ||||
\(917\) | −31229.4 | + | 31229.4i | −1.12463 | + | 1.12463i | ||||
\(918\) | −1785.85 | + | 1785.85i | −0.0642069 | + | 0.0642069i | ||||
\(919\) | − | 34058.0i | − | 1.22249i | −0.791441 | − | 0.611245i | \(-0.790669\pi\) | ||
0.791441 | − | 0.611245i | \(-0.209331\pi\) | |||||||
\(920\) | 1725.94 | 0.0618505 | ||||||||
\(921\) | −15961.0 | − | 15961.0i | −0.571045 | − | 0.571045i | ||||
\(922\) | 3729.66i | 0.133221i | ||||||||
\(923\) | −3272.57 | − | 14616.7i | −0.116704 | − | 0.521253i | ||||
\(924\) | −18712.6 | + | 24895.5i | −0.666232 | + | 0.886366i | ||||
\(925\) | 13317.3 | + | 13317.3i | 0.473373 | + | 0.473373i | ||||
\(926\) | 2693.83i | 0.0955990i | ||||||||
\(927\) | − | 894.749i | − | 0.0317016i | ||||||
\(928\) | −1768.14 | − | 1768.14i | −0.0625452 | − | 0.0625452i | ||||
\(929\) | 2184.76 | + | 2184.76i | 0.0771578 | + | 0.0771578i | 0.744633 | − | 0.667475i | \(-0.232625\pi\) |
−0.667475 | + | 0.744633i | \(0.732625\pi\) | |||||||
\(930\) | 333.132 | + | 333.132i | 0.0117460 | + | 0.0117460i | ||||
\(931\) | 3993.31 | + | 3993.31i | 0.140575 | + | 0.140575i | ||||
\(932\) | 31498.4i | 1.10704i | ||||||||
\(933\) | − | 38363.8i | − | 1.34617i | ||||||
\(934\) | 1340.40 | + | 1340.40i | 0.0469586 | + | 0.0469586i | ||||
\(935\) | −7230.44 | − | 5434.72i | −0.252899 | − | 0.190090i | ||||
\(936\) | −27.8485 | − | 124.384i | −0.000972495 | − | 0.00434360i | ||||
\(937\) | 15443.8i | 0.538449i | 0.963077 | + | 0.269225i | \(0.0867674\pi\) | ||||
−0.963077 | + | 0.269225i | \(0.913233\pi\) | |||||||
\(938\) | 319.251 | + | 319.251i | 0.0111129 | + | 0.0111129i | ||||
\(939\) | 20482.9 | 0.711859 | ||||||||
\(940\) | 3139.32i | 0.108929i | ||||||||
\(941\) | −17156.9 | + | 17156.9i | −0.594366 | + | 0.594366i | −0.938808 | − | 0.344442i | \(-0.888068\pi\) |
0.344442 | + | 0.938808i | \(0.388068\pi\) | |||||||
\(942\) | 527.703 | − | 527.703i | 0.0182521 | − | 0.0182521i | ||||
\(943\) | 19524.5 | + | 19524.5i | 0.674235 | + | 0.674235i | ||||
\(944\) | 3757.78 | − | 3757.78i | 0.129561 | − | 0.129561i | ||||
\(945\) | 9635.15i | 0.331674i | ||||||||
\(946\) | −1875.81 | + | 2495.60i | −0.0644690 | + | 0.0857707i | ||||
\(947\) | −18130.7 | + | 18130.7i | −0.622140 | + | 0.622140i | −0.946078 | − | 0.323938i | \(-0.894993\pi\) |
0.323938 | + | 0.946078i | \(0.394993\pi\) | |||||||
\(948\) | −16375.4 | −0.561021 | ||||||||
\(949\) | −2713.70 | − | 12120.6i | −0.0928244 | − | 0.414595i | ||||
\(950\) | 2142.33 | 0.0731646 | ||||||||
\(951\) | 20256.8 | + | 20256.8i | 0.690716 | + | 0.690716i | ||||
\(952\) | 5942.06i | 0.202293i | ||||||||
\(953\) | 44586.7 | 1.51554 | 0.757768 | − | 0.652524i | \(-0.226290\pi\) | ||||
0.757768 | + | 0.652524i | \(0.226290\pi\) | |||||||
\(954\) | −22.0530 | + | 22.0530i | −0.000748418 | + | 0.000748418i | ||||
\(955\) | 950.529 | + | 950.529i | 0.0322078 | + | 0.0322078i | ||||
\(956\) | −2273.24 | − | 2273.24i | −0.0769057 | − | 0.0769057i | ||||
\(957\) | 1416.17 | + | 9988.18i | 0.0478352 | + | 0.337379i | ||||
\(958\) | −3859.66 | −0.130167 | ||||||||
\(959\) | −53784.7 | −1.81105 | ||||||||
\(960\) | 6180.89 | − | 6180.89i | 0.207799 | − | 0.207799i | ||||
\(961\) | − | 18755.5i | − | 0.629570i | ||||||
\(962\) | 1043.82 | − | 1646.07i | 0.0349836 | − | 0.0551678i | ||||
\(963\) | 1015.96i | 0.0339968i | ||||||||
\(964\) | 8442.82 | − | 8442.82i | 0.282080 | − | 0.282080i | ||||
\(965\) | 1546.52i | 0.0515900i | ||||||||
\(966\) | 3421.68i | 0.113966i | ||||||||
\(967\) | −31193.6 | + | 31193.6i | −1.03735 | + | 1.03735i | −0.0380748 | + | 0.999275i | \(0.512123\pi\) |
−0.999275 | + | 0.0380748i | \(0.987877\pi\) | |||||||
\(968\) | −4652.17 | − | 2563.93i | −0.154469 | − | 0.0851320i | ||||
\(969\) | −20440.4 | + | 20440.4i | −0.677647 | + | 0.677647i | ||||
\(970\) | 446.228 | + | 446.228i | 0.0147706 | + | 0.0147706i | ||||
\(971\) | 40149.3 | 1.32693 | 0.663467 | − | 0.748205i | \(-0.269084\pi\) | ||||
0.663467 | + | 0.748205i | \(0.269084\pi\) | |||||||
\(972\) | 1517.20i | 0.0500660i | ||||||||
\(973\) | 5253.34 | − | 5253.34i | 0.173088 | − | 0.173088i | ||||
\(974\) | 1115.19 | 0.0366867 | ||||||||
\(975\) | −14978.2 | + | 23620.0i | −0.491985 | + | 0.775840i | ||||
\(976\) | 47418.7i | 1.55516i | ||||||||
\(977\) | 42719.6 | + | 42719.6i | 1.39890 | + | 1.39890i | 0.803236 | + | 0.595661i | \(0.203110\pi\) |
0.595661 | + | 0.803236i | \(0.296890\pi\) | |||||||
\(978\) | − | 2947.21i | − | 0.0963613i | ||||||
\(979\) | −27453.2 | + | 36524.3i | −0.896230 | + | 1.19236i | ||||
\(980\) | 1430.29 | + | 1430.29i | 0.0466213 | + | 0.0466213i | ||||
\(981\) | 233.602 | − | 233.602i | 0.00760278 | − | 0.00760278i | ||||
\(982\) | −1507.61 | + | 1507.61i | −0.0489916 | + | 0.0489916i | ||||
\(983\) | −8763.91 | + | 8763.91i | −0.284360 | + | 0.284360i | −0.834845 | − | 0.550485i | \(-0.814443\pi\) |
0.550485 | + | 0.834845i | \(0.314443\pi\) | |||||||
\(984\) | −4563.44 | −0.147842 | ||||||||
\(985\) | 16597.7 | 0.536900 | ||||||||
\(986\) | 677.819 | + | 677.819i | 0.0218927 | + | 0.0218927i | ||||
\(987\) | −12496.6 | −0.403011 | ||||||||
\(988\) | 6131.53 | + | 27386.2i | 0.197439 | + | 0.881852i | ||||
\(989\) | − | 43416.0i | − | 1.39590i | ||||||
\(990\) | 20.9800 | − | 2.97464i | 0.000673523 | − | 9.54952e-5i | ||||
\(991\) | −41111.6 | −1.31781 | −0.658907 | − | 0.752224i | \(-0.728981\pi\) | ||||
−0.658907 | + | 0.752224i | \(0.728981\pi\) | |||||||
\(992\) | −4998.06 | −0.159968 | ||||||||
\(993\) | 17811.0 | + | 17811.0i | 0.569199 | + | 0.569199i | ||||
\(994\) | −1156.69 | − | 1156.69i | −0.0369096 | − | 0.0369096i | ||||
\(995\) | −9716.84 | + | 9716.84i | −0.309592 | + | 0.309592i | ||||
\(996\) | −43750.5 | − | 43750.5i | −1.39185 | − | 1.39185i | ||||
\(997\) | 890.045i | 0.0282728i | 0.999900 | + | 0.0141364i | \(0.00449991\pi\) | ||||
−0.999900 | + | 0.0141364i | \(0.995500\pi\) | |||||||
\(998\) | −1359.67 | −0.0431259 | ||||||||
\(999\) | −16259.6 | + | 16259.6i | −0.514946 | + | 0.514946i |
(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 | 143.4.g.a.21.20 | ✓ | 80 | |
11.10 | odd | 2 | inner | 143.4.g.a.21.21 | yes | 80 | |
13.5 | odd | 4 | inner | 143.4.g.a.109.21 | yes | 80 | |
143.109 | even | 4 | inner | 143.4.g.a.109.20 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.g.a.21.20 | ✓ | 80 | 1.1 | even | 1 | trivial | |
143.4.g.a.21.21 | yes | 80 | 11.10 | odd | 2 | inner | |
143.4.g.a.109.20 | yes | 80 | 143.109 | even | 4 | inner | |
143.4.g.a.109.21 | yes | 80 | 13.5 | odd | 4 | inner |