Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(126,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.126");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.d (of order \(5\), 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: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 501.3 | ||
Root | \(-3.18910i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.501 |
Dual form | 625.2.d.p.126.3 |
$q$-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 \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.154814 | + | 0.476469i | −0.109470 | + | 0.336915i | −0.990754 | − | 0.135674i | \(-0.956680\pi\) |
0.881283 | + | 0.472588i | \(0.156680\pi\) | |||||||
\(3\) | 2.50250 | + | 1.81817i | 1.44482 | + | 1.04972i | 0.987008 | + | 0.160671i | \(0.0513658\pi\) |
0.457809 | + | 0.889050i | \(0.348634\pi\) | |||||||
\(4\) | 1.41498 | + | 1.02804i | 0.707489 | + | 0.514021i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.25372 | + | 0.910884i | −0.511831 | + | 0.371867i | ||||
\(7\) | −0.0237879 | −0.00899097 | −0.00449549 | − | 0.999990i | \(-0.501431\pi\) | ||||
−0.00449549 | + | 0.999990i | \(0.501431\pi\) | |||||||
\(8\) | −1.51951 | + | 1.10399i | −0.537227 | + | 0.390318i | ||||
\(9\) | 2.02970 | + | 6.24676i | 0.676566 | + | 2.08225i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.10730 | − | 3.40791i | 0.333863 | − | 1.02752i | −0.633417 | − | 0.773811i | \(-0.718348\pi\) |
0.967280 | − | 0.253713i | \(-0.0816517\pi\) | |||||||
\(12\) | 1.67182 | + | 5.14535i | 0.482614 | + | 1.48533i | ||||
\(13\) | −1.16681 | − | 3.59107i | −0.323614 | − | 0.995983i | −0.972062 | − | 0.234724i | \(-0.924582\pi\) |
0.648448 | − | 0.761259i | \(-0.275418\pi\) | |||||||
\(14\) | 0.00368270 | − | 0.0113342i | 0.000984243 | − | 0.00302919i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.790173 | + | 2.43190i | 0.197543 | + | 0.607976i | ||||
\(17\) | −2.93109 | + | 2.12956i | −0.710894 | + | 0.516495i | −0.883462 | − | 0.468503i | \(-0.844794\pi\) |
0.172568 | + | 0.984998i | \(0.444794\pi\) | |||||||
\(18\) | −3.29062 | −0.775606 | ||||||||
\(19\) | 1.96659 | − | 1.42881i | 0.451166 | − | 0.327792i | −0.338890 | − | 0.940826i | \(-0.610051\pi\) |
0.790056 | + | 0.613035i | \(0.210051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0595291 | − | 0.0432504i | −0.0129903 | − | 0.00943802i | ||||
\(22\) | 1.45234 | + | 1.05519i | 0.309640 | + | 0.224966i | ||||
\(23\) | −0.530082 | + | 1.63143i | −0.110530 | + | 0.340176i | −0.990988 | − | 0.133947i | \(-0.957235\pi\) |
0.880459 | + | 0.474123i | \(0.157235\pi\) | |||||||
\(24\) | −5.80980 | −1.18592 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.89167 | 0.370987 | ||||||||
\(27\) | −3.41077 | + | 10.4973i | −0.656402 | + | 2.02020i | ||||
\(28\) | −0.0336593 | − | 0.0244549i | −0.00636102 | − | 0.00462155i | ||||
\(29\) | −3.12065 | − | 2.26729i | −0.579491 | − | 0.421025i | 0.259050 | − | 0.965864i | \(-0.416591\pi\) |
−0.838540 | + | 0.544839i | \(0.816591\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.86202 | − | 3.53247i | 0.873245 | − | 0.634449i | −0.0582109 | − | 0.998304i | \(-0.518540\pi\) |
0.931456 | + | 0.363855i | \(0.118540\pi\) | |||||||
\(32\) | −5.03748 | −0.890510 | ||||||||
\(33\) | 8.96717 | − | 6.51503i | 1.56098 | − | 1.13412i | ||||
\(34\) | −0.560896 | − | 1.72626i | −0.0961929 | − | 0.296051i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.54996 | + | 10.9257i | −0.591660 | + | 1.82094i | ||||
\(37\) | 0.114123 | + | 0.351233i | 0.0187616 | + | 0.0577424i | 0.959999 | − | 0.280003i | \(-0.0903356\pi\) |
−0.941237 | + | 0.337746i | \(0.890336\pi\) | |||||||
\(38\) | 0.376328 | + | 1.15822i | 0.0610485 | + | 0.187888i | ||||
\(39\) | 3.60924 | − | 11.1081i | 0.577941 | − | 1.77872i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.41311 | − | 7.42680i | −0.376865 | − | 1.15987i | −0.942212 | − | 0.335018i | \(-0.891258\pi\) |
0.565347 | − | 0.824853i | \(-0.308742\pi\) | |||||||
\(42\) | 0.0298234 | − | 0.0216680i | 0.00460186 | − | 0.00334345i | ||||
\(43\) | −0.174574 | −0.0266224 | −0.0133112 | − | 0.999911i | \(-0.504237\pi\) | ||||
−0.0133112 | + | 0.999911i | \(0.504237\pi\) | |||||||
\(44\) | 5.07027 | − | 3.68377i | 0.764373 | − | 0.555349i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.695260 | − | 0.505136i | −0.102510 | − | 0.0744782i | ||||
\(47\) | 6.31908 | + | 4.59108i | 0.921733 | + | 0.669678i | 0.943955 | − | 0.330075i | \(-0.107074\pi\) |
−0.0222216 | + | 0.999753i | \(0.507074\pi\) | |||||||
\(48\) | −2.44421 | + | 7.52250i | −0.352791 | + | 1.08578i | ||||
\(49\) | −6.99943 | −0.999919 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.2070 | −1.56929 | ||||||||
\(52\) | 2.04076 | − | 6.28081i | 0.283002 | − | 0.870992i | ||||
\(53\) | −7.25837 | − | 5.27352i | −0.997014 | − | 0.724373i | −0.0355683 | − | 0.999367i | \(-0.511324\pi\) |
−0.961446 | + | 0.274994i | \(0.911324\pi\) | |||||||
\(54\) | −4.47359 | − | 3.25025i | −0.608778 | − | 0.442303i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.0361458 | − | 0.0262615i | 0.00483019 | − | 0.00350934i | ||||
\(57\) | 7.51920 | 0.995943 | ||||||||
\(58\) | 1.56341 | − | 1.13589i | 0.205286 | − | 0.149149i | ||||
\(59\) | −1.37678 | − | 4.23730i | −0.179242 | − | 0.551649i | 0.820560 | − | 0.571560i | \(-0.193662\pi\) |
−0.999802 | + | 0.0199113i | \(0.993662\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.84729 | − | 8.76306i | 0.364558 | − | 1.12199i | −0.585699 | − | 0.810529i | \(-0.699180\pi\) |
0.950257 | − | 0.311466i | \(-0.100820\pi\) | |||||||
\(62\) | 0.930401 | + | 2.86348i | 0.118161 | + | 0.363662i | ||||
\(63\) | −0.0482822 | − | 0.148597i | −0.00608298 | − | 0.0187215i | ||||
\(64\) | −0.800472 | + | 2.46360i | −0.100059 | + | 0.307950i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.71597 | + | 5.28120i | 0.211221 | + | 0.650070i | ||||
\(67\) | −3.61942 | + | 2.62967i | −0.442183 | + | 0.321265i | −0.786502 | − | 0.617588i | \(-0.788110\pi\) |
0.344319 | + | 0.938853i | \(0.388110\pi\) | |||||||
\(68\) | −6.33671 | −0.768439 | ||||||||
\(69\) | −4.29274 | + | 3.11886i | −0.516785 | + | 0.375466i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.84308 | + | 5.69833i | 0.930803 | + | 0.676268i | 0.946189 | − | 0.323614i | \(-0.104898\pi\) |
−0.0153866 | + | 0.999882i | \(0.504898\pi\) | |||||||
\(72\) | −9.98048 | − | 7.25125i | −1.17621 | − | 0.854567i | ||||
\(73\) | 1.22181 | − | 3.76035i | 0.143002 | − | 0.440116i | −0.853746 | − | 0.520689i | \(-0.825675\pi\) |
0.996749 | + | 0.0805732i | \(0.0256751\pi\) | |||||||
\(74\) | −0.185020 | −0.0215081 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.25156 | 0.487687 | ||||||||
\(77\) | −0.0263402 | + | 0.0810669i | −0.00300175 | + | 0.00923843i | ||||
\(78\) | 4.73390 | + | 3.43938i | 0.536009 | + | 0.389433i | ||||
\(79\) | 7.83411 | + | 5.69181i | 0.881406 | + | 0.640379i | 0.933623 | − | 0.358257i | \(-0.116629\pi\) |
−0.0522169 | + | 0.998636i | \(0.516629\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.6798 | + | 8.48587i | −1.29776 | + | 0.942875i | ||||
\(82\) | 3.91223 | 0.432033 | ||||||||
\(83\) | −7.24650 | + | 5.26489i | −0.795407 | + | 0.577897i | −0.909563 | − | 0.415566i | \(-0.863584\pi\) |
0.114156 | + | 0.993463i | \(0.463584\pi\) | |||||||
\(84\) | −0.0397691 | − | 0.122397i | −0.00433917 | − | 0.0133546i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.0270266 | − | 0.0831794i | 0.00291435 | − | 0.00896946i | ||||
\(87\) | −3.68711 | − | 11.3478i | −0.395300 | − | 1.21661i | ||||
\(88\) | 2.07974 | + | 6.40078i | 0.221701 | + | 0.682326i | ||||
\(89\) | −5.25794 | + | 16.1823i | −0.557341 | + | 1.71532i | 0.132339 | + | 0.991205i | \(0.457751\pi\) |
−0.689680 | + | 0.724115i | \(0.742249\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0277559 | + | 0.0854239i | 0.00290961 | + | 0.00895485i | ||||
\(92\) | −2.42723 | + | 1.76349i | −0.253056 | + | 0.183856i | ||||
\(93\) | 18.5898 | 1.92767 | ||||||||
\(94\) | −3.16579 | + | 2.30008i | −0.326527 | + | 0.237236i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −12.6063 | − | 9.15901i | −1.28662 | − | 0.934787i | ||||
\(97\) | 2.23643 | + | 1.62486i | 0.227075 | + | 0.164979i | 0.695506 | − | 0.718521i | \(-0.255180\pi\) |
−0.468431 | + | 0.883500i | \(0.655180\pi\) | |||||||
\(98\) | 1.08361 | − | 3.33501i | 0.109461 | − | 0.336887i | ||||
\(99\) | 23.5359 | 2.36545 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3526 | 1.03012 | 0.515062 | − | 0.857153i | \(-0.327769\pi\) | ||||
0.515062 | + | 0.857153i | \(0.327769\pi\) | |||||||
\(102\) | 1.73500 | − | 5.33977i | 0.171790 | − | 0.528716i | ||||
\(103\) | 14.7980 | + | 10.7514i | 1.45809 | + | 1.05937i | 0.983855 | + | 0.178967i | \(0.0572756\pi\) |
0.474236 | + | 0.880398i | \(0.342724\pi\) | |||||||
\(104\) | 5.73746 | + | 4.16851i | 0.562604 | + | 0.408756i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.63637 | − | 2.64198i | 0.353195 | − | 0.256611i | ||||
\(107\) | −15.8786 | −1.53504 | −0.767522 | − | 0.641023i | \(-0.778510\pi\) | ||||
−0.767522 | + | 0.641023i | \(0.778510\pi\) | |||||||
\(108\) | −15.6178 | + | 11.3470i | −1.50282 | + | 1.09186i | ||||
\(109\) | 1.84208 | + | 5.66933i | 0.176439 | + | 0.543024i | 0.999696 | − | 0.0246449i | \(-0.00784550\pi\) |
−0.823257 | + | 0.567669i | \(0.807845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.353011 | + | 1.08645i | −0.0335063 | + | 0.103122i | ||||
\(112\) | −0.0187965 | − | 0.0578498i | −0.00177611 | − | 0.00546629i | ||||
\(113\) | −0.750387 | − | 2.30945i | −0.0705904 | − | 0.217255i | 0.909537 | − | 0.415622i | \(-0.136436\pi\) |
−0.980128 | + | 0.198367i | \(0.936436\pi\) | |||||||
\(114\) | −1.16408 | + | 3.58267i | −0.109026 | + | 0.335548i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.08479 | − | 6.41632i | −0.193568 | − | 0.595741i | ||||
\(117\) | 20.0643 | − | 14.5776i | 1.85494 | − | 1.34770i | ||||
\(118\) | 2.23209 | 0.205480 | ||||||||
\(119\) | 0.0697245 | − | 0.0506578i | 0.00639163 | − | 0.00464379i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.48855 | − | 1.08149i | −0.135323 | − | 0.0983176i | ||||
\(122\) | 3.73453 | + | 2.71329i | 0.338108 | + | 0.245650i | ||||
\(123\) | 7.46438 | − | 22.9730i | 0.673041 | − | 2.07141i | ||||
\(124\) | 10.5112 | 0.943932 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.0782768 | 0.00697345 | ||||||||
\(127\) | 5.28644 | − | 16.2700i | 0.469096 | − | 1.44373i | −0.384661 | − | 0.923058i | \(-0.625682\pi\) |
0.853757 | − | 0.520672i | \(-0.174318\pi\) | |||||||
\(128\) | −9.20073 | − | 6.68472i | −0.813237 | − | 0.590851i | ||||
\(129\) | −0.436872 | − | 0.317406i | −0.0384645 | − | 0.0279461i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.87482 | + | 2.81522i | −0.338545 | + | 0.245967i | −0.744048 | − | 0.668127i | \(-0.767096\pi\) |
0.405503 | + | 0.914094i | \(0.367096\pi\) | |||||||
\(132\) | 19.3861 | 1.68734 | ||||||||
\(133\) | −0.0467810 | + | 0.0339884i | −0.00405642 | + | 0.00294716i | ||||
\(134\) | −0.692616 | − | 2.13165i | −0.0598329 | − | 0.184147i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.10281 | − | 6.47177i | 0.180314 | − | 0.554950i | ||||
\(137\) | −3.95862 | − | 12.1834i | −0.338207 | − | 1.04090i | −0.965120 | − | 0.261806i | \(-0.915682\pi\) |
0.626913 | − | 0.779089i | \(-0.284318\pi\) | |||||||
\(138\) | −0.821463 | − | 2.52820i | −0.0699275 | − | 0.215215i | ||||
\(139\) | −2.45366 | + | 7.55158i | −0.208116 | + | 0.640516i | 0.791455 | + | 0.611228i | \(0.209324\pi\) |
−0.999571 | + | 0.0292885i | \(0.990676\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.46612 | + | 22.9783i | 0.628761 | + | 1.93513i | ||||
\(142\) | −3.92930 | + | 2.85480i | −0.329740 | + | 0.239570i | ||||
\(143\) | −13.5300 | −1.13144 | ||||||||
\(144\) | −13.5877 | + | 9.87205i | −1.13231 | + | 0.822671i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.60254 | + | 1.16431i | 0.132627 | + | 0.0963591i | ||||
\(147\) | −17.5161 | − | 12.7262i | −1.44470 | − | 1.04964i | ||||
\(148\) | −0.199602 | + | 0.614310i | −0.0164071 | + | 0.0504960i | ||||
\(149\) | −5.62724 | −0.461002 | −0.230501 | − | 0.973072i | \(-0.574036\pi\) | ||||
−0.230501 | + | 0.973072i | \(0.574036\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.36960 | −0.599730 | −0.299865 | − | 0.953982i | \(-0.596942\pi\) | ||||
−0.299865 | + | 0.953982i | \(0.596942\pi\) | |||||||
\(152\) | −1.41086 | + | 4.34217i | −0.114436 | + | 0.352197i | ||||
\(153\) | −19.2521 | − | 13.9875i | −1.55644 | − | 1.13082i | ||||
\(154\) | −0.0345480 | − | 0.0251006i | −0.00278396 | − | 0.00202267i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 16.5266 | − | 12.0073i | 1.32319 | − | 0.961350i | ||||
\(157\) | −8.63091 | −0.688822 | −0.344411 | − | 0.938819i | \(-0.611921\pi\) | ||||
−0.344411 | + | 0.938819i | \(0.611921\pi\) | |||||||
\(158\) | −3.92481 | + | 2.85154i | −0.312241 | + | 0.226856i | ||||
\(159\) | −8.57591 | − | 26.3939i | −0.680114 | − | 2.09317i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0126095 | − | 0.0388082i | 0.000993770 | − | 0.00305851i | ||||
\(162\) | −2.23506 | − | 6.87880i | −0.175603 | − | 0.540450i | ||||
\(163\) | −1.46772 | − | 4.51717i | −0.114961 | − | 0.353812i | 0.876978 | − | 0.480530i | \(-0.159556\pi\) |
−0.991939 | + | 0.126718i | \(0.959556\pi\) | |||||||
\(164\) | 4.22056 | − | 12.9895i | 0.329570 | − | 1.01431i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.38670 | − | 4.26782i | −0.107629 | − | 0.331247i | ||||
\(167\) | 15.0451 | − | 10.9309i | 1.16422 | − | 0.845856i | 0.173916 | − | 0.984761i | \(-0.444358\pi\) |
0.990306 | + | 0.138904i | \(0.0443580\pi\) | |||||||
\(168\) | 0.138203 | 0.0106626 | ||||||||
\(169\) | −1.01710 | + | 0.738965i | −0.0782383 | + | 0.0568434i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.9170 | + | 9.38476i | 0.987789 | + | 0.717671i | ||||
\(172\) | −0.247019 | − | 0.179470i | −0.0188350 | − | 0.0136845i | ||||
\(173\) | −4.88114 | + | 15.0226i | −0.371106 | + | 1.14215i | 0.574963 | + | 0.818180i | \(0.305017\pi\) |
−0.946068 | + | 0.323967i | \(0.894983\pi\) | |||||||
\(174\) | 5.97767 | 0.453166 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.16266 | 0.690661 | ||||||||
\(177\) | 4.25874 | − | 13.1070i | 0.320106 | − | 0.985186i | ||||
\(178\) | −6.89636 | − | 5.01050i | −0.516904 | − | 0.375553i | ||||
\(179\) | −7.58005 | − | 5.50723i | −0.566560 | − | 0.411630i | 0.267294 | − | 0.963615i | \(-0.413870\pi\) |
−0.833854 | + | 0.551985i | \(0.813870\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.72975 | − | 3.43637i | 0.351560 | − | 0.255423i | −0.397963 | − | 0.917401i | \(-0.630283\pi\) |
0.749523 | + | 0.661978i | \(0.230283\pi\) | |||||||
\(182\) | −0.0449988 | −0.00333554 | ||||||||
\(183\) | 23.0581 | − | 16.7527i | 1.70450 | − | 1.23839i | ||||
\(184\) | −0.995608 | − | 3.06417i | −0.0733972 | − | 0.225893i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.87797 | + | 8.85748i | −0.211023 | + | 0.649462i | ||||
\(187\) | 4.01177 | + | 12.3470i | 0.293369 | + | 0.902898i | ||||
\(188\) | 4.22154 | + | 12.9926i | 0.307888 | + | 0.947581i | ||||
\(189\) | 0.0811349 | − | 0.249708i | 0.00590170 | − | 0.0181636i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.76584 | − | 20.8231i | −0.489559 | − | 1.50671i | −0.825268 | − | 0.564741i | \(-0.808976\pi\) |
0.335709 | − | 0.941966i | \(-0.391024\pi\) | |||||||
\(192\) | −6.48242 | + | 4.70976i | −0.467829 | + | 0.339897i | ||||
\(193\) | 25.2541 | 1.81783 | 0.908916 | − | 0.416980i | \(-0.136911\pi\) | ||||
0.908916 | + | 0.416980i | \(0.136911\pi\) | |||||||
\(194\) | −1.12043 | + | 0.814037i | −0.0804419 | + | 0.0584445i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.90405 | − | 7.19571i | −0.707432 | − | 0.513979i | ||||
\(197\) | 11.6934 | + | 8.49575i | 0.833120 | + | 0.605297i | 0.920440 | − | 0.390883i | \(-0.127830\pi\) |
−0.0873202 | + | 0.996180i | \(0.527830\pi\) | |||||||
\(198\) | −3.64369 | + | 11.2141i | −0.258946 | + | 0.796953i | ||||
\(199\) | −3.77734 | −0.267768 | −0.133884 | − | 0.990997i | \(-0.542745\pi\) | ||||
−0.133884 | + | 0.990997i | \(0.542745\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.8388 | −0.976112 | ||||||||
\(202\) | −1.60273 | + | 4.93270i | −0.112768 | + | 0.347064i | ||||
\(203\) | 0.0742337 | + | 0.0539339i | 0.00521018 | + | 0.00378542i | ||||
\(204\) | −15.8576 | − | 11.5212i | −1.11025 | − | 0.806647i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.41364 | + | 5.38633i | −0.516533 | + | 0.375283i | ||||
\(207\) | −11.2670 | −0.783113 | ||||||||
\(208\) | 7.81115 | − | 5.67513i | 0.541605 | − | 0.393499i | ||||
\(209\) | −2.69166 | − | 8.28407i | −0.186186 | − | 0.573021i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.84061 | + | 17.9756i | −0.402084 | + | 1.23749i | 0.521221 | + | 0.853422i | \(0.325477\pi\) |
−0.923305 | + | 0.384067i | \(0.874523\pi\) | |||||||
\(212\) | −4.84904 | − | 14.9238i | −0.333034 | − | 1.02497i | ||||
\(213\) | 9.26675 | + | 28.5201i | 0.634947 | + | 1.95417i | ||||
\(214\) | 2.45824 | − | 7.56567i | 0.168042 | − | 0.517179i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.40615 | − | 19.7161i | −0.435883 | − | 1.34151i | ||||
\(217\) | −0.115657 | + | 0.0840299i | −0.00785132 | + | 0.00570432i | ||||
\(218\) | −2.98644 | −0.202267 | ||||||||
\(219\) | 9.89454 | − | 7.18881i | 0.668611 | − | 0.485775i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.0674 | + | 8.04095i | 0.744476 | + | 0.540893i | ||||
\(222\) | −0.463011 | − | 0.336397i | −0.0310753 | − | 0.0225775i | ||||
\(223\) | 3.50907 | − | 10.7998i | 0.234984 | − | 0.723208i | −0.762139 | − | 0.647413i | \(-0.775851\pi\) |
0.997123 | − | 0.0757944i | \(-0.0241493\pi\) | |||||||
\(224\) | 0.119831 | 0.00800655 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.21655 | 0.0809239 | ||||||||
\(227\) | −3.46027 | + | 10.6496i | −0.229666 | + | 0.706841i | 0.768118 | + | 0.640309i | \(0.221194\pi\) |
−0.997784 | + | 0.0665322i | \(0.978806\pi\) | |||||||
\(228\) | 10.6395 | + | 7.73006i | 0.704619 | + | 0.511936i | ||||
\(229\) | −7.80676 | − | 5.67194i | −0.515885 | − | 0.374813i | 0.299166 | − | 0.954201i | \(-0.403291\pi\) |
−0.815052 | + | 0.579388i | \(0.803291\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.213310 | + | 0.154979i | −0.0140348 | + | 0.0101968i | ||||
\(232\) | 7.24491 | 0.475651 | ||||||||
\(233\) | −12.5608 | + | 9.12599i | −0.822889 | + | 0.597864i | −0.917538 | − | 0.397647i | \(-0.869827\pi\) |
0.0946499 | + | 0.995511i | \(0.469827\pi\) | |||||||
\(234\) | 3.83952 | + | 11.8168i | 0.250997 | + | 0.772490i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.40800 | − | 7.41107i | 0.156748 | − | 0.482420i | ||||
\(237\) | 9.25615 | + | 28.4875i | 0.601252 | + | 1.85046i | ||||
\(238\) | 0.0133425 | + | 0.0410641i | 0.000864868 | + | 0.00266179i | ||||
\(239\) | 4.42951 | − | 13.6326i | 0.286521 | − | 0.881822i | −0.699417 | − | 0.714714i | \(-0.746557\pi\) |
0.985938 | − | 0.167109i | \(-0.0534430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.82164 | + | 24.0725i | 0.503836 | + | 1.55065i | 0.802718 | + | 0.596359i | \(0.203386\pi\) |
−0.298882 | + | 0.954290i | \(0.596614\pi\) | |||||||
\(242\) | 0.745747 | − | 0.541817i | 0.0479384 | − | 0.0348293i | ||||
\(243\) | −11.5450 | −0.740613 | ||||||||
\(244\) | 13.0377 | − | 9.47241i | 0.834650 | − | 0.606409i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.79034 | + | 7.11309i | 0.624209 | + | 0.453514i | ||||
\(247\) | −7.42558 | − | 5.39500i | −0.472479 | − | 0.343276i | ||||
\(248\) | −3.48808 | + | 10.7352i | −0.221493 | + | 0.681687i | ||||
\(249\) | −27.7068 | −1.75585 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.23698 | 0.267436 | 0.133718 | − | 0.991019i | \(-0.457308\pi\) | ||||
0.133718 | + | 0.991019i | \(0.457308\pi\) | |||||||
\(252\) | 0.0844460 | − | 0.259898i | 0.00531960 | − | 0.0163720i | ||||
\(253\) | 4.97279 | + | 3.61294i | 0.312637 | + | 0.227144i | ||||
\(254\) | 6.93374 | + | 5.03766i | 0.435061 | + | 0.316091i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.418140 | − | 0.303797i | 0.0261338 | − | 0.0189873i | ||||
\(257\) | 20.4007 | 1.27256 | 0.636281 | − | 0.771458i | \(-0.280472\pi\) | ||||
0.636281 | + | 0.771458i | \(0.280472\pi\) | |||||||
\(258\) | 0.218868 | − | 0.159017i | 0.0136261 | − | 0.00989997i | ||||
\(259\) | −0.00271473 | − | 0.00835509i | −0.000168685 | − | 0.000519160i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.82923 | − | 24.0959i | 0.484617 | − | 1.49150i | ||||
\(262\) | −0.741490 | − | 2.28207i | −0.0458094 | − | 0.140987i | ||||
\(263\) | −8.85883 | − | 27.2647i | −0.546259 | − | 1.68121i | −0.717978 | − | 0.696066i | \(-0.754932\pi\) |
0.171719 | − | 0.985146i | \(-0.445068\pi\) | |||||||
\(264\) | −6.43317 | + | 19.7993i | −0.395934 | + | 1.21856i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.00895205 | − | 0.0275516i | −0.000548885 | − | 0.00168930i | ||||
\(267\) | −42.5802 | + | 30.9363i | −2.60586 | + | 1.89327i | ||||
\(268\) | −7.82481 | −0.477977 | ||||||||
\(269\) | −6.42887 | + | 4.67085i | −0.391975 | + | 0.284786i | −0.766264 | − | 0.642525i | \(-0.777887\pi\) |
0.374289 | + | 0.927312i | \(0.377887\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.73005 | − | 5.61621i | −0.469567 | − | 0.341161i | 0.327705 | − | 0.944780i | \(-0.393725\pi\) |
−0.797273 | + | 0.603619i | \(0.793725\pi\) | |||||||
\(272\) | −7.49496 | − | 5.44541i | −0.454449 | − | 0.330176i | ||||
\(273\) | −0.0858561 | + | 0.264238i | −0.00519625 | + | 0.0159924i | ||||
\(274\) | 6.41785 | 0.387717 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.28045 | −0.558618 | ||||||||
\(277\) | −5.31213 | + | 16.3491i | −0.319175 | + | 0.982320i | 0.654826 | + | 0.755779i | \(0.272742\pi\) |
−0.974002 | + | 0.226541i | \(0.927258\pi\) | |||||||
\(278\) | −3.21823 | − | 2.33818i | −0.193017 | − | 0.140235i | ||||
\(279\) | 31.9349 | + | 23.2021i | 1.91189 | + | 1.38907i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.0200 | + | 15.9985i | −1.31360 | + | 0.954388i | −0.313614 | + | 0.949550i | \(0.601540\pi\) |
−0.999988 | + | 0.00483787i | \(0.998460\pi\) | |||||||
\(282\) | −12.1043 | −0.720803 | ||||||||
\(283\) | −2.81458 | + | 2.04491i | −0.167309 | + | 0.121557i | −0.668289 | − | 0.743902i | \(-0.732973\pi\) |
0.500980 | + | 0.865459i | \(0.332973\pi\) | |||||||
\(284\) | 5.23967 | + | 16.1260i | 0.310917 | + | 0.956904i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.09464 | − | 6.44664i | 0.123859 | − | 0.381198i | ||||
\(287\) | 0.0574029 | + | 0.176668i | 0.00338838 | + | 0.0104284i | ||||
\(288\) | −10.2246 | − | 31.4680i | −0.602488 | − | 1.85427i | ||||
\(289\) | −1.19703 | + | 3.68407i | −0.0704134 | + | 0.216710i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.64238 | + | 8.13241i | 0.154899 | + | 0.476730i | ||||
\(292\) | 5.59464 | − | 4.06474i | 0.327401 | − | 0.237871i | ||||
\(293\) | −23.4941 | −1.37254 | −0.686271 | − | 0.727346i | \(-0.740754\pi\) | ||||
−0.686271 | + | 0.727346i | \(0.740754\pi\) | |||||||
\(294\) | 8.77536 | − | 6.37567i | 0.511790 | − | 0.371837i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.561167 | − | 0.407712i | −0.0326172 | − | 0.0236978i | ||||
\(297\) | 31.9970 | + | 23.2472i | 1.85665 | + | 1.34894i | ||||
\(298\) | 0.871177 | − | 2.68121i | 0.0504659 | − | 0.155318i | ||||
\(299\) | 6.47706 | 0.374578 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.00415276 | 0.000239361 | ||||||||
\(302\) | 1.14092 | − | 3.51139i | 0.0656525 | − | 0.202058i | ||||
\(303\) | 25.9074 | + | 18.8228i | 1.48834 | + | 1.08134i | ||||
\(304\) | 5.02867 | + | 3.65354i | 0.288414 | + | 0.209545i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.64510 | − | 7.00758i | 0.551374 | − | 0.400596i | ||||
\(307\) | −1.11253 | −0.0634952 | −0.0317476 | − | 0.999496i | \(-0.510107\pi\) | ||||
−0.0317476 | + | 0.999496i | \(0.510107\pi\) | |||||||
\(308\) | −0.120611 | + | 0.0876291i | −0.00687245 | + | 0.00499313i | ||||
\(309\) | 17.4841 | + | 53.8106i | 0.994637 | + | 3.06118i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.55890 | + | 14.0308i | −0.258511 | + | 0.795616i | 0.734606 | + | 0.678494i | \(0.237367\pi\) |
−0.993117 | + | 0.117122i | \(0.962633\pi\) | |||||||
\(312\) | 6.77892 | + | 20.8634i | 0.383781 | + | 1.18116i | ||||
\(313\) | −1.52912 | − | 4.70615i | −0.0864310 | − | 0.266007i | 0.898495 | − | 0.438984i | \(-0.144661\pi\) |
−0.984926 | + | 0.172977i | \(0.944661\pi\) | |||||||
\(314\) | 1.33619 | − | 4.11237i | 0.0754055 | − | 0.232074i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.23367 | + | 16.1076i | 0.294417 | + | 0.906123i | ||||
\(317\) | 18.3530 | − | 13.3342i | 1.03080 | − | 0.748923i | 0.0623350 | − | 0.998055i | \(-0.480145\pi\) |
0.968470 | + | 0.249132i | \(0.0801453\pi\) | |||||||
\(318\) | 13.9036 | 0.779673 | ||||||||
\(319\) | −11.1822 | + | 8.12434i | −0.626083 | + | 0.454876i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −39.7362 | − | 28.8700i | −2.21786 | − | 1.61137i | ||||
\(322\) | 0.0165388 | + | 0.0120161i | 0.000921669 | + | 0.000669632i | ||||
\(323\) | −2.72151 | + | 8.37595i | −0.151429 | + | 0.466050i | ||||
\(324\) | −25.2505 | −1.40281 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.37952 | 0.131789 | ||||||||
\(327\) | −5.69802 | + | 17.5367i | −0.315101 | + | 0.969782i | ||||
\(328\) | 11.8658 | + | 8.62103i | 0.655181 | + | 0.476017i | ||||
\(329\) | −0.150318 | − | 0.109212i | −0.00828728 | − | 0.00602106i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.40169 | + | 1.01838i | −0.0770437 | + | 0.0559755i | −0.625640 | − | 0.780112i | \(-0.715162\pi\) |
0.548597 | + | 0.836087i | \(0.315162\pi\) | |||||||
\(332\) | −15.6662 | −0.859793 | ||||||||
\(333\) | −1.96244 | + | 1.42579i | −0.107541 | + | 0.0781330i | ||||
\(334\) | 2.87904 | + | 8.86076i | 0.157534 | + | 0.484839i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.0581425 | − | 0.178944i | 0.00317194 | − | 0.00976221i | ||||
\(337\) | −4.32038 | − | 13.2968i | −0.235346 | − | 0.724321i | −0.997075 | − | 0.0764255i | \(-0.975649\pi\) |
0.761729 | − | 0.647896i | \(-0.224351\pi\) | |||||||
\(338\) | −0.194633 | − | 0.599018i | −0.0105866 | − | 0.0325823i | ||||
\(339\) | 2.32114 | − | 7.14373i | 0.126067 | − | 0.387994i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.65462 | − | 20.4808i | −0.360368 | − | 1.10910i | ||||
\(342\) | −6.47129 | + | 4.70167i | −0.349927 | + | 0.254237i | ||||
\(343\) | 0.333017 | 0.0179812 | ||||||||
\(344\) | 0.265267 | − | 0.192728i | 0.0143022 | − | 0.0103912i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.40213 | − | 4.65142i | −0.344181 | − | 0.250062i | ||||
\(347\) | 4.11121 | + | 2.98697i | 0.220701 | + | 0.160349i | 0.692642 | − | 0.721281i | \(-0.256447\pi\) |
−0.471941 | + | 0.881630i | \(0.656447\pi\) | |||||||
\(348\) | 6.44879 | − | 19.8473i | 0.345691 | − | 1.06393i | ||||
\(349\) | −8.88643 | −0.475680 | −0.237840 | − | 0.971304i | \(-0.576439\pi\) | ||||
−0.237840 | + | 0.971304i | \(0.576439\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 41.6761 | 2.22450 | ||||||||
\(352\) | −5.57799 | + | 17.1673i | −0.297308 | + | 0.915020i | ||||
\(353\) | 7.61641 | + | 5.53364i | 0.405380 | + | 0.294526i | 0.771729 | − | 0.635952i | \(-0.219392\pi\) |
−0.366349 | + | 0.930478i | \(0.619392\pi\) | |||||||
\(354\) | 5.58579 | + | 4.05831i | 0.296881 | + | 0.215697i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −24.0760 | + | 17.4922i | −1.27602 | + | 0.927085i | ||||
\(357\) | 0.266590 | 0.0141094 | ||||||||
\(358\) | 3.79752 | − | 2.75906i | 0.200705 | − | 0.145821i | ||||
\(359\) | 2.81668 | + | 8.66886i | 0.148659 | + | 0.457525i | 0.997463 | − | 0.0711818i | \(-0.0226770\pi\) |
−0.848804 | + | 0.528707i | \(0.822677\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.04535 | + | 12.4503i | −0.212913 | + | 0.655280i | ||||
\(362\) | 0.905090 | + | 2.78558i | 0.0475705 | + | 0.146407i | ||||
\(363\) | −1.75875 | − | 5.41287i | −0.0923103 | − | 0.284102i | ||||
\(364\) | −0.0485453 | + | 0.149407i | −0.00254447 | + | 0.00783106i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.41241 | + | 13.5800i | 0.230641 | + | 0.709839i | ||||
\(367\) | −14.4639 | + | 10.5087i | −0.755012 | + | 0.548548i | −0.897376 | − | 0.441266i | \(-0.854529\pi\) |
0.142365 | + | 0.989814i | \(0.454529\pi\) | |||||||
\(368\) | −4.38633 | −0.228653 | ||||||||
\(369\) | 41.4956 | − | 30.1483i | 2.16017 | − | 1.56946i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.172661 | + | 0.125446i | 0.00896413 | + | 0.00651282i | ||||
\(372\) | 26.3042 | + | 19.1111i | 1.36381 | + | 0.990865i | ||||
\(373\) | 0.949901 | − | 2.92350i | 0.0491840 | − | 0.151373i | −0.923448 | − | 0.383723i | \(-0.874642\pi\) |
0.972632 | + | 0.232350i | \(0.0746416\pi\) | |||||||
\(374\) | −6.50402 | −0.336315 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.6704 | −0.756567 | ||||||||
\(377\) | −4.50077 | + | 13.8520i | −0.231802 | + | 0.713412i | ||||
\(378\) | 0.106417 | + | 0.0773166i | 0.00547351 | + | 0.00397674i | ||||
\(379\) | −20.7000 | − | 15.0394i | −1.06329 | − | 0.772524i | −0.0885946 | − | 0.996068i | \(-0.528238\pi\) |
−0.974694 | + | 0.223543i | \(0.928238\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42.8110 | − | 31.1040i | 2.19327 | − | 1.59351i | ||||
\(382\) | 10.9690 | 0.561224 | ||||||||
\(383\) | −1.80030 | + | 1.30799i | −0.0919909 | + | 0.0668353i | −0.632830 | − | 0.774291i | \(-0.718107\pi\) |
0.540839 | + | 0.841126i | \(0.318107\pi\) | |||||||
\(384\) | −10.8708 | − | 33.4570i | −0.554750 | − | 1.70734i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.90970 | + | 12.0328i | −0.198998 | + | 0.612454i | ||||
\(387\) | −0.354333 | − | 1.09053i | −0.0180118 | − | 0.0554345i | ||||
\(388\) | 1.49407 | + | 4.59828i | 0.0758500 | + | 0.233442i | ||||
\(389\) | 1.43511 | − | 4.41683i | 0.0727632 | − | 0.223942i | −0.908061 | − | 0.418839i | \(-0.862437\pi\) |
0.980824 | + | 0.194897i | \(0.0624372\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.92050 | − | 5.91070i | −0.0971240 | − | 0.298917i | ||||
\(392\) | 10.6357 | − | 7.72728i | 0.537183 | − | 0.390287i | ||||
\(393\) | −14.8153 | −0.747333 | ||||||||
\(394\) | −5.85827 | + | 4.25628i | −0.295135 | + | 0.214428i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 33.3028 | + | 24.1959i | 1.67353 | + | 1.21589i | ||||
\(397\) | −30.6983 | − | 22.3036i | −1.54070 | − | 1.11939i | −0.949892 | − | 0.312578i | \(-0.898807\pi\) |
−0.590812 | − | 0.806809i | \(-0.701193\pi\) | |||||||
\(398\) | 0.584786 | − | 1.79979i | 0.0293127 | − | 0.0902151i | ||||
\(399\) | −0.178866 | −0.00895449 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.7187 | −0.834890 | −0.417445 | − | 0.908702i | \(-0.637074\pi\) | ||||
−0.417445 | + | 0.908702i | \(0.637074\pi\) | |||||||
\(402\) | 2.14244 | − | 6.59375i | 0.106855 | − | 0.328866i | ||||
\(403\) | −18.3584 | − | 13.3381i | −0.914495 | − | 0.664420i | ||||
\(404\) | 14.6487 | + | 10.6429i | 0.728801 | + | 0.529505i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0371903 | + | 0.0270203i | −0.00184572 | + | 0.00134100i | ||||
\(407\) | 1.32334 | 0.0655955 | ||||||||
\(408\) | 17.0291 | − | 12.3723i | 0.843064 | − | 0.612522i | ||||
\(409\) | 0.146206 | + | 0.449975i | 0.00722941 | + | 0.0222498i | 0.954606 | − | 0.297871i | \(-0.0962765\pi\) |
−0.947377 | + | 0.320121i | \(0.896277\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.2450 | − | 37.6863i | 0.604002 | − | 1.85893i | ||||
\(412\) | 9.88599 | + | 30.4259i | 0.487048 | + | 1.49898i | ||||
\(413\) | 0.0327507 | + | 0.100796i | 0.00161156 | + | 0.00495986i | ||||
\(414\) | 1.74430 | − | 5.36840i | 0.0857276 | − | 0.263842i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.87778 | + | 18.0899i | 0.288182 | + | 0.886932i | ||||
\(417\) | −19.8703 | + | 14.4366i | −0.973054 | + | 0.706965i | ||||
\(418\) | 4.36381 | 0.213441 | ||||||||
\(419\) | −19.6064 | + | 14.2449i | −0.957835 | + | 0.695908i | −0.952647 | − | 0.304078i | \(-0.901651\pi\) |
−0.00518829 | + | 0.999987i | \(0.501651\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.3612 | + | 18.4260i | 1.23603 | + | 0.898028i | 0.997327 | − | 0.0730653i | \(-0.0232782\pi\) |
0.238702 | + | 0.971093i | \(0.423278\pi\) | |||||||
\(422\) | −7.66059 | − | 5.56574i | −0.372912 | − | 0.270936i | ||||
\(423\) | −15.8536 | + | 48.7923i | −0.770828 | + | 2.37236i | ||||
\(424\) | 16.8510 | 0.818359 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −15.0236 | −0.727895 | ||||||||
\(427\) | −0.0677310 | + | 0.208455i | −0.00327773 | + | 0.0100878i | ||||
\(428\) | −22.4679 | − | 16.3239i | −1.08603 | − | 0.789045i | ||||
\(429\) | −33.8589 | − | 24.5999i | −1.63472 | − | 1.18769i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.61857 | − | 1.17596i | 0.0779639 | − | 0.0566441i | −0.548121 | − | 0.836399i | \(-0.684657\pi\) |
0.626084 | + | 0.779755i | \(0.284657\pi\) | |||||||
\(432\) | −28.2234 | −1.35790 | ||||||||
\(433\) | 5.72180 | − | 4.15713i | 0.274972 | − | 0.199779i | −0.441749 | − | 0.897138i | \(-0.645642\pi\) |
0.716721 | + | 0.697360i | \(0.245642\pi\) | |||||||
\(434\) | −0.0221323 | − | 0.0681161i | −0.00106238 | − | 0.00326968i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.22181 | + | 9.91572i | −0.154297 | + | 0.474877i | ||||
\(437\) | 1.28854 | + | 3.96573i | 0.0616394 | + | 0.189707i | ||||
\(438\) | 1.89343 | + | 5.82737i | 0.0904715 | + | 0.278443i | ||||
\(439\) | 4.00549 | − | 12.3276i | 0.191171 | − | 0.588365i | −0.808829 | − | 0.588045i | \(-0.799898\pi\) |
1.00000 | 0.000320575i | \(-0.000102042\pi\) | ||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.2067 | − | 43.7238i | −0.676511 | − | 2.08209i | ||||
\(442\) | −5.54466 | + | 4.02843i | −0.263733 | + | 0.191613i | ||||
\(443\) | −21.8687 | −1.03901 | −0.519506 | − | 0.854467i | \(-0.673884\pi\) | ||||
−0.519506 | + | 0.854467i | \(0.673884\pi\) | |||||||
\(444\) | −1.61642 | + | 1.17440i | −0.0767121 | + | 0.0557346i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.60252 | + | 3.34392i | 0.217936 | + | 0.158339i | ||||
\(447\) | −14.0822 | − | 10.2313i | −0.666063 | − | 0.483923i | ||||
\(448\) | 0.0190415 | − | 0.0586038i | 0.000899628 | − | 0.00276877i | ||||
\(449\) | 0.399626 | 0.0188595 | 0.00942976 | − | 0.999956i | \(-0.496998\pi\) | ||||
0.00942976 | + | 0.999956i | \(0.496998\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.9819 | −1.31762 | ||||||||
\(452\) | 1.31243 | − | 4.03925i | 0.0617317 | − | 0.189991i | ||||
\(453\) | −18.4424 | − | 13.3992i | −0.866500 | − | 0.629549i | ||||
\(454\) | −4.53852 | − | 3.29743i | −0.213003 | − | 0.154756i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.4255 | + | 8.30110i | −0.535047 | + | 0.388735i | ||||
\(457\) | 35.2247 | 1.64774 | 0.823872 | − | 0.566777i | \(-0.191810\pi\) | ||||
0.823872 | + | 0.566777i | \(0.191810\pi\) | |||||||
\(458\) | 3.91110 | − | 2.84158i | 0.182754 | − | 0.132778i | ||||
\(459\) | −12.3573 | − | 38.0319i | −0.576790 | − | 1.77518i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.93238 | + | 15.1803i | −0.229724 | + | 0.707017i | 0.768054 | + | 0.640385i | \(0.221225\pi\) |
−0.997778 | + | 0.0666319i | \(0.978775\pi\) | |||||||
\(462\) | −0.0408192 | − | 0.125628i | −0.00189908 | − | 0.00584477i | ||||
\(463\) | 9.41981 | + | 28.9912i | 0.437776 | + | 1.34734i | 0.890215 | + | 0.455540i | \(0.150554\pi\) |
−0.452440 | + | 0.891795i | \(0.649446\pi\) | |||||||
\(464\) | 3.04797 | − | 9.38067i | 0.141498 | − | 0.435487i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.40366 | − | 7.39769i | −0.111347 | − | 0.342691i | ||||
\(467\) | 5.37719 | − | 3.90676i | 0.248827 | − | 0.180783i | −0.456380 | − | 0.889785i | \(-0.650854\pi\) |
0.705207 | + | 0.709002i | \(0.250854\pi\) | |||||||
\(468\) | 43.3769 | 2.00510 | ||||||||
\(469\) | 0.0860984 | − | 0.0625542i | 0.00397566 | − | 0.00288848i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.5988 | − | 15.6925i | −0.995222 | − | 0.723071i | ||||
\(472\) | 6.76995 | + | 4.91865i | 0.311612 | + | 0.226399i | ||||
\(473\) | −0.193306 | + | 0.594934i | −0.00888821 | + | 0.0273551i | ||||
\(474\) | −15.0064 | −0.689267 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.150737 | 0.00690902 | ||||||||
\(477\) | 18.2101 | − | 56.0450i | 0.833784 | − | 2.56612i | ||||
\(478\) | 5.80978 | + | 4.22105i | 0.265733 | + | 0.193067i | ||||
\(479\) | −17.9932 | − | 13.0728i | −0.822129 | − | 0.597312i | 0.0951925 | − | 0.995459i | \(-0.469653\pi\) |
−0.917322 | + | 0.398147i | \(0.869653\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.12814 | − | 0.819644i | 0.0514389 | − | 0.0373725i | ||||
\(482\) | −12.6807 | −0.577591 | ||||||||
\(483\) | 0.102115 | − | 0.0741910i | 0.00464640 | − | 0.00337581i | ||||
\(484\) | −0.994443 | − | 3.06058i | −0.0452020 | − | 0.139117i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.78733 | − | 5.50084i | 0.0810751 | − | 0.249523i | ||||
\(487\) | −3.14737 | − | 9.68660i | −0.142621 | − | 0.438942i | 0.854077 | − | 0.520147i | \(-0.174123\pi\) |
−0.996697 | + | 0.0812055i | \(0.974123\pi\) | |||||||
\(488\) | 5.34782 | + | 16.4589i | 0.242085 | + | 0.745060i | ||||
\(489\) | 4.54003 | − | 13.9728i | 0.205307 | − | 0.631871i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.05189 | + | 6.31505i | 0.0926003 | + | 0.284994i | 0.986621 | − | 0.163032i | \(-0.0521272\pi\) |
−0.894021 | + | 0.448026i | \(0.852127\pi\) | |||||||
\(492\) | 34.1792 | − | 24.8326i | 1.54092 | − | 1.11954i | ||||
\(493\) | 13.9752 | 0.629413 | ||||||||
\(494\) | 3.72014 | − | 2.70284i | 0.167377 | − | 0.121606i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.4325 | + | 9.03270i | 0.558234 | + | 0.405580i | ||||
\(497\) | −0.186570 | − | 0.135551i | −0.00836882 | − | 0.00608030i | ||||
\(498\) | 4.28941 | − | 13.2014i | 0.192213 | − | 0.591571i | ||||
\(499\) | 1.08397 | 0.0485253 | 0.0242626 | − | 0.999706i | \(-0.492276\pi\) | ||||
0.0242626 | + | 0.999706i | \(0.492276\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 57.5244 | 2.57000 | ||||||||
\(502\) | −0.655945 | + | 2.01879i | −0.0292762 | + | 0.0901030i | ||||
\(503\) | −1.60673 | − | 1.16736i | −0.0716405 | − | 0.0520498i | 0.551389 | − | 0.834249i | \(-0.314098\pi\) |
−0.623029 | + | 0.782199i | \(0.714098\pi\) | |||||||
\(504\) | 0.237415 | + | 0.172492i | 0.0105753 | + | 0.00768339i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.49132 | + | 1.81005i | −0.110752 | + | 0.0804664i | ||||
\(507\) | −3.88885 | −0.172710 | ||||||||
\(508\) | 24.2065 | − | 17.5870i | 1.07399 | − | 0.780298i | ||||
\(509\) | 0.713568 | + | 2.19614i | 0.0316283 | + | 0.0973420i | 0.965624 | − | 0.259941i | \(-0.0837031\pi\) |
−0.933996 | + | 0.357283i | \(0.883703\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0290643 | + | 0.0894508i | −0.00128573 | + | 0.00395707i | ||||
\(512\) | −6.94871 | − | 21.3859i | −0.307093 | − | 0.945134i | ||||
\(513\) | 8.29102 | + | 25.5171i | 0.366057 | + | 1.12661i | ||||
\(514\) | −3.15832 | + | 9.72031i | −0.139308 | + | 0.428744i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.291858 | − | 0.898246i | −0.0128483 | − | 0.0395431i | ||||
\(517\) | 22.6431 | − | 16.4512i | 0.995842 | − | 0.723522i | ||||
\(518\) | 0.00440122 | 0.000193379 | ||||||||
\(519\) | −39.5287 | + | 28.7193i | −1.73512 | + | 1.26064i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.93539 | + | 6.49194i | 0.391467 | + | 0.284417i | 0.766056 | − | 0.642774i | \(-0.222216\pi\) |
−0.374590 | + | 0.927191i | \(0.622216\pi\) | |||||||
\(522\) | 10.2689 | + | 7.46077i | 0.449456 | + | 0.326549i | ||||
\(523\) | −8.03522 | + | 24.7299i | −0.351356 | + | 1.08136i | 0.606737 | + | 0.794903i | \(0.292478\pi\) |
−0.958093 | + | 0.286459i | \(0.907522\pi\) | |||||||
\(524\) | −8.37696 | −0.365949 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.3623 | 0.626224 | ||||||||
\(527\) | −6.72842 | + | 20.7080i | −0.293095 | + | 0.902053i | ||||
\(528\) | 22.9295 | + | 16.6593i | 0.997880 | + | 0.725002i | ||||
\(529\) | 16.2268 | + | 11.7895i | 0.705514 | + | 0.512586i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.6749 | − | 17.2009i | 1.02741 | − | 0.746453i | ||||
\(532\) | −0.101136 | −0.00438478 | ||||||||
\(533\) | −23.8545 | + | 17.3313i | −1.03325 | + | 0.750702i | ||||
\(534\) | −8.14818 | − | 25.0775i | −0.352606 | − | 1.08521i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.59663 | − | 7.99159i | 0.112157 | − | 0.345184i | ||||
\(537\) | −8.95597 | − | 27.5637i | −0.386479 | − | 1.18946i | ||||
\(538\) | −1.23023 | − | 3.78627i | −0.0530392 | − | 0.163238i | ||||
\(539\) | −7.75045 | + | 23.8534i | −0.333836 | + | 1.02744i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.00563620 | − | 0.0173465i | −0.000242319 | − | 0.000745782i | 0.950935 | − | 0.309390i | \(-0.100125\pi\) |
−0.951178 | + | 0.308644i | \(0.900125\pi\) | |||||||
\(542\) | 3.87267 | − | 2.81366i | 0.166346 | − | 0.120857i | ||||
\(543\) | 18.0841 | 0.776063 | ||||||||
\(544\) | 14.7653 | − | 10.7276i | 0.633058 | − | 0.459944i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.112609 | − | 0.0818156i | −0.00481924 | − | 0.00350138i | ||||
\(547\) | −8.05820 | − | 5.85462i | −0.344544 | − | 0.250326i | 0.402033 | − | 0.915625i | \(-0.368304\pi\) |
−0.746576 | + | 0.665300i | \(0.768304\pi\) | |||||||
\(548\) | 6.92366 | − | 21.3088i | 0.295764 | − | 0.910268i | ||||
\(549\) | 60.5199 | 2.58293 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.37656 | −0.399455 | ||||||||
\(552\) | 3.07967 | − | 9.47825i | 0.131080 | − | 0.403421i | ||||
\(553\) | −0.186357 | − | 0.135396i | −0.00792470 | − | 0.00575763i | ||||
\(554\) | −6.96743 | − | 5.06214i | −0.296018 | − | 0.215070i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.2352 | + | 8.16286i | −0.476479 | + | 0.346182i | ||||
\(557\) | 34.9291 | 1.47999 | 0.739996 | − | 0.672611i | \(-0.234827\pi\) | ||||
0.739996 | + | 0.672611i | \(0.234827\pi\) | |||||||
\(558\) | −15.9990 | + | 11.6240i | −0.677294 | + | 0.492083i | ||||
\(559\) | 0.203695 | + | 0.626909i | 0.00861538 | + | 0.0265154i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.4094 | + | 38.1923i | −0.523926 | + | 1.61248i | ||||
\(562\) | −4.21377 | − | 12.9686i | −0.177747 | − | 0.547049i | ||||
\(563\) | −4.88059 | − | 15.0209i | −0.205692 | − | 0.633055i | −0.999684 | − | 0.0251273i | \(-0.992001\pi\) |
0.793992 | − | 0.607928i | \(-0.207999\pi\) | |||||||
\(564\) | −13.0583 | + | 40.1894i | −0.549854 | + | 1.69228i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.538601 | − | 1.65764i | −0.0226391 | − | 0.0696759i | ||||
\(567\) | 0.277838 | − | 0.201861i | 0.0116681 | − | 0.00847736i | ||||
\(568\) | −18.2085 | −0.764012 | ||||||||
\(569\) | 11.7797 | − | 8.55845i | 0.493831 | − | 0.358789i | −0.312825 | − | 0.949811i | \(-0.601275\pi\) |
0.806656 | + | 0.591022i | \(0.201275\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.3401 | − | 16.2310i | −0.934903 | − | 0.679246i | 0.0122857 | − | 0.999925i | \(-0.496089\pi\) |
−0.947188 | + | 0.320678i | \(0.896089\pi\) | |||||||
\(572\) | −19.1447 | − | 13.9094i | −0.800480 | − | 0.581583i | ||||
\(573\) | 20.9285 | − | 64.4112i | 0.874299 | − | 2.69082i | ||||
\(574\) | −0.0930636 | −0.00388440 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −17.0142 | −0.708927 | ||||||||
\(577\) | 8.39043 | − | 25.8231i | 0.349298 | − | 1.07503i | −0.609944 | − | 0.792444i | \(-0.708808\pi\) |
0.959242 | − | 0.282585i | \(-0.0911919\pi\) | |||||||
\(578\) | −1.57003 | − | 1.14069i | −0.0653047 | − | 0.0474466i | ||||
\(579\) | 63.1984 | + | 45.9163i | 2.62643 | + | 1.90822i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.172379 | − | 0.125241i | 0.00715148 | − | 0.00519586i | ||||
\(582\) | −4.28392 | −0.177574 | ||||||||
\(583\) | −26.0088 | + | 18.8965i | −1.07718 | + | 0.782614i | ||||
\(584\) | 2.29483 | + | 7.06275i | 0.0949605 | + | 0.292258i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.63723 | − | 11.1942i | 0.150253 | − | 0.462430i | ||||
\(587\) | 3.30761 | + | 10.1798i | 0.136520 | + | 0.420165i | 0.995823 | − | 0.0913013i | \(-0.0291026\pi\) |
−0.859304 | + | 0.511466i | \(0.829103\pi\) | |||||||
\(588\) | −11.7018 | − | 36.0145i | −0.482575 | − | 1.48521i | ||||
\(589\) | 4.51437 | − | 13.8938i | 0.186011 | − | 0.572484i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.8160 | + | 42.5212i | 0.568313 | + | 1.74909i | ||||
\(592\) | −0.763989 | + | 0.555070i | −0.0313997 | + | 0.0228132i | ||||
\(593\) | 3.84629 | 0.157948 | 0.0789740 | − | 0.996877i | \(-0.474836\pi\) | ||||
0.0789740 | + | 0.996877i | \(0.474836\pi\) | |||||||
\(594\) | −16.0301 | + | 11.6466i | −0.657725 | + | 0.477865i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.96242 | − | 5.78504i | −0.326154 | − | 0.236964i | ||||
\(597\) | −9.45278 | − | 6.86784i | −0.386876 | − | 0.281082i | ||||
\(598\) | −1.00274 | + | 3.08612i | −0.0410051 | + | 0.126201i | ||||
\(599\) | 46.1423 | 1.88532 | 0.942662 | − | 0.333750i | \(-0.108314\pi\) | ||||
0.942662 | + | 0.333750i | \(0.108314\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.3119 | −0.543005 | −0.271503 | − | 0.962438i | \(-0.587521\pi\) | ||||
−0.271503 | + | 0.962438i | \(0.587521\pi\) | |||||||
\(602\) | −0.000642906 | 0.00197866i | −2.62029e−5 | 8.06442e-5i | ||||||
\(603\) | −23.7732 | − | 17.2723i | −0.968121 | − | 0.703381i | ||||
\(604\) | −10.4278 | − | 7.57626i | −0.424302 | − | 0.308274i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.9793 | + | 9.43003i | −0.527249 | + | 0.383069i | ||||
\(607\) | −34.0838 | −1.38342 | −0.691709 | − | 0.722176i | \(-0.743142\pi\) | ||||
−0.691709 | + | 0.722176i | \(0.743142\pi\) | |||||||
\(608\) | −9.90666 | + | 7.19761i | −0.401768 | + | 0.291902i | ||||
\(609\) | 0.0877085 | + | 0.269939i | 0.00355413 | + | 0.0109385i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.11373 | − | 28.0492i | 0.368702 | − | 1.13475i | ||||
\(612\) | −12.8616 | − | 39.5839i | −0.519900 | − | 1.60009i | ||||
\(613\) | −7.87404 | − | 24.2338i | −0.318029 | − | 0.978794i | −0.974490 | − | 0.224433i | \(-0.927947\pi\) |
0.656460 | − | 0.754361i | \(-0.272053\pi\) | |||||||
\(614\) | 0.172235 | − | 0.530084i | 0.00695083 | − | 0.0213924i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0494726 | − | 0.152261i | −0.00199331 | − | 0.00613477i | ||||
\(617\) | −21.7992 | + | 15.8381i | −0.877604 | + | 0.637617i | −0.932617 | − | 0.360869i | \(-0.882480\pi\) |
0.0550123 | + | 0.998486i | \(0.482480\pi\) | |||||||
\(618\) | −28.3459 | −1.14024 | ||||||||
\(619\) | −31.8178 | + | 23.1170i | −1.27886 | + | 0.929149i | −0.999518 | − | 0.0310417i | \(-0.990118\pi\) |
−0.279346 | + | 0.960191i | \(0.590118\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.3175 | − | 11.1288i | −0.614671 | − | 0.446584i | ||||
\(622\) | −5.97948 | − | 4.34435i | −0.239755 | − | 0.174193i | ||||
\(623\) | 0.125075 | − | 0.384942i | 0.00501104 | − | 0.0154224i | ||||
\(624\) | 29.8657 | 1.19559 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.47906 | 0.0990833 | ||||||||
\(627\) | 8.32599 | − | 25.6248i | 0.332508 | − | 1.02335i | ||||
\(628\) | −12.2126 | − | 8.87294i | −0.487334 | − | 0.354069i | ||||
\(629\) | −1.08248 | − | 0.786466i | −0.0431612 | − | 0.0313584i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.09686 | + | 6.60926i | −0.362140 | + | 0.263110i | −0.753944 | − | 0.656938i | \(-0.771851\pi\) |
0.391804 | + | 0.920049i | \(0.371851\pi\) | |||||||
\(632\) | −18.1877 | −0.723467 | ||||||||
\(633\) | −47.2988 | + | 34.3646i | −1.87996 | + | 1.36587i | ||||
\(634\) | 3.51204 | + | 10.8089i | 0.139481 | + | 0.429278i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.9993 | − | 46.1632i | 0.594763 | − | 1.83049i | ||||
\(637\) | 8.16700 | + | 25.1354i | 0.323588 | + | 0.995902i | ||||
\(638\) | −2.13983 | − | 6.58573i | −0.0847169 | − | 0.260732i | ||||
\(639\) | −19.6771 | + | 60.5598i | −0.778413 | + | 2.39571i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.40078 | + | 16.6219i | 0.213318 | + | 0.656525i | 0.999269 | + | 0.0382358i | \(0.0121738\pi\) |
−0.785951 | + | 0.618289i | \(0.787826\pi\) | |||||||
\(642\) | 19.9074 | − | 14.4636i | 0.785683 | − | 0.570832i | ||||
\(643\) | 8.72320 | 0.344009 | 0.172005 | − | 0.985096i | \(-0.444976\pi\) | ||||
0.172005 | + | 0.985096i | \(0.444976\pi\) | |||||||
\(644\) | 0.0577386 | − | 0.0419496i | 0.00227522 | − | 0.00165304i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.56955 | − | 2.59343i | −0.140442 | − | 0.102037i | ||||
\(647\) | 20.2783 | + | 14.7330i | 0.797222 | + | 0.579216i | 0.910098 | − | 0.414393i | \(-0.136006\pi\) |
−0.112876 | + | 0.993609i | \(0.536006\pi\) | |||||||
\(648\) | 8.37925 | − | 25.7887i | 0.329168 | − | 1.01308i | ||||
\(649\) | −15.9648 | −0.626674 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.442212 | −0.0173317 | ||||||||
\(652\) | 2.56705 | − | 7.90058i | 0.100534 | − | 0.309411i | ||||
\(653\) | 24.2525 | + | 17.6205i | 0.949073 | + | 0.689542i | 0.950587 | − | 0.310457i | \(-0.100482\pi\) |
−0.00151446 | + | 0.999999i | \(0.500482\pi\) | |||||||
\(654\) | −7.47357 | − | 5.42986i | −0.292240 | − | 0.212324i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 16.1545 | − | 11.7369i | 0.630727 | − | 0.458250i | ||||
\(657\) | 25.9699 | 1.01318 | ||||||||
\(658\) | 0.0753075 | − | 0.0547141i | 0.00293579 | − | 0.00213298i | ||||
\(659\) | −1.34917 | − | 4.15233i | −0.0525563 | − | 0.161752i | 0.921333 | − | 0.388773i | \(-0.127101\pi\) |
−0.973890 | + | 0.227022i | \(0.927101\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.01126 | + | 18.5008i | −0.233811 | + | 0.719596i | 0.763466 | + | 0.645848i | \(0.223496\pi\) |
−0.997277 | + | 0.0737481i | \(0.976504\pi\) | |||||||
\(662\) | −0.268228 | − | 0.825521i | −0.0104250 | − | 0.0320848i | ||||
\(663\) | 13.0764 | + | 40.2449i | 0.507844 | + | 1.56298i | ||||
\(664\) | 5.19874 | − | 16.0001i | 0.201750 | − | 0.620924i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.375534 | − | 1.15577i | −0.0145516 | − | 0.0447853i | ||||
\(667\) | 5.35311 | − | 3.88926i | 0.207273 | − | 0.150593i | ||||
\(668\) | 32.5258 | 1.25846 | ||||||||
\(669\) | 28.4173 | − | 20.6464i | 1.09868 | − | 0.798235i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.7109 | − | 19.4066i | −1.03116 | − | 0.749184i | ||||
\(672\) | 0.299877 | + | 0.217873i | 0.0115680 | + | 0.00840465i | ||||
\(673\) | 11.1949 | − | 34.4544i | 0.431532 | − | 1.32812i | −0.465067 | − | 0.885276i | \(-0.653970\pi\) |
0.896599 | − | 0.442844i | \(-0.146030\pi\) | |||||||
\(674\) | 7.00436 | 0.269798 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.19886 | −0.0845715 | ||||||||
\(677\) | −0.630538 | + | 1.94060i | −0.0242336 | + | 0.0745832i | −0.962442 | − | 0.271488i | \(-0.912484\pi\) |
0.938208 | + | 0.346071i | \(0.112484\pi\) | |||||||
\(678\) | 3.04442 | + | 2.21190i | 0.116920 | + | 0.0849476i | ||||
\(679\) | −0.0531999 | − | 0.0386520i | −0.00204162 | − | 0.00148333i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.0222 | + | 20.3593i | −1.07381 | + | 0.780170i | ||||
\(682\) | 10.7887 | 0.413121 | ||||||||
\(683\) | 12.8719 | − | 9.35197i | 0.492529 | − | 0.357843i | −0.313627 | − | 0.949546i | \(-0.601544\pi\) |
0.806156 | + | 0.591703i | \(0.201544\pi\) | |||||||
\(684\) | 8.62937 | + | 26.5585i | 0.329952 | + | 1.01549i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.0515557 | + | 0.158672i | −0.00196841 | + | 0.00605814i | ||||
\(687\) | −9.22384 | − | 28.3880i | −0.351911 | − | 1.08307i | ||||
\(688\) | −0.137944 | − | 0.424548i | −0.00525907 | − | 0.0161857i | ||||
\(689\) | −10.4684 | + | 32.2185i | −0.398815 | + | 1.22743i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.20568 | − | 3.71070i | −0.0458662 | − | 0.141162i | 0.925501 | − | 0.378746i | \(-0.123644\pi\) |
−0.971367 | + | 0.237584i | \(0.923644\pi\) | |||||||
\(692\) | −22.3506 | + | 16.2386i | −0.849641 | + | 0.617300i | ||||
\(693\) | −0.559869 | −0.0212677 | ||||||||
\(694\) | −2.05967 | + | 1.49644i | −0.0781840 | + | 0.0568040i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 18.1304 | + | 13.1725i | 0.687230 | + | 0.499301i | ||||
\(697\) | 22.8889 | + | 16.6298i | 0.866979 | + | 0.629897i | ||||
\(698\) | 1.37575 | − | 4.23411i | 0.0520728 | − | 0.160264i | ||||
\(699\) | −48.0261 | −1.81651 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.3587 | 1.14663 | 0.573316 | − | 0.819335i | \(-0.305657\pi\) | ||||
0.573316 | + | 0.819335i | \(0.305657\pi\) | |||||||
\(702\) | −6.45205 | + | 19.8574i | −0.243517 | + | 0.749468i | ||||
\(703\) | 0.726278 | + | 0.527672i | 0.0273921 | + | 0.0199015i | ||||
\(704\) | 7.50936 | + | 5.45587i | 0.283020 | + | 0.205626i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.81574 | + | 2.77230i | −0.143607 | + | 0.104337i | ||||
\(707\) | −0.246267 | −0.00926181 | ||||||||
\(708\) | 19.5006 | − | 14.1680i | 0.732878 | − | 0.532467i | ||||
\(709\) | −15.0082 | − | 46.1906i | −0.563646 | − | 1.73472i | −0.671940 | − | 0.740606i | \(-0.734539\pi\) |
0.108293 | − | 0.994119i | \(-0.465461\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.6546 | + | 60.4905i | −0.737103 | + | 2.26857i | ||||
\(712\) | −9.87554 | − | 30.3938i | −0.370102 | − | 1.13906i | ||||
\(713\) | 3.18568 | + | 9.80452i | 0.119305 | + | 0.367182i | ||||
\(714\) | −0.0412719 | + | 0.127022i | −0.00154456 | + | 0.00475367i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.06395 | − | 15.5852i | −0.189249 | − | 0.582447i | ||||
\(717\) | 35.8713 | − | 26.0620i | 1.33964 | − | 0.973305i | ||||
\(718\) | −4.56651 | −0.170421 | ||||||||
\(719\) | −3.85284 | + | 2.79925i | −0.143687 | + | 0.104395i | −0.657306 | − | 0.753623i | \(-0.728304\pi\) |
0.513620 | + | 0.858018i | \(0.328304\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.352013 | − | 0.255753i | −0.0131097 | − | 0.00952472i | ||||
\(722\) | −5.30591 | − | 3.85497i | −0.197466 | − | 0.143467i | ||||
\(723\) | −24.1944 | + | 74.4626i | −0.899798 | + | 2.76929i | ||||
\(724\) | 10.2252 | 0.380018 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.85135 | 0.105823 | ||||||||
\(727\) | 1.04661 | − | 3.22114i | 0.0388167 | − | 0.119466i | −0.929770 | − | 0.368140i | \(-0.879995\pi\) |
0.968587 | + | 0.248674i | \(0.0799948\pi\) | |||||||
\(728\) | −0.136482 | − | 0.0991600i | −0.00505836 | − | 0.00367511i | ||||
\(729\) | 6.14803 | + | 4.46681i | 0.227705 | + | 0.165437i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.511694 | − | 0.371767i | 0.0189257 | − | 0.0137503i | ||||
\(732\) | 49.8491 | 1.84248 | ||||||||
\(733\) | 12.4596 | − | 9.05244i | 0.460207 | − | 0.334360i | −0.333406 | − | 0.942783i | \(-0.608198\pi\) |
0.793612 | + | 0.608424i | \(0.208198\pi\) | |||||||
\(734\) | −2.76783 | − | 8.51852i | −0.102163 | − | 0.314424i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.67028 | − | 8.21828i | 0.0984279 | − | 0.302930i | ||||
\(737\) | 4.95388 | + | 15.2465i | 0.182479 | + | 0.561612i | ||||
\(738\) | 7.94063 | + | 24.4388i | 0.292299 | + | 0.899603i | ||||
\(739\) | 3.08543 | − | 9.49596i | 0.113499 | − | 0.349315i | −0.878132 | − | 0.478419i | \(-0.841210\pi\) |
0.991631 | + | 0.129104i | \(0.0412101\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.77347 | − | 27.0020i | −0.322301 | − | 0.991942i | ||||
\(742\) | −0.0865015 | + | 0.0628470i | −0.00317557 | + | 0.00230719i | ||||
\(743\) | 41.4419 | 1.52036 | 0.760178 | − | 0.649715i | \(-0.225112\pi\) | ||||
0.760178 | + | 0.649715i | \(0.225112\pi\) | |||||||
\(744\) | −28.2474 | + | 20.5229i | −1.03560 | + | 0.752406i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.24590 | + | 0.905198i | 0.0456156 | + | 0.0331416i | ||||
\(747\) | −47.5967 | − | 34.5811i | −1.74147 | − | 1.26525i | ||||
\(748\) | −7.01662 | + | 21.5949i | −0.256553 | + | 0.789589i | ||||
\(749\) | 0.377719 | 0.0138015 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.1036 | 0.770082 | 0.385041 | − | 0.922900i | \(-0.374187\pi\) | ||||
0.385041 | + | 0.922900i | \(0.374187\pi\) | |||||||
\(752\) | −6.17190 | + | 18.9952i | −0.225066 | + | 0.692682i | ||||
\(753\) | 10.6030 | + | 7.70355i | 0.386396 | + | 0.280733i | ||||
\(754\) | −5.90325 | − | 4.28896i | −0.214984 | − | 0.156195i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.371514 | − | 0.269921i | 0.0135118 | − | 0.00981692i | ||||
\(757\) | −40.7168 | −1.47988 | −0.739938 | − | 0.672675i | \(-0.765145\pi\) | ||||
−0.739938 | + | 0.672675i | \(0.765145\pi\) | |||||||
\(758\) | 10.3705 | − | 7.53460i | 0.376673 | − | 0.273669i | ||||
\(759\) | 5.87545 | + | 18.0828i | 0.213265 | + | 0.656363i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.56877 | + | 4.82817i | −0.0568678 | + | 0.175021i | −0.975456 | − | 0.220196i | \(-0.929330\pi\) |
0.918588 | + | 0.395217i | \(0.129330\pi\) | |||||||
\(762\) | 8.19234 | + | 25.2134i | 0.296777 | + | 0.913387i | ||||
\(763\) | −0.0438191 | − | 0.134861i | −0.00158636 | − | 0.00488231i | ||||
\(764\) | 11.8335 | − | 36.4198i | 0.428121 | − | 1.31762i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.344506 | − | 1.06028i | −0.0124475 | − | 0.0383095i | ||||
\(767\) | −13.6100 | + | 9.88822i | −0.491428 | + | 0.357043i | ||||
\(768\) | 1.59875 | 0.0576899 | ||||||||
\(769\) | 37.8367 | − | 27.4899i | 1.36442 | − | 0.991312i | 0.366275 | − | 0.930507i | \(-0.380633\pi\) |
0.998150 | − | 0.0608058i | \(-0.0193670\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 51.0527 | + | 37.0920i | 1.83862 | + | 1.33583i | ||||
\(772\) | 35.7340 | + | 25.9623i | 1.28610 | + | 0.934404i | ||||
\(773\) | −5.90031 | + | 18.1593i | −0.212219 | + | 0.653144i | 0.787120 | + | 0.616800i | \(0.211571\pi\) |
−0.999339 | + | 0.0363441i | \(0.988429\pi\) | |||||||
\(774\) | 0.574458 | 0.0206485 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.19209 | −0.186385 | ||||||||
\(777\) | 0.00839737 | − | 0.0258445i | 0.000301254 | − | 0.000927165i | ||||
\(778\) | 1.88231 | + | 1.36757i | 0.0674839 | + | 0.0490299i | ||||
\(779\) | −15.3571 | − | 11.1576i | −0.550225 | − | 0.399762i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.1040 | − | 20.4188i | 1.00564 | − | 0.730641i | ||||
\(782\) | 3.11359 | 0.111342 | ||||||||
\(783\) | 34.4441 | − | 25.0251i | 1.23093 | − | 0.894325i | ||||
\(784\) | −5.53077 | − | 17.0219i | −0.197527 | − | 0.607927i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.29362 | − | 7.05903i | 0.0818106 | − | 0.251787i | ||||
\(787\) | 1.24383 | + | 3.82813i | 0.0443379 | + | 0.136458i | 0.970775 | − | 0.239992i | \(-0.0771447\pi\) |
−0.926437 | + | 0.376450i | \(0.877145\pi\) | |||||||
\(788\) | 7.81192 | + | 24.0426i | 0.278288 | + | 0.856483i | ||||
\(789\) | 27.4026 | − | 84.3366i | 0.975560 | − | 3.00246i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.0178501 | + | 0.0549370i | 0.000634677 | + | 0.00195333i | ||||
\(792\) | −35.7629 | + | 25.9833i | −1.27078 | + | 0.923276i | ||||
\(793\) | −34.7910 | −1.23546 | ||||||||
\(794\) | 15.3795 | − | 11.1739i | 0.545799 | − | 0.396546i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.34485 | − | 3.88326i | −0.189443 | − | 0.137639i | ||||
\(797\) | −12.9319 | − | 9.39554i | −0.458070 | − | 0.332807i | 0.334704 | − | 0.942323i | \(-0.391364\pi\) |
−0.792774 | + | 0.609516i | \(0.791364\pi\) | |||||||
\(798\) | 0.0276910 | − | 0.0852241i | 0.000980250 | − | 0.00301690i | ||||
\(799\) | −28.2988 | −1.00114 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −111.759 | −3.94881 | ||||||||
\(802\) | 2.58829 | − | 7.96592i | 0.0913955 | − | 0.281287i | ||||
\(803\) | −11.4620 | − | 8.32765i | −0.404486 | − | 0.293876i | ||||
\(804\) | −19.5816 | − | 14.2268i | −0.690589 | − | 0.501742i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.19735 | − | 6.68226i | 0.323963 | − | 0.235373i | ||||
\(807\) | −24.5806 | −0.865279 | ||||||||
\(808\) | −15.7309 | + | 11.4291i | −0.553410 | + | 0.402076i | ||||
\(809\) | −9.02377 | − | 27.7723i | −0.317259 | − | 0.976422i | −0.974815 | − | 0.223016i | \(-0.928410\pi\) |
0.657556 | − | 0.753406i | \(-0.271590\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.19933 | − | 6.76885i | 0.0772290 | − | 0.237686i | −0.904988 | − | 0.425438i | \(-0.860120\pi\) |
0.982217 | + | 0.187752i | \(0.0601200\pi\) | |||||||
\(812\) | 0.0495927 | + | 0.152631i | 0.00174036 | + | 0.00535629i | ||||
\(813\) | −9.13320 | − | 28.1091i | −0.320315 | − | 0.985829i | ||||
\(814\) | −0.204872 | + | 0.630530i | −0.00718075 | + | 0.0221001i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.85544 | − | 27.2542i | −0.310002 | − | 0.954089i | ||||
\(817\) | −0.343316 | + | 0.249434i | −0.0120111 | + | 0.00872658i | ||||
\(818\) | −0.237034 | −0.00828770 | ||||||||
\(819\) | −0.477287 | + | 0.346769i | −0.0166777 | + | 0.0121171i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.3765 | + | 19.1637i | 0.920547 | + | 0.668816i | 0.943660 | − | 0.330917i | \(-0.107358\pi\) |
−0.0231135 | + | 0.999733i | \(0.507358\pi\) | |||||||
\(822\) | 16.0607 | + | 11.6687i | 0.560180 | + | 0.406994i | ||||
\(823\) | −8.38552 | + | 25.8080i | −0.292301 | + | 0.899609i | 0.691814 | + | 0.722076i | \(0.256812\pi\) |
−0.984115 | + | 0.177533i | \(0.943188\pi\) | |||||||
\(824\) | −34.3551 | −1.19681 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.0530966 | −0.00184747 | ||||||||
\(827\) | 16.9413 | − | 52.1400i | 0.589107 | − | 1.81308i | 0.00699443 | − | 0.999976i | \(-0.497774\pi\) |
0.582112 | − | 0.813108i | \(-0.302226\pi\) | |||||||
\(828\) | −15.9426 | − | 11.5830i | −0.554044 | − | 0.402537i | ||||
\(829\) | −0.381831 | − | 0.277416i | −0.0132615 | − | 0.00963506i | 0.581135 | − | 0.813807i | \(-0.302609\pi\) |
−0.594396 | + | 0.804172i | \(0.702609\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −43.0190 | + | 31.2551i | −1.49231 | + | 1.08423i | ||||
\(832\) | 9.78095 | 0.339093 | ||||||||
\(833\) | 20.5160 | − | 14.9057i | 0.710837 | − | 0.516453i | ||||
\(834\) | −3.80240 | − | 11.7026i | −0.131666 | − | 0.405228i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.70773 | − | 14.4889i | 0.162820 | − | 0.501110i | ||||
\(837\) | 20.4980 | + | 63.0863i | 0.708514 | + | 2.18058i | ||||
\(838\) | −3.75190 | − | 11.5472i | −0.129607 | − | 0.398890i | ||||
\(839\) | −11.8890 | + | 36.5906i | −0.410454 | + | 1.26325i | 0.505799 | + | 0.862651i | \(0.331198\pi\) |
−0.916254 | + | 0.400598i | \(0.868802\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.36361 | − | 13.4298i | −0.150469 | − | 0.463097i | ||||
\(842\) | −12.7057 | + | 9.23122i | −0.437867 | + | 0.318129i | ||||
\(843\) | −84.1929 | −2.89976 | ||||||||
\(844\) | −26.7440 | + | 19.4306i | −0.920566 | + | 0.668830i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −20.7937 | − | 15.1075i | −0.714902 | − | 0.519406i | ||||
\(847\) | 0.0354094 | + | 0.0257264i | 0.00121668 | + | 0.000883971i | ||||
\(848\) | 7.08931 | − | 21.8187i | 0.243448 | − | 0.749256i | ||||
\(849\) | −10.7615 | −0.369333 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.633505 | −0.0217163 | ||||||||
\(852\) | −16.2076 | + | 49.8820i | −0.555264 | + | 1.70893i | ||||
\(853\) | −29.0066 | − | 21.0745i | −0.993167 | − | 0.721578i | −0.0325548 | − | 0.999470i | \(-0.510364\pi\) |
−0.960612 | + | 0.277892i | \(0.910364\pi\) | |||||||
\(854\) | −0.0888365 | − | 0.0645435i | −0.00303992 | − | 0.00220863i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24.1277 | − | 17.5298i | 0.824667 | − | 0.599155i | ||||
\(857\) | −0.386299 | −0.0131957 | −0.00659786 | − | 0.999978i | \(-0.502100\pi\) | ||||
−0.00659786 | + | 0.999978i | \(0.502100\pi\) | |||||||
\(858\) | 16.9629 | − | 12.3243i | 0.579105 | − | 0.420744i | ||||
\(859\) | 6.88765 | + | 21.1980i | 0.235003 | + | 0.723266i | 0.997121 | + | 0.0758275i | \(0.0241598\pi\) |
−0.762117 | + | 0.647439i | \(0.775840\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.177562 | + | 0.546479i | −0.00605129 | + | 0.0186240i | ||||
\(862\) | 0.309731 | + | 0.953255i | 0.0105495 | + | 0.0324680i | ||||
\(863\) | −2.87327 | − | 8.84300i | −0.0978071 | − | 0.301019i | 0.890168 | − | 0.455633i | \(-0.150587\pi\) |
−0.987975 | + | 0.154613i | \(0.950587\pi\) | |||||||
\(864\) | 17.1817 | − | 52.8798i | 0.584533 | − | 1.79901i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.09493 | + | 3.36984i | 0.0372072 | + | 0.114512i | ||||
\(867\) | −9.69383 | + | 7.04298i | −0.329220 | + | 0.239192i | ||||
\(868\) | −0.250039 | −0.00848686 | ||||||||
\(869\) | 28.0719 | − | 20.3954i | 0.952273 | − | 0.691867i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.6665 | + | 9.92928i | 0.463071 | + | 0.336441i | ||||
\(872\) | −9.05792 | − | 6.58096i | −0.306740 | − | 0.222860i | ||||
\(873\) | −5.61085 | + | 17.2684i | −0.189898 | + | 0.584447i | ||||
\(874\) | −2.08903 | −0.0706626 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 21.3910 | 0.722734 | ||||||||
\(877\) | −9.01669 | + | 27.7505i | −0.304472 | + | 0.937069i | 0.675402 | + | 0.737450i | \(0.263970\pi\) |
−0.979874 | + | 0.199618i | \(0.936030\pi\) | |||||||
\(878\) | 5.25362 | + | 3.81698i | 0.177301 | + | 0.128817i | ||||
\(879\) | −58.7940 | − | 42.7164i | −1.98307 | − | 1.44079i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.4203 | − | 23.5548i | 1.09227 | − | 0.793580i | 0.112488 | − | 0.993653i | \(-0.464118\pi\) |
0.979781 | + | 0.200073i | \(0.0641180\pi\) | |||||||
\(882\) | 23.0325 | 0.775543 | ||||||||
\(883\) | 24.9452 | − | 18.1237i | 0.839471 | − | 0.609912i | −0.0827515 | − | 0.996570i | \(-0.526371\pi\) |
0.922223 | + | 0.386658i | \(0.126371\pi\) | |||||||
\(884\) | 7.39373 | + | 22.7556i | 0.248678 | + | 0.765352i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.38558 | − | 10.4198i | 0.113741 | − | 0.350058i | ||||
\(887\) | 11.9135 | + | 36.6659i | 0.400016 | + | 1.23112i | 0.924986 | + | 0.380001i | \(0.124076\pi\) |
−0.524971 | + | 0.851120i | \(0.675924\pi\) | |||||||
\(888\) | −0.663029 | − | 2.04059i | −0.0222498 | − | 0.0684779i | ||||
\(889\) | −0.125753 | + | 0.387029i | −0.00421763 | + | 0.0129805i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.9861 | + | 49.2001i | 0.535554 | + | 1.64826i | ||||
\(892\) | 16.0679 | − | 11.6740i | 0.537993 | − | 0.390875i | ||||
\(893\) | 18.9868 | 0.635370 | ||||||||
\(894\) | 7.05501 | − | 5.12576i | 0.235955 | − | 0.171431i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.218866 | + | 0.159015i | 0.00731179 | + | 0.00531233i | ||||
\(897\) | 16.2088 | + | 11.7764i | 0.541197 | + | 0.393203i | ||||
\(898\) | −0.0618678 | + | 0.190410i | −0.00206456 | + | 0.00635405i | ||||
\(899\) | −23.1818 | −0.773156 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.5052 | 1.08291 | ||||||||
\(902\) | 4.33199 | − | 13.3325i | 0.144240 | − | 0.443924i | ||||
\(903\) | 0.0103923 | + | 0.00755042i | 0.000345833 | + | 0.000251262i | ||||
\(904\) | 3.68982 | + | 2.68081i | 0.122722 | + | 0.0891625i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.23945 | − | 6.71285i | 0.306960 | − | 0.223020i | ||||
\(907\) | 4.77670 | 0.158608 | 0.0793038 | − | 0.996850i | \(-0.474730\pi\) | ||||
0.0793038 | + | 0.996850i | \(0.474730\pi\) | |||||||
\(908\) | −15.8445 | + | 11.5117i | −0.525818 | + | 0.382029i | ||||
\(909\) | 21.0127 | + | 64.6703i | 0.696946 | + | 2.14498i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.56395 | + | 10.9687i | −0.118079 | + | 0.363410i | −0.992577 | − | 0.121620i | \(-0.961191\pi\) |
0.874498 | + | 0.485029i | \(0.161191\pi\) | |||||||
\(912\) | 5.94147 | + | 18.2860i | 0.196742 | + | 0.605509i | ||||
\(913\) | 9.91824 | + | 30.5252i | 0.328246 | + | 1.01024i | ||||
\(914\) | −5.45329 | + | 16.7835i | −0.180379 | + | 0.555149i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.21540 | − | 16.0514i | −0.172322 | − | 0.530352i | ||||
\(917\) | 0.0921738 | − | 0.0669682i | 0.00304385 | − | 0.00221148i | ||||
\(918\) | 20.0341 | 0.661224 | ||||||||
\(919\) | 33.4341 | − | 24.2913i | 1.10289 | − | 0.801296i | 0.121360 | − | 0.992609i | \(-0.461274\pi\) |
0.981529 | + | 0.191313i | \(0.0612745\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.78409 | − | 2.02276i | −0.0917389 | − | 0.0666522i | ||||
\(922\) | −6.46934 | − | 4.70025i | −0.213057 | − | 0.154795i | ||||
\(923\) | 11.3117 | − | 34.8139i | 0.372330 | − | 1.14591i | ||||
\(924\) | −0.461153 | −0.0151708 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.2717 | −0.501860 | ||||||||
\(927\) | −37.1259 | + | 114.262i | −1.21937 | + | 3.75285i | ||||
\(928\) | 15.7202 | + | 11.4214i | 0.516042 | + | 0.374927i | ||||
\(929\) | 10.8549 | + | 7.88657i | 0.356139 | + | 0.258750i | 0.751440 | − | 0.659802i | \(-0.229360\pi\) |
−0.395301 | + | 0.918552i | \(0.629360\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.7650 | + | 10.0009i | −0.451130 | + | 0.327765i | ||||
\(932\) | −27.1552 | −0.889499 | ||||||||
\(933\) | −36.9191 | + | 26.8233i | −1.20868 | + | 0.878155i | ||||
\(934\) | 1.02898 | + | 3.16689i | 0.0336694 | + | 0.103624i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −14.3944 | + | 44.3014i | −0.470496 | + | 1.44804i | ||||
\(937\) | −12.9765 | − | 39.9376i | −0.423924 | − | 1.30470i | −0.904021 | − | 0.427488i | \(-0.859398\pi\) |
0.480097 | − | 0.877215i | \(-0.340602\pi\) | |||||||
\(938\) | 0.0164759 | + | 0.0507075i | 0.000537956 | + | 0.00165566i | ||||
\(939\) | 4.72996 | − | 14.5573i | 0.154356 | − | 0.475060i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.3781 | + | 38.0960i | 0.403515 | + | 1.24189i | 0.922129 | + | 0.386884i | \(0.126449\pi\) |
−0.518613 | + | 0.855009i | \(0.673551\pi\) | |||||||
\(942\) | 10.8208 | − | 7.86176i | 0.352560 | − | 0.256150i | ||||
\(943\) | 13.3954 | 0.436215 | ||||||||
\(944\) | 9.21680 | − | 6.69639i | 0.299981 | − | 0.217949i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.253541 | − | 0.184208i | −0.00824334 | − | 0.00598913i | ||||
\(947\) | 35.5766 | + | 25.8479i | 1.15608 | + | 0.839944i | 0.989278 | − | 0.146046i | \(-0.0466547\pi\) |
0.166806 | + | 0.985990i | \(0.446655\pi\) | |||||||
\(948\) | −16.1891 | + | 49.8249i | −0.525797 | + | 1.61824i | ||||
\(949\) | −14.9293 | −0.484625 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 70.1721 | 2.27549 | ||||||||
\(952\) | −0.0500213 | + | 0.153950i | −0.00162120 | + | 0.00498954i | ||||
\(953\) | 32.8600 | + | 23.8742i | 1.06444 | + | 0.773360i | 0.974904 | − | 0.222624i | \(-0.0714622\pi\) |
0.0895340 | + | 0.995984i | \(0.471462\pi\) | |||||||
\(954\) | 23.8845 | + | 17.3531i | 0.773290 | + | 0.561828i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.2826 | − | 14.7362i | 0.655986 | − | 0.476602i | ||||
\(957\) | −42.7548 | −1.38207 | ||||||||
\(958\) | 9.01439 | − | 6.54934i | 0.291242 | − | 0.211599i | ||||
\(959\) | 0.0941671 | + | 0.289817i | 0.00304081 | + | 0.00935866i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.58141 | − | 4.86709i | 0.0510133 | − | 0.157003i | ||||
\(962\) | 0.215882 | + | 0.664418i | 0.00696033 | + | 0.0214217i | ||||
\(963\) | −32.2288 | − | 99.1900i | −1.03856 | − | 3.19635i | ||||
\(964\) | −13.6801 | + | 42.1031i | −0.440607 | + | 1.35605i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.0195409 | + | 0.0601406i | 0.000628717 | + | 0.00193499i | ||||
\(967\) | −12.9444 | + | 9.40466i | −0.416264 | + | 0.302433i | −0.776133 | − | 0.630569i | \(-0.782821\pi\) |
0.359869 | + | 0.933003i | \(0.382821\pi\) | |||||||
\(968\) | 3.45581 | 0.111074 | ||||||||
\(969\) | −22.0395 | + | 16.0126i | −0.708010 | + | 0.514399i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.9167 | − | 32.6339i | −1.44145 | − | 1.04727i | −0.987738 | − | 0.156122i | \(-0.950101\pi\) |
−0.453708 | − | 0.891150i | \(-0.649899\pi\) | |||||||
\(972\) | −16.3360 | − | 11.8688i | −0.523976 | − | 0.380691i | ||||
\(973\) | 0.0583673 | − | 0.179636i | 0.00187117 | − | 0.00575887i | ||||
\(974\) | 5.10263 | 0.163499 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23.5608 | 0.754162 | ||||||||
\(977\) | −1.95465 | + | 6.01580i | −0.0625348 | + | 0.192462i | −0.977443 | − | 0.211200i | \(-0.932263\pi\) |
0.914908 | + | 0.403662i | \(0.132263\pi\) | |||||||
\(978\) | 5.95474 | + | 4.32637i | 0.190411 | + | 0.138342i | ||||
\(979\) | 49.3257 | + | 35.8372i | 1.57645 | + | 1.14536i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.6761 | + | 23.0141i | −1.01134 | + | 0.734782i | ||||
\(982\) | −3.32659 | −0.106156 | ||||||||
\(983\) | 39.3524 | − | 28.5912i | 1.25515 | − | 0.911916i | 0.256636 | − | 0.966508i | \(-0.417386\pi\) |
0.998509 | + | 0.0545918i | \(0.0173858\pi\) | |||||||
\(984\) | 14.0197 | + | 43.1482i | 0.446932 | + | 1.37551i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.16357 | + | 6.65877i | −0.0689020 | + | 0.212059i | ||||
\(987\) | −0.177603 | − | 0.546606i | −0.00565317 | − | 0.0173987i | ||||
\(988\) | −4.96075 | − | 15.2676i | −0.157823 | − | 0.485728i | ||||
\(989\) | 0.0925388 | − | 0.284805i | 0.00294256 | − | 0.00905628i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.6512 | − | 42.0141i | −0.433645 | − | 1.33462i | −0.894469 | − | 0.447131i | \(-0.852446\pi\) |
0.460823 | − | 0.887492i | \(-0.347554\pi\) | |||||||
\(992\) | −24.4924 | + | 17.7947i | −0.777633 | + | 0.564984i | ||||
\(993\) | −5.35931 | −0.170073 | ||||||||
\(994\) | 0.0934697 | − | 0.0679097i | 0.00296468 | − | 0.00215397i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −39.2046 | − | 28.4838i | −1.24224 | − | 0.902543i | ||||
\(997\) | 32.5437 | + | 23.6444i | 1.03067 | + | 0.748825i | 0.968442 | − | 0.249237i | \(-0.0801799\pi\) |
0.0622265 | + | 0.998062i | \(0.480180\pi\) | |||||||
\(998\) | −0.167814 | + | 0.516479i | −0.00531207 | + | 0.0163489i | ||||
\(999\) | −4.07623 | −0.128966 |
(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 | 625.2.d.p.501.3 | 16 | ||
5.2 | odd | 4 | 625.2.e.k.124.4 | 32 | |||
5.3 | odd | 4 | 625.2.e.k.124.5 | 32 | |||
5.4 | even | 2 | 625.2.d.n.501.2 | 16 | |||
25.2 | odd | 20 | 625.2.e.j.249.4 | 32 | |||
25.3 | odd | 20 | 625.2.e.j.374.4 | 32 | |||
25.4 | even | 10 | 625.2.d.m.251.3 | 16 | |||
25.6 | even | 5 | inner | 625.2.d.p.126.3 | 16 | ||
25.8 | odd | 20 | 625.2.e.k.499.4 | 32 | |||
25.9 | even | 10 | 625.2.a.g.1.4 | yes | 8 | ||
25.11 | even | 5 | 625.2.d.q.376.2 | 16 | |||
25.12 | odd | 20 | 625.2.b.d.624.7 | 16 | |||
25.13 | odd | 20 | 625.2.b.d.624.10 | 16 | |||
25.14 | even | 10 | 625.2.d.m.376.3 | 16 | |||
25.16 | even | 5 | 625.2.a.e.1.5 | ✓ | 8 | ||
25.17 | odd | 20 | 625.2.e.k.499.5 | 32 | |||
25.19 | even | 10 | 625.2.d.n.126.2 | 16 | |||
25.21 | even | 5 | 625.2.d.q.251.2 | 16 | |||
25.22 | odd | 20 | 625.2.e.j.374.5 | 32 | |||
25.23 | odd | 20 | 625.2.e.j.249.5 | 32 | |||
75.41 | odd | 10 | 5625.2.a.be.1.4 | 8 | |||
75.59 | odd | 10 | 5625.2.a.s.1.5 | 8 | |||
100.59 | odd | 10 | 10000.2.a.be.1.1 | 8 | |||
100.91 | odd | 10 | 10000.2.a.bn.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.5 | ✓ | 8 | 25.16 | even | 5 | ||
625.2.a.g.1.4 | yes | 8 | 25.9 | even | 10 | ||
625.2.b.d.624.7 | 16 | 25.12 | odd | 20 | |||
625.2.b.d.624.10 | 16 | 25.13 | odd | 20 | |||
625.2.d.m.251.3 | 16 | 25.4 | even | 10 | |||
625.2.d.m.376.3 | 16 | 25.14 | even | 10 | |||
625.2.d.n.126.2 | 16 | 25.19 | even | 10 | |||
625.2.d.n.501.2 | 16 | 5.4 | even | 2 | |||
625.2.d.p.126.3 | 16 | 25.6 | even | 5 | inner | ||
625.2.d.p.501.3 | 16 | 1.1 | even | 1 | trivial | ||
625.2.d.q.251.2 | 16 | 25.21 | even | 5 | |||
625.2.d.q.376.2 | 16 | 25.11 | even | 5 | |||
625.2.e.j.249.4 | 32 | 25.2 | odd | 20 | |||
625.2.e.j.249.5 | 32 | 25.23 | odd | 20 | |||
625.2.e.j.374.4 | 32 | 25.3 | odd | 20 | |||
625.2.e.j.374.5 | 32 | 25.22 | odd | 20 | |||
625.2.e.k.124.4 | 32 | 5.2 | odd | 4 | |||
625.2.e.k.124.5 | 32 | 5.3 | odd | 4 | |||
625.2.e.k.499.4 | 32 | 25.8 | odd | 20 | |||
625.2.e.k.499.5 | 32 | 25.17 | odd | 20 | |||
5625.2.a.s.1.5 | 8 | 75.59 | odd | 10 | |||
5625.2.a.be.1.4 | 8 | 75.41 | odd | 10 | |||
10000.2.a.be.1.1 | 8 | 100.59 | odd | 10 | |||
10000.2.a.bn.1.8 | 8 | 100.91 | odd | 10 |