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 | 64.2 | ||
Root | \(-1.00376 + 0.579521i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.64 |
Dual form | 855.2.be.d.334.2 |
$q$-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 | −0.740342 | − | 0.672231i | \(-0.765336\pi\) |
0.211998 | + | 0.977270i | \(0.432003\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.627804 | + | 1.08739i | −0.313902 | + | 0.543695i | ||||
\(5\) | −1.95987 | − | 1.07652i | −0.876483 | − | 0.481433i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.566520i | 0.214124i | 0.994252 | + | 0.107062i | \(0.0341444\pi\) | ||||
−0.994252 | + | 0.107062i | \(0.965856\pi\) | |||||||
\(8\) | − | 2.80888i | − | 0.993088i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.92880 | − | 0.0411078i | 0.609940 | − | 0.0129994i | ||||
\(11\) | 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 | 0.523180 | − | 0.852222i | \(-0.324745\pi\) |
−0.476456 | + | 0.879199i | \(0.658079\pi\) | |||||||
\(14\) | −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 | −0.939418 | − | 0.342774i | \(-0.888633\pi\) |
−0.172858 | + | 0.984947i | \(0.555300\pi\) | |||||||
\(18\) | 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 | 0.163254 | − | 0.986584i | \(-0.447801\pi\) |
−0.772780 | + | 0.634674i | \(0.781134\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.68222 | + | 4.21968i | 0.536444 | + | 0.843936i | ||||
\(26\) | −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 | ||||
\(35\) | 0.609869 | − | 1.11031i | 0.103087 | − | 0.187676i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.955582i | 0.157097i | 0.996910 | + | 0.0785484i | \(0.0250285\pi\) | ||||
−0.996910 | + | 0.0785484i | \(0.974971\pi\) | |||||||
\(38\) | −0.190988 | + | 3.75592i | −0.0309824 | + | 0.609291i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.02381 | + | 5.50505i | −0.478106 | + | 0.870425i | ||||
\(41\) | 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 | −0.137583 | − | 0.990490i | \(-0.543934\pi\) |
0.788998 | + | 0.614396i | \(0.210600\pi\) | |||||||
\(44\) | −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 | 0.940536 | − | 0.339694i | \(-0.110324\pi\) |
0.176084 | + | 0.984375i | \(0.443657\pi\) | |||||||
\(48\) | 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 | 0.901114 | − | 0.433581i | \(-0.142750\pi\) |
0.0750646 | + | 0.997179i | \(0.476084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.74773 | − | 2.05855i | −0.505344 | − | 0.277575i | ||||
\(56\) | 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 | 0.270594 | − | 0.962693i | \(-0.412780\pi\) |
−0.698420 | + | 0.715688i | \(0.746113\pi\) | |||||||
\(68\) | − | 6.64906i | − | 0.806318i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0232884 | + | 1.09270i | 0.00278349 | + | 0.130603i | ||||
\(71\) | 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 | −0.868051 | − | 0.496475i | \(-0.834627\pi\) |
−0.00406505 | + | 0.999992i | \(0.501294\pi\) | |||||||
\(74\) | −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 | \(0.711742\pi\) | |||||||
\(80\) | 0.00418190 | + | 0.196217i | 0.000467551 | + | 0.0219377i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.50921 | − | 4.33544i | −0.829253 | − | 0.478770i | ||||
\(83\) | − | 4.51737i | − | 0.495845i | −0.968780 | − | 0.247923i | \(-0.920252\pi\) | ||
0.968780 | − | 0.247923i | \(-0.0797479\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.8384 | − | 0.252307i | 1.28405 | − | 0.0273666i | ||||
\(86\) | −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 | ||||||||
\(95\) | −8.58103 | + | 4.62233i | −0.880395 | + | 0.474241i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.1568 | − | 7.59611i | 1.33588 | − | 0.771268i | 0.349683 | − | 0.936868i | \(-0.386289\pi\) |
0.986193 | + | 0.165600i | \(0.0529561\pi\) | |||||||
\(98\) | −4.99053 | + | 2.88128i | −0.504119 | + | 0.291053i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.27234 | + | 0.267482i | −0.627234 | + | 0.0267482i | ||||
\(101\) | 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 | \(-0.718712\pi\) | ||
0.634301 | − | 0.773086i | \(-0.281288\pi\) | |||||||
\(104\) | 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 | \(-0.983725\pi\) | ||
0.998693 | − | 0.0511071i | \(-0.0162750\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.37220 | − | 5.84081i | −0.322998 | − | 0.559449i | 0.658107 | − | 0.752924i | \(-0.271357\pi\) |
−0.981105 | + | 0.193476i | \(0.938024\pi\) | |||||||
\(110\) | 3.68831 | − | 0.0786075i | 0.351666 | − | 0.00749493i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.0430622 | − | 0.0248620i | 0.00406899 | − | 0.00234923i | ||||
\(113\) | − | 7.90091i | − | 0.743255i | −0.928382 | − | 0.371627i | \(-0.878800\pi\) | ||
0.928382 | − | 0.371627i | \(-0.121200\pi\) | |||||||
\(114\) | 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 | 0.788987 | − | 0.614410i | \(-0.210606\pi\) |
−0.137601 | + | 0.990488i | \(0.543939\pi\) | |||||||
\(128\) | −6.32219 | + | 3.65012i | −0.558808 | + | 0.322628i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.328941 | + | 0.180681i | 0.0288501 | + | 0.0158467i | ||||
\(131\) | 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 | 0.884276 | − | 0.466965i | \(-0.154653\pi\) |
0.0377341 | + | 0.999288i | \(0.487986\pi\) | |||||||
\(138\) | 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 | ||||
\(155\) | −11.0863 | − | 6.08945i | −0.890470 | − | 0.489117i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.6572 | − | 7.88498i | 1.08996 | − | 0.629290i | 0.156395 | − | 0.987695i | \(-0.450013\pi\) |
0.933566 | + | 0.358405i | \(0.116679\pi\) | |||||||
\(158\) | −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 | \(-0.882839\pi\) | ||
0.933023 | − | 0.359817i | \(-0.117161\pi\) | |||||||
\(164\) | −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 | 0.393585 | − | 0.919288i | \(-0.371235\pi\) |
−0.599335 | + | 0.800498i | \(0.704568\pi\) | |||||||
\(168\) | 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 | −0.116328 | − | 0.993211i | \(-0.537112\pi\) |
0.801982 | + | 0.597348i | \(0.203779\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.39053 | + | 1.51953i | −0.180707 | + | 0.114866i | ||||
\(176\) | −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 | ||||
\(185\) | 1.02870 | − | 1.87282i | 0.0756316 | − | 0.137693i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.76954 | + | 5.06310i | −0.641292 | + | 0.370250i | ||||
\(188\) | −9.61189 | + | 5.54942i | −0.701019 | + | 0.404733i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.41763 | − | 7.15554i | 0.320489 | − | 0.519117i | ||||
\(191\) | 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 | −0.618806 | − | 0.785544i | \(-0.712383\pi\) |
0.370898 | + | 0.928674i | \(0.379050\pi\) | |||||||
\(194\) | −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 | \(-0.773229\pi\) | ||
0.756781 | − | 0.653669i | \(-0.226771\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.803346 | + | 1.39144i | −0.0569477 | + | 0.0986363i | −0.893094 | − | 0.449870i | \(-0.851470\pi\) |
0.836146 | + | 0.548507i | \(0.184803\pi\) | |||||||
\(200\) | 11.8526 | − | 7.53403i | 0.838103 | − | 0.532736i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.05542i | 0.214978i | ||||||||
\(203\) | 4.28640 | + | 2.47475i | 0.300846 | + | 0.173694i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.478836 | − | 22.4672i | −0.0334433 | − | 1.56918i | ||||
\(206\) | 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 | ||||
\(215\) | −11.0267 | + | 0.235009i | −0.752018 | + | 0.0160275i | ||||
\(216\) | 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 | −0.907938 | − | 0.419106i | \(-0.862344\pi\) |
−0.0910127 | + | 0.995850i | \(0.529010\pi\) | |||||||
\(224\) | −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 | \(-0.987479\pi\) | ||
0.999226 | − | 0.0393271i | \(-0.0125214\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.24791 | −0.412873 | −0.206437 | − | 0.978460i | \(-0.566187\pi\) | ||||
−0.206437 | + | 0.978460i | \(0.566187\pi\) | |||||||
\(230\) | −5.70760 | − | 3.13507i | −0.376348 | − | 0.206720i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.2525 | − | 12.2701i | −1.39530 | − | 0.805574i | ||||
\(233\) | −2.38752 | + | 1.37844i | −0.156412 | + | 0.0903043i | −0.576163 | − | 0.817335i | \(-0.695451\pi\) |
0.419751 | + | 0.907639i | \(0.362117\pi\) | |||||||
\(234\) | 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 | ||||
\(245\) | −13.0901 | − | 7.19012i | −0.836297 | − | 0.459360i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.754923 | − | 0.386131i | 0.0480346 | − | 0.0245689i | ||||
\(248\) | − | 15.8888i | − | 1.00894i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.34692 | + | 8.02866i | 0.338169 | + | 0.507777i | ||||
\(251\) | −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 | −0.240999 | − | 0.970525i | \(-0.577475\pi\) |
−0.960999 | + | 0.276552i | \(0.910808\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.541356 | −0.0336382 | ||||||||
\(260\) | 0.546047 | − | 0.0116377i | 0.0338644 | − | 0.000721740i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.40052 | − | 0.808593i | −0.0865246 | − | 0.0499550i | ||||
\(263\) | 7.63264 | − | 4.40671i | 0.470649 | − | 0.271729i | −0.245863 | − | 0.969305i | \(-0.579071\pi\) |
0.716511 | + | 0.697576i | \(0.245738\pi\) | |||||||
\(264\) | 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 | ||||||||
\(275\) | 5.12902 | + | 8.06900i | 0.309291 | + | 0.486579i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.7724i | 1.96910i | 0.175098 | + | 0.984551i | \(0.443976\pi\) | ||||
−0.175098 | + | 0.984551i | \(0.556024\pi\) | |||||||
\(278\) | − | 0.270258i | − | 0.0162090i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.11872 | − | 1.71305i | −0.186379 | − | 0.102374i | ||||
\(281\) | 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 | −0.435024 | − | 0.900419i | \(-0.643260\pi\) |
0.562273 | + | 0.826951i | \(0.309927\pi\) | |||||||
\(284\) | −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 | ||||
\(290\) | 8.11463 | − | 14.7732i | 0.476507 | − | 0.867515i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 10.8034i | − | 0.632219i | ||||||
\(293\) | 17.0284i | 0.994812i | 0.867518 | + | 0.497406i | \(0.165714\pi\) | ||||
−0.867518 | + | 0.497406i | \(0.834286\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.176968 | + | 8.30344i | 0.0103035 | + | 0.483445i | ||||
\(296\) | 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 | −0.918964 | − | 0.394341i | \(-0.870973\pi\) |
−0.117972 | + | 0.993017i | \(0.537639\pi\) | |||||||
\(308\) | −1.17799 | − | 0.680110i | −0.0671220 | − | 0.0387529i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.9105 | − | 0.232531i | 0.619674 | − | 0.0132069i | ||||
\(311\) | 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 | 0.167985 | − | 0.985790i | \(-0.446274\pi\) |
−0.769726 | + | 0.638374i | \(0.779607\pi\) | |||||||
\(314\) | −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 | 0.752148 | − | 0.658994i | \(-0.229018\pi\) |
−0.194631 | + | 0.980876i | \(0.562351\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.35327 | − | 14.4683i | 0.467694 | − | 0.810069i | ||||
\(320\) | 9.28331 | + | 5.09913i | 0.518953 | + | 0.285050i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.64984i | 0.0919417i | ||||||||
\(323\) | −1.17223 | + | 23.0527i | −0.0652246 | + | 1.28269i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0414409 | + | 0.971773i | 0.00229873 | + | 0.0539043i | ||||
\(326\) | 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 | −0.282968 | − | 0.959129i | \(-0.591319\pi\) |
0.689146 | + | 0.724622i | \(0.257986\pi\) | |||||||
\(338\) | 9.68520 | + | 5.59175i | 0.526805 | + | 0.304151i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.15784 | + | 13.0313i | −0.388188 | + | 0.706723i | ||||
\(341\) | 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 | −0.191900 | − | 0.981414i | \(-0.561465\pi\) |
0.753980 | + | 0.656898i | \(0.228132\pi\) | |||||||
\(348\) | 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 | \(-0.934156\pi\) | ||
0.978682 | − | 0.205383i | \(-0.0658440\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.247535 | − | 11.6145i | −0.0131378 | − | 0.616432i | ||||
\(356\) | −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 | ||||
\(365\) | 19.2350 | − | 0.409948i | 1.00680 | − | 0.0214576i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.1945 | + | 16.8554i | 1.52394 | + | 0.879847i | 0.999598 | + | 0.0283394i | \(0.00902191\pi\) |
0.524342 | + | 0.851508i | \(0.324311\pi\) | |||||||
\(368\) | 0.296261i | 0.0154437i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.0392819 | + | 1.84313i | 0.00204217 | + | 0.0958196i | ||||
\(371\) | −2.32446 | + | 4.02608i | −0.120680 | + | 0.209024i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 10.0097i | − | 0.518281i | −0.965840 | − | 0.259141i | \(-0.916561\pi\) | ||
0.965840 | − | 0.259141i | \(-0.0834393\pi\) | |||||||
\(374\) | 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 | \(0.128492\pi\) | |||||||
\(380\) | 0.360934 | − | 12.2328i | 0.0185155 | − | 0.627531i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.5353 | + | 6.08255i | −0.539032 | + | 0.311210i | ||||
\(383\) | −14.0725 | + | 8.12477i | −0.719072 | + | 0.415156i | −0.814411 | − | 0.580289i | \(-0.802940\pi\) |
0.0953393 | + | 0.995445i | \(0.469606\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.16621 | − | 2.12316i | 0.0594355 | − | 0.108206i | ||||
\(386\) | 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 | ||||
\(395\) | −0.315723 | − | 14.8139i | −0.0158858 | − | 0.745368i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.63682 | − | 2.67707i | 0.232716 | − | 0.134358i | −0.379109 | − | 0.925352i | \(-0.623769\pi\) |
0.611824 | + | 0.790994i | \(0.290436\pi\) | |||||||
\(398\) | − | 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 | ||||||||
\(415\) | −4.86302 | + | 8.85347i | −0.238716 | + | 0.434600i | ||||
\(416\) | 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 | 0.897187 | − | 0.441651i | \(-0.145607\pi\) |
0.0661122 | + | 0.997812i | \(0.478940\pi\) | |||||||
\(434\) | −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 | \(0.537887\pi\) | |||||||
\(440\) | −5.78221 | + | 10.5269i | −0.275656 | + | 0.501851i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.769710 | − | 0.444392i | 0.0366114 | − | 0.0211376i | ||||
\(443\) | 27.1567 | + | 15.6789i | 1.29025 | + | 0.744929i | 0.978699 | − | 0.205299i | \(-0.0658167\pi\) |
0.311555 | + | 0.950228i | \(0.399150\pi\) | |||||||
\(444\) | 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 | \(-0.882728\pi\) | ||
0.932897 | − | 0.360143i | \(-0.117272\pi\) | |||||||
\(458\) | 4.66837 | − | 2.69529i | 0.218139 | − | 0.125943i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.47470 | + | 0.201931i | −0.441760 | + | 0.00941508i | ||||
\(461\) | −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 | \(0.274486\pi\) | ||||
−0.650675 | + | 0.759356i | \(0.725514\pi\) | |||||||
\(464\) | −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 | \(-0.951273\pi\) | ||
0.988306 | − | 0.152484i | \(-0.0487272\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.14540 | − | 1.98390i | 0.0528898 | − | 0.0916078i | ||||
\(470\) | 14.9469 | + | 8.21004i | 0.689451 | + | 0.378701i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.03514 | + | 5.21644i | −0.415876 | + | 0.240106i | ||||
\(473\) | 8.16830 | − | 4.71597i | 0.375579 | − | 0.216841i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.7938 | + | 0.178437i | 0.999966 | + | 0.00818726i | ||||
\(476\) | 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 | ||||
\(485\) | −33.9631 | + | 0.723844i | −1.54219 | + | 0.0328680i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.45475i | − | 0.111235i | −0.998452 | − | 0.0556176i | \(-0.982287\pi\) | ||
0.998452 | − | 0.0556176i | \(-0.0177128\pi\) | |||||||
\(488\) | −8.54125 | − | 4.93129i | −0.386644 | − | 0.223229i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 12.8826 | − | 0.274561i | 0.581975 | − | 0.0124034i | ||||
\(491\) | 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 | \(-0.394155\pi\) | |||||||
\(500\) | 12.5810 | + | 6.22806i | 0.562637 | + | 0.278527i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 22.6462i | − | 1.01075i | ||||||
\(503\) | −25.4939 | − | 14.7189i | −1.13672 | − | 0.656283i | −0.191100 | − | 0.981571i | \(-0.561206\pi\) |
−0.945615 | + | 0.325287i | \(0.894539\pi\) | |||||||
\(504\) | 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 | ||||||||
\(515\) | −16.8927 | + | 30.7542i | −0.744379 | + | 1.35519i | ||||
\(516\) | 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 | −0.387918 | − | 0.921694i | \(-0.626805\pi\) |
−0.992169 | + | 0.124901i | \(0.960139\pi\) | |||||||
\(524\) | −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 | ||||
\(530\) | 13.8760 | + | 7.62182i | 0.602737 | + | 0.331071i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.76047 | + | 1.41193i | −0.119681 | + | 0.0612151i | ||||
\(533\) | 1.95503i | 0.0846816i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.13822 | + | 2.07220i | −0.0492094 | + | 0.0895890i | ||||
\(536\) | −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 | ||||||||
\(545\) | 0.321341 | + | 15.0775i | 0.0137647 | + | 0.645849i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6831 | − | 10.2093i | −0.756073 | − | 0.436519i | 0.0718112 | − | 0.997418i | \(-0.477122\pi\) |
−0.827884 | + | 0.560899i | \(0.810455\pi\) | |||||||
\(548\) | −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 | 0.983180 | − | 0.182641i | \(-0.0584645\pi\) |
0.333418 | + | 0.942779i | \(0.391798\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.959512 | 0.0405830 | ||||||||
\(560\) | −0.111161 | + | 0.00236913i | −0.00469740 | + | 0.000100114i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.55873i | 0.361028i | ||||||||
\(563\) | 37.7708i | 1.59185i | 0.605395 | + | 0.795925i | \(0.293015\pi\) | ||||
−0.605395 | + | 0.795925i | \(0.706985\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.50547 | + | 15.4848i | −0.357828 | + | 0.651450i | ||||
\(566\) | −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 | ||||
\(575\) | −0.719059 | − | 16.8617i | −0.0299869 | − | 0.703180i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 43.8371i | − | 1.82496i | −0.409119 | − | 0.912481i | \(-0.634164\pi\) | ||
0.409119 | − | 0.912481i | \(-0.365836\pi\) | |||||||
\(578\) | 9.52702i | 0.396272i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.522666 | − | 24.5238i | −0.0217025 | − | 1.01829i | ||||
\(581\) | 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 | 0.368315 | − | 0.929701i | \(-0.379935\pi\) |
0.989302 | + | 0.145880i | \(0.0466015\pi\) | |||||||
\(588\) | 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 | 0.401272 | − | 0.915959i | \(-0.368568\pi\) |
−0.592608 | + | 0.805491i | \(0.701902\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.142937 | + | 6.70668i | 0.00585985 | + | 0.274947i | ||||
\(596\) | 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 | ||||
\(605\) | 14.3921 | + | 7.90528i | 0.585122 | + | 0.321395i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 24.5915i | − | 0.998139i | −0.866562 | − | 0.499069i | \(-0.833675\pi\) | ||
0.866562 | − | 0.499069i | \(-0.166325\pi\) | |||||||
\(608\) | 22.0949 | − | 11.3012i | 0.896065 | − | 0.458323i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.26122 | − | 5.93727i | 0.132043 | − | 0.240393i | ||||
\(611\) | 0.859772 | + | 1.48917i | 0.0347826 | + | 0.0602453i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.8856 | − | 14.9450i | 1.04551 | − | 0.603624i | 0.124119 | − | 0.992267i | \(-0.460389\pi\) |
0.921388 | + | 0.388643i | \(0.127056\pi\) | |||||||
\(614\) | 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 | −0.423238 | − | 0.906019i | \(-0.639106\pi\) |
−0.996254 | + | 0.0864749i | \(0.972440\pi\) | |||||||
\(618\) | 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 | ||||||||
\(625\) | −10.6114 | + | 22.6362i | −0.424456 | + | 0.905449i | ||||
\(626\) | 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 | ||||||||
\(640\) | 16.3201 | − | 0.347825i | 0.645110 | − | 0.0137490i | ||||
\(641\) | −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 | −0.821195 | − | 0.570648i | \(-0.806692\pi\) |
0.0835979 | + | 0.996500i | \(0.473359\pi\) | |||||||
\(644\) | 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 | \(0.0797504\pi\) | ||||
−0.968778 | + | 0.247930i | \(0.920250\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.55125 | − | 6.15095i | −0.139399 | − | 0.241446i | ||||
\(650\) | −0.450178 | − | 0.708222i | −0.0176574 | − | 0.0277788i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.99059 | + | 5.76807i | 0.391262 | + | 0.225895i | ||||
\(653\) | − | 26.6312i | − | 1.04216i | −0.853508 | − | 0.521080i | \(-0.825529\pi\) | ||
0.853508 | − | 0.521080i | \(-0.174471\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0893064 | − | 4.19030i | −0.00348949 | − | 0.163729i | ||||
\(656\) | 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 | ||||||||
\(665\) | −2.61864 | − | 4.86132i | −0.101547 | − | 0.188514i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.5389 | + | 14.7449i | −0.988871 | + | 0.570925i | ||||
\(668\) | 3.33851 | − | 1.92749i | 0.129171 | − | 0.0745768i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.83758 | − | 3.75574i | −0.264159 | − | 0.145097i | ||||
\(671\) | 3.35713 | − | 5.81471i | 0.129600 | − | 0.224475i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 34.4110i | − | 1.32645i | −0.748421 | − | 0.663224i | \(-0.769188\pi\) | ||
0.748421 | − | 0.663224i | \(-0.230812\pi\) | |||||||
\(674\) | −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 | \(0.193080\pi\) | ||||
−0.821604 | + | 0.570059i | \(0.806920\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.30335 | + | 7.45361i | 0.165147 | + | 0.286043i | ||||
\(680\) | −0.708700 | − | 33.2526i | −0.0271774 | − | 1.27518i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.08217 | + | 4.66625i | −0.309482 | + | 0.178680i | ||||
\(683\) | − | 27.8978i | − | 1.06748i | −0.845648 | − | 0.533740i | \(-0.820786\pi\) | ||
0.845648 | − | 0.533740i | \(-0.179214\pi\) | |||||||
\(684\) | 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 | ||||||||
\(700\) | −0.151534 | − | 3.55341i | −0.00572744 | − | 0.134306i | ||||
\(701\) | −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 | ||||
\(725\) | 43.6438 | − | 1.86117i | 1.62089 | − | 0.0691222i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.914981 | + | 0.528264i | −0.0339348 | + | 0.0195922i | −0.516871 | − | 0.856063i | \(-0.672903\pi\) |
0.482937 | + | 0.875655i | \(0.339570\pi\) | |||||||
\(728\) | 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 | \(-0.876392\pi\) | ||
0.925545 | − | 0.378639i | \(-0.123608\pi\) | |||||||
\(734\) | −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 | −0.274388 | − | 0.961619i | \(-0.588475\pi\) |
0.695592 | + | 0.718437i | \(0.255142\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.208012 | + | 9.76004i | 0.00762098 | + | 0.357580i | ||||
\(746\) | 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 | ||||
\(755\) | −0.388009 | − | 0.213125i | −0.0141211 | − | 0.00775643i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.9726 | − | 24.2329i | 1.52552 | − | 0.880760i | 0.525980 | − | 0.850497i | \(-0.323699\pi\) |
0.999542 | − | 0.0302631i | \(-0.00963450\pi\) | |||||||
\(758\) | −26.7542 | + | 15.4465i | −0.971756 | + | 0.561044i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.9836 | + | 24.1031i | 0.470963 | + | 0.874310i | ||||
\(761\) | −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 | \(0.865835\pi\) | |||||||
\(770\) | 0.0445327 | + | 2.08950i | 0.00160485 | + | 0.0753003i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 4.99337i | − | 0.179715i | ||||||
\(773\) | −3.19256 | − | 1.84323i | −0.114828 | − | 0.0662962i | 0.441486 | − | 0.897268i | \(-0.354452\pi\) |
−0.556314 | + | 0.830972i | \(0.687785\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.1723 | + | 23.8691i | 0.545005 | + | 0.857404i | ||||
\(776\) | −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 | ||||
\(785\) | −35.2547 | + | 0.751370i | −1.25829 | + | 0.0268175i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.7141i | 1.62953i | 0.579790 | + | 0.814766i | \(0.303135\pi\) | ||||
−0.579790 | + | 0.814766i | \(0.696865\pi\) | |||||||
\(788\) | 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 | \(0.180559\pi\) | ||||
−0.843385 | + | 0.537310i | \(0.819441\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46.8091 | −1.65599 | ||||||||
\(800\) | 1.21288 | + | 28.4416i | 0.0428818 | + | 1.00556i | ||||
\(801\) | 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 | ||||
\(815\) | −9.89071 | + | 18.0067i | −0.346456 | + | 0.630748i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.09186 | − | 21.4722i | 0.0381994 | − | 0.751218i | ||||
\(818\) | − | 30.4757i | − | 1.06556i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.7312 | + | 13.5843i | 0.863652 | + | 0.474386i | ||||
\(821\) | 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 | 0.307662 | − | 0.951496i | \(-0.400453\pi\) |
−0.670189 | + | 0.742191i | \(0.733787\pi\) | |||||||
\(824\) | −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 | 0.623122 | − | 0.782125i | \(-0.285864\pi\) |
−0.365779 | + | 0.930702i | \(0.619197\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.1042 | 0.941369 | 0.470685 | − | 0.882302i | \(-0.344007\pi\) | ||||
0.470685 | + | 0.882302i | \(0.344007\pi\) | |||||||
\(830\) | −0.185699 | − | 8.71309i | −0.00644570 | − | 0.302436i | ||||
\(831\) | 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 | ||||||||
\(845\) | 0.617591 | + | 28.9777i | 0.0212458 | + | 0.996863i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.16017i | − | 0.142945i | ||||||
\(848\) | − | 0.720256i | − | 0.0247337i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 22.8235 | − | 0.973300i | 0.782840 | − | 0.0333839i | ||||
\(851\) | 1.61274 | − | 2.79334i | 0.0552838 | − | 0.0957544i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.8890 | − | 9.17354i | 0.544030 | − | 0.314096i | −0.202680 | − | 0.979245i | \(-0.564965\pi\) |
0.746711 | + | 0.665149i | \(0.231632\pi\) | |||||||
\(854\) | −1.71622 | −0.0587279 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.96986 | −0.101508 | ||||||||
\(857\) | 6.80508 | − | 3.92892i | 0.232457 | − | 0.134209i | −0.379248 | − | 0.925295i | \(-0.623817\pi\) |
0.611705 | + | 0.791086i | \(0.290484\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.1511 | + | 29.7066i | −0.585188 | + | 1.01358i | 0.409664 | + | 0.912237i | \(0.365646\pi\) |
−0.994852 | + | 0.101339i | \(0.967687\pi\) | |||||||
\(860\) | 6.66709 | − | 12.1379i | 0.227346 | − | 0.413899i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 14.6257i | − | 0.498153i | ||||||
\(863\) | − | 35.9451i | − | 1.22359i | −0.791018 | − | 0.611793i | \(-0.790449\pi\) | ||
0.791018 | − | 0.611793i | \(-0.209551\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.2801 | + | 0.496159i | −0.791546 | + | 0.0168699i | ||||
\(866\) | −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 | −0.821505 | − | 0.570202i | \(-0.806865\pi\) |
0.0830567 | + | 0.996545i | \(0.473532\pi\) | |||||||
\(878\) | −25.0651 | − | 14.4713i | −0.845905 | − | 0.488383i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.00799675 | + | 0.375212i | 0.000269570 | + | 0.0126484i | ||||
\(881\) | −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 | 0.606014 | − | 0.795454i | \(-0.292768\pi\) |
−0.385876 | + | 0.922550i | \(0.626101\pi\) | |||||||
\(884\) | 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 | 0.244932 | − | 0.969540i | \(-0.421234\pi\) |
−0.717181 | + | 0.696887i | \(0.754568\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.40101 | + | 4.15867i | −0.0805273 | + | 0.139477i | ||||
\(890\) | −3.13332 | + | 5.70443i | −0.105029 | + | 0.191213i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 21.6282i | − | 0.724165i | ||||||
\(893\) | 34.3034 | − | 17.5456i | 1.14792 | − | 0.587142i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.3471 | + | 14.4719i | 0.880685 | + | 0.483742i | ||||
\(896\) | −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 | −0.738935 | − | 0.673776i | \(-0.764671\pi\) |
0.214040 | + | 0.976825i | \(0.431338\pi\) | |||||||
\(908\) | 1.28861 | + | 0.743977i | 0.0427639 | + | 0.0246897i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.102359 | + | 0.186352i | −0.00339317 | + | 0.00617750i | ||||
\(911\) | −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 | ||||||||
\(925\) | −4.03225 | + | 2.56308i | −0.132580 | + | 0.0842736i | ||||
\(926\) | −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 | ||||
\(935\) | 22.6377 | − | 0.482469i | 0.740332 | − | 0.0157784i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.4401 | + | 21.6160i | 1.22311 | + | 0.706165i | 0.965580 | − | 0.260105i | \(-0.0837571\pi\) |
0.257533 | + | 0.966270i | \(0.417090\pi\) | |||||||
\(938\) | 1.97646i | 0.0645338i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 24.8121 | − | 0.528812i | 0.809283 | − | 0.0172480i | ||||
\(941\) | −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 | −0.165888 | − | 0.986145i | \(-0.553049\pi\) |
0.771083 | + | 0.636735i | \(0.219716\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.67376 | −0.0543327 | ||||||||
\(950\) | −16.3611 | + | 9.26830i | −0.530823 | + | 0.300703i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.29768 | + | 4.21332i | −0.236519 | + | 0.136554i | ||||
\(953\) | 15.3547 | − | 8.86503i | 0.497387 | − | 0.287166i | −0.230247 | − | 0.973132i | \(-0.573953\pi\) |
0.727634 | + | 0.685966i | \(0.240620\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.6340 | − | 15.1787i | −0.894214 | − | 0.491173i | ||||
\(956\) | −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 | ||||
\(965\) | 8.89049 | − | 0.189480i | 0.286195 | − | 0.00609957i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.8239 | + | 6.82652i | −0.380230 | + | 0.219526i | −0.677919 | − | 0.735137i | \(-0.737118\pi\) |
0.297688 | + | 0.954663i | \(0.403784\pi\) | |||||||
\(968\) | 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 | \(-0.907807\pi\) | ||
0.958349 | − | 0.285600i | \(-0.0921929\pi\) | |||||||
\(978\) | 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 | −0.988903 | − | 0.148559i | \(-0.952536\pi\) |
−0.365795 | + | 0.930695i | \(0.619203\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.7534 | + | 35.9625i | −0.629396 | + | 1.14586i | ||||
\(986\) | −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 | 0.0281699 | − | 0.999603i | \(-0.491032\pi\) |
−0.851597 | + | 0.524197i | \(0.824365\pi\) | |||||||
\(998\) | 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.64.2 | 12 | ||
3.2 | odd | 2 | 95.2.i.b.64.5 | yes | 12 | ||
5.4 | even | 2 | inner | 855.2.be.d.64.5 | 12 | ||
15.2 | even | 4 | 475.2.e.g.26.5 | 12 | |||
15.8 | even | 4 | 475.2.e.g.26.2 | 12 | |||
15.14 | odd | 2 | 95.2.i.b.64.2 | yes | 12 | ||
19.11 | even | 3 | inner | 855.2.be.d.334.5 | 12 | ||
57.11 | odd | 6 | 95.2.i.b.49.2 | ✓ | 12 | ||
57.26 | odd | 6 | 1805.2.b.f.1084.5 | 6 | |||
57.50 | even | 6 | 1805.2.b.g.1084.2 | 6 | |||
95.49 | even | 6 | inner | 855.2.be.d.334.2 | 12 | ||
285.68 | even | 12 | 475.2.e.g.201.2 | 12 | |||
285.83 | even | 12 | 9025.2.a.bu.1.5 | 6 | |||
285.107 | odd | 12 | 9025.2.a.bt.1.5 | 6 | |||
285.164 | even | 6 | 1805.2.b.g.1084.5 | 6 | |||
285.182 | even | 12 | 475.2.e.g.201.5 | 12 | |||
285.197 | even | 12 | 9025.2.a.bu.1.2 | 6 | |||
285.239 | odd | 6 | 95.2.i.b.49.5 | yes | 12 | ||
285.254 | odd | 6 | 1805.2.b.f.1084.2 | 6 | |||
285.278 | odd | 12 | 9025.2.a.bt.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.i.b.49.2 | ✓ | 12 | 57.11 | odd | 6 | ||
95.2.i.b.49.5 | yes | 12 | 285.239 | odd | 6 | ||
95.2.i.b.64.2 | yes | 12 | 15.14 | odd | 2 | ||
95.2.i.b.64.5 | yes | 12 | 3.2 | odd | 2 | ||
475.2.e.g.26.2 | 12 | 15.8 | even | 4 | |||
475.2.e.g.26.5 | 12 | 15.2 | even | 4 | |||
475.2.e.g.201.2 | 12 | 285.68 | even | 12 | |||
475.2.e.g.201.5 | 12 | 285.182 | even | 12 | |||
855.2.be.d.64.2 | 12 | 1.1 | even | 1 | trivial | ||
855.2.be.d.64.5 | 12 | 5.4 | even | 2 | inner | ||
855.2.be.d.334.2 | 12 | 95.49 | even | 6 | inner | ||
855.2.be.d.334.5 | 12 | 19.11 | even | 3 | inner | ||
1805.2.b.f.1084.2 | 6 | 285.254 | odd | 6 | |||
1805.2.b.f.1084.5 | 6 | 57.26 | odd | 6 | |||
1805.2.b.g.1084.2 | 6 | 57.50 | even | 6 | |||
1805.2.b.g.1084.5 | 6 | 285.164 | even | 6 | |||
9025.2.a.bt.1.2 | 6 | 285.278 | odd | 12 | |||
9025.2.a.bt.1.5 | 6 | 285.107 | odd | 12 | |||
9025.2.a.bu.1.2 | 6 | 285.197 | even | 12 | |||
9025.2.a.bu.1.5 | 6 | 285.83 | even | 12 |