Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(64,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.be (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6x^{10} + 29x^{8} - 40x^{6} + 43x^{4} - 7x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 64.5 | ||
Root | \(1.00376 - 0.579521i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.64 |
Dual form | 855.2.be.d.334.5 |
$q$-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 \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.747190 | − | 0.431391i | 0.528343 | − | 0.305039i | −0.211998 | − | 0.977270i | \(-0.567997\pi\) |
0.740342 | + | 0.672231i | \(0.234664\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.627804 | + | 1.08739i | −0.313902 | + | 0.543695i | ||||
\(5\) | 0.0476457 | − | 2.23556i | 0.0213078 | − | 0.999773i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.566520i | − | 0.214124i | −0.994252 | − | 0.107062i | \(-0.965856\pi\) | ||
0.994252 | − | 0.107062i | \(-0.0341444\pi\) | |||||||
\(8\) | 2.80888i | 0.993088i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.928799 | − | 1.69094i | −0.293712 | − | 0.534723i | ||||
\(11\) | 1.91223 | 0.576559 | 0.288279 | − | 0.957546i | \(-0.406917\pi\) | ||||
0.288279 | + | 0.957546i | \(0.406917\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.168469 | − | 0.0972656i | −0.0467249 | − | 0.0269766i | 0.476456 | − | 0.879199i | \(-0.341921\pi\) |
−0.523180 | + | 0.852222i | \(0.675255\pi\) | |||||||
\(14\) | −0.244391 | − | 0.423298i | −0.0653163 | − | 0.113131i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.0438854 | − | 0.0760118i | −0.0109714 | − | 0.0190029i | ||||
\(17\) | 4.58603 | − | 2.64775i | 1.11228 | − | 0.642173i | 0.172858 | − | 0.984947i | \(-0.444700\pi\) |
0.939418 | + | 0.342774i | \(0.111367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.36834 | − | 3.65936i | 0.543335 | − | 0.839516i | ||||
\(20\) | 2.40101 | + | 1.45530i | 0.536883 | + | 0.325416i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.42880 | − | 0.824918i | 0.304621 | − | 0.175873i | ||||
\(23\) | 2.92318 | + | 1.68770i | 0.609525 | + | 0.351910i | 0.772780 | − | 0.634674i | \(-0.218866\pi\) |
−0.163254 | + | 0.986584i | \(0.552199\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99546 | − | 0.213030i | −0.999092 | − | 0.0426059i | ||||
\(26\) | −0.167838 | −0.0329157 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.616027 | + | 0.355664i | 0.116418 | + | 0.0672141i | ||||
\(29\) | 4.36834 | − | 7.56619i | 0.811181 | − | 1.40501i | −0.100857 | − | 0.994901i | \(-0.532158\pi\) |
0.912038 | − | 0.410106i | \(-0.134508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65662 | 1.01596 | 0.507980 | − | 0.861369i | \(-0.330393\pi\) | ||||
0.507980 | + | 0.861369i | \(0.330393\pi\) | |||||||
\(32\) | −4.93070 | − | 2.84674i | −0.871633 | − | 0.503238i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.28442 | − | 3.95674i | 0.391776 | − | 0.678575i | ||||
\(35\) | −1.26649 | − | 0.0269922i | −0.214076 | − | 0.00456252i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.955582i | − | 0.157097i | −0.996910 | − | 0.0785484i | \(-0.974971\pi\) | ||
0.996910 | − | 0.0785484i | \(-0.0250285\pi\) | |||||||
\(38\) | 0.190988 | − | 3.75592i | 0.0309824 | − | 0.609291i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.27942 | + | 0.133831i | 0.992863 | + | 0.0211605i | ||||
\(41\) | 5.02496 | + | 8.70349i | 0.784768 | + | 1.35926i | 0.929138 | + | 0.369734i | \(0.120551\pi\) |
−0.144370 | + | 0.989524i | \(0.546116\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.27161 | + | 2.46622i | −0.651415 | + | 0.376094i | −0.788998 | − | 0.614396i | \(-0.789400\pi\) |
0.137583 | + | 0.990490i | \(0.456066\pi\) | |||||||
\(44\) | −1.20051 | + | 2.07934i | −0.180983 | + | 0.313472i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.91223 | 0.429385 | ||||||||
\(47\) | −7.65516 | − | 4.41971i | −1.11662 | − | 0.644681i | −0.176084 | − | 0.984375i | \(-0.556343\pi\) |
−0.940536 | + | 0.339694i | \(0.889676\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.67906 | 0.954151 | ||||||||
\(50\) | −3.82446 | + | 1.99582i | −0.540860 | + | 0.282252i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.211531 | − | 0.122128i | 0.0293341 | − | 0.0169361i | ||||
\(53\) | −7.10669 | − | 4.10305i | −0.976179 | − | 0.563597i | −0.0750646 | − | 0.997179i | \(-0.523916\pi\) |
−0.901114 | + | 0.433581i | \(0.857250\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0911095 | − | 4.27490i | 0.0122852 | − | 0.576428i | ||||
\(56\) | 1.59128 | 0.212644 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 7.53785i | − | 0.989768i | ||||||
\(59\) | −1.85713 | − | 3.21664i | −0.241777 | − | 0.418770i | 0.719443 | − | 0.694551i | \(-0.244397\pi\) |
−0.961221 | + | 0.275781i | \(0.911064\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.75561 | − | 3.04080i | 0.224783 | − | 0.389335i | −0.731472 | − | 0.681872i | \(-0.761166\pi\) |
0.956254 | + | 0.292537i | \(0.0944995\pi\) | |||||||
\(62\) | 4.22657 | − | 2.44021i | 0.536775 | − | 0.309907i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.73669 | −0.592086 | ||||||||
\(65\) | −0.225470 | + | 0.371988i | −0.0279661 | + | 0.0461395i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50190 | + | 2.02182i | 0.427825 | + | 0.247005i | 0.698420 | − | 0.715688i | \(-0.253887\pi\) |
−0.270594 | + | 0.962693i | \(0.587220\pi\) | |||||||
\(68\) | 6.64906i | 0.806318i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.957953 | + | 0.526183i | −0.114497 | + | 0.0628909i | ||||
\(71\) | 2.59767 | + | 4.49929i | 0.308286 | + | 0.533967i | 0.977988 | − | 0.208663i | \(-0.0669112\pi\) |
−0.669701 | + | 0.742631i | \(0.733578\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.45136 | − | 4.30205i | 0.872116 | − | 0.503516i | 0.00406505 | − | 0.999992i | \(-0.498706\pi\) |
0.868051 | + | 0.496475i | \(0.165373\pi\) | |||||||
\(74\) | −0.412229 | − | 0.714002i | −0.0479207 | − | 0.0830010i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.49230 | + | 4.87268i | 0.285886 | + | 0.558934i | ||||
\(77\) | − | 1.08332i | − | 0.123455i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.31324 | + | 5.73870i | 0.372769 | + | 0.645654i | 0.989990 | − | 0.141135i | \(-0.0450751\pi\) |
−0.617222 | + | 0.786789i | \(0.711742\pi\) | |||||||
\(80\) | −0.172020 | + | 0.0944869i | −0.0192324 | + | 0.0105640i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.50921 | + | 4.33544i | 0.829253 | + | 0.478770i | ||||
\(83\) | 4.51737i | 0.495845i | 0.968780 | + | 0.247923i | \(0.0797479\pi\) | ||||
−0.968780 | + | 0.247923i | \(0.920252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.70069 | − | 10.3785i | −0.618327 | − | 1.12571i | ||||
\(86\) | −2.12780 | + | 3.68547i | −0.229447 | + | 0.397414i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.37122i | 0.572574i | ||||||||
\(89\) | −1.68676 | + | 2.92155i | −0.178796 | + | 0.309684i | −0.941468 | − | 0.337101i | \(-0.890554\pi\) |
0.762672 | + | 0.646785i | \(0.223887\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0551029 | + | 0.0954410i | −0.00577635 | + | 0.0100049i | ||||
\(92\) | −3.67037 | + | 2.11909i | −0.382663 | + | 0.220930i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.62648 | −0.786612 | ||||||||
\(95\) | −8.06789 | − | 5.46893i | −0.827748 | − | 0.561100i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.1568 | + | 7.59611i | −1.33588 | + | 0.771268i | −0.986193 | − | 0.165600i | \(-0.947044\pi\) |
−0.349683 | + | 0.936868i | \(0.613711\pi\) | |||||||
\(98\) | 4.99053 | − | 2.88128i | 0.504119 | − | 0.291053i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.36782 | − | 5.29827i | 0.336782 | − | 0.529827i | ||||
\(101\) | 1.77068 | − | 3.06690i | 0.176189 | − | 0.305168i | −0.764383 | − | 0.644762i | \(-0.776956\pi\) |
0.940572 | + | 0.339594i | \(0.110290\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.6919i | 1.54617i | 0.634301 | + | 0.773086i | \(0.281288\pi\) | ||||
−0.634301 | + | 0.773086i | \(0.718712\pi\) | |||||||
\(104\) | 0.273207 | − | 0.473209i | 0.0267902 | − | 0.0464020i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.08007 | −0.687677 | ||||||||
\(107\) | 1.05731i | 0.102214i | 0.998693 | + | 0.0511071i | \(0.0162750\pi\) | ||||
−0.998693 | + | 0.0511071i | \(0.983725\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.37220 | − | 5.84081i | −0.322998 | − | 0.559449i | 0.658107 | − | 0.752924i | \(-0.271357\pi\) |
−0.981105 | + | 0.193476i | \(0.938024\pi\) | |||||||
\(110\) | −1.77608 | − | 3.23347i | −0.169342 | − | 0.308299i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.0430622 | + | 0.0248620i | −0.00406899 | + | 0.00234923i | ||||
\(113\) | 7.90091i | 0.743255i | 0.928382 | + | 0.371627i | \(0.121200\pi\) | ||||
−0.928382 | + | 0.371627i | \(0.878800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.91223 | − | 6.45453i | 0.364817 | − | 0.601888i | ||||
\(116\) | 5.48493 | + | 9.50018i | 0.509263 | + | 0.882069i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.77525 | − | 1.60229i | −0.255483 | − | 0.147503i | ||||
\(119\) | −1.50000 | − | 2.59808i | −0.137505 | − | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.34338 | −0.667580 | ||||||||
\(122\) | − | 3.02941i | − | 0.274270i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.55125 | + | 6.15095i | −0.318912 | + | 0.552371i | ||||
\(125\) | −0.714253 | + | 11.1575i | −0.0638847 | + | 0.997957i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.34074 | − | 4.23818i | −0.651385 | − | 0.376078i | 0.137601 | − | 0.990488i | \(-0.456061\pi\) |
−0.788987 | + | 0.614410i | \(0.789394\pi\) | |||||||
\(128\) | 6.32219 | − | 3.65012i | 0.558808 | − | 0.322628i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.00799675 | + | 0.375212i | −0.000701362 | + | 0.0329083i | ||||
\(131\) | 0.937193 | + | 1.62327i | 0.0818830 | + | 0.141825i | 0.904059 | − | 0.427408i | \(-0.140573\pi\) |
−0.822176 | + | 0.569234i | \(0.807240\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.07310 | − | 1.34171i | −0.179761 | − | 0.116341i | ||||
\(134\) | 3.48878 | 0.301385 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.43719 | + | 12.8816i | 0.637734 | + | 1.10459i | ||||
\(137\) | −10.7918 | − | 6.23068i | −0.922010 | − | 0.532323i | −0.0377341 | − | 0.999288i | \(-0.512014\pi\) |
−0.884276 | + | 0.466965i | \(0.845347\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.156620 | + | 0.271275i | −0.0132844 | + | 0.0230092i | −0.872591 | − | 0.488451i | \(-0.837562\pi\) |
0.859307 | + | 0.511460i | \(0.170895\pi\) | |||||||
\(140\) | 0.824458 | − | 1.36022i | 0.0696794 | − | 0.114960i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.88190 | + | 2.24122i | 0.325762 | + | 0.188079i | ||||
\(143\) | −0.322151 | − | 0.185994i | −0.0269397 | − | 0.0155536i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.7065 | − | 10.1262i | −1.38740 | − | 0.840935i | ||||
\(146\) | 3.71172 | − | 6.42889i | 0.307184 | − | 0.532059i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.03909 | + | 0.599919i | 0.0854127 | + | 0.0493130i | ||||
\(149\) | −2.18291 | − | 3.78091i | −0.178831 | − | 0.309744i | 0.762650 | − | 0.646812i | \(-0.223898\pi\) |
−0.941480 | + | 0.337068i | \(0.890565\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.197977 | 0.0161111 | 0.00805555 | − | 0.999968i | \(-0.497436\pi\) | ||||
0.00805555 | + | 0.999968i | \(0.497436\pi\) | |||||||
\(152\) | 10.2787 | + | 6.65239i | 0.833713 | + | 0.539580i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.467332 | − | 0.809443i | −0.0376587 | − | 0.0652268i | ||||
\(155\) | 0.269514 | − | 12.6457i | 0.0216478 | − | 1.01573i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.6572 | + | 7.88498i | −1.08996 | + | 0.629290i | −0.933566 | − | 0.358405i | \(-0.883321\pi\) |
−0.156395 | + | 0.987695i | \(0.549987\pi\) | |||||||
\(158\) | 4.95124 | + | 2.85860i | 0.393900 | + | 0.227418i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.59899 | + | 10.8872i | −0.521696 | + | 0.860712i | ||||
\(161\) | 0.956115 | − | 1.65604i | 0.0753524 | − | 0.130514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.18768i | 0.719635i | 0.933023 | + | 0.359817i | \(0.117161\pi\) | ||||
−0.933023 | + | 0.359817i | \(0.882839\pi\) | |||||||
\(164\) | −12.6188 | −0.985361 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.94875 | + | 3.37533i | 0.151252 | + | 0.261977i | ||||
\(167\) | 2.65888 | + | 1.53510i | 0.205750 | + | 0.118790i | 0.599335 | − | 0.800498i | \(-0.295432\pi\) |
−0.393585 | + | 0.919288i | \(0.628765\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.48108 | − | 11.2256i | −0.498545 | − | 0.863504i | ||||
\(170\) | −8.73669 | − | 5.29549i | −0.670073 | − | 0.406146i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 6.19320i | − | 0.472227i | ||||||
\(173\) | −9.01838 | + | 5.20676i | −0.685655 | + | 0.395863i | −0.801982 | − | 0.597348i | \(-0.796221\pi\) |
0.116328 | + | 0.993211i | \(0.462888\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.120685 | + | 2.83003i | −0.00912296 | + | 0.213930i | ||||
\(176\) | −0.0839190 | − | 0.145352i | −0.00632563 | − | 0.0109563i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.91061i | 0.218159i | ||||||||
\(179\) | −13.4432 | −1.00479 | −0.502397 | − | 0.864637i | \(-0.667549\pi\) | ||||
−0.502397 | + | 0.864637i | \(0.667549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.98108 | + | 6.89543i | −0.295911 | + | 0.512533i | −0.975196 | − | 0.221341i | \(-0.928957\pi\) |
0.679285 | + | 0.733874i | \(0.262290\pi\) | |||||||
\(182\) | 0.0950835i | 0.00704806i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.74054 | + | 8.21086i | −0.349477 | + | 0.605312i | ||||
\(185\) | −2.13626 | − | 0.0455294i | −0.157061 | − | 0.00334739i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.76954 | − | 5.06310i | 0.641292 | − | 0.370250i | ||||
\(188\) | 9.61189 | − | 5.54942i | 0.701019 | − | 0.404733i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.38749 | − | 0.605920i | −0.608493 | − | 0.0439580i | ||||
\(191\) | 14.0999 | 1.02023 | 0.510115 | − | 0.860106i | \(-0.329603\pi\) | ||||
0.510115 | + | 0.860106i | \(0.329603\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.44405 | − | 1.98842i | 0.247908 | − | 0.143130i | −0.370898 | − | 0.928674i | \(-0.620950\pi\) |
0.618806 | + | 0.785544i | \(0.287617\pi\) | |||||||
\(194\) | −6.55378 | + | 11.3515i | −0.470534 | + | 0.814989i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.19314 | + | 7.26273i | −0.299510 | + | 0.518767i | ||||
\(197\) | 18.3494i | 1.30734i | 0.756781 | + | 0.653669i | \(0.226771\pi\) | ||||
−0.756781 | + | 0.653669i | \(0.773229\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.803346 | + | 1.39144i | −0.0569477 | + | 0.0986363i | −0.893094 | − | 0.449870i | \(-0.851470\pi\) |
0.836146 | + | 0.548507i | \(0.184803\pi\) | |||||||
\(200\) | 0.598374 | − | 14.0316i | 0.0423114 | − | 0.992186i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 3.05542i | − | 0.214978i | ||||||
\(203\) | −4.28640 | − | 2.47475i | −0.300846 | − | 0.173694i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.6966 | − | 10.8189i | 1.37567 | − | 0.755627i | ||||
\(206\) | 6.76936 | + | 11.7249i | 0.471643 | + | 0.816910i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.0170742i | 0.00118388i | ||||||||
\(209\) | 4.52882 | − | 6.99754i | 0.313265 | − | 0.484030i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.04993 | + | 5.28263i | 0.209966 | + | 0.363671i | 0.951703 | − | 0.307019i | \(-0.0993314\pi\) |
−0.741738 | + | 0.670690i | \(0.765998\pi\) | |||||||
\(212\) | 8.92322 | − | 5.15182i | 0.612849 | − | 0.353829i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.456115 | + | 0.790014i | 0.0311794 | + | 0.0540042i | ||||
\(215\) | 5.30985 | + | 9.66695i | 0.362129 | + | 0.659280i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.20459i | − | 0.217542i | ||||||
\(218\) | −5.03934 | − | 2.90947i | −0.341307 | − | 0.197054i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.59128 | + | 2.78287i | 0.309544 | + | 0.187621i | ||||
\(221\) | −1.03014 | −0.0692946 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.9175 | − | 8.61263i | 0.998950 | − | 0.576744i | 0.0910127 | − | 0.995850i | \(-0.470990\pi\) |
0.907938 | + | 0.419106i | \(0.137656\pi\) | |||||||
\(224\) | −1.61274 | + | 2.79334i | −0.107755 | + | 0.186638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.40838 | + | 5.90348i | 0.226722 | + | 0.392694i | ||||
\(227\) | 1.18505i | 0.0786542i | 0.999226 | + | 0.0393271i | \(0.0125214\pi\) | ||||
−0.999226 | + | 0.0393271i | \(0.987479\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.24791 | −0.412873 | −0.206437 | − | 0.978460i | \(-0.566187\pi\) | ||||
−0.206437 | + | 0.978460i | \(0.566187\pi\) | |||||||
\(230\) | 0.138755 | − | 6.51046i | 0.00914924 | − | 0.429287i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 21.2525 | + | 12.2701i | 1.39530 | + | 0.805574i | ||||
\(233\) | 2.38752 | − | 1.37844i | 0.156412 | − | 0.0903043i | −0.419751 | − | 0.907639i | \(-0.637883\pi\) |
0.576163 | + | 0.817335i | \(0.304549\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2453 | + | 16.9030i | −0.668327 | + | 1.10263i | ||||
\(236\) | 4.66365 | 0.303578 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.24157 | − | 1.29417i | −0.145299 | − | 0.0838887i | ||||
\(239\) | 17.3055 | 1.11940 | 0.559701 | − | 0.828695i | \(-0.310916\pi\) | ||||
0.559701 | + | 0.828695i | \(0.310916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.39331 | − | 4.14533i | 0.154167 | − | 0.267024i | −0.778589 | − | 0.627535i | \(-0.784064\pi\) |
0.932755 | + | 0.360510i | \(0.117397\pi\) | |||||||
\(242\) | −5.48690 | + | 3.16786i | −0.352711 | + | 0.203638i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.20436 | + | 3.81806i | 0.141120 | + | 0.244426i | ||||
\(245\) | 0.318228 | − | 14.9314i | 0.0203308 | − | 0.953934i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.754923 | + | 0.386131i | −0.0480346 | + | 0.0245689i | ||||
\(248\) | 15.8888i | 1.00894i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.27956 | + | 8.64490i | 0.270663 | + | 0.546751i | ||||
\(251\) | −13.1240 | + | 22.7314i | −0.828377 | + | 1.43479i | 0.0709346 | + | 0.997481i | \(0.477402\pi\) |
−0.899311 | + | 0.437309i | \(0.855932\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.58979 | + | 3.22727i | 0.351427 | + | 0.202897i | ||||
\(254\) | −7.31324 | −0.458874 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.88594 | − | 13.6589i | 0.492871 | − | 0.853678i | ||||
\(257\) | 19.2695 | + | 11.1252i | 1.20200 | + | 0.693974i | 0.960999 | − | 0.276552i | \(-0.0891917\pi\) |
0.240999 | + | 0.970525i | \(0.422525\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.541356 | −0.0336382 | ||||||||
\(260\) | −0.262945 | − | 0.478710i | −0.0163072 | − | 0.0296883i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.40052 | + | 0.808593i | 0.0865246 | + | 0.0499550i | ||||
\(263\) | −7.63264 | + | 4.40671i | −0.470649 | + | 0.271729i | −0.716511 | − | 0.697576i | \(-0.754262\pi\) |
0.245863 | + | 0.969305i | \(0.420929\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.51122 | + | 15.6919i | −0.584269 | + | 0.963948i | ||||
\(266\) | −2.12780 | − | 0.108199i | −0.130464 | − | 0.00663409i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.39702 | + | 2.53862i | −0.268591 | + | 0.155071i | ||||
\(269\) | 2.38209 | + | 4.12590i | 0.145239 | + | 0.251561i | 0.929462 | − | 0.368918i | \(-0.120272\pi\) |
−0.784223 | + | 0.620479i | \(0.786938\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.75946 | − | 3.04748i | −0.106880 | − | 0.185121i | 0.807625 | − | 0.589696i | \(-0.200753\pi\) |
−0.914505 | + | 0.404576i | \(0.867419\pi\) | |||||||
\(272\) | −0.402520 | − | 0.232395i | −0.0244063 | − | 0.0140910i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.7514 | −0.649517 | ||||||||
\(275\) | −9.55246 | − | 0.407361i | −0.576035 | − | 0.0245648i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 32.7724i | − | 1.96910i | −0.175098 | − | 0.984551i | \(-0.556024\pi\) | ||
0.175098 | − | 0.984551i | \(-0.443976\pi\) | |||||||
\(278\) | 0.270258i | 0.0162090i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0758178 | − | 3.55741i | 0.00453098 | − | 0.212596i | ||||
\(281\) | 4.95997 | − | 8.59091i | 0.295887 | − | 0.512491i | −0.679304 | − | 0.733857i | \(-0.737718\pi\) |
0.975191 | + | 0.221366i | \(0.0710516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.14066 | + | 1.23591i | −0.127249 | + | 0.0734673i | −0.562273 | − | 0.826951i | \(-0.690073\pi\) |
0.435024 | + | 0.900419i | \(0.356740\pi\) | |||||||
\(284\) | −6.52330 | −0.387087 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.320945 | −0.0189779 | ||||||||
\(287\) | 4.93070 | − | 2.84674i | 0.291050 | − | 0.168038i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.52111 | − | 9.56285i | 0.324771 | − | 0.562520i | ||||
\(290\) | −16.8513 | − | 0.359146i | −0.989543 | − | 0.0210898i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.8034i | 0.632219i | ||||||||
\(293\) | − | 17.0284i | − | 0.994812i | −0.867518 | − | 0.497406i | \(-0.834286\pi\) | ||
0.867518 | − | 0.497406i | \(-0.165714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.27947 | + | 3.99846i | −0.423827 | + | 0.232799i | ||||
\(296\) | 2.68411 | 0.156011 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.26209 | − | 1.88337i | −0.188968 | − | 0.109101i | ||||
\(299\) | −0.328310 | − | 0.568650i | −0.0189867 | − | 0.0328859i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.39716 | + | 2.41995i | 0.0805310 | + | 0.139484i | ||||
\(302\) | 0.147926 | − | 0.0854052i | 0.00851220 | − | 0.00491452i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.382090 | − | 0.0194293i | −0.0219144 | − | 0.00111435i | ||||
\(305\) | −6.71425 | − | 4.06965i | −0.384457 | − | 0.233028i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.1686 | − | 10.4896i | 1.03694 | − | 0.598676i | 0.117972 | − | 0.993017i | \(-0.462361\pi\) |
0.918964 | + | 0.394341i | \(0.129027\pi\) | |||||||
\(308\) | 1.17799 | + | 0.680110i | 0.0671220 | + | 0.0387529i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.25386 | − | 9.56502i | −0.298399 | − | 0.543257i | ||||
\(311\) | 3.14805 | 0.178509 | 0.0892547 | − | 0.996009i | \(-0.471551\pi\) | ||||
0.0892547 | + | 0.996009i | \(0.471551\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.6459 | + | 6.14641i | 0.601742 | + | 0.347416i | 0.769726 | − | 0.638374i | \(-0.220393\pi\) |
−0.167985 | + | 0.985790i | \(0.553726\pi\) | |||||||
\(314\) | −6.80301 | + | 11.7832i | −0.383916 | + | 0.664962i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.32027 | −0.468052 | ||||||||
\(317\) | −9.92630 | − | 5.73095i | −0.557517 | − | 0.321882i | 0.194631 | − | 0.980876i | \(-0.437649\pi\) |
−0.752148 | + | 0.658994i | \(0.770982\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.35327 | − | 14.4683i | 0.467694 | − | 0.810069i | ||||
\(320\) | −0.225683 | + | 10.5892i | −0.0126160 | + | 0.591952i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 1.64984i | − | 0.0919417i | ||||||
\(323\) | 1.17223 | − | 23.0527i | 0.0652246 | − | 1.28269i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.820860 | + | 0.521776i | 0.0455331 | + | 0.0289429i | ||||
\(326\) | 3.96348 | + | 6.86495i | 0.219517 | + | 0.380214i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −24.4470 | + | 14.1145i | −1.34986 | + | 0.779343i | ||||
\(329\) | −2.50385 | + | 4.33680i | −0.138042 | + | 0.239095i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.85724 | 0.321943 | 0.160972 | − | 0.986959i | \(-0.448537\pi\) | ||||
0.160972 | + | 0.986959i | \(0.448537\pi\) | |||||||
\(332\) | −4.91213 | − | 2.83602i | −0.269588 | − | 0.155647i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.64892 | 0.144942 | ||||||||
\(335\) | 4.68676 | − | 7.73238i | 0.256065 | − | 0.422465i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.45644 | + | 4.30498i | −0.406178 | + | 0.234507i | −0.689146 | − | 0.724622i | \(-0.742014\pi\) |
0.282968 | + | 0.959129i | \(0.408681\pi\) | |||||||
\(338\) | −9.68520 | − | 5.59175i | −0.526805 | − | 0.304151i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.8644 | + | 0.316799i | 0.806134 | + | 0.0171808i | ||||
\(341\) | 10.8168 | 0.585760 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 7.74945i | − | 0.418431i | ||||||
\(344\) | −6.92730 | − | 11.9984i | −0.373495 | − | 0.646912i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.49230 | + | 7.78089i | −0.241507 | + | 0.418303i | ||||
\(347\) | −10.4704 | + | 6.04507i | −0.562079 | + | 0.324517i | −0.753980 | − | 0.656898i | \(-0.771868\pi\) |
0.191900 | + | 0.981414i | \(0.438535\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.9819 | −1.01608 | −0.508040 | − | 0.861333i | \(-0.669630\pi\) | ||||
−0.508040 | + | 0.861333i | \(0.669630\pi\) | |||||||
\(350\) | 1.13067 | + | 2.16663i | 0.0604369 | + | 0.115811i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.42863 | − | 5.44362i | −0.502548 | − | 0.290146i | ||||
\(353\) | 7.71759i | 0.410766i | 0.978682 | + | 0.205383i | \(0.0658440\pi\) | ||||
−0.978682 | + | 0.205383i | \(0.934156\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.1822 | − | 5.59287i | 0.540415 | − | 0.296839i | ||||
\(356\) | −2.11791 | − | 3.66833i | −0.112249 | − | 0.194421i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.0447 | + | 5.79929i | −0.530877 | + | 0.306502i | ||||
\(359\) | 3.51507 | + | 6.08828i | 0.185518 | + | 0.321327i | 0.943751 | − | 0.330657i | \(-0.107270\pi\) |
−0.758233 | + | 0.651984i | \(0.773937\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.78190 | − | 17.3333i | −0.409573 | − | 0.912277i | ||||
\(362\) | 6.86960i | 0.361058i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.0691877 | − | 0.119837i | −0.00362642 | − | 0.00628114i | ||||
\(365\) | −9.26246 | − | 16.8629i | −0.484819 | − | 0.882647i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.1945 | − | 16.8554i | −1.52394 | − | 0.879847i | −0.999598 | − | 0.0283394i | \(-0.990978\pi\) |
−0.524342 | − | 0.851508i | \(-0.675689\pi\) | |||||||
\(368\) | − | 0.296261i | − | 0.0154437i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.61584 | + | 0.887544i | −0.0840033 | + | 0.0461412i | ||||
\(371\) | −2.32446 | + | 4.02608i | −0.120680 | + | 0.209024i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0097i | 0.518281i | 0.965840 | + | 0.259141i | \(0.0834393\pi\) | ||||
−0.965840 | + | 0.259141i | \(0.916561\pi\) | |||||||
\(374\) | 4.36834 | − | 7.56619i | 0.225882 | − | 0.391239i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.4144 | − | 21.5024i | 0.640225 | − | 1.10890i | ||||
\(377\) | −1.47186 | + | 0.849780i | −0.0758047 | + | 0.0437659i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.8064 | 1.83925 | 0.919626 | − | 0.392796i | \(-0.128492\pi\) | ||||
0.919626 | + | 0.392796i | \(0.128492\pi\) | |||||||
\(380\) | 11.0119 | − | 5.33952i | 0.564899 | − | 0.273911i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.5353 | − | 6.08255i | 0.539032 | − | 0.311210i | ||||
\(383\) | 14.0725 | − | 8.12477i | 0.719072 | − | 0.415156i | −0.0953393 | − | 0.995445i | \(-0.530394\pi\) |
0.814411 | + | 0.580289i | \(0.197060\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.42182 | − | 0.0516153i | −0.123427 | − | 0.00263056i | ||||
\(386\) | 1.71558 | − | 2.97146i | 0.0873205 | − | 0.151244i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 19.0755i | − | 0.968411i | ||||||
\(389\) | 9.69280 | − | 16.7884i | 0.491445 | − | 0.851207i | −0.508507 | − | 0.861058i | \(-0.669802\pi\) |
0.999951 | + | 0.00985094i | \(0.00313570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.8744 | 0.903947 | ||||||||
\(392\) | 18.7607i | 0.947556i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.91574 | + | 13.7105i | 0.398789 | + | 0.690723i | ||||
\(395\) | 12.9871 | − | 7.13353i | 0.653451 | − | 0.358927i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.63682 | + | 2.67707i | −0.232716 | + | 0.134358i | −0.611824 | − | 0.790994i | \(-0.709564\pi\) |
0.379109 | + | 0.925352i | \(0.376231\pi\) | |||||||
\(398\) | 1.38622i | 0.0694851i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.203035 | + | 0.389063i | 0.0101518 | + | 0.0194531i | ||||
\(401\) | 4.16916 | + | 7.22120i | 0.208198 | + | 0.360609i | 0.951147 | − | 0.308739i | \(-0.0999068\pi\) |
−0.742949 | + | 0.669348i | \(0.766574\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.952965 | − | 0.550195i | −0.0474706 | − | 0.0274072i | ||||
\(404\) | 2.22328 | + | 3.85083i | 0.110612 | + | 0.191586i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.27034 | −0.211933 | ||||||||
\(407\) | − | 1.82729i | − | 0.0905755i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.6613 | + | 30.5903i | −0.873297 | + | 1.51259i | −0.0147313 | + | 0.999891i | \(0.504689\pi\) |
−0.858566 | + | 0.512703i | \(0.828644\pi\) | |||||||
\(410\) | 10.0499 | − | 16.5807i | 0.496331 | − | 0.818864i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.0632 | − | 9.85147i | −0.840646 | − | 0.485347i | ||||
\(413\) | −1.82229 | + | 1.05210i | −0.0896689 | + | 0.0517704i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.0988 | + | 0.215233i | 0.495733 | + | 0.0105654i | ||||
\(416\) | 0.553780 | + | 0.959176i | 0.0271513 | + | 0.0470274i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.365214 | − | 7.18219i | 0.0178632 | − | 0.351292i | ||||
\(419\) | 21.2453 | 1.03790 | 0.518949 | − | 0.854805i | \(-0.326323\pi\) | ||||
0.518949 | + | 0.854805i | \(0.326323\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.43719 | + | 12.8816i | 0.362467 | + | 0.627811i | 0.988366 | − | 0.152093i | \(-0.0486013\pi\) |
−0.625900 | + | 0.779904i | \(0.715268\pi\) | |||||||
\(422\) | 4.55775 | + | 2.63142i | 0.221868 | + | 0.128096i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.5250 | − | 19.9618i | 0.559702 | − | 0.969432i | ||||
\(425\) | −23.4734 | + | 12.2497i | −1.13863 | + | 0.594200i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.72268 | − | 0.994587i | −0.0833661 | − | 0.0481314i | ||||
\(428\) | −1.14971 | − | 0.663785i | −0.0555733 | − | 0.0320853i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.13770 | + | 4.93243i | 0.392435 | + | 0.237863i | ||||
\(431\) | −8.47590 | + | 14.6807i | −0.408270 | + | 0.707144i | −0.994696 | − | 0.102858i | \(-0.967201\pi\) |
0.586426 | + | 0.810003i | \(0.300534\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.0450 | − | 11.5730i | −0.963299 | − | 0.556161i | −0.0661122 | − | 0.997812i | \(-0.521060\pi\) |
−0.897187 | + | 0.441651i | \(0.854393\pi\) | |||||||
\(434\) | −1.38243 | − | 2.39444i | −0.0663587 | − | 0.114937i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.46832 | 0.405559 | ||||||||
\(437\) | 13.0990 | − | 6.69993i | 0.626610 | − | 0.320501i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.7729 | + | 29.0515i | 0.800525 | + | 1.38655i | 0.919271 | + | 0.393626i | \(0.128779\pi\) |
−0.118745 | + | 0.992925i | \(0.537887\pi\) | |||||||
\(440\) | 12.0077 | + | 0.255915i | 0.572444 | + | 0.0122003i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.769710 | + | 0.444392i | −0.0366114 | + | 0.0211376i | ||||
\(443\) | −27.1567 | − | 15.6789i | −1.29025 | − | 0.744929i | −0.311555 | − | 0.950228i | \(-0.600850\pi\) |
−0.978699 | + | 0.205299i | \(0.934183\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.45094 | + | 3.91005i | 0.305804 | + | 0.185354i | ||||
\(446\) | 7.43081 | − | 12.8705i | 0.351859 | − | 0.609438i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.68343i | 0.126780i | ||||||||
\(449\) | −16.0301 | −0.756509 | −0.378255 | − | 0.925702i | \(-0.623476\pi\) | ||||
−0.378255 | + | 0.925702i | \(0.623476\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.60888 | + | 16.6431i | 0.452465 | + | 0.783692i | ||||
\(452\) | −8.59136 | − | 4.96022i | −0.404104 | − | 0.233309i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.511217 | + | 0.885455i | 0.0239926 | + | 0.0415564i | ||||
\(455\) | 0.210739 | + | 0.127733i | 0.00987959 | + | 0.00598823i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.3980i | 0.720286i | 0.932897 | + | 0.360143i | \(0.117272\pi\) | ||||
−0.932897 | + | 0.360143i | \(0.882728\pi\) | |||||||
\(458\) | −4.66837 | + | 2.69529i | −0.218139 | + | 0.125943i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.56247 | + | 8.30630i | 0.212726 | + | 0.387283i | ||||
\(461\) | −2.90705 | − | 5.03517i | −0.135395 | − | 0.234511i | 0.790353 | − | 0.612651i | \(-0.209897\pi\) |
−0.925748 | + | 0.378140i | \(0.876564\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 32.6788i | − | 1.51871i | −0.650675 | − | 0.759356i | \(-0.725514\pi\) | ||
0.650675 | − | 0.759356i | \(-0.274486\pi\) | |||||||
\(464\) | −0.766826 | −0.0355990 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.18929 | − | 2.05991i | 0.0550927 | − | 0.0954234i | ||||
\(467\) | 6.59041i | 0.304968i | 0.988306 | + | 0.152484i | \(0.0487272\pi\) | ||||
−0.988306 | + | 0.152484i | \(0.951273\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.14540 | − | 1.98390i | 0.0528898 | − | 0.0916078i | ||||
\(470\) | −0.363369 | + | 17.0495i | −0.0167610 | + | 0.786433i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.03514 | − | 5.21644i | 0.415876 | − | 0.240106i | ||||
\(473\) | −8.16830 | + | 4.71597i | −0.375579 | + | 0.216841i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.6105 | + | 17.7757i | −0.578610 | + | 0.815604i | ||||
\(476\) | 3.76683 | 0.172652 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.9305 | − | 7.46545i | 0.591429 | − | 0.341462i | ||||
\(479\) | 18.4032 | − | 31.8753i | 0.840864 | − | 1.45642i | −0.0483016 | − | 0.998833i | \(-0.515381\pi\) |
0.889165 | − | 0.457586i | \(-0.151286\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0929453 | + | 0.160986i | −0.00423794 | + | 0.00734033i | ||||
\(482\) | − | 4.12980i | − | 0.188107i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.61021 | − | 7.98511i | 0.209555 | − | 0.362960i | ||||
\(485\) | 16.3547 | + | 29.7749i | 0.742628 | + | 1.35201i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.45475i | 0.111235i | 0.998452 | + | 0.0556176i | \(0.0177128\pi\) | ||||
−0.998452 | + | 0.0556176i | \(0.982287\pi\) | |||||||
\(488\) | 8.54125 | + | 4.93129i | 0.386644 | + | 0.223229i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.20350 | − | 11.2939i | −0.280246 | − | 0.510206i | ||||
\(491\) | 8.89716 | + | 15.4103i | 0.401523 | + | 0.695459i | 0.993910 | − | 0.110195i | \(-0.0351476\pi\) |
−0.592387 | + | 0.805654i | \(0.701814\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 46.2651i | − | 2.08367i | ||||||
\(494\) | −0.397498 | + | 0.614180i | −0.0178843 | + | 0.0276333i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.248243 | − | 0.429970i | −0.0111464 | − | 0.0193062i | ||||
\(497\) | 2.54894 | − | 1.47163i | 0.114335 | − | 0.0660116i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.6399 | − | 25.3570i | −0.655371 | − | 1.13514i | −0.981801 | − | 0.189915i | \(-0.939179\pi\) |
0.326429 | − | 0.945222i | \(-0.394155\pi\) | |||||||
\(500\) | −11.6841 | − | 7.78140i | −0.522530 | − | 0.347995i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.6462i | 1.01075i | ||||||||
\(503\) | 25.4939 | + | 14.7189i | 1.13672 | + | 0.656283i | 0.945615 | − | 0.325287i | \(-0.105461\pi\) |
0.191100 | + | 0.981571i | \(0.438794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.77188 | − | 4.10458i | −0.301345 | − | 0.182652i | ||||
\(506\) | 5.56885 | 0.247566 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.21710 | − | 5.32149i | 0.408943 | − | 0.236103i | ||||
\(509\) | −3.34723 | + | 5.79757i | −0.148363 | + | 0.256973i | −0.930623 | − | 0.365980i | \(-0.880734\pi\) |
0.782259 | + | 0.622953i | \(0.214067\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.43719 | − | 4.22134i | −0.107815 | − | 0.186741i | ||||
\(512\) | 0.992797i | 0.0438758i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 19.1973 | 0.846757 | ||||||||
\(515\) | 35.0803 | + | 0.747653i | 1.54582 | + | 0.0329455i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.6384 | − | 8.45150i | −0.643797 | − | 0.371696i | ||||
\(518\) | −0.404496 | + | 0.233536i | −0.0177725 | + | 0.0102610i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.04487 | − | 0.633318i | −0.0458206 | − | 0.0277728i | ||||
\(521\) | −20.0801 | −0.879724 | −0.439862 | − | 0.898065i | \(-0.644973\pi\) | ||||
−0.439862 | + | 0.898065i | \(0.644973\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.5615 | + | 18.2220i | 1.38009 | + | 0.796793i | 0.992169 | − | 0.124901i | \(-0.0398612\pi\) |
0.387918 | + | 0.921694i | \(0.373195\pi\) | |||||||
\(524\) | −2.35350 | −0.102813 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.80202 | + | 6.58530i | −0.165776 | + | 0.287133i | ||||
\(527\) | 25.9414 | − | 14.9773i | 1.13003 | − | 0.652421i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.80335 | − | 10.0517i | −0.252319 | − | 0.437030i | ||||
\(530\) | −0.337335 | + | 15.8279i | −0.0146529 | + | 0.687521i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.76047 | − | 1.41193i | 0.119681 | − | 0.0612151i | ||||
\(533\) | − | 1.95503i | − | 0.0846816i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.36369 | + | 0.0503764i | 0.102191 | + | 0.00217796i | ||||
\(536\) | −5.67906 | + | 9.83641i | −0.245298 | + | 0.424868i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.55975 | + | 2.05522i | 0.153472 | + | 0.0886069i | ||||
\(539\) | 12.7719 | 0.550124 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.31456 | − | 12.6692i | 0.314478 | − | 0.544691i | −0.664849 | − | 0.746978i | \(-0.731504\pi\) |
0.979326 | + | 0.202287i | \(0.0648373\pi\) | |||||||
\(542\) | −2.62930 | − | 1.51803i | −0.112938 | − | 0.0652049i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −30.1498 | −1.29266 | ||||||||
\(545\) | −13.2182 | + | 7.26046i | −0.566204 | + | 0.311004i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.6831 | + | 10.2093i | 0.756073 | + | 0.436519i | 0.827884 | − | 0.560899i | \(-0.189545\pi\) |
−0.0718112 | + | 0.997418i | \(0.522878\pi\) | |||||||
\(548\) | 13.5503 | − | 7.82329i | 0.578842 | − | 0.334194i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.31324 | + | 3.81647i | −0.311838 | + | 0.162735i | ||||
\(551\) | −17.3417 | − | 33.9047i | −0.738782 | − | 1.44439i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.25109 | − | 1.87702i | 0.138250 | − | 0.0798188i | ||||
\(554\) | −14.1377 | − | 24.4872i | −0.600653 | − | 1.04036i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.196654 | − | 0.340615i | −0.00833999 | − | 0.0144453i | ||||
\(557\) | −31.0728 | − | 17.9399i | −1.31660 | − | 0.760138i | −0.333418 | − | 0.942779i | \(-0.608202\pi\) |
−0.983180 | + | 0.182641i | \(0.941535\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.959512 | 0.0405830 | ||||||||
\(560\) | 0.0535287 | + | 0.0974526i | 0.00226200 | + | 0.00411812i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 8.55873i | − | 0.361028i | ||||||
\(563\) | − | 37.7708i | − | 1.59185i | −0.605395 | − | 0.795925i | \(-0.706985\pi\) | ||
0.605395 | − | 0.795925i | \(-0.293015\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.6630 | + | 0.376444i | 0.743086 | + | 0.0158371i | ||||
\(566\) | −1.06632 | + | 1.84692i | −0.0448208 | + | 0.0776319i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.6380 | + | 7.29653i | −0.530277 | + | 0.306155i | ||||
\(569\) | 28.0844 | 1.17736 | 0.588681 | − | 0.808366i | \(-0.299648\pi\) | ||||
0.588681 | + | 0.808366i | \(0.299648\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.6040 | 0.862253 | 0.431126 | − | 0.902292i | \(-0.358116\pi\) | ||||
0.431126 | + | 0.902292i | \(0.358116\pi\) | |||||||
\(572\) | 0.404496 | − | 0.233536i | 0.0169128 | − | 0.00976463i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.45611 | − | 4.25412i | 0.102516 | − | 0.177563i | ||||
\(575\) | −14.2431 | − | 9.05355i | −0.593978 | − | 0.377559i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.8371i | 1.82496i | 0.409119 | + | 0.912481i | \(0.365836\pi\) | ||||
−0.409119 | + | 0.912481i | \(0.634164\pi\) | |||||||
\(578\) | − | 9.52702i | − | 0.396272i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 21.4996 | − | 11.8093i | 0.892720 | − | 0.490352i | ||||
\(581\) | 2.55918 | 0.106173 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.5896 | − | 7.84597i | −0.562825 | − | 0.324947i | ||||
\(584\) | 12.0839 | + | 20.9300i | 0.500036 | + | 0.866088i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.34591 | − | 12.7235i | −0.303457 | − | 0.525602i | ||||
\(587\) | −32.8925 | + | 18.9905i | −1.35762 | + | 0.783821i | −0.989302 | − | 0.145880i | \(-0.953399\pi\) |
−0.368315 | + | 0.929701i | \(0.620065\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.3968 | − | 20.6996i | 0.552006 | − | 0.852914i | ||||
\(590\) | −3.71425 | + | 6.12790i | −0.152913 | + | 0.252282i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.0726355 | + | 0.0419361i | −0.00298530 | + | 0.00172356i | ||||
\(593\) | 4.65934 | + | 2.69007i | 0.191336 | + | 0.110468i | 0.592608 | − | 0.805491i | \(-0.298098\pi\) |
−0.401272 | + | 0.915959i | \(0.631432\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.87962 | + | 3.22955i | −0.241041 | + | 0.132399i | ||||
\(596\) | 5.48175 | 0.224541 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.490620 | − | 0.283260i | −0.0200630 | − | 0.0115834i | ||||
\(599\) | −11.2143 | + | 19.4237i | −0.458202 | + | 0.793629i | −0.998866 | − | 0.0476095i | \(-0.984840\pi\) |
0.540664 | + | 0.841239i | \(0.318173\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.5732 | −1.20632 | −0.603159 | − | 0.797621i | \(-0.706091\pi\) | ||||
−0.603159 | + | 0.797621i | \(0.706091\pi\) | |||||||
\(602\) | 2.08789 | + | 1.20544i | 0.0850960 | + | 0.0491302i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.124291 | + | 0.215278i | −0.00505731 | + | 0.00875952i | ||||
\(605\) | −0.349880 | + | 16.4166i | −0.0142247 | + | 0.667428i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.5915i | 0.998139i | 0.866562 | + | 0.499069i | \(0.166325\pi\) | ||||
−0.866562 | + | 0.499069i | \(0.833675\pi\) | |||||||
\(608\) | −22.0949 | + | 11.3012i | −0.896065 | + | 0.458323i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.77243 | − | 0.144338i | −0.274208 | − | 0.00584409i | ||||
\(611\) | 0.859772 | + | 1.48917i | 0.0347826 | + | 0.0602453i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.8856 | + | 14.9450i | −1.04551 | + | 0.603624i | −0.921388 | − | 0.388643i | \(-0.872944\pi\) |
−0.124119 | + | 0.992267i | \(0.539611\pi\) | |||||||
\(614\) | 9.05027 | − | 15.6755i | 0.365239 | − | 0.632613i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.04290 | 0.122602 | ||||||||
\(617\) | 35.2594 | + | 20.3570i | 1.41949 | + | 0.819544i | 0.996254 | − | 0.0864749i | \(-0.0275603\pi\) |
0.423238 | + | 0.906019i | \(0.360894\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.4784 | 1.14464 | 0.572322 | − | 0.820029i | \(-0.306043\pi\) | ||||
0.572322 | + | 0.820029i | \(0.306043\pi\) | |||||||
\(620\) | 13.5816 | + | 8.23210i | 0.545451 | + | 0.330609i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.35219 | − | 1.35804i | 0.0943143 | − | 0.0544524i | ||||
\(623\) | 1.65512 | + | 0.955582i | 0.0663109 | + | 0.0382846i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9092 | + | 2.12836i | 0.996369 | + | 0.0851345i | ||||
\(626\) | 10.6060 | 0.423902 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 19.8009i | − | 0.790141i | ||||||
\(629\) | −2.53014 | − | 4.38233i | −0.100883 | − | 0.174735i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.2101 | + | 36.7369i | −0.844359 | + | 1.46247i | 0.0418172 | + | 0.999125i | \(0.486685\pi\) |
−0.886176 | + | 0.463348i | \(0.846648\pi\) | |||||||
\(632\) | −16.1193 | + | 9.30649i | −0.641192 | + | 0.370192i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.88912 | −0.392747 | ||||||||
\(635\) | −9.82446 | + | 16.2087i | −0.389872 | + | 0.643224i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.12521 | − | 0.649643i | −0.0445826 | − | 0.0257398i | ||||
\(638\) | − | 14.4141i | − | 0.570659i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.85884 | − | 14.3076i | −0.310648 | − | 0.565556i | ||||
\(641\) | −14.7630 | − | 25.5702i | −0.583102 | − | 1.00996i | −0.995109 | − | 0.0987822i | \(-0.968505\pi\) |
0.412007 | − | 0.911181i | \(-0.364828\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.7036 | − | 10.7985i | 0.737597 | − | 0.425852i | −0.0835979 | − | 0.996500i | \(-0.526641\pi\) |
0.821195 | + | 0.570648i | \(0.193308\pi\) | |||||||
\(644\) | 1.20051 | + | 2.07934i | 0.0473066 | + | 0.0819374i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.06885 | − | 17.7305i | −0.356809 | − | 0.697596i | ||||
\(647\) | − | 12.6128i | − | 0.495861i | −0.968778 | − | 0.247930i | \(-0.920250\pi\) | ||
0.968778 | − | 0.247930i | \(-0.0797504\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.55125 | − | 6.15095i | −0.139399 | − | 0.241446i | ||||
\(650\) | 0.838428 | + | 0.0357544i | 0.0328858 | + | 0.00140240i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.99059 | − | 5.76807i | −0.391262 | − | 0.225895i | ||||
\(653\) | 26.6312i | 1.04216i | 0.853508 | + | 0.521080i | \(0.174471\pi\) | ||||
−0.853508 | + | 0.521080i | \(0.825529\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.67356 | − | 2.01781i | 0.143538 | − | 0.0788424i | ||||
\(656\) | 0.441045 | − | 0.763913i | 0.0172199 | − | 0.0298258i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.32055i | 0.168433i | ||||||||
\(659\) | −19.9772 | + | 34.6016i | −0.778202 | + | 1.34789i | 0.154775 | + | 0.987950i | \(0.450535\pi\) |
−0.932977 | + | 0.359936i | \(0.882798\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.76165 | − | 11.7115i | 0.262998 | − | 0.455526i | −0.704039 | − | 0.710161i | \(-0.748622\pi\) |
0.967037 | + | 0.254635i | \(0.0819555\pi\) | |||||||
\(662\) | 4.37648 | − | 2.52676i | 0.170097 | − | 0.0982053i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.6887 | −0.492418 | ||||||||
\(665\) | −3.09826 | + | 4.57062i | −0.120145 | + | 0.177241i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.5389 | − | 14.7449i | 0.988871 | − | 0.570925i | ||||
\(668\) | −3.33851 | + | 1.92749i | −0.129171 | + | 0.0745768i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.166225 | − | 7.79938i | 0.00642185 | − | 0.301316i | ||||
\(671\) | 3.35713 | − | 5.81471i | 0.129600 | − | 0.224475i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.4110i | 1.32645i | 0.748421 | + | 0.663224i | \(0.230812\pi\) | ||||
−0.748421 | + | 0.663224i | \(0.769188\pi\) | |||||||
\(674\) | −3.71425 | + | 6.43327i | −0.143068 | + | 0.247800i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.2754 | 0.625977 | ||||||||
\(677\) | − | 29.6650i | − | 1.14012i | −0.821604 | − | 0.570059i | \(-0.806920\pi\) | ||
0.821604 | − | 0.570059i | \(-0.193080\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.30335 | + | 7.45361i | 0.165147 | + | 0.286043i | ||||
\(680\) | 29.1519 | − | 16.0125i | 1.11793 | − | 0.614053i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.08217 | − | 4.66625i | 0.309482 | − | 0.178680i | ||||
\(683\) | 27.8978i | 1.06748i | 0.845648 | + | 0.533740i | \(0.179214\pi\) | ||||
−0.845648 | + | 0.533740i | \(0.820786\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.4432 | + | 23.8290i | −0.551848 | + | 0.910458i | ||||
\(686\) | −3.34304 | − | 5.79032i | −0.127638 | − | 0.221075i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.374923 | + | 0.216462i | 0.0142938 | + | 0.00825253i | ||||
\(689\) | 0.798172 | + | 1.38247i | 0.0304079 | + | 0.0526680i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −49.6386 | −1.88834 | −0.944170 | − | 0.329459i | \(-0.893134\pi\) | ||||
−0.944170 | + | 0.329459i | \(0.893134\pi\) | |||||||
\(692\) | − | 13.0753i | − | 0.497049i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.21558 | + | 9.03364i | −0.197981 | + | 0.342912i | ||||
\(695\) | 0.598988 | + | 0.363059i | 0.0227209 | + | 0.0137716i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.0893 | + | 26.6097i | 1.74576 | + | 1.00791i | ||||
\(698\) | −14.1831 | + | 8.18863i | −0.536839 | + | 0.309944i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.00157 | − | 1.90794i | −0.113449 | − | 0.0721132i | ||||
\(701\) | −24.9906 | − | 43.2851i | −0.943883 | − | 1.63485i | −0.757972 | − | 0.652287i | \(-0.773810\pi\) |
−0.185911 | − | 0.982567i | \(-0.559524\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.49682 | − | 2.26315i | −0.131885 | − | 0.0853562i | ||||
\(704\) | −9.05763 | −0.341372 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.32929 | + | 5.76651i | 0.125300 | + | 0.217025i | ||||
\(707\) | −1.73746 | − | 1.00312i | −0.0653440 | − | 0.0377264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.5938 | − | 21.8131i | 0.472971 | − | 0.819209i | −0.526551 | − | 0.850144i | \(-0.676515\pi\) |
0.999521 | + | 0.0309345i | \(0.00984834\pi\) | |||||||
\(710\) | 5.19533 | − | 8.57144i | 0.194977 | − | 0.321680i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.20628 | − | 4.73790i | −0.307543 | − | 0.177560i | ||||
\(713\) | 16.5353 | + | 9.54667i | 0.619253 | + | 0.357526i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.431150 | + | 0.711327i | −0.0161241 | + | 0.0266021i | ||||
\(716\) | 8.43972 | − | 14.6180i | 0.315407 | − | 0.546301i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.25285 | + | 3.03274i | 0.196035 | + | 0.113181i | ||||
\(719\) | −8.58777 | − | 14.8745i | −0.320270 | − | 0.554724i | 0.660274 | − | 0.751025i | \(-0.270440\pi\) |
−0.980544 | + | 0.196301i | \(0.937107\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.88979 | 0.331073 | ||||||||
\(722\) | −13.2920 | − | 9.59421i | −0.494676 | − | 0.357060i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.99868 | − | 8.65796i | −0.185774 | − | 0.321771i | ||||
\(725\) | −23.4337 | + | 36.8660i | −0.870306 | + | 1.36917i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.914981 | − | 0.528264i | 0.0339348 | − | 0.0195922i | −0.482937 | − | 0.875655i | \(-0.660430\pi\) |
0.516871 | + | 0.856063i | \(0.327097\pi\) | |||||||
\(728\) | −0.268082 | − | 0.154777i | −0.00993579 | − | 0.00573643i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14.1953 | − | 8.60409i | −0.525393 | − | 0.318452i | ||||
\(731\) | −13.0598 | + | 22.6203i | −0.483035 | + | 0.836641i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.5025i | 0.757277i | 0.925545 | + | 0.378639i | \(0.123608\pi\) | ||||
−0.925545 | + | 0.378639i | \(0.876392\pi\) | |||||||
\(734\) | −29.0851 | −1.07355 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.60888 | − | 16.6431i | −0.354188 | − | 0.613472i | ||||
\(737\) | 6.69644 | + | 3.86619i | 0.246666 | + | 0.142413i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.4548 | + | 21.5723i | 0.458157 | + | 0.793551i | 0.998864 | − | 0.0476601i | \(-0.0151764\pi\) |
−0.540707 | + | 0.841211i | \(0.681843\pi\) | |||||||
\(740\) | 1.39066 | − | 2.29436i | 0.0511218 | − | 0.0843425i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.01100i | 0.147248i | ||||||||
\(743\) | −11.4812 | + | 6.62867i | −0.421204 | + | 0.243182i | −0.695592 | − | 0.718437i | \(-0.744858\pi\) |
0.274388 | + | 0.961619i | \(0.411525\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.55645 | + | 4.69988i | −0.313484 | + | 0.172190i | ||||
\(746\) | 4.31808 | + | 7.47913i | 0.158096 | + | 0.273830i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.7145i | 0.464889i | ||||||||
\(749\) | 0.598988 | 0.0218866 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.4183 | + | 21.5091i | −0.453149 | + | 0.784877i | −0.998580 | − | 0.0532786i | \(-0.983033\pi\) |
0.545430 | + | 0.838156i | \(0.316366\pi\) | |||||||
\(752\) | 0.775843i | 0.0282921i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.733174 | + | 1.26989i | −0.0267006 | + | 0.0462468i | ||||
\(755\) | 0.00943273 | − | 0.442589i | 0.000343292 | − | 0.0161075i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.9726 | + | 24.2329i | −1.52552 | + | 0.880760i | −0.525980 | + | 0.850497i | \(0.676301\pi\) |
−0.999542 | + | 0.0302631i | \(0.990365\pi\) | |||||||
\(758\) | 26.7542 | − | 15.4465i | 0.971756 | − | 0.561044i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 15.3616 | − | 22.6617i | 0.557222 | − | 0.822027i | ||||
\(761\) | −40.3726 | −1.46351 | −0.731753 | − | 0.681570i | \(-0.761298\pi\) | ||||
−0.731753 | + | 0.681570i | \(0.761298\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.30894 | + | 1.91042i | −0.119792 | + | 0.0691617i | ||||
\(764\) | −8.85195 | + | 15.3320i | −0.320252 | + | 0.554693i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.00989 | − | 12.1415i | 0.253278 | − | 0.438690i | ||||
\(767\) | 0.722538i | 0.0260893i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.4772 | + | 38.9317i | −0.810550 | + | 1.40391i | 0.101930 | + | 0.994792i | \(0.467498\pi\) |
−0.912480 | + | 0.409121i | \(0.865835\pi\) | |||||||
\(770\) | −1.83182 | + | 1.00618i | −0.0660144 | + | 0.0362603i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.99337i | 0.179715i | ||||||||
\(773\) | 3.19256 | + | 1.84323i | 0.114828 | + | 0.0662962i | 0.556314 | − | 0.830972i | \(-0.312215\pi\) |
−0.441486 | + | 0.897268i | \(0.645548\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.2574 | − | 1.20503i | −1.01504 | − | 0.0432859i | ||||
\(776\) | −21.3365 | − | 36.9560i | −0.765937 | − | 1.32664i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 16.7255i | − | 0.599639i | ||||||
\(779\) | 43.7501 | + | 2.22469i | 1.56751 | + | 0.0797078i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.96733 | + | 8.60367i | 0.177745 | + | 0.307864i | ||||
\(782\) | 13.3556 | − | 7.71084i | 0.477594 | − | 0.275739i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.293113 | − | 0.507687i | −0.0104683 | − | 0.0181317i | ||||
\(785\) | 16.9766 | + | 30.9071i | 0.605922 | + | 1.10312i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 45.7141i | − | 1.62953i | −0.579790 | − | 0.814766i | \(-0.696865\pi\) | ||
0.579790 | − | 0.814766i | \(-0.303135\pi\) | |||||||
\(788\) | −19.9529 | − | 11.5198i | −0.710793 | − | 0.410376i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.62648 | − | 10.9326i | 0.235760 | − | 0.388965i | ||||
\(791\) | 4.47602 | 0.159149 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.591531 | + | 0.341521i | −0.0210059 | + | 0.0121278i | ||||
\(794\) | −2.30973 | + | 4.00056i | −0.0819691 | + | 0.141975i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.00869 | − | 1.74710i | −0.0357520 | − | 0.0619243i | ||||
\(797\) | − | 30.3378i | − | 1.07462i | −0.843385 | − | 0.537310i | \(-0.819441\pi\) | ||
0.843385 | − | 0.537310i | \(-0.180559\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46.8091 | −1.65599 | ||||||||
\(800\) | 24.0247 | + | 15.2712i | 0.849401 | + | 0.539917i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.23031 | + | 3.59707i | 0.220000 | + | 0.127017i | ||||
\(803\) | 14.2487 | − | 8.22650i | 0.502826 | − | 0.290307i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.65662 | − | 2.21635i | −0.128879 | − | 0.0781162i | ||||
\(806\) | −0.949395 | −0.0334410 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.61456 | + | 4.97362i | 0.303059 | + | 0.174971i | ||||
\(809\) | 34.5585 | 1.21501 | 0.607506 | − | 0.794315i | \(-0.292170\pi\) | ||||
0.607506 | + | 0.794315i | \(0.292170\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.6377 | + | 28.8173i | −0.584229 | + | 1.01191i | 0.410742 | + | 0.911751i | \(0.365270\pi\) |
−0.994971 | + | 0.100162i | \(0.968064\pi\) | |||||||
\(812\) | 5.38204 | − | 3.10732i | 0.188873 | − | 0.109046i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.788277 | − | 1.36534i | −0.0276291 | − | 0.0478550i | ||||
\(815\) | 20.5396 | + | 0.437753i | 0.719472 | + | 0.0153338i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.09186 | + | 21.4722i | −0.0381994 | + | 0.751218i | ||||
\(818\) | 30.4757i | 1.06556i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.601230 | + | 28.2100i | −0.0209959 | + | 0.985137i | ||||
\(821\) | 6.35063 | − | 10.9996i | 0.221638 | − | 0.383889i | −0.733667 | − | 0.679509i | \(-0.762193\pi\) |
0.955306 | + | 0.295620i | \(0.0955262\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.4002 | + | 6.00454i | 0.362527 | + | 0.209305i | 0.670189 | − | 0.742191i | \(-0.266213\pi\) |
−0.307662 | + | 0.951496i | \(0.599547\pi\) | |||||||
\(824\) | −44.0767 | −1.53549 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.907731 | + | 1.57224i | −0.0315840 | + | 0.0547051i | ||||
\(827\) | −7.40057 | − | 4.27272i | −0.257343 | − | 0.148577i | 0.365779 | − | 0.930702i | \(-0.380803\pi\) |
−0.623122 | + | 0.782125i | \(0.714136\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.1042 | 0.941369 | 0.470685 | − | 0.882302i | \(-0.344007\pi\) | ||||
0.470685 | + | 0.882302i | \(0.344007\pi\) | |||||||
\(830\) | 7.63861 | − | 4.19573i | 0.265140 | − | 0.145636i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.797985 | + | 0.460717i | 0.0276652 | + | 0.0159725i | ||||
\(833\) | 30.6303 | − | 17.6844i | 1.06128 | − | 0.612729i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.55850 | − | 5.87094i | 0.123147 | − | 0.203172i | ||||
\(836\) | 4.76584 | + | 9.31767i | 0.164830 | + | 0.322258i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.8743 | − | 9.16500i | 0.548367 | − | 0.316600i | ||||
\(839\) | 18.2190 | + | 31.5562i | 0.628989 | + | 1.08944i | 0.987755 | + | 0.156013i | \(0.0498642\pi\) |
−0.358766 | + | 0.933427i | \(0.616802\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.6649 | − | 40.9887i | −0.816029 | − | 1.41340i | ||||
\(842\) | 11.1140 | + | 6.41667i | 0.383014 | + | 0.221133i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.65903 | −0.263635 | ||||||||
\(845\) | −25.4042 | + | 13.9540i | −0.873931 | + | 0.480032i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.16017i | 0.142945i | ||||||||
\(848\) | 0.720256i | 0.0247337i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.2547 | + | 19.2791i | −0.420331 | + | 0.661267i | ||||
\(851\) | 1.61274 | − | 2.79334i | 0.0552838 | − | 0.0957544i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.8890 | + | 9.17354i | −0.544030 | + | 0.314096i | −0.746711 | − | 0.665149i | \(-0.768368\pi\) |
0.202680 | + | 0.979245i | \(0.435035\pi\) | |||||||
\(854\) | −1.71622 | −0.0587279 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.96986 | −0.101508 | ||||||||
\(857\) | −6.80508 | + | 3.92892i | −0.232457 | + | 0.134209i | −0.611705 | − | 0.791086i | \(-0.709516\pi\) |
0.379248 | + | 0.925295i | \(0.376183\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.1511 | + | 29.7066i | −0.585188 | + | 1.01358i | 0.409664 | + | 0.912237i | \(0.365646\pi\) |
−0.994852 | + | 0.101339i | \(0.967687\pi\) | |||||||
\(860\) | −13.8453 | − | 0.295079i | −0.472120 | − | 0.0100621i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.6257i | 0.498153i | ||||||||
\(863\) | 35.9451i | 1.22359i | 0.791018 | + | 0.611793i | \(0.209551\pi\) | ||||
−0.791018 | + | 0.611793i | \(0.790449\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.2103 | + | 20.4092i | 0.381163 | + | 0.693934i | ||||
\(866\) | −19.9699 | −0.678604 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.48463 | + | 2.01185i | 0.118276 | + | 0.0682868i | ||||
\(869\) | 6.33568 | + | 10.9737i | 0.214923 | + | 0.372258i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.393308 | − | 0.681229i | −0.0133267 | − | 0.0230826i | ||||
\(872\) | 16.4061 | − | 9.47209i | 0.555582 | − | 0.320765i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.89716 | − | 10.6569i | 0.233300 | − | 0.360475i | ||||
\(875\) | 6.32094 | + | 0.404638i | 0.213687 | + | 0.0136793i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.8685 | − | 12.6258i | 0.738448 | − | 0.426343i | −0.0830567 | − | 0.996545i | \(-0.526468\pi\) |
0.821505 | + | 0.570202i | \(0.193135\pi\) | |||||||
\(878\) | 25.0651 | + | 14.4713i | 0.845905 | + | 0.488383i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.328941 | + | 0.180681i | −0.0110886 | + | 0.00609074i | ||||
\(881\) | −17.7796 | −0.599010 | −0.299505 | − | 0.954095i | \(-0.596821\pi\) | ||||
−0.299505 | + | 0.954095i | \(0.596821\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.54146 | − | 3.77671i | −0.220138 | − | 0.127096i | 0.385876 | − | 0.922550i | \(-0.373899\pi\) |
−0.606014 | + | 0.795454i | \(0.707232\pi\) | |||||||
\(884\) | 0.646726 | − | 1.12016i | 0.0217517 | − | 0.0376751i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.0550 | −0.908930 | ||||||||
\(887\) | 14.0648 | + | 8.12030i | 0.472249 | + | 0.272653i | 0.717181 | − | 0.696887i | \(-0.245432\pi\) |
−0.244932 | + | 0.969540i | \(0.578766\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.40101 | + | 4.15867i | −0.0805273 | + | 0.139477i | ||||
\(890\) | 6.50684 | + | 0.138678i | 0.218110 | + | 0.00464849i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.6282i | 0.724165i | ||||||||
\(893\) | −34.3034 | + | 17.5456i | −1.14792 | + | 0.587142i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.640512 | + | 30.0532i | −0.0214100 | + | 1.00457i | ||||
\(896\) | −2.06787 | − | 3.58165i | −0.0690825 | − | 0.119654i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.9776 | + | 6.91525i | −0.399697 | + | 0.230765i | ||||
\(899\) | 24.7101 | − | 42.7991i | 0.824127 | − | 1.42743i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.4553 | −1.44771 | ||||||||
\(902\) | 14.3593 | + | 8.29036i | 0.478113 | + | 0.276039i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.1927 | −0.738118 | ||||||||
\(905\) | 15.2255 | + | 9.22848i | 0.506112 | + | 0.306765i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.8080 | − | 9.12675i | 0.524896 | − | 0.303049i | −0.214040 | − | 0.976825i | \(-0.568662\pi\) |
0.738935 | + | 0.673776i | \(0.235329\pi\) | |||||||
\(908\) | −1.28861 | − | 0.743977i | −0.0427639 | − | 0.0246897i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.212565 | + | 0.00453032i | 0.00704646 | + | 0.000150179i | ||||
\(911\) | −15.9019 | −0.526853 | −0.263426 | − | 0.964679i | \(-0.584853\pi\) | ||||
−0.263426 | + | 0.964679i | \(0.584853\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.63824i | 0.285884i | ||||||||
\(914\) | 6.64254 | + | 11.5052i | 0.219716 | + | 0.380558i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.92246 | − | 6.79390i | 0.129602 | − | 0.224477i | ||||
\(917\) | 0.919612 | − | 0.530939i | 0.0303683 | − | 0.0175331i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.0748 | 0.992075 | 0.496038 | − | 0.868301i | \(-0.334788\pi\) | ||||
0.496038 | + | 0.868301i | \(0.334788\pi\) | |||||||
\(920\) | 18.1300 | + | 10.9890i | 0.597728 | + | 0.362296i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.34425 | − | 2.50815i | −0.143070 | − | 0.0826016i | ||||
\(923\) | − | 1.01065i | − | 0.0332661i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.203567 | + | 4.77357i | −0.00669325 | + | 0.156954i | ||||
\(926\) | −14.0973 | − | 24.4173i | −0.463267 | − | 0.802402i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −43.0780 | + | 24.8711i | −1.41410 | + | 0.816433i | ||||
\(929\) | 18.4221 | + | 31.9081i | 0.604410 | + | 1.04687i | 0.992144 | + | 0.125098i | \(0.0399245\pi\) |
−0.387734 | + | 0.921771i | \(0.626742\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.8183 | − | 24.4411i | 0.518424 | − | 0.801025i | ||||
\(932\) | 3.46155i | 0.113387i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.84304 | + | 4.92429i | 0.0930272 | + | 0.161128i | ||||
\(935\) | −10.9010 | − | 19.8461i | −0.356502 | − | 0.649036i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.4401 | − | 21.6160i | −1.22311 | − | 0.706165i | −0.257533 | − | 0.966270i | \(-0.582910\pi\) |
−0.965580 | + | 0.260105i | \(0.916243\pi\) | |||||||
\(938\) | − | 1.97646i | − | 0.0645338i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −11.9481 | − | 21.7524i | −0.389704 | − | 0.709484i | ||||
\(941\) | −10.1601 | + | 17.5979i | −0.331211 | + | 0.573674i | −0.982750 | − | 0.184941i | \(-0.940790\pi\) |
0.651539 | + | 0.758615i | \(0.274124\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.9225i | 1.10467i | ||||||||
\(944\) | −0.163001 | + | 0.282327i | −0.00530525 | + | 0.00918896i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.06885 | + | 7.04745i | −0.132290 | + | 0.229133i | ||||
\(947\) | −18.6239 | + | 10.7525i | −0.605195 | + | 0.349409i | −0.771083 | − | 0.636735i | \(-0.780284\pi\) |
0.165888 | + | 0.986145i | \(0.446951\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.67376 | −0.0543327 | ||||||||
\(950\) | −1.75420 | + | 18.7219i | −0.0569137 | + | 0.607418i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.29768 | − | 4.21332i | 0.236519 | − | 0.136554i | ||||
\(953\) | −15.3547 | + | 8.86503i | −0.497387 | + | 0.287166i | −0.727634 | − | 0.685966i | \(-0.759380\pi\) |
0.230247 | + | 0.973132i | \(0.426047\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.671797 | − | 31.5211i | 0.0217388 | − | 1.02000i | ||||
\(956\) | −10.8645 | + | 18.8179i | −0.351383 | + | 0.608613i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 31.7559i | − | 1.02599i | ||||||
\(959\) | −3.52980 | + | 6.11379i | −0.113983 | + | 0.197425i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.997355 | 0.0321727 | ||||||||
\(962\) | 0.160383i | 0.00517095i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.00506 | + | 5.20491i | 0.0967864 | + | 0.167639i | ||||
\(965\) | −4.28115 | − | 7.79413i | −0.137815 | − | 0.250902i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.8239 | − | 6.82652i | 0.380230 | − | 0.219526i | −0.297688 | − | 0.954663i | \(-0.596216\pi\) |
0.677919 | + | 0.735137i | \(0.262882\pi\) | |||||||
\(968\) | − | 20.6267i | − | 0.662966i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 25.0647 | + | 15.1922i | 0.804778 | + | 0.487793i | ||||
\(971\) | 13.9798 | + | 24.2136i | 0.448632 | + | 0.777053i | 0.998297 | − | 0.0583319i | \(-0.0185782\pi\) |
−0.549666 | + | 0.835385i | \(0.685245\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.153682 | + | 0.0887286i | 0.00492683 | + | 0.00284451i | ||||
\(974\) | 1.05895 | + | 1.83416i | 0.0339311 | + | 0.0587704i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.308182 | −0.00986468 | ||||||||
\(977\) | 17.8540i | 0.571200i | 0.958349 | + | 0.285600i | \(0.0921929\pi\) | ||||
−0.958349 | + | 0.285600i | \(0.907807\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.22547 | + | 5.58668i | −0.103086 | + | 0.178551i | ||||
\(980\) | 16.0365 | + | 9.72006i | 0.512267 | + | 0.310496i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.2957 | + | 7.67630i | 0.424284 | + | 0.244961i | ||||
\(983\) | 42.4736 | − | 24.5222i | 1.35470 | − | 0.782136i | 0.365795 | − | 0.930695i | \(-0.380797\pi\) |
0.988903 | + | 0.148559i | \(0.0474636\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.0211 | + | 0.874268i | 1.30704 | + | 0.0278565i | ||||
\(986\) | −19.9583 | − | 34.5688i | −0.635602 | − | 1.10089i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.0540692 | − | 1.06331i | 0.00172017 | − | 0.0338284i | ||||
\(989\) | −16.6489 | −0.529405 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.5337 | + | 21.7089i | 0.398145 | + | 0.689607i | 0.993497 | − | 0.113858i | \(-0.0363209\pi\) |
−0.595352 | + | 0.803465i | \(0.702988\pi\) | |||||||
\(992\) | −27.8911 | − | 16.1029i | −0.885543 | − | 0.511269i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.26969 | − | 2.19917i | 0.0402722 | − | 0.0697536i | ||||
\(995\) | 3.07236 | + | 1.86222i | 0.0974005 | + | 0.0590365i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.0000 | + | 15.0111i | 0.823427 | + | 0.475406i | 0.851597 | − | 0.524197i | \(-0.175635\pi\) |
−0.0281699 | + | 0.999603i | \(0.508968\pi\) | |||||||
\(998\) | −21.8776 | − | 12.6310i | −0.692522 | − | 0.399828i | ||||
\(999\) | 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 | 855.2.be.d.64.5 | 12 | ||
3.2 | odd | 2 | 95.2.i.b.64.2 | yes | 12 | ||
5.4 | even | 2 | inner | 855.2.be.d.64.2 | 12 | ||
15.2 | even | 4 | 475.2.e.g.26.2 | 12 | |||
15.8 | even | 4 | 475.2.e.g.26.5 | 12 | |||
15.14 | odd | 2 | 95.2.i.b.64.5 | yes | 12 | ||
19.11 | even | 3 | inner | 855.2.be.d.334.2 | 12 | ||
57.11 | odd | 6 | 95.2.i.b.49.5 | yes | 12 | ||
57.26 | odd | 6 | 1805.2.b.f.1084.2 | 6 | |||
57.50 | even | 6 | 1805.2.b.g.1084.5 | 6 | |||
95.49 | even | 6 | inner | 855.2.be.d.334.5 | 12 | ||
285.68 | even | 12 | 475.2.e.g.201.5 | 12 | |||
285.83 | even | 12 | 9025.2.a.bu.1.2 | 6 | |||
285.107 | odd | 12 | 9025.2.a.bt.1.2 | 6 | |||
285.164 | even | 6 | 1805.2.b.g.1084.2 | 6 | |||
285.182 | even | 12 | 475.2.e.g.201.2 | 12 | |||
285.197 | even | 12 | 9025.2.a.bu.1.5 | 6 | |||
285.239 | odd | 6 | 95.2.i.b.49.2 | ✓ | 12 | ||
285.254 | odd | 6 | 1805.2.b.f.1084.5 | 6 | |||
285.278 | odd | 12 | 9025.2.a.bt.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.i.b.49.2 | ✓ | 12 | 285.239 | odd | 6 | ||
95.2.i.b.49.5 | yes | 12 | 57.11 | odd | 6 | ||
95.2.i.b.64.2 | yes | 12 | 3.2 | odd | 2 | ||
95.2.i.b.64.5 | yes | 12 | 15.14 | odd | 2 | ||
475.2.e.g.26.2 | 12 | 15.2 | even | 4 | |||
475.2.e.g.26.5 | 12 | 15.8 | even | 4 | |||
475.2.e.g.201.2 | 12 | 285.182 | even | 12 | |||
475.2.e.g.201.5 | 12 | 285.68 | even | 12 | |||
855.2.be.d.64.2 | 12 | 5.4 | even | 2 | inner | ||
855.2.be.d.64.5 | 12 | 1.1 | even | 1 | trivial | ||
855.2.be.d.334.2 | 12 | 19.11 | even | 3 | inner | ||
855.2.be.d.334.5 | 12 | 95.49 | even | 6 | inner | ||
1805.2.b.f.1084.2 | 6 | 57.26 | odd | 6 | |||
1805.2.b.f.1084.5 | 6 | 285.254 | odd | 6 | |||
1805.2.b.g.1084.2 | 6 | 285.164 | even | 6 | |||
1805.2.b.g.1084.5 | 6 | 57.50 | even | 6 | |||
9025.2.a.bt.1.2 | 6 | 285.107 | odd | 12 | |||
9025.2.a.bt.1.5 | 6 | 285.278 | odd | 12 | |||
9025.2.a.bu.1.2 | 6 | 285.83 | even | 12 | |||
9025.2.a.bu.1.5 | 6 | 285.197 | even | 12 |