Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(193,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 2, 12]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bp (of order \(9\), degree \(6\), 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: | \(144\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 193.5 | ||
Character | \(\chi\) | \(=\) | 756.193 |
Dual form | 756.2.bp.a.709.5 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.35655 | − | 1.07693i | −0.783203 | − | 0.621766i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.04264 | − | 0.743461i | 0.913497 | − | 0.332486i | 0.157849 | − | 0.987463i | \(-0.449544\pi\) |
0.755648 | + | 0.654978i | \(0.227322\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.979055 | − | 2.45794i | 0.370048 | − | 0.929013i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.680440 | + | 2.92181i | 0.226813 | + | 0.973938i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.861192 | + | 0.313448i | 0.259659 | + | 0.0945082i | 0.468570 | − | 0.883427i | \(-0.344770\pi\) |
−0.208911 | + | 0.977935i | \(0.566992\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.73996 | − | 1.36123i | 1.03728 | − | 0.377539i | 0.233431 | − | 0.972373i | \(-0.425005\pi\) |
0.803848 | + | 0.594835i | \(0.202783\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.57160 | − | 1.19124i | −0.922182 | − | 0.307578i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.17734 | + | 2.03922i | 0.285547 | + | 0.494583i | 0.972742 | − | 0.231891i | \(-0.0744912\pi\) |
−0.687194 | + | 0.726474i | \(0.741158\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.245736 | − | 0.425627i | 0.0563757 | − | 0.0976455i | −0.836460 | − | 0.548028i | \(-0.815379\pi\) |
0.892836 | + | 0.450382i | \(0.148712\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.97516 | + | 2.27993i | −0.867451 | + | 0.497522i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.385571 | − | 2.18668i | 0.0803971 | − | 0.455954i | −0.917858 | − | 0.396908i | \(-0.870083\pi\) |
0.998255 | − | 0.0590459i | \(-0.0188058\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.210571 | + | 0.176690i | −0.0421143 | + | 0.0353381i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.22354 | − | 4.69637i | 0.427921 | − | 0.903816i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.293857 | − | 0.106955i | −0.0545679 | − | 0.0198611i | 0.314592 | − | 0.949227i | \(-0.398132\pi\) |
−0.369160 | + | 0.929366i | \(0.620355\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.57219 | + | 0.572230i | −0.282373 | + | 0.102776i | −0.479324 | − | 0.877638i | \(-0.659118\pi\) |
0.196951 | + | 0.980413i | \(0.436896\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.830685 | − | 1.35265i | −0.144604 | − | 0.235466i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.172480 | − | 5.74857i | 0.0291544 | − | 0.971686i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.644777 | −0.106001 | −0.0530003 | − | 0.998594i | \(-0.516878\pi\) | ||||
−0.0530003 | + | 0.998594i | \(0.516878\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.53939 | − | 2.18110i | −1.04714 | − | 0.349256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.02951 | − | 2.55853i | 1.09783 | − | 0.399576i | 0.271311 | − | 0.962492i | \(-0.412543\pi\) |
0.826514 | + | 0.562916i | \(0.190321\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.47268 | − | 8.35201i | −0.224582 | − | 1.27367i | −0.863482 | − | 0.504379i | \(-0.831721\pi\) |
0.638900 | − | 0.769290i | \(-0.279390\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.56215 | + | 5.46234i | 0.531014 | + | 0.814278i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.31936 | − | 0.844179i | −0.338314 | − | 0.123136i | 0.167276 | − | 0.985910i | \(-0.446503\pi\) |
−0.505590 | + | 0.862774i | \(0.668725\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.08290 | − | 4.81291i | −0.726129 | − | 0.687559i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.598975 | − | 4.03421i | 0.0838733 | − | 0.564902i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.387704 | − | 0.671523i | 0.0532552 | − | 0.0922408i | −0.838169 | − | 0.545411i | \(-0.816374\pi\) |
0.891424 | + | 0.453170i | \(0.149707\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.99214 | 0.268620 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.791723 | + | 0.312743i | −0.104866 | + | 0.0414238i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.649562 | + | 0.545047i | 0.0845657 | + | 0.0709591i | 0.684091 | − | 0.729397i | \(-0.260199\pi\) |
−0.599525 | + | 0.800356i | \(0.704644\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.88514 | − | 2.86996i | −1.00959 | − | 0.367460i | −0.216314 | − | 0.976324i | \(-0.569403\pi\) |
−0.793275 | + | 0.608864i | \(0.791626\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.84782 | + | 1.18814i | 0.988733 | + | 0.149691i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.62738 | − | 5.56103i | 0.822025 | − | 0.689761i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.858765 | − | 4.87030i | 0.104915 | − | 0.595001i | −0.886339 | − | 0.463036i | \(-0.846760\pi\) |
0.991254 | − | 0.131966i | \(-0.0421288\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.87795 | + | 2.55110i | −0.346464 | + | 0.307117i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.26653 | + | 7.38984i | −0.506344 | + | 0.877013i | 0.493630 | + | 0.869672i | \(0.335670\pi\) |
−0.999973 | + | 0.00734044i | \(0.997663\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.22271 | 0.962396 | 0.481198 | − | 0.876612i | \(-0.340202\pi\) | ||||
0.481198 | + | 0.876612i | \(0.340202\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.475933 | − | 0.0129180i | 0.0549560 | − | 0.00149164i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.61359 | − | 1.80987i | 0.183886 | − | 0.206254i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.72096 | − | 15.4313i | −0.306132 | − | 1.73616i | −0.618130 | − | 0.786076i | \(-0.712110\pi\) |
0.311999 | − | 0.950083i | \(-0.399002\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.07400 | + | 3.97624i | −0.897111 | + | 0.441805i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.7930 | + | 5.38420i | 1.62374 | + | 0.590993i | 0.984090 | − | 0.177673i | \(-0.0568570\pi\) |
0.639650 | + | 0.768666i | \(0.279079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.92097 | + | 3.29008i | 0.425288 | + | 0.356859i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.283448 | + | 0.461554i | 0.0303888 | + | 0.0494837i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.775187 | − | 1.34266i | 0.0821697 | − | 0.142322i | −0.822012 | − | 0.569470i | \(-0.807148\pi\) |
0.904182 | + | 0.427148i | \(0.140482\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.315801 | − | 10.5253i | 0.0331050 | − | 1.10335i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.74900 | + | 0.916882i | 0.285058 | + | 0.0950762i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.185513 | − | 1.05210i | 0.0190333 | − | 0.107943i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.191971 | − | 1.08872i | −0.0194917 | − | 0.110543i | 0.973510 | − | 0.228646i | \(-0.0734298\pi\) |
−0.993001 | + | 0.118103i | \(0.962319\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.329848 | + | 2.72953i | −0.0331510 | + | 0.274328i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.78746 | + | 15.8085i | 0.277363 | + | 1.57300i | 0.731355 | + | 0.681997i | \(0.238888\pi\) |
−0.453992 | + | 0.891006i | \(0.650001\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.1945 | + | 5.89430i | −1.59569 | + | 0.580783i | −0.978539 | − | 0.206063i | \(-0.933935\pi\) |
−0.617150 | + | 0.786846i | \(0.711713\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.42479 | + | 7.61246i | −0.626995 | + | 0.742900i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.57310 | − | 4.45674i | −0.248751 | − | 0.430849i | 0.714429 | − | 0.699708i | \(-0.246687\pi\) |
−0.963179 | + | 0.268859i | \(0.913353\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.52203 | + | 7.83239i | −0.433132 | + | 0.750207i | −0.997141 | − | 0.0755615i | \(-0.975925\pi\) |
0.564009 | + | 0.825769i | \(0.309258\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.874670 | + | 0.694380i | 0.0830200 | + | 0.0659076i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.746948 | + | 4.23615i | −0.0702669 | + | 0.398504i | 0.929307 | + | 0.369309i | \(0.120405\pi\) |
−0.999574 | + | 0.0291949i | \(0.990706\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.838128 | − | 4.75326i | −0.0781559 | − | 0.443244i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.52210 | + | 10.0012i | 0.602968 | + | 0.924614i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.16495 | − | 0.897326i | 0.565140 | − | 0.0822578i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.78309 | − | 6.53079i | −0.707553 | − | 0.593708i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.2912 | − | 4.09953i | −1.10826 | − | 0.369642i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.73309 | + | 9.93001i | −0.512784 | + | 0.888167i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.36039 | + | 7.55242i | 0.386922 | + | 0.670169i | 0.992034 | − | 0.125972i | \(-0.0402048\pi\) |
−0.605112 | + | 0.796141i | \(0.706872\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.99677 | + | 12.9159i | −0.616031 | + | 1.13718i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.43614 | + | 19.4873i | −0.300217 | + | 1.70261i | 0.344991 | + | 0.938606i | \(0.387882\pi\) |
−0.645208 | + | 0.764007i | \(0.723229\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.805575 | − | 1.02072i | −0.0698522 | − | 0.0885073i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.05034 | − | 11.2461i | 0.0903986 | − | 0.967911i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.0527142 | − | 0.0442325i | 0.00450368 | − | 0.00377904i | −0.640533 | − | 0.767931i | \(-0.721287\pi\) |
0.645037 | + | 0.764152i | \(0.276842\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.91073 | + | 4.12059i | 0.416522 | + | 0.349504i | 0.826838 | − | 0.562440i | \(-0.190137\pi\) |
−0.410316 | + | 0.911943i | \(0.634582\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.23720 | + | 3.64296i | 0.188406 | + | 0.306793i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.64750 | 0.305019 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.679762 | −0.0564511 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.71202 | + | 12.0029i | 0.141205 | + | 0.989980i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.1707 | + | 11.0515i | 1.07898 | + | 0.905375i | 0.995836 | − | 0.0911623i | \(-0.0290582\pi\) |
0.0831477 | + | 0.996537i | \(0.473503\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.96837 | + | 2.90025i | 0.648457 | + | 0.236019i | 0.645245 | − | 0.763976i | \(-0.276755\pi\) |
0.00321191 | + | 0.999995i | \(0.498978\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.15710 | + | 4.82754i | −0.416927 | + | 0.390284i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.78599 | + | 2.33772i | −0.223776 | + | 0.187770i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.03664 | + | 0.869844i | 0.0827329 | + | 0.0694211i | 0.683216 | − | 0.730216i | \(-0.260581\pi\) |
−0.600483 | + | 0.799637i | \(0.705025\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.24912 | + | 0.493422i | −0.0990619 | + | 0.0391309i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.99723 | − | 3.08859i | −0.393837 | − | 0.243415i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.57730 | + | 13.1243i | 0.593500 | + | 1.02797i | 0.993757 | + | 0.111569i | \(0.0355877\pi\) |
−0.400256 | + | 0.916403i | \(0.631079\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.70244 | − | 2.14540i | −0.210384 | − | 0.167019i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.19499 | + | 23.7910i | −0.324618 | + | 1.84100i | 0.187727 | + | 0.982221i | \(0.439888\pi\) |
−0.512345 | + | 0.858780i | \(0.671223\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.17577 | − | 1.82569i | 0.167367 | − | 0.140438i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.41081 | + | 0.428381i | 0.107887 | + | 0.0327591i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.0004 | − | 15.1041i | 1.36854 | − | 1.14834i | 0.395302 | − | 0.918551i | \(-0.370640\pi\) |
0.973240 | − | 0.229792i | \(-0.0738047\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.228133 | + | 0.690561i | 0.0172452 | + | 0.0522015i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.294183 | − | 1.43891i | −0.0221122 | − | 0.108155i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.01203 | − | 5.21699i | −0.225130 | − | 0.389936i | 0.731229 | − | 0.682132i | \(-0.238947\pi\) |
−0.956358 | + | 0.292196i | \(0.905614\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.25877 | + | 2.18025i | 0.0935635 | + | 0.162057i | 0.909008 | − | 0.416778i | \(-0.136841\pi\) |
−0.815445 | + | 0.578835i | \(0.803508\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.60582 | + | 12.3850i | 0.562238 | + | 0.915524i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.31705 | + | 0.479366i | −0.0968313 | + | 0.0352437i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.374729 | + | 2.12519i | 0.0274029 | + | 0.155409i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.36640 | − | 10.0633i | −0.681305 | − | 0.731999i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.24794 | − | 12.7487i | −0.162656 | − | 0.922465i | −0.951449 | − | 0.307807i | \(-0.900405\pi\) |
0.788793 | − | 0.614659i | \(-0.210706\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.57449 | − | 1.30101i | 0.257298 | − | 0.0936487i | −0.210151 | − | 0.977669i | \(-0.567396\pi\) |
0.467449 | + | 0.884020i | \(0.345173\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.9792 | + | 0.406573i | −1.07268 | + | 0.0291153i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.33263 | + | 5.77229i | 0.237440 | + | 0.411258i | 0.959979 | − | 0.280072i | \(-0.0903583\pi\) |
−0.722539 | + | 0.691330i | \(0.757025\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.81597 | − | 11.8056i | −0.483171 | − | 0.836877i | 0.516642 | − | 0.856202i | \(-0.327182\pi\) |
−0.999813 | + | 0.0193244i | \(0.993848\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.40993 | + | 5.68196i | −0.452121 | + | 0.400774i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.550591 | + | 0.617567i | −0.0386439 | + | 0.0433447i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.4566 | − | 10.4523i | 0.870007 | − | 0.730022i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.65143 | − | 0.361339i | 0.462307 | − | 0.0251148i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.345038 | − | 0.289521i | 0.0238668 | − | 0.0200266i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.13814 | + | 12.1260i | −0.147196 | + | 0.834789i | 0.818382 | + | 0.574675i | \(0.194871\pi\) |
−0.965578 | + | 0.260115i | \(0.916240\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.7461 | − | 5.42991i | 0.941867 | − | 0.372052i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.21755 | − | 15.9653i | −0.628632 | − | 1.08882i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.132755 | + | 4.42459i | −0.00901201 | + | 0.300360i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.1545 | − | 8.85529i | −0.753751 | − | 0.598385i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.17907 | + | 6.02395i | 0.482916 | + | 0.405215i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.20459 | + | 1.84987i | −0.147630 | + | 0.123877i | −0.713612 | − | 0.700542i | \(-0.752942\pi\) |
0.565981 | + | 0.824418i | \(0.308497\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.659538 | − | 0.495023i | −0.0439692 | − | 0.0330015i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.6442 | + | 4.23814i | 0.772851 | + | 0.281295i | 0.698189 | − | 0.715914i | \(-0.253990\pi\) |
0.0746629 | + | 0.997209i | \(0.476212\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.4648 | − | 16.3329i | −1.28627 | − | 1.07931i | −0.992347 | − | 0.123483i | \(-0.960594\pi\) |
−0.293926 | − | 0.955828i | \(-0.594962\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.13802 | + | 0.717451i | −0.272262 | + | 0.0472048i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.5061 | −1.08135 | −0.540674 | − | 0.841232i | \(-0.681831\pi\) | ||||
−0.540674 | + | 0.841232i | \(0.681831\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.36524 | −0.349990 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.9273 | + | 23.8636i | −0.839722 | + | 1.55011i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.5905 | − | 16.4384i | −1.26720 | − | 1.06331i | −0.994876 | − | 0.101107i | \(-0.967762\pi\) |
−0.272329 | − | 0.962204i | \(-0.587794\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.55019 | − | 8.01356i | 0.615182 | − | 0.516199i | −0.281103 | − | 0.959678i | \(-0.590700\pi\) |
0.896285 | + | 0.443479i | \(0.146256\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2349 | + | 3.30118i | 0.977319 | + | 0.211771i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.9608 | − | 6.05212i | −0.891920 | − | 0.386655i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.339664 | − | 1.92633i | 0.0216123 | − | 0.122570i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.2690 | − | 23.2349i | −0.904258 | − | 1.47245i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.88142 | + | 17.1151i | 0.623710 | + | 1.08030i | 0.988789 | + | 0.149320i | \(0.0477086\pi\) |
−0.365079 | + | 0.930976i | \(0.618958\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.01746 | − | 1.76229i | 0.0639672 | − | 0.110795i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.77579 | − | 8.68576i | −0.111204 | − | 0.543923i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.7362 | + | 14.8825i | 1.10636 | + | 0.928342i | 0.997836 | − | 0.0657522i | \(-0.0209447\pi\) |
0.108519 | + | 0.994094i | \(0.465389\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.631272 | + | 1.58482i | −0.0392253 | + | 0.0984759i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.112551 | − | 0.931373i | 0.00696674 | − | 0.0576505i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.34411 | − | 18.9654i | −0.206207 | − | 1.16946i | −0.895530 | − | 0.445001i | \(-0.853203\pi\) |
0.689323 | − | 0.724454i | \(-0.257908\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.292689 | − | 1.65992i | 0.0179798 | − | 0.101968i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.49753 | + | 0.986564i | −0.152847 | + | 0.0603767i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.13138 | − | 7.15576i | 0.251895 | − | 0.436294i | −0.712153 | − | 0.702025i | \(-0.752280\pi\) |
0.964047 | + | 0.265730i | \(0.0856130\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.8009 | + | 22.1718i | 0.777601 | + | 1.34684i | 0.933321 | + | 0.359043i | \(0.116897\pi\) |
−0.155720 | + | 0.987801i | \(0.549770\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.7634 | + | 13.9380i | −0.711955 | + | 0.843565i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.236726 | + | 0.0861611i | −0.0142751 | + | 0.00519571i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.32599 | + | 13.1913i | 0.139755 | + | 0.792591i | 0.971430 | + | 0.237328i | \(0.0762715\pi\) |
−0.831674 | + | 0.555264i | \(0.812617\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.74173 | − | 4.20428i | −0.164143 | − | 0.251703i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.54264 | − | 25.7626i | −0.270991 | − | 1.53687i | −0.751415 | − | 0.659830i | \(-0.770628\pi\) |
0.480423 | − | 0.877037i | \(-0.340483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.09916 | + | 11.9050i | −0.124782 | + | 0.707676i | 0.856654 | + | 0.515891i | \(0.172539\pi\) |
−0.981437 | + | 0.191785i | \(0.938572\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.38469 | + | 1.22744i | −0.0820222 | + | 0.0727070i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.593570 | − | 19.7830i | 0.0350373 | − | 1.16776i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.72773 | − | 9.92072i | 0.336925 | − | 0.583572i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.912058 | + | 1.68364i | −0.0534658 | + | 0.0986966i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.0697 | + | 11.8058i | 0.821958 | + | 0.689705i | 0.953430 | − | 0.301615i | \(-0.0975258\pi\) |
−0.131472 | + | 0.991320i | \(0.541970\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.73204 | + | 0.630412i | 0.100843 | + | 0.0367040i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.38696 | − | 3.34751i | 0.196532 | − | 0.194242i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.53457 | − | 8.70295i | −0.0887462 | − | 0.503305i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.9705 | − | 4.55731i | −1.26636 | − | 0.262679i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.2433 | − | 24.4469i | 0.760809 | − | 1.40443i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.2402 | −1.04443 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.40312 | − | 16.2867i | 0.536664 | − | 0.929530i | −0.462417 | − | 0.886663i | \(-0.653018\pi\) |
0.999081 | − | 0.0428668i | \(-0.0136491\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.3163 | + | 9.44442i | 1.61086 | + | 0.537274i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.28943 | − | 12.9840i | 0.129821 | − | 0.736254i | −0.848505 | − | 0.529187i | \(-0.822497\pi\) |
0.978327 | − | 0.207067i | \(-0.0663918\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.84541 | + | 5.74398i | −0.386925 | + | 0.324669i | −0.815414 | − | 0.578878i | \(-0.803491\pi\) |
0.428489 | + | 0.903547i | \(0.359046\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.9136 | − | 3.40761i | 0.952975 | − | 0.191997i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.2370 | + | 11.0054i | 1.69828 | + | 0.618122i | 0.995627 | − | 0.0934144i | \(-0.0297782\pi\) |
0.702649 | + | 0.711537i | \(0.252000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.219542 | − | 0.184218i | −0.0122920 | − | 0.0103142i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.30907 | + | 8.81682i | −0.0730650 | + | 0.492107i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.15726 | 0.0643917 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.547012 | + | 0.947452i | −0.0303427 | + | 0.0525552i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.5693 | − | 5.75509i | 0.805684 | − | 0.318257i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.34572 | + | 4.87435i | −0.239587 | + | 0.268731i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.8908 | + | 9.78746i | 1.47805 | + | 0.537968i | 0.950274 | − | 0.311414i | \(-0.100803\pi\) |
0.527779 | + | 0.849381i | \(0.323025\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.438732 | − | 1.88392i | −0.0240424 | − | 0.103238i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.86673 | − | 10.5867i | −0.101990 | − | 0.578415i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.9957 | + | 4.73003i | −0.707919 | + | 0.257661i | −0.670788 | − | 0.741649i | \(-0.734044\pi\) |
−0.0371307 | + | 0.999310i | \(0.511822\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.57531 | − | 4.94213i | 0.302809 | − | 0.268420i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.53332 | −0.0830340 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.8063 | + | 7.78134i | −0.907453 | + | 0.420153i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.98197 | + | 7.35063i | −0.214382 | + | 0.395745i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.4899 | + | 12.5533i | −1.85152 | + | 0.673897i | −0.867077 | + | 0.498173i | \(0.834004\pi\) |
−0.984440 | + | 0.175724i | \(0.943773\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.1826 | − | 5.16203i | −0.759176 | − | 0.276317i | −0.0667142 | − | 0.997772i | \(-0.521252\pi\) |
−0.692462 | + | 0.721455i | \(0.743474\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.92311 | − | 20.5910i | 0.102648 | − | 1.09907i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.24502 | + | 3.56200i | −0.225940 | + | 0.189586i | −0.748729 | − | 0.662876i | \(-0.769336\pi\) |
0.522790 | + | 0.852462i | \(0.324891\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.22093 | + | 18.2668i | −0.170949 | + | 0.969501i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.32940 | − | 5.42196i | −0.493764 | − | 0.286960i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.89688 | + | 5.01755i | −0.152892 | + | 0.264816i | −0.932289 | − | 0.361713i | \(-0.882192\pi\) |
0.779398 | + | 0.626530i | \(0.215525\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.37923 | + | 16.2453i | 0.493644 | + | 0.855016i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.52492 | + | 17.2412i | 0.185010 | + | 0.904926i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.7961 | − | 6.11327i | 0.879146 | − | 0.319983i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.2206 | + | 8.08765i | 1.15991 | + | 0.422172i | 0.849064 | − | 0.528289i | \(-0.177166\pi\) |
0.310843 | + | 0.950461i | \(0.399389\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.2587 | + | 18.7980i | 0.638164 | + | 0.978585i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.27098 | − | 1.61041i | −0.0659858 | − | 0.0836083i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.60475 | + | 1.67599i | −0.238425 | + | 0.0867796i | −0.458469 | − | 0.888710i | \(-0.651602\pi\) |
0.220044 | + | 0.975490i | \(0.429380\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.4711 | − | 7.29638i | 0.953846 | − | 0.376784i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.24461 | −0.0641004 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.93187 | −0.150600 | −0.0753000 | − | 0.997161i | \(-0.523991\pi\) | ||||
−0.0753000 | + | 0.997161i | \(0.523991\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.21836 | − | 14.9411i | 0.113650 | − | 0.765454i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.8697 | + | 9.77979i | −1.37298 | + | 0.499724i | −0.920043 | − | 0.391819i | \(-0.871846\pi\) |
−0.452937 | + | 0.891542i | \(0.649624\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.95042 | − | 4.89656i | 0.0994025 | − | 0.249552i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 23.4009 | − | 9.98595i | 1.18954 | − | 0.507614i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.1371 | − | 9.51313i | −1.32520 | − | 0.482335i | −0.420081 | − | 0.907486i | \(-0.637998\pi\) |
−0.905122 | + | 0.425152i | \(0.860221\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.91306 | − | 1.78821i | 0.248464 | − | 0.0904336i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.6477 | − | 22.7350i | 1.29376 | − | 1.14683i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.0305 | − | 29.4977i | −0.856898 | − | 1.48419i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.05330 | − | 13.9487i | 0.404184 | − | 0.700066i | −0.590043 | − | 0.807372i | \(-0.700889\pi\) |
0.994226 | + | 0.107306i | \(0.0342224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.00643936 | + | 2.25220i | −0.000322371 | + | 0.112751i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.69554 | + | 15.2872i | −0.134609 | + | 0.763406i | 0.840522 | + | 0.541777i | \(0.182248\pi\) |
−0.975131 | + | 0.221629i | \(0.928863\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.10099 | + | 4.28024i | −0.254098 | + | 0.213214i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.5361 | + | 14.1247i | −0.672615 | + | 0.701864i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.555277 | − | 0.202104i | −0.0275240 | − | 0.0100179i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.70699 | + | 3.53305i | −0.479980 | + | 0.174698i | −0.570668 | − | 0.821181i | \(-0.693316\pi\) |
0.0906882 | + | 0.995879i | \(0.471093\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.119145 | + | 0.00323388i | −0.00587697 | + | 0.000159516i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.97565 | − | 1.06295i | 0.0972152 | − | 0.0523043i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.2197 | 1.67978 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.22404 | − | 10.8783i | −0.108912 | − | 0.532712i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.4103 | − | 7.06476i | 0.948254 | − | 0.345136i | 0.178834 | − | 0.983879i | \(-0.442768\pi\) |
0.769420 | + | 0.638743i | \(0.220545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.55192 | − | 31.4865i | −0.270584 | − | 1.53456i | −0.752649 | − | 0.658422i | \(-0.771224\pi\) |
0.482065 | − | 0.876135i | \(-0.339887\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.888346 | − | 7.35116i | 0.0431929 | − | 0.357426i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.608224 | − | 0.221376i | −0.0295032 | − | 0.0107383i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.7742 | + | 16.5713i | −0.714972 | + | 0.801943i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.94801 | − | 3.92811i | −0.238892 | − | 0.189651i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.7881 | + | 18.6856i | −0.519646 | + | 0.900053i | 0.480093 | + | 0.877217i | \(0.340603\pi\) |
−0.999739 | + | 0.0228358i | \(0.992731\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.5628 | 0.555671 | 0.277836 | − | 0.960629i | \(-0.410383\pi\) | ||||
0.277836 | + | 0.960629i | \(0.410383\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.922129 | + | 0.732056i | 0.0442127 | + | 0.0350994i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.835962 | − | 0.701455i | −0.0399895 | − | 0.0335551i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.9568 | − | 11.6313i | −1.52522 | − | 0.555133i | −0.562772 | − | 0.826612i | \(-0.690265\pi\) |
−0.962444 | + | 0.271479i | \(0.912487\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.6038 | − | 18.1262i | 0.504944 | − | 0.863152i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.32517 | + | 5.30745i | −0.300518 | + | 0.252165i | −0.780560 | − | 0.625081i | \(-0.785066\pi\) |
0.480042 | + | 0.877246i | \(0.340621\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.585212 | − | 3.31890i | 0.0277417 | − | 0.157331i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.96493 | − | 29.1758i | −0.282132 | − | 1.37997i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.496435 | − | 0.859850i | 0.0234282 | − | 0.0405788i | −0.854074 | − | 0.520152i | \(-0.825875\pi\) |
0.877502 | + | 0.479573i | \(0.159209\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.85573 | 0.322823 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.68610 | − | 12.5157i | −0.361125 | − | 0.588039i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.18009 | − | 21.7342i | −0.336608 | − | 1.01892i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.45136 | − | 30.9162i | −0.255004 | − | 1.44620i | −0.796063 | − | 0.605214i | \(-0.793088\pi\) |
0.541059 | − | 0.840985i | \(-0.318024\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.1948 | − | 0.994946i | 0.569204 | − | 0.0464401i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.7389 | + | 4.27260i | 0.546734 | + | 0.198995i | 0.600595 | − | 0.799554i | \(-0.294931\pi\) |
−0.0538610 | + | 0.998548i | \(0.517153\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.14281 | + | 7.67173i | 0.424902 | + | 0.356535i | 0.830024 | − | 0.557727i | \(-0.188326\pi\) |
−0.405122 | + | 0.914263i | \(0.632771\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.29689 | − | 0.170913i | 0.292011 | − | 0.00792592i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.23637 | − | 14.2658i | 0.381134 | − | 0.660143i | −0.610091 | − | 0.792331i | \(-0.708867\pi\) |
0.991225 | + | 0.132188i | \(0.0422004\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.1301 | − | 6.87908i | −0.513940 | − | 0.317646i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.469489 | − | 2.29637i | −0.0216329 | − | 0.105811i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.34966 | − | 7.65429i | 0.0620573 | − | 0.351945i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0234592 | + | 0.133044i | 0.00107638 | + | 0.00610448i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.22588 | + | 0.675868i | 0.101916 | + | 0.0309459i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.525860 | − | 2.98230i | −0.0240272 | − | 0.136265i | 0.970435 | − | 0.241365i | \(-0.0775949\pi\) |
−0.994462 | + | 0.105100i | \(0.966484\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.41144 | + | 0.877692i | −0.109952 | + | 0.0400193i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.45278 | + | 9.57148i | 0.157107 | + | 0.435518i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.20155 | − | 2.08114i | −0.0545594 | − | 0.0944997i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.4221 | + | 23.2478i | −0.608214 | + | 1.05346i | 0.383321 | + | 0.923615i | \(0.374780\pi\) |
−0.991535 | + | 0.129842i | \(0.958553\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.85497 | − | 25.9639i | 0.174328 | − | 1.17413i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.98415 | + | 16.9239i | −0.134673 | + | 0.763766i | 0.840414 | + | 0.541944i | \(0.182312\pi\) |
−0.975087 | + | 0.221822i | \(0.928800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.127865 | − | 0.725161i | −0.00575877 | − | 0.0326596i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.35553 | + | 5.82067i | 0.0609267 | + | 0.261620i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.9866 | + | 17.7219i | 0.627384 | + | 0.794936i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.3206 | + | 23.7638i | 1.26781 | + | 1.06382i | 0.994805 | + | 0.101801i | \(0.0324606\pi\) |
0.273001 | + | 0.962014i | \(0.411984\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.3119 | − | 27.7559i | 1.39891 | − | 1.24004i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.27791 | + | 5.67751i | −0.146155 | + | 0.253148i | −0.929803 | − | 0.368057i | \(-0.880023\pi\) |
0.783648 | + | 0.621205i | \(0.213356\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.4468 | + | 30.2187i | 0.776371 | + | 1.34471i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.91768 | + | 0.133478i | −0.218402 | + | 0.00592797i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.896915 | − | 5.08666i | 0.0397550 | − | 0.225462i | −0.958457 | − | 0.285238i | \(-0.907927\pi\) |
0.998212 | + | 0.0597757i | \(0.0190385\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.05049 | − | 20.2109i | 0.356133 | − | 0.894078i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.45250 | − | 2.10047i | −0.0641293 | − | 0.0927378i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28.6973 | + | 24.0799i | −1.26455 | + | 1.06109i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.73281 | − | 1.45400i | −0.0762089 | − | 0.0639468i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −40.6844 | + | 1.10428i | −1.78585 | + | 0.0484724i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.7393 | −0.689549 | −0.344775 | − | 0.938685i | \(-0.612045\pi\) | ||||
−0.344775 | + | 0.938685i | \(0.612045\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.3835 | 1.10994 | 0.554972 | − | 0.831869i | \(-0.312729\pi\) | ||||
0.554972 | + | 0.831869i | \(0.312729\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.434213 | − | 1.18246i | 0.0189506 | − | 0.0516068i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.01791 | − | 2.53232i | −0.131462 | − | 0.110310i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.9800 | + | 6.18022i | 0.738262 | + | 0.268705i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.15054 | + | 2.26877i | −0.0499291 | + | 0.0984563i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.8073 | − | 19.1376i | 0.987895 | − | 0.828943i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.56932 | − | 7.19052i | −0.370484 | − | 0.310873i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.53238 | + | 10.3208i | −0.0661269 | + | 0.445377i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.86875 | − | 5.73807i | −0.123566 | − | 0.247156i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.35804 | − | 2.35220i | −0.0583868 | − | 0.101129i | 0.835355 | − | 0.549711i | \(-0.185262\pi\) |
−0.893741 | + | 0.448583i | \(0.851929\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.640400 | − | 4.31322i | 0.0274822 | − | 0.185098i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.41382 | + | 19.3607i | −0.146232 | + | 0.829323i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.5876 | + | 18.1142i | −0.923019 | + | 0.774505i | −0.974551 | − | 0.224166i | \(-0.928034\pi\) |
0.0515315 | + | 0.998671i | \(0.483590\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.02011 | − | 24.9918i | 0.128895 | − | 1.06662i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.117734 | + | 0.0987908i | −0.00501565 | + | 0.00420863i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −40.5931 | − | 8.42017i | −1.72620 | − | 0.358062i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.30288 | + | 0.768086i | 0.0977519 | + | 0.0326035i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.5892 | + | 30.4654i | 0.745278 | + | 1.29086i | 0.950065 | + | 0.312052i | \(0.101016\pi\) |
−0.204788 | + | 0.978806i | \(0.565650\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.8768 | − | 29.2315i | −0.713813 | − | 1.23636i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.78035 | − | 3.28648i | 0.0751664 | − | 0.138755i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.1266 | + | 8.78135i | −1.01681 | + | 0.370090i | −0.796046 | − | 0.605236i | \(-0.793079\pi\) |
−0.220768 | + | 0.975326i | \(0.570856\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.62367 | + | 9.20826i | 0.0683081 | + | 0.387395i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.86845 | + | 23.7383i | 0.0784676 | + | 0.996917i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.39253 | − | 7.89743i | −0.0583779 | − | 0.331077i | 0.941606 | − | 0.336716i | \(-0.109316\pi\) |
−0.999984 | + | 0.00563874i | \(0.998205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.7749 | − | 7.56144i | 0.869401 | − | 0.316436i | 0.131477 | − | 0.991319i | \(-0.458028\pi\) |
0.737925 | + | 0.674883i | \(0.235806\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.6801 | + | 19.7151i | −0.446166 | + | 0.823611i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.305175 | + | 0.528579i | 0.0127267 | + | 0.0220433i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.1011 | + | 36.5482i | 0.878451 | + | 1.52152i | 0.853040 | + | 0.521845i | \(0.174756\pi\) |
0.0254109 | + | 0.999677i | \(0.491911\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.25006 | − | 2.08460i | −0.259744 | − | 0.0866331i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.7172 | − | 31.0888i | 1.14990 | − | 1.28978i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.544375 | − | 0.456785i | 0.0225457 | − | 0.0189181i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 20.7578 | + | 15.5800i | 0.858231 | + | 0.644154i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.04599 | + | 1.71679i | −0.0844471 | + | 0.0708595i | −0.684034 | − | 0.729450i | \(-0.739776\pi\) |
0.599587 | + | 0.800310i | \(0.295332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.142787 | + | 0.809784i | −0.00588342 | + | 0.0333665i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.69548 | − | 11.4194i | 0.0697428 | − | 0.469731i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.0319 | − | 36.4283i | −0.863677 | − | 1.49593i | −0.868355 | − | 0.495943i | \(-0.834823\pi\) |
0.00467857 | − | 0.999989i | \(-0.498511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.9257 | − | 6.41631i | 0.488904 | − | 0.263043i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.46764 | + | 23.3552i | −0.141921 | + | 0.955864i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.7818 | − | 13.2425i | −0.644826 | − | 0.541073i | 0.260670 | − | 0.965428i | \(-0.416056\pi\) |
−0.905496 | + | 0.424355i | \(0.860501\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.5157 | − | 27.2839i | 1.32634 | − | 1.11293i | 0.341424 | − | 0.939909i | \(-0.389091\pi\) |
0.984918 | − | 0.173024i | \(-0.0553537\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.8144 | − | 0.804795i | 0.603291 | − | 0.0327738i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.7534 | − | 7.55363i | −0.843747 | − | 0.307099i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.9845 | + | 17.6081i | 0.851736 | + | 0.714692i | 0.960171 | − | 0.279412i | \(-0.0901395\pi\) |
−0.108435 | + | 0.994104i | \(0.534584\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.41198 | − | 0.244810i | 0.0572163 | − | 0.00992019i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.82345 | −0.397414 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.4798 | −0.625225 | −0.312612 | − | 0.949881i | \(-0.601204\pi\) | ||||
−0.312612 | + | 0.949881i | \(0.601204\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −28.1544 | + | 0.764181i | −1.13530 | + | 0.0308148i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.5496 | − | 24.7951i | −1.18962 | − | 0.998212i | −0.999866 | − | 0.0163810i | \(-0.994786\pi\) |
−0.189757 | − | 0.981831i | \(-0.560770\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.7500 | + | 19.9286i | −0.954593 | + | 0.800999i | −0.980065 | − | 0.198677i | \(-0.936336\pi\) |
0.0254717 | + | 0.999676i | \(0.491891\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.41212 | − | 6.67296i | −0.377695 | − | 0.267777i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.54123 | − | 3.21990i | −0.101812 | − | 0.129003i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.08942 | + | 23.1923i | −0.163577 | + | 0.927690i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.779854 | + | 0.0211672i | −0.0311444 | + | 0.000845336i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.759123 | − | 1.31484i | −0.0302682 | − | 0.0524261i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.9592 | + | 36.3024i | −0.834372 | + | 1.44517i | 0.0601695 | + | 0.998188i | \(0.480836\pi\) |
−0.894541 | + | 0.446986i | \(0.852497\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.9594 | − | 14.1469i | 0.634328 | − | 0.562288i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.5216 | + | 12.1851i | 0.576274 | + | 0.483551i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.5614 | − | 11.0811i | −1.01278 | − | 0.439048i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.4949 | − | 7.43765i | −0.969002 | − | 0.294229i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.30244 | − | 13.0578i | −0.0909408 | − | 0.515751i | −0.995916 | − | 0.0902863i | \(-0.971222\pi\) |
0.904975 | − | 0.425465i | \(-0.139889\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.800161 | + | 4.53794i | −0.0315553 | + | 0.178959i | −0.996512 | − | 0.0834505i | \(-0.973406\pi\) |
0.964957 | + | 0.262409i | \(0.0845171\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.68945 | + | 31.5843i | −0.184647 | + | 1.24363i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.66162 | + | 13.2703i | −0.301209 | + | 0.521710i | −0.976410 | − | 0.215924i | \(-0.930724\pi\) |
0.675201 | + | 0.737634i | \(0.264057\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.388553 | + | 0.672994i | 0.0152520 | + | 0.0264173i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.94506 | − | 5.85919i | 0.193812 | − | 0.229640i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.4735 | + | 8.17968i | −0.879456 | + | 0.320096i | −0.741990 | − | 0.670411i | \(-0.766118\pi\) |
−0.137466 | + | 0.990507i | \(0.543896\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.46925 | + | 42.3602i | 0.291848 | + | 1.65515i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.59507 | + | 24.0252i | 0.218284 | + | 0.937314i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.65033 | + | 49.0584i | 0.336969 | + | 1.91105i | 0.406860 | + | 0.913491i | \(0.366624\pi\) |
−0.0698911 | + | 0.997555i | \(0.522265\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.07549 | + | 28.7845i | −0.197414 | + | 1.11959i | 0.711526 | + | 0.702660i | \(0.248005\pi\) |
−0.908939 | + | 0.416928i | \(0.863107\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.25136 | − | 15.9031i | −0.126272 | − | 0.617627i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.40436 | − | 1.48604i | −0.0932372 | − | 0.0576263i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.347180 | + | 0.601333i | −0.0134428 | + | 0.0232837i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.98281 | − | 0.135246i | 0.192647 | − | 0.00522891i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.89104 | − | 4.94317i | −0.227421 | − | 0.190829i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.37079 | + | 2.68275i | 0.284123 | + | 0.103412i | 0.480151 | − | 0.877186i | \(-0.340582\pi\) |
−0.196027 | + | 0.980598i | \(0.562804\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.361588 | + | 1.38180i | 0.0139175 | + | 0.0531855i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.71900 | − | 38.1053i | −0.258232 | − | 1.46451i | −0.787638 | − | 0.616138i | \(-0.788696\pi\) |
0.529406 | − | 0.848369i | \(-0.322415\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.86395 | − | 0.594065i | −0.109908 | − | 0.0227981i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.2317 | − | 18.2892i | −0.430400 | − | 0.700844i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.0563 | −1.11181 | −0.555905 | − | 0.831246i | \(-0.687628\pi\) | ||||
−0.555905 | + | 0.831246i | \(0.687628\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.0747911 | − | 0.129542i | 0.00285762 | − | 0.00494955i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.81553 | + | 43.1187i | 0.336333 | + | 1.64508i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.535897 | − | 3.03923i | 0.0204161 | − | 0.115785i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.9798 | + | 12.5696i | −0.569860 | + | 0.478169i | −0.881599 | − | 0.471998i | \(-0.843533\pi\) |
0.311739 | + | 0.950168i | \(0.399088\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.38606 | + | 3.48310i | 0.242586 | + | 0.132312i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.0944 | + | 4.76595i | 0.496697 | + | 0.180783i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.4935 | + | 11.3224i | 0.511104 | + | 0.428868i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.3912 | + | 17.7759i | 0.846915 | + | 0.672346i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.2829 | 0.501688 | 0.250844 | − | 0.968028i | \(-0.419292\pi\) | ||||
0.250844 | + | 0.968028i | \(0.419292\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.158445 | + | 0.274434i | −0.00597586 | + | 0.0103505i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.27820 | + | 5.77799i | 0.274113 | + | 0.217612i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 41.5853 | + | 8.62597i | 1.56398 | + | 0.324413i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.8649 | − | 6.13833i | −0.633375 | − | 0.230530i | 0.00532452 | − | 0.999986i | \(-0.498305\pi\) |
−0.638700 | + | 0.769456i | \(0.720527\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 43.2360 | − | 18.4502i | 1.62148 | − | 0.691937i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.645094 | + | 3.65851i | 0.0241590 | + | 0.137012i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.45054 | − | 2.71177i | 0.278634 | − | 0.101415i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.87244 | + | 43.3971i | 0.331347 | + | 1.62069i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.15770 | −0.155056 | −0.0775280 | − | 0.996990i | \(-0.524703\pi\) | ||||
−0.0775280 | + | 0.996990i | \(0.524703\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.36746 | + | 45.5758i | −0.0509267 | + | 1.69733i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.5853 | + | 0.585880i | −0.802767 | + | 0.0217891i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.0807758 | − | 0.0294000i | 0.00299994 | − | 0.00109189i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.1268 | − | 8.41747i | −0.857726 | − | 0.312187i | −0.124540 | − | 0.992215i | \(-0.539745\pi\) |
−0.733186 | + | 0.680028i | \(0.761968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.1117 | − | 20.8851i | −0.633767 | − | 0.773524i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.2977 | − | 12.8363i | 0.565806 | − | 0.474767i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.60656 | − | 9.11124i | 0.0593396 | − | 0.336531i | −0.940656 | − | 0.339360i | \(-0.889789\pi\) |
0.999996 | + | 0.00282903i | \(0.000900510\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.4207 | + | 23.2447i | 0.458145 | + | 0.857395i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.26615 | − | 3.92508i | 0.0834746 | − | 0.144582i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.81739 | + | 13.5401i | 0.287567 | + | 0.498081i | 0.973229 | − | 0.229840i | \(-0.0738202\pi\) |
−0.685661 | + | 0.727921i | \(0.740487\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.53530 | + | 2.24737i | −0.0931365 | + | 0.0825590i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.39183 | − | 0.506586i | 0.0510614 | − | 0.0185848i | −0.316363 | − | 0.948638i | \(-0.602462\pi\) |
0.367425 | + | 0.930053i | \(0.380240\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.1193 | + | 12.7824i | 1.28667 | + | 0.468311i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.66590 | + | 46.8860i | −0.207305 | + | 1.71547i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.4736 | + | 1.96112i | −0.492314 | + | 0.0716577i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.6022 | − | 9.68241i | 0.970728 | − | 0.353316i | 0.192500 | − | 0.981297i | \(-0.438341\pi\) |
0.778229 | + | 0.627981i | \(0.216118\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.02719 | − | 33.8591i | 0.183201 | − | 1.23389i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.4327 | 0.670836 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.48414 | −0.344707 | −0.172353 | − | 0.985035i | \(-0.555137\pi\) | ||||
−0.172353 | + | 0.985035i | \(0.555137\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.27810 | + | 1.29490i | −0.118988 | + | 0.0470019i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.7036 | + | 3.89577i | −0.388003 | + | 0.141222i | −0.528654 | − | 0.848838i | \(-0.677303\pi\) |
0.140650 | + | 0.990059i | \(0.455081\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.8242 | + | 18.7832i | 0.536672 | + | 0.679998i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.94502 | + | 13.6950i | −0.251098 | + | 0.495145i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.17127 | + | 1.15425i | 0.114508 | + | 0.0416775i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.3493 | − | 13.5940i | 1.34685 | − | 0.490213i | 0.434887 | − | 0.900485i | \(-0.356788\pi\) |
0.911963 | + | 0.410272i | \(0.134566\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.03265 | − | 39.2894i | −0.289289 | − | 1.41497i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.13102 | − | 7.15513i | −0.148582 | − | 0.257352i | 0.782121 | − | 0.623126i | \(-0.214138\pi\) |
−0.930704 | + | 0.365774i | \(0.880804\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.229950 | − | 0.398286i | 0.00826006 | − | 0.0143069i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.56309 | − | 1.47005i | 0.0919504 | − | 0.0527376i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.638422 | − | 3.62067i | 0.0228739 | − | 0.129724i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.99063 | + | 5.02674i | −0.214362 | + | 0.179871i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.15570 | + | 1.14224i | −0.0413015 | + | 0.0408204i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.76418 | + | 1.00608i | 0.0986578 | + | 0.0359085i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5434 | − | 5.65733i | 0.554062 | − | 0.201662i | −0.0497885 | − | 0.998760i | \(-0.515855\pi\) |
0.603850 | + | 0.797098i | \(0.293632\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.8880 | + | 29.3288i | −0.565626 | + | 1.04413i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.68089 | + | 5.98338i | 0.344213 | + | 0.212744i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.3968 | −1.18596 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.18467 | + | 1.93656i | −0.0774822 | + | 0.0686826i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 50.9520 | − | 18.5450i | 1.80481 | − | 0.656898i | 0.807019 | − | 0.590526i | \(-0.201080\pi\) |
0.997795 | − | 0.0663722i | \(-0.0211425\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.00922 | − | 5.72357i | −0.0357036 | − | 0.202485i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.45048 | + | 1.35135i | 0.157250 | + | 0.0477476i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.08133 | + | 2.57740i | 0.249895 | + | 0.0909543i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.5038 | − | 2.59364i | −0.440701 | − | 0.0914138i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.3107 | + | 5.25792i | −0.468558 | + | 0.185087i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.0155 | + | 22.5436i | −0.457602 | + | 0.792590i | −0.998834 | − | 0.0482838i | \(-0.984625\pi\) |
0.541232 | + | 0.840873i | \(0.317958\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.752228 | −0.0264143 | −0.0132072 | − | 0.999913i | \(-0.504204\pi\) | ||||
−0.0132072 | + | 0.999913i | \(0.504204\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.51249 | − | 43.8629i | 0.228403 | − | 1.53834i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.2351 | + | 21.1748i | 0.883947 | + | 0.741720i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.91673 | − | 1.42557i | −0.137029 | − | 0.0498745i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 30.9679 | − | 6.23913i | 1.08211 | − | 0.218013i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.9525 | + | 22.6158i | −0.940648 | + | 0.789297i | −0.977698 | − | 0.210016i | \(-0.932648\pi\) |
0.0370502 | + | 0.999313i | \(0.488204\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.54189 | − | 37.1009i | 0.228036 | − | 1.29326i | −0.628759 | − | 0.777600i | \(-0.716437\pi\) |
0.856795 | − | 0.515657i | \(-0.172452\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.413919 | + | 0.138056i | 0.0144108 | + | 0.00480648i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.74484 | + | 13.4145i | −0.269314 | + | 0.466466i | −0.968685 | − | 0.248293i | \(-0.920130\pi\) |
0.699371 | + | 0.714759i | \(0.253464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.0359 | −0.661146 | −0.330573 | − | 0.943781i | \(-0.607242\pi\) | ||||
−0.330573 | + | 0.943781i | \(0.607242\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.0508 | − | 20.3996i | 0.383350 | − | 0.707655i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.83025 | − | 16.0316i | 0.132710 | − | 0.555461i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.11879 | + | 51.7152i | 0.315569 | + | 1.78968i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.808428 | + | 8.65595i | −0.0279433 | + | 0.299194i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.80913 | − | 2.47832i | −0.235077 | − | 0.0855611i | 0.221795 | − | 0.975093i | \(-0.428808\pi\) |
−0.456873 | + | 0.889532i | \(0.651030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.1404 | − | 18.5780i | −0.763461 | − | 0.640620i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.5822 | + | 39.8403i | −0.743331 | + | 1.37217i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.08699 | − | 5.34683i | 0.106196 | − | 0.183937i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.6723 | + | 12.7363i | −0.813391 | + | 0.437626i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.6684 | − | 13.8890i | 0.537739 | − | 0.476668i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.248607 | + | 1.40992i | −0.00852214 | + | 0.0483315i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.80413 | − | 27.2456i | −0.164490 | − | 0.932872i | −0.949588 | − | 0.313500i | \(-0.898498\pi\) |
0.785098 | − | 0.619372i | \(-0.212613\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.20027 | − | 0.173855i | 0.109447 | − | 0.00594570i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.37631 | + | 24.8193i | 0.149492 | + | 0.847811i | 0.963650 | + | 0.267168i | \(0.0860878\pi\) |
−0.814158 | + | 0.580643i | \(0.802801\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.35293 | + | 2.31228i | −0.216759 | + | 0.0788938i | −0.448117 | − | 0.893975i | \(-0.647905\pi\) |
0.231358 | + | 0.972869i | \(0.425683\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.1102 | + | 26.1974i | −0.753512 | + | 0.892805i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.12740 | + | 12.3450i | 0.242620 | + | 0.420230i | 0.961460 | − | 0.274946i | \(-0.0886600\pi\) |
−0.718840 | + | 0.695176i | \(0.755327\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.5390 | − | 44.2348i | 0.868352 | − | 1.50403i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.4539 | + | 7.28955i | −0.626726 | + | 0.247566i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.49365 | − | 14.1422i | 0.0845913 | − | 0.479741i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.41787 | − | 19.3837i | −0.115810 | − | 0.656792i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.05041 | − | 1.30171i | 0.103241 | − | 0.0440562i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.7943 | + | 23.8136i | 0.635364 | + | 0.805047i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.3008 | − | 23.7472i | −0.955650 | − | 0.801886i | 0.0245896 | − | 0.999698i | \(-0.492172\pi\) |
−0.980240 | + | 0.197812i | \(0.936617\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.37208 | − | 31.1672i | −0.214925 | − | 1.05124i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.5123 | + | 37.2604i | −0.724768 | + | 1.25533i | 0.234302 | + | 0.972164i | \(0.424720\pi\) |
−0.959069 | + | 0.283171i | \(0.908614\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.95611 | − | 6.85218i | −0.133134 | − | 0.230594i | 0.791749 | − | 0.610846i | \(-0.209171\pi\) |
−0.924883 | + | 0.380252i | \(0.875837\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.67069 | − | 2.72047i | −0.0561595 | − | 0.0914477i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.81832 | − | 21.6547i | 0.128206 | − | 0.727095i | −0.851145 | − | 0.524931i | \(-0.824091\pi\) |
0.979352 | − | 0.202165i | \(-0.0647976\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.8324 | − | 3.32333i | 0.765775 | − | 0.111461i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.19961 | + | 0.893525i | −0.274697 | + | 0.0299342i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.929256 | + | 0.779738i | −0.0310964 | + | 0.0260929i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.0311 | − | 8.41712i | −0.335304 | − | 0.281353i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.29077 | + | 13.4586i | −0.243432 | + | 0.449369i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.523202 | 0.0174498 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.82584 | 0.0608276 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.8962 | + | 29.8430i | 0.828492 | + | 0.993111i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.19214 | + | 3.51762i | 0.139351 | + | 0.116930i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.0346 | + | 4.38024i | 0.399603 | + | 0.145444i | 0.534001 | − | 0.845484i | \(-0.320688\pi\) |
−0.134398 | + | 0.990927i | \(0.542910\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −44.2927 | + | 18.9012i | −1.46910 | + | 0.626912i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.9130 | + | 21.7436i | −0.858536 | + | 0.720397i | −0.961652 | − | 0.274272i | \(-0.911563\pi\) |
0.103116 | + | 0.994669i | \(0.467119\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.0519 | + | 9.27366i | 0.365765 | + | 0.306913i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.7437 | + | 19.6434i | 0.818002 | + | 0.649392i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 44.5344 | + | 27.5249i | 1.47065 | + | 0.908954i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.6409 | − | 32.2870i | −0.614907 | − | 1.06505i | −0.990401 | − | 0.138225i | \(-0.955860\pi\) |
0.375494 | − | 0.926825i | \(-0.377473\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.2954 | + | 11.9671i | −0.998267 | + | 0.394331i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.89734 | + | 33.4455i | −0.194113 | + | 1.10087i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.135772 | − | 0.113926i | 0.00446414 | − | 0.00374586i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −28.2414 | − | 43.3065i | −0.927570 | − | 1.42237i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.1449 | − | 22.7773i | 0.890595 | − | 0.747298i | −0.0777341 | − | 0.996974i | \(-0.524769\pi\) |
0.968329 | + | 0.249676i | \(0.0803241\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.29756 | + | 0.980715i | −0.108073 | + | 0.0321416i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.0886 | + | 15.1478i | −0.559454 | + | 0.495918i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.34543 | + | 4.06241i | 0.0767039 | + | 0.132855i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.54931 | − | 14.8078i | −0.279294 | − | 0.483751i | 0.691916 | − | 0.721978i | \(-0.256767\pi\) |
−0.971209 | + | 0.238227i | \(0.923434\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.4720 | − | 0.419948i | 0.504909 | − | 0.0137045i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.1779 | + | 12.4397i | −1.11417 | + | 0.405524i | −0.832521 | − | 0.553994i | \(-0.813103\pi\) |
−0.281648 | + | 0.959518i | \(0.590881\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.88432 | − | 16.3578i | −0.0939264 | − | 0.532683i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −26.6139 | − | 13.5922i | −0.865750 | − | 0.442155i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.88894 | + | 27.7266i | 0.158869 | + | 0.900993i | 0.955163 | + | 0.296082i | \(0.0956801\pi\) |
−0.796293 | + | 0.604911i | \(0.793209\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.7526 | − | 11.1930i | 0.998273 | − | 0.363342i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.1659 | − | 47.4924i | −0.945768 | − | 1.54005i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.5144 | − | 38.9960i | −0.729312 | − | 1.26320i | −0.957175 | − | 0.289511i | \(-0.906507\pi\) |
0.227863 | − | 0.973693i | \(-0.426826\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.0699 | − | 24.3698i | −0.455292 | − | 0.788589i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.0994296 | + | 0.486332i | 0.00321410 | + | 0.0157209i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.0571105 | − | 0.172874i | −0.00184419 | − | 0.00558240i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.6030 | + | 18.1271i | −0.696872 | + | 0.584745i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.2709 | − | 10.5507i | 0.363200 | − | 0.339990i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.33416 | − | 5.31499i | 0.203904 | − | 0.171096i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.219291 | + | 1.24366i | −0.00705192 | + | 0.0399934i | −0.988131 | − | 0.153616i | \(-0.950908\pi\) |
0.981079 | + | 0.193609i | \(0.0620193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.56988 | − | 1.24629i | −0.0504318 | − | 0.0400366i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.3239 | − | 43.8622i | −0.812682 | − | 1.40761i | −0.910981 | − | 0.412449i | \(-0.864674\pi\) |
0.0982991 | − | 0.995157i | \(-0.468660\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.9360 | − | 8.03597i | 0.478827 | − | 0.257621i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.76239 | − | 0.696170i | 0.0564416 | − | 0.0222953i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.1670 | + | 33.7041i | 1.28506 | + | 1.07829i | 0.992526 | + | 0.122033i | \(0.0389414\pi\) |
0.292530 | + | 0.956256i | \(0.405503\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.08844 | − | 0.913310i | 0.0347867 | − | 0.0291895i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.9618 | − | 7.88307i | −0.828896 | − | 0.251687i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.9421 | + | 11.2620i | 0.986901 | + | 0.359203i | 0.784519 | − | 0.620104i | \(-0.212910\pi\) |
0.202381 | + | 0.979307i | \(0.435132\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.0988 | + | 9.31303i | 0.353638 | + | 0.296738i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.1445 | − | 1.93224i | 0.354734 | − | 0.0615039i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.8310 | −0.598791 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.48076 | −0.301166 | −0.150583 | − | 0.988597i | \(-0.548115\pi\) | ||||
−0.150583 | + | 0.988597i | \(0.548115\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.9383 | − | 42.2367i | −0.823126 | − | 1.34034i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.6996 | − | 19.0472i | −0.719625 | − | 0.603837i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.33794 | − | 1.12266i | 0.0423729 | − | 0.0355551i | −0.621355 | − | 0.783529i | \(-0.713418\pi\) |
0.663728 | + | 0.747974i | \(0.268973\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.43369 | + | 3.02811i | −0.0453599 | + | 0.0958051i |
(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.bp.a.193.5 | ✓ | 144 | |
7.2 | even | 3 | 756.2.bq.a.625.22 | yes | 144 | ||
27.7 | even | 9 | 756.2.bq.a.277.22 | yes | 144 | ||
189.142 | even | 9 | inner | 756.2.bp.a.709.5 | yes | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.bp.a.193.5 | ✓ | 144 | 1.1 | even | 1 | trivial | |
756.2.bp.a.709.5 | yes | 144 | 189.142 | even | 9 | inner | |
756.2.bq.a.277.22 | yes | 144 | 27.7 | even | 9 | ||
756.2.bq.a.625.22 | yes | 144 | 7.2 | even | 3 |