Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(577,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.i (of order \(3\), degree \(2\), not 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: | \(9.70980888579\) |
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: | \( x^{12} - 28 x^{9} - 121 x^{8} - 238 x^{7} + 392 x^{6} + 2534 x^{5} + 5589 x^{4} + 6426 x^{3} + 4802 x^{2} + 2548 x + 676 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 608) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.3 | ||
Root | \(-1.15100 - 1.56354i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.961 |
Dual form | 1216.2.i.r.577.3 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.866025 | + | 1.50000i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.09926 | − | 3.63603i | 0.938818 | − | 1.62608i | 0.171139 | − | 0.985247i | \(-0.445255\pi\) |
0.767679 | − | 0.640834i | \(-0.221411\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.28918 | 1.62116 | 0.810578 | − | 0.585630i | \(-0.199153\pi\) | ||||
0.810578 | + | 0.585630i | \(0.199153\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.71493 | 1.42160 | 0.710802 | − | 0.703392i | \(-0.248332\pi\) | ||||
0.710802 | + | 0.703392i | \(0.248332\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.615275 | − | 1.06569i | −0.170647 | − | 0.295569i | 0.767999 | − | 0.640451i | \(-0.221252\pi\) |
−0.938646 | + | 0.344882i | \(0.887919\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.63603 | + | 6.29778i | 0.938818 | + | 1.62608i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.61528 | + | 2.79774i | −0.391762 | + | 0.678551i | −0.992682 | − | 0.120758i | \(-0.961468\pi\) |
0.600920 | + | 0.799309i | \(0.294801\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.625413 | − | 4.31380i | −0.143480 | − | 0.989653i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.71454 | + | 6.43377i | −0.810578 | + | 1.40396i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.90398 | + | 3.29778i | 0.397007 | + | 0.687636i | 0.993355 | − | 0.115090i | \(-0.0367157\pi\) |
−0.596348 | + | 0.802726i | \(0.703382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.31380 | − | 10.9358i | −1.26276 | − | 2.18716i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.09926 | − | 3.63603i | −0.389823 | − | 0.675193i | 0.602602 | − | 0.798042i | \(-0.294131\pi\) |
−0.992425 | + | 0.122848i | \(0.960797\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.825076 | 0.148188 | 0.0740940 | − | 0.997251i | \(-0.476394\pi\) | ||||
0.0740940 | + | 0.997251i | \(0.476394\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.08325 | + | 7.07239i | −0.710802 | + | 1.23115i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.00411 | − | 15.5956i | 1.52197 | − | 2.63613i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.96797 | −0.487932 | −0.243966 | − | 0.969784i | \(-0.578448\pi\) | ||||
−0.243966 | + | 0.969784i | \(0.578448\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.13138 | 0.341293 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.69852 | − | 4.67398i | 0.421439 | − | 0.729953i | −0.574642 | − | 0.818405i | \(-0.694859\pi\) |
0.996080 | + | 0.0884520i | \(0.0281920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.49144 | + | 2.58325i | −0.227442 | + | 0.393942i | −0.957049 | − | 0.289925i | \(-0.906370\pi\) |
0.729607 | + | 0.683867i | \(0.239703\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.653150 | − | 1.13129i | −0.0952717 | − | 0.165015i | 0.814450 | − | 0.580233i | \(-0.197039\pi\) |
−0.909722 | + | 0.415218i | \(0.863705\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.3970 | 1.62815 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.79774 | − | 4.84583i | −0.391762 | − | 0.678551i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.38472 | − | 2.39841i | −0.190207 | − | 0.329447i | 0.755112 | − | 0.655596i | \(-0.227582\pi\) |
−0.945319 | + | 0.326148i | \(0.894249\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.89787 | − | 17.1436i | 1.33463 | − | 2.31164i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.01232 | + | 2.79774i | 0.928805 | + | 0.370570i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.31300 | + | 12.6665i | −0.952072 | + | 1.64904i | −0.211142 | + | 0.977455i | \(0.567718\pi\) |
−0.740930 | + | 0.671582i | \(0.765615\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.09926 | + | 7.10013i | 0.524857 | + | 0.909078i | 0.999581 | + | 0.0289439i | \(0.00921441\pi\) |
−0.474724 | + | 0.880135i | \(0.657452\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.16650 | −0.640825 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.69110 | + | 2.92907i | 0.206601 | + | 0.357843i | 0.950642 | − | 0.310291i | \(-0.100426\pi\) |
−0.744041 | + | 0.668134i | \(0.767093\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.59557 | −0.794013 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.04857 | + | 7.01232i | −0.480476 | + | 0.832209i | −0.999749 | − | 0.0223991i | \(-0.992870\pi\) |
0.519273 | + | 0.854609i | \(0.326203\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.69852 | + | 8.13808i | −0.549921 | + | 0.952490i | 0.448359 | + | 0.893854i | \(0.352009\pi\) |
−0.998279 | + | 0.0586367i | \(0.981325\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 21.8716 | 2.52552 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 20.2232 | 2.30464 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.31652 | − | 4.01232i | 0.260628 | − | 0.451421i | −0.705781 | − | 0.708430i | \(-0.749404\pi\) |
0.966409 | + | 0.257009i | \(0.0827370\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.32753 | −0.804301 | −0.402150 | − | 0.915574i | \(-0.631737\pi\) | ||||
−0.402150 | + | 0.915574i | \(0.631737\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.78177 | + | 11.7464i | 0.735586 | + | 1.27407i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.27206 | 0.779646 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.61528 | − | 9.72594i | −0.595218 | − | 1.03095i | −0.993516 | − | 0.113692i | \(-0.963732\pi\) |
0.398298 | − | 0.917256i | \(-0.369601\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.63903 | − | 4.57093i | −0.276645 | − | 0.479163i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.714537 | + | 1.23761i | −0.0740940 | + | 0.128335i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.9980 | − | 6.78177i | −1.74396 | − | 0.695795i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.92907 | + | 10.2695i | −0.602006 | + | 1.04271i | 0.390511 | + | 0.920598i | \(0.372298\pi\) |
−0.992517 | + | 0.122107i | \(0.961035\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.868711 | + | 1.50465i | 0.0864400 | + | 0.149718i | 0.906004 | − | 0.423269i | \(-0.139118\pi\) |
−0.819564 | + | 0.572988i | \(0.805784\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.42986 | 0.929151 | 0.464576 | − | 0.885533i | \(-0.346207\pi\) | ||||
0.464576 | + | 0.885533i | \(0.346207\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 15.5956 | + | 27.0123i | 1.52197 | + | 2.63613i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.5066 | 1.49908 | 0.749538 | − | 0.661962i | \(-0.230276\pi\) | ||||
0.749538 | + | 0.661962i | \(0.230276\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0123 | − | 17.3419i | 0.959006 | − | 1.66105i | 0.234085 | − | 0.972216i | \(-0.424790\pi\) |
0.724921 | − | 0.688832i | \(-0.241876\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.57034 | − | 4.45196i | 0.243966 | − | 0.422561i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.23055 | 0.209833 | 0.104916 | − | 0.994481i | \(-0.466543\pi\) | ||||
0.104916 | + | 0.994481i | \(0.466543\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.9878 | 1.49087 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.92820 | + | 12.0000i | −0.635107 | + | 1.10004i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.2306 | 1.02096 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.67398 | + | 8.09557i | 0.421439 | + | 0.729953i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −32.0246 | −2.86437 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.39841 | + | 4.15417i | 0.212825 | + | 0.368623i | 0.952597 | − | 0.304234i | \(-0.0984003\pi\) |
−0.739773 | + | 0.672857i | \(0.765067\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.58325 | − | 4.47432i | −0.227442 | − | 0.393942i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.50505 | + | 6.07093i | −0.306238 | + | 0.530419i | −0.977536 | − | 0.210768i | \(-0.932404\pi\) |
0.671298 | + | 0.741187i | \(0.265737\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.68251 | − | 18.5026i | −0.232603 | − | 1.60438i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.9081 | + | 18.8934i | −0.938818 | + | 1.62608i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.89705 | − | 15.4101i | −0.760126 | − | 1.31658i | −0.942785 | − | 0.333401i | \(-0.891804\pi\) |
0.182659 | − | 0.983176i | \(-0.441529\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.71233 | + | 13.3581i | 0.654151 | + | 1.13302i | 0.982106 | + | 0.188330i | \(0.0603074\pi\) |
−0.327955 | + | 0.944694i | \(0.606359\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.26258 | 0.190543 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.90098 | − | 5.02464i | −0.242592 | − | 0.420182i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.6276 | −1.46389 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.87013 | + | 17.0956i | −0.814075 | + | 1.41002i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.09926 | − | 1.90398i | 0.0900550 | − | 0.155980i | −0.817479 | − | 0.575958i | \(-0.804629\pi\) |
0.907534 | + | 0.419978i | \(0.137962\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.7190 | 1.11644 | 0.558220 | − | 0.829693i | \(-0.311485\pi\) | ||||
0.558220 | + | 0.829693i | \(0.311485\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.73205 | − | 3.00000i | 0.139122 | − | 0.240966i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.78177 | − | 8.28227i | 0.381627 | − | 0.660997i | −0.609668 | − | 0.792657i | \(-0.708697\pi\) |
0.991295 | + | 0.131660i | \(0.0420306\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.79683 | 0.380413 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.16650 | + | 14.1448i | 0.643610 | + | 1.11477i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.563122 | 0.0441071 | 0.0220536 | − | 0.999757i | \(-0.492980\pi\) | ||||
0.0220536 | + | 0.999757i | \(0.492980\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 17.1436 | + | 29.6936i | 1.33463 | + | 2.31164i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.64924 | − | 6.32067i | −0.282387 | − | 0.489108i | 0.689585 | − | 0.724204i | \(-0.257793\pi\) |
−0.971972 | + | 0.235096i | \(0.924459\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.74287 | − | 9.94695i | 0.441759 | − | 0.765150i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.78177 | + | 16.9425i | −0.743694 | + | 1.28812i | 0.207108 | + | 0.978318i | \(0.433595\pi\) |
−0.950802 | + | 0.309798i | \(0.899739\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −27.0810 | − | 46.9057i | −2.04713 | − | 3.54574i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.6665 | − | 21.9390i | −0.952072 | − | 1.64904i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.7198 | −1.32444 | −0.662221 | − | 0.749308i | \(-0.730386\pi\) | ||||
−0.662221 | + | 0.749308i | \(0.730386\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.29778 | + | 16.1042i | 0.691099 | + | 1.19702i | 0.971478 | + | 0.237129i | \(0.0762064\pi\) |
−0.280379 | + | 0.959889i | \(0.590460\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.2003 | −1.04971 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.23055 | + | 10.7916i | −0.458079 | + | 0.793416i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.61591 | + | 13.1911i | −0.556930 | + | 0.964632i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.2872 | −1.62116 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8564 | 1.00261 | 0.501307 | − | 0.865269i | \(-0.332853\pi\) | ||||
0.501307 | + | 0.865269i | \(0.332853\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.01232 | − | 3.48544i | 0.144850 | − | 0.250888i | −0.784467 | − | 0.620171i | \(-0.787063\pi\) |
0.929317 | + | 0.369283i | \(0.120397\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.47432 | − | 7.74974i | 0.320412 | − | 0.554971i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.96797 | −0.211459 | −0.105730 | − | 0.994395i | \(-0.533718\pi\) | ||||
−0.105730 | + | 0.994395i | \(0.533718\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.51267 | − | 13.0123i | −0.532559 | − | 0.922419i | −0.999277 | − | 0.0380130i | \(-0.987897\pi\) |
0.466718 | − | 0.884406i | \(-0.345436\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.85815 | −0.413202 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.00411 | − | 15.5956i | −0.631964 | − | 1.09459i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.3298 | − | 19.6238i | −0.791308 | − | 1.37059i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.94878 | − | 20.3393i | −0.203971 | − | 1.40690i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.54691 | + | 2.67933i | −0.106494 | + | 0.184453i | −0.914348 | − | 0.404930i | \(-0.867296\pi\) |
0.807854 | + | 0.589383i | \(0.200629\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.01232 | − | 12.1457i | −0.480476 | − | 0.832209i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.26184 | + | 10.8458i | 0.427054 | + | 0.739679i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.53890 | 0.240236 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.13808 | − | 14.0956i | −0.549921 | − | 0.952490i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.97536 | 0.267411 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.21028 | + | 5.56036i | −0.214976 | + | 0.372349i | −0.953265 | − | 0.302135i | \(-0.902301\pi\) |
0.738289 | + | 0.674484i | \(0.235634\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.8716 | −1.45167 | −0.725836 | − | 0.687868i | \(-0.758547\pi\) | ||||
−0.725836 | + | 0.687868i | \(0.758547\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.9222 | −1.11825 | −0.559125 | − | 0.829083i | \(-0.688863\pi\) | ||||
−0.559125 | + | 0.829083i | \(0.688863\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.5138 | + | 30.3348i | −1.15232 | + | 1.99588i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.07093 | − | 3.58695i | 0.135671 | − | 0.234989i | −0.790183 | − | 0.612871i | \(-0.790014\pi\) |
0.925854 | + | 0.377883i | \(0.123348\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.48453 | −0.357771 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.01232 | + | 6.94955i | 0.260628 | + | 0.451421i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.26275 | −0.275735 | −0.137867 | − | 0.990451i | \(-0.544025\pi\) | ||||
−0.137867 | + | 0.990451i | \(0.544025\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.12760 | + | 10.6133i | 0.394713 | + | 0.683663i | 0.993065 | − | 0.117571i | \(-0.0375106\pi\) |
−0.598351 | + | 0.801234i | \(0.704177\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.9254 | − | 41.4400i | 1.52854 | − | 2.64750i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.21236 | + | 3.32067i | −0.268026 | + | 0.211289i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.34583 | − | 10.9913i | 0.402150 | − | 0.696545i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.51618 | − | 4.35815i | −0.158820 | − | 0.275084i | 0.775624 | − | 0.631196i | \(-0.217436\pi\) |
−0.934443 | + | 0.356112i | \(0.884102\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.97712 | + | 15.5488i | 0.564386 | + | 0.977546i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −23.4927 | −1.47117 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.30148 | + | 5.71833i | 0.205940 | + | 0.356699i | 0.950432 | − | 0.310933i | \(-0.100641\pi\) |
−0.744492 | + | 0.667632i | \(0.767308\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.7302 | −0.791014 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.58135 | − | 13.1313i | 0.467486 | − | 0.809710i | −0.531824 | − | 0.846855i | \(-0.678493\pi\) |
0.999310 | + | 0.0371452i | \(0.0118264\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.6276 | −0.714278 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.4519 | 1.19044 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.01232 | − | 10.4136i | 0.366578 | − | 0.634931i | −0.622450 | − | 0.782659i | \(-0.713863\pi\) |
0.989028 | + | 0.147728i | \(0.0471960\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.5642 | + | 18.2978i | −0.641731 | + | 1.11151i | 0.343315 | + | 0.939220i | \(0.388450\pi\) |
−0.985046 | + | 0.172291i | \(0.944883\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.14185 | 0.553290 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −29.7691 | − | 51.5616i | −1.79514 | − | 3.10928i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.5709 | −0.995650 | −0.497825 | − | 0.867277i | \(-0.665868\pi\) | ||||
−0.497825 | + | 0.867277i | \(0.665868\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.69852 | + | 9.87013i | 0.339945 | + | 0.588803i | 0.984422 | − | 0.175821i | \(-0.0562581\pi\) |
−0.644477 | + | 0.764624i | \(0.722925\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.866025 | + | 1.50000i | −0.0514799 | + | 0.0891657i | −0.890617 | − | 0.454754i | \(-0.849727\pi\) |
0.839137 | + | 0.543920i | \(0.183060\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.8934 | − | 19.6238i | 1.47456 | − | 1.16241i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.5744 | − | 20.0475i | 0.683218 | − | 1.18337i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.28177 | + | 5.68419i | 0.193045 | + | 0.334364i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.2695 | − | 17.7872i | −0.602006 | − | 1.04271i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.44282 | 0.259552 | 0.129776 | − | 0.991543i | \(-0.458574\pi\) | ||||
0.129776 | + | 0.991543i | \(0.458574\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.7038 | + | 53.1806i | 1.78765 | + | 3.09629i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.4995 | −1.42160 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.34294 | − | 4.05809i | 0.135496 | − | 0.234685i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.39705 | + | 11.0800i | −0.368720 | + | 0.638641i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00930 | −0.172880 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34.4217 | 1.97098 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.4656 | + | 26.7872i | −0.882669 | + | 1.52883i | −0.0343067 | + | 0.999411i | \(0.510922\pi\) |
−0.848362 | + | 0.529416i | \(0.822411\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.16650 | + | 14.1448i | −0.464576 | + | 0.804669i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.9133 | −1.69623 | −0.848114 | − | 0.529814i | \(-0.822262\pi\) | ||||
−0.848114 | + | 0.529814i | \(0.822262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.15962 | + | 5.47263i | 0.178593 | + | 0.309331i | 0.941399 | − | 0.337296i | \(-0.109512\pi\) |
−0.762806 | + | 0.646627i | \(0.776179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.38472 | + | 12.7907i | 0.414767 | + | 0.718398i | 0.995404 | − | 0.0957646i | \(-0.0305296\pi\) |
−0.580637 | + | 0.814163i | \(0.697196\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.89787 | − | 17.1436i | −0.554174 | − | 0.959858i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.4291 | + | 23.2598i | −0.749538 | + | 1.29824i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.0791 | + | 5.21823i | 0.727740 | + | 0.290350i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.76945 | + | 13.4571i | −0.430972 | + | 0.746465i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.3419 | + | 30.0370i | 0.959006 | + | 1.66105i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.80148 | − | 4.85230i | −0.154450 | − | 0.267516i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.563122 | −0.0309520 | −0.0154760 | − | 0.999880i | \(-0.504926\pi\) | ||||
−0.0154760 | + | 0.999880i | \(0.504926\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.2003 | 0.775843 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.30148 | + | 2.25422i | −0.0708960 | + | 0.122795i | −0.899294 | − | 0.437344i | \(-0.855919\pi\) |
0.828398 | + | 0.560140i | \(0.189252\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.93171 | + | 3.34583i | −0.104916 | + | 0.181720i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.89018 | 0.210665 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.8597 | 1.01833 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.8458 | + | 23.9817i | −0.745434 | + | 1.29113i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.6022 | + | 20.0956i | −0.622838 | + | 1.07879i | 0.366117 | + | 0.930569i | \(0.380687\pi\) |
−0.988955 | + | 0.148218i | \(0.952646\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0000 | 0.856460 | 0.428230 | − | 0.903670i | \(-0.359137\pi\) | ||||
0.428230 | + | 0.903670i | \(0.359137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.19706 | + | 5.53748i | 0.170647 | + | 0.295569i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.29461 | 0.228579 | 0.114289 | − | 0.993447i | \(-0.463541\pi\) | ||||
0.114289 | + | 0.993447i | \(0.463541\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.9980 | + | 29.4414i | 0.902160 | + | 1.56259i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.0000 | − | 20.7846i | −0.635107 | − | 1.10004i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.571252 | + | 0.989437i | −0.0301495 | + | 0.0522205i | −0.880706 | − | 0.473662i | \(-0.842932\pi\) |
0.850557 | + | 0.525883i | \(0.176265\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2177 | + | 5.39582i | −0.958827 | + | 0.283990i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.72594 | + | 16.8458i | −0.510480 | + | 0.884177i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.7269 | + | 34.1679i | 1.03255 | + | 1.78843i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.06178 | + | 7.03521i | 0.212023 | + | 0.367235i | 0.952348 | − | 0.305015i | \(-0.0986615\pi\) |
−0.740324 | + | 0.672250i | \(0.765328\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.93933 | − | 10.2872i | −0.308355 | − | 0.534086i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.4611 | 0.955880 | 0.477940 | − | 0.878393i | \(-0.341384\pi\) | ||||
0.477940 | + | 0.878393i | \(0.341384\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 27.7342 | − | 48.0370i | 1.43219 | − | 2.48062i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.58325 | + | 4.47432i | −0.133044 | + | 0.230439i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.6584 | −1.00978 | −0.504891 | − | 0.863183i | \(-0.668467\pi\) | ||||
−0.504891 | + | 0.863183i | \(0.668467\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.30835 | −0.425650 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.0455 | + | 19.1313i | −0.564396 | + | 0.977563i | 0.432709 | + | 0.901534i | \(0.357558\pi\) |
−0.997106 | + | 0.0760296i | \(0.975776\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 42.4537 | − | 73.5320i | 2.16364 | − | 3.74754i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.55122 | − | 16.5432i | −0.484266 | − | 0.838773i | 0.515571 | − | 0.856847i | \(-0.327580\pi\) |
−0.999837 | + | 0.0180736i | \(0.994247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.3018 | −0.622128 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.07093 | − | 10.5152i | −0.306238 | − | 0.530419i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.72594 | − | 16.8458i | −0.489365 | − | 0.847605i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.49631 | + | 9.51988i | −0.275852 | + | 0.477789i | −0.970350 | − | 0.241705i | \(-0.922293\pi\) |
0.694498 | + | 0.719495i | \(0.255627\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 30.0771 | + | 12.0000i | 1.50574 | + | 0.600751i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.8330 | + | 32.6197i | −0.940475 | + | 1.62895i | −0.175907 | + | 0.984407i | \(0.556286\pi\) |
−0.764568 | + | 0.644543i | \(0.777048\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.507649 | − | 0.879274i | −0.0252878 | − | 0.0437998i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.8934 | − | 32.7242i | −0.938818 | − | 1.62608i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.9938 | −0.693646 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.50000 | + | 7.79423i | 0.222511 | + | 0.385400i | 0.955570 | − | 0.294765i | \(-0.0952414\pi\) |
−0.733059 | + | 0.680165i | \(0.761908\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 30.8203 | 1.52025 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −31.3668 | + | 54.3289i | −1.54346 | + | 2.67335i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.3824 | + | 26.6431i | −0.755092 | + | 1.30786i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.7163 | −1.30830 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.63121 | 0.421662 | 0.210831 | − | 0.977523i | \(-0.432383\pi\) | ||||
0.210831 | + | 0.977523i | \(0.432383\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.2658 | − | 24.7090i | 0.695270 | − | 1.20424i | −0.274819 | − | 0.961496i | \(-0.588618\pi\) |
0.970089 | − | 0.242748i | \(-0.0780487\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 40.7941 | 1.97880 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.5825 | + | 30.4537i | 0.850875 | + | 1.47376i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.0493 | 0.485184 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.03144 | − | 12.1788i | −0.338693 | − | 0.586633i | 0.645494 | − | 0.763765i | \(-0.276651\pi\) |
−0.984187 | + | 0.177132i | \(0.943318\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.27490 | − | 14.3325i | −0.397666 | − | 0.688778i | 0.595771 | − | 0.803154i | \(-0.296846\pi\) |
−0.993438 | + | 0.114376i | \(0.963513\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.2659 | − | 26.4414i | 0.731946 | − | 1.26777i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.0352 | − | 10.2759i | 0.623558 | − | 0.491561i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.8262 | − | 18.7515i | 0.516706 | − | 0.894960i | −0.483106 | − | 0.875562i | \(-0.660492\pi\) |
0.999812 | − | 0.0193986i | \(-0.00617516\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.9460 | − | 20.6911i | −0.567573 | − | 0.983066i | −0.996805 | − | 0.0798714i | \(-0.974549\pi\) |
0.429232 | − | 0.903194i | \(-0.358784\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −47.1517 | −2.23521 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.90398 | + | 3.29778i | 0.0900550 | + | 0.155980i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.9606 | 0.611648 | 0.305824 | − | 0.952088i | \(-0.401068\pi\) | ||||
0.305824 | + | 0.952088i | \(0.401068\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.7233 | − | 22.0375i | 0.599119 | − | 1.03770i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.8810 | + | 20.5786i | −0.558220 | + | 0.966865i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22.1600 | −1.03888 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.70539 | 0.266887 | 0.133444 | − | 0.991056i | \(-0.457397\pi\) | ||||
0.133444 | + | 0.991056i | \(0.457397\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.39322 | − | 14.5375i | 0.391762 | − | 0.678551i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.61528 | + | 4.52979i | −0.121806 | + | 0.210973i | −0.920480 | − | 0.390790i | \(-0.872202\pi\) |
0.798674 | + | 0.601764i | \(0.205535\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.46741 | 0.393514 | 0.196757 | − | 0.980452i | \(-0.436959\pi\) | ||||
0.196757 | + | 0.980452i | \(0.436959\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.00000 | + | 5.19615i | 0.139122 | + | 0.240966i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.5985 | 1.36965 | 0.684827 | − | 0.728705i | \(-0.259878\pi\) | ||||
0.684827 | + | 0.728705i | \(0.259878\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.25344 | + | 12.5633i | 0.334933 | + | 0.580120i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.28227 | + | 14.3453i | 0.381627 | + | 0.660997i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.03203 | + | 12.1798i | −0.323333 | + | 0.560029i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −43.2262 | + | 34.0759i | −1.98335 | + | 1.56351i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.3761 | − | 19.7040i | −0.519787 | − | 0.900298i | −0.999735 | − | 0.0230008i | \(-0.992678\pi\) |
0.479948 | − | 0.877297i | \(-0.340655\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.82612 | + | 3.16293i | 0.0832639 | + | 0.144217i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −28.2896 | −1.28722 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.8934 | + | 43.1166i | 1.13035 | + | 1.95782i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.14068 | 0.232946 | 0.116473 | − | 0.993194i | \(-0.462841\pi\) | ||||
0.116473 | + | 0.993194i | \(0.462841\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.487678 | + | 0.844683i | −0.0220536 | + | 0.0381979i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.95554 | − | 8.58325i | 0.223640 | − | 0.387357i | −0.732270 | − | 0.681014i | \(-0.761539\pi\) |
0.955911 | + | 0.293658i | \(0.0948725\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.5635 | 0.610871 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.3650 | + | 30.0771i | −0.778928 | + | 1.34914i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.69110 | − | 2.92907i | 0.0757041 | − | 0.131123i | −0.825688 | − | 0.564127i | \(-0.809213\pi\) |
0.901392 | + | 0.433003i | \(0.142546\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.6413 | 0.564773 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.03535 | − | 6.98944i | −0.179928 | − | 0.311644i | 0.761928 | − | 0.647662i | \(-0.224253\pi\) |
−0.941856 | + | 0.336018i | \(0.890920\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.29461 | 0.324606 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.94695 | + | 17.2286i | 0.441759 | + | 0.765150i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.7818 | − | 29.0669i | −0.743839 | − | 1.28837i | −0.950735 | − | 0.310004i | \(-0.899670\pi\) |
0.206896 | − | 0.978363i | \(-0.433664\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.1528 | + | 34.9057i | −0.891507 | + | 1.54414i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.24974 | + | 22.4152i | 0.143480 | + | 0.989653i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.7957 | − | 34.2872i | 0.872304 | − | 1.51088i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.07956 | − | 5.33395i | −0.135439 | − | 0.234587i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.9425 | − | 29.3453i | −0.743694 | − | 1.28812i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.1665 | 0.971132 | 0.485566 | − | 0.874200i | \(-0.338614\pi\) | ||||
0.485566 | + | 0.874200i | \(0.338614\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.3683 | + | 30.0827i | 0.759462 | + | 1.31543i | 0.943125 | + | 0.332437i | \(0.107871\pi\) |
−0.183664 | + | 0.982989i | \(0.558796\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 93.8114 | 4.09426 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.33273 | + | 2.30835i | −0.0580544 | + | 0.100553i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.24974 | − | 7.36077i | 0.184771 | − | 0.320034i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.64134 | −0.287668 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.5523 | − | 56.3823i | 1.40736 | − | 2.43762i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.3458 | − | 26.5798i | 0.662221 | − | 1.14700i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 53.7363 | 2.31458 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.2429 | − | 29.8655i | −0.741329 | − | 1.28402i | −0.951890 | − | 0.306439i | \(-0.900863\pi\) |
0.210561 | − | 0.977581i | \(-0.432471\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.2085 | −1.38220 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −42.0370 | − | 72.8102i | −1.80067 | − | 3.11884i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.75237 | − | 16.8916i | −0.416981 | − | 0.722232i | 0.578653 | − | 0.815574i | \(-0.303579\pi\) |
−0.995634 | + | 0.0933413i | \(0.970245\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.3722 | + | 11.3298i | −0.612276 | + | 0.482666i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.93594 | − | 17.2096i | 0.422519 | − | 0.731825i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.7916 | − | 18.6917i | −0.458079 | − | 0.793416i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.4734 | − | 25.0687i | −0.613259 | − | 1.06220i | −0.990687 | − | 0.136156i | \(-0.956525\pi\) |
0.377429 | − | 0.926039i | \(-0.376808\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.67058 | 0.155249 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.1911 | − | 22.8477i | −0.556930 | − | 0.964632i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.5713 | −0.782688 | −0.391344 | − | 0.920244i | \(-0.627990\pi\) | ||||
−0.391344 | + | 0.920244i | \(0.627990\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.68251 | − | 8.11034i | 0.196995 | − | 0.341205i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.3013 | − | 33.4308i | 0.810578 | − | 1.40396i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.9222 | 0.541727 | 0.270863 | − | 0.962618i | \(-0.412691\pi\) | ||||
0.270863 | + | 0.962618i | \(0.412691\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.5969 | 0.903802 | 0.451901 | − | 0.892068i | \(-0.350746\pi\) | ||||
0.451901 | + | 0.892068i | \(0.350746\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.0000 | + | 20.7846i | −0.501307 | + | 0.868290i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0427 | − | 41.6431i | 1.00265 | − | 1.73664i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.43646 | 0.226323 | 0.113161 | − | 0.993577i | \(-0.463902\pi\) | ||||
0.113161 | + | 0.993577i | \(0.463902\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.48544 | + | 6.03697i | 0.144850 | + | 0.250888i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.4291 | −1.30390 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.52888 | − | 11.3083i | −0.270398 | − | 0.468344i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.7028 | + | 25.4660i | −0.606851 | + | 1.05110i | 0.384906 | + | 0.922956i | \(0.374234\pi\) |
−0.991756 | + | 0.128140i | \(0.959099\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.516014 | − | 3.55921i | −0.0212620 | − | 0.146655i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.57034 | − | 4.45196i | 0.105730 | − | 0.183129i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.3902 | + | 23.1925i | 0.549869 | + | 0.952400i | 0.998283 | + | 0.0585746i | \(0.0186555\pi\) |
−0.448414 | + | 0.893826i | \(0.648011\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 29.0882 | + | 50.3823i | 1.19250 | + | 2.06547i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.0246 | 1.06512 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.5419 | − | 33.8476i | −0.798461 | − | 1.38297i | −0.920618 | − | 0.390464i | \(-0.872315\pi\) |
0.122157 | − | 0.992511i | \(-0.461019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.7409 | −1.49869 | −0.749347 | − | 0.662177i | \(-0.769633\pi\) | ||||
−0.749347 | + | 0.662177i | \(0.769633\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.5759 | − | 40.8346i | 0.958495 | − | 1.66016i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.7272 | 1.28777 | 0.643885 | − | 0.765123i | \(-0.277322\pi\) | ||||
0.643885 | + | 0.765123i | \(0.277322\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 31.1911 | 1.26393 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.803734 | + | 1.39211i | −0.0325156 | + | 0.0563187i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.551220 | + | 0.954742i | −0.0222636 | + | 0.0385617i | −0.876943 | − | 0.480595i | \(-0.840421\pi\) |
0.854679 | + | 0.519157i | \(0.173754\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 39.2476 | 1.58262 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.09557 | + | 15.7540i | 0.366174 | + | 0.634232i | 0.988964 | − | 0.148157i | \(-0.0473342\pi\) |
−0.622790 | + | 0.782389i | \(0.714001\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.6666 | −1.51395 | −0.756974 | − | 0.653445i | \(-0.773323\pi\) | ||||
−0.756974 | + | 0.653445i | \(0.773323\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.89335 | − | 17.1358i | −0.397007 | − | 0.687636i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.0849 | − | 41.7163i | −0.964942 | − | 1.67133i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −35.6591 | + | 61.7634i | −1.42636 | + | 2.47054i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 33.0626 | + | 13.1911i | 1.32039 | + | 0.526803i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.79409 | − | 8.30361i | 0.191153 | − | 0.331087i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.8534 | + | 25.7269i | 0.591305 | + | 1.02417i | 0.994057 | + | 0.108861i | \(0.0347203\pi\) |
−0.402752 | + | 0.915309i | \(0.631946\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.67933 | − | 4.64074i | −0.106494 | − | 0.184453i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.1396 | 0.799215 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.01232 | − | 12.1457i | −0.277838 | − | 0.481230i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.86502 | − | 10.1585i | 0.231654 | − | 0.401237i | −0.726641 | − | 0.687018i | \(-0.758920\pi\) |
0.958295 | + | 0.285781i | \(0.0922528\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.84371 | − | 17.0498i | 0.388198 | − | 0.672378i | −0.604009 | − | 0.796977i | \(-0.706431\pi\) |
0.992207 | + | 0.124599i | \(0.0397644\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21.6917 | −0.854108 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.8869 | −1.17497 | −0.587487 | − | 0.809234i | \(-0.699883\pi\) | ||||
−0.587487 | + | 0.809234i | \(0.699883\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34.4803 | + | 59.7216i | −1.35347 | + | 2.34428i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.06478 | + | 5.30835i | −0.120118 | + | 0.208051i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.5882 | −1.62747 | −0.813736 | − | 0.581235i | \(-0.802570\pi\) | ||||
−0.813736 | + | 0.581235i | \(0.802570\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.7160 | + | 25.4889i | 0.575003 | + | 0.995935i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.502566 | − | 0.870470i | −0.0195772 | − | 0.0339087i | 0.856071 | − | 0.516859i | \(-0.172899\pi\) |
−0.875648 | + | 0.482950i | \(0.839565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.69483 | + | 4.66758i | 0.104817 | + | 0.181548i | 0.913663 | − | 0.406472i | \(-0.133241\pi\) |
−0.808847 | + | 0.588020i | \(0.799908\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.44276 | + | 5.96303i | −0.133706 | + | 0.231585i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −72.9074 | − | 29.0882i | −2.82723 | − | 1.12799i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.99389 | − | 13.8458i | 0.309525 | − | 0.536113i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.56036 | − | 9.63083i | −0.214976 | − | 0.372349i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.3277 | + | 33.4766i | 0.746139 | + | 1.29235i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.7300 | −0.567801 | −0.283901 | − | 0.958854i | \(-0.591629\pi\) | ||||
−0.283901 | + | 0.958854i | \(0.591629\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 32.8075 | + | 56.8242i | 1.26276 | + | 2.18716i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.0493 | −0.539958 | −0.269979 | − | 0.962866i | \(-0.587017\pi\) | ||||
−0.269979 | + | 0.962866i | \(0.587017\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.4309 | + | 44.0475i | −0.975947 | + | 1.69039i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.9414 | − | 32.8075i | 0.725836 | − | 1.25718i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.2792 | 1.54124 | 0.770620 | − | 0.637295i | \(-0.219947\pi\) | ||||
0.770620 | + | 0.637295i | \(0.219947\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −74.7089 | −2.85448 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.6551 | − | 25.3833i | 0.559125 | − | 0.968433i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.70397 | + | 2.95137i | −0.0649162 | + | 0.112438i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.0882 | 1.10657 | 0.553284 | − | 0.832993i | \(-0.313374\pi\) | ||||
0.553284 | + | 0.832993i | \(0.313374\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 64.7608 | 2.45652 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.71772 | + | 15.0995i | 0.330207 | + | 0.571935i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.58695 | + | 6.21278i | 0.135671 | + | 0.234989i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.52834 | + | 6.11126i | −0.133263 | + | 0.230819i | −0.924933 | − | 0.380131i | \(-0.875879\pi\) |
0.791669 | + | 0.610950i | \(0.209212\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.85621 | + | 12.8032i | 0.0700083 | + | 0.482883i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.74974 | − | 8.22680i | 0.178886 | − | 0.309839i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.72606 | + | 6.45372i | 0.140133 | + | 0.242717i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.6948 | + | 27.1842i | 0.589432 | + | 1.02093i | 0.994307 | + | 0.106554i | \(0.0339816\pi\) |
−0.404875 | + | 0.914372i | \(0.632685\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.57093 | + | 2.72092i | 0.0588316 | + | 0.101899i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.3597 | −0.911000 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.69165 | − | 6.39413i | 0.137867 | − | 0.238793i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.08612 | − | 5.34531i | 0.115093 | − | 0.199347i | −0.802724 | − | 0.596351i | \(-0.796617\pi\) |
0.917817 | + | 0.397004i | \(0.129950\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.4463 | 1.50630 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.2266 | −0.789426 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26.5086 | + | 45.9143i | −0.984506 | + | 1.70521i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.78062 | + | 10.0123i | −0.214391 | + | 0.371336i | −0.953084 | − | 0.302706i | \(-0.902110\pi\) |
0.738693 | + | 0.674042i | \(0.235443\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.81817 | − | 8.34531i | −0.178206 | − | 0.308663i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.4784 | 1.08881 | 0.544404 | − | 0.838823i | \(-0.316756\pi\) | ||||
0.544404 | + | 0.838823i | \(0.316756\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 41.4400 | + | 71.7761i | 1.52854 | + | 2.64750i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.97342 | + | 13.8104i | 0.293705 | + | 0.508712i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.2523 | + | 22.9537i | −0.487495 | + | 0.844366i | −0.999897 | − | 0.0143798i | \(-0.995423\pi\) |
0.512402 | + | 0.858746i | \(0.328756\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.33299 | − | 9.19433i | −0.0489687 | − | 0.337762i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.2792 | + | 26.4643i | −0.560538 | + | 0.970880i | 0.436911 | + | 0.899504i | \(0.356072\pi\) |
−0.997449 | + | 0.0713758i | \(0.977261\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.61528 | − | 7.99389i | −0.169091 | − | 0.292874i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 66.5104 | 2.43024 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.2377 | − | 33.3207i | −0.701994 | − | 1.21589i | −0.967766 | − | 0.251853i | \(-0.918960\pi\) |
0.265772 | − | 0.964036i | \(-0.414373\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.71630 | 0.317639 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.7998 | − | 49.8828i | 1.04813 | − | 1.81542i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.6399 | + | 35.7494i | −0.750171 | + | 1.29933i | 0.197569 | + | 0.980289i | \(0.436695\pi\) |
−0.947740 | + | 0.319045i | \(0.896638\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31.0976 | −1.12877 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.8325 | −1.77018 | −0.885088 | − | 0.465424i | \(-0.845902\pi\) | ||||
−0.885088 | + | 0.465424i | \(0.845902\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.9446 | − | 74.3823i | 1.55470 | − | 2.69282i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.9980 | 0.649872 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.0049 | − | 46.7739i | −0.973823 | − | 1.68671i | −0.683766 | − | 0.729702i | \(-0.739659\pi\) |
−0.290057 | − | 0.957009i | \(-0.593674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.4367 | −0.411881 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.13129 | + | 8.88765i | 0.184560 | + | 0.319667i | 0.943428 | − | 0.331577i | \(-0.107581\pi\) |
−0.758868 | + | 0.651244i | \(0.774247\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.20936 | − | 9.02288i | −0.187126 | − | 0.324112i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.0246 | − | 19.0952i | 0.395507 | − | 0.685038i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.8503 | − | 8.71772i | −0.782868 | − | 0.312345i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.0887 | + | 33.0626i | −0.683047 | + | 1.18307i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.9081 | + | 18.8934i | 0.389823 | + | 0.675193i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.0764 | − | 34.7733i | −0.716557 | − | 1.24111i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.0061 | 1.46171 | 0.730855 | − | 0.682533i | \(-0.239122\pi\) | ||||
0.730855 | + | 0.682533i | \(0.239122\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.1313 | + | 22.7441i | 0.467486 | + | 0.809710i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.56723 | 0.340171 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.04435 | − | 8.73707i | 0.179130 | − | 0.310262i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.0698 | − | 17.4414i | 0.357139 | − | 0.618583i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.7483 | 0.947474 | 0.473737 | − | 0.880666i | \(-0.342905\pi\) | ||||
0.473737 | + | 0.880666i | \(0.342905\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.22007 | 0.149295 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.1532 | + | 38.3705i | −0.781769 | + | 1.35406i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 68.5744 | 2.41693 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.4136 | + | 18.0370i | 0.366578 | + | 0.634931i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.61385 | −0.267689 | −0.133844 | − | 0.991002i | \(-0.542732\pi\) | ||||
−0.133844 | + | 0.991002i | \(0.542732\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.1498 | − | 36.6325i | −0.742670 | − | 1.28634i | −0.951275 | − | 0.308342i | \(-0.900226\pi\) |
0.208605 | − | 0.978000i | \(-0.433108\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.2978 | − | 31.6927i | −0.641731 | − | 1.11151i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.18214 | − | 2.04753i | 0.0414086 | − | 0.0717218i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0764 | + | 4.81817i | 0.422499 | + | 0.168566i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.2429 | + | 17.7412i | 0.357479 | + | 0.619171i | 0.987539 | − | 0.157375i | \(-0.0503031\pi\) |
−0.630060 | + | 0.776546i | \(0.716970\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.2395 | − | 26.3956i | −0.531216 | − | 0.920094i | −0.999336 | − | 0.0364287i | \(-0.988402\pi\) |
0.468120 | − | 0.883665i | \(-0.344932\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 103.123 | 3.59029 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.84970 | + | 13.5961i | 0.272961 | + | 0.472782i | 0.969619 | − | 0.244622i | \(-0.0786637\pi\) |
−0.696658 | + | 0.717404i | \(0.745330\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.1271 | 1.63679 | 0.818396 | − | 0.574655i | \(-0.194864\pi\) | ||||
0.818396 | + | 0.574655i | \(0.194864\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.3508 | − | 24.8564i | 0.497825 | − | 0.862259i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.4094 | + | 31.8860i | −0.637847 | + | 1.10478i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.6428 | −1.06044 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.28722 | −0.148188 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.57536 | + | 16.5850i | −0.330578 | + | 0.572578i | −0.982625 | − | 0.185600i | \(-0.940577\pi\) |
0.652047 | + | 0.758178i | \(0.273910\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.68620 | − | 9.84879i | 0.196076 | − | 0.339613i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.7403 | −0.679891 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.1116 | − | 41.7625i | −0.829464 | − | 1.43667i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.1698 | 1.65513 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.50000 | − | 2.59808i | −0.0514799 | − | 0.0891657i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.65095 | − | 9.78773i | −0.193712 | − | 0.335519i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.0123 | − | 46.7867i | 0.924884 | − | 1.60195i | 0.133137 | − | 0.991098i | \(-0.457495\pi\) |
0.791747 | − | 0.610849i | \(-0.209172\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.0635 | − | 19.1626i | 0.377923 | − | 0.654583i | −0.612837 | − | 0.790210i | \(-0.709972\pi\) |
0.990760 | + | 0.135627i | \(0.0433049\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.04506 | + | 15.6665i | 0.308613 | + | 0.534534i | 0.978059 | − | 0.208327i | \(-0.0668018\pi\) |
−0.669446 | + | 0.742861i | \(0.733468\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.0475 | + | 34.7233i | 0.683218 | + | 1.18337i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.2070 | 0.789975 | 0.394988 | − | 0.918686i | \(-0.370749\pi\) | ||||
0.394988 | + | 0.918686i | \(0.370749\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41.0690 | + | 71.1336i | 1.39639 | + | 2.41861i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.3684 | −0.386091 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.9222 | − | 18.9178i | 0.370510 | − | 0.641743i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.08099 | − | 3.60437i | 0.0705115 | − | 0.122130i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −137.359 | −4.64359 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.06723 | + | 12.2408i | −0.238644 | + | 0.413343i | −0.960325 | − | 0.278882i | \(-0.910036\pi\) |
0.721682 | + | 0.692225i | \(0.243369\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.84759 | + | 6.66422i | −0.129776 | + | 0.224779i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.4217 | 1.66506 | 0.832530 | − | 0.553981i | \(-0.186892\pi\) | ||||
0.832530 | + | 0.553981i | \(0.186892\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.3596 | + | 49.1202i | 0.954375 | + | 1.65303i | 0.735791 | + | 0.677209i | \(0.236811\pi\) |
0.218585 | + | 0.975818i | \(0.429856\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −106.361 | −3.57529 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.2325 | − | 43.7040i | −0.847224 | − | 1.46744i | −0.883675 | − | 0.468100i | \(-0.844939\pi\) |
0.0364508 | − | 0.999335i | \(-0.488395\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.2872 | + | 17.8180i | 0.345022 | + | 0.597596i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.2172 | − | 36.7492i | 0.710802 | − | 1.23115i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.47166 | + | 3.52508i | −0.149639 | + | 0.117962i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37.1986 | + | 64.4298i | −1.24341 | + | 2.15365i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.05809 | + | 7.02882i | 0.135496 | + | 0.234685i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.73205 | − | 3.00000i | −0.0577671 | − | 0.100056i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.94685 | 0.298063 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.0800 | − | 19.1911i | −0.368720 | − | 0.638641i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 78.0739 | 2.59527 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.12878 | − | 8.88330i | 0.170298 | − | 0.294965i | −0.768226 | − | 0.640179i | \(-0.778860\pi\) |
0.938524 | + | 0.345214i | \(0.112194\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.9971 | −0.629402 | −0.314701 | − | 0.949191i | \(-0.601904\pi\) | ||||
−0.314701 | + | 0.949191i | \(0.601904\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.5488 | −1.14340 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −29.8101 | + | 51.6325i | −0.985490 | + | 1.70692i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.0338 | + | 26.0393i | −0.496459 | + | 0.859893i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.5866 | 0.877010 | 0.438505 | − | 0.898729i | \(-0.355508\pi\) | ||||
0.438505 | + | 0.898729i | \(0.355508\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.7872 | − | 46.3968i | −0.882669 | − | 1.52883i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.96393 | 0.327967 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.7392 | + | 32.4572i | 0.616140 | + | 1.06719i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.7306 | − | 18.5859i | 0.352058 | − | 0.609782i | −0.634552 | − | 0.772880i | \(-0.718815\pi\) |
0.986610 | + | 0.163098i | \(0.0521487\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.12787 | − | 49.1646i | −0.233606 | − | 1.61130i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.9057 | − | 44.8699i | 0.848114 | − | 1.46898i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.9756 | + | 55.3833i | 1.04571 | + | 1.81123i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.6207 | + | 18.3956i | 0.346964 | + | 0.600959i | 0.985709 | − | 0.168460i | \(-0.0538793\pi\) |
−0.638745 | + | 0.769419i | \(0.720546\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.9453 | −0.357185 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.5759 | − | 35.6384i | −0.670754 | − | 1.16178i | −0.977691 | − | 0.210050i | \(-0.932637\pi\) |
0.306937 | − | 0.951730i | \(-0.400696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.5517 | 0.669256 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −46.7867 | + | 81.0370i | −1.52197 | + | 2.63613i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.2872 | + | 36.8705i | −0.691740 | + | 1.19813i | 0.279527 | + | 0.960138i | \(0.409822\pi\) |
−0.971267 | + | 0.237991i | \(0.923511\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.5635 | 0.375368 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.5814 | −0.829535 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.3261 | + | 43.8661i | −0.820394 | + | 1.42096i | 0.0849960 | + | 0.996381i | \(0.472912\pi\) |
−0.905390 | + | 0.424582i | \(0.860421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.0882 | − | 50.3823i | 0.941273 | − | 1.63033i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 34.2872 | 1.10835 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −38.1610 | − | 66.0968i | −1.23228 | − | 2.13438i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3192 | −0.978040 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.44878 | − | 14.6337i | −0.271976 | − | 0.471076i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.02814 | − | 3.51283i | 0.0652205 | − | 0.112965i | −0.831571 | − | 0.555418i | \(-0.812558\pi\) |
0.896792 | + | 0.442453i | \(0.145892\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19.1542 | + | 15.0995i | −0.615321 | + | 0.485067i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.9085 | − | 22.3581i | 0.414253 | − | 0.717507i | −0.581097 | − | 0.813834i | \(-0.697376\pi\) |
0.995350 | + | 0.0963273i | \(0.0307096\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.0796 | + | 57.2955i | 1.06048 | + | 1.83681i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.4571 | − | 23.3083i | −0.430972 | − | 0.746465i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.8828 | −0.700093 | −0.350046 | − | 0.936732i | \(-0.613834\pi\) | ||||
−0.350046 | + | 0.936732i | \(0.613834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.4756 | − | 45.8571i | −0.846165 | − | 1.46560i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.4765 | − | 42.3946i | 0.780680 | − | 1.35218i | −0.150866 | − | 0.988554i | \(-0.548206\pi\) |
0.931546 | − | 0.363624i | \(-0.118461\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.23055 | + | 10.7916i | −0.198522 | + | 0.343850i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.70460 | 0.308901 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.3587 | −0.361184 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.185139 | + | 0.320670i | −0.00588112 | + | 0.0101864i | −0.868951 | − | 0.494898i | \(-0.835205\pi\) |
0.863070 | + | 0.505085i | \(0.168539\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.487678 | − | 0.844683i | 0.0154760 | − | 0.0268052i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −63.0842 | −1.99990 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.66280 | − | 13.2724i | −0.242683 | − | 0.420340i | 0.718794 | − | 0.695223i | \(-0.244694\pi\) |
−0.961478 | + | 0.274883i | \(0.911361\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.4220 | 0.487932 |
(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 | 1216.2.i.r.961.3 | 12 | ||
4.3 | odd | 2 | inner | 1216.2.i.r.961.6 | 12 | ||
8.3 | odd | 2 | 608.2.i.f.353.1 | ✓ | 12 | ||
8.5 | even | 2 | 608.2.i.f.353.4 | yes | 12 | ||
19.7 | even | 3 | inner | 1216.2.i.r.577.3 | 12 | ||
76.7 | odd | 6 | inner | 1216.2.i.r.577.6 | 12 | ||
152.45 | even | 6 | 608.2.i.f.577.4 | yes | 12 | ||
152.83 | odd | 6 | 608.2.i.f.577.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.i.f.353.1 | ✓ | 12 | 8.3 | odd | 2 | ||
608.2.i.f.353.4 | yes | 12 | 8.5 | even | 2 | ||
608.2.i.f.577.1 | yes | 12 | 152.83 | odd | 6 | ||
608.2.i.f.577.4 | yes | 12 | 152.45 | even | 6 | ||
1216.2.i.r.577.3 | 12 | 19.7 | even | 3 | inner | ||
1216.2.i.r.577.6 | 12 | 76.7 | odd | 6 | inner | ||
1216.2.i.r.961.3 | 12 | 1.1 | even | 1 | trivial | ||
1216.2.i.r.961.6 | 12 | 4.3 | odd | 2 | inner |