Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [440,2,Mod(81,440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(440, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("440.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 440 = 2^{3} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 440.y (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: | \(3.51341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 15 x^{10} - 22 x^{9} + 89 x^{8} - 118 x^{7} + 205 x^{6} - 68 x^{5} + 1061 x^{4} + \cdots + 400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 81.1 | ||
Root | \(-0.866917 - 2.66810i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 440.81 |
Dual form | 440.2.y.b.201.1 |
$q$-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 \(\left(\mathbb{Z}/440\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(221\) | \(321\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 | ||||||||
\(3\) | −0.535784 | + | 1.64897i | −0.309335 | + | 0.952036i | 0.668689 | + | 0.743542i | \(0.266856\pi\) |
−0.978024 | + | 0.208493i | \(0.933144\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.809017 | − | 0.587785i | 0.361803 | − | 0.262866i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.386966 | − | 1.19096i | −0.146259 | − | 0.450140i | 0.850912 | − | 0.525309i | \(-0.176050\pi\) |
−0.997171 | + | 0.0751693i | \(0.976050\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.00499969 | − | 0.00363249i | −0.00166656 | − | 0.00121083i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.45751 | + | 2.22725i | 0.740967 | + | 0.671541i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.02882 | + | 1.47403i | 0.562695 | + | 0.408822i | 0.832444 | − | 0.554109i | \(-0.186941\pi\) |
−0.269749 | + | 0.962931i | \(0.586941\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.535784 | + | 1.64897i | 0.138339 | + | 0.425763i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.91579 | − | 2.11845i | 0.707183 | − | 0.513799i | −0.175081 | − | 0.984554i | \(-0.556019\pi\) |
0.882264 | + | 0.470756i | \(0.156019\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.18093 | + | 6.71222i | −0.500340 | + | 1.53989i | 0.308125 | + | 0.951346i | \(0.400299\pi\) |
−0.808465 | + | 0.588544i | \(0.799701\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.17119 | 0.473792 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.20737 | −0.460268 | −0.230134 | − | 0.973159i | \(-0.573916\pi\) | ||||
−0.230134 | + | 0.973159i | \(0.573916\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.309017 | − | 0.951057i | 0.0618034 | − | 0.190211i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.19943 | + | 3.05107i | −0.808182 | + | 0.587178i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.834223 | + | 2.56747i | 0.154911 | + | 0.476768i | 0.998152 | − | 0.0607684i | \(-0.0193551\pi\) |
−0.843241 | + | 0.537536i | \(0.819355\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.29231 | + | 1.66546i | 0.411712 | + | 0.299126i | 0.774294 | − | 0.632826i | \(-0.218105\pi\) |
−0.362583 | + | 0.931952i | \(0.618105\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.98937 | + | 2.85905i | −0.868538 | + | 0.497696i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.01309 | − | 0.736053i | −0.171243 | − | 0.124416i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.49468 | − | 7.67782i | −0.410122 | − | 1.26223i | −0.916542 | − | 0.399939i | \(-0.869031\pi\) |
0.506420 | − | 0.862287i | \(-0.330969\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.51765 | + | 2.55572i | −0.563274 | + | 0.409243i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.19109 | + | 9.82117i | −0.498365 | + | 1.53381i | 0.313282 | + | 0.949660i | \(0.398571\pi\) |
−0.811647 | + | 0.584148i | \(0.801429\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.88581 | 1.05008 | 0.525038 | − | 0.851079i | \(-0.324051\pi\) | ||||
0.525038 | + | 0.851079i | \(0.324051\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.00617996 | −0.000921254 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.493365 | − | 1.51842i | 0.0719647 | − | 0.221485i | −0.908605 | − | 0.417657i | \(-0.862851\pi\) |
0.980569 | + | 0.196173i | \(0.0628513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.39448 | − | 3.19278i | 0.627783 | − | 0.456111i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.93103 | + | 5.94309i | 0.270398 | + | 0.832199i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.43514 | − | 1.04269i | −0.197132 | − | 0.143225i | 0.484841 | − | 0.874602i | \(-0.338878\pi\) |
−0.681972 | + | 0.731378i | \(0.738878\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.29731 | + | 0.357394i | 0.444610 | + | 0.0481910i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.89977 | − | 7.19261i | −1.31126 | − | 0.952684i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.35006 | − | 4.15504i | −0.175762 | − | 0.540941i | 0.823905 | − | 0.566728i | \(-0.191791\pi\) |
−0.999667 | + | 0.0257871i | \(0.991791\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.74173 | − | 4.89816i | 0.863191 | − | 0.627145i | −0.0655605 | − | 0.997849i | \(-0.520884\pi\) |
0.928751 | + | 0.370704i | \(0.120884\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.00239143 | + | 0.00736007i | −0.000301292 | + | 0.000927282i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.50777 | 0.311050 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.43293 | 0.663738 | 0.331869 | − | 0.943326i | \(-0.392321\pi\) | ||||
0.331869 | + | 0.943326i | \(0.392321\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.18267 | − | 3.63989i | 0.142377 | − | 0.438191i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.75112 | − | 2.72535i | 0.445176 | − | 0.323439i | −0.342512 | − | 0.939513i | \(-0.611278\pi\) |
0.787688 | + | 0.616074i | \(0.211278\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.628770 | − | 1.93515i | −0.0735919 | − | 0.226493i | 0.907494 | − | 0.420065i | \(-0.137993\pi\) |
−0.981086 | + | 0.193572i | \(0.937993\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.40270 | + | 1.01912i | 0.161970 | + | 0.117678i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.70159 | − | 3.78866i | 0.193914 | − | 0.431758i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.5612 | − | 9.85278i | −1.52575 | − | 1.10852i | −0.958542 | − | 0.284951i | \(-0.908023\pi\) |
−0.567210 | − | 0.823573i | \(-0.691977\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.78687 | − | 8.57710i | −0.309652 | − | 0.953012i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.55121 | − | 3.30665i | 0.499561 | − | 0.362952i | −0.309288 | − | 0.950968i | \(-0.600091\pi\) |
0.808849 | + | 0.588016i | \(0.200091\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.11373 | − | 3.42772i | 0.120801 | − | 0.371788i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.68066 | −0.501820 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.72832 | −0.501200 | −0.250600 | − | 0.968091i | \(-0.580628\pi\) | ||||
−0.250600 | + | 0.968091i | \(0.580628\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.970419 | − | 2.98664i | 0.101728 | − | 0.313085i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.97449 | + | 2.88764i | −0.412135 | + | 0.299434i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.18093 | + | 6.71222i | 0.223759 | + | 0.688660i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.4476 | − | 11.2233i | −1.56847 | − | 1.13956i | −0.928608 | − | 0.371063i | \(-0.878993\pi\) |
−0.639858 | − | 0.768493i | \(-0.721007\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.00419634 | − | 0.0200624i | −0.000421748 | − | 0.00201635i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.5085 | + | 8.36138i | 1.14513 | + | 0.831989i | 0.987826 | − | 0.155561i | \(-0.0497185\pi\) |
0.157308 | + | 0.987550i | \(0.449719\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.90766 | − | 15.1042i | −0.483566 | − | 1.48826i | −0.834047 | − | 0.551693i | \(-0.813982\pi\) |
0.350481 | − | 0.936570i | \(-0.386018\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.75653 | − | 1.27619i | 0.171420 | − | 0.124544i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.25132 | + | 3.85116i | −0.120969 | + | 0.372306i | −0.993145 | − | 0.116887i | \(-0.962708\pi\) |
0.872176 | + | 0.489193i | \(0.162708\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.89844 | 0.564968 | 0.282484 | − | 0.959272i | \(-0.408842\pi\) | ||||
0.282484 | + | 0.959272i | \(0.408842\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.9971 | 1.32855 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.05499 | − | 3.24692i | 0.0992448 | − | 0.305444i | −0.889092 | − | 0.457729i | \(-0.848663\pi\) |
0.988337 | + | 0.152285i | \(0.0486630\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.78580 | + | 1.29746i | −0.166526 | + | 0.120989i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.00478911 | − | 0.0147394i | −0.000442753 | − | 0.00136265i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.65129 | − | 2.65282i | −0.334713 | − | 0.243183i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.07872 | + | 10.9470i | 0.0980656 | + | 0.995180i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.4851 | − | 10.5241i | −1.30608 | − | 0.948922i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.309017 | − | 0.951057i | −0.0276393 | − | 0.0850651i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.00949 | + | 3.63961i | −0.444521 | + | 0.322963i | −0.787429 | − | 0.616406i | \(-0.788588\pi\) |
0.342908 | + | 0.939369i | \(0.388588\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.68931 | + | 11.3545i | −0.324826 | + | 0.999710i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.39924 | −0.646475 | −0.323237 | − | 0.946318i | \(-0.604771\pi\) | ||||
−0.323237 | + | 0.946318i | \(0.604771\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.83792 | 0.766345 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.60404 | + | 4.93673i | −0.138054 | + | 0.424886i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.9530 | + | 10.8640i | −1.27752 | + | 0.928175i | −0.999475 | − | 0.0323920i | \(-0.989687\pi\) |
−0.278048 | + | 0.960567i | \(0.589687\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.51361 | − | 16.9691i | −0.467658 | − | 1.43930i | −0.855608 | − | 0.517624i | \(-0.826817\pi\) |
0.387950 | − | 0.921680i | \(-0.373183\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.23950 | + | 1.62709i | 0.188600 | + | 0.137026i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.70283 | + | 8.14114i | 0.142398 | + | 0.680796i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.18402 | + | 1.58679i | 0.181373 | + | 0.131775i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.91031 | + | 8.95702i | 0.240039 | + | 0.738763i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.98599 | − | 4.34908i | 0.490392 | − | 0.356290i | −0.314943 | − | 0.949111i | \(-0.601985\pi\) |
0.805335 | + | 0.592820i | \(0.201985\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.36436 | − | 4.19906i | 0.111030 | − | 0.341714i | −0.880069 | − | 0.474847i | \(-0.842504\pi\) |
0.991098 | + | 0.133132i | \(0.0425035\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0222733 | −0.00180069 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.83345 | 0.227589 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.720185 | + | 2.21650i | −0.0574770 | + | 0.176896i | −0.975673 | − | 0.219230i | \(-0.929646\pi\) |
0.918196 | + | 0.396126i | \(0.129646\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.48830 | − | 1.80785i | 0.197335 | − | 0.143372i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.854175 | + | 2.62888i | 0.0673184 | + | 0.207185i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.21850 | − | 0.885295i | −0.0954406 | − | 0.0693416i | 0.539042 | − | 0.842279i | \(-0.318787\pi\) |
−0.634482 | + | 0.772938i | \(0.718787\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.35598 | + | 5.24570i | −0.183413 | + | 0.408377i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.92620 | − | 5.75872i | −0.613347 | − | 0.445623i | 0.237244 | − | 0.971450i | \(-0.423756\pi\) |
−0.850591 | + | 0.525827i | \(0.823756\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.07385 | − | 6.38265i | −0.159527 | − | 0.490973i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0352861 | − | 0.0256368i | 0.00269839 | − | 0.00196050i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.20927 | + | 19.1102i | −0.472082 | + | 1.45292i | 0.377771 | + | 0.925899i | \(0.376691\pi\) |
−0.849853 | + | 0.527020i | \(0.823309\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.25225 | −0.0946610 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.57490 | 0.569364 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.00760 | − | 15.4118i | 0.374285 | − | 1.15193i | −0.569674 | − | 0.821871i | \(-0.692931\pi\) |
0.943960 | − | 0.330061i | \(-0.107069\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.62800 | − | 5.54207i | 0.566985 | − | 0.411939i | −0.267024 | − | 0.963690i | \(-0.586040\pi\) |
0.834009 | + | 0.551751i | \(0.186040\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.46482 | + | 13.7413i | 0.330049 | + | 1.01579i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.53115 | − | 4.74516i | −0.480179 | − | 0.348871i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.8839 | + | 1.28809i | 0.869036 | + | 0.0941943i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.25873 | + | 3.82069i | 0.382516 | + | 0.277914i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.52639 | + | 7.77542i | 0.182803 | + | 0.562610i | 0.999904 | − | 0.0138853i | \(-0.00441998\pi\) |
−0.817101 | + | 0.576495i | \(0.804420\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.04119 | − | 2.93610i | 0.290891 | − | 0.211345i | −0.432763 | − | 0.901508i | \(-0.642461\pi\) |
0.723654 | + | 0.690163i | \(0.242461\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.34362 | + | 4.13524i | −0.0962187 | + | 0.296131i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.00790 | −0.499292 | −0.249646 | − | 0.968337i | \(-0.580314\pi\) | ||||
−0.249646 | + | 0.968337i | \(0.580314\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.8762 | 1.33810 | 0.669050 | − | 0.743217i | \(-0.266701\pi\) | ||||
0.669050 | + | 0.743217i | \(0.266701\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.91088 | + | 8.95875i | −0.205317 | + | 0.631902i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.73494 | − | 1.98705i | 0.191955 | − | 0.139463i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.19109 | + | 9.82117i | 0.222875 | + | 0.685940i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.0110362 | + | 0.00801823i | 0.000767066 | + | 0.000557306i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.3095 | + | 11.6379i | −1.40483 | + | 0.805009i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1392 | − | 8.09308i | −0.766852 | − | 0.557150i | 0.134153 | − | 0.990961i | \(-0.457169\pi\) |
−0.901004 | + | 0.433810i | \(0.857169\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.48424 | + | 7.64569i | 0.170217 | + | 0.523874i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.57074 | − | 4.04738i | 0.379921 | − | 0.276029i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.09645 | − | 3.37453i | 0.0744319 | − | 0.229078i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.52790 | 0.238394 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.03828 | 0.607980 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.89894 | − | 27.3881i | 0.595917 | − | 1.83404i | 0.0458095 | − | 0.998950i | \(-0.485413\pi\) |
0.550108 | − | 0.835094i | \(-0.314587\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.00499969 | + | 0.00363249i | −0.000333313 | + | 0.000242166i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.50197 | + | 23.0887i | 0.497923 | + | 1.53245i | 0.812351 | + | 0.583168i | \(0.198187\pi\) |
−0.314428 | + | 0.949281i | \(0.601813\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.2625 | + | 9.63574i | 0.876408 | + | 0.636748i | 0.932299 | − | 0.361689i | \(-0.117800\pi\) |
−0.0558905 | + | 0.998437i | \(0.517800\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.33572 | + | 4.83578i | 0.351065 | + | 0.318171i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.03746 | + | 1.48030i | 0.133478 | + | 0.0969776i | 0.652521 | − | 0.757771i | \(-0.273711\pi\) |
−0.519043 | + | 0.854748i | \(0.673711\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.493365 | − | 1.51842i | −0.0321836 | − | 0.0990509i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.5128 | − | 17.0831i | 1.52732 | − | 1.10967i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.06369 | − | 6.35138i | 0.133489 | − | 0.410837i | −0.861863 | − | 0.507141i | \(-0.830702\pi\) |
0.995352 | + | 0.0963045i | \(0.0307022\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.14310 | −0.138049 | −0.0690247 | − | 0.997615i | \(-0.521989\pi\) | ||||
−0.0690247 | + | 0.997615i | \(0.521989\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.0642239 | 0.00411997 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.67854 | − | 5.16602i | 0.107238 | − | 0.330045i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.3187 | + | 10.4032i | −0.911079 | + | 0.661938i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.01411 | + | 9.27649i | 0.191012 | + | 0.587873i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.6422 | − | 8.45856i | −0.734850 | − | 0.533900i | 0.156244 | − | 0.987718i | \(-0.450061\pi\) |
−0.891094 | + | 0.453819i | \(0.850061\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.42463 | − | 4.91636i | −0.341043 | − | 0.309089i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.05550 | + | 3.67303i | 0.316587 | + | 0.230014i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.54105 | + | 23.2090i | 0.470398 | + | 1.44774i | 0.852065 | + | 0.523436i | \(0.175350\pi\) |
−0.381667 | + | 0.924300i | \(0.624650\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.17861 | + | 5.94211i | −0.508194 | + | 0.369225i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.00515546 | − | 0.0158669i | 0.000319115 | − | 0.000982135i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.992957 | 0.0612283 | 0.0306142 | − | 0.999531i | \(-0.490254\pi\) | ||||
0.0306142 | + | 0.999531i | \(0.490254\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.77393 | −0.108972 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.53336 | − | 7.79687i | 0.155039 | − | 0.477161i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.6128 | + | 17.8822i | −1.50067 | + | 1.09030i | −0.530551 | + | 0.847653i | \(0.678015\pi\) |
−0.970115 | + | 0.242645i | \(0.921985\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.01666 | + | 24.6728i | 0.486978 | + | 1.49876i | 0.829096 | + | 0.559106i | \(0.188856\pi\) |
−0.342119 | + | 0.939657i | \(0.611144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.40496 | + | 3.20039i | 0.266600 | + | 0.193697i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.87765 | − | 1.64897i | 0.173529 | − | 0.0994369i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.07624 | + | 2.96156i | 0.244917 | + | 0.177943i | 0.703471 | − | 0.710724i | \(-0.251632\pi\) |
−0.458554 | + | 0.888667i | \(0.651632\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.00541108 | − | 0.0166536i | −0.000323953 | − | 0.000997025i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.8065 | + | 12.2106i | −1.00259 | + | 0.728424i | −0.962642 | − | 0.270778i | \(-0.912719\pi\) |
−0.0399476 | + | 0.999202i | \(0.512719\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.40797 | + | 4.33329i | −0.0836952 | + | 0.257587i | −0.984143 | − | 0.177377i | \(-0.943239\pi\) |
0.900448 | + | 0.434964i | \(0.143239\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.2368 | −0.724845 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.9314 | 0.763319 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.23927 | + | 3.81407i | −0.0728981 | + | 0.224357i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 26.7836 | − | 19.4594i | 1.57008 | − | 1.14073i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.738834 | − | 2.27390i | −0.0431631 | − | 0.132842i | 0.927153 | − | 0.374684i | \(-0.122249\pi\) |
−0.970316 | + | 0.241841i | \(0.922249\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.53449 | − | 2.56796i | −0.205786 | − | 0.149512i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −17.1156 | − | 1.85515i | −0.993150 | − | 0.107647i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.47836 | − | 3.25372i | −0.258990 | − | 0.188167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.66457 | − | 8.20071i | −0.153583 | − | 0.472681i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.9538 | + | 14.4972i | −1.14631 | + | 0.832845i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.57511 | − | 7.92538i | 0.147451 | − | 0.453806i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.26648 | 0.186428 | 0.0932138 | − | 0.995646i | \(-0.470286\pi\) | ||||
0.0932138 | + | 0.995646i | \(0.470286\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.5359 | 1.56646 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.845368 | − | 2.60177i | 0.0479364 | − | 0.147533i | −0.924223 | − | 0.381853i | \(-0.875286\pi\) |
0.972160 | + | 0.234320i | \(0.0752862\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.38026 | − | 6.08861i | 0.473680 | − | 0.344149i | −0.325194 | − | 0.945647i | \(-0.605430\pi\) |
0.798874 | + | 0.601499i | \(0.205430\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.00239143 | + | 0.00736007i | 0.000134742 | + | 0.000414693i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.2866 | − | 18.3718i | −1.42024 | − | 1.03186i | −0.991732 | − | 0.128323i | \(-0.959041\pi\) |
−0.428504 | − | 0.903540i | \(-0.640959\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.66829 | + | 8.16762i | −0.205385 | + | 0.457299i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.68003 | − | 4.12678i | −0.317028 | − | 0.230334i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.86034 | + | 24.1916i | 0.437361 | + | 1.34606i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.02882 | − | 1.47403i | 0.112539 | − | 0.0817643i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.16029 | + | 9.72638i | −0.174765 | + | 0.537870i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.99929 | −0.110224 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.7878 | −1.63729 | −0.818644 | − | 0.574302i | \(-0.805274\pi\) | ||||
−0.818644 | + | 0.574302i | \(0.805274\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0154170 | + | 0.0474486i | −0.000844846 | + | 0.00260017i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.39533 | − | 3.19339i | 0.240143 | − | 0.174474i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.21954 | − | 28.3748i | −0.502220 | − | 1.54568i | −0.805394 | − | 0.592740i | \(-0.798046\pi\) |
0.303173 | − | 0.952935i | \(-0.401954\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.78884 | + | 3.47929i | 0.260094 | + | 0.188969i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.92398 | + | 9.19845i | 0.104190 | + | 0.498124i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.5946 | − | 9.15051i | −0.680045 | − | 0.494081i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.18267 | − | 3.63989i | −0.0636729 | − | 0.195965i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.9739 | − | 13.0588i | 0.964891 | − | 0.701035i | 0.0106099 | − | 0.999944i | \(-0.496623\pi\) |
0.954282 | + | 0.298909i | \(0.0966227\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.93726 | + | 18.2730i | −0.317814 | + | 0.978132i | 0.656766 | + | 0.754094i | \(0.271924\pi\) |
−0.974581 | + | 0.224038i | \(0.928076\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.0173 | −0.694811 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.0691 | 1.65364 | 0.826821 | − | 0.562466i | \(-0.190147\pi\) | ||||
0.826821 | + | 0.562466i | \(0.190147\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.43280 | − | 4.40970i | 0.0760451 | − | 0.234043i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.33073 | − | 4.59955i | 0.335058 | − | 0.243434i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.50924 | − | 26.1887i | −0.449100 | − | 1.38219i | −0.877924 | − | 0.478801i | \(-0.841072\pi\) |
0.428823 | − | 0.903388i | \(-0.358928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −24.9262 | − | 18.1099i | −1.31190 | − | 0.953153i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.6292 | − | 4.08643i | −0.977782 | − | 0.214482i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.64614 | − | 1.19599i | −0.0861629 | − | 0.0626010i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.35123 | + | 22.6248i | 0.383731 | + | 1.18100i | 0.937397 | + | 0.348264i | \(0.113229\pi\) |
−0.553665 | + | 0.832739i | \(0.686771\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.0516297 | − | 0.0375112i | 0.00268774 | − | 0.00195275i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.686451 | + | 2.11268i | −0.0356387 | + | 0.109685i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.5085 | −0.803000 | −0.401500 | − | 0.915859i | \(-0.631511\pi\) | ||||
−0.401500 | + | 0.915859i | \(0.631511\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.73383 | 0.0895348 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.09203 | + | 6.43862i | −0.107745 | + | 0.331606i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.4087 | − | 11.1950i | 0.791489 | − | 0.575051i | −0.116916 | − | 0.993142i | \(-0.537301\pi\) |
0.908405 | + | 0.418091i | \(0.137301\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.31762 | − | 10.2106i | −0.169967 | − | 0.523103i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.8006 | + | 9.30018i | 0.654080 | + | 0.475217i | 0.864659 | − | 0.502360i | \(-0.167535\pi\) |
−0.210578 | + | 0.977577i | \(0.567535\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.850306 | − | 4.06526i | −0.0433356 | − | 0.207185i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.0344269 | − | 0.0250126i | −0.00175002 | − | 0.00127146i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.01448 | − | 15.4330i | −0.254244 | − | 0.782483i | −0.993978 | − | 0.109583i | \(-0.965048\pi\) |
0.739733 | − | 0.672900i | \(-0.234952\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.43622 | + | 4.67619i | −0.325494 | + | 0.236485i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.96440 | − | 12.2012i | 0.199977 | − | 0.615467i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.7625 | −0.843415 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.3002 | 1.57091 | 0.785455 | − | 0.618919i | \(-0.212429\pi\) | ||||
0.785455 | + | 0.618919i | \(0.212429\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.73522 | + | 14.5735i | −0.237057 | + | 0.729588i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.55064 | − | 4.03277i | 0.277186 | − | 0.201387i | −0.440503 | − | 0.897751i | \(-0.645200\pi\) |
0.717689 | + | 0.696364i | \(0.245200\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.19576 | + | 6.75786i | 0.109379 | + | 0.336633i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.29612 | − | 5.30094i | −0.362547 | − | 0.263406i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.9697 | − | 24.4246i | 0.543749 | − | 1.21068i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.4691 | + | 13.4186i | 0.913238 | + | 0.663506i | 0.941832 | − | 0.336085i | \(-0.109103\pi\) |
−0.0285937 | + | 0.999591i | \(0.509103\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.90288 | − | 30.4779i | −0.488473 | − | 1.50336i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.42606 | + | 3.21572i | −0.217792 | + | 0.158235i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.73841 | − | 5.35027i | 0.0853352 | − | 0.262635i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.9358 | 1.51493 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.98106 | 0.292194 | 0.146097 | − | 0.989270i | \(-0.453329\pi\) | ||||
0.146097 | + | 0.989270i | \(0.453329\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.6887 | − | 35.9742i | 0.569674 | − | 1.75328i | −0.0839652 | − | 0.996469i | \(-0.526758\pi\) |
0.653639 | − | 0.756807i | \(-0.273242\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.00798232 | + | 0.00579949i | −0.000388114 | + | 0.000281981i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.11373 | − | 3.42772i | −0.0540240 | − | 0.166269i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.44232 | − | 6.13370i | −0.408552 | − | 0.296831i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.3369 | − | 1.55397i | −0.692191 | − | 0.0750262i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.27409 | − | 3.83185i | −0.254044 | − | 0.184574i | 0.453473 | − | 0.891270i | \(-0.350185\pi\) |
−0.707517 | + | 0.706696i | \(0.750185\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.96761 | − | 27.5995i | −0.430956 | − | 1.32635i | −0.897175 | − | 0.441676i | \(-0.854384\pi\) |
0.466219 | − | 0.884669i | \(-0.345616\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.78673 | + | 2.75122i | −0.181560 | + | 0.131911i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.81412 | − | 14.8163i | 0.230291 | − | 0.708762i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.2777 | 0.585984 | 0.292992 | − | 0.956115i | \(-0.405349\pi\) | ||||
0.292992 | + | 0.956115i | \(0.405349\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0335688 | −0.00159851 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.70527 | − | 8.32598i | 0.128531 | − | 0.395579i | −0.865996 | − | 0.500050i | \(-0.833315\pi\) |
0.994528 | + | 0.104471i | \(0.0333149\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.82529 | + | 2.77923i | −0.181336 | + | 0.131748i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.96432 | + | 12.2009i | 0.187506 | + | 0.577084i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.9978 | + | 12.3496i | 0.802175 | + | 0.582814i | 0.911551 | − | 0.411186i | \(-0.134885\pi\) |
−0.109376 | + | 0.994000i | \(0.534885\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.7163 | + | 17.0283i | −1.39929 | + | 0.801830i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.19313 | + | 4.49957i | 0.290979 | + | 0.211408i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.970419 | − | 2.98664i | −0.0454940 | − | 0.140016i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.1794 | − | 8.12230i | 0.522950 | − | 0.379945i | −0.294764 | − | 0.955570i | \(-0.595241\pi\) |
0.817714 | + | 0.575625i | \(0.195241\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.78115 | + | 17.7925i | −0.269841 | + | 0.830485i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −38.6522 | −1.80021 | −0.900106 | − | 0.435672i | \(-0.856511\pi\) | ||||
−0.900106 | + | 0.435672i | \(0.856511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.0206 | −0.698066 | −0.349033 | − | 0.937110i | \(-0.613490\pi\) | ||||
−0.349033 | + | 0.937110i | \(0.613490\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.51812 | + | 4.67229i | −0.0704011 | + | 0.216672i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.53857 | + | 6.93018i | −0.441393 | + | 0.320690i | −0.786188 | − | 0.617987i | \(-0.787948\pi\) |
0.344795 | + | 0.938678i | \(0.387948\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.10236 | − | 6.47039i | −0.0970778 | − | 0.298775i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.26909 | − | 2.37513i | −0.150632 | − | 0.109440i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.9220 | + | 15.3364i | 0.778072 | + | 0.705169i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.70976 | + | 4.14838i | 0.261982 | + | 0.190341i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.00338770 | + | 0.0104263i | 0.000155112 | + | 0.000477386i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.8577 | + | 10.7948i | −0.678866 | + | 0.493225i | −0.872981 | − | 0.487754i | \(-0.837816\pi\) |
0.194115 | + | 0.980979i | \(0.437816\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.25606 | − | 19.2542i | 0.285252 | − | 0.877915i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.79261 | −0.218071 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.0943 | −0.867026 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.90222 | − | 21.2428i | 0.312769 | − | 0.962605i | −0.663893 | − | 0.747827i | \(-0.731097\pi\) |
0.976663 | − | 0.214778i | \(-0.0689028\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.11268 | − | 1.53495i | 0.0955388 | − | 0.0694130i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.69256 | + | 8.28684i | 0.121513 | + | 0.373980i | 0.993250 | − | 0.115995i | \(-0.0370058\pi\) |
−0.871736 | + | 0.489975i | \(0.837006\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.87147 | + | 5.71896i | 0.354513 | + | 0.257569i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0151873 | − | 0.0137643i | −0.000682619 | − | 0.000618660i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.69733 | − | 3.41281i | −0.210704 | − | 0.153085i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0473 | + | 37.0779i | 0.539312 | + | 1.65983i | 0.734142 | + | 0.678996i | \(0.237585\pi\) |
−0.194830 | + | 0.980837i | \(0.562415\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.7427 | − | 9.98466i | 0.613979 | − | 0.446082i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.94916 | − | 12.1543i | 0.176084 | − | 0.541932i | −0.823597 | − | 0.567175i | \(-0.808036\pi\) |
0.999681 | + | 0.0252436i | \(0.00803613\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.2252 | 0.633015 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.6360 | 0.516771 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.4262 | − | 35.1664i | 0.506459 | − | 1.55872i | −0.291844 | − | 0.956466i | \(-0.594269\pi\) |
0.798303 | − | 0.602256i | \(-0.205731\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.06137 | + | 1.49768i | −0.0911899 | + | 0.0662533i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.3208 | − | 34.8417i | −0.499824 | − | 1.53830i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.8484 | − | 9.33492i | −0.566169 | − | 0.411346i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.59435 | − | 2.63269i | 0.202059 | − | 0.115786i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.1853 | − | 20.4779i | −1.23720 | − | 0.898878i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.77225 | − | 8.53211i | −0.121454 | − | 0.373798i | 0.871784 | − | 0.489891i | \(-0.162963\pi\) |
−0.993238 | + | 0.116092i | \(0.962963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.50362 | + | 1.81899i | −0.109476 | + | 0.0795387i | −0.641176 | − | 0.767394i | \(-0.721553\pi\) |
0.531701 | + | 0.846932i | \(0.321553\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.670934 | − | 2.06492i | 0.0292820 | − | 0.0901206i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.2121 | 0.444846 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.1275 | −0.788154 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.00834329 | + | 0.0256780i | −0.000362068 | + | 0.00111433i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.9508 | + | 15.2217i | −0.907481 | + | 0.659324i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.25132 | + | 3.85116i | 0.0540992 | + | 0.166500i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.7307 | + | 16.5148i | 0.980900 | + | 0.712666i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.9106 | + | 1.94132i | 0.771464 | + | 0.0836185i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.2808 | + | 11.1022i | 0.656974 | + | 0.477320i | 0.865640 | − | 0.500667i | \(-0.166912\pi\) |
−0.208665 | + | 0.977987i | \(0.566912\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.05176 | + | 15.5477i | 0.216792 | + | 0.667217i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.77194 | − | 3.46702i | 0.204407 | − | 0.148511i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.5202 | + | 32.3777i | −0.449810 | + | 1.38437i | 0.427312 | + | 0.904104i | \(0.359461\pi\) |
−0.877122 | + | 0.480268i | \(0.840539\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0514991 | −0.00219793 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.0528 | −0.811678 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.48653 | + | 19.9635i | −0.275835 | + | 0.848934i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.3239 | − | 8.22731i | 0.480674 | − | 0.349230i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.13777 | + | 18.8901i | 0.260065 | + | 0.800399i | 0.992789 | + | 0.119873i | \(0.0382487\pi\) |
−0.732724 | + | 0.680526i | \(0.761751\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.9701 | + | 10.1499i | 0.590873 | + | 0.429294i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.49123 | + | 18.9061i | −0.358500 | + | 0.798216i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.2154 | + | 13.9608i | 0.809834 | + | 0.588379i | 0.913782 | − | 0.406204i | \(-0.133148\pi\) |
−0.103949 | + | 0.994583i | \(0.533148\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.05499 | − | 3.24692i | −0.0443836 | − | 0.136599i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.13655 | + | 6.63809i | −0.383699 | + | 0.278774i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.2508 | − | 34.6264i | 0.471658 | − | 1.45161i | −0.378755 | − | 0.925497i | \(-0.623648\pi\) |
0.850413 | − | 0.526116i | \(-0.176352\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.49673 | −0.0626362 | −0.0313181 | − | 0.999509i | \(-0.509970\pi\) | ||||
−0.0313181 | + | 0.999509i | \(0.509970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.1751 | −0.592172 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.682114 | + | 2.09933i | −0.0284461 | + | 0.0875481i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.3772 | + | 24.2500i | −1.38951 | + | 1.00954i | −0.393594 | + | 0.919284i | \(0.628768\pi\) |
−0.995919 | + | 0.0902557i | \(0.971232\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.67634 | + | 8.23693i | 0.111225 | + | 0.342315i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.69925 | − | 4.14075i | −0.236445 | − | 0.171787i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.20454 | − | 5.75884i | −0.0498870 | − | 0.238507i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0125381 | − | 0.00910943i | −0.000518385 | − | 0.000376628i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.8847 | + | 39.6551i | 0.531810 | + | 1.63674i | 0.750443 | + | 0.660935i | \(0.229840\pi\) |
−0.218634 | + | 0.975807i | \(0.570160\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.1783 | + | 11.7543i | −0.666617 | + | 0.484326i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.75472 | − | 11.5558i | 0.154449 | − | 0.475344i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.0656 | 0.659736 | 0.329868 | − | 0.944027i | \(-0.392996\pi\) | ||||
0.329868 | + | 0.944027i | \(0.392996\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.51324 | −0.185025 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.1136 | + | 31.1264i | −0.413921 | + | 1.27392i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.5746 | − | 14.9483i | 0.840655 | − | 0.610771i | −0.0818988 | − | 0.996641i | \(-0.526098\pi\) |
0.922553 | + | 0.385869i | \(0.126098\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.15982 | + | 12.8026i | 0.169682 | + | 0.522229i | 0.999351 | − | 0.0360277i | \(-0.0114704\pi\) |
−0.829668 | + | 0.558257i | \(0.811470\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.0271630 | − | 0.0197350i | −0.00110616 | − | 0.000803673i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.30718 | + | 8.22224i | 0.297079 | + | 0.334281i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.66478 | + | 1.20953i | 0.0675712 | + | 0.0490933i | 0.621058 | − | 0.783765i | \(-0.286703\pi\) |
−0.553487 | + | 0.832858i | \(0.686703\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.81126 | + | 5.57447i | 0.0733958 | + | 0.225889i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.23915 | − | 2.35338i | 0.131042 | − | 0.0952074i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.8489 | + | 36.4670i | −0.478571 | + | 1.47289i | 0.362510 | + | 0.931980i | \(0.381920\pi\) |
−0.841081 | + | 0.540909i | \(0.818080\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.9046 | −0.721982 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.25724 | 0.292166 | 0.146083 | − | 0.989272i | \(-0.453333\pi\) | ||||
0.146083 | + | 0.989272i | \(0.453333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.44221 | + | 16.7494i | −0.218741 | + | 0.673215i | 0.780126 | + | 0.625622i | \(0.215155\pi\) |
−0.998867 | + | 0.0475925i | \(0.984845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.26969 | − | 6.73483i | 0.371980 | − | 0.270259i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.82970 | + | 5.63123i | 0.0733052 | + | 0.225610i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.809017 | − | 0.587785i | −0.0323607 | − | 0.0235114i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.30907 | − | 39.7252i | −0.331832 | − | 1.58647i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.5390 | − | 17.1021i | −0.938562 | − | 0.681905i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.78700 | − | 27.0436i | −0.349805 | − | 1.07659i | −0.958961 | − | 0.283539i | \(-0.908492\pi\) |
0.609156 | − | 0.793051i | \(-0.291508\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.3135 | − | 14.0320i | 0.767641 | − | 0.557724i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.91346 | + | 5.88901i | −0.0759332 | + | 0.233698i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.6219 | 0.539718 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.0286542 | −0.00113354 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.1372 | + | 40.4322i | −0.518889 | + | 1.59698i | 0.257205 | + | 0.966357i | \(0.417199\pi\) |
−0.776093 | + | 0.630618i | \(0.782801\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.5865 | − | 13.5039i | 0.732981 | − | 0.532542i | −0.157524 | − | 0.987515i | \(-0.550351\pi\) |
0.890505 | + | 0.454973i | \(0.150351\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.68931 | + | 11.3545i | 0.145266 | + | 0.447084i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.5392 | + | 8.38372i | 0.453653 | + | 0.329598i | 0.791036 | − | 0.611769i | \(-0.209542\pi\) |
−0.337383 | + | 0.941367i | \(0.609542\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.93654 | − | 13.2180i | 0.233030 | − | 0.518851i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.97704 | + | 3.61603i | 0.195066 | + | 0.141724i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.29334 | − | 25.5243i | −0.324543 | − | 0.998842i | −0.971646 | − | 0.236439i | \(-0.924020\pi\) |
0.647103 | − | 0.762403i | \(-0.275980\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.98611 | + | 4.34917i | −0.233897 | + | 0.169936i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.00388577 | + | 0.0119592i | −0.000151598 | + | 0.000466572i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.8747 | 1.12480 | 0.562400 | − | 0.826865i | \(-0.309878\pi\) | ||||
0.562400 | + | 0.826865i | \(0.309878\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.6938 | −0.921582 | −0.460791 | − | 0.887509i | \(-0.652434\pi\) | ||||
−0.460791 | + | 0.887509i | \(0.652434\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.84256 | + | 14.9039i | −0.188070 | + | 0.578819i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.15003 | − | 5.19480i | 0.277266 | − | 0.201446i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.84144 | − | 5.66736i | −0.0713007 | − | 0.219441i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.3944 | + | 29.3482i | 1.56174 | + | 1.13467i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.4773 | + | 2.97825i | 1.06075 | + | 0.114974i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.77758 | + | 3.47111i | 0.184162 | + | 0.133802i | 0.676047 | − | 0.736859i | \(-0.263692\pi\) |
−0.491885 | + | 0.870660i | \(0.663692\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.60404 | + | 4.93673i | 0.0617396 | + | 0.190015i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.6423 | + | 17.9036i | −0.947079 | + | 0.688093i | −0.950114 | − | 0.311903i | \(-0.899034\pi\) |
0.00303550 | + | 0.999995i | \(0.499034\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.38883 | + | 22.7405i | −0.283557 | + | 0.872699i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.0921 | −1.61297 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.95068 | −0.112905 | −0.0564524 | − | 0.998405i | \(-0.517979\pi\) | ||||
−0.0564524 | + | 0.998405i | \(0.517979\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.71155 | + | 17.5783i | −0.218227 | + | 0.671634i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.9949 | + | 16.7068i | −0.877310 | + | 0.637403i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.37469 | − | 4.23087i | −0.0523717 | − | 0.161183i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.2400 | + | 22.6972i | 1.18842 | + | 0.863441i | 0.993097 | − | 0.117297i | \(-0.0374231\pi\) |
0.195327 | + | 0.980738i | \(0.437423\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0222697 | + | 0.0127611i | −0.000845955 | + | 0.000484756i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.4348 | − | 10.4875i | −0.547544 | − | 0.397814i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.5011 | + | 35.3966i | 0.435634 | + | 1.34074i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.53261 | + | 2.56659i | −0.133616 | + | 0.0970775i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.2324 | − | 31.4922i | 0.386474 | − | 1.18944i | −0.548931 | − | 0.835867i | \(-0.684965\pi\) |
0.935405 | − | 0.353577i | \(-0.115035\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 56.9760 | 2.14889 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.76817 | 0.104255 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.50468 | − | 16.9417i | 0.207025 | − | 0.637157i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.7941 | + | 12.9282i | −0.668272 | + | 0.485528i | −0.869446 | − | 0.494027i | \(-0.835524\pi\) |
0.201174 | + | 0.979555i | \(0.435524\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0320116 | + | 0.0985217i | 0.00120053 | + | 0.00369485i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.05998 | − | 3.67629i | −0.189498 | − | 0.137678i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.16286 | + | 5.58542i | 0.230478 | + | 0.208883i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.36757 | + | 6.80594i | 0.349838 | + | 0.254172i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.85139 | − | 5.69798i | −0.0690450 | − | 0.212499i | 0.910580 | − | 0.413332i | \(-0.135635\pi\) |
−0.979625 | + | 0.200833i | \(0.935635\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0894 | + | 11.6896i | −0.599200 | + | 0.435344i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.14824 | − | 3.53392i | 0.0427035 | − | 0.131428i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.69960 | 0.100261 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.06512 | −0.150767 | −0.0753834 | − | 0.997155i | \(-0.524018\pi\) | ||||
−0.0753834 | + | 0.997155i | \(0.524018\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.32620 | − | 25.6254i | 0.308378 | − | 0.949089i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.0776 | − | 14.5872i | 0.742596 | − | 0.539528i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.24807 | − | 28.4626i | −0.341585 | − | 1.05129i | −0.963386 | − | 0.268117i | \(-0.913599\pi\) |
0.621801 | − | 0.783175i | \(-0.286401\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.61930 | + | 5.53574i | 0.281042 | + | 0.204189i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.3515 | + | 12.1005i | 0.491808 | + | 0.445727i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.9174 | + | 11.5646i | 0.585530 | + | 0.425412i | 0.840713 | − | 0.541480i | \(-0.182136\pi\) |
−0.255184 | + | 0.966893i | \(0.582136\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.48281 | − | 29.1851i | −0.348360 | − | 1.07214i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.5791 | − | 15.6782i | 0.791662 | − | 0.575176i | −0.116794 | − | 0.993156i | \(-0.537262\pi\) |
0.908456 | + | 0.417980i | \(0.137262\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.28645 | − | 7.03696i | 0.0837689 | − | 0.257814i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0347660 | −0.00127202 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.07079 | 0.185282 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.43053 | − | 7.48041i | 0.0886914 | − | 0.272964i | −0.896867 | − | 0.442301i | \(-0.854162\pi\) |
0.985558 | + | 0.169336i | \(0.0541625\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.1857 | − | 14.6657i | 0.735607 | − | 0.534449i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.36436 | − | 4.19906i | −0.0496540 | − | 0.152819i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.7853 | + | 14.3748i | 0.719108 | + | 0.522463i | 0.886099 | − | 0.463496i | \(-0.153405\pi\) |
−0.166991 | + | 0.985958i | \(0.553405\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.0134 | − | 6.31097i | 0.399760 | − | 0.229074i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.2329 | + | 30.6840i | 1.53094 | + | 1.11229i | 0.955712 | + | 0.294302i | \(0.0950873\pi\) |
0.575230 | + | 0.817992i | \(0.304913\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.28249 | − | 7.02480i | −0.0826319 | − | 0.254315i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0180195 | + | 0.0130919i | −0.000651495 | + | 0.000473339i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.38562 | − | 10.4199i | 0.122248 | − | 0.376240i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.7480 | 0.964558 | 0.482279 | − | 0.876018i | \(-0.339809\pi\) | ||||
0.482279 | + | 0.876018i | \(0.339809\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −42.3114 | −1.52381 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.5257 | + | 47.7833i | −0.558422 | + | 1.71865i | 0.128307 | + | 0.991734i | \(0.459046\pi\) |
−0.686730 | + | 0.726913i | \(0.740954\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.29231 | − | 1.66546i | 0.0823423 | − | 0.0598252i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.41641 | − | 16.6700i | −0.194313 | − | 0.598033i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −58.9623 | − | 42.8386i | −2.11254 | − | 1.53485i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.2884 | + | 1.65710i | 0.547063 | + | 0.0592959i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.3368 | − | 8.23667i | −0.405144 | − | 0.294354i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.720185 | + | 2.21650i | 0.0257045 | + | 0.0791104i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.1647 | − | 19.0098i | 0.932672 | − | 0.677626i | −0.0139739 | − | 0.999902i | \(-0.504448\pi\) |
0.946645 | + | 0.322277i | \(0.104448\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.532010 | + | 1.63736i | −0.0189401 | + | 0.0582915i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.27518 | −0.152008 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.8978 | 0.742103 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.950444 | − | 2.92517i | 0.0337088 | − | 0.103745i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.2484 | + | 22.7033i | −1.10688 | + | 0.804193i | −0.982169 | − | 0.188001i | \(-0.939799\pi\) |
−0.124707 | + | 0.992194i | \(0.539799\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.77814 | − | 5.47257i | −0.0629062 | − | 0.193605i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.0236401 | + | 0.0171756i | 0.000835283 | + | 0.000606868i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.76486 | − | 6.15609i | 0.0975699 | − | 0.217244i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.23626 | + | 1.62474i | 0.0788178 | + | 0.0572645i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.3002 | − | 50.1668i | −0.573794 | − | 1.76596i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.9627 | − | 17.4099i | 0.842484 | − | 0.612101i | −0.0805792 | − | 0.996748i | \(-0.525677\pi\) |
0.923064 | + | 0.384648i | \(0.125677\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.51727 | + | 13.9027i | −0.158623 | + | 0.488191i | −0.998510 | − | 0.0545700i | \(-0.982621\pi\) |
0.839887 | + | 0.542761i | \(0.182621\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −44.9799 | −1.57751 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.50615 | −0.0527583 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.0175 | + | 46.2191i | −0.525396 | + | 1.61700i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.0157007 | + | 0.0114073i | −0.000548628 | + | 0.000398602i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.64907 | + | 26.6191i | 0.301855 | + | 0.929013i | 0.980832 | + | 0.194854i | \(0.0624233\pi\) |
−0.678978 | + | 0.734159i | \(0.737577\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.2865 | − | 10.3797i | −0.497995 | − | 0.361815i | 0.310256 | − | 0.950653i | \(-0.399585\pi\) |
−0.808251 | + | 0.588839i | \(0.799585\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.17731 | + | 5.62867i | 0.0409888 | + | 0.195965i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.13665 | + | 2.27891i | 0.109072 | + | 0.0792455i | 0.640984 | − | 0.767554i | \(-0.278526\pi\) |
−0.531912 | + | 0.846800i | \(0.678526\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.43603 | − | 19.8081i | −0.223532 | − | 0.687962i | −0.998437 | − | 0.0558842i | \(-0.982202\pi\) |
0.774905 | − | 0.632078i | \(-0.217798\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.06752 | + | 5.13485i | −0.245170 | + | 0.178126i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.04966 | − | 18.6189i | 0.209608 | − | 0.645108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.79732 | −0.339050 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.7079 | −0.508378 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.02525 | + | 27.7769i | −0.311586 | + | 0.958964i | 0.665551 | + | 0.746353i | \(0.268197\pi\) |
−0.977137 | + | 0.212611i | \(0.931803\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.5655 | − | 12.7621i | 0.605707 | − | 0.440072i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.1303 | − | 34.2557i | −0.383349 | − | 1.17983i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.42940 | − | 3.94469i | −0.186777 | − | 0.135702i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.6200 | − | 5.52082i | 0.433627 | − | 0.189698i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.39111 | − | 4.64342i | −0.219342 | − | 0.159362i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.50667 | + | 16.9478i | 0.188766 | + | 0.580962i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.3786 | + | 33.6960i | −1.58797 | + | 1.15373i | −0.681207 | + | 0.732091i | \(0.738545\pi\) |
−0.906764 | + | 0.421638i | \(0.861455\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0134781 | − | 0.0414813i | 0.000460941 | − | 0.00141863i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.7938 | 1.49597 | 0.747984 | − | 0.663717i | \(-0.231022\pi\) | ||||
0.747984 | + | 0.663717i | \(0.231022\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.0382 | −1.09313 | −0.546564 | − | 0.837417i | \(-0.684065\pi\) | ||||
−0.546564 | + | 0.837417i | \(0.684065\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.92846 | + | 21.3236i | −0.236121 | + | 0.726707i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.9055 | + | 29.7196i | −1.39244 | + | 1.01167i | −0.396846 | + | 0.917885i | \(0.629895\pi\) |
−0.995593 | + | 0.0937806i | \(0.970105\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.20927 | + | 19.1102i | 0.211122 | + | 0.649765i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.62533 | − | 4.08704i | −0.191046 | − | 0.138803i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.3822 | − | 54.4174i | −0.386114 | − | 1.84599i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.0225 | + | 8.00828i | 0.373482 | + | 0.271350i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.0364646 | + | 0.112226i | 0.00123414 | + | 0.00379829i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.01309 | + | 0.736053i | −0.0342487 | + | 0.0248831i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.17959 | − | 19.0188i | 0.208670 | − | 0.642220i | −0.790873 | − | 0.611981i | \(-0.790373\pi\) |
0.999543 | − | 0.0302393i | \(-0.00962694\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.14545 | 0.139823 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.7712 | −0.666108 | −0.333054 | − | 0.942908i | \(-0.608079\pi\) | ||||
−0.333054 | + | 0.942908i | \(0.608079\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.69759 | + | 8.30232i | −0.0907810 | + | 0.279395i | −0.986131 | − | 0.165968i | \(-0.946925\pi\) |
0.895350 | + | 0.445363i | \(0.146925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.12822 | − | 4.45241i | 0.205998 | − | 0.149666i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.4955 | − | 47.6902i | −0.520287 | − | 1.60128i | −0.773452 | − | 0.633855i | \(-0.781471\pi\) |
0.253165 | − | 0.967423i | \(-0.418529\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.27313 | + | 4.55769i | 0.210394 | + | 0.152860i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.2546 | − | 27.2854i | 0.410544 | − | 0.914095i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.11599 | + | 6.62315i | 0.305055 | + | 0.221635i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.00760 | − | 15.4118i | −0.167385 | − | 0.515159i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.76473 | − | 5.64141i | 0.259257 | − | 0.188361i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.36373 | + | 7.27482i | −0.0788349 | + | 0.242629i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.39345 | −0.212997 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.9504 | 0.497518 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.91364 | − | 8.96725i | 0.0968526 | − | 0.298082i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.4459 | + | 12.6752i | −0.579281 | + | 0.420872i | −0.838465 | − | 0.544956i | \(-0.816547\pi\) |
0.259184 | + | 0.965828i | \(0.416547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.0271661 | − | 0.0836087i | −0.000901043 | − | 0.00277312i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.9688 | − | 15.2347i | −0.694728 | − | 0.504749i | 0.183483 | − | 0.983023i | \(-0.441263\pi\) |
−0.878211 | + | 0.478274i | \(0.841263\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.5494 | + | 2.01056i | 0.613895 | + | 0.0665398i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.6890 | + | 8.49259i | 0.386428 | + | 0.280756i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.86325 | + | 8.81219i | 0.0945530 | + | 0.291004i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.6510 | + | 7.73843i | −0.351345 | + | 0.255267i | −0.749433 | − | 0.662080i | \(-0.769674\pi\) |
0.398088 | + | 0.917347i | \(0.369674\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.75013 | + | 5.38633i | −0.0576686 | + | 0.177486i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.6276 | 0.382727 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.07294 | −0.265437 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.0303291 | + | 0.0933434i | −0.000996139 | + | 0.00306580i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.5849 | + | 23.6743i | −1.06908 | + | 0.776728i | −0.975746 | − | 0.218907i | \(-0.929751\pi\) |
−0.0933293 | + | 0.995635i | \(0.529751\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.8466 | + | 36.4600i | 0.388255 | + | 1.19493i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.83732 | + | 2.78798i | 0.125628 | + | 0.0912743i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.3714 | − | 5.94309i | 0.339181 | − | 0.194360i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.2387 | − | 21.9697i | −0.987855 | − | 0.717719i | −0.0284047 | − | 0.999597i | \(-0.509043\pi\) |
−0.959450 | + | 0.281878i | \(0.909043\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.54995 | + | 17.0810i | 0.181116 | + | 0.557418i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.9226 | − | 22.4666i | 1.00805 | − | 0.732389i | 0.0442485 | − | 0.999021i | \(-0.485911\pi\) |
0.963799 | + | 0.266632i | \(0.0859107\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.04391 | − | 21.6789i | 0.229381 | − | 0.705963i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.50015 | 0.211450 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −58.9505 | −1.91564 | −0.957818 | − | 0.287377i | \(-0.907217\pi\) | ||||
−0.957818 | + | 0.287377i | \(0.907217\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.57681 | − | 4.85291i | 0.0511853 | − | 0.157532i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43.8428 | − | 31.8536i | 1.42170 | − | 1.03292i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.37363 | + | 19.6160i | 0.206462 | + | 0.635425i | 0.999650 | + | 0.0264484i | \(0.00841976\pi\) |
−0.793188 | + | 0.608977i | \(0.791580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.61417 | + | 4.80547i | 0.214029 | + | 0.155502i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.5028 | − | 10.4250i | −0.371832 | − | 0.336992i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.7249 | + | 13.6044i | 0.604658 | + | 0.439310i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.09859 | − | 21.8472i | −0.228987 | − | 0.704749i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0202455 | − | 0.0147092i | 0.000652402 | − | 0.000473998i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.54360 | − | 4.75070i | 0.0496901 | − | 0.152931i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.8174 | −1.15181 | −0.575904 | − | 0.817517i | \(-0.695350\pi\) | ||||
−0.575904 | + | 0.817517i | \(0.695350\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −44.1028 | −1.41679 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.49481 | − | 10.7559i | 0.112154 | − | 0.345174i | −0.879189 | − | 0.476473i | \(-0.841915\pi\) |
0.991343 | + | 0.131299i | \(0.0419149\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.0760 | + | 13.1330i | −0.579489 | + | 0.421023i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.34362 | + | 4.13524i | 0.0430303 | + | 0.132434i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.7803 | − | 13.6447i | −0.600834 | − | 0.436531i | 0.245341 | − | 0.969437i | \(-0.421100\pi\) |
−0.846175 | + | 0.532906i | \(0.821100\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.6199 | − | 10.5311i | −0.371373 | − | 0.336577i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.0294904 | − | 0.0214260i | −0.000941556 | − | 0.000684080i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.5567 | + | 32.4901i | 0.336706 | + | 1.03627i | 0.965876 | + | 0.259006i | \(0.0833949\pi\) |
−0.629170 | + | 0.777268i | \(0.716605\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.66951 | + | 4.11914i | −0.180646 | + | 0.131247i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.07119 | − | 3.29678i | 0.0340963 | − | 0.104938i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.1995 | −0.483316 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.7516 | −0.881560 | −0.440780 | − | 0.897615i | \(-0.645298\pi\) | ||||
−0.440780 | + | 0.897615i | \(0.645298\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.9598 | − | 49.1194i | 0.506470 | − | 1.55876i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.2712 | − | 11.0952i | 0.484129 | − | 0.351740i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.3489 | − | 41.0836i | −0.422763 | − | 1.30113i | −0.905120 | − | 0.425155i | \(-0.860219\pi\) |
0.482358 | − | 0.875974i | \(-0.339781\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33.9018 | + | 24.6311i | 1.07261 | + | 0.779293i |
(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 | 440.2.y.b.81.1 | ✓ | 12 | |
4.3 | odd | 2 | 880.2.bo.j.81.3 | 12 | |||
11.3 | even | 5 | inner | 440.2.y.b.201.1 | yes | 12 | |
11.5 | even | 5 | 4840.2.a.bf.1.2 | 6 | |||
11.6 | odd | 10 | 4840.2.a.be.1.2 | 6 | |||
44.3 | odd | 10 | 880.2.bo.j.641.3 | 12 | |||
44.27 | odd | 10 | 9680.2.a.cx.1.5 | 6 | |||
44.39 | even | 10 | 9680.2.a.cy.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.y.b.81.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
440.2.y.b.201.1 | yes | 12 | 11.3 | even | 5 | inner | |
880.2.bo.j.81.3 | 12 | 4.3 | odd | 2 | |||
880.2.bo.j.641.3 | 12 | 44.3 | odd | 10 | |||
4840.2.a.be.1.2 | 6 | 11.6 | odd | 10 | |||
4840.2.a.bf.1.2 | 6 | 11.5 | even | 5 | |||
9680.2.a.cx.1.5 | 6 | 44.27 | odd | 10 | |||
9680.2.a.cy.1.5 | 6 | 44.39 | even | 10 |