Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(289,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.s (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 802.5 | ||
Root | \(1.16700 + 2.02131i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.802 |
Dual form | 819.2.s.d.289.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.90556 | 1.34743 | 0.673717 | − | 0.738989i | \(-0.264697\pi\) | ||||
0.673717 | + | 0.738989i | \(0.264697\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.63116 | 0.815580 | ||||||||
\(5\) | −0.736565 | − | 1.27577i | −0.329402 | − | 0.570541i | 0.652991 | − | 0.757365i | \(-0.273514\pi\) |
−0.982393 | + | 0.186825i | \(0.940180\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.58334 | − | 2.11968i | 0.598447 | − | 0.801162i | ||||
\(8\) | −0.702849 | −0.248495 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.40357 | − | 2.43105i | −0.443847 | − | 0.768766i | ||||
\(11\) | −2.19681 | − | 3.80498i | −0.662362 | − | 1.14725i | −0.979993 | − | 0.199031i | \(-0.936221\pi\) |
0.317631 | − | 0.948214i | \(-0.397113\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.69752 | − | 2.39236i | 0.748158 | − | 0.663520i | ||||
\(14\) | 3.01715 | − | 4.03917i | 0.806368 | − | 1.07951i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.60164 | −1.15041 | ||||||||
\(17\) | 1.20271 | 0.291700 | 0.145850 | − | 0.989307i | \(-0.453408\pi\) | ||||
0.145850 | + | 0.989307i | \(0.453408\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.62105 | + | 2.80773i | −0.371893 | + | 0.644138i | −0.989857 | − | 0.142068i | \(-0.954625\pi\) |
0.617963 | + | 0.786207i | \(0.287958\pi\) | |||||||
\(20\) | −1.20145 | − | 2.08098i | −0.268653 | − | 0.465321i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.18615 | − | 7.25062i | −0.892490 | − | 1.54584i | ||||
\(23\) | 4.43710 | 0.925200 | 0.462600 | − | 0.886567i | \(-0.346917\pi\) | ||||
0.462600 | + | 0.886567i | \(0.346917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.41494 | − | 2.45075i | 0.282989 | − | 0.490151i | ||||
\(26\) | 5.14029 | − | 4.55878i | 1.00809 | − | 0.894050i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.58268 | − | 3.45753i | 0.488081 | − | 0.653412i | ||||
\(29\) | 0.0837807 | − | 0.145112i | 0.0155577 | − | 0.0269467i | −0.858142 | − | 0.513413i | \(-0.828381\pi\) |
0.873699 | + | 0.486466i | \(0.161714\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.62272 | + | 4.54268i | −0.471054 | + | 0.815889i | −0.999452 | − | 0.0331076i | \(-0.989460\pi\) |
0.528398 | + | 0.848997i | \(0.322793\pi\) | |||||||
\(32\) | −7.36300 | −1.30161 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.29184 | 0.393047 | ||||||||
\(35\) | −3.87045 | − | 0.458697i | −0.654225 | − | 0.0775340i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.05055 | 1.15910 | 0.579552 | − | 0.814936i | \(-0.303228\pi\) | ||||
0.579552 | + | 0.814936i | \(0.303228\pi\) | |||||||
\(38\) | −3.08900 | + | 5.35031i | −0.501102 | + | 0.867934i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.517694 | + | 0.896672i | 0.0818546 | + | 0.141776i | ||||
\(41\) | 2.58195 | − | 4.47206i | 0.403233 | − | 0.698419i | −0.590881 | − | 0.806758i | \(-0.701220\pi\) |
0.994114 | + | 0.108339i | \(0.0345533\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0113752 | − | 0.0197024i | −0.00173470 | − | 0.00300459i | 0.865157 | − | 0.501502i | \(-0.167219\pi\) |
−0.866891 | + | 0.498497i | \(0.833886\pi\) | |||||||
\(44\) | −3.58334 | − | 6.20653i | −0.540209 | − | 0.935670i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.45516 | 1.24665 | ||||||||
\(47\) | 5.84178 | + | 10.1183i | 0.852111 | + | 1.47590i | 0.879300 | + | 0.476269i | \(0.158011\pi\) |
−0.0271891 | + | 0.999630i | \(0.508656\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.98606 | − | 6.71235i | −0.283722 | − | 0.958906i | ||||
\(50\) | 2.69626 | − | 4.67006i | 0.381309 | − | 0.660446i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.40009 | − | 3.90231i | 0.610183 | − | 0.541154i | ||||
\(53\) | −0.0708929 | + | 0.122790i | −0.00973788 | + | 0.0168665i | −0.870853 | − | 0.491543i | \(-0.836433\pi\) |
0.861115 | + | 0.508410i | \(0.169766\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.23618 | + | 5.60523i | −0.436367 | + | 0.755809i | ||||
\(56\) | −1.11285 | + | 1.48981i | −0.148711 | + | 0.199084i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.159649 | − | 0.276520i | 0.0209630 | − | 0.0363089i | ||||
\(59\) | 5.34354 | 0.695670 | 0.347835 | − | 0.937556i | \(-0.386917\pi\) | ||||
0.347835 | + | 0.937556i | \(0.386917\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.77287 | + | 9.99891i | −0.739141 | + | 1.28023i | 0.213742 | + | 0.976890i | \(0.431435\pi\) |
−0.952883 | + | 0.303339i | \(0.901898\pi\) | |||||||
\(62\) | −4.99774 | + | 8.65635i | −0.634714 | + | 1.09936i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.82736 | −0.603420 | ||||||||
\(65\) | −5.03899 | − | 1.67929i | −0.625010 | − | 0.208290i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.06773 | − | 3.58141i | −0.252613 | − | 0.437539i | 0.711631 | − | 0.702553i | \(-0.247957\pi\) |
−0.964245 | + | 0.265014i | \(0.914623\pi\) | |||||||
\(68\) | 1.96181 | 0.237905 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.37537 | − | 0.874075i | −0.881526 | − | 0.104472i | ||||
\(71\) | −4.98486 | − | 8.63403i | −0.591594 | − | 1.02467i | −0.994018 | − | 0.109217i | \(-0.965166\pi\) |
0.402424 | − | 0.915453i | \(-0.368168\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.62080 | + | 13.1996i | −0.891947 | + | 1.54490i | −0.0544080 | + | 0.998519i | \(0.517327\pi\) |
−0.837539 | + | 0.546378i | \(0.816006\pi\) | |||||||
\(74\) | 13.4352 | 1.56182 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.64418 | + | 4.57986i | −0.303309 | + | 0.525346i | ||||
\(77\) | −11.5436 | − | 1.36807i | −1.31552 | − | 0.155906i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.387251 | − | 0.670738i | −0.0435691 | − | 0.0754639i | 0.843418 | − | 0.537257i | \(-0.180540\pi\) |
−0.886988 | + | 0.461793i | \(0.847206\pi\) | |||||||
\(80\) | 3.38941 | + | 5.87062i | 0.378947 | + | 0.656356i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.92006 | − | 8.52179i | 0.543329 | − | 0.941074i | ||||
\(83\) | 16.0186 | 1.75827 | 0.879136 | − | 0.476571i | \(-0.158121\pi\) | ||||
0.879136 | + | 0.476571i | \(0.158121\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.885875 | − | 1.53438i | −0.0960866 | − | 0.166427i | ||||
\(86\) | −0.0216761 | − | 0.0375441i | −0.00233740 | − | 0.00404849i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.54402 | + | 2.67433i | 0.164593 | + | 0.285084i | ||||
\(89\) | −6.55760 | −0.695104 | −0.347552 | − | 0.937661i | \(-0.612987\pi\) | ||||
−0.347552 | + | 0.937661i | \(0.612987\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.799921 | − | 9.50579i | −0.0838545 | − | 0.996478i | ||||
\(92\) | 7.23762 | 0.754574 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.1319 | + | 19.2809i | 1.14816 | + | 1.98868i | ||||
\(95\) | 4.77602 | 0.490010 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.74583 | − | 3.02387i | −0.177262 | − | 0.307027i | 0.763680 | − | 0.645595i | \(-0.223391\pi\) |
−0.940942 | + | 0.338568i | \(0.890057\pi\) | |||||||
\(98\) | −3.78455 | − | 12.7908i | −0.382297 | − | 1.29206i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.30800 | − | 3.99757i | 0.230800 | − | 0.399757i | ||||
\(101\) | 1.28890 | + | 2.23244i | 0.128250 | + | 0.222136i | 0.922999 | − | 0.384803i | \(-0.125731\pi\) |
−0.794749 | + | 0.606939i | \(0.792397\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.43173 | + | 14.6042i | 0.830803 | + | 1.43899i | 0.897402 | + | 0.441213i | \(0.145452\pi\) |
−0.0665997 | + | 0.997780i | \(0.521215\pi\) | |||||||
\(104\) | −1.89595 | + | 1.68146i | −0.185913 | + | 0.164881i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.135091 | + | 0.233984i | −0.0131212 | + | 0.0227265i | ||||
\(107\) | −8.68265 | −0.839383 | −0.419692 | − | 0.907667i | \(-0.637862\pi\) | ||||
−0.419692 | + | 0.907667i | \(0.637862\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.02026 | − | 10.4274i | 0.576637 | − | 0.998764i | −0.419225 | − | 0.907882i | \(-0.637698\pi\) |
0.995862 | − | 0.0908816i | \(-0.0289685\pi\) | |||||||
\(110\) | −6.16674 | + | 10.6811i | −0.587976 | + | 1.01840i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.28597 | + | 9.75398i | −0.688459 | + | 0.921665i | ||||
\(113\) | 4.68616 | + | 8.11667i | 0.440837 | + | 0.763552i | 0.997752 | − | 0.0670176i | \(-0.0213484\pi\) |
−0.556915 | + | 0.830570i | \(0.688015\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.26821 | − | 5.66071i | −0.304763 | − | 0.527864i | ||||
\(116\) | 0.136660 | − | 0.236701i | 0.0126885 | − | 0.0219772i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.1824 | 0.937369 | ||||||||
\(119\) | 1.90430 | − | 2.54936i | 0.174567 | − | 0.233699i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.15192 | + | 7.19134i | −0.377448 | + | 0.653758i | ||||
\(122\) | −11.0006 | + | 19.0535i | −0.995944 | + | 1.72503i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.27807 | + | 7.40983i | −0.384182 | + | 0.665423i | ||||
\(125\) | −11.5344 | −1.03167 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.94269 | + | 13.7571i | −0.704800 | + | 1.22075i | 0.261964 | + | 0.965078i | \(0.415630\pi\) |
−0.966764 | + | 0.255672i | \(0.917703\pi\) | |||||||
\(128\) | 5.52717 | 0.488537 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.60210 | − | 3.19998i | −0.842160 | − | 0.280657i | ||||
\(131\) | 0.928725 | + | 1.60860i | 0.0811430 | + | 0.140544i | 0.903741 | − | 0.428079i | \(-0.140810\pi\) |
−0.822598 | + | 0.568623i | \(0.807476\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.38482 | + | 7.88170i | 0.293501 | + | 0.683430i | ||||
\(134\) | −3.94018 | − | 6.82459i | −0.340380 | − | 0.589555i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.845324 | −0.0724859 | ||||||||
\(137\) | 12.8002 | 1.09360 | 0.546798 | − | 0.837264i | \(-0.315847\pi\) | ||||
0.546798 | + | 0.837264i | \(0.315847\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.169365 | + | 0.293348i | 0.0143653 | + | 0.0248815i | 0.873119 | − | 0.487508i | \(-0.162094\pi\) |
−0.858753 | + | 0.512389i | \(0.828761\pi\) | |||||||
\(140\) | −6.31332 | − | 0.748208i | −0.533573 | − | 0.0632351i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.49894 | − | 16.4527i | −0.797134 | − | 1.38068i | ||||
\(143\) | −15.0288 | − | 5.00848i | −1.25677 | − | 0.418830i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.246840 | −0.0204989 | ||||||||
\(146\) | −14.5219 | + | 25.1526i | −1.20184 | + | 2.08165i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.5006 | 0.945341 | ||||||||
\(149\) | 1.96158 | − | 3.39756i | 0.160699 | − | 0.278339i | −0.774421 | − | 0.632671i | \(-0.781959\pi\) |
0.935120 | + | 0.354332i | \(0.115292\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.05939 | − | 1.83492i | 0.0862122 | − | 0.149324i | −0.819695 | − | 0.572800i | \(-0.805857\pi\) |
0.905907 | + | 0.423476i | \(0.139190\pi\) | |||||||
\(152\) | 1.13935 | − | 1.97341i | 0.0924135 | − | 0.160065i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −21.9971 | − | 2.60693i | −1.77257 | − | 0.210073i | ||||
\(155\) | 7.72721 | 0.620664 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0564 | − | 19.1502i | 0.882397 | − | 1.52836i | 0.0337285 | − | 0.999431i | \(-0.489262\pi\) |
0.848668 | − | 0.528925i | \(-0.177405\pi\) | |||||||
\(158\) | −0.737929 | − | 1.27813i | −0.0587065 | − | 0.101683i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.42333 | + | 9.39348i | 0.428752 | + | 0.742620i | ||||
\(161\) | 7.02545 | − | 9.40522i | 0.553683 | − | 0.741235i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.92607 | + | 3.33605i | −0.150861 | + | 0.261299i | −0.931544 | − | 0.363628i | \(-0.881538\pi\) |
0.780683 | + | 0.624927i | \(0.214871\pi\) | |||||||
\(164\) | 4.21157 | − | 7.29465i | 0.328868 | − | 0.569616i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 30.5244 | 2.36916 | ||||||||
\(167\) | 1.06947 | − | 1.85238i | 0.0827582 | − | 0.143341i | −0.821676 | − | 0.569956i | \(-0.806960\pi\) |
0.904434 | + | 0.426614i | \(0.140294\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.55326 | − | 12.9069i | 0.119482 | − | 0.992836i | ||||
\(170\) | −1.68809 | − | 2.92385i | −0.129470 | − | 0.224249i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0185547 | − | 0.0321378i | −0.00141479 | − | 0.00245048i | ||||
\(173\) | −8.30664 | + | 14.3875i | −0.631542 | + | 1.09386i | 0.355695 | + | 0.934602i | \(0.384244\pi\) |
−0.987237 | + | 0.159260i | \(0.949089\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.95447 | − | 6.87961i | −0.223337 | − | 0.520049i | ||||
\(176\) | 10.1089 | + | 17.5091i | 0.761988 | + | 1.31980i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.4959 | −0.936607 | ||||||||
\(179\) | −0.269748 | − | 0.467217i | −0.0201619 | − | 0.0349214i | 0.855768 | − | 0.517359i | \(-0.173085\pi\) |
−0.875930 | + | 0.482438i | \(0.839752\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.77164 | 0.206014 | 0.103007 | − | 0.994681i | \(-0.467154\pi\) | ||||
0.103007 | + | 0.994681i | \(0.467154\pi\) | |||||||
\(182\) | −1.52430 | − | 18.1139i | −0.112988 | − | 1.34269i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.11861 | −0.229907 | ||||||||
\(185\) | −5.19319 | − | 8.99486i | −0.381811 | − | 0.661316i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.64213 | − | 4.57629i | −0.193211 | − | 0.334652i | ||||
\(188\) | 9.52887 | + | 16.5045i | 0.694964 | + | 1.20371i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.10100 | 0.660256 | ||||||||
\(191\) | −10.1204 | + | 17.5290i | −0.732284 | + | 1.26835i | 0.223621 | + | 0.974676i | \(0.428212\pi\) |
−0.955905 | + | 0.293677i | \(0.905121\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.18856 | + | 14.1830i | 0.589425 | + | 1.02091i | 0.994308 | + | 0.106546i | \(0.0339791\pi\) |
−0.404882 | + | 0.914369i | \(0.632688\pi\) | |||||||
\(194\) | −3.32678 | − | 5.76216i | −0.238849 | − | 0.413699i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.23958 | − | 10.9489i | −0.231398 | − | 0.782064i | ||||
\(197\) | 9.86676 | − | 17.0897i | 0.702977 | − | 1.21759i | −0.264439 | − | 0.964402i | \(-0.585187\pi\) |
0.967417 | − | 0.253190i | \(-0.0814798\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.1175 | −1.00076 | −0.500380 | − | 0.865806i | \(-0.666806\pi\) | ||||
−0.500380 | + | 0.865806i | \(0.666806\pi\) | |||||||
\(200\) | −0.994491 | + | 1.72251i | −0.0703212 | + | 0.121800i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.45607 | + | 4.25404i | 0.172809 | + | 0.299313i | ||||
\(203\) | −0.174938 | − | 0.407351i | −0.0122782 | − | 0.0285904i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.60709 | −0.531302 | ||||||||
\(206\) | 16.0672 | + | 27.8291i | 1.11945 | + | 1.93895i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.4130 | + | 11.0088i | −0.860688 | + | 0.763320i | ||||
\(209\) | 14.2445 | 0.985313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.31317 | − | 4.00652i | 0.159245 | − | 0.275820i | −0.775352 | − | 0.631530i | \(-0.782427\pi\) |
0.934597 | + | 0.355709i | \(0.115761\pi\) | |||||||
\(212\) | −0.115638 | + | 0.200290i | −0.00794202 | + | 0.0137560i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.5453 | −1.13101 | ||||||||
\(215\) | −0.0167571 | + | 0.0290242i | −0.00114283 | + | 0.00197943i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.47635 | + | 12.7519i | 0.371759 | + | 0.865657i | ||||
\(218\) | 11.4720 | − | 19.8700i | 0.776980 | − | 1.34577i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.27873 | + | 9.14303i | −0.355892 | + | 0.616423i | ||||
\(221\) | 3.24434 | − | 2.87731i | 0.218238 | − | 0.193549i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.6761 | − | 18.4916i | 0.714926 | − | 1.23829i | −0.248061 | − | 0.968744i | \(-0.579793\pi\) |
0.962988 | − | 0.269545i | \(-0.0868732\pi\) | |||||||
\(224\) | −11.6581 | + | 15.6072i | −0.778943 | + | 1.04280i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.92976 | + | 15.4668i | 0.593999 | + | 1.02884i | ||||
\(227\) | 10.4490 | 0.693526 | 0.346763 | − | 0.937953i | \(-0.387281\pi\) | ||||
0.346763 | + | 0.937953i | \(0.387281\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.22901 | − | 12.5210i | −0.477706 | − | 0.827412i | 0.521967 | − | 0.852966i | \(-0.325198\pi\) |
−0.999673 | + | 0.0255538i | \(0.991865\pi\) | |||||||
\(230\) | −6.22778 | − | 10.7868i | −0.410648 | − | 0.711262i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.0588852 | + | 0.101992i | −0.00386600 | + | 0.00669611i | ||||
\(233\) | −4.64413 | − | 8.04388i | −0.304247 | − | 0.526972i | 0.672846 | − | 0.739783i | \(-0.265072\pi\) |
−0.977093 | + | 0.212811i | \(0.931738\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.60570 | − | 14.9055i | 0.561374 | − | 0.972328i | ||||
\(236\) | 8.71616 | 0.567374 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.62876 | − | 4.85796i | 0.235218 | − | 0.314895i | ||||
\(239\) | −19.6332 | −1.26997 | −0.634983 | − | 0.772526i | \(-0.718993\pi\) | ||||
−0.634983 | + | 0.772526i | \(0.718993\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.31105 | 0.470946 | 0.235473 | − | 0.971881i | \(-0.424336\pi\) | ||||
0.235473 | + | 0.971881i | \(0.424336\pi\) | |||||||
\(242\) | −7.91174 | + | 13.7035i | −0.508586 | + | 0.880897i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.41648 | + | 16.3098i | −0.602828 | + | 1.04413i | ||||
\(245\) | −7.10053 | + | 7.47783i | −0.453637 | + | 0.477741i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.34429 | + | 11.4520i | 0.149164 | + | 0.728676i | ||||
\(248\) | 1.84337 | − | 3.19282i | 0.117054 | − | 0.202744i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −21.9796 | −1.39011 | ||||||||
\(251\) | −5.93191 | − | 10.2744i | −0.374419 | − | 0.648512i | 0.615821 | − | 0.787886i | \(-0.288824\pi\) |
−0.990240 | + | 0.139374i | \(0.955491\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.74746 | − | 16.8831i | −0.612817 | − | 1.06143i | ||||
\(254\) | −15.1353 | + | 26.2151i | −0.949672 | + | 1.64488i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.1871 | 1.26169 | ||||||||
\(257\) | 15.1722 | 0.946413 | 0.473206 | − | 0.880952i | \(-0.343096\pi\) | ||||
0.473206 | + | 0.880952i | \(0.343096\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.1634 | − | 14.9449i | 0.693662 | − | 0.928630i | ||||
\(260\) | −8.21940 | − | 2.73919i | −0.509745 | − | 0.169877i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.76974 | + | 3.06528i | 0.109335 | + | 0.189374i | ||||
\(263\) | 8.59820 | + | 14.8925i | 0.530187 | + | 0.918312i | 0.999380 | + | 0.0352156i | \(0.0112118\pi\) |
−0.469192 | + | 0.883096i | \(0.655455\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.208869 | 0.0128307 | ||||||||
\(266\) | 6.44997 | + | 15.0190i | 0.395473 | + | 0.920877i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.37279 | − | 5.84185i | −0.206026 | − | 0.356848i | ||||
\(269\) | −18.9220 | −1.15370 | −0.576849 | − | 0.816851i | \(-0.695718\pi\) | ||||
−0.576849 | + | 0.816851i | \(0.695718\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.1334 | 1.95196 | 0.975982 | − | 0.217853i | \(-0.0699054\pi\) | ||||
0.975982 | + | 0.217853i | \(0.0699054\pi\) | |||||||
\(272\) | −5.53444 | −0.335575 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 24.3916 | 1.47355 | ||||||||
\(275\) | −12.4334 | −0.749764 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.4054 | 1.10587 | 0.552936 | − | 0.833224i | \(-0.313507\pi\) | ||||
0.552936 | + | 0.833224i | \(0.313507\pi\) | |||||||
\(278\) | 0.322734 | + | 0.558992i | 0.0193563 | + | 0.0335261i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.72034 | + | 0.322395i | 0.162571 | + | 0.0192668i | ||||
\(281\) | 14.2252 | 0.848603 | 0.424302 | − | 0.905521i | \(-0.360520\pi\) | ||||
0.424302 | + | 0.905521i | \(0.360520\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.71446 | + | 9.89773i | 0.339689 | + | 0.588359i | 0.984374 | − | 0.176089i | \(-0.0563448\pi\) |
−0.644685 | + | 0.764448i | \(0.723011\pi\) | |||||||
\(284\) | −8.13109 | − | 14.0835i | −0.482492 | − | 0.835700i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −28.6383 | − | 9.54396i | −1.69342 | − | 0.564346i | ||||
\(287\) | −5.39123 | − | 12.5537i | −0.318234 | − | 0.741022i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5535 | −0.914911 | ||||||||
\(290\) | −0.470368 | −0.0276210 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.4307 | + | 21.5307i | −0.727453 | + | 1.25999i | ||||
\(293\) | −6.60231 | − | 11.4355i | −0.385711 | − | 0.668071i | 0.606156 | − | 0.795345i | \(-0.292711\pi\) |
−0.991868 | + | 0.127274i | \(0.959377\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.93586 | − | 6.81712i | −0.229155 | − | 0.396908i | ||||
\(296\) | −4.95547 | −0.288031 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.73791 | − | 6.47425i | 0.216531 | − | 0.375043i | ||||
\(299\) | 11.9692 | − | 10.6151i | 0.692196 | − | 0.613889i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0597736 | − | 0.00708392i | −0.00344529 | − | 0.000408310i | ||||
\(302\) | 2.01874 | − | 3.49656i | 0.116165 | − | 0.201204i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.45947 | − | 12.9202i | 0.427830 | − | 0.741023i | ||||
\(305\) | 17.0084 | 0.973898 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.65903 | −0.380051 | −0.190026 | − | 0.981779i | \(-0.560857\pi\) | ||||
−0.190026 | + | 0.981779i | \(0.560857\pi\) | |||||||
\(308\) | −18.8295 | − | 2.23153i | −1.07291 | − | 0.127153i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.7247 | 0.836304 | ||||||||
\(311\) | −1.02298 | + | 1.77186i | −0.0580081 | + | 0.100473i | −0.893571 | − | 0.448922i | \(-0.851808\pi\) |
0.835563 | + | 0.549395i | \(0.185142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.70883 | − | 8.15594i | −0.266159 | − | 0.461001i | 0.701708 | − | 0.712465i | \(-0.252421\pi\) |
−0.967867 | + | 0.251464i | \(0.919088\pi\) | |||||||
\(314\) | 21.0686 | − | 36.4919i | 1.18897 | − | 2.05936i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.631667 | − | 1.09408i | −0.0355341 | − | 0.0615468i | ||||
\(317\) | −16.6856 | − | 28.9004i | −0.937159 | − | 1.62321i | −0.770738 | − | 0.637153i | \(-0.780112\pi\) |
−0.166421 | − | 0.986055i | \(-0.553221\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.736200 | −0.0412193 | ||||||||
\(320\) | 3.55567 | + | 6.15860i | 0.198768 | + | 0.344276i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.3874 | − | 17.9222i | 0.746051 | − | 0.998766i | ||||
\(323\) | −1.94965 | + | 3.37689i | −0.108481 | + | 0.187895i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.04624 | − | 9.99602i | −0.113505 | − | 0.554479i | ||||
\(326\) | −3.67024 | + | 6.35704i | −0.203276 | + | 0.352084i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.81472 | + | 3.14318i | −0.100201 | + | 0.173553i | ||||
\(329\) | 30.6970 | + | 3.63798i | 1.69238 | + | 0.200568i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.53298 | + | 16.5116i | −0.523980 | + | 0.907560i | 0.475631 | + | 0.879645i | \(0.342220\pi\) |
−0.999610 | + | 0.0279144i | \(0.991113\pi\) | |||||||
\(332\) | 26.1289 | 1.43401 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.03794 | − | 3.52982i | 0.111511 | − | 0.193143i | ||||
\(335\) | −3.04603 | + | 5.27588i | −0.166423 | + | 0.288252i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.2849 | −1.70420 | −0.852098 | − | 0.523382i | \(-0.824670\pi\) | ||||
−0.852098 | + | 0.523382i | \(0.824670\pi\) | |||||||
\(338\) | 2.95983 | − | 24.5948i | 0.160994 | − | 1.33778i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.44500 | − | 2.50282i | −0.0783663 | − | 0.135734i | ||||
\(341\) | 23.0464 | 1.24803 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.3726 | − | 6.41814i | −0.938033 | − | 0.346547i | ||||
\(344\) | 0.00799504 | + | 0.0138478i | 0.000431064 | + | 0.000746624i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.8288 | + | 27.4163i | −0.850961 | + | 1.47391i | ||||
\(347\) | −11.6752 | −0.626757 | −0.313378 | − | 0.949628i | \(-0.601461\pi\) | ||||
−0.313378 | + | 0.949628i | \(0.601461\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.9952 | + | 20.7763i | −0.642089 | + | 1.11213i | 0.342877 | + | 0.939380i | \(0.388599\pi\) |
−0.984966 | + | 0.172750i | \(0.944735\pi\) | |||||||
\(350\) | −5.62992 | − | 13.1095i | −0.300932 | − | 0.700732i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.1751 | + | 28.0161i | 0.862135 | + | 1.49326i | ||||
\(353\) | 6.39668 | + | 11.0794i | 0.340461 | + | 0.589696i | 0.984518 | − | 0.175282i | \(-0.0560836\pi\) |
−0.644057 | + | 0.764977i | \(0.722750\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.34334 | + | 12.7190i | −0.389744 | + | 0.675057i | ||||
\(356\) | −10.6965 | −0.566912 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.514021 | − | 0.890310i | −0.0271668 | − | 0.0470544i | ||||
\(359\) | 6.16986 | + | 10.6865i | 0.325633 | + | 0.564012i | 0.981640 | − | 0.190742i | \(-0.0610894\pi\) |
−0.656008 | + | 0.754754i | \(0.727756\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.24442 | + | 7.35155i | 0.223390 | + | 0.386924i | ||||
\(362\) | 5.28152 | 0.277591 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.30480 | − | 15.5055i | −0.0683900 | − | 0.812707i | ||||
\(365\) | 22.4528 | 1.17524 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.01538 | − | 1.75870i | −0.0530026 | − | 0.0918032i | 0.838307 | − | 0.545199i | \(-0.183546\pi\) |
−0.891309 | + | 0.453396i | \(0.850212\pi\) | |||||||
\(368\) | −20.4179 | −1.06436 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.89593 | − | 17.1403i | −0.514465 | − | 0.891079i | ||||
\(371\) | 0.148028 | + | 0.344689i | 0.00768521 | + | 0.0178953i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.93700 | − | 3.35498i | 0.100294 | − | 0.173714i | −0.811512 | − | 0.584336i | \(-0.801355\pi\) |
0.911806 | + | 0.410622i | \(0.134688\pi\) | |||||||
\(374\) | −5.03473 | − | 8.72040i | −0.260340 | − | 0.450921i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.10588 | − | 7.11160i | −0.211745 | − | 0.366753i | ||||
\(377\) | −0.121160 | − | 0.591877i | −0.00624007 | − | 0.0304832i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.28396 | − | 12.6162i | 0.374152 | − | 0.648050i | −0.616048 | − | 0.787709i | \(-0.711267\pi\) |
0.990200 | + | 0.139659i | \(0.0446006\pi\) | |||||||
\(380\) | 7.79045 | 0.399642 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −19.2850 | + | 33.4025i | −0.986705 | + | 1.70902i | ||||
\(383\) | −13.3909 | + | 23.1937i | −0.684243 | + | 1.18514i | 0.289430 | + | 0.957199i | \(0.406534\pi\) |
−0.973674 | + | 0.227945i | \(0.926799\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.75730 | + | 15.7347i | 0.344384 | + | 0.801912i | ||||
\(386\) | 15.6038 | + | 27.0266i | 0.794212 | + | 1.37562i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.84773 | − | 4.93241i | −0.144571 | − | 0.250405i | ||||
\(389\) | 6.00738 | − | 10.4051i | 0.304586 | − | 0.527559i | −0.672583 | − | 0.740022i | \(-0.734815\pi\) |
0.977169 | + | 0.212463i | \(0.0681485\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.33655 | 0.269881 | ||||||||
\(392\) | 1.39590 | + | 4.71776i | 0.0705035 | + | 0.238283i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.8017 | − | 32.5655i | 0.947216 | − | 1.64063i | ||||
\(395\) | −0.570470 | + | 0.988084i | −0.0287035 | + | 0.0497159i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.828825 | − | 1.43557i | 0.0415975 | − | 0.0720491i | −0.844477 | − | 0.535592i | \(-0.820089\pi\) |
0.886075 | + | 0.463543i | \(0.153422\pi\) | |||||||
\(398\) | −26.9017 | −1.34846 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.51106 | + | 11.2775i | −0.325553 | + | 0.563874i | ||||
\(401\) | 20.4828 | 1.02286 | 0.511430 | − | 0.859325i | \(-0.329116\pi\) | ||||
0.511430 | + | 0.859325i | \(0.329116\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.79287 | + | 18.5285i | 0.188936 | + | 0.922968i | ||||
\(404\) | 2.10240 | + | 3.64146i | 0.104598 | + | 0.181169i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.333355 | − | 0.776231i | −0.0165441 | − | 0.0385237i | ||||
\(407\) | −15.4887 | − | 26.8272i | −0.767746 | − | 1.32978i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.8659 | 0.735070 | 0.367535 | − | 0.930010i | \(-0.380202\pi\) | ||||
0.367535 | + | 0.930010i | \(0.380202\pi\) | |||||||
\(410\) | −14.4958 | −0.715895 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.7535 | + | 23.8217i | 0.677586 | + | 1.17361i | ||||
\(413\) | 8.46065 | − | 11.3266i | 0.416321 | − | 0.557344i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.7988 | − | 20.4360i | −0.579178 | − | 1.00317i | ||||
\(416\) | −19.8619 | + | 17.6149i | −0.973808 | + | 0.863643i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 27.1438 | 1.32764 | ||||||||
\(419\) | −11.8087 | + | 20.4533i | −0.576895 | + | 0.999211i | 0.418938 | + | 0.908015i | \(0.362402\pi\) |
−0.995833 | + | 0.0911962i | \(0.970931\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0822 | 1.27117 | 0.635585 | − | 0.772031i | \(-0.280759\pi\) | ||||
0.635585 | + | 0.772031i | \(0.280759\pi\) | |||||||
\(422\) | 4.40788 | − | 7.63467i | 0.214572 | − | 0.371650i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.0498269 | − | 0.0863028i | 0.00241981 | − | 0.00419123i | ||||
\(425\) | 1.70177 | − | 2.94755i | 0.0825479 | − | 0.142977i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0540 | + | 28.0683i | 0.583335 | + | 1.35832i | ||||
\(428\) | −14.1628 | −0.684584 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.0319317 | + | 0.0553074i | −0.00153988 | + | 0.00266716i | ||||
\(431\) | −6.65859 | − | 11.5330i | −0.320733 | − | 0.555526i | 0.659906 | − | 0.751348i | \(-0.270596\pi\) |
−0.980640 | + | 0.195822i | \(0.937263\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.2110 | − | 17.6860i | −0.490711 | − | 0.849937i | 0.509232 | − | 0.860629i | \(-0.329930\pi\) |
−0.999943 | + | 0.0106929i | \(0.996596\pi\) | |||||||
\(434\) | 10.4355 | + | 24.2996i | 0.500921 | + | 1.16642i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.82001 | − | 17.0087i | 0.470293 | − | 0.814571i | ||||
\(437\) | −7.19275 | + | 12.4582i | −0.344076 | + | 0.595957i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.77074 | −0.466332 | −0.233166 | − | 0.972437i | \(-0.574909\pi\) | ||||
−0.233166 | + | 0.972437i | \(0.574909\pi\) | |||||||
\(440\) | 2.27455 | − | 3.93963i | 0.108435 | − | 0.187814i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.18229 | − | 5.48290i | 0.294061 | − | 0.260795i | ||||
\(443\) | 10.5819 | + | 18.3285i | 0.502763 | + | 0.870811i | 0.999995 | + | 0.00319331i | \(0.00101646\pi\) |
−0.497232 | + | 0.867618i | \(0.665650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.83010 | + | 8.36597i | 0.228968 | + | 0.396585i | ||||
\(446\) | 20.3440 | − | 35.2368i | 0.963317 | − | 1.66851i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.64337 | + | 10.2324i | −0.361115 | + | 0.483438i | ||||
\(449\) | −9.07320 | − | 15.7152i | −0.428191 | − | 0.741648i | 0.568522 | − | 0.822668i | \(-0.307516\pi\) |
−0.996712 | + | 0.0810200i | \(0.974182\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.6882 | −1.06834 | ||||||||
\(452\) | 7.64387 | + | 13.2396i | 0.359538 | + | 0.622737i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.9112 | 0.934480 | ||||||||
\(455\) | −11.5380 | + | 8.02215i | −0.540910 | + | 0.376084i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.0198 | −0.842932 | −0.421466 | − | 0.906844i | \(-0.638484\pi\) | ||||
−0.421466 | + | 0.906844i | \(0.638484\pi\) | |||||||
\(458\) | −13.7753 | − | 23.8595i | −0.643678 | − | 1.11488i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.33098 | − | 9.23352i | −0.248558 | − | 0.430515i | ||||
\(461\) | −14.8873 | − | 25.7855i | −0.693370 | − | 1.20095i | −0.970727 | − | 0.240185i | \(-0.922792\pi\) |
0.277357 | − | 0.960767i | \(-0.410542\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7067 | 0.822900 | 0.411450 | − | 0.911432i | \(-0.365023\pi\) | ||||
0.411450 | + | 0.911432i | \(0.365023\pi\) | |||||||
\(464\) | −0.385529 | + | 0.667755i | −0.0178977 | + | 0.0309997i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.84968 | − | 15.3281i | −0.409953 | − | 0.710060i | ||||
\(467\) | −2.91461 | − | 5.04825i | −0.134872 | − | 0.233605i | 0.790677 | − | 0.612234i | \(-0.209729\pi\) |
−0.925549 | + | 0.378629i | \(0.876396\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.8654 | − | 1.28768i | −0.501715 | − | 0.0594596i | ||||
\(470\) | 16.3987 | − | 28.4033i | 0.756414 | − | 1.31015i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.75570 | −0.172870 | ||||||||
\(473\) | −0.0499782 | + | 0.0865648i | −0.00229800 | + | 0.00398025i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.58738 | + | 7.94557i | 0.210483 | + | 0.364568i | ||||
\(476\) | 3.10622 | − | 4.15841i | 0.142373 | − | 0.190600i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −37.4122 | −1.71120 | ||||||||
\(479\) | 7.24565 | + | 12.5498i | 0.331062 | + | 0.573417i | 0.982720 | − | 0.185096i | \(-0.0592596\pi\) |
−0.651658 | + | 0.758513i | \(0.725926\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.0190 | − | 16.8674i | 0.867193 | − | 0.769088i | ||||
\(482\) | 13.9316 | 0.634569 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.77245 | + | 11.7302i | −0.307839 | + | 0.533192i | ||||
\(485\) | −2.57183 | + | 4.45455i | −0.116781 | + | 0.202271i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.9601 | −0.813851 | −0.406926 | − | 0.913461i | \(-0.633399\pi\) | ||||
−0.406926 | + | 0.913461i | \(0.633399\pi\) | |||||||
\(488\) | 4.05746 | − | 7.02772i | 0.183672 | − | 0.318130i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.5305 | + | 14.2494i | −0.611245 | + | 0.643724i | ||||
\(491\) | −18.1505 | + | 31.4375i | −0.819119 | + | 1.41876i | 0.0872134 | + | 0.996190i | \(0.472204\pi\) |
−0.906332 | + | 0.422566i | \(0.861130\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.100764 | − | 0.174528i | 0.00453818 | − | 0.00786036i | ||||
\(494\) | 4.46719 | + | 21.8226i | 0.200988 | + | 0.981844i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.0688 | − | 20.9038i | 0.541905 | − | 0.938607i | ||||
\(497\) | −26.1941 | − | 3.10433i | −1.17496 | − | 0.139248i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.8538 | − | 20.5314i | −0.530649 | − | 0.919112i | −0.999360 | − | 0.0357602i | \(-0.988615\pi\) |
0.468711 | − | 0.883352i | \(-0.344719\pi\) | |||||||
\(500\) | −18.8145 | −0.841410 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.3036 | − | 19.5784i | −0.504505 | − | 0.873828i | ||||
\(503\) | 13.8876 | + | 24.0540i | 0.619217 | + | 1.07252i | 0.989629 | + | 0.143648i | \(0.0458834\pi\) |
−0.370411 | + | 0.928868i | \(0.620783\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.89871 | − | 3.28867i | 0.0844916 | − | 0.146344i | ||||
\(506\) | −18.5744 | − | 32.1717i | −0.825731 | − | 1.43021i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.9558 | + | 22.4401i | −0.574820 | + | 0.995618i | ||||
\(509\) | −8.70416 | −0.385805 | −0.192902 | − | 0.981218i | \(-0.561790\pi\) | ||||
−0.192902 | + | 0.981218i | \(0.561790\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.9126 | + | 37.0531i | 0.703931 | + | 1.63913i | ||||
\(512\) | 27.4134 | 1.21151 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.9114 | 1.27523 | ||||||||
\(515\) | 12.4210 | − | 21.5139i | 0.547336 | − | 0.948014i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.6665 | − | 44.4557i | 1.12881 | − | 1.95516i | ||||
\(518\) | 21.2726 | − | 28.4784i | 0.934664 | − | 1.25127i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.54165 | + | 1.18028i | 0.155312 | + | 0.0517589i | ||||
\(521\) | −4.28573 | + | 7.42310i | −0.187761 | + | 0.325212i | −0.944504 | − | 0.328501i | \(-0.893456\pi\) |
0.756742 | + | 0.653713i | \(0.226790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.9493 | 1.30959 | 0.654796 | − | 0.755806i | \(-0.272755\pi\) | ||||
0.654796 | + | 0.755806i | \(0.272755\pi\) | |||||||
\(524\) | 1.51490 | + | 2.62388i | 0.0661786 | + | 0.114625i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.3844 | + | 28.3786i | 0.714393 | + | 1.23736i | ||||
\(527\) | −3.15437 | + | 5.46353i | −0.137407 | + | 0.237995i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.31212 | −0.144005 | ||||||||
\(530\) | 0.398012 | 0.0172885 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.52118 | + | 12.8563i | 0.239373 | + | 0.557391i | ||||
\(533\) | −3.73391 | − | 18.2404i | −0.161734 | − | 0.790081i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.39534 | + | 11.0770i | 0.276494 | + | 0.478902i | ||||
\(536\) | 1.45330 | + | 2.51719i | 0.0627730 | + | 0.108726i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −36.0571 | −1.55453 | ||||||||
\(539\) | −21.1774 | + | 22.3026i | −0.912174 | + | 0.960643i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.24095 | − | 9.07760i | −0.225326 | − | 0.390276i | 0.731091 | − | 0.682280i | \(-0.239011\pi\) |
−0.956417 | + | 0.292003i | \(0.905678\pi\) | |||||||
\(542\) | 61.2321 | 2.63014 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.85557 | −0.379679 | ||||||||
\(545\) | −17.7373 | −0.759781 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.2216 | 0.650829 | 0.325415 | − | 0.945571i | \(-0.394496\pi\) | ||||
0.325415 | + | 0.945571i | \(0.394496\pi\) | |||||||
\(548\) | 20.8792 | 0.891915 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −23.6927 | −1.01026 | ||||||||
\(551\) | 0.271625 | + | 0.470468i | 0.0115716 | + | 0.0200426i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.03490 | − | 0.241161i | −0.0865326 | − | 0.0102552i | ||||
\(554\) | 35.0726 | 1.49009 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.276261 | + | 0.478497i | 0.0117161 | + | 0.0202928i | ||||
\(557\) | 5.92986 | + | 10.2708i | 0.251256 | + | 0.435189i | 0.963872 | − | 0.266366i | \(-0.0858230\pi\) |
−0.712616 | + | 0.701555i | \(0.752490\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.0778200 | − | 0.0259342i | −0.00329144 | − | 0.00109690i | ||||
\(560\) | 17.8104 | + | 2.11076i | 0.752627 | + | 0.0891958i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.1069 | 1.14344 | ||||||||
\(563\) | −7.69349 | −0.324242 | −0.162121 | − | 0.986771i | \(-0.551834\pi\) | ||||
−0.162121 | + | 0.986771i | \(0.551834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.90332 | − | 11.9569i | 0.290425 | − | 0.503031i | ||||
\(566\) | 10.8892 | + | 18.8607i | 0.457709 | + | 0.792775i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.50360 | + | 6.06841i | 0.147008 | + | 0.254625i | ||||
\(569\) | −37.4196 | −1.56871 | −0.784355 | − | 0.620312i | \(-0.787006\pi\) | ||||
−0.784355 | + | 0.620312i | \(0.787006\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.08285 | + | 12.2679i | −0.296408 | + | 0.513394i | −0.975311 | − | 0.220834i | \(-0.929122\pi\) |
0.678903 | + | 0.734228i | \(0.262456\pi\) | |||||||
\(572\) | −24.5144 | − | 8.16963i | −1.02500 | − | 0.341589i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.2733 | − | 23.9218i | −0.428799 | − | 0.998478i | ||||
\(575\) | 6.27825 | − | 10.8742i | 0.261821 | − | 0.453488i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.48776 | − | 12.9692i | 0.311720 | − | 0.539914i | −0.667015 | − | 0.745044i | \(-0.732428\pi\) |
0.978735 | + | 0.205130i | \(0.0657617\pi\) | |||||||
\(578\) | −29.6381 | −1.23278 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.402635 | −0.0167185 | ||||||||
\(581\) | 25.3629 | − | 33.9543i | 1.05223 | − | 1.40866i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.622952 | 0.0258000 | ||||||||
\(584\) | 5.35627 | − | 9.27732i | 0.221644 | − | 0.383898i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.5811 | − | 21.7911i | −0.519720 | − | 0.900182i | ||||
\(587\) | −6.58821 | + | 11.4111i | −0.271925 | + | 0.470987i | −0.969355 | − | 0.245666i | \(-0.920993\pi\) |
0.697430 | + | 0.716653i | \(0.254327\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.50309 | − | 14.7278i | −0.350364 | − | 0.606848i | ||||
\(590\) | −7.50003 | − | 12.9904i | −0.308771 | − | 0.534807i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −32.4441 | −1.33344 | ||||||||
\(593\) | −22.0663 | − | 38.2200i | −0.906156 | − | 1.56951i | −0.819357 | − | 0.573283i | \(-0.805670\pi\) |
−0.0867989 | − | 0.996226i | \(-0.527664\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.65503 | − | 0.551680i | −0.190838 | − | 0.0226167i | ||||
\(596\) | 3.19965 | − | 5.54195i | 0.131063 | − | 0.227007i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 22.8080 | − | 20.2278i | 0.932689 | − | 0.827175i | ||||
\(599\) | −3.01349 | + | 5.21952i | −0.123128 | + | 0.213264i | −0.921000 | − | 0.389564i | \(-0.872626\pi\) |
0.797872 | + | 0.602827i | \(0.205959\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.86260 | + | 3.22612i | −0.0759770 | + | 0.131596i | −0.901511 | − | 0.432757i | \(-0.857541\pi\) |
0.825534 | + | 0.564353i | \(0.190874\pi\) | |||||||
\(602\) | −0.113902 | − | 0.0134988i | −0.00464230 | − | 0.000550172i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.72804 | − | 2.99305i | 0.0703129 | − | 0.121786i | ||||
\(605\) | 12.2326 | 0.497328 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.00825 | − | 5.21045i | 0.122101 | − | 0.211486i | −0.798495 | − | 0.602002i | \(-0.794370\pi\) |
0.920596 | + | 0.390516i | \(0.127703\pi\) | |||||||
\(608\) | 11.9358 | − | 20.6733i | 0.484059 | − | 0.838415i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 32.4105 | 1.31226 | ||||||||
\(611\) | 39.9648 | + | 13.3186i | 1.61680 | + | 0.538813i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.90413 | − | 8.49420i | −0.198076 | − | 0.343077i | 0.749829 | − | 0.661632i | \(-0.230136\pi\) |
−0.947904 | + | 0.318555i | \(0.896803\pi\) | |||||||
\(614\) | −12.6892 | −0.512094 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.11342 | + | 0.961543i | 0.326899 | + | 0.0387417i | ||||
\(617\) | 16.8838 | + | 29.2436i | 0.679716 | + | 1.17730i | 0.975066 | + | 0.221914i | \(0.0712304\pi\) |
−0.295350 | + | 0.955389i | \(0.595436\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.04671 | + | 3.54501i | −0.0822644 | + | 0.142486i | −0.904222 | − | 0.427062i | \(-0.859549\pi\) |
0.821958 | + | 0.569548i | \(0.192882\pi\) | |||||||
\(620\) | 12.6043 | 0.506201 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.94936 | + | 3.37639i | −0.0781621 | + | 0.135381i | ||||
\(623\) | −10.3829 | + | 13.9000i | −0.415983 | + | 0.556891i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.42115 | + | 2.46150i | 0.0568459 | + | 0.0984599i | ||||
\(626\) | −8.97297 | − | 15.5416i | −0.358632 | − | 0.621169i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.0347 | − | 31.2371i | 0.719665 | − | 1.24650i | ||||
\(629\) | 8.47978 | 0.338111 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.3868 | + | 23.1866i | 0.532921 | + | 0.923046i | 0.999261 | + | 0.0384402i | \(0.0122389\pi\) |
−0.466340 | + | 0.884605i | \(0.654428\pi\) | |||||||
\(632\) | 0.272179 | + | 0.471427i | 0.0108267 | + | 0.0187524i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −31.7955 | − | 55.0714i | −1.26276 | − | 2.18717i | ||||
\(635\) | 23.4012 | 0.928650 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.4158 | − | 13.3553i | −0.848523 | − | 0.529158i | ||||
\(638\) | −1.40287 | −0.0555403 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.07112 | − | 7.05139i | −0.160925 | − | 0.278731i | ||||
\(641\) | 18.5722 | 0.733558 | 0.366779 | − | 0.930308i | \(-0.380461\pi\) | ||||
0.366779 | + | 0.930308i | \(0.380461\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.96695 | + | 3.40686i | 0.0775690 | + | 0.134353i | 0.902201 | − | 0.431317i | \(-0.141951\pi\) |
−0.824632 | + | 0.565670i | \(0.808618\pi\) | |||||||
\(644\) | 11.4596 | − | 15.3414i | 0.451572 | − | 0.604536i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.71518 | + | 6.43487i | −0.146172 | + | 0.253177i | ||||
\(647\) | −0.0985378 | − | 0.170672i | −0.00387392 | − | 0.00670983i | 0.864082 | − | 0.503351i | \(-0.167900\pi\) |
−0.867956 | + | 0.496641i | \(0.834566\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.7387 | − | 20.3321i | −0.460785 | − | 0.798104i | ||||
\(650\) | −3.89922 | − | 19.0480i | −0.152940 | − | 0.747125i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.14172 | + | 5.44163i | −0.123039 | + | 0.213110i | ||||
\(653\) | 14.4673 | 0.566148 | 0.283074 | − | 0.959098i | \(-0.408646\pi\) | ||||
0.283074 | + | 0.959098i | \(0.408646\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.36813 | − | 2.36967i | 0.0534573 | − | 0.0925908i | ||||
\(656\) | −11.8812 | + | 20.5788i | −0.463883 | + | 0.803468i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 58.4949 | + | 6.93238i | 2.28037 | + | 0.270252i | ||||
\(659\) | −11.7066 | − | 20.2764i | −0.456024 | − | 0.789857i | 0.542722 | − | 0.839912i | \(-0.317394\pi\) |
−0.998746 | + | 0.0500552i | \(0.984060\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.02409 | + | 3.50582i | 0.0787278 | + | 0.136361i | 0.902701 | − | 0.430268i | \(-0.141581\pi\) |
−0.823973 | + | 0.566628i | \(0.808248\pi\) | |||||||
\(662\) | −18.1657 | + | 31.4638i | −0.706028 | + | 1.22288i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.2587 | −0.436921 | ||||||||
\(665\) | 7.56208 | − | 10.1236i | 0.293245 | − | 0.392577i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.371744 | − | 0.643879i | 0.0143940 | − | 0.0249311i | ||||
\(668\) | 1.74448 | − | 3.02153i | 0.0674959 | − | 0.116906i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.80440 | + | 10.0535i | −0.224243 | + | 0.388401i | ||||
\(671\) | 50.7276 | 1.95832 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.64704 | + | 6.31685i | −0.140583 | + | 0.243497i | −0.927716 | − | 0.373286i | \(-0.878231\pi\) |
0.787133 | + | 0.616783i | \(0.211564\pi\) | |||||||
\(674\) | −59.6152 | −2.29629 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.53362 | − | 21.0532i | 0.0974468 | − | 0.809737i | ||||
\(677\) | −7.87553 | − | 13.6408i | −0.302681 | − | 0.524259i | 0.674061 | − | 0.738676i | \(-0.264548\pi\) |
−0.976742 | + | 0.214416i | \(0.931215\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.17387 | − | 1.08722i | −0.352061 | − | 0.0417236i | ||||
\(680\) | 0.622636 | + | 1.07844i | 0.0238770 | + | 0.0413562i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 43.9163 | 1.68164 | ||||||||
\(683\) | −41.4854 | −1.58739 | −0.793697 | − | 0.608314i | \(-0.791846\pi\) | ||||
−0.793697 | + | 0.608314i | \(0.791846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.42819 | − | 16.3301i | −0.360233 | − | 0.623941i | ||||
\(686\) | −33.1045 | − | 12.2301i | −1.26394 | − | 0.466949i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.0523445 | + | 0.0906634i | 0.00199562 | + | 0.00345651i | ||||
\(689\) | 0.102522 | + | 0.500830i | 0.00390579 | + | 0.0190801i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −46.8216 | −1.78118 | −0.890589 | − | 0.454809i | \(-0.849708\pi\) | ||||
−0.890589 | + | 0.454809i | \(0.849708\pi\) | |||||||
\(692\) | −13.5494 | + | 23.4683i | −0.515073 | + | 0.892132i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.2478 | −0.844514 | ||||||||
\(695\) | 0.249496 | − | 0.432140i | 0.00946392 | − | 0.0163920i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.10534 | − | 5.37860i | 0.117623 | − | 0.203729i | ||||
\(698\) | −22.8576 | + | 39.5905i | −0.865172 | + | 1.49852i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.81921 | − | 11.2217i | −0.182149 | − | 0.424142i | ||||
\(701\) | −29.8626 | −1.12790 | −0.563948 | − | 0.825810i | \(-0.690718\pi\) | ||||
−0.563948 | + | 0.825810i | \(0.690718\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.4293 | + | 19.7961i | −0.431063 | + | 0.746623i | ||||
\(704\) | 10.6048 | + | 18.3680i | 0.399683 | + | 0.692271i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.1893 | + | 21.1124i | 0.458749 | + | 0.794576i | ||||
\(707\) | 6.77281 | + | 0.802663i | 0.254718 | + | 0.0301873i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.4666 | + | 23.3249i | −0.505750 | + | 0.875984i | 0.494228 | + | 0.869332i | \(0.335451\pi\) |
−0.999978 | + | 0.00665185i | \(0.997883\pi\) | |||||||
\(710\) | −13.9932 | + | 24.2369i | −0.525155 | + | 0.909595i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.60900 | 0.172729 | ||||||||
\(713\) | −11.6373 | + | 20.1563i | −0.435819 | + | 0.754861i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.68004 | + | 22.8623i | 0.175023 | + | 0.855003i | ||||
\(716\) | −0.440002 | − | 0.762105i | −0.0164436 | − | 0.0284812i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11.7570 | + | 20.3638i | 0.438769 | + | 0.759969i | ||||
\(719\) | −7.24938 | + | 12.5563i | −0.270356 | + | 0.468271i | −0.968953 | − | 0.247245i | \(-0.920475\pi\) |
0.698597 | + | 0.715516i | \(0.253808\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.3064 | + | 5.25087i | 1.65006 | + | 0.195553i | ||||
\(722\) | 8.08799 | + | 14.0088i | 0.301004 | + | 0.521354i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.52098 | 0.168021 | ||||||||
\(725\) | −0.237090 | − | 0.410652i | −0.00880530 | − | 0.0152512i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.26424 | −0.232328 | −0.116164 | − | 0.993230i | \(-0.537060\pi\) | ||||
−0.116164 | + | 0.993230i | \(0.537060\pi\) | |||||||
\(728\) | 0.562223 | + | 6.68113i | 0.0208374 | + | 0.247619i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 42.7852 | 1.58355 | ||||||||
\(731\) | −0.0136811 | − | 0.0236963i | −0.000506013 | − | 0.000876440i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.99189 | + | 10.3783i | 0.221316 | + | 0.383330i | 0.955208 | − | 0.295936i | \(-0.0956316\pi\) |
−0.733892 | + | 0.679266i | \(0.762298\pi\) | |||||||
\(734\) | −1.93487 | − | 3.35130i | −0.0714175 | − | 0.123699i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32.6704 | −1.20425 | ||||||||
\(737\) | −9.08480 | + | 15.7353i | −0.334643 | + | 0.579619i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.76269 | − | 11.7133i | −0.248770 | − | 0.430882i | 0.714415 | − | 0.699722i | \(-0.246693\pi\) |
−0.963185 | + | 0.268840i | \(0.913360\pi\) | |||||||
\(740\) | −8.47091 | − | 14.6721i | −0.311397 | − | 0.539355i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.282075 | + | 0.656825i | 0.0103553 | + | 0.0241128i | ||||
\(743\) | −19.2299 | + | 33.3072i | −0.705477 | + | 1.22192i | 0.261043 | + | 0.965327i | \(0.415934\pi\) |
−0.966519 | + | 0.256594i | \(0.917400\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.77932 | −0.211738 | ||||||||
\(746\) | 3.69107 | − | 6.39312i | 0.135140 | − | 0.234069i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.30973 | − | 7.46466i | −0.157579 | − | 0.272935i | ||||
\(749\) | −13.7476 | + | 18.4044i | −0.502326 | + | 0.672482i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.7115 | 0.427357 | 0.213679 | − | 0.976904i | \(-0.431455\pi\) | ||||
0.213679 | + | 0.976904i | \(0.431455\pi\) | |||||||
\(752\) | −26.8817 | − | 46.5605i | −0.980276 | − | 1.69789i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.230878 | − | 1.12786i | −0.00840809 | − | 0.0410742i | ||||
\(755\) | −3.12125 | −0.113594 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.65791 | + | 8.06773i | −0.169295 | + | 0.293227i | −0.938172 | − | 0.346169i | \(-0.887482\pi\) |
0.768877 | + | 0.639396i | \(0.220816\pi\) | |||||||
\(758\) | 13.8800 | − | 24.0409i | 0.504145 | − | 0.873205i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.35682 | −0.121765 | ||||||||
\(761\) | −21.9691 | + | 38.0515i | −0.796378 | + | 1.37937i | 0.125582 | + | 0.992083i | \(0.459920\pi\) |
−0.921960 | + | 0.387284i | \(0.873413\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.5706 | − | 29.2712i | −0.455086 | − | 1.05969i | ||||
\(764\) | −16.5079 | + | 28.5926i | −0.597236 | + | 1.03444i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.5172 | + | 44.1971i | −0.921973 | + | 1.59690i | ||||
\(767\) | 14.4143 | − | 12.7837i | 0.520471 | − | 0.461591i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.6771 | + | 21.9573i | −0.457147 | + | 0.791802i | −0.998809 | − | 0.0487946i | \(-0.984462\pi\) |
0.541662 | + | 0.840597i | \(0.317795\pi\) | |||||||
\(770\) | 12.8764 | + | 29.9833i | 0.464035 | + | 1.08052i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.3568 | + | 23.1347i | 0.480723 | + | 0.832637i | ||||
\(773\) | 23.1084 | 0.831152 | 0.415576 | − | 0.909559i | \(-0.363580\pi\) | ||||
0.415576 | + | 0.909559i | \(0.363580\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.42200 | + | 12.8553i | 0.266606 | + | 0.461775i | ||||
\(776\) | 1.22705 | + | 2.12532i | 0.0440487 | + | 0.0762946i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.4474 | − | 19.8275i | 0.410410 | − | 0.710851i | ||||
\(779\) | 8.37091 | + | 14.4988i | 0.299919 | + | 0.519475i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.9015 | + | 37.9346i | −0.783699 | + | 1.35741i | ||||
\(782\) | 10.1691 | 0.363647 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.13912 | + | 30.8878i | 0.326397 | + | 1.10314i | ||||
\(785\) | −32.5750 | −1.16265 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.6692 | −0.879364 | −0.439682 | − | 0.898154i | \(-0.644909\pi\) | ||||
−0.439682 | + | 0.898154i | \(0.644909\pi\) | |||||||
\(788\) | 16.0943 | − | 27.8761i | 0.573334 | − | 0.993044i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.08707 | + | 1.88285i | −0.0386761 | + | 0.0669889i | ||||
\(791\) | 24.6245 | + | 2.91832i | 0.875547 | + | 0.103763i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.34850 | + | 40.7831i | 0.296464 | + | 1.44825i | ||||
\(794\) | 1.57938 | − | 2.73556i | 0.0560500 | − | 0.0970814i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23.0278 | −0.816199 | ||||||||
\(797\) | 5.65686 | + | 9.79797i | 0.200376 | + | 0.347062i | 0.948650 | − | 0.316329i | \(-0.102450\pi\) |
−0.748273 | + | 0.663390i | \(0.769117\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.02597 | + | 12.1693i | 0.248561 | + | 0.430520i | ||||
\(800\) | −10.4182 | + | 18.0449i | −0.368340 | + | 0.637984i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 39.0311 | 1.37824 | ||||||||
\(803\) | 66.9657 | 2.36317 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.1736 | − | 2.03529i | −0.605289 | − | 0.0717344i | ||||
\(806\) | 7.22754 | + | 35.3071i | 0.254579 | + | 1.24364i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.905900 | − | 1.56906i | −0.0318694 | − | 0.0551995i | ||||
\(809\) | 8.18540 | + | 14.1775i | 0.287783 | + | 0.498455i | 0.973280 | − | 0.229620i | \(-0.0737484\pi\) |
−0.685497 | + | 0.728075i | \(0.740415\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.0412 | −1.01978 | −0.509888 | − | 0.860241i | \(-0.670313\pi\) | ||||
−0.509888 | + | 0.860241i | \(0.670313\pi\) | |||||||
\(812\) | −0.285352 | − | 0.664454i | −0.0100139 | − | 0.0233178i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29.5146 | − | 51.1209i | −1.03449 | − | 1.79179i | ||||
\(815\) | 5.67470 | 0.198776 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0737588 | 0.00258050 | ||||||||
\(818\) | 28.3278 | 0.990458 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.4084 | −0.433319 | ||||||||
\(821\) | 13.7518 | 0.479940 | 0.239970 | − | 0.970780i | \(-0.422862\pi\) | ||||
0.239970 | + | 0.970780i | \(0.422862\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.1153 | −1.01490 | −0.507448 | − | 0.861682i | \(-0.669411\pi\) | ||||
−0.507448 | + | 0.861682i | \(0.669411\pi\) | |||||||
\(824\) | −5.92623 | − | 10.2645i | −0.206450 | − | 0.357582i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.1223 | − | 21.5835i | 0.560966 | − | 0.750985i | ||||
\(827\) | 22.9118 | 0.796722 | 0.398361 | − | 0.917229i | \(-0.369579\pi\) | ||||
0.398361 | + | 0.917229i | \(0.369579\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.6914 | + | 20.2502i | 0.406061 | + | 0.703317i | 0.994444 | − | 0.105264i | \(-0.0335689\pi\) |
−0.588384 | + | 0.808582i | \(0.700236\pi\) | |||||||
\(830\) | −22.4832 | − | 38.9421i | −0.780404 | − | 1.35170i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13.0219 | + | 11.5488i | −0.451454 | + | 0.400382i | ||||
\(833\) | −2.38865 | − | 8.07301i | −0.0827620 | − | 0.279713i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.15094 | −0.109043 | ||||||||
\(836\) | 23.2350 | 0.803601 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.5023 | + | 38.9751i | −0.777328 | + | 1.34637i | ||||
\(839\) | 0.367168 | + | 0.635954i | 0.0126761 | + | 0.0219556i | 0.872294 | − | 0.488982i | \(-0.162632\pi\) |
−0.859618 | + | 0.510938i | \(0.829298\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4860 | + | 25.0904i | 0.499516 | + | 0.865187i | ||||
\(842\) | 49.7013 | 1.71282 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.77314 | − | 6.53528i | 0.129877 | − | 0.224954i | ||||
\(845\) | −17.6103 | + | 7.52515i | −0.605811 | + | 0.258873i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.66941 | + | 20.1871i | 0.297884 | + | 0.693637i | ||||
\(848\) | 0.326223 | − | 0.565035i | 0.0112026 | − | 0.0194034i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.24282 | − | 5.61674i | 0.111228 | − | 0.192652i | ||||
\(851\) | 31.2840 | 1.07240 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 54.3567 | 1.86114 | 0.930569 | − | 0.366118i | \(-0.119313\pi\) | ||||
0.930569 | + | 0.366118i | \(0.119313\pi\) | |||||||
\(854\) | 22.9697 | + | 53.4859i | 0.786006 | + | 1.83025i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.10259 | 0.208582 | ||||||||
\(857\) | −10.5106 | + | 18.2048i | −0.359034 | + | 0.621864i | −0.987800 | − | 0.155730i | \(-0.950227\pi\) |
0.628766 | + | 0.777595i | \(0.283560\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.6814 | + | 44.4816i | 0.876240 | + | 1.51769i | 0.855436 | + | 0.517908i | \(0.173289\pi\) |
0.0208035 | + | 0.999784i | \(0.493378\pi\) | |||||||
\(860\) | −0.0273336 | + | 0.0473431i | −0.000932066 | + | 0.00161439i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.6884 | − | 21.9769i | −0.432167 | − | 0.748535i | ||||
\(863\) | 3.55660 | + | 6.16021i | 0.121068 | + | 0.209696i | 0.920189 | − | 0.391474i | \(-0.128035\pi\) |
−0.799121 | + | 0.601170i | \(0.794701\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.4735 | 0.832124 | ||||||||
\(866\) | −19.4577 | − | 33.7018i | −0.661201 | − | 1.14523i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.93280 | + | 20.8004i | 0.303199 | + | 0.706012i | ||||
\(869\) | −1.70143 | + | 2.94696i | −0.0577171 | + | 0.0999689i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.1458 | − | 4.71419i | −0.479311 | − | 0.159734i | ||||
\(872\) | −4.23133 | + | 7.32888i | −0.143291 | + | 0.248187i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.7062 | + | 23.7399i | −0.463620 | + | 0.803013i | ||||
\(875\) | −18.2630 | + | 24.4493i | −0.617401 | + | 0.826537i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.256238 | + | 0.443818i | −0.00865255 | + | 0.0149867i | −0.870319 | − | 0.492488i | \(-0.836088\pi\) |
0.861667 | + | 0.507475i | \(0.169421\pi\) | |||||||
\(878\) | −18.6187 | −0.628352 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 14.8917 | − | 25.7933i | 0.502000 | − | 0.869490i | ||||
\(881\) | −18.5464 | + | 32.1232i | −0.624843 | + | 1.08226i | 0.363729 | + | 0.931505i | \(0.381503\pi\) |
−0.988571 | + | 0.150754i | \(0.951830\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.5667 | −0.523860 | −0.261930 | − | 0.965087i | \(-0.584359\pi\) | ||||
−0.261930 | + | 0.965087i | \(0.584359\pi\) | |||||||
\(884\) | 5.29204 | − | 4.69336i | 0.177990 | − | 0.157855i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.1645 | + | 34.9260i | 0.677440 | + | 1.17336i | ||||
\(887\) | −27.5799 | −0.926043 | −0.463022 | − | 0.886347i | \(-0.653235\pi\) | ||||
−0.463022 | + | 0.886347i | \(0.653235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.5847 | + | 38.6182i | 0.556233 | + | 1.29521i | ||||
\(890\) | 9.20404 | + | 15.9419i | 0.308520 | + | 0.534372i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.4145 | − | 30.1627i | 0.583079 | − | 1.00992i | ||||
\(893\) | −37.8792 | −1.26758 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.397374 | + | 0.688272i | −0.0132827 | + | 0.0230064i | ||||
\(896\) | 8.75140 | − | 11.7158i | 0.292364 | − | 0.391398i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.2895 | − | 29.9463i | −0.576959 | − | 0.999323i | ||||
\(899\) | 0.439466 | + | 0.761178i | 0.0146570 | + | 0.0253867i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.0852637 | + | 0.147681i | −0.00284054 | + | 0.00491997i | ||||
\(902\) | −43.2337 | −1.43952 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.29366 | − | 5.70479i | −0.109546 | − | 0.189738i | ||||
\(905\) | −2.04149 | − | 3.53597i | −0.0678615 | − | 0.117539i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.5236 | + | 39.0119i | 0.747882 | + | 1.29537i | 0.948836 | + | 0.315769i | \(0.102263\pi\) |
−0.200954 | + | 0.979601i | \(0.564404\pi\) | |||||||
\(908\) | 17.0440 | 0.565625 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −21.9863 | + | 15.2867i | −0.728840 | + | 0.506749i | ||||
\(911\) | −35.4678 | −1.17510 | −0.587550 | − | 0.809188i | \(-0.699907\pi\) | ||||
−0.587550 | + | 0.809188i | \(0.699907\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.1898 | − | 60.9505i | −1.16461 | − | 2.01717i | ||||
\(914\) | −34.3379 | −1.13580 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.7917 | − | 20.4238i | −0.389608 | − | 0.674820i | ||||
\(917\) | 4.88020 | + | 0.578365i | 0.161158 | + | 0.0190993i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.68622 | + | 15.0450i | −0.286532 | + | 0.496288i | −0.972980 | − | 0.230891i | \(-0.925836\pi\) |
0.686447 | + | 0.727179i | \(0.259169\pi\) | |||||||
\(920\) | 2.29706 | + | 3.97862i | 0.0757318 | + | 0.131171i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28.3686 | − | 49.1359i | −0.934271 | − | 1.61820i | ||||
\(923\) | −34.1024 | − | 11.3649i | −1.12250 | − | 0.374081i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.97613 | − | 17.2792i | 0.328013 | − | 0.568136i | ||||
\(926\) | 33.7412 | 1.10880 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.616877 | + | 1.06846i | −0.0202500 | + | 0.0350740i | ||||
\(929\) | 5.38001 | − | 9.31845i | 0.176512 | − | 0.305729i | −0.764171 | − | 0.645013i | \(-0.776852\pi\) |
0.940684 | + | 0.339285i | \(0.110185\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.0660 | + | 5.30470i | 0.723183 | + | 0.173854i | ||||
\(932\) | −7.57532 | − | 13.1208i | −0.248138 | − | 0.429788i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.55396 | − | 9.61975i | −0.181731 | − | 0.314768i | ||||
\(935\) | −3.89219 | + | 6.74148i | −0.127288 | + | 0.220470i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.9816 | −0.358755 | −0.179377 | − | 0.983780i | \(-0.557408\pi\) | ||||
−0.179377 | + | 0.983780i | \(0.557408\pi\) | |||||||
\(938\) | −20.7046 | − | 2.45375i | −0.676029 | − | 0.0801179i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 14.0373 | − | 24.3132i | 0.457845 | − | 0.793011i | ||||
\(941\) | 4.08897 | − | 7.08231i | 0.133297 | − | 0.230877i | −0.791649 | − | 0.610976i | \(-0.790777\pi\) |
0.924946 | + | 0.380100i | \(0.124110\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.4564 | − | 19.8430i | 0.373071 | − | 0.646177i | ||||
\(944\) | −24.5890 | −0.800305 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.0952365 | + | 0.164954i | −0.00309640 | + | 0.00536313i | ||||
\(947\) | 4.59378 | 0.149278 | 0.0746389 | − | 0.997211i | \(-0.476220\pi\) | ||||
0.0746389 | + | 0.997211i | \(0.476220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.0209 | + | 53.8379i | 0.357753 | + | 1.74765i | ||||
\(950\) | 8.74153 | + | 15.1408i | 0.283613 | + | 0.491231i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.33844 | + | 1.79181i | −0.0433790 | + | 0.0580730i | ||||
\(953\) | 10.5714 | + | 18.3102i | 0.342442 | + | 0.593126i | 0.984886 | − | 0.173206i | \(-0.0554128\pi\) |
−0.642444 | + | 0.766333i | \(0.722079\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.8172 | 0.964863 | ||||||||
\(956\) | −32.0249 | −1.03576 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.8070 | + | 23.9145i | 0.446085 | + | 0.772641i | ||||
\(959\) | 20.2671 | − | 27.1323i | 0.654459 | − | 0.876148i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.74271 | + | 3.01846i | 0.0562164 | + | 0.0973697i | ||||
\(962\) | 36.2419 | − | 32.1419i | 1.16849 | − | 1.03630i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.9255 | 0.384094 | ||||||||
\(965\) | 12.0628 | − | 20.8934i | 0.388316 | − | 0.672582i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.0750 | −1.03146 | −0.515731 | − | 0.856750i | \(-0.672480\pi\) | ||||
−0.515731 | + | 0.856750i | \(0.672480\pi\) | |||||||
\(968\) | 2.91817 | − | 5.05442i | 0.0937936 | − | 0.162455i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.90079 | + | 8.48841i | −0.157355 | + | 0.272546i | ||||
\(971\) | −26.0417 | + | 45.1056i | −0.835719 | + | 1.44751i | 0.0577245 | + | 0.998333i | \(0.481616\pi\) |
−0.893444 | + | 0.449175i | \(0.851718\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.889965 | + | 0.105472i | 0.0285310 | + | 0.00338128i | ||||
\(974\) | −34.2241 | −1.09661 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.5647 | − | 46.0114i | 0.850315 | − | 1.47279i | ||||
\(977\) | 9.62898 | + | 16.6779i | 0.308058 | + | 0.533573i | 0.977938 | − | 0.208897i | \(-0.0669874\pi\) |
−0.669879 | + | 0.742470i | \(0.733654\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.4058 | + | 24.9515i | 0.460410 | + | 0.797454i | ||||
\(980\) | −11.5821 | + | 12.1975i | −0.369977 | + | 0.389636i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −34.5868 | + | 59.9061i | −1.10371 | + | 1.91168i | ||||
\(983\) | −8.03657 | + | 13.9197i | −0.256327 | + | 0.443971i | −0.965255 | − | 0.261310i | \(-0.915846\pi\) |
0.708928 | + | 0.705280i | \(0.249179\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.0700 | −0.926248 | ||||||||
\(986\) | 0.192012 | − | 0.332574i | 0.00611490 | − | 0.0105913i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.82391 | + | 18.6801i | 0.121655 | + | 0.594294i | ||||
\(989\) | −0.0504729 | − | 0.0874216i | −0.00160494 | − | 0.00277985i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.7132 | − | 18.5559i | −0.340317 | − | 0.589447i | 0.644174 | − | 0.764879i | \(-0.277201\pi\) |
−0.984492 | + | 0.175432i | \(0.943868\pi\) | |||||||
\(992\) | 19.3111 | − | 33.4478i | 0.613127 | − | 1.06197i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −49.9144 | − | 5.91549i | −1.58319 | − | 0.187628i | ||||
\(995\) | 10.3984 | + | 18.0106i | 0.329652 | + | 0.570974i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.9537 | −0.536931 | −0.268465 | − | 0.963289i | \(-0.586516\pi\) | ||||
−0.268465 | + | 0.963289i | \(0.586516\pi\) | |||||||
\(998\) | −22.5881 | − | 39.1238i | −0.715015 | − | 1.23844i | ||||
\(999\) | 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 | 819.2.s.d.802.5 | 12 | ||
3.2 | odd | 2 | 91.2.h.b.74.2 | yes | 12 | ||
7.2 | even | 3 | 819.2.n.d.100.2 | 12 | |||
13.3 | even | 3 | 819.2.n.d.172.2 | 12 | |||
21.2 | odd | 6 | 91.2.g.b.9.5 | ✓ | 12 | ||
21.5 | even | 6 | 637.2.g.l.373.5 | 12 | |||
21.11 | odd | 6 | 637.2.f.k.295.5 | 12 | |||
21.17 | even | 6 | 637.2.f.j.295.5 | 12 | |||
21.20 | even | 2 | 637.2.h.l.165.2 | 12 | |||
39.17 | odd | 6 | 1183.2.e.g.508.2 | 12 | |||
39.29 | odd | 6 | 91.2.g.b.81.5 | yes | 12 | ||
39.35 | odd | 6 | 1183.2.e.h.508.5 | 12 | |||
91.16 | even | 3 | inner | 819.2.s.d.289.5 | 12 | ||
273.17 | even | 6 | 8281.2.a.cf.1.5 | 6 | |||
273.68 | even | 6 | 637.2.h.l.471.2 | 12 | |||
273.74 | odd | 6 | 8281.2.a.bz.1.2 | 6 | |||
273.95 | odd | 6 | 8281.2.a.ce.1.5 | 6 | |||
273.107 | odd | 6 | 91.2.h.b.16.2 | yes | 12 | ||
273.146 | even | 6 | 637.2.g.l.263.5 | 12 | |||
273.185 | even | 6 | 637.2.f.j.393.5 | 12 | |||
273.191 | odd | 6 | 1183.2.e.h.170.5 | 12 | |||
273.212 | odd | 6 | 1183.2.e.g.170.2 | 12 | |||
273.263 | odd | 6 | 637.2.f.k.393.5 | 12 | |||
273.269 | even | 6 | 8281.2.a.ca.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.5 | ✓ | 12 | 21.2 | odd | 6 | ||
91.2.g.b.81.5 | yes | 12 | 39.29 | odd | 6 | ||
91.2.h.b.16.2 | yes | 12 | 273.107 | odd | 6 | ||
91.2.h.b.74.2 | yes | 12 | 3.2 | odd | 2 | ||
637.2.f.j.295.5 | 12 | 21.17 | even | 6 | |||
637.2.f.j.393.5 | 12 | 273.185 | even | 6 | |||
637.2.f.k.295.5 | 12 | 21.11 | odd | 6 | |||
637.2.f.k.393.5 | 12 | 273.263 | odd | 6 | |||
637.2.g.l.263.5 | 12 | 273.146 | even | 6 | |||
637.2.g.l.373.5 | 12 | 21.5 | even | 6 | |||
637.2.h.l.165.2 | 12 | 21.20 | even | 2 | |||
637.2.h.l.471.2 | 12 | 273.68 | even | 6 | |||
819.2.n.d.100.2 | 12 | 7.2 | even | 3 | |||
819.2.n.d.172.2 | 12 | 13.3 | even | 3 | |||
819.2.s.d.289.5 | 12 | 91.16 | even | 3 | inner | ||
819.2.s.d.802.5 | 12 | 1.1 | even | 1 | trivial | ||
1183.2.e.g.170.2 | 12 | 273.212 | odd | 6 | |||
1183.2.e.g.508.2 | 12 | 39.17 | odd | 6 | |||
1183.2.e.h.170.5 | 12 | 273.191 | odd | 6 | |||
1183.2.e.h.508.5 | 12 | 39.35 | odd | 6 | |||
8281.2.a.bz.1.2 | 6 | 273.74 | odd | 6 | |||
8281.2.a.ca.1.2 | 6 | 273.269 | even | 6 | |||
8281.2.a.ce.1.5 | 6 | 273.95 | odd | 6 | |||
8281.2.a.cf.1.5 | 6 | 273.17 | even | 6 |