Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(57,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.57");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 953.1 | ||
Character | \(\chi\) | \(=\) | 1148.953 |
Dual form | 1148.2.n.e.365.1 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 | ||||||||
\(3\) | −2.28641 | −1.32006 | −0.660029 | − | 0.751240i | \(-0.729456\pi\) | ||||
−0.660029 | + | 0.751240i | \(0.729456\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.815322 | − | 2.50930i | −0.364623 | − | 1.12219i | −0.950217 | − | 0.311589i | \(-0.899139\pi\) |
0.585594 | − | 0.810605i | \(-0.300861\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.809017 | − | 0.587785i | 0.305780 | − | 0.222162i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.22766 | 0.742554 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.72446 | + | 5.30734i | −0.519944 | + | 1.60022i | 0.254159 | + | 0.967162i | \(0.418201\pi\) |
−0.774103 | + | 0.633060i | \(0.781799\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00138 | + | 0.727546i | 0.277733 | + | 0.201785i | 0.717928 | − | 0.696117i | \(-0.245091\pi\) |
−0.440195 | + | 0.897902i | \(0.645091\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.86416 | + | 5.73729i | 0.481323 | + | 1.48136i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.144210 | + | 0.443834i | −0.0349762 | + | 0.107646i | −0.967020 | − | 0.254699i | \(-0.918024\pi\) |
0.932044 | + | 0.362345i | \(0.118024\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.66632 | + | 1.93720i | −0.611697 | + | 0.444424i | −0.850011 | − | 0.526764i | \(-0.823405\pi\) |
0.238315 | + | 0.971188i | \(0.423405\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.84974 | + | 1.34392i | −0.403647 | + | 0.293267i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.607844 | + | 0.441625i | 0.126744 | + | 0.0920851i | 0.649351 | − | 0.760489i | \(-0.275040\pi\) |
−0.522607 | + | 0.852574i | \(0.675040\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.58676 | + | 1.15285i | −0.317352 | + | 0.230570i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.76588 | 0.339844 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.433514 | − | 1.33422i | −0.0805015 | − | 0.247758i | 0.902703 | − | 0.430263i | \(-0.141579\pi\) |
−0.983205 | + | 0.182505i | \(0.941579\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.42526 | − | 4.38651i | 0.255985 | − | 0.787840i | −0.737649 | − | 0.675184i | \(-0.764064\pi\) |
0.993634 | − | 0.112656i | \(-0.0359359\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.94282 | − | 12.1347i | 0.686356 | − | 2.11239i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.13454 | − | 1.55083i | −0.360803 | − | 0.262139i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.000945850 | − | 0.00291103i | −0.000155497 | − | 0.000478570i | 0.950979 | − | 0.309256i | \(-0.100080\pi\) |
−0.951134 | + | 0.308778i | \(0.900080\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.28957 | − | 1.66347i | −0.366624 | − | 0.266368i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.18765 | − | 5.55328i | 0.497827 | − | 0.867277i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.80937 | + | 3.49421i | 0.733422 | + | 0.532862i | 0.890644 | − | 0.454701i | \(-0.150254\pi\) |
−0.157222 | + | 0.987563i | \(0.550254\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.81626 | − | 5.58987i | −0.270752 | − | 0.833289i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.92558 | + | 2.12556i | 0.426740 | + | 0.310045i | 0.780344 | − | 0.625351i | \(-0.215044\pi\) |
−0.353604 | + | 0.935395i | \(0.615044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.329724 | − | 1.01479i | 0.0461706 | − | 0.142098i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.30725 | + | 4.02329i | 0.179564 | + | 0.552641i | 0.999812 | − | 0.0193663i | \(-0.00616487\pi\) |
−0.820248 | + | 0.572007i | \(0.806165\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.7237 | 1.98534 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.09630 | − | 4.42922i | 0.807475 | − | 0.586665i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.140019 | + | 0.101730i | 0.0182290 | + | 0.0132441i | 0.596862 | − | 0.802344i | \(-0.296414\pi\) |
−0.578633 | + | 0.815588i | \(0.696414\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.52668 | − | 6.92154i | 1.21977 | − | 0.886212i | 0.223685 | − | 0.974661i | \(-0.428191\pi\) |
0.996081 | + | 0.0884496i | \(0.0281912\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.80222 | − | 1.30939i | 0.227058 | − | 0.164967i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00919 | − | 3.10595i | 0.125174 | − | 0.385246i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.51906 | + | 4.67519i | 0.185583 | + | 0.571165i | 0.999958 | − | 0.00917352i | \(-0.00292006\pi\) |
−0.814375 | + | 0.580339i | \(0.802920\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.38978 | − | 1.00973i | −0.167310 | − | 0.121558i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.221011 | − | 0.680201i | 0.0262291 | − | 0.0807250i | −0.937085 | − | 0.349101i | \(-0.886487\pi\) |
0.963314 | + | 0.268376i | \(0.0864870\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.00251 | −0.351418 | −0.175709 | − | 0.984442i | \(-0.556222\pi\) | ||||
−0.175709 | + | 0.984442i | \(0.556222\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.62799 | − | 2.63589i | 0.418924 | − | 0.304366i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.72446 | + | 5.30734i | 0.196520 | + | 0.604827i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9295 | 1.22966 | 0.614832 | − | 0.788658i | \(-0.289224\pi\) | ||||
0.614832 | + | 0.788658i | \(0.289224\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7205 | −1.19117 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.64278 | 0.619376 | 0.309688 | − | 0.950838i | \(-0.399775\pi\) | ||||
0.309688 | + | 0.950838i | \(0.399775\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.23129 | 0.133552 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.991190 | + | 3.05057i | 0.106267 | + | 0.327055i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.96074 | − | 5.05728i | 0.737837 | − | 0.536070i | −0.154196 | − | 0.988040i | \(-0.549279\pi\) |
0.892033 | + | 0.451970i | \(0.149279\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.23778 | 0.129754 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.25873 | + | 10.0294i | −0.337915 | + | 1.04000i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.03492 | + | 5.11117i | 0.721768 | + | 0.524395i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.25934 | + | 3.87584i | 0.127866 | + | 0.393532i | 0.994412 | − | 0.105565i | \(-0.0336651\pi\) |
−0.866546 | + | 0.499097i | \(0.833665\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.84151 | + | 11.8229i | −0.386086 | + | 1.18825i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.46711 | + | 6.15172i | −0.842509 | + | 0.612119i | −0.923070 | − | 0.384631i | \(-0.874329\pi\) |
0.0805614 | + | 0.996750i | \(0.474329\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.9526 | − | 10.8637i | 1.47332 | − | 1.07043i | 0.493687 | − | 0.869639i | \(-0.335649\pi\) |
0.979634 | − | 0.200791i | \(-0.0643513\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.88043 | + | 3.54584i | 0.476281 | + | 0.346038i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.29753 | + | 4.57542i | −0.608805 | + | 0.442323i | −0.848993 | − | 0.528403i | \(-0.822791\pi\) |
0.240188 | + | 0.970726i | \(0.422791\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.1629 | 1.73969 | 0.869846 | − | 0.493323i | \(-0.164218\pi\) | ||||
0.869846 | + | 0.493323i | \(0.164218\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.00216260 | + | 0.00665580i | 0.000205265 | + | 0.000631740i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.19207 | − | 3.66881i | 0.112140 | − | 0.345132i | −0.879200 | − | 0.476454i | \(-0.841922\pi\) |
0.991340 | + | 0.131321i | \(0.0419220\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.612581 | − | 1.88533i | 0.0571235 | − | 0.175808i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.23074 | + | 1.62073i | 0.206232 | + | 0.149836i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.144210 | + | 0.443834i | 0.0132197 | + | 0.0406862i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.2949 | − | 11.8389i | −1.48135 | − | 1.07627i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.28826 | + | 12.6971i | −0.657160 | + | 1.14486i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.48613 | − | 4.71245i | −0.580137 | − | 0.421494i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.33300 | + | 4.10255i | 0.118284 | + | 0.364042i | 0.992618 | − | 0.121284i | \(-0.0387010\pi\) |
−0.874333 | + | 0.485326i | \(0.838701\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.9962 | − | 7.98919i | −0.968160 | − | 0.703409i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.12252 | + | 6.53244i | −0.185445 | + | 0.570742i | −0.999956 | − | 0.00940693i | \(-0.997006\pi\) |
0.814510 | + | 0.580149i | \(0.197006\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.01844 | + | 3.13445i | −0.0883104 | + | 0.271791i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.43976 | − | 4.43113i | −0.123915 | − | 0.381371i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.12510 | 0.352431 | 0.176215 | − | 0.984352i | \(-0.443614\pi\) | ||||
0.176215 | + | 0.984352i | \(0.443614\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.4255 | − | 9.75417i | 1.13873 | − | 0.827338i | 0.151790 | − | 0.988413i | \(-0.451496\pi\) |
0.986942 | + | 0.161075i | \(0.0514961\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.68907 | − | 4.85990i | −0.563321 | − | 0.409277i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.58818 | + | 4.06005i | −0.467307 | + | 0.339518i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.99450 | + | 2.17563i | −0.248680 | + | 0.180677i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.706539 | + | 2.17450i | −0.0582743 | + | 0.179350i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.317187 | + | 0.976200i | 0.0259849 | + | 0.0799734i | 0.963208 | − | 0.268757i | \(-0.0866129\pi\) |
−0.937223 | + | 0.348730i | \(0.886613\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.18087 | + | 2.31104i | 0.258856 | + | 0.188070i | 0.709642 | − | 0.704562i | \(-0.248857\pi\) |
−0.450787 | + | 0.892632i | \(0.648857\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.321252 | + | 0.988712i | −0.0259717 | + | 0.0799326i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.1691 | −0.977448 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.59131 | + | 3.33578i | −0.366427 | + | 0.266225i | −0.755728 | − | 0.654886i | \(-0.772717\pi\) |
0.389301 | + | 0.921111i | \(0.372717\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.98890 | − | 9.19888i | −0.237035 | − | 0.729518i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.751337 | 0.0592137 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.5161 | −1.05866 | −0.529332 | − | 0.848415i | \(-0.677557\pi\) | ||||
−0.529332 | + | 0.848415i | \(0.677557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −33.6644 | −2.62077 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.2733 | −0.949740 | −0.474870 | − | 0.880056i | \(-0.657505\pi\) | ||||
−0.474870 | + | 0.880056i | \(0.657505\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.54378 | − | 10.9066i | −0.272598 | − | 0.838972i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.93966 | + | 4.31542i | −0.454218 | + | 0.330008i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.4998 | 1.86268 | 0.931341 | − | 0.364149i | \(-0.118640\pi\) | ||||
0.931341 | + | 0.364149i | \(0.118640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.606089 | + | 1.86535i | −0.0458160 | + | 0.141007i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.320141 | − | 0.232596i | −0.0240633 | − | 0.0174830i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.29543 | + | 13.2200i | 0.321055 | + | 0.988107i | 0.973190 | + | 0.230003i | \(0.0738737\pi\) |
−0.652135 | + | 0.758103i | \(0.726126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.541715 | + | 1.66723i | −0.0402654 | + | 0.123924i | −0.969169 | − | 0.246398i | \(-0.920753\pi\) |
0.928903 | + | 0.370323i | \(0.120753\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.7819 | + | 15.8255i | −1.61016 | + | 1.16985i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.00653348 | + | 0.00474685i | −0.000480351 | + | 0.000348995i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.10689 | − | 1.53075i | −0.154071 | − | 0.111939i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.42863 | − | 1.03796i | 0.103917 | − | 0.0755004i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.32091 | 0.457365 | 0.228683 | − | 0.973501i | \(-0.426558\pi\) | ||||
0.228683 | + | 0.973501i | \(0.426558\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.02996 | − | 24.7137i | −0.578009 | − | 1.77893i | −0.625696 | − | 0.780067i | \(-0.715185\pi\) |
0.0476869 | − | 0.998862i | \(-0.484815\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.30741 | + | 7.10148i | −0.165237 | + | 0.508547i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.89014 | + | 11.9726i | −0.277161 | + | 0.853014i | 0.711478 | + | 0.702708i | \(0.248026\pi\) |
−0.988639 | + | 0.150306i | \(0.951974\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.6741 | + | 14.2941i | 1.39466 | + | 1.01328i | 0.995336 | + | 0.0964739i | \(0.0307564\pi\) |
0.399328 | + | 0.916808i | \(0.369244\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.47319 | − | 10.6894i | −0.244980 | − | 0.753972i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.13495 | − | 0.824593i | −0.0796582 | − | 0.0578750i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.5338 | − | 3.47106i | −1.15477 | − | 0.242429i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.35407 | + | 0.983791i | 0.0941145 | + | 0.0683782i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.68340 | − | 17.4917i | −0.393129 | − | 1.20993i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.97480 | − | 5.06749i | −0.480165 | − | 0.348860i | 0.321225 | − | 0.947003i | \(-0.395906\pi\) |
−0.801390 | + | 0.598143i | \(0.795906\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.505320 | + | 1.55522i | −0.0346240 | + | 0.106562i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.84685 | − | 14.9171i | 0.330552 | − | 1.01734i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.42526 | − | 4.38651i | −0.0967532 | − | 0.297776i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.86497 | 0.463892 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.467320 | + | 0.339527i | −0.0314353 | + | 0.0228391i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.26908 | + | 6.00784i | 0.553739 | + | 0.402315i | 0.829162 | − | 0.559008i | \(-0.188818\pi\) |
−0.275423 | + | 0.961323i | \(0.588818\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.53477 | + | 2.56816i | −0.235651 | + | 0.171211i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.5788 | + | 15.6779i | −1.43224 | + | 1.04058i | −0.442641 | + | 0.896699i | \(0.645958\pi\) |
−0.989595 | + | 0.143881i | \(0.954042\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.94238 | − | 9.05570i | 0.194438 | − | 0.598418i | −0.805545 | − | 0.592535i | \(-0.798127\pi\) |
0.999983 | − | 0.00588307i | \(-0.00187265\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.94282 | − | 12.1347i | −0.259418 | − | 0.798407i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.65893 | + | 4.11145i | 0.370729 | + | 0.269350i | 0.757513 | − | 0.652820i | \(-0.226414\pi\) |
−0.386784 | + | 0.922170i | \(0.626414\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.94838 | − | 9.07418i | 0.192331 | − | 0.591934i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −24.9893 | −1.62323 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.25004 | + | 5.26746i | −0.468966 | + | 0.340724i | −0.797038 | − | 0.603929i | \(-0.793601\pi\) |
0.328072 | + | 0.944653i | \(0.393601\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.16855 | + | 15.9072i | 0.332935 | + | 1.02467i | 0.967730 | + | 0.251989i | \(0.0810846\pi\) |
−0.634795 | + | 0.772681i | \(0.718915\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.2138 | 1.23257 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.63844 | −0.168564 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.07941 | −0.259567 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.9017 | −0.817612 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.58483 | − | 11.0330i | −0.226272 | − | 0.696394i | −0.998160 | − | 0.0606356i | \(-0.980687\pi\) |
0.771888 | − | 0.635759i | \(-0.219313\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.39205 | + | 2.46447i | −0.213257 | + | 0.154940i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.81523 | −0.176297 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.20278 | + | 9.85714i | −0.199784 | + | 0.614872i | 0.800103 | + | 0.599862i | \(0.204778\pi\) |
−0.999887 | + | 0.0150096i | \(0.995222\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.00247627 | − | 0.00179911i | −0.000153868 | − | 0.000111792i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.965722 | − | 2.97219i | −0.0597767 | − | 0.183974i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.03630 | + | 12.4225i | −0.248889 | + | 0.766002i | 0.746083 | + | 0.665853i | \(0.231932\pi\) |
−0.994972 | + | 0.100149i | \(0.968068\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.02982 | − | 6.56055i | 0.554697 | − | 0.403011i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.9151 | + | 11.5630i | −0.973988 | + | 0.707644i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.9699 | + | 10.8762i | 0.912728 | + | 0.663136i | 0.941703 | − | 0.336444i | \(-0.109224\pi\) |
−0.0289751 | + | 0.999580i | \(0.509224\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.08633 | − | 2.96889i | 0.248227 | − | 0.180347i | −0.456714 | − | 0.889614i | \(-0.650974\pi\) |
0.704940 | + | 0.709266i | \(0.250974\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.83006 | −0.171283 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.38226 | − | 10.4095i | −0.203958 | − | 0.627718i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.46421 | + | 26.0502i | −0.508565 | + | 1.56520i | 0.286128 | + | 0.958191i | \(0.407632\pi\) |
−0.794693 | + | 0.607011i | \(0.792368\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.17500 | − | 9.77166i | 0.190083 | − | 0.585014i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.4452 | + | 11.9482i | 0.981041 | + | 0.712768i | 0.957941 | − | 0.286965i | \(-0.0926465\pi\) |
0.0230997 | + | 0.999733i | \(0.492646\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.881266 | + | 2.71226i | 0.0523858 | + | 0.161227i | 0.973827 | − | 0.227291i | \(-0.0729870\pi\) |
−0.921441 | + | 0.388518i | \(0.872987\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.0847 | − | 11.6862i | −0.952776 | − | 0.692232i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.685276 | − | 6.36635i | −0.0404506 | − | 0.375794i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5771 | + | 9.86434i | 0.798653 | + | 0.580255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.87936 | − | 8.86176i | −0.168791 | − | 0.519485i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.9126 | − | 12.2878i | −0.988048 | − | 0.717859i | −0.0285549 | − | 0.999592i | \(-0.509091\pi\) |
−0.959493 | + | 0.281734i | \(0.909091\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.141111 | − | 0.434294i | 0.00821577 | − | 0.0252855i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.04519 | + | 9.37213i | −0.176700 | + | 0.543826i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.287382 | + | 0.884470i | 0.0166197 | + | 0.0511502i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.94471 | 0.342647 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.3593 | − | 14.0653i | 1.11216 | − | 0.808032i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −25.1355 | − | 18.2620i | −1.43926 | − | 1.04568i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.90843 | + | 6.47236i | −0.508431 | + | 0.369397i | −0.812228 | − | 0.583340i | \(-0.801746\pi\) |
0.303797 | + | 0.952737i | \(0.401746\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −34.1877 | + | 24.8388i | −1.94487 | + | 1.41303i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.83605 | + | 5.65077i | −0.104113 | + | 0.320426i | −0.989521 | − | 0.144388i | \(-0.953879\pi\) |
0.885408 | + | 0.464814i | \(0.153879\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.56973 | − | 7.90880i | −0.145249 | − | 0.447032i | 0.851794 | − | 0.523878i | \(-0.175515\pi\) |
−0.997043 | + | 0.0768457i | \(0.975515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.75503 | − | 3.45473i | −0.267916 | − | 0.194652i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.09067 | + | 6.43441i | −0.117424 | + | 0.361393i | −0.992445 | − | 0.122692i | \(-0.960847\pi\) |
0.875021 | + | 0.484085i | \(0.160847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.82873 | 0.438324 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.3987 | − | 10.4613i | 0.803659 | − | 0.583892i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.475282 | − | 1.46277i | −0.0264454 | − | 0.0813906i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.42771 | −0.134665 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −41.5279 | −2.29650 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.61622 | 0.199369 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6233 | 0.583912 | 0.291956 | − | 0.956432i | \(-0.405694\pi\) | ||||
0.291956 | + | 0.956432i | \(0.405694\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.00210703 | − | 0.00648478i | −0.000115465 | − | 0.000355364i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.4929 | − | 7.62357i | 0.573291 | − | 0.416520i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.5785 | 0.903091 | 0.451546 | − | 0.892248i | \(-0.350873\pi\) | ||||
0.451546 | + | 0.892248i | \(0.350873\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.72555 | + | 8.38839i | −0.148032 | + | 0.455595i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.8229 | + | 15.1287i | 1.12762 | + | 0.819265i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.309017 | − | 0.951057i | −0.0166853 | − | 0.0513522i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.40061 | + | 4.31064i | −0.0754064 | + | 0.232077i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7842 | − | 15.1006i | 1.11576 | − | 0.810645i | 0.132196 | − | 0.991224i | \(-0.457797\pi\) |
0.983561 | + | 0.180579i | \(0.0577971\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.2627 | − | 13.9952i | 1.03111 | − | 0.749146i | 0.0625803 | − | 0.998040i | \(-0.480067\pi\) |
0.968531 | + | 0.248894i | \(0.0800670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.76832 | + | 1.28476i | 0.0943860 | + | 0.0685755i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.9575 | + | 11.5938i | −0.849335 | + | 0.617078i | −0.924962 | − | 0.380058i | \(-0.875904\pi\) |
0.0756279 | + | 0.997136i | \(0.475904\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.88702 | −0.100153 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.329724 | − | 1.01479i | −0.0174508 | − | 0.0537081i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.17638 | + | 12.8536i | −0.220421 | + | 0.678385i | 0.778303 | + | 0.627888i | \(0.216081\pi\) |
−0.998724 | + | 0.0504970i | \(0.983919\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.51478 | + | 7.73969i | −0.132357 | + | 0.407352i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 37.2567 | + | 27.0686i | 1.95547 | + | 1.42073i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.44801 | + | 7.53422i | 0.128135 | + | 0.394359i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.45693 | − | 5.41778i | −0.389249 | − | 0.282806i | 0.375899 | − | 0.926661i | \(-0.377334\pi\) |
−0.765148 | + | 0.643855i | \(0.777334\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.10099 | − | 12.3708i | 0.369663 | − | 0.643999i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.42241 | + | 2.48653i | 0.177683 | + | 0.129094i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.410404 | − | 1.26309i | −0.0212499 | − | 0.0654005i | 0.939869 | − | 0.341535i | \(-0.110947\pi\) |
−0.961119 | + | 0.276134i | \(0.910947\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.8299 | + | 10.7746i | 0.765815 | + | 0.556397i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.536593 | − | 1.65146i | 0.0276360 | − | 0.0850547i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.76235 | + | 8.50165i | −0.141893 | + | 0.436700i | −0.996598 | − | 0.0824125i | \(-0.973738\pi\) |
0.854706 | + | 0.519113i | \(0.173738\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.04778 | − | 9.38009i | −0.156142 | − | 0.480557i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.1670 | −0.672804 | −0.336402 | − | 0.941718i | \(-0.609210\pi\) | ||||
−0.336402 | + | 0.941718i | \(0.609210\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.9117 | − | 8.65437i | 0.607078 | − | 0.441068i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.7136 | + | 7.78392i | 0.544605 | + | 0.395679i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.5805 | − | 16.4057i | 1.14488 | − | 0.831803i | 0.157087 | − | 0.987585i | \(-0.449790\pi\) |
0.987791 | + | 0.155782i | \(0.0497898\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.283666 | + | 0.206095i | −0.0143456 | + | 0.0104227i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.85294 | − | 14.9358i | 0.244799 | − | 0.753413i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.91106 | − | 27.4254i | −0.448364 | − | 1.37992i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.0855 | + | 17.4991i | 1.20882 | + | 0.878256i | 0.995123 | − | 0.0986446i | \(-0.0314507\pi\) |
0.213693 | + | 0.976901i | \(0.431451\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.32858 | − | 7.16663i | 0.116575 | − | 0.358780i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.3933 | 1.56771 | 0.783854 | − | 0.620945i | \(-0.213251\pi\) | ||||
0.783854 | + | 0.620945i | \(0.213251\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.61862 | − | 3.35563i | 0.230070 | − | 0.167156i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.74066 | + | 26.9010i | 0.434327 | + | 1.33672i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.0170809 | 0.000846668 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.6785 | −0.528017 | −0.264008 | − | 0.964520i | \(-0.585045\pi\) | ||||
−0.264008 | + | 0.964520i | \(0.585045\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.43166 | −0.465229 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.173073 | 0.00851639 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.60068 | − | 14.1594i | −0.225839 | − | 0.695060i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.6961 | + | 22.3020i | −1.50319 | + | 1.09213i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.8955 | −1.41164 | −0.705819 | − | 0.708392i | \(-0.749421\pi\) | ||||
−0.705819 | + | 0.708392i | \(0.749421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.59607 | + | 20.3006i | −0.321473 | + | 0.989391i | 0.651535 | + | 0.758619i | \(0.274125\pi\) |
−0.973008 | + | 0.230773i | \(0.925875\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.51720 | + | 4.73503i | 0.316877 | + | 0.230225i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.282846 | − | 0.870512i | −0.0137201 | − | 0.0422260i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.63887 | − | 11.1993i | 0.176097 | − | 0.541971i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.7768 | − | 9.28292i | 0.616872 | − | 0.448184i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.8580 | − | 18.0604i | 1.19737 | − | 0.869940i | 0.203346 | − | 0.979107i | \(-0.434818\pi\) |
0.994023 | + | 0.109167i | \(0.0348183\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.3218 | + | 11.8585i | 0.784377 | + | 0.569883i | 0.906290 | − | 0.422657i | \(-0.138903\pi\) |
−0.121912 | + | 0.992541i | \(0.538903\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.84666 | − | 4.97439i | 0.328272 | − | 0.238504i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.47622 | −0.118454 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.52453 | + | 4.69202i | 0.0727618 | + | 0.223938i | 0.980823 | − | 0.194899i | \(-0.0624379\pi\) |
−0.908062 | + | 0.418837i | \(0.862438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.688385 | − | 2.11863i | 0.0327802 | − | 0.100887i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.13252 | + | 3.48553i | −0.0538075 | + | 0.165602i | −0.974349 | − | 0.225042i | \(-0.927748\pi\) |
0.920541 | + | 0.390645i | \(0.127748\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.3655 | − | 13.3433i | −0.870607 | − | 0.632533i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.725218 | − | 2.23199i | −0.0343016 | − | 0.105570i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.8314 | − | 16.5880i | −1.07748 | − | 0.782835i | −0.100239 | − | 0.994963i | \(-0.531961\pi\) |
−0.977242 | + | 0.212128i | \(0.931961\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.9762 | + | 26.4943i | 1.12899 | + | 1.24757i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.27277 | − | 5.28397i | −0.341704 | − | 0.248263i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.00919 | − | 3.10595i | −0.0473113 | − | 0.145609i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.8737 | + | 22.4310i | 1.44421 | + | 1.04928i | 0.987142 | + | 0.159847i | \(0.0511001\pi\) |
0.457067 | + | 0.889432i | \(0.348900\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.254658 | + | 0.783758i | −0.0118864 | + | 0.0365827i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.26868 | − | 25.4484i | 0.385111 | − | 1.18525i | −0.551289 | − | 0.834315i | \(-0.685864\pi\) |
0.936400 | − | 0.350935i | \(-0.114136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.7429 | − | 36.1408i | −0.545737 | − | 1.67961i | −0.719231 | − | 0.694771i | \(-0.755506\pi\) |
0.173494 | − | 0.984835i | \(-0.444494\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 27.8236 | 1.29029 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.9597 | + | 23.2201i | −1.47892 | + | 1.07450i | −0.501016 | + | 0.865438i | \(0.667040\pi\) |
−0.977903 | + | 0.209059i | \(0.932960\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.97695 | + | 2.88943i | 0.183639 | + | 0.133421i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.4976 | − | 7.62696i | 0.483705 | − | 0.351432i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.8385 | + | 19.4993i | −1.23404 | + | 0.896580i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.99752 | − | 6.14774i | 0.0916526 | − | 0.282078i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.91210 | + | 8.96252i | 0.133336 | + | 0.410366i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.5835 | − | 22.9468i | −1.44309 | − | 1.04846i | −0.987386 | − | 0.158331i | \(-0.949389\pi\) |
−0.455701 | − | 0.890133i | \(-0.650611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.00117075 | − | 0.00360320i | 5.33816e−5 | − | 0.000164292i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.71786 | −0.0781655 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.69889 | − | 6.32012i | 0.394996 | − | 0.286982i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.681748 | − | 2.09820i | −0.0308929 | − | 0.0950787i | 0.934421 | − | 0.356170i | \(-0.115918\pi\) |
−0.965314 | + | 0.261091i | \(0.915918\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 30.9034 | 1.39750 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.5676 | −1.33437 | −0.667184 | − | 0.744893i | \(-0.732500\pi\) | ||||
−0.667184 | + | 0.744893i | \(0.732500\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.654689 | 0.0294857 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 32.7994 | 1.47422 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.221011 | − | 0.680201i | −0.00991368 | − | 0.0305112i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.7606 | − | 16.5365i | 1.01890 | − | 0.740276i | 0.0528446 | − | 0.998603i | \(-0.483171\pi\) |
0.966058 | + | 0.258327i | \(0.0831712\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.0619 | 1.25371 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.03506 | − | 12.4186i | 0.179914 | − | 0.553720i | −0.819909 | − | 0.572493i | \(-0.805976\pi\) |
0.999824 | + | 0.0187737i | \(0.00597621\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.3399 | + | 16.2309i | 0.994114 | + | 0.722266i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.10253 | + | 24.9370i | 0.359846 | + | 1.10749i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.15735 | + | 15.8727i | −0.228596 | + | 0.703545i | 0.769311 | + | 0.638875i | \(0.220600\pi\) |
−0.997907 | + | 0.0646707i | \(0.979400\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.42909 | + | 1.76483i | −0.107456 | + | 0.0780716i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.70841 | + | 3.42086i | −0.207881 | + | 0.151035i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −39.4514 | − | 28.6631i | −1.73844 | − | 1.26305i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.3261 | + | 11.8616i | −0.718021 | + | 0.521673i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −56.0164 | −2.45885 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.66470 | − | 14.3565i | −0.204364 | − | 0.628968i | −0.999739 | − | 0.0228500i | \(-0.992726\pi\) |
0.795375 | − | 0.606118i | \(-0.207274\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.44354 | + | 13.6758i | −0.194303 | + | 0.598002i | 0.805682 | + | 0.592349i | \(0.201799\pi\) |
−0.999984 | + | 0.00565266i | \(0.998201\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.38577 | − | 4.26495i | 0.0604798 | − | 0.186138i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.74134 | + | 1.26516i | 0.0758542 | + | 0.0551113i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.93295 | − | 21.3374i | −0.301433 | − | 0.927714i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.311916 | + | 0.226620i | 0.0135360 | + | 0.00983447i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.23232 | − | 3.24179i | 0.313267 | − | 0.140418i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.6156 | + | 12.0720i | 0.718357 | + | 0.521917i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.82110 | − | 30.2262i | −0.423812 | − | 1.30436i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.51469 | + | 3.28011i | 0.194461 | + | 0.141285i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.65991 | − | 11.2640i | 0.157352 | − | 0.484279i | −0.841040 | − | 0.540973i | \(-0.818056\pi\) |
0.998392 | + | 0.0566941i | \(0.0180560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.23858 | − | 3.81196i | 0.0531526 | − | 0.163587i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.8086 | − | 45.5763i | −0.634332 | − | 1.95227i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.9572 | −1.02434 | −0.512169 | − | 0.858885i | \(-0.671158\pi\) | ||||
−0.512169 | + | 0.858885i | \(0.671158\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 21.2222 | − | 15.4188i | 0.905742 | − | 0.658060i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.74053 | + | 2.71766i | 0.159352 | + | 0.115776i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.84215 | − | 6.42420i | 0.376006 | − | 0.273185i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.0149382 | − | 0.0108532i | 0.000634091 | − | 0.000460694i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.04695 | + | 15.5329i | −0.213846 | + | 0.658151i | 0.785387 | + | 0.619005i | \(0.212464\pi\) |
−0.999233 | + | 0.0391461i | \(0.987536\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.27381 | + | 6.99808i | 0.0961721 | + | 0.295987i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.81721 | + | 3.49991i | 0.203383 | + | 0.147766i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.6705 | − | 38.9959i | 0.534000 | − | 1.64348i | −0.211801 | − | 0.977313i | \(-0.567933\pi\) |
0.745801 | − | 0.666169i | \(-0.232067\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.1781 | −0.428194 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.67307 | + | 6.30136i | −0.364235 | + | 0.264632i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.806540 | − | 2.48228i | −0.0338119 | − | 0.104062i | 0.932726 | − | 0.360585i | \(-0.117423\pi\) |
−0.966538 | + | 0.256523i | \(0.917423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.0516 | 1.50871 | 0.754355 | − | 0.656466i | \(-0.227950\pi\) | ||||
0.754355 | + | 0.656466i | \(0.227950\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.4522 | −0.603749 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.47363 | −0.0614547 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.2244 | 1.09174 | 0.545869 | − | 0.837871i | \(-0.316200\pi\) | ||||
0.545869 | + | 0.837871i | \(0.316200\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.3598 | + | 56.5055i | 0.763006 | + | 2.34829i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.56511 | − | 3.31674i | 0.189393 | − | 0.137602i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.6072 | −0.977712 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.24812 | − | 6.91901i | 0.0929485 | − | 0.286066i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.3714 | − | 14.8007i | −0.840817 | − | 0.610889i | 0.0817819 | − | 0.996650i | \(-0.473939\pi\) |
−0.922599 | + | 0.385761i | \(0.873939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.69732 | + | 14.4569i | 0.193550 | + | 0.595685i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.89445 | − | 27.3743i | 0.365869 | − | 1.12603i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.6856 | − | 11.3963i | 0.644131 | − | 0.467988i | −0.217136 | − | 0.976141i | \(-0.569672\pi\) |
0.861267 | + | 0.508153i | \(0.169672\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.996136 | − | 0.723735i | 0.0408376 | − | 0.0296702i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −44.9831 | − | 32.6822i | −1.84104 | − | 1.33759i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.8777 | − | 10.0828i | 0.567029 | − | 0.411971i | −0.266995 | − | 0.963698i | \(-0.586031\pi\) |
0.834025 | + | 0.551727i | \(0.186031\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.65422 | −0.0674769 | −0.0337384 | − | 0.999431i | \(-0.510741\pi\) | ||||
−0.0337384 | + | 0.999431i | \(0.510741\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.38395 | + | 10.4147i | 0.137805 | + | 0.424121i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.4219 | + | 50.5413i | −0.667644 | + | 2.05480i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.869906 | + | 2.67730i | −0.0353084 | + | 0.108668i | −0.967157 | − | 0.254178i | \(-0.918195\pi\) |
0.931849 | + | 0.362846i | \(0.118195\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.59497 | + | 1.88535i | 0.105153 | + | 0.0763984i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.38318 | + | 4.25699i | 0.0559575 | + | 0.172219i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.43454 | − | 2.49534i | −0.138720 | − | 0.100786i | 0.516261 | − | 0.856431i | \(-0.327323\pi\) |
−0.654981 | + | 0.755645i | \(0.727323\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 37.8030 | + | 7.93625i | 1.52437 | + | 0.320021i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.1814 | + | 16.1158i | 0.892991 | + | 0.648796i | 0.936656 | − | 0.350250i | \(-0.113903\pi\) |
−0.0436652 | + | 0.999046i | \(0.513903\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.36021 | + | 4.18629i | 0.0546714 | + | 0.168261i | 0.974664 | − | 0.223675i | \(-0.0718054\pi\) |
−0.919992 | + | 0.391936i | \(0.871805\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.07338 | + | 0.779857i | 0.0430733 | + | 0.0312946i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.65877 | − | 8.18284i | 0.106521 | − | 0.327839i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.56712 | + | 29.4446i | −0.382685 | + | 1.17778i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.9946 | + | 39.9931i | 0.518953 | + | 1.59717i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.00142841 | 5.69546e−5 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.79107 | + | 6.38709i | −0.349967 | + | 0.254266i | −0.748855 | − | 0.662734i | \(-0.769396\pi\) |
0.398888 | + | 0.917000i | \(0.369396\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.9472 | + | 11.5863i | 0.633846 | + | 0.460516i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.20771 | − | 6.68979i | 0.365397 | − | 0.265476i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00138 | − | 0.727546i | 0.0396762 | − | 0.0288264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.492337 | − | 1.51526i | 0.0194765 | − | 0.0599426i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.682266 | + | 2.09980i | 0.0269479 | + | 0.0829370i | 0.963626 | − | 0.267255i | \(-0.0861165\pi\) |
−0.936678 | + | 0.350192i | \(0.886116\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.28643 | − | 6.74699i | −0.366221 | − | 0.266075i | 0.389421 | − | 0.921060i | \(-0.372675\pi\) |
−0.755642 | + | 0.654985i | \(0.772675\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.0819 | + | 34.1065i | −0.436348 | + | 1.34294i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.4167 | −1.39237 | −0.696187 | − | 0.717861i | \(-0.745122\pi\) | ||||
−0.696187 | + | 0.717861i | \(0.745122\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.781373 | + | 0.567701i | −0.0306716 | + | 0.0222842i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.25873 | + | 10.0294i | 0.127720 | + | 0.393081i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.1244 | 1.49192 | 0.745962 | − | 0.665988i | \(-0.231990\pi\) | ||||
0.745962 | + | 0.665988i | \(0.231990\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.1224 | 0.708101 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.68858 | −0.260947 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.35522 | 0.247564 | 0.123782 | − | 0.992309i | \(-0.460498\pi\) | ||||
0.123782 | + | 0.992309i | \(0.460498\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.90427 | − | 30.4822i | −0.385232 | − | 1.18562i | −0.936312 | − | 0.351169i | \(-0.885784\pi\) |
0.551080 | − | 0.834452i | \(-0.314216\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.06848 | − | 0.776298i | 0.0414964 | − | 0.0301489i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.69564 | 0.337203 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.325715 | − | 1.00245i | 0.0126117 | − | 0.0388149i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.9065 | − | 13.7364i | −0.730967 | − | 0.531079i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.3066 | + | 62.4972i | 0.783926 | + | 2.41268i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.09495 | + | 18.7583i | −0.234943 | + | 0.723080i | 0.762186 | + | 0.647358i | \(0.224126\pi\) |
−0.997129 | + | 0.0757222i | \(0.975874\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.80203 | + | 2.03580i | −0.107850 | + | 0.0783579i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.9798 | + | 15.2427i | −0.806319 | + | 0.585825i | −0.912761 | − | 0.408494i | \(-0.866054\pi\) |
0.106442 | + | 0.994319i | \(0.466054\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.29699 | + | 2.39540i | 0.126527 | + | 0.0919271i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 49.3380 | − | 35.8461i | 1.89063 | − | 1.37363i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.6465 | 1.55529 | 0.777647 | − | 0.628701i | \(-0.216413\pi\) | ||||
0.777647 | + | 0.628701i | \(0.216413\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.36328 | − | 10.3511i | −0.128504 | − | 0.395496i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.72747 | + | 20.7050i | −0.256669 | + | 0.789946i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.61808 | + | 4.97993i | −0.0616438 | + | 0.189720i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.2139 | + | 14.6863i | 0.768975 | + | 0.558693i | 0.901650 | − | 0.432467i | \(-0.142357\pi\) |
−0.132675 | + | 0.991160i | \(0.542357\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.84151 | + | 11.8229i | 0.145927 | + | 0.449117i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.4222 | − | 25.7357i | −1.34364 | − | 0.976213i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.00504 | + | 2.21563i | 0.0759464 | + | 0.0839228i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.9386 | − | 9.40046i | −0.489384 | − | 0.355558i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.97639 | − | 12.2381i | −0.150186 | − | 0.462225i | 0.847455 | − | 0.530867i | \(-0.178134\pi\) |
−0.997641 | + | 0.0686415i | \(0.978134\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.00816118 | + | 0.00592944i | 0.000307805 | + | 0.000223633i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.74120 | + | 20.7473i | −0.253888 | + | 0.781388i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.23415 | + | 9.95369i | −0.121633 | + | 0.374347i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.37040 | − | 22.6838i | −0.276801 | − | 0.851906i | −0.988737 | − | 0.149662i | \(-0.952181\pi\) |
0.711936 | − | 0.702244i | \(-0.247819\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.3472 | 0.913092 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.80353 | − | 2.03688i | 0.104993 | − | 0.0762819i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.7440 | + | 10.7122i | 0.551396 | + | 0.400613i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.5765 | − | 12.0436i | 0.619062 | − | 0.449775i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.5486 | + | 9.84362i | −0.505277 | + | 0.367105i | −0.811029 | − | 0.585006i | \(-0.801092\pi\) |
0.305752 | + | 0.952111i | \(0.401092\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.71138 | − | 17.5778i | 0.212703 | − | 0.654632i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.8174 | − | 36.3702i | −0.439494 | − | 1.35262i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.22604 | + | 1.61731i | 0.0826730 | + | 0.0600654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.5939 | + | 32.6046i | −0.392905 | + | 1.20924i | 0.537676 | + | 0.843152i | \(0.319302\pi\) |
−0.930581 | + | 0.366086i | \(0.880698\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.7691 | −0.435892 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.24441 | + | 1.63066i | −0.0830126 | + | 0.0603122i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.9989 | − | 40.0065i | −0.480125 | − | 1.47767i | −0.838919 | − | 0.544256i | \(-0.816812\pi\) |
0.358795 | − | 0.933416i | \(-0.383188\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.03254 | 0.222514 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27.4324 | −1.01048 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.7018 | 0.577600 | 0.288800 | − | 0.957389i | \(-0.406744\pi\) | ||||
0.288800 | + | 0.957389i | \(0.406744\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.32719 | 0.342643 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.97576 | + | 27.6246i | 0.329289 | + | 1.01345i | 0.969467 | + | 0.245221i | \(0.0788604\pi\) |
−0.640179 | + | 0.768226i | \(0.721140\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.19097 | − | 1.59183i | 0.0802710 | − | 0.0583203i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.5702 | 0.459920 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.40544 | + | 7.40319i | −0.0878930 | + | 0.270507i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.6421 | − | 9.18504i | −0.461317 | − | 0.335167i | 0.332730 | − | 0.943022i | \(-0.392030\pi\) |
−0.794048 | + | 0.607855i | \(0.792030\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.19638 | + | 25.2259i | 0.298693 | + | 0.919281i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.20566 | − | 9.86600i | 0.116666 | − | 0.359061i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.25239 | − | 3.81609i | 0.190901 | − | 0.138698i | −0.488229 | − | 0.872715i | \(-0.662357\pi\) |
0.679131 | + | 0.734017i | \(0.262357\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.75562 | − | 5.63479i | 0.281511 | − | 0.204530i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.40426 | + | 3.92642i | 0.195904 | + | 0.142333i | 0.681413 | − | 0.731899i | \(-0.261366\pi\) |
−0.485509 | + | 0.874232i | \(0.661366\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.6941 | − | 10.6759i | 0.531963 | − | 0.386493i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.74290 | 0.0991698 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.0661995 | + | 0.203741i | 0.00239033 | + | 0.00735667i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.565091 | + | 1.73917i | −0.0203777 | + | 0.0627162i | −0.960728 | − | 0.277491i | \(-0.910497\pi\) |
0.940351 | + | 0.340207i | \(0.110497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.32286 | − | 22.5374i | 0.263726 | − | 0.811666i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.9107 | − | 8.65367i | −0.428400 | − | 0.311251i | 0.352609 | − | 0.935771i | \(-0.385295\pi\) |
−0.781009 | + | 0.624520i | \(0.785295\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.79543 | + | 8.60346i | 0.100415 | + | 0.309046i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.00566176 | + | 0.00411351i | 0.000203114 | + | 0.000147571i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.25850 | + | 20.9819i | 0.0809193 | + | 0.751756i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.22893 | + | 2.34596i | 0.115540 | + | 0.0839449i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.765534 | − | 2.35607i | −0.0273580 | − | 0.0841991i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.1139 | + | 8.80125i | 0.432363 | + | 0.314130i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.3528 | − | 47.2511i | 0.547268 | − | 1.68432i | −0.168266 | − | 0.985742i | \(-0.553817\pi\) |
0.715535 | − | 0.698577i | \(-0.246183\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.22864 | − | 28.4028i | 0.328548 | − | 1.01117i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.19207 | − | 3.66881i | −0.0423850 | − | 0.130448i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.5756 | 0.517594 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −20.6458 | + | 15.0001i | −0.732233 | + | 0.531998i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.47696 | − | 2.52616i | −0.123160 | − | 0.0894812i | 0.524500 | − | 0.851411i | \(-0.324252\pi\) |
−0.647660 | + | 0.761929i | \(0.724252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.36529 | + | 0.991945i | −0.0483007 | + | 0.0350925i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.5062 | − | 11.2659i | 0.547884 | − | 0.398061i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.17771 | − | 15.9354i | 0.182717 | − | 0.562346i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.612581 | − | 1.88533i | −0.0215907 | − | 0.0664492i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34.2272 | − | 24.8675i | −1.20485 | − | 0.875378i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.36904 | − | 13.4465i | 0.153607 | − | 0.472755i | −0.844410 | − | 0.535698i | \(-0.820049\pi\) |
0.998017 | + | 0.0629431i | \(0.0200487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.7031 | −1.49951 | −0.749755 | − | 0.661716i | \(-0.769828\pi\) | ||||
−0.749755 | + | 0.661716i | \(0.769828\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.34301 | + | 6.78809i | −0.327674 | + | 0.238069i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.0200 | + | 33.9160i | 0.386013 | + | 1.18803i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.5923 | −0.685448 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.75735 | 0.0963494 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.35907 | −0.326634 | −0.163317 | − | 0.986574i | \(-0.552219\pi\) | ||||
−0.163317 | + | 0.986574i | \(0.552219\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.2836 | 1.82249 | 0.911246 | − | 0.411862i | \(-0.135121\pi\) | ||||
0.911246 | + | 0.411862i | \(0.135121\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.73322 | + | 23.8004i | 0.269236 | + | 0.828624i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.8139 | − | 20.2080i | 0.967184 | − | 0.702700i | 0.0123757 | − | 0.999923i | \(-0.496061\pi\) |
0.954808 | + | 0.297223i | \(0.0960606\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.5609 | −0.609915 | −0.304957 | − | 0.952366i | \(-0.598642\pi\) | ||||
−0.304957 | + | 0.952366i | \(0.598642\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.3526 | − | 59.5613i | 0.671336 | − | 2.06616i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.377548 | + | 0.274304i | 0.0130813 | + | 0.00950409i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.0067 | + | 30.7975i | 0.346297 | + | 1.06579i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.51685 | − | 7.74606i | 0.0869949 | − | 0.267743i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.7779 | − | 25.9942i | 1.23519 | − | 0.897419i | 0.237923 | − | 0.971284i | \(-0.423533\pi\) |
0.997268 | + | 0.0738651i | \(0.0235334\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.8693 | − | 15.8890i | 0.754113 | − | 0.547895i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −37.6005 | − | 27.3184i | −1.29503 | − | 0.940895i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.4787 | + | 17.7848i | −0.842093 | + | 0.611817i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.1416 | −0.692073 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.01493 | − | 6.20133i | −0.0691523 | − | 0.212829i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.000710652 | − | 0.00218716i | 2.43608e−5 | − | 7.49750e-5i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.84738 | + | 21.0741i | −0.234450 | + | 0.721563i | 0.762744 | + | 0.646701i | \(0.223852\pi\) |
−0.997194 | + | 0.0748620i | \(0.976148\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.6714 | + | 11.3860i | 0.535952 | + | 0.389392i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.6528 | + | 32.7860i | 0.363893 | + | 1.11995i | 0.950671 | + | 0.310201i | \(0.100396\pi\) |
−0.586778 | + | 0.809748i | \(0.699604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.4654 | − | 28.6733i | −1.34654 | − | 0.978319i | −0.999176 | − | 0.0405886i | \(-0.987077\pi\) |
−0.347364 | − | 0.937730i | \(-0.612923\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.56682 | + | 14.5561i | 0.0533971 | + | 0.496070i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.9508 | + | 17.4012i | 0.815293 | + | 0.592345i | 0.915360 | − | 0.402636i | \(-0.131906\pi\) |
−0.100067 | + | 0.994981i | \(0.531906\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.9752 | − | 61.4773i | −0.679176 | − | 2.09029i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −31.0428 | − | 22.5539i | −1.05427 | − | 0.765971i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.8475 | + | 58.0065i | −0.639356 | + | 1.96774i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.88026 | + | 5.78684i | −0.0637101 | + | 0.196080i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.80538 | + | 8.63406i | 0.0949476 | + | 0.292219i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.01730 | −0.271034 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.71389 | − | 2.69830i | 0.125409 | − | 0.0911152i | −0.523312 | − | 0.852141i | \(-0.675304\pi\) |
0.648722 | + | 0.761026i | \(0.275304\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38.6692 | + | 28.0948i | 1.30428 | + | 0.947615i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.7784 | − | 20.9088i | 0.969570 | − | 0.704434i | 0.0142168 | − | 0.999899i | \(-0.495475\pi\) |
0.955354 | + | 0.295465i | \(0.0954745\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.1667 | − | 10.2927i | 0.476749 | − | 0.346378i | −0.323317 | − | 0.946291i | \(-0.604798\pi\) |
0.800066 | + | 0.599912i | \(0.204798\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.322636 | + | 0.992972i | −0.0108453 | + | 0.0333784i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.27284 | − | 6.99508i | −0.0763145 | − | 0.234872i | 0.905621 | − | 0.424088i | \(-0.139405\pi\) |
−0.981935 | + | 0.189216i | \(0.939405\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.48983 | + | 2.53551i | 0.117045 | + | 0.0850384i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.4871 | − | 56.8974i | 0.619340 | − | 1.90613i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.9182 | −0.398826 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.6707 | − | 21.5570i | 0.991783 | − | 0.720573i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.657072 | − | 2.02226i | −0.0219390 | − | 0.0675213i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.47044 | −0.215801 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.97419 | −0.0657698 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.5920 | −0.452314 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.62525 | 0.153749 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.96084 | + | 12.1902i | 0.131517 | + | 0.404769i | 0.995032 | − | 0.0995548i | \(-0.0317418\pi\) |
−0.863515 | + | 0.504324i | \(0.831742\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.8619 | + | 13.7039i | −0.625608 | + | 0.454531i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.8819 | −0.857505 | −0.428753 | − | 0.903422i | \(-0.641047\pi\) | ||||
−0.428753 | + | 0.903422i | \(0.641047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.73074 | + | 29.9481i | −0.322041 | + | 0.991139i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 57.4701 | + | 41.7544i | 1.89990 | + | 1.38036i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.12252 | + | 6.53244i | 0.0700917 | + | 0.215720i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.7771 | + | 39.3239i | −0.421478 | + | 1.29718i | 0.484849 | + | 0.874598i | \(0.338875\pi\) |
−0.906327 | + | 0.422577i | \(0.861125\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.3683 | − | 14.7984i | 0.671159 | − | 0.487625i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.716194 | − | 0.520345i | 0.0235738 | − | 0.0171274i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.00485682 | + | 0.00352868i | 0.000159691 | + | 0.000116022i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 33.3093 | − | 24.2006i | 1.09402 | − | 0.794852i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.1094 | −0.659768 | −0.329884 | − | 0.944022i | \(-0.607010\pi\) | ||||
−0.329884 | + | 0.944022i | \(0.607010\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.01844 | + | 3.13445i | 0.0333782 | + | 0.102727i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.19795 | − | 12.9200i | 0.137435 | − | 0.422981i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.12331 | + | 6.53488i | −0.0694397 | + | 0.213713i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.2019 | + | 16.1307i | 0.725306 | + | 0.526966i | 0.888075 | − | 0.459699i | \(-0.152043\pi\) |
−0.162769 | + | 0.986664i | \(0.552043\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.87544 | + | 18.0827i | 0.191738 | + | 0.590108i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.37987 | + | 6.08833i | 0.273176 | + | 0.198474i | 0.715936 | − | 0.698166i | \(-0.246000\pi\) |
−0.442759 | + | 0.896640i | \(0.646000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.39006 | − | 1.96779i | 0.142960 | − | 0.0640800i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.76934 | − | 2.73859i | −0.122617 | − | 0.0890863i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.98252 | + | 21.4900i | 0.226901 | + | 0.698330i | 0.998093 | + | 0.0617275i | \(0.0196610\pi\) |
−0.771192 | + | 0.636603i | \(0.780339\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.00666 | − | 2.18447i | −0.0976004 | − | 0.0709109i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.78012 | − | 14.7117i | 0.155006 | − | 0.477059i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.1718 | + | 43.6162i | −0.459069 | + | 1.41287i | 0.407223 | + | 0.913329i | \(0.366497\pi\) |
−0.866291 | + | 0.499539i | \(0.833503\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.15358 | − | 15.8611i | −0.166766 | − | 0.513253i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.8997 | −0.578614 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.33727 | − | 2.42467i | 0.107766 | − | 0.0782967i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.86943 | + | 5.71748i | 0.253853 | + | 0.184435i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.0288 | + | 10.1925i | −0.452071 | + | 0.328449i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −55.4671 | + | 40.2992i | −1.78555 | + | 1.29728i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.38564 | − | 19.6530i | 0.205348 | − | 0.631997i | −0.794351 | − | 0.607459i | \(-0.792189\pi\) |
0.999699 | − | 0.0245373i | \(-0.00781126\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.08669 | + | 3.34449i | 0.0349095 | + | 0.107440i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.8298 | − | 25.3054i | −1.11774 | − | 0.812088i | −0.133877 | − | 0.990998i | \(-0.542743\pi\) |
−0.983865 | + | 0.178910i | \(0.942743\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.12807 | − | 15.7826i | 0.164398 | − | 0.505966i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.55073 | 0.177766 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.69896 | + | 4.14054i | −0.182326 | + | 0.132467i | −0.675205 | − | 0.737631i | \(-0.735945\pi\) |
0.492879 | + | 0.870098i | \(0.335945\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.8372 | + | 45.6641i | 0.474198 | + | 1.45943i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 40.4608 | 1.29182 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.1451 | −0.483054 | −0.241527 | − | 0.970394i | \(-0.577648\pi\) | ||||
−0.241527 | + | 0.970394i | \(0.577648\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.2146 | 1.05831 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.26815 | −0.263178 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.38022 | + | 4.24788i | 0.0438884 | + | 0.135075i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.8468 | + | 25.3177i | −1.10695 | + | 0.804243i | −0.982180 | − | 0.187943i | \(-0.939818\pi\) |
−0.124766 | + | 0.992186i | \(0.539818\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.2893 | −0.770797 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.8275 | − | 61.0227i | 0.628573 | − | 1.93455i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.5608 | − | 30.1957i | −1.31624 | − | 0.956307i | −0.999971 | − | 0.00763802i | \(-0.997569\pi\) |
−0.316272 | − | 0.948668i | \(-0.602431\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.00167026 | − | 0.00514053i | −5.28447e−5 | − | 0.000162639i |
(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 | 1148.2.n.e.953.1 | yes | 24 | |
41.37 | even | 5 | inner | 1148.2.n.e.365.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.n.e.365.1 | ✓ | 24 | 41.37 | even | 5 | inner | |
1148.2.n.e.953.1 | yes | 24 | 1.1 | even | 1 | trivial |