Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [125,2,Mod(24,125)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(125, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("125.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 125 = 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 125.e (of order \(10\), 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: | \(0.998130025266\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(0.951057 - 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 125.49 |
Dual form | 125.2.e.a.74.1 |
$q$-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 \(\left(\mathbb{Z}/125\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.363271 | + | 0.500000i | −0.256872 | + | 0.353553i | −0.917903 | − | 0.396805i | \(-0.870119\pi\) |
0.661031 | + | 0.750358i | \(0.270119\pi\) | |||||||
\(3\) | −0.951057 | + | 0.309017i | −0.549093 | + | 0.178411i | −0.570408 | − | 0.821362i | \(-0.693215\pi\) |
0.0213149 | + | 0.999773i | \(0.493215\pi\) | |||||||
\(4\) | 0.500000 | + | 1.53884i | 0.250000 | + | 0.769421i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.190983 | − | 0.587785i | 0.0779685 | − | 0.239962i | ||||
\(7\) | 1.61803i | 0.611559i | 0.952102 | + | 0.305780i | \(0.0989171\pi\) | ||||
−0.952102 | + | 0.305780i | \(0.901083\pi\) | |||||||
\(8\) | −2.12663 | − | 0.690983i | −0.751876 | − | 0.244299i | ||||
\(9\) | −1.61803 | + | 1.17557i | −0.539345 | + | 0.391857i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.618034 | + | 0.449028i | 0.186344 | + | 0.135387i | 0.677046 | − | 0.735940i | \(-0.263260\pi\) |
−0.490702 | + | 0.871327i | \(0.663260\pi\) | |||||||
\(12\) | −0.951057 | − | 1.30902i | −0.274546 | − | 0.377881i | ||||
\(13\) | 2.85317 | + | 3.92705i | 0.791327 | + | 1.08917i | 0.993942 | + | 0.109909i | \(0.0350561\pi\) |
−0.202615 | + | 0.979259i | \(0.564944\pi\) | |||||||
\(14\) | −0.809017 | − | 0.587785i | −0.216219 | − | 0.157092i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | + | 1.08981i | −0.375000 | + | 0.272453i | ||||
\(17\) | 0.726543 | + | 0.236068i | 0.176212 | + | 0.0572549i | 0.395794 | − | 0.918339i | \(-0.370469\pi\) |
−0.219582 | + | 0.975594i | \(0.570469\pi\) | |||||||
\(18\) | − | 1.23607i | − | 0.291344i | ||||||
\(19\) | 1.80902 | − | 5.56758i | 0.415017 | − | 1.27729i | −0.497219 | − | 0.867625i | \(-0.665645\pi\) |
0.912236 | − | 0.409666i | \(-0.134355\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | − | 1.53884i | −0.109109 | − | 0.335803i | ||||
\(22\) | −0.449028 | + | 0.145898i | −0.0957331 | + | 0.0311056i | ||||
\(23\) | 4.84104 | − | 6.66312i | 1.00943 | − | 1.38936i | 0.0900679 | − | 0.995936i | \(-0.471292\pi\) |
0.919359 | − | 0.393421i | \(-0.128708\pi\) | |||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | 2.93893 | − | 4.04508i | 0.565597 | − | 0.778477i | ||||
\(28\) | −2.48990 | + | 0.809017i | −0.470547 | + | 0.152890i | ||||
\(29\) | 0.427051 | + | 1.31433i | 0.0793014 | + | 0.244065i | 0.982846 | − | 0.184430i | \(-0.0590440\pi\) |
−0.903544 | + | 0.428495i | \(0.859044\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.927051 | + | 2.85317i | −0.166503 | + | 0.512444i | −0.999144 | − | 0.0413693i | \(-0.986828\pi\) |
0.832641 | + | 0.553814i | \(0.186828\pi\) | |||||||
\(32\) | − | 5.61803i | − | 0.993137i | ||||||
\(33\) | −0.726543 | − | 0.236068i | −0.126475 | − | 0.0410942i | ||||
\(34\) | −0.381966 | + | 0.277515i | −0.0655066 | + | 0.0475934i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.61803 | − | 1.90211i | −0.436339 | − | 0.317019i | ||||
\(37\) | 2.48990 | + | 3.42705i | 0.409337 | + | 0.563404i | 0.963057 | − | 0.269299i | \(-0.0867921\pi\) |
−0.553720 | + | 0.832703i | \(0.686792\pi\) | |||||||
\(38\) | 2.12663 | + | 2.92705i | 0.344984 | + | 0.474830i | ||||
\(39\) | −3.92705 | − | 2.85317i | −0.628831 | − | 0.456873i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.23607 | − | 3.07768i | 0.661563 | − | 0.480653i | −0.205628 | − | 0.978630i | \(-0.565924\pi\) |
0.867190 | + | 0.497977i | \(0.165924\pi\) | |||||||
\(42\) | 0.951057 | + | 0.309017i | 0.146751 | + | 0.0476824i | ||||
\(43\) | 1.85410i | 0.282748i | 0.989956 | + | 0.141374i | \(0.0451520\pi\) | ||||
−0.989956 | + | 0.141374i | \(0.954848\pi\) | |||||||
\(44\) | −0.381966 | + | 1.17557i | −0.0575835 | + | 0.177224i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.57295 | + | 4.84104i | 0.231919 | + | 0.713772i | ||||
\(47\) | −1.53884 | + | 0.500000i | −0.224463 | + | 0.0729325i | −0.419089 | − | 0.907945i | \(-0.637651\pi\) |
0.194626 | + | 0.980877i | \(0.437651\pi\) | |||||||
\(48\) | 1.08981 | − | 1.50000i | 0.157301 | − | 0.216506i | ||||
\(49\) | 4.38197 | 0.625995 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.763932 | −0.106972 | ||||||||
\(52\) | −4.61653 | + | 6.35410i | −0.640197 | + | 0.881155i | ||||
\(53\) | −5.20431 | + | 1.69098i | −0.714867 | + | 0.232274i | −0.643796 | − | 0.765197i | \(-0.722642\pi\) |
−0.0710707 | + | 0.997471i | \(0.522642\pi\) | |||||||
\(54\) | 0.954915 | + | 2.93893i | 0.129947 | + | 0.399937i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.11803 | − | 3.44095i | 0.149404 | − | 0.459817i | ||||
\(57\) | 5.85410i | 0.775395i | ||||||||
\(58\) | −0.812299 | − | 0.263932i | −0.106660 | − | 0.0346560i | ||||
\(59\) | −3.35410 | + | 2.43690i | −0.436667 | + | 0.317257i | −0.784309 | − | 0.620370i | \(-0.786982\pi\) |
0.347642 | + | 0.937627i | \(0.386982\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.80902 | + | 2.76741i | 0.487695 | + | 0.354331i | 0.804297 | − | 0.594227i | \(-0.202542\pi\) |
−0.316602 | + | 0.948558i | \(0.602542\pi\) | |||||||
\(62\) | −1.08981 | − | 1.50000i | −0.138406 | − | 0.190500i | ||||
\(63\) | −1.90211 | − | 2.61803i | −0.239644 | − | 0.329841i | ||||
\(64\) | −0.190983 | − | 0.138757i | −0.0238729 | − | 0.0173447i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.381966 | − | 0.277515i | 0.0470168 | − | 0.0341597i | ||||
\(67\) | −8.78402 | − | 2.85410i | −1.07314 | − | 0.348684i | −0.281430 | − | 0.959582i | \(-0.590809\pi\) |
−0.791709 | + | 0.610898i | \(0.790809\pi\) | |||||||
\(68\) | 1.23607i | 0.149895i | ||||||||
\(69\) | −2.54508 | + | 7.83297i | −0.306392 | + | 0.942978i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.35410 | − | 4.16750i | −0.160702 | − | 0.494591i | 0.837992 | − | 0.545683i | \(-0.183730\pi\) |
−0.998694 | + | 0.0510922i | \(0.983730\pi\) | |||||||
\(72\) | 4.25325 | − | 1.38197i | 0.501251 | − | 0.162866i | ||||
\(73\) | −5.29007 | + | 7.28115i | −0.619156 | + | 0.852194i | −0.997291 | − | 0.0735557i | \(-0.976565\pi\) |
0.378136 | + | 0.925750i | \(0.376565\pi\) | |||||||
\(74\) | −2.61803 | −0.304340 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.47214 | 1.08653 | ||||||||
\(77\) | −0.726543 | + | 1.00000i | −0.0827972 | + | 0.113961i | ||||
\(78\) | 2.85317 | − | 0.927051i | 0.323058 | − | 0.104968i | ||||
\(79\) | −0.954915 | − | 2.93893i | −0.107436 | − | 0.330655i | 0.882858 | − | 0.469640i | \(-0.155616\pi\) |
−0.990295 | + | 0.138985i | \(0.955616\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 3.23607i | 0.357364i | ||||||||
\(83\) | −1.67760 | − | 0.545085i | −0.184140 | − | 0.0598308i | 0.215495 | − | 0.976505i | \(-0.430863\pi\) |
−0.399636 | + | 0.916674i | \(0.630863\pi\) | |||||||
\(84\) | 2.11803 | − | 1.53884i | 0.231096 | − | 0.167901i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.927051 | − | 0.673542i | −0.0999665 | − | 0.0726299i | ||||
\(87\) | −0.812299 | − | 1.11803i | −0.0870876 | − | 0.119866i | ||||
\(88\) | −1.00406 | − | 1.38197i | −0.107033 | − | 0.147318i | ||||
\(89\) | 7.23607 | + | 5.25731i | 0.767022 | + | 0.557274i | 0.901056 | − | 0.433703i | \(-0.142793\pi\) |
−0.134034 | + | 0.990977i | \(0.542793\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.35410 | + | 4.61653i | −0.666091 | + | 0.483943i | ||||
\(92\) | 12.6740 | + | 4.11803i | 1.32136 | + | 0.429335i | ||||
\(93\) | − | 3.00000i | − | 0.311086i | ||||||
\(94\) | 0.309017 | − | 0.951057i | 0.0318727 | − | 0.0980940i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.73607 | + | 5.34307i | 0.177187 | + | 0.545325i | ||||
\(97\) | 2.71441 | − | 0.881966i | 0.275607 | − | 0.0895501i | −0.167953 | − | 0.985795i | \(-0.553716\pi\) |
0.443559 | + | 0.896245i | \(0.353716\pi\) | |||||||
\(98\) | −1.59184 | + | 2.19098i | −0.160800 | + | 0.221323i | ||||
\(99\) | −1.52786 | −0.153556 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.47214 | −0.743505 | −0.371753 | − | 0.928332i | \(-0.621243\pi\) | ||||
−0.371753 | + | 0.928332i | \(0.621243\pi\) | |||||||
\(102\) | 0.277515 | − | 0.381966i | 0.0274780 | − | 0.0378203i | ||||
\(103\) | 10.9964 | − | 3.57295i | 1.08351 | − | 0.352053i | 0.287773 | − | 0.957699i | \(-0.407085\pi\) |
0.795735 | + | 0.605645i | \(0.207085\pi\) | |||||||
\(104\) | −3.35410 | − | 10.3229i | −0.328897 | − | 1.01224i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.04508 | − | 3.21644i | 0.101508 | − | 0.312408i | ||||
\(107\) | − | 10.4164i | − | 1.00699i | −0.863998 | − | 0.503496i | \(-0.832047\pi\) | ||
0.863998 | − | 0.503496i | \(-0.167953\pi\) | |||||||
\(108\) | 7.69421 | + | 2.50000i | 0.740376 | + | 0.240563i | ||||
\(109\) | 8.09017 | − | 5.87785i | 0.774898 | − | 0.562996i | −0.128546 | − | 0.991704i | \(-0.541031\pi\) |
0.903443 | + | 0.428707i | \(0.141031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.42705 | − | 2.48990i | −0.325281 | − | 0.236331i | ||||
\(112\) | −1.76336 | − | 2.42705i | −0.166621 | − | 0.229335i | ||||
\(113\) | −5.96361 | − | 8.20820i | −0.561009 | − | 0.772163i | 0.430445 | − | 0.902617i | \(-0.358357\pi\) |
−0.991454 | + | 0.130454i | \(0.958357\pi\) | |||||||
\(114\) | −2.92705 | − | 2.12663i | −0.274143 | − | 0.199177i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.80902 | + | 1.31433i | −0.167963 | + | 0.122032i | ||||
\(117\) | −9.23305 | − | 3.00000i | −0.853596 | − | 0.277350i | ||||
\(118\) | − | 2.56231i | − | 0.235879i | ||||||
\(119\) | −0.381966 | + | 1.17557i | −0.0350148 | + | 0.107764i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.21885 | − | 9.90659i | −0.292622 | − | 0.900599i | ||||
\(122\) | −2.76741 | + | 0.899187i | −0.250550 | + | 0.0814086i | ||||
\(123\) | −3.07768 | + | 4.23607i | −0.277505 | + | 0.381953i | ||||
\(124\) | −4.85410 | −0.435911 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.00000 | 0.178174 | ||||||||
\(127\) | 9.33905 | − | 12.8541i | 0.828707 | − | 1.14062i | −0.159455 | − | 0.987205i | \(-0.550974\pi\) |
0.988162 | − | 0.153412i | \(-0.0490262\pi\) | |||||||
\(128\) | 10.8249 | − | 3.51722i | 0.956794 | − | 0.310881i | ||||
\(129\) | −0.572949 | − | 1.76336i | −0.0504453 | − | 0.155255i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.50000 | + | 16.9273i | −0.480537 | + | 1.47894i | 0.357805 | + | 0.933797i | \(0.383525\pi\) |
−0.838342 | + | 0.545145i | \(0.816475\pi\) | |||||||
\(132\) | − | 1.23607i | − | 0.107586i | ||||||
\(133\) | 9.00854 | + | 2.92705i | 0.781139 | + | 0.253808i | ||||
\(134\) | 4.61803 | − | 3.35520i | 0.398937 | − | 0.289845i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.38197 | − | 1.00406i | −0.118503 | − | 0.0860972i | ||||
\(137\) | 3.49396 | + | 4.80902i | 0.298509 | + | 0.410862i | 0.931755 | − | 0.363089i | \(-0.118278\pi\) |
−0.633246 | + | 0.773951i | \(0.718278\pi\) | |||||||
\(138\) | −2.99193 | − | 4.11803i | −0.254690 | − | 0.350550i | ||||
\(139\) | 4.04508 | + | 2.93893i | 0.343100 | + | 0.249276i | 0.745968 | − | 0.665981i | \(-0.231987\pi\) |
−0.402869 | + | 0.915258i | \(0.631987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.30902 | − | 0.951057i | 0.110239 | − | 0.0800934i | ||||
\(142\) | 2.57565 | + | 0.836881i | 0.216144 | + | 0.0702295i | ||||
\(143\) | 3.70820i | 0.310096i | ||||||||
\(144\) | 1.14590 | − | 3.52671i | 0.0954915 | − | 0.293893i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.71885 | − | 5.29007i | −0.142253 | − | 0.437809i | ||||
\(147\) | −4.16750 | + | 1.35410i | −0.343729 | + | 0.111684i | ||||
\(148\) | −4.02874 | + | 5.54508i | −0.331160 | + | 0.455803i | ||||
\(149\) | −13.9443 | −1.14236 | −0.571180 | − | 0.820825i | \(-0.693514\pi\) | ||||
−0.571180 | + | 0.820825i | \(0.693514\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.56231 | −0.452654 | −0.226327 | − | 0.974051i | \(-0.572672\pi\) | ||||
−0.226327 | + | 0.974051i | \(0.572672\pi\) | |||||||
\(152\) | −7.69421 | + | 10.5902i | −0.624083 | + | 0.858976i | ||||
\(153\) | −1.45309 | + | 0.472136i | −0.117475 | + | 0.0381699i | ||||
\(154\) | −0.236068 | − | 0.726543i | −0.0190229 | − | 0.0585465i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.42705 | − | 7.46969i | 0.194320 | − | 0.598054i | ||||
\(157\) | 9.18034i | 0.732671i | 0.930483 | + | 0.366335i | \(0.119388\pi\) | ||||
−0.930483 | + | 0.366335i | \(0.880612\pi\) | |||||||
\(158\) | 1.81636 | + | 0.590170i | 0.144502 | + | 0.0469514i | ||||
\(159\) | 4.42705 | − | 3.21644i | 0.351088 | − | 0.255080i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.7812 | + | 7.83297i | 0.849674 | + | 0.617324i | ||||
\(162\) | 0.363271 | + | 0.500000i | 0.0285413 | + | 0.0392837i | ||||
\(163\) | −6.46564 | − | 8.89919i | −0.506428 | − | 0.697038i | 0.476884 | − | 0.878966i | \(-0.341766\pi\) |
−0.983312 | + | 0.181928i | \(0.941766\pi\) | |||||||
\(164\) | 6.85410 | + | 4.97980i | 0.535215 | + | 0.388857i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.881966 | − | 0.640786i | 0.0684538 | − | 0.0497346i | ||||
\(167\) | 5.29007 | + | 1.71885i | 0.409358 | + | 0.133008i | 0.506455 | − | 0.862267i | \(-0.330956\pi\) |
−0.0970971 | + | 0.995275i | \(0.530956\pi\) | |||||||
\(168\) | 3.61803i | 0.279137i | ||||||||
\(169\) | −3.26393 | + | 10.0453i | −0.251072 | + | 0.772719i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.61803 | + | 11.1352i | 0.276678 | + | 0.851527i | ||||
\(172\) | −2.85317 | + | 0.927051i | −0.217552 | + | 0.0706870i | ||||
\(173\) | −9.92684 | + | 13.6631i | −0.754723 | + | 1.03879i | 0.242911 | + | 0.970049i | \(0.421898\pi\) |
−0.997635 | + | 0.0687392i | \(0.978102\pi\) | |||||||
\(174\) | 0.854102 | 0.0647493 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.41641 | −0.106766 | ||||||||
\(177\) | 2.43690 | − | 3.35410i | 0.183168 | − | 0.252110i | ||||
\(178\) | −5.25731 | + | 1.70820i | −0.394052 | + | 0.128035i | ||||
\(179\) | 2.92705 | + | 9.00854i | 0.218778 | + | 0.673330i | 0.998864 | + | 0.0476570i | \(0.0151754\pi\) |
−0.780086 | + | 0.625673i | \(0.784825\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.23607 | − | 13.0373i | 0.314864 | − | 0.969053i | −0.660946 | − | 0.750434i | \(-0.729845\pi\) |
0.975810 | − | 0.218619i | \(-0.0701553\pi\) | |||||||
\(182\) | − | 4.85410i | − | 0.359810i | ||||||
\(183\) | −4.47777 | − | 1.45492i | −0.331006 | − | 0.107550i | ||||
\(184\) | −14.8992 | + | 10.8249i | −1.09838 | + | 0.798022i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.50000 | + | 1.08981i | 0.109985 | + | 0.0799090i | ||||
\(187\) | 0.343027 | + | 0.472136i | 0.0250846 | + | 0.0345260i | ||||
\(188\) | −1.53884 | − | 2.11803i | −0.112232 | − | 0.154474i | ||||
\(189\) | 6.54508 | + | 4.75528i | 0.476085 | + | 0.345896i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.5623 | − | 14.2128i | 1.41548 | − | 1.02841i | 0.422982 | − | 0.906138i | \(-0.360984\pi\) |
0.992497 | − | 0.122267i | \(-0.0390165\pi\) | |||||||
\(192\) | 0.224514 | + | 0.0729490i | 0.0162029 | + | 0.00526464i | ||||
\(193\) | − | 5.70820i | − | 0.410886i | −0.978669 | − | 0.205443i | \(-0.934137\pi\) | ||
0.978669 | − | 0.205443i | \(-0.0658634\pi\) | |||||||
\(194\) | −0.545085 | + | 1.67760i | −0.0391348 | + | 0.120445i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.19098 | + | 6.74315i | 0.156499 | + | 0.481654i | ||||
\(197\) | −9.23305 | + | 3.00000i | −0.657828 | + | 0.213741i | −0.618862 | − | 0.785499i | \(-0.712406\pi\) |
−0.0389652 | + | 0.999241i | \(0.512406\pi\) | |||||||
\(198\) | 0.555029 | − | 0.763932i | 0.0394442 | − | 0.0542903i | ||||
\(199\) | −2.56231 | −0.181637 | −0.0908185 | − | 0.995867i | \(-0.528948\pi\) | ||||
−0.0908185 | + | 0.995867i | \(0.528948\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.23607 | 0.651462 | ||||||||
\(202\) | 2.71441 | − | 3.73607i | 0.190985 | − | 0.262869i | ||||
\(203\) | −2.12663 | + | 0.690983i | −0.149260 | + | 0.0484975i | ||||
\(204\) | −0.381966 | − | 1.17557i | −0.0267430 | − | 0.0823064i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.20820 | + | 6.79615i | −0.153853 | + | 0.473510i | ||||
\(207\) | 16.4721i | 1.14489i | ||||||||
\(208\) | −8.55951 | − | 2.78115i | −0.593495 | − | 0.192838i | ||||
\(209\) | 3.61803 | − | 2.62866i | 0.250265 | − | 0.181828i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6631 | − | 7.74721i | −0.734079 | − | 0.533340i | 0.156772 | − | 0.987635i | \(-0.449891\pi\) |
−0.890851 | + | 0.454295i | \(0.849891\pi\) | |||||||
\(212\) | −5.20431 | − | 7.16312i | −0.357434 | − | 0.491965i | ||||
\(213\) | 2.57565 | + | 3.54508i | 0.176481 | + | 0.242905i | ||||
\(214\) | 5.20820 | + | 3.78398i | 0.356025 | + | 0.258668i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −9.04508 | + | 6.57164i | −0.615440 | + | 0.447143i | ||||
\(217\) | −4.61653 | − | 1.50000i | −0.313390 | − | 0.101827i | ||||
\(218\) | 6.18034i | 0.418585i | ||||||||
\(219\) | 2.78115 | − | 8.55951i | 0.187933 | − | 0.578398i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.14590 | + | 3.52671i | 0.0770814 | + | 0.237232i | ||||
\(222\) | 2.48990 | − | 0.809017i | 0.167111 | − | 0.0542977i | ||||
\(223\) | 13.0373 | − | 17.9443i | 0.873041 | − | 1.20164i | −0.105260 | − | 0.994445i | \(-0.533567\pi\) |
0.978300 | − | 0.207193i | \(-0.0664327\pi\) | |||||||
\(224\) | 9.09017 | 0.607363 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.27051 | 0.417108 | ||||||||
\(227\) | −11.3067 | + | 15.5623i | −0.750451 | + | 1.03291i | 0.247498 | + | 0.968888i | \(0.420392\pi\) |
−0.997949 | + | 0.0640182i | \(0.979608\pi\) | |||||||
\(228\) | −9.00854 | + | 2.92705i | −0.596605 | + | 0.193849i | ||||
\(229\) | −2.56231 | − | 7.88597i | −0.169322 | − | 0.521119i | 0.830007 | − | 0.557753i | \(-0.188336\pi\) |
−0.999329 | + | 0.0366339i | \(0.988336\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.381966 | − | 1.17557i | 0.0251315 | − | 0.0773469i | ||||
\(232\) | − | 3.09017i | − | 0.202880i | ||||||
\(233\) | 14.2128 | + | 4.61803i | 0.931115 | + | 0.302537i | 0.735018 | − | 0.678047i | \(-0.237174\pi\) |
0.196096 | + | 0.980585i | \(0.437174\pi\) | |||||||
\(234\) | 4.85410 | − | 3.52671i | 0.317323 | − | 0.230548i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.42705 | − | 3.94298i | −0.353271 | − | 0.256666i | ||||
\(237\) | 1.81636 | + | 2.50000i | 0.117985 | + | 0.162392i | ||||
\(238\) | −0.449028 | − | 0.618034i | −0.0291062 | − | 0.0400612i | ||||
\(239\) | −23.8435 | − | 17.3233i | −1.54231 | − | 1.12055i | −0.948869 | − | 0.315669i | \(-0.897771\pi\) |
−0.593436 | − | 0.804881i | \(-0.702229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.28115 | + | 6.74315i | −0.597852 | + | 0.434365i | −0.845116 | − | 0.534584i | \(-0.820468\pi\) |
0.247264 | + | 0.968948i | \(0.420468\pi\) | |||||||
\(242\) | 6.12261 | + | 1.98936i | 0.393576 | + | 0.127881i | ||||
\(243\) | 16.0000i | 1.02640i | ||||||||
\(244\) | −2.35410 | + | 7.24518i | −0.150706 | + | 0.463825i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.00000 | − | 3.07768i | −0.0637577 | − | 0.196226i | ||||
\(247\) | 27.0256 | − | 8.78115i | 1.71960 | − | 0.558731i | ||||
\(248\) | 3.94298 | − | 5.42705i | 0.250380 | − | 0.344618i | ||||
\(249\) | 1.76393 | 0.111785 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.81966 | −0.430453 | −0.215227 | − | 0.976564i | \(-0.569049\pi\) | ||||
−0.215227 | + | 0.976564i | \(0.569049\pi\) | |||||||
\(252\) | 3.07768 | − | 4.23607i | 0.193876 | − | 0.266847i | ||||
\(253\) | 5.98385 | − | 1.94427i | 0.376202 | − | 0.122235i | ||||
\(254\) | 3.03444 | + | 9.33905i | 0.190398 | + | 0.585984i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.02786 | + | 6.24112i | −0.126742 | + | 0.390070i | ||||
\(257\) | − | 16.1459i | − | 1.00715i | −0.863951 | − | 0.503577i | \(-0.832017\pi\) | ||
0.863951 | − | 0.503577i | \(-0.167983\pi\) | |||||||
\(258\) | 1.08981 | + | 0.354102i | 0.0678488 | + | 0.0220454i | ||||
\(259\) | −5.54508 | + | 4.02874i | −0.344555 | + | 0.250334i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.23607 | − | 1.62460i | −0.138409 | − | 0.100560i | ||||
\(262\) | −6.46564 | − | 8.89919i | −0.399448 | − | 0.549794i | ||||
\(263\) | 12.9843 | + | 17.8713i | 0.800645 | + | 1.10199i | 0.992700 | + | 0.120609i | \(0.0384847\pi\) |
−0.192055 | + | 0.981384i | \(0.561515\pi\) | |||||||
\(264\) | 1.38197 | + | 1.00406i | 0.0850541 | + | 0.0617954i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.73607 | + | 3.44095i | −0.290387 | + | 0.210978i | ||||
\(267\) | −8.50651 | − | 2.76393i | −0.520590 | − | 0.169150i | ||||
\(268\) | − | 14.9443i | − | 0.912867i | ||||||
\(269\) | 5.32624 | − | 16.3925i | 0.324746 | − | 0.999467i | −0.646808 | − | 0.762652i | \(-0.723897\pi\) |
0.971555 | − | 0.236814i | \(-0.0761033\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.47214 | − | 7.60845i | −0.150172 | − | 0.462181i | 0.847468 | − | 0.530846i | \(-0.178126\pi\) |
−0.997640 | + | 0.0686657i | \(0.978126\pi\) | |||||||
\(272\) | −1.34708 | + | 0.437694i | −0.0816790 | + | 0.0265391i | ||||
\(273\) | 4.61653 | − | 6.35410i | 0.279405 | − | 0.384568i | ||||
\(274\) | −3.67376 | −0.221940 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.3262 | −0.802145 | ||||||||
\(277\) | 6.63715 | − | 9.13525i | 0.398788 | − | 0.548884i | −0.561651 | − | 0.827374i | \(-0.689834\pi\) |
0.960439 | + | 0.278490i | \(0.0898338\pi\) | |||||||
\(278\) | −2.93893 | + | 0.954915i | −0.176265 | + | 0.0572720i | ||||
\(279\) | −1.85410 | − | 5.70634i | −0.111002 | − | 0.341630i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.336881 | + | 1.03681i | −0.0200966 | + | 0.0618511i | −0.960602 | − | 0.277928i | \(-0.910352\pi\) |
0.940505 | + | 0.339779i | \(0.110352\pi\) | |||||||
\(282\) | 1.00000i | 0.0595491i | ||||||||
\(283\) | −22.0131 | − | 7.15248i | −1.30854 | − | 0.425171i | −0.429996 | − | 0.902831i | \(-0.641485\pi\) |
−0.878545 | + | 0.477660i | \(0.841485\pi\) | |||||||
\(284\) | 5.73607 | − | 4.16750i | 0.340373 | − | 0.247295i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.85410 | − | 1.34708i | −0.109635 | − | 0.0796547i | ||||
\(287\) | 4.97980 | + | 6.85410i | 0.293948 | + | 0.404585i | ||||
\(288\) | 6.60440 | + | 9.09017i | 0.389168 | + | 0.535643i | ||||
\(289\) | −13.2812 | − | 9.64932i | −0.781244 | − | 0.567607i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.30902 | + | 1.67760i | −0.135357 | + | 0.0983426i | ||||
\(292\) | −13.8496 | − | 4.50000i | −0.810485 | − | 0.263343i | ||||
\(293\) | − | 28.4721i | − | 1.66336i | −0.555255 | − | 0.831680i | \(-0.687379\pi\) | ||
0.555255 | − | 0.831680i | \(-0.312621\pi\) | |||||||
\(294\) | 0.836881 | − | 2.57565i | 0.0488079 | − | 0.150215i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.92705 | − | 9.00854i | −0.170131 | − | 0.523611i | ||||
\(297\) | 3.63271 | − | 1.18034i | 0.210791 | − | 0.0684903i | ||||
\(298\) | 5.06555 | − | 6.97214i | 0.293440 | − | 0.403885i | ||||
\(299\) | 39.9787 | 2.31203 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | −0.172917 | ||||||||
\(302\) | 2.02063 | − | 2.78115i | 0.116274 | − | 0.160037i | ||||
\(303\) | 7.10642 | − | 2.30902i | 0.408253 | − | 0.132650i | ||||
\(304\) | 3.35410 | + | 10.3229i | 0.192371 | + | 0.592057i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.291796 | − | 0.898056i | 0.0166809 | − | 0.0513384i | ||||
\(307\) | − | 4.76393i | − | 0.271892i | −0.990716 | − | 0.135946i | \(-0.956593\pi\) | ||
0.990716 | − | 0.135946i | \(-0.0434074\pi\) | |||||||
\(308\) | −1.90211 | − | 0.618034i | −0.108383 | − | 0.0352158i | ||||
\(309\) | −9.35410 | + | 6.79615i | −0.532136 | + | 0.386620i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.8713 | + | 17.3435i | 1.35362 | + | 0.983461i | 0.998822 | + | 0.0485178i | \(0.0154498\pi\) |
0.354796 | + | 0.934944i | \(0.384550\pi\) | |||||||
\(312\) | 6.37988 | + | 8.78115i | 0.361190 | + | 0.497135i | ||||
\(313\) | 12.4822 | + | 17.1803i | 0.705538 | + | 0.971090i | 0.999882 | + | 0.0153904i | \(0.00489912\pi\) |
−0.294343 | + | 0.955700i | \(0.595101\pi\) | |||||||
\(314\) | −4.59017 | − | 3.33495i | −0.259038 | − | 0.188202i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.04508 | − | 2.93893i | 0.227554 | − | 0.165328i | ||||
\(317\) | 22.4948 | + | 7.30902i | 1.26344 | + | 0.410515i | 0.862718 | − | 0.505686i | \(-0.168761\pi\) |
0.400719 | + | 0.916201i | \(0.368761\pi\) | |||||||
\(318\) | 3.38197i | 0.189651i | ||||||||
\(319\) | −0.326238 | + | 1.00406i | −0.0182658 | + | 0.0562164i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.21885 | + | 9.90659i | 0.179659 | + | 0.552932i | ||||
\(322\) | −7.83297 | + | 2.54508i | −0.436514 | + | 0.141832i | ||||
\(323\) | 2.62866 | − | 3.61803i | 0.146262 | − | 0.201313i | ||||
\(324\) | 1.61803 | 0.0898908 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.79837 | 0.376527 | ||||||||
\(327\) | −5.87785 | + | 8.09017i | −0.325046 | + | 0.447387i | ||||
\(328\) | −11.1352 | + | 3.61803i | −0.614837 | + | 0.199773i | ||||
\(329\) | −0.809017 | − | 2.48990i | −0.0446026 | − | 0.137273i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.29180 | − | 16.2865i | 0.290863 | − | 0.895186i | −0.693716 | − | 0.720248i | \(-0.744028\pi\) |
0.984580 | − | 0.174937i | \(-0.0559722\pi\) | |||||||
\(332\) | − | 2.85410i | − | 0.156639i | ||||||
\(333\) | −8.05748 | − | 2.61803i | −0.441547 | − | 0.143467i | ||||
\(334\) | −2.78115 | + | 2.02063i | −0.152178 | + | 0.110564i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.42705 | + | 1.76336i | 0.132406 | + | 0.0961989i | ||||
\(337\) | 0.673542 | + | 0.927051i | 0.0366902 | + | 0.0504997i | 0.826968 | − | 0.562249i | \(-0.190064\pi\) |
−0.790278 | + | 0.612749i | \(0.790064\pi\) | |||||||
\(338\) | −3.83698 | − | 5.28115i | −0.208704 | − | 0.287257i | ||||
\(339\) | 8.20820 | + | 5.96361i | 0.445808 | + | 0.323899i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.85410 | + | 1.34708i | −0.100405 | + | 0.0729487i | ||||
\(342\) | −6.88191 | − | 2.23607i | −0.372131 | − | 0.120913i | ||||
\(343\) | 18.4164i | 0.994393i | ||||||||
\(344\) | 1.28115 | − | 3.94298i | 0.0690751 | − | 0.212591i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.22542 | − | 9.92684i | −0.173400 | − | 0.533670i | ||||
\(347\) | −29.5685 | + | 9.60739i | −1.58732 | + | 0.515752i | −0.963929 | − | 0.266158i | \(-0.914246\pi\) |
−0.623391 | + | 0.781910i | \(0.714246\pi\) | |||||||
\(348\) | 1.31433 | − | 1.80902i | 0.0704554 | − | 0.0969735i | ||||
\(349\) | −8.29180 | −0.443850 | −0.221925 | − | 0.975064i | \(-0.571234\pi\) | ||||
−0.221925 | + | 0.975064i | \(0.571234\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.2705 | 1.29546 | ||||||||
\(352\) | 2.52265 | − | 3.47214i | 0.134458 | − | 0.185065i | ||||
\(353\) | −22.9111 | + | 7.44427i | −1.21944 | + | 0.396219i | −0.846876 | − | 0.531790i | \(-0.821520\pi\) |
−0.372559 | + | 0.928008i | \(0.621520\pi\) | |||||||
\(354\) | 0.791796 | + | 2.43690i | 0.0420835 | + | 0.129520i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.47214 | + | 13.7638i | −0.237023 | + | 0.729481i | ||||
\(357\) | − | 1.23607i | − | 0.0654197i | ||||||
\(358\) | −5.56758 | − | 1.80902i | −0.294256 | − | 0.0956095i | ||||
\(359\) | −23.2533 | + | 16.8945i | −1.22726 | + | 0.891658i | −0.996682 | − | 0.0813956i | \(-0.974062\pi\) |
−0.230580 | + | 0.973053i | \(0.574062\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3541 | − | 8.97578i | −0.650216 | − | 0.472409i | ||||
\(362\) | 4.97980 | + | 6.85410i | 0.261732 | + | 0.360244i | ||||
\(363\) | 6.12261 | + | 8.42705i | 0.321354 | + | 0.442305i | ||||
\(364\) | −10.2812 | − | 7.46969i | −0.538879 | − | 0.391518i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.35410 | − | 1.71036i | 0.123051 | − | 0.0894017i | ||||
\(367\) | 5.17155 | + | 1.68034i | 0.269953 | + | 0.0877130i | 0.440866 | − | 0.897573i | \(-0.354672\pi\) |
−0.170913 | + | 0.985286i | \(0.554672\pi\) | |||||||
\(368\) | 15.2705i | 0.796030i | ||||||||
\(369\) | −3.23607 | + | 9.95959i | −0.168463 | + | 0.518476i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.73607 | − | 8.42075i | −0.142050 | − | 0.437184i | ||||
\(372\) | 4.61653 | − | 1.50000i | 0.239356 | − | 0.0777714i | ||||
\(373\) | 3.09793 | − | 4.26393i | 0.160405 | − | 0.220778i | −0.721248 | − | 0.692677i | \(-0.756431\pi\) |
0.881653 | + | 0.471899i | \(0.156431\pi\) | |||||||
\(374\) | −0.360680 | −0.0186503 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.61803 | 0.186586 | ||||||||
\(377\) | −3.94298 | + | 5.42705i | −0.203074 | + | 0.279507i | ||||
\(378\) | −4.75528 | + | 1.54508i | −0.244585 | + | 0.0794706i | ||||
\(379\) | 10.6910 | + | 32.9035i | 0.549159 | + | 1.69014i | 0.710891 | + | 0.703303i | \(0.248292\pi\) |
−0.161732 | + | 0.986835i | \(0.551708\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.90983 | + | 15.1109i | −0.251538 | + | 0.774155i | ||||
\(382\) | 14.9443i | 0.764615i | ||||||||
\(383\) | −10.8046 | − | 3.51064i | −0.552092 | − | 0.179385i | 0.0196680 | − | 0.999807i | \(-0.493739\pi\) |
−0.571760 | + | 0.820421i | \(0.693739\pi\) | |||||||
\(384\) | −9.20820 | + | 6.69015i | −0.469904 | + | 0.341405i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.85410 | + | 2.07363i | 0.145270 | + | 0.105545i | ||||
\(387\) | −2.17963 | − | 3.00000i | −0.110797 | − | 0.152499i | ||||
\(388\) | 2.71441 | + | 3.73607i | 0.137803 | + | 0.189670i | ||||
\(389\) | 12.1353 | + | 8.81678i | 0.615282 | + | 0.447028i | 0.851270 | − | 0.524727i | \(-0.175833\pi\) |
−0.235988 | + | 0.971756i | \(0.575833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.09017 | − | 3.69822i | 0.257421 | − | 0.187027i | ||||
\(392\) | −9.31881 | − | 3.02786i | −0.470671 | − | 0.152930i | ||||
\(393\) | − | 17.7984i | − | 0.897809i | ||||||
\(394\) | 1.85410 | − | 5.70634i | 0.0934083 | − | 0.287481i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.763932 | − | 2.35114i | −0.0383890 | − | 0.118149i | ||||
\(397\) | −0.0327561 | + | 0.0106431i | −0.00164398 | + | 0.000534163i | −0.309839 | − | 0.950789i | \(-0.600275\pi\) |
0.308195 | + | 0.951323i | \(0.400275\pi\) | |||||||
\(398\) | 0.930812 | − | 1.28115i | 0.0466574 | − | 0.0642184i | ||||
\(399\) | −9.47214 | −0.474200 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.5967 | −1.12843 | −0.564214 | − | 0.825629i | \(-0.690821\pi\) | ||||
−0.564214 | + | 0.825629i | \(0.690821\pi\) | |||||||
\(402\) | −3.35520 | + | 4.61803i | −0.167342 | + | 0.230327i | ||||
\(403\) | −13.8496 | + | 4.50000i | −0.689897 | + | 0.224161i | ||||
\(404\) | −3.73607 | − | 11.4984i | −0.185876 | − | 0.572069i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.427051 | − | 1.31433i | 0.0211942 | − | 0.0652290i | ||||
\(407\) | 3.23607i | 0.160406i | ||||||||
\(408\) | 1.62460 | + | 0.527864i | 0.0804296 | + | 0.0261332i | ||||
\(409\) | 22.9894 | − | 16.7027i | 1.13675 | − | 0.825898i | 0.150087 | − | 0.988673i | \(-0.452045\pi\) |
0.986663 | + | 0.162775i | \(0.0520445\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.80902 | − | 3.49396i | −0.237211 | − | 0.172344i | ||||
\(412\) | 10.9964 | + | 15.1353i | 0.541754 | + | 0.745660i | ||||
\(413\) | −3.94298 | − | 5.42705i | −0.194022 | − | 0.267048i | ||||
\(414\) | −8.23607 | − | 5.98385i | −0.404781 | − | 0.294090i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 22.0623 | − | 16.0292i | 1.08169 | − | 0.785896i | ||||
\(417\) | −4.75528 | − | 1.54508i | −0.232867 | − | 0.0756631i | ||||
\(418\) | 2.76393i | 0.135188i | ||||||||
\(419\) | 0.163119 | − | 0.502029i | 0.00796888 | − | 0.0245257i | −0.946993 | − | 0.321254i | \(-0.895896\pi\) |
0.954962 | + | 0.296728i | \(0.0958956\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.88854 | + | 30.4338i | 0.481938 | + | 1.48325i | 0.836367 | + | 0.548170i | \(0.184675\pi\) |
−0.354429 | + | 0.935083i | \(0.615325\pi\) | |||||||
\(422\) | 7.74721 | − | 2.51722i | 0.377128 | − | 0.122536i | ||||
\(423\) | 1.90211 | − | 2.61803i | 0.0924839 | − | 0.127293i | ||||
\(424\) | 12.2361 | 0.594236 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.70820 | −0.131213 | ||||||||
\(427\) | −4.47777 | + | 6.16312i | −0.216694 | + | 0.298254i | ||||
\(428\) | 16.0292 | − | 5.20820i | 0.774801 | − | 0.251748i | ||||
\(429\) | −1.14590 | − | 3.52671i | −0.0553245 | − | 0.170271i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.36475 | − | 22.6664i | 0.354747 | − | 1.09180i | −0.601409 | − | 0.798942i | \(-0.705394\pi\) |
0.956156 | − | 0.292858i | \(-0.0946064\pi\) | |||||||
\(432\) | 9.27051i | 0.446028i | ||||||||
\(433\) | 19.1599 | + | 6.22542i | 0.920765 | + | 0.299175i | 0.730781 | − | 0.682612i | \(-0.239156\pi\) |
0.189985 | + | 0.981787i | \(0.439156\pi\) | |||||||
\(434\) | 2.42705 | − | 1.76336i | 0.116502 | − | 0.0846438i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.0902 | + | 9.51057i | 0.626905 | + | 0.455473i | ||||
\(437\) | −28.3399 | − | 39.0066i | −1.35568 | − | 1.86594i | ||||
\(438\) | 3.26944 | + | 4.50000i | 0.156220 | + | 0.215018i | ||||
\(439\) | 4.83688 | + | 3.51420i | 0.230852 | + | 0.167724i | 0.697198 | − | 0.716879i | \(-0.254430\pi\) |
−0.466346 | + | 0.884602i | \(0.654430\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.09017 | + | 5.15131i | −0.337627 | + | 0.245300i | ||||
\(442\) | −2.17963 | − | 0.708204i | −0.103674 | − | 0.0336858i | ||||
\(443\) | 12.0557i | 0.572785i | 0.958112 | + | 0.286392i | \(0.0924561\pi\) | ||||
−0.958112 | + | 0.286392i | \(0.907544\pi\) | |||||||
\(444\) | 2.11803 | − | 6.51864i | 0.100517 | − | 0.309361i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.23607 | + | 13.0373i | 0.200584 | + | 0.617333i | ||||
\(447\) | 13.2618 | − | 4.30902i | 0.627261 | − | 0.203810i | ||||
\(448\) | 0.224514 | − | 0.309017i | 0.0106073 | − | 0.0145997i | ||||
\(449\) | −20.3262 | −0.959254 | −0.479627 | − | 0.877472i | \(-0.659228\pi\) | ||||
−0.479627 | + | 0.877472i | \(0.659228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | 9.64932 | − | 13.2812i | 0.453866 | − | 0.624693i | ||||
\(453\) | 5.29007 | − | 1.71885i | 0.248549 | − | 0.0807585i | ||||
\(454\) | −3.67376 | − | 11.3067i | −0.172418 | − | 0.530649i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.04508 | − | 12.4495i | 0.189428 | − | 0.583001i | ||||
\(457\) | − | 5.41641i | − | 0.253369i | −0.991943 | − | 0.126684i | \(-0.959566\pi\) | ||
0.991943 | − | 0.126684i | \(-0.0404336\pi\) | |||||||
\(458\) | 4.87380 | + | 1.58359i | 0.227738 | + | 0.0739964i | ||||
\(459\) | 3.09017 | − | 2.24514i | 0.144237 | − | 0.104794i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.7533 | − | 13.6251i | −0.873428 | − | 0.634582i | 0.0580768 | − | 0.998312i | \(-0.481503\pi\) |
−0.931505 | + | 0.363730i | \(0.881503\pi\) | |||||||
\(462\) | 0.449028 | + | 0.618034i | 0.0208907 | + | 0.0287535i | ||||
\(463\) | −9.47781 | − | 13.0451i | −0.440471 | − | 0.606257i | 0.529846 | − | 0.848094i | \(-0.322250\pi\) |
−0.970317 | + | 0.241838i | \(0.922250\pi\) | |||||||
\(464\) | −2.07295 | − | 1.50609i | −0.0962342 | − | 0.0699183i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.47214 | + | 5.42882i | −0.346140 | + | 0.251485i | ||||
\(467\) | 27.0584 | + | 8.79180i | 1.25211 | + | 0.406836i | 0.858677 | − | 0.512517i | \(-0.171287\pi\) |
0.393435 | + | 0.919353i | \(0.371287\pi\) | |||||||
\(468\) | − | 15.7082i | − | 0.726112i | ||||||
\(469\) | 4.61803 | − | 14.2128i | 0.213241 | − | 0.656288i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.83688 | − | 8.73102i | −0.130717 | − | 0.402304i | ||||
\(472\) | 8.81678 | − | 2.86475i | 0.405825 | − | 0.131861i | ||||
\(473\) | −0.832544 | + | 1.14590i | −0.0382804 | + | 0.0526884i | ||||
\(474\) | −1.90983 | −0.0877214 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.00000 | −0.0916698 | ||||||||
\(477\) | 6.43288 | − | 8.85410i | 0.294541 | − | 0.405401i | ||||
\(478\) | 17.3233 | − | 5.62868i | 0.792349 | − | 0.257450i | ||||
\(479\) | 1.28115 | + | 3.94298i | 0.0585374 | + | 0.180160i | 0.976050 | − | 0.217548i | \(-0.0698059\pi\) |
−0.917512 | + | 0.397708i | \(0.869806\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.35410 | + | 19.5559i | −0.289722 | + | 0.891673i | ||||
\(482\) | − | 7.09017i | − | 0.322948i | ||||||
\(483\) | −12.6740 | − | 4.11803i | −0.576687 | − | 0.187377i | ||||
\(484\) | 13.6353 | − | 9.90659i | 0.619784 | − | 0.450300i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.00000 | − | 5.81234i | −0.362887 | − | 0.263653i | ||||
\(487\) | −5.63309 | − | 7.75329i | −0.255260 | − | 0.351335i | 0.662085 | − | 0.749429i | \(-0.269672\pi\) |
−0.917345 | + | 0.398094i | \(0.869672\pi\) | |||||||
\(488\) | −6.18812 | − | 8.51722i | −0.280123 | − | 0.385556i | ||||
\(489\) | 8.89919 | + | 6.46564i | 0.402435 | + | 0.292386i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.1353 | + | 21.8945i | −1.35999 | + | 0.988087i | −0.361539 | + | 0.932357i | \(0.617749\pi\) |
−0.998446 | + | 0.0557300i | \(0.982251\pi\) | |||||||
\(492\) | −8.05748 | − | 2.61803i | −0.363259 | − | 0.118030i | ||||
\(493\) | 1.05573i | 0.0475476i | ||||||||
\(494\) | −5.42705 | + | 16.7027i | −0.244175 | + | 0.751492i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.71885 | − | 5.29007i | −0.0771785 | − | 0.237531i | ||||
\(497\) | 6.74315 | − | 2.19098i | 0.302472 | − | 0.0982790i | ||||
\(498\) | −0.640786 | + | 0.881966i | −0.0287143 | + | 0.0395218i | ||||
\(499\) | 12.5623 | 0.562366 | 0.281183 | − | 0.959654i | \(-0.409273\pi\) | ||||
0.281183 | + | 0.959654i | \(0.409273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.56231 | −0.248506 | ||||||||
\(502\) | 2.47739 | − | 3.40983i | 0.110571 | − | 0.152188i | ||||
\(503\) | 10.0656 | − | 3.27051i | 0.448803 | − | 0.145825i | −0.0758907 | − | 0.997116i | \(-0.524180\pi\) |
0.524693 | + | 0.851291i | \(0.324180\pi\) | |||||||
\(504\) | 2.23607 | + | 6.88191i | 0.0996024 | + | 0.306545i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.20163 | + | 3.69822i | −0.0534188 | + | 0.164406i | ||||
\(507\) | − | 10.5623i | − | 0.469088i | ||||||
\(508\) | 24.4500 | + | 7.94427i | 1.08479 | + | 0.352470i | ||||
\(509\) | −3.78115 | + | 2.74717i | −0.167597 | + | 0.121766i | −0.668422 | − | 0.743782i | \(-0.733030\pi\) |
0.500825 | + | 0.865548i | \(0.333030\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.7812 | − | 8.55951i | −0.521168 | − | 0.378650i | ||||
\(512\) | 10.9964 | + | 15.1353i | 0.485977 | + | 0.668890i | ||||
\(513\) | −17.2048 | − | 23.6803i | −0.759609 | − | 1.04551i | ||||
\(514\) | 8.07295 | + | 5.86534i | 0.356083 | + | 0.258709i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.42705 | − | 1.76336i | 0.106845 | − | 0.0776274i | ||||
\(517\) | −1.17557 | − | 0.381966i | −0.0517015 | − | 0.0167988i | ||||
\(518\) | − | 4.23607i | − | 0.186122i | ||||||
\(519\) | 5.21885 | − | 16.0620i | 0.229082 | − | 0.705042i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.74671 | − | 14.6089i | −0.207957 | − | 0.640026i | −0.999579 | − | 0.0290150i | \(-0.990763\pi\) |
0.791622 | − | 0.611011i | \(-0.209237\pi\) | |||||||
\(522\) | 1.62460 | − | 0.527864i | 0.0711067 | − | 0.0231040i | ||||
\(523\) | −11.6699 | + | 16.0623i | −0.510291 | + | 0.702356i | −0.983968 | − | 0.178343i | \(-0.942926\pi\) |
0.473677 | + | 0.880699i | \(0.342926\pi\) | |||||||
\(524\) | −28.7984 | −1.25806 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.6525 | −0.595276 | ||||||||
\(527\) | −1.34708 | + | 1.85410i | −0.0586799 | + | 0.0807660i | ||||
\(528\) | 1.34708 | − | 0.437694i | 0.0586243 | − | 0.0190482i | ||||
\(529\) | −13.8541 | − | 42.6385i | −0.602352 | − | 1.85385i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.56231 | − | 7.88597i | 0.111195 | − | 0.342222i | ||||
\(532\) | 15.3262i | 0.664477i | ||||||||
\(533\) | 24.1724 | + | 7.85410i | 1.04702 | + | 0.340199i | ||||
\(534\) | 4.47214 | − | 3.24920i | 0.193528 | − | 0.140607i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 16.7082 | + | 12.1392i | 0.721684 | + | 0.524334i | ||||
\(537\) | −5.56758 | − | 7.66312i | −0.240259 | − | 0.330688i | ||||
\(538\) | 6.26137 | + | 8.61803i | 0.269947 | + | 0.371550i | ||||
\(539\) | 2.70820 | + | 1.96763i | 0.116651 | + | 0.0847516i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.6180 | − | 7.71445i | 0.456505 | − | 0.331670i | −0.335654 | − | 0.941985i | \(-0.608957\pi\) |
0.792159 | + | 0.610315i | \(0.208957\pi\) | |||||||
\(542\) | 4.70228 | + | 1.52786i | 0.201980 | + | 0.0656274i | ||||
\(543\) | 13.7082i | 0.588275i | ||||||||
\(544\) | 1.32624 | − | 4.08174i | 0.0568620 | − | 0.175003i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.50000 | + | 4.61653i | 0.0641941 | + | 0.197569i | ||||
\(547\) | −33.0095 | + | 10.7254i | −1.41138 | + | 0.458586i | −0.912854 | − | 0.408287i | \(-0.866126\pi\) |
−0.498529 | + | 0.866873i | \(0.666126\pi\) | |||||||
\(548\) | −5.65334 | + | 7.78115i | −0.241499 | + | 0.332394i | ||||
\(549\) | −9.41641 | −0.401882 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.09017 | 0.344653 | ||||||||
\(552\) | 10.8249 | − | 14.8992i | 0.460738 | − | 0.634152i | ||||
\(553\) | 4.75528 | − | 1.54508i | 0.202215 | − | 0.0657037i | ||||
\(554\) | 2.15654 | + | 6.63715i | 0.0916227 | + | 0.281986i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.50000 | + | 7.69421i | −0.106024 | + | 0.326307i | ||||
\(557\) | − | 9.23607i | − | 0.391345i | −0.980669 | − | 0.195672i | \(-0.937311\pi\) | ||
0.980669 | − | 0.195672i | \(-0.0626889\pi\) | |||||||
\(558\) | 3.52671 | + | 1.14590i | 0.149298 | + | 0.0485097i | ||||
\(559\) | −7.28115 | + | 5.29007i | −0.307960 | + | 0.223746i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.472136 | − | 0.343027i | −0.0199336 | − | 0.0144826i | ||||
\(562\) | −0.396027 | − | 0.545085i | −0.0167054 | − | 0.0229930i | ||||
\(563\) | −5.65334 | − | 7.78115i | −0.238260 | − | 0.327936i | 0.673097 | − | 0.739555i | \(-0.264964\pi\) |
−0.911356 | + | 0.411618i | \(0.864964\pi\) | |||||||
\(564\) | 2.11803 | + | 1.53884i | 0.0891853 | + | 0.0647969i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.5729 | − | 8.40824i | 0.486447 | − | 0.353425i | ||||
\(567\) | 1.53884 | + | 0.500000i | 0.0646253 | + | 0.0209980i | ||||
\(568\) | 9.79837i | 0.411131i | ||||||||
\(569\) | −9.10739 | + | 28.0297i | −0.381802 | + | 1.17506i | 0.556972 | + | 0.830531i | \(0.311963\pi\) |
−0.938774 | + | 0.344534i | \(0.888037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.92705 | + | 30.5523i | 0.415434 | + | 1.27857i | 0.911862 | + | 0.410497i | \(0.134645\pi\) |
−0.496428 | + | 0.868078i | \(0.665355\pi\) | |||||||
\(572\) | −5.70634 | + | 1.85410i | −0.238594 | + | 0.0775239i | ||||
\(573\) | −14.2128 | + | 19.5623i | −0.593750 | + | 0.817227i | ||||
\(574\) | −5.23607 | −0.218549 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.472136 | 0.0196723 | ||||||||
\(577\) | −22.2048 | + | 30.5623i | −0.924399 | + | 1.27233i | 0.0376062 | + | 0.999293i | \(0.488027\pi\) |
−0.962005 | + | 0.273033i | \(0.911973\pi\) | |||||||
\(578\) | 9.64932 | − | 3.13525i | 0.401359 | − | 0.130409i | ||||
\(579\) | 1.76393 | + | 5.42882i | 0.0733065 | + | 0.225614i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.881966 | − | 2.71441i | 0.0365901 | − | 0.112613i | ||||
\(582\) | − | 1.76393i | − | 0.0731173i | ||||||
\(583\) | −3.97574 | − | 1.29180i | −0.164658 | − | 0.0535007i | ||||
\(584\) | 16.2812 | − | 11.8290i | 0.673719 | − | 0.489485i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.2361 | + | 10.3431i | 0.588087 | + | 0.427270i | ||||
\(587\) | 10.9964 | + | 15.1353i | 0.453870 | + | 0.624699i | 0.973224 | − | 0.229861i | \(-0.0738271\pi\) |
−0.519353 | + | 0.854560i | \(0.673827\pi\) | |||||||
\(588\) | −4.16750 | − | 5.73607i | −0.171865 | − | 0.236551i | ||||
\(589\) | 14.2082 | + | 10.3229i | 0.585439 | + | 0.425346i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.85410 | − | 5.70634i | 0.323075 | − | 0.234727i | ||||
\(592\) | −7.46969 | − | 2.42705i | −0.307003 | − | 0.0997512i | ||||
\(593\) | − | 22.0902i | − | 0.907135i | −0.891222 | − | 0.453567i | \(-0.850151\pi\) | ||
0.891222 | − | 0.453567i | \(-0.149849\pi\) | |||||||
\(594\) | −0.729490 | + | 2.24514i | −0.0299313 | + | 0.0921192i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.97214 | − | 21.4580i | −0.285590 | − | 0.878955i | ||||
\(597\) | 2.43690 | − | 0.791796i | 0.0997356 | − | 0.0324061i | ||||
\(598\) | −14.5231 | + | 19.9894i | −0.593894 | + | 0.817426i | ||||
\(599\) | 0.527864 | 0.0215679 | 0.0107840 | − | 0.999942i | \(-0.496567\pi\) | ||||
0.0107840 | + | 0.999942i | \(0.496567\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2705 | 1.47950 | 0.739752 | − | 0.672879i | \(-0.234943\pi\) | ||||
0.739752 | + | 0.672879i | \(0.234943\pi\) | |||||||
\(602\) | 1.08981 | − | 1.50000i | 0.0444175 | − | 0.0611354i | ||||
\(603\) | 17.5680 | − | 5.70820i | 0.715426 | − | 0.232456i | ||||
\(604\) | −2.78115 | − | 8.55951i | −0.113164 | − | 0.348281i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.42705 | + | 4.39201i | −0.0579700 | + | 0.178413i | ||||
\(607\) | 15.4377i | 0.626597i | 0.949655 | + | 0.313298i | \(0.101434\pi\) | ||||
−0.949655 | + | 0.313298i | \(0.898566\pi\) | |||||||
\(608\) | −31.2789 | − | 10.1631i | −1.26853 | − | 0.412169i | ||||
\(609\) | 1.80902 | − | 1.31433i | 0.0733051 | − | 0.0532592i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.35410 | − | 4.61653i | −0.257059 | − | 0.186765i | ||||
\(612\) | −1.45309 | − | 2.00000i | −0.0587375 | − | 0.0808452i | ||||
\(613\) | −18.7966 | − | 25.8713i | −0.759188 | − | 1.04493i | −0.997281 | − | 0.0736905i | \(-0.976522\pi\) |
0.238093 | − | 0.971242i | \(-0.423478\pi\) | |||||||
\(614\) | 2.38197 | + | 1.73060i | 0.0961283 | + | 0.0698413i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.23607 | − | 1.62460i | 0.0900937 | − | 0.0654569i | ||||
\(617\) | −9.28605 | − | 3.01722i | −0.373842 | − | 0.121469i | 0.116069 | − | 0.993241i | \(-0.462971\pi\) |
−0.489911 | + | 0.871772i | \(0.662971\pi\) | |||||||
\(618\) | − | 7.14590i | − | 0.287450i | ||||||
\(619\) | −12.1976 | + | 37.5402i | −0.490261 | + | 1.50887i | 0.333952 | + | 0.942590i | \(0.391618\pi\) |
−0.824213 | + | 0.566279i | \(0.808382\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.7254 | − | 39.1648i | −0.510654 | − | 1.57163i | ||||
\(622\) | −17.3435 | + | 5.63525i | −0.695412 | + | 0.225953i | ||||
\(623\) | −8.50651 | + | 11.7082i | −0.340806 | + | 0.469079i | ||||
\(624\) | 9.00000 | 0.360288 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −13.1246 | −0.524565 | ||||||||
\(627\) | −2.62866 | + | 3.61803i | −0.104978 | + | 0.144490i | ||||
\(628\) | −14.1271 | + | 4.59017i | −0.563732 | + | 0.183168i | ||||
\(629\) | 1.00000 | + | 3.07768i | 0.0398726 | + | 0.122715i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.78115 | + | 5.48183i | −0.0709066 | + | 0.218228i | −0.980230 | − | 0.197862i | \(-0.936600\pi\) |
0.909323 | + | 0.416090i | \(0.136600\pi\) | |||||||
\(632\) | 6.90983i | 0.274858i | ||||||||
\(633\) | 12.5352 | + | 4.07295i | 0.498231 | + | 0.161885i | ||||
\(634\) | −11.8262 | + | 8.59226i | −0.469680 | + | 0.341242i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.16312 | + | 5.20431i | 0.284036 | + | 0.206364i | ||||
\(637\) | 12.5025 | + | 17.2082i | 0.495367 | + | 0.681814i | ||||
\(638\) | −0.383516 | − | 0.527864i | −0.0151835 | − | 0.0208983i | ||||
\(639\) | 7.09017 | + | 5.15131i | 0.280483 | + | 0.203783i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.16312 | + | 5.93085i | −0.322424 | + | 0.234255i | −0.737209 | − | 0.675665i | \(-0.763857\pi\) |
0.414785 | + | 0.909919i | \(0.363857\pi\) | |||||||
\(642\) | −6.12261 | − | 1.98936i | −0.241640 | − | 0.0785137i | ||||
\(643\) | 22.8328i | 0.900438i | 0.892918 | + | 0.450219i | \(0.148654\pi\) | ||||
−0.892918 | + | 0.450219i | \(0.851346\pi\) | |||||||
\(644\) | −6.66312 | + | 20.5070i | −0.262564 | + | 0.808088i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.854102 | + | 2.62866i | 0.0336042 | + | 0.103423i | ||||
\(647\) | 29.0462 | − | 9.43769i | 1.14193 | − | 0.371034i | 0.323829 | − | 0.946116i | \(-0.395030\pi\) |
0.818096 | + | 0.575082i | \(0.195030\pi\) | |||||||
\(648\) | −1.31433 | + | 1.80902i | −0.0516317 | + | 0.0710649i | ||||
\(649\) | −3.16718 | −0.124323 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.85410 | 0.190247 | ||||||||
\(652\) | 10.4616 | − | 14.3992i | 0.409709 | − | 0.563916i | ||||
\(653\) | −7.52270 | + | 2.44427i | −0.294386 | + | 0.0956518i | −0.452487 | − | 0.891771i | \(-0.649463\pi\) |
0.158101 | + | 0.987423i | \(0.449463\pi\) | |||||||
\(654\) | −1.90983 | − | 5.87785i | −0.0746803 | − | 0.229842i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.00000 | + | 9.23305i | −0.117130 | + | 0.360490i | ||||
\(657\) | − | 18.0000i | − | 0.702247i | ||||||
\(658\) | 1.53884 | + | 0.500000i | 0.0599903 | + | 0.0194920i | ||||
\(659\) | 19.7984 | − | 14.3844i | 0.771235 | − | 0.560335i | −0.131101 | − | 0.991369i | \(-0.541851\pi\) |
0.902336 | + | 0.431034i | \(0.141851\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.9164 | + | 23.9152i | 1.28030 | + | 0.930192i | 0.999562 | − | 0.0295922i | \(-0.00942086\pi\) |
0.280738 | + | 0.959784i | \(0.409421\pi\) | |||||||
\(662\) | 6.22088 | + | 8.56231i | 0.241781 | + | 0.332783i | ||||
\(663\) | −2.17963 | − | 3.00000i | −0.0846497 | − | 0.116510i | ||||
\(664\) | 3.19098 | + | 2.31838i | 0.123834 | + | 0.0899708i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.23607 | − | 3.07768i | 0.164144 | − | 0.119258i | ||||
\(667\) | 10.8249 | + | 3.51722i | 0.419142 | + | 0.136187i | ||||
\(668\) | 9.00000i | 0.348220i | ||||||||
\(669\) | −6.85410 | + | 21.0948i | −0.264995 | + | 0.815570i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.11146 | + | 3.42071i | 0.0429073 | + | 0.132055i | ||||
\(672\) | −8.64527 | + | 2.80902i | −0.333498 | + | 0.108360i | ||||
\(673\) | −5.98385 | + | 8.23607i | −0.230661 | + | 0.317477i | −0.908621 | − | 0.417621i | \(-0.862864\pi\) |
0.677961 | + | 0.735098i | \(0.262864\pi\) | |||||||
\(674\) | −0.708204 | −0.0272790 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.0902 | −0.657314 | ||||||||
\(677\) | −4.92680 | + | 6.78115i | −0.189352 | + | 0.260621i | −0.893129 | − | 0.449800i | \(-0.851495\pi\) |
0.703777 | + | 0.710421i | \(0.251495\pi\) | |||||||
\(678\) | −5.96361 | + | 1.93769i | −0.229031 | + | 0.0744167i | ||||
\(679\) | 1.42705 | + | 4.39201i | 0.0547652 | + | 0.168550i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.94427 | − | 18.2946i | 0.227785 | − | 0.701050i | ||||
\(682\) | − | 1.41641i | − | 0.0542371i | ||||||
\(683\) | −4.30625 | − | 1.39919i | −0.164774 | − | 0.0535384i | 0.225468 | − | 0.974251i | \(-0.427609\pi\) |
−0.390242 | + | 0.920712i | \(0.627609\pi\) | |||||||
\(684\) | −15.3262 | + | 11.1352i | −0.586013 | + | 0.425764i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.20820 | − | 6.69015i | −0.351571 | − | 0.255431i | ||||
\(687\) | 4.87380 | + | 6.70820i | 0.185947 | + | 0.255934i | ||||
\(688\) | −2.02063 | − | 2.78115i | −0.0770356 | − | 0.106030i | ||||
\(689\) | −21.4894 | − | 15.6129i | −0.818679 | − | 0.594805i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.20820 | + | 1.60435i | −0.0840040 | + | 0.0610325i | −0.628995 | − | 0.777410i | \(-0.716533\pi\) |
0.544991 | + | 0.838442i | \(0.316533\pi\) | |||||||
\(692\) | −25.9888 | − | 8.44427i | −0.987946 | − | 0.321003i | ||||
\(693\) | − | 2.47214i | − | 0.0939087i | ||||||
\(694\) | 5.93769 | − | 18.2743i | 0.225392 | − | 0.693685i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.954915 | + | 2.93893i | 0.0361960 | + | 0.111400i | ||||
\(697\) | 3.80423 | − | 1.23607i | 0.144095 | − | 0.0468194i | ||||
\(698\) | 3.01217 | − | 4.14590i | 0.114012 | − | 0.156925i | ||||
\(699\) | −14.9443 | −0.565244 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.0132 | 1.32243 | 0.661214 | − | 0.750197i | \(-0.270041\pi\) | ||||
0.661214 | + | 0.750197i | \(0.270041\pi\) | |||||||
\(702\) | −8.81678 | + | 12.1353i | −0.332768 | + | 0.458016i | ||||
\(703\) | 23.5847 | − | 7.66312i | 0.889512 | − | 0.289020i | ||||
\(704\) | −0.0557281 | − | 0.171513i | −0.00210033 | − | 0.00646416i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.60081 | − | 14.1598i | 0.173154 | − | 0.532913i | ||||
\(707\) | − | 12.0902i | − | 0.454698i | ||||||
\(708\) | 6.37988 | + | 2.07295i | 0.239771 | + | 0.0779062i | ||||
\(709\) | 27.1353 | − | 19.7149i | 1.01909 | − | 0.740409i | 0.0529906 | − | 0.998595i | \(-0.483125\pi\) |
0.966095 | + | 0.258186i | \(0.0831247\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.00000 | + | 3.63271i | 0.187515 | + | 0.136237i | ||||
\(712\) | −11.7557 | − | 16.1803i | −0.440564 | − | 0.606384i | ||||
\(713\) | 14.5231 | + | 19.9894i | 0.543895 | + | 0.748607i | ||||
\(714\) | 0.618034 | + | 0.449028i | 0.0231293 | + | 0.0168044i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.3992 | + | 9.00854i | −0.463379 | + | 0.336665i | ||||
\(717\) | 28.0297 | + | 9.10739i | 1.04679 | + | 0.340122i | ||||
\(718\) | − | 17.7639i | − | 0.662944i | ||||||
\(719\) | 11.3435 | − | 34.9116i | 0.423040 | − | 1.30198i | −0.481819 | − | 0.876271i | \(-0.660024\pi\) |
0.904859 | − | 0.425712i | \(-0.139976\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.78115 | + | 17.7926i | 0.215301 | + | 0.662630i | ||||
\(722\) | 8.97578 | − | 2.91641i | 0.334044 | − | 0.108537i | ||||
\(723\) | 6.74315 | − | 9.28115i | 0.250781 | − | 0.345170i | ||||
\(724\) | 22.1803 | 0.824326 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.43769 | −0.238925 | ||||||||
\(727\) | −2.60841 | + | 3.59017i | −0.0967406 | + | 0.133152i | −0.854643 | − | 0.519216i | \(-0.826224\pi\) |
0.757903 | + | 0.652368i | \(0.226224\pi\) | |||||||
\(728\) | 16.7027 | − | 5.42705i | 0.619045 | − | 0.201140i | ||||
\(729\) | −4.01722 | − | 12.3637i | −0.148786 | − | 0.457916i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.437694 | + | 1.34708i | −0.0161887 | + | 0.0498237i | ||||
\(732\) | − | 7.61803i | − | 0.281571i | ||||||
\(733\) | 25.6583 | + | 8.33688i | 0.947710 | + | 0.307930i | 0.741785 | − | 0.670638i | \(-0.233980\pi\) |
0.205925 | + | 0.978568i | \(0.433980\pi\) | |||||||
\(734\) | −2.71885 | + | 1.97536i | −0.100354 | + | 0.0729118i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −37.4336 | − | 27.1971i | −1.37982 | − | 1.00250i | ||||
\(737\) | −4.14725 | − | 5.70820i | −0.152766 | − | 0.210264i | ||||
\(738\) | −3.80423 | − | 5.23607i | −0.140035 | − | 0.192742i | ||||
\(739\) | −25.0623 | − | 18.2088i | −0.921932 | − | 0.669823i | 0.0220723 | − | 0.999756i | \(-0.492974\pi\) |
−0.944004 | + | 0.329934i | \(0.892974\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.9894 | + | 16.7027i | −0.844535 | + | 0.613591i | ||||
\(742\) | 5.20431 | + | 1.69098i | 0.191056 | + | 0.0620779i | ||||
\(743\) | − | 16.3607i | − | 0.600215i | −0.953905 | − | 0.300108i | \(-0.902977\pi\) | ||
0.953905 | − | 0.300108i | \(-0.0970226\pi\) | |||||||
\(744\) | −2.07295 | + | 6.37988i | −0.0759980 | + | 0.233898i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.00658 | + | 3.09793i | 0.0368534 | + | 0.113423i | ||||
\(747\) | 3.35520 | − | 1.09017i | 0.122760 | − | 0.0398872i | ||||
\(748\) | −0.555029 | + | 0.763932i | −0.0202939 | + | 0.0279321i | ||||
\(749\) | 16.8541 | 0.615835 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.8885 | −1.49204 | −0.746022 | − | 0.665921i | \(-0.768039\pi\) | ||||
−0.746022 | + | 0.665921i | \(0.768039\pi\) | |||||||
\(752\) | 1.76336 | − | 2.42705i | 0.0643030 | − | 0.0885054i | ||||
\(753\) | 6.48588 | − | 2.10739i | 0.236359 | − | 0.0767976i | ||||
\(754\) | −1.28115 | − | 3.94298i | −0.0466568 | − | 0.143595i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.04508 | + | 12.4495i | −0.147118 | + | 0.452784i | ||||
\(757\) | − | 3.58359i | − | 0.130248i | −0.997877 | − | 0.0651239i | \(-0.979256\pi\) | ||
0.997877 | − | 0.0651239i | \(-0.0207443\pi\) | |||||||
\(758\) | −20.3355 | − | 6.60739i | −0.738617 | − | 0.239991i | ||||
\(759\) | −5.09017 | + | 3.69822i | −0.184761 | + | 0.134237i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.2984 | − | 22.0131i | −1.09832 | − | 0.797973i | −0.117531 | − | 0.993069i | \(-0.537498\pi\) |
−0.980784 | + | 0.195096i | \(0.937498\pi\) | |||||||
\(762\) | −5.77185 | − | 7.94427i | −0.209092 | − | 0.287791i | ||||
\(763\) | 9.51057 | + | 13.0902i | 0.344306 | + | 0.473896i | ||||
\(764\) | 31.6525 | + | 22.9969i | 1.14515 | + | 0.831998i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.68034 | − | 4.12701i | 0.205239 | − | 0.149115i | ||||
\(767\) | −19.1396 | − | 6.21885i | −0.691092 | − | 0.224550i | ||||
\(768\) | − | 6.56231i | − | 0.236797i | ||||||
\(769\) | 4.14590 | − | 12.7598i | 0.149505 | − | 0.460129i | −0.848058 | − | 0.529904i | \(-0.822228\pi\) |
0.997563 | + | 0.0697749i | \(0.0222281\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.98936 | + | 15.3557i | 0.179687 | + | 0.553021i | ||||
\(772\) | 8.78402 | − | 2.85410i | 0.316144 | − | 0.102721i | ||||
\(773\) | 19.4904 | − | 26.8262i | 0.701021 | − | 0.964873i | −0.298923 | − | 0.954277i | \(-0.596627\pi\) |
0.999944 | − | 0.0105954i | \(-0.00337269\pi\) | |||||||
\(774\) | 2.29180 | 0.0823769 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.38197 | −0.229099 | ||||||||
\(777\) | 4.02874 | − | 5.54508i | 0.144530 | − | 0.198929i | ||||
\(778\) | −8.81678 | + | 2.86475i | −0.316097 | + | 0.102706i | ||||
\(779\) | −9.47214 | − | 29.1522i | −0.339374 | − | 1.04449i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.03444 | − | 3.18368i | 0.0370152 | − | 0.113921i | ||||
\(782\) | 3.88854i | 0.139054i | ||||||||
\(783\) | 6.57164 | + | 2.13525i | 0.234851 | + | 0.0763078i | ||||
\(784\) | −6.57295 | + | 4.77553i | −0.234748 | + | 0.170555i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.89919 | + | 6.46564i | 0.317423 | + | 0.230622i | ||||
\(787\) | −20.0907 | − | 27.6525i | −0.716156 | − | 0.985704i | −0.999643 | − | 0.0267281i | \(-0.991491\pi\) |
0.283487 | − | 0.958976i | \(-0.408509\pi\) | |||||||
\(788\) | −9.23305 | − | 12.7082i | −0.328914 | − | 0.452711i | ||||
\(789\) | −17.8713 | − | 12.9843i | −0.636236 | − | 0.462252i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.2812 | − | 9.64932i | 0.472223 | − | 0.343090i | ||||
\(792\) | 3.24920 | + | 1.05573i | 0.115455 | + | 0.0375137i | ||||
\(793\) | 22.8541i | 0.811573i | ||||||||
\(794\) | 0.00657781 | − | 0.0202444i | 0.000233438 | − | 0.000718447i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.28115 | − | 3.94298i | −0.0454093 | − | 0.139755i | ||||
\(797\) | 13.5393 | − | 4.39919i | 0.479587 | − | 0.155827i | −0.0592400 | − | 0.998244i | \(-0.518868\pi\) |
0.538827 | + | 0.842417i | \(0.318868\pi\) | |||||||
\(798\) | 3.44095 | − | 4.73607i | 0.121808 | − | 0.167655i | ||||
\(799\) | −1.23607 | −0.0437289 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.8885 | −0.632061 | ||||||||
\(802\) | 8.20875 | − | 11.2984i | 0.289861 | − | 0.398959i | ||||
\(803\) | −6.53888 | + | 2.12461i | −0.230752 | + | 0.0749759i | ||||
\(804\) | 4.61803 | + | 14.2128i | 0.162866 | + | 0.501248i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.78115 | − | 8.55951i | 0.0979619 | − | 0.301496i | ||||
\(807\) | 17.2361i | 0.606738i | ||||||||
\(808\) | 15.8904 | + | 5.16312i | 0.559024 | + | 0.181638i | ||||
\(809\) | −12.9271 | + | 9.39205i | −0.454491 | + | 0.330207i | −0.791366 | − | 0.611342i | \(-0.790630\pi\) |
0.336875 | + | 0.941549i | \(0.390630\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.04508 | + | 0.759299i | 0.0366979 | + | 0.0266626i | 0.605983 | − | 0.795478i | \(-0.292780\pi\) |
−0.569285 | + | 0.822140i | \(0.692780\pi\) | |||||||
\(812\) | −2.12663 | − | 2.92705i | −0.0746300 | − | 0.102719i | ||||
\(813\) | 4.70228 | + | 6.47214i | 0.164916 | + | 0.226988i | ||||
\(814\) | −1.61803 | − | 1.17557i | −0.0567121 | − | 0.0412037i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.14590 | − | 0.832544i | 0.0401145 | − | 0.0291449i | ||||
\(817\) | 10.3229 | + | 3.35410i | 0.361151 | + | 0.117345i | ||||
\(818\) | 17.5623i | 0.614052i | ||||||||
\(819\) | 4.85410 | − | 14.9394i | 0.169616 | − | 0.522025i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.08359 | + | 18.7234i | 0.212319 | + | 0.653450i | 0.999333 | + | 0.0365154i | \(0.0116258\pi\) |
−0.787014 | + | 0.616935i | \(0.788374\pi\) | |||||||
\(822\) | 3.49396 | − | 1.13525i | 0.121866 | − | 0.0395966i | ||||
\(823\) | 20.1562 | − | 27.7426i | 0.702601 | − | 0.967048i | −0.297323 | − | 0.954777i | \(-0.596094\pi\) |
0.999925 | − | 0.0122710i | \(-0.00390607\pi\) | |||||||
\(824\) | −25.8541 | −0.900670 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.14590 | 0.144254 | ||||||||
\(827\) | 17.6538 | − | 24.2984i | 0.613883 | − | 0.844937i | −0.383007 | − | 0.923745i | \(-0.625111\pi\) |
0.996890 | + | 0.0788082i | \(0.0251115\pi\) | |||||||
\(828\) | −25.3480 | + | 8.23607i | −0.880904 | + | 0.286223i | ||||
\(829\) | 9.00658 | + | 27.7194i | 0.312811 | + | 0.962734i | 0.976646 | + | 0.214855i | \(0.0689279\pi\) |
−0.663835 | + | 0.747879i | \(0.731072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.48936 | + | 10.7391i | −0.121044 | + | 0.372537i | ||||
\(832\) | − | 1.14590i | − | 0.0397269i | ||||||
\(833\) | 3.18368 | + | 1.03444i | 0.110308 | + | 0.0358413i | ||||
\(834\) | 2.50000 | − | 1.81636i | 0.0865679 | − | 0.0628953i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.85410 | + | 4.25325i | 0.202468 | + | 0.147102i | ||||
\(837\) | 8.81678 | + | 12.1353i | 0.304752 | + | 0.419456i | ||||
\(838\) | 0.191758 | + | 0.263932i | 0.00662416 | + | 0.00911738i | ||||
\(839\) | 3.35410 | + | 2.43690i | 0.115796 | + | 0.0841311i | 0.644176 | − | 0.764877i | \(-0.277200\pi\) |
−0.528380 | + | 0.849008i | \(0.677200\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.9164 | − | 15.9232i | 0.755738 | − | 0.549076i | ||||
\(842\) | −18.8091 | − | 6.11146i | −0.648205 | − | 0.210615i | ||||
\(843\) | − | 1.09017i | − | 0.0375474i | ||||||
\(844\) | 6.59017 | − | 20.2825i | 0.226843 | − | 0.698151i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.618034 | + | 1.90211i | 0.0212484 | + | 0.0653960i | ||||
\(847\) | 16.0292 | − | 5.20820i | 0.550770 | − | 0.178956i | ||||
\(848\) | 5.96361 | − | 8.20820i | 0.204791 | − | 0.281871i | ||||
\(849\) | 23.1459 | 0.794365 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.8885 | 1.19596 | ||||||||
\(852\) | −4.16750 | + | 5.73607i | −0.142776 | + | 0.196514i | ||||
\(853\) | −44.9897 | + | 14.6180i | −1.54042 | + | 0.500512i | −0.951491 | − | 0.307675i | \(-0.900449\pi\) |
−0.588926 | + | 0.808187i | \(0.700449\pi\) | |||||||
\(854\) | −1.45492 | − | 4.47777i | −0.0497862 | − | 0.153226i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.19756 | + | 22.1518i | −0.246008 | + | 0.757133i | ||||
\(857\) | 40.6869i | 1.38984i | 0.719088 | + | 0.694919i | \(0.244560\pi\) | ||||
−0.719088 | + | 0.694919i | \(0.755440\pi\) | |||||||
\(858\) | 2.17963 | + | 0.708204i | 0.0744113 | + | 0.0241777i | ||||
\(859\) | −22.9894 | + | 16.7027i | −0.784387 | + | 0.569890i | −0.906292 | − | 0.422651i | \(-0.861099\pi\) |
0.121906 | + | 0.992542i | \(0.461099\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.85410 | − | 4.97980i | −0.233587 | − | 0.169711i | ||||
\(862\) | 8.65778 | + | 11.9164i | 0.294885 | + | 0.405874i | ||||
\(863\) | 24.4297 | + | 33.6246i | 0.831597 | + | 1.14460i | 0.987624 | + | 0.156842i | \(0.0501314\pi\) |
−0.156027 | + | 0.987753i | \(0.549869\pi\) | |||||||
\(864\) | −22.7254 | − | 16.5110i | −0.773135 | − | 0.561715i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10.0729 | + | 7.31843i | −0.342293 | + | 0.248690i | ||||
\(867\) | 15.6129 | + | 5.07295i | 0.530243 | + | 0.172286i | ||||
\(868\) | − | 7.85410i | − | 0.266586i | ||||||
\(869\) | 0.729490 | − | 2.24514i | 0.0247463 | − | 0.0761612i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.8541 | − | 42.6385i | −0.469428 | − | 1.44475i | ||||
\(872\) | −21.2663 | + | 6.90983i | −0.720167 | + | 0.233996i | ||||
\(873\) | −3.35520 | + | 4.61803i | −0.113556 | + | 0.156297i | ||||
\(874\) | 29.7984 | 1.00795 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.5623 | 0.492015 | ||||||||
\(877\) | −17.9516 | + | 24.7082i | −0.606181 | + | 0.834337i | −0.996257 | − | 0.0864462i | \(-0.972449\pi\) |
0.390075 | + | 0.920783i | \(0.372449\pi\) | |||||||
\(878\) | −3.51420 | + | 1.14183i | −0.118598 | + | 0.0385350i | ||||
\(879\) | 8.79837 | + | 27.0786i | 0.296762 | + | 0.913339i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.34752 | − | 4.14725i | 0.0453992 | − | 0.139725i | −0.925787 | − | 0.378044i | \(-0.876597\pi\) |
0.971187 | + | 0.238320i | \(0.0765967\pi\) | |||||||
\(882\) | − | 5.41641i | − | 0.182380i | ||||||
\(883\) | −45.0957 | − | 14.6525i | −1.51759 | − | 0.493095i | −0.572500 | − | 0.819904i | \(-0.694026\pi\) |
−0.945090 | + | 0.326809i | \(0.894026\pi\) | |||||||
\(884\) | −4.85410 | + | 3.52671i | −0.163261 | + | 0.118616i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.02786 | − | 4.37950i | −0.202510 | − | 0.147132i | ||||
\(887\) | −3.46120 | − | 4.76393i | −0.116216 | − | 0.159957i | 0.746946 | − | 0.664885i | \(-0.231519\pi\) |
−0.863162 | + | 0.504927i | \(0.831519\pi\) | |||||||
\(888\) | 5.56758 | + | 7.66312i | 0.186836 | + | 0.257157i | ||||
\(889\) | 20.7984 | + | 15.1109i | 0.697555 | + | 0.506803i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.618034 | − | 0.449028i | 0.0207049 | − | 0.0150430i | ||||
\(892\) | 34.1320 | + | 11.0902i | 1.14283 | + | 0.371326i | ||||
\(893\) | 9.47214i | 0.316973i | ||||||||
\(894\) | −2.66312 | + | 8.19624i | −0.0890680 | + | 0.274123i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.69098 | + | 17.5150i | 0.190122 | + | 0.585137i | ||||
\(897\) | −38.0220 | + | 12.3541i | −1.26952 | + | 0.412491i | ||||
\(898\) | 7.38394 | − | 10.1631i | 0.246405 | − | 0.339148i | ||||
\(899\) | −4.14590 | −0.138273 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.18034 | −0.139267 | ||||||||
\(902\) | −1.45309 | + | 2.00000i | −0.0483824 | + | 0.0665927i | ||||
\(903\) | 2.85317 | − | 0.927051i | 0.0949475 | − | 0.0308503i | ||||
\(904\) | 7.01064 | + | 21.5765i | 0.233171 | + | 0.717625i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.06231 | + | 3.26944i | −0.0352927 | + | 0.108620i | ||||
\(907\) | − | 47.2492i | − | 1.56888i | −0.620202 | − | 0.784442i | \(-0.712949\pi\) | ||
0.620202 | − | 0.784442i | \(-0.287051\pi\) | |||||||
\(908\) | −29.6013 | − | 9.61803i | −0.982352 | − | 0.319186i | ||||
\(909\) | 12.0902 | − | 8.78402i | 0.401006 | − | 0.291348i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.9336 | + | 21.0215i | 0.958614 | + | 0.696474i | 0.952828 | − | 0.303510i | \(-0.0981584\pi\) |
0.00578548 | + | 0.999983i | \(0.498158\pi\) | |||||||
\(912\) | −6.37988 | − | 8.78115i | −0.211259 | − | 0.290773i | ||||
\(913\) | −0.792055 | − | 1.09017i | −0.0262132 | − | 0.0360794i | ||||
\(914\) | 2.70820 | + | 1.96763i | 0.0895794 | + | 0.0650833i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.8541 | − | 7.88597i | 0.358630 | − | 0.260560i | ||||
\(917\) | −27.3889 | − | 8.89919i | −0.904461 | − | 0.293877i | ||||
\(918\) | 2.36068i | 0.0779140i | ||||||||
\(919\) | 0.551663 | − | 1.69784i | 0.0181977 | − | 0.0560067i | −0.941545 | − | 0.336886i | \(-0.890626\pi\) |
0.959743 | + | 0.280880i | \(0.0906262\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.47214 | + | 4.53077i | 0.0485085 | + | 0.149294i | ||||
\(922\) | 13.6251 | − | 4.42705i | 0.448718 | − | 0.145797i | ||||
\(923\) | 12.5025 | − | 17.2082i | 0.411525 | − | 0.566415i | ||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.96556 | 0.327489 | ||||||||
\(927\) | −13.5923 | + | 18.7082i | −0.446430 | + | 0.614458i | ||||
\(928\) | 7.38394 | − | 2.39919i | 0.242390 | − | 0.0787572i | ||||
\(929\) | 11.3197 | + | 34.8383i | 0.371386 | + | 1.14301i | 0.945885 | + | 0.324503i | \(0.105197\pi\) |
−0.574499 | + | 0.818506i | \(0.694803\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.92705 | − | 24.3970i | 0.259799 | − | 0.799578i | ||||
\(932\) | 24.1803i | 0.792053i | ||||||||
\(933\) | −28.0624 | − | 9.11803i | −0.918722 | − | 0.298511i | ||||
\(934\) | −14.2254 | + | 10.3354i | −0.465470 | + | 0.338184i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 17.5623 | + | 12.7598i | 0.574042 | + | 0.417066i | ||||
\(937\) | 30.1360 | + | 41.4787i | 0.984502 | + | 1.35505i | 0.934369 | + | 0.356308i | \(0.115965\pi\) |
0.0501333 | + | 0.998743i | \(0.484035\pi\) | |||||||
\(938\) | 5.42882 | + | 7.47214i | 0.177257 | + | 0.243974i | ||||
\(939\) | −17.1803 | − | 12.4822i | −0.560659 | − | 0.407343i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.8435 | − | 11.5109i | 0.516482 | − | 0.375246i | −0.298795 | − | 0.954317i | \(-0.596585\pi\) |
0.815277 | + | 0.579071i | \(0.196585\pi\) | |||||||
\(942\) | 5.39607 | + | 1.75329i | 0.175813 | + | 0.0571252i | ||||
\(943\) | − | 43.1246i | − | 1.40433i | ||||||
\(944\) | 2.37539 | − | 7.31069i | 0.0773123 | − | 0.237943i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.270510 | − | 0.832544i | −0.00879503 | − | 0.0270683i | ||||
\(947\) | −27.2501 | + | 8.85410i | −0.885510 | + | 0.287720i | −0.716243 | − | 0.697851i | \(-0.754140\pi\) |
−0.169267 | + | 0.985570i | \(0.554140\pi\) | |||||||
\(948\) | −2.93893 | + | 4.04508i | −0.0954519 | + | 0.131378i | ||||
\(949\) | −43.6869 | −1.41814 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.6525 | −0.766984 | ||||||||
\(952\) | 1.62460 | − | 2.23607i | 0.0526535 | − | 0.0724714i | ||||
\(953\) | −33.0422 | + | 10.7361i | −1.07034 | + | 0.347775i | −0.790621 | − | 0.612306i | \(-0.790242\pi\) |
−0.279721 | + | 0.960081i | \(0.590242\pi\) | |||||||
\(954\) | 2.09017 | + | 6.43288i | 0.0676718 | + | 0.208272i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.7361 | − | 45.3530i | 0.476598 | − | 1.46682i | ||||
\(957\) | − | 1.05573i | − | 0.0341268i | ||||||
\(958\) | −2.43690 | − | 0.791796i | −0.0787326 | − | 0.0255818i | ||||
\(959\) | −7.78115 | + | 5.65334i | −0.251267 | + | 0.182556i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.7984 | + | 12.9313i | 0.574141 | + | 0.417138i | ||||
\(962\) | −7.46969 | − | 10.2812i | −0.240833 | − | 0.331478i | ||||
\(963\) | 12.2452 | + | 16.8541i | 0.394597 | + | 0.543116i | ||||
\(964\) | −15.0172 | − | 10.9106i | −0.483672 | − | 0.351408i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.66312 | − | 4.84104i | 0.214382 | − | 0.155758i | ||||
\(967\) | −37.9363 | − | 12.3262i | −1.21995 | − | 0.396385i | −0.372885 | − | 0.927878i | \(-0.621631\pi\) |
−0.847063 | + | 0.531493i | \(0.821631\pi\) | |||||||
\(968\) | 23.2918i | 0.748627i | ||||||||
\(969\) | −1.38197 | + | 4.25325i | −0.0443951 | + | 0.136634i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.04508 | + | 3.21644i | 0.0335384 | + | 0.103220i | 0.966424 | − | 0.256951i | \(-0.0827180\pi\) |
−0.932886 | + | 0.360172i | \(0.882718\pi\) | |||||||
\(972\) | −24.6215 | + | 8.00000i | −0.789734 | + | 0.256600i | ||||
\(973\) | −4.75528 | + | 6.54508i | −0.152447 | + | 0.209826i | ||||
\(974\) | 5.92299 | 0.189785 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.72949 | −0.279424 | ||||||||
\(977\) | 19.7804 | − | 27.2254i | 0.632832 | − | 0.871019i | −0.365376 | − | 0.930860i | \(-0.619060\pi\) |
0.998208 | + | 0.0598416i | \(0.0190595\pi\) | |||||||
\(978\) | −6.46564 | + | 2.10081i | −0.206748 | + | 0.0671766i | ||||
\(979\) | 2.11146 | + | 6.49839i | 0.0674824 | + | 0.207690i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.18034 | + | 19.0211i | −0.197323 | + | 0.607298i | ||||
\(982\) | − | 23.0213i | − | 0.734639i | ||||||
\(983\) | 7.02067 | + | 2.28115i | 0.223924 | + | 0.0727575i | 0.418830 | − | 0.908064i | \(-0.362440\pi\) |
−0.194906 | + | 0.980822i | \(0.562440\pi\) | |||||||
\(984\) | 9.47214 | − | 6.88191i | 0.301961 | − | 0.219387i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.527864 | − | 0.383516i | −0.0168106 | − | 0.0122136i | ||||
\(987\) | 1.53884 | + | 2.11803i | 0.0489819 | + | 0.0674178i | ||||
\(988\) | 27.0256 | + | 37.1976i | 0.859799 | + | 1.18341i | ||||
\(989\) | 12.3541 | + | 8.97578i | 0.392838 | + | 0.285413i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.7533 | + | 17.2578i | −0.754548 | + | 0.548211i | −0.897233 | − | 0.441557i | \(-0.854426\pi\) |
0.142685 | + | 0.989768i | \(0.454426\pi\) | |||||||
\(992\) | 16.0292 | + | 5.20820i | 0.508928 | + | 0.165361i | ||||
\(993\) | 17.1246i | 0.543433i | ||||||||
\(994\) | −1.35410 | + | 4.16750i | −0.0429495 | + | 0.132185i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.881966 | + | 2.71441i | 0.0279462 | + | 0.0860094i | ||||
\(997\) | −10.3556 | + | 3.36475i | −0.327966 | + | 0.106563i | −0.468372 | − | 0.883531i | \(-0.655159\pi\) |
0.140406 | + | 0.990094i | \(0.455159\pi\) | |||||||
\(998\) | −4.56352 | + | 6.28115i | −0.144456 | + | 0.198826i | ||||
\(999\) | 21.1803 | 0.670116 |
(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 | 125.2.e.a.49.1 | 8 | ||
5.2 | odd | 4 | 25.2.d.a.16.1 | yes | 4 | ||
5.3 | odd | 4 | 125.2.d.a.76.1 | 4 | |||
5.4 | even | 2 | inner | 125.2.e.a.49.2 | 8 | ||
15.2 | even | 4 | 225.2.h.b.91.1 | 4 | |||
20.7 | even | 4 | 400.2.u.b.241.1 | 4 | |||
25.2 | odd | 20 | 25.2.d.a.11.1 | ✓ | 4 | ||
25.3 | odd | 20 | 625.2.d.b.126.1 | 4 | |||
25.4 | even | 10 | 625.2.e.c.499.1 | 8 | |||
25.6 | even | 5 | 625.2.b.a.624.2 | 4 | |||
25.8 | odd | 20 | 625.2.a.c.1.1 | 2 | |||
25.9 | even | 10 | 625.2.e.c.124.2 | 8 | |||
25.11 | even | 5 | inner | 125.2.e.a.74.2 | 8 | ||
25.12 | odd | 20 | 625.2.d.h.501.1 | 4 | |||
25.13 | odd | 20 | 625.2.d.b.501.1 | 4 | |||
25.14 | even | 10 | inner | 125.2.e.a.74.1 | 8 | ||
25.16 | even | 5 | 625.2.e.c.124.1 | 8 | |||
25.17 | odd | 20 | 625.2.a.b.1.2 | 2 | |||
25.19 | even | 10 | 625.2.b.a.624.3 | 4 | |||
25.21 | even | 5 | 625.2.e.c.499.2 | 8 | |||
25.22 | odd | 20 | 625.2.d.h.126.1 | 4 | |||
25.23 | odd | 20 | 125.2.d.a.51.1 | 4 | |||
75.2 | even | 20 | 225.2.h.b.136.1 | 4 | |||
75.8 | even | 20 | 5625.2.a.d.1.2 | 2 | |||
75.17 | even | 20 | 5625.2.a.f.1.1 | 2 | |||
100.27 | even | 20 | 400.2.u.b.161.1 | 4 | |||
100.67 | even | 20 | 10000.2.a.c.1.2 | 2 | |||
100.83 | even | 20 | 10000.2.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.d.a.11.1 | ✓ | 4 | 25.2 | odd | 20 | ||
25.2.d.a.16.1 | yes | 4 | 5.2 | odd | 4 | ||
125.2.d.a.51.1 | 4 | 25.23 | odd | 20 | |||
125.2.d.a.76.1 | 4 | 5.3 | odd | 4 | |||
125.2.e.a.49.1 | 8 | 1.1 | even | 1 | trivial | ||
125.2.e.a.49.2 | 8 | 5.4 | even | 2 | inner | ||
125.2.e.a.74.1 | 8 | 25.14 | even | 10 | inner | ||
125.2.e.a.74.2 | 8 | 25.11 | even | 5 | inner | ||
225.2.h.b.91.1 | 4 | 15.2 | even | 4 | |||
225.2.h.b.136.1 | 4 | 75.2 | even | 20 | |||
400.2.u.b.161.1 | 4 | 100.27 | even | 20 | |||
400.2.u.b.241.1 | 4 | 20.7 | even | 4 | |||
625.2.a.b.1.2 | 2 | 25.17 | odd | 20 | |||
625.2.a.c.1.1 | 2 | 25.8 | odd | 20 | |||
625.2.b.a.624.2 | 4 | 25.6 | even | 5 | |||
625.2.b.a.624.3 | 4 | 25.19 | even | 10 | |||
625.2.d.b.126.1 | 4 | 25.3 | odd | 20 | |||
625.2.d.b.501.1 | 4 | 25.13 | odd | 20 | |||
625.2.d.h.126.1 | 4 | 25.22 | odd | 20 | |||
625.2.d.h.501.1 | 4 | 25.12 | odd | 20 | |||
625.2.e.c.124.1 | 8 | 25.16 | even | 5 | |||
625.2.e.c.124.2 | 8 | 25.9 | even | 10 | |||
625.2.e.c.499.1 | 8 | 25.4 | even | 10 | |||
625.2.e.c.499.2 | 8 | 25.21 | even | 5 | |||
5625.2.a.d.1.2 | 2 | 75.8 | even | 20 | |||
5625.2.a.f.1.1 | 2 | 75.17 | even | 20 | |||
10000.2.a.c.1.2 | 2 | 100.67 | even | 20 | |||
10000.2.a.l.1.1 | 2 | 100.83 | even | 20 |