Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,5,Mod(15,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.15");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.h (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2313552747\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 47.2 | ||
Character | \(\chi\) | \(=\) | 128.47 |
Dual form | 128.5.h.a.79.2 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −5.09563 | + | 12.3019i | −0.566181 | + | 1.36688i | 0.338569 | + | 0.940941i | \(0.390057\pi\) |
−0.904751 | + | 0.425941i | \(0.859943\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.07195 | − | 14.6590i | −0.242878 | − | 0.586359i | 0.754688 | − | 0.656083i | \(-0.227788\pi\) |
−0.997566 | + | 0.0697242i | \(0.977788\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.01401 | − | 3.01401i | −0.0615103 | − | 0.0615103i | 0.675682 | − | 0.737193i | \(-0.263849\pi\) |
−0.737193 | + | 0.675682i | \(0.763849\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −68.0967 | − | 68.0967i | −0.840700 | − | 0.840700i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −58.0733 | − | 140.201i | −0.479945 | − | 1.15869i | −0.959634 | − | 0.281251i | \(-0.909251\pi\) |
0.479690 | − | 0.877438i | \(-0.340749\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −80.2328 | + | 193.699i | −0.474750 | + | 1.14615i | 0.487290 | + | 0.873240i | \(0.337986\pi\) |
−0.962040 | + | 0.272908i | \(0.912014\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 211.274 | 0.938997 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 483.394i | − | 1.67264i | −0.548238 | − | 0.836322i | \(-0.684701\pi\) | ||
0.548238 | − | 0.836322i | \(-0.315299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 331.005 | + | 137.107i | 0.916912 | + | 0.379797i | 0.790698 | − | 0.612206i | \(-0.209718\pi\) |
0.126213 | + | 0.992003i | \(0.459718\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 52.4364 | − | 21.7199i | 0.118903 | − | 0.0492514i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 541.798 | − | 541.798i | 1.02419 | − | 1.02419i | 0.0244925 | − | 0.999700i | \(-0.492203\pi\) |
0.999700 | − | 0.0244925i | \(-0.00779697\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 263.925 | − | 263.925i | 0.422279 | − | 0.422279i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 188.260 | − | 77.9800i | 0.258245 | − | 0.106968i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 806.524 | + | 334.073i | 0.959006 | + | 0.397233i | 0.806609 | − | 0.591086i | \(-0.201301\pi\) |
0.152398 | + | 0.988319i | \(0.451301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 388.265i | 0.404021i | 0.979383 | + | 0.202011i | \(0.0647476\pi\) | ||||
−0.979383 | + | 0.202011i | \(0.935252\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2020.67 | 1.85553 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −25.8814 | + | 62.4832i | −0.0211276 | + | 0.0510067i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −355.906 | − | 859.232i | −0.259975 | − | 0.627635i | 0.738961 | − | 0.673748i | \(-0.235317\pi\) |
−0.998936 | + | 0.0461129i | \(0.985317\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1974.04 | − | 1974.04i | −1.29786 | − | 1.29786i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −840.019 | − | 840.019i | −0.499714 | − | 0.499714i | 0.411635 | − | 0.911349i | \(-0.364958\pi\) |
−0.911349 | + | 0.411635i | \(0.864958\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −574.540 | − | 1387.06i | −0.310730 | − | 0.750169i | −0.999678 | − | 0.0253583i | \(-0.991927\pi\) |
0.688948 | − | 0.724810i | \(-0.258073\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −584.749 | + | 1411.71i | −0.288765 | + | 0.697140i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3447.34 | −1.56059 | −0.780294 | − | 0.625412i | \(-0.784931\pi\) | ||||
−0.780294 | + | 0.625412i | \(0.784931\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 2382.83i | − | 0.992433i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5946.69 | + | 2463.20i | 2.28631 | + | 0.947020i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −151.487 | + | 62.7482i | −0.0539293 | + | 0.0223383i | −0.409485 | − | 0.912317i | \(-0.634292\pi\) |
0.355556 | + | 0.934655i | \(0.384292\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1702.59 | + | 1702.59i | −0.562840 | + | 0.562840i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3373.36 | + | 3373.36i | −1.03828 | + | 1.03828i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2509.57 | − | 1039.50i | 0.720935 | − | 0.298621i | 0.00811390 | − | 0.999967i | \(-0.497417\pi\) |
0.712821 | + | 0.701346i | \(0.247417\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4711.50 | − | 1951.57i | −1.26619 | − | 0.524474i | −0.354388 | − | 0.935099i | \(-0.615311\pi\) |
−0.911805 | + | 0.410625i | \(0.865311\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 410.488i | 0.103424i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3326.60 | 0.787361 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1405.29 | + | 3392.68i | −0.313053 | + | 0.755776i | 0.686536 | + | 0.727096i | \(0.259130\pi\) |
−0.999589 | + | 0.0286801i | \(0.990870\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3904.36 | + | 9425.97i | 0.820072 | + | 1.97983i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1504.88 | − | 1504.88i | −0.298528 | − | 0.298528i | 0.541909 | − | 0.840437i | \(-0.317702\pi\) |
−0.840437 | + | 0.541909i | \(0.817702\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −74.3394 | − | 74.3394i | −0.0139500 | − | 0.0139500i | 0.700097 | − | 0.714047i | \(-0.253140\pi\) |
−0.714047 | + | 0.700097i | \(0.753140\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1901.92 | + | 4591.65i | 0.338120 | + | 0.816293i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −247.534 | + | 597.601i | −0.0417498 | + | 0.100793i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9234.62 | 1.47967 | 0.739835 | − | 0.672788i | \(-0.234904\pi\) | ||||
0.739835 | + | 0.672788i | \(0.234904\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 5087.24i | − | 0.775376i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6924.43 | − | 2868.19i | −1.00514 | − | 0.416344i | −0.181463 | − | 0.983398i | \(-0.558083\pi\) |
−0.823681 | + | 0.567054i | \(0.808083\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7086.07 | + | 2935.15i | −0.980771 | + | 0.406249i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8219.50 | + | 8219.50i | −1.08594 | + | 1.08594i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3449.37 | − | 3449.37i | 0.435471 | − | 0.435471i | −0.455013 | − | 0.890485i | \(-0.650366\pi\) |
0.890485 | + | 0.455013i | \(0.150366\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 825.633 | − | 341.988i | 0.0997021 | − | 0.0412979i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4776.41 | − | 1978.45i | −0.552250 | − | 0.228749i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 5684.70i | − | 0.629884i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7821.64 | −0.831294 | −0.415647 | − | 0.909526i | \(-0.636445\pi\) | ||||
−0.415647 | + | 0.909526i | \(0.636445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5592.65 | + | 13501.9i | −0.570620 | + | 1.37760i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5450.00 | + | 13157.5i | 0.534261 | + | 1.28982i | 0.928677 | + | 0.370889i | \(0.120947\pi\) |
−0.394416 | + | 0.918932i | \(0.629053\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4438.23 | − | 4438.23i | −0.418346 | − | 0.418346i | 0.466287 | − | 0.884633i | \(-0.345591\pi\) |
−0.884633 | + | 0.466287i | \(0.845591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −636.782 | − | 636.782i | −0.0577580 | − | 0.0577580i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6827.27 | − | 16482.5i | −0.596321 | − | 1.43965i | −0.877305 | − | 0.479933i | \(-0.840661\pi\) |
0.280985 | − | 0.959712i | \(-0.409339\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3294.72 | − | 7954.16i | 0.277310 | − | 0.669486i | −0.722449 | − | 0.691424i | \(-0.756984\pi\) |
0.999759 | + | 0.0219383i | \(0.00698375\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12383.8 | 1.00510 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3385.06i | 0.265100i | 0.991176 | + | 0.132550i | \(0.0423165\pi\) | ||||
−0.991176 | + | 0.132550i | \(0.957684\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11232.0 | − | 4652.44i | −0.849298 | − | 0.351791i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18653.9 | − | 7726.69i | 1.36269 | − | 0.564445i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1456.95 | + | 1456.95i | −0.102885 | + | 0.102885i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5931.16 | + | 5931.16i | −0.405106 | + | 0.405106i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14614.3 | − | 6053.44i | 0.965979 | − | 0.400122i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −14633.3 | − | 6061.30i | −0.936529 | − | 0.387923i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2472.15i | 0.153274i | 0.997059 | + | 0.0766370i | \(0.0244182\pi\) | ||||
−0.997059 | + | 0.0766370i | \(0.975582\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19991.2 | 1.20132 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 858.517 | − | 2072.64i | 0.0500272 | − | 0.120776i | −0.896890 | − | 0.442253i | \(-0.854179\pi\) |
0.946917 | + | 0.321477i | \(0.104179\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −584.411 | − | 1410.89i | −0.0330381 | − | 0.0797610i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2286.22 | − | 2286.22i | −0.125444 | − | 0.125444i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12881.6 | + | 12881.6i | 0.686323 | + | 0.686323i | 0.961417 | − | 0.275094i | \(-0.0887091\pi\) |
−0.275094 | + | 0.961417i | \(0.588709\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2777.72 | − | 6706.01i | −0.143767 | − | 0.347084i | 0.835551 | − | 0.549414i | \(-0.185149\pi\) |
−0.979318 | + | 0.202329i | \(0.935149\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17566.4 | − | 42409.0i | 0.883576 | − | 2.13314i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 31816.3 | 1.55588 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 13851.3i | − | 0.658801i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 29313.5 | + | 12142.0i | 1.35654 | + | 0.561897i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22793.5 | − | 9441.39i | 1.02669 | − | 0.425268i | 0.195173 | − | 0.980769i | \(-0.437473\pi\) |
0.831516 | + | 0.555500i | \(0.187473\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6711.21 | + | 6711.21i | −0.294338 | + | 0.294338i | −0.838791 | − | 0.544453i | \(-0.816737\pi\) |
0.544453 | + | 0.838791i | \(0.316737\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −32917.6 | + | 32917.6i | −1.40619 | + | 1.40619i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5691.56 | − | 2357.52i | 0.236902 | − | 0.0981279i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2712.43 | − | 1123.52i | −0.110042 | − | 0.0455809i | 0.326983 | − | 0.945030i | \(-0.393968\pi\) |
−0.437025 | + | 0.899449i | \(0.643968\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 2183.33i | − | 0.0863626i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3265.96 | −0.125997 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2887.41 | − | 6970.83i | 0.108676 | − | 0.262367i | −0.860181 | − | 0.509990i | \(-0.829649\pi\) |
0.968857 | + | 0.247623i | \(0.0796493\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12269.4 | − | 29621.0i | −0.450667 | − | 1.08801i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4391.08 | + | 4391.08i | 0.157449 | + | 0.157449i | 0.781435 | − | 0.623986i | \(-0.214488\pi\) |
−0.623986 | + | 0.781435i | \(0.714488\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10886.4 | − | 10886.4i | −0.381162 | − | 0.381162i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13203.8 | − | 31876.9i | −0.451552 | − | 1.09014i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10260.8 | + | 24771.8i | −0.342839 | + | 0.827687i | 0.654587 | + | 0.755987i | \(0.272843\pi\) |
−0.997426 | + | 0.0717004i | \(0.977157\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1590.94 | −0.0519491 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 36169.5i | 1.15451i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14278.4 | − | 5914.30i | −0.445628 | − | 0.184585i | 0.148573 | − | 0.988901i | \(-0.452532\pi\) |
−0.594202 | + | 0.804316i | \(0.702532\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −34585.7 | + | 14325.9i | −1.05570 | + | 0.437284i | −0.841922 | − | 0.539599i | \(-0.818576\pi\) |
−0.213775 | + | 0.976883i | \(0.568576\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 48016.2 | − | 48016.2i | 1.43379 | − | 1.43379i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10434.4 | + | 10434.4i | −0.304877 | + | 0.304877i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −67772.5 | + | 28072.3i | −1.93807 | + | 0.802777i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −802.450 | − | 332.386i | −0.0224644 | − | 0.00930506i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 52388.7i | 1.43605i | 0.696015 | + | 0.718027i | \(0.254955\pi\) | ||||
−0.696015 | + | 0.718027i | \(0.745045\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 48694.8 | 1.30728 | 0.653639 | − | 0.756807i | \(-0.273242\pi\) | ||||
0.653639 | + | 0.756807i | \(0.273242\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16951.1 | + | 40923.7i | −0.445789 | + | 1.07623i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1166.09 | − | 2815.18i | −0.0300468 | − | 0.0725393i | 0.908144 | − | 0.418658i | \(-0.137499\pi\) |
−0.938191 | + | 0.346119i | \(0.887499\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8460.16 | + | 8460.16i | 0.213635 | + | 0.213635i | 0.805810 | − | 0.592175i | \(-0.201730\pi\) |
−0.592175 | + | 0.805810i | \(0.701730\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −34575.7 | − | 34575.7i | −0.855812 | − | 0.855812i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1423.97 | − | 3437.77i | −0.0345548 | − | 0.0834228i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7213.27 | + | 17414.4i | −0.171642 | + | 0.414381i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −73789.3 | −1.72208 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 54369.6i | − | 1.24470i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −29788.0 | − | 12338.6i | −0.669077 | − | 0.277141i | 0.0221757 | − | 0.999754i | \(-0.492941\pi\) |
−0.691252 | + | 0.722613i | \(0.742941\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 26181.2 | − | 10844.6i | 0.577073 | − | 0.239032i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16844.3 | + | 16844.3i | −0.364399 | + | 0.364399i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1170.23 | − | 1170.23i | 0.0248515 | − | 0.0248515i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1293.33 | − | 535.713i | 0.0269662 | − | 0.0111698i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 93633.1 | + | 38784.1i | 1.91710 | + | 0.794089i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12606.2i | 0.253498i | 0.991935 | + | 0.126749i | \(0.0404542\pi\) | ||||
−0.991935 | + | 0.126749i | \(0.959546\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −35944.8 | −0.710021 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14926.8 | − | 36036.4i | 0.289677 | − | 0.699343i | −0.710312 | − | 0.703887i | \(-0.751446\pi\) |
0.999990 | + | 0.00454381i | \(0.00144634\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23771.0 | + | 57388.3i | 0.453291 | + | 1.09434i | 0.971063 | + | 0.238823i | \(0.0767614\pi\) |
−0.517772 | + | 0.855518i | \(0.673239\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6090.31 | − | 6090.31i | −0.114134 | − | 0.114134i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 49723.7 | + | 49723.7i | 0.915907 | + | 0.915907i | 0.996729 | − | 0.0808219i | \(-0.0257545\pi\) |
−0.0808219 | + | 0.996729i | \(0.525755\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20932.1 | + | 50534.5i | 0.379033 | + | 0.915066i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −47056.2 | + | 113604.i | −0.837762 | + | 2.02254i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 61477.2 | 1.07626 | 0.538131 | − | 0.842861i | \(-0.319130\pi\) | ||||
0.538131 | + | 0.842861i | \(0.319130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 41588.9i | 0.716050i | 0.933712 | + | 0.358025i | \(0.116550\pi\) | ||||
−0.933712 | + | 0.358025i | \(0.883450\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 77832.1 | + | 32239.1i | 1.31809 | + | 0.545972i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −34929.9 | + | 14468.4i | −0.581922 | + | 0.241040i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −53115.0 | + | 53115.0i | −0.870609 | + | 0.870609i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 70568.7 | − | 70568.7i | 1.13819 | − | 1.13819i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24760.6 | − | 10256.2i | 0.393020 | − | 0.162794i | −0.177417 | − | 0.984136i | \(-0.556774\pi\) |
0.570437 | + | 0.821342i | \(0.306774\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −107425. | − | 44496.8i | −1.67828 | − | 0.695165i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 102129.i | − | 1.57061i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −73168.6 | −1.10779 | −0.553897 | − | 0.832585i | \(-0.686860\pi\) | ||||
−0.553897 | + | 0.832585i | \(0.686860\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1517.03 | + | 3662.43i | −0.0226149 | + | 0.0545972i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −32172.4 | − | 77671.0i | −0.472283 | − | 1.14019i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2748.13 | + | 2748.13i | 0.0397306 | + | 0.0397306i | 0.726693 | − | 0.686962i | \(-0.241056\pi\) |
−0.686962 | + | 0.726693i | \(0.741056\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1839.65 | + | 1839.65i | 0.0261965 | + | 0.0261965i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24857.2 | + | 60010.7i | 0.348682 | + | 0.841794i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 49335.7 | − | 119107.i | 0.681799 | − | 1.64601i | −0.0788830 | − | 0.996884i | \(-0.525135\pi\) |
0.760682 | − | 0.649125i | \(-0.224865\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −83389.5 | −1.13546 | −0.567731 | − | 0.823214i | \(-0.692179\pi\) | ||||
−0.567731 | + | 0.823214i | \(0.692179\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11899.5i | 0.159663i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −52329.6 | − | 21675.6i | −0.691961 | − | 0.286620i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −102973. | + | 42652.7i | −1.34203 | + | 0.555887i | −0.934063 | − | 0.357109i | \(-0.883762\pi\) |
−0.407967 | + | 0.912996i | \(0.633762\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 26439.5 | − | 26439.5i | 0.339661 | − | 0.339661i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 81592.0 | − | 81592.0i | 1.03332 | − | 1.03332i | 0.0338942 | − | 0.999425i | \(-0.489209\pi\) |
0.999425 | − | 0.0338942i | \(-0.0107909\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 116760. | − | 48363.5i | 1.45788 | − | 0.603872i | 0.493818 | − | 0.869565i | \(-0.335601\pi\) |
0.964058 | + | 0.265694i | \(0.0856009\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 69932.9 | + | 28967.2i | 0.860978 | + | 0.356629i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5063.65i | 0.0614751i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −150149. | −1.79774 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 39856.2 | − | 96221.4i | 0.470663 | − | 1.13628i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13133.0 | − | 31705.8i | −0.152978 | − | 0.369320i | 0.828748 | − | 0.559622i | \(-0.189054\pi\) |
−0.981726 | + | 0.190301i | \(0.939054\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30476.0 | − | 30476.0i | −0.350198 | − | 0.350198i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21865.8 | − | 21865.8i | −0.247886 | − | 0.247886i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 61475.8 | + | 148416.i | 0.687641 | + | 1.66011i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2448.95 | + | 5912.28i | −0.0270300 | + | 0.0652562i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −189634. | −2.06552 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 80915.6i | 0.869827i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4481.70 | − | 1856.38i | −0.0475517 | − | 0.0196966i | 0.358781 | − | 0.933422i | \(-0.383193\pi\) |
−0.406333 | + | 0.913725i | \(0.633193\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 77214.5 | − | 31983.3i | 0.808690 | − | 0.334970i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 36754.8 | − | 36754.8i | 0.380008 | − | 0.380008i | −0.491097 | − | 0.871105i | \(-0.663404\pi\) |
0.871105 | + | 0.491097i | \(0.163404\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 60596.3 | − | 60596.3i | 0.618525 | − | 0.618525i | −0.326628 | − | 0.945153i | \(-0.605912\pi\) |
0.945153 | + | 0.326628i | \(0.105912\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6017.33 | − | 2492.46i | 0.0606433 | − | 0.0251193i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10177.0 | + | 4215.46i | 0.101275 | + | 0.0419495i | 0.432746 | − | 0.901516i | \(-0.357545\pi\) |
−0.331471 | + | 0.943466i | \(0.607545\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 132477.i | − | 1.30184i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 237556. | 2.30545 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 66276.7 | − | 160006.i | 0.635266 | − | 1.53367i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29946.6 | + | 72297.4i | 0.283518 | + | 0.684472i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 81062.9 | + | 81062.9i | 0.758100 | + | 0.758100i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10390.3 | + | 10390.3i | 0.0959923 | + | 0.0959923i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16494.0 | + | 39820.1i | 0.150547 | + | 0.363452i | 0.981104 | − | 0.193481i | \(-0.0619779\pi\) |
−0.830557 | + | 0.556933i | \(0.811978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −34274.9 | + | 82746.9i | −0.309092 | + | 0.746214i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 58266.1 | 0.519190 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 156650.i | − | 1.37933i | −0.724126 | − | 0.689667i | \(-0.757757\pi\) | ||
0.724126 | − | 0.689667i | \(-0.242243\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −41642.8 | − | 17249.0i | −0.362360 | − | 0.150095i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 54435.2 | − | 22547.8i | 0.468135 | − | 0.193908i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14418.5 | + | 14418.5i | −0.122555 | + | 0.122555i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 114468. | − | 114468.i | 0.961714 | − | 0.961714i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −98109.2 | + | 40638.2i | −0.814800 | + | 0.337501i | −0.750867 | − | 0.660453i | \(-0.770364\pi\) |
−0.0639325 | + | 0.997954i | \(0.520364\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 149888. | + | 62085.6i | 1.23060 | + | 0.509730i | 0.900763 | − | 0.434310i | \(-0.143008\pi\) |
0.329832 | + | 0.944039i | \(0.393008\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 42722.4i | 0.346770i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −191637. | −1.53791 | −0.768954 | − | 0.639304i | \(-0.779223\pi\) | ||||
−0.768954 | + | 0.639304i | \(0.779223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12922.4 | + | 31197.5i | −0.102539 | + | 0.247550i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10499.3 | − | 25347.5i | −0.0823801 | − | 0.198883i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 160315. | + | 160315.i | 1.24390 | + | 1.24390i | 0.958368 | + | 0.285535i | \(0.0921711\pi\) |
0.285535 | + | 0.958368i | \(0.407829\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1384.70 | − | 1384.70i | −0.0106253 | − | 0.0106253i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −42741.8 | − | 103188.i | −0.324369 | − | 0.783096i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −638.355 | + | 1541.13i | −0.00479156 | + | 0.0115678i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 76746.2 | 0.569803 | 0.284902 | − | 0.958557i | \(-0.408039\pi\) | ||||
0.284902 | + | 0.958557i | \(0.408039\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 114405.i | 0.840219i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 645.708 | + | 267.461i | 0.00469124 | + | 0.00194318i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −105599. | + | 43740.6i | −0.759002 | + | 0.314389i | −0.728408 | − | 0.685143i | \(-0.759740\pi\) |
−0.0305932 | + | 0.999532i | \(0.509740\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 149131. | − | 149131.i | 1.06049 | − | 1.06049i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −129419. | + | 129419.i | −0.910577 | + | 0.910577i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −145215. | + | 60150.1i | −1.01096 | + | 0.418753i | −0.825805 | − | 0.563956i | \(-0.809279\pi\) |
−0.185155 | + | 0.982709i | \(0.559279\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −30412.3 | − | 12597.2i | −0.209507 | − | 0.0867808i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 106466.i | 0.725795i | 0.931829 | + | 0.362898i | \(0.118213\pi\) | ||||
−0.931829 | + | 0.362898i | \(0.881787\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10263.2 | 0.0692409 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −55330.1 | + | 133579.i | −0.369436 | + | 0.891898i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19486.5 | − | 47044.6i | −0.128776 | − | 0.310893i | 0.846320 | − | 0.532674i | \(-0.178813\pi\) |
−0.975096 | + | 0.221781i | \(0.928813\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −261902. | − | 261902.i | −1.71311 | − | 1.71311i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21122.9 | + | 21122.9i | 0.136763 | + | 0.136763i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −56072.1 | − | 135370.i | −0.359379 | − | 0.867618i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33934.6 | − | 81925.3i | 0.215309 | − | 0.519801i | −0.778915 | − | 0.627129i | \(-0.784230\pi\) |
0.994224 | + | 0.107329i | \(0.0342297\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20334.7 | 0.127730 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 55161.3i | − | 0.343041i | −0.985181 | − | 0.171520i | \(-0.945132\pi\) | ||
0.985181 | − | 0.171520i | \(-0.0548680\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −75206.5 | − | 31151.6i | −0.463069 | − | 0.191809i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −74573.8 | + | 30889.5i | −0.454649 | + | 0.188322i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −99796.9 | + | 99796.9i | −0.602460 | + | 0.602460i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −168061. | + | 168061.i | −1.00466 | + | 1.00466i | −0.00467264 | + | 0.999989i | \(0.501487\pi\) |
−0.999989 | + | 0.00467264i | \(0.998513\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −224109. | + | 92828.8i | −1.32671 | + | 0.549540i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10696.9 | − | 4430.81i | −0.0627132 | − | 0.0259767i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 118921.i | 0.690496i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 96651.3 | 0.555822 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6549.88 | − | 15812.8i | 0.0373083 | − | 0.0900701i | −0.904127 | − | 0.427264i | \(-0.859478\pi\) |
0.941435 | + | 0.337193i | \(0.109478\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −124106. | − | 299618.i | −0.700209 | − | 1.69045i | −0.723126 | − | 0.690716i | \(-0.757295\pi\) |
0.0229168 | − | 0.999737i | \(-0.492705\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 234753. | + | 234753.i | 1.31199 | + | 1.31199i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −127580. | − | 127580.i | −0.706323 | − | 0.706323i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8318.46 | + | 20082.5i | 0.0456233 | + | 0.110144i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −162124. | + | 391402.i | −0.880912 | + | 2.12671i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −131817. | −0.709606 | −0.354803 | − | 0.934941i | \(-0.615452\pi\) | ||||
−0.354803 | + | 0.934941i | \(0.615452\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 265921.i | 1.41833i | 0.705042 | + | 0.709165i | \(0.250928\pi\) | ||||
−0.705042 | + | 0.709165i | \(0.749072\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 170398. | + | 70581.1i | 0.900504 | + | 0.373001i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 253622. | − | 105054.i | 1.32808 | − | 0.550109i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 121945. | − | 121945.i | 0.632755 | − | 0.632755i | −0.316003 | − | 0.948758i | \(-0.602341\pi\) |
0.948758 | + | 0.316003i | \(0.102341\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −162263. | + | 162263.i | −0.834339 | + | 0.834339i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 176173. | − | 72973.2i | 0.897701 | − | 0.371840i | 0.114365 | − | 0.993439i | \(-0.463517\pi\) |
0.783336 | + | 0.621599i | \(0.213517\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −71508.6 | − | 29619.8i | −0.361109 | − | 0.149576i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 328514.i | 1.64414i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −91589.3 | −0.454310 | −0.227155 | − | 0.973859i | \(-0.572942\pi\) | ||||
−0.227155 | + | 0.973859i | \(0.572942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −68989.1 | + | 166554.i | −0.339178 | + | 0.818848i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −48363.0 | − | 116759.i | −0.235677 | − | 0.568975i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10026.4 | − | 10026.4i | −0.0484309 | − | 0.0484309i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 135201. | + | 135201.i | 0.647361 | + | 0.647361i | 0.952355 | − | 0.304993i | \(-0.0986542\pi\) |
−0.304993 | + | 0.952355i | \(0.598654\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −37695.1 | − | 91004.0i | −0.178920 | − | 0.431952i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 135453. | − | 327012.i | 0.637362 | − | 1.53873i | −0.192819 | − | 0.981234i | \(-0.561763\pi\) |
0.830181 | − | 0.557493i | \(-0.188237\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 119356. | 0.556776 | 0.278388 | − | 0.960469i | \(-0.410200\pi\) | ||||
0.278388 | + | 0.960469i | \(0.410200\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 82030.4i | 0.379375i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12897.7 | + | 5342.40i | 0.0591395 | + | 0.0244964i | 0.412057 | − | 0.911158i | \(-0.364810\pi\) |
−0.352918 | + | 0.935654i | \(0.614810\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14461.1 | − | 5989.99i | 0.0657440 | − | 0.0272321i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 27643.0 | − | 27643.0i | 0.124607 | − | 0.124607i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −161103. | + | 161103.i | −0.720079 | + | 0.720079i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 123546. | − | 51174.5i | 0.547574 | − | 0.226812i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14588.7 | + | 6042.86i | 0.0641182 | + | 0.0265586i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 199300.i | − | 0.868631i | −0.900761 | − | 0.434316i | \(-0.856990\pi\) | ||
0.900761 | − | 0.434316i | \(-0.143010\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 194988. | 0.842786 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16642.2 | − | 40177.7i | 0.0713371 | − | 0.172223i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 47492.6 | + | 114657.i | 0.201903 | + | 0.487437i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −157594. | − | 157594.i | −0.664478 | − | 0.664478i | 0.291954 | − | 0.956432i | \(-0.405695\pi\) |
−0.956432 | + | 0.291954i | \(0.905695\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 71041.6 | + | 71041.6i | 0.297095 | + | 0.297095i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −81254.0 | − | 196165.i | −0.337040 | − | 0.813688i | −0.997997 | − | 0.0632633i | \(-0.979849\pi\) |
0.660956 | − | 0.750424i | \(-0.270151\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 161489. | − | 389869.i | 0.664430 | − | 1.60408i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 231882. | 0.946359 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9071.42i | 0.0367251i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27115.5 | − | 11231.6i | −0.108897 | − | 0.0451066i | 0.327570 | − | 0.944827i | \(-0.393770\pi\) |
−0.436467 | + | 0.899720i | \(0.643770\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −76394.2 | + | 31643.5i | −0.304358 | + | 0.126069i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −275981. | + | 275981.i | −1.09080 | + | 1.09080i | −0.0953523 | + | 0.995444i | \(0.530398\pi\) |
−0.995444 | + | 0.0953523i | \(0.969602\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 159783. | − | 159783.i | 0.626538 | − | 0.626538i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 189397. | − | 78450.7i | 0.736811 | − | 0.305197i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 89441.7 | + | 37047.9i | 0.345227 | + | 0.142998i | 0.548558 | − | 0.836112i | \(-0.315177\pi\) |
−0.203332 | + | 0.979110i | \(0.565177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 448.119i | 0.00171614i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 73006.8 | 0.277414 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −38111.2 | + | 92008.7i | −0.143694 | + | 0.346908i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 200198. | + | 483322.i | 0.748996 | + | 1.80824i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −252456. | − | 252456.i | −0.937242 | − | 0.937242i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5129.50 | − | 5129.50i | −0.0188973 | − | 0.0188973i | 0.697595 | − | 0.716492i | \(-0.254254\pi\) |
−0.716492 | + | 0.697595i | \(0.754254\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34860.2 | + | 84160.0i | 0.127446 | + | 0.307682i | 0.974704 | − | 0.223499i | \(-0.0717481\pi\) |
−0.847258 | + | 0.531182i | \(0.821748\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8106.85 | − | 19571.7i | 0.0294126 | − | 0.0710083i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 187685. | 0.675784 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 307249.i | − | 1.09794i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −241680. | − | 100107.i | −0.857141 | − | 0.355039i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 230108. | − | 95313.9i | 0.809986 | − | 0.335507i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −200162. | + | 200162.i | −0.699316 | + | 0.699316i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 145515. | − | 145515.i | 0.504613 | − | 0.504613i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −334076. | + | 138379.i | −1.14992 | + | 0.476313i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −409834. | − | 169759.i | −1.40028 | − | 0.580013i | −0.450453 | − | 0.892800i | \(-0.648737\pi\) |
−0.949823 | + | 0.312787i | \(0.898737\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 498471.i | − | 1.69060i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −136605. | −0.459912 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 53977.4 | − | 130313.i | 0.180400 | − | 0.435525i | −0.807649 | − | 0.589664i | \(-0.799260\pi\) |
0.988049 | + | 0.154139i | \(0.0492603\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 187942. | + | 453733.i | 0.623563 | + | 1.50541i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 221160. | + | 221160.i | 0.728456 | + | 0.728456i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27833.2 | − | 27833.2i | −0.0910150 | − | 0.0910150i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −75193.8 | − | 181534.i | −0.244116 | − | 0.589348i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11809.8 | − | 28511.4i | 0.0380655 | − | 0.0918983i | −0.903703 | − | 0.428159i | \(-0.859162\pi\) |
0.941769 | + | 0.336261i | \(0.109162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 314770. | 1.00732 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 976780.i | − | 3.10364i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35846.1 | − | 14847.9i | −0.113090 | − | 0.0468435i | 0.325421 | − | 0.945569i | \(-0.394494\pi\) |
−0.438511 | + | 0.898726i | \(0.644494\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 49621.5 | − | 20553.9i | 0.155444 | − | 0.0643869i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15333.0 | + | 15333.0i | −0.0476936 | + | 0.0476936i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −56554.8 | + | 56554.8i | −0.174681 | + | 0.174681i | −0.789032 | − | 0.614352i | \(-0.789418\pi\) |
0.614352 | + | 0.789032i | \(0.289418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 436193. | − | 180677.i | 1.33785 | − | 0.554155i | 0.404965 | − | 0.914332i | \(-0.367284\pi\) |
0.932884 | + | 0.360177i | \(0.117284\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −644483. | − | 266954.i | −1.96292 | − | 0.813068i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 285988.i | − | 0.864991i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 399675. | 1.20048 | 0.600240 | − | 0.799820i | \(-0.295072\pi\) | ||||
0.600240 | + | 0.799820i | \(0.295072\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −248131. | + | 599040.i | −0.740156 | + | 1.78689i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12225.5 | + | 29515.0i | 0.0362172 | + | 0.0874362i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17594.8 | + | 17594.8i | 0.0517662 | + | 0.0517662i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −226531. | − | 226531.i | −0.661935 | − | 0.661935i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1130.83 | + | 2730.08i | 0.00328188 | + | 0.00792316i | 0.925512 | − | 0.378718i | \(-0.123635\pi\) |
−0.922230 | + | 0.386641i | \(0.873635\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −53233.7 | + | 128518.i | −0.153446 | + | 0.370452i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40574.1 | 0.116165 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 457093.i | 1.29986i | 0.759996 | + | 0.649928i | \(0.225201\pi\) | ||||
−0.759996 | + | 0.649928i | \(0.774799\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30204.0 | + | 12510.9i | 0.0853160 | + | 0.0353391i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −147186. | + | 60966.6i | −0.412970 | + | 0.171058i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 155176. | − | 155176.i | 0.432485 | − | 0.432485i | −0.456988 | − | 0.889473i | \(-0.651072\pi\) |
0.889473 | + | 0.456988i | \(0.151072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −64063.7 | + | 64063.7i | −0.177363 | + | 0.177363i | −0.790205 | − | 0.612842i | \(-0.790026\pi\) |
0.612842 | + | 0.790205i | \(0.290026\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 326726. | − | 135334.i | 0.898564 | − | 0.372198i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 122958. | + | 50931.1i | 0.335929 | + | 0.139146i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 92224.8i | 0.250305i | 0.992137 | + | 0.125153i | \(0.0399421\pi\) | ||||
−0.992137 | + | 0.125153i | \(0.960058\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 49547.3 | 0.133593 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 276590. | − | 667747.i | 0.740890 | − | 1.78867i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 218845. | + | 528338.i | 0.582392 | + | 1.40602i | 0.890638 | + | 0.454713i | \(0.150258\pi\) |
−0.308246 | + | 0.951307i | \(0.599742\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −177475. | − | 177475.i | −0.469230 | − | 0.469230i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 112085. | + | 112085.i | 0.294427 | + | 0.294427i | 0.838826 | − | 0.544399i | \(-0.183242\pi\) |
−0.544399 | + | 0.838826i | \(0.683242\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 188744. | + | 455668.i | 0.492596 | + | 1.18923i | 0.953394 | + | 0.301728i | \(0.0975634\pi\) |
−0.460798 | + | 0.887505i | \(0.652437\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 59749.7 | − | 144249.i | 0.154936 | − | 0.374049i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20792.8 | −0.0535720 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18034.1i | 0.0461672i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 668852. | + | 277048.i | 1.70136 | + | 0.704724i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −415348. | + | 172043.i | −1.04981 | + | 0.434846i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 250089. | − | 250089.i | 0.628110 | − | 0.628110i | −0.319482 | − | 0.947592i | \(-0.603509\pi\) |
0.947592 | + | 0.319482i | \(0.103509\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 303577. | − | 303577.i | 0.757638 | − | 0.757638i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36239.3 | − | 15010.8i | 0.0898736 | − | 0.0372269i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 461552. | + | 191181.i | 1.13748 | + | 0.471158i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 204955.i | 0.501945i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −417319. | −1.01567 | −0.507835 | − | 0.861455i | \(-0.669554\pi\) | ||||
−0.507835 | + | 0.861455i | \(0.669554\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −296774. | + | 716476.i | −0.717801 | + | 1.73293i | −0.0382831 | + | 0.999267i | \(0.512189\pi\) |
−0.679518 | + | 0.733659i | \(0.737811\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −121386. | − | 293051.i | −0.291775 | − | 0.704406i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −363142. | − | 363142.i | −0.867498 | − | 0.867498i | 0.124697 | − | 0.992195i | \(-0.460204\pi\) |
−0.992195 | + | 0.124697i | \(0.960204\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −291478. | − | 291478.i | −0.692018 | − | 0.692018i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8433.06 | + | 20359.2i | 0.0198986 | + | 0.0480395i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −199241. | + | 481012.i | −0.467254 | + | 1.12805i | 0.498102 | + | 0.867118i | \(0.334030\pi\) |
−0.965357 | + | 0.260934i | \(0.915970\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −35595.7 | −0.0829689 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10124.5i | 0.0234555i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −300618. | − | 124520.i | −0.692220 | − | 0.286727i | 0.00870482 | − | 0.999962i | \(-0.497229\pi\) |
−0.700925 | + | 0.713235i | \(0.747229\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6388.54 | + | 2646.22i | −0.0146217 | + | 0.00605652i | −0.389982 | − | 0.920822i | \(-0.627519\pi\) |
0.375361 | + | 0.926879i | \(0.377519\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −954240. | + | 954240.i | −2.17085 | + | 2.17085i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17133.7 | + | 17133.7i | −0.0387444 | + | 0.0387444i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 617973. | − | 255973.i | 1.38905 | − | 0.575364i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −155081. | − | 64236.5i | −0.346501 | − | 0.143526i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 773893.i | 1.71884i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 652582. | 1.44080 | 0.720402 | − | 0.693556i | \(-0.243957\pi\) | ||||
0.720402 | + | 0.693556i | \(0.243957\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 29105.7 | − | 70267.4i | 0.0638809 | − | 0.154222i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32037.9 | − | 77346.3i | −0.0699015 | − | 0.168757i | 0.885068 | − | 0.465463i | \(-0.154112\pi\) |
−0.954969 | + | 0.296705i | \(0.904112\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23574.5 | + | 23574.5i | 0.0511332 | + | 0.0511332i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 367257. | + | 367257.i | 0.791910 | + | 0.791910i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −122223. | − | 295072.i | −0.262006 | − | 0.632539i | 0.737056 | − | 0.675831i | \(-0.236215\pi\) |
−0.999062 | + | 0.0432925i | \(0.986215\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 110615. | − | 267047.i | 0.235739 | − | 0.569124i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −827117. | −1.75248 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 34377.5i | − | 0.0724161i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 800274. | + | 331484.i | 1.67603 | + | 0.694235i | 0.999125 | − | 0.0418321i | \(-0.0133195\pi\) |
0.676908 | + | 0.736068i | \(0.263319\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 57551.0 | − | 23838.4i | 0.119836 | − | 0.0496376i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −81437.1 | + | 81437.1i | −0.168598 | + | 0.168598i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −406060. | + | 406060.i | −0.835844 | + | 0.835844i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −865071. | + | 358324.i | −1.77051 | + | 0.733368i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 460670. | + | 190816.i | 0.937462 | + | 0.388309i | 0.798504 | − | 0.601989i | \(-0.205625\pi\) |
0.138957 | + | 0.990298i | \(0.455625\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 333207.i | − | 0.674224i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −728335. | −1.46539 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23230.3 | − | 56083.0i | 0.0464747 | − | 0.112200i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −109077. | − | 263335.i | −0.216991 | − | 0.523862i | 0.777476 | − | 0.628912i | \(-0.216500\pi\) |
−0.994467 | + | 0.105050i | \(0.966500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −628847. | − | 628847.i | −1.24396 | − | 1.24396i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 210361. | + | 210361.i | 0.413796 | + | 0.413796i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −193187. | − | 466394.i | −0.377890 | − | 0.912307i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −313265. | + | 756289.i | −0.609360 | + | 1.47113i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −620275. | −1.19985 | −0.599924 | − | 0.800057i | \(-0.704803\pi\) | ||||
−0.599924 | + | 0.800057i | \(0.704803\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26753.7i | 0.0514652i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −511625. | − | 211922.i | −0.978757 | − | 0.405414i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 301032. | − | 124691.i | 0.572712 | − | 0.237225i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 202721. | − | 202721.i | 0.383558 | − | 0.383558i | −0.488825 | − | 0.872382i | \(-0.662574\pi\) |
0.872382 | + | 0.488825i | \(0.162574\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −501832. | + | 501832.i | −0.944285 | + | 0.944285i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −670498. | + | 277729.i | −1.25477 | + | 0.519741i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −786303. | − | 325697.i | −1.46346 | − | 0.606186i | −0.498106 | − | 0.867116i | \(-0.665971\pi\) |
−0.965358 | + | 0.260930i | \(0.915971\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 503431.i | − | 0.931892i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 557268. | 1.02596 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −183482. | + | 442965.i | −0.335973 | + | 0.811111i | 0.662121 | + | 0.749397i | \(0.269657\pi\) |
−0.998094 | + | 0.0617138i | \(0.980343\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −382763. | − | 924072.i | −0.697097 | − | 1.68294i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 569790. | + | 569790.i | 1.03214 | + | 1.03214i | 0.999466 | + | 0.0326698i | \(0.0104010\pi\) |
0.0326698 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −276802. | − | 276802.i | −0.498720 | − | 0.498720i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 276217. | + | 666846.i | 0.495004 | + | 1.19504i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29100.9 | + | 70255.8i | −0.0518732 | + | 0.125233i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 625561. | 1.10915 | 0.554575 | − | 0.832134i | \(-0.312881\pi\) | ||||
0.554575 | + | 0.832134i | \(0.312881\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 356866.i | 0.629383i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 139130. | + | 57629.3i | 0.244076 | + | 0.101100i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −111355. | + | 46124.6i | −0.194319 | + | 0.0804898i | −0.477721 | − | 0.878512i | \(-0.658537\pi\) |
0.283402 | + | 0.959001i | \(0.408537\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.09479e6 | − | 1.09479e6i | 1.90042 | − | 1.90042i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −177072. | + | 177072.i | −0.305760 | + | 0.305760i | −0.843262 | − | 0.537502i | \(-0.819368\pi\) |
0.537502 | + | 0.843262i | \(0.319368\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33904.2 | + | 14043.6i | −0.0582377 | + | 0.0241228i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 682412. | + | 282664.i | 1.16607 | + | 0.483001i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 569504.i | 0.968069i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 654747. | 1.10719 | 0.553593 | − | 0.832787i | \(-0.313256\pi\) | ||||
0.553593 | + | 0.832787i | \(0.313256\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 372840. | − | 900116.i | 0.627212 | − | 1.51422i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30117.2 | + | 72709.3i | 0.0504029 | + | 0.121683i | 0.947075 | − | 0.321011i | \(-0.104023\pi\) |
−0.896673 | + | 0.442694i | \(0.854023\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 102473. | + | 102473.i | 0.170610 | + | 0.170610i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −37324.8 | − | 37324.8i | −0.0618238 | − | 0.0618238i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −162878. | − | 393223.i | −0.268404 | − | 0.647984i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −123593. | + | 298379.i | −0.202624 | + | 0.489177i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 177888. | 0.290150 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46583.4i | 0.0755947i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −104049. | − | 43098.4i | −0.167992 | − | 0.0695844i | 0.297103 | − | 0.954846i | \(-0.403980\pi\) |
−0.465094 | + | 0.885261i | \(0.653980\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −47810.7 | + | 19803.9i | −0.0768018 | + | 0.0318123i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10202.6 | − | 10202.6i | 0.0163064 | − | 0.0163064i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 756034. | − | 756034.i | 1.20225 | − | 1.20225i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −32005.4 | + | 13257.1i | −0.0506395 | + | 0.0209756i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 397059. | + | 164467.i | 0.625084 | + | 0.258918i | 0.672663 | − | 0.739949i | \(-0.265151\pi\) |
−0.0475789 | + | 0.998867i | \(0.515151\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.66643e6i | 2.61031i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −469781. | −0.732202 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6105.35 | + | 14739.6i | −0.00946847 | + | 0.0228589i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19830.8 | + | 47875.7i | 0.0306019 | + | 0.0738794i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.21385e6 | + | 1.21385e6i | 1.86388 | + | 1.86388i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −447404. | − | 447404.i | −0.683601 | − | 0.683601i | 0.277209 | − | 0.960810i | \(-0.410591\pi\) |
−0.960810 | + | 0.277209i | \(0.910591\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −263162. | − | 635329.i | −0.400112 | − | 0.965955i | −0.987638 | − | 0.156750i | \(-0.949898\pi\) |
0.587527 | − | 0.809205i | \(-0.300102\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 424922. | − | 1.02585e6i | 0.642878 | − | 1.55204i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −119717. | −0.180236 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 537898.i | − | 0.805853i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −79511.2 | − | 32934.6i | −0.118539 | − | 0.0491004i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 132367. | − | 54828.4i | 0.196379 | − | 0.0813428i | −0.282327 | − | 0.959318i | \(-0.591106\pi\) |
0.478705 | + | 0.877976i | \(0.341106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 898841. | − | 898841.i | 1.32704 | − | 1.32704i | 0.419096 | − | 0.907942i | \(-0.362347\pi\) |
0.907942 | − | 0.419096i | \(-0.137653\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 533304. | − | 533304.i | 0.783551 | − | 0.783551i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −487581. | + | 201963.i | −0.712911 | + | 0.295298i | −0.709509 | − | 0.704697i | \(-0.751083\pi\) |
−0.00340260 | + | 0.999994i | \(0.501083\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.03969e6 | + | 430653.i | 1.51284 | + | 0.626640i | 0.976142 | − | 0.217133i | \(-0.0696704\pi\) |
0.536701 | + | 0.843773i | \(0.319670\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1.48411e6i | − | 2.14913i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.15185e6 | −1.65999 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 37706.4 | − | 91031.3i | 0.0540807 | − | 0.130562i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30276.9 | + | 73094.9i | 0.0432176 | + | 0.104336i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 598087. | + | 598087.i | 0.849651 | + | 0.849651i | 0.990089 | − | 0.140439i | \(-0.0448513\pi\) |
−0.140439 | + | 0.990089i | \(0.544851\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38753.2 | + | 38753.2i | 0.0547919 | + | 0.0547919i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 587977. | + | 1.41950e6i | 0.827380 | + | 1.99747i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −93481.7 | + | 225685.i | −0.130922 | + | 0.316074i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35753.1 | 0.0498364 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.68281e6i | 2.33465i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −658359. | − | 272701.i | −0.909083 | − | 0.376555i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −223688. | + | 92654.4i | −0.307428 | + | 0.127341i | −0.531064 | − | 0.847332i | \(-0.678208\pi\) |
0.223635 | + | 0.974673i | \(0.428208\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −387110. | + | 387110.i | −0.529544 | + | 0.529544i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 209053. | − | 209053.i | 0.284639 | − | 0.284639i | −0.550317 | − | 0.834956i | \(-0.685493\pi\) |
0.834956 | + | 0.550317i | \(0.185493\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 551958. | − | 228629.i | 0.748032 | − | 0.309845i | 0.0240935 | − | 0.999710i | \(-0.492330\pi\) |
0.723938 | + | 0.689865i | \(0.242330\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −62292.7 | − | 25802.5i | −0.0840293 | − | 0.0348061i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.44496e6i | − | 1.94015i | −0.242807 | − | 0.970075i | \(-0.578068\pi\) | ||
0.242807 | − | 0.970075i | \(-0.421932\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 425433. | 0.568590 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 765105. | − | 1.84713e6i | 1.01785 | − | 2.45730i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −536285. | − | 1.29471e6i | −0.710160 | − | 1.71448i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −544408. | − | 544408.i | −0.717610 | − | 0.717610i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 532628. | + | 532628.i | 0.698869 | + | 0.698869i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25836.0 | + | 62373.5i | 0.0337449 | + | 0.0814675i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 141976. | − | 342760.i | 0.184593 | − | 0.445646i | −0.804310 | − | 0.594210i | \(-0.797465\pi\) |
0.988903 | + | 0.148563i | \(0.0474649\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 456964. | 0.591431 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 842005.i | − | 1.08483i | −0.840110 | − | 0.542416i | \(-0.817509\pi\) | ||
0.840110 | − | 0.542416i | \(-0.182491\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.15603e6 | − | 478843.i | −1.48268 | − | 0.614146i | −0.512970 | − | 0.858407i | \(-0.671455\pi\) |
−0.969710 | + | 0.244261i | \(0.921455\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 530209. | − | 219620.i | 0.676956 | − | 0.280404i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 200436. | − | 200436.i | 0.254759 | − | 0.254759i | −0.568160 | − | 0.822918i | \(-0.692344\pi\) |
0.822918 | + | 0.568160i | \(0.192344\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7451.09 | − | 7451.09i | 0.00942793 | − | 0.00942793i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −713238. | + | 295433.i | −0.898419 | + | 0.372137i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.14109e6 | − | 472654.i | −1.43092 | − | 0.592707i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 245218.i | 0.306130i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.13906e6 | −2.65851 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −129709. | + | 313145.i | −0.160491 | + | 0.387459i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30332.1 | + | 73228.2i | 0.0373640 | + | 0.0902046i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −60253.6 | − | 60253.6i | −0.0738937 | − | 0.0738937i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 420005. | + | 420005.i | 0.512811 | + | 0.512811i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7840.87 | + | 18929.5i | 0.00953125 | + | 0.0230105i | 0.928574 | − | 0.371149i | \(-0.121036\pi\) |
−0.919042 | + | 0.394159i | \(0.871036\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 524853. | − | 1.26711e6i | 0.635199 | − | 1.53351i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51624.2 | −0.0622038 | −0.0311019 | − | 0.999516i | \(-0.509902\pi\) | ||||
−0.0311019 | + | 0.999516i | \(0.509902\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.13738e6i | 1.36447i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −995420. | − | 412316.i | −1.18895 | − | 0.492480i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8834.54 | + | 3659.39i | −0.0105062 | + | 0.00435181i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.06428e6 | + | 1.06428e6i | −1.26016 | + | 1.26016i | −0.309146 | + | 0.951015i | \(0.600043\pi\) |
−0.951015 | + | 0.309146i | \(0.899957\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 45674.2 | − | 45674.2i | 0.0538458 | − | 0.0538458i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 412234. | − | 170753.i | 0.483883 | − | 0.200431i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −320705. | − | 132840.i | −0.374819 | − | 0.155255i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 604458.i | 0.703407i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 211113. | 0.244615 | 0.122307 | − | 0.992492i | \(-0.460971\pi\) | ||||
0.122307 | + | 0.992492i | \(0.460971\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 326703. | − | 788730.i | 0.376923 | − | 0.909974i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 264866. | + | 639444.i | 0.304273 | + | 0.734580i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 823023. | + | 823023.i | 0.941431 | + | 0.941431i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −452514. | − | 452514.i | −0.515410 | − | 0.515410i | 0.400769 | − | 0.916179i | \(-0.368743\pi\) |
−0.916179 | + | 0.400769i | \(0.868743\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 436676. | + | 1.05423e6i | 0.495254 | + | 1.19565i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −141554. | + | 341741.i | −0.159861 | + | 0.385938i | −0.983433 | − | 0.181274i | \(-0.941978\pi\) |
0.823572 | + | 0.567212i | \(0.191978\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −910241. | −1.02361 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13781.3i | 0.0154322i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.22812e6 | + | 508702.i | 1.36943 | + | 0.567236i | 0.941633 | − | 0.336640i | \(-0.109291\pi\) |
0.427795 | + | 0.903876i | \(0.359291\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20363.9 | − | 8435.02i | 0.0226115 | − | 0.00936599i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −103717. | + | 103717.i | −0.114680 | + | 0.114680i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 483747. | − | 483747.i | 0.532638 | − | 0.532638i | −0.388718 | − | 0.921357i | \(-0.627082\pi\) |
0.921357 | + | 0.388718i | \(0.127082\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 767965. | − | 318102.i | 0.842044 | − | 0.348786i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.62972e6 | + | 675052.i | 1.77946 | + | 0.737077i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 77650.4i | − | 0.0844319i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 772772. | 0.836767 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −657489. | + | 1.58732e6i | −0.708983 | + | 1.71164i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −295672. | − | 713816.i | −0.317509 | − | 0.766534i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −684162. | − | 684162.i | −0.731655 | − | 0.731655i | 0.239293 | − | 0.970948i | \(-0.423084\pi\) |
−0.970948 | + | 0.239293i | \(0.923084\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.63066e6 | + | 1.63066e6i | 1.73667 | + | 1.73667i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22015.7 | − | 53150.6i | −0.0233504 | − | 0.0563728i | 0.911774 | − | 0.410692i | \(-0.134713\pi\) |
−0.935125 | + | 0.354319i | \(0.884713\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11839.9 | + | 28584.0i | −0.0125061 | + | 0.0301924i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.04200e6 | −1.09612 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 631988.i | 0.662094i | 0.943614 | + | 0.331047i | \(0.107402\pi\) | ||||
−0.943614 | + | 0.331047i | \(0.892598\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −683922. | − | 283290.i | −0.713578 | − | 0.295574i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −766012. | + | 317292.i | −0.795971 | + | 0.329702i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 298315. | − | 298315.i | 0.308722 | − | 0.308722i | −0.535691 | − | 0.844414i | \(-0.679949\pi\) |
0.844414 | + | 0.535691i | \(0.179949\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34187.2 | + | 34187.2i | −0.0352364 | + | 0.0352364i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −180766. | + | 74875.8i | −0.185559 | + | 0.0768612i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.06279e6 | − | 440223.i | −1.08656 | − | 0.450070i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.21567e6i | − | 1.23785i | −0.785449 | − | 0.618927i | \(-0.787568\pi\) | ||
0.785449 | − | 0.618927i | \(-0.212432\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −573913. | −0.582033 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 72647.7 | − | 175387.i | 0.0733796 | − | 0.177154i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 344654. | + | 832068.i | 0.346731 | + | 0.837083i | 0.997002 | + | 0.0773805i | \(0.0246556\pi\) |
−0.650270 | + | 0.759703i | \(0.725344\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −134006. | − | 134006.i | −0.134274 | − | 0.134274i |
(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 | 128.5.h.a.47.2 | 60 | ||
4.3 | odd | 2 | 32.5.h.a.3.14 | ✓ | 60 | ||
32.11 | odd | 8 | inner | 128.5.h.a.79.2 | 60 | ||
32.21 | even | 8 | 32.5.h.a.11.14 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.5.h.a.3.14 | ✓ | 60 | 4.3 | odd | 2 | ||
32.5.h.a.11.14 | yes | 60 | 32.21 | even | 8 | ||
128.5.h.a.47.2 | 60 | 1.1 | even | 1 | trivial | ||
128.5.h.a.79.2 | 60 | 32.11 | odd | 8 | inner |