Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [644,2,Mod(93,644)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(644, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("644.93");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 644 = 2^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 644.i (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: | \(5.14236589017\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 13 x^{12} - 8 x^{11} + 130 x^{10} - 78 x^{9} + 505 x^{8} - 519 x^{7} + 1508 x^{6} - 955 x^{5} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.3 | ||
Root | \(0.0453148 - 0.0784875i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 644.277 |
Dual form | 644.2.i.a.93.3 |
$q$-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 \(\left(\mathbb{Z}/644\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) | \(323\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.03959 | + | 1.80062i | −0.600205 | + | 1.03959i | 0.392584 | + | 0.919716i | \(0.371581\pi\) |
−0.992790 | + | 0.119870i | \(0.961752\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.832793 | + | 1.44244i | 0.372436 | + | 0.645079i | 0.989940 | − | 0.141490i | \(-0.0451892\pi\) |
−0.617503 | + | 0.786568i | \(0.711856\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64459 | − | 0.0784875i | −0.999560 | − | 0.0296655i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.661478 | − | 1.14571i | −0.220493 | − | 0.381905i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.494262 | + | 0.856087i | −0.149026 | + | 0.258120i | −0.930868 | − | 0.365357i | \(-0.880947\pi\) |
0.781842 | + | 0.623477i | \(0.214280\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.84085 | −0.787911 | −0.393955 | − | 0.919130i | \(-0.628894\pi\) | ||||
−0.393955 | + | 0.919130i | \(0.628894\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.46304 | −0.894153 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.02169 | + | 1.76962i | −0.247796 | + | 0.429196i | −0.962914 | − | 0.269808i | \(-0.913040\pi\) |
0.715118 | + | 0.699004i | \(0.246373\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.57247 | − | 2.72360i | −0.360750 | − | 0.624836i | 0.627335 | − | 0.778750i | \(-0.284146\pi\) |
−0.988084 | + | 0.153913i | \(0.950812\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.89060 | − | 4.68029i | 0.630781 | − | 1.02132i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.11291 | − | 1.92762i | 0.222582 | − | 0.385524i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.48686 | −0.671047 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.06771 | 0.569660 | 0.284830 | − | 0.958578i | \(-0.408063\pi\) | ||||
0.284830 | + | 0.958578i | \(0.408063\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.31480 | + | 5.74140i | −0.595355 | + | 1.03119i | 0.398141 | + | 0.917324i | \(0.369655\pi\) |
−0.993497 | + | 0.113862i | \(0.963678\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.02766 | − | 1.77995i | −0.178892 | − | 0.309850i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.08918 | − | 3.88002i | −0.353136 | − | 0.655843i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00232 | − | 6.93223i | −0.657978 | − | 1.13965i | −0.981138 | − | 0.193307i | \(-0.938079\pi\) |
0.323161 | − | 0.946344i | \(-0.395255\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.95331 | − | 5.11528i | 0.472908 | − | 0.819101i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.47285 | 0.230021 | 0.115010 | − | 0.993364i | \(-0.463310\pi\) | ||||
0.115010 | + | 0.993364i | \(0.463310\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.79477 | −0.731196 | −0.365598 | − | 0.930773i | \(-0.619135\pi\) | ||||
−0.365598 | + | 0.930773i | \(0.619135\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.10175 | − | 1.90829i | 0.164239 | − | 0.284470i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.26758 | − | 9.12372i | −0.768356 | − | 1.33083i | −0.938454 | − | 0.345404i | \(-0.887742\pi\) |
0.170098 | − | 0.985427i | \(-0.445591\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98768 | + | 0.415134i | 0.998240 | + | 0.0593048i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.12427 | − | 3.67934i | −0.297457 | − | 0.515211i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.05423 | + | 1.82598i | −0.144810 | + | 0.250818i | −0.929302 | − | 0.369321i | \(-0.879590\pi\) |
0.784492 | + | 0.620139i | \(0.212924\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.64647 | −0.222010 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.53887 | 0.866095 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.30091 | + | 9.18145i | −0.690120 | + | 1.19532i | 0.281678 | + | 0.959509i | \(0.409109\pi\) |
−0.971798 | + | 0.235814i | \(0.924224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.886494 | + | 1.53545i | 0.113504 | + | 0.196595i | 0.917181 | − | 0.398472i | \(-0.130459\pi\) |
−0.803677 | + | 0.595066i | \(0.797126\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.65941 | + | 3.08186i | 0.209066 | + | 0.388278i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.36584 | − | 4.09776i | −0.293447 | − | 0.508264i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.30965 | + | 4.00044i | −0.282169 | + | 0.488731i | −0.971919 | − | 0.235317i | \(-0.924387\pi\) |
0.689750 | + | 0.724048i | \(0.257721\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.07917 | −0.250303 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.86351 | 0.458514 | 0.229257 | − | 0.973366i | \(-0.426370\pi\) | ||||
0.229257 | + | 0.973366i | \(0.426370\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.12559 | + | 8.87778i | −0.599905 | + | 1.03907i | 0.392930 | + | 0.919569i | \(0.371462\pi\) |
−0.992835 | + | 0.119497i | \(0.961872\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.31393 | + | 4.00785i | 0.267190 | + | 0.462787i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.37431 | − | 2.22520i | 0.156617 | − | 0.253586i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.641961 | − | 1.11191i | −0.0722263 | − | 0.125100i | 0.827650 | − | 0.561244i | \(-0.189677\pi\) |
−0.899877 | + | 0.436144i | \(0.856344\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.60933 | − | 9.71564i | 0.623259 | − | 1.07952i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.51653 | −0.934811 | −0.467405 | − | 0.884043i | \(-0.654811\pi\) | ||||
−0.467405 | + | 0.884043i | \(0.654811\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.40343 | −0.369153 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.18915 | + | 5.52378i | −0.341913 | + | 0.592211i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.35745 | + | 7.54733i | 0.461889 | + | 0.800015i | 0.999055 | − | 0.0434611i | \(-0.0138385\pi\) |
−0.537166 | + | 0.843477i | \(0.680505\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.51288 | + | 0.222971i | 0.787564 | + | 0.0233737i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.89204 | − | 11.9374i | −0.714671 | − | 1.23785i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.61909 | − | 4.53639i | 0.268712 | − | 0.465424i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.2838 | 1.04416 | 0.522080 | − | 0.852896i | \(-0.325156\pi\) | ||||
0.522080 | + | 0.852896i | \(0.325156\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.30778 | 0.131436 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.74071 | + | 11.6753i | −0.670726 | + | 1.16173i | 0.306972 | + | 0.951718i | \(0.400684\pi\) |
−0.977699 | + | 0.210013i | \(0.932649\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.35673 | + | 5.81403i | 0.330748 | + | 0.572873i | 0.982659 | − | 0.185423i | \(-0.0593655\pi\) |
−0.651910 | + | 0.758296i | \(0.726032\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.15831 | + | 0.271805i | 0.893760 | + | 0.0265255i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.0996616 | − | 0.172619i | −0.00963466 | − | 0.0166877i | 0.861168 | − | 0.508321i | \(-0.169734\pi\) |
−0.870803 | + | 0.491633i | \(0.836400\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.87314 | + | 17.1008i | −0.945676 | + | 1.63796i | −0.191283 | + | 0.981535i | \(0.561265\pi\) |
−0.754393 | + | 0.656423i | \(0.772069\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.6430 | 1.57969 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.53986 | 0.333002 | 0.166501 | − | 0.986041i | \(-0.446753\pi\) | ||||
0.166501 | + | 0.986041i | \(0.446753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.832793 | + | 1.44244i | −0.0776583 | + | 0.134508i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.87916 | + | 3.25481i | 0.173729 | + | 0.300907i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.84084 | − | 4.59972i | 0.260420 | − | 0.421656i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.01141 | + | 8.68002i | 0.455583 | + | 0.789092i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.53116 | + | 2.65204i | −0.138060 | + | 0.239126i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0352 | 1.07646 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.50216 | 0.133295 | 0.0666475 | − | 0.997777i | \(-0.478770\pi\) | ||||
0.0666475 | + | 0.997777i | \(0.478770\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.98458 | − | 8.63354i | 0.438867 | − | 0.760141i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.12937 | + | 10.6164i | 0.535525 | + | 0.927557i | 0.999138 | + | 0.0415190i | \(0.0132197\pi\) |
−0.463612 | + | 0.886038i | \(0.653447\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.94477 | + | 7.32621i | 0.342055 | + | 0.635263i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.90383 | − | 5.02959i | −0.249922 | − | 0.432878i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.62370 | − | 6.27642i | 0.309593 | − | 0.536231i | −0.668680 | − | 0.743550i | \(-0.733140\pi\) |
0.978273 | + | 0.207319i | \(0.0664738\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.73017 | 0.570846 | 0.285423 | − | 0.958402i | \(-0.407866\pi\) | ||||
0.285423 | + | 0.958402i | \(0.407866\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.9044 | 1.84468 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.40413 | − | 2.43202i | 0.117419 | − | 0.203376i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.55477 | + | 4.42499i | 0.212162 | + | 0.367476i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.01179 | + | 12.1506i | −0.660801 | + | 1.00216i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.21743 | − | 7.30480i | −0.345505 | − | 0.598433i | 0.639940 | − | 0.768425i | \(-0.278959\pi\) |
−0.985445 | + | 0.169992i | \(0.945626\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.65419 | + | 2.86515i | −0.134616 | + | 0.233162i | −0.925451 | − | 0.378868i | \(-0.876314\pi\) |
0.790835 | + | 0.612030i | \(0.209647\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.70330 | 0.218549 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.0422 | −0.886928 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.36542 | + | 2.36498i | −0.108972 | + | 0.188746i | −0.915354 | − | 0.402649i | \(-0.868089\pi\) |
0.806382 | + | 0.591395i | \(0.201423\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.19192 | − | 3.79653i | −0.173831 | − | 0.301084i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.25432 | − | 2.32952i | −0.0988544 | − | 0.183592i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4458 | + | 18.0927i | 0.818179 | + | 1.41713i | 0.907023 | + | 0.421082i | \(0.138349\pi\) |
−0.0888439 | + | 0.996046i | \(0.528317\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.71165 | − | 2.96467i | 0.133252 | − | 0.230799i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.58070 | 0.354465 | 0.177233 | − | 0.984169i | \(-0.443285\pi\) | ||||
0.177233 | + | 0.984169i | \(0.443285\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.92955 | −0.379197 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.08031 | + | 3.60320i | −0.159085 | + | 0.275544i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.89064 | − | 3.27469i | −0.143743 | − | 0.248970i | 0.785160 | − | 0.619293i | \(-0.212581\pi\) |
−0.928903 | + | 0.370322i | \(0.879247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.09449 | + | 5.01041i | −0.233921 | + | 0.378751i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.0215 | − | 19.0898i | −0.828427 | − | 1.43488i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.3563 | − | 19.6696i | 0.848806 | − | 1.47018i | −0.0334679 | − | 0.999440i | \(-0.510655\pi\) |
0.882274 | − | 0.470736i | \(-0.156012\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.78760 | −0.355859 | −0.177930 | − | 0.984043i | \(-0.556940\pi\) | ||||
−0.177930 | + | 0.984043i | \(0.556940\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.68635 | −0.272503 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.66621 | − | 11.5462i | 0.490110 | − | 0.848895i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.00997 | − | 1.74931i | −0.0738561 | − | 0.127922i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.22131 | + | 0.273675i | 0.670752 | + | 0.0199069i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.82929 | − | 3.16843i | −0.132363 | − | 0.229259i | 0.792224 | − | 0.610230i | \(-0.208923\pi\) |
−0.924587 | + | 0.380971i | \(0.875590\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.28068 | + | 16.0746i | −0.668038 | + | 1.15708i | 0.310414 | + | 0.950601i | \(0.399532\pi\) |
−0.978452 | + | 0.206474i | \(0.933801\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.83799 | 0.704513 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.2158 | −0.870341 | −0.435170 | − | 0.900348i | \(-0.643312\pi\) | ||||
−0.435170 | + | 0.900348i | \(0.643312\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.1874 | + | 17.6451i | −0.722166 | + | 1.25083i | 0.237964 | + | 0.971274i | \(0.423520\pi\) |
−0.960130 | + | 0.279554i | \(0.909813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.80217 | − | 8.31760i | −0.338719 | − | 0.586678i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.11284 | − | 0.240777i | −0.569410 | − | 0.0168992i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.22658 | + | 2.12450i | 0.0856681 | + | 0.148381i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.661478 | − | 1.14571i | 0.0459759 | − | 0.0796326i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.10885 | 0.215044 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.76436 | 0.190306 | 0.0951532 | − | 0.995463i | \(-0.469666\pi\) | ||||
0.0951532 | + | 0.995463i | \(0.469666\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.01645 | + | 6.95669i | −0.275202 | + | 0.476664i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.99305 | − | 6.91617i | −0.272324 | − | 0.471679i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.21690 | − | 14.9235i | 0.625684 | − | 1.01307i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.6570 | − | 18.4584i | −0.720132 | − | 1.24731i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.90247 | − | 5.02723i | 0.195241 | − | 0.338168i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.7299 | 0.986389 | 0.493194 | − | 0.869919i | \(-0.335829\pi\) | ||||
0.493194 | + | 0.869919i | \(0.335829\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.94467 | −0.196311 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.2577 | + | 21.2309i | −0.813570 | + | 1.40914i | 0.0967799 | + | 0.995306i | \(0.469146\pi\) |
−0.910350 | + | 0.413839i | \(0.864188\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.8456 | − | 20.5172i | −0.782781 | − | 1.35582i | −0.930316 | − | 0.366759i | \(-0.880467\pi\) |
0.147535 | − | 0.989057i | \(-0.452866\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.57802 | + | 4.78790i | 0.169621 | + | 0.315021i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.24516 | − | 9.08488i | −0.343622 | − | 0.595170i | 0.641481 | − | 0.767139i | \(-0.278320\pi\) |
−0.985102 | + | 0.171969i | \(0.944987\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.77361 | − | 15.1963i | 0.572327 | − | 0.991300i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.66949 | 0.173402 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.4871 | −1.19583 | −0.597916 | − | 0.801559i | \(-0.704004\pi\) | ||||
−0.597916 | + | 0.801559i | \(0.704004\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.94815 | − | 10.3025i | 0.383154 | − | 0.663642i | −0.608357 | − | 0.793663i | \(-0.708171\pi\) |
0.991511 | + | 0.130021i | \(0.0415045\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.43247 | + | 11.1414i | 0.412643 | + | 0.714718i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.22048 | + | 10.4250i | 0.333525 | + | 0.666031i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.46716 | + | 7.73734i | 0.284238 | + | 0.492315i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.85367 | − | 15.3350i | 0.561078 | − | 0.971816i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.3755 | 1.03361 | 0.516805 | − | 0.856103i | \(-0.327121\pi\) | ||||
0.516805 | + | 0.856103i | \(0.327121\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.988525 | −0.0621480 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.53816 | − | 6.12826i | 0.221568 | − | 0.383767i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.59191 | − | 7.95343i | −0.286436 | − | 0.496121i | 0.686521 | − | 0.727110i | \(-0.259137\pi\) |
−0.972956 | + | 0.230989i | \(0.925804\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0404 | + | 18.6470i | 0.623880 | + | 1.15867i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.02923 | − | 3.51472i | −0.125606 | − | 0.217556i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.01599 | − | 6.95591i | 0.247637 | − | 0.428920i | −0.715233 | − | 0.698886i | \(-0.753679\pi\) |
0.962870 | + | 0.269967i | \(0.0870127\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.51182 | −0.215729 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.1198 | −1.10891 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.19305 | − | 7.26258i | 0.255655 | − | 0.442808i | −0.709418 | − | 0.704788i | \(-0.751042\pi\) |
0.965073 | + | 0.261980i | \(0.0843755\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.85582 | + | 4.94642i | 0.173479 | + | 0.300474i | 0.939634 | − | 0.342182i | \(-0.111166\pi\) |
−0.766155 | + | 0.642656i | \(0.777833\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.21177 | + | 13.2960i | −0.496999 | + | 0.804712i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.10014 | + | 1.90550i | 0.0663410 | + | 0.114906i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.29343 | + | 14.3646i | −0.498304 | + | 0.863088i | −0.999998 | − | 0.00195715i | \(-0.999377\pi\) |
0.501694 | + | 0.865045i | \(0.332710\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.77067 | 0.525086 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.8040 | −0.763824 | −0.381912 | − | 0.924199i | \(-0.624734\pi\) | ||||
−0.381912 | + | 0.924199i | \(0.624734\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.24196 | + | 10.8114i | −0.371046 | + | 0.642671i | −0.989727 | − | 0.142972i | \(-0.954334\pi\) |
0.618681 | + | 0.785643i | \(0.287668\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.44553 | + | 9.43193i | 0.322565 | + | 0.558699i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.89508 | − | 0.115600i | −0.229920 | − | 0.00682368i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.41230 | + | 11.1064i | 0.377194 | + | 0.653319i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.6909 | + | 18.5172i | −0.626711 | + | 1.08549i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.3771 | −1.07360 | −0.536800 | − | 0.843710i | \(-0.680367\pi\) | ||||
−0.536800 | + | 0.843710i | \(0.680367\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.6583 | −1.02810 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.72342 | − | 2.98506i | 0.100003 | − | 0.173211i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.42043 | − | 2.46025i | −0.0821454 | − | 0.142280i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.6802 | + | 0.376329i | 0.730874 | + | 0.0216913i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.0151 | − | 24.2749i | −0.805147 | − | 1.39456i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.47653 | + | 2.55743i | −0.0845459 | + | 0.146438i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.5832 | 1.17474 | 0.587371 | − | 0.809318i | \(-0.300163\pi\) | ||||
0.587371 | + | 0.809318i | \(0.300163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.9584 | −0.794068 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.0743 | − | 22.6454i | 0.741377 | − | 1.28410i | −0.210492 | − | 0.977596i | \(-0.567507\pi\) |
0.951869 | − | 0.306507i | \(-0.0991601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.40691 | − | 11.0971i | −0.362140 | − | 0.627245i | 0.626173 | − | 0.779684i | \(-0.284620\pi\) |
−0.988313 | + | 0.152439i | \(0.951287\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.06345 | + | 4.96015i | −0.172606 | + | 0.279473i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.213486 | + | 0.369769i | 0.0119906 | + | 0.0207683i | 0.871958 | − | 0.489580i | \(-0.162850\pi\) |
−0.859968 | + | 0.510348i | \(0.829517\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.51626 | + | 2.62623i | −0.0848940 | + | 0.147041i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.414427 | 0.0231311 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.42631 | 0.357570 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.16162 | + | 5.47608i | −0.175375 | + | 0.303758i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.5280 | − | 35.5555i | −1.13520 | − | 1.96622i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.2145 | + | 24.5419i | 0.728538 | + | 1.35304i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.3241 | + | 24.8101i | 0.787324 | + | 1.36368i | 0.927601 | + | 0.373573i | \(0.121867\pi\) |
−0.140277 | + | 0.990112i | \(0.544799\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.29490 | + | 9.17103i | −0.290159 | + | 0.502570i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.69385 | −0.420360 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.28857 | −0.179140 | −0.0895698 | − | 0.995981i | \(-0.528549\pi\) | ||||
−0.0895698 | + | 0.995981i | \(0.528549\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.67999 | + | 6.37392i | −0.199869 | + | 0.346184i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.27676 | − | 5.67552i | −0.177447 | − | 0.307346i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4469 | − | 1.64630i | −0.996041 | − | 0.0888920i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.73152 | − | 2.99908i | −0.0932219 | − | 0.161465i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.1179 | − | 27.9171i | 0.865257 | − | 1.49867i | −0.00153529 | − | 0.999999i | \(-0.500489\pi\) |
0.866792 | − | 0.498670i | \(-0.166178\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.7933 | −1.00598 | −0.502992 | − | 0.864291i | \(-0.667767\pi\) | ||||
−0.502992 | + | 0.864291i | \(0.667767\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.90566 | 0.528725 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.1794 | + | 22.8274i | −0.701470 | + | 1.21498i | 0.266480 | + | 0.963840i | \(0.414139\pi\) |
−0.967950 | + | 0.251142i | \(0.919194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.21750 | + | 5.57287i | 0.170767 | + | 0.295777i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.32904 | + | 9.89707i | 0.282042 | + | 0.523809i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.18487 | − | 14.1766i | −0.431981 | − | 0.748212i | 0.565063 | − | 0.825048i | \(-0.308852\pi\) |
−0.997044 | + | 0.0768352i | \(0.975518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.55467 | − | 7.88892i | 0.239720 | − | 0.415207i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.8392 | −1.09377 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.0742 | −0.893706 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.98291 | − | 12.0948i | 0.364505 | − | 0.631341i | −0.624192 | − | 0.781271i | \(-0.714572\pi\) |
0.988697 | + | 0.149930i | \(0.0479049\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.974259 | − | 1.68747i | −0.0507179 | − | 0.0878460i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.93132 | − | 4.74622i | 0.152186 | − | 0.246411i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.21829 | − | 3.84219i | −0.114859 | − | 0.198941i | 0.802865 | − | 0.596161i | \(-0.203308\pi\) |
−0.917723 | + | 0.397220i | \(0.869975\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.5117 | + | 21.6708i | −0.646099 | + | 1.11908i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.71493 | −0.448842 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.47569 | 0.178534 | 0.0892670 | − | 0.996008i | \(-0.471548\pi\) | ||||
0.0892670 | + | 0.996008i | \(0.471548\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.56162 | + | 2.70481i | −0.0800044 | + | 0.138572i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.31187 | − | 12.6645i | −0.373619 | − | 0.647127i | 0.616500 | − | 0.787355i | \(-0.288550\pi\) |
−0.990119 | + | 0.140228i | \(0.955217\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.35424 | + | 0.129227i | 0.221913 | + | 0.00658604i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.17164 | + | 5.49344i | 0.161223 | + | 0.279247i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.20978 | + | 14.2198i | −0.416252 | + | 0.720970i | −0.995559 | − | 0.0941396i | \(-0.969990\pi\) |
0.579307 | + | 0.815110i | \(0.303323\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.04338 | −0.103338 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −25.4880 | −1.28570 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.06924 | − | 1.85198i | 0.0537994 | − | 0.0931832i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.10084 | + | 1.90671i | 0.0552497 | + | 0.0956953i | 0.892327 | − | 0.451389i | \(-0.149071\pi\) |
−0.837078 | + | 0.547084i | \(0.815738\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.2926 | − | 0.513220i | −0.865714 | − | 0.0256931i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.42622 | + | 7.66643i | 0.221035 | + | 0.382843i | 0.955122 | − | 0.296211i | \(-0.0957233\pi\) |
−0.734088 | + | 0.679055i | \(0.762390\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.41686 | − | 16.3105i | 0.469087 | − | 0.812483i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.6856 | 0.928497 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.91279 | 0.392222 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.83363 | − | 3.17595i | 0.0906673 | − | 0.157040i | −0.817125 | − | 0.576461i | \(-0.804433\pi\) |
0.907792 | + | 0.419420i | \(0.137767\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.53429 | + | 13.0498i | 0.371639 | + | 0.643698i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.7394 | − | 23.8651i | 0.725276 | − | 1.17432i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.09251 | − | 12.2846i | −0.348157 | − | 0.603026i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.99659 | + | 12.1185i | −0.342625 | + | 0.593443i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.0724 | −1.56684 | −0.783420 | − | 0.621493i | \(-0.786526\pi\) | ||||
−0.783420 | + | 0.621493i | \(0.786526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.5009 | −0.511781 | −0.255891 | − | 0.966706i | \(-0.582369\pi\) | ||||
−0.255891 | + | 0.966706i | \(0.582369\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.96878 | + | 12.0703i | −0.338834 | + | 0.586877i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.27410 | + | 3.93886i | 0.110310 | + | 0.191063i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.22390 | − | 4.13022i | −0.107622 | − | 0.199875i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.91942 | + | 5.05659i | 0.140951 | + | 0.244134i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.8228 | − | 32.6021i | 0.906663 | − | 1.57039i | 0.0879936 | − | 0.996121i | \(-0.471954\pi\) |
0.818669 | − | 0.574265i | \(-0.194712\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.15378 | 0.439903 | 0.219951 | − | 0.975511i | \(-0.429410\pi\) | ||||
0.219951 | + | 0.975511i | \(0.429410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.6236 | −0.509364 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.57247 | − | 2.72360i | 0.0752215 | − | 0.130287i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.59019 | − | 16.6107i | −0.457715 | − | 0.792785i | 0.541125 | − | 0.840942i | \(-0.317999\pi\) |
−0.998840 | + | 0.0481571i | \(0.984665\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.14657 | − | 8.28048i | −0.197456 | − | 0.394309i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.351260 | − | 0.608399i | −0.0166888 | − | 0.0289059i | 0.857560 | − | 0.514383i | \(-0.171979\pi\) |
−0.874249 | + | 0.485477i | \(0.838646\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.25771 | + | 12.5707i | −0.344049 | + | 0.595910i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.5375 | 0.829496 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.3683 | 1.33878 | 0.669392 | − | 0.742910i | \(-0.266555\pi\) | ||||
0.669392 | + | 0.742910i | \(0.266555\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.727975 | + | 1.26089i | −0.0342790 | + | 0.0593730i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.43935 | − | 5.95713i | −0.161595 | − | 0.279890i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.93505 | + | 11.0226i | 0.278240 | + | 0.516746i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.49028 | − | 4.31329i | −0.116490 | − | 0.201767i | 0.801884 | − | 0.597480i | \(-0.203831\pi\) |
−0.918375 | + | 0.395712i | \(0.870498\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.56249 | − | 6.17042i | 0.166283 | − | 0.288011i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.4498 | 1.55791 | 0.778956 | − | 0.627078i | \(-0.215749\pi\) | ||||
0.778956 | + | 0.627078i | \(0.215749\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.58397 | −0.398931 | −0.199465 | − | 0.979905i | \(-0.563921\pi\) | ||||
−0.199465 | + | 0.979905i | \(0.563921\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.4793 | − | 19.8827i | 0.532339 | − | 0.922038i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.68463 | + | 11.5781i | 0.309328 | + | 0.535772i | 0.978216 | − | 0.207592i | \(-0.0665626\pi\) |
−0.668888 | + | 0.743364i | \(0.733229\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.42206 | − | 10.3982i | 0.296543 | − | 0.480145i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.83895 | − | 4.91720i | −0.130812 | − | 0.226572i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.36987 | − | 4.10474i | 0.108967 | − | 0.188736i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.00008 | −0.321186 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.78940 | 0.127718 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.98362 | − | 17.2921i | 0.456163 | − | 0.790098i | −0.542591 | − | 0.839997i | \(-0.682557\pi\) |
0.998754 | + | 0.0498991i | \(0.0158900\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.3700 | + | 19.6934i | 0.518428 | + | 0.897943i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.49855 | + | 0.163189i | 0.250193 | + | 0.00742535i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.56427 | + | 14.8337i | 0.388883 | + | 0.673566i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.6255 | − | 30.5283i | 0.798689 | − | 1.38337i | −0.121781 | − | 0.992557i | \(-0.538861\pi\) |
0.920470 | − | 0.390813i | \(-0.127806\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −43.4373 | −1.96430 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.6733 | 0.481680 | 0.240840 | − | 0.970565i | \(-0.422577\pi\) | ||||
0.240840 | + | 0.970565i | \(0.422577\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.13426 | + | 5.42869i | −0.141160 | + | 0.244496i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.08911 | + | 1.88639i | 0.0489517 | + | 0.0847868i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.2174 | − | 0.303237i | −0.458312 | − | 0.0136020i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0916 | + | 34.7997i | 0.899424 | + | 1.55785i | 0.828231 | + | 0.560386i | \(0.189347\pi\) |
0.0711930 | + | 0.997463i | \(0.477319\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.76204 | + | 8.24809i | −0.212752 | + | 0.368497i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.89782 | 0.441322 | 0.220661 | − | 0.975351i | \(-0.429179\pi\) | ||||
0.220661 | + | 0.975351i | \(0.429179\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.4545 | −0.999211 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.12470 | − | 8.87623i | 0.227596 | − | 0.394207i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.02205 | + | 10.4305i | 0.266923 | + | 0.462324i | 0.968066 | − | 0.250697i | \(-0.0806598\pi\) |
−0.701143 | + | 0.713021i | \(0.747326\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.2519 | − | 23.0758i | 0.630465 | − | 1.02081i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.48299 | + | 9.49681i | 0.242080 | + | 0.419295i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.59092 | + | 9.68376i | −0.246366 | + | 0.426718i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.4143 | 0.458019 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.86195 | 0.345101 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.8928 | − | 34.4553i | 0.871518 | − | 1.50951i | 0.0110927 | − | 0.999938i | \(-0.496469\pi\) |
0.860426 | − | 0.509576i | \(-0.170198\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.1822 | − | 29.7605i | −0.751327 | − | 1.30134i | −0.947180 | − | 0.320703i | \(-0.896081\pi\) |
0.195853 | − | 0.980633i | \(-0.437252\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.80484 | − | 10.7807i | −0.253344 | − | 0.470510i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.77340 | − | 11.7319i | −0.295054 | − | 0.511048i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.0258 | 0.608666 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.18415 | −0.181236 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.165995 | − | 0.287512i | 0.00717659 | − | 0.0124302i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.6116 | + | 40.8965i | 1.01892 | + | 1.76481i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.80914 | + | 5.77688i | −0.164071 | + | 0.248828i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.68562 | − | 2.91959i | −0.0724706 | − | 0.125523i | 0.827513 | − | 0.561447i | \(-0.189755\pi\) |
−0.899984 | + | 0.435924i | \(0.856422\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.97712 | − | 8.62062i | 0.213589 | − | 0.369946i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −32.8891 | −1.40882 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.9057 | 0.509050 | 0.254525 | − | 0.967066i | \(-0.418081\pi\) | ||||
0.254525 | + | 0.967066i | \(0.418081\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.17279 | − | 2.03134i | 0.0500536 | − | 0.0866953i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.82389 | − | 8.35522i | −0.205505 | − | 0.355945i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.61045 | + | 2.99093i | 0.0684833 | + | 0.127187i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.8602 | + | 24.0066i | 0.588333 | + | 1.01902i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.7090 | − | 30.6729i | 0.750355 | − | 1.29965i | −0.197295 | − | 0.980344i | \(-0.563216\pi\) |
0.947651 | − | 0.319309i | \(-0.103451\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.6212 | 0.576117 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.19979 | 0.177315 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.0435 | + | 34.7164i | −0.844733 | + | 1.46312i | 0.0411201 | + | 0.999154i | \(0.486907\pi\) |
−0.885853 | + | 0.463966i | \(0.846426\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.94797 | + | 5.10603i | 0.124022 | + | 0.214812i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.5969 | + | 25.2536i | −0.655009 | + | 1.06055i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.6226 | + | 35.7194i | 0.864544 | + | 1.49743i | 0.867499 | + | 0.497438i | \(0.165726\pi\) |
−0.00295553 | + | 0.999996i | \(0.500941\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.2410 | − | 17.7379i | 0.428571 | − | 0.742307i | −0.568175 | − | 0.822907i | \(-0.692351\pi\) |
0.996746 | + | 0.0806007i | \(0.0256838\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.60683 | 0.317780 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.22582 | 0.0928233 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.0890 | + | 24.4029i | −0.586534 | + | 1.01591i | 0.408148 | + | 0.912916i | \(0.366175\pi\) |
−0.994682 | + | 0.102991i | \(0.967159\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.2961 | − | 33.4219i | −0.801920 | − | 1.38897i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.5227 | + | 0.668441i | 0.934399 | + | 0.0277316i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.04213 | − | 1.80503i | −0.0431607 | − | 0.0747565i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.12991 | + | 5.42116i | −0.129406 | + | 0.224137i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.7008 | −1.18461 | −0.592304 | − | 0.805715i | \(-0.701781\pi\) | ||||
−0.592304 | + | 0.805715i | \(0.701781\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.8497 | 0.859097 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.6994 | − | 21.9960i | 0.522383 | − | 0.904794i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.8741 | + | 36.1551i | 0.857198 | + | 1.48471i | 0.874591 | + | 0.484862i | \(0.161130\pi\) |
−0.0173926 | + | 0.999849i | \(0.505537\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.00066 | + | 0.267126i | 0.368991 | + | 0.0109511i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.1814 | − | 36.6872i | −0.866896 | − | 1.50151i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.1173 | + | 17.5237i | −0.413381 | + | 0.715997i | −0.995257 | − | 0.0972803i | \(-0.968986\pi\) |
0.581876 | + | 0.813278i | \(0.302319\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.85589 | −0.238867 | −0.119433 | − | 0.992842i | \(-0.538108\pi\) | ||||
−0.119433 | + | 0.992842i | \(0.538108\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.11114 | 0.248865 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.34693 | + | 14.4573i | −0.339351 | + | 0.587773i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.1393 | + | 38.3464i | 0.898606 | + | 1.55643i | 0.829277 | + | 0.558838i | \(0.188753\pi\) |
0.0693298 | + | 0.997594i | \(0.477914\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.86754 | − | 14.3578i | 0.359331 | − | 0.581807i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.9644 | + | 25.9191i | 0.605396 | + | 1.04858i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.8218 | + | 36.0645i | −0.840986 | + | 1.45663i | 0.0480763 | + | 0.998844i | \(0.484691\pi\) |
−0.889062 | + | 0.457787i | \(0.848642\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.10054 | −0.205674 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.3910 | −1.18324 | −0.591619 | − | 0.806217i | \(-0.701511\pi\) | ||||
−0.591619 | + | 0.806217i | \(0.701511\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.28116 | + | 9.14724i | −0.212268 | + | 0.367659i | −0.952424 | − | 0.304777i | \(-0.901418\pi\) |
0.740156 | + | 0.672435i | \(0.234752\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.74343 | − | 3.01971i | −0.0699615 | − | 0.121177i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.9313 | − | 20.3016i | −0.437953 | − | 0.813366i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.45830 | + | 7.72200i | 0.178332 | + | 0.308880i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.23192 | + | 5.59785i | −0.129070 | + | 0.223557i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.3565 | 0.652178 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.5742 | 1.85409 | 0.927045 | − | 0.374950i | \(-0.122340\pi\) | ||||
0.927045 | + | 0.374950i | \(0.122340\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.87379 | + | 4.97755i | −0.114223 | + | 0.197840i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.25099 | + | 2.16677i | 0.0496439 | + | 0.0859858i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.8510 | − | 1.17933i | −0.786524 | − | 0.0467269i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.55562 | − | 4.42647i | −0.101099 | − | 0.175109i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.53229 | + | 6.11811i | −0.139517 | + | 0.241651i | −0.927314 | − | 0.374284i | \(-0.877888\pi\) |
0.787797 | + | 0.615935i | \(0.211222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.6500 | 0.577741 | 0.288870 | − | 0.957368i | \(-0.406720\pi\) | ||||
0.288870 | + | 0.957368i | \(0.406720\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.6045 | 0.653801 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.61862 | + | 2.80354i | −0.0636347 | + | 0.110219i | −0.896088 | − | 0.443877i | \(-0.853603\pi\) |
0.832453 | + | 0.554096i | \(0.186936\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.24008 | − | 9.07609i | −0.205691 | − | 0.356268i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.2897 | + | 32.1103i | 0.677635 | + | 1.25850i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.9334 | + | 39.7217i | 0.897451 | + | 1.55443i | 0.830741 | + | 0.556659i | \(0.187917\pi\) |
0.0667105 | + | 0.997772i | \(0.478750\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.2090 | + | 17.6825i | −0.398898 | + | 0.690912i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.5619 | 0.529099 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.3690 | 1.29987 | 0.649937 | − | 0.759988i | \(-0.274795\pi\) | ||||
0.649937 | + | 0.759988i | \(0.274795\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.54098 | + | 9.59726i | −0.215519 | + | 0.373290i | −0.953433 | − | 0.301605i | \(-0.902478\pi\) |
0.737914 | + | 0.674895i | \(0.235811\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.03474 | + | 10.4525i | 0.234370 | + | 0.405941i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.28245 | + | 11.7913i | −0.282401 | + | 0.457247i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.53386 | + | 2.65672i | 0.0593912 | + | 0.102869i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.3130 | + | 26.5229i | −0.592036 | + | 1.02544i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.75264 | −0.0676600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.48730 | 0.172973 | 0.0864863 | − | 0.996253i | \(-0.472436\pi\) | ||||
0.0864863 | + | 0.996253i | \(0.472436\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.88057 | + | 6.72134i | −0.149363 | + | 0.258705i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.99559 | − | 5.18852i | −0.115130 | − | 0.199411i | 0.802702 | − | 0.596381i | \(-0.203395\pi\) |
−0.917832 | + | 0.396970i | \(0.870062\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.1964 | − | 0.807149i | −1.04370 | − | 0.0309755i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.4858 | − | 44.1427i | −0.976618 | − | 1.69155i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.51795 | + | 4.36121i | −0.0963466 | + | 0.166877i | −0.910170 | − | 0.414235i | \(-0.864049\pi\) |
0.813823 | + | 0.581112i | \(0.197382\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0712 | 0.461215 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 49.2582 | 1.87932 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.99491 | − | 5.18734i | 0.114097 | − | 0.197622i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.03556 | − | 15.6500i | −0.343729 | − | 0.595356i | 0.641393 | − | 0.767212i | \(-0.278357\pi\) |
−0.985122 | + | 0.171857i | \(0.945023\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.45853 | − | 0.102644i | −0.131379 | − | 0.00389912i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.60484 | + | 9.70787i | 0.212604 | + | 0.368240i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.50480 | + | 2.60639i | −0.0569983 | + | 0.0987240i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.8112 | 0.824974 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.4949 | −0.811851 | −0.405926 | − | 0.913906i | \(-0.633051\pi\) | ||||
−0.405926 | + | 0.913906i | \(0.633051\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.5871 | + | 21.8014i | −0.474730 | + | 0.822257i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.2418 | + | 31.5958i | 0.687028 | + | 1.18997i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.7428 | − | 30.3472i | 0.704894 | − | 1.14132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.1340 | − | 22.7488i | −0.493259 | − | 0.854349i | 0.506711 | − | 0.862116i | \(-0.330861\pi\) |
−0.999970 | + | 0.00776668i | \(0.997528\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.849286 | + | 1.47101i | −0.0318507 | + | 0.0551671i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.62960 | −0.248280 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.67739 | 0.174924 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.2189 | − | 33.2882i | 0.717745 | − | 1.24317i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.10584 | + | 10.5756i | 0.227709 | + | 0.394404i | 0.957129 | − | 0.289663i | \(-0.0935431\pi\) |
−0.729420 | + | 0.684067i | \(0.760210\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.42084 | − | 15.6392i | −0.313608 | − | 0.582433i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.3672 | + | 21.4207i | 0.459942 | + | 0.796643i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.41410 | − | 5.91339i | 0.126796 | − | 0.219618i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.7476 | 1.17745 | 0.588726 | − | 0.808333i | \(-0.299630\pi\) | ||||
0.588726 | + | 0.808333i | \(0.299630\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.90756 | 0.255836 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.89877 | − | 8.48492i | 0.181188 | − | 0.313826i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.4666 | − | 19.8607i | −0.423528 | − | 0.733572i | 0.572754 | − | 0.819728i | \(-0.305875\pi\) |
−0.996282 | + | 0.0861555i | \(0.972542\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −24.1986 | − | 1.43763i | −0.892579 | − | 0.0530276i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.28315 | − | 3.95453i | −0.0841009 | − | 0.145667i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.2469 | + | 31.6046i | −0.671225 | + | 1.16260i | 0.306332 | + | 0.951925i | \(0.400898\pi\) |
−0.977557 | + | 0.210671i | \(0.932435\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.5760 | −0.682406 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.3428 | 1.59009 | 0.795046 | − | 0.606549i | \(-0.207446\pi\) | ||||
0.795046 | + | 0.606549i | \(0.207446\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.02449 | − | 12.1668i | 0.257357 | − | 0.445756i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.63350 | + | 9.75751i | 0.206119 | + | 0.357009i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.250015 | + | 0.464328i | 0.00913537 | + | 0.0169662i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.1136 | − | 45.2302i | −0.952901 | − | 1.65047i | −0.739101 | − | 0.673595i | \(-0.764749\pi\) |
−0.213800 | − | 0.976878i | \(-0.568584\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.0237 | + | 29.4859i | −0.620379 | + | 1.07453i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.51040 | −0.200544 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.29338 | 0.301428 | 0.150714 | − | 0.988577i | \(-0.451843\pi\) | ||||
0.150714 | + | 0.988577i | \(0.451843\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.02766 | − | 1.77995i | 0.0373016 | − | 0.0646082i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.72204 | + | 2.98266i | 0.0624239 | + | 0.108121i | 0.895548 | − | 0.444964i | \(-0.146784\pi\) |
−0.833124 | + | 0.553086i | \(0.813450\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.4526 | − | 44.4496i | 0.993850 | − | 1.60918i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.25129 | + | 3.89935i | 0.0813957 | + | 0.140981i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.0591 | − | 26.0831i | 0.543753 | − | 0.941808i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.2297 | −1.30648 | −0.653239 | − | 0.757152i | \(-0.726590\pi\) | ||||
−0.653239 | + | 0.757152i | \(0.726590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.0948 | 0.687681 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.5220 | − | 33.8131i | 0.702157 | − | 1.21617i | −0.265550 | − | 0.964097i | \(-0.585554\pi\) |
0.967708 | − | 0.252075i | \(-0.0811130\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.37816 | + | 12.7793i | 0.265031 | + | 0.459048i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −44.0139 | − | 1.30627i | −1.57899 | − | 0.0468622i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.31602 | − | 4.01146i | −0.0829799 | − | 0.143725i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.90959 | + | 3.30750i | −0.0683303 | + | 0.118352i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.6967 | −0.382269 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.54845 | −0.162341 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.22694 | + | 2.12512i | −0.0437357 | + | 0.0757525i | −0.887065 | − | 0.461645i | \(-0.847259\pi\) |
0.843329 | + | 0.537398i | \(0.180593\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.34994 | + | 14.4625i | 0.297266 | + | 0.514880i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.36146 | − | 0.277834i | −0.332855 | − | 0.00987866i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.51840 | − | 4.36199i | −0.0894309 | − | 0.154899i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.65084 | − | 6.32344i | 0.129482 | − | 0.224269i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.36871 | −0.190170 | −0.0950848 | − | 0.995469i | \(-0.530312\pi\) | ||||
−0.0950848 | + | 0.995469i | \(0.530312\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.5274 | 0.761583 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.76472 | − | 9.98479i | 0.203686 | − | 0.352795i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.06677 | − | 8.77591i | −0.178802 | − | 0.309695i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.31561 | − | 3.74929i | 0.0816144 | − | 0.132145i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.71808 | + | 15.1002i | 0.306891 | + | 0.531551i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.9603 | − | 29.3762i | 0.596294 | − | 1.03281i | −0.397069 | − | 0.917789i | \(-0.629973\pi\) |
0.993363 | − | 0.115023i | \(-0.0366941\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.2078 | −1.16608 | −0.583042 | − | 0.812442i | \(-0.698138\pi\) | ||||
−0.583042 | + | 0.812442i | \(0.698138\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.8755 | −0.416491 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.3984 | + | 30.1349i | −0.609439 | + | 1.05558i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.53963 | + | 13.0590i | 0.263778 | + | 0.456878i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.71415 | − | 8.75511i | −0.164726 | − | 0.305928i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.5519 | − | 37.3290i | −0.752167 | − | 1.30279i | −0.946770 | − | 0.321909i | \(-0.895675\pi\) |
0.194604 | − | 0.980882i | \(-0.437658\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.7391 | + | 25.5289i | −0.513773 | + | 0.889882i | 0.486099 | + | 0.873904i | \(0.338419\pi\) |
−0.999872 | + | 0.0159778i | \(0.994914\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.57476 | −0.159273 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.2293 | 1.01640 | 0.508202 | − | 0.861238i | \(-0.330310\pi\) | ||||
0.508202 | + | 0.861238i | \(0.330310\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.3456 | − | 26.5793i | 0.532974 | − | 0.923138i | −0.466284 | − | 0.884635i | \(-0.654408\pi\) |
0.999258 | − | 0.0385033i | \(-0.0122590\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.2435 | − | 29.8666i | −0.598170 | − | 1.03606i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.87388 | + | 11.9414i | −0.272814 | + | 0.413745i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.81478 | + | 6.60739i | 0.132016 | + | 0.228658i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.5582 | − | 20.0195i | 0.399511 | − | 0.691974i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.3773 | −1.63565 | −0.817823 | − | 0.575470i | \(-0.804819\pi\) | ||||
−0.817823 | + | 0.575470i | \(0.804819\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.5891 | −0.675487 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.3109 | − | 23.0551i | 0.458451 | − | 0.794061i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.10530 | − | 7.11059i | −0.141227 | − | 0.244612i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.5718 | − | 23.3484i | −0.431973 | − | 0.802260i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.9781 | − | 22.4788i | −0.445408 | − | 0.771469i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00232 | − | 6.93223i | 0.137198 | − | 0.237634i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.0607 | −1.44013 | −0.720065 | − | 0.693907i | \(-0.755888\pi\) | ||||
−0.720065 | + | 0.693907i | \(0.755888\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.92987 | −0.236997 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.1953 | + | 43.6395i | −0.860654 | + | 1.49070i | 0.0106449 | + | 0.999943i | \(0.496612\pi\) |
−0.871299 | + | 0.490753i | \(0.836722\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.0150 | − | 27.7387i | −0.546423 | − | 0.946433i | −0.998516 | − | 0.0544616i | \(-0.982656\pi\) |
0.452093 | − | 0.891971i | \(-0.350678\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.25743 | − | 6.89337i | 0.145093 | − | 0.234926i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.8475 | − | 30.9128i | −0.607536 | − | 1.05228i | −0.991645 | − | 0.128995i | \(-0.958825\pi\) |
0.384109 | − | 0.923288i | \(-0.374509\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.14903 | − | 5.45428i | 0.107070 | − | 0.185451i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.6645 | −0.905575 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.26919 | 0.0430543 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.56138 | − | 11.3647i | 0.222324 | − | 0.385076i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.80250 | − | 11.7823i | −0.230230 | − | 0.398770i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.8282 | − | 0.944615i | −1.07599 | − | 0.0319338i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.9051 | + | 34.4767i | 0.672148 | + | 1.16419i | 0.977294 | + | 0.211889i | \(0.0679616\pi\) |
−0.305145 | + | 0.952306i | \(0.598705\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.1045 | − | 33.0900i | 0.644380 | − | 1.11610i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.3634 | −0.483915 | −0.241957 | − | 0.970287i | \(-0.577789\pi\) | ||||
−0.241957 | + | 0.970287i | \(0.577789\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.5239 | 0.858949 | 0.429474 | − | 0.903079i | \(-0.358699\pi\) | ||||
0.429474 | + | 0.903079i | \(0.358699\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.3573 | − | 31.7957i | 0.617073 | − | 1.06880i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.01897 | + | 8.69311i | 0.168520 | + | 0.291886i | 0.937900 | − | 0.346906i | \(-0.112768\pi\) |
−0.769379 | + | 0.638792i | \(0.779434\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.97259 | − | 0.117901i | −0.133236 | − | 0.00395426i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.54496 | + | 9.60415i | 0.185763 | + | 0.321751i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.5662 | + | 28.6936i | −0.554368 | + | 0.960193i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.8296 | 1.26451 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.90662 | 0.197216 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.1689 | + | 17.6130i | −0.339150 | + | 0.587426i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.15419 | − | 3.73117i | −0.0717666 | − | 0.124303i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.8598 | + | 22.4409i | −0.461224 | + | 0.746787i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.98708 | − | 6.90582i | −0.132535 | − | 0.229557i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.9224 | + | 20.6502i | −0.395878 | + | 0.685680i | −0.993213 | − | 0.116312i | \(-0.962893\pi\) |
0.597335 | + | 0.801992i | \(0.296226\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.8353 | 0.591561 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.6212 | −0.418159 | −0.209080 | − | 0.977899i | \(-0.567047\pi\) | ||||
−0.209080 | + | 0.977899i | \(0.567047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.20940 | − | 7.29090i | 0.139311 | − | 0.241293i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.06996 | − | 5.31733i | −0.101490 | − | 0.175786i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.3764 | − | 28.5570i | −0.507773 | − | 0.943036i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.89196 | + | 15.4013i | 0.293319 | + | 0.508043i | 0.974592 | − | 0.223986i | \(-0.0719070\pi\) |
−0.681274 | + | 0.732029i | \(0.738574\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.3980 | + | 37.0624i | −0.705087 | + | 1.22125i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.9756 | −0.361268 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.8169 | −0.585817 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.44081 | − | 7.69171i | 0.145855 | − | 0.252629i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.7301 | + | 25.5132i | 0.483278 | + | 0.837063i | 0.999816 | − | 0.0192021i | \(-0.00611260\pi\) |
−0.516537 | + | 0.856265i | \(0.672779\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.85726 | − | 19.6844i | −0.323059 | − | 0.645131i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.1838 | + | 47.0837i | 0.889956 | + | 1.54145i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.68219 | − | 2.91363i | 0.0550134 | − | 0.0952859i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.6168 | 0.346837 | 0.173418 | − | 0.984848i | \(-0.444519\pi\) | ||||
0.173418 | + | 0.984848i | \(0.444519\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.6421 | 0.869433 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.0935 | − | 45.1952i | 0.850622 | − | 1.47332i | −0.0300249 | − | 0.999549i | \(-0.509559\pi\) |
0.880647 | − | 0.473772i | \(-0.157108\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.736426 | + | 1.27553i | 0.0239813 | + | 0.0415369i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.28468 | + | 13.5291i | 0.236971 | + | 0.440102i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.1715 | + | 34.9381i | 0.655487 | + | 1.13534i | 0.981771 | + | 0.190065i | \(0.0608700\pi\) |
−0.326284 | + | 0.945272i | \(0.605797\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.5610 | − | 25.2205i | 0.472672 | − | 0.818691i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.887750 | −0.0287873 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.5027 | −1.24722 | −0.623612 | − | 0.781734i | \(-0.714335\pi\) | ||||
−0.623612 | + | 0.781734i | \(0.714335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.04685 | − | 5.27729i | 0.0985936 | − | 0.170769i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.15256 | − | 5.46039i | −0.101908 | − | 0.176509i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.0758 | + | 16.3141i | −0.325364 | + | 0.526811i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.47578 | − | 11.2164i | −0.208896 | − | 0.361819i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.131848 | + | 0.228367i | −0.00424874 | + | 0.00735904i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30.9155 | −0.995206 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.0101 | −0.354061 | −0.177030 | − | 0.984205i | \(-0.556649\pi\) | ||||
−0.177030 | + | 0.984205i | \(0.556649\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.68071 | + | 11.5713i | −0.214615 | + | 0.371724i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.93481 | + | 10.2794i | 0.190457 | + | 0.329881i | 0.945402 | − | 0.325907i | \(-0.105670\pi\) |
−0.754945 | + | 0.655788i | \(0.772336\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.7985 | − | 0.528234i | −0.570594 | − | 0.0169344i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.57355 | − | 11.3857i | −0.210522 | − | 0.364635i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.2511 | − | 22.9517i | 0.423942 | − | 0.734289i | −0.572379 | − | 0.819989i | \(-0.693979\pi\) |
0.996321 | + | 0.0857003i | \(0.0273128\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.61490 | −0.275333 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.1235 | 0.834059 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.3654 | − | 24.8816i | 0.458185 | − | 0.793600i | −0.540680 | − | 0.841228i | \(-0.681833\pi\) |
0.998865 | + | 0.0476287i | \(0.0151664\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.1732 | − | 17.6206i | −0.324146 | − | 0.561438i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −57.9281 | − | 1.71922i | −1.84387 | − | 0.0547235i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.39738 | − | 4.15239i | −0.0762324 | − | 0.132038i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.6344 | + | 40.9359i | −0.750770 | + | 1.30037i | 0.196679 | + | 0.980468i | \(0.436984\pi\) |
−0.947450 | + | 0.319905i | \(0.896349\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −59.5645 | −1.89022 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.9360 | −1.07584 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.58911 | − | 16.6088i | 0.303690 | − | 0.526007i | −0.673279 | − | 0.739389i | \(-0.735115\pi\) |
0.976969 | + | 0.213382i | \(0.0684479\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.9555 | + | 24.1717i | 0.441534 | + | 0.764759i |
(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 | 644.2.i.a.277.3 | yes | 14 | |
7.2 | even | 3 | inner | 644.2.i.a.93.3 | ✓ | 14 | |
7.3 | odd | 6 | 4508.2.a.l.1.3 | 7 | |||
7.4 | even | 3 | 4508.2.a.m.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
644.2.i.a.93.3 | ✓ | 14 | 7.2 | even | 3 | inner | |
644.2.i.a.277.3 | yes | 14 | 1.1 | even | 1 | trivial | |
4508.2.a.l.1.3 | 7 | 7.3 | odd | 6 | |||
4508.2.a.m.1.5 | 7 | 7.4 | even | 3 |