Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(157,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(12))
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("1050.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.bc (of order \(12\), degree \(4\), 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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 943.4 | ||
Root | \(0.792206 + 1.03242i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.943 |
Dual form | 1050.2.bc.g.157.4 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | + | 0.965926i | 0.183013 | + | 0.683013i | ||||
\(3\) | −0.965926 | − | 0.258819i | −0.557678 | − | 0.149429i | ||||
\(4\) | −0.866025 | + | 0.500000i | −0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 1.52856 | + | 2.15951i | 0.577743 | + | 0.816219i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0.866025 | + | 0.500000i | 0.288675 | + | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.883028 | + | 1.52945i | 0.266243 | + | 0.461147i | 0.967889 | − | 0.251380i | \(-0.0808843\pi\) |
−0.701645 | + | 0.712526i | \(0.747551\pi\) | |||||||
\(12\) | 0.965926 | − | 0.258819i | 0.278839 | − | 0.0747146i | ||||
\(13\) | −2.71395 | + | 2.71395i | −0.752713 | + | 0.752713i | −0.974985 | − | 0.222272i | \(-0.928653\pi\) |
0.222272 | + | 0.974985i | \(0.428653\pi\) | |||||||
\(14\) | −1.69031 | + | 2.03540i | −0.451754 | + | 0.543984i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 0.574830 | − | 2.14529i | 0.139417 | − | 0.520310i | −0.860524 | − | 0.509410i | \(-0.829864\pi\) |
0.999941 | − | 0.0109000i | \(-0.00346965\pi\) | |||||||
\(18\) | −0.258819 | + | 0.965926i | −0.0610042 | + | 0.227671i | ||||
\(19\) | 0.886994 | − | 1.53632i | 0.203490 | − | 0.352456i | −0.746160 | − | 0.665766i | \(-0.768105\pi\) |
0.949651 | + | 0.313311i | \(0.101438\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.917556 | − | 2.48155i | −0.200227 | − | 0.541519i | ||||
\(22\) | −1.24879 | + | 1.24879i | −0.266243 | + | 0.266243i | ||||
\(23\) | 3.90900 | − | 1.04741i | 0.815082 | − | 0.218401i | 0.172887 | − | 0.984942i | \(-0.444691\pi\) |
0.642195 | + | 0.766541i | \(0.278024\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.32389 | − | 1.91905i | −0.651869 | − | 0.376356i | ||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | −2.40353 | − | 1.10591i | −0.454225 | − | 0.208998i | ||||
\(29\) | 3.84628i | 0.714236i | 0.934059 | + | 0.357118i | \(0.116241\pi\) | ||||
−0.934059 | + | 0.357118i | \(0.883759\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.94554 | + | 5.16471i | −1.60667 | + | 0.927610i | −0.616558 | + | 0.787310i | \(0.711473\pi\) |
−0.990109 | + | 0.140300i | \(0.955193\pi\) | |||||||
\(32\) | 0.965926 | + | 0.258819i | 0.170753 | + | 0.0457532i | ||||
\(33\) | −0.457089 | − | 1.70588i | −0.0795690 | − | 0.296956i | ||||
\(34\) | 2.22097 | 0.380893 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 0.861499 | + | 3.21516i | 0.141630 | + | 0.528569i | 0.999882 | + | 0.0153416i | \(0.00488357\pi\) |
−0.858253 | + | 0.513227i | \(0.828450\pi\) | |||||||
\(38\) | 1.71354 | + | 0.459142i | 0.277973 | + | 0.0744827i | ||||
\(39\) | 3.32389 | − | 1.91905i | 0.532248 | − | 0.307294i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.8993i | 1.85836i | 0.369622 | + | 0.929182i | \(0.379487\pi\) | ||||
−0.369622 | + | 0.929182i | \(0.620513\pi\) | |||||||
\(42\) | 2.15951 | − | 1.52856i | 0.333220 | − | 0.235862i | ||||
\(43\) | −3.46335 | − | 3.46335i | −0.528155 | − | 0.528155i | 0.391867 | − | 0.920022i | \(-0.371829\pi\) |
−0.920022 | + | 0.391867i | \(0.871829\pi\) | |||||||
\(44\) | −1.52945 | − | 0.883028i | −0.230573 | − | 0.133122i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.02344 | + | 3.50471i | 0.298341 | + | 0.516741i | ||||
\(47\) | −5.93837 | + | 1.59118i | −0.866200 | + | 0.232098i | −0.664444 | − | 0.747338i | \(-0.731332\pi\) |
−0.201756 | + | 0.979436i | \(0.564665\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | −2.32699 | + | 6.60190i | −0.332427 | + | 0.943129i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.11049 | + | 1.92342i | −0.155499 | + | 0.269332i | ||||
\(52\) | 0.993373 | − | 3.70732i | 0.137756 | − | 0.514113i | ||||
\(53\) | −0.106258 | + | 0.396561i | −0.0145957 | + | 0.0544719i | −0.972840 | − | 0.231480i | \(-0.925643\pi\) |
0.958244 | + | 0.285952i | \(0.0923098\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.446149 | − | 2.60786i | 0.0596191 | − | 0.348490i | ||||
\(57\) | −1.25440 | + | 1.25440i | −0.166149 | + | 0.166149i | ||||
\(58\) | −3.71522 | + | 0.995491i | −0.487833 | + | 0.130714i | ||||
\(59\) | 5.18379 | + | 8.97859i | 0.674872 | + | 1.16891i | 0.976506 | + | 0.215489i | \(0.0691346\pi\) |
−0.301634 | + | 0.953424i | \(0.597532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.87936 | − | 3.39445i | −0.752775 | − | 0.434615i | 0.0739204 | − | 0.997264i | \(-0.476449\pi\) |
−0.826696 | + | 0.562649i | \(0.809782\pi\) | |||||||
\(62\) | −7.30401 | − | 7.30401i | −0.927610 | − | 0.927610i | ||||
\(63\) | 0.244018 | + | 2.63447i | 0.0307434 | + | 0.331913i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.52945 | − | 0.883028i | 0.188262 | − | 0.108693i | ||||
\(67\) | 7.37834 | + | 1.97702i | 0.901408 | + | 0.241532i | 0.679621 | − | 0.733563i | \(-0.262144\pi\) |
0.221787 | + | 0.975095i | \(0.428811\pi\) | |||||||
\(68\) | 0.574830 | + | 2.14529i | 0.0697083 | + | 0.260155i | ||||
\(69\) | −4.04689 | −0.487188 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7193 | −1.27214 | −0.636072 | − | 0.771629i | \(-0.719442\pi\) | ||||
−0.636072 | + | 0.771629i | \(0.719442\pi\) | |||||||
\(72\) | −0.258819 | − | 0.965926i | −0.0305021 | − | 0.113835i | ||||
\(73\) | −10.2705 | − | 2.75198i | −1.20207 | − | 0.322095i | −0.398426 | − | 0.917200i | \(-0.630444\pi\) |
−0.803647 | + | 0.595106i | \(0.797110\pi\) | |||||||
\(74\) | −2.88263 | + | 1.66429i | −0.335099 | + | 0.193470i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.77399i | 0.203490i | ||||||||
\(77\) | −1.95310 | + | 4.24477i | −0.222577 | + | 0.483737i | ||||
\(78\) | 2.71395 | + | 2.71395i | 0.307294 | + | 0.307294i | ||||
\(79\) | −10.9907 | − | 6.34546i | −1.23655 | − | 0.713920i | −0.268159 | − | 0.963375i | \(-0.586415\pi\) |
−0.968386 | + | 0.249455i | \(0.919749\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | −11.4939 | + | 3.07978i | −1.26929 | + | 0.340104i | ||||
\(83\) | 1.94227 | − | 1.94227i | 0.213191 | − | 0.213191i | −0.592430 | − | 0.805622i | \(-0.701831\pi\) |
0.805622 | + | 0.592430i | \(0.201831\pi\) | |||||||
\(84\) | 2.03540 | + | 1.69031i | 0.222081 | + | 0.184428i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.44896 | − | 4.24172i | 0.264078 | − | 0.457396i | ||||
\(87\) | 0.995491 | − | 3.71522i | 0.106728 | − | 0.398314i | ||||
\(88\) | 0.457089 | − | 1.70588i | 0.0487259 | − | 0.181847i | ||||
\(89\) | −0.558127 | + | 0.966705i | −0.0591614 | + | 0.102471i | −0.894089 | − | 0.447889i | \(-0.852176\pi\) |
0.834928 | + | 0.550359i | \(0.185509\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0092 | − | 1.71236i | −1.04925 | − | 0.179504i | ||||
\(92\) | −2.86158 | + | 2.86158i | −0.298341 | + | 0.298341i | ||||
\(93\) | 9.97746 | − | 2.67345i | 1.03461 | − | 0.277224i | ||||
\(94\) | −3.07393 | − | 5.32419i | −0.317051 | − | 0.549149i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | 7.26720 | + | 7.26720i | 0.737872 | + | 0.737872i | 0.972166 | − | 0.234293i | \(-0.0752777\pi\) |
−0.234293 | + | 0.972166i | \(0.575278\pi\) | |||||||
\(98\) | −6.97922 | − | 0.539001i | −0.705007 | − | 0.0544473i | ||||
\(99\) | 1.76606i | 0.177495i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.8887 | − | 9.17333i | 1.58098 | − | 0.912780i | 0.586265 | − | 0.810119i | \(-0.300598\pi\) |
0.994716 | − | 0.102661i | \(-0.0327358\pi\) | |||||||
\(102\) | −2.14529 | − | 0.574830i | −0.212416 | − | 0.0569166i | ||||
\(103\) | −2.36040 | − | 8.80911i | −0.232577 | − | 0.867988i | −0.979226 | − | 0.202770i | \(-0.935006\pi\) |
0.746650 | − | 0.665217i | \(-0.231661\pi\) | |||||||
\(104\) | 3.83810 | 0.376356 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.410550 | −0.0398762 | ||||||||
\(107\) | 3.81880 | + | 14.2519i | 0.369177 | + | 1.37779i | 0.861669 | + | 0.507471i | \(0.169419\pi\) |
−0.492492 | + | 0.870317i | \(0.663914\pi\) | |||||||
\(108\) | 0.965926 | + | 0.258819i | 0.0929463 | + | 0.0249049i | ||||
\(109\) | 17.4494 | − | 10.0744i | 1.67135 | − | 0.964955i | 0.704467 | − | 0.709736i | \(-0.251186\pi\) |
0.966883 | − | 0.255218i | \(-0.0821474\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.32858i | − | 0.315935i | ||||||
\(112\) | 2.63447 | − | 0.244018i | 0.248934 | − | 0.0230576i | ||||
\(113\) | 6.54677 | + | 6.54677i | 0.615869 | + | 0.615869i | 0.944469 | − | 0.328600i | \(-0.106577\pi\) |
−0.328600 | + | 0.944469i | \(0.606577\pi\) | |||||||
\(114\) | −1.53632 | − | 0.886994i | −0.143889 | − | 0.0830746i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.92314 | − | 3.33098i | −0.178559 | − | 0.309273i | ||||
\(117\) | −3.70732 | + | 0.993373i | −0.342742 | + | 0.0918374i | ||||
\(118\) | −7.33099 | + | 7.33099i | −0.674872 | + | 0.674872i | ||||
\(119\) | 5.51145 | − | 2.03786i | 0.505234 | − | 0.186811i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.94052 | − | 6.82518i | 0.358229 | − | 0.620471i | ||||
\(122\) | 1.75710 | − | 6.55758i | 0.159080 | − | 0.593695i | ||||
\(123\) | 3.07978 | − | 11.4939i | 0.277694 | − | 1.03637i | ||||
\(124\) | 5.16471 | − | 8.94554i | 0.463805 | − | 0.803333i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.48155 | + | 0.917556i | −0.221074 | + | 0.0817424i | ||||
\(127\) | −12.5444 | + | 12.5444i | −1.11313 | + | 1.11313i | −0.120409 | + | 0.992724i | \(0.538421\pi\) |
−0.992724 | + | 0.120409i | \(0.961579\pi\) | |||||||
\(128\) | −0.965926 | + | 0.258819i | −0.0853766 | + | 0.0228766i | ||||
\(129\) | 2.44896 | + | 4.24172i | 0.215619 | + | 0.373462i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.830756 | + | 0.479637i | 0.0725835 | + | 0.0419061i | 0.535853 | − | 0.844312i | \(-0.319990\pi\) |
−0.463269 | + | 0.886218i | \(0.653324\pi\) | |||||||
\(132\) | 1.24879 | + | 1.24879i | 0.108693 | + | 0.108693i | ||||
\(133\) | 4.67353 | − | 0.432886i | 0.405246 | − | 0.0375359i | ||||
\(134\) | 7.63862i | 0.659877i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.92342 | + | 1.11049i | −0.164932 | + | 0.0952233i | ||||
\(137\) | 10.7669 | + | 2.88499i | 0.919880 | + | 0.246481i | 0.687534 | − | 0.726152i | \(-0.258693\pi\) |
0.232346 | + | 0.972633i | \(0.425360\pi\) | |||||||
\(138\) | −1.04741 | − | 3.90900i | −0.0891616 | − | 0.332756i | ||||
\(139\) | −13.5695 | −1.15095 | −0.575477 | − | 0.817818i | \(-0.695184\pi\) | ||||
−0.575477 | + | 0.817818i | \(0.695184\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.14785 | 0.517742 | ||||||||
\(142\) | −2.77435 | − | 10.3540i | −0.232819 | − | 0.868891i | ||||
\(143\) | −6.54733 | − | 1.75435i | −0.547516 | − | 0.146706i | ||||
\(144\) | 0.866025 | − | 0.500000i | 0.0721688 | − | 0.0416667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 10.6328i | − | 0.879979i | ||||||
\(147\) | 3.95640 | − | 5.77468i | 0.326318 | − | 0.476288i | ||||
\(148\) | −2.35366 | − | 2.35366i | −0.193470 | − | 0.193470i | ||||
\(149\) | 8.74565 | + | 5.04930i | 0.716471 | + | 0.413655i | 0.813453 | − | 0.581631i | \(-0.197585\pi\) |
−0.0969812 | + | 0.995286i | \(0.530919\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.15497 | + | 12.3928i | 0.582263 | + | 1.00851i | 0.995211 | + | 0.0977541i | \(0.0311659\pi\) |
−0.412948 | + | 0.910755i | \(0.635501\pi\) | |||||||
\(152\) | −1.71354 | + | 0.459142i | −0.138987 | + | 0.0372413i | ||||
\(153\) | 1.57046 | − | 1.57046i | 0.126964 | − | 0.126964i | ||||
\(154\) | −4.60563 | − | 0.787924i | −0.371133 | − | 0.0634927i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.91905 | + | 3.32389i | −0.153647 | + | 0.266124i | ||||
\(157\) | 2.48036 | − | 9.25683i | 0.197954 | − | 0.738776i | −0.793528 | − | 0.608534i | \(-0.791758\pi\) |
0.991482 | − | 0.130242i | \(-0.0415754\pi\) | |||||||
\(158\) | 3.28465 | − | 12.2585i | 0.261313 | − | 0.975233i | ||||
\(159\) | 0.205275 | − | 0.355547i | 0.0162794 | − | 0.0281967i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.23705 | + | 6.84049i | 0.649170 | + | 0.539106i | ||||
\(162\) | −0.707107 | + | 0.707107i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 11.4401 | − | 3.06537i | 0.896058 | − | 0.240098i | 0.218736 | − | 0.975784i | \(-0.429807\pi\) |
0.677323 | + | 0.735686i | \(0.263140\pi\) | |||||||
\(164\) | −5.94967 | − | 10.3051i | −0.464591 | − | 0.804695i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.37878 | + | 1.37339i | 0.184629 | + | 0.106596i | ||||
\(167\) | −6.95883 | − | 6.95883i | −0.538490 | − | 0.538490i | 0.384595 | − | 0.923085i | \(-0.374341\pi\) |
−0.923085 | + | 0.384595i | \(0.874341\pi\) | |||||||
\(168\) | −1.10591 | + | 2.40353i | −0.0853229 | + | 0.185436i | ||||
\(169\) | − | 1.73100i | − | 0.133154i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.53632 | − | 0.886994i | 0.117485 | − | 0.0678301i | ||||
\(172\) | 4.73102 | + | 1.26767i | 0.360737 | + | 0.0966592i | ||||
\(173\) | 2.24296 | + | 8.37084i | 0.170529 | + | 0.636423i | 0.997270 | + | 0.0738403i | \(0.0235255\pi\) |
−0.826741 | + | 0.562583i | \(0.809808\pi\) | |||||||
\(174\) | 3.84628 | 0.291586 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.76606 | 0.133122 | ||||||||
\(177\) | −2.68333 | − | 10.0143i | −0.201691 | − | 0.752722i | ||||
\(178\) | −1.07822 | − | 0.288908i | −0.0808160 | − | 0.0216546i | ||||
\(179\) | 11.5646 | − | 6.67682i | 0.864378 | − | 0.499049i | −0.00109809 | − | 0.999999i | \(-0.500350\pi\) |
0.865476 | + | 0.500951i | \(0.167016\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.73922i | 0.649581i | 0.945786 | + | 0.324791i | \(0.105294\pi\) | ||||
−0.945786 | + | 0.324791i | \(0.894706\pi\) | |||||||
\(182\) | −0.936566 | − | 10.1114i | −0.0694229 | − | 0.749505i | ||||
\(183\) | 4.80048 | + | 4.80048i | 0.354862 | + | 0.354862i | ||||
\(184\) | −3.50471 | − | 2.02344i | −0.258371 | − | 0.149170i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.16471 | + | 8.94554i | 0.378695 | + | 0.655919i | ||||
\(187\) | 3.78871 | − | 1.01518i | 0.277058 | − | 0.0742374i | ||||
\(188\) | 4.34719 | − | 4.34719i | 0.317051 | − | 0.317051i | ||||
\(189\) | 0.446149 | − | 2.60786i | 0.0324525 | − | 0.189694i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.43796 | − | 9.41883i | 0.393477 | − | 0.681523i | −0.599428 | − | 0.800429i | \(-0.704605\pi\) |
0.992906 | + | 0.118906i | \(0.0379386\pi\) | |||||||
\(192\) | 0.258819 | − | 0.965926i | 0.0186787 | − | 0.0697097i | ||||
\(193\) | −2.89908 | + | 10.8195i | −0.208680 | + | 0.778806i | 0.779616 | + | 0.626258i | \(0.215414\pi\) |
−0.988296 | + | 0.152548i | \(0.951252\pi\) | |||||||
\(194\) | −5.13869 | + | 8.90047i | −0.368936 | + | 0.639016i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.28572 | − | 6.88091i | −0.0918371 | − | 0.491494i | ||||
\(197\) | 10.3775 | − | 10.3775i | 0.739367 | − | 0.739367i | −0.233088 | − | 0.972456i | \(-0.574883\pi\) |
0.972456 | + | 0.233088i | \(0.0748831\pi\) | |||||||
\(198\) | −1.70588 | + | 0.457089i | −0.121232 | + | 0.0324839i | ||||
\(199\) | −9.28152 | − | 16.0761i | −0.657949 | − | 1.13960i | −0.981146 | − | 0.193270i | \(-0.938091\pi\) |
0.323197 | − | 0.946332i | \(-0.395243\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.61524 | − | 3.81931i | −0.466603 | − | 0.269394i | ||||
\(202\) | 12.9730 | + | 12.9730i | 0.912780 | + | 0.912780i | ||||
\(203\) | −8.30609 | + | 5.87928i | −0.582973 | + | 0.412645i | ||||
\(204\) | − | 2.22097i | − | 0.155499i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.89804 | − | 4.55993i | 0.550282 | − | 0.317706i | ||||
\(207\) | 3.90900 | + | 1.04741i | 0.271694 | + | 0.0728002i | ||||
\(208\) | 0.993373 | + | 3.70732i | 0.0688780 | + | 0.257056i | ||||
\(209\) | 3.13296 | 0.216712 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.453133 | −0.0311950 | −0.0155975 | − | 0.999878i | \(-0.504965\pi\) | ||||
−0.0155975 | + | 0.999878i | \(0.504965\pi\) | |||||||
\(212\) | −0.106258 | − | 0.396561i | −0.00729784 | − | 0.0272359i | ||||
\(213\) | 10.3540 | + | 2.77435i | 0.709446 | + | 0.190096i | ||||
\(214\) | −12.7779 | + | 7.37735i | −0.873483 | + | 0.504305i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −24.8271 | − | 11.4234i | −1.68537 | − | 0.775473i | ||||
\(218\) | 14.2474 | + | 14.2474i | 0.964955 | + | 0.964955i | ||||
\(219\) | 9.20830 | + | 5.31641i | 0.622239 | + | 0.359250i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.26215 | + | 7.38226i | 0.286703 | + | 0.496585i | ||||
\(222\) | 3.21516 | − | 0.861499i | 0.215787 | − | 0.0578201i | ||||
\(223\) | −4.67260 | + | 4.67260i | −0.312901 | + | 0.312901i | −0.846032 | − | 0.533132i | \(-0.821015\pi\) |
0.533132 | + | 0.846032i | \(0.321015\pi\) | |||||||
\(224\) | 0.917556 | + | 2.48155i | 0.0613068 | + | 0.165806i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.62927 | + | 8.01813i | −0.307934 | + | 0.533358i | ||||
\(227\) | 4.29835 | − | 16.0416i | 0.285291 | − | 1.06472i | −0.663335 | − | 0.748323i | \(-0.730860\pi\) |
0.948626 | − | 0.316399i | \(-0.102474\pi\) | |||||||
\(228\) | 0.459142 | − | 1.71354i | 0.0304074 | − | 0.113482i | ||||
\(229\) | −6.77075 | + | 11.7273i | −0.447423 | + | 0.774960i | −0.998217 | − | 0.0596810i | \(-0.980992\pi\) |
0.550794 | + | 0.834641i | \(0.314325\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.98518 | − | 3.59463i | 0.196410 | − | 0.236510i | ||||
\(232\) | 2.71973 | − | 2.71973i | 0.178559 | − | 0.178559i | ||||
\(233\) | 11.1838 | − | 2.99668i | 0.732672 | − | 0.196319i | 0.126853 | − | 0.991922i | \(-0.459512\pi\) |
0.605819 | + | 0.795603i | \(0.292846\pi\) | |||||||
\(234\) | −1.91905 | − | 3.32389i | −0.125452 | − | 0.217290i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.97859 | − | 5.18379i | −0.584456 | − | 0.337436i | ||||
\(237\) | 8.97383 | + | 8.97383i | 0.582913 | + | 0.582913i | ||||
\(238\) | 3.39489 | + | 4.79621i | 0.220058 | + | 0.310892i | ||||
\(239\) | − | 17.0264i | − | 1.10135i | −0.834721 | − | 0.550673i | \(-0.814371\pi\) | ||
0.834721 | − | 0.550673i | \(-0.185629\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.3866 | − | 9.46081i | 1.05555 | − | 0.609424i | 0.131355 | − | 0.991335i | \(-0.458067\pi\) |
0.924199 | + | 0.381911i | \(0.124734\pi\) | |||||||
\(242\) | 7.61250 | + | 2.03976i | 0.489350 | + | 0.131121i | ||||
\(243\) | −0.258819 | − | 0.965926i | −0.0166032 | − | 0.0619642i | ||||
\(244\) | 6.78891 | 0.434615 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.8993 | 0.758674 | ||||||||
\(247\) | 1.76223 | + | 6.57674i | 0.112128 | + | 0.418468i | ||||
\(248\) | 9.97746 | + | 2.67345i | 0.633569 | + | 0.169764i | ||||
\(249\) | −2.37878 | + | 1.37339i | −0.150749 | + | 0.0870350i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.1527i | 1.14579i | 0.819629 | + | 0.572894i | \(0.194179\pi\) | ||||
−0.819629 | + | 0.572894i | \(0.805821\pi\) | |||||||
\(252\) | −1.52856 | − | 2.15951i | −0.0962904 | − | 0.136037i | ||||
\(253\) | 5.05372 | + | 5.05372i | 0.317725 | + | 0.317725i | ||||
\(254\) | −15.3637 | − | 8.87021i | −0.964002 | − | 0.556567i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 23.2500 | − | 6.22983i | 1.45030 | − | 0.388606i | 0.554170 | − | 0.832403i | \(-0.313036\pi\) |
0.896127 | + | 0.443797i | \(0.146369\pi\) | |||||||
\(258\) | −3.46335 | + | 3.46335i | −0.215619 | + | 0.215619i | ||||
\(259\) | −5.62632 | + | 6.77499i | −0.349603 | + | 0.420978i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.92314 | + | 3.33098i | −0.119039 | + | 0.206182i | ||||
\(262\) | −0.248279 | + | 0.926588i | −0.0153387 | + | 0.0572448i | ||||
\(263\) | −3.63274 | + | 13.5576i | −0.224004 | + | 0.835995i | 0.758797 | + | 0.651328i | \(0.225788\pi\) |
−0.982801 | + | 0.184668i | \(0.940879\pi\) | |||||||
\(264\) | −0.883028 | + | 1.52945i | −0.0543466 | + | 0.0941311i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.62773 | + | 4.40224i | 0.0998027 | + | 0.269919i | ||||
\(267\) | 0.789311 | − | 0.789311i | 0.0483051 | − | 0.0483051i | ||||
\(268\) | −7.37834 | + | 1.97702i | −0.450704 | + | 0.120766i | ||||
\(269\) | −13.2762 | − | 22.9951i | −0.809466 | − | 1.40204i | −0.913234 | − | 0.407435i | \(-0.866423\pi\) |
0.103768 | − | 0.994602i | \(-0.466910\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.3582 | + | 5.98031i | 0.629216 | + | 0.363278i | 0.780448 | − | 0.625220i | \(-0.214991\pi\) |
−0.151232 | + | 0.988498i | \(0.548324\pi\) | |||||||
\(272\) | −1.57046 | − | 1.57046i | −0.0952233 | − | 0.0952233i | ||||
\(273\) | 9.22499 | + | 4.24460i | 0.558322 | + | 0.256895i | ||||
\(274\) | 11.1467i | 0.673399i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.50471 | − | 2.02344i | 0.210959 | − | 0.121797i | ||||
\(277\) | −2.28118 | − | 0.611241i | −0.137063 | − | 0.0367259i | 0.189635 | − | 0.981855i | \(-0.439269\pi\) |
−0.326698 | + | 0.945129i | \(0.605936\pi\) | |||||||
\(278\) | −3.51206 | − | 13.1072i | −0.210639 | − | 0.786116i | ||||
\(279\) | −10.3294 | −0.618406 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0306 | −0.658033 | −0.329017 | − | 0.944324i | \(-0.606717\pi\) | ||||
−0.329017 | + | 0.944324i | \(0.606717\pi\) | |||||||
\(282\) | 1.59118 | + | 5.93837i | 0.0947534 | + | 0.353625i | ||||
\(283\) | −22.6131 | − | 6.05917i | −1.34421 | − | 0.360180i | −0.486217 | − | 0.873838i | \(-0.661623\pi\) |
−0.857995 | + | 0.513658i | \(0.828290\pi\) | |||||||
\(284\) | 9.28317 | − | 5.35964i | 0.550855 | − | 0.318036i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 6.77830i | − | 0.400809i | ||||||
\(287\) | −25.6968 | + | 18.1889i | −1.51683 | + | 1.07366i | ||||
\(288\) | 0.707107 | + | 0.707107i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 10.4506 | + | 6.03364i | 0.614740 | + | 0.354920i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.13869 | − | 8.90047i | −0.301235 | − | 0.521755i | ||||
\(292\) | 10.2705 | − | 2.75198i | 0.601037 | − | 0.161047i | ||||
\(293\) | 15.4837 | − | 15.4837i | 0.904565 | − | 0.904565i | −0.0912620 | − | 0.995827i | \(-0.529090\pi\) |
0.995827 | + | 0.0912620i | \(0.0290901\pi\) | |||||||
\(294\) | 6.60190 | + | 2.32699i | 0.385031 | + | 0.135713i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.66429 | − | 2.88263i | 0.0967348 | − | 0.167550i | ||||
\(297\) | 0.457089 | − | 1.70588i | 0.0265230 | − | 0.0989852i | ||||
\(298\) | −2.61371 | + | 9.75450i | −0.151408 | + | 0.565063i | ||||
\(299\) | −7.76618 | + | 13.4514i | −0.449130 | + | 0.777916i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.18520 | − | 12.7731i | 0.125953 | − | 0.736228i | ||||
\(302\) | −10.1186 | + | 10.1186i | −0.582263 | + | 0.582263i | ||||
\(303\) | −17.7215 | + | 4.74846i | −1.01807 | + | 0.272792i | ||||
\(304\) | −0.886994 | − | 1.53632i | −0.0508726 | − | 0.0881139i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.92342 | + | 1.11049i | 0.109954 | + | 0.0634822i | ||||
\(307\) | −2.12149 | − | 2.12149i | −0.121080 | − | 0.121080i | 0.643971 | − | 0.765050i | \(-0.277286\pi\) |
−0.765050 | + | 0.643971i | \(0.777286\pi\) | |||||||
\(308\) | −0.430950 | − | 4.65263i | −0.0245557 | − | 0.265108i | ||||
\(309\) | 9.11987i | 0.518811i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.0082 | − | 7.51027i | 0.737626 | − | 0.425868i | −0.0835796 | − | 0.996501i | \(-0.526635\pi\) |
0.821205 | + | 0.570633i | \(0.193302\pi\) | |||||||
\(312\) | −3.70732 | − | 0.993373i | −0.209886 | − | 0.0562387i | ||||
\(313\) | 3.44701 | + | 12.8644i | 0.194836 | + | 0.727139i | 0.992309 | + | 0.123784i | \(0.0395031\pi\) |
−0.797473 | + | 0.603355i | \(0.793830\pi\) | |||||||
\(314\) | 9.58338 | 0.540821 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.6909 | 0.713920 | ||||||||
\(317\) | −3.59802 | − | 13.4280i | −0.202085 | − | 0.754192i | −0.990318 | − | 0.138815i | \(-0.955671\pi\) |
0.788233 | − | 0.615377i | \(-0.210996\pi\) | |||||||
\(318\) | 0.396561 | + | 0.106258i | 0.0222380 | + | 0.00595867i | ||||
\(319\) | −5.88269 | + | 3.39638i | −0.329368 | + | 0.190160i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 14.7547i | − | 0.823527i | ||||||
\(322\) | −4.47550 | + | 9.72682i | −0.249410 | + | 0.542055i | ||||
\(323\) | −2.78598 | − | 2.78598i | −0.155016 | − | 0.155016i | ||||
\(324\) | −0.866025 | − | 0.500000i | −0.0481125 | − | 0.0277778i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.92183 | + | 10.2569i | 0.327980 | + | 0.568078i | ||||
\(327\) | −19.4623 | + | 5.21491i | −1.07627 | + | 0.288385i | ||||
\(328\) | 8.41410 | − | 8.41410i | 0.464591 | − | 0.464591i | ||||
\(329\) | −12.5133 | − | 10.3918i | −0.689883 | − | 0.572916i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.31631 | − | 16.1363i | 0.512071 | − | 0.886932i | −0.487832 | − | 0.872938i | \(-0.662212\pi\) |
0.999902 | − | 0.0139944i | \(-0.00445470\pi\) | |||||||
\(332\) | −0.710918 | + | 2.65318i | −0.0390167 | + | 0.145612i | ||||
\(333\) | −0.861499 | + | 3.21516i | −0.0472099 | + | 0.176190i | ||||
\(334\) | 4.92063 | − | 8.52279i | 0.269245 | − | 0.466346i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.60786 | − | 0.446149i | −0.142271 | − | 0.0243394i | ||||
\(337\) | −9.63568 | + | 9.63568i | −0.524889 | + | 0.524889i | −0.919044 | − | 0.394155i | \(-0.871037\pi\) |
0.394155 | + | 0.919044i | \(0.371037\pi\) | |||||||
\(338\) | 1.67202 | − | 0.448015i | 0.0909456 | − | 0.0243688i | ||||
\(339\) | −4.62927 | − | 8.01813i | −0.251427 | − | 0.435485i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.7983 | − | 9.12117i | −0.855528 | − | 0.493939i | ||||
\(342\) | 1.25440 | + | 1.25440i | 0.0678301 | + | 0.0678301i | ||||
\(343\) | −17.8138 | + | 5.06626i | −0.961857 | + | 0.273552i | ||||
\(344\) | 4.89791i | 0.264078i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.50509 | + | 4.33306i | −0.403476 | + | 0.232947i | ||||
\(347\) | 33.6890 | + | 9.02693i | 1.80852 | + | 0.484591i | 0.995255 | − | 0.0973042i | \(-0.0310220\pi\) |
0.813264 | + | 0.581895i | \(0.197689\pi\) | |||||||
\(348\) | 0.995491 | + | 3.71522i | 0.0533639 | + | 0.199157i | ||||
\(349\) | −1.49727 | −0.0801469 | −0.0400735 | − | 0.999197i | \(-0.512759\pi\) | ||||
−0.0400735 | + | 0.999197i | \(0.512759\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.83810 | 0.204863 | ||||||||
\(352\) | 0.457089 | + | 1.70588i | 0.0243629 | + | 0.0909237i | ||||
\(353\) | 5.76343 | + | 1.54431i | 0.306756 | + | 0.0821951i | 0.408913 | − | 0.912573i | \(-0.365908\pi\) |
−0.102157 | + | 0.994768i | \(0.532574\pi\) | |||||||
\(354\) | 8.97859 | − | 5.18379i | 0.477207 | − | 0.275515i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 1.11625i | − | 0.0591614i | ||||||
\(357\) | −5.85109 | + | 0.541957i | −0.309673 | + | 0.0286834i | ||||
\(358\) | 9.44244 | + | 9.44244i | 0.499049 | + | 0.499049i | ||||
\(359\) | 14.9989 | + | 8.65964i | 0.791613 | + | 0.457038i | 0.840530 | − | 0.541765i | \(-0.182244\pi\) |
−0.0489170 | + | 0.998803i | \(0.515577\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.92648 | + | 13.7291i | 0.417183 | + | 0.722583i | ||||
\(362\) | −8.44144 | + | 2.26188i | −0.443672 | + | 0.118882i | ||||
\(363\) | −5.57274 | + | 5.57274i | −0.292493 | + | 0.292493i | ||||
\(364\) | 9.52443 | − | 3.52167i | 0.499216 | − | 0.184586i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.39445 | + | 5.87936i | −0.177431 | + | 0.307319i | ||||
\(367\) | −1.41960 | + | 5.29802i | −0.0741025 | + | 0.276554i | −0.993028 | − | 0.117876i | \(-0.962391\pi\) |
0.918926 | + | 0.394430i | \(0.129058\pi\) | |||||||
\(368\) | 1.04741 | − | 3.90900i | 0.0546001 | − | 0.203770i | ||||
\(369\) | −5.94967 | + | 10.3051i | −0.309727 | + | 0.536464i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.01880 | + | 0.376703i | −0.0528935 | + | 0.0195574i | ||||
\(372\) | −7.30401 | + | 7.30401i | −0.378695 | + | 0.378695i | ||||
\(373\) | 29.7901 | − | 7.98224i | 1.54247 | − | 0.413305i | 0.615410 | − | 0.788207i | \(-0.288991\pi\) |
0.927064 | + | 0.374903i | \(0.122324\pi\) | |||||||
\(374\) | 1.96118 | + | 3.39686i | 0.101410 | + | 0.175648i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.32419 | + | 3.07393i | 0.274574 | + | 0.158526i | ||||
\(377\) | −10.4386 | − | 10.4386i | −0.537615 | − | 0.537615i | ||||
\(378\) | 2.63447 | − | 0.244018i | 0.135503 | − | 0.0125509i | ||||
\(379\) | − | 12.9203i | − | 0.663670i | −0.943337 | − | 0.331835i | \(-0.892332\pi\) | ||
0.943337 | − | 0.331835i | \(-0.107668\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.3637 | − | 8.87021i | 0.787104 | − | 0.454435i | ||||
\(382\) | 10.5053 | + | 2.81490i | 0.537500 | + | 0.144023i | ||||
\(383\) | 0.308002 | + | 1.14948i | 0.0157382 | + | 0.0587356i | 0.973348 | − | 0.229332i | \(-0.0736540\pi\) |
−0.957610 | + | 0.288067i | \(0.906987\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.2012 | −0.570126 | ||||||||
\(387\) | −1.26767 | − | 4.73102i | −0.0644394 | − | 0.240491i | ||||
\(388\) | −9.92718 | − | 2.65998i | −0.503976 | − | 0.135040i | ||||
\(389\) | −8.25213 | + | 4.76437i | −0.418400 | + | 0.241563i | −0.694392 | − | 0.719597i | \(-0.744327\pi\) |
0.275993 | + | 0.961160i | \(0.410993\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8.98802i | − | 0.454544i | ||||||
\(392\) | 6.31368 | − | 3.02282i | 0.318889 | − | 0.152675i | ||||
\(393\) | −0.678310 | − | 0.678310i | −0.0342162 | − | 0.0342162i | ||||
\(394\) | 12.7098 | + | 7.33801i | 0.640311 | + | 0.369684i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.883028 | − | 1.52945i | −0.0443738 | − | 0.0768578i | ||||
\(397\) | 27.5610 | − | 7.38494i | 1.38324 | − | 0.370639i | 0.510946 | − | 0.859613i | \(-0.329295\pi\) |
0.872299 | + | 0.488974i | \(0.162629\pi\) | |||||||
\(398\) | 13.1260 | − | 13.1260i | 0.657949 | − | 0.657949i | ||||
\(399\) | −4.62632 | − | 0.791463i | −0.231606 | − | 0.0396227i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.6150 | + | 33.9741i | −0.979526 | + | 1.69659i | −0.315415 | + | 0.948954i | \(0.602144\pi\) |
−0.664111 | + | 0.747634i | \(0.731190\pi\) | |||||||
\(402\) | 1.97702 | − | 7.37834i | 0.0986049 | − | 0.367998i | ||||
\(403\) | 10.2610 | − | 38.2945i | 0.511135 | − | 1.90758i | ||||
\(404\) | −9.17333 | + | 15.8887i | −0.456390 | + | 0.790491i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.82873 | − | 6.50140i | −0.388533 | − | 0.322659i | ||||
\(407\) | −4.15670 | + | 4.15670i | −0.206040 | + | 0.206040i | ||||
\(408\) | 2.14529 | − | 0.574830i | 0.106208 | − | 0.0284583i | ||||
\(409\) | 4.32912 | + | 7.49826i | 0.214061 | + | 0.370765i | 0.952982 | − | 0.303028i | \(-0.0979974\pi\) |
−0.738920 | + | 0.673793i | \(0.764664\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.65336 | − | 5.57337i | −0.476165 | − | 0.274914i | ||||
\(412\) | 6.44872 | + | 6.44872i | 0.317706 | + | 0.317706i | ||||
\(413\) | −11.4656 | + | 24.9188i | −0.564187 | + | 1.22617i | ||||
\(414\) | 4.04689i | 0.198894i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.32389 | + | 1.91905i | −0.162967 | + | 0.0940891i | ||||
\(417\) | 13.1072 | + | 3.51206i | 0.641861 | + | 0.171986i | ||||
\(418\) | 0.810871 | + | 3.02621i | 0.0396610 | + | 0.148017i | ||||
\(419\) | 4.29623 | 0.209884 | 0.104942 | − | 0.994478i | \(-0.466534\pi\) | ||||
0.104942 | + | 0.994478i | \(0.466534\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.8346 | −0.917945 | −0.458972 | − | 0.888451i | \(-0.651782\pi\) | ||||
−0.458972 | + | 0.888451i | \(0.651782\pi\) | |||||||
\(422\) | −0.117279 | − | 0.437693i | −0.00570907 | − | 0.0213066i | ||||
\(423\) | −5.93837 | − | 1.59118i | −0.288733 | − | 0.0773659i | ||||
\(424\) | 0.355547 | − | 0.205275i | 0.0172669 | − | 0.00996904i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.7193i | 0.519351i | ||||||||
\(427\) | −1.65662 | − | 17.8852i | −0.0801693 | − | 0.865525i | ||||
\(428\) | −10.4332 | − | 10.4332i | −0.504305 | − | 0.504305i | ||||
\(429\) | 5.87018 | + | 3.38915i | 0.283415 | + | 0.163630i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.46231 | − | 5.99690i | −0.166774 | − | 0.288860i | 0.770510 | − | 0.637428i | \(-0.220002\pi\) |
−0.937284 | + | 0.348567i | \(0.886668\pi\) | |||||||
\(432\) | −0.965926 | + | 0.258819i | −0.0464731 | + | 0.0124524i | ||||
\(433\) | −11.5154 | + | 11.5154i | −0.553393 | + | 0.553393i | −0.927419 | − | 0.374025i | \(-0.877977\pi\) |
0.374025 | + | 0.927419i | \(0.377977\pi\) | |||||||
\(434\) | 4.60846 | − | 26.9377i | 0.221213 | − | 1.29305i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0744 | + | 17.4494i | −0.482477 | + | 0.835675i | ||||
\(437\) | 1.85810 | − | 6.93451i | 0.0888848 | − | 0.331723i | ||||
\(438\) | −2.75198 | + | 10.2705i | −0.131495 | + | 0.490745i | ||||
\(439\) | 9.11194 | − | 15.7823i | 0.434889 | − | 0.753250i | −0.562397 | − | 0.826867i | \(-0.690121\pi\) |
0.997287 | + | 0.0736169i | \(0.0234542\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.31618 | + | 4.55392i | −0.253152 | + | 0.216853i | ||||
\(442\) | −6.02759 | + | 6.02759i | −0.286703 | + | 0.286703i | ||||
\(443\) | −31.7136 | + | 8.49765i | −1.50676 | + | 0.403735i | −0.915358 | − | 0.402641i | \(-0.868092\pi\) |
−0.591403 | + | 0.806376i | \(0.701426\pi\) | |||||||
\(444\) | 1.66429 | + | 2.88263i | 0.0789837 | + | 0.136804i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.72275 | − | 3.30403i | −0.270980 | − | 0.156450i | ||||
\(447\) | −7.14079 | − | 7.14079i | −0.337748 | − | 0.337748i | ||||
\(448\) | −2.15951 | + | 1.52856i | −0.102027 | + | 0.0722178i | ||||
\(449\) | − | 8.14032i | − | 0.384165i | −0.981379 | − | 0.192083i | \(-0.938476\pi\) | ||
0.981379 | − | 0.192083i | \(-0.0615242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.1994 | + | 10.5075i | −0.856978 | + | 0.494777i | ||||
\(452\) | −8.94306 | − | 2.39629i | −0.420646 | − | 0.112712i | ||||
\(453\) | −3.70368 | − | 13.8223i | −0.174014 | − | 0.649430i | ||||
\(454\) | 16.6075 | 0.779430 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.77399 | 0.0830746 | ||||||||
\(457\) | −1.18177 | − | 4.41041i | −0.0552806 | − | 0.206310i | 0.932762 | − | 0.360494i | \(-0.117392\pi\) |
−0.988042 | + | 0.154184i | \(0.950725\pi\) | |||||||
\(458\) | −13.0801 | − | 3.50480i | −0.611192 | − | 0.163768i | ||||
\(459\) | −1.92342 | + | 1.11049i | −0.0897774 | + | 0.0518330i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.54894i | − | 0.351589i | −0.984427 | − | 0.175795i | \(-0.943751\pi\) | ||
0.984427 | − | 0.175795i | \(-0.0562495\pi\) | |||||||
\(462\) | 4.24477 | + | 1.95310i | 0.197485 | + | 0.0908665i | ||||
\(463\) | 8.87647 | + | 8.87647i | 0.412525 | + | 0.412525i | 0.882617 | − | 0.470092i | \(-0.155779\pi\) |
−0.470092 | + | 0.882617i | \(0.655779\pi\) | |||||||
\(464\) | 3.33098 | + | 1.92314i | 0.154637 | + | 0.0892796i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.78914 | + | 10.0271i | 0.268177 | + | 0.464495i | ||||
\(467\) | −11.1162 | + | 2.97858i | −0.514397 | + | 0.137832i | −0.506674 | − | 0.862138i | \(-0.669125\pi\) |
−0.00772331 | + | 0.999970i | \(0.502458\pi\) | |||||||
\(468\) | 2.71395 | − | 2.71395i | 0.125452 | − | 0.125452i | ||||
\(469\) | 7.00886 | + | 18.9556i | 0.323639 | + | 0.875290i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.79169 | + | 8.29945i | −0.220789 | + | 0.382418i | ||||
\(472\) | 2.68333 | − | 10.0143i | 0.123510 | − | 0.460946i | ||||
\(473\) | 2.23878 | − | 8.35525i | 0.102939 | − | 0.384175i | ||||
\(474\) | −6.34546 | + | 10.9907i | −0.291457 | + | 0.504817i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.75412 | + | 4.52057i | −0.172070 | + | 0.207200i | ||||
\(477\) | −0.290303 | + | 0.290303i | −0.0132921 | + | 0.0132921i | ||||
\(478\) | 16.4462 | − | 4.40676i | 0.752233 | − | 0.201560i | ||||
\(479\) | 6.17379 | + | 10.6933i | 0.282088 | + | 0.488590i | 0.971899 | − | 0.235399i | \(-0.0756398\pi\) |
−0.689811 | + | 0.723989i | \(0.742306\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.0638 | − | 6.38770i | −0.504467 | − | 0.291254i | ||||
\(482\) | 13.3796 | + | 13.3796i | 0.609424 | + | 0.609424i | ||||
\(483\) | −6.18593 | − | 8.73931i | −0.281469 | − | 0.397652i | ||||
\(484\) | 7.88104i | 0.358229i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | −15.0556 | − | 4.03414i | −0.682235 | − | 0.182804i | −0.0989752 | − | 0.995090i | \(-0.531556\pi\) |
−0.583260 | + | 0.812286i | \(0.698223\pi\) | |||||||
\(488\) | 1.75710 | + | 6.55758i | 0.0795401 | + | 0.296848i | ||||
\(489\) | −11.8437 | −0.535589 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.67474 | −0.120709 | −0.0603547 | − | 0.998177i | \(-0.519223\pi\) | ||||
−0.0603547 | + | 0.998177i | \(0.519223\pi\) | |||||||
\(492\) | 3.07978 | + | 11.4939i | 0.138847 | + | 0.518184i | ||||
\(493\) | 8.25140 | + | 2.21096i | 0.371624 | + | 0.0995764i | ||||
\(494\) | −5.89654 | + | 3.40437i | −0.265298 | + | 0.153170i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.3294i | 0.463805i | ||||||||
\(497\) | −16.3851 | − | 23.1484i | −0.734972 | − | 1.03835i | ||||
\(498\) | −1.94227 | − | 1.94227i | −0.0870350 | − | 0.0870350i | ||||
\(499\) | −15.7413 | − | 9.08825i | −0.704678 | − | 0.406846i | 0.104410 | − | 0.994534i | \(-0.466705\pi\) |
−0.809087 | + | 0.587688i | \(0.800038\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.92063 | + | 8.52279i | 0.219838 | + | 0.380770i | ||||
\(502\) | −17.5342 | + | 4.69827i | −0.782588 | + | 0.209694i | ||||
\(503\) | 3.59630 | − | 3.59630i | 0.160351 | − | 0.160351i | −0.622371 | − | 0.782722i | \(-0.713831\pi\) |
0.782722 | + | 0.622371i | \(0.213831\pi\) | |||||||
\(504\) | 1.69031 | − | 2.03540i | 0.0752923 | − | 0.0906640i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.57352 | + | 6.18952i | −0.158862 | + | 0.275158i | ||||
\(507\) | −0.448015 | + | 1.67202i | −0.0198971 | + | 0.0742568i | ||||
\(508\) | 4.59156 | − | 17.1359i | 0.203718 | − | 0.760284i | ||||
\(509\) | 2.40629 | − | 4.16782i | 0.106657 | − | 0.184735i | −0.807757 | − | 0.589516i | \(-0.799319\pi\) |
0.914414 | + | 0.404780i | \(0.132652\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.75621 | − | 26.3859i | −0.431589 | − | 1.16724i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −1.71354 | + | 0.459142i | −0.0756547 | + | 0.0202716i | ||||
\(514\) | 12.0351 | + | 20.8454i | 0.530846 | + | 0.919452i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.24172 | − | 2.44896i | −0.186731 | − | 0.107809i | ||||
\(517\) | −7.67738 | − | 7.67738i | −0.337651 | − | 0.337651i | ||||
\(518\) | −8.00034 | − | 3.68111i | −0.351515 | − | 0.161739i | ||||
\(519\) | − | 8.66613i | − | 0.380401i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.61481 | − | 2.66436i | 0.202178 | − | 0.116728i | −0.395493 | − | 0.918469i | \(-0.629426\pi\) |
0.597671 | + | 0.801741i | \(0.296093\pi\) | |||||||
\(522\) | −3.71522 | − | 0.995491i | −0.162611 | − | 0.0435714i | ||||
\(523\) | −1.58561 | − | 5.91757i | −0.0693338 | − | 0.258757i | 0.922555 | − | 0.385866i | \(-0.126097\pi\) |
−0.991889 | + | 0.127108i | \(0.959430\pi\) | |||||||
\(524\) | −0.959275 | −0.0419061 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.0358 | −0.611991 | ||||||||
\(527\) | 5.93766 | + | 22.1596i | 0.258648 | + | 0.965289i | ||||
\(528\) | −1.70588 | − | 0.457089i | −0.0742389 | − | 0.0198923i | ||||
\(529\) | −5.73541 | + | 3.31134i | −0.249366 | + | 0.143971i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3676i | 0.449915i | ||||||||
\(532\) | −3.83095 | + | 2.71165i | −0.166093 | + | 0.117565i | ||||
\(533\) | −32.2942 | − | 32.2942i | −1.39881 | − | 1.39881i | ||||
\(534\) | 0.966705 | + | 0.558127i | 0.0418334 | + | 0.0241525i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.81931 | − | 6.61524i | −0.164969 | − | 0.285735i | ||||
\(537\) | −12.8986 | + | 3.45617i | −0.556617 | + | 0.149145i | ||||
\(538\) | 18.7754 | − | 18.7754i | 0.809466 | − | 0.809466i | ||||
\(539\) | −12.1521 | + | 2.27065i | −0.523427 | + | 0.0978040i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.81239 | − | 11.7994i | 0.292887 | − | 0.507296i | −0.681604 | − | 0.731721i | \(-0.738717\pi\) |
0.974491 | + | 0.224426i | \(0.0720506\pi\) | |||||||
\(542\) | −3.09564 | + | 11.5531i | −0.132969 | + | 0.496247i | ||||
\(543\) | 2.26188 | − | 8.44144i | 0.0970664 | − | 0.362257i | ||||
\(544\) | 1.11049 | − | 1.92342i | 0.0476117 | − | 0.0824658i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.71236 | + | 10.0092i | −0.0732823 | + | 0.428356i | ||||
\(547\) | 14.8290 | − | 14.8290i | 0.634042 | − | 0.634042i | −0.315037 | − | 0.949079i | \(-0.602017\pi\) |
0.949079 | + | 0.315037i | \(0.102017\pi\) | |||||||
\(548\) | −10.7669 | + | 2.88499i | −0.459940 | + | 0.123241i | ||||
\(549\) | −3.39445 | − | 5.87936i | −0.144872 | − | 0.250925i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.90911 | + | 3.41163i | 0.251737 | + | 0.145340i | ||||
\(552\) | 2.86158 | + | 2.86158i | 0.121797 | + | 0.121797i | ||||
\(553\) | −3.09681 | − | 33.4339i | −0.131690 | − | 1.42175i | ||||
\(554\) | − | 2.36165i | − | 0.100337i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.7516 | − | 6.78477i | 0.498378 | − | 0.287738i | ||||
\(557\) | 0.0387479 | + | 0.0103825i | 0.00164180 | + | 0.000439920i | 0.259640 | − | 0.965706i | \(-0.416396\pi\) |
−0.257998 | + | 0.966145i | \(0.583063\pi\) | |||||||
\(558\) | −2.67345 | − | 9.97746i | −0.113176 | − | 0.422379i | ||||
\(559\) | 18.7987 | 0.795099 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.92236 | −0.165602 | ||||||||
\(562\) | −2.85494 | − | 10.6548i | −0.120428 | − | 0.449445i | ||||
\(563\) | −13.4327 | − | 3.59929i | −0.566122 | − | 0.151692i | −0.0356047 | − | 0.999366i | \(-0.511336\pi\) |
−0.530518 | + | 0.847674i | \(0.678002\pi\) | |||||||
\(564\) | −5.32419 | + | 3.07393i | −0.224189 | + | 0.129436i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 23.4108i | − | 0.984031i | ||||||
\(567\) | −1.10591 | + | 2.40353i | −0.0464439 | + | 0.100939i | ||||
\(568\) | 7.57968 | + | 7.57968i | 0.318036 | + | 0.318036i | ||||
\(569\) | 17.1817 | + | 9.91984i | 0.720293 | + | 0.415861i | 0.814860 | − | 0.579657i | \(-0.196814\pi\) |
−0.0945677 | + | 0.995518i | \(0.530147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.94454 | + | 5.10010i | 0.123225 | + | 0.213432i | 0.921038 | − | 0.389473i | \(-0.127343\pi\) |
−0.797813 | + | 0.602906i | \(0.794010\pi\) | |||||||
\(572\) | 6.54733 | − | 1.75435i | 0.273758 | − | 0.0733532i | ||||
\(573\) | −7.69044 | + | 7.69044i | −0.321273 | + | 0.321273i | ||||
\(574\) | −24.2199 | − | 20.1135i | −1.01092 | − | 0.839523i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −3.85984 | + | 14.4051i | −0.160687 | + | 0.599692i | 0.837864 | + | 0.545879i | \(0.183804\pi\) |
−0.998551 | + | 0.0538132i | \(0.982862\pi\) | |||||||
\(578\) | −3.12324 | + | 11.6561i | −0.129910 | + | 0.484830i | ||||
\(579\) | 5.60060 | − | 9.70052i | 0.232753 | − | 0.403140i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.16322 | + | 1.22547i | 0.297180 | + | 0.0508411i | ||||
\(582\) | 7.26720 | − | 7.26720i | 0.301235 | − | 0.301235i | ||||
\(583\) | −0.700349 | + | 0.187658i | −0.0290055 | + | 0.00777200i | ||||
\(584\) | 5.31641 | + | 9.20830i | 0.219995 | + | 0.381042i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.9635 | + | 10.9486i | 0.783376 | + | 0.452282i | ||||
\(587\) | 4.86057 | + | 4.86057i | 0.200617 | + | 0.200617i | 0.800264 | − | 0.599647i | \(-0.204692\pi\) |
−0.599647 | + | 0.800264i | \(0.704692\pi\) | |||||||
\(588\) | −0.539001 | + | 6.97922i | −0.0222280 | + | 0.287818i | ||||
\(589\) | 18.3243i | 0.755039i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.7098 | + | 7.33801i | −0.522812 | + | 0.301846i | ||||
\(592\) | 3.21516 | + | 0.861499i | 0.132142 | + | 0.0354074i | ||||
\(593\) | 5.48532 | + | 20.4715i | 0.225255 | + | 0.840664i | 0.982302 | + | 0.187304i | \(0.0599748\pi\) |
−0.757047 | + | 0.653361i | \(0.773359\pi\) | |||||||
\(594\) | 1.76606 | 0.0724622 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.0986 | −0.413655 | ||||||||
\(597\) | 4.80447 | + | 17.9305i | 0.196634 | + | 0.733847i | ||||
\(598\) | −15.0031 | − | 4.02007i | −0.613523 | − | 0.164393i | ||||
\(599\) | 10.0409 | − | 5.79712i | 0.410260 | − | 0.236864i | −0.280641 | − | 0.959813i | \(-0.590547\pi\) |
0.690902 | + | 0.722949i | \(0.257214\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.3561i | 0.626387i | 0.949689 | + | 0.313193i | \(0.101399\pi\) | ||||
−0.949689 | + | 0.313193i | \(0.898601\pi\) | |||||||
\(602\) | 12.9034 | − | 1.19518i | 0.525904 | − | 0.0487119i | ||||
\(603\) | 5.40132 | + | 5.40132i | 0.219959 | + | 0.219959i | ||||
\(604\) | −12.3928 | − | 7.15497i | −0.504254 | − | 0.291131i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.17333 | − | 15.8887i | −0.372641 | − | 0.645433i | ||||
\(607\) | −21.7853 | + | 5.83734i | −0.884237 | + | 0.236931i | −0.672234 | − | 0.740339i | \(-0.734665\pi\) |
−0.212003 | + | 0.977269i | \(0.567999\pi\) | |||||||
\(608\) | 1.25440 | − | 1.25440i | 0.0508726 | − | 0.0508726i | ||||
\(609\) | 9.54474 | − | 3.52918i | 0.386772 | − | 0.143009i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.7980 | − | 20.4348i | 0.477297 | − | 0.826703i | ||||
\(612\) | −0.574830 | + | 2.14529i | −0.0232361 | + | 0.0867183i | ||||
\(613\) | 1.23846 | − | 4.62200i | 0.0500209 | − | 0.186681i | −0.936395 | − | 0.350948i | \(-0.885859\pi\) |
0.986416 | + | 0.164267i | \(0.0525260\pi\) | |||||||
\(614\) | 1.50012 | − | 2.59828i | 0.0605399 | − | 0.104858i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.38256 | − | 1.62046i | 0.176578 | − | 0.0652900i | ||||
\(617\) | −17.3498 | + | 17.3498i | −0.698475 | + | 0.698475i | −0.964082 | − | 0.265606i | \(-0.914428\pi\) |
0.265606 | + | 0.964082i | \(0.414428\pi\) | |||||||
\(618\) | −8.80911 | + | 2.36040i | −0.354355 | + | 0.0949490i | ||||
\(619\) | 10.4801 | + | 18.1521i | 0.421232 | + | 0.729596i | 0.996060 | − | 0.0886786i | \(-0.0282644\pi\) |
−0.574828 | + | 0.818274i | \(0.694931\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.50471 | − | 2.02344i | −0.140639 | − | 0.0811980i | ||||
\(622\) | 10.6211 | + | 10.6211i | 0.425868 | + | 0.425868i | ||||
\(623\) | −2.94074 | + | 0.272387i | −0.117818 | + | 0.0109129i | ||||
\(624\) | − | 3.83810i | − | 0.153647i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.5339 | + | 6.65911i | −0.460988 | + | 0.266152i | ||||
\(627\) | −3.02621 | − | 0.810871i | −0.120855 | − | 0.0323831i | ||||
\(628\) | 2.48036 | + | 9.25683i | 0.0989772 | + | 0.369388i | ||||
\(629\) | 7.39267 | 0.294765 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −48.7823 | −1.94199 | −0.970996 | − | 0.239095i | \(-0.923149\pi\) | ||||
−0.970996 | + | 0.239095i | \(0.923149\pi\) | |||||||
\(632\) | 3.28465 | + | 12.2585i | 0.130656 | + | 0.487616i | ||||
\(633\) | 0.437693 | + | 0.117279i | 0.0173967 | + | 0.00466144i | ||||
\(634\) | 12.0392 | − | 6.95084i | 0.478138 | − | 0.276053i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.410550i | 0.0162794i | ||||||||
\(637\) | −11.6019 | − | 24.2325i | −0.459683 | − | 0.960128i | ||||
\(638\) | −4.80320 | − | 4.80320i | −0.190160 | − | 0.190160i | ||||
\(639\) | −9.28317 | − | 5.35964i | −0.367237 | − | 0.212024i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.03196 | − | 10.4477i | −0.238248 | − | 0.412658i | 0.721964 | − | 0.691931i | \(-0.243240\pi\) |
−0.960212 | + | 0.279273i | \(0.909906\pi\) | |||||||
\(642\) | 14.2519 | − | 3.81880i | 0.562480 | − | 0.150716i | ||||
\(643\) | −15.5935 | + | 15.5935i | −0.614947 | + | 0.614947i | −0.944231 | − | 0.329284i | \(-0.893193\pi\) |
0.329284 | + | 0.944231i | \(0.393193\pi\) | |||||||
\(644\) | −10.5537 | − | 1.80551i | −0.415875 | − | 0.0711472i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.96999 | − | 3.41212i | 0.0775082 | − | 0.134248i | ||||
\(647\) | 1.69672 | − | 6.33226i | 0.0667051 | − | 0.248947i | −0.924520 | − | 0.381135i | \(-0.875533\pi\) |
0.991225 | + | 0.132188i | \(0.0422001\pi\) | |||||||
\(648\) | 0.258819 | − | 0.965926i | 0.0101674 | − | 0.0379452i | ||||
\(649\) | −9.15487 | + | 15.8567i | −0.359360 | + | 0.622430i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.0245 | + | 17.4599i | 0.824016 | + | 0.684308i | ||||
\(652\) | −8.37474 | + | 8.37474i | −0.327980 | + | 0.327980i | ||||
\(653\) | −22.3037 | + | 5.97625i | −0.872811 | + | 0.233869i | −0.667303 | − | 0.744787i | \(-0.732551\pi\) |
−0.205508 | + | 0.978655i | \(0.565885\pi\) | |||||||
\(654\) | −10.0744 | − | 17.4494i | −0.393941 | − | 0.682326i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.3051 | + | 5.94967i | 0.402348 | + | 0.232296i | ||||
\(657\) | −7.51854 | − | 7.51854i | −0.293326 | − | 0.293326i | ||||
\(658\) | 6.79898 | − | 14.7765i | 0.265052 | − | 0.576050i | ||||
\(659\) | − | 8.89429i | − | 0.346472i | −0.984880 | − | 0.173236i | \(-0.944578\pi\) | ||
0.984880 | − | 0.173236i | \(-0.0554224\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.24046 | − | 4.18028i | 0.281621 | − | 0.162594i | −0.352536 | − | 0.935798i | \(-0.614681\pi\) |
0.634157 | + | 0.773204i | \(0.281347\pi\) | |||||||
\(662\) | 17.9977 | + | 4.82248i | 0.699501 | + | 0.187431i | ||||
\(663\) | −2.20625 | − | 8.23385i | −0.0856837 | − | 0.319776i | ||||
\(664\) | −2.74678 | −0.106596 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.32858 | −0.128980 | ||||||||
\(667\) | 4.02864 | + | 15.0351i | 0.155990 | + | 0.582161i | ||||
\(668\) | 9.50594 | + | 2.54711i | 0.367796 | + | 0.0985506i | ||||
\(669\) | 5.72275 | − | 3.30403i | 0.221254 | − | 0.127741i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 11.9896i | − | 0.462853i | ||||||
\(672\) | −0.244018 | − | 2.63447i | −0.00941321 | − | 0.101627i | ||||
\(673\) | 11.1305 | + | 11.1305i | 0.429048 | + | 0.429048i | 0.888304 | − | 0.459256i | \(-0.151884\pi\) |
−0.459256 | + | 0.888304i | \(0.651884\pi\) | |||||||
\(674\) | −11.8013 | − | 6.81346i | −0.454567 | − | 0.262444i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.865499 | + | 1.49909i | 0.0332884 | + | 0.0576572i | ||||
\(677\) | −41.9335 | + | 11.2360i | −1.61163 | + | 0.431836i | −0.948529 | − | 0.316690i | \(-0.897429\pi\) |
−0.663106 | + | 0.748526i | \(0.730762\pi\) | |||||||
\(678\) | 6.54677 | − | 6.54677i | 0.251427 | − | 0.251427i | ||||
\(679\) | −4.58524 | + | 26.8020i | −0.175965 | + | 1.02857i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.30377 | + | 14.3825i | −0.318201 | + | 0.551140i | ||||
\(682\) | 4.72147 | − | 17.6208i | 0.180794 | − | 0.674734i | ||||
\(683\) | 4.62860 | − | 17.2742i | 0.177108 | − | 0.660977i | −0.819075 | − | 0.573687i | \(-0.805513\pi\) |
0.996183 | − | 0.0872904i | \(-0.0278208\pi\) | |||||||
\(684\) | −0.886994 | + | 1.53632i | −0.0339151 | + | 0.0587426i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.50420 | − | 15.8956i | −0.362872 | − | 0.606897i | ||||
\(687\) | 9.57528 | − | 9.57528i | 0.365320 | − | 0.365320i | ||||
\(688\) | −4.73102 | + | 1.26767i | −0.180368 | + | 0.0483296i | ||||
\(689\) | −0.787866 | − | 1.36462i | −0.0300153 | − | 0.0519880i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.5564 | + | 17.6417i | 1.16242 | + | 0.671123i | 0.951883 | − | 0.306463i | \(-0.0991456\pi\) |
0.210537 | + | 0.977586i | \(0.432479\pi\) | |||||||
\(692\) | −6.12788 | − | 6.12788i | −0.232947 | − | 0.232947i | ||||
\(693\) | −3.81382 | + | 2.69953i | −0.144875 | + | 0.102547i | ||||
\(694\) | 34.8774i | 1.32393i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.33098 | + | 1.92314i | −0.126260 | + | 0.0728964i | ||||
\(697\) | 25.5276 | + | 6.84009i | 0.966926 | + | 0.259087i | ||||
\(698\) | −0.387522 | − | 1.44625i | −0.0146679 | − | 0.0547414i | ||||
\(699\) | −11.5783 | −0.437930 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.9862 | −0.566020 | −0.283010 | − | 0.959117i | \(-0.591333\pi\) | ||||
−0.283010 | + | 0.959117i | \(0.591333\pi\) | |||||||
\(702\) | 0.993373 | + | 3.70732i | 0.0374924 | + | 0.139924i | ||||
\(703\) | 5.70366 | + | 1.52829i | 0.215117 | + | 0.0576405i | ||||
\(704\) | −1.52945 | + | 0.883028i | −0.0576433 | + | 0.0332804i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.96674i | 0.224561i | ||||||||
\(707\) | 44.0968 | + | 20.2898i | 1.65843 | + | 0.763075i | ||||
\(708\) | 7.33099 | + | 7.33099i | 0.275515 | + | 0.275515i | ||||
\(709\) | 7.19605 | + | 4.15464i | 0.270253 | + | 0.156031i | 0.629003 | − | 0.777403i | \(-0.283463\pi\) |
−0.358750 | + | 0.933434i | \(0.616797\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.34546 | − | 10.9907i | −0.237973 | − | 0.412182i | ||||
\(712\) | 1.07822 | − | 0.288908i | 0.0404080 | − | 0.0108273i | ||||
\(713\) | −29.5585 | + | 29.5585i | −1.10697 | + | 1.10697i | ||||
\(714\) | −2.03786 | − | 5.51145i | −0.0762652 | − | 0.206261i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.67682 | + | 11.5646i | −0.249524 | + | 0.432189i | ||||
\(717\) | −4.40676 | + | 16.4462i | −0.164573 | + | 0.614196i | ||||
\(718\) | −4.48256 | + | 16.7291i | −0.167288 | + | 0.624326i | ||||
\(719\) | 7.07678 | − | 12.2574i | 0.263920 | − | 0.457122i | −0.703360 | − | 0.710833i | \(-0.748318\pi\) |
0.967280 | + | 0.253711i | \(0.0816513\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.4154 | − | 18.5626i | 0.574099 | − | 0.691307i | ||||
\(722\) | −11.2097 | + | 11.2097i | −0.417183 | + | 0.417183i | ||||
\(723\) | −18.2769 | + | 4.89728i | −0.679725 | + | 0.182132i | ||||
\(724\) | −4.36961 | − | 7.56839i | −0.162395 | − | 0.281277i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.82518 | − | 3.94052i | −0.253306 | − | 0.146246i | ||||
\(727\) | −19.9622 | − | 19.9622i | −0.740357 | − | 0.740357i | 0.232290 | − | 0.972647i | \(-0.425378\pi\) |
−0.972647 | + | 0.232290i | \(0.925378\pi\) | |||||||
\(728\) | 5.86678 | + | 8.28842i | 0.217437 | + | 0.307189i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.42073 | + | 5.43906i | −0.348438 | + | 0.201171i | ||||
\(732\) | −6.55758 | − | 1.75710i | −0.242375 | − | 0.0649442i | ||||
\(733\) | 12.0119 | + | 44.8290i | 0.443670 | + | 1.65580i | 0.719425 | + | 0.694570i | \(0.244405\pi\) |
−0.275755 | + | 0.961228i | \(0.588928\pi\) | |||||||
\(734\) | −5.48491 | −0.202452 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.04689 | 0.149170 | ||||||||
\(737\) | 3.49153 | + | 13.0306i | 0.128612 | + | 0.479987i | ||||
\(738\) | −11.4939 | − | 3.07978i | −0.423095 | − | 0.113368i | ||||
\(739\) | 15.1424 | − | 8.74246i | 0.557022 | − | 0.321597i | −0.194927 | − | 0.980818i | \(-0.562447\pi\) |
0.751949 | + | 0.659221i | \(0.229114\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 6.80874i | − | 0.250125i | ||||||
\(742\) | −0.627552 | − | 0.886588i | −0.0230382 | − | 0.0325477i | ||||
\(743\) | 12.2427 | + | 12.2427i | 0.449143 | + | 0.449143i | 0.895069 | − | 0.445927i | \(-0.147126\pi\) |
−0.445927 | + | 0.895069i | \(0.647126\pi\) | |||||||
\(744\) | −8.94554 | − | 5.16471i | −0.327960 | − | 0.189348i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.4205 | + | 26.7091i | 0.564585 | + | 0.977889i | ||||
\(747\) | 2.65318 | − | 0.710918i | 0.0970749 | − | 0.0260111i | ||||
\(748\) | −2.77353 | + | 2.77353i | −0.101410 | + | 0.101410i | ||||
\(749\) | −24.9400 | + | 30.0317i | −0.911287 | + | 1.09734i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.4732 | − | 21.6042i | 0.455154 | − | 0.788350i | −0.543543 | − | 0.839381i | \(-0.682917\pi\) |
0.998697 | + | 0.0510312i | \(0.0162508\pi\) | |||||||
\(752\) | −1.59118 | + | 5.93837i | −0.0580244 | + | 0.216550i | ||||
\(753\) | 4.69827 | − | 17.5342i | 0.171214 | − | 0.638981i | ||||
\(754\) | 7.38120 | − | 12.7846i | 0.268808 | − | 0.465588i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.917556 | + | 2.48155i | 0.0333712 | + | 0.0902531i | ||||
\(757\) | 32.4637 | − | 32.4637i | 1.17991 | − | 1.17991i | 0.200149 | − | 0.979765i | \(-0.435857\pi\) |
0.979765 | − | 0.200149i | \(-0.0641427\pi\) | |||||||
\(758\) | 12.4800 | − | 3.34401i | 0.453295 | − | 0.121460i | ||||
\(759\) | −3.57352 | − | 6.18952i | −0.129711 | − | 0.224665i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.5750 | + | 16.4978i | 1.03584 | + | 0.598045i | 0.918653 | − | 0.395065i | \(-0.129278\pi\) |
0.117191 | + | 0.993109i | \(0.462611\pi\) | |||||||
\(762\) | 12.5444 | + | 12.5444i | 0.454435 | + | 0.454435i | ||||
\(763\) | 48.4284 | + | 22.2828i | 1.75322 | + | 0.806693i | ||||
\(764\) | 10.8759i | 0.393477i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.03059 | + | 0.595014i | −0.0372369 | + | 0.0214987i | ||||
\(767\) | −38.4359 | − | 10.2989i | −1.38784 | − | 0.371871i | ||||
\(768\) | 0.258819 | + | 0.965926i | 0.00933933 | + | 0.0348548i | ||||
\(769\) | 10.0980 | 0.364144 | 0.182072 | − | 0.983285i | \(-0.441720\pi\) | ||||
0.182072 | + | 0.983285i | \(0.441720\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0702 | −0.866867 | ||||||||
\(772\) | −2.89908 | − | 10.8195i | −0.104340 | − | 0.389403i | ||||
\(773\) | 11.4236 | + | 3.06094i | 0.410878 | + | 0.110094i | 0.458336 | − | 0.888779i | \(-0.348446\pi\) |
−0.0474585 | + | 0.998873i | \(0.515112\pi\) | |||||||
\(774\) | 4.24172 | − | 2.44896i | 0.152465 | − | 0.0880259i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 10.2774i | − | 0.368936i | ||||||
\(777\) | 7.18811 | − | 5.08794i | 0.257872 | − | 0.182529i | ||||
\(778\) | −6.73784 | − | 6.73784i | −0.241563 | − | 0.241563i | ||||
\(779\) | 18.2812 | + | 10.5546i | 0.654991 | + | 0.378159i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.46543 | − | 16.3946i | −0.338700 | − | 0.586645i | ||||
\(782\) | 8.68176 | − | 2.32627i | 0.310459 | − | 0.0831873i | ||||
\(783\) | 2.71973 | − | 2.71973i | 0.0971953 | − | 0.0971953i | ||||
\(784\) | 4.55392 | + | 5.31618i | 0.162640 | + | 0.189864i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.479637 | − | 0.830756i | 0.0171081 | − | 0.0296321i | ||||
\(787\) | 2.27001 | − | 8.47179i | 0.0809171 | − | 0.301987i | −0.913593 | − | 0.406631i | \(-0.866704\pi\) |
0.994510 | + | 0.104644i | \(0.0333703\pi\) | |||||||
\(788\) | −3.79843 | + | 14.1760i | −0.135314 | + | 0.504997i | ||||
\(789\) | 7.01791 | − | 12.1554i | 0.249844 | − | 0.432743i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.13068 | + | 24.1450i | −0.146870 | + | 0.858497i | ||||
\(792\) | 1.24879 | − | 1.24879i | 0.0443738 | − | 0.0443738i | ||||
\(793\) | 25.1686 | − | 6.74391i | 0.893764 | − | 0.239483i | ||||
\(794\) | 14.2666 | + | 24.7105i | 0.506303 | + | 0.876942i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.0761 | + | 9.28152i | 0.569801 | + | 0.328975i | ||||
\(797\) | 26.4972 | + | 26.4972i | 0.938580 | + | 0.938580i | 0.998220 | − | 0.0596400i | \(-0.0189953\pi\) |
−0.0596400 | + | 0.998220i | \(0.518995\pi\) | |||||||
\(798\) | −0.432886 | − | 4.67353i | −0.0153240 | − | 0.165441i | ||||
\(799\) | 13.6542i | 0.483051i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.966705 | + | 0.558127i | −0.0341568 | + | 0.0197205i | ||||
\(802\) | −37.8932 | − | 10.1535i | −1.33806 | − | 0.358531i | ||||
\(803\) | −4.86015 | − | 18.1383i | −0.171511 | − | 0.640088i | ||||
\(804\) | 7.63862 | 0.269394 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 39.6453 | 1.39645 | ||||||||
\(807\) | 6.87229 | + | 25.6477i | 0.241916 | + | 0.902842i | ||||
\(808\) | −17.7215 | − | 4.74846i | −0.623441 | − | 0.167050i | ||||
\(809\) | −34.0232 | + | 19.6433i | −1.19619 | + | 0.690622i | −0.959704 | − | 0.281012i | \(-0.909330\pi\) |
−0.236489 | + | 0.971634i | \(0.575997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.61165i | 0.337511i | 0.985658 | + | 0.168755i | \(0.0539748\pi\) | ||||
−0.985658 | + | 0.168755i | \(0.946025\pi\) | |||||||
\(812\) | 4.25364 | − | 9.24465i | 0.149274 | − | 0.324424i | ||||
\(813\) | −8.45744 | − | 8.45744i | −0.296615 | − | 0.296615i | ||||
\(814\) | −5.09089 | − | 2.93923i | −0.178436 | − | 0.103020i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.11049 | + | 1.92342i | 0.0388748 | + | 0.0673331i | ||||
\(817\) | −8.39277 | + | 2.24884i | −0.293626 | + | 0.0786769i | ||||
\(818\) | −6.12230 | + | 6.12230i | −0.214061 | + | 0.214061i | ||||
\(819\) | −7.81207 | − | 6.48757i | −0.272976 | − | 0.226694i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.9357 | + | 44.9219i | −0.905162 | + | 1.56779i | −0.0844618 | + | 0.996427i | \(0.526917\pi\) |
−0.820700 | + | 0.571359i | \(0.806416\pi\) | |||||||
\(822\) | 2.88499 | − | 10.7669i | 0.100626 | − | 0.375540i | ||||
\(823\) | −2.69263 | + | 10.0490i | −0.0938592 | + | 0.350287i | −0.996844 | − | 0.0793852i | \(-0.974704\pi\) |
0.902985 | + | 0.429672i | \(0.141371\pi\) | |||||||
\(824\) | −4.55993 | + | 7.89804i | −0.158853 | + | 0.275141i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.0372 | − | 4.62548i | −0.940746 | − | 0.160941i | ||||
\(827\) | −7.55951 | + | 7.55951i | −0.262870 | + | 0.262870i | −0.826219 | − | 0.563349i | \(-0.809513\pi\) |
0.563349 | + | 0.826219i | \(0.309513\pi\) | |||||||
\(828\) | −3.90900 | + | 1.04741i | −0.135847 | + | 0.0364001i | ||||
\(829\) | 16.1525 | + | 27.9770i | 0.561001 | + | 0.971682i | 0.997409 | + | 0.0719331i | \(0.0229168\pi\) |
−0.436409 | + | 0.899748i | \(0.643750\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.04525 | + | 1.18083i | 0.0709490 | + | 0.0409624i | ||||
\(832\) | −2.71395 | − | 2.71395i | −0.0940891 | − | 0.0940891i | ||||
\(833\) | 12.8254 | + | 8.78704i | 0.444374 | + | 0.304453i | ||||
\(834\) | 13.5695i | 0.469875i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.71323 | + | 1.56648i | −0.0938389 | + | 0.0541779i | ||||
\(837\) | 9.97746 | + | 2.67345i | 0.344871 | + | 0.0924080i | ||||
\(838\) | 1.11195 | + | 4.14984i | 0.0384115 | + | 0.143354i | ||||
\(839\) | −24.7218 | −0.853490 | −0.426745 | − | 0.904372i | \(-0.640340\pi\) | ||||
−0.426745 | + | 0.904372i | \(0.640340\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.2061 | 0.489866 | ||||||||
\(842\) | −4.87477 | − | 18.1929i | −0.167996 | − | 0.626968i | ||||
\(843\) | 10.6548 | + | 2.85494i | 0.366970 | + | 0.0983294i | ||||
\(844\) | 0.392425 | − | 0.226566i | 0.0135078 | − | 0.00779874i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 6.14785i | − | 0.211367i | ||||||
\(847\) | 20.7624 | − | 1.92312i | 0.713405 | − | 0.0660791i | ||||
\(848\) | 0.290303 | + | 0.290303i | 0.00996904 | + | 0.00996904i | ||||
\(849\) | 20.2744 | + | 11.7054i | 0.695815 | + | 0.401729i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.73519 | + | 11.6657i | 0.230879 | + | 0.399895i | ||||
\(852\) | −10.3540 | + | 2.77435i | −0.354723 | + | 0.0950478i | ||||
\(853\) | 28.0435 | − | 28.0435i | 0.960191 | − | 0.960191i | −0.0390463 | − | 0.999237i | \(-0.512432\pi\) |
0.999237 | + | 0.0390463i | \(0.0124320\pi\) | |||||||
\(854\) | 16.8470 | − | 6.22920i | 0.576493 | − | 0.213159i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.37735 | − | 12.7779i | 0.252153 | − | 0.436741i | ||||
\(857\) | 12.3144 | − | 45.9579i | 0.420652 | − | 1.56989i | −0.352587 | − | 0.935779i | \(-0.614698\pi\) |
0.773239 | − | 0.634115i | \(-0.218635\pi\) | |||||||
\(858\) | −1.75435 | + | 6.54733i | −0.0598926 | + | 0.223522i | ||||
\(859\) | 26.8560 | − | 46.5160i | 0.916315 | − | 1.58710i | 0.111351 | − | 0.993781i | \(-0.464482\pi\) |
0.804964 | − | 0.593324i | \(-0.202185\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.5288 | − | 10.9183i | 1.00634 | − | 0.372095i | ||||
\(862\) | 4.89645 | − | 4.89645i | 0.166774 | − | 0.166774i | ||||
\(863\) | 38.6139 | − | 10.3466i | 1.31443 | − | 0.352201i | 0.467544 | − | 0.883970i | \(-0.345139\pi\) |
0.846890 | + | 0.531768i | \(0.178472\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.1034 | − | 8.14260i | −0.479253 | − | 0.276697i | ||||
\(867\) | −8.53286 | − | 8.53286i | −0.289791 | − | 0.289791i | ||||
\(868\) | 27.2126 | − | 2.52057i | 0.923656 | − | 0.0855536i | ||||
\(869\) | − | 22.4129i | − | 0.760305i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.3900 | + | 14.6589i | −0.860306 | + | 0.496698i | ||||
\(872\) | −19.4623 | − | 5.21491i | −0.659076 | − | 0.176599i | ||||
\(873\) | 2.65998 | + | 9.92718i | 0.0900267 | + | 0.335984i | ||||
\(874\) | 7.17914 | 0.242838 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.6328 | −0.359250 | ||||||||
\(877\) | 1.96884 | + | 7.34780i | 0.0664829 | + | 0.248118i | 0.991167 | − | 0.132617i | \(-0.0423379\pi\) |
−0.924685 | + | 0.380734i | \(0.875671\pi\) | |||||||
\(878\) | 17.6029 | + | 4.71669i | 0.594070 | + | 0.159180i | ||||
\(879\) | −18.9635 | + | 10.9486i | −0.639624 | + | 0.369287i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 37.1659i | − | 1.25215i | −0.779763 | − | 0.626075i | \(-0.784660\pi\) | ||
0.779763 | − | 0.626075i | \(-0.215340\pi\) | |||||||
\(882\) | −5.77468 | − | 3.95640i | −0.194444 | − | 0.133219i | ||||
\(883\) | −25.7803 | − | 25.7803i | −0.867577 | − | 0.867577i | 0.124627 | − | 0.992204i | \(-0.460227\pi\) |
−0.992204 | + | 0.124627i | \(0.960227\pi\) | |||||||
\(884\) | −7.38226 | − | 4.26215i | −0.248292 | − | 0.143352i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.4162 | − | 28.4337i | −0.551513 | − | 0.955248i | ||||
\(887\) | 14.4006 | − | 3.85864i | 0.483526 | − | 0.129560i | −0.00881809 | − | 0.999961i | \(-0.502807\pi\) |
0.492344 | + | 0.870401i | \(0.336140\pi\) | |||||||
\(888\) | −2.35366 | + | 2.35366i | −0.0789837 | + | 0.0789837i | ||||
\(889\) | −46.2646 | − | 7.91487i | −1.55167 | − | 0.265456i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.883028 | + | 1.52945i | −0.0295826 | + | 0.0512385i | ||||
\(892\) | 1.71029 | − | 6.38289i | 0.0572648 | − | 0.213715i | ||||
\(893\) | −2.82274 | + | 10.5346i | −0.0944593 | + | 0.352527i | ||||
\(894\) | 5.04930 | − | 8.74565i | 0.168874 | − | 0.292498i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.03540 | − | 1.69031i | −0.0679980 | − | 0.0564692i | ||||
\(897\) | 10.9830 | − | 10.9830i | 0.366713 | − | 0.366713i | ||||
\(898\) | 7.86295 | − | 2.10687i | 0.262390 | − | 0.0703072i | ||||
\(899\) | −19.8649 | − | 34.4071i | −0.662533 | − | 1.14754i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.789659 | + | 0.455910i | 0.0263074 | + | 0.0151886i | ||||
\(902\) | −14.8598 | − | 14.8598i | −0.494777 | − | 0.494777i | ||||
\(903\) | −5.41666 | + | 11.7723i | −0.180255 | + | 0.391757i | ||||
\(904\) | − | 9.25854i | − | 0.307934i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.3928 | − | 7.15497i | 0.411722 | − | 0.237708i | ||||
\(907\) | 20.7799 | + | 5.56795i | 0.689984 | + | 0.184881i | 0.586740 | − | 0.809775i | \(-0.300411\pi\) |
0.103244 | + | 0.994656i | \(0.467078\pi\) | |||||||
\(908\) | 4.29835 | + | 16.0416i | 0.142646 | + | 0.532361i | ||||
\(909\) | 18.3467 | 0.608520 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.6120 | 0.782301 | 0.391151 | − | 0.920327i | \(-0.372077\pi\) | ||||
0.391151 | + | 0.920327i | \(0.372077\pi\) | |||||||
\(912\) | 0.459142 | + | 1.71354i | 0.0152037 | + | 0.0567410i | ||||
\(913\) | 4.68567 | + | 1.25552i | 0.155073 | + | 0.0415517i | ||||
\(914\) | 3.95426 | − | 2.28300i | 0.130795 | − | 0.0755148i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 13.5415i | − | 0.447423i | ||||||
\(917\) | 0.234081 | + | 2.52719i | 0.00773002 | + | 0.0834550i | ||||
\(918\) | −1.57046 | − | 1.57046i | −0.0518330 | − | 0.0518330i | ||||
\(919\) | −38.2901 | − | 22.1068i | −1.26307 | − | 0.729236i | −0.289406 | − | 0.957207i | \(-0.593458\pi\) |
−0.973668 | + | 0.227971i | \(0.926791\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.50012 | + | 2.59828i | 0.0494306 | + | 0.0856163i | ||||
\(922\) | 7.29172 | − | 1.95381i | 0.240140 | − | 0.0643453i | ||||
\(923\) | 29.0915 | − | 29.0915i | 0.957560 | − | 0.957560i | ||||
\(924\) | −0.787924 | + | 4.60563i | −0.0259208 | + | 0.151514i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.27661 | + | 10.8714i | −0.206262 | + | 0.357257i | ||||
\(927\) | 2.36040 | − | 8.80911i | 0.0775255 | − | 0.289329i | ||||
\(928\) | −0.995491 | + | 3.71522i | −0.0326786 | + | 0.121958i | ||||
\(929\) | −0.388224 | + | 0.672424i | −0.0127372 | + | 0.0220615i | −0.872324 | − | 0.488929i | \(-0.837388\pi\) |
0.859587 | + | 0.510990i | \(0.170721\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.07860 | + | 9.43085i | 0.264766 | + | 0.309084i | ||||
\(932\) | −8.18707 | + | 8.18707i | −0.268177 | + | 0.268177i | ||||
\(933\) | −14.5087 | + | 3.88760i | −0.474995 | + | 0.127274i | ||||
\(934\) | −5.75418 | − | 9.96652i | −0.188282 | − | 0.326115i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.32389 | + | 1.91905i | 0.108645 | + | 0.0627261i | ||||
\(937\) | −0.494892 | − | 0.494892i | −0.0161674 | − | 0.0161674i | 0.698977 | − | 0.715144i | \(-0.253639\pi\) |
−0.715144 | + | 0.698977i | \(0.753639\pi\) | |||||||
\(938\) | −16.4957 | + | 11.6761i | −0.538604 | + | 0.381239i | ||||
\(939\) | − | 13.3182i | − | 0.434624i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.9777 | − | 9.22471i | 0.520857 | − | 0.300717i | −0.216428 | − | 0.976299i | \(-0.569441\pi\) |
0.737285 | + | 0.675582i | \(0.236107\pi\) | |||||||
\(942\) | −9.25683 | − | 2.48036i | −0.301604 | − | 0.0808145i | ||||
\(943\) | 12.4635 | + | 46.5145i | 0.405868 | + | 1.51472i | ||||
\(944\) | 10.3676 | 0.337436 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.64999 | 0.281235 | ||||||||
\(947\) | 2.67536 | + | 9.98459i | 0.0869376 | + | 0.324456i | 0.995674 | − | 0.0929149i | \(-0.0296184\pi\) |
−0.908736 | + | 0.417370i | \(0.862952\pi\) | |||||||
\(948\) | −12.2585 | − | 3.28465i | −0.398137 | − | 0.106680i | ||||
\(949\) | 35.3424 | − | 20.4049i | 1.14726 | − | 0.662372i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.9017i | 0.450793i | ||||||||
\(952\) | −5.33817 | − | 2.45620i | −0.173011 | − | 0.0796058i | ||||
\(953\) | −11.1833 | − | 11.1833i | −0.362263 | − | 0.362263i | 0.502383 | − | 0.864645i | \(-0.332457\pi\) |
−0.864645 | + | 0.502383i | \(0.832457\pi\) | |||||||
\(954\) | −0.355547 | − | 0.205275i | −0.0115113 | − | 0.00664603i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.51320 | + | 14.7453i | 0.275336 | + | 0.476897i | ||||
\(957\) | 6.56129 | − | 1.75809i | 0.212096 | − | 0.0568311i | ||||
\(958\) | −8.73106 | + | 8.73106i | −0.282088 | + | 0.282088i | ||||
\(959\) | 10.2278 | + | 27.6612i | 0.330271 | + | 0.893227i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.8485 | − | 65.5555i | 1.22092 | − | 2.11469i | ||||
\(962\) | 3.30652 | − | 12.3401i | 0.106606 | − | 0.397861i | ||||
\(963\) | −3.81880 | + | 14.2519i | −0.123059 | + | 0.459263i | ||||
\(964\) | −9.46081 | + | 16.3866i | −0.304712 | + | 0.527777i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.84049 | − | 8.23705i | 0.220089 | − | 0.265023i | ||||
\(967\) | 3.47333 | − | 3.47333i | 0.111695 | − | 0.111695i | −0.649051 | − | 0.760745i | \(-0.724834\pi\) |
0.760745 | + | 0.649051i | \(0.224834\pi\) | |||||||
\(968\) | −7.61250 | + | 2.03976i | −0.244675 | + | 0.0655605i | ||||
\(969\) | 1.96999 | + | 3.41212i | 0.0632851 | + | 0.109613i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.5326 | + | 18.2054i | 1.01193 | + | 0.584238i | 0.911756 | − | 0.410732i | \(-0.134727\pi\) |
0.100174 | + | 0.994970i | \(0.468060\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −20.7419 | − | 29.3036i | −0.664955 | − | 0.939430i | ||||
\(974\) | − | 15.5867i | − | 0.499431i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.87936 | + | 3.39445i | −0.188194 | + | 0.108654i | ||||
\(977\) | −23.2951 | − | 6.24191i | −0.745278 | − | 0.199697i | −0.133855 | − | 0.991001i | \(-0.542736\pi\) |
−0.611422 | + | 0.791304i | \(0.709402\pi\) | |||||||
\(978\) | −3.06537 | − | 11.4401i | −0.0980196 | − | 0.365814i | ||||
\(979\) | −1.97137 | −0.0630052 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.1488 | 0.643303 | ||||||||
\(982\) | −0.692274 | − | 2.58360i | −0.0220913 | − | 0.0824460i | ||||
\(983\) | 24.7118 | + | 6.62151i | 0.788184 | + | 0.211193i | 0.630390 | − | 0.776279i | \(-0.282895\pi\) |
0.157794 | + | 0.987472i | \(0.449562\pi\) | |||||||
\(984\) | −10.3051 | + | 5.94967i | −0.328516 | + | 0.189669i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.54248i | 0.272048i | ||||||||
\(987\) | 9.39738 | + | 13.2764i | 0.299122 | + | 0.422591i | ||||
\(988\) | −4.81451 | − | 4.81451i | −0.153170 | − | 0.153170i | ||||
\(989\) | −17.1658 | − | 9.91066i | −0.545839 | − | 0.315141i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.1174 | − | 22.7201i | −0.416689 | − | 0.721726i | 0.578915 | − | 0.815388i | \(-0.303476\pi\) |
−0.995604 | + | 0.0936614i | \(0.970143\pi\) | |||||||
\(992\) | −9.97746 | + | 2.67345i | −0.316785 | + | 0.0848822i | ||||
\(993\) | −13.1752 | + | 13.1752i | −0.418104 | + | 0.418104i | ||||
\(994\) | 18.1189 | − | 21.8180i | 0.574696 | − | 0.692026i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.37339 | − | 2.37878i | 0.0435175 | − | 0.0753745i | ||||
\(997\) | −9.65822 | + | 36.0450i | −0.305879 | + | 1.14156i | 0.626307 | + | 0.779577i | \(0.284566\pi\) |
−0.932186 | + | 0.361980i | \(0.882101\pi\) | |||||||
\(998\) | 4.70442 | − | 17.5571i | 0.148916 | − | 0.555762i | ||||
\(999\) | 1.66429 | − | 2.88263i | 0.0526558 | − | 0.0912025i |
(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 | 1050.2.bc.g.943.4 | 16 | ||
5.2 | odd | 4 | 1050.2.bc.h.607.1 | 16 | |||
5.3 | odd | 4 | 210.2.u.a.187.3 | yes | 16 | ||
5.4 | even | 2 | 210.2.u.b.103.2 | yes | 16 | ||
7.3 | odd | 6 | 1050.2.bc.h.493.1 | 16 | |||
15.8 | even | 4 | 630.2.bv.a.397.2 | 16 | |||
15.14 | odd | 2 | 630.2.bv.b.523.3 | 16 | |||
35.3 | even | 12 | 210.2.u.b.157.2 | yes | 16 | ||
35.9 | even | 6 | 1470.2.m.e.1273.2 | 16 | |||
35.17 | even | 12 | inner | 1050.2.bc.g.157.4 | 16 | ||
35.19 | odd | 6 | 1470.2.m.d.1273.3 | 16 | |||
35.23 | odd | 12 | 1470.2.m.d.97.3 | 16 | |||
35.24 | odd | 6 | 210.2.u.a.73.3 | ✓ | 16 | ||
35.33 | even | 12 | 1470.2.m.e.97.2 | 16 | |||
105.38 | odd | 12 | 630.2.bv.b.577.3 | 16 | |||
105.59 | even | 6 | 630.2.bv.a.73.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.u.a.73.3 | ✓ | 16 | 35.24 | odd | 6 | ||
210.2.u.a.187.3 | yes | 16 | 5.3 | odd | 4 | ||
210.2.u.b.103.2 | yes | 16 | 5.4 | even | 2 | ||
210.2.u.b.157.2 | yes | 16 | 35.3 | even | 12 | ||
630.2.bv.a.73.2 | 16 | 105.59 | even | 6 | |||
630.2.bv.a.397.2 | 16 | 15.8 | even | 4 | |||
630.2.bv.b.523.3 | 16 | 15.14 | odd | 2 | |||
630.2.bv.b.577.3 | 16 | 105.38 | odd | 12 | |||
1050.2.bc.g.157.4 | 16 | 35.17 | even | 12 | inner | ||
1050.2.bc.g.943.4 | 16 | 1.1 | even | 1 | trivial | ||
1050.2.bc.h.493.1 | 16 | 7.3 | odd | 6 | |||
1050.2.bc.h.607.1 | 16 | 5.2 | odd | 4 | |||
1470.2.m.d.97.3 | 16 | 35.23 | odd | 12 | |||
1470.2.m.d.1273.3 | 16 | 35.19 | odd | 6 | |||
1470.2.m.e.97.2 | 16 | 35.33 | even | 12 | |||
1470.2.m.e.1273.2 | 16 | 35.9 | even | 6 |