Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(65,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.n (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 263.2 | ||
Root | \(2.13746 - 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.263 |
Dual form | 462.2.n.c.65.2 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −1.50000 | − | 0.866025i | −0.866025 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.63746 | − | 1.52274i | 1.17951 | − | 0.680989i | 0.223607 | − | 0.974679i | \(-0.428217\pi\) |
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | − | 1.73205i | − | 0.707107i | ||||||
\(7\) | −2.63746 | − | 0.209313i | −0.996866 | − | 0.0791130i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 2.63746 | + | 1.52274i | 0.834038 | + | 0.481532i | ||||
\(11\) | 3.13746 | + | 1.07534i | 0.945979 | + | 0.324227i | ||||
\(12\) | 1.50000 | − | 0.866025i | 0.433013 | − | 0.250000i | ||||
\(13\) | − | 6.09095i | − | 1.68933i | −0.535299 | − | 0.844663i | \(-0.679801\pi\) | ||
0.535299 | − | 0.844663i | \(-0.320199\pi\) | |||||||
\(14\) | −1.13746 | − | 2.38876i | −0.303999 | − | 0.638424i | ||||
\(15\) | −5.27492 | −1.36198 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.13746 | − | 3.70219i | 0.518410 | − | 0.897912i | −0.481361 | − | 0.876522i | \(-0.659858\pi\) |
0.999771 | − | 0.0213900i | \(-0.00680916\pi\) | |||||||
\(18\) | −1.50000 | + | 2.59808i | −0.353553 | + | 0.612372i | ||||
\(19\) | −1.86254 | + | 1.07534i | −0.427296 | + | 0.246700i | −0.698194 | − | 0.715908i | \(-0.746013\pi\) |
0.270898 | + | 0.962608i | \(0.412679\pi\) | |||||||
\(20\) | 3.04547i | 0.680989i | ||||||||
\(21\) | 3.77492 | + | 2.59808i | 0.823754 | + | 0.566947i | ||||
\(22\) | 0.637459 | + | 3.25479i | 0.135907 | + | 0.693923i | ||||
\(23\) | 6.41238 | − | 3.70219i | 1.33707 | − | 0.771959i | 0.350700 | − | 0.936488i | \(-0.385944\pi\) |
0.986372 | + | 0.164528i | \(0.0526102\pi\) | |||||||
\(24\) | 1.50000 | + | 0.866025i | 0.306186 | + | 0.176777i | ||||
\(25\) | 2.13746 | − | 3.70219i | 0.427492 | − | 0.740437i | ||||
\(26\) | 5.27492 | − | 3.04547i | 1.03450 | − | 0.597267i | ||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 1.50000 | − | 2.17945i | 0.283473 | − | 0.411877i | ||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | −2.63746 | − | 4.56821i | −0.481532 | − | 0.834038i | ||||
\(31\) | 1.36254 | − | 2.35999i | 0.244720 | − | 0.423867i | −0.717333 | − | 0.696730i | \(-0.754637\pi\) |
0.962053 | + | 0.272863i | \(0.0879707\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −3.77492 | − | 4.33013i | −0.657129 | − | 0.753778i | ||||
\(34\) | 4.27492 | 0.733142 | ||||||||
\(35\) | −7.27492 | + | 3.46410i | −1.22969 | + | 0.585540i | ||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | −0.137459 | − | 0.238085i | −0.0225981 | − | 0.0391410i | 0.854505 | − | 0.519443i | \(-0.173860\pi\) |
−0.877103 | + | 0.480302i | \(0.840527\pi\) | |||||||
\(38\) | −1.86254 | − | 1.07534i | −0.302144 | − | 0.174443i | ||||
\(39\) | −5.27492 | + | 9.13642i | −0.844663 | + | 1.46300i | ||||
\(40\) | −2.63746 | + | 1.52274i | −0.417019 | + | 0.240766i | ||||
\(41\) | 8.54983 | 1.33526 | 0.667630 | − | 0.744493i | \(-0.267309\pi\) | ||||
0.667630 | + | 0.744493i | \(0.267309\pi\) | |||||||
\(42\) | −0.362541 | + | 4.56821i | −0.0559414 | + | 0.704890i | ||||
\(43\) | 5.61478i | 0.856246i | 0.903721 | + | 0.428123i | \(0.140825\pi\) | ||||
−0.903721 | + | 0.428123i | \(0.859175\pi\) | |||||||
\(44\) | −2.50000 | + | 2.17945i | −0.376889 | + | 0.328564i | ||||
\(45\) | 7.91238 | + | 4.56821i | 1.17951 | + | 0.680989i | ||||
\(46\) | 6.41238 | + | 3.70219i | 0.945453 | + | 0.545858i | ||||
\(47\) | −9.41238 | + | 5.43424i | −1.37294 | + | 0.792665i | −0.991297 | − | 0.131646i | \(-0.957974\pi\) |
−0.381639 | + | 0.924311i | \(0.624640\pi\) | |||||||
\(48\) | 1.73205i | 0.250000i | ||||||||
\(49\) | 6.91238 | + | 1.10411i | 0.987482 | + | 0.157730i | ||||
\(50\) | 4.27492 | 0.604565 | ||||||||
\(51\) | −6.41238 | + | 3.70219i | −0.897912 | + | 0.518410i | ||||
\(52\) | 5.27492 | + | 3.04547i | 0.731499 | + | 0.422331i | ||||
\(53\) | −7.18729 | − | 4.14959i | −0.987251 | − | 0.569989i | −0.0827993 | − | 0.996566i | \(-0.526386\pi\) |
−0.904451 | + | 0.426577i | \(0.859719\pi\) | |||||||
\(54\) | 4.50000 | − | 2.59808i | 0.612372 | − | 0.353553i | ||||
\(55\) | 9.91238 | − | 1.94136i | 1.33658 | − | 0.261773i | ||||
\(56\) | 2.63746 | + | 0.209313i | 0.352445 | + | 0.0279707i | ||||
\(57\) | 3.72508 | 0.493399 | ||||||||
\(58\) | 0.500000 | + | 0.866025i | 0.0656532 | + | 0.113715i | ||||
\(59\) | 1.50000 | + | 0.866025i | 0.195283 | + | 0.112747i | 0.594454 | − | 0.804130i | \(-0.297368\pi\) |
−0.399170 | + | 0.916877i | \(0.630702\pi\) | |||||||
\(60\) | 2.63746 | − | 4.56821i | 0.340494 | − | 0.589754i | ||||
\(61\) | −6.00000 | + | 3.46410i | −0.768221 | + | 0.443533i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.0640184 | + | 0.997949i | \(0.479608\pi\) | |||||||
\(62\) | 2.72508 | 0.346086 | ||||||||
\(63\) | −3.41238 | − | 7.16629i | −0.429919 | − | 0.902867i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.27492 | − | 16.0646i | −1.15041 | − | 1.99257i | ||||
\(66\) | 1.86254 | − | 5.43424i | 0.229263 | − | 0.668908i | ||||
\(67\) | −3.27492 | + | 5.67232i | −0.400095 | + | 0.692985i | −0.993737 | − | 0.111745i | \(-0.964356\pi\) |
0.593642 | + | 0.804729i | \(0.297689\pi\) | |||||||
\(68\) | 2.13746 | + | 3.70219i | 0.259205 | + | 0.448956i | ||||
\(69\) | −12.8248 | −1.54392 | ||||||||
\(70\) | −6.63746 | − | 4.56821i | −0.793328 | − | 0.546006i | ||||
\(71\) | − | 5.61478i | − | 0.666352i | −0.942865 | − | 0.333176i | \(-0.891880\pi\) | ||
0.942865 | − | 0.333176i | \(-0.108120\pi\) | |||||||
\(72\) | −1.50000 | − | 2.59808i | −0.176777 | − | 0.306186i | ||||
\(73\) | 10.5498 | + | 6.09095i | 1.23476 | + | 0.712892i | 0.968019 | − | 0.250875i | \(-0.0807184\pi\) |
0.266745 | + | 0.963767i | \(0.414052\pi\) | |||||||
\(74\) | 0.137459 | − | 0.238085i | 0.0159792 | − | 0.0276769i | ||||
\(75\) | −6.41238 | + | 3.70219i | −0.740437 | + | 0.427492i | ||||
\(76\) | − | 2.15068i | − | 0.246700i | ||||||
\(77\) | −8.04983 | − | 3.49287i | −0.917364 | − | 0.398050i | ||||
\(78\) | −10.5498 | −1.19453 | ||||||||
\(79\) | −5.63746 | + | 3.25479i | −0.634264 | + | 0.366192i | −0.782401 | − | 0.622774i | \(-0.786005\pi\) |
0.148138 | + | 0.988967i | \(0.452672\pi\) | |||||||
\(80\) | −2.63746 | − | 1.52274i | −0.294877 | − | 0.170247i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 4.27492 | + | 7.40437i | 0.472086 | + | 0.817676i | ||||
\(83\) | 2.72508 | 0.299117 | 0.149558 | − | 0.988753i | \(-0.452215\pi\) | ||||
0.149558 | + | 0.988753i | \(0.452215\pi\) | |||||||
\(84\) | −4.13746 | + | 1.97014i | −0.451434 | + | 0.214959i | ||||
\(85\) | − | 13.0192i | − | 1.41213i | ||||||
\(86\) | −4.86254 | + | 2.80739i | −0.524341 | + | 0.302729i | ||||
\(87\) | −1.50000 | − | 0.866025i | −0.160817 | − | 0.0928477i | ||||
\(88\) | −3.13746 | − | 1.07534i | −0.334454 | − | 0.114631i | ||||
\(89\) | −5.27492 | + | 3.04547i | −0.559140 | + | 0.322820i | −0.752800 | − | 0.658249i | \(-0.771297\pi\) |
0.193660 | + | 0.981069i | \(0.437964\pi\) | |||||||
\(90\) | 9.13642i | 0.963064i | ||||||||
\(91\) | −1.27492 | + | 16.0646i | −0.133648 | + | 1.68403i | ||||
\(92\) | 7.40437i | 0.771959i | ||||||||
\(93\) | −4.08762 | + | 2.35999i | −0.423867 | + | 0.244720i | ||||
\(94\) | −9.41238 | − | 5.43424i | −0.970812 | − | 0.560499i | ||||
\(95\) | −3.27492 | + | 5.67232i | −0.335999 | + | 0.581968i | ||||
\(96\) | −1.50000 | + | 0.866025i | −0.153093 | + | 0.0883883i | ||||
\(97\) | 1.54983 | 0.157362 | 0.0786809 | − | 0.996900i | \(-0.474929\pi\) | ||||
0.0786809 | + | 0.996900i | \(0.474929\pi\) | |||||||
\(98\) | 2.50000 | + | 6.53835i | 0.252538 | + | 0.660473i | ||||
\(99\) | 1.91238 | + | 9.76436i | 0.192201 | + | 0.981356i | ||||
\(100\) | 2.13746 | + | 3.70219i | 0.213746 | + | 0.370219i | ||||
\(101\) | −6.41238 | + | 11.1066i | −0.638055 | + | 1.10514i | 0.347804 | + | 0.937567i | \(0.386928\pi\) |
−0.985859 | + | 0.167577i | \(0.946406\pi\) | |||||||
\(102\) | −6.41238 | − | 3.70219i | −0.634920 | − | 0.366571i | ||||
\(103\) | −8.54983 | − | 14.8087i | −0.842440 | − | 1.45915i | −0.887826 | − | 0.460180i | \(-0.847785\pi\) |
0.0453856 | − | 0.998970i | \(-0.485548\pi\) | |||||||
\(104\) | 6.09095i | 0.597267i | ||||||||
\(105\) | 13.9124 | + | 1.10411i | 1.35771 | + | 0.107750i | ||||
\(106\) | − | 8.29917i | − | 0.806087i | ||||||
\(107\) | −3.36254 | − | 5.82409i | −0.325069 | − | 0.563036i | 0.656457 | − | 0.754363i | \(-0.272054\pi\) |
−0.981526 | + | 0.191327i | \(0.938721\pi\) | |||||||
\(108\) | 4.50000 | + | 2.59808i | 0.433013 | + | 0.250000i | ||||
\(109\) | −11.2749 | − | 6.50958i | −1.07994 | − | 0.623504i | −0.149061 | − | 0.988828i | \(-0.547625\pi\) |
−0.930881 | + | 0.365324i | \(0.880958\pi\) | |||||||
\(110\) | 6.63746 | + | 7.61369i | 0.632857 | + | 0.725937i | ||||
\(111\) | 0.476171i | 0.0451961i | ||||||||
\(112\) | 1.13746 | + | 2.38876i | 0.107480 | + | 0.225717i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 1.86254 | + | 3.22602i | 0.174443 | + | 0.302144i | ||||
\(115\) | 11.2749 | − | 19.5287i | 1.05139 | − | 1.82106i | ||||
\(116\) | −0.500000 | + | 0.866025i | −0.0464238 | + | 0.0804084i | ||||
\(117\) | 15.8248 | − | 9.13642i | 1.46300 | − | 0.844663i | ||||
\(118\) | 1.73205i | 0.159448i | ||||||||
\(119\) | −6.41238 | + | 9.31697i | −0.587822 | + | 0.854085i | ||||
\(120\) | 5.27492 | 0.481532 | ||||||||
\(121\) | 8.68729 | + | 6.74766i | 0.789754 | + | 0.613424i | ||||
\(122\) | −6.00000 | − | 3.46410i | −0.543214 | − | 0.313625i | ||||
\(123\) | −12.8248 | − | 7.40437i | −1.15637 | − | 0.667630i | ||||
\(124\) | 1.36254 | + | 2.35999i | 0.122360 | + | 0.211933i | ||||
\(125\) | 2.20822i | 0.197509i | ||||||||
\(126\) | 4.50000 | − | 6.53835i | 0.400892 | − | 0.582482i | ||||
\(127\) | 13.9140i | 1.23466i | 0.786703 | + | 0.617332i | \(0.211786\pi\) | ||||
−0.786703 | + | 0.617332i | \(0.788214\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 4.86254 | − | 8.42217i | 0.428123 | − | 0.741531i | ||||
\(130\) | 9.27492 | − | 16.0646i | 0.813464 | − | 1.40896i | ||||
\(131\) | 1.36254 | + | 2.35999i | 0.119046 | + | 0.206193i | 0.919390 | − | 0.393348i | \(-0.128683\pi\) |
−0.800344 | + | 0.599541i | \(0.795350\pi\) | |||||||
\(132\) | 5.63746 | − | 1.10411i | 0.490678 | − | 0.0961005i | ||||
\(133\) | 5.13746 | − | 2.44631i | 0.445474 | − | 0.212122i | ||||
\(134\) | −6.54983 | −0.565820 | ||||||||
\(135\) | −7.91238 | − | 13.7046i | −0.680989 | − | 1.17951i | ||||
\(136\) | −2.13746 | + | 3.70219i | −0.183286 | + | 0.317460i | ||||
\(137\) | 11.2749 | + | 6.50958i | 0.963281 | + | 0.556151i | 0.897181 | − | 0.441662i | \(-0.145611\pi\) |
0.0660998 | + | 0.997813i | \(0.478944\pi\) | |||||||
\(138\) | −6.41238 | − | 11.1066i | −0.545858 | − | 0.945453i | ||||
\(139\) | 4.77753i | 0.405224i | 0.979259 | + | 0.202612i | \(0.0649431\pi\) | ||||
−0.979259 | + | 0.202612i | \(0.935057\pi\) | |||||||
\(140\) | 0.637459 | − | 8.03231i | 0.0538751 | − | 0.678854i | ||||
\(141\) | 18.8248 | 1.58533 | ||||||||
\(142\) | 4.86254 | − | 2.80739i | 0.408055 | − | 0.235591i | ||||
\(143\) | 6.54983 | − | 19.1101i | 0.547725 | − | 1.59807i | ||||
\(144\) | 1.50000 | − | 2.59808i | 0.125000 | − | 0.216506i | ||||
\(145\) | 2.63746 | − | 1.52274i | 0.219029 | − | 0.126456i | ||||
\(146\) | 12.1819i | 1.00818i | ||||||||
\(147\) | −9.41238 | − | 7.64246i | −0.776320 | − | 0.630339i | ||||
\(148\) | 0.274917 | 0.0225981 | ||||||||
\(149\) | 0.137459 | + | 0.238085i | 0.0112610 | + | 0.0195047i | 0.871601 | − | 0.490216i | \(-0.163082\pi\) |
−0.860340 | + | 0.509721i | \(0.829749\pi\) | |||||||
\(150\) | −6.41238 | − | 3.70219i | −0.523568 | − | 0.302282i | ||||
\(151\) | 10.5000 | + | 6.06218i | 0.854478 | + | 0.493333i | 0.862159 | − | 0.506637i | \(-0.169112\pi\) |
−0.00768132 | + | 0.999970i | \(0.502445\pi\) | |||||||
\(152\) | 1.86254 | − | 1.07534i | 0.151072 | − | 0.0872215i | ||||
\(153\) | 12.8248 | 1.03682 | ||||||||
\(154\) | −1.00000 | − | 8.71780i | −0.0805823 | − | 0.702500i | ||||
\(155\) | − | 8.29917i | − | 0.666605i | ||||||
\(156\) | −5.27492 | − | 9.13642i | −0.422331 | − | 0.731499i | ||||
\(157\) | −4.86254 | + | 8.42217i | −0.388073 | + | 0.672162i | −0.992190 | − | 0.124733i | \(-0.960193\pi\) |
0.604117 | + | 0.796895i | \(0.293526\pi\) | |||||||
\(158\) | −5.63746 | − | 3.25479i | −0.448492 | − | 0.258937i | ||||
\(159\) | 7.18729 | + | 12.4488i | 0.569989 | + | 0.987251i | ||||
\(160\) | − | 3.04547i | − | 0.240766i | ||||||
\(161\) | −17.6873 | + | 8.42217i | −1.39395 | + | 0.663760i | ||||
\(162\) | −9.00000 | −0.707107 | ||||||||
\(163\) | −0.725083 | − | 1.25588i | −0.0567929 | − | 0.0983681i | 0.836231 | − | 0.548377i | \(-0.184754\pi\) |
−0.893024 | + | 0.450009i | \(0.851421\pi\) | |||||||
\(164\) | −4.27492 | + | 7.40437i | −0.333815 | + | 0.578184i | ||||
\(165\) | −16.5498 | − | 5.67232i | −1.28840 | − | 0.441590i | ||||
\(166\) | 1.36254 | + | 2.35999i | 0.105754 | + | 0.183171i | ||||
\(167\) | 22.5498 | 1.74496 | 0.872479 | − | 0.488651i | \(-0.162511\pi\) | ||||
0.872479 | + | 0.488651i | \(0.162511\pi\) | |||||||
\(168\) | −3.77492 | − | 2.59808i | −0.291241 | − | 0.200446i | ||||
\(169\) | −24.0997 | −1.85382 | ||||||||
\(170\) | 11.2749 | − | 6.50958i | 0.864747 | − | 0.499262i | ||||
\(171\) | −5.58762 | − | 3.22602i | −0.427296 | − | 0.246700i | ||||
\(172\) | −4.86254 | − | 2.80739i | −0.370765 | − | 0.214061i | ||||
\(173\) | 7.00000 | + | 12.1244i | 0.532200 | + | 0.921798i | 0.999293 | + | 0.0375896i | \(0.0119679\pi\) |
−0.467093 | + | 0.884208i | \(0.654699\pi\) | |||||||
\(174\) | − | 1.73205i | − | 0.131306i | ||||||
\(175\) | −6.41238 | + | 9.31697i | −0.484730 | + | 0.704296i | ||||
\(176\) | −0.637459 | − | 3.25479i | −0.0480503 | − | 0.245339i | ||||
\(177\) | −1.50000 | − | 2.59808i | −0.112747 | − | 0.195283i | ||||
\(178\) | −5.27492 | − | 3.04547i | −0.395372 | − | 0.228268i | ||||
\(179\) | 16.1375 | + | 9.31697i | 1.20617 | + | 0.696383i | 0.961920 | − | 0.273330i | \(-0.0881250\pi\) |
0.244250 | + | 0.969712i | \(0.421458\pi\) | |||||||
\(180\) | −7.91238 | + | 4.56821i | −0.589754 | + | 0.340494i | ||||
\(181\) | 8.54983 | 0.635504 | 0.317752 | − | 0.948174i | \(-0.397072\pi\) | ||||
0.317752 | + | 0.948174i | \(0.397072\pi\) | |||||||
\(182\) | −14.5498 | + | 6.92820i | −1.07851 | + | 0.513553i | ||||
\(183\) | 12.0000 | 0.887066 | ||||||||
\(184\) | −6.41238 | + | 3.70219i | −0.472727 | + | 0.272929i | ||||
\(185\) | −0.725083 | − | 0.418627i | −0.0533091 | − | 0.0307781i | ||||
\(186\) | −4.08762 | − | 2.35999i | −0.299719 | − | 0.173043i | ||||
\(187\) | 10.6873 | − | 9.31697i | 0.781532 | − | 0.681324i | ||||
\(188\) | − | 10.8685i | − | 0.792665i | ||||||
\(189\) | −1.08762 | + | 13.7046i | −0.0791130 | + | 0.996866i | ||||
\(190\) | −6.54983 | −0.475175 | ||||||||
\(191\) | 12.8248 | − | 7.40437i | 0.927966 | − | 0.535762i | 0.0417986 | − | 0.999126i | \(-0.486691\pi\) |
0.886168 | + | 0.463364i | \(0.153358\pi\) | |||||||
\(192\) | −1.50000 | − | 0.866025i | −0.108253 | − | 0.0625000i | ||||
\(193\) | 15.3625 | + | 8.86957i | 1.10582 | + | 0.638445i | 0.937744 | − | 0.347329i | \(-0.112911\pi\) |
0.168076 | + | 0.985774i | \(0.446244\pi\) | |||||||
\(194\) | 0.774917 | + | 1.34220i | 0.0556358 | + | 0.0963641i | ||||
\(195\) | 32.1293i | 2.30082i | ||||||||
\(196\) | −4.41238 | + | 5.43424i | −0.315170 | + | 0.388160i | ||||
\(197\) | −20.2749 | −1.44453 | −0.722264 | − | 0.691617i | \(-0.756898\pi\) | ||||
−0.722264 | + | 0.691617i | \(0.756898\pi\) | |||||||
\(198\) | −7.50000 | + | 6.53835i | −0.533002 | + | 0.464660i | ||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | −2.13746 | + | 3.70219i | −0.151141 | + | 0.261784i | ||||
\(201\) | 9.82475 | − | 5.67232i | 0.692985 | − | 0.400095i | ||||
\(202\) | −12.8248 | −0.902346 | ||||||||
\(203\) | −2.63746 | − | 0.209313i | −0.185113 | − | 0.0146909i | ||||
\(204\) | − | 7.40437i | − | 0.518410i | ||||||
\(205\) | 22.5498 | − | 13.0192i | 1.57495 | − | 0.909297i | ||||
\(206\) | 8.54983 | − | 14.8087i | 0.595695 | − | 1.03177i | ||||
\(207\) | 19.2371 | + | 11.1066i | 1.33707 | + | 0.771959i | ||||
\(208\) | −5.27492 | + | 3.04547i | −0.365750 | + | 0.211166i | ||||
\(209\) | −7.00000 | + | 1.37097i | −0.484200 | + | 0.0948318i | ||||
\(210\) | 6.00000 | + | 12.6005i | 0.414039 | + | 0.869519i | ||||
\(211\) | − | 11.2296i | − | 0.773075i | −0.922274 | − | 0.386537i | \(-0.873671\pi\) | ||
0.922274 | − | 0.386537i | \(-0.126329\pi\) | |||||||
\(212\) | 7.18729 | − | 4.14959i | 0.493625 | − | 0.284995i | ||||
\(213\) | −4.86254 | + | 8.42217i | −0.333176 | + | 0.577077i | ||||
\(214\) | 3.36254 | − | 5.82409i | 0.229859 | − | 0.398127i | ||||
\(215\) | 8.54983 | + | 14.8087i | 0.583094 | + | 1.00995i | ||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | −4.08762 | + | 5.93918i | −0.277486 | + | 0.403178i | ||||
\(218\) | − | 13.0192i | − | 0.881768i | ||||||
\(219\) | −10.5498 | − | 18.2728i | −0.712892 | − | 1.23476i | ||||
\(220\) | −3.27492 | + | 9.55505i | −0.220795 | + | 0.644201i | ||||
\(221\) | −22.5498 | − | 13.0192i | −1.51687 | − | 0.875763i | ||||
\(222\) | −0.412376 | + | 0.238085i | −0.0276769 | + | 0.0159792i | ||||
\(223\) | −19.8248 | −1.32756 | −0.663782 | − | 0.747926i | \(-0.731050\pi\) | ||||
−0.663782 | + | 0.747926i | \(0.731050\pi\) | |||||||
\(224\) | −1.50000 | + | 2.17945i | −0.100223 | + | 0.145621i | ||||
\(225\) | 12.8248 | 0.854983 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.18729 | − | 12.4488i | 0.477037 | − | 0.826253i | −0.522616 | − | 0.852568i | \(-0.675044\pi\) |
0.999654 | + | 0.0263150i | \(0.00837729\pi\) | |||||||
\(228\) | −1.86254 | + | 3.22602i | −0.123350 | + | 0.213648i | ||||
\(229\) | −4.27492 | − | 7.40437i | −0.282494 | − | 0.489295i | 0.689504 | − | 0.724282i | \(-0.257829\pi\) |
−0.971998 | + | 0.234987i | \(0.924495\pi\) | |||||||
\(230\) | 22.5498 | 1.48689 | ||||||||
\(231\) | 9.04983 | + | 12.2107i | 0.595435 | + | 0.803403i | ||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −2.41238 | − | 4.17836i | −0.158040 | − | 0.273733i | 0.776122 | − | 0.630583i | \(-0.217184\pi\) |
−0.934162 | + | 0.356850i | \(0.883851\pi\) | |||||||
\(234\) | 15.8248 | + | 9.13642i | 1.03450 | + | 0.597267i | ||||
\(235\) | −16.5498 | + | 28.6652i | −1.07959 | + | 1.86991i | ||||
\(236\) | −1.50000 | + | 0.866025i | −0.0976417 | + | 0.0563735i | ||||
\(237\) | 11.2749 | 0.732385 | ||||||||
\(238\) | −11.2749 | − | 0.894797i | −0.730844 | − | 0.0580011i | ||||
\(239\) | 2.54983 | 0.164935 | 0.0824675 | − | 0.996594i | \(-0.473720\pi\) | ||||
0.0824675 | + | 0.996594i | \(0.473720\pi\) | |||||||
\(240\) | 2.63746 | + | 4.56821i | 0.170247 | + | 0.294877i | ||||
\(241\) | −7.91238 | − | 4.56821i | −0.509681 | − | 0.294264i | 0.223022 | − | 0.974814i | \(-0.428408\pi\) |
−0.732702 | + | 0.680549i | \(0.761741\pi\) | |||||||
\(242\) | −1.50000 | + | 10.8972i | −0.0964237 | + | 0.700502i | ||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | − | 6.92820i | − | 0.443533i | ||||||
\(245\) | 19.9124 | − | 7.61369i | 1.27216 | − | 0.486421i | ||||
\(246\) | − | 14.8087i | − | 0.944171i | ||||||
\(247\) | 6.54983 | + | 11.3446i | 0.416756 | + | 0.721843i | ||||
\(248\) | −1.36254 | + | 2.35999i | −0.0865215 | + | 0.149860i | ||||
\(249\) | −4.08762 | − | 2.35999i | −0.259043 | − | 0.149558i | ||||
\(250\) | −1.91238 | + | 1.10411i | −0.120949 | + | 0.0698301i | ||||
\(251\) | − | 7.82300i | − | 0.493783i | −0.969043 | − | 0.246892i | \(-0.920591\pi\) | ||
0.969043 | − | 0.246892i | \(-0.0794092\pi\) | |||||||
\(252\) | 7.91238 | + | 0.627940i | 0.498433 | + | 0.0395565i | ||||
\(253\) | 24.0997 | − | 4.71998i | 1.51513 | − | 0.296743i | ||||
\(254\) | −12.0498 | + | 6.95698i | −0.756074 | + | 0.436519i | ||||
\(255\) | −11.2749 | + | 19.5287i | −0.706063 | + | 1.22294i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.72508 | − | 3.88273i | 0.419499 | − | 0.242198i | −0.275364 | − | 0.961340i | \(-0.588798\pi\) |
0.694863 | + | 0.719142i | \(0.255465\pi\) | |||||||
\(258\) | 9.72508 | 0.605457 | ||||||||
\(259\) | 0.312707 | + | 0.656712i | 0.0194307 | + | 0.0408061i | ||||
\(260\) | 18.5498 | 1.15041 | ||||||||
\(261\) | 1.50000 | + | 2.59808i | 0.0928477 | + | 0.160817i | ||||
\(262\) | −1.36254 | + | 2.35999i | −0.0841781 | + | 0.145801i | ||||
\(263\) | 0.549834 | − | 0.952341i | 0.0339042 | − | 0.0587239i | −0.848575 | − | 0.529074i | \(-0.822539\pi\) |
0.882480 | + | 0.470351i | \(0.155873\pi\) | |||||||
\(264\) | 3.77492 | + | 4.33013i | 0.232330 | + | 0.266501i | ||||
\(265\) | −25.2749 | −1.55263 | ||||||||
\(266\) | 4.68729 | + | 3.22602i | 0.287396 | + | 0.197800i | ||||
\(267\) | 10.5498 | 0.645639 | ||||||||
\(268\) | −3.27492 | − | 5.67232i | −0.200047 | − | 0.346492i | ||||
\(269\) | 13.9124 | + | 8.03231i | 0.848253 | + | 0.489739i | 0.860061 | − | 0.510191i | \(-0.170425\pi\) |
−0.0118083 | + | 0.999930i | \(0.503759\pi\) | |||||||
\(270\) | 7.91238 | − | 13.7046i | 0.481532 | − | 0.834038i | ||||
\(271\) | −26.7371 | + | 15.4367i | −1.62416 | + | 0.937712i | −0.638376 | + | 0.769725i | \(0.720393\pi\) |
−0.985789 | + | 0.167987i | \(0.946273\pi\) | |||||||
\(272\) | −4.27492 | −0.259205 | ||||||||
\(273\) | 15.8248 | − | 22.9928i | 0.957758 | − | 1.39159i | ||||
\(274\) | 13.0192i | 0.786516i | ||||||||
\(275\) | 10.6873 | − | 9.31697i | 0.644468 | − | 0.561834i | ||||
\(276\) | 6.41238 | − | 11.1066i | 0.385980 | − | 0.668536i | ||||
\(277\) | 22.5498 | + | 13.0192i | 1.35489 | + | 0.782245i | 0.988930 | − | 0.148386i | \(-0.0474078\pi\) |
0.365959 | + | 0.930631i | \(0.380741\pi\) | |||||||
\(278\) | −4.13746 | + | 2.38876i | −0.248148 | + | 0.143268i | ||||
\(279\) | 8.17525 | 0.489439 | ||||||||
\(280\) | 7.27492 | − | 3.46410i | 0.434759 | − | 0.207020i | ||||
\(281\) | 3.72508 | 0.222220 | 0.111110 | − | 0.993808i | \(-0.464559\pi\) | ||||
0.111110 | + | 0.993808i | \(0.464559\pi\) | |||||||
\(282\) | 9.41238 | + | 16.3027i | 0.560499 | + | 0.970812i | ||||
\(283\) | −2.27492 | − | 1.31342i | −0.135230 | − | 0.0780750i | 0.430859 | − | 0.902419i | \(-0.358211\pi\) |
−0.566089 | + | 0.824344i | \(0.691544\pi\) | |||||||
\(284\) | 4.86254 | + | 2.80739i | 0.288539 | + | 0.166588i | ||||
\(285\) | 9.82475 | − | 5.67232i | 0.581968 | − | 0.335999i | ||||
\(286\) | 19.8248 | − | 3.88273i | 1.17226 | − | 0.229591i | ||||
\(287\) | −22.5498 | − | 1.78959i | −1.33107 | − | 0.105636i | ||||
\(288\) | 3.00000 | 0.176777 | ||||||||
\(289\) | −0.637459 | − | 1.10411i | −0.0374976 | − | 0.0649477i | ||||
\(290\) | 2.63746 | + | 1.52274i | 0.154877 | + | 0.0894182i | ||||
\(291\) | −2.32475 | − | 1.34220i | −0.136279 | − | 0.0786809i | ||||
\(292\) | −10.5498 | + | 6.09095i | −0.617382 | + | 0.356446i | ||||
\(293\) | −24.0997 | −1.40792 | −0.703959 | − | 0.710241i | \(-0.748586\pi\) | ||||
−0.703959 | + | 0.710241i | \(0.748586\pi\) | |||||||
\(294\) | 1.91238 | − | 11.9726i | 0.111532 | − | 0.698255i | ||||
\(295\) | 5.27492 | 0.307118 | ||||||||
\(296\) | 0.137459 | + | 0.238085i | 0.00798962 | + | 0.0138384i | ||||
\(297\) | 5.58762 | − | 16.3027i | 0.324227 | − | 0.945979i | ||||
\(298\) | −0.137459 | + | 0.238085i | −0.00796276 | + | 0.0137919i | ||||
\(299\) | −22.5498 | − | 39.0575i | −1.30409 | − | 2.25875i | ||||
\(300\) | − | 7.40437i | − | 0.427492i | ||||||
\(301\) | 1.17525 | − | 14.8087i | 0.0677402 | − | 0.853562i | ||||
\(302\) | 12.1244i | 0.697678i | ||||||||
\(303\) | 19.2371 | − | 11.1066i | 1.10514 | − | 0.638055i | ||||
\(304\) | 1.86254 | + | 1.07534i | 0.106824 | + | 0.0616749i | ||||
\(305\) | −10.5498 | + | 18.2728i | −0.604082 | + | 1.04630i | ||||
\(306\) | 6.41238 | + | 11.1066i | 0.366571 | + | 0.634920i | ||||
\(307\) | − | 15.6460i | − | 0.892964i | −0.894793 | − | 0.446482i | \(-0.852677\pi\) | ||
0.894793 | − | 0.446482i | \(-0.147323\pi\) | |||||||
\(308\) | 7.04983 | − | 5.22492i | 0.401702 | − | 0.297718i | ||||
\(309\) | 29.6175i | 1.68488i | ||||||||
\(310\) | 7.18729 | − | 4.14959i | 0.408211 | − | 0.235681i | ||||
\(311\) | −19.1375 | − | 11.0490i | −1.08519 | − | 0.626532i | −0.152895 | − | 0.988242i | \(-0.548860\pi\) |
−0.932291 | + | 0.361710i | \(0.882193\pi\) | |||||||
\(312\) | 5.27492 | − | 9.13642i | 0.298633 | − | 0.517248i | ||||
\(313\) | −3.50000 | − | 6.06218i | −0.197832 | − | 0.342655i | 0.749993 | − | 0.661445i | \(-0.230057\pi\) |
−0.947825 | + | 0.318791i | \(0.896723\pi\) | |||||||
\(314\) | −9.72508 | −0.548818 | ||||||||
\(315\) | −19.9124 | − | 13.7046i | −1.12194 | − | 0.772169i | ||||
\(316\) | − | 6.50958i | − | 0.366192i | ||||||
\(317\) | 7.18729 | − | 4.14959i | 0.403679 | − | 0.233064i | −0.284391 | − | 0.958708i | \(-0.591792\pi\) |
0.688070 | + | 0.725644i | \(0.258458\pi\) | |||||||
\(318\) | −7.18729 | + | 12.4488i | −0.403043 | + | 0.698092i | ||||
\(319\) | 3.13746 | + | 1.07534i | 0.175664 | + | 0.0602074i | ||||
\(320\) | 2.63746 | − | 1.52274i | 0.147438 | − | 0.0851236i | ||||
\(321\) | 11.6482i | 0.650138i | ||||||||
\(322\) | −16.1375 | − | 11.1066i | −0.899305 | − | 0.618944i | ||||
\(323\) | 9.19397i | 0.511566i | ||||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | −22.5498 | − | 13.0192i | −1.25084 | − | 0.722173i | ||||
\(326\) | 0.725083 | − | 1.25588i | 0.0401586 | − | 0.0695568i | ||||
\(327\) | 11.2749 | + | 19.5287i | 0.623504 | + | 1.07994i | ||||
\(328\) | −8.54983 | −0.472086 | ||||||||
\(329\) | 25.9622 | − | 12.3624i | 1.43134 | − | 0.681563i | ||||
\(330\) | −3.36254 | − | 17.1687i | −0.185102 | − | 0.945108i | ||||
\(331\) | −12.5498 | − | 21.7370i | −0.689801 | − | 1.19477i | −0.971902 | − | 0.235386i | \(-0.924365\pi\) |
0.282101 | − | 0.959385i | \(-0.408969\pi\) | |||||||
\(332\) | −1.36254 | + | 2.35999i | −0.0747792 | + | 0.129521i | ||||
\(333\) | 0.412376 | − | 0.714256i | 0.0225981 | − | 0.0391410i | ||||
\(334\) | 11.2749 | + | 19.5287i | 0.616936 | + | 1.06856i | ||||
\(335\) | 19.9474i | 1.08984i | ||||||||
\(336\) | 0.362541 | − | 4.56821i | 0.0197783 | − | 0.249216i | ||||
\(337\) | 21.3183i | 1.16128i | 0.814159 | + | 0.580642i | \(0.197198\pi\) | ||||
−0.814159 | + | 0.580642i | \(0.802802\pi\) | |||||||
\(338\) | −12.0498 | − | 20.8709i | −0.655425 | − | 1.13523i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.2749 | + | 6.50958i | 0.611468 | + | 0.353031i | ||||
\(341\) | 6.81271 | − | 5.93918i | 0.368929 | − | 0.321625i | ||||
\(342\) | − | 6.45203i | − | 0.348886i | ||||||
\(343\) | −18.0000 | − | 4.35890i | −0.971909 | − | 0.235358i | ||||
\(344\) | − | 5.61478i | − | 0.302729i | ||||||
\(345\) | −33.8248 | + | 19.5287i | −1.82106 | + | 1.05139i | ||||
\(346\) | −7.00000 | + | 12.1244i | −0.376322 | + | 0.651809i | ||||
\(347\) | 2.00000 | − | 3.46410i | 0.107366 | − | 0.185963i | −0.807337 | − | 0.590091i | \(-0.799092\pi\) |
0.914702 | + | 0.404128i | \(0.132425\pi\) | |||||||
\(348\) | 1.50000 | − | 0.866025i | 0.0804084 | − | 0.0464238i | ||||
\(349\) | − | 35.7084i | − | 1.91143i | −0.294295 | − | 0.955715i | \(-0.595085\pi\) | ||
0.294295 | − | 0.955715i | \(-0.404915\pi\) | |||||||
\(350\) | −11.2749 | − | 0.894797i | −0.602670 | − | 0.0478289i | ||||
\(351\) | −31.6495 | −1.68933 | ||||||||
\(352\) | 2.50000 | − | 2.17945i | 0.133250 | − | 0.116165i | ||||
\(353\) | −13.6495 | − | 7.88054i | −0.726490 | − | 0.419439i | 0.0906469 | − | 0.995883i | \(-0.471107\pi\) |
−0.817137 | + | 0.576444i | \(0.804440\pi\) | |||||||
\(354\) | 1.50000 | − | 2.59808i | 0.0797241 | − | 0.138086i | ||||
\(355\) | −8.54983 | − | 14.8087i | −0.453778 | − | 0.785967i | ||||
\(356\) | − | 6.09095i | − | 0.322820i | ||||||
\(357\) | 17.6873 | − | 8.42217i | 0.936111 | − | 0.445748i | ||||
\(358\) | 18.6339i | 0.984834i | ||||||||
\(359\) | 9.82475 | + | 17.0170i | 0.518531 | + | 0.898121i | 0.999768 | + | 0.0215311i | \(0.00685409\pi\) |
−0.481238 | + | 0.876590i | \(0.659813\pi\) | |||||||
\(360\) | −7.91238 | − | 4.56821i | −0.417019 | − | 0.240766i | ||||
\(361\) | −7.18729 | + | 12.4488i | −0.378279 | + | 0.655198i | ||||
\(362\) | 4.27492 | + | 7.40437i | 0.224685 | + | 0.389165i | ||||
\(363\) | −7.18729 | − | 17.6449i | −0.377235 | − | 0.926118i | ||||
\(364\) | −13.2749 | − | 9.13642i | −0.695795 | − | 0.478879i | ||||
\(365\) | 37.0997 | 1.94189 | ||||||||
\(366\) | 6.00000 | + | 10.3923i | 0.313625 | + | 0.543214i | ||||
\(367\) | −12.6375 | + | 21.8887i | −0.659670 | + | 1.14258i | 0.321031 | + | 0.947069i | \(0.395971\pi\) |
−0.980701 | + | 0.195513i | \(0.937363\pi\) | |||||||
\(368\) | −6.41238 | − | 3.70219i | −0.334268 | − | 0.192990i | ||||
\(369\) | 12.8248 | + | 22.2131i | 0.667630 | + | 1.15637i | ||||
\(370\) | − | 0.837253i | − | 0.0435267i | ||||||
\(371\) | 18.0876 | + | 12.4488i | 0.939063 | + | 0.646307i | ||||
\(372\) | − | 4.71998i | − | 0.244720i | ||||||
\(373\) | 22.5498 | − | 13.0192i | 1.16759 | − | 0.674106i | 0.214476 | − | 0.976729i | \(-0.431196\pi\) |
0.953110 | + | 0.302623i | \(0.0978623\pi\) | |||||||
\(374\) | 13.4124 | + | 4.59698i | 0.693537 | + | 0.237704i | ||||
\(375\) | 1.91238 | − | 3.31233i | 0.0987547 | − | 0.171048i | ||||
\(376\) | 9.41238 | − | 5.43424i | 0.485406 | − | 0.280249i | ||||
\(377\) | − | 6.09095i | − | 0.313700i | ||||||
\(378\) | −12.4124 | + | 5.91041i | −0.638424 | + | 0.303999i | ||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | −3.27492 | − | 5.67232i | −0.168000 | − | 0.290984i | ||||
\(381\) | 12.0498 | − | 20.8709i | 0.617332 | − | 1.06925i | ||||
\(382\) | 12.8248 | + | 7.40437i | 0.656171 | + | 0.378841i | ||||
\(383\) | 15.5120 | − | 8.95588i | 0.792628 | − | 0.457624i | −0.0482586 | − | 0.998835i | \(-0.515367\pi\) |
0.840887 | + | 0.541211i | \(0.182034\pi\) | |||||||
\(384\) | − | 1.73205i | − | 0.0883883i | ||||||
\(385\) | −26.5498 | + | 3.04547i | −1.35310 | + | 0.155212i | ||||
\(386\) | 17.7391i | 0.902898i | ||||||||
\(387\) | −14.5876 | + | 8.42217i | −0.741531 | + | 0.428123i | ||||
\(388\) | −0.774917 | + | 1.34220i | −0.0393405 | + | 0.0681397i | ||||
\(389\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(390\) | −27.8248 | + | 16.0646i | −1.40896 | + | 0.813464i | ||||
\(391\) | − | 31.6531i | − | 1.60077i | ||||||
\(392\) | −6.91238 | − | 1.10411i | −0.349128 | − | 0.0557660i | ||||
\(393\) | − | 4.71998i | − | 0.238092i | ||||||
\(394\) | −10.1375 | − | 17.5586i | −0.510718 | − | 0.884589i | ||||
\(395\) | −9.91238 | + | 17.1687i | −0.498746 | + | 0.863853i | ||||
\(396\) | −9.41238 | − | 3.22602i | −0.472990 | − | 0.162113i | ||||
\(397\) | 9.13746 | + | 15.8265i | 0.458596 | + | 0.794311i | 0.998887 | − | 0.0471668i | \(-0.0150192\pi\) |
−0.540291 | + | 0.841478i | \(0.681686\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.82475 | − | 0.779710i | −0.491853 | − | 0.0390343i | ||||
\(400\) | −4.27492 | −0.213746 | ||||||||
\(401\) | −25.6495 | + | 14.8087i | −1.28088 | + | 0.739514i | −0.977008 | − | 0.213201i | \(-0.931611\pi\) |
−0.303867 | + | 0.952715i | \(0.598278\pi\) | |||||||
\(402\) | 9.82475 | + | 5.67232i | 0.490014 | + | 0.282910i | ||||
\(403\) | −14.3746 | − | 8.29917i | −0.716049 | − | 0.413411i | ||||
\(404\) | −6.41238 | − | 11.1066i | −0.319028 | − | 0.552572i | ||||
\(405\) | 27.4093i | 1.36198i | ||||||||
\(406\) | −1.13746 | − | 2.38876i | −0.0564511 | − | 0.118552i | ||||
\(407\) | −0.175248 | − | 0.894797i | −0.00868674 | − | 0.0443535i | ||||
\(408\) | 6.41238 | − | 3.70219i | 0.317460 | − | 0.183286i | ||||
\(409\) | 31.1873 | + | 18.0060i | 1.54211 | + | 0.890339i | 0.998705 | + | 0.0508697i | \(0.0161993\pi\) |
0.543407 | + | 0.839469i | \(0.317134\pi\) | |||||||
\(410\) | 22.5498 | + | 13.0192i | 1.11366 | + | 0.642970i | ||||
\(411\) | −11.2749 | − | 19.5287i | −0.556151 | − | 0.963281i | ||||
\(412\) | 17.0997 | 0.842440 | ||||||||
\(413\) | −3.77492 | − | 2.59808i | −0.185752 | − | 0.127843i | ||||
\(414\) | 22.2131i | 1.09172i | ||||||||
\(415\) | 7.18729 | − | 4.14959i | 0.352810 | − | 0.203695i | ||||
\(416\) | −5.27492 | − | 3.04547i | −0.258624 | − | 0.149317i | ||||
\(417\) | 4.13746 | − | 7.16629i | 0.202612 | − | 0.350935i | ||||
\(418\) | −4.68729 | − | 5.37669i | −0.229263 | − | 0.262983i | ||||
\(419\) | 22.9353i | 1.12046i | 0.828336 | + | 0.560231i | \(0.189288\pi\) | ||||
−0.828336 | + | 0.560231i | \(0.810712\pi\) | |||||||
\(420\) | −7.91238 | + | 11.4964i | −0.386084 | + | 0.560968i | ||||
\(421\) | −15.3746 | −0.749311 | −0.374656 | − | 0.927164i | \(-0.622239\pi\) | ||||
−0.374656 | + | 0.927164i | \(0.622239\pi\) | |||||||
\(422\) | 9.72508 | − | 5.61478i | 0.473410 | − | 0.273323i | ||||
\(423\) | −28.2371 | − | 16.3027i | −1.37294 | − | 0.792665i | ||||
\(424\) | 7.18729 | + | 4.14959i | 0.349046 | + | 0.201522i | ||||
\(425\) | −9.13746 | − | 15.8265i | −0.443232 | − | 0.767700i | ||||
\(426\) | −9.72508 | −0.471182 | ||||||||
\(427\) | 16.5498 | − | 7.88054i | 0.800903 | − | 0.381366i | ||||
\(428\) | 6.72508 | 0.325069 | ||||||||
\(429\) | −26.3746 | + | 22.9928i | −1.27338 | + | 1.11010i | ||||
\(430\) | −8.54983 | + | 14.8087i | −0.412310 | + | 0.714141i | ||||
\(431\) | 6.00000 | − | 10.3923i | 0.289010 | − | 0.500580i | −0.684564 | − | 0.728953i | \(-0.740007\pi\) |
0.973574 | + | 0.228373i | \(0.0733406\pi\) | |||||||
\(432\) | −4.50000 | + | 2.59808i | −0.216506 | + | 0.125000i | ||||
\(433\) | 4.27492 | 0.205439 | 0.102720 | − | 0.994710i | \(-0.467246\pi\) | ||||
0.102720 | + | 0.994710i | \(0.467246\pi\) | |||||||
\(434\) | −7.18729 | − | 0.570396i | −0.345001 | − | 0.0273799i | ||||
\(435\) | −5.27492 | −0.252913 | ||||||||
\(436\) | 11.2749 | − | 6.50958i | 0.539971 | − | 0.311752i | ||||
\(437\) | −7.96221 | + | 13.7910i | −0.380884 | + | 0.659711i | ||||
\(438\) | 10.5498 | − | 18.2728i | 0.504091 | − | 0.873111i | ||||
\(439\) | −20.3248 | + | 11.7345i | −0.970047 | + | 0.560057i | −0.899251 | − | 0.437434i | \(-0.855888\pi\) |
−0.0707968 | + | 0.997491i | \(0.522554\pi\) | |||||||
\(440\) | −9.91238 | + | 1.94136i | −0.472554 | + | 0.0925509i | ||||
\(441\) | 7.50000 | + | 19.6150i | 0.357143 | + | 0.934050i | ||||
\(442\) | − | 26.0383i | − | 1.23852i | ||||||
\(443\) | −12.0498 | + | 6.95698i | −0.572505 | + | 0.330536i | −0.758149 | − | 0.652081i | \(-0.773896\pi\) |
0.185644 | + | 0.982617i | \(0.440563\pi\) | |||||||
\(444\) | −0.412376 | − | 0.238085i | −0.0195705 | − | 0.0112990i | ||||
\(445\) | −9.27492 | + | 16.0646i | −0.439673 | + | 0.761536i | ||||
\(446\) | −9.91238 | − | 17.1687i | −0.469365 | − | 0.812963i | ||||
\(447\) | − | 0.476171i | − | 0.0225221i | ||||||
\(448\) | −2.63746 | − | 0.209313i | −0.124608 | − | 0.00988913i | ||||
\(449\) | 13.0192i | 0.614412i | 0.951643 | + | 0.307206i | \(0.0993940\pi\) | ||||
−0.951643 | + | 0.307206i | \(0.900606\pi\) | |||||||
\(450\) | 6.41238 | + | 11.1066i | 0.302282 | + | 0.523568i | ||||
\(451\) | 26.8248 | + | 9.19397i | 1.26313 | + | 0.432927i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.5000 | − | 18.1865i | −0.493333 | − | 0.854478i | ||||
\(454\) | 14.3746 | 0.674633 | ||||||||
\(455\) | 21.0997 | + | 44.3112i | 0.989168 | + | 2.07734i | ||||
\(456\) | −3.72508 | −0.174443 | ||||||||
\(457\) | −32.8368 | + | 18.9583i | −1.53604 | + | 0.886833i | −0.536976 | + | 0.843598i | \(0.680433\pi\) |
−0.999065 | + | 0.0432357i | \(0.986233\pi\) | |||||||
\(458\) | 4.27492 | − | 7.40437i | 0.199754 | − | 0.345984i | ||||
\(459\) | −19.2371 | − | 11.1066i | −0.897912 | − | 0.518410i | ||||
\(460\) | 11.2749 | + | 19.5287i | 0.525696 | + | 0.910532i | ||||
\(461\) | 12.8248 | 0.597308 | 0.298654 | − | 0.954361i | \(-0.403462\pi\) | ||||
0.298654 | + | 0.954361i | \(0.403462\pi\) | |||||||
\(462\) | −6.04983 | + | 13.9427i | −0.281464 | + | 0.648674i | ||||
\(463\) | 20.0000 | 0.929479 | 0.464739 | − | 0.885448i | \(-0.346148\pi\) | ||||
0.464739 | + | 0.885448i | \(0.346148\pi\) | |||||||
\(464\) | −0.500000 | − | 0.866025i | −0.0232119 | − | 0.0402042i | ||||
\(465\) | −7.18729 | + | 12.4488i | −0.333303 | + | 0.577297i | ||||
\(466\) | 2.41238 | − | 4.17836i | 0.111751 | − | 0.193559i | ||||
\(467\) | −20.6873 | + | 11.9438i | −0.957294 | + | 0.552694i | −0.895339 | − | 0.445385i | \(-0.853067\pi\) |
−0.0619547 | + | 0.998079i | \(0.519733\pi\) | |||||||
\(468\) | 18.2728i | 0.844663i | ||||||||
\(469\) | 9.82475 | − | 14.2750i | 0.453665 | − | 0.659160i | ||||
\(470\) | −33.0997 | −1.52677 | ||||||||
\(471\) | 14.5876 | − | 8.42217i | 0.672162 | − | 0.388073i | ||||
\(472\) | −1.50000 | − | 0.866025i | −0.0690431 | − | 0.0398621i | ||||
\(473\) | −6.03779 | + | 17.6161i | −0.277618 | + | 0.809991i | ||||
\(474\) | 5.63746 | + | 9.76436i | 0.258937 | + | 0.448492i | ||||
\(475\) | 9.19397i | 0.421848i | ||||||||
\(476\) | −4.86254 | − | 10.2118i | −0.222874 | − | 0.468055i | ||||
\(477\) | − | 24.8975i | − | 1.13998i | ||||||
\(478\) | 1.27492 | + | 2.20822i | 0.0583134 | + | 0.101002i | ||||
\(479\) | 14.0000 | − | 24.2487i | 0.639676 | − | 1.10795i | −0.345827 | − | 0.938298i | \(-0.612402\pi\) |
0.985504 | − | 0.169654i | \(-0.0542649\pi\) | |||||||
\(480\) | −2.63746 | + | 4.56821i | −0.120383 | + | 0.208509i | ||||
\(481\) | −1.45017 | + | 0.837253i | −0.0661219 | + | 0.0381755i | ||||
\(482\) | − | 9.13642i | − | 0.416153i | ||||||
\(483\) | 33.8248 | + | 2.68439i | 1.53908 | + | 0.122144i | ||||
\(484\) | −10.1873 | + | 4.14959i | −0.463059 | + | 0.188618i | ||||
\(485\) | 4.08762 | − | 2.35999i | 0.185609 | − | 0.107162i | ||||
\(486\) | 13.5000 | + | 7.79423i | 0.612372 | + | 0.353553i | ||||
\(487\) | −9.18729 | + | 15.9129i | −0.416316 | + | 0.721080i | −0.995566 | − | 0.0940698i | \(-0.970012\pi\) |
0.579250 | + | 0.815150i | \(0.303346\pi\) | |||||||
\(488\) | 6.00000 | − | 3.46410i | 0.271607 | − | 0.156813i | ||||
\(489\) | 2.51176i | 0.113586i | ||||||||
\(490\) | 16.5498 | + | 13.4378i | 0.747645 | + | 0.607057i | ||||
\(491\) | 22.3746 | 1.00975 | 0.504875 | − | 0.863192i | \(-0.331538\pi\) | ||||
0.504875 | + | 0.863192i | \(0.331538\pi\) | |||||||
\(492\) | 12.8248 | − | 7.40437i | 0.578184 | − | 0.333815i | ||||
\(493\) | 2.13746 | − | 3.70219i | 0.0962663 | − | 0.166738i | ||||
\(494\) | −6.54983 | + | 11.3446i | −0.294691 | + | 0.510420i | ||||
\(495\) | 19.9124 | + | 22.8411i | 0.894995 | + | 1.02663i | ||||
\(496\) | −2.72508 | −0.122360 | ||||||||
\(497\) | −1.17525 | + | 14.8087i | −0.0527171 | + | 0.664263i | ||||
\(498\) | − | 4.71998i | − | 0.211507i | ||||||
\(499\) | −9.27492 | − | 16.0646i | −0.415202 | − | 0.719152i | 0.580247 | − | 0.814440i | \(-0.302956\pi\) |
−0.995450 | + | 0.0952888i | \(0.969623\pi\) | |||||||
\(500\) | −1.91238 | − | 1.10411i | −0.0855240 | − | 0.0493773i | ||||
\(501\) | −33.8248 | − | 19.5287i | −1.51118 | − | 0.872479i | ||||
\(502\) | 6.77492 | − | 3.91150i | 0.302379 | − | 0.174579i | ||||
\(503\) | −11.6495 | −0.519426 | −0.259713 | − | 0.965686i | \(-0.583628\pi\) | ||||
−0.259713 | + | 0.965686i | \(0.583628\pi\) | |||||||
\(504\) | 3.41238 | + | 7.16629i | 0.151999 | + | 0.319212i | ||||
\(505\) | 39.0575i | 1.73803i | ||||||||
\(506\) | 16.1375 | + | 18.5109i | 0.717398 | + | 0.822911i | ||||
\(507\) | 36.1495 | + | 20.8709i | 1.60546 | + | 0.926910i | ||||
\(508\) | −12.0498 | − | 6.95698i | −0.534625 | − | 0.308666i | ||||
\(509\) | −31.9124 | + | 18.4246i | −1.41449 | + | 0.816657i | −0.995807 | − | 0.0914752i | \(-0.970842\pi\) |
−0.418684 | + | 0.908132i | \(0.637508\pi\) | |||||||
\(510\) | −22.5498 | −0.998523 | ||||||||
\(511\) | −26.5498 | − | 18.2728i | −1.17450 | − | 0.808343i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.58762 | + | 9.67805i | 0.246700 | + | 0.427296i | ||||
\(514\) | 6.72508 | + | 3.88273i | 0.296631 | + | 0.171260i | ||||
\(515\) | −45.0997 | − | 26.0383i | −1.98733 | − | 1.14738i | ||||
\(516\) | 4.86254 | + | 8.42217i | 0.214061 | + | 0.370765i | ||||
\(517\) | −35.3746 | + | 6.92820i | −1.55577 | + | 0.304702i | ||||
\(518\) | −0.412376 | + | 0.599168i | −0.0181188 | + | 0.0263259i | ||||
\(519\) | − | 24.2487i | − | 1.06440i | ||||||
\(520\) | 9.27492 | + | 16.0646i | 0.406732 | + | 0.704481i | ||||
\(521\) | 15.0997 | + | 8.71780i | 0.661529 | + | 0.381934i | 0.792859 | − | 0.609405i | \(-0.208592\pi\) |
−0.131331 | + | 0.991339i | \(0.541925\pi\) | |||||||
\(522\) | −1.50000 | + | 2.59808i | −0.0656532 | + | 0.113715i | ||||
\(523\) | 6.09967 | − | 3.52165i | 0.266720 | − | 0.153991i | −0.360676 | − | 0.932691i | \(-0.617454\pi\) |
0.627396 | + | 0.778700i | \(0.284121\pi\) | |||||||
\(524\) | −2.72508 | −0.119046 | ||||||||
\(525\) | 17.6873 | − | 8.42217i | 0.771937 | − | 0.367574i | ||||
\(526\) | 1.09967 | 0.0479478 | ||||||||
\(527\) | −5.82475 | − | 10.0888i | −0.253730 | − | 0.439474i | ||||
\(528\) | −1.86254 | + | 5.43424i | −0.0810567 | + | 0.236495i | ||||
\(529\) | 15.9124 | − | 27.5610i | 0.691842 | − | 1.19831i | ||||
\(530\) | −12.6375 | − | 21.8887i | −0.548936 | − | 0.950785i | ||||
\(531\) | 5.19615i | 0.225494i | ||||||||
\(532\) | −0.450166 | + | 5.67232i | −0.0195172 | + | 0.245926i | ||||
\(533\) | − | 52.0766i | − | 2.25569i | ||||||
\(534\) | 5.27492 | + | 9.13642i | 0.228268 | + | 0.395372i | ||||
\(535\) | −17.7371 | − | 10.2405i | −0.766843 | − | 0.442737i | ||||
\(536\) | 3.27492 | − | 5.67232i | 0.141455 | − | 0.245007i | ||||
\(537\) | −16.1375 | − | 27.9509i | −0.696383 | − | 1.20617i | ||||
\(538\) | 16.0646i | 0.692595i | ||||||||
\(539\) | 20.5000 | + | 10.8972i | 0.882998 | + | 0.469378i | ||||
\(540\) | 15.8248 | 0.680989 | ||||||||
\(541\) | −22.5498 | + | 13.0192i | −0.969493 | + | 0.559737i | −0.899082 | − | 0.437781i | \(-0.855765\pi\) |
−0.0704114 | + | 0.997518i | \(0.522431\pi\) | |||||||
\(542\) | −26.7371 | − | 15.4367i | −1.14846 | − | 0.663063i | ||||
\(543\) | −12.8248 | − | 7.40437i | −0.550363 | − | 0.317752i | ||||
\(544\) | −2.13746 | − | 3.70219i | −0.0916428 | − | 0.158730i | ||||
\(545\) | −39.6495 | −1.69840 | ||||||||
\(546\) | 27.8248 | + | 2.20822i | 1.19079 | + | 0.0945032i | ||||
\(547\) | 22.2131i | 0.949764i | 0.880049 | + | 0.474882i | \(0.157509\pi\) | ||||
−0.880049 | + | 0.474882i | \(0.842491\pi\) | |||||||
\(548\) | −11.2749 | + | 6.50958i | −0.481641 | + | 0.278075i | ||||
\(549\) | −18.0000 | − | 10.3923i | −0.768221 | − | 0.443533i | ||||
\(550\) | 13.4124 | + | 4.59698i | 0.571906 | + | 0.196016i | ||||
\(551\) | −1.86254 | + | 1.07534i | −0.0793469 | + | 0.0458110i | ||||
\(552\) | 12.8248 | 0.545858 | ||||||||
\(553\) | 15.5498 | − | 7.40437i | 0.661246 | − | 0.314866i | ||||
\(554\) | 26.0383i | 1.10626i | ||||||||
\(555\) | 0.725083 | + | 1.25588i | 0.0307781 | + | 0.0533091i | ||||
\(556\) | −4.13746 | − | 2.38876i | −0.175467 | − | 0.101306i | ||||
\(557\) | 15.3248 | − | 26.5432i | 0.649331 | − | 1.12467i | −0.333952 | − | 0.942590i | \(-0.608383\pi\) |
0.983283 | − | 0.182084i | \(-0.0582842\pi\) | |||||||
\(558\) | 4.08762 | + | 7.07997i | 0.173043 | + | 0.299719i | ||||
\(559\) | 34.1993 | 1.44648 | ||||||||
\(560\) | 6.63746 | + | 4.56821i | 0.280484 | + | 0.193042i | ||||
\(561\) | −24.0997 | + | 4.71998i | −1.01749 | + | 0.199278i | ||||
\(562\) | 1.86254 | + | 3.22602i | 0.0785666 | + | 0.136081i | ||||
\(563\) | −15.3625 | + | 26.6087i | −0.647454 | + | 1.12142i | 0.336275 | + | 0.941764i | \(0.390833\pi\) |
−0.983729 | + | 0.179659i | \(0.942500\pi\) | |||||||
\(564\) | −9.41238 | + | 16.3027i | −0.396333 | + | 0.686468i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 2.62685i | − | 0.110415i | ||||||
\(567\) | 13.5000 | − | 19.6150i | 0.566947 | − | 0.823754i | ||||
\(568\) | 5.61478i | 0.235591i | ||||||||
\(569\) | 14.6873 | + | 25.4391i | 0.615723 | + | 1.06646i | 0.990257 | + | 0.139251i | \(0.0444694\pi\) |
−0.374534 | + | 0.927213i | \(0.622197\pi\) | |||||||
\(570\) | 9.82475 | + | 5.67232i | 0.411514 | + | 0.237587i | ||||
\(571\) | −7.96221 | − | 4.59698i | −0.333208 | − | 0.192378i | 0.324056 | − | 0.946038i | \(-0.394953\pi\) |
−0.657265 | + | 0.753660i | \(0.728287\pi\) | |||||||
\(572\) | 13.2749 | + | 15.2274i | 0.555052 | + | 0.636689i | ||||
\(573\) | −25.6495 | −1.07152 | ||||||||
\(574\) | −9.72508 | − | 20.4235i | −0.405917 | − | 0.852462i | ||||
\(575\) | − | 31.6531i | − | 1.32002i | ||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | −0.187293 | + | 0.324401i | −0.00779711 | + | 0.0135050i | −0.869898 | − | 0.493232i | \(-0.835815\pi\) |
0.862101 | + | 0.506737i | \(0.169149\pi\) | |||||||
\(578\) | 0.637459 | − | 1.10411i | 0.0265148 | − | 0.0459250i | ||||
\(579\) | −15.3625 | − | 26.6087i | −0.638445 | − | 1.10582i | ||||
\(580\) | 3.04547i | 0.126456i | ||||||||
\(581\) | −7.18729 | − | 0.570396i | −0.298179 | − | 0.0236640i | ||||
\(582\) | − | 2.68439i | − | 0.111272i | ||||||
\(583\) | −18.0876 | − | 20.7479i | −0.749113 | − | 0.859291i | ||||
\(584\) | −10.5498 | − | 6.09095i | −0.436555 | − | 0.252045i | ||||
\(585\) | 27.8248 | − | 48.1939i | 1.15041 | − | 1.99257i | ||||
\(586\) | −12.0498 | − | 20.8709i | −0.497774 | − | 0.862170i | ||||
\(587\) | − | 26.4569i | − | 1.09199i | −0.837787 | − | 0.545997i | \(-0.816151\pi\) | ||
0.837787 | − | 0.545997i | \(-0.183849\pi\) | |||||||
\(588\) | 11.3248 | − | 4.33013i | 0.467025 | − | 0.178571i | ||||
\(589\) | 5.86077i | 0.241489i | ||||||||
\(590\) | 2.63746 | + | 4.56821i | 0.108582 | + | 0.188070i | ||||
\(591\) | 30.4124 | + | 17.5586i | 1.25100 | + | 0.722264i | ||||
\(592\) | −0.137459 | + | 0.238085i | −0.00564951 | + | 0.00978525i | ||||
\(593\) | −6.41238 | − | 11.1066i | −0.263325 | − | 0.456092i | 0.703799 | − | 0.710400i | \(-0.251486\pi\) |
−0.967123 | + | 0.254308i | \(0.918152\pi\) | |||||||
\(594\) | 16.9124 | − | 3.31233i | 0.693923 | − | 0.135907i | ||||
\(595\) | −2.72508 | + | 34.3375i | −0.111718 | + | 1.40770i | ||||
\(596\) | −0.274917 | −0.0112610 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 22.5498 | − | 39.0575i | 0.922131 | − | 1.59718i | ||||
\(599\) | 24.0997 | + | 13.9140i | 0.984686 | + | 0.568509i | 0.903682 | − | 0.428205i | \(-0.140854\pi\) |
0.0810042 | + | 0.996714i | \(0.474187\pi\) | |||||||
\(600\) | 6.41238 | − | 3.70219i | 0.261784 | − | 0.151141i | ||||
\(601\) | − | 1.37097i | − | 0.0559229i | −0.999609 | − | 0.0279615i | \(-0.991098\pi\) | ||
0.999609 | − | 0.0279615i | \(-0.00890157\pi\) | |||||||
\(602\) | 13.4124 | − | 6.38658i | 0.546648 | − | 0.260298i | ||||
\(603\) | −19.6495 | −0.800190 | ||||||||
\(604\) | −10.5000 | + | 6.06218i | −0.427239 | + | 0.246667i | ||||
\(605\) | 33.1873 | + | 4.56821i | 1.34926 | + | 0.185724i | ||||
\(606\) | 19.2371 | + | 11.1066i | 0.781455 | + | 0.451173i | ||||
\(607\) | 18.3625 | − | 10.6016i | 0.745313 | − | 0.430306i | −0.0786852 | − | 0.996900i | \(-0.525072\pi\) |
0.823998 | + | 0.566593i | \(0.191739\pi\) | |||||||
\(608\) | 2.15068i | 0.0872215i | ||||||||
\(609\) | 3.77492 | + | 2.59808i | 0.152967 | + | 0.105279i | ||||
\(610\) | −21.0997 | −0.854301 | ||||||||
\(611\) | 33.0997 | + | 57.3303i | 1.33907 | + | 2.31934i | ||||
\(612\) | −6.41238 | + | 11.1066i | −0.259205 | + | 0.448956i | ||||
\(613\) | −8.17525 | − | 4.71998i | −0.330195 | − | 0.190638i | 0.325733 | − | 0.945462i | \(-0.394389\pi\) |
−0.655928 | + | 0.754824i | \(0.727722\pi\) | |||||||
\(614\) | 13.5498 | − | 7.82300i | 0.546827 | − | 0.315711i | ||||
\(615\) | −45.0997 | −1.81859 | ||||||||
\(616\) | 8.04983 | + | 3.49287i | 0.324337 | + | 0.140732i | ||||
\(617\) | − | 3.57919i | − | 0.144093i | −0.997401 | − | 0.0720464i | \(-0.977047\pi\) | ||
0.997401 | − | 0.0720464i | \(-0.0229530\pi\) | |||||||
\(618\) | −25.6495 | + | 14.8087i | −1.03177 | + | 0.595695i | ||||
\(619\) | 8.54983 | − | 14.8087i | 0.343647 | − | 0.595214i | −0.641460 | − | 0.767156i | \(-0.721671\pi\) |
0.985107 | + | 0.171943i | \(0.0550044\pi\) | |||||||
\(620\) | 7.18729 | + | 4.14959i | 0.288649 | + | 0.166651i | ||||
\(621\) | −19.2371 | − | 33.3197i | −0.771959 | − | 1.33707i | ||||
\(622\) | − | 22.0980i | − | 0.886050i | ||||||
\(623\) | 14.5498 | − | 6.92820i | 0.582927 | − | 0.277573i | ||||
\(624\) | 10.5498 | 0.422331 | ||||||||
\(625\) | 14.0498 | + | 24.3350i | 0.561993 | + | 0.973401i | ||||
\(626\) | 3.50000 | − | 6.06218i | 0.139888 | − | 0.242293i | ||||
\(627\) | 11.6873 | + | 4.00573i | 0.466746 | + | 0.159973i | ||||
\(628\) | −4.86254 | − | 8.42217i | −0.194037 | − | 0.336081i | ||||
\(629\) | −1.17525 | −0.0468602 | ||||||||
\(630\) | 1.91238 | − | 24.0969i | 0.0761909 | − | 0.960045i | ||||
\(631\) | 24.9244 | 0.992226 | 0.496113 | − | 0.868258i | \(-0.334760\pi\) | ||||
0.496113 | + | 0.868258i | \(0.334760\pi\) | |||||||
\(632\) | 5.63746 | − | 3.25479i | 0.224246 | − | 0.129469i | ||||
\(633\) | −9.72508 | + | 16.8443i | −0.386537 | + | 0.669502i | ||||
\(634\) | 7.18729 | + | 4.14959i | 0.285444 | + | 0.164801i | ||||
\(635\) | 21.1873 | + | 36.6975i | 0.840792 | + | 1.45629i | ||||
\(636\) | −14.3746 | −0.569989 | ||||||||
\(637\) | 6.72508 | − | 42.1029i | 0.266457 | − | 1.66818i | ||||
\(638\) | 0.637459 | + | 3.25479i | 0.0252372 | + | 0.128858i | ||||
\(639\) | 14.5876 | − | 8.42217i | 0.577077 | − | 0.333176i | ||||
\(640\) | 2.63746 | + | 1.52274i | 0.104255 | + | 0.0601915i | ||||
\(641\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | −10.0876 | + | 5.82409i | −0.398127 | + | 0.229859i | ||||
\(643\) | 11.6495 | 0.459412 | 0.229706 | − | 0.973260i | \(-0.426224\pi\) | ||||
0.229706 | + | 0.973260i | \(0.426224\pi\) | |||||||
\(644\) | 1.54983 | − | 19.5287i | 0.0610720 | − | 0.769540i | ||||
\(645\) | − | 29.6175i | − | 1.16619i | ||||||
\(646\) | −7.96221 | + | 4.59698i | −0.313269 | + | 0.180866i | ||||
\(647\) | −0.824752 | − | 0.476171i | −0.0324243 | − | 0.0187202i | 0.483700 | − | 0.875234i | \(-0.339293\pi\) |
−0.516125 | + | 0.856514i | \(0.672626\pi\) | |||||||
\(648\) | 4.50000 | − | 7.79423i | 0.176777 | − | 0.306186i | ||||
\(649\) | 3.77492 | + | 4.33013i | 0.148178 | + | 0.169972i | ||||
\(650\) | − | 26.0383i | − | 1.02131i | ||||||
\(651\) | 11.2749 | − | 5.36878i | 0.441899 | − | 0.210419i | ||||
\(652\) | 1.45017 | 0.0567929 | ||||||||
\(653\) | 15.3625 | − | 8.86957i | 0.601183 | − | 0.347093i | −0.168324 | − | 0.985732i | \(-0.553835\pi\) |
0.769507 | + | 0.638639i | \(0.220502\pi\) | |||||||
\(654\) | −11.2749 | + | 19.5287i | −0.440884 | + | 0.763634i | ||||
\(655\) | 7.18729 | + | 4.14959i | 0.280831 | + | 0.162138i | ||||
\(656\) | −4.27492 | − | 7.40437i | −0.166907 | − | 0.289092i | ||||
\(657\) | 36.5457i | 1.42578i | ||||||||
\(658\) | 23.6873 | + | 16.3027i | 0.923427 | + | 0.635546i | ||||
\(659\) | −20.0000 | −0.779089 | −0.389545 | − | 0.921008i | \(-0.627368\pi\) | ||||
−0.389545 | + | 0.921008i | \(0.627368\pi\) | |||||||
\(660\) | 13.1873 | − | 11.4964i | 0.513315 | − | 0.447497i | ||||
\(661\) | 9.13746 | − | 15.8265i | 0.355406 | − | 0.615581i | −0.631781 | − | 0.775147i | \(-0.717676\pi\) |
0.987187 | + | 0.159565i | \(0.0510093\pi\) | |||||||
\(662\) | 12.5498 | − | 21.7370i | 0.487763 | − | 0.844831i | ||||
\(663\) | 22.5498 | + | 39.0575i | 0.875763 | + | 1.51687i | ||||
\(664\) | −2.72508 | −0.105754 | ||||||||
\(665\) | 9.82475 | − | 14.2750i | 0.380988 | − | 0.553562i | ||||
\(666\) | 0.824752 | 0.0319585 | ||||||||
\(667\) | 6.41238 | − | 3.70219i | 0.248288 | − | 0.143349i | ||||
\(668\) | −11.2749 | + | 19.5287i | −0.436240 | + | 0.755589i | ||||
\(669\) | 29.7371 | + | 17.1687i | 1.14970 | + | 0.663782i | ||||
\(670\) | −17.2749 | + | 9.97368i | −0.667388 | + | 0.385317i | ||||
\(671\) | −22.5498 | + | 4.41644i | −0.870527 | + | 0.170495i | ||||
\(672\) | 4.13746 | − | 1.97014i | 0.159606 | − | 0.0759997i | ||||
\(673\) | − | 17.7391i | − | 0.683793i | −0.939738 | − | 0.341897i | \(-0.888931\pi\) | ||
0.939738 | − | 0.341897i | \(-0.111069\pi\) | |||||||
\(674\) | −18.4622 | + | 10.6592i | −0.711138 | + | 0.410576i | ||||
\(675\) | −19.2371 | − | 11.1066i | −0.740437 | − | 0.427492i | ||||
\(676\) | 12.0498 | − | 20.8709i | 0.463455 | − | 0.802728i | ||||
\(677\) | −13.5997 | − | 23.5553i | −0.522678 | − | 0.905304i | −0.999652 | − | 0.0263870i | \(-0.991600\pi\) |
0.476974 | − | 0.878917i | \(-0.341734\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.08762 | − | 0.324401i | −0.156869 | − | 0.0124494i | ||||
\(680\) | 13.0192i | 0.499262i | ||||||||
\(681\) | −21.5619 | + | 12.4488i | −0.826253 | + | 0.477037i | ||||
\(682\) | 8.54983 | + | 2.93039i | 0.327390 | + | 0.112210i | ||||
\(683\) | −18.6752 | − | 10.7822i | −0.714589 | − | 0.412568i | 0.0981692 | − | 0.995170i | \(-0.468701\pi\) |
−0.812758 | + | 0.582602i | \(0.802035\pi\) | |||||||
\(684\) | 5.58762 | − | 3.22602i | 0.213648 | − | 0.123350i | ||||
\(685\) | 39.6495 | 1.51493 | ||||||||
\(686\) | −5.22508 | − | 17.7679i | −0.199495 | − | 0.678382i | ||||
\(687\) | 14.8087i | 0.564989i | ||||||||
\(688\) | 4.86254 | − | 2.80739i | 0.185383 | − | 0.107031i | ||||
\(689\) | −25.2749 | + | 43.7774i | −0.962898 | + | 1.66779i | ||||
\(690\) | −33.8248 | − | 19.5287i | −1.28769 | − | 0.743446i | ||||
\(691\) | 14.0000 | + | 24.2487i | 0.532585 | + | 0.922464i | 0.999276 | + | 0.0380440i | \(0.0121127\pi\) |
−0.466691 | + | 0.884420i | \(0.654554\pi\) | |||||||
\(692\) | −14.0000 | −0.532200 | ||||||||
\(693\) | −3.00000 | − | 26.1534i | −0.113961 | − | 0.993485i | ||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | 7.27492 | + | 12.6005i | 0.275953 | + | 0.477965i | ||||
\(696\) | 1.50000 | + | 0.866025i | 0.0568574 | + | 0.0328266i | ||||
\(697\) | 18.2749 | − | 31.6531i | 0.692212 | − | 1.19895i | ||||
\(698\) | 30.9244 | − | 17.8542i | 1.17051 | − | 0.675792i | ||||
\(699\) | 8.35671i | 0.316080i | ||||||||
\(700\) | −4.86254 | − | 10.2118i | −0.183787 | − | 0.385968i | ||||
\(701\) | −40.0997 | −1.51454 | −0.757272 | − | 0.653100i | \(-0.773468\pi\) | ||||
−0.757272 | + | 0.653100i | \(0.773468\pi\) | |||||||
\(702\) | −15.8248 | − | 27.4093i | −0.597267 | − | 1.03450i | ||||
\(703\) | 0.512045 | + | 0.295629i | 0.0193121 | + | 0.0111499i | ||||
\(704\) | 3.13746 | + | 1.07534i | 0.118247 | + | 0.0405284i | ||||
\(705\) | 49.6495 | − | 28.6652i | 1.86991 | − | 1.07959i | ||||
\(706\) | − | 15.7611i | − | 0.593176i | ||||||
\(707\) | 19.2371 | − | 27.9509i | 0.723487 | − | 1.05120i | ||||
\(708\) | 3.00000 | 0.112747 | ||||||||
\(709\) | 13.8625 | + | 24.0106i | 0.520619 | + | 0.901738i | 0.999713 | + | 0.0239743i | \(0.00763200\pi\) |
−0.479094 | + | 0.877764i | \(0.659035\pi\) | |||||||
\(710\) | 8.54983 | − | 14.8087i | 0.320870 | − | 0.555762i | ||||
\(711\) | −16.9124 | − | 9.76436i | −0.634264 | − | 0.366192i | ||||
\(712\) | 5.27492 | − | 3.04547i | 0.197686 | − | 0.114134i | ||||
\(713\) | − | 20.1775i | − | 0.755654i | ||||||
\(714\) | 16.1375 | + | 11.1066i | 0.603929 | + | 0.415653i | ||||
\(715\) | −11.8248 | − | 60.3758i | −0.442221 | − | 2.25793i | ||||
\(716\) | −16.1375 | + | 9.31697i | −0.603085 | + | 0.348191i | ||||
\(717\) | −3.82475 | − | 2.20822i | −0.142838 | − | 0.0824675i | ||||
\(718\) | −9.82475 | + | 17.0170i | −0.366656 | + | 0.635068i | ||||
\(719\) | 24.4124 | − | 14.0945i | 0.910428 | − | 0.525636i | 0.0298592 | − | 0.999554i | \(-0.490494\pi\) |
0.880569 | + | 0.473918i | \(0.157161\pi\) | |||||||
\(720\) | − | 9.13642i | − | 0.340494i | ||||||
\(721\) | 19.4502 | + | 40.8471i | 0.724362 | + | 1.52122i | ||||
\(722\) | −14.3746 | −0.534967 | ||||||||
\(723\) | 7.91238 | + | 13.7046i | 0.294264 | + | 0.509681i | ||||
\(724\) | −4.27492 | + | 7.40437i | −0.158876 | + | 0.275181i | ||||
\(725\) | 2.13746 | − | 3.70219i | 0.0793832 | − | 0.137496i | ||||
\(726\) | 11.6873 | − | 15.0468i | 0.433756 | − | 0.558440i | ||||
\(727\) | 2.72508 | 0.101068 | 0.0505339 | − | 0.998722i | \(-0.483908\pi\) | ||||
0.0505339 | + | 0.998722i | \(0.483908\pi\) | |||||||
\(728\) | 1.27492 | − | 16.0646i | 0.0472516 | − | 0.595395i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 18.5498 | + | 32.1293i | 0.686560 | + | 1.18916i | ||||
\(731\) | 20.7870 | + | 12.0014i | 0.768834 | + | 0.443886i | ||||
\(732\) | −6.00000 | + | 10.3923i | −0.221766 | + | 0.384111i | ||||
\(733\) | −2.90033 | + | 1.67451i | −0.107126 | + | 0.0618493i | −0.552606 | − | 0.833443i | \(-0.686366\pi\) |
0.445480 | + | 0.895292i | \(0.353033\pi\) | |||||||
\(734\) | −25.2749 | −0.932914 | ||||||||
\(735\) | −36.4622 | − | 5.82409i | −1.34493 | − | 0.214825i | ||||
\(736\) | − | 7.40437i | − | 0.272929i | ||||||
\(737\) | −16.3746 | + | 14.2750i | −0.603166 | + | 0.525828i | ||||
\(738\) | −12.8248 | + | 22.2131i | −0.472086 | + | 0.817676i | ||||
\(739\) | 24.0997 | + | 13.9140i | 0.886521 | + | 0.511833i | 0.872803 | − | 0.488073i | \(-0.162300\pi\) |
0.0137178 | + | 0.999906i | \(0.495633\pi\) | |||||||
\(740\) | 0.725083 | − | 0.418627i | 0.0266546 | − | 0.0153890i | ||||
\(741\) | − | 22.6893i | − | 0.833512i | ||||||
\(742\) | −1.73713 | + | 21.8887i | −0.0637720 | + | 0.803560i | ||||
\(743\) | 47.6495 | 1.74809 | 0.874045 | − | 0.485844i | \(-0.161488\pi\) | ||||
0.874045 | + | 0.485844i | \(0.161488\pi\) | |||||||
\(744\) | 4.08762 | − | 2.35999i | 0.149860 | − | 0.0865215i | ||||
\(745\) | 0.725083 | + | 0.418627i | 0.0265650 | + | 0.0153373i | ||||
\(746\) | 22.5498 | + | 13.0192i | 0.825608 | + | 0.476665i | ||||
\(747\) | 4.08762 | + | 7.07997i | 0.149558 | + | 0.259043i | ||||
\(748\) | 2.72508 | + | 13.9140i | 0.0996389 | + | 0.508744i | ||||
\(749\) | 7.64950 | + | 16.0646i | 0.279507 | + | 0.586989i | ||||
\(750\) | 3.82475 | 0.139660 | ||||||||
\(751\) | −13.3625 | − | 23.1446i | −0.487606 | − | 0.844558i | 0.512292 | − | 0.858811i | \(-0.328796\pi\) |
−0.999898 | + | 0.0142526i | \(0.995463\pi\) | |||||||
\(752\) | 9.41238 | + | 5.43424i | 0.343234 | + | 0.198166i | ||||
\(753\) | −6.77492 | + | 11.7345i | −0.246892 | + | 0.427629i | ||||
\(754\) | 5.27492 | − | 3.04547i | 0.192101 | − | 0.110910i | ||||
\(755\) | 36.9244 | 1.34382 | ||||||||
\(756\) | −11.3248 | − | 7.79423i | −0.411877 | − | 0.283473i | ||||
\(757\) | −32.4743 | −1.18030 | −0.590148 | − | 0.807295i | \(-0.700931\pi\) | ||||
−0.590148 | + | 0.807295i | \(0.700931\pi\) | |||||||
\(758\) | 10.0000 | + | 17.3205i | 0.363216 | + | 0.629109i | ||||
\(759\) | −40.2371 | − | 13.7910i | −1.46052 | − | 0.500580i | ||||
\(760\) | 3.27492 | − | 5.67232i | 0.118794 | − | 0.205757i | ||||
\(761\) | 10.0997 | + | 17.4931i | 0.366113 | + | 0.634126i | 0.988954 | − | 0.148222i | \(-0.0473551\pi\) |
−0.622841 | + | 0.782348i | \(0.714022\pi\) | |||||||
\(762\) | 24.0997 | 0.873039 | ||||||||
\(763\) | 28.3746 | + | 19.5287i | 1.02723 | + | 0.706987i | ||||
\(764\) | 14.8087i | 0.535762i | ||||||||
\(765\) | 33.8248 | − | 19.5287i | 1.22294 | − | 0.706063i | ||||
\(766\) | 15.5120 | + | 8.95588i | 0.560473 | + | 0.323589i | ||||
\(767\) | 5.27492 | − | 9.13642i | 0.190466 | − | 0.329897i | ||||
\(768\) | 1.50000 | − | 0.866025i | 0.0541266 | − | 0.0312500i | ||||
\(769\) | 18.8066i | 0.678182i | 0.940754 | + | 0.339091i | \(0.110119\pi\) | ||||
−0.940754 | + | 0.339091i | \(0.889881\pi\) | |||||||
\(770\) | −15.9124 | − | 21.4701i | −0.573442 | − | 0.773728i | ||||
\(771\) | −13.4502 | −0.484396 | ||||||||
\(772\) | −15.3625 | + | 8.86957i | −0.552910 | + | 0.319223i | ||||
\(773\) | 12.0000 | + | 6.92820i | 0.431610 | + | 0.249190i | 0.700032 | − | 0.714111i | \(-0.253169\pi\) |
−0.268422 | + | 0.963301i | \(0.586502\pi\) | |||||||
\(774\) | −14.5876 | − | 8.42217i | −0.524341 | − | 0.302729i | ||||
\(775\) | −5.82475 | − | 10.0888i | −0.209231 | − | 0.362399i | ||||
\(776\) | −1.54983 | −0.0556358 | ||||||||
\(777\) | 0.0996689 | − | 1.25588i | 0.00357560 | − | 0.0450545i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.9244 | + | 9.19397i | −0.570552 | + | 0.329408i | ||||
\(780\) | −27.8248 | − | 16.0646i | −0.996286 | − | 0.575206i | ||||
\(781\) | 6.03779 | − | 17.6161i | 0.216049 | − | 0.630355i | ||||
\(782\) | 27.4124 | − | 15.8265i | 0.980265 | − | 0.565956i | ||||
\(783\) | − | 5.19615i | − | 0.185695i | ||||||
\(784\) | −2.50000 | − | 6.53835i | −0.0892857 | − | 0.233512i | ||||
\(785\) | 29.6175i | 1.05709i | ||||||||
\(786\) | 4.08762 | − | 2.35999i | 0.145801 | − | 0.0841781i | ||||
\(787\) | −13.7629 | − | 7.94600i | −0.490593 | − | 0.283244i | 0.234227 | − | 0.972182i | \(-0.424744\pi\) |
−0.724821 | + | 0.688938i | \(0.758077\pi\) | |||||||
\(788\) | 10.1375 | − | 17.5586i | 0.361132 | − | 0.625499i | ||||
\(789\) | −1.64950 | + | 0.952341i | −0.0587239 | + | 0.0339042i | ||||
\(790\) | −19.8248 | −0.705333 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.91238 | − | 9.76436i | −0.0679533 | − | 0.346962i | ||||
\(793\) | 21.0997 | + | 36.5457i | 0.749271 | + | 1.29778i | ||||
\(794\) | −9.13746 | + | 15.8265i | −0.324276 | + | 0.561663i | ||||
\(795\) | 37.9124 | + | 21.8887i | 1.34461 | + | 0.776313i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 11.6482i | − | 0.412600i | −0.978489 | − | 0.206300i | \(-0.933858\pi\) | ||
0.978489 | − | 0.206300i | \(-0.0661423\pi\) | |||||||
\(798\) | −4.23713 | − | 8.89834i | −0.149993 | − | 0.314998i | ||||
\(799\) | 46.4618i | 1.64370i | ||||||||
\(800\) | −2.13746 | − | 3.70219i | −0.0755706 | − | 0.130892i | ||||
\(801\) | −15.8248 | − | 9.13642i | −0.559140 | − | 0.322820i | ||||
\(802\) | −25.6495 | − | 14.8087i | −0.905715 | − | 0.522915i | ||||
\(803\) | 26.5498 | + | 30.4547i | 0.936923 | + | 1.07472i | ||||
\(804\) | 11.3446i | 0.400095i | ||||||||
\(805\) | −33.8248 | + | 49.1462i | −1.19217 | + | 1.73218i | ||||
\(806\) | − | 16.5983i | − | 0.584652i | ||||||
\(807\) | −13.9124 | − | 24.0969i | −0.489739 | − | 0.848253i | ||||
\(808\) | 6.41238 | − | 11.1066i | 0.225587 | − | 0.390727i | ||||
\(809\) | −6.82475 | + | 11.8208i | −0.239945 | + | 0.415598i | −0.960698 | − | 0.277594i | \(-0.910463\pi\) |
0.720753 | + | 0.693192i | \(0.243796\pi\) | |||||||
\(810\) | −23.7371 | + | 13.7046i | −0.834038 | + | 0.481532i | ||||
\(811\) | − | 17.3205i | − | 0.608205i | −0.952639 | − | 0.304103i | \(-0.901643\pi\) | ||
0.952639 | − | 0.304103i | \(-0.0983566\pi\) | |||||||
\(812\) | 1.50000 | − | 2.17945i | 0.0526397 | − | 0.0764837i | ||||
\(813\) | 53.4743 | 1.87542 | ||||||||
\(814\) | 0.687293 | − | 0.599168i | 0.0240896 | − | 0.0210008i | ||||
\(815\) | −3.82475 | − | 2.20822i | −0.133975 | − | 0.0773506i | ||||
\(816\) | 6.41238 | + | 3.70219i | 0.224478 | + | 0.129602i | ||||
\(817\) | −6.03779 | − | 10.4578i | −0.211236 | − | 0.365871i | ||||
\(818\) | 36.0120i | 1.25913i | ||||||||
\(819\) | −43.6495 | + | 20.7846i | −1.52524 | + | 0.726273i | ||||
\(820\) | 26.0383i | 0.909297i | ||||||||
\(821\) | −13.4622 | − | 23.3172i | −0.469834 | − | 0.813777i | 0.529571 | − | 0.848266i | \(-0.322353\pi\) |
−0.999405 | + | 0.0344888i | \(0.989020\pi\) | |||||||
\(822\) | 11.2749 | − | 19.5287i | 0.393258 | − | 0.681143i | ||||
\(823\) | −28.5498 | + | 49.4498i | −0.995185 | + | 1.72371i | −0.412706 | + | 0.910864i | \(0.635416\pi\) |
−0.582478 | + | 0.812846i | \(0.697917\pi\) | |||||||
\(824\) | 8.54983 | + | 14.8087i | 0.297848 | + | 0.515887i | ||||
\(825\) | −24.0997 | + | 4.71998i | −0.839043 | + | 0.164329i | ||||
\(826\) | 0.362541 | − | 4.56821i | 0.0126144 | − | 0.158948i | ||||
\(827\) | −23.4743 | −0.816280 | −0.408140 | − | 0.912919i | \(-0.633822\pi\) | ||||
−0.408140 | + | 0.912919i | \(0.633822\pi\) | |||||||
\(828\) | −19.2371 | + | 11.1066i | −0.668536 | + | 0.385980i | ||||
\(829\) | −10.6873 | + | 18.5109i | −0.371185 | + | 0.642911i | −0.989748 | − | 0.142824i | \(-0.954382\pi\) |
0.618563 | + | 0.785735i | \(0.287715\pi\) | |||||||
\(830\) | 7.18729 | + | 4.14959i | 0.249475 | + | 0.144034i | ||||
\(831\) | −22.5498 | − | 39.0575i | −0.782245 | − | 1.35489i | ||||
\(832\) | − | 6.09095i | − | 0.211166i | ||||||
\(833\) | 18.8625 | − | 23.2309i | 0.653548 | − | 0.804904i | ||||
\(834\) | 8.27492 | 0.286537 | ||||||||
\(835\) | 59.4743 | − | 34.3375i | 2.05819 | − | 1.18830i | ||||
\(836\) | 2.31271 | − | 6.74766i | 0.0799866 | − | 0.233373i | ||||
\(837\) | −12.2629 | − | 7.07997i | −0.423867 | − | 0.244720i | ||||
\(838\) | −19.8625 | + | 11.4676i | −0.686140 | + | 0.396143i | ||||
\(839\) | 39.7796i | 1.37335i | 0.726967 | + | 0.686673i | \(0.240929\pi\) | ||||
−0.726967 | + | 0.686673i | \(0.759071\pi\) | |||||||
\(840\) | −13.9124 | − | 1.10411i | −0.480023 | − | 0.0380954i | ||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −7.68729 | − | 13.3148i | −0.264922 | − | 0.458858i | ||||
\(843\) | −5.58762 | − | 3.22602i | −0.192448 | − | 0.111110i | ||||
\(844\) | 9.72508 | + | 5.61478i | 0.334751 | + | 0.193269i | ||||
\(845\) | −63.5619 | + | 36.6975i | −2.18660 | + | 1.26243i | ||||
\(846\) | − | 32.6054i | − | 1.12100i | ||||||
\(847\) | −21.5000 | − | 19.6150i | −0.738749 | − | 0.673981i | ||||
\(848\) | 8.29917i | 0.284995i | ||||||||
\(849\) | 2.27492 | + | 3.94027i | 0.0780750 | + | 0.135230i | ||||
\(850\) | 9.13746 | − | 15.8265i | 0.313412 | − | 0.542846i | ||||
\(851\) | −1.76287 | − | 1.01779i | −0.0604305 | − | 0.0348896i | ||||
\(852\) | −4.86254 | − | 8.42217i | −0.166588 | − | 0.288539i | ||||
\(853\) | − | 30.4547i | − | 1.04275i | −0.853327 | − | 0.521375i | \(-0.825419\pi\) | ||
0.853327 | − | 0.521375i | \(-0.174581\pi\) | |||||||
\(854\) | 15.0997 | + | 10.3923i | 0.516700 | + | 0.355617i | ||||
\(855\) | −19.6495 | −0.671999 | ||||||||
\(856\) | 3.36254 | + | 5.82409i | 0.114929 | + | 0.199063i | ||||
\(857\) | 4.86254 | − | 8.42217i | 0.166101 | − | 0.287696i | −0.770945 | − | 0.636902i | \(-0.780215\pi\) |
0.937046 | + | 0.349206i | \(0.113549\pi\) | |||||||
\(858\) | −33.0997 | − | 11.3446i | −1.13000 | − | 0.387300i | ||||
\(859\) | −14.0000 | − | 24.2487i | −0.477674 | − | 0.827355i | 0.521999 | − | 0.852946i | \(-0.325187\pi\) |
−0.999672 | + | 0.0255910i | \(0.991853\pi\) | |||||||
\(860\) | −17.0997 | −0.583094 | ||||||||
\(861\) | 32.2749 | + | 22.2131i | 1.09993 | + | 0.757021i | ||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | 27.1993 | − | 15.7035i | 0.925876 | − | 0.534555i | 0.0403712 | − | 0.999185i | \(-0.487146\pi\) |
0.885505 | + | 0.464630i | \(0.153813\pi\) | |||||||
\(864\) | −4.50000 | − | 2.59808i | −0.153093 | − | 0.0883883i | ||||
\(865\) | 36.9244 | + | 21.3183i | 1.25547 | + | 0.724845i | ||||
\(866\) | 2.13746 | + | 3.70219i | 0.0726338 | + | 0.125805i | ||||
\(867\) | 2.20822i | 0.0749951i | ||||||||
\(868\) | −3.09967 | − | 6.50958i | −0.105210 | − | 0.220949i | ||||
\(869\) | −21.1873 | + | 4.14959i | −0.718730 | + | 0.140765i | ||||
\(870\) | −2.63746 | − | 4.56821i | −0.0894182 | − | 0.154877i | ||||
\(871\) | 34.5498 | + | 19.9474i | 1.17068 | + | 0.675890i | ||||
\(872\) | 11.2749 | + | 6.50958i | 0.381817 | + | 0.220442i | ||||
\(873\) | 2.32475 | + | 4.02659i | 0.0786809 | + | 0.136279i | ||||
\(874\) | −15.9244 | −0.538652 | ||||||||
\(875\) | 0.462210 | − | 5.82409i | 0.0156256 | − | 0.196890i | ||||
\(876\) | 21.0997 | 0.712892 | ||||||||
\(877\) | −25.6495 | + | 14.8087i | −0.866122 | + | 0.500056i | −0.866058 | − | 0.499944i | \(-0.833354\pi\) |
−6.45221e−5 | 1.00000i | \(0.500021\pi\) | ||||||||
\(878\) | −20.3248 | − | 11.7345i | −0.685927 | − | 0.396020i | ||||
\(879\) | 36.1495 | + | 20.8709i | 1.21929 | + | 0.703959i | ||||
\(880\) | −6.63746 | − | 7.61369i | −0.223749 | − | 0.256657i | ||||
\(881\) | − | 49.5649i | − | 1.66988i | −0.550339 | − | 0.834941i | \(-0.685502\pi\) | ||
0.550339 | − | 0.834941i | \(-0.314498\pi\) | |||||||
\(882\) | −13.2371 | + | 16.3027i | −0.445717 | + | 0.548941i | ||||
\(883\) | 26.1993 | 0.881678 | 0.440839 | − | 0.897586i | \(-0.354681\pi\) | ||||
0.440839 | + | 0.897586i | \(0.354681\pi\) | |||||||
\(884\) | 22.5498 | − | 13.0192i | 0.758433 | − | 0.437882i | ||||
\(885\) | −7.91238 | − | 4.56821i | −0.265972 | − | 0.153559i | ||||
\(886\) | −12.0498 | − | 6.95698i | −0.404822 | − | 0.233724i | ||||
\(887\) | −11.2749 | − | 19.5287i | −0.378575 | − | 0.655711i | 0.612280 | − | 0.790641i | \(-0.290252\pi\) |
−0.990855 | + | 0.134930i | \(0.956919\pi\) | |||||||
\(888\) | − | 0.476171i | − | 0.0159792i | ||||||
\(889\) | 2.91238 | − | 36.6975i | 0.0976780 | − | 1.23079i | ||||
\(890\) | −18.5498 | −0.621792 | ||||||||
\(891\) | −22.5000 | + | 19.6150i | −0.753778 | + | 0.657129i | ||||
\(892\) | 9.91238 | − | 17.1687i | 0.331891 | − | 0.574852i | ||||
\(893\) | 11.6873 | − | 20.2430i | 0.391100 | − | 0.677406i | ||||
\(894\) | 0.412376 | − | 0.238085i | 0.0137919 | − | 0.00796276i | ||||
\(895\) | 56.7492 | 1.89692 | ||||||||
\(896\) | −1.13746 | − | 2.38876i | −0.0379998 | − | 0.0798030i | ||||
\(897\) | 78.1149i | 2.60818i | ||||||||
\(898\) | −11.2749 | + | 6.50958i | −0.376249 | + | 0.217227i | ||||
\(899\) | 1.36254 | − | 2.35999i | 0.0454433 | − | 0.0787101i | ||||
\(900\) | −6.41238 | + | 11.1066i | −0.213746 | + | 0.370219i | ||||
\(901\) | −30.7251 | + | 17.7391i | −1.02360 | + | 0.590976i | ||||
\(902\) | 5.45017 | + | 27.8279i | 0.181471 | + | 0.926568i | ||||
\(903\) | −14.5876 | + | 21.1953i | −0.485446 | + | 0.705336i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.5498 | − | 13.0192i | 0.749582 | − | 0.432771i | ||||
\(906\) | 10.5000 | − | 18.1865i | 0.348839 | − | 0.604207i | ||||
\(907\) | −13.2749 | + | 22.9928i | −0.440786 | + | 0.763464i | −0.997748 | − | 0.0670738i | \(-0.978634\pi\) |
0.556962 | + | 0.830538i | \(0.311967\pi\) | |||||||
\(908\) | 7.18729 | + | 12.4488i | 0.238519 | + | 0.413127i | ||||
\(909\) | −38.4743 | −1.27611 | ||||||||
\(910\) | −27.8248 | + | 40.4284i | −0.922382 | + | 1.34019i | ||||
\(911\) | − | 12.7732i | − | 0.423194i | −0.977357 | − | 0.211597i | \(-0.932134\pi\) | ||
0.977357 | − | 0.211597i | \(-0.0678664\pi\) | |||||||
\(912\) | −1.86254 | − | 3.22602i | −0.0616749 | − | 0.106824i | ||||
\(913\) | 8.54983 | + | 2.93039i | 0.282958 | + | 0.0969817i | ||||
\(914\) | −32.8368 | − | 18.9583i | −1.08614 | − | 0.627086i | ||||
\(915\) | 31.6495 | − | 18.2728i | 1.04630 | − | 0.604082i | ||||
\(916\) | 8.54983 | 0.282494 | ||||||||
\(917\) | −3.09967 | − | 6.50958i | −0.102360 | − | 0.214965i | ||||
\(918\) | − | 22.2131i | − | 0.733142i | ||||||
\(919\) | 38.6873 | − | 22.3361i | 1.27618 | − | 0.736801i | 0.300033 | − | 0.953929i | \(-0.403002\pi\) |
0.976143 | + | 0.217128i | \(0.0696690\pi\) | |||||||
\(920\) | −11.2749 | + | 19.5287i | −0.371723 | + | 0.643843i | ||||
\(921\) | −13.5498 | + | 23.4690i | −0.446482 | + | 0.773330i | ||||
\(922\) | 6.41238 | + | 11.1066i | 0.211180 | + | 0.365775i | ||||
\(923\) | −34.1993 | −1.12568 | ||||||||
\(924\) | −15.0997 | + | 1.73205i | −0.496743 | + | 0.0569803i | ||||
\(925\) | −1.17525 | −0.0386419 | ||||||||
\(926\) | 10.0000 | + | 17.3205i | 0.328620 | + | 0.569187i | ||||
\(927\) | 25.6495 | − | 44.4262i | 0.842440 | − | 1.45915i | ||||
\(928\) | 0.500000 | − | 0.866025i | 0.0164133 | − | 0.0284287i | ||||
\(929\) | −1.45017 | + | 0.837253i | −0.0475784 | + | 0.0274694i | −0.523601 | − | 0.851964i | \(-0.675412\pi\) |
0.476022 | + | 0.879433i | \(0.342078\pi\) | |||||||
\(930\) | −14.3746 | −0.471361 | ||||||||
\(931\) | −14.0619 | + | 5.37669i | −0.460859 | + | 0.176214i | ||||
\(932\) | 4.82475 | 0.158040 | ||||||||
\(933\) | 19.1375 | + | 33.1471i | 0.626532 | + | 1.08519i | ||||
\(934\) | −20.6873 | − | 11.9438i | −0.676909 | − | 0.390814i | ||||
\(935\) | 14.0000 | − | 40.8471i | 0.457849 | − | 1.33584i | ||||
\(936\) | −15.8248 | + | 9.13642i | −0.517248 | + | 0.298633i | ||||
\(937\) | 16.9019i | 0.552160i | 0.961135 | + | 0.276080i | \(0.0890355\pi\) | ||||
−0.961135 | + | 0.276080i | \(0.910964\pi\) | |||||||
\(938\) | 17.2749 | + | 1.37097i | 0.564046 | + | 0.0447637i | ||||
\(939\) | 12.1244i | 0.395663i | ||||||||
\(940\) | −16.5498 | − | 28.6652i | −0.539796 | − | 0.934954i | ||||
\(941\) | −13.5997 | + | 23.5553i | −0.443337 | + | 0.767881i | −0.997935 | − | 0.0642369i | \(-0.979539\pi\) |
0.554598 | + | 0.832118i | \(0.312872\pi\) | |||||||
\(942\) | 14.5876 | + | 8.42217i | 0.475290 | + | 0.274409i | ||||
\(943\) | 54.8248 | − | 31.6531i | 1.78534 | − | 1.03077i | ||||
\(944\) | − | 1.73205i | − | 0.0563735i | ||||||
\(945\) | 18.0000 | + | 37.8016i | 0.585540 | + | 1.22969i | ||||
\(946\) | −18.2749 | + | 3.57919i | −0.594169 | + | 0.116369i | ||||
\(947\) | −19.2371 | + | 11.1066i | −0.625123 | + | 0.360915i | −0.778861 | − | 0.627197i | \(-0.784202\pi\) |
0.153738 | + | 0.988112i | \(0.450869\pi\) | |||||||
\(948\) | −5.63746 | + | 9.76436i | −0.183096 | + | 0.317132i | ||||
\(949\) | 37.0997 | − | 64.2585i | 1.20431 | − | 2.08592i | ||||
\(950\) | −7.96221 | + | 4.59698i | −0.258328 | + | 0.149146i | ||||
\(951\) | −14.3746 | −0.466128 | ||||||||
\(952\) | 6.41238 | − | 9.31697i | 0.207826 | − | 0.301965i | ||||
\(953\) | −17.6495 | −0.571723 | −0.285862 | − | 0.958271i | \(-0.592280\pi\) | ||||
−0.285862 | + | 0.958271i | \(0.592280\pi\) | |||||||
\(954\) | 21.5619 | − | 12.4488i | 0.698092 | − | 0.403043i | ||||
\(955\) | 22.5498 | − | 39.0575i | 0.729696 | − | 1.26387i | ||||
\(956\) | −1.27492 | + | 2.20822i | −0.0412338 | + | 0.0714190i | ||||
\(957\) | −3.77492 | − | 4.33013i | −0.122026 | − | 0.139973i | ||||
\(958\) | 28.0000 | 0.904639 | ||||||||
\(959\) | −28.3746 | − | 19.5287i | −0.916263 | − | 0.630616i | ||||
\(960\) | −5.27492 | −0.170247 | ||||||||
\(961\) | 11.7870 | + | 20.4156i | 0.380225 | + | 0.658568i | ||||
\(962\) | −1.45017 | − | 0.837253i | −0.0467552 | − | 0.0269941i | ||||
\(963\) | 10.0876 | − | 17.4723i | 0.325069 | − | 0.563036i | ||||
\(964\) | 7.91238 | − | 4.56821i | 0.254840 | − | 0.147132i | ||||
\(965\) | 54.0241 | 1.73910 | ||||||||
\(966\) | 14.5876 | + | 30.6353i | 0.469349 | + | 0.985674i | ||||
\(967\) | 10.3348i | 0.332344i | 0.986097 | + | 0.166172i | \(0.0531406\pi\) | ||||
−0.986097 | + | 0.166172i | \(0.946859\pi\) | |||||||
\(968\) | −8.68729 | − | 6.74766i | −0.279220 | − | 0.216878i | ||||
\(969\) | 7.96221 | − | 13.7910i | 0.255783 | − | 0.443029i | ||||
\(970\) | 4.08762 | + | 2.35999i | 0.131246 | + | 0.0757747i | ||||
\(971\) | −15.2629 | + | 8.81202i | −0.489809 | + | 0.282791i | −0.724495 | − | 0.689280i | \(-0.757927\pi\) |
0.234686 | + | 0.972071i | \(0.424594\pi\) | |||||||
\(972\) | 15.5885i | 0.500000i | ||||||||
\(973\) | 1.00000 | − | 12.6005i | 0.0320585 | − | 0.403954i | ||||
\(974\) | −18.3746 | −0.588760 | ||||||||
\(975\) | 22.5498 | + | 39.0575i | 0.722173 | + | 1.25084i | ||||
\(976\) | 6.00000 | + | 3.46410i | 0.192055 | + | 0.110883i | ||||
\(977\) | −3.09967 | − | 1.78959i | −0.0991672 | − | 0.0572542i | 0.449596 | − | 0.893232i | \(-0.351568\pi\) |
−0.548763 | + | 0.835978i | \(0.684901\pi\) | |||||||
\(978\) | −2.17525 | + | 1.25588i | −0.0695568 | + | 0.0401586i | ||||
\(979\) | −19.8248 | + | 3.88273i | −0.633602 | + | 0.124093i | ||||
\(980\) | −3.36254 | + | 21.0515i | −0.107412 | + | 0.672464i | ||||
\(981\) | − | 39.0575i | − | 1.24701i | ||||||
\(982\) | 11.1873 | + | 19.3770i | 0.357001 | + | 0.618344i | ||||
\(983\) | 0.312707 | + | 0.180541i | 0.00997380 | + | 0.00575838i | 0.504979 | − | 0.863132i | \(-0.331500\pi\) |
−0.495005 | + | 0.868890i | \(0.664834\pi\) | |||||||
\(984\) | 12.8248 | + | 7.40437i | 0.408838 | + | 0.236043i | ||||
\(985\) | −53.4743 | + | 30.8734i | −1.70383 | + | 0.983708i | ||||
\(986\) | 4.27492 | 0.136141 | ||||||||
\(987\) | −49.6495 | − | 3.94027i | −1.58036 | − | 0.125420i | ||||
\(988\) | −13.0997 | −0.416756 | ||||||||
\(989\) | 20.7870 | + | 36.0041i | 0.660987 | + | 1.14486i | ||||
\(990\) | −9.82475 | + | 28.6652i | −0.312251 | + | 0.911038i | ||||
\(991\) | 3.91238 | − | 6.77643i | 0.124281 | − | 0.215261i | −0.797171 | − | 0.603754i | \(-0.793671\pi\) |
0.921452 | + | 0.388493i | \(0.127004\pi\) | |||||||
\(992\) | −1.36254 | − | 2.35999i | −0.0432607 | − | 0.0749298i | ||||
\(993\) | 43.4739i | 1.37960i | ||||||||
\(994\) | −13.4124 | + | 6.38658i | −0.425415 | + | 0.202570i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.08762 | − | 2.35999i | 0.129521 | − | 0.0747792i | ||||
\(997\) | −32.3746 | − | 18.6915i | −1.02531 | − | 0.591965i | −0.109675 | − | 0.993968i | \(-0.534981\pi\) |
−0.915639 | + | 0.402003i | \(0.868314\pi\) | |||||||
\(998\) | 9.27492 | − | 16.0646i | 0.293592 | − | 0.508517i | ||||
\(999\) | −1.23713 | + | 0.714256i | −0.0391410 | + | 0.0225981i |
(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 | 462.2.n.c.263.2 | yes | 4 | |
3.2 | odd | 2 | 462.2.n.b.263.1 | yes | 4 | ||
7.2 | even | 3 | 462.2.n.d.65.1 | yes | 4 | ||
11.10 | odd | 2 | 462.2.n.a.263.2 | yes | 4 | ||
21.2 | odd | 6 | 462.2.n.a.65.2 | ✓ | 4 | ||
33.32 | even | 2 | 462.2.n.d.263.1 | yes | 4 | ||
77.65 | odd | 6 | 462.2.n.b.65.1 | yes | 4 | ||
231.65 | even | 6 | inner | 462.2.n.c.65.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.n.a.65.2 | ✓ | 4 | 21.2 | odd | 6 | ||
462.2.n.a.263.2 | yes | 4 | 11.10 | odd | 2 | ||
462.2.n.b.65.1 | yes | 4 | 77.65 | odd | 6 | ||
462.2.n.b.263.1 | yes | 4 | 3.2 | odd | 2 | ||
462.2.n.c.65.2 | yes | 4 | 231.65 | even | 6 | inner | |
462.2.n.c.263.2 | yes | 4 | 1.1 | even | 1 | trivial | |
462.2.n.d.65.1 | yes | 4 | 7.2 | even | 3 | ||
462.2.n.d.263.1 | yes | 4 | 33.32 | even | 2 |