Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(289,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.m (of order \(3\), 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: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 546) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1621.1 | ||
Root | \(-1.10337 + 1.91109i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.1621 |
Dual form | 1638.2.m.k.289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.10337 | − | 1.91109i | −0.493442 | − | 0.854666i | 0.506530 | − | 0.862223i | \(-0.330928\pi\) |
−0.999971 | + | 0.00755619i | \(0.997595\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.19230 | + | 2.36187i | 0.450648 | + | 0.892702i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.10337 | − | 1.91109i | −0.348916 | − | 0.604340i | ||||
\(11\) | −0.527733 | − | 0.914061i | −0.159118 | − | 0.275600i | 0.775433 | − | 0.631430i | \(-0.217532\pi\) |
−0.934551 | + | 0.355830i | \(0.884198\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.18376 | − | 1.69224i | 0.883015 | − | 0.469344i | ||||
\(14\) | 1.19230 | + | 2.36187i | 0.318657 | + | 0.631235i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.944533 | 0.229083 | 0.114541 | − | 0.993418i | \(-0.463460\pi\) | ||||
0.114541 | + | 0.993418i | \(0.463460\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.96372 | + | 3.40126i | −0.450508 | + | 0.780303i | −0.998418 | − | 0.0562346i | \(-0.982091\pi\) |
0.547909 | + | 0.836538i | \(0.315424\pi\) | |||||||
\(20\) | −1.10337 | − | 1.91109i | −0.246721 | − | 0.427333i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.527733 | − | 0.914061i | −0.112513 | − | 0.194879i | ||||
\(23\) | 6.22771 | 1.29857 | 0.649284 | − | 0.760546i | \(-0.275069\pi\) | ||||
0.649284 | + | 0.760546i | \(0.275069\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0651512 | − | 0.112845i | 0.0130302 | − | 0.0225690i | ||||
\(26\) | 3.18376 | − | 1.69224i | 0.624386 | − | 0.331876i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.19230 | + | 2.36187i | 0.225324 | + | 0.446351i | ||||
\(29\) | −0.888084 | + | 1.53821i | −0.164913 | + | 0.285638i | −0.936624 | − | 0.350335i | \(-0.886068\pi\) |
0.771711 | + | 0.635973i | \(0.219401\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.63304 | − | 6.29261i | 0.652513 | − | 1.13019i | −0.329997 | − | 0.943982i | \(-0.607048\pi\) |
0.982511 | − | 0.186205i | \(-0.0596188\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.944533 | 0.161986 | ||||||||
\(35\) | 3.19819 | − | 4.88461i | 0.540593 | − | 0.825650i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.26221 | 0.371904 | 0.185952 | − | 0.982559i | \(-0.440463\pi\) | ||||
0.185952 | + | 0.982559i | \(0.440463\pi\) | |||||||
\(38\) | −1.96372 | + | 3.40126i | −0.318557 | + | 0.551758i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.10337 | − | 1.91109i | −0.174458 | − | 0.302170i | ||||
\(41\) | 1.63110 | − | 2.82515i | 0.254735 | − | 0.441215i | −0.710088 | − | 0.704113i | \(-0.751345\pi\) |
0.964824 | + | 0.262898i | \(0.0846783\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.537418 | + | 0.930835i | 0.0819554 | + | 0.141951i | 0.904090 | − | 0.427343i | \(-0.140550\pi\) |
−0.822134 | + | 0.569293i | \(0.807217\pi\) | |||||||
\(44\) | −0.527733 | − | 0.914061i | −0.0795588 | − | 0.137800i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.22771 | 0.918226 | ||||||||
\(47\) | −2.42678 | − | 4.20330i | −0.353982 | − | 0.613114i | 0.632961 | − | 0.774183i | \(-0.281839\pi\) |
−0.986943 | + | 0.161069i | \(0.948506\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.15682 | + | 5.63212i | −0.593832 | + | 0.804589i | ||||
\(50\) | 0.0651512 | − | 0.112845i | 0.00921377 | − | 0.0159587i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.18376 | − | 1.69224i | 0.441508 | − | 0.234672i | ||||
\(53\) | 4.94074 | − | 8.55761i | 0.678663 | − | 1.17548i | −0.296721 | − | 0.954964i | \(-0.595893\pi\) |
0.975384 | − | 0.220514i | \(-0.0707734\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.16457 | + | 2.01709i | −0.157031 | + | 0.271985i | ||||
\(56\) | 1.19230 | + | 2.36187i | 0.159328 | + | 0.315618i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.888084 | + | 1.53821i | −0.116611 | + | 0.201976i | ||||
\(59\) | 1.01937 | 0.132710 | 0.0663552 | − | 0.997796i | \(-0.478863\pi\) | ||||
0.0663552 | + | 0.997796i | \(0.478863\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0382184 | + | 0.0661962i | −0.00489336 | + | 0.00847555i | −0.868462 | − | 0.495756i | \(-0.834891\pi\) |
0.863568 | + | 0.504232i | \(0.168224\pi\) | |||||||
\(62\) | 3.63304 | − | 6.29261i | 0.461397 | − | 0.799163i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.74690 | − | 4.21728i | −0.836849 | − | 0.523089i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.85308 | + | 10.1378i | 0.715067 | + | 1.23853i | 0.962934 | + | 0.269739i | \(0.0869373\pi\) |
−0.247866 | + | 0.968794i | \(0.579729\pi\) | |||||||
\(68\) | 0.944533 | 0.114541 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.19819 | − | 4.88461i | 0.382257 | − | 0.583823i | ||||
\(71\) | 4.20868 | + | 7.28964i | 0.499478 | + | 0.865121i | 1.00000 | 0.000602515i | \(-0.000191787\pi\) | |
−0.500522 | + | 0.865724i | \(0.666858\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.57264 | − | 11.3841i | 0.769269 | − | 1.33241i | −0.168690 | − | 0.985669i | \(-0.553954\pi\) |
0.937960 | − | 0.346745i | \(-0.112713\pi\) | |||||||
\(74\) | 2.26221 | 0.262976 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.96372 | + | 3.40126i | −0.225254 | + | 0.390152i | ||||
\(77\) | 1.52967 | − | 2.33627i | 0.174322 | − | 0.266243i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.00194 | + | 5.19951i | 0.337744 | + | 0.584991i | 0.984008 | − | 0.178124i | \(-0.0570027\pi\) |
−0.646264 | + | 0.763114i | \(0.723669\pi\) | |||||||
\(80\) | −1.10337 | − | 1.91109i | −0.123360 | − | 0.213667i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.63110 | − | 2.82515i | 0.180125 | − | 0.311986i | ||||
\(83\) | 1.77617 | 0.194960 | 0.0974799 | − | 0.995237i | \(-0.468922\pi\) | ||||
0.0974799 | + | 0.995237i | \(0.468922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.04217 | − | 1.80509i | −0.113039 | − | 0.195789i | ||||
\(86\) | 0.537418 | + | 0.930835i | 0.0579512 | + | 0.100374i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.527733 | − | 0.914061i | −0.0562566 | − | 0.0974393i | ||||
\(89\) | −13.3353 | −1.41354 | −0.706769 | − | 0.707444i | \(-0.749848\pi\) | ||||
−0.706769 | + | 0.707444i | \(0.749848\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.79286 | + | 5.50194i | 0.816914 | + | 0.576760i | ||||
\(92\) | 6.22771 | 0.649284 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.42678 | − | 4.20330i | −0.250303 | − | 0.433537i | ||||
\(95\) | 8.66684 | 0.889199 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.99467 | − | 15.5792i | −0.913270 | − | 1.58183i | −0.809415 | − | 0.587238i | \(-0.800215\pi\) |
−0.103855 | − | 0.994592i | \(-0.533118\pi\) | |||||||
\(98\) | −4.15682 | + | 5.63212i | −0.419903 | + | 0.568930i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0651512 | − | 0.112845i | 0.00651512 | − | 0.0112845i | ||||
\(101\) | 6.75018 | + | 11.6917i | 0.671668 | + | 1.16336i | 0.977431 | + | 0.211256i | \(0.0677553\pi\) |
−0.305763 | + | 0.952108i | \(0.598911\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.46258 | + | 2.53327i | 0.144113 | + | 0.249610i | 0.929041 | − | 0.369976i | \(-0.120634\pi\) |
−0.784929 | + | 0.619586i | \(0.787301\pi\) | |||||||
\(104\) | 3.18376 | − | 1.69224i | 0.312193 | − | 0.165938i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.94074 | − | 8.55761i | 0.479887 | − | 0.831188i | ||||
\(107\) | −14.1092 | −1.36399 | −0.681993 | − | 0.731359i | \(-0.738887\pi\) | ||||
−0.681993 | + | 0.731359i | \(0.738887\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.723832 | − | 1.25371i | 0.0693306 | − | 0.120084i | −0.829276 | − | 0.558839i | \(-0.811247\pi\) |
0.898607 | + | 0.438755i | \(0.144580\pi\) | |||||||
\(110\) | −1.16457 | + | 2.01709i | −0.111037 | + | 0.192322i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.19230 | + | 2.36187i | 0.112662 | + | 0.223175i | ||||
\(113\) | 1.67707 | + | 2.90477i | 0.157765 | + | 0.273257i | 0.934062 | − | 0.357110i | \(-0.116238\pi\) |
−0.776297 | + | 0.630367i | \(0.782904\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.87146 | − | 11.9017i | −0.640767 | − | 1.10984i | ||||
\(116\) | −0.888084 | + | 1.53821i | −0.0824565 | + | 0.142819i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.01937 | 0.0938405 | ||||||||
\(119\) | 1.12617 | + | 2.23086i | 0.103236 | + | 0.204503i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.94299 | − | 8.56152i | 0.449363 | − | 0.778320i | ||||
\(122\) | −0.0382184 | + | 0.0661962i | −0.00346013 | + | 0.00599312i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.63304 | − | 6.29261i | 0.326257 | − | 0.565093i | ||||
\(125\) | −11.3212 | −1.01260 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.80963 | + | 8.33053i | −0.426786 | + | 0.739215i | −0.996585 | − | 0.0825687i | \(-0.973688\pi\) |
0.569799 | + | 0.821784i | \(0.307021\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.74690 | − | 4.21728i | −0.591742 | − | 0.369880i | ||||
\(131\) | 3.27649 | + | 5.67504i | 0.286268 | + | 0.495831i | 0.972916 | − | 0.231159i | \(-0.0742519\pi\) |
−0.686648 | + | 0.726990i | \(0.740919\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.3747 | − | 0.582706i | −0.899599 | − | 0.0505270i | ||||
\(134\) | 5.85308 | + | 10.1378i | 0.505629 | + | 0.875775i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.944533 | 0.0809930 | ||||||||
\(137\) | −7.12468 | −0.608702 | −0.304351 | − | 0.952560i | \(-0.598440\pi\) | ||||
−0.304351 | + | 0.952560i | \(0.598440\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.09957 | − | 5.36862i | −0.262902 | − | 0.455360i | 0.704109 | − | 0.710091i | \(-0.251346\pi\) |
−0.967012 | + | 0.254731i | \(0.918013\pi\) | |||||||
\(140\) | 3.19819 | − | 4.88461i | 0.270297 | − | 0.412825i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.20868 | + | 7.28964i | 0.353184 | + | 0.611733i | ||||
\(143\) | −3.22699 | − | 2.01709i | −0.269854 | − | 0.168678i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.91954 | 0.325500 | ||||||||
\(146\) | 6.57264 | − | 11.3841i | 0.543956 | − | 0.942159i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.26221 | 0.185952 | ||||||||
\(149\) | −10.9374 | + | 18.9442i | −0.896028 | + | 1.55197i | −0.0635010 | + | 0.997982i | \(0.520227\pi\) |
−0.832527 | + | 0.553984i | \(0.813107\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.25658 | − | 12.5688i | 0.590532 | − | 1.02283i | −0.403629 | − | 0.914923i | \(-0.632251\pi\) |
0.994161 | − | 0.107909i | \(-0.0344154\pi\) | |||||||
\(152\) | −1.96372 | + | 3.40126i | −0.159279 | + | 0.275879i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.52967 | − | 2.33627i | 0.123264 | − | 0.188262i | ||||
\(155\) | −16.0343 | −1.28791 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.13538 | − | 3.69859i | 0.170422 | − | 0.295179i | −0.768146 | − | 0.640275i | \(-0.778820\pi\) |
0.938567 | + | 0.345096i | \(0.112154\pi\) | |||||||
\(158\) | 3.00194 | + | 5.19951i | 0.238821 | + | 0.413651i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.10337 | − | 1.91109i | −0.0872290 | − | 0.151085i | ||||
\(161\) | 7.42532 | + | 14.7090i | 0.585197 | + | 1.15923i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.03208 | + | 5.25172i | −0.237491 | + | 0.411347i | −0.959994 | − | 0.280021i | \(-0.909658\pi\) |
0.722503 | + | 0.691368i | \(0.242992\pi\) | |||||||
\(164\) | 1.63110 | − | 2.82515i | 0.127368 | − | 0.220607i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.77617 | 0.137857 | ||||||||
\(167\) | 7.86930 | − | 13.6300i | 0.608944 | − | 1.05472i | −0.382470 | − | 0.923968i | \(-0.624927\pi\) |
0.991415 | − | 0.130755i | \(-0.0417401\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.27262 | − | 10.7754i | 0.559432 | − | 0.828876i | ||||
\(170\) | −1.04217 | − | 1.80509i | −0.0799307 | − | 0.138444i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.537418 | + | 0.930835i | 0.0409777 | + | 0.0709755i | ||||
\(173\) | −5.29220 | + | 9.16635i | −0.402358 | + | 0.696905i | −0.994010 | − | 0.109289i | \(-0.965143\pi\) |
0.591652 | + | 0.806194i | \(0.298476\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.344205 | + | 0.0193327i | 0.0260195 | + | 0.00146141i | ||||
\(176\) | −0.527733 | − | 0.914061i | −0.0397794 | − | 0.0689000i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.3353 | −0.999522 | ||||||||
\(179\) | 7.11908 | + | 12.3306i | 0.532105 | + | 0.921633i | 0.999297 | + | 0.0374773i | \(0.0119322\pi\) |
−0.467192 | + | 0.884156i | \(0.654734\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.7312 | −1.02063 | −0.510314 | − | 0.859988i | \(-0.670471\pi\) | ||||
−0.510314 | + | 0.859988i | \(0.670471\pi\) | |||||||
\(182\) | 7.79286 | + | 5.50194i | 0.577645 | + | 0.407831i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.22771 | 0.459113 | ||||||||
\(185\) | −2.49605 | − | 4.32328i | −0.183513 | − | 0.317854i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.498462 | − | 0.863361i | −0.0364511 | − | 0.0631352i | ||||
\(188\) | −2.42678 | − | 4.20330i | −0.176991 | − | 0.306557i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.66684 | 0.628758 | ||||||||
\(191\) | 0.437999 | − | 0.758636i | 0.0316925 | − | 0.0548930i | −0.849744 | − | 0.527195i | \(-0.823244\pi\) |
0.881437 | + | 0.472302i | \(0.156577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.3312 | + | 19.6263i | 0.815640 | + | 1.41273i | 0.908867 | + | 0.417085i | \(0.136948\pi\) |
−0.0932273 | + | 0.995645i | \(0.529718\pi\) | |||||||
\(194\) | −8.99467 | − | 15.5792i | −0.645779 | − | 1.11852i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.15682 | + | 5.63212i | −0.296916 | + | 0.402295i | ||||
\(197\) | −8.44249 | + | 14.6228i | −0.601502 | + | 1.04183i | 0.391092 | + | 0.920352i | \(0.372098\pi\) |
−0.992594 | + | 0.121481i | \(0.961236\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.90084 | −0.418300 | −0.209150 | − | 0.977884i | \(-0.567070\pi\) | ||||
−0.209150 | + | 0.977884i | \(0.567070\pi\) | |||||||
\(200\) | 0.0651512 | − | 0.112845i | 0.00460688 | − | 0.00797936i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.75018 | + | 11.6917i | 0.474941 | + | 0.822622i | ||||
\(203\) | −4.69190 | − | 0.263526i | −0.329307 | − | 0.0184959i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.19884 | −0.502789 | ||||||||
\(206\) | 1.46258 | + | 2.53327i | 0.101903 | + | 0.176501i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.18376 | − | 1.69224i | 0.220754 | − | 0.117336i | ||||
\(209\) | 4.14528 | 0.286735 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.7856 | + | 20.4132i | −0.811353 | + | 1.40531i | 0.100564 | + | 0.994931i | \(0.467935\pi\) |
−0.911917 | + | 0.410375i | \(0.865398\pi\) | |||||||
\(212\) | 4.94074 | − | 8.55761i | 0.339331 | − | 0.587739i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.1092 | −0.964484 | ||||||||
\(215\) | 1.18594 | − | 2.05411i | 0.0808805 | − | 0.140089i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.1940 | + | 1.07805i | 1.30297 | + | 0.0731830i | ||||
\(218\) | 0.723832 | − | 1.25371i | 0.0490241 | − | 0.0849123i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.16457 | + | 2.01709i | −0.0785153 | + | 0.135992i | ||||
\(221\) | 3.00716 | − | 1.59838i | 0.202284 | − | 0.107519i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.87906 | + | 4.98667i | −0.192796 | + | 0.333932i | −0.946176 | − | 0.323653i | \(-0.895089\pi\) |
0.753380 | + | 0.657586i | \(0.228422\pi\) | |||||||
\(224\) | 1.19230 | + | 2.36187i | 0.0796641 | + | 0.157809i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.67707 | + | 2.90477i | 0.111557 | + | 0.193222i | ||||
\(227\) | −19.6805 | −1.30624 | −0.653121 | − | 0.757254i | \(-0.726541\pi\) | ||||
−0.653121 | + | 0.757254i | \(0.726541\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0430 | + | 17.3951i | 0.663663 | + | 1.14950i | 0.979646 | + | 0.200733i | \(0.0643324\pi\) |
−0.315983 | + | 0.948765i | \(0.602334\pi\) | |||||||
\(230\) | −6.87146 | − | 11.9017i | −0.453091 | − | 0.784777i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.888084 | + | 1.53821i | −0.0583056 | + | 0.100988i | ||||
\(233\) | 2.82261 | + | 4.88890i | 0.184915 | + | 0.320282i | 0.943548 | − | 0.331236i | \(-0.107466\pi\) |
−0.758633 | + | 0.651518i | \(0.774132\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.35526 | + | 9.27559i | −0.349339 | + | 0.605073i | ||||
\(236\) | 1.01937 | 0.0663552 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.12617 | + | 2.23086i | 0.0729988 | + | 0.144605i | ||||
\(239\) | −8.20960 | −0.531035 | −0.265517 | − | 0.964106i | \(-0.585543\pi\) | ||||
−0.265517 | + | 0.964106i | \(0.585543\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.0169 | −1.35382 | −0.676908 | − | 0.736068i | \(-0.736681\pi\) | ||||
−0.676908 | + | 0.736068i | \(0.736681\pi\) | |||||||
\(242\) | 4.94299 | − | 8.56152i | 0.317748 | − | 0.550355i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.0382184 | + | 0.0661962i | −0.00244668 | + | 0.00423778i | ||||
\(245\) | 15.3500 | + | 1.72976i | 0.980677 | + | 0.110510i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.496239 | + | 14.1519i | −0.0315749 | + | 0.900463i | ||||
\(248\) | 3.63304 | − | 6.29261i | 0.230698 | − | 0.399581i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.3212 | −0.716018 | ||||||||
\(251\) | 12.0281 | + | 20.8333i | 0.759209 | + | 1.31499i | 0.943254 | + | 0.332071i | \(0.107747\pi\) |
−0.184045 | + | 0.982918i | \(0.558919\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.28657 | − | 5.69251i | −0.206625 | − | 0.357885i | ||||
\(254\) | −4.80963 | + | 8.33053i | −0.301783 | + | 0.522704i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.59910 | 0.224506 | 0.112253 | − | 0.993680i | \(-0.464193\pi\) | ||||
0.112253 | + | 0.993680i | \(0.464193\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.69724 | + | 5.34303i | 0.167598 | + | 0.332000i | ||||
\(260\) | −6.74690 | − | 4.21728i | −0.418425 | − | 0.261545i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.27649 | + | 5.67504i | 0.202422 | + | 0.350605i | ||||
\(263\) | −15.1196 | − | 26.1880i | −0.932317 | − | 1.61482i | −0.779350 | − | 0.626588i | \(-0.784451\pi\) |
−0.152966 | − | 0.988231i | \(-0.548883\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.8058 | −1.33952 | ||||||||
\(266\) | −10.3747 | − | 0.582706i | −0.636112 | − | 0.0357280i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.85308 | + | 10.1378i | 0.357534 | + | 0.619266i | ||||
\(269\) | −10.4393 | −0.636494 | −0.318247 | − | 0.948008i | \(-0.603094\pi\) | ||||
−0.318247 | + | 0.948008i | \(0.603094\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.6691 | −0.648102 | −0.324051 | − | 0.946040i | \(-0.605045\pi\) | ||||
−0.324051 | + | 0.946040i | \(0.605045\pi\) | |||||||
\(272\) | 0.944533 | 0.0572707 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.12468 | −0.430417 | ||||||||
\(275\) | −0.137530 | −0.00829336 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.0706 | 1.14584 | 0.572920 | − | 0.819611i | \(-0.305810\pi\) | ||||
0.572920 | + | 0.819611i | \(0.305810\pi\) | |||||||
\(278\) | −3.09957 | − | 5.36862i | −0.185900 | − | 0.321988i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.19819 | − | 4.88461i | 0.191129 | − | 0.291911i | ||||
\(281\) | −23.3309 | −1.39181 | −0.695903 | − | 0.718136i | \(-0.744995\pi\) | ||||
−0.695903 | + | 0.718136i | \(0.744995\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.11466 | − | 7.12679i | −0.244591 | − | 0.423644i | 0.717426 | − | 0.696635i | \(-0.245320\pi\) |
−0.962017 | + | 0.272991i | \(0.911987\pi\) | |||||||
\(284\) | 4.20868 | + | 7.28964i | 0.249739 | + | 0.432561i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.22699 | − | 2.01709i | −0.190816 | − | 0.119273i | ||||
\(287\) | 8.61740 | + | 0.484007i | 0.508669 | + | 0.0285700i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1079 | −0.947521 | ||||||||
\(290\) | 3.91954 | 0.230163 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.57264 | − | 11.3841i | 0.384635 | − | 0.666207i | ||||
\(293\) | −9.34471 | − | 16.1855i | −0.545924 | − | 0.945568i | −0.998548 | − | 0.0538667i | \(-0.982845\pi\) |
0.452624 | − | 0.891701i | \(-0.350488\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.12474 | − | 1.94811i | −0.0654849 | − | 0.113423i | ||||
\(296\) | 2.26221 | 0.131488 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.9374 | + | 18.9442i | −0.633588 | + | 1.09741i | ||||
\(299\) | 19.8275 | − | 10.5388i | 1.14665 | − | 0.609475i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.55774 | + | 2.37915i | −0.0897868 | + | 0.137132i | ||||
\(302\) | 7.25658 | − | 12.5688i | 0.417569 | − | 0.723251i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.96372 | + | 3.40126i | −0.112627 | + | 0.195076i | ||||
\(305\) | 0.168676 | 0.00965836 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0495 | 1.03014 | 0.515069 | − | 0.857149i | \(-0.327766\pi\) | ||||
0.515069 | + | 0.857149i | \(0.327766\pi\) | |||||||
\(308\) | 1.52967 | − | 2.33627i | 0.0871611 | − | 0.133122i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.0343 | −0.910690 | ||||||||
\(311\) | 8.46321 | − | 14.6587i | 0.479905 | − | 0.831219i | −0.519830 | − | 0.854270i | \(-0.674005\pi\) |
0.999734 | + | 0.0230506i | \(0.00733790\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0035 | − | 19.0587i | −0.621957 | − | 1.07726i | −0.989121 | − | 0.147105i | \(-0.953004\pi\) |
0.367163 | − | 0.930156i | \(-0.380329\pi\) | |||||||
\(314\) | 2.13538 | − | 3.69859i | 0.120506 | − | 0.208723i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.00194 | + | 5.19951i | 0.168872 | + | 0.292495i | ||||
\(317\) | −4.46606 | − | 7.73544i | −0.250839 | − | 0.434466i | 0.712918 | − | 0.701247i | \(-0.247373\pi\) |
−0.963757 | + | 0.266782i | \(0.914040\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.87469 | 0.104962 | ||||||||
\(320\) | −1.10337 | − | 1.91109i | −0.0616802 | − | 0.106833i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.42532 | + | 14.7090i | 0.413797 | + | 0.819701i | ||||
\(323\) | −1.85480 | + | 3.21260i | −0.103204 | + | 0.178754i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0164639 | − | 0.469523i | 0.000913254 | − | 0.0260445i | ||||
\(326\) | −3.03208 | + | 5.25172i | −0.167932 | + | 0.290866i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.63110 | − | 2.82515i | 0.0900626 | − | 0.155993i | ||||
\(329\) | 7.03418 | − | 10.7433i | 0.387807 | − | 0.592299i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.16425 | + | 3.74859i | −0.118958 | + | 0.206041i | −0.919355 | − | 0.393429i | \(-0.871289\pi\) |
0.800397 | + | 0.599470i | \(0.204622\pi\) | |||||||
\(332\) | 1.77617 | 0.0974799 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.86930 | − | 13.6300i | 0.430589 | − | 0.745802i | ||||
\(335\) | 12.9162 | − | 22.3715i | 0.705688 | − | 1.22229i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.416096 | −0.0226662 | −0.0113331 | − | 0.999936i | \(-0.503608\pi\) | ||||
−0.0113331 | + | 0.999936i | \(0.503608\pi\) | |||||||
\(338\) | 7.27262 | − | 10.7754i | 0.395578 | − | 0.586104i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.04217 | − | 1.80509i | −0.0565196 | − | 0.0978947i | ||||
\(341\) | −7.66911 | −0.415306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.2585 | − | 3.10266i | −0.985867 | − | 0.167528i | ||||
\(344\) | 0.537418 | + | 0.930835i | 0.0289756 | + | 0.0501872i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.29220 | + | 9.16635i | −0.284510 | + | 0.492786i | ||||
\(347\) | −21.7452 | −1.16734 | −0.583671 | − | 0.811990i | \(-0.698384\pi\) | ||||
−0.583671 | + | 0.811990i | \(0.698384\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.8128 | − | 27.3885i | 0.846438 | − | 1.46607i | −0.0379278 | − | 0.999280i | \(-0.512076\pi\) |
0.884366 | − | 0.466794i | \(-0.154591\pi\) | |||||||
\(350\) | 0.344205 | + | 0.0193327i | 0.0183985 | + | 0.00103338i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.527733 | − | 0.914061i | −0.0281283 | − | 0.0487196i | ||||
\(353\) | 13.8944 | + | 24.0658i | 0.739523 | + | 1.28089i | 0.952710 | + | 0.303880i | \(0.0982821\pi\) |
−0.213188 | + | 0.977011i | \(0.568385\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.28745 | − | 16.0863i | 0.492927 | − | 0.853774i | ||||
\(356\) | −13.3353 | −0.706769 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.11908 | + | 12.3306i | 0.376255 | + | 0.651693i | ||||
\(359\) | −4.17747 | − | 7.23559i | −0.220478 | − | 0.381880i | 0.734475 | − | 0.678636i | \(-0.237428\pi\) |
−0.954953 | + | 0.296756i | \(0.904095\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.78761 | + | 3.09623i | 0.0940847 | + | 0.162959i | ||||
\(362\) | −13.7312 | −0.721693 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.79286 | + | 5.50194i | 0.408457 | + | 0.288380i | ||||
\(365\) | −29.0082 | −1.51836 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.3905 | + | 17.9969i | 0.542379 | + | 0.939429i | 0.998767 | + | 0.0496476i | \(0.0158098\pi\) |
−0.456387 | + | 0.889781i | \(0.650857\pi\) | |||||||
\(368\) | 6.22771 | 0.324642 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.49605 | − | 4.32328i | −0.129763 | − | 0.224757i | ||||
\(371\) | 26.1028 | + | 1.46609i | 1.35519 | + | 0.0761158i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.72840 | + | 13.3860i | −0.400161 | + | 0.693100i | −0.993745 | − | 0.111672i | \(-0.964379\pi\) |
0.593584 | + | 0.804772i | \(0.297713\pi\) | |||||||
\(374\) | −0.498462 | − | 0.863361i | −0.0257748 | − | 0.0446433i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.42678 | − | 4.20330i | −0.125151 | − | 0.216769i | ||||
\(377\) | −0.224422 | + | 6.40013i | −0.0115583 | + | 0.329623i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.1123 | − | 20.9792i | 0.622169 | − | 1.07763i | −0.366912 | − | 0.930256i | \(-0.619585\pi\) |
0.989081 | − | 0.147372i | \(-0.0470816\pi\) | |||||||
\(380\) | 8.66684 | 0.444599 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.437999 | − | 0.758636i | 0.0224100 | − | 0.0388152i | ||||
\(383\) | 7.49967 | − | 12.9898i | 0.383215 | − | 0.663749i | −0.608304 | − | 0.793704i | \(-0.708150\pi\) |
0.991520 | + | 0.129955i | \(0.0414834\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.15263 | − | 0.345570i | −0.313567 | − | 0.0176119i | ||||
\(386\) | 11.3312 | + | 19.6263i | 0.576745 | + | 0.998951i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.99467 | − | 15.5792i | −0.456635 | − | 0.790915i | ||||
\(389\) | −4.37986 | + | 7.58613i | −0.222068 | + | 0.384632i | −0.955436 | − | 0.295200i | \(-0.904614\pi\) |
0.733368 | + | 0.679832i | \(0.237947\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.88228 | 0.297480 | ||||||||
\(392\) | −4.15682 | + | 5.63212i | −0.209951 | + | 0.284465i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.44249 | + | 14.6228i | −0.425326 | + | 0.736687i | ||||
\(395\) | 6.62449 | − | 11.4740i | 0.333315 | − | 0.577318i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.4400 | + | 30.2070i | −0.875289 | + | 1.51604i | −0.0188334 | + | 0.999823i | \(0.505995\pi\) |
−0.856455 | + | 0.516222i | \(0.827338\pi\) | |||||||
\(398\) | −5.90084 | −0.295783 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.0651512 | − | 0.112845i | 0.00325756 | − | 0.00564226i | ||||
\(401\) | 12.9474 | 0.646565 | 0.323282 | − | 0.946303i | \(-0.395214\pi\) | ||||
0.323282 | + | 0.946303i | \(0.395214\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.918082 | − | 26.1821i | 0.0457329 | − | 1.30423i | ||||
\(404\) | 6.75018 | + | 11.6917i | 0.335834 | + | 0.581682i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.69190 | − | 0.263526i | −0.232855 | − | 0.0130786i | ||||
\(407\) | −1.19384 | − | 2.06779i | −0.0591765 | − | 0.102497i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.1242 | −1.68733 | −0.843666 | − | 0.536869i | \(-0.819607\pi\) | ||||
−0.843666 | + | 0.536869i | \(0.819607\pi\) | |||||||
\(410\) | −7.19884 | −0.355525 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.46258 | + | 2.53327i | 0.0720563 | + | 0.124805i | ||||
\(413\) | 1.21540 | + | 2.40761i | 0.0598058 | + | 0.118471i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.95977 | − | 3.39442i | −0.0962013 | − | 0.166626i | ||||
\(416\) | 3.18376 | − | 1.69224i | 0.156097 | − | 0.0829691i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.14528 | 0.202752 | ||||||||
\(419\) | −11.0690 | + | 19.1720i | −0.540754 | + | 0.936613i | 0.458107 | + | 0.888897i | \(0.348528\pi\) |
−0.998861 | + | 0.0477160i | \(0.984806\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.1012 | −1.51578 | −0.757890 | − | 0.652382i | \(-0.773770\pi\) | ||||
−0.757890 | + | 0.652382i | \(0.773770\pi\) | |||||||
\(422\) | −11.7856 | + | 20.4132i | −0.573713 | + | 0.993701i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.94074 | − | 8.55761i | 0.239943 | − | 0.415594i | ||||
\(425\) | 0.0615374 | − | 0.106586i | 0.00298500 | − | 0.00517018i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.201914 | − | 0.0113408i | −0.00977133 | − | 0.000548818i | ||||
\(428\) | −14.1092 | −0.681993 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.18594 | − | 2.05411i | 0.0571911 | − | 0.0990580i | ||||
\(431\) | 5.65730 | + | 9.79873i | 0.272502 | + | 0.471988i | 0.969502 | − | 0.245083i | \(-0.0788154\pi\) |
−0.697000 | + | 0.717072i | \(0.745482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.0285 | − | 32.9583i | −0.914450 | − | 1.58387i | −0.807704 | − | 0.589588i | \(-0.799290\pi\) |
−0.106746 | − | 0.994286i | \(-0.534043\pi\) | |||||||
\(434\) | 19.1940 | + | 1.07805i | 0.921341 | + | 0.0517482i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.723832 | − | 1.25371i | 0.0346653 | − | 0.0600420i | ||||
\(437\) | −12.2295 | + | 21.1821i | −0.585015 | + | 1.01328i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.96609 | −0.141564 | −0.0707818 | − | 0.997492i | \(-0.522549\pi\) | ||||
−0.0707818 | + | 0.997492i | \(0.522549\pi\) | |||||||
\(440\) | −1.16457 | + | 2.01709i | −0.0555187 | + | 0.0961612i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.00716 | − | 1.59838i | 0.143036 | − | 0.0760272i | ||||
\(443\) | 10.1253 | + | 17.5375i | 0.481067 | + | 0.833233i | 0.999764 | − | 0.0217253i | \(-0.00691593\pi\) |
−0.518697 | + | 0.854958i | \(0.673583\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.7138 | + | 25.4850i | 0.697499 | + | 1.20810i | ||||
\(446\) | −2.87906 | + | 4.98667i | −0.136327 | + | 0.236126i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.19230 | + | 2.36187i | 0.0563311 | + | 0.111588i | ||||
\(449\) | −5.97830 | − | 10.3547i | −0.282133 | − | 0.488669i | 0.689777 | − | 0.724022i | \(-0.257709\pi\) |
−0.971910 | + | 0.235353i | \(0.924375\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.44315 | −0.162132 | ||||||||
\(452\) | 1.67707 | + | 2.90477i | 0.0788826 | + | 0.136629i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.6805 | −0.923652 | ||||||||
\(455\) | 1.91631 | − | 20.9635i | 0.0898379 | − | 0.982786i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.0842 | 1.07983 | 0.539916 | − | 0.841719i | \(-0.318456\pi\) | ||||
0.539916 | + | 0.841719i | \(0.318456\pi\) | |||||||
\(458\) | 10.0430 | + | 17.3951i | 0.469281 | + | 0.812818i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.87146 | − | 11.9017i | −0.320384 | − | 0.554921i | ||||
\(461\) | 9.46131 | + | 16.3875i | 0.440657 | + | 0.763240i | 0.997738 | − | 0.0672176i | \(-0.0214122\pi\) |
−0.557081 | + | 0.830458i | \(0.688079\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.7770 | −1.52328 | −0.761638 | − | 0.648002i | \(-0.775605\pi\) | ||||
−0.761638 | + | 0.648002i | \(0.775605\pi\) | |||||||
\(464\) | −0.888084 | + | 1.53821i | −0.0412283 | + | 0.0714094i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.82261 | + | 4.88890i | 0.130755 | + | 0.226474i | ||||
\(467\) | 10.7307 | + | 18.5861i | 0.496557 | + | 0.860061i | 0.999992 | − | 0.00397163i | \(-0.00126421\pi\) |
−0.503436 | + | 0.864033i | \(0.667931\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.9655 | + | 25.9116i | −0.783396 | + | 1.19648i | ||||
\(470\) | −5.35526 | + | 9.27559i | −0.247020 | + | 0.427851i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.01937 | 0.0469202 | ||||||||
\(473\) | 0.567227 | − | 0.982465i | 0.0260811 | − | 0.0451738i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.255877 | + | 0.443193i | 0.0117405 | + | 0.0203351i | ||||
\(476\) | 1.12617 | + | 2.23086i | 0.0516179 | + | 0.102251i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.20960 | −0.375498 | ||||||||
\(479\) | −15.9460 | − | 27.6194i | −0.728593 | − | 1.26196i | −0.957478 | − | 0.288507i | \(-0.906841\pi\) |
0.228884 | − | 0.973454i | \(-0.426492\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.20231 | − | 3.82821i | 0.328397 | − | 0.174551i | ||||
\(482\) | −21.0169 | −0.957293 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.94299 | − | 8.56152i | 0.224682 | − | 0.389160i | ||||
\(485\) | −19.8489 | + | 34.3793i | −0.901291 | + | 1.56108i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.744679 | 0.0337446 | 0.0168723 | − | 0.999858i | \(-0.494629\pi\) | ||||
0.0168723 | + | 0.999858i | \(0.494629\pi\) | |||||||
\(488\) | −0.0382184 | + | 0.0661962i | −0.00173007 | + | 0.00299656i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15.3500 | + | 1.72976i | 0.693443 | + | 0.0781426i | ||||
\(491\) | 20.5033 | − | 35.5127i | 0.925301 | − | 1.60267i | 0.134224 | − | 0.990951i | \(-0.457146\pi\) |
0.791077 | − | 0.611717i | \(-0.209521\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.838824 | + | 1.45289i | −0.0377788 | + | 0.0654347i | ||||
\(494\) | −0.496239 | + | 14.1519i | −0.0223268 | + | 0.636724i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.63304 | − | 6.29261i | 0.163128 | − | 0.282547i | ||||
\(497\) | −12.1991 | + | 18.6318i | −0.547206 | + | 0.835750i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.61372 | + | 9.72324i | 0.251305 | + | 0.435272i | 0.963885 | − | 0.266318i | \(-0.0858071\pi\) |
−0.712581 | + | 0.701590i | \(0.752474\pi\) | |||||||
\(500\) | −11.3212 | −0.506301 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0281 | + | 20.8333i | 0.536842 | + | 0.929837i | ||||
\(503\) | 19.4719 | + | 33.7264i | 0.868211 | + | 1.50379i | 0.863823 | + | 0.503796i | \(0.168064\pi\) |
0.00438828 | + | 0.999990i | \(0.498603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.8959 | − | 25.8004i | 0.662859 | − | 1.14810i | ||||
\(506\) | −3.28657 | − | 5.69251i | −0.146106 | − | 0.253063i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.80963 | + | 8.33053i | −0.213393 | + | 0.369608i | ||||
\(509\) | 21.6152 | 0.958079 | 0.479039 | − | 0.877793i | \(-0.340985\pi\) | ||||
0.479039 | + | 0.877793i | \(0.340985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.7244 | + | 1.95034i | 1.53612 | + | 0.0862779i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.59910 | 0.158749 | ||||||||
\(515\) | 3.22754 | − | 5.59026i | 0.142222 | − | 0.246336i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.56138 | + | 4.43644i | −0.112649 | + | 0.195115i | ||||
\(518\) | 2.69724 | + | 5.34303i | 0.118510 | + | 0.234759i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.74690 | − | 4.21728i | −0.295871 | − | 0.184940i | ||||
\(521\) | −3.75964 | + | 6.51188i | −0.164713 | + | 0.285291i | −0.936553 | − | 0.350525i | \(-0.886003\pi\) |
0.771840 | + | 0.635816i | \(0.219336\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.6196 | 1.47008 | 0.735041 | − | 0.678023i | \(-0.237163\pi\) | ||||
0.735041 | + | 0.678023i | \(0.237163\pi\) | |||||||
\(524\) | 3.27649 | + | 5.67504i | 0.143134 | + | 0.247915i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.1196 | − | 26.1880i | −0.659247 | − | 1.14185i | ||||
\(527\) | 3.43153 | − | 5.94358i | 0.149480 | − | 0.258906i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.7844 | 0.686276 | ||||||||
\(530\) | −21.8058 | −0.947185 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.3747 | − | 0.582706i | −0.449799 | − | 0.0252635i | ||||
\(533\) | 0.412185 | − | 11.7548i | 0.0178537 | − | 0.509158i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.5676 | + | 26.9640i | 0.673048 | + | 1.16575i | ||||
\(536\) | 5.85308 | + | 10.1378i | 0.252814 | + | 0.437888i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.4393 | −0.450069 | ||||||||
\(539\) | 7.34180 | + | 0.827332i | 0.316234 | + | 0.0356357i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.62006 | + | 6.27013i | 0.155639 | + | 0.269574i | 0.933291 | − | 0.359120i | \(-0.116923\pi\) |
−0.777653 | + | 0.628694i | \(0.783590\pi\) | |||||||
\(542\) | −10.6691 | −0.458278 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.944533 | 0.0404965 | ||||||||
\(545\) | −3.19462 | −0.136842 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.7236 | 0.586779 | 0.293390 | − | 0.955993i | \(-0.405217\pi\) | ||||
0.293390 | + | 0.955993i | \(0.405217\pi\) | |||||||
\(548\) | −7.12468 | −0.304351 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.137530 | −0.00586429 | ||||||||
\(551\) | −3.48790 | − | 6.04121i | −0.148589 | − | 0.257364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.70132 | + | 13.2896i | −0.370018 | + | 0.565130i | ||||
\(554\) | 19.0706 | 0.810232 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.09957 | − | 5.36862i | −0.131451 | − | 0.227680i | ||||
\(557\) | −11.6122 | − | 20.1129i | −0.492024 | − | 0.852210i | 0.507934 | − | 0.861396i | \(-0.330409\pi\) |
−0.999958 | + | 0.00918575i | \(0.997076\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.28621 | + | 2.05411i | 0.138992 | + | 0.0868796i | ||||
\(560\) | 3.19819 | − | 4.88461i | 0.135148 | − | 0.206413i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.3309 | −0.984155 | ||||||||
\(563\) | 15.6123 | 0.657981 | 0.328990 | − | 0.944333i | \(-0.393292\pi\) | ||||
0.328990 | + | 0.944333i | \(0.393292\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.70085 | − | 6.41006i | 0.155696 | − | 0.269673i | ||||
\(566\) | −4.11466 | − | 7.12679i | −0.172952 | − | 0.299561i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.20868 | + | 7.28964i | 0.176592 | + | 0.305867i | ||||
\(569\) | 13.3032 | 0.557698 | 0.278849 | − | 0.960335i | \(-0.410047\pi\) | ||||
0.278849 | + | 0.960335i | \(0.410047\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.4972 | − | 26.8420i | 0.648539 | − | 1.12330i | −0.334933 | − | 0.942242i | \(-0.608714\pi\) |
0.983472 | − | 0.181061i | \(-0.0579530\pi\) | |||||||
\(572\) | −3.22699 | − | 2.01709i | −0.134927 | − | 0.0843390i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.61740 | + | 0.484007i | 0.359684 | + | 0.0202020i | ||||
\(575\) | 0.405743 | − | 0.702767i | 0.0169206 | − | 0.0293074i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.8416 | + | 39.5629i | −0.950910 | + | 1.64702i | −0.207449 | + | 0.978246i | \(0.566516\pi\) |
−0.743462 | + | 0.668779i | \(0.766817\pi\) | |||||||
\(578\) | −16.1079 | −0.669999 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.91954 | 0.162750 | ||||||||
\(581\) | 2.11773 | + | 4.19507i | 0.0878583 | + | 0.174041i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.4296 | −0.431949 | ||||||||
\(584\) | 6.57264 | − | 11.3841i | 0.271978 | − | 0.471079i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.34471 | − | 16.1855i | −0.386027 | − | 0.668618i | ||||
\(587\) | 1.75183 | − | 3.03426i | 0.0723057 | − | 0.125237i | −0.827606 | − | 0.561310i | \(-0.810298\pi\) |
0.899911 | + | 0.436073i | \(0.143631\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.2686 | + | 24.7139i | 0.587925 | + | 1.01832i | ||||
\(590\) | −1.12474 | − | 1.94811i | −0.0463048 | − | 0.0802023i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.26221 | 0.0929761 | ||||||||
\(593\) | 6.29875 | + | 10.9098i | 0.258659 | + | 0.448010i | 0.965883 | − | 0.258979i | \(-0.0833862\pi\) |
−0.707224 | + | 0.706989i | \(0.750053\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.02080 | − | 4.61368i | 0.123841 | − | 0.189142i | ||||
\(596\) | −10.9374 | + | 18.9442i | −0.448014 | + | 0.775983i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 19.8275 | − | 10.5388i | 0.810807 | − | 0.430964i | ||||
\(599\) | 15.2844 | − | 26.4733i | 0.624503 | − | 1.08167i | −0.364134 | − | 0.931347i | \(-0.618635\pi\) |
0.988637 | − | 0.150324i | \(-0.0480318\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.11682 | − | 12.3267i | 0.290301 | − | 0.502817i | −0.683580 | − | 0.729876i | \(-0.739578\pi\) |
0.973881 | + | 0.227059i | \(0.0729112\pi\) | |||||||
\(602\) | −1.55774 | + | 2.37915i | −0.0634888 | + | 0.0969668i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.25658 | − | 12.5688i | 0.295266 | − | 0.511416i | ||||
\(605\) | −21.8158 | −0.886938 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.20981 | + | 2.09546i | −0.0491049 | + | 0.0850521i | −0.889533 | − | 0.456871i | \(-0.848970\pi\) |
0.840428 | + | 0.541923i | \(0.182304\pi\) | |||||||
\(608\) | −1.96372 | + | 3.40126i | −0.0796394 | + | 0.137939i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.168676 | 0.00682949 | ||||||||
\(611\) | −14.8393 | − | 9.27559i | −0.600333 | − | 0.375250i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.269478 | − | 0.466750i | −0.0108841 | − | 0.0188518i | 0.860532 | − | 0.509396i | \(-0.170131\pi\) |
−0.871416 | + | 0.490544i | \(0.836798\pi\) | |||||||
\(614\) | 18.0495 | 0.728418 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.52967 | − | 2.33627i | 0.0616322 | − | 0.0941312i | ||||
\(617\) | −22.1866 | − | 38.4283i | −0.893198 | − | 1.54706i | −0.836020 | − | 0.548700i | \(-0.815123\pi\) |
−0.0571781 | − | 0.998364i | \(-0.518210\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.10976 | − | 15.7786i | 0.366152 | − | 0.634194i | −0.622808 | − | 0.782375i | \(-0.714008\pi\) |
0.988960 | + | 0.148180i | \(0.0473416\pi\) | |||||||
\(620\) | −16.0343 | −0.643955 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.46321 | − | 14.6587i | 0.339344 | − | 0.587761i | ||||
\(623\) | −15.8997 | − | 31.4962i | −0.637009 | − | 1.26187i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.1658 | + | 21.0717i | 0.486630 | + | 0.842868i | ||||
\(626\) | −11.0035 | − | 19.0587i | −0.439790 | − | 0.761739i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.13538 | − | 3.69859i | 0.0852110 | − | 0.147590i | ||||
\(629\) | 2.13673 | 0.0851969 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.76140 | − | 3.05083i | −0.0701200 | − | 0.121451i | 0.828834 | − | 0.559495i | \(-0.189005\pi\) |
−0.898954 | + | 0.438044i | \(0.855672\pi\) | |||||||
\(632\) | 3.00194 | + | 5.19951i | 0.119411 | + | 0.206825i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.46606 | − | 7.73544i | −0.177370 | − | 0.307214i | ||||
\(635\) | 21.2272 | 0.842376 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.70339 | + | 24.9657i | −0.146734 | + | 0.989176i | ||||
\(638\) | 1.87469 | 0.0742195 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.10337 | − | 1.91109i | −0.0436145 | − | 0.0755426i | ||||
\(641\) | 27.2176 | 1.07503 | 0.537515 | − | 0.843254i | \(-0.319363\pi\) | ||||
0.537515 | + | 0.843254i | \(0.319363\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.1450 | − | 34.8922i | −0.794442 | − | 1.37601i | −0.923193 | − | 0.384338i | \(-0.874430\pi\) |
0.128750 | − | 0.991677i | \(-0.458903\pi\) | |||||||
\(644\) | 7.42532 | + | 14.7090i | 0.292599 | + | 0.579616i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.85480 | + | 3.21260i | −0.0729761 | + | 0.126398i | ||||
\(647\) | −15.5929 | − | 27.0077i | −0.613020 | − | 1.06178i | −0.990728 | − | 0.135857i | \(-0.956621\pi\) |
0.377709 | − | 0.925925i | \(-0.376712\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.537955 | − | 0.931765i | −0.0211166 | − | 0.0365750i | ||||
\(650\) | 0.0164639 | − | 0.469523i | 0.000645768 | − | 0.0184162i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.03208 | + | 5.25172i | −0.118746 | + | 0.205673i | ||||
\(653\) | −0.465996 | −0.0182358 | −0.00911792 | − | 0.999958i | \(-0.502902\pi\) | ||||
−0.00911792 | + | 0.999958i | \(0.502902\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.23035 | − | 12.5233i | 0.282513 | − | 0.489327i | ||||
\(656\) | 1.63110 | − | 2.82515i | 0.0636839 | − | 0.110304i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.03418 | − | 10.7433i | 0.274221 | − | 0.418819i | ||||
\(659\) | 22.1490 | + | 38.3632i | 0.862803 | + | 1.49442i | 0.869212 | + | 0.494439i | \(0.164627\pi\) |
−0.00640903 | + | 0.999979i | \(0.502040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.9918 | − | 27.6986i | −0.622008 | − | 1.07735i | −0.989111 | − | 0.147169i | \(-0.952984\pi\) |
0.367103 | − | 0.930180i | \(-0.380350\pi\) | |||||||
\(662\) | −2.16425 | + | 3.74859i | −0.0841160 | + | 0.145693i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.77617 | 0.0689287 | ||||||||
\(665\) | 10.3335 | + | 20.4699i | 0.400716 | + | 0.793789i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.53073 | + | 9.57950i | −0.214151 | + | 0.370920i | ||||
\(668\) | 7.86930 | − | 13.6300i | 0.304472 | − | 0.527361i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.9162 | − | 22.3715i | 0.498997 | − | 0.864288i | ||||
\(671\) | 0.0806765 | 0.00311448 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.49379 | − | 4.31938i | 0.0961286 | − | 0.166500i | −0.813950 | − | 0.580934i | \(-0.802687\pi\) |
0.910079 | + | 0.414435i | \(0.136021\pi\) | |||||||
\(674\) | −0.416096 | −0.0160274 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.27262 | − | 10.7754i | 0.279716 | − | 0.414438i | ||||
\(677\) | 17.6543 | + | 30.5782i | 0.678511 | + | 1.17522i | 0.975429 | + | 0.220312i | \(0.0707076\pi\) |
−0.296919 | + | 0.954903i | \(0.595959\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.0717 | − | 39.8194i | 1.00054 | − | 1.52813i | ||||
\(680\) | −1.04217 | − | 1.80509i | −0.0399654 | − | 0.0692220i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.66911 | −0.293665 | ||||||||
\(683\) | 35.6076 | 1.36249 | 0.681243 | − | 0.732057i | \(-0.261440\pi\) | ||||
0.681243 | + | 0.732057i | \(0.261440\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.86115 | + | 13.6159i | 0.300359 | + | 0.520237i | ||||
\(686\) | −18.2585 | − | 3.10266i | −0.697113 | − | 0.118460i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.537418 | + | 0.930835i | 0.0204889 | + | 0.0354877i | ||||
\(689\) | 1.24854 | − | 35.6063i | 0.0475656 | − | 1.35649i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.0171 | −0.647361 | −0.323680 | − | 0.946166i | \(-0.604920\pi\) | ||||
−0.323680 | + | 0.946166i | \(0.604920\pi\) | |||||||
\(692\) | −5.29220 | + | 9.16635i | −0.201179 | + | 0.348452i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.7452 | −0.825435 | ||||||||
\(695\) | −6.83995 | + | 11.8471i | −0.259454 | + | 0.449388i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.54063 | − | 2.66845i | 0.0583555 | − | 0.101075i | ||||
\(698\) | 15.8128 | − | 27.3885i | 0.598522 | − | 1.03667i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.344205 | + | 0.0193327i | 0.0130097 | + | 0.000730707i | ||||
\(701\) | 24.2469 | 0.915792 | 0.457896 | − | 0.889006i | \(-0.348603\pi\) | ||||
0.457896 | + | 0.889006i | \(0.348603\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.44234 | + | 7.69436i | −0.167546 | + | 0.290198i | ||||
\(704\) | −0.527733 | − | 0.914061i | −0.0198897 | − | 0.0344500i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.8944 | + | 24.0658i | 0.522922 | + | 0.905727i | ||||
\(707\) | −19.5659 | + | 29.8830i | −0.735850 | + | 1.12387i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.13933 | + | 5.43748i | −0.117900 | + | 0.204209i | −0.918935 | − | 0.394408i | \(-0.870950\pi\) |
0.801035 | + | 0.598617i | \(0.204283\pi\) | |||||||
\(710\) | 9.28745 | − | 16.0863i | 0.348552 | − | 0.603710i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.3353 | −0.499761 | ||||||||
\(713\) | 22.6255 | − | 39.1886i | 0.847333 | − | 1.46762i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.294291 | + | 8.39268i | −0.0110059 | + | 0.313868i | ||||
\(716\) | 7.11908 | + | 12.3306i | 0.266053 | + | 0.460816i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.17747 | − | 7.23559i | −0.155902 | − | 0.270030i | ||||
\(719\) | −9.96438 | + | 17.2588i | −0.371609 | + | 0.643645i | −0.989813 | − | 0.142372i | \(-0.954527\pi\) |
0.618204 | + | 0.786017i | \(0.287860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.23940 | + | 6.47485i | −0.157883 | + | 0.241136i | ||||
\(722\) | 1.78761 | + | 3.09623i | 0.0665279 | + | 0.115230i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.7312 | −0.510314 | ||||||||
\(725\) | 0.115719 | + | 0.200432i | 0.00429771 | + | 0.00744385i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.1916 | 0.377984 | 0.188992 | − | 0.981979i | \(-0.439478\pi\) | ||||
0.188992 | + | 0.981979i | \(0.439478\pi\) | |||||||
\(728\) | 7.79286 | + | 5.50194i | 0.288823 | + | 0.203915i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −29.0082 | −1.07364 | ||||||||
\(731\) | 0.507609 | + | 0.879204i | 0.0187746 | + | 0.0325185i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.7321 | + | 25.5168i | 0.544144 | + | 0.942485i | 0.998660 | + | 0.0517467i | \(0.0164788\pi\) |
−0.454516 | + | 0.890738i | \(0.650188\pi\) | |||||||
\(734\) | 10.3905 | + | 17.9969i | 0.383520 | + | 0.664276i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.22771 | 0.229556 | ||||||||
\(737\) | 6.17773 | − | 10.7001i | 0.227560 | − | 0.394145i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.3475 | − | 28.3148i | −0.601354 | − | 1.04158i | −0.992616 | − | 0.121296i | \(-0.961295\pi\) |
0.391263 | − | 0.920279i | \(-0.372038\pi\) | |||||||
\(740\) | −2.49605 | − | 4.32328i | −0.0917566 | − | 0.158927i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26.1028 | + | 1.46609i | 0.958263 | + | 0.0538220i | ||||
\(743\) | 10.7085 | − | 18.5477i | 0.392857 | − | 0.680448i | −0.599968 | − | 0.800024i | \(-0.704820\pi\) |
0.992825 | + | 0.119576i | \(0.0381535\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.2720 | 1.76855 | ||||||||
\(746\) | −7.72840 | + | 13.3860i | −0.282957 | + | 0.490096i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.498462 | − | 0.863361i | −0.0182256 | − | 0.0315676i | ||||
\(749\) | −16.8224 | − | 33.3240i | −0.614678 | − | 1.21763i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.4156 | −1.14637 | −0.573185 | − | 0.819426i | \(-0.694292\pi\) | ||||
−0.573185 | + | 0.819426i | \(0.694292\pi\) | |||||||
\(752\) | −2.42678 | − | 4.20330i | −0.0884954 | − | 0.153279i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.224422 | + | 6.40013i | −0.00817296 | + | 0.233079i | ||||
\(755\) | −32.0268 | −1.16557 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.28891 | + | 16.0889i | −0.337611 | + | 0.584760i | −0.983983 | − | 0.178263i | \(-0.942952\pi\) |
0.646372 | + | 0.763023i | \(0.276286\pi\) | |||||||
\(758\) | 12.1123 | − | 20.9792i | 0.439940 | − | 0.761998i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.66684 | 0.314379 | ||||||||
\(761\) | 12.9141 | − | 22.3679i | 0.468137 | − | 0.810838i | −0.531200 | − | 0.847247i | \(-0.678259\pi\) |
0.999337 | + | 0.0364091i | \(0.0115919\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.82413 | + | 0.214787i | 0.138443 | + | 0.00777581i | ||||
\(764\) | 0.437999 | − | 0.758636i | 0.0158462 | − | 0.0274465i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.49967 | − | 12.9898i | 0.270974 | − | 0.469341i | ||||
\(767\) | 3.24542 | − | 1.72502i | 0.117185 | − | 0.0622869i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.92009 | + | 17.1821i | −0.357727 | + | 0.619602i | −0.987581 | − | 0.157112i | \(-0.949782\pi\) |
0.629853 | + | 0.776714i | \(0.283115\pi\) | |||||||
\(770\) | −6.15263 | − | 0.345570i | −0.221725 | − | 0.0124535i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.3312 | + | 19.6263i | 0.407820 | + | 0.706365i | ||||
\(773\) | −43.0325 | −1.54777 | −0.773885 | − | 0.633326i | \(-0.781689\pi\) | ||||
−0.773885 | + | 0.633326i | \(0.781689\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.473394 | − | 0.819942i | −0.0170048 | − | 0.0294532i | ||||
\(776\) | −8.99467 | − | 15.5792i | −0.322890 | − | 0.559261i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.37986 | + | 7.58613i | −0.157025 | + | 0.271976i | ||||
\(779\) | 6.40606 | + | 11.0956i | 0.229521 | + | 0.397542i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.44212 | − | 7.69398i | 0.158952 | − | 0.275312i | ||||
\(782\) | 5.88228 | 0.210350 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.15682 | + | 5.63212i | −0.148458 | + | 0.201147i | ||||
\(785\) | −9.42445 | −0.336373 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.28254 | −0.330887 | −0.165443 | − | 0.986219i | \(-0.552906\pi\) | ||||
−0.165443 | + | 0.986219i | \(0.552906\pi\) | |||||||
\(788\) | −8.44249 | + | 14.6228i | −0.300751 | + | 0.520916i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.62449 | − | 11.4740i | 0.235689 | − | 0.408225i | ||||
\(791\) | −4.86110 | + | 7.42437i | −0.172841 | + | 0.263980i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.00965792 | + | 0.275427i | −0.000342963 | + | 0.00978072i | ||||
\(794\) | −17.4400 | + | 30.2070i | −0.618922 | + | 1.07201i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.90084 | −0.209150 | ||||||||
\(797\) | −19.2169 | − | 33.2847i | −0.680698 | − | 1.17900i | −0.974768 | − | 0.223219i | \(-0.928343\pi\) |
0.294071 | − | 0.955784i | \(-0.404990\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.29217 | − | 3.97016i | −0.0810912 | − | 0.140454i | ||||
\(800\) | 0.0651512 | − | 0.112845i | 0.00230344 | − | 0.00398968i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.9474 | 0.457190 | ||||||||
\(803\) | −13.8744 | −0.489617 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.9174 | − | 30.4200i | 0.701997 | − | 1.07216i | ||||
\(806\) | 0.918082 | − | 26.1821i | 0.0323381 | − | 0.922227i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.75018 | + | 11.6917i | 0.237471 | + | 0.411311i | ||||
\(809\) | 15.7351 | + | 27.2540i | 0.553217 | + | 0.958200i | 0.998040 | + | 0.0625814i | \(0.0199333\pi\) |
−0.444823 | + | 0.895619i | \(0.646733\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.9386 | 1.78870 | 0.894348 | − | 0.447373i | \(-0.147640\pi\) | ||||
0.894348 | + | 0.447373i | \(0.147640\pi\) | |||||||
\(812\) | −4.69190 | − | 0.263526i | −0.164654 | − | 0.00924796i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.19384 | − | 2.06779i | −0.0418441 | − | 0.0724762i | ||||
\(815\) | 13.3820 | 0.468752 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.22135 | −0.147686 | ||||||||
\(818\) | −34.1242 | −1.19312 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.19884 | −0.251394 | ||||||||
\(821\) | −40.3254 | −1.40736 | −0.703682 | − | 0.710515i | \(-0.748462\pi\) | ||||
−0.703682 | + | 0.710515i | \(0.748462\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.4715 | 0.748450 | 0.374225 | − | 0.927338i | \(-0.377909\pi\) | ||||
0.374225 | + | 0.927338i | \(0.377909\pi\) | |||||||
\(824\) | 1.46258 | + | 2.53327i | 0.0509515 | + | 0.0882505i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.21540 | + | 2.40761i | 0.0422891 | + | 0.0837715i | ||||
\(827\) | 48.0554 | 1.67105 | 0.835525 | − | 0.549452i | \(-0.185164\pi\) | ||||
0.835525 | + | 0.549452i | \(0.185164\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.41512 | − | 7.64722i | −0.153344 | − | 0.265599i | 0.779111 | − | 0.626886i | \(-0.215671\pi\) |
−0.932455 | + | 0.361287i | \(0.882337\pi\) | |||||||
\(830\) | −1.95977 | − | 3.39442i | −0.0680246 | − | 0.117822i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.18376 | − | 1.69224i | 0.110377 | − | 0.0586680i | ||||
\(833\) | −3.92626 | + | 5.31973i | −0.136037 | + | 0.184318i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.7310 | −1.20191 | ||||||||
\(836\) | 4.14528 | 0.143368 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.0690 | + | 19.1720i | −0.382371 | + | 0.662285i | ||||
\(839\) | 10.3799 | + | 17.9786i | 0.358355 | + | 0.620689i | 0.987686 | − | 0.156448i | \(-0.0500043\pi\) |
−0.629331 | + | 0.777137i | \(0.716671\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.9226 | + | 22.3826i | 0.445607 | + | 0.771815i | ||||
\(842\) | −31.1012 | −1.07182 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.7856 | + | 20.4132i | −0.405677 | + | 0.702653i | ||||
\(845\) | −28.6171 | − | 2.00940i | −0.984460 | − | 0.0691256i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.1147 | + | 1.46676i | 0.897312 | + | 0.0503986i | ||||
\(848\) | 4.94074 | − | 8.55761i | 0.169666 | − | 0.293869i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.0615374 | − | 0.106586i | 0.00211072 | − | 0.00365587i | ||||
\(851\) | 14.0884 | 0.482943 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.67377 | 0.331224 | 0.165612 | − | 0.986191i | \(-0.447040\pi\) | ||||
0.165612 | + | 0.986191i | \(0.447040\pi\) | |||||||
\(854\) | −0.201914 | − | 0.0113408i | −0.00690937 | − | 0.000388073i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.1092 | −0.482242 | ||||||||
\(857\) | −5.94275 | + | 10.2931i | −0.203000 | + | 0.351607i | −0.949494 | − | 0.313786i | \(-0.898403\pi\) |
0.746493 | + | 0.665393i | \(0.231736\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.4094 | − | 21.4937i | −0.423404 | − | 0.733357i | 0.572866 | − | 0.819649i | \(-0.305832\pi\) |
−0.996270 | + | 0.0862919i | \(0.972498\pi\) | |||||||
\(860\) | 1.18594 | − | 2.05411i | 0.0404402 | − | 0.0700446i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.65730 | + | 9.79873i | 0.192688 | + | 0.333746i | ||||
\(863\) | 19.3325 | + | 33.4848i | 0.658084 | + | 1.13984i | 0.981111 | + | 0.193446i | \(0.0619663\pi\) |
−0.323027 | + | 0.946390i | \(0.604700\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.3570 | 0.794162 | ||||||||
\(866\) | −19.0285 | − | 32.9583i | −0.646614 | − | 1.11997i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 19.1940 | + | 1.07805i | 0.651487 | + | 0.0365915i | ||||
\(869\) | 3.16845 | − | 5.48791i | 0.107482 | − | 0.186165i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.7905 | + | 22.3715i | 1.21271 | + | 0.758031i | ||||
\(872\) | 0.723832 | − | 1.25371i | 0.0245121 | − | 0.0424561i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.2295 | + | 21.1821i | −0.413668 | + | 0.716494i | ||||
\(875\) | −13.4984 | − | 26.7393i | −0.456328 | − | 0.903952i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.8476 | + | 48.2335i | −0.940347 | + | 1.62873i | −0.175537 | + | 0.984473i | \(0.556166\pi\) |
−0.764810 | + | 0.644256i | \(0.777167\pi\) | |||||||
\(878\) | −2.96609 | −0.100101 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.16457 | + | 2.01709i | −0.0392577 | + | 0.0679962i | ||||
\(881\) | 1.98870 | − | 3.44454i | 0.0670011 | − | 0.116049i | −0.830579 | − | 0.556901i | \(-0.811990\pi\) |
0.897580 | + | 0.440852i | \(0.145324\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.3816 | −0.349370 | −0.174685 | − | 0.984624i | \(-0.555891\pi\) | ||||
−0.174685 | + | 0.984624i | \(0.555891\pi\) | |||||||
\(884\) | 3.00716 | − | 1.59838i | 0.101142 | − | 0.0537594i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.1253 | + | 17.5375i | 0.340166 | + | 0.589185i | ||||
\(887\) | 1.35095 | 0.0453604 | 0.0226802 | − | 0.999743i | \(-0.492780\pi\) | ||||
0.0226802 | + | 0.999743i | \(0.492780\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.4101 | − | 1.42719i | −0.852229 | − | 0.0478664i | ||||
\(890\) | 14.7138 | + | 25.4850i | 0.493206 | + | 0.854258i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.87906 | + | 4.98667i | −0.0963979 | + | 0.166966i | ||||
\(893\) | 19.0620 | 0.637887 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.7100 | − | 27.2104i | 0.525126 | − | 0.909545i | ||||
\(896\) | 1.19230 | + | 2.36187i | 0.0398321 | + | 0.0789044i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.97830 | − | 10.3547i | −0.199498 | − | 0.345541i | ||||
\(899\) | 6.45289 | + | 11.1767i | 0.215216 | + | 0.372765i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.66669 | − | 8.08294i | 0.155470 | − | 0.269282i | ||||
\(902\) | −3.44315 | −0.114644 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.67707 | + | 2.90477i | 0.0557784 | + | 0.0966111i | ||||
\(905\) | 15.1505 | + | 26.2415i | 0.503621 | + | 0.872297i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.3731 | − | 23.1628i | −0.444045 | − | 0.769109i | 0.553940 | − | 0.832557i | \(-0.313124\pi\) |
−0.997985 | + | 0.0634476i | \(0.979790\pi\) | |||||||
\(908\) | −19.6805 | −0.653121 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.91631 | − | 20.9635i | 0.0635250 | − | 0.694935i | ||||
\(911\) | 13.3116 | 0.441034 | 0.220517 | − | 0.975383i | \(-0.429226\pi\) | ||||
0.220517 | + | 0.975383i | \(0.429226\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.937343 | − | 1.62353i | −0.0310215 | − | 0.0537309i | ||||
\(914\) | 23.0842 | 0.763557 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.0430 | + | 17.3951i | 0.331831 | + | 0.574749i | ||||
\(917\) | −9.49712 | + | 14.5050i | −0.313623 | + | 0.478997i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.4317 | + | 28.4606i | −0.542032 | + | 0.938827i | 0.456755 | + | 0.889592i | \(0.349012\pi\) |
−0.998787 | + | 0.0492346i | \(0.984322\pi\) | |||||||
\(920\) | −6.87146 | − | 11.9017i | −0.226545 | − | 0.392388i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.46131 | + | 16.3875i | 0.311592 | + | 0.539692i | ||||
\(923\) | 25.7353 | + | 16.0863i | 0.847087 | + | 0.529488i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.147385 | − | 0.255279i | 0.00484600 | − | 0.00839352i | ||||
\(926\) | −32.7770 | −1.07712 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.888084 | + | 1.53821i | −0.0291528 | + | 0.0504941i | ||||
\(929\) | 22.3652 | − | 38.7377i | 0.733780 | − | 1.27094i | −0.221477 | − | 0.975166i | \(-0.571088\pi\) |
0.955257 | − | 0.295779i | \(-0.0955790\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.9935 | − | 25.1984i | −0.360297 | − | 0.825843i | ||||
\(932\) | 2.82261 | + | 4.88890i | 0.0924575 | + | 0.160141i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.7307 | + | 18.5861i | 0.351118 | + | 0.608155i | ||||
\(935\) | −1.09997 | + | 1.90521i | −0.0359730 | + | 0.0623071i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.6286 | 0.869917 | 0.434958 | − | 0.900451i | \(-0.356763\pi\) | ||||
0.434958 | + | 0.900451i | \(0.356763\pi\) | |||||||
\(938\) | −16.9655 | + | 25.9116i | −0.553945 | + | 0.846042i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.35526 | + | 9.27559i | −0.174669 | + | 0.302536i | ||||
\(941\) | 5.48027 | − | 9.49210i | 0.178652 | − | 0.309434i | −0.762767 | − | 0.646673i | \(-0.776160\pi\) |
0.941419 | + | 0.337239i | \(0.109493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.1580 | − | 17.5942i | 0.330791 | − | 0.572947i | ||||
\(944\) | 1.01937 | 0.0331776 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.567227 | − | 0.982465i | 0.0184421 | − | 0.0319427i | ||||
\(947\) | 53.7000 | 1.74501 | 0.872507 | − | 0.488602i | \(-0.162493\pi\) | ||||
0.872507 | + | 0.488602i | \(0.162493\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.66093 | − | 47.3669i | 0.0539160 | − | 1.53759i | ||||
\(950\) | 0.255877 | + | 0.443193i | 0.00830176 | + | 0.0143791i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.12617 | + | 2.23086i | 0.0364994 | + | 0.0723026i | ||||
\(953\) | −15.5264 | − | 26.8924i | −0.502948 | − | 0.871131i | −0.999994 | − | 0.00340721i | \(-0.998915\pi\) |
0.497046 | − | 0.867724i | \(-0.334418\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.93310 | −0.0625536 | ||||||||
\(956\) | −8.20960 | −0.265517 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.9460 | − | 27.6194i | −0.515193 | − | 0.892341i | ||||
\(959\) | −8.49478 | − | 16.8275i | −0.274311 | − | 0.543389i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.8980 | − | 18.8759i | −0.351548 | − | 0.608898i | ||||
\(962\) | 7.20231 | − | 3.82821i | 0.232212 | − | 0.123426i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.0169 | −0.676908 | ||||||||
\(965\) | 25.0051 | − | 43.3101i | 0.804942 | − | 1.39420i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.7062 | −1.59844 | −0.799221 | − | 0.601037i | \(-0.794754\pi\) | ||||
−0.799221 | + | 0.601037i | \(0.794754\pi\) | |||||||
\(968\) | 4.94299 | − | 8.56152i | 0.158874 | − | 0.275178i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.8489 | + | 34.3793i | −0.637309 | + | 1.10385i | ||||
\(971\) | −25.5570 | + | 44.2660i | −0.820163 | + | 1.42056i | 0.0853971 | + | 0.996347i | \(0.472784\pi\) |
−0.905560 | + | 0.424217i | \(0.860549\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.98433 | − | 13.7218i | 0.288024 | − | 0.439901i | ||||
\(974\) | 0.744679 | 0.0238610 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.0382184 | + | 0.0661962i | −0.00122334 | + | 0.00211889i | ||||
\(977\) | −2.31793 | − | 4.01477i | −0.0741571 | − | 0.128444i | 0.826562 | − | 0.562845i | \(-0.190293\pi\) |
−0.900719 | + | 0.434401i | \(0.856960\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.03748 | + | 12.1893i | 0.224919 | + | 0.389571i | ||||
\(980\) | 15.3500 | + | 1.72976i | 0.490338 | + | 0.0552552i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 20.5033 | − | 35.5127i | 0.654286 | − | 1.13326i | ||||
\(983\) | −5.80348 | + | 10.0519i | −0.185102 | + | 0.320607i | −0.943611 | − | 0.331056i | \(-0.892595\pi\) |
0.758509 | + | 0.651663i | \(0.225928\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37.2607 | 1.18723 | ||||||||
\(986\) | −0.838824 | + | 1.45289i | −0.0267136 | + | 0.0462693i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.496239 | + | 14.1519i | −0.0157875 | + | 0.450232i | ||||
\(989\) | 3.34688 | + | 5.79697i | 0.106425 | + | 0.184333i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.7478 | + | 41.1323i | 0.754373 | + | 1.30661i | 0.945686 | + | 0.325083i | \(0.105392\pi\) |
−0.191313 | + | 0.981529i | \(0.561274\pi\) | |||||||
\(992\) | 3.63304 | − | 6.29261i | 0.115349 | − | 0.199791i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.1991 | + | 18.6318i | −0.386933 | + | 0.590965i | ||||
\(995\) | 6.51081 | + | 11.2771i | 0.206407 | + | 0.357507i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.47510 | 0.0467168 | 0.0233584 | − | 0.999727i | \(-0.492564\pi\) | ||||
0.0233584 | + | 0.999727i | \(0.492564\pi\) | |||||||
\(998\) | 5.61372 | + | 9.72324i | 0.177699 | + | 0.307784i | ||||
\(999\) | 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 | 1638.2.m.k.1621.1 | 10 | ||
3.2 | odd | 2 | 546.2.j.e.529.5 | yes | 10 | ||
7.2 | even | 3 | 1638.2.p.j.919.1 | 10 | |||
13.3 | even | 3 | 1638.2.p.j.991.1 | 10 | |||
21.2 | odd | 6 | 546.2.k.e.373.5 | yes | 10 | ||
39.29 | odd | 6 | 546.2.k.e.445.5 | yes | 10 | ||
91.16 | even | 3 | inner | 1638.2.m.k.289.1 | 10 | ||
273.107 | odd | 6 | 546.2.j.e.289.5 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.e.289.5 | ✓ | 10 | 273.107 | odd | 6 | ||
546.2.j.e.529.5 | yes | 10 | 3.2 | odd | 2 | ||
546.2.k.e.373.5 | yes | 10 | 21.2 | odd | 6 | ||
546.2.k.e.445.5 | yes | 10 | 39.29 | odd | 6 | ||
1638.2.m.k.289.1 | 10 | 91.16 | even | 3 | inner | ||
1638.2.m.k.1621.1 | 10 | 1.1 | even | 1 | trivial | ||
1638.2.p.j.919.1 | 10 | 7.2 | even | 3 | |||
1638.2.p.j.991.1 | 10 | 13.3 | even | 3 |