Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(107,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.be (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.5 | ||
Character | \(\chi\) | \(=\) | 756.107 |
Dual form | 756.2.be.d.431.5 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.498187 | − | 1.32356i | −0.352271 | − | 0.935898i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.50362 | + | 1.31876i | −0.751810 | + | 0.659380i | ||||
\(5\) | −0.936239 | − | 0.540538i | −0.418699 | − | 0.241736i | 0.275822 | − | 0.961209i | \(-0.411050\pi\) |
−0.694520 | + | 0.719473i | \(0.744383\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.749282 | + | 2.53743i | 0.283202 | + | 0.959060i | ||||
\(8\) | 2.49454 | + | 1.33314i | 0.881953 | + | 0.471337i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.249012 | + | 1.50846i | −0.0787446 | + | 0.477016i | ||||
\(11\) | −2.43972 | − | 4.22571i | −0.735602 | − | 1.27410i | −0.954459 | − | 0.298343i | \(-0.903566\pi\) |
0.218856 | − | 0.975757i | \(-0.429767\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.815997 | 0.226317 | 0.113158 | − | 0.993577i | \(-0.463903\pi\) | ||||
0.113158 | + | 0.993577i | \(0.463903\pi\) | |||||||
\(14\) | 2.98516 | − | 2.25584i | 0.797819 | − | 0.602897i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.521749 | − | 3.96583i | 0.130437 | − | 0.991457i | ||||
\(17\) | −1.47016 | + | 0.848796i | −0.356566 | + | 0.205863i | −0.667573 | − | 0.744544i | \(-0.732667\pi\) |
0.311007 | + | 0.950407i | \(0.399334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.58740 | − | 2.07119i | −0.823006 | − | 0.475163i | 0.0284462 | − | 0.999595i | \(-0.490944\pi\) |
−0.851452 | + | 0.524433i | \(0.824277\pi\) | |||||||
\(20\) | 2.12059 | − | 0.421910i | 0.474178 | − | 0.0943419i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.37755 | + | 5.33430i | −0.933297 | + | 1.13728i | ||||
\(23\) | −1.75645 | + | 3.04226i | −0.366245 | + | 0.634354i | −0.988975 | − | 0.148082i | \(-0.952690\pi\) |
0.622730 | + | 0.782436i | \(0.286023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.91564 | − | 3.31798i | −0.383128 | − | 0.663596i | ||||
\(26\) | −0.406519 | − | 1.08002i | −0.0797249 | − | 0.211810i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.47290 | − | 2.82722i | −0.845299 | − | 0.534294i | ||||
\(29\) | − | 9.61003i | − | 1.78454i | −0.451504 | − | 0.892269i | \(-0.649112\pi\) | ||
0.451504 | − | 0.892269i | \(-0.350888\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.73929 | + | 4.46828i | −1.39002 | + | 0.802527i | −0.993317 | − | 0.115422i | \(-0.963178\pi\) |
−0.396700 | + | 0.917948i | \(0.629845\pi\) | |||||||
\(32\) | −5.50894 | + | 1.28516i | −0.973851 | + | 0.227186i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.85585 | + | 1.52298i | 0.318275 | + | 0.261190i | ||||
\(35\) | 0.670072 | − | 2.78066i | 0.113263 | − | 0.470017i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.37978 | + | 5.85395i | −0.555632 | + | 0.962383i | 0.442222 | + | 0.896906i | \(0.354190\pi\) |
−0.997854 | + | 0.0654777i | \(0.979143\pi\) | |||||||
\(38\) | −0.954144 | + | 5.77997i | −0.154783 | + | 0.937635i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.61487 | − | 2.59653i | −0.255334 | − | 0.410548i | ||||
\(41\) | − | 6.96667i | − | 1.08801i | −0.839082 | − | 0.544005i | \(-0.816907\pi\) | ||
0.839082 | − | 0.544005i | \(-0.183093\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.510241i | 0.0778110i | 0.999243 | + | 0.0389055i | \(0.0123871\pi\) | ||||
−0.999243 | + | 0.0389055i | \(0.987613\pi\) | |||||||
\(44\) | 9.24111 | + | 3.13647i | 1.39315 | + | 0.472841i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.90165 | + | 0.809152i | 0.722708 | + | 0.119303i | ||||
\(47\) | −3.40777 | + | 5.90243i | −0.497074 | + | 0.860958i | −0.999994 | − | 0.00337527i | \(-0.998926\pi\) |
0.502920 | + | 0.864333i | \(0.332259\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.87715 | + | 3.80251i | −0.839593 | + | 0.543216i | ||||
\(50\) | −3.43720 | + | 4.18843i | −0.486094 | + | 0.592334i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.22695 | + | 1.07610i | −0.170147 | + | 0.149229i | ||||
\(53\) | −2.99884 | + | 1.73138i | −0.411922 | + | 0.237824i | −0.691615 | − | 0.722266i | \(-0.743101\pi\) |
0.279693 | + | 0.960090i | \(0.409767\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.27504i | 0.711286i | ||||||||
\(56\) | −1.51365 | + | 7.32863i | −0.202270 | + | 0.979330i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12.7195 | + | 4.78759i | −1.67015 | + | 0.628641i | ||||
\(59\) | 2.50722 | + | 4.34263i | 0.326412 | + | 0.565362i | 0.981797 | − | 0.189933i | \(-0.0608270\pi\) |
−0.655385 | + | 0.755295i | \(0.727494\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.85713 | − | 11.8769i | 0.877966 | − | 1.52068i | 0.0243965 | − | 0.999702i | \(-0.492234\pi\) |
0.853569 | − | 0.520979i | \(-0.174433\pi\) | |||||||
\(62\) | 9.76964 | + | 8.01737i | 1.24075 | + | 1.01821i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.44546 | + | 6.65116i | 0.555682 | + | 0.831395i | ||||
\(65\) | −0.763968 | − | 0.441077i | −0.0947586 | − | 0.0547089i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.66826 | − | 2.11787i | 0.448150 | − | 0.258739i | −0.258899 | − | 0.965904i | \(-0.583360\pi\) |
0.707048 | + | 0.707165i | \(0.250026\pi\) | |||||||
\(68\) | 1.09120 | − | 3.21505i | 0.132328 | − | 0.389882i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.01419 | + | 0.498407i | −0.479788 | + | 0.0595711i | ||||
\(71\) | −11.8557 | −1.40701 | −0.703503 | − | 0.710692i | \(-0.748382\pi\) | ||||
−0.703503 | + | 0.710692i | \(0.748382\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.49777 | − | 2.59421i | −0.175301 | − | 0.303630i | 0.764965 | − | 0.644072i | \(-0.222756\pi\) |
−0.940265 | + | 0.340443i | \(0.889423\pi\) | |||||||
\(74\) | 9.43181 | + | 1.55698i | 1.09643 | + | 0.180995i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.12548 | − | 1.61664i | 0.932056 | − | 0.185441i | ||||
\(77\) | 8.89444 | − | 9.35688i | 1.01362 | − | 1.06631i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.41517 | − | 1.97175i | −0.384237 | − | 0.221839i | 0.295423 | − | 0.955366i | \(-0.404539\pi\) |
−0.679660 | + | 0.733527i | \(0.737873\pi\) | |||||||
\(80\) | −2.63216 | + | 3.43094i | −0.294284 | + | 0.383590i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.22080 | + | 3.47070i | −1.01827 | + | 0.383275i | ||||
\(83\) | −11.3326 | −1.24392 | −0.621960 | − | 0.783049i | \(-0.713663\pi\) | ||||
−0.621960 | + | 0.783049i | \(0.713663\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.83523 | 0.199058 | ||||||||
\(86\) | 0.675334 | − | 0.254195i | 0.0728232 | − | 0.0274106i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.452489 | − | 13.7937i | −0.0482355 | − | 1.47041i | ||||
\(89\) | 0.313438 | + | 0.180963i | 0.0332243 | + | 0.0191821i | 0.516520 | − | 0.856275i | \(-0.327227\pi\) |
−0.483296 | + | 0.875457i | \(0.660560\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.611412 | + | 2.07054i | 0.0640934 | + | 0.217052i | ||||
\(92\) | −1.37097 | − | 6.89073i | −0.142934 | − | 0.718408i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.50992 | + | 1.56987i | 0.980873 | + | 0.161920i | ||||
\(95\) | 2.23911 | + | 3.87825i | 0.229728 | + | 0.397900i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.12677 | 0.825148 | 0.412574 | − | 0.910924i | \(-0.364630\pi\) | ||||
0.412574 | + | 0.910924i | \(0.364630\pi\) | |||||||
\(98\) | 7.96077 | + | 5.88440i | 0.804159 | + | 0.594414i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.25601 | + | 2.46272i | 0.725601 | + | 0.246272i | ||||
\(101\) | −1.32037 | + | 0.762317i | −0.131382 | + | 0.0758534i | −0.564250 | − | 0.825604i | \(-0.690835\pi\) |
0.432869 | + | 0.901457i | \(0.357501\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.69999 | + | 3.86824i | 0.660170 | + | 0.381149i | 0.792342 | − | 0.610078i | \(-0.208862\pi\) |
−0.132172 | + | 0.991227i | \(0.542195\pi\) | |||||||
\(104\) | 2.03554 | + | 1.08784i | 0.199601 | + | 0.106672i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.78557 | + | 3.10659i | 0.367687 | + | 0.301739i | ||||
\(107\) | 0.602928 | − | 1.04430i | 0.0582873 | − | 0.100957i | −0.835409 | − | 0.549628i | \(-0.814769\pi\) |
0.893697 | + | 0.448672i | \(0.148103\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.314166 | + | 0.544151i | 0.0300916 | + | 0.0521202i | 0.880679 | − | 0.473713i | \(-0.157087\pi\) |
−0.850587 | + | 0.525834i | \(0.823753\pi\) | |||||||
\(110\) | 6.98183 | − | 2.62795i | 0.665691 | − | 0.250565i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.4540 | − | 1.64762i | 0.987807 | − | 0.155686i | ||||
\(113\) | − | 11.7870i | − | 1.10882i | −0.832242 | − | 0.554412i | \(-0.812943\pi\) | ||
0.832242 | − | 0.554412i | \(-0.187057\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.28891 | − | 1.89885i | 0.306692 | − | 0.177069i | ||||
\(116\) | 12.6733 | + | 14.4498i | 1.17669 | + | 1.34163i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.49867 | − | 5.48189i | 0.414136 | − | 0.504649i | ||||
\(119\) | −3.25533 | − | 3.09444i | −0.298416 | − | 0.283667i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.40444 | + | 11.0928i | −0.582222 | + | 1.00844i | ||||
\(122\) | −19.1359 | − | 3.15891i | −1.73248 | − | 0.285994i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.74436 | − | 16.9248i | 0.515859 | − | 1.51990i | ||||
\(125\) | 9.54728i | 0.853934i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.46528i | − | 0.484966i | −0.970156 | − | 0.242483i | \(-0.922038\pi\) | ||
0.970156 | − | 0.242483i | \(-0.0779618\pi\) | |||||||
\(128\) | 6.58854 | − | 9.19735i | 0.582350 | − | 0.812938i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.203193 | + | 1.23090i | −0.0178212 | + | 0.107957i | ||||
\(131\) | −7.94069 | + | 13.7537i | −0.693782 | + | 1.20167i | 0.276808 | + | 0.960925i | \(0.410723\pi\) |
−0.970590 | + | 0.240740i | \(0.922610\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.56752 | − | 10.6547i | 0.222633 | − | 0.923879i | ||||
\(134\) | −4.63061 | − | 3.80007i | −0.400024 | − | 0.328276i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.79894 | + | 0.157424i | −0.411505 | + | 0.0134990i | ||||
\(137\) | −10.7072 | + | 6.18180i | −0.914777 | + | 0.528147i | −0.881965 | − | 0.471315i | \(-0.843780\pi\) |
−0.0328121 | + | 0.999462i | \(0.510446\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.2243i | − | 1.46095i | −0.682941 | − | 0.730473i | \(-0.739299\pi\) | ||
0.682941 | − | 0.730473i | \(-0.260701\pi\) | |||||||
\(140\) | 2.65949 | + | 5.06472i | 0.224768 | + | 0.428047i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.90633 | + | 15.6917i | 0.495648 | + | 1.31682i | ||||
\(143\) | −1.99080 | − | 3.44817i | −0.166479 | − | 0.288350i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.19459 | + | 8.99729i | −0.431387 | + | 0.747184i | ||||
\(146\) | −2.68743 | + | 3.27479i | −0.222413 | + | 0.271024i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.63804 | − | 13.2592i | −0.216846 | − | 1.08990i | ||||
\(149\) | 9.97002 | + | 5.75619i | 0.816776 | + | 0.471566i | 0.849303 | − | 0.527905i | \(-0.177022\pi\) |
−0.0325274 | + | 0.999471i | \(0.510356\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.30760 | − | 5.37375i | 0.757442 | − | 0.437309i | −0.0709346 | − | 0.997481i | \(-0.522598\pi\) |
0.828377 | + | 0.560172i | \(0.189265\pi\) | |||||||
\(152\) | −6.18772 | − | 9.94917i | −0.501890 | − | 0.806984i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16.8155 | − | 7.11085i | −1.35503 | − | 0.573008i | ||||
\(155\) | 9.66109 | 0.775998 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.7042 | + | 20.2723i | 0.934099 | + | 1.61791i | 0.776233 | + | 0.630446i | \(0.217128\pi\) |
0.157865 | + | 0.987461i | \(0.449539\pi\) | |||||||
\(158\) | −0.908337 | + | 5.50248i | −0.0722634 | + | 0.437754i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.85236 | + | 1.77458i | 0.462669 | + | 0.140292i | ||||
\(161\) | −9.03560 | − | 2.17736i | −0.712105 | − | 0.171600i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.35163 | − | 1.35771i | −0.184193 | − | 0.106344i | 0.405068 | − | 0.914287i | \(-0.367248\pi\) |
−0.589261 | + | 0.807942i | \(0.700581\pi\) | |||||||
\(164\) | 9.18736 | + | 10.4752i | 0.717412 | + | 0.817978i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.64577 | + | 14.9994i | 0.438197 | + | 1.16418i | ||||
\(167\) | 6.84595 | 0.529756 | 0.264878 | − | 0.964282i | \(-0.414668\pi\) | ||||
0.264878 | + | 0.964282i | \(0.414668\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3341 | −0.948781 | ||||||||
\(170\) | −0.914285 | − | 2.42903i | −0.0701224 | − | 0.186298i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.672885 | − | 0.767209i | −0.0513070 | − | 0.0584991i | ||||
\(173\) | −7.19348 | − | 4.15316i | −0.546910 | − | 0.315759i | 0.200965 | − | 0.979599i | \(-0.435592\pi\) |
−0.747875 | + | 0.663840i | \(0.768926\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.98381 | − | 7.34691i | 0.527926 | − | 0.555374i | ||||
\(176\) | −18.0314 | + | 7.47073i | −1.35917 | + | 0.563128i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.0833654 | − | 0.505007i | 0.00624850 | − | 0.0378519i | ||||
\(179\) | −10.4832 | − | 18.1575i | −0.783554 | − | 1.35716i | −0.929859 | − | 0.367917i | \(-0.880071\pi\) |
0.146304 | − | 0.989240i | \(-0.453262\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.8558 | 1.32721 | 0.663605 | − | 0.748083i | \(-0.269026\pi\) | ||||
0.663605 | + | 0.748083i | \(0.269026\pi\) | |||||||
\(182\) | 2.43589 | − | 1.84076i | 0.180560 | − | 0.136446i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.43729 | + | 5.24743i | −0.622005 | + | 0.386846i | ||||
\(185\) | 6.32856 | − | 3.65380i | 0.465285 | − | 0.268633i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.17354 | + | 4.14165i | 0.524581 | + | 0.302867i | ||||
\(188\) | −2.65989 | − | 13.3690i | −0.193992 | − | 0.975037i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.01760 | − | 4.89568i | 0.291467 | − | 0.355170i | ||||
\(191\) | 9.10942 | − | 15.7780i | 0.659135 | − | 1.14165i | −0.321705 | − | 0.946840i | \(-0.604256\pi\) |
0.980840 | − | 0.194815i | \(-0.0624106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.35386 | − | 16.2014i | −0.673306 | − | 1.16620i | −0.976961 | − | 0.213418i | \(-0.931540\pi\) |
0.303655 | − | 0.952782i | \(-0.401793\pi\) | |||||||
\(194\) | −4.04865 | − | 10.7563i | −0.290676 | − | 0.772255i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.82241 | − | 13.4681i | 0.273029 | − | 0.962006i | ||||
\(197\) | − | 22.2223i | − | 1.58327i | −0.610994 | − | 0.791635i | \(-0.709230\pi\) | ||
0.610994 | − | 0.791635i | \(-0.290770\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.8519 | − | 7.99738i | 0.981934 | − | 0.566920i | 0.0790802 | − | 0.996868i | \(-0.474802\pi\) |
0.902853 | + | 0.429949i | \(0.141468\pi\) | |||||||
\(200\) | −0.355289 | − | 10.8307i | −0.0251227 | − | 0.765843i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.66676 | + | 1.36781i | 0.117273 | + | 0.0962391i | ||||
\(203\) | 24.3848 | − | 7.20063i | 1.71148 | − | 0.505385i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.76575 | + | 6.52247i | −0.263011 | + | 0.455549i | ||||
\(206\) | 1.78200 | − | 10.7949i | 0.124158 | − | 0.752120i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.425745 | − | 3.23610i | 0.0295201 | − | 0.224383i | ||||
\(209\) | 20.2124i | 1.39812i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.32079i | 0.572827i | 0.958106 | + | 0.286414i | \(0.0924631\pi\) | ||||
−0.958106 | + | 0.286414i | \(0.907537\pi\) | |||||||
\(212\) | 2.22584 | − | 6.55809i | 0.152872 | − | 0.450411i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.68257 | − | 0.277754i | −0.115018 | − | 0.0189869i | ||||
\(215\) | 0.275804 | − | 0.477707i | 0.0188097 | − | 0.0325794i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.1369 | − | 16.2899i | −1.16333 | − | 1.10583i | ||||
\(218\) | 0.563704 | − | 0.686906i | 0.0381788 | − | 0.0465232i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.95650 | − | 7.93165i | −0.469007 | − | 0.534752i | ||||
\(221\) | −1.19965 | + | 0.692615i | −0.0806969 | + | 0.0465904i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.91285i | 0.596848i | 0.954433 | + | 0.298424i | \(0.0964610\pi\) | ||||
−0.954433 | + | 0.298424i | \(0.903539\pi\) | |||||||
\(224\) | −7.38875 | − | 13.0156i | −0.493681 | − | 0.869643i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.6007 | + | 5.87210i | −1.03775 | + | 0.390607i | ||||
\(227\) | 10.2145 | + | 17.6920i | 0.677957 | + | 1.17426i | 0.975595 | + | 0.219578i | \(0.0704679\pi\) |
−0.297638 | + | 0.954679i | \(0.596199\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.21367 | − | 10.7624i | 0.410611 | − | 0.711199i | −0.584346 | − | 0.811505i | \(-0.698649\pi\) |
0.994957 | + | 0.100306i | \(0.0319821\pi\) | |||||||
\(230\) | −4.15173 | − | 3.40708i | −0.273757 | − | 0.224657i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.8116 | − | 23.9726i | 0.841120 | − | 1.57388i | ||||
\(233\) | 2.18246 | + | 1.26005i | 0.142978 | + | 0.0825484i | 0.569783 | − | 0.821796i | \(-0.307027\pi\) |
−0.426805 | + | 0.904344i | \(0.640361\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.38097 | − | 3.68405i | 0.416249 | − | 0.240321i | ||||
\(236\) | −9.49679 | − | 3.22325i | −0.618188 | − | 0.209816i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.47392 | + | 5.85023i | −0.160360 | + | 0.379214i | ||||
\(239\) | 25.2624 | 1.63409 | 0.817045 | − | 0.576574i | \(-0.195611\pi\) | ||||
0.817045 | + | 0.576574i | \(0.195611\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.31705 | + | 12.6735i | 0.471333 | + | 0.816372i | 0.999462 | − | 0.0327917i | \(-0.0104398\pi\) |
−0.528130 | + | 0.849164i | \(0.677106\pi\) | |||||||
\(242\) | 17.8726 | + | 2.95037i | 1.14889 | + | 0.189657i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.35225 | + | 26.9013i | 0.342643 | + | 1.72218i | ||||
\(245\) | 7.55782 | − | 0.383236i | 0.482851 | − | 0.0244841i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.92731 | − | 1.69008i | −0.186260 | − | 0.107537i | ||||
\(248\) | −25.2628 | + | 0.828722i | −1.60419 | + | 0.0526239i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.6364 | − | 4.75632i | 0.799195 | − | 0.300816i | ||||
\(251\) | −11.3947 | −0.719227 | −0.359613 | − | 0.933101i | \(-0.617091\pi\) | ||||
−0.359613 | + | 0.933101i | \(0.617091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.1409 | 1.07764 | ||||||||
\(254\) | −7.23363 | + | 2.72273i | −0.453878 | + | 0.170839i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.4556 | − | 4.13833i | −0.965972 | − | 0.258646i | ||||
\(257\) | 19.8884 | + | 11.4826i | 1.24060 | + | 0.716263i | 0.969217 | − | 0.246208i | \(-0.0791846\pi\) |
0.271386 | + | 0.962471i | \(0.412518\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.3864 | − | 4.18971i | −1.08034 | − | 0.260336i | ||||
\(260\) | 1.73039 | − | 0.344277i | 0.107314 | − | 0.0213512i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.1598 | + | 3.65808i | 1.36904 | + | 0.225997i | ||||
\(263\) | −11.6566 | − | 20.1898i | −0.718775 | − | 1.24495i | −0.961485 | − | 0.274856i | \(-0.911370\pi\) |
0.242711 | − | 0.970099i | \(-0.421963\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.74351 | 0.229962 | ||||||||
\(266\) | −15.3812 | + | 1.90975i | −0.943084 | + | 0.117094i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.72271 | + | 8.02203i | −0.166316 | + | 0.490024i | ||||
\(269\) | −25.3140 | + | 14.6150i | −1.54342 | + | 0.891094i | −0.544801 | + | 0.838565i | \(0.683395\pi\) |
−0.998619 | + | 0.0525290i | \(0.983272\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.829286 | − | 0.478788i | −0.0503755 | − | 0.0290843i | 0.474601 | − | 0.880201i | \(-0.342592\pi\) |
−0.524976 | + | 0.851117i | \(0.675926\pi\) | |||||||
\(272\) | 2.59913 | + | 6.27325i | 0.157595 | + | 0.380372i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.5162 | + | 11.0919i | 0.816541 | + | 0.670087i | ||||
\(275\) | −9.34723 | + | 16.1899i | −0.563659 | + | 0.976286i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.06856 | − | 10.5111i | −0.364624 | − | 0.631548i | 0.624091 | − | 0.781351i | \(-0.285469\pi\) |
−0.988716 | + | 0.149803i | \(0.952136\pi\) | |||||||
\(278\) | −22.7974 | + | 8.58092i | −1.36730 | + | 0.514649i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.37854 | − | 6.04317i | 0.321429 | − | 0.361148i | ||||
\(281\) | 23.7714i | 1.41808i | 0.705168 | + | 0.709041i | \(0.250872\pi\) | ||||
−0.705168 | + | 0.709041i | \(0.749128\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.93570 | + | 1.69493i | −0.174509 | + | 0.100753i | −0.584710 | − | 0.811242i | \(-0.698792\pi\) |
0.410201 | + | 0.911995i | \(0.365458\pi\) | |||||||
\(284\) | 17.8264 | − | 15.6347i | 1.05780 | − | 0.927752i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.57207 | + | 4.35278i | −0.211221 | + | 0.257385i | ||||
\(287\) | 17.6775 | − | 5.22000i | 1.04347 | − | 0.308127i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.05909 | + | 12.2267i | −0.415241 | + | 0.719218i | ||||
\(290\) | 14.4963 | + | 2.39302i | 0.851253 | + | 0.140523i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.67322 | + | 1.92552i | 0.332000 | + | 0.112682i | ||||
\(293\) | 14.2017i | 0.829673i | 0.909896 | + | 0.414837i | \(0.136161\pi\) | ||||
−0.909896 | + | 0.414837i | \(0.863839\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5.42099i | − | 0.315622i | ||||||
\(296\) | −16.2351 | + | 10.0972i | −0.943649 | + | 0.586887i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.65174 | − | 16.0636i | 0.153611 | − | 0.930538i | ||||
\(299\) | −1.43326 | + | 2.48247i | −0.0828873 | + | 0.143565i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.29470 | + | 0.382315i | −0.0746254 | + | 0.0220362i | ||||
\(302\) | −11.7494 | − | 9.64204i | −0.676102 | − | 0.554837i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.0857 | + | 13.1464i | −0.578454 | + | 0.753995i | ||||
\(305\) | −12.8398 | + | 7.41308i | −0.735206 | + | 0.424472i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.7078i | 1.46722i | 0.679571 | + | 0.733610i | \(0.262166\pi\) | ||||
−0.679571 | + | 0.733610i | \(0.737834\pi\) | |||||||
\(308\) | −1.03439 | + | 25.7988i | −0.0589399 | + | 1.47002i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.81303 | − | 12.7870i | −0.273362 | − | 0.726255i | ||||
\(311\) | 4.39864 | + | 7.61867i | 0.249424 | + | 0.432015i | 0.963366 | − | 0.268190i | \(-0.0864254\pi\) |
−0.713942 | + | 0.700205i | \(0.753092\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.87877 | + | 11.9144i | −0.388811 | + | 0.673440i | −0.992290 | − | 0.123939i | \(-0.960447\pi\) |
0.603479 | + | 0.797379i | \(0.293781\pi\) | |||||||
\(314\) | 21.0007 | − | 25.5906i | 1.18514 | − | 1.44416i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.73539 | − | 1.53902i | 0.435149 | − | 0.0865769i | ||||
\(317\) | 9.53960 | + | 5.50769i | 0.535797 | + | 0.309343i | 0.743374 | − | 0.668876i | \(-0.233224\pi\) |
−0.207577 | + | 0.978219i | \(0.566558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −40.6092 | + | 23.4458i | −2.27368 | + | 1.31271i | ||||
\(320\) | −0.566808 | − | 8.63001i | −0.0316855 | − | 0.482432i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.61955 | + | 13.0439i | 0.0902538 | + | 0.726908i | ||||
\(323\) | 7.03206 | 0.391274 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.56316 | − | 2.70746i | −0.0867082 | − | 0.150183i | ||||
\(326\) | −0.625464 | + | 3.78891i | −0.0346413 | + | 0.209848i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.28757 | − | 17.3786i | 0.512820 | − | 0.959574i | ||||
\(329\) | −17.5304 | − | 4.22440i | −0.966483 | − | 0.232899i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.42290 | − | 1.39886i | −0.133175 | − | 0.0768884i | 0.431933 | − | 0.901906i | \(-0.357832\pi\) |
−0.565107 | + | 0.825017i | \(0.691165\pi\) | |||||||
\(332\) | 17.0400 | − | 14.9450i | 0.935191 | − | 0.820215i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.41056 | − | 9.06103i | −0.186618 | − | 0.495797i | ||||
\(335\) | −4.57916 | −0.250186 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.38341 | −0.184306 | −0.0921530 | − | 0.995745i | \(-0.529375\pi\) | ||||
−0.0921530 | + | 0.995745i | \(0.529375\pi\) | |||||||
\(338\) | 6.14471 | + | 16.3250i | 0.334228 | + | 0.887962i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.75948 | + | 2.42022i | −0.149654 | + | 0.131255i | ||||
\(341\) | 37.7633 | + | 21.8027i | 2.04500 | + | 1.18068i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.0523 | − | 12.0637i | −0.758751 | − | 0.651380i | ||||
\(344\) | −0.680224 | + | 1.27282i | −0.0366752 | + | 0.0686257i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.91326 | + | 11.5901i | −0.102857 | + | 0.623085i | ||||
\(347\) | 1.96566 | + | 3.40462i | 0.105522 | + | 0.182770i | 0.913951 | − | 0.405824i | \(-0.133015\pi\) |
−0.808429 | + | 0.588593i | \(0.799682\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.1233 | 0.863058 | 0.431529 | − | 0.902099i | \(-0.357974\pi\) | ||||
0.431529 | + | 0.902099i | \(0.357974\pi\) | |||||||
\(350\) | −13.2033 | − | 5.58336i | −0.705747 | − | 0.298443i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 18.8709 | + | 20.1438i | 1.00582 | + | 1.07367i | ||||
\(353\) | 32.2263 | − | 18.6059i | 1.71523 | − | 0.990290i | 0.788106 | − | 0.615539i | \(-0.211062\pi\) |
0.927126 | − | 0.374750i | \(-0.122272\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.0997 | + | 6.40843i | 0.589112 | + | 0.340124i | ||||
\(356\) | −0.709939 | + | 0.141249i | −0.0376267 | + | 0.00748617i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.8099 | + | 22.9210i | −0.994136 | + | 1.21141i | ||||
\(359\) | −10.7770 | + | 18.6664i | −0.568790 | + | 0.985173i | 0.427896 | + | 0.903828i | \(0.359255\pi\) |
−0.996686 | + | 0.0813452i | \(0.974078\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.920383 | − | 1.59415i | −0.0484412 | − | 0.0839026i | ||||
\(362\) | −8.89551 | − | 23.6332i | −0.467538 | − | 1.24213i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.64988 | − | 2.30700i | −0.191305 | − | 0.120920i | ||||
\(365\) | 3.23841i | 0.169506i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.45961 | − | 0.842704i | 0.0761908 | − | 0.0439888i | −0.461421 | − | 0.887182i | \(-0.652660\pi\) |
0.537611 | + | 0.843193i | \(0.319327\pi\) | |||||||
\(368\) | 11.1486 | + | 8.55306i | 0.581163 | + | 0.445859i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.98882 | − | 6.55596i | −0.415319 | − | 0.340828i | ||||
\(371\) | −6.64025 | − | 6.31207i | −0.344744 | − | 0.327706i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.14560 | − | 3.71630i | 0.111095 | − | 0.192422i | −0.805117 | − | 0.593116i | \(-0.797897\pi\) |
0.916212 | + | 0.400694i | \(0.131231\pi\) | |||||||
\(374\) | 1.90795 | − | 11.5579i | 0.0986579 | − | 0.597646i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16.3696 | + | 10.1808i | −0.844197 | + | 0.525035i | ||||
\(377\) | − | 7.84176i | − | 0.403871i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.00059i | 0.154130i | 0.997026 | + | 0.0770650i | \(0.0245549\pi\) | ||||
−0.997026 | + | 0.0770650i | \(0.975445\pi\) | |||||||
\(380\) | −8.48124 | − | 2.87857i | −0.435079 | − | 0.147668i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −25.4213 | − | 4.19649i | −1.30067 | − | 0.214711i | ||||
\(383\) | −10.5636 | + | 18.2967i | −0.539774 | + | 0.934916i | 0.459142 | + | 0.888363i | \(0.348157\pi\) |
−0.998916 | + | 0.0465530i | \(0.985176\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.3851 | + | 3.95249i | −0.682166 | + | 0.201438i | ||||
\(386\) | −16.7835 | + | 20.4517i | −0.854258 | + | 1.04096i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.2196 | + | 10.7172i | −0.620355 | + | 0.544086i | ||||
\(389\) | −29.5830 | + | 17.0798i | −1.49992 | + | 0.865979i | −1.00000 | 9.28896e-5i | \(-0.999970\pi\) | |
−0.499920 | + | 0.866072i | \(0.666637\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.96347i | − | 0.301585i | ||||||
\(392\) | −19.7301 | + | 1.65043i | −0.996520 | + | 0.0833593i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −29.4125 | + | 11.0708i | −1.48178 | + | 0.557740i | ||||
\(395\) | 2.13161 | + | 3.69206i | 0.107253 | + | 0.185768i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.42503 | − | 14.5926i | 0.422840 | − | 0.732380i | −0.573376 | − | 0.819292i | \(-0.694367\pi\) |
0.996216 | + | 0.0869120i | \(0.0276999\pi\) | |||||||
\(398\) | −17.4858 | − | 14.3496i | −0.876486 | − | 0.719280i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.1580 | + | 5.86593i | −0.707901 | + | 0.293297i | ||||
\(401\) | 8.58950 | + | 4.95915i | 0.428939 | + | 0.247648i | 0.698894 | − | 0.715225i | \(-0.253676\pi\) |
−0.269956 | + | 0.962873i | \(0.587009\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.31524 | + | 3.64610i | −0.314584 | + | 0.181625i | ||||
\(404\) | 0.980025 | − | 2.88749i | 0.0487581 | − | 0.143658i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.6787 | − | 28.6875i | −1.07589 | − | 1.42374i | ||||
\(407\) | 32.9828 | 1.63490 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.0859 | − | 31.3257i | −0.894291 | − | 1.54896i | −0.834680 | − | 0.550736i | \(-0.814347\pi\) |
−0.0596111 | − | 0.998222i | \(-0.518986\pi\) | |||||||
\(410\) | 10.5089 | + | 1.73479i | 0.518998 | + | 0.0856750i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.1755 | + | 3.01931i | −0.747645 | + | 0.148751i | ||||
\(413\) | −9.14053 | + | 9.61576i | −0.449776 | + | 0.473161i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.6101 | + | 6.12572i | 0.520828 | + | 0.300700i | ||||
\(416\) | −4.49528 | + | 1.04868i | −0.220399 | + | 0.0514159i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 26.7523 | − | 10.0696i | 1.30850 | − | 0.492518i | ||||
\(419\) | 30.7098 | 1.50027 | 0.750137 | − | 0.661283i | \(-0.229988\pi\) | ||||
0.750137 | + | 0.661283i | \(0.229988\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.9036 | 0.531411 | 0.265706 | − | 0.964054i | \(-0.414395\pi\) | ||||
0.265706 | + | 0.964054i | \(0.414395\pi\) | |||||||
\(422\) | 11.0131 | − | 4.14531i | 0.536108 | − | 0.201790i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.78891 | + | 0.321116i | −0.475391 | + | 0.0155947i | ||||
\(425\) | 5.63258 | + | 3.25197i | 0.273220 | + | 0.157744i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.2748 | + | 8.50037i | 1.70707 | + | 0.411362i | ||||
\(428\) | 0.470608 | + | 2.36535i | 0.0227477 | + | 0.114334i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.769676 | − | 0.127056i | −0.0371171 | − | 0.00612720i | ||||
\(431\) | −7.83169 | − | 13.5649i | −0.377239 | − | 0.653398i | 0.613420 | − | 0.789757i | \(-0.289793\pi\) |
−0.990659 | + | 0.136359i | \(0.956460\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.8956 | −1.10029 | −0.550145 | − | 0.835069i | \(-0.685428\pi\) | ||||
−0.550145 | + | 0.835069i | \(0.685428\pi\) | |||||||
\(434\) | −13.0233 | + | 30.7971i | −0.625140 | + | 1.47831i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.18999 | − | 0.403888i | −0.0569902 | − | 0.0193427i | ||||
\(437\) | 12.6022 | − | 7.27586i | 0.602843 | − | 0.348051i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.9901 | − | 8.65454i | −0.715438 | − | 0.413059i | 0.0976331 | − | 0.995222i | \(-0.468873\pi\) |
−0.813071 | + | 0.582164i | \(0.802206\pi\) | |||||||
\(440\) | −7.03238 | + | 13.1588i | −0.335256 | + | 0.627321i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.51436 | + | 1.24275i | 0.0720310 | + | 0.0591116i | ||||
\(443\) | 5.69268 | − | 9.86000i | 0.270467 | − | 0.468463i | −0.698514 | − | 0.715596i | \(-0.746155\pi\) |
0.968982 | + | 0.247133i | \(0.0794885\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.195635 | − | 0.338850i | −0.00927400 | − | 0.0160630i | ||||
\(446\) | 11.7967 | − | 4.44026i | 0.558589 | − | 0.210252i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −13.5460 | + | 16.2637i | −0.639987 | + | 0.768386i | ||||
\(449\) | 11.1088i | 0.524258i | 0.965033 | + | 0.262129i | \(0.0844245\pi\) | ||||
−0.965033 | + | 0.262129i | \(0.915575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.4391 | + | 16.9967i | −1.38624 | + | 0.800343i | ||||
\(452\) | 15.5442 | + | 17.7231i | 0.731136 | + | 0.833625i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.3277 | − | 22.3333i | 0.860160 | − | 1.04816i | ||||
\(455\) | 0.546777 | − | 2.26901i | 0.0256333 | − | 0.106373i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.5658 | + | 23.4967i | −0.634582 | + | 1.09913i | 0.352022 | + | 0.935992i | \(0.385494\pi\) |
−0.986604 | + | 0.163136i | \(0.947839\pi\) | |||||||
\(458\) | −17.3402 | − | 2.86248i | −0.810256 | − | 0.133755i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.44114 | + | 7.19243i | −0.113819 | + | 0.335349i | ||||
\(461\) | 13.2528i | 0.617246i | 0.951184 | + | 0.308623i | \(0.0998682\pi\) | ||||
−0.951184 | + | 0.308623i | \(0.900132\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.07186i | − | 0.189235i | −0.995514 | − | 0.0946176i | \(-0.969837\pi\) | ||
0.995514 | − | 0.0946176i | \(-0.0301629\pi\) | |||||||
\(464\) | −38.1117 | − | 5.01402i | −1.76929 | − | 0.232770i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.580472 | − | 3.51636i | 0.0268899 | − | 0.162892i | ||||
\(467\) | 11.7529 | − | 20.3565i | 0.543857 | − | 0.941988i | −0.454821 | − | 0.890583i | \(-0.650297\pi\) |
0.998678 | − | 0.0514053i | \(-0.0163700\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.12253 | + | 7.72109i | 0.375064 | + | 0.356527i | ||||
\(470\) | −8.05498 | − | 6.61025i | −0.371549 | − | 0.304908i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.465008 | + | 14.1753i | 0.0214037 | + | 0.652473i | ||||
\(473\) | 2.15613 | − | 1.24484i | 0.0991390 | − | 0.0572380i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.8706i | 0.728191i | ||||||||
\(476\) | 8.97560 | + | 0.359872i | 0.411396 | + | 0.0164947i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.5854 | − | 33.4363i | −0.575643 | − | 1.52934i | ||||
\(479\) | 1.86090 | + | 3.22317i | 0.0850266 | + | 0.147270i | 0.905403 | − | 0.424554i | \(-0.139569\pi\) |
−0.820376 | + | 0.571825i | \(0.806236\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.75789 | + | 4.77681i | −0.125749 | + | 0.217804i | ||||
\(482\) | 13.1289 | − | 15.9983i | 0.598004 | − | 0.728704i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.99890 | − | 25.1253i | −0.227223 | − | 1.14206i | ||||
\(485\) | −7.60860 | − | 4.39283i | −0.345489 | − | 0.199468i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.5697 | − | 8.41182i | 0.660216 | − | 0.381176i | −0.132143 | − | 0.991231i | \(-0.542186\pi\) |
0.792359 | + | 0.610055i | \(0.208853\pi\) | |||||||
\(488\) | 32.9390 | − | 20.4859i | 1.49108 | − | 0.927352i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.27244 | − | 9.81230i | −0.193009 | − | 0.443275i | ||||
\(491\) | −6.75735 | −0.304955 | −0.152477 | − | 0.988307i | \(-0.548725\pi\) | ||||
−0.152477 | + | 0.988307i | \(0.548725\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.15696 | + | 14.1283i | 0.367371 | + | 0.636305i | ||||
\(494\) | −0.778579 | + | 4.71644i | −0.0350299 | + | 0.212203i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.6825 | + | 33.0240i | 0.614360 | + | 1.48282i | ||||
\(497\) | −8.88323 | − | 30.0829i | −0.398467 | − | 1.34940i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.9780 | − | 8.64752i | −0.670505 | − | 0.387116i | 0.125763 | − | 0.992060i | \(-0.459862\pi\) |
−0.796268 | + | 0.604944i | \(0.793195\pi\) | |||||||
\(500\) | −12.5906 | − | 14.3555i | −0.563067 | − | 0.641997i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.67668 | + | 15.0816i | 0.253363 | + | 0.673123i | ||||
\(503\) | −6.05186 | −0.269839 | −0.134920 | − | 0.990857i | \(-0.543078\pi\) | ||||
−0.134920 | + | 0.990857i | \(0.543078\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.64824 | 0.0733459 | ||||||||
\(506\) | −8.53938 | − | 22.6871i | −0.379622 | − | 1.00856i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.20739 | + | 8.21771i | 0.319776 | + | 0.364602i | ||||
\(509\) | −15.4989 | − | 8.94831i | −0.686978 | − | 0.396627i | 0.115501 | − | 0.993307i | \(-0.463153\pi\) |
−0.802479 | + | 0.596681i | \(0.796486\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.46040 | − | 5.74429i | 0.241554 | − | 0.254113i | ||||
\(512\) | 2.22242 | + | 22.5180i | 0.0982182 | + | 0.995165i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.28973 | − | 32.0439i | 0.233320 | − | 1.41340i | ||||
\(515\) | −4.18186 | − | 7.24320i | −0.184275 | − | 0.319173i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.2560 | 1.46260 | ||||||||
\(518\) | 3.11635 | + | 25.0992i | 0.136925 | + | 1.10280i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.31773 | − | 2.11876i | −0.0577863 | − | 0.0929140i | ||||
\(521\) | 6.17964 | − | 3.56782i | 0.270735 | − | 0.156309i | −0.358487 | − | 0.933535i | \(-0.616707\pi\) |
0.629222 | + | 0.777226i | \(0.283374\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.1480 | − | 21.4474i | −1.62437 | − | 0.937830i | −0.985732 | − | 0.168323i | \(-0.946165\pi\) |
−0.638638 | − | 0.769507i | \(-0.720502\pi\) | |||||||
\(524\) | −6.19801 | − | 31.1522i | −0.270761 | − | 1.36089i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.9152 | + | 25.4864i | −0.911947 | + | 1.11126i | ||||
\(527\) | 7.58532 | − | 13.1382i | 0.330422 | − | 0.572307i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.32978 | + | 9.23146i | 0.231730 | + | 0.401368i | ||||
\(530\) | −1.86497 | − | 4.95476i | −0.0810089 | − | 0.215221i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.1904 | + | 19.4066i | 0.441810 | + | 0.841381i | ||||
\(533\) | − | 5.68478i | − | 0.246235i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.12897 | + | 0.651811i | −0.0488096 | + | 0.0281803i | ||||
\(536\) | 11.9741 | − | 0.392797i | 0.517200 | − | 0.0169663i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.9550 | + | 26.2235i | 1.37768 | + | 1.13058i | ||||
\(539\) | 30.4069 | + | 15.5581i | 1.30972 | + | 0.670135i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.68983 | − | 11.5871i | 0.287618 | − | 0.498170i | −0.685622 | − | 0.727957i | \(-0.740470\pi\) |
0.973241 | + | 0.229788i | \(0.0738032\pi\) | |||||||
\(542\) | −0.220566 | + | 1.33614i | −0.00947412 | + | 0.0573919i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.00817 | − | 6.56535i | 0.300473 | − | 0.281487i | ||||
\(545\) | − | 0.679274i | − | 0.0290969i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.1576i | 0.690849i | 0.938447 | + | 0.345424i | \(0.112265\pi\) | ||||
−0.938447 | + | 0.345424i | \(0.887735\pi\) | |||||||
\(548\) | 7.94725 | − | 23.4153i | 0.339490 | − | 1.00025i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 26.0849 | + | 4.30604i | 1.11226 | + | 0.183610i | ||||
\(551\) | −19.9042 | + | 34.4750i | −0.847946 | + | 1.46869i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.44426 | − | 10.1432i | 0.103940 | − | 0.431332i | ||||
\(554\) | −10.8887 | + | 13.2686i | −0.462618 | + | 0.563727i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.7147 | + | 25.8988i | 0.963318 | + | 1.09835i | ||||
\(557\) | −4.80203 | + | 2.77245i | −0.203469 | + | 0.117473i | −0.598272 | − | 0.801293i | \(-0.704146\pi\) |
0.394804 | + | 0.918765i | \(0.370813\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.416355i | 0.0176099i | ||||||||
\(560\) | −10.6780 | − | 4.10820i | −0.451228 | − | 0.173603i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 31.4628 | − | 11.8426i | 1.32718 | − | 0.499549i | ||||
\(563\) | −21.7530 | − | 37.6772i | −0.916778 | − | 1.58791i | −0.804277 | − | 0.594255i | \(-0.797447\pi\) |
−0.112501 | − | 0.993652i | \(-0.535886\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.37130 | + | 11.0354i | −0.268042 | + | 0.464263i | ||||
\(566\) | 3.70586 | + | 3.04118i | 0.155769 | + | 0.127830i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −29.5744 | − | 15.8053i | −1.24091 | − | 0.663175i | ||||
\(569\) | −31.6927 | − | 18.2978i | −1.32863 | − | 0.767083i | −0.343539 | − | 0.939138i | \(-0.611626\pi\) |
−0.985087 | + | 0.172056i | \(0.944959\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5668 | − | 10.1422i | 0.735148 | − | 0.424438i | −0.0851545 | − | 0.996368i | \(-0.527138\pi\) |
0.820303 | + | 0.571930i | \(0.193805\pi\) | |||||||
\(572\) | 7.54072 | + | 2.55935i | 0.315293 | + | 0.107012i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15.7157 | − | 20.7966i | −0.655959 | − | 0.868035i | ||||
\(575\) | 13.4589 | 0.561274 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.86675 | + | 8.42945i | 0.202605 | + | 0.350923i | 0.949367 | − | 0.314169i | \(-0.101726\pi\) |
−0.746762 | + | 0.665092i | \(0.768392\pi\) | |||||||
\(578\) | 19.6995 | + | 3.25195i | 0.819392 | + | 0.135263i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.05457 | − | 20.3789i | −0.168357 | − | 0.846188i | ||||
\(581\) | −8.49135 | − | 28.7559i | −0.352281 | − | 1.19299i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.6326 | + | 8.44816i | 0.606022 | + | 0.349887i | ||||
\(584\) | −0.277788 | − | 8.46811i | −0.0114950 | − | 0.350413i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.7968 | − | 7.07510i | 0.776489 | − | 0.292270i | ||||
\(587\) | −32.9781 | −1.36115 | −0.680576 | − | 0.732678i | \(-0.738270\pi\) | ||||
−0.680576 | + | 0.732678i | \(0.738270\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.0185 | 1.52532 | ||||||||
\(590\) | −7.17500 | + | 2.70066i | −0.295390 | + | 0.111184i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 21.4524 | + | 16.4579i | 0.881686 | + | 0.676416i | ||||
\(593\) | 30.7424 | + | 17.7491i | 1.26244 | + | 0.728869i | 0.973546 | − | 0.228493i | \(-0.0733798\pi\) |
0.288892 | + | 0.957362i | \(0.406713\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.37510 | + | 4.65677i | 0.0563737 | + | 0.190909i | ||||
\(596\) | −22.5822 | + | 4.49293i | −0.925001 | + | 0.184037i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.99973 | + | 0.660266i | 0.163561 | + | 0.0270003i | ||||
\(599\) | −14.8924 | − | 25.7944i | −0.608488 | − | 1.05393i | −0.991490 | − | 0.130185i | \(-0.958443\pi\) |
0.383002 | − | 0.923748i | \(-0.374890\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.8743 | −1.91204 | −0.956021 | − | 0.293298i | \(-0.905247\pi\) | ||||
−0.956021 | + | 0.293298i | \(0.905247\pi\) | |||||||
\(602\) | 1.15102 | + | 1.52315i | 0.0469121 | + | 0.0620791i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.90842 | + | 20.3546i | −0.281100 | + | 0.828215i | ||||
\(605\) | 11.9922 | − | 6.92368i | 0.487551 | − | 0.281488i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.2150 | + | 11.0938i | 0.779912 | + | 0.450283i | 0.836399 | − | 0.548121i | \(-0.184657\pi\) |
−0.0564869 | + | 0.998403i | \(0.517990\pi\) | |||||||
\(608\) | 22.4245 | + | 6.79966i | 0.909435 | + | 0.275763i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.2083 | + | 13.3012i | 0.656254 | + | 0.538549i | ||||
\(611\) | −2.78073 | + | 4.81636i | −0.112496 | + | 0.194849i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.05599 | − | 10.4893i | −0.244599 | − | 0.423658i | 0.717420 | − | 0.696641i | \(-0.245323\pi\) |
−0.962019 | + | 0.272983i | \(0.911990\pi\) | |||||||
\(614\) | 34.0258 | − | 12.8073i | 1.37317 | − | 0.516859i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 34.6616 | − | 11.4835i | 1.39655 | − | 0.462685i | ||||
\(617\) | 19.5363i | 0.786501i | 0.919431 | + | 0.393250i | \(0.128649\pi\) | ||||
−0.919431 | + | 0.393250i | \(0.871351\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.819203 | − | 0.472967i | 0.0329265 | − | 0.0190102i | −0.483446 | − | 0.875374i | \(-0.660615\pi\) |
0.516373 | + | 0.856364i | \(0.327282\pi\) | |||||||
\(620\) | −14.5266 | + | 12.7407i | −0.583403 | + | 0.511677i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.89242 | − | 9.61738i | 0.316457 | − | 0.385622i | ||||
\(623\) | −0.224329 | + | 0.930921i | −0.00898757 | + | 0.0372966i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.41753 | + | 7.65138i | −0.176701 | + | 0.306055i | ||||
\(626\) | 19.1963 | + | 3.16888i | 0.767238 | + | 0.126654i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −44.3330 | − | 15.0468i | −1.76908 | − | 0.600433i | ||||
\(629\) | − | 11.4750i | − | 0.457537i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6.23847i | − | 0.248350i | −0.992260 | − | 0.124175i | \(-0.960372\pi\) | ||
0.992260 | − | 0.124175i | \(-0.0396284\pi\) | |||||||
\(632\) | −5.89066 | − | 9.47152i | −0.234318 | − | 0.376757i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.53726 | − | 15.3701i | 0.100767 | − | 0.610424i | ||||
\(635\) | −2.95419 | + | 5.11681i | −0.117234 | + | 0.203054i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.79574 | + | 3.10284i | −0.190014 | + | 0.122939i | ||||
\(638\) | 51.2628 | + | 42.0684i | 2.02952 | + | 1.66550i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.1400 | + | 5.04956i | −0.440346 | + | 0.199601i | ||||
\(641\) | −6.36278 | + | 3.67355i | −0.251315 | + | 0.145097i | −0.620366 | − | 0.784312i | \(-0.713016\pi\) |
0.369051 | + | 0.929409i | \(0.379683\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 44.8033i | − | 1.76687i | −0.468553 | − | 0.883436i | \(-0.655224\pi\) | ||
0.468553 | − | 0.883436i | \(-0.344776\pi\) | |||||||
\(644\) | 16.4575 | − | 8.64186i | 0.648518 | − | 0.340537i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.50328 | − | 9.30735i | −0.137835 | − | 0.366193i | ||||
\(647\) | 4.89449 | + | 8.47750i | 0.192422 | + | 0.333285i | 0.946052 | − | 0.324014i | \(-0.105032\pi\) |
−0.753630 | + | 0.657299i | \(0.771699\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.2338 | − | 21.1896i | 0.480219 | − | 0.831764i | ||||
\(650\) | −2.80475 | + | 3.41775i | −0.110011 | + | 0.134055i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.32645 | − | 1.05974i | 0.208600 | − | 0.0415028i | ||||
\(653\) | −0.378115 | − | 0.218305i | −0.0147968 | − | 0.00854292i | 0.492583 | − | 0.870265i | \(-0.336053\pi\) |
−0.507380 | + | 0.861722i | \(0.669386\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.8688 | − | 8.58449i | 0.580971 | − | 0.335424i | ||||
\(656\) | −27.6286 | − | 3.63485i | −1.07872 | − | 0.141917i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.14216 | + | 25.3071i | 0.122494 | + | 0.986573i | ||||
\(659\) | 26.0531 | 1.01489 | 0.507443 | − | 0.861685i | \(-0.330591\pi\) | ||||
0.507443 | + | 0.861685i | \(0.330591\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.9044 | − | 34.4754i | −0.774191 | − | 1.34094i | −0.935248 | − | 0.353993i | \(-0.884824\pi\) |
0.161057 | − | 0.986945i | \(-0.448510\pi\) | |||||||
\(662\) | −0.644421 | + | 3.90375i | −0.0250461 | + | 0.151723i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −28.2697 | − | 15.1080i | −1.09708 | − | 0.586306i | ||||
\(665\) | −8.16308 | + | 8.58749i | −0.316551 | + | 0.333009i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.2362 | + | 16.8795i | 1.13203 | + | 0.653578i | ||||
\(668\) | −10.2937 | + | 9.02816i | −0.398276 | + | 0.349310i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.28128 | + | 6.06079i | 0.0881334 | + | 0.234149i | ||||
\(671\) | −66.9179 | −2.58333 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.26652 | −0.318651 | −0.159326 | − | 0.987226i | \(-0.550932\pi\) | ||||
−0.159326 | + | 0.987226i | \(0.550932\pi\) | |||||||
\(674\) | 1.68557 | + | 4.47814i | 0.0649257 | + | 0.172492i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.5459 | − | 16.2658i | 0.713303 | − | 0.625607i | ||||
\(677\) | 3.77905 | + | 2.18184i | 0.145241 | + | 0.0838548i | 0.570859 | − | 0.821048i | \(-0.306610\pi\) |
−0.425619 | + | 0.904903i | \(0.639943\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.08924 | + | 20.6211i | 0.233684 | + | 0.791367i | ||||
\(680\) | 4.57804 | + | 2.44662i | 0.175560 | + | 0.0938236i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.0440 | − | 60.8438i | 0.384603 | − | 2.32983i | ||||
\(683\) | −11.8552 | − | 20.5339i | −0.453628 | − | 0.785706i | 0.544981 | − | 0.838449i | \(-0.316537\pi\) |
−0.998608 | + | 0.0527426i | \(0.983204\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.3660 | 0.510688 | ||||||||
\(686\) | −8.96642 | + | 24.6090i | −0.342340 | + | 0.939576i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.02353 | + | 0.266218i | 0.0771462 | + | 0.0101494i | ||||
\(689\) | −2.44705 | + | 1.41280i | −0.0932250 | + | 0.0538235i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.8985 | − | 11.4884i | −0.756974 | − | 0.437039i | 0.0712345 | − | 0.997460i | \(-0.477306\pi\) |
−0.828208 | + | 0.560421i | \(0.810639\pi\) | |||||||
\(692\) | 16.2933 | − | 3.24170i | 0.619378 | − | 0.123231i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.52695 | − | 4.29780i | 0.133881 | − | 0.163142i | ||||
\(695\) | −9.31039 | + | 16.1261i | −0.353163 | + | 0.611697i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.91328 | + | 10.2421i | 0.223982 | + | 0.387947i | ||||
\(698\) | −8.03239 | − | 21.3401i | −0.304030 | − | 0.807735i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.812191 | + | 20.2569i | −0.0306979 | + | 0.765640i | ||||
\(701\) | − | 37.9118i | − | 1.43191i | −0.698146 | − | 0.715955i | \(-0.745991\pi\) | ||
0.698146 | − | 0.715955i | \(-0.254009\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.2492 | − | 14.0003i | 0.914577 | − | 0.528031i | ||||
\(704\) | 17.2602 | − | 35.0122i | 0.650519 | − | 1.31957i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −40.6807 | − | 33.3842i | −1.53104 | − | 1.25643i | ||||
\(707\) | −2.92366 | − | 2.77917i | −0.109956 | − | 0.104521i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.4546 | − | 25.0361i | 0.542855 | − | 0.940252i | −0.455884 | − | 0.890039i | \(-0.650677\pi\) |
0.998739 | − | 0.0502127i | \(-0.0159899\pi\) | |||||||
\(710\) | 2.95220 | − | 17.8837i | 0.110794 | − | 0.671165i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.540633 | + | 0.869278i | 0.0202611 | + | 0.0325776i | ||||
\(713\) | − | 31.3932i | − | 1.17568i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.30441i | 0.160976i | ||||||||
\(716\) | 39.7082 | + | 13.4771i | 1.48397 | + | 0.503664i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 30.0750 | + | 4.96471i | 1.12239 | + | 0.185281i | ||||
\(719\) | −15.2533 | + | 26.4195i | −0.568852 | + | 0.985280i | 0.427828 | + | 0.903860i | \(0.359279\pi\) |
−0.996680 | + | 0.0814198i | \(0.974055\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.79523 | + | 19.8992i | −0.178584 | + | 0.741085i | ||||
\(722\) | −1.65143 | + | 2.01237i | −0.0614599 | + | 0.0748925i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −26.8483 | + | 23.5475i | −0.997810 | + | 0.875135i | ||||
\(725\) | −31.8859 | + | 18.4093i | −1.18421 | + | 0.683706i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 19.4515i | − | 0.721415i | −0.932679 | − | 0.360708i | \(-0.882535\pi\) | ||
0.932679 | − | 0.360708i | \(-0.117465\pi\) | |||||||
\(728\) | −1.23513 | + | 5.98014i | −0.0457771 | + | 0.221639i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.28622 | − | 1.61333i | 0.158640 | − | 0.0597120i | ||||
\(731\) | −0.433091 | − | 0.750135i | −0.0160184 | − | 0.0277447i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.52314 | + | 16.4946i | −0.351745 | + | 0.609241i | −0.986555 | − | 0.163428i | \(-0.947745\pi\) |
0.634810 | + | 0.772668i | \(0.281078\pi\) | |||||||
\(734\) | −1.84253 | − | 1.51205i | −0.0680089 | − | 0.0558109i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.76638 | − | 19.0169i | 0.212552 | − | 0.700972i | ||||
\(737\) | −17.8990 | − | 10.3340i | −0.659320 | − | 0.380658i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.3030 | − | 15.1860i | 0.967571 | − | 0.558628i | 0.0690765 | − | 0.997611i | \(-0.477995\pi\) |
0.898495 | + | 0.438984i | \(0.144661\pi\) | |||||||
\(740\) | −4.69728 | + | 13.8398i | −0.172675 | + | 0.508760i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.04632 | + | 11.9334i | −0.185256 | + | 0.438087i | ||||
\(743\) | 13.1841 | 0.483676 | 0.241838 | − | 0.970317i | \(-0.422250\pi\) | ||||
0.241838 | + | 0.970317i | \(0.422250\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.22288 | − | 10.7783i | −0.227989 | − | 0.394888i | ||||
\(746\) | −5.98765 | − | 0.988427i | −0.219223 | − | 0.0361889i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −16.2481 | + | 3.23271i | −0.594090 | + | 0.118200i | ||||
\(749\) | 3.10161 | + | 0.747414i | 0.113331 | + | 0.0273099i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.5934 | − | 16.5084i | −1.04339 | − | 0.602400i | −0.122596 | − | 0.992457i | \(-0.539122\pi\) |
−0.920791 | + | 0.390057i | \(0.872455\pi\) | |||||||
\(752\) | 21.6300 | + | 16.5942i | 0.788765 | + | 0.605128i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.3790 | + | 3.90666i | −0.377982 | + | 0.142272i | ||||
\(755\) | −11.6189 | −0.422853 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.2886 | −1.13720 | −0.568601 | − | 0.822613i | \(-0.692515\pi\) | ||||
−0.568601 | + | 0.822613i | \(0.692515\pi\) | |||||||
\(758\) | 3.97146 | − | 1.49485i | 0.144250 | − | 0.0542956i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.415282 | + | 12.6595i | 0.0150639 | + | 0.459208i | ||||
\(761\) | −4.37627 | − | 2.52664i | −0.158640 | − | 0.0915906i | 0.418579 | − | 0.908181i | \(-0.362528\pi\) |
−0.577218 | + | 0.816590i | \(0.695862\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.14535 | + | 1.20490i | −0.0414644 | + | 0.0436203i | ||||
\(764\) | 7.11024 | + | 35.7372i | 0.257240 | + | 1.29293i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.4794 | + | 4.86638i | 1.06513 | + | 0.175830i | ||||
\(767\) | 2.04588 | + | 3.54357i | 0.0738726 | + | 0.127951i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.29930 | −0.191098 | −0.0955489 | − | 0.995425i | \(-0.530461\pi\) | ||||
−0.0955489 | + | 0.995425i | \(0.530461\pi\) | |||||||
\(770\) | 11.8996 | + | 15.7468i | 0.428832 | + | 0.567477i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 35.4304 | + | 12.0252i | 1.27517 | + | 0.432797i | ||||
\(773\) | 20.1963 | − | 11.6604i | 0.726411 | − | 0.419394i | −0.0906965 | − | 0.995879i | \(-0.528909\pi\) |
0.817108 | + | 0.576485i | \(0.195576\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.6513 | + | 17.1192i | 1.06511 | + | 0.614940i | ||||
\(776\) | 20.2725 | + | 10.8341i | 0.727742 | + | 0.388923i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.3440 | + | 30.6460i | 1.33885 | + | 1.09871i | ||||
\(779\) | −14.4293 | + | 24.9922i | −0.516982 | + | 0.895439i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.9244 | + | 50.0986i | 1.03500 | + | 1.79267i | ||||
\(782\) | −7.89300 | + | 2.97092i | −0.282253 | + | 0.106240i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.0137 | + | 25.2917i | 0.429061 | + | 0.903276i | ||||
\(785\) | − | 25.3063i | − | 0.903220i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.4126 | − | 21.0228i | 1.29797 | − | 0.749383i | 0.317917 | − | 0.948119i | \(-0.397017\pi\) |
0.980053 | + | 0.198735i | \(0.0636834\pi\) | |||||||
\(788\) | 29.3058 | + | 33.4138i | 1.04398 | + | 1.19032i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.82472 | − | 4.66065i | 0.136077 | − | 0.165818i | ||||
\(791\) | 29.9086 | − | 8.83176i | 1.06343 | − | 0.314021i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.59540 | − | 9.69152i | 0.198699 | − | 0.344156i | ||||
\(794\) | −23.5114 | − | 3.88120i | −0.834388 | − | 0.137739i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.2813 | + | 30.2923i | −0.364412 | + | 1.07368i | ||||
\(797\) | − | 21.9503i | − | 0.777519i | −0.921339 | − | 0.388760i | \(-0.872904\pi\) | ||
0.921339 | − | 0.388760i | \(-0.127096\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 11.5700i | − | 0.409317i | ||||||
\(800\) | 14.8172 | + | 15.8167i | 0.523869 | + | 0.559203i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.28456 | − | 13.8393i | 0.0806705 | − | 0.488682i | ||||
\(803\) | −7.30827 | + | 12.6583i | −0.257903 | + | 0.446702i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.28254 | + | 6.92262i | 0.256676 | + | 0.243990i | ||||
\(806\) | 7.97200 | + | 6.54215i | 0.280802 | + | 0.230437i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.31000 | + | 0.141385i | −0.151625 | + | 0.00497392i | ||||
\(809\) | 42.1387 | − | 24.3288i | 1.48152 | − | 0.855355i | 0.481739 | − | 0.876315i | \(-0.340005\pi\) |
0.999780 | + | 0.0209595i | \(0.00667210\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.14916i | − | 0.0754672i | −0.999288 | − | 0.0377336i | \(-0.987986\pi\) | ||
0.999288 | − | 0.0377336i | \(-0.0120138\pi\) | |||||||
\(812\) | −27.1696 | + | 42.9847i | −0.953467 | + | 1.50847i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.4316 | − | 43.6547i | −0.575927 | − | 1.53010i | ||||
\(815\) | 1.46779 | + | 2.54228i | 0.0514144 | + | 0.0890523i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.05680 | − | 1.83044i | 0.0369729 | − | 0.0640389i | ||||
\(818\) | −32.4513 | + | 39.5438i | −1.13463 | + | 1.38262i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.93931 | − | 14.7734i | −0.102645 | − | 0.515910i | ||||
\(821\) | 11.4656 | + | 6.61966i | 0.400152 | + | 0.231028i | 0.686549 | − | 0.727083i | \(-0.259125\pi\) |
−0.286398 | + | 0.958111i | \(0.592458\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.8020 | + | 28.1759i | −1.70113 | + | 0.982149i | −0.756514 | + | 0.653977i | \(0.773099\pi\) |
−0.944618 | + | 0.328172i | \(0.893568\pi\) | |||||||
\(824\) | 11.5565 | + | 18.5815i | 0.402589 | + | 0.647319i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.2807 | + | 7.30759i | 0.601273 | + | 0.254264i | ||||
\(827\) | −44.4024 | −1.54402 | −0.772011 | − | 0.635609i | \(-0.780749\pi\) | ||||
−0.772011 | + | 0.635609i | \(0.780749\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.2282 | + | 28.1080i | 0.563627 | + | 0.976231i | 0.997176 | + | 0.0751011i | \(0.0239279\pi\) |
−0.433549 | + | 0.901130i | \(0.642739\pi\) | |||||||
\(830\) | 2.82197 | − | 17.0948i | 0.0979520 | − | 0.593369i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.62748 | + | 5.42733i | 0.125760 | + | 0.188159i | ||||
\(833\) | 5.41279 | − | 10.5788i | 0.187542 | − | 0.366534i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.40945 | − | 3.70050i | −0.221808 | − | 0.128061i | ||||
\(836\) | −26.6553 | − | 30.3918i | −0.921893 | − | 1.05112i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.2992 | − | 40.6463i | −0.528503 | − | 1.40410i | ||||
\(839\) | 25.8761 | 0.893342 | 0.446671 | − | 0.894698i | \(-0.352609\pi\) | ||||
0.446671 | + | 0.894698i | \(0.352609\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −63.3527 | −2.18458 | ||||||||
\(842\) | −5.43205 | − | 14.4316i | −0.187201 | − | 0.497347i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.9731 | − | 12.5113i | −0.377710 | − | 0.430657i | ||||
\(845\) | 11.5477 | + | 6.66707i | 0.397253 | + | 0.229354i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.9460 | − | 7.93919i | −1.13204 | − | 0.272794i | ||||
\(848\) | 5.30172 | + | 12.7962i | 0.182062 | + | 0.439424i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.49810 | − | 9.07515i | 0.0513845 | − | 0.311275i | ||||
\(851\) | −11.8728 | − | 20.5643i | −0.406995 | − | 0.704936i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.9017 | 0.510225 | 0.255113 | − | 0.966911i | \(-0.417887\pi\) | ||||
0.255113 | + | 0.966911i | \(0.417887\pi\) | |||||||
\(854\) | −6.32268 | − | 50.9231i | −0.216358 | − | 1.74255i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.89623 | − | 1.80126i | 0.0989912 | − | 0.0615660i | ||||
\(857\) | 17.4299 | − | 10.0632i | 0.595395 | − | 0.343751i | −0.171833 | − | 0.985126i | \(-0.554969\pi\) |
0.767228 | + | 0.641375i | \(0.221636\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.71584 | − | 5.60944i | −0.331500 | − | 0.191392i | 0.325007 | − | 0.945712i | \(-0.394633\pi\) |
−0.656507 | + | 0.754320i | \(0.727967\pi\) | |||||||
\(860\) | 0.215276 | + | 1.08201i | 0.00734084 | + | 0.0368962i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.0523 | + | 17.1236i | −0.478623 | + | 0.583231i | ||||
\(863\) | −16.4955 | + | 28.5711i | −0.561514 | + | 0.972571i | 0.435850 | + | 0.900019i | \(0.356448\pi\) |
−0.997365 | + | 0.0725520i | \(0.976886\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.48988 | + | 7.77670i | 0.152660 | + | 0.264416i | ||||
\(866\) | 11.4063 | + | 30.3036i | 0.387600 | + | 1.02976i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 47.2499 | + | 1.89446i | 1.60376 | + | 0.0643021i | ||||
\(869\) | 19.2420i | 0.652742i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.99329 | − | 1.72818i | 0.101424 | − | 0.0585571i | ||||
\(872\) | 0.0582677 | + | 1.77624i | 0.00197319 | + | 0.0601509i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.9083 | − | 13.0550i | −0.538105 | − | 0.441591i | ||||
\(875\) | −24.2256 | + | 7.15361i | −0.818974 | + | 0.241836i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.8909 | − | 30.9880i | 0.604134 | − | 1.04639i | −0.388054 | − | 0.921637i | \(-0.626852\pi\) |
0.992188 | − | 0.124754i | \(-0.0398142\pi\) | |||||||
\(878\) | −3.98693 | + | 24.1519i | −0.134552 | + | 0.815086i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 20.9199 | + | 2.75224i | 0.705209 | + | 0.0927781i | ||||
\(881\) | 3.68853i | 0.124270i | 0.998068 | + | 0.0621348i | \(0.0197909\pi\) | ||||
−0.998068 | + | 0.0621348i | \(0.980209\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 12.4938i | − | 0.420449i | −0.977653 | − | 0.210224i | \(-0.932581\pi\) | ||
0.977653 | − | 0.210224i | \(-0.0674195\pi\) | |||||||
\(884\) | 0.890418 | − | 2.62347i | 0.0299480 | − | 0.0882370i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.8863 | − | 2.62248i | −0.533711 | − | 0.0881038i | ||||
\(887\) | 0.427511 | − | 0.740471i | 0.0143544 | − | 0.0248626i | −0.858759 | − | 0.512380i | \(-0.828764\pi\) |
0.873113 | + | 0.487517i | \(0.162097\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.8678 | − | 4.09504i | 0.465111 | − | 0.137343i | ||||
\(890\) | −0.351025 | + | 0.427745i | −0.0117664 | + | 0.0143381i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.7539 | − | 13.4015i | −0.393550 | − | 0.448717i | ||||
\(893\) | 24.4500 | − | 14.1162i | 0.818190 | − | 0.472382i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.6664i | 0.757653i | ||||||||
\(896\) | 28.2743 | + | 9.82658i | 0.944579 | + | 0.328283i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.7032 | − | 5.53426i | 0.490652 | − | 0.184681i | ||||
\(899\) | 42.9403 | + | 74.3748i | 1.43214 | + | 2.48054i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.93918 | − | 5.09081i | 0.0979183 | − | 0.169599i | ||||
\(902\) | 37.1623 | + | 30.4969i | 1.23737 | + | 1.01544i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.7137 | − | 29.4030i | 0.522630 | − | 0.977930i | ||||
\(905\) | −16.7173 | − | 9.65172i | −0.555701 | − | 0.320834i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.5068 | − | 14.7264i | 0.846939 | − | 0.488981i | −0.0126776 | − | 0.999920i | \(-0.504036\pi\) |
0.859617 | + | 0.510939i | \(0.170702\pi\) | |||||||
\(908\) | −38.6901 | − | 13.1316i | −1.28398 | − | 0.435787i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.27557 | + | 0.406699i | −0.108584 | + | 0.0134819i | ||||
\(911\) | −9.62988 | −0.319052 | −0.159526 | − | 0.987194i | \(-0.550997\pi\) | ||||
−0.159526 | + | 0.987194i | \(0.550997\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.6484 | + | 47.8885i | 0.915030 | + | 1.58488i | ||||
\(914\) | 37.8575 | + | 6.24943i | 1.25222 | + | 0.206713i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.85000 | + | 24.3769i | 0.160249 | + | 0.805435i | ||||
\(917\) | −40.8489 | − | 9.84360i | −1.34895 | − | 0.325064i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.68583 | − | 3.28272i | −0.187558 | − | 0.108287i | 0.403281 | − | 0.915076i | \(-0.367870\pi\) |
−0.590839 | + | 0.806790i | \(0.701203\pi\) | |||||||
\(920\) | 10.7358 | − | 0.352176i | 0.353947 | − | 0.0116109i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17.5409 | − | 6.60239i | 0.577680 | − | 0.217438i | ||||
\(923\) | −9.67418 | −0.318429 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.8977 | 0.851512 | ||||||||
\(926\) | −5.38935 | + | 2.02854i | −0.177105 | + | 0.0666621i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 12.3504 | + | 52.9411i | 0.405421 | + | 1.73788i | ||||
\(929\) | −18.6881 | − | 10.7896i | −0.613137 | − | 0.353995i | 0.161055 | − | 0.986945i | \(-0.448510\pi\) |
−0.774192 | + | 0.632951i | \(0.781844\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.9594 | − | 1.46845i | 0.949106 | − | 0.0481265i | ||||
\(932\) | −4.94330 | + | 0.983513i | −0.161923 | + | 0.0322161i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32.7982 | − | 5.41425i | −1.07319 | − | 0.177160i | ||||
\(935\) | −4.47743 | − | 7.75514i | −0.146428 | − | 0.253620i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.5055 | −1.25792 | −0.628960 | − | 0.777437i | \(-0.716519\pi\) | ||||
−0.628960 | + | 0.777437i | \(0.716519\pi\) | |||||||
\(938\) | 6.17279 | − | 14.5972i | 0.201549 | − | 0.476615i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.73618 | + | 13.9544i | −0.154477 | + | 0.455142i | ||||
\(941\) | 1.30779 | − | 0.755052i | 0.0426327 | − | 0.0246140i | −0.478532 | − | 0.878070i | \(-0.658831\pi\) |
0.521165 | + | 0.853456i | \(0.325498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.1944 | + | 12.2366i | 0.690184 | + | 0.398478i | ||||
\(944\) | 18.5303 | − | 7.67743i | 0.603108 | − | 0.249879i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.72178 | − | 2.23361i | −0.0884927 | − | 0.0726208i | ||||
\(947\) | 2.64972 | − | 4.58945i | 0.0861044 | − | 0.149137i | −0.819757 | − | 0.572712i | \(-0.805891\pi\) |
0.905861 | + | 0.423574i | \(0.139225\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.22218 | − | 2.11687i | −0.0396735 | − | 0.0687166i | ||||
\(950\) | 21.0056 | − | 7.90650i | 0.681513 | − | 0.256521i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.99521 | − | 12.0590i | −0.129486 | − | 0.390835i | ||||
\(953\) | − | 60.6268i | − | 1.96390i | −0.189151 | − | 0.981948i | \(-0.560574\pi\) | ||
0.189151 | − | 0.981948i | \(-0.439426\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.0572 | + | 9.84797i | −0.551958 | + | 0.318673i | ||||
\(956\) | −37.9851 | + | 33.3150i | −1.22853 | + | 1.07749i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.33899 | − | 4.06875i | 0.107878 | − | 0.131455i | ||||
\(959\) | −23.7086 | − | 22.5369i | −0.765592 | − | 0.727754i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4310 | − | 42.3158i | 0.788098 | − | 1.36503i | ||||
\(962\) | 7.69633 | + | 1.27049i | 0.248140 | + | 0.0409623i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −27.7154 | − | 9.40671i | −0.892652 | − | 0.302970i | ||||
\(965\) | 20.2245i | 0.651049i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.5917i | 1.40181i | 0.713253 | + | 0.700907i | \(0.247221\pi\) | ||||
−0.713253 | + | 0.700907i | \(0.752779\pi\) | |||||||
\(968\) | −30.7644 | + | 19.1334i | −0.988806 | + | 0.614972i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.02367 | + | 12.2589i | −0.0649760 | + | 0.393609i | ||||
\(971\) | 9.75149 | − | 16.8901i | 0.312940 | − | 0.542028i | −0.666057 | − | 0.745901i | \(-0.732019\pi\) |
0.978997 | + | 0.203872i | \(0.0653527\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43.7056 | − | 12.9059i | 1.40114 | − | 0.413743i | ||||
\(974\) | −18.3920 | − | 15.0932i | −0.589317 | − | 0.483618i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −43.5240 | − | 33.3910i | −1.39317 | − | 1.06882i | ||||
\(977\) | −51.2227 | + | 29.5734i | −1.63876 | + | 0.946137i | −0.657496 | + | 0.753458i | \(0.728384\pi\) |
−0.981262 | + | 0.192679i | \(0.938282\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.76600i | − | 0.0564416i | ||||||
\(980\) | −10.8587 | + | 10.5432i | −0.346868 | + | 0.336790i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.36642 | + | 8.94376i | 0.107427 | + | 0.285407i | ||||
\(983\) | −21.1885 | − | 36.6996i | −0.675809 | − | 1.17054i | −0.976232 | − | 0.216729i | \(-0.930461\pi\) |
0.300423 | − | 0.953806i | \(-0.402872\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0120 | + | 20.8053i | −0.382733 | + | 0.662913i | ||||
\(986\) | 14.6359 | − | 17.8347i | 0.466103 | − | 0.567974i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.63037 | − | 1.31917i | 0.210940 | − | 0.0419684i | ||||
\(989\) | −1.55228 | − | 0.896211i | −0.0493597 | − | 0.0284979i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.1417 | − | 9.89678i | 0.544525 | − | 0.314381i | −0.202386 | − | 0.979306i | \(-0.564870\pi\) |
0.746911 | + | 0.664924i | \(0.231536\pi\) | |||||||
\(992\) | 36.8928 | − | 34.5616i | 1.17135 | − | 1.09733i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −35.3911 | + | 26.7444i | −1.12254 | + | 0.848281i | ||||
\(995\) | −17.2916 | −0.548179 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.1621 | − | 34.9217i | −0.638539 | − | 1.10598i | −0.985753 | − | 0.168197i | \(-0.946206\pi\) |
0.347214 | − | 0.937786i | \(-0.387128\pi\) | |||||||
\(998\) | −3.98370 | + | 24.1323i | −0.126102 | + | 0.763894i | ||||
\(999\) | 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 | 756.2.be.d.107.5 | yes | 28 | |
3.2 | odd | 2 | inner | 756.2.be.d.107.10 | yes | 28 | |
4.3 | odd | 2 | 756.2.be.c.107.1 | ✓ | 28 | ||
7.4 | even | 3 | 756.2.be.c.431.14 | yes | 28 | ||
12.11 | even | 2 | 756.2.be.c.107.14 | yes | 28 | ||
21.11 | odd | 6 | 756.2.be.c.431.1 | yes | 28 | ||
28.11 | odd | 6 | inner | 756.2.be.d.431.10 | yes | 28 | |
84.11 | even | 6 | inner | 756.2.be.d.431.5 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.be.c.107.1 | ✓ | 28 | 4.3 | odd | 2 | ||
756.2.be.c.107.14 | yes | 28 | 12.11 | even | 2 | ||
756.2.be.c.431.1 | yes | 28 | 21.11 | odd | 6 | ||
756.2.be.c.431.14 | yes | 28 | 7.4 | even | 3 | ||
756.2.be.d.107.5 | yes | 28 | 1.1 | even | 1 | trivial | |
756.2.be.d.107.10 | yes | 28 | 3.2 | odd | 2 | inner | |
756.2.be.d.431.5 | yes | 28 | 84.11 | even | 6 | inner | |
756.2.be.d.431.10 | yes | 28 | 28.11 | odd | 6 | inner |