Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(136,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.136");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.et (of order \(12\), degree \(4\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 136.5 | ||
Character | \(\chi\) | \(=\) | 819.136 |
Dual form | 819.2.et.b.271.5 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.270646 | − | 0.270646i | 0.191376 | − | 0.191376i | −0.604915 | − | 0.796290i | \(-0.706793\pi\) |
0.796290 | + | 0.604915i | \(0.206793\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.85350i | 0.926751i | ||||||||
\(5\) | −0.959617 | + | 3.58134i | −0.429154 | + | 1.60162i | 0.325528 | + | 0.945533i | \(0.394458\pi\) |
−0.754681 | + | 0.656091i | \(0.772209\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.30385 | + | 2.30217i | 0.492809 | + | 0.870137i | ||||
\(8\) | 1.04293 | + | 1.04293i | 0.368733 | + | 0.368733i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.709559 | + | 1.22899i | 0.224382 | + | 0.388641i | ||||
\(11\) | −0.0226729 | + | 0.0846164i | −0.00683614 | + | 0.0255128i | −0.969260 | − | 0.246040i | \(-0.920871\pi\) |
0.962424 | + | 0.271553i | \(0.0875372\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.63590 | − | 3.21307i | 0.453716 | − | 0.891146i | ||||
\(14\) | 0.975954 | + | 0.270190i | 0.260835 | + | 0.0722114i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.14247 | −0.785618 | ||||||||
\(17\) | 5.89043 | 1.42864 | 0.714319 | − | 0.699820i | \(-0.246736\pi\) | ||||
0.714319 | + | 0.699820i | \(0.246736\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.58643 | + | 0.960980i | −0.822782 | + | 0.220464i | −0.645563 | − | 0.763707i | \(-0.723377\pi\) |
−0.177220 | + | 0.984171i | \(0.556710\pi\) | |||||||
\(20\) | −6.63802 | − | 1.77865i | −1.48431 | − | 0.397719i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0167648 | + | 0.0290374i | 0.00357426 | + | 0.00619080i | ||||
\(23\) | 0.446373i | 0.0930753i | 0.998917 | + | 0.0465377i | \(0.0148187\pi\) | ||||
−0.998917 | + | 0.0465377i | \(0.985181\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.57501 | − | 4.37343i | −1.51500 | − | 0.874686i | ||||
\(26\) | −0.426856 | − | 1.31235i | −0.0837133 | − | 0.257374i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.26707 | + | 2.41669i | −0.806401 | + | 0.456711i | ||||
\(29\) | −0.706429 | + | 1.22357i | −0.131181 | + | 0.227212i | −0.924132 | − | 0.382073i | \(-0.875210\pi\) |
0.792951 | + | 0.609285i | \(0.208543\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.94183 | + | 0.520311i | −0.348762 | + | 0.0934505i | −0.428947 | − | 0.903329i | \(-0.641115\pi\) |
0.0801853 | + | 0.996780i | \(0.474449\pi\) | |||||||
\(32\) | −2.93637 | + | 2.93637i | −0.519081 | + | 0.519081i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.59422 | − | 1.59422i | 0.273406 | − | 0.273406i | ||||
\(35\) | −9.49604 | + | 2.46033i | −1.60512 | + | 0.415872i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.87469 | + | 1.87469i | 0.308197 | + | 0.308197i | 0.844210 | − | 0.536013i | \(-0.180070\pi\) |
−0.536013 | + | 0.844210i | \(0.680070\pi\) | |||||||
\(38\) | −0.710566 | + | 1.23074i | −0.115269 | + | 0.199652i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.73592 | + | 2.73428i | −0.748815 | + | 0.432328i | ||||
\(41\) | −3.00264 | + | 0.804556i | −0.468934 | + | 0.125651i | −0.485545 | − | 0.874211i | \(-0.661379\pi\) |
0.0166112 | + | 0.999862i | \(0.494712\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.64788 | − | 4.99286i | 1.31879 | − | 0.761404i | 0.335256 | − | 0.942127i | \(-0.391177\pi\) |
0.983534 | + | 0.180724i | \(0.0578439\pi\) | |||||||
\(44\) | −0.156837 | − | 0.0420243i | −0.0236440 | − | 0.00633539i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.120809 | + | 0.120809i | 0.0178123 | + | 0.0178123i | ||||
\(47\) | −8.84037 | − | 2.36877i | −1.28950 | − | 0.345521i | −0.452030 | − | 0.892003i | \(-0.649300\pi\) |
−0.837471 | + | 0.546482i | \(0.815967\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.59995 | + | 6.00336i | −0.514278 | + | 0.857623i | ||||
\(50\) | −3.23380 | + | 0.866493i | −0.457328 | + | 0.122541i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.95544 | + | 3.03214i | 0.825870 | + | 0.420482i | ||||
\(53\) | 6.28118 | − | 10.8793i | 0.862786 | − | 1.49439i | −0.00644326 | − | 0.999979i | \(-0.502051\pi\) |
0.869229 | − | 0.494410i | \(-0.164616\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.281283 | − | 0.162399i | −0.0379282 | − | 0.0218978i | ||||
\(56\) | −1.04118 | + | 3.76084i | −0.139133 | + | 0.502563i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.139962 | + | 0.522347i | 0.0183780 | + | 0.0685875i | ||||
\(59\) | −5.05813 | + | 5.05813i | −0.658513 | + | 0.658513i | −0.955028 | − | 0.296515i | \(-0.904175\pi\) |
0.296515 | + | 0.955028i | \(0.404175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.110587 | + | 0.0638473i | 0.0141592 | + | 0.00817481i | 0.507063 | − | 0.861909i | \(-0.330731\pi\) |
−0.492904 | + | 0.870084i | \(0.664065\pi\) | |||||||
\(62\) | −0.384727 | + | 0.666367i | −0.0488604 | + | 0.0846287i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 4.69551i | − | 0.586939i | ||||||
\(65\) | 9.93727 | + | 8.94203i | 1.23257 | + | 1.10912i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.61759 | + | 2.57703i | 1.17498 | + | 0.314834i | 0.792932 | − | 0.609310i | \(-0.208554\pi\) |
0.382044 | + | 0.924144i | \(0.375220\pi\) | |||||||
\(68\) | 10.9179i | 1.32399i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.90419 | + | 3.23594i | −0.227594 | + | 0.386769i | ||||
\(71\) | 9.83277 | + | 2.63468i | 1.16694 | + | 0.312679i | 0.789732 | − | 0.613451i | \(-0.210219\pi\) |
0.377203 | + | 0.926131i | \(0.376886\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.37094 | − | 8.84847i | −0.277498 | − | 1.03563i | −0.954149 | − | 0.299332i | \(-0.903236\pi\) |
0.676652 | − | 0.736303i | \(-0.263430\pi\) | |||||||
\(74\) | 1.01475 | 0.117963 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.78118 | − | 6.64744i | −0.204315 | − | 0.762514i | ||||
\(77\) | −0.224363 | + | 0.0581303i | −0.0255686 | + | 0.00662457i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.75744 | + | 3.04398i | 0.197728 | + | 0.342474i | 0.947791 | − | 0.318891i | \(-0.103311\pi\) |
−0.750064 | + | 0.661366i | \(0.769977\pi\) | |||||||
\(80\) | 3.01557 | − | 11.2543i | 0.337151 | − | 1.25826i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.594903 | + | 1.03040i | −0.0656961 | + | 0.113789i | ||||
\(83\) | 2.17980 | + | 2.17980i | 0.239264 | + | 0.239264i | 0.816545 | − | 0.577281i | \(-0.195886\pi\) |
−0.577281 | + | 0.816545i | \(0.695886\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.65256 | + | 21.0956i | −0.613106 | + | 2.28814i | ||||
\(86\) | 0.989217 | − | 3.69181i | 0.106670 | − | 0.398098i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.111896 | + | 0.0646030i | −0.0119281 | + | 0.00688670i | ||||
\(89\) | −1.19449 | + | 1.19449i | −0.126616 | + | 0.126616i | −0.767575 | − | 0.640959i | \(-0.778537\pi\) |
0.640959 | + | 0.767575i | \(0.278537\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.53000 | − | 0.423256i | 0.999015 | − | 0.0443693i | ||||
\(92\) | −0.827354 | −0.0862576 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.03371 | + | 1.75151i | −0.312903 | + | 0.180655i | ||||
\(95\) | − | 13.7664i | − | 1.41240i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.452103 | + | 1.68727i | −0.0459041 | + | 0.171317i | −0.985072 | − | 0.172141i | \(-0.944932\pi\) |
0.939168 | + | 0.343458i | \(0.111598\pi\) | |||||||
\(98\) | 0.650474 | + | 2.59910i | 0.0657078 | + | 0.262548i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.10616 | − | 14.0403i | 0.810616 | − | 1.40403i | ||||
\(101\) | 3.41120 | + | 5.90838i | 0.339427 | + | 0.587905i | 0.984325 | − | 0.176363i | \(-0.0564334\pi\) |
−0.644898 | + | 0.764269i | \(0.723100\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.00029 | + | 8.66076i | 0.492693 | + | 0.853370i | 0.999965 | − | 0.00841640i | \(-0.00267906\pi\) |
−0.507271 | + | 0.861787i | \(0.669346\pi\) | |||||||
\(104\) | 5.05716 | − | 1.64489i | 0.495895 | − | 0.161295i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.24447 | − | 4.64442i | −0.120873 | − | 0.451106i | ||||
\(107\) | 0.0598871 | 0.00578950 | 0.00289475 | − | 0.999996i | \(-0.499079\pi\) | ||||
0.00289475 | + | 0.999996i | \(0.499079\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.25671 | − | 15.8862i | −0.407719 | − | 1.52163i | −0.798986 | − | 0.601350i | \(-0.794630\pi\) |
0.391267 | − | 0.920277i | \(-0.372037\pi\) | |||||||
\(110\) | −0.120081 | + | 0.0321755i | −0.0114492 | + | 0.00306781i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.09731 | − | 7.23450i | −0.387160 | − | 0.683596i | ||||
\(113\) | −2.74673 | − | 4.75748i | −0.258391 | − | 0.447546i | 0.707420 | − | 0.706793i | \(-0.249859\pi\) |
−0.965811 | + | 0.259247i | \(0.916526\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.59862 | − | 0.428348i | −0.149072 | − | 0.0399436i | ||||
\(116\) | −2.26789 | − | 1.30937i | −0.210569 | − | 0.121572i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.73793i | 0.252047i | ||||||||
\(119\) | 7.68024 | + | 13.5608i | 0.704046 | + | 1.24311i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.51963 | + | 5.49616i | 0.865421 | + | 0.499651i | ||||
\(122\) | 0.0472098 | − | 0.0126498i | 0.00427418 | − | 0.00114526i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.964397 | − | 3.59918i | −0.0866054 | − | 0.323216i | ||||
\(125\) | 9.82324 | − | 9.82324i | 0.878617 | − | 0.878617i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.7405 | + | 8.51045i | 1.30801 | + | 0.755180i | 0.981764 | − | 0.190104i | \(-0.0608826\pi\) |
0.326247 | + | 0.945285i | \(0.394216\pi\) | |||||||
\(128\) | −7.14355 | − | 7.14355i | −0.631407 | − | 0.631407i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.10960 | − | 0.269359i | 0.448142 | − | 0.0236243i | ||||
\(131\) | −2.35567 | + | 1.36005i | −0.205816 | + | 0.118828i | −0.599365 | − | 0.800475i | \(-0.704580\pi\) |
0.393549 | + | 0.919303i | \(0.371247\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.88850 | − | 7.00358i | −0.597309 | − | 0.607287i | ||||
\(134\) | 3.30042 | − | 1.90550i | 0.285113 | − | 0.164610i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.14333 | + | 6.14333i | 0.526786 | + | 0.526786i | ||||
\(137\) | 3.04603 | + | 3.04603i | 0.260240 | + | 0.260240i | 0.825152 | − | 0.564911i | \(-0.191090\pi\) |
−0.564911 | + | 0.825152i | \(0.691090\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.1251 | + | 7.00040i | −1.02843 | + | 0.593766i | −0.916535 | − | 0.399953i | \(-0.869026\pi\) |
−0.111898 | + | 0.993720i | \(0.535693\pi\) | |||||||
\(140\) | −4.56023 | − | 17.6009i | −0.385410 | − | 1.48755i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.37426 | − | 1.94813i | 0.283162 | − | 0.163484i | ||||
\(143\) | 0.234788 | + | 0.211273i | 0.0196340 | + | 0.0176676i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.70412 | − | 3.70412i | −0.307611 | − | 0.307611i | ||||
\(146\) | −3.03649 | − | 1.75312i | −0.251301 | − | 0.145089i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.47473 | + | 3.47473i | −0.285621 | + | 0.285621i | ||||
\(149\) | 2.37346 | + | 8.85786i | 0.194441 | + | 0.725664i | 0.992411 | + | 0.122967i | \(0.0392408\pi\) |
−0.797970 | + | 0.602698i | \(0.794092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.33161 | + | 1.96450i | −0.596638 | + | 0.159869i | −0.544485 | − | 0.838770i | \(-0.683275\pi\) |
−0.0521530 | + | 0.998639i | \(0.516608\pi\) | |||||||
\(152\) | −4.74264 | − | 2.73817i | −0.384679 | − | 0.222095i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0449902 | + | 0.0764557i | −0.00362542 | + | 0.00616098i | ||||
\(155\) | − | 7.45364i | − | 0.598691i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.438021 | − | 0.252891i | −0.0349578 | − | 0.0201829i | 0.482419 | − | 0.875940i | \(-0.339758\pi\) |
−0.517377 | + | 0.855758i | \(0.673092\pi\) | |||||||
\(158\) | 1.29948 | + | 0.348196i | 0.103381 | + | 0.0277010i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.69834 | − | 13.3339i | −0.608607 | − | 1.05414i | ||||
\(161\) | −1.02763 | + | 0.582004i | −0.0809883 | + | 0.0458684i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.28976 | + | 1.14944i | −0.336000 | + | 0.0900308i | −0.422874 | − | 0.906188i | \(-0.638979\pi\) |
0.0868745 | + | 0.996219i | \(0.472312\pi\) | |||||||
\(164\) | −1.49125 | − | 5.56541i | −0.116447 | − | 0.434585i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.17991 | 0.0915785 | ||||||||
\(167\) | 2.07730 | + | 7.75258i | 0.160746 | + | 0.599913i | 0.998545 | + | 0.0539330i | \(0.0171757\pi\) |
−0.837798 | + | 0.545980i | \(0.816158\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.64768 | − | 10.5125i | −0.588283 | − | 0.808655i | ||||
\(170\) | 4.17960 | + | 7.23929i | 0.320561 | + | 0.555228i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.25427 | + | 16.0289i | 0.705631 | + | 1.22219i | ||||
\(173\) | −0.631547 | + | 1.09387i | −0.0480157 | + | 0.0831656i | −0.889034 | − | 0.457841i | \(-0.848623\pi\) |
0.841019 | + | 0.541006i | \(0.181956\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.191697 | − | 23.1412i | 0.0144909 | − | 1.74931i | ||||
\(176\) | 0.0712489 | − | 0.265905i | 0.00537059 | − | 0.0200433i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.646569i | 0.0484624i | ||||||||
\(179\) | −1.46377 | + | 0.845110i | −0.109408 | + | 0.0631665i | −0.553705 | − | 0.832713i | \(-0.686787\pi\) |
0.444298 | + | 0.895879i | \(0.353453\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.30825 | −0.617547 | −0.308774 | − | 0.951136i | \(-0.599919\pi\) | ||||
−0.308774 | + | 0.951136i | \(0.599919\pi\) | |||||||
\(182\) | 2.46470 | − | 2.69381i | 0.182696 | − | 0.199678i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.465538 | + | 0.465538i | −0.0343199 | + | 0.0343199i | ||||
\(185\) | −8.51287 | + | 4.91491i | −0.625879 | + | 0.361351i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.133553 | + | 0.498427i | −0.00976637 | + | 0.0364486i | ||||
\(188\) | 4.39052 | − | 16.3856i | 0.320211 | − | 1.19505i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.72581 | − | 3.72581i | −0.270299 | − | 0.270299i | ||||
\(191\) | 10.3140 | − | 17.8644i | 0.746296 | − | 1.29262i | −0.203290 | − | 0.979119i | \(-0.565164\pi\) |
0.949587 | − | 0.313505i | \(-0.101503\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.47003 | + | 12.9503i | −0.249779 | + | 0.932186i | 0.721143 | + | 0.692787i | \(0.243617\pi\) |
−0.970921 | + | 0.239400i | \(0.923049\pi\) | |||||||
\(194\) | 0.334293 | + | 0.579013i | 0.0240009 | + | 0.0415707i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.1272 | − | 6.67251i | −0.794803 | − | 0.476608i | ||||
\(197\) | −4.28034 | − | 15.9744i | −0.304961 | − | 1.13813i | −0.932979 | − | 0.359932i | \(-0.882800\pi\) |
0.628017 | − | 0.778199i | \(-0.283867\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.9622 | 0.918863 | 0.459432 | − | 0.888213i | \(-0.348053\pi\) | ||||
0.459432 | + | 0.888213i | \(0.348053\pi\) | |||||||
\(200\) | −3.33903 | − | 12.4614i | −0.236105 | − | 0.881157i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.52231 | + | 0.675850i | 0.177469 | + | 0.0475526i | ||||
\(203\) | −3.73795 | − | 0.0309644i | −0.262352 | − | 0.00217327i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 11.5256i | − | 0.804980i | ||||||
\(206\) | 3.69731 | + | 0.990691i | 0.257604 | + | 0.0690247i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.14076 | + | 10.0970i | −0.356448 | + | 0.700100i | ||||
\(209\) | − | 0.325259i | − | 0.0224986i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.19052 | + | 5.52614i | −0.219644 | + | 0.380435i | −0.954699 | − | 0.297572i | \(-0.903823\pi\) |
0.735055 | + | 0.678008i | \(0.237156\pi\) | |||||||
\(212\) | 20.1648 | + | 11.6422i | 1.38493 | + | 0.799587i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.0162082 | − | 0.0162082i | 0.00110797 | − | 0.00110797i | ||||
\(215\) | 9.58246 | + | 35.7622i | 0.653519 | + | 2.43896i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.72969 | − | 3.79200i | −0.253188 | − | 0.257418i | ||||
\(218\) | −5.45161 | − | 3.14749i | −0.369229 | − | 0.213175i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.301006 | − | 0.521358i | 0.0202938 | − | 0.0351500i | ||||
\(221\) | 9.63614 | − | 18.9264i | 0.648197 | − | 1.27313i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3622 | − | 3.31244i | 0.827834 | − | 0.221817i | 0.180065 | − | 0.983655i | \(-0.442369\pi\) |
0.647769 | + | 0.761837i | \(0.275702\pi\) | |||||||
\(224\) | −10.5886 | − | 2.93142i | −0.707480 | − | 0.195864i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.03098 | − | 0.544201i | −0.135099 | − | 0.0361997i | ||||
\(227\) | 8.38467 | + | 8.38467i | 0.556510 | + | 0.556510i | 0.928312 | − | 0.371802i | \(-0.121260\pi\) |
−0.371802 | + | 0.928312i | \(0.621260\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.2594 | + | 4.08875i | 1.00837 | + | 0.270192i | 0.724949 | − | 0.688803i | \(-0.241863\pi\) |
0.283423 | + | 0.958995i | \(0.408530\pi\) | |||||||
\(230\) | −0.548589 | + | 0.316728i | −0.0361729 | + | 0.0208844i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.01286 | + | 0.539345i | −0.132151 | + | 0.0354098i | ||||
\(233\) | −11.6063 | + | 6.70088i | −0.760352 | + | 0.438989i | −0.829422 | − | 0.558623i | \(-0.811330\pi\) |
0.0690703 | + | 0.997612i | \(0.477997\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.9667 | − | 29.3873i | 1.10679 | − | 1.91701i | ||||
\(236\) | −9.37526 | − | 9.37526i | −0.610277 | − | 0.610277i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.74879 | + | 1.59154i | 0.372638 | + | 0.103164i | ||||
\(239\) | 14.4526 | − | 14.4526i | 0.934861 | − | 0.934861i | −0.0631438 | − | 0.998004i | \(-0.520113\pi\) |
0.998004 | + | 0.0631438i | \(0.0201127\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.721809 | − | 0.721809i | 0.0464958 | − | 0.0464958i | −0.683477 | − | 0.729972i | \(-0.739533\pi\) |
0.729972 | + | 0.683477i | \(0.239533\pi\) | |||||||
\(242\) | 4.06396 | − | 1.08894i | 0.261241 | − | 0.0699994i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.118341 | + | 0.204973i | −0.00757601 | + | 0.0131220i | ||||
\(245\) | −18.0455 | − | 18.6536i | −1.15289 | − | 1.19173i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.77933 | + | 13.0955i | −0.176844 | + | 0.833247i | ||||
\(248\) | −2.56785 | − | 1.48255i | −0.163058 | − | 0.0941418i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 5.31724i | − | 0.336292i | ||||||
\(251\) | 5.59470 | + | 9.69030i | 0.353134 | + | 0.611646i | 0.986797 | − | 0.161963i | \(-0.0517826\pi\) |
−0.633663 | + | 0.773609i | \(0.718449\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.0377705 | − | 0.0101206i | −0.00237461 | − | 0.000636275i | ||||
\(254\) | 6.29278 | − | 1.68615i | 0.394844 | − | 0.105798i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.52428 | 0.345267 | ||||||||
\(257\) | 9.42673 | 0.588023 | 0.294012 | − | 0.955802i | \(-0.405010\pi\) | ||||
0.294012 | + | 0.955802i | \(0.405010\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.87153 | + | 6.76015i | −0.116291 | + | 0.420055i | ||||
\(260\) | −16.5741 | + | 18.4187i | −1.02788 | + | 1.14228i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.269462 | + | 1.00564i | −0.0166474 | + | 0.0621289i | ||||
\(263\) | 6.87360 | + | 11.9054i | 0.423844 | + | 0.734120i | 0.996312 | − | 0.0858074i | \(-0.0273470\pi\) |
−0.572467 | + | 0.819928i | \(0.694014\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.9350 | + | 32.9350i | 2.02318 | + | 2.02318i | ||||
\(266\) | −3.75983 | − | 0.0311457i | −0.230530 | − | 0.00190966i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.77652 | + | 17.8262i | −0.291772 | + | 1.08891i | ||||
\(269\) | − | 23.5848i | − | 1.43799i | −0.695015 | − | 0.718995i | \(-0.744602\pi\) | ||
0.695015 | − | 0.718995i | \(-0.255398\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.42801 | + | 6.42801i | −0.390474 | + | 0.390474i | −0.874856 | − | 0.484382i | \(-0.839044\pi\) |
0.484382 | + | 0.874856i | \(0.339044\pi\) | |||||||
\(272\) | −18.5105 | −1.12236 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.64879 | 0.0996072 | ||||||||
\(275\) | 0.541811 | − | 0.541811i | 0.0326725 | − | 0.0326725i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 12.6627i | − | 0.760828i | −0.924816 | − | 0.380414i | \(-0.875781\pi\) | ||
0.924816 | − | 0.380414i | \(-0.124219\pi\) | |||||||
\(278\) | −1.38697 | + | 5.17622i | −0.0831846 | + | 0.310449i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.4697 | − | 7.33778i | −0.745208 | − | 0.438516i | ||||
\(281\) | 23.5896 | + | 23.5896i | 1.40724 | + | 1.40724i | 0.773769 | + | 0.633468i | \(0.218369\pi\) |
0.633468 | + | 0.773769i | \(0.281631\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.4194 | − | 19.7790i | −0.678813 | − | 1.17574i | −0.975339 | − | 0.220713i | \(-0.929162\pi\) |
0.296526 | − | 0.955025i | \(-0.404172\pi\) | |||||||
\(284\) | −4.88339 | + | 18.2251i | −0.289776 | + | 1.08146i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.120725 | − | 0.00636415i | 0.00713860 | − | 0.000376320i | ||||
\(287\) | −5.76722 | − | 5.86357i | −0.340428 | − | 0.346115i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.6971 | 1.04101 | ||||||||
\(290\) | −2.00501 | −0.117738 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.4007 | − | 4.39454i | 0.959776 | − | 0.257171i | ||||
\(293\) | −11.5762 | − | 3.10184i | −0.676290 | − | 0.181211i | −0.0957036 | − | 0.995410i | \(-0.530510\pi\) |
−0.580587 | + | 0.814198i | \(0.697177\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.2610 | − | 22.9688i | −0.772087 | − | 1.33729i | ||||
\(296\) | 3.91035i | 0.227284i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.03971 | + | 1.75498i | 0.176086 | + | 0.101663i | ||||
\(299\) | 1.43423 | + | 0.730221i | 0.0829437 | + | 0.0422298i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.7699 | + | 13.3989i | 1.31244 | + | 0.772302i | ||||
\(302\) | −1.45259 | + | 2.51596i | −0.0835870 | + | 0.144777i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.2702 | − | 3.01985i | 0.646393 | − | 0.173200i | ||||
\(305\) | −0.334780 | + | 0.334780i | −0.0191694 | + | 0.0191694i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.9842 | + | 18.9842i | −1.08348 | + | 1.08348i | −0.0873012 | + | 0.996182i | \(0.527824\pi\) |
−0.996182 | + | 0.0873012i | \(0.972176\pi\) | |||||||
\(308\) | −0.107745 | − | 0.415858i | −0.00613932 | − | 0.0236957i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.01730 | − | 2.01730i | −0.114575 | − | 0.114575i | ||||
\(311\) | 14.8991 | − | 25.8060i | 0.844851 | − | 1.46333i | −0.0408993 | − | 0.999163i | \(-0.513022\pi\) |
0.885750 | − | 0.464162i | \(-0.153644\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.1617 | − | 8.17629i | 0.800469 | − | 0.462151i | −0.0431661 | − | 0.999068i | \(-0.513744\pi\) |
0.843635 | + | 0.536917i | \(0.180411\pi\) | |||||||
\(314\) | −0.186992 | + | 0.0501045i | −0.0105526 | + | 0.00282756i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.64202 | + | 3.25742i | −0.317388 | + | 0.183244i | ||||
\(317\) | 16.4961 | + | 4.42013i | 0.926516 | + | 0.248259i | 0.690368 | − | 0.723458i | \(-0.257449\pi\) |
0.236147 | + | 0.971717i | \(0.424115\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0875174 | − | 0.0875174i | −0.00490004 | − | 0.00490004i | ||||
\(320\) | 16.8162 | + | 4.50589i | 0.940056 | + | 0.251887i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.120606 | + | 0.435640i | −0.00672110 | + | 0.0242773i | ||||
\(323\) | −21.1256 | + | 5.66058i | −1.17546 | + | 0.314963i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.4441 | + | 17.1846i | −1.46685 | + | 0.953228i | ||||
\(326\) | −0.849915 | + | 1.47210i | −0.0470724 | + | 0.0815318i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.97066 | − | 2.29246i | −0.219243 | − | 0.126580i | ||||
\(329\) | −6.07321 | − | 23.4405i | −0.334827 | − | 1.29232i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.63617 | + | 21.0345i | 0.309792 | + | 1.15616i | 0.928742 | + | 0.370728i | \(0.120892\pi\) |
−0.618950 | + | 0.785430i | \(0.712442\pi\) | |||||||
\(332\) | −4.04026 | + | 4.04026i | −0.221738 | + | 0.221738i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.66042 | + | 1.53599i | 0.145571 | + | 0.0840457i | ||||
\(335\) | −18.4584 | + | 31.9709i | −1.00849 | + | 1.74676i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.6556i | − | 1.23413i | −0.786912 | − | 0.617066i | \(-0.788321\pi\) | ||
0.786912 | − | 0.617066i | \(-0.211679\pi\) | |||||||
\(338\) | −4.91498 | − | 0.775358i | −0.267340 | − | 0.0421739i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −39.1008 | − | 10.4770i | −2.12054 | − | 0.568196i | ||||
\(341\) | − | 0.176107i | − | 0.00953674i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5145 | − | 0.460196i | −0.999691 | − | 0.0248483i | ||||
\(344\) | 14.2264 | + | 3.81195i | 0.767036 | + | 0.205527i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.125126 | + | 0.466978i | 0.00672683 | + | 0.0251049i | ||||
\(347\) | −11.8708 | −0.637259 | −0.318630 | − | 0.947879i | \(-0.603223\pi\) | ||||
−0.318630 | + | 0.947879i | \(0.603223\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.38273 | − | 20.0886i | −0.288131 | − | 1.07532i | −0.946521 | − | 0.322642i | \(-0.895429\pi\) |
0.658390 | − | 0.752677i | \(-0.271238\pi\) | |||||||
\(350\) | −6.21120 | − | 6.31496i | −0.332002 | − | 0.337549i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.181889 | − | 0.315041i | −0.00969470 | − | 0.0167917i | ||||
\(353\) | −7.23488 | + | 27.0009i | −0.385074 | + | 1.43712i | 0.452977 | + | 0.891522i | \(0.350362\pi\) |
−0.838050 | + | 0.545593i | \(0.816305\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.8714 | + | 32.6862i | −1.00159 | + | 1.73480i | ||||
\(356\) | −2.21400 | − | 2.21400i | −0.117342 | − | 0.117342i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.167439 | + | 0.624890i | −0.00884941 | + | 0.0330265i | ||||
\(359\) | −4.06106 | + | 15.1561i | −0.214334 | + | 0.799907i | 0.772065 | + | 0.635543i | \(0.219224\pi\) |
−0.986400 | + | 0.164364i | \(0.947443\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.51552 | + | 2.60704i | −0.237659 | + | 0.137212i | ||||
\(362\) | −2.24859 | + | 2.24859i | −0.118183 | + | 0.118183i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.784506 | + | 17.6639i | 0.0411193 | + | 0.925838i | ||||
\(365\) | 33.9646 | 1.77779 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.15012 | − | 2.39607i | 0.216635 | − | 0.125074i | −0.387756 | − | 0.921762i | \(-0.626750\pi\) |
0.604391 | + | 0.796688i | \(0.293416\pi\) | |||||||
\(368\) | − | 1.40272i | − | 0.0731216i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.973774 | + | 3.63417i | −0.0506241 | + | 0.188932i | ||||
\(371\) | 33.2357 | + | 0.275318i | 1.72551 | + | 0.0142938i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.941886 | + | 1.63140i | −0.0487690 | + | 0.0844704i | −0.889379 | − | 0.457170i | \(-0.848863\pi\) |
0.840610 | + | 0.541640i | \(0.182196\pi\) | |||||||
\(374\) | 0.0987516 | + | 0.171043i | 0.00510632 | + | 0.00884441i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.74945 | − | 11.6904i | −0.348076 | − | 0.602886i | ||||
\(377\) | 2.77578 | + | 4.27145i | 0.142960 | + | 0.219991i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.368612 | − | 1.37568i | −0.0189343 | − | 0.0706638i | 0.955812 | − | 0.293978i | \(-0.0949792\pi\) |
−0.974747 | + | 0.223314i | \(0.928312\pi\) | |||||||
\(380\) | 25.5160 | 1.30894 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.04348 | − | 7.62638i | −0.104554 | − | 0.390199i | ||||
\(383\) | −10.5704 | + | 2.83233i | −0.540122 | + | 0.144725i | −0.518559 | − | 0.855042i | \(-0.673531\pi\) |
−0.0215638 | + | 0.999767i | \(0.506865\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.00711829 | − | 0.859304i | 0.000362782 | − | 0.0437942i | ||||
\(386\) | 2.56581 | + | 4.44411i | 0.130596 | + | 0.226199i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.12736 | − | 0.837974i | −0.158768 | − | 0.0425417i | ||||
\(389\) | −23.9984 | − | 13.8555i | −1.21677 | − | 0.702502i | −0.252544 | − | 0.967586i | \(-0.581267\pi\) |
−0.964225 | + | 0.265084i | \(0.914600\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.62933i | 0.132971i | ||||||||
\(392\) | −10.0156 | + | 2.50660i | −0.505865 | + | 0.126603i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.48187 | − | 3.16496i | −0.276173 | − | 0.159448i | ||||
\(395\) | −12.5880 | + | 3.37294i | −0.633371 | + | 0.169711i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.25335 | − | 12.1417i | −0.163281 | − | 0.609373i | −0.998253 | − | 0.0590806i | \(-0.981183\pi\) |
0.834972 | − | 0.550292i | \(-0.185484\pi\) | |||||||
\(398\) | 3.50816 | − | 3.50816i | 0.175848 | − | 0.175848i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 23.8042 | + | 13.7434i | 1.19021 | + | 0.687169i | ||||
\(401\) | 17.4913 | + | 17.4913i | 0.873475 | + | 0.873475i | 0.992849 | − | 0.119374i | \(-0.0380887\pi\) |
−0.119374 | + | 0.992849i | \(0.538089\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.50483 | + | 7.09040i | −0.0749610 | + | 0.353198i | ||||
\(404\) | −10.9512 | + | 6.32267i | −0.544842 | + | 0.314565i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.02004 | + | 1.00328i | −0.0506237 | + | 0.0497919i | ||||
\(407\) | −0.201134 | + | 0.116125i | −0.00996983 | + | 0.00575609i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.05291 | + | 8.05291i | 0.398191 | + | 0.398191i | 0.877594 | − | 0.479404i | \(-0.159147\pi\) |
−0.479404 | + | 0.877594i | \(0.659147\pi\) | |||||||
\(410\) | −3.11934 | − | 3.11934i | −0.154053 | − | 0.154053i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16.0527 | + | 9.26805i | −0.790861 | + | 0.456604i | ||||
\(413\) | −18.2397 | − | 5.04962i | −0.897518 | − | 0.248476i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.89837 | + | 5.71482i | −0.485892 | + | 0.280530i | ||||
\(416\) | 4.63116 | + | 14.2384i | 0.227061 | + | 0.698093i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0880299 | − | 0.0880299i | −0.00430568 | − | 0.00430568i | ||||
\(419\) | −25.2233 | − | 14.5627i | −1.23224 | − | 0.711435i | −0.264744 | − | 0.964319i | \(-0.585288\pi\) |
−0.967497 | + | 0.252884i | \(0.918621\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.9431 | − | 24.9431i | 1.21565 | − | 1.21565i | 0.246512 | − | 0.969140i | \(-0.420715\pi\) |
0.969140 | − | 0.246512i | \(-0.0792845\pi\) | |||||||
\(422\) | 0.632127 | + | 2.35913i | 0.0307714 | + | 0.114841i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 17.8973 | − | 4.79556i | 0.869168 | − | 0.232893i | ||||
\(425\) | −44.6200 | − | 25.7614i | −2.16439 | − | 1.24961i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.00279857 | + | 0.337836i | −0.000135432 | + | 0.0163491i | ||||
\(428\) | 0.111001i | 0.00536543i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.2724 | + | 7.08545i | 0.591826 | + | 0.341691i | ||||
\(431\) | −3.15664 | − | 0.845820i | −0.152050 | − | 0.0407417i | 0.181991 | − | 0.983300i | \(-0.441746\pi\) |
−0.334041 | + | 0.942558i | \(0.608412\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.82888 | − | 17.0241i | −0.472346 | − | 0.818127i | 0.527153 | − | 0.849770i | \(-0.323259\pi\) |
−0.999499 | + | 0.0316430i | \(0.989926\pi\) | |||||||
\(434\) | −2.03572 | − | 0.0168634i | −0.0977174 | − | 0.000809471i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29.4452 | − | 7.88981i | 1.41017 | − | 0.377854i | ||||
\(437\) | −0.428956 | − | 1.60089i | −0.0205197 | − | 0.0765807i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.8075 | −1.80445 | −0.902226 | − | 0.431263i | \(-0.858068\pi\) | ||||
−0.902226 | + | 0.431263i | \(0.858068\pi\) | |||||||
\(440\) | −0.123988 | − | 0.462731i | −0.00591091 | − | 0.0220598i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.51436 | − | 7.73033i | −0.119596 | − | 0.367694i | ||||
\(443\) | −2.31623 | − | 4.01183i | −0.110047 | − | 0.190608i | 0.805742 | − | 0.592267i | \(-0.201767\pi\) |
−0.915789 | + | 0.401659i | \(0.868434\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.13163 | − | 5.42414i | −0.148454 | − | 0.257129i | ||||
\(446\) | 2.44928 | − | 4.24228i | 0.115977 | − | 0.200878i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.8099 | − | 6.12225i | 0.510718 | − | 0.289249i | ||||
\(449\) | 3.43957 | − | 12.8367i | 0.162324 | − | 0.605800i | −0.836043 | − | 0.548664i | \(-0.815137\pi\) |
0.998366 | − | 0.0571356i | \(-0.0181967\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 0.272315i | − | 0.0128228i | ||||||
\(452\) | 8.81800 | − | 5.09107i | 0.414764 | − | 0.239464i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.53855 | 0.213005 | ||||||||
\(455\) | −7.62933 | + | 34.5363i | −0.357668 | + | 1.61909i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.254661 | + | 0.254661i | −0.0119125 | + | 0.0119125i | −0.713038 | − | 0.701125i | \(-0.752681\pi\) |
0.701125 | + | 0.713038i | \(0.252681\pi\) | |||||||
\(458\) | 5.23651 | − | 3.02330i | 0.244686 | − | 0.141270i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.793943 | − | 2.96304i | 0.0370178 | − | 0.138152i | ||||
\(461\) | 6.55396 | − | 24.4597i | 0.305249 | − | 1.13920i | −0.627483 | − | 0.778631i | \(-0.715915\pi\) |
0.932731 | − | 0.360573i | \(-0.117419\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.4801 | + | 18.4801i | 0.858844 | + | 0.858844i | 0.991202 | − | 0.132358i | \(-0.0422548\pi\) |
−0.132358 | + | 0.991202i | \(0.542255\pi\) | |||||||
\(464\) | 2.21993 | − | 3.84504i | 0.103058 | − | 0.178501i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.32762 | + | 4.95475i | −0.0615009 | + | 0.229525i | ||||
\(467\) | 15.6223 | + | 27.0587i | 0.722916 | + | 1.25213i | 0.959826 | + | 0.280595i | \(0.0905318\pi\) |
−0.236911 | + | 0.971531i | \(0.576135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.60715 | + | 25.5014i | 0.305090 | + | 1.17754i | ||||
\(470\) | −3.36156 | − | 12.5455i | −0.155057 | − | 0.578682i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.5506 | −0.485631 | ||||||||
\(473\) | 0.226405 | + | 0.844955i | 0.0104101 | + | 0.0388511i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.3700 | + | 8.40556i | 1.43935 | + | 0.385673i | ||||
\(476\) | −25.1349 | + | 14.2353i | −1.15206 | + | 0.652475i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 7.82307i | − | 0.357819i | ||||||
\(479\) | −28.7805 | − | 7.71172i | −1.31502 | − | 0.352357i | −0.467907 | − | 0.883778i | \(-0.654992\pi\) |
−0.847108 | + | 0.531420i | \(0.821659\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.09030 | − | 2.95671i | 0.414482 | − | 0.134814i | ||||
\(482\) | − | 0.390709i | − | 0.0177963i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.1871 | + | 17.6447i | −0.463052 | + | 0.802030i | ||||
\(485\) | −5.60885 | − | 3.23827i | −0.254685 | − | 0.147042i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.1388 | + | 10.1388i | −0.459433 | + | 0.459433i | −0.898469 | − | 0.439037i | \(-0.855320\pi\) |
0.439037 | + | 0.898469i | \(0.355320\pi\) | |||||||
\(488\) | 0.0487462 | + | 0.181923i | 0.00220664 | + | 0.00823528i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.93246 | − | 0.164568i | −0.448703 | − | 0.00743443i | ||||
\(491\) | −16.5417 | − | 9.55034i | −0.746515 | − | 0.431001i | 0.0779183 | − | 0.996960i | \(-0.475173\pi\) |
−0.824433 | + | 0.565959i | \(0.808506\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.16117 | + | 7.20736i | −0.187410 | + | 0.324603i | ||||
\(494\) | 2.79203 | + | 4.29646i | 0.125619 | + | 0.193307i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.10213 | − | 1.63506i | 0.273994 | − | 0.0734164i | ||||
\(497\) | 6.75498 | + | 26.0719i | 0.303002 | + | 1.16949i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.3030 | − | 5.97607i | −0.998420 | − | 0.267526i | −0.277636 | − | 0.960686i | \(-0.589551\pi\) |
−0.720783 | + | 0.693160i | \(0.756218\pi\) | |||||||
\(500\) | 18.2074 | + | 18.2074i | 0.814259 | + | 0.814259i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.13682 | + | 1.10846i | 0.184635 | + | 0.0494729i | ||||
\(503\) | −10.9978 | + | 6.34957i | −0.490367 | + | 0.283113i | −0.724727 | − | 0.689036i | \(-0.758034\pi\) |
0.234360 | + | 0.972150i | \(0.424701\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.4334 | + | 6.54690i | −1.08727 | + | 0.291333i | ||||
\(506\) | −0.0129615 | + | 0.00748334i | −0.000576210 | + | 0.000332675i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.7741 | + | 27.3216i | −0.699864 | + | 1.21220i | ||||
\(509\) | −7.68399 | − | 7.68399i | −0.340587 | − | 0.340587i | 0.516001 | − | 0.856588i | \(-0.327420\pi\) |
−0.856588 | + | 0.516001i | \(0.827420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.2793 | − | 16.9954i | 0.764391 | − | 0.751831i | ||||
\(512\) | 15.7822 | − | 15.7822i | 0.697483 | − | 0.697483i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.55130 | − | 2.55130i | 0.112533 | − | 0.112533i | ||||
\(515\) | −35.8155 | + | 9.59673i | −1.57822 | + | 0.422883i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.400874 | − | 0.694333i | 0.0176304 | − | 0.0305367i | ||||
\(518\) | 1.32309 | + | 2.33613i | 0.0581330 | + | 0.102644i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.03798 | + | 19.6899i | 0.0455182 | + | 0.863458i | ||||
\(521\) | 28.6041 | + | 16.5146i | 1.25317 | + | 0.723518i | 0.971738 | − | 0.236064i | \(-0.0758574\pi\) |
0.281432 | + | 0.959581i | \(0.409191\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.6359i | 0.683712i | 0.939752 | + | 0.341856i | \(0.111055\pi\) | ||||
−0.939752 | + | 0.341856i | \(0.888945\pi\) | |||||||
\(524\) | −2.52085 | − | 4.36624i | −0.110124 | − | 0.190740i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.08247 | + | 1.36184i | 0.221606 | + | 0.0593792i | ||||
\(527\) | −11.4382 | + | 3.06485i | −0.498255 | + | 0.133507i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.8008 | 0.991337 | ||||||||
\(530\) | 17.8274 | 0.774375 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.9811 | − | 12.7678i | 0.562804 | − | 0.553556i | ||||
\(533\) | −2.32692 | + | 10.9639i | −0.100790 | + | 0.474899i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.0574687 | + | 0.214476i | −0.00248459 | + | 0.00927261i | ||||
\(536\) | 7.34285 | + | 12.7182i | 0.317163 | + | 0.549342i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.38313 | − | 6.38313i | −0.275196 | − | 0.275196i | ||||
\(539\) | −0.426362 | − | 0.440728i | −0.0183647 | − | 0.0189835i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.18712 | − | 11.8945i | 0.137025 | − | 0.511384i | −0.862956 | − | 0.505278i | \(-0.831390\pi\) |
0.999981 | − | 0.00610564i | \(-0.00194350\pi\) | |||||||
\(542\) | 3.47943i | 0.149454i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17.2965 | + | 17.2965i | −0.741579 | + | 0.741579i | ||||
\(545\) | 60.9789 | 2.61205 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.99754 | 0.170922 | 0.0854611 | − | 0.996342i | \(-0.472764\pi\) | ||||
0.0854611 | + | 0.996342i | \(0.472764\pi\) | |||||||
\(548\) | −5.64583 | + | 5.64583i | −0.241178 | + | 0.241178i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 0.293278i | − | 0.0125054i | ||||||
\(551\) | 1.35773 | − | 5.06711i | 0.0578412 | − | 0.215866i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.71631 | + | 8.01482i | −0.200558 | + | 0.340825i | ||||
\(554\) | −3.42711 | − | 3.42711i | −0.145604 | − | 0.145604i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.9753 | − | 22.4738i | −0.550273 | − | 0.953101i | ||||
\(557\) | 3.31424 | − | 12.3689i | 0.140429 | − | 0.524088i | −0.859488 | − | 0.511157i | \(-0.829217\pi\) |
0.999916 | − | 0.0129309i | \(-0.00411614\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.89536 | − | 35.9541i | −0.0801653 | − | 1.52070i | ||||
\(560\) | 29.8410 | − | 7.73152i | 1.26101 | − | 0.326717i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.7689 | 0.538621 | ||||||||
\(563\) | 10.0474 | 0.423447 | 0.211723 | − | 0.977330i | \(-0.432092\pi\) | ||||
0.211723 | + | 0.977330i | \(0.432092\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.6740 | − | 5.27162i | 0.827690 | − | 0.221779i | ||||
\(566\) | −8.44371 | − | 2.26249i | −0.354916 | − | 0.0950993i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.50713 | + | 13.0027i | 0.314992 | + | 0.545583i | ||||
\(569\) | − | 5.89515i | − | 0.247138i | −0.992336 | − | 0.123569i | \(-0.960566\pi\) | ||
0.992336 | − | 0.123569i | \(-0.0394340\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.761139 | + | 0.439444i | 0.0318527 | + | 0.0183901i | 0.515842 | − | 0.856684i | \(-0.327479\pi\) |
−0.483989 | + | 0.875074i | \(0.660813\pi\) | |||||||
\(572\) | −0.391596 | + | 0.435180i | −0.0163734 | + | 0.0181958i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.14782 | − | 0.0260759i | −0.131388 | − | 0.00108839i | ||||
\(575\) | 1.95218 | − | 3.38128i | 0.0814117 | − | 0.141009i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.150636 | + | 0.0403629i | −0.00627107 | + | 0.00168033i | −0.261953 | − | 0.965081i | \(-0.584367\pi\) |
0.255682 | + | 0.966761i | \(0.417700\pi\) | |||||||
\(578\) | 4.78966 | − | 4.78966i | 0.199224 | − | 0.199224i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.86560 | − | 6.86560i | 0.285079 | − | 0.285079i | ||||
\(581\) | −2.17613 | + | 7.86039i | −0.0902810 | + | 0.326104i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.778156 | + | 0.778156i | 0.0322279 | + | 0.0322279i | ||||
\(584\) | 6.75564 | − | 11.7011i | 0.279550 | − | 0.484195i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.97256 | + | 2.29356i | −0.164105 | + | 0.0947460i | ||||
\(587\) | 38.7558 | − | 10.3846i | 1.59962 | − | 0.428617i | 0.654693 | − | 0.755895i | \(-0.272798\pi\) |
0.944928 | + | 0.327278i | \(0.106131\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.46420 | − | 3.73211i | 0.266353 | − | 0.153779i | ||||
\(590\) | −9.80544 | − | 2.62736i | −0.403684 | − | 0.108167i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.89115 | − | 5.89115i | −0.242125 | − | 0.242125i | ||||
\(593\) | 2.34322 | + | 0.627863i | 0.0962244 | + | 0.0257833i | 0.306610 | − | 0.951835i | \(-0.400805\pi\) |
−0.210386 | + | 0.977618i | \(0.567472\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −55.9357 | + | 14.4924i | −2.29314 | + | 0.594131i | ||||
\(596\) | −16.4181 | + | 4.39921i | −0.672510 | + | 0.180199i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.585800 | − | 0.190537i | 0.0239551 | − | 0.00779164i | ||||
\(599\) | −5.34796 | + | 9.26293i | −0.218512 | + | 0.378473i | −0.954353 | − | 0.298681i | \(-0.903453\pi\) |
0.735842 | + | 0.677154i | \(0.236787\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.2246 | − | 17.4502i | −1.23289 | − | 0.711807i | −0.265255 | − | 0.964178i | \(-0.585456\pi\) |
−0.967630 | + | 0.252371i | \(0.918790\pi\) | |||||||
\(602\) | 9.78896 | − | 2.53622i | 0.398968 | − | 0.103369i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.64120 | − | 13.5892i | −0.148159 | − | 0.552935i | ||||
\(605\) | −28.8188 | + | 28.8188i | −1.17165 | + | 1.17165i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.7887 | − | 7.38356i | −0.519078 | − | 0.299690i | 0.217480 | − | 0.976065i | \(-0.430216\pi\) |
−0.736557 | + | 0.676375i | \(0.763550\pi\) | |||||||
\(608\) | 7.70927 | − | 13.3528i | 0.312652 | − | 0.541529i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.181214i | 0.00733712i | ||||||||
\(611\) | −22.0730 | + | 24.5297i | −0.892977 | + | 0.992365i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.1947 | + | 3.53552i | 0.532930 | + | 0.142798i | 0.515241 | − | 0.857045i | \(-0.327702\pi\) |
0.0176892 | + | 0.999844i | \(0.494369\pi\) | |||||||
\(614\) | 10.2760i | 0.414704i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.294622 | − | 0.173370i | −0.0118707 | − | 0.00698527i | ||||
\(617\) | 14.8331 | + | 3.97453i | 0.597160 | + | 0.160008i | 0.544723 | − | 0.838616i | \(-0.316635\pi\) |
0.0524363 | + | 0.998624i | \(0.483301\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.22023 | + | 4.55397i | 0.0490453 | + | 0.183039i | 0.986103 | − | 0.166135i | \(-0.0531287\pi\) |
−0.937058 | + | 0.349174i | \(0.886462\pi\) | |||||||
\(620\) | 13.8153 | 0.554837 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.95191 | − | 11.0167i | −0.118361 | − | 0.441728i | ||||
\(623\) | −4.30736 | − | 1.19248i | −0.172571 | − | 0.0477758i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.88665 | + | 6.73187i | 0.155466 | + | 0.269275i | ||||
\(626\) | 1.61994 | − | 6.04570i | 0.0647458 | − | 0.241635i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.468734 | − | 0.811872i | 0.0187045 | − | 0.0323972i | ||||
\(629\) | 11.0427 | + | 11.0427i | 0.440302 | + | 0.440302i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.57205 | + | 17.0631i | −0.182011 | + | 0.679273i | 0.813240 | + | 0.581928i | \(0.197702\pi\) |
−0.995251 | + | 0.0973445i | \(0.968965\pi\) | |||||||
\(632\) | −1.34177 | + | 5.00757i | −0.0533729 | + | 0.199190i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.66090 | − | 3.26832i | 0.224823 | − | 0.129802i | ||||
\(635\) | −44.6241 | + | 44.6241i | −1.77085 | + | 1.77085i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.4001 | + | 21.3878i | 0.530931 | + | 0.847415i | ||||
\(638\) | −0.0473725 | −0.00187549 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 32.4386 | − | 18.7284i | 1.28225 | − | 0.740306i | ||||
\(641\) | − | 37.2148i | − | 1.46990i | −0.678124 | − | 0.734948i | \(-0.737207\pi\) | ||
0.678124 | − | 0.734948i | \(-0.262793\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.17224 | − | 8.10691i | 0.0856648 | − | 0.319705i | −0.909774 | − | 0.415103i | \(-0.863746\pi\) |
0.995439 | + | 0.0953976i | \(0.0304122\pi\) | |||||||
\(644\) | −1.07875 | − | 1.90471i | −0.0425085 | − | 0.0750560i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.18554 | + | 7.24956i | −0.164678 | + | 0.285230i | ||||
\(647\) | −12.9222 | − | 22.3819i | −0.508024 | − | 0.879923i | −0.999957 | − | 0.00928983i | \(-0.997043\pi\) |
0.491933 | − | 0.870633i | \(-0.336290\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.313319 | − | 0.542684i | −0.0122988 | − | 0.0213022i | ||||
\(650\) | −2.50605 | + | 11.8079i | −0.0982955 | + | 0.463144i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.13048 | − | 7.95107i | −0.0834362 | − | 0.311388i | ||||
\(653\) | −32.0109 | −1.25268 | −0.626341 | − | 0.779549i | \(-0.715448\pi\) | ||||
−0.626341 | + | 0.779549i | \(0.715448\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.61025 | − | 9.74159i | −0.101991 | − | 0.380636i | ||||
\(656\) | 9.43572 | − | 2.52829i | 0.368403 | − | 0.0987133i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.98777 | − | 4.70039i | −0.311396 | − | 0.183240i | ||||
\(659\) | −1.93932 | − | 3.35900i | −0.0755452 | − | 0.130848i | 0.825778 | − | 0.563995i | \(-0.190736\pi\) |
−0.901323 | + | 0.433147i | \(0.857403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.97619 | − | 2.40516i | −0.349133 | − | 0.0935500i | 0.0799905 | − | 0.996796i | \(-0.474511\pi\) |
−0.429124 | + | 0.903246i | \(0.641178\pi\) | |||||||
\(662\) | 7.21829 | + | 4.16748i | 0.280547 | + | 0.161974i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.54677i | 0.176449i | ||||||||
\(665\) | 31.6925 | − | 17.9493i | 1.22898 | − | 0.696044i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.546170 | − | 0.315331i | −0.0211478 | − | 0.0122097i | ||||
\(668\) | −14.3694 | + | 3.85027i | −0.555969 | + | 0.148972i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.65710 | + | 13.6485i | 0.141286 | + | 0.527287i | ||||
\(671\) | −0.00790985 | + | 0.00790985i | −0.000305356 | + | 0.000305356i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.3896 | + | 14.0814i | 0.940151 | + | 0.542797i | 0.890008 | − | 0.455945i | \(-0.150699\pi\) |
0.0501436 | + | 0.998742i | \(0.484032\pi\) | |||||||
\(674\) | −6.13166 | − | 6.13166i | −0.236183 | − | 0.236183i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.4850 | − | 14.1750i | 0.749422 | − | 0.545192i | ||||
\(677\) | 24.5782 | − | 14.1902i | 0.944617 | − | 0.545375i | 0.0532122 | − | 0.998583i | \(-0.483054\pi\) |
0.891405 | + | 0.453209i | \(0.149721\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.47386 | + | 1.15913i | −0.171691 | + | 0.0444835i | ||||
\(680\) | −27.8966 | + | 16.1061i | −1.06979 | + | 0.617641i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.0476627 | − | 0.0476627i | −0.00182510 | − | 0.00182510i | ||||
\(683\) | −17.2778 | − | 17.2778i | −0.661118 | − | 0.661118i | 0.294526 | − | 0.955644i | \(-0.404838\pi\) |
−0.955644 | + | 0.294526i | \(0.904838\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.8319 | + | 7.98586i | −0.528490 | + | 0.305124i | ||||
\(686\) | −5.13543 | + | 4.88633i | −0.196072 | + | 0.186561i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −27.1757 | + | 15.6899i | −1.03606 | + | 0.598172i | ||||
\(689\) | −24.6807 | − | 37.9793i | −0.940259 | − | 1.44690i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.9402 | − | 22.9402i | −0.872688 | − | 0.872688i | 0.120077 | − | 0.992765i | \(-0.461686\pi\) |
−0.992765 | + | 0.120077i | \(0.961686\pi\) | |||||||
\(692\) | −2.02749 | − | 1.17057i | −0.0770738 | − | 0.0444986i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.21279 | + | 3.21279i | −0.121956 | + | 0.121956i | ||||
\(695\) | −13.4354 | − | 50.1416i | −0.509634 | − | 1.90198i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.6869 | + | 4.73918i | −0.669937 | + | 0.179509i | ||||
\(698\) | −6.89372 | − | 3.98009i | −0.260931 | − | 0.150649i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 42.8923 | + | 0.355311i | 1.62118 | + | 0.0134295i | ||||
\(701\) | − | 49.4461i | − | 1.86755i | −0.357856 | − | 0.933777i | \(-0.616492\pi\) | ||
0.357856 | − | 0.933777i | \(-0.383508\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.52496 | − | 4.92189i | −0.321525 | − | 0.185632i | ||||
\(704\) | 0.397317 | + | 0.106461i | 0.0149745 | + | 0.00401240i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.34960 | + | 9.26578i | 0.201335 | + | 0.348722i | ||||
\(707\) | −9.15437 | + | 15.5568i | −0.344286 | + | 0.585074i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.2101 | − | 4.61145i | 0.646341 | − | 0.173186i | 0.0792669 | − | 0.996853i | \(-0.474742\pi\) |
0.567074 | + | 0.823667i | \(0.308075\pi\) | |||||||
\(710\) | 3.73892 | + | 13.9539i | 0.140319 | + | 0.523679i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.49156 | −0.0933750 | ||||||||
\(713\) | −0.232253 | − | 0.866779i | −0.00869794 | − | 0.0324611i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.981949 | + | 0.638115i | −0.0367228 | + | 0.0238641i | ||||
\(716\) | −1.56641 | − | 2.71311i | −0.0585396 | − | 0.101394i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.00282 | + | 5.20104i | 0.112064 | + | 0.194101i | ||||
\(719\) | 13.9168 | − | 24.1047i | 0.519011 | − | 0.898953i | −0.480745 | − | 0.876860i | \(-0.659634\pi\) |
0.999756 | − | 0.0220927i | \(-0.00703289\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4189 | + | 22.8038i | −0.499745 | + | 0.849260i | ||||
\(722\) | −0.516523 | + | 1.92769i | −0.0192230 | + | 0.0717412i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 15.3994i | − | 0.572312i | ||||||
\(725\) | 10.7024 | − | 6.17904i | 0.397478 | − | 0.229484i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.3797 | 1.75722 | 0.878608 | − | 0.477544i | \(-0.158473\pi\) | ||||
0.878608 | + | 0.477544i | \(0.158473\pi\) | |||||||
\(728\) | 10.3806 | + | 9.49773i | 0.384730 | + | 0.352009i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.19237 | − | 9.19237i | 0.340225 | − | 0.340225i | ||||
\(731\) | 50.9397 | − | 29.4101i | 1.88407 | − | 1.08777i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.74821 | − | 28.9167i | 0.286187 | − | 1.06806i | −0.661781 | − | 0.749697i | \(-0.730199\pi\) |
0.947968 | − | 0.318366i | \(-0.103134\pi\) | |||||||
\(734\) | 0.474726 | − | 1.77170i | 0.0175225 | − | 0.0653947i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.31072 | − | 1.31072i | −0.0483136 | − | 0.0483136i | ||||
\(737\) | −0.436117 | + | 0.755377i | −0.0160646 | + | 0.0278247i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.28151 | − | 12.2468i | 0.120712 | − | 0.450505i | −0.878938 | − | 0.476936i | \(-0.841748\pi\) |
0.999651 | + | 0.0264308i | \(0.00841417\pi\) | |||||||
\(740\) | −9.10979 | − | 15.7786i | −0.334883 | − | 0.580034i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.06962 | − | 8.92060i | 0.332956 | − | 0.327485i | ||||
\(743\) | 5.17566 | + | 19.3158i | 0.189877 | + | 0.708629i | 0.993534 | + | 0.113537i | \(0.0362180\pi\) |
−0.803657 | + | 0.595093i | \(0.797115\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.0006 | −1.24569 | ||||||||
\(746\) | 0.186613 | + | 0.696448i | 0.00683238 | + | 0.0254988i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.923835 | − | 0.247541i | −0.0337788 | − | 0.00905099i | ||||
\(749\) | 0.0780838 | + | 0.137870i | 0.00285312 | + | 0.00503766i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 31.9306i | − | 1.16516i | −0.812772 | − | 0.582582i | \(-0.802042\pi\) | ||
0.812772 | − | 0.582582i | \(-0.197958\pi\) | |||||||
\(752\) | 27.7806 | + | 7.44379i | 1.01305 | + | 0.271447i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.90730 | + | 0.404797i | 0.0694599 | + | 0.0147418i | ||||
\(755\) | − | 28.1422i | − | 1.02420i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.983838 | − | 1.70406i | 0.0357582 | − | 0.0619350i | −0.847592 | − | 0.530648i | \(-0.821949\pi\) |
0.883351 | + | 0.468713i | \(0.155282\pi\) | |||||||
\(758\) | −0.472085 | − | 0.272558i | −0.0171469 | − | 0.00989976i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 14.3574 | − | 14.3574i | 0.520799 | − | 0.520799i | ||||
\(761\) | −1.79980 | − | 6.71695i | −0.0652427 | − | 0.243489i | 0.925601 | − | 0.378500i | \(-0.123560\pi\) |
−0.990844 | + | 0.135010i | \(0.956893\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.0227 | − | 30.5129i | 1.12310 | − | 1.10464i | ||||
\(764\) | 33.1117 | + | 19.1171i | 1.19794 | + | 0.691631i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.09428 | + | 3.62739i | −0.0756693 | + | 0.131063i | ||||
\(767\) | 7.97756 | + | 24.5267i | 0.288053 | + | 0.885609i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.45316 | − | 0.657322i | 0.0884631 | − | 0.0237036i | −0.214316 | − | 0.976764i | \(-0.568752\pi\) |
0.302779 | + | 0.953061i | \(0.402086\pi\) | |||||||
\(770\) | −0.230640 | − | 0.234494i | −0.00831171 | − | 0.00845056i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24.0035 | − | 6.43171i | −0.863904 | − | 0.231482i | ||||
\(773\) | 6.08636 | + | 6.08636i | 0.218911 | + | 0.218911i | 0.808039 | − | 0.589128i | \(-0.200529\pi\) |
−0.589128 | + | 0.808039i | \(0.700529\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.9849 | + | 4.55109i | 0.610115 | + | 0.163480i | ||||
\(776\) | −2.23123 | + | 1.28820i | −0.0800964 | + | 0.0462437i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.2450 | + | 2.74514i | −0.367302 | + | 0.0984181i | ||||
\(779\) | 9.99560 | − | 5.77096i | 0.358129 | − | 0.206766i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.445875 | + | 0.772278i | −0.0159547 | + | 0.0276343i | ||||
\(782\) | 0.711618 | + | 0.711618i | 0.0254474 | + | 0.0254474i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.3127 | − | 18.8654i | 0.404026 | − | 0.673764i | ||||
\(785\) | 1.32602 | − | 1.32602i | 0.0473277 | − | 0.0473277i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.29200 | − | 4.29200i | 0.152993 | − | 0.152993i | −0.626460 | − | 0.779453i | \(-0.715497\pi\) |
0.779453 | + | 0.626460i | \(0.215497\pi\) | |||||||
\(788\) | 29.6086 | − | 7.93361i | 1.05476 | − | 0.282623i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.49402 | + | 4.31976i | −0.0887331 | + | 0.153690i | ||||
\(791\) | 7.37119 | − | 12.5265i | 0.262089 | − | 0.445390i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.386055 | − | 0.250876i | 0.0137092 | − | 0.00890885i | ||||
\(794\) | −4.16660 | − | 2.40559i | −0.147867 | − | 0.0853710i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.0254i | 0.851557i | ||||||||
\(797\) | −0.799767 | − | 1.38524i | −0.0283292 | − | 0.0490676i | 0.851513 | − | 0.524333i | \(-0.175685\pi\) |
−0.879842 | + | 0.475266i | \(0.842352\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −52.0736 | − | 13.9531i | −1.84223 | − | 0.493624i | ||||
\(800\) | 35.0850 | − | 9.40099i | 1.24044 | − | 0.332375i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.46791 | 0.334324 | ||||||||
\(803\) | 0.802482 | 0.0283190 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.09823 | − | 4.23878i | −0.0387074 | − | 0.149397i | ||||
\(806\) | 1.51171 | + | 2.32626i | 0.0532478 | + | 0.0819392i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.60439 | + | 9.71971i | −0.0916221 | + | 0.341938i | ||||
\(809\) | 21.3018 | + | 36.8958i | 0.748932 | + | 1.29719i | 0.948335 | + | 0.317270i | \(0.102766\pi\) |
−0.199403 | + | 0.979918i | \(0.563900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.5518 | + | 36.5518i | 1.28351 | + | 1.28351i | 0.938658 | + | 0.344850i | \(0.112070\pi\) |
0.344850 | + | 0.938658i | \(0.387930\pi\) | |||||||
\(812\) | 0.0573925 | − | 6.92829i | 0.00201408 | − | 0.243135i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.0230074 | + | 0.0858647i | −0.000806408 | + | 0.00300956i | ||||
\(815\) | − | 16.4661i | − | 0.576782i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.2169 | + | 26.2169i | −0.917215 | + | 0.917215i | ||||
\(818\) | 4.35897 | 0.152408 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 21.3626 | 0.746016 | ||||||||
\(821\) | 14.6049 | − | 14.6049i | 0.509714 | − | 0.509714i | −0.404725 | − | 0.914439i | \(-0.632633\pi\) |
0.914439 | + | 0.404725i | \(0.132633\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 51.9954i | 1.81245i | 0.422799 | + | 0.906224i | \(0.361048\pi\) | ||||
−0.422799 | + | 0.906224i | \(0.638952\pi\) | |||||||
\(824\) | −3.81763 | + | 14.2476i | −0.132993 | + | 0.496338i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.30316 | + | 3.56985i | −0.219315 | + | 0.124211i | ||||
\(827\) | −30.9176 | − | 30.9176i | −1.07511 | − | 1.07511i | −0.996940 | − | 0.0781709i | \(-0.975092\pi\) |
−0.0781709 | − | 0.996940i | \(-0.524908\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.5718 | + | 39.0955i | 0.783951 | + | 1.35784i | 0.929624 | + | 0.368510i | \(0.120132\pi\) |
−0.145673 | + | 0.989333i | \(0.546535\pi\) | |||||||
\(830\) | −1.13226 | + | 4.22565i | −0.0393013 | + | 0.146674i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15.0870 | − | 7.68138i | −0.523048 | − | 0.266304i | ||||
\(833\) | −21.2052 | + | 35.3624i | −0.734718 | + | 1.22523i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.7580 | −1.02982 | ||||||||
\(836\) | 0.602867 | 0.0208506 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.7679 | + | 2.88526i | −0.371972 | + | 0.0996696i | ||||
\(839\) | 29.8547 | + | 7.99955i | 1.03070 | + | 0.276175i | 0.734254 | − | 0.678875i | \(-0.237532\pi\) |
0.296445 | + | 0.955050i | \(0.404199\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5019 | + | 23.3860i | 0.465583 | + | 0.806414i | ||||
\(842\) | − | 13.5015i | − | 0.465292i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.2427 | − | 5.91363i | −0.352569 | − | 0.203556i | ||||
\(845\) | 44.9877 | − | 17.3009i | 1.54763 | − | 0.595170i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.240909 | + | 29.0820i | −0.00827773 | + | 0.999268i | ||||
\(848\) | −19.7384 | + | 34.1879i | −0.677820 | + | 1.17402i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −19.0484 | + | 5.10401i | −0.653356 | + | 0.175066i | ||||
\(851\) | −0.836810 | + | 0.836810i | −0.0286855 | + | 0.0286855i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.8132 | − | 22.8132i | 0.781108 | − | 0.781108i | −0.198910 | − | 0.980018i | \(-0.563740\pi\) |
0.980018 | + | 0.198910i | \(0.0637401\pi\) | |||||||
\(854\) | 0.0906766 | + | 0.0921915i | 0.00310289 | + | 0.00315473i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.0624583 | + | 0.0624583i | 0.00213478 | + | 0.00213478i | ||||
\(857\) | −12.8148 | + | 22.1959i | −0.437745 | + | 0.758196i | −0.997515 | − | 0.0704518i | \(-0.977556\pi\) |
0.559771 | + | 0.828648i | \(0.310889\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.71477 | − | 3.29942i | 0.194985 | − | 0.112575i | −0.399329 | − | 0.916808i | \(-0.630757\pi\) |
0.594314 | + | 0.804233i | \(0.297424\pi\) | |||||||
\(860\) | −66.2854 | + | 17.7611i | −2.26031 | + | 0.605649i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.08325 | + | 0.625415i | −0.0368956 | + | 0.0213017i | ||||
\(863\) | −42.9816 | − | 11.5169i | −1.46311 | − | 0.392039i | −0.562548 | − | 0.826765i | \(-0.690179\pi\) |
−0.900563 | + | 0.434725i | \(0.856846\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.31148 | − | 3.31148i | −0.112594 | − | 0.112594i | ||||
\(866\) | −7.26766 | − | 1.94736i | −0.246965 | − | 0.0661741i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.02848 | − | 6.91299i | 0.238562 | − | 0.234642i | ||||
\(869\) | −0.297417 | + | 0.0796926i | −0.0100892 | + | 0.00270339i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0136 | − | 26.6863i | 0.813669 | − | 0.904230i | ||||
\(872\) | 12.1288 | − | 21.0078i | 0.410735 | − | 0.711413i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.549368 | − | 0.317178i | −0.0185827 | − | 0.0107287i | ||||
\(875\) | 35.4228 | + | 9.80670i | 1.19751 | + | 0.331527i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.6400 | − | 50.9050i | −0.460589 | − | 1.71894i | −0.671115 | − | 0.741353i | \(-0.734185\pi\) |
0.210527 | − | 0.977588i | \(-0.432482\pi\) | |||||||
\(878\) | −10.2324 | + | 10.2324i | −0.345328 | + | 0.345328i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.883923 | + | 0.510333i | 0.0297970 | + | 0.0172033i | ||||
\(881\) | −14.4790 | + | 25.0784i | −0.487811 | + | 0.844914i | −0.999902 | − | 0.0140175i | \(-0.995538\pi\) |
0.512090 | + | 0.858932i | \(0.328871\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 56.4022i | − | 1.89808i | −0.315149 | − | 0.949042i | \(-0.602054\pi\) | ||
0.315149 | − | 0.949042i | \(-0.397946\pi\) | |||||||
\(884\) | 35.0801 | + | 17.8606i | 1.17987 | + | 0.600717i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.71266 | − | 0.458907i | −0.0575381 | − | 0.0154173i | ||||
\(887\) | − | 44.1021i | − | 1.48080i | −0.672165 | − | 0.740402i | \(-0.734635\pi\) | ||
0.672165 | − | 0.740402i | \(-0.265365\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.373032 | + | 45.0315i | −0.0125111 | + | 1.51031i | ||||
\(890\) | −2.31558 | − | 0.620459i | −0.0776186 | − | 0.0207978i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.13962 | + | 22.9134i | 0.205570 | + | 0.767196i | ||||
\(893\) | 33.9817 | 1.13715 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.62196 | − | 6.05325i | −0.0542163 | − | 0.202338i | ||||
\(896\) | 7.13153 | − | 25.7598i | 0.238248 | − | 0.860574i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.54328 | − | 4.40510i | −0.0848705 | − | 0.147000i | ||||
\(899\) | 0.735125 | − | 2.74353i | 0.0245178 | − | 0.0915017i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.9988 | − | 64.0838i | 1.23261 | − | 2.13494i | ||||
\(902\) | −0.0737008 | − | 0.0737008i | −0.00245397 | − | 0.00245397i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.09708 | − | 7.82640i | 0.0697478 | − | 0.260302i | ||||
\(905\) | 7.97274 | − | 29.7547i | 0.265023 | − | 0.989079i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.56547 | − | 4.94528i | 0.284412 | − | 0.164205i | −0.351007 | − | 0.936373i | \(-0.614161\pi\) |
0.635419 | + | 0.772168i | \(0.280827\pi\) | |||||||
\(908\) | −15.5410 | + | 15.5410i | −0.515746 | + | 0.515746i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.28227 | + | 11.4120i | 0.241405 | + | 0.378303i | ||||
\(911\) | −11.6807 | −0.387000 | −0.193500 | − | 0.981100i | \(-0.561984\pi\) | ||||
−0.193500 | + | 0.981100i | \(0.561984\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.233869 | + | 0.135024i | −0.00773993 | + | 0.00446865i | ||||
\(914\) | 0.137846i | 0.00455953i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.57851 | + | 28.2834i | −0.250401 | + | 0.934510i | ||||
\(917\) | −6.20250 | − | 3.64985i | −0.204825 | − | 0.120529i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.44586 | − | 7.70045i | 0.146655 | − | 0.254014i | −0.783334 | − | 0.621601i | \(-0.786483\pi\) |
0.929989 | + | 0.367587i | \(0.119816\pi\) | |||||||
\(920\) | −1.22051 | − | 2.11399i | −0.0402391 | − | 0.0696962i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.84612 | − | 8.39373i | −0.159598 | − | 0.276433i | ||||
\(923\) | 24.5508 | − | 27.2833i | 0.808101 | − | 0.898042i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.00195 | − | 22.3996i | −0.197343 | − | 0.736493i | ||||
\(926\) | 10.0031 | 0.328724 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.51852 | − | 5.66719i | −0.0498478 | − | 0.186035i | ||||
\(929\) | 4.93637 | − | 1.32270i | 0.161957 | − | 0.0433963i | −0.176929 | − | 0.984224i | \(-0.556616\pi\) |
0.338886 | + | 0.940827i | \(0.389950\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.14184 | − | 24.9901i | 0.234064 | − | 0.819017i | ||||
\(932\) | −12.4201 | − | 21.5122i | −0.406834 | − | 0.704657i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.5514 | + | 3.09520i | 0.377975 | + | 0.101278i | ||||
\(935\) | −1.65688 | − | 0.956598i | −0.0541856 | − | 0.0312841i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.6472i | − | 0.641846i | −0.947105 | − | 0.320923i | \(-0.896007\pi\) | ||
0.947105 | − | 0.320923i | \(-0.103993\pi\) | |||||||
\(938\) | 8.69004 | + | 5.11364i | 0.283740 | + | 0.166966i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 54.4693 | + | 31.4479i | 1.77659 | + | 1.02572i | ||||
\(941\) | −22.9818 | + | 6.15795i | −0.749185 | + | 0.200743i | −0.613156 | − | 0.789962i | \(-0.710100\pi\) |
−0.136028 | + | 0.990705i | \(0.543434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.359132 | − | 1.34030i | −0.0116950 | − | 0.0436462i | ||||
\(944\) | 15.8950 | − | 15.8950i | 0.517339 | − | 0.517339i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.289959 | + | 0.167408i | 0.00942739 | + | 0.00544291i | ||||
\(947\) | −38.2822 | − | 38.2822i | −1.24400 | − | 1.24400i | −0.958326 | − | 0.285678i | \(-0.907781\pi\) |
−0.285678 | − | 0.958326i | \(-0.592219\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.3094 | − | 6.85719i | −1.04881 | − | 0.222594i | ||||
\(950\) | 10.7651 | − | 6.21522i | 0.349265 | − | 0.201648i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.13299 | + | 22.1530i | −0.198771 | + | 0.717981i | ||||
\(953\) | −33.5390 | + | 19.3637i | −1.08643 | + | 0.627253i | −0.932625 | − | 0.360848i | \(-0.882487\pi\) |
−0.153809 | + | 0.988101i | \(0.549154\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54.0810 | + | 54.0810i | 1.75002 | + | 1.75002i | ||||
\(956\) | 26.7879 | + | 26.7879i | 0.866383 | + | 0.866383i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.87648 | + | 5.70219i | −0.319094 | + | 0.184229i | ||||
\(959\) | −3.04091 | + | 10.9841i | −0.0981960 | + | 0.354693i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.3468 | + | 13.4793i | −0.753123 | + | 0.434816i | ||||
\(962\) | 1.66003 | − | 3.26047i | 0.0535216 | − | 0.105122i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.33787 | + | 1.33787i | 0.0430900 | + | 0.0430900i | ||||
\(965\) | −43.0497 | − | 24.8547i | −1.38582 | − | 0.800103i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.90329 | − | 1.90329i | 0.0612056 | − | 0.0612056i | −0.675841 | − | 0.737047i | \(-0.736220\pi\) |
0.737047 | + | 0.675841i | \(0.236220\pi\) | |||||||
\(968\) | 4.19622 | + | 15.6605i | 0.134871 | + | 0.503347i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.39444 | + | 0.641587i | −0.0768807 | + | 0.0206001i | ||||
\(971\) | 0.711680 | + | 0.410888i | 0.0228389 | + | 0.0131860i | 0.511376 | − | 0.859357i | \(-0.329136\pi\) |
−0.488537 | + | 0.872543i | \(0.662469\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.9253 | − | 18.7864i | −1.02348 | − | 0.602265i | ||||
\(974\) | 5.48805i | 0.175848i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.347516 | − | 0.200638i | −0.0111237 | − | 0.00642227i | ||||
\(977\) | −11.3007 | − | 3.02801i | −0.361540 | − | 0.0968745i | 0.0734760 | − | 0.997297i | \(-0.476591\pi\) |
−0.435016 | + | 0.900423i | \(0.643257\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0739911 | − | 0.128156i | −0.00236477 | − | 0.00409589i | ||||
\(980\) | 34.5744 | − | 33.4474i | 1.10444 | − | 1.06844i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.06169 | + | 1.89217i | −0.225348 | + | 0.0603817i | ||||
\(983\) | 3.25273 | + | 12.1393i | 0.103746 | + | 0.387185i | 0.998200 | − | 0.0599750i | \(-0.0191021\pi\) |
−0.894454 | + | 0.447160i | \(0.852435\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 61.3174 | 1.95373 | ||||||||
\(986\) | 0.824439 | + | 3.07685i | 0.0262555 | + | 0.0979868i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.2726 | − | 5.15149i | −0.772213 | − | 0.163891i | ||||
\(989\) | 2.22868 | + | 3.86019i | 0.0708679 | + | 0.122747i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.39652 | + | 9.34706i | 0.171426 | + | 0.296919i | 0.938919 | − | 0.344139i | \(-0.111829\pi\) |
−0.767492 | + | 0.641058i | \(0.778496\pi\) | |||||||
\(992\) | 4.17409 | − | 7.22973i | 0.132527 | − | 0.229544i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.88446 | + | 5.22805i | 0.281798 | + | 0.165824i | ||||
\(995\) | −12.4387 | + | 46.4219i | −0.394334 | + | 1.47167i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 35.3997i | − | 1.12112i | −0.828114 | − | 0.560560i | \(-0.810586\pi\) | ||
0.828114 | − | 0.560560i | \(-0.189414\pi\) | |||||||
\(998\) | −7.65362 | + | 4.41882i | −0.242271 | + | 0.139875i | ||||
\(999\) | 0 | 0 |
(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 | 819.2.et.b.136.5 | 28 | ||
3.2 | odd | 2 | 91.2.ba.a.45.3 | yes | 28 | ||
7.5 | odd | 6 | 819.2.gh.b.19.3 | 28 | |||
13.11 | odd | 12 | 819.2.gh.b.388.3 | 28 | |||
21.2 | odd | 6 | 637.2.x.a.19.5 | 28 | |||
21.5 | even | 6 | 91.2.w.a.19.5 | ✓ | 28 | ||
21.11 | odd | 6 | 637.2.bd.b.97.3 | 28 | |||
21.17 | even | 6 | 637.2.bd.a.97.3 | 28 | |||
21.20 | even | 2 | 637.2.bb.a.227.3 | 28 | |||
39.11 | even | 12 | 91.2.w.a.24.5 | yes | 28 | ||
91.89 | even | 12 | inner | 819.2.et.b.271.5 | 28 | ||
273.11 | even | 12 | 637.2.bd.a.440.3 | 28 | |||
273.89 | odd | 12 | 91.2.ba.a.89.3 | yes | 28 | ||
273.128 | even | 12 | 637.2.bb.a.362.3 | 28 | |||
273.167 | odd | 12 | 637.2.x.a.570.5 | 28 | |||
273.206 | odd | 12 | 637.2.bd.b.440.3 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.w.a.19.5 | ✓ | 28 | 21.5 | even | 6 | ||
91.2.w.a.24.5 | yes | 28 | 39.11 | even | 12 | ||
91.2.ba.a.45.3 | yes | 28 | 3.2 | odd | 2 | ||
91.2.ba.a.89.3 | yes | 28 | 273.89 | odd | 12 | ||
637.2.x.a.19.5 | 28 | 21.2 | odd | 6 | |||
637.2.x.a.570.5 | 28 | 273.167 | odd | 12 | |||
637.2.bb.a.227.3 | 28 | 21.20 | even | 2 | |||
637.2.bb.a.362.3 | 28 | 273.128 | even | 12 | |||
637.2.bd.a.97.3 | 28 | 21.17 | even | 6 | |||
637.2.bd.a.440.3 | 28 | 273.11 | even | 12 | |||
637.2.bd.b.97.3 | 28 | 21.11 | odd | 6 | |||
637.2.bd.b.440.3 | 28 | 273.206 | odd | 12 | |||
819.2.et.b.136.5 | 28 | 1.1 | even | 1 | trivial | ||
819.2.et.b.271.5 | 28 | 91.89 | even | 12 | inner | ||
819.2.gh.b.19.3 | 28 | 7.5 | odd | 6 | |||
819.2.gh.b.388.3 | 28 | 13.11 | odd | 12 |