Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.2 | ||
Character | \(\chi\) | \(=\) | 3024.2305 |
Dual form | 3024.2.q.l.2881.2 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.89970 | − | 3.29038i | −0.849572 | − | 1.47150i | −0.881591 | − | 0.472014i | \(-0.843527\pi\) |
0.0320189 | − | 0.999487i | \(-0.489806\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.841809 | − | 2.50826i | 0.318174 | − | 0.948032i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.25706 | + | 3.90934i | −0.680529 | + | 1.17871i | 0.294290 | + | 0.955716i | \(0.404917\pi\) |
−0.974820 | + | 0.222995i | \(0.928417\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.588451 | − | 1.01923i | 0.163207 | − | 0.282683i | −0.772810 | − | 0.634637i | \(-0.781150\pi\) |
0.936017 | + | 0.351955i | \(0.114483\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.95973 | + | 5.12641i | 0.717841 | + | 1.24334i | 0.961853 | + | 0.273565i | \(0.0882029\pi\) |
−0.244012 | + | 0.969772i | \(0.578464\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.55676 | + | 4.42844i | −0.586562 | + | 1.01595i | 0.408117 | + | 0.912930i | \(0.366185\pi\) |
−0.994679 | + | 0.103025i | \(0.967148\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.09082 | + | 3.62140i | 0.435966 | + | 0.755115i | 0.997374 | − | 0.0724243i | \(-0.0230736\pi\) |
−0.561408 | + | 0.827539i | \(0.689740\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.71772 | + | 8.17134i | −0.943545 | + | 1.63427i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.11164 | − | 3.65747i | −0.392122 | − | 0.679175i | 0.600607 | − | 0.799544i | \(-0.294925\pi\) |
−0.992729 | + | 0.120369i | \(0.961592\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.24283 | 1.12124 | 0.560622 | − | 0.828072i | \(-0.310562\pi\) | ||||
0.560622 | + | 0.828072i | \(0.310562\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.85230 | + | 1.99507i | −1.66534 | + | 0.337229i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.87179 | + | 6.70614i | −0.636519 | + | 1.10248i | 0.349672 | + | 0.936872i | \(0.386293\pi\) |
−0.986191 | + | 0.165611i | \(0.947040\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.754693 | + | 1.30717i | −0.117863 | + | 0.204145i | −0.918921 | − | 0.394442i | \(-0.870938\pi\) |
0.801057 | + | 0.598587i | \(0.204271\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.01709 | + | 8.68986i | 0.765099 | + | 1.32519i | 0.940194 | + | 0.340639i | \(0.110643\pi\) |
−0.175095 | + | 0.984552i | \(0.556023\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.23665 | −0.326248 | −0.163124 | − | 0.986606i | \(-0.552157\pi\) | ||||
−0.163124 | + | 0.986606i | \(0.552157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.58272 | − | 4.22295i | −0.797531 | − | 0.603278i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.49368 | − | 11.2474i | −0.891975 | − | 1.54495i | −0.837504 | − | 0.546431i | \(-0.815986\pi\) |
−0.0544716 | − | 0.998515i | \(-0.517347\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.1510 | 2.31263 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.3922 | 1.61332 | 0.806662 | − | 0.591013i | \(-0.201272\pi\) | ||||
0.806662 | + | 0.591013i | \(0.201272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.45834 | 0.186722 | 0.0933608 | − | 0.995632i | \(-0.470239\pi\) | ||||
0.0933608 | + | 0.995632i | \(0.470239\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.47152 | −0.554624 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.62638 | −0.198694 | −0.0993472 | − | 0.995053i | \(-0.531675\pi\) | ||||
−0.0993472 | + | 0.995053i | \(0.531675\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.48517 | 1.00700 | 0.503502 | − | 0.863994i | \(-0.332045\pi\) | ||||
0.503502 | + | 0.863994i | \(0.332045\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.72984 | + | 6.46027i | 0.436544 | + | 0.756117i | 0.997420 | − | 0.0717827i | \(-0.0228688\pi\) |
−0.560876 | + | 0.827900i | \(0.689535\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.90563 | + | 8.95221i | 0.900930 | + | 1.02020i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.84185 | 0.207224 | 0.103612 | − | 0.994618i | \(-0.466960\pi\) | ||||
0.103612 | + | 0.994618i | \(0.466960\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.307606 | − | 0.532789i | −0.0337641 | − | 0.0584812i | 0.848650 | − | 0.528956i | \(-0.177416\pi\) |
−0.882414 | + | 0.470474i | \(0.844083\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.2452 | − | 19.4773i | 1.21972 | − | 2.11261i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.25572 | − | 2.17496i | 0.133106 | − | 0.230546i | −0.791767 | − | 0.610824i | \(-0.790838\pi\) |
0.924872 | + | 0.380278i | \(0.124172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.06112 | − | 2.33398i | −0.216064 | − | 0.244668i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.4283 | 1.99330 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.36751 | + | 4.10064i | 0.240384 | + | 0.416357i | 0.960824 | − | 0.277160i | \(-0.0893934\pi\) |
−0.720440 | + | 0.693517i | \(0.756060\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.71081 | + | 9.89141i | −0.568247 | + | 0.984232i | 0.428493 | + | 0.903545i | \(0.359045\pi\) |
−0.996739 | + | 0.0806872i | \(0.974289\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.18752 | − | 5.52095i | −0.314076 | − | 0.543996i | 0.665165 | − | 0.746697i | \(-0.268361\pi\) |
−0.979241 | + | 0.202701i | \(0.935028\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.11999 | − | 1.93988i | 0.108274 | − | 0.187536i | −0.806797 | − | 0.590828i | \(-0.798801\pi\) |
0.915071 | + | 0.403293i | \(0.132134\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.73089 | − | 4.73005i | −0.261572 | − | 0.453056i | 0.705088 | − | 0.709120i | \(-0.250908\pi\) |
−0.966660 | + | 0.256064i | \(0.917574\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.45456 | − | 7.71553i | 0.419050 | − | 0.725816i | −0.576794 | − | 0.816890i | \(-0.695696\pi\) |
0.995844 | + | 0.0910734i | \(0.0290298\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.94386 | − | 13.7592i | 0.740768 | − | 1.28305i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.3499 | − | 3.10832i | 1.40712 | − | 0.284939i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.68864 | − | 8.12096i | −0.426240 | − | 0.738269i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 16.8520 | 1.50729 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.434918 | −0.0385927 | −0.0192964 | − | 0.999814i | \(-0.506143\pi\) | ||||
−0.0192964 | + | 0.999814i | \(0.506143\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.67633 | + | 4.63553i | 0.233832 | + | 0.405009i | 0.958933 | − | 0.283634i | \(-0.0915402\pi\) |
−0.725101 | + | 0.688643i | \(0.758207\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.95537 | + | 10.1409i | 0.776529 | + | 0.879329i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.95121 | − | 5.11165i | 0.252139 | − | 0.436718i | −0.711976 | − | 0.702204i | \(-0.752199\pi\) |
0.964115 | + | 0.265487i | \(0.0855326\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.33649 | + | 7.51102i | −0.367816 | + | 0.637077i | −0.989224 | − | 0.146411i | \(-0.953228\pi\) |
0.621407 | + | 0.783488i | \(0.286561\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.65634 | + | 4.60091i | 0.222134 | + | 0.384747i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.02297 | + | 13.8962i | −0.666271 | + | 1.15402i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.38860 | − | 9.33333i | −0.441451 | − | 0.764616i | 0.556346 | − | 0.830951i | \(-0.312203\pi\) |
−0.997797 | + | 0.0663346i | \(0.978870\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.41310 | + | 14.5719i | −0.684648 | + | 1.18585i | 0.288899 | + | 0.957360i | \(0.406711\pi\) |
−0.973547 | + | 0.228486i | \(0.926622\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.8595 | − | 20.5413i | −0.952578 | − | 1.64991i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.96136 | 0.715194 | 0.357597 | − | 0.933876i | \(-0.383596\pi\) | ||||
0.357597 | + | 0.933876i | \(0.383596\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.8435 | − | 2.19578i | 0.854586 | − | 0.173052i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.71319 | − | 6.43144i | 0.290840 | − | 0.503749i | −0.683169 | − | 0.730261i | \(-0.739399\pi\) |
0.974009 | + | 0.226511i | \(0.0727320\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.13764 | + | 8.89866i | −0.397563 | + | 0.688599i | −0.993425 | − | 0.114488i | \(-0.963477\pi\) |
0.595862 | + | 0.803087i | \(0.296811\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.80745 | + | 10.0588i | 0.446727 | + | 0.773754i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.2099 | 0.776246 | 0.388123 | − | 0.921608i | \(-0.373124\pi\) | ||||
0.388123 | + | 0.921608i | \(0.373124\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.5244 | + | 18.7120i | 1.24913 | + | 1.41449i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.62985 | + | 16.6794i | 0.719769 | + | 1.24668i | 0.961091 | + | 0.276231i | \(0.0890854\pi\) |
−0.241323 | + | 0.970445i | \(0.577581\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.39163 | −0.103439 | −0.0517195 | − | 0.998662i | \(-0.516470\pi\) | ||||
−0.0517195 | + | 0.998662i | \(0.516470\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 29.4210 | 2.16307 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.7212 | −1.95405 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.71483 | −0.196438 | −0.0982190 | − | 0.995165i | \(-0.531315\pi\) | ||||
−0.0982190 | + | 0.995165i | \(0.531315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.84169 | 0.132568 | 0.0662839 | − | 0.997801i | \(-0.478886\pi\) | ||||
0.0662839 | + | 0.997801i | \(0.478886\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.9198 | −1.56172 | −0.780860 | − | 0.624706i | \(-0.785219\pi\) | ||||
−0.780860 | + | 0.624706i | \(0.785219\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.726101 | + | 1.25764i | 0.0514719 | + | 0.0891520i | 0.890613 | − | 0.454761i | \(-0.150275\pi\) |
−0.839141 | + | 0.543913i | \(0.816942\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.9515 | + | 2.21765i | −0.768643 | + | 0.155649i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.73476 | 0.400533 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.5415 | − | 19.9905i | −0.798344 | − | 1.38277i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.771347 | + | 1.33601i | −0.0531017 | + | 0.0919749i | −0.891354 | − | 0.453307i | \(-0.850244\pi\) |
0.838253 | + | 0.545282i | \(0.183577\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.0619 | − | 33.0162i | 1.30001 | − | 2.25169i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.25527 | − | 15.6586i | 0.356751 | − | 1.06298i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.96663 | 0.468626 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.346045 | + | 0.599368i | 0.0231729 | + | 0.0401366i | 0.877379 | − | 0.479797i | \(-0.159290\pi\) |
−0.854206 | + | 0.519934i | \(0.825957\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.20797 | + | 15.9487i | −0.611155 | + | 1.05855i | 0.379892 | + | 0.925031i | \(0.375961\pi\) |
−0.991046 | + | 0.133520i | \(0.957372\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.69696 | + | 4.67127i | 0.178220 | + | 0.308686i | 0.941271 | − | 0.337652i | \(-0.109633\pi\) |
−0.763051 | + | 0.646338i | \(0.776299\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.27352 | − | 14.3302i | 0.542016 | − | 0.938800i | −0.456772 | − | 0.889584i | \(-0.650994\pi\) |
0.998788 | − | 0.0492161i | \(-0.0156723\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.24896 | + | 7.35941i | 0.277171 | + | 0.480075i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.56724 | + | 2.71454i | −0.101376 | + | 0.175589i | −0.912252 | − | 0.409630i | \(-0.865658\pi\) |
0.810876 | + | 0.585219i | \(0.198991\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.23730 | − | 14.2674i | 0.530611 | − | 0.919046i | −0.468751 | − | 0.883330i | \(-0.655296\pi\) |
0.999362 | − | 0.0357151i | \(-0.0113709\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.28960 | + | 26.3916i | −0.210165 | + | 1.68610i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.00906 | + | 5.21184i | 0.191462 | + | 0.331621i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.8939 | 0.813858 | 0.406929 | − | 0.913460i | \(-0.366600\pi\) | ||||
0.406929 | + | 0.913460i | \(0.366600\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.8764 | −1.18675 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.3045 | + | 17.8478i | 0.642774 | + | 1.11332i | 0.984811 | + | 0.173631i | \(0.0555501\pi\) |
−0.342036 | + | 0.939687i | \(0.611117\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.5614 | + | 15.3567i | 0.842666 | + | 0.954222i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.56616 | + | 7.90883i | −0.281562 | + | 0.487679i | −0.971770 | − | 0.235932i | \(-0.924186\pi\) |
0.690208 | + | 0.723611i | \(0.257519\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.6721 | + | 42.7333i | −1.51559 | + | 2.62509i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.4387 | + | 21.5445i | 0.758401 | + | 1.31359i | 0.943666 | + | 0.330900i | \(0.107352\pi\) |
−0.185265 | + | 0.982689i | \(0.559314\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.70814 | + | 9.88679i | −0.346745 | + | 0.600580i | −0.985669 | − | 0.168690i | \(-0.946046\pi\) |
0.638924 | + | 0.769270i | \(0.279380\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.2964 | − | 36.8864i | −1.28422 | − | 2.22433i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.4938 | + | 26.8360i | −0.930932 | + | 1.61242i | −0.149200 | + | 0.988807i | \(0.547670\pi\) |
−0.781732 | + | 0.623615i | \(0.785663\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.40910 | + | 12.8329i | 0.441990 | + | 0.765549i | 0.997837 | − | 0.0657354i | \(-0.0209393\pi\) |
−0.555847 | + | 0.831285i | \(0.687606\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.7431 | −1.53027 | −0.765134 | − | 0.643872i | \(-0.777327\pi\) | ||||
−0.765134 | + | 0.643872i | \(0.777327\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.64340 | + | 2.99335i | 0.156035 | + | 0.176692i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.02006 | + | 15.6232i | −0.530592 | + | 0.919012i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.41185 | + | 14.5697i | −0.491425 | + | 0.851174i | −0.999951 | − | 0.00987288i | \(-0.996857\pi\) |
0.508526 | + | 0.861047i | \(0.330191\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.5414 | − | 40.7749i | −1.37063 | − | 2.37401i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.92137 | 0.284610 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.0198 | − | 5.26896i | 1.49976 | − | 0.303698i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.77041 | − | 4.79849i | −0.158633 | − | 0.274761i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.2972 | 1.61501 | 0.807504 | − | 0.589862i | \(-0.200818\pi\) | ||||
0.807504 | + | 0.589862i | \(0.200818\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.8695 | 1.12670 | 0.563349 | − | 0.826219i | \(-0.309513\pi\) | ||||
0.563349 | + | 0.826219i | \(0.309513\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.2859 | −1.03358 | −0.516789 | − | 0.856113i | \(-0.672873\pi\) | ||||
−0.516789 | + | 0.856113i | \(0.672873\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.9480 | −0.783399 | −0.391700 | − | 0.920093i | \(-0.628113\pi\) | ||||
−0.391700 | + | 0.920093i | \(0.628113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.0644 | 1.06740 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −30.2694 | −1.68423 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.55230 | + | 9.61686i | 0.307986 | + | 0.533447i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.88283 | + | 5.61009i | −0.103804 | + | 0.309294i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.8399 | −1.14547 | −0.572733 | − | 0.819742i | \(-0.694117\pi\) | ||||
−0.572733 | + | 0.819742i | \(0.694117\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.08964 | + | 5.35142i | 0.168805 | + | 0.292379i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.4376 | − | 26.7387i | 0.840939 | − | 1.45655i | −0.0481619 | − | 0.998840i | \(-0.515336\pi\) |
0.889101 | − | 0.457710i | \(-0.151330\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.0904 | + | 24.4054i | −0.763040 | + | 1.32162i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.2918 | + | 10.4480i | −0.825681 | + | 0.564138i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.2685 | −0.551244 | −0.275622 | − | 0.961266i | \(-0.588884\pi\) | ||||
−0.275622 | + | 0.961266i | \(0.588884\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.61262 | + | 7.98930i | 0.246908 | + | 0.427657i | 0.962666 | − | 0.270691i | \(-0.0872521\pi\) |
−0.715758 | + | 0.698348i | \(0.753919\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.08660 | − | 7.07820i | 0.217508 | − | 0.376735i | −0.736538 | − | 0.676397i | \(-0.763541\pi\) |
0.954045 | + | 0.299662i | \(0.0968739\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.1193 | − | 27.9194i | −0.855522 | − | 1.48181i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.35957 | − | 11.0151i | 0.335645 | − | 0.581355i | −0.647963 | − | 0.761672i | \(-0.724379\pi\) |
0.983609 | + | 0.180317i | \(0.0577123\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.57407 | − | 6.19047i | −0.188109 | − | 0.325814i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.1711 | − | 24.5452i | 0.741752 | − | 1.28475i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.9431 | + | 18.9540i | −0.571224 | + | 0.989388i | 0.425217 | + | 0.905091i | \(0.360198\pi\) |
−0.996441 | + | 0.0842970i | \(0.973136\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −33.6778 | + | 6.81968i | −1.74846 | + | 0.354060i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.73126 | + | 11.6589i | 0.348531 | + | 0.603674i | 0.985989 | − | 0.166811i | \(-0.0533471\pi\) |
−0.637457 | + | 0.770486i | \(0.720014\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.97038 | −0.255988 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.2180 | 0.576231 | 0.288115 | − | 0.957596i | \(-0.406971\pi\) | ||||
0.288115 | + | 0.957596i | \(0.406971\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.00330 | + | 6.93392i | 0.204559 | + | 0.354307i | 0.949992 | − | 0.312274i | \(-0.101091\pi\) |
−0.745433 | + | 0.666581i | \(0.767757\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.4378 | − | 43.0190i | 0.735819 | − | 2.19245i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.3931 | − | 24.9296i | 0.729759 | − | 1.26398i | −0.227226 | − | 0.973842i | \(-0.572966\pi\) |
0.956985 | − | 0.290137i | \(-0.0937009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.3765 | + | 21.4368i | −0.625908 | + | 1.08410i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.49897 | − | 6.06039i | −0.176052 | − | 0.304931i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.8138 | − | 18.7301i | 0.542731 | − | 0.940037i | −0.456015 | − | 0.889972i | \(-0.650724\pi\) |
0.998746 | − | 0.0500651i | \(-0.0159429\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.4966 | + | 23.3768i | 0.673987 | + | 1.16738i | 0.976764 | + | 0.214318i | \(0.0687530\pi\) |
−0.302777 | + | 0.953062i | \(0.597914\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.67360 | − | 6.36285i | 0.182995 | − | 0.316956i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.4777 | − | 30.2723i | −0.866339 | − | 1.50054i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.9473 | −1.03578 | −0.517889 | − | 0.855448i | \(-0.673282\pi\) | ||||
−0.517889 | + | 0.855448i | \(0.673282\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.4318 | − | 31.0828i | 0.513317 | − | 1.52948i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.16872 | + | 2.02428i | −0.0573701 | + | 0.0993680i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.91450 | − | 11.9763i | 0.337795 | − | 0.585079i | −0.646222 | − | 0.763149i | \(-0.723652\pi\) |
0.984018 | + | 0.178070i | \(0.0569855\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.86872 | − | 11.8970i | −0.334761 | − | 0.579823i | 0.648678 | − | 0.761063i | \(-0.275322\pi\) |
−0.983439 | + | 0.181240i | \(0.941989\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −55.8529 | −2.70926 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.22764 | − | 3.65790i | 0.0594099 | − | 0.177018i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.20392 | − | 15.9417i | −0.443337 | − | 0.767882i | 0.554598 | − | 0.832119i | \(-0.312872\pi\) |
−0.997935 | + | 0.0642362i | \(0.979539\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.3558 | 1.17047 | 0.585233 | − | 0.810865i | \(-0.301003\pi\) | ||||
0.585233 | + | 0.810865i | \(0.301003\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.3829 | −1.02288 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.83655 | 0.278564 | 0.139282 | − | 0.990253i | \(-0.455521\pi\) | ||||
0.139282 | + | 0.990253i | \(0.455521\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.8400 | 0.705071 | 0.352536 | − | 0.935798i | \(-0.385320\pi\) | ||||
0.352536 | + | 0.935798i | \(0.385320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.54194 | −0.452331 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.26289 | 0.201178 | 0.100589 | − | 0.994928i | \(-0.467927\pi\) | ||||
0.100589 | + | 0.994928i | \(0.467927\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.40677 | − | 5.90070i | −0.160419 | − | 0.277853i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.76416 | + | 11.2157i | −0.176467 | + | 0.525801i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 39.7459 | 1.85924 | 0.929618 | − | 0.368525i | \(-0.120137\pi\) | ||||
0.929618 | + | 0.368525i | \(0.120137\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.68671 | + | 4.65353i | 0.125133 | + | 0.216736i | 0.921785 | − | 0.387702i | \(-0.126731\pi\) |
−0.796652 | + | 0.604438i | \(0.793398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.8205 | + | 34.3301i | −0.921136 | + | 1.59545i | −0.123474 | + | 0.992348i | \(0.539404\pi\) |
−0.797661 | + | 0.603106i | \(0.793930\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.43069 | − | 16.3344i | 0.436400 | − | 0.755867i | −0.561009 | − | 0.827810i | \(-0.689587\pi\) |
0.997409 | + | 0.0719427i | \(0.0229199\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.36910 | + | 4.07939i | −0.0632193 | + | 0.188369i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −45.2955 | −2.08269 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.1242 | − | 41.7843i | −1.10689 | − | 1.91720i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.50287 | + | 16.4595i | −0.434197 | + | 0.752052i | −0.997230 | − | 0.0743830i | \(-0.976301\pi\) |
0.563032 | + | 0.826435i | \(0.309635\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.55672 | + | 7.89247i | 0.207768 | + | 0.359866i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.99511 | − | 15.5800i | 0.408447 | − | 0.707451i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.21626 | + | 9.03482i | 0.236371 | + | 0.409407i | 0.959670 | − | 0.281128i | \(-0.0907085\pi\) |
−0.723299 | + | 0.690535i | \(0.757375\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.3311 | + | 24.8221i | −0.646752 | + | 1.12021i | 0.337142 | + | 0.941454i | \(0.390540\pi\) |
−0.983894 | + | 0.178753i | \(0.942794\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.4998 | − | 21.6503i | 0.562962 | − | 0.975079i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.14289 | − | 21.2830i | 0.320402 | − | 0.954673i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.5396 | − | 28.6475i | −0.740416 | − | 1.28244i | −0.952306 | − | 0.305145i | \(-0.901295\pi\) |
0.211890 | − | 0.977294i | \(-0.432038\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.9523 | −1.29092 | −0.645460 | − | 0.763794i | \(-0.723334\pi\) | ||||
−0.645460 | + | 0.763794i | \(0.723334\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.3953 | 1.93107 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.8820 | + | 27.5085i | 0.703959 | + | 1.21929i | 0.967066 | + | 0.254526i | \(0.0819194\pi\) |
−0.263107 | + | 0.964767i | \(0.584747\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.3438 | − | 3.91709i | 0.855721 | − | 0.173282i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.1107 | + | 20.9763i | −0.533660 | + | 0.924327i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.04825 | − | 8.74382i | 0.222022 | − | 0.384553i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.87897 | + | 4.98652i | 0.126130 | + | 0.218463i | 0.922174 | − | 0.386775i | \(-0.126411\pi\) |
−0.796044 | + | 0.605239i | \(0.793078\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.3123 | − | 38.6461i | 0.975650 | − | 1.68987i | 0.297875 | − | 0.954605i | \(-0.403722\pi\) |
0.677774 | − | 0.735270i | \(-0.262945\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.4771 | + | 32.0033i | 0.804876 | + | 1.39409i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.75696 | − | 4.77520i | 0.119868 | − | 0.207617i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.888199 | + | 1.53841i | 0.0384722 | + | 0.0666357i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.51060 | −0.367945 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.1095 | − | 12.2933i | 1.25383 | − | 0.529510i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.6719 | − | 27.1445i | 0.673786 | − | 1.16703i | −0.303036 | − | 0.952979i | \(-0.598000\pi\) |
0.976822 | − | 0.214053i | \(-0.0686665\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.3758 | + | 17.9713i | −0.444449 | + | 0.769808i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.37567 | − | 2.38273i | −0.0588195 | − | 0.101878i | 0.835116 | − | 0.550073i | \(-0.185400\pi\) |
−0.893936 | + | 0.448195i | \(0.852067\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.5959 | 0.920014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.55049 | − | 4.61984i | 0.0659334 | − | 0.196455i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.42197 | − | 5.92703i | −0.144994 | − | 0.251136i | 0.784377 | − | 0.620284i | \(-0.212983\pi\) |
−0.929371 | + | 0.369148i | \(0.879650\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.8092 | 0.499478 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.1001 | 0.636395 | 0.318197 | − | 0.948025i | \(-0.396923\pi\) | ||||
0.318197 | + | 0.948025i | \(0.396923\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.8494 | −1.42405 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.5276 | 1.15402 | 0.577008 | − | 0.816738i | \(-0.304220\pi\) | ||||
0.577008 | + | 0.816738i | \(0.304220\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.8755 | 1.62689 | 0.813444 | − | 0.581643i | \(-0.197590\pi\) | ||||
0.813444 | + | 0.581643i | \(0.197590\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.4556 | −1.64541 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.84330 | − | 17.0491i | −0.409782 | − | 0.709763i | 0.585083 | − | 0.810973i | \(-0.301062\pi\) |
−0.994865 | + | 0.101210i | \(0.967729\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.59532 | + | 0.323049i | −0.0661849 | + | 0.0134023i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 58.6265 | 2.42806 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.14068 | + | 5.43982i | 0.129630 | + | 0.224525i | 0.923533 | − | 0.383519i | \(-0.125288\pi\) |
−0.793903 | + | 0.608044i | \(0.791954\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.9614 | + | 27.6460i | −0.657679 | + | 1.13913i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.79280 | + | 13.4975i | −0.320012 | + | 0.554277i | −0.980490 | − | 0.196568i | \(-0.937020\pi\) |
0.660478 | + | 0.750845i | \(0.270354\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −39.3877 | − | 44.6021i | −1.61474 | − | 1.82851i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.05557 | 0.0431292 | 0.0215646 | − | 0.999767i | \(-0.493135\pi\) | ||||
0.0215646 | + | 0.999767i | \(0.493135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1622 | − | 21.0656i | −0.496107 | − | 0.859283i | 0.503883 | − | 0.863772i | \(-0.331904\pi\) |
−0.999990 | + | 0.00448941i | \(0.998571\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.8140 | + | 30.8548i | −0.724243 | + | 1.25443i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.16502 | + | 3.74993i | 0.0878756 | + | 0.152205i | 0.906613 | − | 0.421963i | \(-0.138659\pi\) |
−0.818737 | + | 0.574168i | \(0.805326\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.31616 | + | 2.27965i | −0.0532460 | + | 0.0922247i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.3556 | − | 42.1852i | −0.983714 | − | 1.70384i | −0.647518 | − | 0.762050i | \(-0.724193\pi\) |
−0.336196 | − | 0.941792i | \(-0.609140\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.6366 | + | 25.3514i | −0.589249 | + | 1.02061i | 0.405082 | + | 0.914280i | \(0.367243\pi\) |
−0.994331 | + | 0.106329i | \(0.966090\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.2381 | + | 31.5893i | −0.733050 | + | 1.26968i | 0.222523 | + | 0.974927i | \(0.428571\pi\) |
−0.955573 | + | 0.294753i | \(0.904763\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.39830 | − | 4.98056i | −0.176214 | − | 0.199542i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.42523 | − | 14.5929i | −0.337009 | − | 0.583717i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −45.8379 | −1.82768 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.501625 | −0.0199694 | −0.00998468 | − | 0.999950i | \(-0.503178\pi\) | ||||
−0.00998468 | + | 0.999950i | \(0.503178\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.826214 | + | 1.43104i | 0.0327873 | + | 0.0567893i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.58929 | + | 3.20506i | −0.300699 | + | 0.126989i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.5112 | + | 30.3303i | −0.691651 | + | 1.19797i | 0.279646 | + | 0.960103i | \(0.409783\pi\) |
−0.971297 | + | 0.237871i | \(0.923551\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.29049 | + | 12.6275i | −0.287509 | + | 0.497980i | −0.973215 | − | 0.229899i | \(-0.926160\pi\) |
0.685706 | + | 0.727879i | \(0.259494\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.6503 | − | 20.1790i | −0.458022 | − | 0.793318i | 0.540834 | − | 0.841129i | \(-0.318109\pi\) |
−0.998856 | + | 0.0478116i | \(0.984775\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.9699 | + | 48.4453i | −1.09791 | + | 1.90164i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.26780 | − | 7.39204i | −0.167012 | − | 0.289273i | 0.770356 | − | 0.637614i | \(-0.220078\pi\) |
−0.937368 | + | 0.348341i | \(0.886745\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.1684 | − | 17.6123i | 0.397314 | − | 0.688168i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.81616 | − | 3.14568i | −0.0707476 | − | 0.122538i | 0.828482 | − | 0.560016i | \(-0.189205\pi\) |
−0.899229 | + | 0.437478i | \(0.855872\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.0231 | −1.20666 | −0.603330 | − | 0.797492i | \(-0.706160\pi\) | ||||
−0.603330 | + | 0.797492i | \(0.706160\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.3549 | − | 48.7313i | 0.634217 | − | 1.88972i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.83011 | − | 15.2942i | 0.341903 | − | 0.592194i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.29156 | + | 5.70116i | −0.127069 | + | 0.220091i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.291838 | + | 0.505478i | 0.0112495 | + | 0.0194848i | 0.871595 | − | 0.490226i | \(-0.163086\pi\) |
−0.860346 | + | 0.509711i | \(0.829752\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.7332 | 1.29647 | 0.648237 | − | 0.761439i | \(-0.275507\pi\) | ||||
0.648237 | + | 0.761439i | \(0.275507\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.2785 | − | 2.48636i | 0.471204 | − | 0.0954178i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.60312 | − | 2.77668i | −0.0613417 | − | 0.106247i | 0.833724 | − | 0.552182i | \(-0.186205\pi\) |
−0.895065 | + | 0.445935i | \(0.852871\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.4257 | −0.856841 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.2848 | −0.582306 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.3674 | 1.23131 | 0.615657 | − | 0.788014i | \(-0.288891\pi\) | ||||
0.615657 | + | 0.788014i | \(0.288891\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.9521 | 1.24995 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.93476 | −0.338428 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.2591 | −0.802943 | −0.401472 | − | 0.915871i | \(-0.631501\pi\) | ||||
−0.401472 | + | 0.915871i | \(0.631501\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.7985 | − | 34.2920i | −0.746715 | − | 1.29335i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.0028 | + | 22.6509i | 0.752283 | + | 0.851873i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.6544 | 1.18880 | 0.594402 | − | 0.804168i | \(-0.297389\pi\) | ||||
0.594402 | + | 0.804168i | \(0.297389\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.0526 | + | 22.6078i | 0.488824 | + | 0.846669i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.0925 | − | 17.4807i | 0.377438 | − | 0.653741i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.9776 | + | 25.9420i | −0.558571 | + | 0.967473i | 0.439045 | + | 0.898465i | \(0.355317\pi\) |
−0.997616 | + | 0.0690079i | \(0.978017\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.5313 | + | 3.34755i | −0.615656 | + | 0.124669i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 39.8486 | 1.47994 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.6310 | + | 23.6095i | 0.505544 | + | 0.875629i | 0.999979 | + | 0.00641398i | \(0.00204165\pi\) |
−0.494435 | + | 0.869215i | \(0.664625\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.6985 | + | 51.4393i | −1.09844 | + | 1.90255i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.2717 | + | 19.5232i | 0.416330 | + | 0.721105i | 0.995567 | − | 0.0940545i | \(-0.0299828\pi\) |
−0.579237 | + | 0.815159i | \(0.696649\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.67085 | − | 6.35809i | 0.135217 | − | 0.234203i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.82742 | + | 15.2895i | 0.324722 | + | 0.562435i | 0.981456 | − | 0.191687i | \(-0.0613960\pi\) |
−0.656734 | + | 0.754122i | \(0.728063\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.31474 | + | 5.74130i | −0.121606 | + | 0.210628i | −0.920401 | − | 0.390975i | \(-0.872138\pi\) |
0.798795 | + | 0.601603i | \(0.205471\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.4735 | + | 35.4611i | −0.750089 | + | 1.29919i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.92291 | − | 4.44224i | −0.143340 | − | 0.162316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.93721 | + | 6.81944i | 0.143671 | + | 0.248845i | 0.928876 | − | 0.370390i | \(-0.120776\pi\) |
−0.785206 | + | 0.619235i | \(0.787443\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 63.9295 | 2.32663 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.1503 | −1.35025 | −0.675125 | − | 0.737703i | \(-0.735910\pi\) | ||||
−0.675125 | + | 0.737703i | \(0.735910\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.2273 | − | 28.1065i | −0.588238 | − | 1.01886i | −0.994463 | − | 0.105085i | \(-0.966488\pi\) |
0.406225 | − | 0.913773i | \(-0.366845\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.1631 | + | 2.86799i | −0.512737 | + | 0.103828i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.29218 | − | 12.6304i | 0.263305 | − | 0.456058i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.4992 | − | 19.9172i | 0.414671 | − | 0.718232i | −0.580723 | − | 0.814101i | \(-0.697230\pi\) |
0.995394 | + | 0.0958699i | \(0.0305633\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.2117 | − | 22.8834i | −0.475194 | − | 0.823059i | 0.524403 | − | 0.851470i | \(-0.324289\pi\) |
−0.999596 | + | 0.0284109i | \(0.990955\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.4519 | + | 51.0123i | −1.05794 | + | 1.83241i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.85914 | − | 6.68423i | −0.138268 | − | 0.239487i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.1515 | + | 33.1714i | −0.685296 | + | 1.18697i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.0239 | − | 29.4862i | −0.607609 | − | 1.05241i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.11300 | 0.324843 | 0.162422 | − | 0.986721i | \(-0.448069\pi\) | ||||
0.162422 | + | 0.986721i | \(0.448069\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.6027 | − | 17.6682i | −0.554767 | − | 0.628209i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.858162 | − | 1.48638i | 0.0304742 | − | 0.0527829i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.5330 | − | 47.6886i | 0.975270 | − | 1.68922i | 0.296228 | − | 0.955117i | \(-0.404271\pi\) |
0.679042 | − | 0.734099i | \(-0.262395\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.61988 | − | 11.4660i | −0.234195 | − | 0.405637i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33.6739 | −1.18833 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.8243 | − | 31.5078i | −0.980679 | − | 1.11050i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.0961 | − | 19.2191i | −0.390119 | − | 0.675707i | 0.602346 | − | 0.798235i | \(-0.294233\pi\) |
−0.992465 | + | 0.122529i | \(0.960900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.0941 | −1.82927 | −0.914636 | − | 0.404279i | \(-0.867522\pi\) | ||||
−0.914636 | + | 0.404279i | \(0.867522\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.2158 | −0.988357 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −51.3100 | −1.79511 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.6107 | −1.38242 | −0.691212 | − | 0.722652i | \(-0.742923\pi\) | ||||
−0.691212 | + | 0.722652i | \(0.742923\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.3470 | 1.12755 | 0.563773 | − | 0.825930i | \(-0.309349\pi\) | ||||
0.563773 | + | 0.825930i | \(0.309349\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.1724 | −1.32738 | −0.663692 | − | 0.748006i | \(-0.731012\pi\) | ||||
−0.663692 | + | 0.748006i | \(0.731012\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.7372 | + | 48.0422i | 0.963353 | + | 1.66858i | 0.713977 | + | 0.700169i | \(0.246892\pi\) |
0.249375 | + | 0.968407i | \(0.419775\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.12520 | − | 41.1181i | 0.177578 | − | 1.42466i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39.0399 | 1.35103 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.35256 | + | 4.07475i | 0.0812193 | + | 0.140676i | 0.903774 | − | 0.428010i | \(-0.140785\pi\) |
−0.822555 | + | 0.568686i | \(0.807452\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.58195 | − | 9.66822i | 0.192481 | − | 0.333387i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.0648 | − | 38.2174i | 0.759054 | − | 1.31472i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.3164 | + | 4.92402i | −0.835522 | + | 0.169191i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.3809 | −1.11000 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.87889 | + | 3.25434i | 0.0643321 | + | 0.111426i | 0.896398 | − | 0.443251i | \(-0.146175\pi\) |
−0.832065 | + | 0.554678i | \(0.812842\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.5780 | + | 46.0345i | −0.907888 | + | 1.57251i | −0.0908957 | + | 0.995860i | \(0.528973\pi\) |
−0.816993 | + | 0.576648i | \(0.804360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.4888 | − | 45.8799i | −0.903786 | − | 1.56540i | −0.822538 | − | 0.568709i | \(-0.807443\pi\) |
−0.0812476 | − | 0.996694i | \(-0.525890\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.57834 | − | 16.5902i | 0.326051 | − | 0.564736i | −0.655674 | − | 0.755044i | \(-0.727615\pi\) |
0.981724 | + | 0.190308i | \(0.0609487\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.3958 | − | 33.5945i | −0.659477 | − | 1.14225i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.15717 | + | 7.20043i | −0.141022 | + | 0.244258i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.957046 | + | 1.65765i | −0.0324283 | + | 0.0561674i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.1862 | − | 42.2693i | 0.479581 | − | 1.42896i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.83865 | − | 3.18463i | −0.0620868 | − | 0.107537i | 0.833311 | − | 0.552804i | \(-0.186442\pi\) |
−0.895398 | + | 0.445267i | \(0.853109\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.8862 | 0.501529 | 0.250765 | − | 0.968048i | \(-0.419318\pi\) | ||||
0.250765 | + | 0.968048i | \(0.419318\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.9262 | −1.34362 | −0.671811 | − | 0.740722i | \(-0.734483\pi\) | ||||
−0.671811 | + | 0.740722i | \(0.734483\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.25124 | + | 7.36336i | 0.142743 | + | 0.247237i | 0.928528 | − | 0.371261i | \(-0.121075\pi\) |
−0.785786 | + | 0.618499i | \(0.787741\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.366118 | + | 1.09089i | −0.0122792 | + | 0.0365872i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.71857 | − | 9.90486i | 0.191365 | − | 0.331453i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.5877 | − | 63.3717i | 1.22299 | − | 2.11828i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.1826 | − | 22.8329i | −0.439665 | − | 0.761521i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.4391 | − | 66.5785i | 1.28059 | − | 2.21805i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.64368 | + | 4.57899i | 0.0878789 | + | 0.152211i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.59544 | + | 2.76339i | −0.0529758 | + | 0.0917568i | −0.891297 | − | 0.453419i | \(-0.850204\pi\) |
0.838321 | + | 0.545176i | \(0.183537\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.63889 | + | 13.2309i | 0.253088 | + | 0.438361i | 0.964374 | − | 0.264541i | \(-0.0852206\pi\) |
−0.711287 | + | 0.702902i | \(0.751887\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.77714 | 0.0919099 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.8801 | − | 2.81069i | 0.458360 | − | 0.0928170i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.2681 | + | 43.7656i | −0.833516 | + | 1.44369i | 0.0617164 | + | 0.998094i | \(0.480343\pi\) |
−0.895233 | + | 0.445599i | \(0.852991\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.99310 | − | 8.64831i | 0.164350 | − | 0.284662i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.5321 | − | 63.2755i | −1.20117 | − | 2.08048i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47.9781 | −1.57411 | −0.787055 | − | 0.616883i | \(-0.788395\pi\) | ||||
−0.787055 | + | 0.616883i | \(0.788395\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.9748 | − | 13.9257i | 1.08070 | − | 0.456395i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 50.7623 | + | 87.9228i | 1.66010 | + | 2.87538i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.5226 | 0.670443 | 0.335222 | − | 0.942139i | \(-0.391189\pi\) | ||||
0.335222 | + | 0.942139i | \(0.391189\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.95586 | 0.324552 | 0.162276 | − | 0.986745i | \(-0.448117\pi\) | ||||
0.162276 | + | 0.986745i | \(0.448117\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.31170 | −0.205537 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.2213 | −0.689601 | −0.344800 | − | 0.938676i | \(-0.612053\pi\) | ||||
−0.344800 | + | 0.938676i | \(0.612053\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.77930 | 0.284988 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.9191 | 1.16353 | 0.581767 | − | 0.813355i | \(-0.302361\pi\) | ||||
0.581767 | + | 0.813355i | \(0.302361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.15736 | + | 8.93281i | 0.166888 | + | 0.289059i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.3370 | − | 11.7054i | −0.333798 | − | 0.377988i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.97290 | 0.257190 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.49866 | − | 6.05986i | −0.112626 | − | 0.195074i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.9559 | + | 27.6365i | −0.513108 | + | 0.888729i | 0.486777 | + | 0.873526i | \(0.338173\pi\) |
−0.999884 | + | 0.0152023i | \(0.995161\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.6645 | + | 49.6483i | −0.919886 | + | 1.59329i | −0.120301 | + | 0.992737i | \(0.538386\pi\) |
−0.799585 | + | 0.600553i | \(0.794947\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.1891 | + | 17.1999i | 0.486940 | + | 0.551403i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.58455 | −0.274644 | −0.137322 | − | 0.990526i | \(-0.543850\pi\) | ||||
−0.137322 | + | 0.990526i | \(0.543850\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.66845 | + | 9.81805i | 0.181164 | + | 0.313786i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.2504 | − | 19.4863i | 0.358834 | − | 0.621518i | −0.628933 | − | 0.777460i | \(-0.716508\pi\) |
0.987766 | + | 0.155942i | \(0.0498412\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.6411 | + | 72.1244i | 1.32679 | + | 2.29807i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.9796 | + | 36.3378i | −0.667114 | + | 1.15548i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.3652 | − | 33.5415i | −0.615156 | − | 1.06548i | −0.990357 | − | 0.138538i | \(-0.955760\pi\) |
0.375201 | − | 0.926944i | \(-0.377574\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.75875 | − | 4.77829i | 0.0874582 | − | 0.151482i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.3955 | + | 31.8619i | −0.582590 | + | 1.00908i | 0.412581 | + | 0.910921i | \(0.364627\pi\) |
−0.995171 | + | 0.0981549i | \(0.968706\pi\) | |||||||
\(998\) | 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 | 3024.2.q.l.2305.2 | 22 | ||
3.2 | odd | 2 | 1008.2.q.l.625.9 | 22 | |||
4.3 | odd | 2 | 1512.2.q.d.793.2 | 22 | |||
7.4 | even | 3 | 3024.2.t.k.1873.10 | 22 | |||
9.2 | odd | 6 | 1008.2.t.l.961.2 | 22 | |||
9.7 | even | 3 | 3024.2.t.k.289.10 | 22 | |||
12.11 | even | 2 | 504.2.q.c.121.3 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.t.l.193.2 | 22 | |||
28.11 | odd | 6 | 1512.2.t.c.361.10 | 22 | |||
36.7 | odd | 6 | 1512.2.t.c.289.10 | 22 | |||
36.11 | even | 6 | 504.2.t.c.457.10 | yes | 22 | ||
63.11 | odd | 6 | 1008.2.q.l.529.9 | 22 | |||
63.25 | even | 3 | inner | 3024.2.q.l.2881.2 | 22 | ||
84.11 | even | 6 | 504.2.t.c.193.10 | yes | 22 | ||
252.11 | even | 6 | 504.2.q.c.25.3 | ✓ | 22 | ||
252.151 | odd | 6 | 1512.2.q.d.1369.2 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.3 | ✓ | 22 | 252.11 | even | 6 | ||
504.2.q.c.121.3 | yes | 22 | 12.11 | even | 2 | ||
504.2.t.c.193.10 | yes | 22 | 84.11 | even | 6 | ||
504.2.t.c.457.10 | yes | 22 | 36.11 | even | 6 | ||
1008.2.q.l.529.9 | 22 | 63.11 | odd | 6 | |||
1008.2.q.l.625.9 | 22 | 3.2 | odd | 2 | |||
1008.2.t.l.193.2 | 22 | 21.11 | odd | 6 | |||
1008.2.t.l.961.2 | 22 | 9.2 | odd | 6 | |||
1512.2.q.d.793.2 | 22 | 4.3 | odd | 2 | |||
1512.2.q.d.1369.2 | 22 | 252.151 | odd | 6 | |||
1512.2.t.c.289.10 | 22 | 36.7 | odd | 6 | |||
1512.2.t.c.361.10 | 22 | 28.11 | odd | 6 | |||
3024.2.q.l.2305.2 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.q.l.2881.2 | 22 | 63.25 | even | 3 | inner | ||
3024.2.t.k.289.10 | 22 | 9.7 | even | 3 | |||
3024.2.t.k.1873.10 | 22 | 7.4 | even | 3 |