Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1084,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1084");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.b (of order \(2\), degree \(1\), 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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.14 | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.k.1084.11 |
$q$-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 \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.249751i | 0.176600i | 0.996094 | + | 0.0883002i | \(0.0281435\pi\) | ||||
−0.996094 | + | 0.0883002i | \(0.971857\pi\) | |||||||
\(3\) | 2.30156i | 1.32881i | 0.747374 | + | 0.664403i | \(0.231314\pi\) | ||||
−0.747374 | + | 0.664403i | \(0.768686\pi\) | |||||||
\(4\) | 1.93762 | 0.968812 | ||||||||
\(5\) | −2.08007 | + | 0.820550i | −0.930236 | + | 0.366961i | ||||
\(6\) | −0.574816 | −0.234668 | ||||||||
\(7\) | − | 3.96043i | − | 1.49690i | −0.663191 | − | 0.748450i | \(-0.730798\pi\) | ||
0.663191 | − | 0.748450i | \(-0.269202\pi\) | |||||||
\(8\) | 0.983424i | 0.347693i | ||||||||
\(9\) | −2.29718 | −0.765727 | ||||||||
\(10\) | −0.204933 | − | 0.519499i | −0.0648055 | − | 0.164280i | ||||
\(11\) | 3.13464 | 0.945131 | 0.472565 | − | 0.881296i | \(-0.343328\pi\) | ||||
0.472565 | + | 0.881296i | \(0.343328\pi\) | |||||||
\(12\) | 4.45956i | 1.28736i | ||||||||
\(13\) | − | 2.65927i | − | 0.737548i | −0.929519 | − | 0.368774i | \(-0.879778\pi\) | ||
0.929519 | − | 0.368774i | \(-0.120222\pi\) | |||||||
\(14\) | 0.989119 | 0.264353 | ||||||||
\(15\) | −1.88855 | − | 4.78741i | −0.487621 | − | 1.23610i | ||||
\(16\) | 3.62964 | 0.907410 | ||||||||
\(17\) | − | 2.25718i | − | 0.547446i | −0.961809 | − | 0.273723i | \(-0.911745\pi\) | ||
0.961809 | − | 0.273723i | \(-0.0882551\pi\) | |||||||
\(18\) | − | 0.573722i | − | 0.135228i | ||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −4.03040 | + | 1.58992i | −0.901224 | + | 0.355517i | ||||
\(21\) | 9.11516 | 1.98909 | ||||||||
\(22\) | 0.782879i | 0.166910i | ||||||||
\(23\) | − | 7.58941i | − | 1.58250i | −0.611492 | − | 0.791251i | \(-0.709430\pi\) | ||
0.611492 | − | 0.791251i | \(-0.290570\pi\) | |||||||
\(24\) | −2.26341 | −0.462017 | ||||||||
\(25\) | 3.65339 | − | 3.41361i | 0.730679 | − | 0.682721i | ||||
\(26\) | 0.664153 | 0.130251 | ||||||||
\(27\) | 1.61758i | 0.311303i | ||||||||
\(28\) | − | 7.67382i | − | 1.45022i | ||||||
\(29\) | −1.36269 | −0.253044 | −0.126522 | − | 0.991964i | \(-0.540381\pi\) | ||||
−0.126522 | + | 0.991964i | \(0.540381\pi\) | |||||||
\(30\) | 1.19566 | − | 0.471666i | 0.218296 | − | 0.0861140i | ||||
\(31\) | 0.894474 | 0.160652 | 0.0803261 | − | 0.996769i | \(-0.474404\pi\) | ||||
0.0803261 | + | 0.996769i | \(0.474404\pi\) | |||||||
\(32\) | 2.87335i | 0.507942i | ||||||||
\(33\) | 7.21457i | 1.25590i | ||||||||
\(34\) | 0.563731 | 0.0966791 | ||||||||
\(35\) | 3.24973 | + | 8.23797i | 0.549304 | + | 1.39247i | ||||
\(36\) | −4.45107 | −0.741846 | ||||||||
\(37\) | − | 6.62537i | − | 1.08920i | −0.838695 | − | 0.544602i | \(-0.816681\pi\) | ||
0.838695 | − | 0.544602i | \(-0.183319\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.12046 | 0.980058 | ||||||||
\(40\) | −0.806949 | − | 2.04559i | −0.127590 | − | 0.323437i | ||||
\(41\) | 6.23645 | 0.973970 | 0.486985 | − | 0.873410i | \(-0.338097\pi\) | ||||
0.486985 | + | 0.873410i | \(0.338097\pi\) | |||||||
\(42\) | 2.27652i | 0.351274i | ||||||||
\(43\) | − | 1.77237i | − | 0.270283i | −0.990826 | − | 0.135142i | \(-0.956851\pi\) | ||
0.990826 | − | 0.135142i | \(-0.0431489\pi\) | |||||||
\(44\) | 6.07376 | 0.915654 | ||||||||
\(45\) | 4.77830 | − | 1.88495i | 0.712307 | − | 0.280992i | ||||
\(46\) | 1.89546 | 0.279470 | ||||||||
\(47\) | − | 0.176361i | − | 0.0257249i | −0.999917 | − | 0.0128625i | \(-0.995906\pi\) | ||
0.999917 | − | 0.0128625i | \(-0.00409436\pi\) | |||||||
\(48\) | 8.35383i | 1.20577i | ||||||||
\(49\) | −8.68497 | −1.24071 | ||||||||
\(50\) | 0.852550 | + | 0.912438i | 0.120569 | + | 0.129038i | ||||
\(51\) | 5.19503 | 0.727450 | ||||||||
\(52\) | − | 5.15266i | − | 0.714545i | ||||||
\(53\) | 6.77526i | 0.930653i | 0.885139 | + | 0.465326i | \(0.154063\pi\) | ||||
−0.885139 | + | 0.465326i | \(0.845937\pi\) | |||||||
\(54\) | −0.403992 | −0.0549763 | ||||||||
\(55\) | −6.52028 | + | 2.57213i | −0.879195 | + | 0.346826i | ||||
\(56\) | 3.89478 | 0.520462 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 0.340331i | − | 0.0446877i | ||||||
\(59\) | 7.81595 | 1.01755 | 0.508775 | − | 0.860899i | \(-0.330098\pi\) | ||||
0.508775 | + | 0.860899i | \(0.330098\pi\) | |||||||
\(60\) | −3.65929 | − | 9.27620i | −0.472413 | − | 1.19755i | ||||
\(61\) | −1.03941 | −0.133082 | −0.0665412 | − | 0.997784i | \(-0.521196\pi\) | ||||
−0.0665412 | + | 0.997784i | \(0.521196\pi\) | |||||||
\(62\) | 0.223395i | 0.0283712i | ||||||||
\(63\) | 9.09781i | 1.14622i | ||||||||
\(64\) | 6.54166 | 0.817707 | ||||||||
\(65\) | 2.18206 | + | 5.53146i | 0.270651 | + | 0.686094i | ||||
\(66\) | −1.80184 | −0.221792 | ||||||||
\(67\) | − | 15.2111i | − | 1.85834i | −0.369656 | − | 0.929169i | \(-0.620524\pi\) | ||
0.369656 | − | 0.929169i | \(-0.379476\pi\) | |||||||
\(68\) | − | 4.37356i | − | 0.530372i | ||||||
\(69\) | 17.4675 | 2.10284 | ||||||||
\(70\) | −2.05744 | + | 0.811622i | −0.245911 | + | 0.0970073i | ||||
\(71\) | 10.4376 | 1.23872 | 0.619360 | − | 0.785107i | \(-0.287392\pi\) | ||||
0.619360 | + | 0.785107i | \(0.287392\pi\) | |||||||
\(72\) | − | 2.25910i | − | 0.266238i | ||||||
\(73\) | 4.18114i | 0.489366i | 0.969603 | + | 0.244683i | \(0.0786839\pi\) | ||||
−0.969603 | + | 0.244683i | \(0.921316\pi\) | |||||||
\(74\) | 1.65469 | 0.192354 | ||||||||
\(75\) | 7.85662 | + | 8.40851i | 0.907205 | + | 0.970931i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 12.4145i | − | 1.41477i | ||||||
\(78\) | 1.52859i | 0.173079i | ||||||||
\(79\) | −11.2084 | −1.26105 | −0.630524 | − | 0.776170i | \(-0.717160\pi\) | ||||
−0.630524 | + | 0.776170i | \(0.717160\pi\) | |||||||
\(80\) | −7.54991 | + | 2.97830i | −0.844105 | + | 0.332984i | ||||
\(81\) | −10.6145 | −1.17939 | ||||||||
\(82\) | 1.55756i | 0.172004i | ||||||||
\(83\) | 13.2542i | 1.45484i | 0.686192 | + | 0.727421i | \(0.259281\pi\) | ||||
−0.686192 | + | 0.727421i | \(0.740719\pi\) | |||||||
\(84\) | 17.6618 | 1.92706 | ||||||||
\(85\) | 1.85213 | + | 4.69509i | 0.200891 | + | 0.509254i | ||||
\(86\) | 0.442650 | 0.0477321 | ||||||||
\(87\) | − | 3.13630i | − | 0.336247i | ||||||
\(88\) | 3.08269i | 0.328615i | ||||||||
\(89\) | −1.48477 | −0.157385 | −0.0786925 | − | 0.996899i | \(-0.525075\pi\) | ||||
−0.0786925 | + | 0.996899i | \(0.525075\pi\) | |||||||
\(90\) | 0.470768 | + | 1.19338i | 0.0496233 | + | 0.125794i | ||||
\(91\) | −10.5318 | −1.10404 | ||||||||
\(92\) | − | 14.7054i | − | 1.53315i | ||||||
\(93\) | 2.05869i | 0.213476i | ||||||||
\(94\) | 0.0440463 | 0.00454303 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −6.61320 | −0.674956 | ||||||||
\(97\) | 15.3864i | 1.56225i | 0.624372 | + | 0.781127i | \(0.285355\pi\) | ||||
−0.624372 | + | 0.781127i | \(0.714645\pi\) | |||||||
\(98\) | − | 2.16908i | − | 0.219110i | ||||||
\(99\) | −7.20085 | −0.723712 | ||||||||
\(100\) | 7.07891 | − | 6.61429i | 0.707891 | − | 0.661429i | ||||
\(101\) | 5.92336 | 0.589396 | 0.294698 | − | 0.955590i | \(-0.404781\pi\) | ||||
0.294698 | + | 0.955590i | \(0.404781\pi\) | |||||||
\(102\) | 1.29746i | 0.128468i | ||||||||
\(103\) | − | 5.00736i | − | 0.493390i | −0.969093 | − | 0.246695i | \(-0.920655\pi\) | ||
0.969093 | − | 0.246695i | \(-0.0793446\pi\) | |||||||
\(104\) | 2.61519 | 0.256440 | ||||||||
\(105\) | −18.9602 | + | 7.47945i | −1.85032 | + | 0.729919i | ||||
\(106\) | −1.69212 | −0.164354 | ||||||||
\(107\) | − | 2.81845i | − | 0.272470i | −0.990677 | − | 0.136235i | \(-0.956500\pi\) | ||
0.990677 | − | 0.136235i | \(-0.0435002\pi\) | |||||||
\(108\) | 3.13426i | 0.301595i | ||||||||
\(109\) | −6.74762 | −0.646305 | −0.323153 | − | 0.946347i | \(-0.604743\pi\) | ||||
−0.323153 | + | 0.946347i | \(0.604743\pi\) | |||||||
\(110\) | −0.642392 | − | 1.62845i | −0.0612497 | − | 0.155266i | ||||
\(111\) | 15.2487 | 1.44734 | ||||||||
\(112\) | − | 14.3749i | − | 1.35830i | ||||||
\(113\) | 7.76636i | 0.730598i | 0.930890 | + | 0.365299i | \(0.119033\pi\) | ||||
−0.930890 | + | 0.365299i | \(0.880967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.22750 | + | 15.7865i | 0.580717 | + | 1.47210i | ||||
\(116\) | −2.64037 | −0.245152 | ||||||||
\(117\) | 6.10882i | 0.564760i | ||||||||
\(118\) | 1.95204i | 0.179700i | ||||||||
\(119\) | −8.93938 | −0.819472 | ||||||||
\(120\) | 4.70806 | − | 1.85724i | 0.429785 | − | 0.169542i | ||||
\(121\) | −1.17400 | −0.106728 | ||||||||
\(122\) | − | 0.259593i | − | 0.0235024i | ||||||
\(123\) | 14.3536i | 1.29422i | ||||||||
\(124\) | 1.73315 | 0.155642 | ||||||||
\(125\) | −4.79828 | + | 10.0983i | −0.429172 | + | 0.903223i | ||||
\(126\) | −2.27218 | −0.202422 | ||||||||
\(127\) | 1.68249i | 0.149297i | 0.997210 | + | 0.0746485i | \(0.0237835\pi\) | ||||
−0.997210 | + | 0.0746485i | \(0.976217\pi\) | |||||||
\(128\) | 7.38049i | 0.652349i | ||||||||
\(129\) | 4.07921 | 0.359154 | ||||||||
\(130\) | −1.38149 | + | 0.544971i | −0.121164 | + | 0.0477971i | ||||
\(131\) | −7.67994 | −0.670999 | −0.335500 | − | 0.942040i | \(-0.608905\pi\) | ||||
−0.335500 | + | 0.942040i | \(0.608905\pi\) | |||||||
\(132\) | 13.9791i | 1.21673i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.79899 | 0.328183 | ||||||||
\(135\) | −1.32731 | − | 3.36468i | −0.114236 | − | 0.289586i | ||||
\(136\) | 2.21976 | 0.190343 | ||||||||
\(137\) | 9.69477i | 0.828280i | 0.910213 | + | 0.414140i | \(0.135918\pi\) | ||||
−0.910213 | + | 0.414140i | \(0.864082\pi\) | |||||||
\(138\) | 4.36252i | 0.371362i | ||||||||
\(139\) | 6.40361 | 0.543147 | 0.271573 | − | 0.962418i | \(-0.412456\pi\) | ||||
0.271573 | + | 0.962418i | \(0.412456\pi\) | |||||||
\(140\) | 6.29675 | + | 15.9621i | 0.532173 | + | 1.34904i | ||||
\(141\) | 0.405906 | 0.0341835 | ||||||||
\(142\) | 2.60681i | 0.218758i | ||||||||
\(143\) | − | 8.33585i | − | 0.697079i | ||||||
\(144\) | −8.33794 | −0.694828 | ||||||||
\(145\) | 2.83448 | − | 1.11815i | 0.235391 | − | 0.0928574i | ||||
\(146\) | −1.04424 | −0.0864222 | ||||||||
\(147\) | − | 19.9890i | − | 1.64866i | ||||||
\(148\) | − | 12.8375i | − | 1.05523i | ||||||
\(149\) | 1.94517 | 0.159355 | 0.0796773 | − | 0.996821i | \(-0.474611\pi\) | ||||
0.0796773 | + | 0.996821i | \(0.474611\pi\) | |||||||
\(150\) | −2.10003 | + | 1.96220i | −0.171467 | + | 0.160213i | ||||
\(151\) | −16.7168 | −1.36040 | −0.680199 | − | 0.733028i | \(-0.738107\pi\) | ||||
−0.680199 | + | 0.733028i | \(0.738107\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.18514i | 0.419194i | ||||||||
\(154\) | 3.10054 | 0.249848 | ||||||||
\(155\) | −1.86057 | + | 0.733961i | −0.149445 | + | 0.0589531i | ||||
\(156\) | 11.8592 | 0.949493 | ||||||||
\(157\) | − | 9.81019i | − | 0.782938i | −0.920191 | − | 0.391469i | \(-0.871967\pi\) | ||
0.920191 | − | 0.391469i | \(-0.128033\pi\) | |||||||
\(158\) | − | 2.79932i | − | 0.222702i | ||||||
\(159\) | −15.5937 | −1.23666 | ||||||||
\(160\) | −2.35773 | − | 5.97678i | −0.186395 | − | 0.472506i | ||||
\(161\) | −30.0573 | −2.36885 | ||||||||
\(162\) | − | 2.65098i | − | 0.208281i | ||||||
\(163\) | 5.06581i | 0.396785i | 0.980123 | + | 0.198393i | \(0.0635721\pi\) | ||||
−0.980123 | + | 0.198393i | \(0.936428\pi\) | |||||||
\(164\) | 12.0839 | 0.943595 | ||||||||
\(165\) | −5.91992 | − | 15.0068i | −0.460865 | − | 1.16828i | ||||
\(166\) | −3.31025 | −0.256926 | ||||||||
\(167\) | 20.1611i | 1.56011i | 0.625710 | + | 0.780056i | \(0.284809\pi\) | ||||
−0.625710 | + | 0.780056i | \(0.715191\pi\) | |||||||
\(168\) | 8.96407i | 0.691593i | ||||||||
\(169\) | 5.92830 | 0.456023 | ||||||||
\(170\) | −1.17260 | + | 0.462570i | −0.0899344 | + | 0.0354775i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 3.43418i | − | 0.261854i | ||||||
\(173\) | 1.94875i | 0.148161i | 0.997252 | + | 0.0740805i | \(0.0236022\pi\) | ||||
−0.997252 | + | 0.0740805i | \(0.976398\pi\) | |||||||
\(174\) | 0.783293 | 0.0593813 | ||||||||
\(175\) | −13.5193 | − | 14.4690i | −1.02197 | − | 1.09375i | ||||
\(176\) | 11.3776 | 0.857621 | ||||||||
\(177\) | 17.9889i | 1.35213i | ||||||||
\(178\) | − | 0.370821i | − | 0.0277942i | ||||||
\(179\) | −17.2710 | −1.29089 | −0.645447 | − | 0.763805i | \(-0.723329\pi\) | ||||
−0.645447 | + | 0.763805i | \(0.723329\pi\) | |||||||
\(180\) | 9.25855 | − | 3.65233i | 0.690092 | − | 0.272229i | ||||
\(181\) | 14.4378 | 1.07315 | 0.536575 | − | 0.843852i | \(-0.319718\pi\) | ||||
0.536575 | + | 0.843852i | \(0.319718\pi\) | |||||||
\(182\) | − | 2.63033i | − | 0.194973i | ||||||
\(183\) | − | 2.39226i | − | 0.176841i | ||||||
\(184\) | 7.46361 | 0.550225 | ||||||||
\(185\) | 5.43645 | + | 13.7812i | 0.399696 | + | 1.01322i | ||||
\(186\) | −0.514158 | −0.0376999 | ||||||||
\(187\) | − | 7.07545i | − | 0.517408i | ||||||
\(188\) | − | 0.341722i | − | 0.0249226i | ||||||
\(189\) | 6.40631 | 0.465990 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.05176 | −0.582605 | −0.291302 | − | 0.956631i | \(-0.594089\pi\) | ||||
−0.291302 | + | 0.956631i | \(0.594089\pi\) | |||||||
\(192\) | 15.0560i | 1.08657i | ||||||||
\(193\) | − | 6.13649i | − | 0.441714i | −0.975306 | − | 0.220857i | \(-0.929115\pi\) | ||
0.975306 | − | 0.220857i | \(-0.0708855\pi\) | |||||||
\(194\) | −3.84277 | −0.275895 | ||||||||
\(195\) | −12.7310 | + | 5.02215i | −0.911686 | + | 0.359643i | ||||
\(196\) | −16.8282 | −1.20201 | ||||||||
\(197\) | − | 17.4160i | − | 1.24084i | −0.784271 | − | 0.620418i | \(-0.786963\pi\) | ||
0.784271 | − | 0.620418i | \(-0.213037\pi\) | |||||||
\(198\) | − | 1.79842i | − | 0.127808i | ||||||
\(199\) | −0.0105972 | −0.000751213 | −0.000375607 | − | 1.00000i | \(-0.500120\pi\) | ||||
−0.000375607 | 1.00000i | \(0.500120\pi\) | ||||||||
\(200\) | 3.35702 | + | 3.59284i | 0.237377 | + | 0.254052i | ||||
\(201\) | 35.0094 | 2.46937 | ||||||||
\(202\) | 1.47936i | 0.104088i | ||||||||
\(203\) | 5.39681i | 0.378782i | ||||||||
\(204\) | 10.0660 | 0.704762 | ||||||||
\(205\) | −12.9723 | + | 5.11732i | −0.906023 | + | 0.357409i | ||||
\(206\) | 1.25059 | 0.0871329 | ||||||||
\(207\) | 17.4343i | 1.21176i | ||||||||
\(208\) | − | 9.65218i | − | 0.669258i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.86800 | − | 4.73532i | −0.128904 | − | 0.326768i | ||||
\(211\) | 27.1262 | 1.86745 | 0.933723 | − | 0.357997i | \(-0.116540\pi\) | ||||
0.933723 | + | 0.357997i | \(0.116540\pi\) | |||||||
\(212\) | 13.1279i | 0.901628i | ||||||||
\(213\) | 24.0228i | 1.64602i | ||||||||
\(214\) | 0.703909 | 0.0481183 | ||||||||
\(215\) | 1.45432 | + | 3.68665i | 0.0991835 | + | 0.251427i | ||||
\(216\) | −1.59077 | −0.108238 | ||||||||
\(217\) | − | 3.54250i | − | 0.240480i | ||||||
\(218\) | − | 1.68522i | − | 0.114138i | ||||||
\(219\) | −9.62316 | −0.650273 | ||||||||
\(220\) | −12.6339 | + | 4.98383i | −0.851775 | + | 0.336010i | ||||
\(221\) | −6.00243 | −0.403767 | ||||||||
\(222\) | 3.80837i | 0.255601i | ||||||||
\(223\) | − | 7.65043i | − | 0.512311i | −0.966636 | − | 0.256155i | \(-0.917544\pi\) | ||
0.966636 | − | 0.256155i | \(-0.0824558\pi\) | |||||||
\(224\) | 11.3797 | 0.760338 | ||||||||
\(225\) | −8.39251 | + | 7.84167i | −0.559501 | + | 0.522778i | ||||
\(226\) | −1.93965 | −0.129024 | ||||||||
\(227\) | − | 25.9617i | − | 1.72314i | −0.507638 | − | 0.861571i | \(-0.669481\pi\) | ||
0.507638 | − | 0.861571i | \(-0.330519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.42130 | 0.424332 | 0.212166 | − | 0.977234i | \(-0.431948\pi\) | ||||
0.212166 | + | 0.977234i | \(0.431948\pi\) | |||||||
\(230\) | −3.94269 | + | 1.55532i | −0.259974 | + | 0.102555i | ||||
\(231\) | 28.5728 | 1.87995 | ||||||||
\(232\) | − | 1.34010i | − | 0.0879817i | ||||||
\(233\) | − | 19.0954i | − | 1.25098i | −0.780231 | − | 0.625492i | \(-0.784898\pi\) | ||
0.780231 | − | 0.625492i | \(-0.215102\pi\) | |||||||
\(234\) | −1.52568 | −0.0997369 | ||||||||
\(235\) | 0.144713 | + | 0.366844i | 0.00944005 | + | 0.0239303i | ||||
\(236\) | 15.1444 | 0.985815 | ||||||||
\(237\) | − | 25.7969i | − | 1.67569i | ||||||
\(238\) | − | 2.23262i | − | 0.144719i | ||||||
\(239\) | 8.39178 | 0.542819 | 0.271409 | − | 0.962464i | \(-0.412510\pi\) | ||||
0.271409 | + | 0.962464i | \(0.412510\pi\) | |||||||
\(240\) | −6.85474 | − | 17.3766i | −0.442472 | − | 1.12165i | ||||
\(241\) | −8.61689 | −0.555063 | −0.277531 | − | 0.960717i | \(-0.589516\pi\) | ||||
−0.277531 | + | 0.960717i | \(0.589516\pi\) | |||||||
\(242\) | − | 0.293208i | − | 0.0188481i | ||||||
\(243\) | − | 19.5772i | − | 1.25588i | ||||||
\(244\) | −2.01398 | −0.128932 | ||||||||
\(245\) | 18.0654 | − | 7.12645i | 1.15415 | − | 0.455292i | ||||
\(246\) | −3.58481 | −0.228559 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.879647i | 0.0558576i | ||||||||
\(249\) | −30.5054 | −1.93320 | ||||||||
\(250\) | −2.52207 | − | 1.19837i | −0.159509 | − | 0.0757919i | ||||
\(251\) | 29.2619 | 1.84700 | 0.923498 | − | 0.383604i | \(-0.125317\pi\) | ||||
0.923498 | + | 0.383604i | \(0.125317\pi\) | |||||||
\(252\) | 17.6281i | 1.11047i | ||||||||
\(253\) | − | 23.7901i | − | 1.49567i | ||||||
\(254\) | −0.420203 | −0.0263659 | ||||||||
\(255\) | −10.8060 | + | 4.26278i | −0.676700 | + | 0.266946i | ||||
\(256\) | 11.2400 | 0.702502 | ||||||||
\(257\) | 5.48068i | 0.341876i | 0.985282 | + | 0.170938i | \(0.0546797\pi\) | ||||
−0.985282 | + | 0.170938i | \(0.945320\pi\) | |||||||
\(258\) | 1.01878i | 0.0634268i | ||||||||
\(259\) | −26.2393 | −1.63043 | ||||||||
\(260\) | 4.22802 | + | 10.7179i | 0.262210 | + | 0.664696i | ||||
\(261\) | 3.13033 | 0.193763 | ||||||||
\(262\) | − | 1.91807i | − | 0.118499i | ||||||
\(263\) | − | 0.568281i | − | 0.0350417i | −0.999846 | − | 0.0175209i | \(-0.994423\pi\) | ||
0.999846 | − | 0.0175209i | \(-0.00557735\pi\) | |||||||
\(264\) | −7.09499 | −0.436666 | ||||||||
\(265\) | −5.55944 | − | 14.0930i | −0.341514 | − | 0.865727i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3.41728i | − | 0.209134i | ||||||
\(268\) | − | 29.4735i | − | 1.80038i | ||||||
\(269\) | 4.44312 | 0.270902 | 0.135451 | − | 0.990784i | \(-0.456752\pi\) | ||||
0.135451 | + | 0.990784i | \(0.456752\pi\) | |||||||
\(270\) | 0.840332 | − | 0.331496i | 0.0511409 | − | 0.0201742i | ||||
\(271\) | 17.7660 | 1.07921 | 0.539605 | − | 0.841919i | \(-0.318574\pi\) | ||||
0.539605 | + | 0.841919i | \(0.318574\pi\) | |||||||
\(272\) | − | 8.19274i | − | 0.496758i | ||||||
\(273\) | − | 24.2396i | − | 1.46705i | ||||||
\(274\) | −2.42127 | −0.146275 | ||||||||
\(275\) | 11.4521 | − | 10.7004i | 0.690587 | − | 0.645261i | ||||
\(276\) | 33.8454 | 2.03726 | ||||||||
\(277\) | − | 8.10450i | − | 0.486952i | −0.969907 | − | 0.243476i | \(-0.921712\pi\) | ||
0.969907 | − | 0.243476i | \(-0.0782877\pi\) | |||||||
\(278\) | 1.59930i | 0.0959199i | ||||||||
\(279\) | −2.05477 | −0.123016 | ||||||||
\(280\) | −8.10142 | + | 3.19586i | −0.484152 | + | 0.190989i | ||||
\(281\) | 7.05224 | 0.420701 | 0.210351 | − | 0.977626i | \(-0.432539\pi\) | ||||
0.210351 | + | 0.977626i | \(0.432539\pi\) | |||||||
\(282\) | 0.101375i | 0.00603681i | ||||||||
\(283\) | 1.29862i | 0.0771949i | 0.999255 | + | 0.0385975i | \(0.0122890\pi\) | ||||
−0.999255 | + | 0.0385975i | \(0.987711\pi\) | |||||||
\(284\) | 20.2242 | 1.20009 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.08188 | 0.123104 | ||||||||
\(287\) | − | 24.6990i | − | 1.45794i | ||||||
\(288\) | − | 6.60061i | − | 0.388945i | ||||||
\(289\) | 11.9052 | 0.700303 | ||||||||
\(290\) | 0.279259 | + | 0.707914i | 0.0163987 | + | 0.0415701i | ||||
\(291\) | −35.4128 | −2.07593 | ||||||||
\(292\) | 8.10149i | 0.474104i | ||||||||
\(293\) | 14.9498i | 0.873376i | 0.899613 | + | 0.436688i | \(0.143849\pi\) | ||||
−0.899613 | + | 0.436688i | \(0.856151\pi\) | |||||||
\(294\) | 4.99226 | 0.291155 | ||||||||
\(295\) | −16.2577 | + | 6.41338i | −0.946562 | + | 0.373401i | ||||
\(296\) | 6.51555 | 0.378708 | ||||||||
\(297\) | 5.07054i | 0.294223i | ||||||||
\(298\) | 0.485808i | 0.0281421i | ||||||||
\(299\) | −20.1823 | −1.16717 | ||||||||
\(300\) | 15.2232 | + | 16.2925i | 0.878911 | + | 0.940650i | ||||
\(301\) | −7.01932 | −0.404587 | ||||||||
\(302\) | − | 4.17504i | − | 0.240247i | ||||||
\(303\) | 13.6330i | 0.783194i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.16204 | − | 0.852886i | 0.123798 | − | 0.0488361i | ||||
\(306\) | −1.29499 | −0.0740298 | ||||||||
\(307\) | − | 5.01371i | − | 0.286147i | −0.989712 | − | 0.143074i | \(-0.954301\pi\) | ||
0.989712 | − | 0.143074i | \(-0.0456986\pi\) | |||||||
\(308\) | − | 24.0547i | − | 1.37064i | ||||||
\(309\) | 11.5248 | 0.655620 | ||||||||
\(310\) | −0.183307 | − | 0.464678i | −0.0104111 | − | 0.0263920i | ||||
\(311\) | −16.7443 | −0.949481 | −0.474741 | − | 0.880126i | \(-0.657458\pi\) | ||||
−0.474741 | + | 0.880126i | \(0.657458\pi\) | |||||||
\(312\) | 6.01901i | 0.340759i | ||||||||
\(313\) | 5.73858i | 0.324363i | 0.986761 | + | 0.162182i | \(0.0518531\pi\) | ||||
−0.986761 | + | 0.162182i | \(0.948147\pi\) | |||||||
\(314\) | 2.45010 | 0.138267 | ||||||||
\(315\) | −7.46521 | − | 18.9241i | −0.420617 | − | 1.06625i | ||||
\(316\) | −21.7178 | −1.22172 | ||||||||
\(317\) | − | 7.94635i | − | 0.446312i | −0.974783 | − | 0.223156i | \(-0.928364\pi\) | ||
0.974783 | − | 0.223156i | \(-0.0716359\pi\) | |||||||
\(318\) | − | 3.89453i | − | 0.218394i | ||||||
\(319\) | −4.27153 | −0.239160 | ||||||||
\(320\) | −13.6071 | + | 5.36776i | −0.760661 | + | 0.300067i | ||||
\(321\) | 6.48683 | 0.362060 | ||||||||
\(322\) | − | 7.50683i | − | 0.418339i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −20.5669 | −1.14261 | ||||||||
\(325\) | −9.07769 | − | 9.71535i | −0.503540 | − | 0.538911i | ||||
\(326\) | −1.26519 | −0.0700724 | ||||||||
\(327\) | − | 15.5301i | − | 0.858814i | ||||||
\(328\) | 6.13308i | 0.338643i | ||||||||
\(329\) | −0.698465 | −0.0385076 | ||||||||
\(330\) | 3.74797 | − | 1.47850i | 0.206319 | − | 0.0813890i | ||||
\(331\) | −20.8177 | −1.14424 | −0.572121 | − | 0.820169i | \(-0.693879\pi\) | ||||
−0.572121 | + | 0.820169i | \(0.693879\pi\) | |||||||
\(332\) | 25.6817i | 1.40947i | ||||||||
\(333\) | 15.2197i | 0.834033i | ||||||||
\(334\) | −5.03525 | −0.275516 | ||||||||
\(335\) | 12.4815 | + | 31.6403i | 0.681938 | + | 1.72869i | ||||
\(336\) | 33.0847 | 1.80492 | ||||||||
\(337\) | 27.3618i | 1.49049i | 0.666790 | + | 0.745245i | \(0.267668\pi\) | ||||
−0.666790 | + | 0.745245i | \(0.732332\pi\) | |||||||
\(338\) | 1.48060i | 0.0805339i | ||||||||
\(339\) | −17.8748 | −0.970824 | ||||||||
\(340\) | 3.58873 | + | 9.09732i | 0.194626 | + | 0.493371i | ||||
\(341\) | 2.80386 | 0.151837 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.67319i | 0.360318i | ||||||||
\(344\) | 1.74299 | 0.0939756 | ||||||||
\(345\) | −36.3336 | + | 14.3330i | −1.95614 | + | 0.771660i | ||||
\(346\) | −0.486703 | −0.0261653 | ||||||||
\(347\) | 20.1999i | 1.08439i | 0.840254 | + | 0.542194i | \(0.182406\pi\) | ||||
−0.840254 | + | 0.542194i | \(0.817594\pi\) | |||||||
\(348\) | − | 6.07698i | − | 0.325760i | ||||||
\(349\) | 15.6240 | 0.836332 | 0.418166 | − | 0.908371i | \(-0.362673\pi\) | ||||
0.418166 | + | 0.908371i | \(0.362673\pi\) | |||||||
\(350\) | 3.61364 | − | 3.37646i | 0.193157 | − | 0.180479i | ||||
\(351\) | 4.30158 | 0.229601 | ||||||||
\(352\) | 9.00694i | 0.480072i | ||||||||
\(353\) | 4.59743i | 0.244696i | 0.992487 | + | 0.122348i | \(0.0390424\pi\) | ||||
−0.992487 | + | 0.122348i | \(0.960958\pi\) | |||||||
\(354\) | −4.49274 | −0.238786 | ||||||||
\(355\) | −21.7110 | + | 8.56460i | −1.15230 | + | 0.454562i | ||||
\(356\) | −2.87692 | −0.152476 | ||||||||
\(357\) | − | 20.5745i | − | 1.08892i | ||||||
\(358\) | − | 4.31344i | − | 0.227972i | ||||||
\(359\) | 10.8302 | 0.571598 | 0.285799 | − | 0.958290i | \(-0.407741\pi\) | ||||
0.285799 | + | 0.958290i | \(0.407741\pi\) | |||||||
\(360\) | 1.85371 | + | 4.69910i | 0.0976990 | + | 0.247664i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 3.60584i | 0.189519i | ||||||||
\(363\) | − | 2.70204i | − | 0.141820i | ||||||
\(364\) | −20.4067 | −1.06960 | ||||||||
\(365\) | −3.43084 | − | 8.69708i | −0.179578 | − | 0.455226i | ||||
\(366\) | 0.597468 | 0.0312302 | ||||||||
\(367\) | − | 6.66237i | − | 0.347773i | −0.984766 | − | 0.173887i | \(-0.944367\pi\) | ||
0.984766 | − | 0.173887i | \(-0.0556326\pi\) | |||||||
\(368\) | − | 27.5468i | − | 1.43598i | ||||||
\(369\) | −14.3263 | −0.745795 | ||||||||
\(370\) | −3.44187 | + | 1.35776i | −0.178934 | + | 0.0705864i | ||||
\(371\) | 26.8329 | 1.39309 | ||||||||
\(372\) | 3.98896i | 0.206818i | ||||||||
\(373\) | − | 18.1212i | − | 0.938279i | −0.883124 | − | 0.469139i | \(-0.844564\pi\) | ||
0.883124 | − | 0.469139i | \(-0.155436\pi\) | |||||||
\(374\) | 1.76710 | 0.0913744 | ||||||||
\(375\) | −23.2419 | − | 11.0435i | −1.20021 | − | 0.570286i | ||||
\(376\) | 0.173438 | 0.00894438 | ||||||||
\(377\) | 3.62374i | 0.186632i | ||||||||
\(378\) | 1.59998i | 0.0822940i | ||||||||
\(379\) | −31.9277 | −1.64002 | −0.820008 | − | 0.572352i | \(-0.806031\pi\) | ||||
−0.820008 | + | 0.572352i | \(0.806031\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.87236 | −0.198387 | ||||||||
\(382\) | − | 2.01093i | − | 0.102888i | ||||||
\(383\) | 13.7847i | 0.704367i | 0.935931 | + | 0.352183i | \(0.114561\pi\) | ||||
−0.935931 | + | 0.352183i | \(0.885439\pi\) | |||||||
\(384\) | −16.9866 | −0.866846 | ||||||||
\(385\) | 10.1867 | + | 25.8231i | 0.519164 | + | 1.31607i | ||||
\(386\) | 1.53259 | 0.0780069 | ||||||||
\(387\) | 4.07145i | 0.206963i | ||||||||
\(388\) | 29.8131i | 1.51353i | ||||||||
\(389\) | 24.6819 | 1.25142 | 0.625712 | − | 0.780054i | \(-0.284809\pi\) | ||||
0.625712 | + | 0.780054i | \(0.284809\pi\) | |||||||
\(390\) | −1.25428 | − | 3.17958i | −0.0635132 | − | 0.161004i | ||||
\(391\) | −17.1306 | −0.866334 | ||||||||
\(392\) | − | 8.54101i | − | 0.431386i | ||||||
\(393\) | − | 17.6758i | − | 0.891628i | ||||||
\(394\) | 4.34965 | 0.219132 | ||||||||
\(395\) | 23.3144 | − | 9.19709i | 1.17307 | − | 0.462756i | ||||
\(396\) | −13.9525 | −0.701141 | ||||||||
\(397\) | − | 17.8679i | − | 0.896762i | −0.893842 | − | 0.448381i | \(-0.852001\pi\) | ||
0.893842 | − | 0.448381i | \(-0.147999\pi\) | |||||||
\(398\) | − | 0.00264665i | − | 0.000132665i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.2605 | − | 12.3902i | 0.663025 | − | 0.619508i | ||||
\(401\) | −22.9321 | −1.14517 | −0.572587 | − | 0.819844i | \(-0.694060\pi\) | ||||
−0.572587 | + | 0.819844i | \(0.694060\pi\) | |||||||
\(402\) | 8.74361i | 0.436092i | ||||||||
\(403\) | − | 2.37864i | − | 0.118489i | ||||||
\(404\) | 11.4772 | 0.571014 | ||||||||
\(405\) | 22.0789 | − | 8.70973i | 1.09711 | − | 0.432790i | ||||
\(406\) | −1.34786 | −0.0668930 | ||||||||
\(407\) | − | 20.7682i | − | 1.02944i | ||||||
\(408\) | 5.10892i | 0.252929i | ||||||||
\(409\) | −25.1805 | −1.24509 | −0.622547 | − | 0.782583i | \(-0.713902\pi\) | ||||
−0.622547 | + | 0.782583i | \(0.713902\pi\) | |||||||
\(410\) | −1.27805 | − | 3.23983i | −0.0631186 | − | 0.160004i | ||||
\(411\) | −22.3131 | −1.10062 | ||||||||
\(412\) | − | 9.70239i | − | 0.478003i | ||||||
\(413\) | − | 30.9545i | − | 1.52317i | ||||||
\(414\) | −4.35422 | −0.213998 | ||||||||
\(415\) | −10.8758 | − | 27.5698i | −0.533870 | − | 1.35335i | ||||
\(416\) | 7.64101 | 0.374631 | ||||||||
\(417\) | 14.7383i | 0.721737i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.249578 | −0.0121927 | −0.00609635 | − | 0.999981i | \(-0.501941\pi\) | ||||
−0.00609635 | + | 0.999981i | \(0.501941\pi\) | |||||||
\(420\) | −36.7377 | + | 14.4924i | −1.79262 | + | 0.707155i | ||||
\(421\) | 30.1682 | 1.47031 | 0.735154 | − | 0.677900i | \(-0.237110\pi\) | ||||
0.735154 | + | 0.677900i | \(0.237110\pi\) | |||||||
\(422\) | 6.77479i | 0.329792i | ||||||||
\(423\) | 0.405134i | 0.0196983i | ||||||||
\(424\) | −6.66295 | −0.323581 | ||||||||
\(425\) | −7.70511 | − | 8.24636i | −0.373753 | − | 0.400007i | ||||
\(426\) | −5.99972 | −0.290687 | ||||||||
\(427\) | 4.11649i | 0.199211i | ||||||||
\(428\) | − | 5.46110i | − | 0.263972i | ||||||
\(429\) | 19.1855 | 0.926283 | ||||||||
\(430\) | −0.920743 | + | 0.363216i | −0.0444022 | + | 0.0175158i | ||||
\(431\) | 15.4165 | 0.742588 | 0.371294 | − | 0.928515i | \(-0.378914\pi\) | ||||
0.371294 | + | 0.928515i | \(0.378914\pi\) | |||||||
\(432\) | 5.87123i | 0.282480i | ||||||||
\(433\) | 12.5378i | 0.602529i | 0.953541 | + | 0.301264i | \(0.0974087\pi\) | ||||
−0.953541 | + | 0.301264i | \(0.902591\pi\) | |||||||
\(434\) | 0.884741 | 0.0424689 | ||||||||
\(435\) | 2.57349 | + | 6.52373i | 0.123390 | + | 0.312789i | ||||
\(436\) | −13.0744 | −0.626148 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 2.40339i | − | 0.114838i | ||||||
\(439\) | −25.3236 | −1.20863 | −0.604315 | − | 0.796746i | \(-0.706553\pi\) | ||||
−0.604315 | + | 0.796746i | \(0.706553\pi\) | |||||||
\(440\) | −2.52950 | − | 6.41221i | −0.120589 | − | 0.305690i | ||||
\(441\) | 19.9509 | 0.950045 | ||||||||
\(442\) | − | 1.49911i | − | 0.0713055i | ||||||
\(443\) | 7.41736i | 0.352410i | 0.984354 | + | 0.176205i | \(0.0563821\pi\) | ||||
−0.984354 | + | 0.176205i | \(0.943618\pi\) | |||||||
\(444\) | 29.5462 | 1.40220 | ||||||||
\(445\) | 3.08842 | − | 1.21833i | 0.146405 | − | 0.0577542i | ||||
\(446\) | 1.91070 | 0.0904742 | ||||||||
\(447\) | 4.47693i | 0.211752i | ||||||||
\(448\) | − | 25.9077i | − | 1.22403i | ||||||
\(449\) | −24.0580 | −1.13537 | −0.567684 | − | 0.823247i | \(-0.692160\pi\) | ||||
−0.567684 | + | 0.823247i | \(0.692160\pi\) | |||||||
\(450\) | −1.95846 | − | 2.09603i | −0.0923228 | − | 0.0988080i | ||||
\(451\) | 19.5491 | 0.920529 | ||||||||
\(452\) | 15.0483i | 0.707812i | ||||||||
\(453\) | − | 38.4748i | − | 1.80771i | ||||||
\(454\) | 6.48396 | 0.304307 | ||||||||
\(455\) | 21.9069 | − | 8.64189i | 1.02701 | − | 0.405138i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.39908i | 0.299337i | 0.988736 | + | 0.149668i | \(0.0478206\pi\) | ||||
−0.988736 | + | 0.149668i | \(0.952179\pi\) | |||||||
\(458\) | 1.60372i | 0.0749371i | ||||||||
\(459\) | 3.65116 | 0.170422 | ||||||||
\(460\) | 12.0665 | + | 30.5884i | 0.562606 | + | 1.42619i | ||||
\(461\) | −15.2501 | −0.710268 | −0.355134 | − | 0.934815i | \(-0.615565\pi\) | ||||
−0.355134 | + | 0.934815i | \(0.615565\pi\) | |||||||
\(462\) | 7.13607i | 0.332000i | ||||||||
\(463\) | 36.4298i | 1.69304i | 0.532359 | + | 0.846518i | \(0.321306\pi\) | ||||
−0.532359 | + | 0.846518i | \(0.678694\pi\) | |||||||
\(464\) | −4.94605 | −0.229615 | ||||||||
\(465\) | −1.68926 | − | 4.28221i | −0.0783373 | − | 0.198583i | ||||
\(466\) | 4.76910 | 0.220924 | ||||||||
\(467\) | 28.1967i | 1.30479i | 0.757880 | + | 0.652395i | \(0.226235\pi\) | ||||
−0.757880 | + | 0.652395i | \(0.773765\pi\) | |||||||
\(468\) | 11.8366i | 0.547147i | ||||||||
\(469\) | −60.2426 | −2.78175 | ||||||||
\(470\) | −0.0916195 | + | 0.0361422i | −0.00422609 | + | 0.00166712i | ||||
\(471\) | 22.5787 | 1.04037 | ||||||||
\(472\) | 7.68640i | 0.353795i | ||||||||
\(473\) | − | 5.55574i | − | 0.255453i | ||||||
\(474\) | 6.44279 | 0.295927 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −17.3212 | −0.793914 | ||||||||
\(477\) | − | 15.5640i | − | 0.712626i | ||||||
\(478\) | 2.09585i | 0.0958620i | ||||||||
\(479\) | −29.4311 | −1.34474 | −0.672371 | − | 0.740215i | \(-0.734724\pi\) | ||||
−0.672371 | + | 0.740215i | \(0.734724\pi\) | |||||||
\(480\) | 13.7559 | − | 5.42646i | 0.627869 | − | 0.247683i | ||||
\(481\) | −17.6186 | −0.803340 | ||||||||
\(482\) | − | 2.15207i | − | 0.0980243i | ||||||
\(483\) | − | 69.1787i | − | 3.14774i | ||||||
\(484\) | −2.27478 | −0.103399 | ||||||||
\(485\) | −12.6253 | − | 32.0048i | −0.573287 | − | 1.45326i | ||||
\(486\) | 4.88941 | 0.221788 | ||||||||
\(487\) | 2.72017i | 0.123263i | 0.998099 | + | 0.0616313i | \(0.0196303\pi\) | ||||
−0.998099 | + | 0.0616313i | \(0.980370\pi\) | |||||||
\(488\) | − | 1.02218i | − | 0.0462718i | ||||||
\(489\) | −11.6593 | −0.527251 | ||||||||
\(490\) | 1.77984 | + | 4.51183i | 0.0804048 | + | 0.203824i | ||||
\(491\) | 18.9629 | 0.855783 | 0.427891 | − | 0.903830i | \(-0.359257\pi\) | ||||
0.427891 | + | 0.903830i | \(0.359257\pi\) | |||||||
\(492\) | 27.8118i | 1.25385i | ||||||||
\(493\) | 3.07582i | 0.138528i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.9783 | − | 5.90866i | 0.673223 | − | 0.265574i | ||||
\(496\) | 3.24662 | 0.145777 | ||||||||
\(497\) | − | 41.3375i | − | 1.85424i | ||||||
\(498\) | − | 7.61875i | − | 0.341404i | ||||||
\(499\) | 6.02343 | 0.269646 | 0.134823 | − | 0.990870i | \(-0.456953\pi\) | ||||
0.134823 | + | 0.990870i | \(0.456953\pi\) | |||||||
\(500\) | −9.29728 | + | 19.5668i | −0.415787 | + | 0.875054i | ||||
\(501\) | −46.4020 | −2.07309 | ||||||||
\(502\) | 7.30818i | 0.326180i | ||||||||
\(503\) | − | 18.6186i | − | 0.830164i | −0.909784 | − | 0.415082i | \(-0.863753\pi\) | ||
0.909784 | − | 0.415082i | \(-0.136247\pi\) | |||||||
\(504\) | −8.94701 | −0.398532 | ||||||||
\(505\) | −12.3210 | + | 4.86041i | −0.548278 | + | 0.216286i | ||||
\(506\) | 5.94159 | 0.264136 | ||||||||
\(507\) | 13.6443i | 0.605967i | ||||||||
\(508\) | 3.26004i | 0.144641i | ||||||||
\(509\) | −26.1610 | −1.15957 | −0.579784 | − | 0.814770i | \(-0.696863\pi\) | ||||
−0.579784 | + | 0.814770i | \(0.696863\pi\) | |||||||
\(510\) | −1.06463 | − | 2.69881i | −0.0471427 | − | 0.119505i | ||||
\(511\) | 16.5591 | 0.732532 | ||||||||
\(512\) | 17.5682i | 0.776411i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.36880 | −0.0603754 | ||||||||
\(515\) | 4.10879 | + | 10.4157i | 0.181055 | + | 0.458969i | ||||
\(516\) | 7.90397 | 0.347953 | ||||||||
\(517\) | − | 0.552830i | − | 0.0243134i | ||||||
\(518\) | − | 6.55327i | − | 0.287934i | ||||||
\(519\) | −4.48518 | −0.196877 | ||||||||
\(520\) | −5.43978 | + | 2.14589i | −0.238550 | + | 0.0941036i | ||||
\(521\) | −3.06917 | −0.134463 | −0.0672315 | − | 0.997737i | \(-0.521417\pi\) | ||||
−0.0672315 | + | 0.997737i | \(0.521417\pi\) | |||||||
\(522\) | 0.781803i | 0.0342186i | ||||||||
\(523\) | − | 11.5164i | − | 0.503576i | −0.967782 | − | 0.251788i | \(-0.918981\pi\) | ||
0.967782 | − | 0.251788i | \(-0.0810186\pi\) | |||||||
\(524\) | −14.8808 | −0.650072 | ||||||||
\(525\) | 33.3013 | − | 31.1156i | 1.45339 | − | 1.35799i | ||||
\(526\) | 0.141929 | 0.00618838 | ||||||||
\(527\) | − | 2.01899i | − | 0.0879484i | ||||||
\(528\) | 26.1863i | 1.13961i | ||||||||
\(529\) | −34.5992 | −1.50431 | ||||||||
\(530\) | 3.51974 | − | 1.38847i | 0.152888 | − | 0.0603114i | ||||
\(531\) | −17.9547 | −0.779166 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 16.5844i | − | 0.718350i | ||||||
\(534\) | 0.853468 | 0.0369332 | ||||||||
\(535\) | 2.31268 | + | 5.86258i | 0.0999859 | + | 0.253461i | ||||
\(536\) | 14.9590 | 0.646131 | ||||||||
\(537\) | − | 39.7502i | − | 1.71535i | ||||||
\(538\) | 1.10967i | 0.0478413i | ||||||||
\(539\) | −27.2243 | −1.17263 | ||||||||
\(540\) | −2.57182 | − | 6.51949i | −0.110674 | − | 0.280554i | ||||
\(541\) | −29.8468 | −1.28322 | −0.641608 | − | 0.767033i | \(-0.721732\pi\) | ||||
−0.641608 | + | 0.767033i | \(0.721732\pi\) | |||||||
\(542\) | 4.43708i | 0.190589i | ||||||||
\(543\) | 33.2294i | 1.42601i | ||||||||
\(544\) | 6.48567 | 0.278071 | ||||||||
\(545\) | 14.0355 | − | 5.53676i | 0.601216 | − | 0.237169i | ||||
\(546\) | 6.05386 | 0.259081 | ||||||||
\(547\) | − | 1.17678i | − | 0.0503155i | −0.999683 | − | 0.0251578i | \(-0.991991\pi\) | ||
0.999683 | − | 0.0251578i | \(-0.00800881\pi\) | |||||||
\(548\) | 18.7848i | 0.802448i | ||||||||
\(549\) | 2.38771 | 0.101905 | ||||||||
\(550\) | 2.67244 | + | 2.86017i | 0.113953 | + | 0.121958i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 17.1780i | 0.731142i | ||||||||
\(553\) | 44.3902i | 1.88766i | ||||||||
\(554\) | 2.02410 | 0.0859959 | ||||||||
\(555\) | −31.7184 | + | 12.5123i | −1.34637 | + | 0.531118i | ||||
\(556\) | 12.4078 | 0.526207 | ||||||||
\(557\) | − | 45.9826i | − | 1.94834i | −0.225807 | − | 0.974172i | \(-0.572502\pi\) | ||
0.225807 | − | 0.974172i | \(-0.427498\pi\) | |||||||
\(558\) | − | 0.513180i | − | 0.0217246i | ||||||
\(559\) | −4.71319 | −0.199347 | ||||||||
\(560\) | 11.7953 | + | 29.9008i | 0.498444 | + | 1.26354i | ||||
\(561\) | 16.2846 | 0.687535 | ||||||||
\(562\) | 1.76130i | 0.0742960i | ||||||||
\(563\) | − | 23.7250i | − | 0.999890i | −0.866057 | − | 0.499945i | \(-0.833353\pi\) | ||
0.866057 | − | 0.499945i | \(-0.166647\pi\) | |||||||
\(564\) | 0.786493 | 0.0331173 | ||||||||
\(565\) | −6.37269 | − | 16.1546i | −0.268101 | − | 0.679629i | ||||
\(566\) | −0.324331 | −0.0136327 | ||||||||
\(567\) | 42.0379i | 1.76543i | ||||||||
\(568\) | 10.2646i | 0.430694i | ||||||||
\(569\) | −7.42753 | −0.311378 | −0.155689 | − | 0.987806i | \(-0.549760\pi\) | ||||
−0.155689 | + | 0.987806i | \(0.549760\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.2355 | 1.47456 | 0.737279 | − | 0.675588i | \(-0.236110\pi\) | ||||
0.737279 | + | 0.675588i | \(0.236110\pi\) | |||||||
\(572\) | − | 16.1518i | − | 0.675339i | ||||||
\(573\) | − | 18.5316i | − | 0.774169i | ||||||
\(574\) | 6.16859 | 0.257472 | ||||||||
\(575\) | −25.9073 | − | 27.7271i | −1.08041 | − | 1.15630i | ||||
\(576\) | −15.0274 | −0.626140 | ||||||||
\(577\) | 31.5680i | 1.31419i | 0.753807 | + | 0.657096i | \(0.228216\pi\) | ||||
−0.753807 | + | 0.657096i | \(0.771784\pi\) | |||||||
\(578\) | 2.97332i | 0.123674i | ||||||||
\(579\) | 14.1235 | 0.586953 | ||||||||
\(580\) | 5.49216 | − | 2.16656i | 0.228050 | − | 0.0899614i | ||||
\(581\) | 52.4924 | 2.17775 | ||||||||
\(582\) | − | 8.84436i | − | 0.366610i | ||||||
\(583\) | 21.2380i | 0.879589i | ||||||||
\(584\) | −4.11184 | −0.170149 | ||||||||
\(585\) | −5.01259 | − | 12.7068i | −0.207245 | − | 0.525360i | ||||
\(586\) | −3.73372 | −0.154238 | ||||||||
\(587\) | 37.2187i | 1.53618i | 0.640342 | + | 0.768090i | \(0.278793\pi\) | ||||
−0.640342 | + | 0.768090i | \(0.721207\pi\) | |||||||
\(588\) | − | 38.7311i | − | 1.59725i | ||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −1.60175 | − | 4.06038i | −0.0659428 | − | 0.167163i | ||||
\(591\) | 40.0839 | 1.64883 | ||||||||
\(592\) | − | 24.0477i | − | 0.988354i | ||||||
\(593\) | 37.5290i | 1.54113i | 0.637360 | + | 0.770566i | \(0.280026\pi\) | ||||
−0.637360 | + | 0.770566i | \(0.719974\pi\) | |||||||
\(594\) | −1.26637 | −0.0519598 | ||||||||
\(595\) | 18.5945 | − | 7.33521i | 0.762302 | − | 0.300714i | ||||
\(596\) | 3.76901 | 0.154385 | ||||||||
\(597\) | − | 0.0243900i | − | 0.000998217i | ||||||
\(598\) | − | 5.04053i | − | 0.206123i | ||||||
\(599\) | −2.13127 | −0.0870813 | −0.0435406 | − | 0.999052i | \(-0.513864\pi\) | ||||
−0.0435406 | + | 0.999052i | \(0.513864\pi\) | |||||||
\(600\) | −8.26913 | + | 7.72639i | −0.337586 | + | 0.315429i | ||||
\(601\) | −0.0853415 | −0.00348115 | −0.00174058 | − | 0.999998i | \(-0.500554\pi\) | ||||
−0.00174058 | + | 0.999998i | \(0.500554\pi\) | |||||||
\(602\) | − | 1.75308i | − | 0.0714502i | ||||||
\(603\) | 34.9428i | 1.42298i | ||||||||
\(604\) | −32.3910 | −1.31797 | ||||||||
\(605\) | 2.44201 | − | 0.963329i | 0.0992819 | − | 0.0391649i | ||||
\(606\) | −3.40484 | −0.138312 | ||||||||
\(607\) | 21.0800i | 0.855610i | 0.903871 | + | 0.427805i | \(0.140713\pi\) | ||||
−0.903871 | + | 0.427805i | \(0.859287\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.4211 | −0.503328 | ||||||||
\(610\) | 0.213009 | + | 0.539971i | 0.00862447 | + | 0.0218628i | ||||
\(611\) | −0.468991 | −0.0189734 | ||||||||
\(612\) | 10.0469i | 0.406120i | ||||||||
\(613\) | 17.8897i | 0.722559i | 0.932458 | + | 0.361280i | \(0.117660\pi\) | ||||
−0.932458 | + | 0.361280i | \(0.882340\pi\) | |||||||
\(614\) | 1.25218 | 0.0505337 | ||||||||
\(615\) | −11.7778 | − | 29.8565i | −0.474928 | − | 1.20393i | ||||
\(616\) | 12.2087 | 0.491904 | ||||||||
\(617\) | − | 1.52526i | − | 0.0614045i | −0.999529 | − | 0.0307022i | \(-0.990226\pi\) | ||
0.999529 | − | 0.0307022i | \(-0.00977436\pi\) | |||||||
\(618\) | 2.87831i | 0.115783i | ||||||||
\(619\) | −11.8121 | −0.474769 | −0.237384 | − | 0.971416i | \(-0.576290\pi\) | ||||
−0.237384 | + | 0.971416i | \(0.576290\pi\) | |||||||
\(620\) | −3.60508 | + | 1.42214i | −0.144784 | + | 0.0571145i | ||||
\(621\) | 12.2765 | 0.492638 | ||||||||
\(622\) | − | 4.18190i | − | 0.167679i | ||||||
\(623\) | 5.88031i | 0.235589i | ||||||||
\(624\) | 22.2151 | 0.889314 | ||||||||
\(625\) | 1.69458 | − | 24.9425i | 0.0677832 | − | 0.997700i | ||||
\(626\) | −1.43321 | −0.0572827 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 19.0085i | − | 0.758520i | ||||||
\(629\) | −14.9546 | −0.596280 | ||||||||
\(630\) | 4.72631 | − | 1.86444i | 0.188301 | − | 0.0742811i | ||||
\(631\) | 8.02047 | 0.319290 | 0.159645 | − | 0.987174i | \(-0.448965\pi\) | ||||
0.159645 | + | 0.987174i | \(0.448965\pi\) | |||||||
\(632\) | − | 11.0227i | − | 0.438458i | ||||||
\(633\) | 62.4326i | 2.48147i | ||||||||
\(634\) | 1.98461 | 0.0788188 | ||||||||
\(635\) | −1.38057 | − | 3.49970i | −0.0547862 | − | 0.138881i | ||||
\(636\) | −30.2147 | −1.19809 | ||||||||
\(637\) | 23.0956i | 0.915083i | ||||||||
\(638\) | − | 1.06682i | − | 0.0422357i | ||||||
\(639\) | −23.9771 | −0.948521 | ||||||||
\(640\) | −6.05606 | − | 15.3519i | −0.239387 | − | 0.606839i | ||||
\(641\) | −42.0011 | −1.65894 | −0.829472 | − | 0.558548i | \(-0.811358\pi\) | ||||
−0.829472 | + | 0.558548i | \(0.811358\pi\) | |||||||
\(642\) | 1.62009i | 0.0639399i | ||||||||
\(643\) | − | 12.7588i | − | 0.503158i | −0.967837 | − | 0.251579i | \(-0.919050\pi\) | ||
0.967837 | − | 0.251579i | \(-0.0809498\pi\) | |||||||
\(644\) | −58.2398 | −2.29497 | ||||||||
\(645\) | −8.48504 | + | 3.34720i | −0.334098 | + | 0.131796i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.1646i | 1.73629i | 0.496311 | + | 0.868145i | \(0.334688\pi\) | ||||
−0.496311 | + | 0.868145i | \(0.665312\pi\) | |||||||
\(648\) | − | 10.4386i | − | 0.410065i | ||||||
\(649\) | 24.5002 | 0.961718 | ||||||||
\(650\) | 2.42641 | − | 2.26716i | 0.0951718 | − | 0.0889253i | ||||
\(651\) | 8.15327 | 0.319552 | ||||||||
\(652\) | 9.81565i | 0.384410i | ||||||||
\(653\) | 21.7731i | 0.852048i | 0.904712 | + | 0.426024i | \(0.140086\pi\) | ||||
−0.904712 | + | 0.426024i | \(0.859914\pi\) | |||||||
\(654\) | 3.87864 | 0.151667 | ||||||||
\(655\) | 15.9748 | − | 6.30178i | 0.624188 | − | 0.246231i | ||||
\(656\) | 22.6361 | 0.883790 | ||||||||
\(657\) | − | 9.60485i | − | 0.374721i | ||||||
\(658\) | − | 0.174442i | − | 0.00680046i | ||||||
\(659\) | 41.1821 | 1.60423 | 0.802114 | − | 0.597171i | \(-0.203709\pi\) | ||||
0.802114 | + | 0.597171i | \(0.203709\pi\) | |||||||
\(660\) | −11.4706 | − | 29.0776i | −0.446492 | − | 1.13184i | ||||
\(661\) | −13.6157 | −0.529588 | −0.264794 | − | 0.964305i | \(-0.585304\pi\) | ||||
−0.264794 | + | 0.964305i | \(0.585304\pi\) | |||||||
\(662\) | − | 5.19923i | − | 0.202074i | ||||||
\(663\) | − | 13.8150i | − | 0.536529i | ||||||
\(664\) | −13.0345 | −0.505838 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.80112 | −0.147290 | ||||||||
\(667\) | 10.3420i | 0.400443i | ||||||||
\(668\) | 39.0646i | 1.51146i | ||||||||
\(669\) | 17.6079 | 0.680762 | ||||||||
\(670\) | −7.90218 | + | 3.11727i | −0.305288 | + | 0.120430i | ||||
\(671\) | −3.25817 | −0.125780 | ||||||||
\(672\) | 26.1911i | 1.01034i | ||||||||
\(673\) | − | 16.0356i | − | 0.618129i | −0.951041 | − | 0.309064i | \(-0.899984\pi\) | ||
0.951041 | − | 0.309064i | \(-0.100016\pi\) | |||||||
\(674\) | −6.83362 | −0.263221 | ||||||||
\(675\) | 5.52178 | + | 5.90966i | 0.212534 | + | 0.227463i | ||||
\(676\) | 11.4868 | 0.441801 | ||||||||
\(677\) | − | 21.8215i | − | 0.838668i | −0.907832 | − | 0.419334i | \(-0.862264\pi\) | ||
0.907832 | − | 0.419334i | \(-0.137736\pi\) | |||||||
\(678\) | − | 4.46423i | − | 0.171448i | ||||||
\(679\) | 60.9367 | 2.33854 | ||||||||
\(680\) | −4.61726 | + | 1.82143i | −0.177064 | + | 0.0698485i | ||||
\(681\) | 59.7525 | 2.28972 | ||||||||
\(682\) | 0.700265i | 0.0268145i | ||||||||
\(683\) | 13.5921i | 0.520088i | 0.965597 | + | 0.260044i | \(0.0837370\pi\) | ||||
−0.965597 | + | 0.260044i | \(0.916263\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.95505 | − | 20.1658i | −0.303947 | − | 0.770496i | ||||
\(686\) | −1.66663 | −0.0636323 | ||||||||
\(687\) | 14.7790i | 0.563855i | ||||||||
\(688\) | − | 6.43305i | − | 0.245258i | ||||||
\(689\) | 18.0172 | 0.686401 | ||||||||
\(690\) | −3.57967 | − | 9.07435i | −0.136276 | − | 0.345455i | ||||
\(691\) | 18.1458 | 0.690300 | 0.345150 | − | 0.938547i | \(-0.387828\pi\) | ||||
0.345150 | + | 0.938547i | \(0.387828\pi\) | |||||||
\(692\) | 3.77596i | 0.143540i | ||||||||
\(693\) | 28.5184i | 1.08332i | ||||||||
\(694\) | −5.04494 | −0.191503 | ||||||||
\(695\) | −13.3200 | + | 5.25448i | −0.505255 | + | 0.199314i | ||||
\(696\) | 3.08432 | 0.116911 | ||||||||
\(697\) | − | 14.0768i | − | 0.533196i | ||||||
\(698\) | 3.90210i | 0.147697i | ||||||||
\(699\) | 43.9493 | 1.66232 | ||||||||
\(700\) | −26.1954 | − | 28.0355i | −0.990093 | − | 1.05964i | ||||
\(701\) | −26.8748 | −1.01505 | −0.507523 | − | 0.861638i | \(-0.669439\pi\) | ||||
−0.507523 | + | 0.861638i | \(0.669439\pi\) | |||||||
\(702\) | 1.07432i | 0.0405477i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 20.5058 | 0.772840 | ||||||||
\(705\) | −0.844313 | + | 0.333066i | −0.0317987 | + | 0.0125440i | ||||
\(706\) | −1.14821 | −0.0432134 | ||||||||
\(707\) | − | 23.4590i | − | 0.882267i | ||||||
\(708\) | 34.8557i | 1.30996i | ||||||||
\(709\) | −20.6855 | −0.776861 | −0.388431 | − | 0.921478i | \(-0.626983\pi\) | ||||
−0.388431 | + | 0.921478i | \(0.626983\pi\) | |||||||
\(710\) | −2.13901 | − | 5.42234i | −0.0802758 | − | 0.203497i | ||||
\(711\) | 25.7478 | 0.965619 | ||||||||
\(712\) | − | 1.46016i | − | 0.0547216i | ||||||
\(713\) | − | 6.78853i | − | 0.254232i | ||||||
\(714\) | 5.13850 | 0.192304 | ||||||||
\(715\) | 6.83999 | + | 17.3392i | 0.255801 | + | 0.648448i | ||||
\(716\) | −33.4647 | −1.25063 | ||||||||
\(717\) | 19.3142i | 0.721301i | ||||||||
\(718\) | 2.70486i | 0.100944i | ||||||||
\(719\) | 29.1011 | 1.08529 | 0.542644 | − | 0.839963i | \(-0.317423\pi\) | ||||
0.542644 | + | 0.839963i | \(0.317423\pi\) | |||||||
\(720\) | 17.3435 | − | 6.84170i | 0.646354 | − | 0.254975i | ||||
\(721\) | −19.8313 | −0.738556 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 19.8323i | − | 0.737571i | ||||||
\(724\) | 27.9750 | 1.03968 | ||||||||
\(725\) | −4.97843 | + | 4.65167i | −0.184894 | + | 0.172759i | ||||
\(726\) | 0.674837 | 0.0250455 | ||||||||
\(727\) | 10.8609i | 0.402808i | 0.979508 | + | 0.201404i | \(0.0645504\pi\) | ||||
−0.979508 | + | 0.201404i | \(0.935450\pi\) | |||||||
\(728\) | − | 10.3573i | − | 0.383865i | ||||||
\(729\) | 13.2146 | 0.489428 | ||||||||
\(730\) | 2.17210 | − | 0.856854i | 0.0803931 | − | 0.0317136i | ||||
\(731\) | −4.00054 | −0.147965 | ||||||||
\(732\) | − | 4.63530i | − | 0.171326i | ||||||
\(733\) | − | 49.4817i | − | 1.82765i | −0.406108 | − | 0.913825i | \(-0.633114\pi\) | ||
0.406108 | − | 0.913825i | \(-0.366886\pi\) | |||||||
\(734\) | 1.66393 | 0.0614169 | ||||||||
\(735\) | 16.4020 | + | 41.5785i | 0.604996 | + | 1.53365i | ||||
\(736\) | 21.8071 | 0.803819 | ||||||||
\(737\) | − | 47.6815i | − | 1.75637i | ||||||
\(738\) | − | 3.57799i | − | 0.131708i | ||||||
\(739\) | 31.5052 | 1.15894 | 0.579468 | − | 0.814995i | \(-0.303260\pi\) | ||||
0.579468 | + | 0.814995i | \(0.303260\pi\) | |||||||
\(740\) | 10.5338 | + | 26.7029i | 0.387230 | + | 0.981617i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.70153i | 0.246021i | ||||||||
\(743\) | 35.6669i | 1.30849i | 0.756282 | + | 0.654246i | \(0.227014\pi\) | ||||
−0.756282 | + | 0.654246i | \(0.772986\pi\) | |||||||
\(744\) | −2.02456 | −0.0742240 | ||||||||
\(745\) | −4.04610 | + | 1.59611i | −0.148237 | + | 0.0584770i | ||||
\(746\) | 4.52577 | 0.165700 | ||||||||
\(747\) | − | 30.4474i | − | 1.11401i | ||||||
\(748\) | − | 13.7096i | − | 0.501271i | ||||||
\(749\) | −11.1623 | −0.407860 | ||||||||
\(750\) | 2.75813 | − | 5.80469i | 0.100713 | − | 0.211957i | ||||
\(751\) | −2.10024 | −0.0766389 | −0.0383194 | − | 0.999266i | \(-0.512200\pi\) | ||||
−0.0383194 | + | 0.999266i | \(0.512200\pi\) | |||||||
\(752\) | − | 0.640127i | − | 0.0233430i | ||||||
\(753\) | 67.3481i | 2.45430i | ||||||||
\(754\) | −0.905032 | −0.0329593 | ||||||||
\(755\) | 34.7722 | − | 13.7170i | 1.26549 | − | 0.499213i | ||||
\(756\) | 12.4130 | 0.451457 | ||||||||
\(757\) | 1.15817i | 0.0420945i | 0.999778 | + | 0.0210473i | \(0.00670004\pi\) | ||||
−0.999778 | + | 0.0210473i | \(0.993300\pi\) | |||||||
\(758\) | − | 7.97396i | − | 0.289627i | ||||||
\(759\) | 54.7544 | 1.98746 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −44.6406 | −1.61822 | −0.809111 | − | 0.587656i | \(-0.800051\pi\) | ||||
−0.809111 | + | 0.587656i | \(0.800051\pi\) | |||||||
\(762\) | − | 0.967123i | − | 0.0350352i | ||||||
\(763\) | 26.7235i | 0.967454i | ||||||||
\(764\) | −15.6013 | −0.564435 | ||||||||
\(765\) | −4.25467 | − | 10.7855i | −0.153828 | − | 0.389950i | ||||
\(766\) | −3.44275 | −0.124391 | ||||||||
\(767\) | − | 20.7847i | − | 0.750492i | ||||||
\(768\) | 25.8696i | 0.933489i | ||||||||
\(769\) | −29.7532 | −1.07293 | −0.536465 | − | 0.843923i | \(-0.680241\pi\) | ||||
−0.536465 | + | 0.843923i | \(0.680241\pi\) | |||||||
\(770\) | −6.44933 | + | 2.54415i | −0.232418 | + | 0.0916846i | ||||
\(771\) | −12.6141 | −0.454287 | ||||||||
\(772\) | − | 11.8902i | − | 0.427938i | ||||||
\(773\) | 13.6612i | 0.491360i | 0.969351 | + | 0.245680i | \(0.0790112\pi\) | ||||
−0.969351 | + | 0.245680i | \(0.920989\pi\) | |||||||
\(774\) | −1.01685 | −0.0365498 | ||||||||
\(775\) | 3.26787 | − | 3.05338i | 0.117385 | − | 0.109681i | ||||
\(776\) | −15.1314 | −0.543185 | ||||||||
\(777\) | − | 60.3913i | − | 2.16652i | ||||||
\(778\) | 6.16433i | 0.221002i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −24.6679 | + | 9.73104i | −0.883252 | + | 0.348427i | ||||
\(781\) | 32.7183 | 1.17075 | ||||||||
\(782\) | − | 4.27839i | − | 0.152995i | ||||||
\(783\) | − | 2.20425i | − | 0.0787736i | ||||||
\(784\) | −31.5233 | −1.12583 | ||||||||
\(785\) | 8.04976 | + | 20.4059i | 0.287308 | + | 0.728318i | ||||
\(786\) | 4.41455 | 0.157462 | ||||||||
\(787\) | 49.9989i | 1.78227i | 0.453740 | + | 0.891134i | \(0.350089\pi\) | ||||
−0.453740 | + | 0.891134i | \(0.649911\pi\) | |||||||
\(788\) | − | 33.7456i | − | 1.20214i | ||||||
\(789\) | 1.30793 | 0.0465637 | ||||||||
\(790\) | 2.29698 | + | 5.82278i | 0.0817228 | + | 0.207165i | ||||
\(791\) | 30.7581 | 1.09363 | ||||||||
\(792\) | − | 7.08149i | − | 0.251630i | ||||||
\(793\) | 2.76406i | 0.0981547i | ||||||||
\(794\) | 4.46251 | 0.158369 | ||||||||
\(795\) | 32.4359 | − | 12.7954i | 1.15038 | − | 0.453805i | ||||
\(796\) | −0.0205333 | −0.000727785 | ||||||||
\(797\) | 11.0649i | 0.391939i | 0.980610 | + | 0.195969i | \(0.0627853\pi\) | ||||
−0.980610 | + | 0.195969i | \(0.937215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.398078 | −0.0140830 | ||||||||
\(800\) | 9.80850 | + | 10.4975i | 0.346783 | + | 0.371142i | ||||
\(801\) | 3.41078 | 0.120514 | ||||||||
\(802\) | − | 5.72730i | − | 0.202238i | ||||||
\(803\) | 13.1064i | 0.462515i | ||||||||
\(804\) | 67.8350 | 2.39236 | ||||||||
\(805\) | 62.5213 | − | 24.6635i | 2.20359 | − | 0.869275i | ||||
\(806\) | 0.594068 | 0.0209251 | ||||||||
\(807\) | 10.2261i | 0.359976i | ||||||||
\(808\) | 5.82518i | 0.204929i | ||||||||
\(809\) | −6.05426 | −0.212857 | −0.106428 | − | 0.994320i | \(-0.533941\pi\) | ||||
−0.106428 | + | 0.994320i | \(0.533941\pi\) | |||||||
\(810\) | 2.17526 | + | 5.51422i | 0.0764309 | + | 0.193750i | ||||
\(811\) | 6.97028 | 0.244760 | 0.122380 | − | 0.992483i | \(-0.460947\pi\) | ||||
0.122380 | + | 0.992483i | \(0.460947\pi\) | |||||||
\(812\) | 10.4570i | 0.366969i | ||||||||
\(813\) | 40.8896i | 1.43406i | ||||||||
\(814\) | 5.18686 | 0.181799 | ||||||||
\(815\) | −4.15676 | − | 10.5373i | −0.145605 | − | 0.369104i | ||||
\(816\) | 18.8561 | 0.660095 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 6.28883i | − | 0.219884i | ||||||
\(819\) | 24.1935 | 0.845390 | ||||||||
\(820\) | −25.1354 | + | 9.91545i | −0.877766 | + | 0.346263i | ||||
\(821\) | 9.65335 | 0.336904 | 0.168452 | − | 0.985710i | \(-0.446123\pi\) | ||||
0.168452 | + | 0.985710i | \(0.446123\pi\) | |||||||
\(822\) | − | 5.57271i | − | 0.194371i | ||||||
\(823\) | − | 14.4949i | − | 0.505261i | −0.967563 | − | 0.252631i | \(-0.918704\pi\) | ||
0.967563 | − | 0.252631i | \(-0.0812957\pi\) | |||||||
\(824\) | 4.92436 | 0.171548 | ||||||||
\(825\) | 24.6277 | + | 26.3577i | 0.857427 | + | 0.917657i | ||||
\(826\) | 7.73090 | 0.268993 | ||||||||
\(827\) | 27.7016i | 0.963279i | 0.876369 | + | 0.481639i | \(0.159959\pi\) | ||||
−0.876369 | + | 0.481639i | \(0.840041\pi\) | |||||||
\(828\) | 33.7810i | 1.17397i | ||||||||
\(829\) | 32.2071 | 1.11860 | 0.559299 | − | 0.828966i | \(-0.311070\pi\) | ||||
0.559299 | + | 0.828966i | \(0.311070\pi\) | |||||||
\(830\) | 6.88556 | − | 2.71623i | 0.239001 | − | 0.0942817i | ||||
\(831\) | 18.6530 | 0.647065 | ||||||||
\(832\) | − | 17.3960i | − | 0.603098i | ||||||
\(833\) | 19.6035i | 0.679221i | ||||||||
\(834\) | −3.68090 | −0.127459 | ||||||||
\(835\) | −16.5432 | − | 41.9365i | −0.572501 | − | 1.45127i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.44688i | 0.0500116i | ||||||||
\(838\) | − | 0.0623324i | − | 0.00215324i | ||||||
\(839\) | −45.1856 | −1.55998 | −0.779990 | − | 0.625791i | \(-0.784776\pi\) | ||||
−0.779990 | + | 0.625791i | \(0.784776\pi\) | |||||||
\(840\) | −7.35547 | − | 18.6459i | −0.253788 | − | 0.643345i | ||||
\(841\) | −27.1431 | −0.935969 | ||||||||
\(842\) | 7.53453i | 0.259657i | ||||||||
\(843\) | 16.2312i | 0.559031i | ||||||||
\(844\) | 52.5604 | 1.80920 | ||||||||
\(845\) | −12.3313 | + | 4.86447i | −0.424209 | + | 0.167343i | ||||
\(846\) | −0.101182 | −0.00347872 | ||||||||
\(847\) | 4.64956i | 0.159761i | ||||||||
\(848\) | 24.5917i | 0.844483i | ||||||||
\(849\) | −2.98885 | −0.102577 | ||||||||
\(850\) | 2.05953 | − | 1.92436i | 0.0706414 | − | 0.0660049i | ||||
\(851\) | −50.2826 | −1.72367 | ||||||||
\(852\) | 46.5473i | 1.59468i | ||||||||
\(853\) | 41.8087i | 1.43150i | 0.698355 | + | 0.715751i | \(0.253916\pi\) | ||||
−0.698355 | + | 0.715751i | \(0.746084\pi\) | |||||||
\(854\) | −1.02810 | −0.0351808 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.77173 | 0.0947358 | ||||||||
\(857\) | − | 42.4772i | − | 1.45099i | −0.688226 | − | 0.725497i | \(-0.741610\pi\) | ||
0.688226 | − | 0.725497i | \(-0.258390\pi\) | |||||||
\(858\) | 4.79158i | 0.163582i | ||||||||
\(859\) | −2.27865 | −0.0777467 | −0.0388733 | − | 0.999244i | \(-0.512377\pi\) | ||||
−0.0388733 | + | 0.999244i | \(0.512377\pi\) | |||||||
\(860\) | 2.81792 | + | 7.14334i | 0.0960902 | + | 0.243586i | ||||
\(861\) | 56.8463 | 1.93732 | ||||||||
\(862\) | 3.85029i | 0.131141i | ||||||||
\(863\) | 41.6831i | 1.41891i | 0.704751 | + | 0.709455i | \(0.251059\pi\) | ||||
−0.704751 | + | 0.709455i | \(0.748941\pi\) | |||||||
\(864\) | −4.64788 | −0.158124 | ||||||||
\(865\) | −1.59905 | − | 4.05355i | −0.0543694 | − | 0.137825i | ||||
\(866\) | −3.13133 | −0.106407 | ||||||||
\(867\) | 27.4004i | 0.930567i | ||||||||
\(868\) | − | 6.86403i | − | 0.232980i | ||||||
\(869\) | −35.1345 | −1.19186 | ||||||||
\(870\) | −1.62931 | + | 0.642732i | −0.0552387 | + | 0.0217906i | ||||
\(871\) | −40.4505 | −1.37061 | ||||||||
\(872\) | − | 6.63578i | − | 0.224716i | ||||||
\(873\) | − | 35.3454i | − | 1.19626i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 39.9937 | + | 19.0032i | 1.35203 | + | 0.642427i | ||||
\(876\) | −18.6461 | −0.629992 | ||||||||
\(877\) | 5.34370i | 0.180444i | 0.995922 | + | 0.0902220i | \(0.0287577\pi\) | ||||
−0.995922 | + | 0.0902220i | \(0.971242\pi\) | |||||||
\(878\) | − | 6.32458i | − | 0.213444i | ||||||
\(879\) | −34.4078 | −1.16055 | ||||||||
\(880\) | −23.6663 | + | 9.33591i | −0.797790 | + | 0.314714i | ||||
\(881\) | 19.1989 | 0.646827 | 0.323414 | − | 0.946258i | \(-0.395169\pi\) | ||||
0.323414 | + | 0.946258i | \(0.395169\pi\) | |||||||
\(882\) | 4.98276i | 0.167778i | ||||||||
\(883\) | − | 28.7091i | − | 0.966138i | −0.875582 | − | 0.483069i | \(-0.839522\pi\) | ||
0.875582 | − | 0.483069i | \(-0.160478\pi\) | |||||||
\(884\) | −11.6305 | −0.391175 | ||||||||
\(885\) | −14.7608 | − | 37.4182i | −0.496178 | − | 1.25780i | ||||
\(886\) | −1.85249 | −0.0622357 | ||||||||
\(887\) | − | 10.1948i | − | 0.342307i | −0.985244 | − | 0.171153i | \(-0.945251\pi\) | ||
0.985244 | − | 0.171153i | \(-0.0547494\pi\) | |||||||
\(888\) | 14.9959i | 0.503230i | ||||||||
\(889\) | 6.66338 | 0.223483 | ||||||||
\(890\) | 0.304278 | + | 0.771335i | 0.0101994 | + | 0.0258552i | ||||
\(891\) | −33.2727 | −1.11468 | ||||||||
\(892\) | − | 14.8237i | − | 0.496333i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −1.11812 | −0.0373954 | ||||||||
\(895\) | 35.9249 | − | 14.1717i | 1.20084 | − | 0.473708i | ||||
\(896\) | 29.2299 | 0.976501 | ||||||||
\(897\) | − | 46.4507i | − | 1.55094i | ||||||
\(898\) | − | 6.00850i | − | 0.200506i | ||||||
\(899\) | −1.21889 | −0.0406521 | ||||||||
\(900\) | −16.2615 | + | 15.1942i | −0.542051 | + | 0.506474i | ||||
\(901\) | 15.2930 | 0.509482 | ||||||||
\(902\) | 4.88239i | 0.162566i | ||||||||
\(903\) | − | 16.1554i | − | 0.537618i | ||||||
\(904\) | −7.63763 | −0.254024 | ||||||||
\(905\) | −30.0316 | + | 11.8469i | −0.998283 | + | 0.393805i | ||||
\(906\) | 9.60911 | 0.319241 | ||||||||
\(907\) | 39.0849i | 1.29779i | 0.760877 | + | 0.648896i | \(0.224769\pi\) | ||||
−0.760877 | + | 0.648896i | \(0.775231\pi\) | |||||||
\(908\) | − | 50.3041i | − | 1.66940i | ||||||
\(909\) | −13.6070 | −0.451317 | ||||||||
\(910\) | 2.15832 | + | 5.47127i | 0.0715475 | + | 0.181371i | ||||
\(911\) | 36.6728 | 1.21502 | 0.607512 | − | 0.794310i | \(-0.292168\pi\) | ||||
0.607512 | + | 0.794310i | \(0.292168\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41.5473i | 1.37502i | ||||||||
\(914\) | −1.59818 | −0.0528629 | ||||||||
\(915\) | 1.96297 | + | 4.97607i | 0.0648937 | + | 0.164504i | ||||
\(916\) | 12.4421 | 0.411098 | ||||||||
\(917\) | 30.4158i | 1.00442i | ||||||||
\(918\) | 0.911881i | 0.0300965i | ||||||||
\(919\) | 20.4855 | 0.675753 | 0.337877 | − | 0.941190i | \(-0.390291\pi\) | ||||
0.337877 | + | 0.941190i | \(0.390291\pi\) | |||||||
\(920\) | −15.5248 | + | 6.12427i | −0.511839 | + | 0.201911i | ||||
\(921\) | 11.5394 | 0.380235 | ||||||||
\(922\) | − | 3.80872i | − | 0.125434i | ||||||
\(923\) | − | 27.7564i | − | 0.913615i | ||||||
\(924\) | 55.3633 | 1.82132 | ||||||||
\(925\) | −22.6164 | − | 24.2051i | −0.743623 | − | 0.795858i | ||||
\(926\) | −9.09837 | −0.298991 | ||||||||
\(927\) | 11.5028i | 0.377802i | ||||||||
\(928\) | − | 3.91547i | − | 0.128532i | ||||||
\(929\) | −17.3877 | −0.570472 | −0.285236 | − | 0.958457i | \(-0.592072\pi\) | ||||
−0.285236 | + | 0.958457i | \(0.592072\pi\) | |||||||
\(930\) | 1.06949 | − | 0.421893i | 0.0350698 | − | 0.0138344i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 36.9998i | − | 1.21197i | ||||||
\(933\) | − | 38.5380i | − | 1.26168i | ||||||
\(934\) | −7.04215 | −0.230426 | ||||||||
\(935\) | 5.80576 | + | 14.7174i | 0.189869 | + | 0.481312i | ||||
\(936\) | −6.00756 | −0.196363 | ||||||||
\(937\) | 33.2075i | 1.08484i | 0.840107 | + | 0.542421i | \(0.182492\pi\) | ||||
−0.840107 | + | 0.542421i | \(0.817508\pi\) | |||||||
\(938\) | − | 15.0456i | − | 0.491257i | ||||||
\(939\) | −13.2077 | −0.431016 | ||||||||
\(940\) | 0.280400 | + | 0.710806i | 0.00914564 | + | 0.0231839i | ||||
\(941\) | −36.7788 | −1.19895 | −0.599477 | − | 0.800392i | \(-0.704625\pi\) | ||||
−0.599477 | + | 0.800392i | \(0.704625\pi\) | |||||||
\(942\) | 5.63906i | 0.183730i | ||||||||
\(943\) | − | 47.3310i | − | 1.54131i | ||||||
\(944\) | 28.3691 | 0.923335 | ||||||||
\(945\) | −13.3256 | + | 5.25670i | −0.433481 | + | 0.171000i | ||||
\(946\) | 1.38755 | 0.0451131 | ||||||||
\(947\) | 34.9882i | 1.13696i | 0.822696 | + | 0.568482i | \(0.192469\pi\) | ||||
−0.822696 | + | 0.568482i | \(0.807531\pi\) | |||||||
\(948\) | − | 49.9847i | − | 1.62343i | ||||||
\(949\) | 11.1188 | 0.360931 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.2890 | 0.593062 | ||||||||
\(952\) | − | 8.79120i | − | 0.284925i | ||||||
\(953\) | − | 53.8985i | − | 1.74594i | −0.487771 | − | 0.872972i | \(-0.662190\pi\) | ||
0.487771 | − | 0.872972i | \(-0.337810\pi\) | |||||||
\(954\) | 3.88712 | 0.125850 | ||||||||
\(955\) | 16.7482 | − | 6.60687i | 0.541960 | − | 0.213793i | ||||
\(956\) | 16.2601 | 0.525890 | ||||||||
\(957\) | − | 9.83119i | − | 0.317797i | ||||||
\(958\) | − | 7.35043i | − | 0.237482i | ||||||
\(959\) | 38.3954 | 1.23985 | ||||||||
\(960\) | −12.3542 | − | 31.3176i | −0.398731 | − | 1.01077i | ||||
\(961\) | −30.1999 | −0.974191 | ||||||||
\(962\) | − | 4.40026i | − | 0.141870i | ||||||
\(963\) | 6.47449i | 0.208637i | ||||||||
\(964\) | −16.6963 | −0.537752 | ||||||||
\(965\) | 5.03530 | + | 12.7643i | 0.162092 | + | 0.410899i | ||||
\(966\) | 17.2774 | 0.555892 | ||||||||
\(967\) | 49.8831i | 1.60413i | 0.597236 | + | 0.802066i | \(0.296266\pi\) | ||||
−0.597236 | + | 0.802066i | \(0.703734\pi\) | |||||||
\(968\) | − | 1.15454i | − | 0.0371084i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.99323 | − | 3.15318i | 0.256647 | − | 0.101243i | ||||
\(971\) | 13.8066 | 0.443074 | 0.221537 | − | 0.975152i | \(-0.428893\pi\) | ||||
0.221537 | + | 0.975152i | \(0.428893\pi\) | |||||||
\(972\) | − | 37.9332i | − | 1.21671i | ||||||
\(973\) | − | 25.3610i | − | 0.813037i | ||||||
\(974\) | −0.679364 | −0.0217682 | ||||||||
\(975\) | 22.3605 | − | 20.8929i | 0.716108 | − | 0.669107i | ||||
\(976\) | −3.77267 | −0.120760 | ||||||||
\(977\) | − | 31.6433i | − | 1.01236i | −0.862428 | − | 0.506180i | \(-0.831057\pi\) | ||
0.862428 | − | 0.506180i | \(-0.168943\pi\) | |||||||
\(978\) | − | 2.91191i | − | 0.0931127i | ||||||
\(979\) | −4.65421 | −0.148749 | ||||||||
\(980\) | 35.0039 | − | 13.8084i | 1.11816 | − | 0.441093i | ||||
\(981\) | 15.5005 | 0.494893 | ||||||||
\(982\) | 4.73599i | 0.151132i | ||||||||
\(983\) | − | 40.1898i | − | 1.28186i | −0.767601 | − | 0.640928i | \(-0.778550\pi\) | ||
0.767601 | − | 0.640928i | \(-0.221450\pi\) | |||||||
\(984\) | −14.1157 | −0.449991 | ||||||||
\(985\) | 14.2907 | + | 36.2264i | 0.455339 | + | 1.15427i | ||||
\(986\) | −0.768188 | −0.0244641 | ||||||||
\(987\) | − | 1.60756i | − | 0.0511692i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.4512 | −0.427724 | ||||||||
\(990\) | 1.47569 | + | 3.74083i | 0.0469005 | + | 0.118891i | ||||
\(991\) | −19.4757 | −0.618667 | −0.309333 | − | 0.950954i | \(-0.600106\pi\) | ||||
−0.309333 | + | 0.950954i | \(0.600106\pi\) | |||||||
\(992\) | 2.57014i | 0.0816020i | ||||||||
\(993\) | − | 47.9131i | − | 1.52048i | ||||||
\(994\) | 10.3241 | 0.327459 | ||||||||
\(995\) | 0.0220429 | − | 0.00869551i | 0.000698806 | − | 0.000275666i | ||||
\(996\) | −59.1081 | −1.87291 | ||||||||
\(997\) | − | 14.1426i | − | 0.447901i | −0.974601 | − | 0.223950i | \(-0.928105\pi\) | ||
0.974601 | − | 0.223950i | \(-0.0718953\pi\) | |||||||
\(998\) | 1.50436i | 0.0476195i | ||||||||
\(999\) | 10.7171 | 0.339073 |
(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 | 1805.2.b.k.1084.14 | 24 | ||
5.2 | odd | 4 | 9025.2.a.cu.1.11 | 24 | |||
5.3 | odd | 4 | 9025.2.a.cu.1.14 | 24 | |||
5.4 | even | 2 | inner | 1805.2.b.k.1084.11 | 24 | ||
19.9 | even | 9 | 95.2.p.a.24.4 | yes | 48 | ||
19.17 | even | 9 | 95.2.p.a.4.5 | yes | 48 | ||
19.18 | odd | 2 | 1805.2.b.l.1084.11 | 24 | |||
57.17 | odd | 18 | 855.2.da.b.289.4 | 48 | |||
57.47 | odd | 18 | 855.2.da.b.784.5 | 48 | |||
95.9 | even | 18 | 95.2.p.a.24.5 | yes | 48 | ||
95.17 | odd | 36 | 475.2.l.f.251.5 | 48 | |||
95.18 | even | 4 | 9025.2.a.ct.1.11 | 24 | |||
95.28 | odd | 36 | 475.2.l.f.176.4 | 48 | |||
95.37 | even | 4 | 9025.2.a.ct.1.14 | 24 | |||
95.47 | odd | 36 | 475.2.l.f.176.5 | 48 | |||
95.74 | even | 18 | 95.2.p.a.4.4 | ✓ | 48 | ||
95.93 | odd | 36 | 475.2.l.f.251.4 | 48 | |||
95.94 | odd | 2 | 1805.2.b.l.1084.14 | 24 | |||
285.74 | odd | 18 | 855.2.da.b.289.5 | 48 | |||
285.104 | odd | 18 | 855.2.da.b.784.4 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.4.4 | ✓ | 48 | 95.74 | even | 18 | ||
95.2.p.a.4.5 | yes | 48 | 19.17 | even | 9 | ||
95.2.p.a.24.4 | yes | 48 | 19.9 | even | 9 | ||
95.2.p.a.24.5 | yes | 48 | 95.9 | even | 18 | ||
475.2.l.f.176.4 | 48 | 95.28 | odd | 36 | |||
475.2.l.f.176.5 | 48 | 95.47 | odd | 36 | |||
475.2.l.f.251.4 | 48 | 95.93 | odd | 36 | |||
475.2.l.f.251.5 | 48 | 95.17 | odd | 36 | |||
855.2.da.b.289.4 | 48 | 57.17 | odd | 18 | |||
855.2.da.b.289.5 | 48 | 285.74 | odd | 18 | |||
855.2.da.b.784.4 | 48 | 285.104 | odd | 18 | |||
855.2.da.b.784.5 | 48 | 57.47 | odd | 18 | |||
1805.2.b.k.1084.11 | 24 | 5.4 | even | 2 | inner | ||
1805.2.b.k.1084.14 | 24 | 1.1 | even | 1 | trivial | ||
1805.2.b.l.1084.11 | 24 | 19.18 | odd | 2 | |||
1805.2.b.l.1084.14 | 24 | 95.94 | odd | 2 | |||
9025.2.a.ct.1.11 | 24 | 95.18 | even | 4 | |||
9025.2.a.ct.1.14 | 24 | 95.37 | even | 4 | |||
9025.2.a.cu.1.11 | 24 | 5.2 | odd | 4 | |||
9025.2.a.cu.1.14 | 24 | 5.3 | odd | 4 |