Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(17,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bl (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.3 | ||
Root | \(0.587308 - 2.01725i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.89 |
Dual form | 504.2.bl.a.17.3 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.587308 | + | 1.01725i | −0.262652 | + | 0.454926i | −0.966946 | − | 0.254982i | \(-0.917930\pi\) |
0.704294 | + | 0.709909i | \(0.251264\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.35282 | + | 1.21006i | 0.889281 | + | 0.457361i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.44725 | + | 0.835571i | −0.436363 | + | 0.251934i | −0.702054 | − | 0.712124i | \(-0.747733\pi\) |
0.265691 | + | 0.964058i | \(0.414400\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.14525i | 0.317635i | 0.987308 | + | 0.158818i | \(0.0507682\pi\) | ||||
−0.987308 | + | 0.158818i | \(0.949232\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.07609 | + | 3.59589i | 0.503525 | + | 0.872131i | 0.999992 | + | 0.00407535i | \(0.00129723\pi\) |
−0.496466 | + | 0.868056i | \(0.665369\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.83453 | + | 1.05917i | 0.420870 | + | 0.242989i | 0.695449 | − | 0.718575i | \(-0.255205\pi\) |
−0.274579 | + | 0.961564i | \(0.588539\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.22379 | − | 2.43860i | −0.880720 | − | 0.508484i | −0.00982439 | − | 0.999952i | \(-0.503127\pi\) |
−0.870896 | + | 0.491468i | \(0.836461\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.81014 | + | 3.13525i | 0.362028 | + | 0.627051i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.32591i | 1.54608i | 0.634355 | + | 0.773042i | \(0.281266\pi\) | ||||
−0.634355 | + | 0.773042i | \(0.718734\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.18124 | − | 4.14609i | 1.28979 | − | 0.744660i | 0.311173 | − | 0.950353i | \(-0.399278\pi\) |
0.978617 | + | 0.205693i | \(0.0659448\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.61276 | + | 1.68272i | −0.441637 | + | 0.284431i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.19996 | + | 3.81045i | −0.361672 | + | 0.626434i | −0.988236 | − | 0.152936i | \(-0.951127\pi\) |
0.626564 | + | 0.779370i | \(0.284461\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.67577 | 0.417885 | 0.208942 | − | 0.977928i | \(-0.432998\pi\) | ||||
0.208942 | + | 0.977928i | \(0.432998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.08536 | 0.623011 | 0.311505 | − | 0.950244i | \(-0.399167\pi\) | ||||
0.311505 | + | 0.950244i | \(0.399167\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.75282 | − | 3.03597i | 0.255674 | − | 0.442841i | −0.709404 | − | 0.704802i | \(-0.751036\pi\) |
0.965078 | + | 0.261961i | \(0.0843692\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.07150 | + | 5.69411i | 0.581643 | + | 0.813444i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.59764 | − | 0.922398i | 0.219453 | − | 0.126701i | −0.386244 | − | 0.922397i | \(-0.626228\pi\) |
0.605697 | + | 0.795695i | \(0.292894\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.96295i | − | 0.264684i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.98667 | − | 5.17306i | −0.388831 | − | 0.673475i | 0.603462 | − | 0.797392i | \(-0.293788\pi\) |
−0.992293 | + | 0.123917i | \(0.960454\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.8011 | − | 7.39071i | −1.63901 | − | 0.946284i | −0.981174 | − | 0.193124i | \(-0.938138\pi\) |
−0.657838 | − | 0.753160i | \(-0.728529\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.16500 | − | 0.672614i | −0.144501 | − | 0.0834275i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.22435 | − | 7.31679i | −0.516087 | − | 0.893889i | −0.999826 | − | 0.0186762i | \(-0.994055\pi\) |
0.483739 | − | 0.875212i | \(-0.339279\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.48320i | − | 0.650736i | −0.945587 | − | 0.325368i | \(-0.894512\pi\) | ||
0.945587 | − | 0.325368i | \(-0.105488\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.846715 | − | 0.488851i | 0.0991004 | − | 0.0572157i | −0.449631 | − | 0.893215i | \(-0.648444\pi\) |
0.548731 | + | 0.835999i | \(0.315111\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.41621 | + | 0.214682i | −0.503274 | + | 0.0244652i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.56097 | + | 9.63187i | −0.625657 | + | 1.08367i | 0.362756 | + | 0.931884i | \(0.381836\pi\) |
−0.988413 | + | 0.151786i | \(0.951497\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.2258 | 1.12242 | 0.561212 | − | 0.827672i | \(-0.310335\pi\) | ||||
0.561212 | + | 0.827672i | \(0.310335\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.87721 | −0.529007 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.29987 | − | 10.9117i | 0.667785 | − | 1.15664i | −0.310737 | − | 0.950496i | \(-0.600576\pi\) |
0.978522 | − | 0.206142i | \(-0.0660909\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.38582 | + | 2.69456i | −0.145274 | + | 0.282467i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.15487 | + | 1.24411i | −0.221085 | + | 0.127643i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.52049i | − | 0.966660i | −0.875438 | − | 0.483330i | \(-0.839427\pi\) | ||
0.875438 | − | 0.483330i | \(-0.160573\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.65944 | + | 16.7306i | 0.961150 | + | 1.66476i | 0.719621 | + | 0.694367i | \(0.244315\pi\) |
0.241528 | + | 0.970394i | \(0.422351\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.0730 | − | 7.54769i | −1.28812 | − | 0.743696i | −0.309801 | − | 0.950801i | \(-0.600262\pi\) |
−0.978319 | + | 0.207105i | \(0.933596\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.46986 | − | 5.46743i | −0.915486 | − | 0.528556i | −0.0332936 | − | 0.999446i | \(-0.510600\pi\) |
−0.882192 | + | 0.470890i | \(0.843933\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.25885 | − | 5.64449i | −0.312141 | − | 0.540644i | 0.666685 | − | 0.745340i | \(-0.267713\pi\) |
−0.978826 | + | 0.204696i | \(0.934379\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.8743i | − | 1.02296i | −0.859294 | − | 0.511482i | \(-0.829097\pi\) | ||
0.859294 | − | 0.511482i | \(-0.170903\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.96132 | − | 2.86442i | 0.462646 | − | 0.267109i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.533405 | + | 10.9727i | 0.0488972 | + | 1.00586i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.10364 | + | 7.10772i | −0.373058 | + | 0.646156i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.1255 | −0.905653 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.56264 | −0.138662 | −0.0693308 | − | 0.997594i | \(-0.522086\pi\) | ||||
−0.0693308 | + | 0.997594i | \(0.522086\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2969 | − | 17.8347i | 0.899642 | − | 1.55823i | 0.0716899 | − | 0.997427i | \(-0.477161\pi\) |
0.827952 | − | 0.560799i | \(-0.189506\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.03466 | + | 4.71192i | 0.263138 | + | 0.408575i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.4299 | − | 10.6405i | 1.57457 | − | 0.909078i | 0.578972 | − | 0.815348i | \(-0.303454\pi\) |
0.995598 | − | 0.0937303i | \(-0.0298791\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.50746i | − | 0.551955i | −0.961164 | − | 0.275978i | \(-0.910998\pi\) | ||
0.961164 | − | 0.275978i | \(-0.0890016\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.956937 | − | 1.65746i | −0.0800231 | − | 0.138604i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.46951 | − | 4.88987i | −0.703354 | − | 0.406082i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.4565 | − | 7.19178i | −1.02048 | − | 0.589173i | −0.106236 | − | 0.994341i | \(-0.533880\pi\) |
−0.914242 | + | 0.405168i | \(0.867213\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.12846 | − | 8.88276i | −0.417348 | − | 0.722869i | 0.578323 | − | 0.815808i | \(-0.303707\pi\) |
−0.995672 | + | 0.0929389i | \(0.970374\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.74013i | 0.782346i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.399926 | − | 0.230897i | 0.0319176 | − | 0.0184276i | −0.483956 | − | 0.875092i | \(-0.660801\pi\) |
0.515874 | + | 0.856665i | \(0.327467\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.98693 | − | 10.8486i | −0.550648 | − | 0.854992i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.1644 | + | 19.3374i | −0.874467 | + | 1.51462i | −0.0171370 | + | 0.999853i | \(0.505455\pi\) |
−0.857330 | + | 0.514768i | \(0.827878\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.42604 | 0.419879 | 0.209940 | − | 0.977714i | \(-0.432673\pi\) | ||||
0.209940 | + | 0.977714i | \(0.432673\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6884 | 0.899108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.75719 | + | 8.23970i | −0.361683 | + | 0.626453i | −0.988238 | − | 0.152924i | \(-0.951131\pi\) |
0.626555 | + | 0.779377i | \(0.284464\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.465076 | + | 9.56706i | 0.0351564 | + | 0.723202i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.95968 | + | 1.13142i | −0.146474 | + | 0.0845665i | −0.571446 | − | 0.820640i | \(-0.693617\pi\) |
0.424972 | + | 0.905206i | \(0.360284\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.7987i | − | 1.62029i | −0.586231 | − | 0.810144i | \(-0.699389\pi\) | ||
0.586231 | − | 0.810144i | \(-0.300611\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.58411 | − | 4.47581i | −0.189988 | − | 0.329068i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00924 | − | 3.46944i | −0.439439 | − | 0.253710i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.8301 | + | 10.8716i | 1.36250 | + | 0.786638i | 0.989956 | − | 0.141378i | \(-0.0451533\pi\) |
0.372541 | + | 0.928016i | \(0.378487\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.8259 | + | 18.7510i | 0.779266 | + | 1.34973i | 0.932365 | + | 0.361518i | \(0.117741\pi\) |
−0.153099 | + | 0.988211i | \(0.548925\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.58787i | 0.398119i | 0.979987 | + | 0.199060i | \(0.0637887\pi\) | ||||
−0.979987 | + | 0.199060i | \(0.936211\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.2081 | − | 8.20308i | 1.00719 | − | 0.581501i | 0.0968215 | − | 0.995302i | \(-0.469132\pi\) |
0.910367 | + | 0.413801i | \(0.135799\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.0749 | + | 19.5894i | −0.707118 | + | 1.37490i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.57150 | + | 2.72192i | −0.109758 | + | 0.190107i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.54003 | −0.244869 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.11777 | 0.558850 | 0.279425 | − | 0.960168i | \(-0.409856\pi\) | ||||
0.279425 | + | 0.960168i | \(0.409856\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.39936 | + | 4.15581i | −0.163635 | + | 0.283424i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.9132 | − | 1.06525i | 1.48756 | − | 0.0723138i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.11819 | + | 2.37764i | −0.277020 | + | 0.159937i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.1486i | 1.41621i | 0.706105 | + | 0.708107i | \(0.250451\pi\) | ||||
−0.706105 | + | 0.708107i | \(0.749549\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.7990 | + | 20.4365i | 0.783130 | + | 1.35642i | 0.930110 | + | 0.367281i | \(0.119711\pi\) |
−0.146980 | + | 0.989139i | \(0.546955\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.969507 | − | 0.559745i | −0.0640668 | − | 0.0369890i | 0.467624 | − | 0.883927i | \(-0.345110\pi\) |
−0.531691 | + | 0.846938i | \(0.678443\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.9299 | − | 12.0839i | −1.37116 | − | 0.791642i | −0.380089 | − | 0.924950i | \(-0.624107\pi\) |
−0.991075 | + | 0.133309i | \(0.957440\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.05888 | + | 3.56609i | 0.134307 | + | 0.232626i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.484062i | 0.0313114i | 0.999877 | + | 0.0156557i | \(0.00498356\pi\) | ||||
−0.999877 | + | 0.0156557i | \(0.995016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3783 | − | 6.56924i | 0.732938 | − | 0.423162i | −0.0865578 | − | 0.996247i | \(-0.527587\pi\) |
0.819496 | + | 0.573085i | \(0.194253\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.18354 | + | 0.797524i | −0.522827 | + | 0.0509519i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.21301 | + | 2.10099i | −0.0771820 | + | 0.133683i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.4221 | 0.847193 | 0.423597 | − | 0.905851i | \(-0.360767\pi\) | ||||
0.423597 | + | 0.905851i | \(0.360767\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.15051 | 0.512418 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.22980 | − | 9.05827i | 0.326226 | − | 0.565040i | −0.655534 | − | 0.755166i | \(-0.727556\pi\) |
0.981760 | + | 0.190126i | \(0.0608897\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.78699 | + | 6.30320i | −0.608134 | + | 0.391662i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.4998 | + | 11.8356i | −1.26407 | + | 0.729813i | −0.973860 | − | 0.227148i | \(-0.927060\pi\) |
−0.290214 | + | 0.956962i | \(0.593726\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.16693i | 0.133113i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.05065 | + | 15.6762i | 0.551828 | + | 0.955794i | 0.998143 | + | 0.0609178i | \(0.0194028\pi\) |
−0.446315 | + | 0.894876i | \(0.647264\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.79002 | + | 3.34287i | 0.351718 | + | 0.203065i | 0.665442 | − | 0.746450i | \(-0.268243\pi\) |
−0.313723 | + | 0.949514i | \(0.601576\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.23945 | − | 3.02500i | −0.315951 | − | 0.182414i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.72478 | + | 2.98741i | 0.103632 | + | 0.179496i | 0.913179 | − | 0.407560i | \(-0.133620\pi\) |
−0.809546 | + | 0.587056i | \(0.800287\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.58198i | 0.571613i | 0.958287 | + | 0.285807i | \(0.0922615\pi\) | ||||
−0.958287 | + | 0.285807i | \(0.907739\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.02161 | − | 4.05393i | 0.417391 | − | 0.240981i | −0.276569 | − | 0.960994i | \(-0.589198\pi\) |
0.693961 | + | 0.720013i | \(0.255864\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.29559 | + | 3.23785i | 0.371617 | + | 0.191124i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.120279 | + | 0.208330i | −0.00707526 | + | 0.0122547i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.9122 | −0.754339 | −0.377170 | − | 0.926144i | \(-0.623103\pi\) | ||||
−0.377170 | + | 0.926144i | \(0.623103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.01637 | 0.408509 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.79281 | − | 4.83729i | 0.161512 | − | 0.279748i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.61209 | + | 4.94353i | 0.554032 | + | 0.284941i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.0364 | − | 8.68124i | 0.860979 | − | 0.497087i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.9163i | 0.680099i | 0.940408 | + | 0.340049i | \(0.110444\pi\) | ||||
−0.940408 | + | 0.340049i | \(0.889556\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.3295 | − | 26.5516i | −0.869259 | − | 1.50560i | −0.862755 | − | 0.505622i | \(-0.831263\pi\) |
−0.00650358 | − | 0.999979i | \(-0.502070\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.14799 | + | 4.70425i | 0.460552 | + | 0.265900i | 0.712276 | − | 0.701899i | \(-0.247664\pi\) |
−0.251724 | + | 0.967799i | \(0.580998\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.23712 | − | 0.714251i | −0.0694835 | − | 0.0401163i | 0.464856 | − | 0.885386i | \(-0.346106\pi\) |
−0.534339 | + | 0.845270i | \(0.679440\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.95689 | − | 12.0497i | −0.389511 | − | 0.674653i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.79569i | 0.489405i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.59065 | + | 2.07306i | −0.199173 | + | 0.114993i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.79776 | − | 5.02206i | 0.429904 | − | 0.276875i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.20798 | − | 12.4846i | 0.396187 | − | 0.686215i | −0.597065 | − | 0.802193i | \(-0.703667\pi\) |
0.993252 | + | 0.115977i | \(0.0370000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.92398 | 0.542205 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.62914 | 0.197692 | 0.0988460 | − | 0.995103i | \(-0.468485\pi\) | ||||
0.0988460 | + | 0.995103i | \(0.468485\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.92871 | + | 12.0009i | −0.375211 | + | 0.649884i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.68927 | + | 18.3240i | 0.145207 | + | 0.989401i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.7433 | + | 14.8629i | −1.38197 | + | 0.797883i | −0.992393 | − | 0.123109i | \(-0.960714\pi\) |
−0.389581 | + | 0.920992i | \(0.627380\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.41027i | − | 0.289605i | −0.989461 | − | 0.144802i | \(-0.953745\pi\) | ||
0.989461 | − | 0.144802i | \(-0.0462547\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.02520 | + | 12.1680i | 0.373914 | + | 0.647637i | 0.990164 | − | 0.139913i | \(-0.0446824\pi\) |
−0.616250 | + | 0.787550i | \(0.711349\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.57777 | + | 3.22032i | 0.296037 | + | 0.170917i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.69438 | + | 3.86500i | 0.353316 | + | 0.203987i | 0.666145 | − | 0.745823i | \(-0.267943\pi\) |
−0.312829 | + | 0.949810i | \(0.601277\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.25633 | − | 12.5683i | −0.381912 | − | 0.661491i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.14842i | 0.0601112i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.80239 | − | 3.92736i | 0.355082 | − | 0.205006i | −0.311839 | − | 0.950135i | \(-0.600945\pi\) |
0.666921 | + | 0.745128i | \(0.267612\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.87512 | − | 0.236990i | 0.253103 | − | 0.0123039i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.94428 | + | 6.83169i | −0.204227 | + | 0.353731i | −0.949886 | − | 0.312596i | \(-0.898801\pi\) |
0.745659 | + | 0.666327i | \(0.232135\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.53525 | −0.491090 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.9349 | −0.613052 | −0.306526 | − | 0.951862i | \(-0.599167\pi\) | ||||
−0.306526 | + | 0.951862i | \(0.599167\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.35936 | − | 2.35449i | 0.0694603 | − | 0.120309i | −0.829204 | − | 0.558947i | \(-0.811206\pi\) |
0.898664 | + | 0.438638i | \(0.144539\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.37529 | − | 4.61846i | 0.121056 | − | 0.235378i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.2510 | − | 9.95985i | 0.874659 | − | 0.504984i | 0.00576514 | − | 0.999983i | \(-0.498165\pi\) |
0.868894 | + | 0.494999i | \(0.164832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 20.2510i | − | 1.02414i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.53199 | − | 11.3137i | −0.328660 | − | 0.569256i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.5532 | − | 8.40230i | −0.730405 | − | 0.421699i | 0.0881655 | − | 0.996106i | \(-0.471900\pi\) |
−0.818570 | + | 0.574406i | \(0.805233\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.31347 | + | 4.22244i | 0.365217 | + | 0.210858i | 0.671367 | − | 0.741125i | \(-0.265707\pi\) |
−0.306150 | + | 0.951983i | \(0.599041\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.74831 | + | 8.22432i | 0.236530 | + | 0.409682i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7.35290i | − | 0.364470i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.5958 | + | 12.4684i | −1.06785 | + | 0.616521i | −0.927592 | − | 0.373595i | \(-0.878125\pi\) |
−0.140253 | + | 0.990116i | \(0.544792\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.767359 | − | 15.7853i | −0.0377593 | − | 0.776745i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00567 | + | 10.4021i | −0.294807 | + | 0.510620i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.2386 | 1.57496 | 0.787480 | − | 0.616340i | \(-0.211385\pi\) | ||||
0.787480 | + | 0.616340i | \(0.211385\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.4958 | −1.77869 | −0.889347 | − | 0.457232i | \(-0.848841\pi\) | ||||
−0.889347 | + | 0.457232i | \(0.848841\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.51602 | + | 13.0181i | −0.364580 | + | 0.631472i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.1754 | − | 32.8791i | −1.02475 | − | 1.59113i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.1694 | − | 9.33541i | 0.778853 | − | 0.449671i | −0.0571709 | − | 0.998364i | \(-0.518208\pi\) |
0.836023 | + | 0.548694i | \(0.184875\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.4261i | 0.597163i | 0.954384 | + | 0.298581i | \(0.0965134\pi\) | ||||
−0.954384 | + | 0.298581i | \(0.903487\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.16577 | − | 8.94738i | −0.247112 | − | 0.428011i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.2673 | − | 9.96928i | −0.824123 | − | 0.475808i | 0.0277131 | − | 0.999616i | \(-0.491178\pi\) |
−0.851836 | + | 0.523808i | \(0.824511\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.3854 | − | 14.6563i | −1.20610 | − | 0.696340i | −0.244192 | − | 0.969727i | \(-0.578523\pi\) |
−0.961904 | + | 0.273387i | \(0.911856\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.39993 | + | 12.8170i | 0.350790 | + | 0.607586i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.58492i | − | 0.169183i | −0.996416 | − | 0.0845915i | \(-0.973041\pi\) | ||
0.996416 | − | 0.0845915i | \(-0.0269585\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.87251 | + | 2.23579i | −0.182349 | + | 0.105279i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.92713 | − | 2.99226i | −0.0903453 | − | 0.140279i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.39741 | − | 14.5447i | 0.392814 | − | 0.680375i | −0.600005 | − | 0.799996i | \(-0.704835\pi\) |
0.992820 | + | 0.119622i | \(0.0381681\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.3775 | 0.529903 | 0.264951 | − | 0.964262i | \(-0.414644\pi\) | ||||
0.264951 | + | 0.964262i | \(0.414644\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.48145 | 0.115323 | 0.0576613 | − | 0.998336i | \(-0.481636\pi\) | ||||
0.0576613 | + | 0.998336i | \(0.481636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.9839 | − | 20.7568i | 0.554550 | − | 0.960508i | −0.443389 | − | 0.896329i | \(-0.646224\pi\) |
0.997938 | − | 0.0641788i | \(-0.0204428\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.08536 | − | 22.3268i | −0.0501171 | − | 1.03096i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.91254 | + | 3.41360i | −0.271859 | + | 0.156958i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.66896i | 0.351876i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.2447 | − | 19.4764i | −0.513784 | − | 0.889899i | −0.999872 | − | 0.0159898i | \(-0.994910\pi\) |
0.486089 | − | 0.873910i | \(-0.338423\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.36391 | − | 2.51951i | −0.198977 | − | 0.114880i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.68469 | + | 5.59146i | 0.439759 | + | 0.253895i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.9567 | − | 18.9776i | −0.496497 | − | 0.859958i | 0.503495 | − | 0.863998i | \(-0.332047\pi\) |
−0.999992 | + | 0.00404053i | \(0.998714\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 22.5875i | − | 1.01936i | −0.860364 | − | 0.509681i | \(-0.829764\pi\) | ||
0.860364 | − | 0.509681i | \(-0.170236\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29.9391 | + | 17.2853i | −1.34839 | + | 0.778492i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.63501 | − | 12.9010i | 0.297621 | − | 0.578687i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.3299 | − | 24.8201i | 0.641495 | − | 1.11110i | −0.343604 | − | 0.939115i | \(-0.611648\pi\) |
0.985099 | − | 0.171987i | \(-0.0550188\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.4762 | −1.76016 | −0.880078 | − | 0.474830i | \(-0.842510\pi\) | ||||
−0.880078 | + | 0.474830i | \(0.842510\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.6922 | −1.00979 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.73501 | − | 4.73717i | 0.121227 | − | 0.209971i | −0.799025 | − | 0.601298i | \(-0.794650\pi\) |
0.920252 | + | 0.391327i | \(0.127984\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.58370 | − | 0.125600i | 0.114296 | − | 0.00555620i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.3557 | − | 8.86563i | 0.676654 | − | 0.390666i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.85841i | 0.257652i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.1796 | + | 26.2918i | 0.665029 | + | 1.15186i | 0.979277 | + | 0.202524i | \(0.0649143\pi\) |
−0.314248 | + | 0.949341i | \(0.601752\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.4905 | + | 18.7584i | 1.42071 | + | 0.820248i | 0.996360 | − | 0.0852494i | \(-0.0271687\pi\) |
0.424352 | + | 0.905497i | \(0.360502\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.8178 | + | 17.2153i | 1.29888 | + | 0.749911i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.393577 | + | 0.681695i | 0.0171120 | + | 0.0296389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.06442i | 0.132735i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.1234 | − | 6.42212i | 0.480908 | − | 0.277652i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.6503 | − | 4.83878i | −0.458742 | − | 0.208421i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5259 | − | 18.2314i | 0.452543 | − | 0.783827i | −0.546000 | − | 0.837785i | \(-0.683850\pi\) |
0.998543 | + | 0.0539578i | \(0.0171836\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.65578 | 0.327938 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.57620 | 0.110150 | 0.0550751 | − | 0.998482i | \(-0.482460\pi\) | ||||
0.0550751 | + | 0.998482i | \(0.482460\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.81853 | + | 15.2741i | −0.375682 | + | 0.650700i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.7391 | + | 15.9329i | −1.05201 | + | 0.677537i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.7118 | − | 11.3806i | 0.835215 | − | 0.482211i | −0.0204201 | − | 0.999791i | \(-0.506500\pi\) |
0.855635 | + | 0.517580i | \(0.173167\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.67875i | 0.197890i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.2404 | − | 22.9331i | −0.558018 | − | 0.966516i | −0.997662 | − | 0.0683439i | \(-0.978229\pi\) |
0.439643 | − | 0.898172i | \(-0.355105\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.0618 | + | 6.38654i | 0.465374 | + | 0.268684i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.2254 | + | 8.79038i | 0.638281 | + | 0.368512i | 0.783952 | − | 0.620821i | \(-0.213201\pi\) |
−0.145671 | + | 0.989333i | \(0.546534\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.1117 | − | 20.9780i | −0.506857 | − | 0.877903i | −0.999969 | − | 0.00793637i | \(-0.997474\pi\) |
0.493111 | − | 0.869966i | \(-0.335860\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 17.6569i | − | 0.736342i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.5934 | + | 10.7349i | −0.774052 | + | 0.446899i | −0.834318 | − | 0.551283i | \(-0.814138\pi\) |
0.0602665 | + | 0.998182i | \(0.480805\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.0594 | + | 12.3738i | 0.998151 | + | 0.513352i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.54146 | + | 2.66988i | −0.0638407 | + | 0.110575i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.2492 | −1.24852 | −0.624260 | − | 0.781217i | \(-0.714599\pi\) | ||||
−0.624260 | + | 0.781217i | \(0.714599\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.5656 | 0.723778 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.9023 | + | 29.2757i | −0.694095 | + | 1.20221i | 0.276390 | + | 0.961046i | \(0.410862\pi\) |
−0.970485 | + | 0.241162i | \(0.922472\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.4752 | − | 5.90172i | −0.470436 | − | 0.241947i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.0568 | + | 19.0854i | −1.35066 | + | 0.779806i | −0.988343 | − | 0.152247i | \(-0.951349\pi\) |
−0.362322 | + | 0.932053i | \(0.618016\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 37.6195i | − | 1.53453i | −0.641329 | − | 0.767266i | \(-0.721616\pi\) | ||
0.641329 | − | 0.767266i | \(-0.278384\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.82020 | − | 8.34883i | −0.195969 | − | 0.339428i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.749770 | − | 0.432880i | −0.0304322 | − | 0.0175700i | 0.484707 | − | 0.874677i | \(-0.338926\pi\) |
−0.515139 | + | 0.857107i | \(0.672260\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.47694 | + | 2.00741i | 0.140662 | + | 0.0812112i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.5564 | + | 18.2842i | 0.426368 | + | 0.738491i | 0.996547 | − | 0.0830296i | \(-0.0264596\pi\) |
−0.570179 | + | 0.821520i | \(0.693126\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.6262i | 0.427795i | 0.976856 | + | 0.213897i | \(0.0686158\pi\) | ||||
−0.976856 | + | 0.213897i | \(0.931384\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.8636 | + | 11.4683i | −0.798385 | + | 0.460948i | −0.842906 | − | 0.538060i | \(-0.819157\pi\) |
0.0445209 | + | 0.999008i | \(0.485824\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.0263 | − | 18.0500i | 1.12285 | − | 0.723158i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.10391 | + | 5.37613i | −0.124156 | + | 0.215045i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.2693 | −0.728443 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.19211 | −0.166885 | −0.0834425 | − | 0.996513i | \(-0.526592\pi\) | ||||
−0.0834425 | + | 0.996513i | \(0.526592\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.917748 | − | 1.58959i | 0.0364197 | − | 0.0630808i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.52118 | + | 4.66288i | −0.258379 | + | 0.184750i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.4895 | + | 8.94287i | −0.611799 | + | 0.353222i | −0.773669 | − | 0.633590i | \(-0.781581\pi\) |
0.161870 | + | 0.986812i | \(0.448247\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.8980i | 1.21850i | 0.792980 | + | 0.609248i | \(0.208529\pi\) | ||||
−0.792980 | + | 0.609248i | \(0.791471\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.81704 | − | 6.61130i | −0.150063 | − | 0.259917i | 0.781187 | − | 0.624297i | \(-0.214614\pi\) |
−0.931250 | + | 0.364380i | \(0.881281\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.64492 | + | 4.99114i | 0.339343 | + | 0.195920i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.2668 | + | 11.1237i | 0.753967 | + | 0.435303i | 0.827125 | − | 0.562017i | \(-0.189975\pi\) |
−0.0731587 | + | 0.997320i | \(0.523308\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0949 | + | 20.9489i | 0.472585 | + | 0.818542i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 8.74939i | − | 0.340828i | −0.985373 | − | 0.170414i | \(-0.945490\pi\) | ||
0.985373 | − | 0.170414i | \(-0.0545105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.46910 | − | 3.73493i | 0.251619 | − | 0.145272i | −0.368887 | − | 0.929474i | \(-0.620261\pi\) |
0.620505 | + | 0.784202i | \(0.286928\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.57546 | + | 0.319648i | −0.254985 | + | 0.0123954i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.3036 | − | 35.1669i | 0.786159 | − | 1.36167i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.7019 | 0.953605 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.388583 | −0.0149788 | −0.00748938 | − | 0.999972i | \(-0.502384\pi\) | ||||
−0.00748938 | + | 0.999972i | \(0.502384\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.45942 | − | 16.3842i | 0.363555 | − | 0.629696i | −0.624988 | − | 0.780634i | \(-0.714896\pi\) |
0.988543 | + | 0.150938i | \(0.0482295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.5204 | − | 22.4000i | 0.442112 | − | 0.859633i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.95105 | + | 2.85849i | −0.189447 | + | 0.109377i | −0.591723 | − | 0.806141i | \(-0.701552\pi\) |
0.402277 | + | 0.915518i | \(0.368219\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.9969i | 0.955084i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.05638 | + | 1.82970i | 0.0402447 | + | 0.0697059i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.7605 | + | 25.2652i | 1.66473 | + | 0.961132i | 0.970410 | + | 0.241465i | \(0.0776277\pi\) |
0.694319 | + | 0.719667i | \(0.255706\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.61969 | + | 3.82188i | 0.251099 | + | 0.144972i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.55513 | + | 9.62177i | 0.210416 | + | 0.364450i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.5025i | − | 0.547752i | −0.961765 | − | 0.273876i | \(-0.911694\pi\) | ||
0.961765 | − | 0.273876i | \(-0.0883058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.07180 | + | 4.66025i | −0.304434 | + | 0.175765i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.48178 | + | 51.0526i | 0.0933370 | + | 1.92003i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.03657 | − | 15.6518i | 0.339376 | − | 0.587816i | −0.644940 | − | 0.764233i | \(-0.723118\pi\) |
0.984315 | + | 0.176417i | \(0.0564509\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −40.4427 | −1.51459 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.24807 | 0.0840729 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.3720 | + | 43.9456i | −0.946216 | + | 1.63889i | −0.192918 | + | 0.981215i | \(0.561795\pi\) |
−0.753298 | + | 0.657679i | \(0.771538\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.6252 | − | 33.5775i | −0.805363 | − | 1.25049i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26.1039 | + | 15.0711i | −0.969473 | + | 0.559725i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.77139i | 0.251137i | 0.992085 | + | 0.125568i | \(0.0400755\pi\) | ||||
−0.992085 | + | 0.125568i | \(0.959925\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.48156 | + | 14.6905i | 0.313702 | + | 0.543347i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.8337 | + | 25.3074i | 1.61903 | + | 0.934750i | 0.987170 | + | 0.159671i | \(0.0510433\pi\) |
0.631864 | + | 0.775079i | \(0.282290\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.2274 | + | 7.05949i | 0.450402 | + | 0.260040i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.3510 | + | 26.5887i | 0.564695 | + | 0.978080i | 0.997078 | + | 0.0763904i | \(0.0243395\pi\) |
−0.432383 | + | 0.901690i | \(0.642327\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.18883i | 0.190360i | 0.995460 | + | 0.0951799i | \(0.0303426\pi\) | ||||
−0.995460 | + | 0.0951799i | \(0.969657\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.6316 | − | 8.44757i | 0.536061 | − | 0.309495i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.6649 | − | 24.3230i | −0.572384 | − | 0.888742i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.618608 | − | 1.07146i | 0.0225733 | − | 0.0390981i | −0.854518 | − | 0.519422i | \(-0.826147\pi\) |
0.877091 | + | 0.480324i | \(0.159481\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0479 | 0.438470 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 51.3970 | 1.86806 | 0.934028 | − | 0.357200i | \(-0.116268\pi\) | ||||
0.934028 | + | 0.357200i | \(0.116268\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.8191 | + | 25.6674i | −0.537190 | + | 0.930441i | 0.461864 | + | 0.886951i | \(0.347181\pi\) |
−0.999054 | + | 0.0434899i | \(0.986152\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.837289 | − | 17.2239i | −0.0303119 | − | 0.623545i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.92445 | − | 3.42048i | 0.213919 | − | 0.123506i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.1387i | 1.01471i | 0.861738 | + | 0.507354i | \(0.169376\pi\) | ||||
−0.861738 | + | 0.507354i | \(0.830624\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.95227 | − | 10.3096i | −0.214088 | − | 0.370812i | 0.738902 | − | 0.673813i | \(-0.235345\pi\) |
−0.952990 | + | 0.303001i | \(0.902011\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.9981 | + | 15.0100i | 0.933880 | + | 0.539176i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.90878 | + | 2.83408i | 0.175875 | + | 0.101542i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.58160 | + | 7.93557i | 0.163943 | + | 0.283957i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.542431i | 0.0193602i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.4945 | + | 17.0287i | −1.05137 | + | 0.607007i | −0.923031 | − | 0.384724i | \(-0.874296\pi\) |
−0.128335 | + | 0.991731i | \(0.540963\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.1585 | − | 25.5852i | 0.467864 | − | 0.909703i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.46421 | − | 14.6604i | 0.300573 | − | 0.520608i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.8088 | 1.16215 | 0.581074 | − | 0.813851i | \(-0.302633\pi\) | ||||
0.581074 | + | 0.813851i | \(0.302633\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.5560 | 0.514954 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.816939 | + | 1.41498i | −0.0288292 | + | 0.0499336i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.1392 | − | 0.735950i | 0.533587 | − | 0.0259388i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.88851 | − | 3.97708i | 0.242187 | − | 0.139827i | −0.373994 | − | 0.927431i | \(-0.622012\pi\) |
0.616182 | + | 0.787604i | \(0.288679\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.4200i | − | 0.787273i | −0.919266 | − | 0.393636i | \(-0.871217\pi\) | ||
0.919266 | − | 0.393636i | \(-0.128783\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.1139 | − | 22.7140i | −0.459361 | − | 0.795636i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.49471 | + | 4.32707i | 0.262207 | + | 0.151385i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.65642 | − | 2.68839i | −0.162510 | − | 0.0938254i | 0.416539 | − | 0.909118i | \(-0.363243\pi\) |
−0.579050 | + | 0.815292i | \(0.696576\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.55129 | + | 6.15102i | 0.123790 | + | 0.214411i | 0.921259 | − | 0.388949i | \(-0.127162\pi\) |
−0.797469 | + | 0.603360i | \(0.793828\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.1228i | 1.70817i | 0.520135 | + | 0.854084i | \(0.325882\pi\) | ||||
−0.520135 | + | 0.854084i | \(0.674118\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.147346 | + | 0.0850705i | −0.00511755 | + | 0.00295462i | −0.502557 | − | 0.864544i | \(-0.667607\pi\) |
0.497439 | + | 0.867499i | \(0.334274\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.0226 | + | 26.4621i | −0.416558 | + | 0.916859i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.18675 | + | 5.51962i | −0.110282 | + | 0.191014i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.2416 | −1.49287 | −0.746434 | − | 0.665460i | \(-0.768235\pi\) | ||||
−0.746434 | + | 0.665460i | \(0.768235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −40.3208 | −1.39037 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.86469 | + | 11.8900i | −0.236152 | + | 0.409028i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.2559 | + | 11.7575i | −0.627280 | + | 0.403992i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.5843 | − | 10.7297i | 0.637063 | − | 0.367809i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.3097i | 0.661153i | 0.943779 | + | 0.330577i | \(0.107243\pi\) | ||||
−0.943779 | + | 0.330577i | \(0.892757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.7997 | − | 46.4185i | −0.915461 | − | 1.58562i | −0.806225 | − | 0.591608i | \(-0.798493\pi\) |
−0.109235 | − | 0.994016i | \(-0.534840\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.59883 | + | 1.50044i | 0.0886710 | + | 0.0511943i | 0.543680 | − | 0.839293i | \(-0.317031\pi\) |
−0.455009 | + | 0.890487i | \(0.650364\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.0064 | + | 20.7883i | 1.22567 | + | 0.707641i | 0.966121 | − | 0.258089i | \(-0.0830927\pi\) |
0.259549 | + | 0.965730i | \(0.416426\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.58787 | − | 9.67847i | −0.189993 | − | 0.329078i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 18.5863i | − | 0.630498i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.37956 | − | 4.83794i | 0.283930 | − | 0.163927i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.8235 | − | 12.2525i | −0.805380 | − | 0.414210i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.7460 | − | 30.7371i | 0.599241 | − | 1.03792i | −0.393692 | − | 0.919242i | \(-0.628802\pi\) |
0.992933 | − | 0.118674i | \(-0.0378644\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.7343 | −0.429030 | −0.214515 | − | 0.976721i | \(-0.568817\pi\) | ||||
−0.214515 | + | 0.976721i | \(0.568817\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.0274 | −0.976849 | −0.488425 | − | 0.872606i | \(-0.662428\pi\) | ||||
−0.488425 | + | 0.872606i | \(0.662428\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.3243 | + | 38.6668i | −0.749575 | + | 1.29830i | 0.198451 | + | 0.980111i | \(0.436409\pi\) |
−0.948026 | + | 0.318192i | \(0.896924\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.67660 | − | 1.89089i | −0.123309 | − | 0.0634183i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.43118 | − | 3.71305i | 0.215211 | − | 0.124252i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.65797i | − | 0.0888462i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34.5200 | + | 59.7904i | 1.15131 | + | 1.99412i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.63368 | + | 3.82996i | 0.221000 | + | 0.127594i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.1747 | + | 12.8026i | 0.737112 | + | 0.425572i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.8863 | − | 25.7838i | −0.494291 | − | 0.856137i | 0.505687 | − | 0.862717i | \(-0.331239\pi\) |
−0.999978 | + | 0.00657974i | \(0.997906\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 33.4911i | − | 1.10961i | −0.831981 | − | 0.554804i | \(-0.812793\pi\) | ||
0.831981 | − | 0.554804i | \(-0.187207\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.7993 | + | 8.54436i | −0.489784 | + | 0.282777i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.8078 | − | 29.5020i | 1.51271 | − | 0.974240i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.79202 | + | 11.7641i | −0.224048 | + | 0.388062i | −0.956033 | − | 0.293258i | \(-0.905261\pi\) |
0.731985 | + | 0.681320i | \(0.238594\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.27963 | 0.206697 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.9290 | −0.523741 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.0268156 | − | 0.0464460i | 0.000879793 | − | 0.00152385i | −0.865585 | − | 0.500762i | \(-0.833053\pi\) |
0.866465 | + | 0.499238i | \(0.166387\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.43828 | + | 14.7584i | 0.0471376 | + | 0.483687i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.05854 | − | 4.07525i | 0.230839 | − | 0.133275i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.3633i | 0.469230i | 0.972088 | + | 0.234615i | \(0.0753829\pi\) | ||||
−0.972088 | + | 0.234615i | \(0.924617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.9562 | − | 29.3690i | −0.552757 | − | 0.957403i | −0.998074 | − | 0.0620301i | \(-0.980243\pi\) |
0.445318 | − | 0.895373i | \(-0.353091\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.3019 | − | 6.52514i | −0.368040 | − | 0.212488i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.3993 | − | 16.3964i | −0.922854 | − | 0.532810i | −0.0383093 | − | 0.999266i | \(-0.512197\pi\) |
−0.884544 | + | 0.466456i | \(0.845531\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.559856 | + | 0.969700i | 0.0181737 | + | 0.0314778i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.2186i | 0.816912i | 0.912778 | + | 0.408456i | \(0.133933\pi\) | ||||
−0.912778 | + | 0.408456i | \(0.866067\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.1181 | + | 12.7699i | −0.715725 | + | 0.413224i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 56.2377 | − | 2.73384i | 1.81601 | − | 0.0882803i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.8802 | − | 32.7014i | 0.609038 | − | 1.05488i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.4326 | −0.818703 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.0565 | −0.484183 | −0.242091 | − | 0.970253i | \(-0.577833\pi\) | ||||
−0.242091 | + | 0.970253i | \(0.577833\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.30245 | − | 10.9162i | 0.202255 | − | 0.350316i | −0.747000 | − | 0.664825i | \(-0.768506\pi\) |
0.949255 | + | 0.314508i | \(0.101840\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.87443 | − | 15.3109i | 0.252443 | − | 0.490844i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.0439 | + | 26.5835i | −1.47307 | + | 0.850480i | −0.999541 | − | 0.0302958i | \(-0.990355\pi\) |
−0.473534 | + | 0.880776i | \(0.657022\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.0560i | 0.672951i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.43065 | − | 7.67412i | −0.141316 | − | 0.244766i | 0.786677 | − | 0.617365i | \(-0.211800\pi\) |
−0.927992 | + | 0.372599i | \(0.878467\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.68424 | − | 3.28180i | −0.181115 | − | 0.104567i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.2557 | − | 9.96256i | −0.548698 | − | 0.316791i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.9235 | + | 25.8482i | 0.474059 | + | 0.821095i | 0.999559 | − | 0.0296992i | \(-0.00945495\pi\) |
−0.525500 | + | 0.850794i | \(0.676122\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.2709i | 0.610929i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0516 | − | 6.38062i | 0.350006 | − | 0.202076i | −0.314682 | − | 0.949197i | \(-0.601898\pi\) |
0.664688 | + | 0.747121i | \(0.268564\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.2.bl.a.89.3 | yes | 16 | |
3.2 | odd | 2 | inner | 504.2.bl.a.89.6 | yes | 16 | |
4.3 | odd | 2 | 1008.2.bt.d.593.3 | 16 | |||
7.2 | even | 3 | 3528.2.k.b.881.11 | 16 | |||
7.3 | odd | 6 | inner | 504.2.bl.a.17.6 | yes | 16 | |
7.4 | even | 3 | 3528.2.bl.a.521.3 | 16 | |||
7.5 | odd | 6 | 3528.2.k.b.881.5 | 16 | |||
7.6 | odd | 2 | 3528.2.bl.a.1097.6 | 16 | |||
12.11 | even | 2 | 1008.2.bt.d.593.6 | 16 | |||
21.2 | odd | 6 | 3528.2.k.b.881.6 | 16 | |||
21.5 | even | 6 | 3528.2.k.b.881.12 | 16 | |||
21.11 | odd | 6 | 3528.2.bl.a.521.6 | 16 | |||
21.17 | even | 6 | inner | 504.2.bl.a.17.3 | ✓ | 16 | |
21.20 | even | 2 | 3528.2.bl.a.1097.3 | 16 | |||
28.3 | even | 6 | 1008.2.bt.d.17.6 | 16 | |||
28.19 | even | 6 | 7056.2.k.h.881.6 | 16 | |||
28.23 | odd | 6 | 7056.2.k.h.881.12 | 16 | |||
84.23 | even | 6 | 7056.2.k.h.881.5 | 16 | |||
84.47 | odd | 6 | 7056.2.k.h.881.11 | 16 | |||
84.59 | odd | 6 | 1008.2.bt.d.17.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bl.a.17.3 | ✓ | 16 | 21.17 | even | 6 | inner | |
504.2.bl.a.17.6 | yes | 16 | 7.3 | odd | 6 | inner | |
504.2.bl.a.89.3 | yes | 16 | 1.1 | even | 1 | trivial | |
504.2.bl.a.89.6 | yes | 16 | 3.2 | odd | 2 | inner | |
1008.2.bt.d.17.3 | 16 | 84.59 | odd | 6 | |||
1008.2.bt.d.17.6 | 16 | 28.3 | even | 6 | |||
1008.2.bt.d.593.3 | 16 | 4.3 | odd | 2 | |||
1008.2.bt.d.593.6 | 16 | 12.11 | even | 2 | |||
3528.2.k.b.881.5 | 16 | 7.5 | odd | 6 | |||
3528.2.k.b.881.6 | 16 | 21.2 | odd | 6 | |||
3528.2.k.b.881.11 | 16 | 7.2 | even | 3 | |||
3528.2.k.b.881.12 | 16 | 21.5 | even | 6 | |||
3528.2.bl.a.521.3 | 16 | 7.4 | even | 3 | |||
3528.2.bl.a.521.6 | 16 | 21.11 | odd | 6 | |||
3528.2.bl.a.1097.3 | 16 | 21.20 | even | 2 | |||
3528.2.bl.a.1097.6 | 16 | 7.6 | odd | 2 | |||
7056.2.k.h.881.5 | 16 | 84.23 | even | 6 | |||
7056.2.k.h.881.6 | 16 | 28.19 | even | 6 | |||
7056.2.k.h.881.11 | 16 | 84.47 | odd | 6 | |||
7056.2.k.h.881.12 | 16 | 28.23 | odd | 6 |