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 | 17.6 | ||
Root | \(-0.587308 - 2.01725i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.17 |
Dual form | 504.2.bl.a.89.6 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | \(-0.0820696\pi\) |
−0.704294 | + | 0.709909i | \(0.748736\pi\) | |||||||
\(6\) | 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 | \(-0.252267\pi\) |
−0.265691 | + | 0.964058i | \(0.585600\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.14525i | − | 0.317635i | −0.987308 | − | 0.158818i | \(-0.949232\pi\) | ||
0.987308 | − | 0.158818i | \(-0.0507682\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.07609 | + | 3.59589i | −0.503525 | + | 0.872131i | 0.496466 | + | 0.868056i | \(0.334631\pi\) |
−0.999992 | + | 0.00407535i | \(0.998703\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.83453 | − | 1.05917i | 0.420870 | − | 0.242989i | −0.274579 | − | 0.961564i | \(-0.588539\pi\) |
0.695449 | + | 0.718575i | \(0.255205\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.22379 | − | 2.43860i | 0.880720 | − | 0.508484i | 0.00982439 | − | 0.999952i | \(-0.496873\pi\) |
0.870896 | + | 0.491468i | \(0.163539\pi\) | |||||||
\(24\) | 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 | 0.978617 | − | 0.205693i | \(-0.0659448\pi\) |
0.311173 | + | 0.950353i | \(0.399278\pi\) | |||||||
\(32\) | 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 | 0.626564 | − | 0.779370i | \(-0.284461\pi\) |
−0.988236 | + | 0.152936i | \(0.951127\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.67577 | −0.417885 | −0.208942 | − | 0.977928i | \(-0.567002\pi\) | ||||
−0.208942 | + | 0.977928i | \(0.567002\pi\) | |||||||
\(42\) | 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 | \(-0.248964\pi\) |
−0.965078 | + | 0.261961i | \(0.915631\pi\) | |||||||
\(48\) | 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 | \(-0.373772\pi\) |
−0.605697 | + | 0.795695i | \(0.707106\pi\) | |||||||
\(54\) | 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 | \(-0.706212\pi\) |
0.992293 | + | 0.123917i | \(0.0395457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.8011 | + | 7.39071i | −1.63901 | + | 0.946284i | −0.657838 | + | 0.753160i | \(0.728529\pi\) |
−0.981174 | + | 0.193124i | \(0.938138\pi\) | |||||||
\(62\) | 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 | 0.483739 | + | 0.875212i | \(0.339279\pi\) |
−0.999826 | + | 0.0186762i | \(0.994055\pi\) | |||||||
\(68\) | 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 | 0.548731 | − | 0.835999i | \(-0.315111\pi\) |
−0.449631 | + | 0.893215i | \(0.648444\pi\) | |||||||
\(74\) | 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 | −0.988413 | − | 0.151786i | \(-0.951497\pi\) |
0.362756 | − | 0.931884i | \(-0.381836\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.2258 | −1.12242 | −0.561212 | − | 0.827672i | \(-0.689665\pi\) | ||||
−0.561212 | + | 0.827672i | \(0.689665\pi\) | |||||||
\(84\) | 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 | −0.978522 | − | 0.206142i | \(-0.933909\pi\) |
0.310737 | − | 0.950496i | \(-0.399424\pi\) | |||||||
\(90\) | 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 | \(0.160573\pi\) | ||||
−0.875438 | + | 0.483330i | \(0.839427\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.65944 | + | 16.7306i | −0.961150 | + | 1.66476i | −0.241528 | + | 0.970394i | \(0.577649\pi\) |
−0.719621 | + | 0.694367i | \(0.755685\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.0730 | + | 7.54769i | −1.28812 | + | 0.743696i | −0.978319 | − | 0.207105i | \(-0.933596\pi\) |
−0.309801 | + | 0.950801i | \(0.600262\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.46986 | − | 5.46743i | 0.915486 | − | 0.528556i | 0.0332936 | − | 0.999446i | \(-0.489400\pi\) |
0.882192 | + | 0.470890i | \(0.156067\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.25885 | + | 5.64449i | −0.312141 | + | 0.540644i | −0.978826 | − | 0.204696i | \(-0.934379\pi\) |
0.666685 | + | 0.745340i | \(0.267713\pi\) | |||||||
\(110\) | 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 | −0.827952 | − | 0.560799i | \(-0.810494\pi\) |
−0.0716899 | − | 0.997427i | \(-0.522839\pi\) | |||||||
\(132\) | 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 | −0.995598 | − | 0.0937303i | \(-0.970121\pi\) |
−0.578972 | − | 0.815348i | \(-0.696546\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50746i | 0.551955i | 0.961164 | + | 0.275978i | \(0.0890016\pi\) | ||||
−0.961164 | + | 0.275978i | \(0.910998\pi\) | |||||||
\(140\) | 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 | \(-0.466120\pi\) |
0.914242 | + | 0.405168i | \(0.132787\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.12846 | + | 8.88276i | −0.417348 | + | 0.722869i | −0.995672 | − | 0.0929389i | \(-0.970374\pi\) |
0.578323 | + | 0.815808i | \(0.303707\pi\) | |||||||
\(152\) | 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 | 0.515874 | − | 0.856665i | \(-0.327467\pi\) |
−0.483956 | + | 0.875092i | \(0.660801\pi\) | |||||||
\(158\) | 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 | −0.857330 | − | 0.514768i | \(-0.827878\pi\) |
−0.0171370 | − | 0.999853i | \(-0.505455\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.42604 | −0.419879 | −0.209940 | − | 0.977714i | \(-0.567327\pi\) | ||||
−0.209940 | + | 0.977714i | \(0.567327\pi\) | |||||||
\(168\) | 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 | \(-0.0488691\pi\) |
−0.626555 | + | 0.779377i | \(0.715536\pi\) | |||||||
\(174\) | 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 | \(-0.306383\pi\) |
−0.424972 | + | 0.905206i | \(0.639716\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.7987i | 1.62029i | 0.586231 | + | 0.810144i | \(0.300611\pi\) | ||||
−0.586231 | + | 0.810144i | \(0.699389\pi\) | |||||||
\(182\) | 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 | \(-0.954847\pi\) |
−0.372541 | + | 0.928016i | \(0.621513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.8259 | − | 18.7510i | 0.779266 | − | 1.34973i | −0.153099 | − | 0.988211i | \(-0.548925\pi\) |
0.932365 | − | 0.361518i | \(-0.117741\pi\) | |||||||
\(194\) | 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 | 0.910367 | − | 0.413801i | \(-0.135799\pi\) |
0.0968215 | + | 0.995302i | \(0.469132\pi\) | |||||||
\(200\) | 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 | \(-0.749549\pi\) | ||
0.706105 | − | 0.708107i | \(-0.250451\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.7990 | + | 20.4365i | −0.783130 | + | 1.35642i | 0.146980 | + | 0.989139i | \(0.453045\pi\) |
−0.930110 | + | 0.367281i | \(0.880289\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.969507 | + | 0.559745i | −0.0640668 | + | 0.0369890i | −0.531691 | − | 0.846938i | \(-0.678443\pi\) |
0.467624 | + | 0.883927i | \(0.345110\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.9299 | − | 12.0839i | 1.37116 | − | 0.791642i | 0.380089 | − | 0.924950i | \(-0.375893\pi\) |
0.991075 | + | 0.133309i | \(0.0425601\pi\) | |||||||
\(234\) | 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 | 0.819496 | − | 0.573085i | \(-0.194253\pi\) |
−0.0865578 | + | 0.996247i | \(0.527587\pi\) | |||||||
\(242\) | 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 | \(-0.639233\pi\) | ||||
−0.423597 | + | 0.905851i | \(0.639233\pi\) | |||||||
\(252\) | 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 | \(-0.272444\pi\) |
−0.981760 | + | 0.190126i | \(0.939110\pi\) | |||||||
\(258\) | 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 | \(-0.0729402\pi\) |
0.290214 | + | 0.956962i | \(0.406274\pi\) | |||||||
\(264\) | 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 | 0.446315 | + | 0.894876i | \(0.352736\pi\) |
−0.998143 | + | 0.0609178i | \(0.980597\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.79002 | − | 3.34287i | 0.351718 | − | 0.203065i | −0.313723 | − | 0.949514i | \(-0.601576\pi\) |
0.665442 | + | 0.746450i | \(0.268243\pi\) | |||||||
\(272\) | 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 | −0.809546 | − | 0.587056i | \(-0.800287\pi\) |
0.913179 | + | 0.407560i | \(0.133620\pi\) | |||||||
\(278\) | 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 | 0.693961 | − | 0.720013i | \(-0.255864\pi\) |
−0.276569 | + | 0.960994i | \(0.589198\pi\) | |||||||
\(284\) | 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 | \(-0.376897\pi\) | ||||
0.377170 | + | 0.926144i | \(0.376897\pi\) | |||||||
\(294\) | 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 | \(-0.889556\pi\) | ||
0.940408 | − | 0.340049i | \(-0.110444\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.3295 | − | 26.5516i | 0.869259 | − | 1.50560i | 0.00650358 | − | 0.999979i | \(-0.497930\pi\) |
0.862755 | − | 0.505622i | \(-0.168737\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.14799 | − | 4.70425i | 0.460552 | − | 0.265900i | −0.251724 | − | 0.967799i | \(-0.580998\pi\) |
0.712276 | + | 0.701899i | \(0.247664\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.23712 | − | 0.714251i | 0.0694835 | − | 0.0401163i | −0.464856 | − | 0.885386i | \(-0.653894\pi\) |
0.534339 | + | 0.845270i | \(0.320560\pi\) | |||||||
\(318\) | 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 | 0.993252 | − | 0.115977i | \(-0.0370000\pi\) |
−0.597065 | + | 0.802193i | \(0.703667\pi\) | |||||||
\(332\) | 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 | \(-0.0392864\pi\) |
0.389581 | + | 0.920992i | \(0.372620\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.41027i | 0.289605i | 0.989461 | + | 0.144802i | \(0.0462547\pi\) | ||||
−0.989461 | + | 0.144802i | \(0.953745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.02520 | + | 12.1680i | −0.373914 | + | 0.647637i | −0.990164 | − | 0.139913i | \(-0.955318\pi\) |
0.616250 | + | 0.787550i | \(0.288651\pi\) | |||||||
\(354\) | 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 | \(-0.732057\pi\) |
0.312829 | + | 0.949810i | \(0.398723\pi\) | |||||||
\(360\) | 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 | 0.666921 | − | 0.745128i | \(-0.267612\pi\) |
−0.311839 | + | 0.950135i | \(0.600945\pi\) | |||||||
\(368\) | 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 | 0.745659 | − | 0.666327i | \(-0.232135\pi\) |
−0.949886 | + | 0.312596i | \(0.898801\pi\) | |||||||
\(374\) | 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 | \(-0.188794\pi\) |
−0.898664 | + | 0.438638i | \(0.855461\pi\) | |||||||
\(384\) | 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 | \(-0.501835\pi\) |
−0.868894 | + | 0.494999i | \(0.835168\pi\) | |||||||
\(390\) | 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 | −0.818570 | − | 0.574406i | \(-0.805233\pi\) |
0.0881655 | + | 0.996106i | \(0.471900\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.31347 | + | 4.22244i | −0.365217 | + | 0.210858i | −0.671367 | − | 0.741125i | \(-0.734293\pi\) |
0.306150 | + | 0.951983i | \(0.400959\pi\) | |||||||
\(402\) | 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 | −0.140253 | − | 0.990116i | \(-0.544792\pi\) |
−0.927592 | + | 0.373595i | \(0.878125\pi\) | |||||||
\(410\) | 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 | \(-0.788615\pi\) | ||||
−0.787480 | + | 0.616340i | \(0.788615\pi\) | |||||||
\(420\) | 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 | \(-0.481792\pi\) |
−0.836023 | + | 0.548694i | \(0.815125\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.4261i | − | 0.597163i | −0.954384 | − | 0.298581i | \(-0.903487\pi\) | ||
0.954384 | − | 0.298581i | \(-0.0965134\pi\) | |||||||
\(434\) | 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 | −0.851836 | − | 0.523808i | \(-0.824511\pi\) |
0.0277131 | + | 0.999616i | \(0.491178\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.3854 | − | 14.6563i | 1.20610 | − | 0.696340i | 0.244192 | − | 0.969727i | \(-0.421477\pi\) |
0.961904 | + | 0.273387i | \(0.0881440\pi\) | |||||||
\(444\) | 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 | 0.992820 | − | 0.119622i | \(-0.0381681\pi\) |
−0.600005 | + | 0.799996i | \(0.704835\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.3775 | −0.529903 | −0.264951 | − | 0.964262i | \(-0.585356\pi\) | ||||
−0.264951 | + | 0.964262i | \(0.585356\pi\) | |||||||
\(462\) | 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 | −0.997938 | − | 0.0641788i | \(-0.979557\pi\) |
0.443389 | − | 0.896329i | \(-0.353776\pi\) | |||||||
\(468\) | 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 | −0.486089 | − | 0.873910i | \(-0.661577\pi\) |
0.999872 | − | 0.0159898i | \(-0.00508992\pi\) | |||||||
\(480\) | 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 | −0.999992 | − | 0.00404053i | \(-0.998714\pi\) |
0.503495 | + | 0.863998i | \(0.332047\pi\) | |||||||
\(488\) | 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 | 0.985099 | + | 0.171987i | \(0.0550188\pi\) |
−0.343604 | + | 0.939115i | \(0.611648\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.4762 | 1.76016 | 0.880078 | − | 0.474830i | \(-0.157490\pi\) | ||||
0.880078 | + | 0.474830i | \(0.157490\pi\) | |||||||
\(504\) | 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 | \(-0.205350\pi\) |
−0.920252 | + | 0.391327i | \(0.872016\pi\) | |||||||
\(510\) | 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 | 0.314248 | + | 0.949341i | \(0.398248\pi\) |
−0.979277 | + | 0.202524i | \(0.935086\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.4905 | − | 18.7584i | 1.42071 | − | 0.820248i | 0.424352 | − | 0.905497i | \(-0.360502\pi\) |
0.996360 | + | 0.0852494i | \(0.0271687\pi\) | |||||||
\(524\) | 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 | 0.998543 | − | 0.0539578i | \(-0.0171836\pi\) |
−0.546000 | + | 0.837785i | \(0.683850\pi\) | |||||||
\(542\) | 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 | \(-0.493500\pi\) |
−0.855635 | + | 0.517580i | \(0.826833\pi\) | |||||||
\(558\) | 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 | −0.439643 | − | 0.898172i | \(-0.644895\pi\) |
0.997662 | − | 0.0683439i | \(-0.0217715\pi\) | |||||||
\(564\) | 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 | \(-0.786799\pi\) |
0.145671 | + | 0.989333i | \(0.453466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.1117 | + | 20.9780i | −0.506857 | + | 0.877903i | 0.493111 | + | 0.869966i | \(0.335860\pi\) |
−0.999969 | + | 0.00793637i | \(0.997474\pi\) | |||||||
\(572\) | 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 | 0.0602665 | − | 0.998182i | \(-0.480805\pi\) |
−0.834318 | + | 0.551283i | \(0.814138\pi\) | |||||||
\(578\) | 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 | \(-0.285401\pi\) | ||||
0.624260 | + | 0.781217i | \(0.285401\pi\) | |||||||
\(588\) | 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 | 0.970485 | + | 0.241162i | \(0.0775285\pi\) |
−0.276390 | + | 0.961046i | \(0.589138\pi\) | |||||||
\(594\) | 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 | \(-0.0486508\pi\) |
0.362322 | + | 0.932053i | \(0.381984\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.6195i | 1.53453i | 0.641329 | + | 0.767266i | \(0.278384\pi\) | ||||
−0.641329 | + | 0.767266i | \(0.721616\pi\) | |||||||
\(602\) | 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 | −0.515139 | − | 0.857107i | \(-0.672260\pi\) |
0.484707 | + | 0.874677i | \(0.338926\pi\) | |||||||
\(608\) | 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 | −0.570179 | − | 0.821520i | \(-0.693126\pi\) |
0.996547 | + | 0.0830296i | \(0.0264596\pi\) | |||||||
\(614\) | 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 | 0.0445209 | − | 0.999008i | \(-0.485824\pi\) |
−0.842906 | + | 0.538060i | \(0.819157\pi\) | |||||||
\(620\) | 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 | \(-0.218419\pi\) |
−0.161870 | + | 0.986812i | \(0.551753\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 30.8980i | − | 1.21850i | −0.792980 | − | 0.609248i | \(-0.791471\pi\) | ||
0.792980 | − | 0.609248i | \(-0.208529\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.81704 | − | 6.61130i | 0.150063 | − | 0.259917i | −0.781187 | − | 0.624297i | \(-0.785386\pi\) |
0.931250 | + | 0.364380i | \(0.118719\pi\) | |||||||
\(648\) | 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 | \(-0.810025\pi\) |
0.0731587 | + | 0.997320i | \(0.476692\pi\) | |||||||
\(654\) | 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 | 0.620505 | − | 0.784202i | \(-0.286928\pi\) |
−0.368887 | + | 0.929474i | \(0.620261\pi\) | |||||||
\(662\) | 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 | \(-0.285104\pi\) |
−0.988543 | + | 0.150938i | \(0.951771\pi\) | |||||||
\(678\) | 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 | \(-0.298448\pi\) |
−0.402277 | + | 0.915518i | \(0.631781\pi\) | |||||||
\(684\) | 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 | 0.694319 | − | 0.719667i | \(-0.255706\pi\) |
0.970410 | − | 0.241465i | \(-0.0776277\pi\) | |||||||
\(692\) | 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 | 0.984315 | − | 0.176417i | \(-0.0564509\pi\) |
−0.644940 | + | 0.764233i | \(0.723118\pi\) | |||||||
\(710\) | 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 | 0.753298 | + | 0.657679i | \(0.228462\pi\) |
0.192918 | + | 0.981215i | \(0.438205\pi\) | |||||||
\(720\) | 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 | \(-0.959925\pi\) | ||
0.992085 | − | 0.125568i | \(-0.0400755\pi\) | |||||||
\(728\) | 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 | 0.631864 | − | 0.775079i | \(-0.282290\pi\) |
0.987170 | − | 0.159671i | \(-0.0510433\pi\) | |||||||
\(734\) | 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 | −0.432383 | − | 0.901690i | \(-0.642327\pi\) |
0.997078 | − | 0.0763904i | \(-0.0243395\pi\) | |||||||
\(740\) | 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 | 0.877091 | − | 0.480324i | \(-0.159481\pi\) |
−0.854518 | + | 0.519422i | \(0.826147\pi\) | |||||||
\(752\) | 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 | 0.999054 | + | 0.0434899i | \(0.0138476\pi\) |
−0.461864 | + | 0.886951i | \(0.652819\pi\) | |||||||
\(762\) | 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 | \(-0.830624\pi\) | ||
0.861738 | − | 0.507354i | \(-0.169376\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.95227 | − | 10.3096i | 0.214088 | − | 0.370812i | −0.738902 | − | 0.673813i | \(-0.764655\pi\) |
0.952990 | + | 0.303001i | \(0.0979886\pi\) | |||||||
\(774\) | 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 | −0.128335 | − | 0.991731i | \(-0.540963\pi\) |
−0.923031 | + | 0.384724i | \(0.874296\pi\) | |||||||
\(788\) | 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 | \(-0.697367\pi\) | ||||
−0.581074 | + | 0.813851i | \(0.697367\pi\) | |||||||
\(798\) | 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 | \(-0.377988\pi\) |
−0.616182 | + | 0.787604i | \(0.711321\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.4200i | 0.787273i | 0.919266 | + | 0.393636i | \(0.128783\pi\) | ||||
−0.919266 | + | 0.393636i | \(0.871217\pi\) | |||||||
\(812\) | 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 | \(-0.636757\pi\) |
0.579050 | + | 0.815292i | \(0.303424\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.55129 | − | 6.15102i | 0.123790 | − | 0.214411i | −0.797469 | − | 0.603360i | \(-0.793828\pi\) |
0.921259 | + | 0.388949i | \(0.127162\pi\) | |||||||
\(824\) | 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 | 0.497439 | − | 0.867499i | \(-0.334274\pi\) |
−0.502557 | + | 0.864544i | \(0.667607\pi\) | |||||||
\(830\) | 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 | \(-0.231765\pi\) | ||||
0.746434 | + | 0.665460i | \(0.231765\pi\) | |||||||
\(840\) | 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 | \(-0.892757\pi\) | ||
0.943779 | − | 0.330577i | \(-0.107243\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.7997 | − | 46.4185i | 0.915461 | − | 1.58562i | 0.109235 | − | 0.994016i | \(-0.465160\pi\) |
0.806225 | − | 0.591608i | \(-0.201507\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.59883 | − | 1.50044i | 0.0886710 | − | 0.0511943i | −0.455009 | − | 0.890487i | \(-0.650364\pi\) |
0.543680 | + | 0.839293i | \(0.317031\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.0064 | + | 20.7883i | −1.22567 | + | 0.707641i | −0.966121 | − | 0.258089i | \(-0.916907\pi\) |
−0.259549 | + | 0.965730i | \(0.583574\pi\) | |||||||
\(864\) | 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 | 0.992933 | + | 0.118674i | \(0.0378644\pi\) |
−0.393692 | + | 0.919242i | \(0.628802\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.7343 | 0.429030 | 0.214515 | − | 0.976721i | \(-0.431183\pi\) | ||||
0.214515 | + | 0.976721i | \(0.431183\pi\) | |||||||
\(882\) | 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 | 0.948026 | + | 0.318192i | \(0.103076\pi\) |
−0.198451 | + | 0.980111i | \(0.563591\pi\) | |||||||
\(888\) | 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 | −0.999978 | − | 0.00657974i | \(-0.997906\pi\) |
0.505687 | + | 0.862717i | \(0.331239\pi\) | |||||||
\(908\) | 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 | 0.731985 | − | 0.681320i | \(-0.238594\pi\) |
−0.956033 | + | 0.293258i | \(0.905261\pi\) | |||||||
\(920\) | 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 | \(-0.166947\pi\) |
−0.866465 | + | 0.499238i | \(0.833613\pi\) | |||||||
\(930\) | 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 | \(-0.924617\pi\) | ||
0.972088 | − | 0.234615i | \(-0.0753829\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.9562 | − | 29.3690i | 0.552757 | − | 0.957403i | −0.445318 | − | 0.895373i | \(-0.646909\pi\) |
0.998074 | − | 0.0620301i | \(-0.0197575\pi\) | |||||||
\(942\) | 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 | \(-0.487803\pi\) |
0.884544 | + | 0.466456i | \(0.154469\pi\) | |||||||
\(948\) | 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 | \(-0.231494\pi\) |
−0.949255 | + | 0.314508i | \(0.898160\pi\) | |||||||
\(972\) | 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 | \(-0.00964493\pi\) |
0.473534 | + | 0.880776i | \(0.342978\pi\) | |||||||
\(978\) | 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 | \(-0.788200\pi\) |
0.927992 | + | 0.372599i | \(0.121533\pi\) | |||||||
\(984\) | 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 | −0.525500 | − | 0.850794i | \(-0.676122\pi\) |
0.999559 | + | 0.0296992i | \(0.00945495\pi\) | |||||||
\(992\) | 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 | 0.664688 | − | 0.747121i | \(-0.268564\pi\) |
−0.314682 | + | 0.949197i | \(0.601898\pi\) | |||||||
\(998\) | 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.17.6 | yes | 16 | |
3.2 | odd | 2 | inner | 504.2.bl.a.17.3 | ✓ | 16 | |
4.3 | odd | 2 | 1008.2.bt.d.17.6 | 16 | |||
7.2 | even | 3 | 3528.2.bl.a.1097.6 | 16 | |||
7.3 | odd | 6 | 3528.2.k.b.881.11 | 16 | |||
7.4 | even | 3 | 3528.2.k.b.881.5 | 16 | |||
7.5 | odd | 6 | inner | 504.2.bl.a.89.3 | yes | 16 | |
7.6 | odd | 2 | 3528.2.bl.a.521.3 | 16 | |||
12.11 | even | 2 | 1008.2.bt.d.17.3 | 16 | |||
21.2 | odd | 6 | 3528.2.bl.a.1097.3 | 16 | |||
21.5 | even | 6 | inner | 504.2.bl.a.89.6 | yes | 16 | |
21.11 | odd | 6 | 3528.2.k.b.881.12 | 16 | |||
21.17 | even | 6 | 3528.2.k.b.881.6 | 16 | |||
21.20 | even | 2 | 3528.2.bl.a.521.6 | 16 | |||
28.3 | even | 6 | 7056.2.k.h.881.12 | 16 | |||
28.11 | odd | 6 | 7056.2.k.h.881.6 | 16 | |||
28.19 | even | 6 | 1008.2.bt.d.593.3 | 16 | |||
84.11 | even | 6 | 7056.2.k.h.881.11 | 16 | |||
84.47 | odd | 6 | 1008.2.bt.d.593.6 | 16 | |||
84.59 | odd | 6 | 7056.2.k.h.881.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bl.a.17.3 | ✓ | 16 | 3.2 | odd | 2 | inner | |
504.2.bl.a.17.6 | yes | 16 | 1.1 | even | 1 | trivial | |
504.2.bl.a.89.3 | yes | 16 | 7.5 | odd | 6 | inner | |
504.2.bl.a.89.6 | yes | 16 | 21.5 | even | 6 | inner | |
1008.2.bt.d.17.3 | 16 | 12.11 | even | 2 | |||
1008.2.bt.d.17.6 | 16 | 4.3 | odd | 2 | |||
1008.2.bt.d.593.3 | 16 | 28.19 | even | 6 | |||
1008.2.bt.d.593.6 | 16 | 84.47 | odd | 6 | |||
3528.2.k.b.881.5 | 16 | 7.4 | even | 3 | |||
3528.2.k.b.881.6 | 16 | 21.17 | even | 6 | |||
3528.2.k.b.881.11 | 16 | 7.3 | odd | 6 | |||
3528.2.k.b.881.12 | 16 | 21.11 | odd | 6 | |||
3528.2.bl.a.521.3 | 16 | 7.6 | odd | 2 | |||
3528.2.bl.a.521.6 | 16 | 21.20 | even | 2 | |||
3528.2.bl.a.1097.3 | 16 | 21.2 | odd | 6 | |||
3528.2.bl.a.1097.6 | 16 | 7.2 | even | 3 | |||
7056.2.k.h.881.5 | 16 | 84.59 | odd | 6 | |||
7056.2.k.h.881.6 | 16 | 28.11 | odd | 6 | |||
7056.2.k.h.881.11 | 16 | 84.11 | even | 6 | |||
7056.2.k.h.881.12 | 16 | 28.3 | even | 6 |