Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(364,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, 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("605.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + x^{10} + 34 x^{9} - 123 x^{8} - 20 x^{7} + 516 x^{6} - 668 x^{5} - 67 x^{4} + \cdots + 1089 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 364.9 | ||
Root | \(1.38187 - 2.46878i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.364 |
Dual form | 605.2.b.h.364.4 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.02281i | 1.43034i | 0.698951 | + | 0.715170i | \(0.253651\pi\) | ||||
−0.698951 | + | 0.715170i | \(0.746349\pi\) | |||||||
\(3\) | − | 2.91475i | − | 1.68283i | −0.540386 | − | 0.841417i | \(-0.681722\pi\) | ||
0.540386 | − | 0.841417i | \(-0.318278\pi\) | |||||||
\(4\) | −2.09174 | −1.04587 | ||||||||
\(5\) | 1.20202 | + | 1.88551i | 0.537561 | + | 0.843225i | ||||
\(6\) | 5.89598 | 2.40702 | ||||||||
\(7\) | 3.21128i | 1.21375i | 0.794798 | + | 0.606874i | \(0.207577\pi\) | ||||
−0.794798 | + | 0.606874i | \(0.792423\pi\) | |||||||
\(8\) | − | 0.185581i | − | 0.0656129i | ||||||
\(9\) | −5.49579 | −1.83193 | ||||||||
\(10\) | −3.81402 | + | 2.43146i | −1.20610 | + | 0.768895i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 6.09692i | 1.76003i | ||||||||
\(13\) | 0.648753i | 0.179932i | 0.995945 | + | 0.0899659i | \(0.0286758\pi\) | ||||
−0.995945 | + | 0.0899659i | \(0.971324\pi\) | |||||||
\(14\) | −6.49579 | −1.73607 | ||||||||
\(15\) | 5.49579 | − | 3.50360i | 1.41901 | − | 0.904626i | ||||
\(16\) | −3.80809 | −0.952023 | ||||||||
\(17\) | 1.18847i | 0.288247i | 0.989560 | + | 0.144123i | \(0.0460362\pi\) | ||||
−0.989560 | + | 0.144123i | \(0.953964\pi\) | |||||||
\(18\) | − | 11.1169i | − | 2.62028i | ||||||
\(19\) | −1.89096 | −0.433815 | −0.216908 | − | 0.976192i | \(-0.569597\pi\) | ||||
−0.216908 | + | 0.976192i | \(0.569597\pi\) | |||||||
\(20\) | −2.51433 | − | 3.94400i | −0.562220 | − | 0.881905i | ||||
\(21\) | 9.36008 | 2.04254 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.35986i | 0.909095i | 0.890723 | + | 0.454547i | \(0.150199\pi\) | ||||
−0.890723 | + | 0.454547i | \(0.849801\pi\) | |||||||
\(24\) | −0.540924 | −0.110416 | ||||||||
\(25\) | −2.11028 | + | 4.53285i | −0.422056 | + | 0.906570i | ||||
\(26\) | −1.31230 | −0.257364 | ||||||||
\(27\) | 7.27462i | 1.40000i | ||||||||
\(28\) | − | 6.71717i | − | 1.26943i | ||||||
\(29\) | 4.16393 | 0.773223 | 0.386611 | − | 0.922243i | \(-0.373645\pi\) | ||||
0.386611 | + | 0.922243i | \(0.373645\pi\) | |||||||
\(30\) | 7.08711 | + | 11.1169i | 1.29392 | + | 2.02966i | ||||
\(31\) | 7.89984 | 1.41885 | 0.709426 | − | 0.704779i | \(-0.248954\pi\) | ||||
0.709426 | + | 0.704779i | \(0.248954\pi\) | |||||||
\(32\) | − | 8.07420i | − | 1.42733i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.40405 | −0.412291 | ||||||||
\(35\) | −6.05489 | + | 3.86003i | −1.02346 | + | 0.652464i | ||||
\(36\) | 11.4958 | 1.91597 | ||||||||
\(37\) | 2.05849i | 0.338414i | 0.985581 | + | 0.169207i | \(0.0541207\pi\) | ||||
−0.985581 | + | 0.169207i | \(0.945879\pi\) | |||||||
\(38\) | − | 3.82504i | − | 0.620503i | ||||||
\(39\) | 1.89096 | 0.302795 | ||||||||
\(40\) | 0.349915 | − | 0.223073i | 0.0553264 | − | 0.0352709i | ||||
\(41\) | −3.30520 | −0.516185 | −0.258092 | − | 0.966120i | \(-0.583094\pi\) | ||||
−0.258092 | + | 0.966120i | \(0.583094\pi\) | |||||||
\(42\) | 18.9336i | 2.92152i | ||||||||
\(43\) | 10.9313i | 1.66701i | 0.552509 | + | 0.833507i | \(0.313670\pi\) | ||||
−0.552509 | + | 0.833507i | \(0.686330\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.60607 | − | 10.3624i | −0.984775 | − | 1.54473i | ||||
\(46\) | −8.81916 | −1.30031 | ||||||||
\(47\) | − | 2.91475i | − | 0.425161i | −0.977144 | − | 0.212580i | \(-0.931813\pi\) | ||
0.977144 | − | 0.212580i | \(-0.0681867\pi\) | |||||||
\(48\) | 11.0997i | 1.60210i | ||||||||
\(49\) | −3.31230 | −0.473186 | ||||||||
\(50\) | −9.16908 | − | 4.26869i | −1.29670 | − | 0.603683i | ||||
\(51\) | 3.46410 | 0.485071 | ||||||||
\(52\) | − | 1.35703i | − | 0.188186i | ||||||
\(53\) | − | 6.41836i | − | 0.881629i | −0.897598 | − | 0.440815i | \(-0.854690\pi\) | ||
0.897598 | − | 0.440815i | \(-0.145310\pi\) | |||||||
\(54\) | −14.7151 | −2.00248 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.595953 | 0.0796376 | ||||||||
\(57\) | 5.51167i | 0.730039i | ||||||||
\(58\) | 8.42283i | 1.10597i | ||||||||
\(59\) | 3.71635 | 0.483827 | 0.241914 | − | 0.970298i | \(-0.422225\pi\) | ||||
0.241914 | + | 0.970298i | \(0.422225\pi\) | |||||||
\(60\) | −11.4958 | + | 7.32864i | −1.48410 | + | 0.946124i | ||||
\(61\) | −7.78694 | −0.997015 | −0.498508 | − | 0.866885i | \(-0.666118\pi\) | ||||
−0.498508 | + | 0.866885i | \(0.666118\pi\) | |||||||
\(62\) | 15.9798i | 2.02944i | ||||||||
\(63\) | − | 17.6485i | − | 2.22350i | ||||||
\(64\) | 8.71635 | 1.08954 | ||||||||
\(65\) | −1.22323 | + | 0.779817i | −0.151723 | + | 0.0967244i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.37993i | 0.290755i | 0.989376 | + | 0.145377i | \(0.0464396\pi\) | ||||
−0.989376 | + | 0.145377i | \(0.953560\pi\) | |||||||
\(68\) | − | 2.48598i | − | 0.301469i | ||||||
\(69\) | 12.7079 | 1.52986 | ||||||||
\(70\) | −7.80809 | − | 12.2479i | −0.933246 | − | 1.46390i | ||||
\(71\) | 15.7163 | 1.86519 | 0.932594 | − | 0.360928i | \(-0.117540\pi\) | ||||
0.932594 | + | 0.360928i | \(0.117540\pi\) | |||||||
\(72\) | 1.01992i | 0.120198i | ||||||||
\(73\) | − | 5.71428i | − | 0.668806i | −0.942430 | − | 0.334403i | \(-0.891465\pi\) | ||
0.942430 | − | 0.334403i | \(-0.108535\pi\) | |||||||
\(74\) | −4.16393 | −0.484047 | ||||||||
\(75\) | 13.2121 | + | 6.15094i | 1.52561 | + | 0.710250i | ||||
\(76\) | 3.95540 | 0.453715 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.82504i | 0.433100i | ||||||||
\(79\) | 15.2561 | 1.71644 | 0.858221 | − | 0.513281i | \(-0.171570\pi\) | ||||
0.858221 | + | 0.513281i | \(0.171570\pi\) | |||||||
\(80\) | −4.57742 | − | 7.18019i | −0.511771 | − | 0.802770i | ||||
\(81\) | 4.71635 | 0.524039 | ||||||||
\(82\) | − | 6.68577i | − | 0.738320i | ||||||
\(83\) | − | 10.6367i | − | 1.16753i | −0.811922 | − | 0.583766i | \(-0.801579\pi\) | ||
0.811922 | − | 0.583766i | \(-0.198421\pi\) | |||||||
\(84\) | −19.5789 | −2.13623 | ||||||||
\(85\) | −2.24087 | + | 1.42857i | −0.243057 | + | 0.154950i | ||||
\(86\) | −22.1120 | −2.38440 | ||||||||
\(87\) | − | 12.1368i | − | 1.30121i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 20.9610 | − | 13.3628i | 2.20949 | − | 1.40856i | ||||
\(91\) | −2.08333 | −0.218392 | ||||||||
\(92\) | − | 9.11972i | − | 0.950797i | ||||||
\(93\) | − | 23.0261i | − | 2.38769i | ||||||
\(94\) | 5.89598 | 0.608124 | ||||||||
\(95\) | −2.27297 | − | 3.56541i | −0.233202 | − | 0.365804i | ||||
\(96\) | −23.5343 | −2.40196 | ||||||||
\(97\) | − | 15.1381i | − | 1.53704i | −0.639826 | − | 0.768520i | \(-0.720994\pi\) | ||
0.639826 | − | 0.768520i | \(-0.279006\pi\) | |||||||
\(98\) | − | 6.70015i | − | 0.676817i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.41416 | − | 9.48156i | 0.441416 | − | 0.948156i | ||||
\(101\) | −5.57817 | −0.555049 | −0.277524 | − | 0.960719i | \(-0.589514\pi\) | ||||
−0.277524 | + | 0.960719i | \(0.589514\pi\) | |||||||
\(102\) | 7.00721i | 0.693817i | ||||||||
\(103\) | − | 3.18217i | − | 0.313548i | −0.987634 | − | 0.156774i | \(-0.949891\pi\) | ||
0.987634 | − | 0.156774i | \(-0.0501095\pi\) | |||||||
\(104\) | 0.120397 | 0.0118058 | ||||||||
\(105\) | 11.2510 | + | 17.6485i | 1.09799 | + | 1.72232i | ||||
\(106\) | 12.9831 | 1.26103 | ||||||||
\(107\) | − | 3.96907i | − | 0.383704i | −0.981424 | − | 0.191852i | \(-0.938551\pi\) | ||
0.981424 | − | 0.191852i | \(-0.0614494\pi\) | |||||||
\(108\) | − | 15.2166i | − | 1.46422i | ||||||
\(109\) | 15.4150 | 1.47649 | 0.738243 | − | 0.674535i | \(-0.235656\pi\) | ||||
0.738243 | + | 0.674535i | \(0.235656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | − | 12.2288i | − | 1.15552i | ||||||
\(113\) | − | 10.1353i | − | 0.953453i | −0.879052 | − | 0.476727i | \(-0.841823\pi\) | ||
0.879052 | − | 0.476727i | \(-0.158177\pi\) | |||||||
\(114\) | −11.1490 | −1.04420 | ||||||||
\(115\) | −8.22056 | + | 5.24066i | −0.766571 | + | 0.488694i | ||||
\(116\) | −8.70988 | −0.808692 | ||||||||
\(117\) | − | 3.56541i | − | 0.329623i | ||||||
\(118\) | 7.51745i | 0.692038i | ||||||||
\(119\) | −3.81651 | −0.349859 | ||||||||
\(120\) | −0.650203 | − | 1.01992i | −0.0593552 | − | 0.0931052i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 15.7515i | − | 1.42607i | ||||||
\(123\) | 9.63383i | 0.868653i | ||||||||
\(124\) | −16.5244 | −1.48394 | ||||||||
\(125\) | −11.0833 | + | 1.46964i | −0.991323 | + | 0.131449i | ||||
\(126\) | 35.6995 | 3.18037 | ||||||||
\(127\) | 16.4430i | 1.45908i | 0.683937 | + | 0.729541i | \(0.260266\pi\) | ||||
−0.683937 | + | 0.729541i | \(0.739734\pi\) | |||||||
\(128\) | 1.48309i | 0.131088i | ||||||||
\(129\) | 31.8622 | 2.80531 | ||||||||
\(130\) | −1.57742 | − | 2.47436i | −0.138349 | − | 0.217015i | ||||
\(131\) | −14.0007 | −1.22325 | −0.611625 | − | 0.791148i | \(-0.709484\pi\) | ||||
−0.611625 | + | 0.791148i | \(0.709484\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.07239i | − | 0.526543i | ||||||
\(134\) | −4.81413 | −0.415878 | ||||||||
\(135\) | −13.7163 | + | 8.74426i | −1.18052 | + | 0.752586i | ||||
\(136\) | 0.220558 | 0.0189127 | ||||||||
\(137\) | 13.7715i | 1.17658i | 0.808650 | + | 0.588291i | \(0.200199\pi\) | ||||
−0.808650 | + | 0.588291i | \(0.799801\pi\) | |||||||
\(138\) | 25.7057i | 2.18821i | ||||||||
\(139\) | 6.75472 | 0.572928 | 0.286464 | − | 0.958091i | \(-0.407520\pi\) | ||||
0.286464 | + | 0.958091i | \(0.407520\pi\) | |||||||
\(140\) | 12.6653 | − | 8.07420i | 1.07041 | − | 0.682394i | ||||
\(141\) | −8.49579 | −0.715475 | ||||||||
\(142\) | 31.7911i | 2.66785i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 20.9285 | 1.74404 | ||||||||
\(145\) | 5.00514 | + | 7.85113i | 0.415655 | + | 0.652000i | ||||
\(146\) | 11.5589 | 0.956620 | ||||||||
\(147\) | 9.65455i | 0.796294i | ||||||||
\(148\) | − | 4.30584i | − | 0.353938i | ||||||
\(149\) | −19.1969 | −1.57267 | −0.786335 | − | 0.617800i | \(-0.788024\pi\) | ||||
−0.786335 | + | 0.617800i | \(0.788024\pi\) | |||||||
\(150\) | −12.4422 | + | 26.7256i | −1.01590 | + | 2.18214i | ||||
\(151\) | 3.29062 | 0.267787 | 0.133893 | − | 0.990996i | \(-0.457252\pi\) | ||||
0.133893 | + | 0.990996i | \(0.457252\pi\) | |||||||
\(152\) | 0.350926i | 0.0284639i | ||||||||
\(153\) | − | 6.53159i | − | 0.528048i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.49579 | + | 14.8952i | 0.762720 | + | 1.19641i | ||||
\(156\) | −3.95540 | −0.316685 | ||||||||
\(157\) | − | 14.0144i | − | 1.11847i | −0.829009 | − | 0.559236i | \(-0.811095\pi\) | ||
0.829009 | − | 0.559236i | \(-0.188905\pi\) | |||||||
\(158\) | 30.8601i | 2.45509i | ||||||||
\(159\) | −18.7079 | −1.48364 | ||||||||
\(160\) | 15.2240 | − | 9.70538i | 1.20356 | − | 0.767277i | ||||
\(161\) | −14.0007 | −1.10341 | ||||||||
\(162\) | 9.54026i | 0.749554i | ||||||||
\(163\) | 10.3220i | 0.808478i | 0.914653 | + | 0.404239i | \(0.132464\pi\) | ||||
−0.914653 | + | 0.404239i | \(0.867536\pi\) | |||||||
\(164\) | 6.91362 | 0.539863 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 21.5160 | 1.66997 | ||||||||
\(167\) | − | 14.6058i | − | 1.13023i | −0.825012 | − | 0.565115i | \(-0.808832\pi\) | ||
0.825012 | − | 0.565115i | \(-0.191168\pi\) | |||||||
\(168\) | − | 1.73706i | − | 0.134017i | ||||||
\(169\) | 12.5791 | 0.967625 | ||||||||
\(170\) | −2.88972 | − | 4.53285i | −0.221631 | − | 0.347654i | ||||
\(171\) | 10.3923 | 0.794719 | ||||||||
\(172\) | − | 22.8656i | − | 1.74348i | ||||||
\(173\) | 2.20839i | 0.167901i | 0.996470 | + | 0.0839503i | \(0.0267537\pi\) | ||||
−0.996470 | + | 0.0839503i | \(0.973246\pi\) | |||||||
\(174\) | 24.5505 | 1.86117 | ||||||||
\(175\) | −14.5562 | − | 6.77669i | −1.10035 | − | 0.512270i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 10.8322i | − | 0.814201i | ||||||
\(178\) | − | 18.2053i | − | 1.36454i | ||||||
\(179\) | −10.8081 | −0.807835 | −0.403917 | − | 0.914795i | \(-0.632352\pi\) | ||||
−0.403917 | + | 0.914795i | \(0.632352\pi\) | |||||||
\(180\) | 13.8182 | + | 21.6754i | 1.02995 | + | 1.61559i | ||||
\(181\) | −3.36698 | −0.250265 | −0.125133 | − | 0.992140i | \(-0.539936\pi\) | ||||
−0.125133 | + | 0.992140i | \(0.539936\pi\) | |||||||
\(182\) | − | 4.21417i | − | 0.312375i | ||||||
\(183\) | 22.6970i | 1.67781i | ||||||||
\(184\) | 0.809109 | 0.0596483 | ||||||||
\(185\) | −3.88130 | + | 2.47436i | −0.285359 | + | 0.181918i | ||||
\(186\) | 46.5773 | 3.41521 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.09692i | 0.444664i | ||||||||
\(189\) | −23.3608 | −1.69925 | ||||||||
\(190\) | 7.21214 | − | 4.59779i | 0.523224 | − | 0.333559i | ||||
\(191\) | 9.27523 | 0.671132 | 0.335566 | − | 0.942017i | \(-0.391072\pi\) | ||||
0.335566 | + | 0.942017i | \(0.391072\pi\) | |||||||
\(192\) | − | 25.4060i | − | 1.83352i | ||||||
\(193\) | − | 4.86292i | − | 0.350041i | −0.984565 | − | 0.175020i | \(-0.944001\pi\) | ||
0.984565 | − | 0.175020i | \(-0.0559991\pi\) | |||||||
\(194\) | 30.6214 | 2.19849 | ||||||||
\(195\) | 2.27297 | + | 3.56541i | 0.162771 | + | 0.255325i | ||||
\(196\) | 6.92849 | 0.494892 | ||||||||
\(197\) | − | 11.8747i | − | 0.846038i | −0.906121 | − | 0.423019i | \(-0.860970\pi\) | ||
0.906121 | − | 0.423019i | \(-0.139030\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.99158 | 0.353844 | 0.176922 | − | 0.984225i | \(-0.443386\pi\) | ||||
0.176922 | + | 0.984225i | \(0.443386\pi\) | |||||||
\(200\) | 0.841212 | + | 0.391628i | 0.0594827 | + | 0.0276923i | ||||
\(201\) | 6.93691 | 0.489292 | ||||||||
\(202\) | − | 11.2836i | − | 0.793908i | ||||||
\(203\) | 13.3715i | 0.938498i | ||||||||
\(204\) | −7.24602 | −0.507323 | ||||||||
\(205\) | −3.97292 | − | 6.23197i | −0.277481 | − | 0.435260i | ||||
\(206\) | 6.43691 | 0.448481 | ||||||||
\(207\) | − | 23.9609i | − | 1.66540i | ||||||
\(208\) | − | 2.47051i | − | 0.171299i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −35.6995 | + | 22.7587i | −2.46350 | + | 1.57050i | ||||
\(211\) | −1.57314 | −0.108300 | −0.0541499 | − | 0.998533i | \(-0.517245\pi\) | ||||
−0.0541499 | + | 0.998533i | \(0.517245\pi\) | |||||||
\(212\) | 13.4256i | 0.922071i | ||||||||
\(213\) | − | 45.8093i | − | 3.13880i | ||||||
\(214\) | 8.02865 | 0.548827 | ||||||||
\(215\) | −20.6111 | + | 13.1397i | −1.40567 | + | 0.896122i | ||||
\(216\) | 1.35003 | 0.0918581 | ||||||||
\(217\) | 25.3686i | 1.72213i | ||||||||
\(218\) | 31.1815i | 2.11188i | ||||||||
\(219\) | −16.6557 | −1.12549 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.771025 | −0.0518647 | ||||||||
\(222\) | 12.1368i | 0.814571i | ||||||||
\(223\) | − | 3.31475i | − | 0.221972i | −0.993822 | − | 0.110986i | \(-0.964599\pi\) | ||
0.993822 | − | 0.110986i | \(-0.0354009\pi\) | |||||||
\(224\) | 25.9285 | 1.73242 | ||||||||
\(225\) | 11.5977 | − | 24.9116i | 0.773177 | − | 1.66077i | ||||
\(226\) | 20.5018 | 1.36376 | ||||||||
\(227\) | − | 2.84011i | − | 0.188505i | −0.995548 | − | 0.0942525i | \(-0.969954\pi\) | ||
0.995548 | − | 0.0942525i | \(-0.0300461\pi\) | |||||||
\(228\) | − | 11.5290i | − | 0.763528i | ||||||
\(229\) | 1.99158 | 0.131608 | 0.0658038 | − | 0.997833i | \(-0.479039\pi\) | ||||
0.0658038 | + | 0.997833i | \(0.479039\pi\) | |||||||
\(230\) | −10.6008 | − | 16.6286i | −0.698999 | − | 1.09646i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 0.772748i | − | 0.0507334i | ||||||
\(233\) | − | 20.2535i | − | 1.32685i | −0.748242 | − | 0.663426i | \(-0.769102\pi\) | ||
0.748242 | − | 0.663426i | \(-0.230898\pi\) | |||||||
\(234\) | 7.21214 | 0.471472 | ||||||||
\(235\) | 5.49579 | − | 3.50360i | 0.358506 | − | 0.228550i | ||||
\(236\) | −7.77365 | −0.506022 | ||||||||
\(237\) | − | 44.4677i | − | 2.88849i | ||||||
\(238\) | − | 7.72006i | − | 0.500417i | ||||||
\(239\) | −1.89096 | −0.122316 | −0.0611579 | − | 0.998128i | \(-0.519479\pi\) | ||||
−0.0611579 | + | 0.998128i | \(0.519479\pi\) | |||||||
\(240\) | −20.9285 | + | 13.3420i | −1.35093 | + | 0.861226i | ||||
\(241\) | 4.00503 | 0.257986 | 0.128993 | − | 0.991645i | \(-0.458825\pi\) | ||||
0.128993 | + | 0.991645i | \(0.458825\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.07686i | 0.518131i | ||||||||
\(244\) | 16.2883 | 1.04275 | ||||||||
\(245\) | −3.98147 | − | 6.24537i | −0.254366 | − | 0.399002i | ||||
\(246\) | −19.4874 | −1.24247 | ||||||||
\(247\) | − | 1.22676i | − | 0.0780572i | ||||||
\(248\) | − | 1.46606i | − | 0.0930950i | ||||||
\(249\) | −31.0034 | −1.96476 | ||||||||
\(250\) | −2.97280 | − | 22.4194i | −0.188017 | − | 1.41793i | ||||
\(251\) | 22.7079 | 1.43331 | 0.716656 | − | 0.697427i | \(-0.245672\pi\) | ||||
0.716656 | + | 0.697427i | \(0.245672\pi\) | |||||||
\(252\) | 36.9162i | 2.32550i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −33.2610 | −2.08698 | ||||||||
\(255\) | 4.16393 | + | 6.53159i | 0.260756 | + | 0.409024i | ||||
\(256\) | 14.4327 | 0.902044 | ||||||||
\(257\) | − | 4.06296i | − | 0.253441i | −0.991938 | − | 0.126720i | \(-0.959555\pi\) | ||
0.991938 | − | 0.126720i | \(-0.0404451\pi\) | |||||||
\(258\) | 64.4510i | 4.01254i | ||||||||
\(259\) | −6.61039 | −0.410750 | ||||||||
\(260\) | 2.55868 | − | 1.63118i | 0.158683 | − | 0.101161i | ||||
\(261\) | −22.8841 | −1.41649 | ||||||||
\(262\) | − | 28.3208i | − | 1.74966i | ||||||
\(263\) | 12.3054i | 0.758783i | 0.925236 | + | 0.379391i | \(0.123867\pi\) | ||||
−0.925236 | + | 0.379391i | \(0.876133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1019 | − | 7.71502i | 0.743411 | − | 0.473930i | ||||
\(266\) | 12.2833 | 0.753135 | ||||||||
\(267\) | 26.2328i | 1.60542i | ||||||||
\(268\) | − | 4.97820i | − | 0.304092i | ||||||
\(269\) | 7.70793 | 0.469961 | 0.234980 | − | 0.972000i | \(-0.424497\pi\) | ||||
0.234980 | + | 0.972000i | \(0.424497\pi\) | |||||||
\(270\) | −17.6879 | − | 27.7455i | −1.07645 | − | 1.68854i | ||||
\(271\) | 15.5739 | 0.946046 | 0.473023 | − | 0.881050i | \(-0.343163\pi\) | ||||
0.473023 | + | 0.881050i | \(0.343163\pi\) | |||||||
\(272\) | − | 4.52581i | − | 0.274418i | ||||||
\(273\) | 6.07239i | 0.367518i | ||||||||
\(274\) | −27.8571 | −1.68291 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −26.5817 | −1.60003 | ||||||||
\(277\) | 20.3030i | 1.21989i | 0.792443 | + | 0.609946i | \(0.208809\pi\) | ||||
−0.792443 | + | 0.609946i | \(0.791191\pi\) | |||||||
\(278\) | 13.6635i | 0.819481i | ||||||||
\(279\) | −43.4159 | −2.59924 | ||||||||
\(280\) | 0.716350 | + | 1.12367i | 0.0428101 | + | 0.0671524i | ||||
\(281\) | 24.2196 | 1.44482 | 0.722409 | − | 0.691466i | \(-0.243035\pi\) | ||||
0.722409 | + | 0.691466i | \(0.243035\pi\) | |||||||
\(282\) | − | 17.1853i | − | 1.02337i | ||||||
\(283\) | 14.4372i | 0.858204i | 0.903256 | + | 0.429102i | \(0.141170\pi\) | ||||
−0.903256 | + | 0.429102i | \(0.858830\pi\) | |||||||
\(284\) | −32.8746 | −1.95075 | ||||||||
\(285\) | −10.3923 | + | 6.62516i | −0.615587 | + | 0.392441i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 10.6139i | − | 0.626519i | ||||||
\(288\) | 44.3741i | 2.61477i | ||||||||
\(289\) | 15.5875 | 0.916914 | ||||||||
\(290\) | −15.8813 | + | 10.1244i | −0.932582 | + | 0.594527i | ||||
\(291\) | −44.1238 | −2.58658 | ||||||||
\(292\) | 11.9528i | 0.699486i | ||||||||
\(293\) | 15.1625i | 0.885805i | 0.896570 | + | 0.442902i | \(0.146051\pi\) | ||||
−0.896570 | + | 0.442902i | \(0.853949\pi\) | |||||||
\(294\) | −19.5293 | −1.13897 | ||||||||
\(295\) | 4.46714 | + | 7.00721i | 0.260087 | + | 0.407975i | ||||
\(296\) | 0.382018 | 0.0222043 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 38.8316i | − | 2.24945i | ||||||
\(299\) | −2.82848 | −0.163575 | ||||||||
\(300\) | −27.6364 | − | 12.8662i | −1.59559 | − | 0.742831i | ||||
\(301\) | −35.1036 | −2.02334 | ||||||||
\(302\) | 6.65628i | 0.383026i | ||||||||
\(303\) | 16.2590i | 0.934055i | ||||||||
\(304\) | 7.20094 | 0.413002 | ||||||||
\(305\) | −9.36008 | − | 14.6823i | −0.535957 | − | 0.840708i | ||||
\(306\) | 13.2121 | 0.755288 | ||||||||
\(307\) | − | 8.04171i | − | 0.458965i | −0.973313 | − | 0.229482i | \(-0.926297\pi\) | ||
0.973313 | − | 0.229482i | \(-0.0737033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.27523 | −0.527650 | ||||||||
\(310\) | −30.1301 | + | 19.2081i | −1.71128 | + | 1.09095i | ||||
\(311\) | 22.2668 | 1.26264 | 0.631318 | − | 0.775524i | \(-0.282514\pi\) | ||||
0.631318 | + | 0.775524i | \(0.282514\pi\) | |||||||
\(312\) | − | 0.350926i | − | 0.0198673i | ||||||
\(313\) | − | 2.35044i | − | 0.132855i | −0.997791 | − | 0.0664273i | \(-0.978840\pi\) | ||
0.997791 | − | 0.0664273i | \(-0.0211601\pi\) | |||||||
\(314\) | 28.3484 | 1.59979 | ||||||||
\(315\) | 33.2764 | − | 21.2139i | 1.87491 | − | 1.19527i | ||||
\(316\) | −31.9118 | −1.79518 | ||||||||
\(317\) | 18.0233i | 1.01229i | 0.862448 | + | 0.506146i | \(0.168930\pi\) | ||||
−0.862448 | + | 0.506146i | \(0.831070\pi\) | |||||||
\(318\) | − | 37.8425i | − | 2.12210i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 10.4773 | + | 16.4347i | 0.585696 | + | 0.918730i | ||||
\(321\) | −11.5689 | −0.645710 | ||||||||
\(322\) | − | 28.3208i | − | 1.57825i | ||||||
\(323\) | − | 2.24735i | − | 0.125046i | ||||||
\(324\) | −9.86540 | −0.548078 | ||||||||
\(325\) | −2.94070 | − | 1.36905i | −0.163121 | − | 0.0759413i | ||||
\(326\) | −20.8793 | −1.15640 | ||||||||
\(327\) | − | 44.9309i | − | 2.48468i | ||||||
\(328\) | 0.613382i | 0.0338684i | ||||||||
\(329\) | 9.36008 | 0.516038 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.09174 | −0.169938 | −0.0849688 | − | 0.996384i | \(-0.527079\pi\) | ||||
−0.0849688 | + | 0.996384i | \(0.527079\pi\) | |||||||
\(332\) | 22.2493i | 1.22109i | ||||||||
\(333\) | − | 11.3130i | − | 0.619951i | ||||||
\(334\) | 29.5447 | 1.61661 | ||||||||
\(335\) | −4.48737 | + | 2.86073i | −0.245171 | + | 0.156298i | ||||
\(336\) | −35.6441 | −1.94454 | ||||||||
\(337\) | − | 35.9458i | − | 1.95809i | −0.203641 | − | 0.979046i | \(-0.565278\pi\) | ||
0.203641 | − | 0.979046i | \(-0.434722\pi\) | |||||||
\(338\) | 25.4451i | 1.38403i | ||||||||
\(339\) | −29.5420 | −1.60450 | ||||||||
\(340\) | 4.68733 | − | 2.98820i | 0.254206 | − | 0.162058i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 21.0216i | 1.13672i | ||||||||
\(343\) | 11.8422i | 0.639420i | ||||||||
\(344\) | 2.02865 | 0.109378 | ||||||||
\(345\) | 15.2752 | + | 23.9609i | 0.822391 | + | 1.29001i | ||||
\(346\) | −4.46714 | −0.240155 | ||||||||
\(347\) | − | 12.2629i | − | 0.658307i | −0.944276 | − | 0.329153i | \(-0.893237\pi\) | ||
0.944276 | − | 0.329153i | \(-0.106763\pi\) | |||||||
\(348\) | 25.3872i | 1.36089i | ||||||||
\(349\) | −17.6734 | −0.946034 | −0.473017 | − | 0.881053i | \(-0.656835\pi\) | ||||
−0.473017 | + | 0.881053i | \(0.656835\pi\) | |||||||
\(350\) | 13.7079 | − | 29.4444i | 0.732720 | − | 1.57387i | ||||
\(351\) | −4.71943 | −0.251905 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.7202i | 0.996378i | 0.867068 | + | 0.498189i | \(0.166001\pi\) | ||||
−0.867068 | + | 0.498189i | \(0.833999\pi\) | |||||||
\(354\) | 21.9115 | 1.16458 | ||||||||
\(355\) | 18.8914 | + | 29.6333i | 1.00265 | + | 1.57277i | ||||
\(356\) | 18.8257 | 0.997760 | ||||||||
\(357\) | 11.1242i | 0.588755i | ||||||||
\(358\) | − | 21.8627i | − | 1.15548i | ||||||
\(359\) | −37.2669 | −1.96687 | −0.983435 | − | 0.181263i | \(-0.941981\pi\) | ||||
−0.983435 | + | 0.181263i | \(0.941981\pi\) | |||||||
\(360\) | −1.92306 | + | 1.22596i | −0.101354 | + | 0.0646139i | ||||
\(361\) | −15.4243 | −0.811804 | ||||||||
\(362\) | − | 6.81074i | − | 0.357965i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.35779 | 0.228410 | ||||||||
\(365\) | 10.7743 | − | 6.86870i | 0.563954 | − | 0.359524i | ||||
\(366\) | −45.9117 | −2.39984 | ||||||||
\(367\) | 17.9988i | 0.939531i | 0.882791 | + | 0.469765i | \(0.155661\pi\) | ||||
−0.882791 | + | 0.469765i | \(0.844339\pi\) | |||||||
\(368\) | − | 16.6028i | − | 0.865479i | ||||||
\(369\) | 18.1647 | 0.945615 | ||||||||
\(370\) | −5.00514 | − | 7.85113i | −0.260205 | − | 0.408161i | ||||
\(371\) | 20.6111 | 1.07008 | ||||||||
\(372\) | 48.1647i | 2.49722i | ||||||||
\(373\) | 0.202607i | 0.0104906i | 0.999986 | + | 0.00524531i | \(0.00166964\pi\) | ||||
−0.999986 | + | 0.00524531i | \(0.998330\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.28365 | + | 32.3052i | 0.221207 | + | 1.66823i | ||||
\(376\) | −0.540924 | −0.0278960 | ||||||||
\(377\) | 2.70137i | 0.139127i | ||||||||
\(378\) | − | 47.2544i | − | 2.43050i | ||||||
\(379\) | 33.9832 | 1.74560 | 0.872799 | − | 0.488080i | \(-0.162303\pi\) | ||||
0.872799 | + | 0.488080i | \(0.162303\pi\) | |||||||
\(380\) | 4.75448 | + | 7.45793i | 0.243900 | + | 0.382584i | ||||
\(381\) | 47.9273 | 2.45539 | ||||||||
\(382\) | 18.7620i | 0.959947i | ||||||||
\(383\) | 7.14204i | 0.364941i | 0.983211 | + | 0.182471i | \(0.0584094\pi\) | ||||
−0.983211 | + | 0.182471i | \(0.941591\pi\) | |||||||
\(384\) | 4.32284 | 0.220599 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.83675 | 0.500677 | ||||||||
\(387\) | − | 60.0764i | − | 3.05385i | ||||||
\(388\) | 31.6650i | 1.60755i | ||||||||
\(389\) | −13.2668 | −0.672654 | −0.336327 | − | 0.941745i | \(-0.609185\pi\) | ||||
−0.336327 | + | 0.941745i | \(0.609185\pi\) | |||||||
\(390\) | −7.21214 | + | 4.59779i | −0.365201 | + | 0.232818i | ||||
\(391\) | −5.18157 | −0.262043 | ||||||||
\(392\) | 0.614701i | 0.0310471i | ||||||||
\(393\) | 40.8087i | 2.05853i | ||||||||
\(394\) | 24.0202 | 1.21012 | ||||||||
\(395\) | 18.3382 | + | 28.7654i | 0.922692 | + | 1.44735i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.5614i | 1.68440i | 0.539165 | + | 0.842200i | \(0.318740\pi\) | ||||
−0.539165 | + | 0.842200i | \(0.681260\pi\) | |||||||
\(398\) | 10.0970i | 0.506117i | ||||||||
\(399\) | −17.6995 | −0.886084 | ||||||||
\(400\) | 8.03614 | − | 17.2615i | 0.401807 | − | 0.863076i | ||||
\(401\) | 33.5909 | 1.67745 | 0.838726 | − | 0.544554i | \(-0.183301\pi\) | ||||
0.838726 | + | 0.544554i | \(0.183301\pi\) | |||||||
\(402\) | 14.0320i | 0.699853i | ||||||||
\(403\) | 5.12505i | 0.255297i | ||||||||
\(404\) | 11.6681 | 0.580510 | ||||||||
\(405\) | 5.66916 | + | 8.89271i | 0.281703 | + | 0.441882i | ||||
\(406\) | −27.0480 | −1.34237 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − | 0.642872i | − | 0.0318269i | ||||||
\(409\) | −8.16896 | −0.403929 | −0.201964 | − | 0.979393i | \(-0.564733\pi\) | ||||
−0.201964 | + | 0.979393i | \(0.564733\pi\) | |||||||
\(410\) | 12.6061 | − | 8.03645i | 0.622569 | − | 0.396892i | ||||
\(411\) | 40.1406 | 1.97999 | ||||||||
\(412\) | 6.65628i | 0.327931i | ||||||||
\(413\) | 11.9342i | 0.587245i | ||||||||
\(414\) | 48.4683 | 2.38209 | ||||||||
\(415\) | 20.0556 | − | 12.7856i | 0.984492 | − | 0.627620i | ||||
\(416\) | 5.23816 | 0.256822 | ||||||||
\(417\) | − | 19.6883i | − | 0.964142i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.5329 | −0.954243 | −0.477121 | − | 0.878837i | \(-0.658320\pi\) | ||||
−0.477121 | + | 0.878837i | \(0.658320\pi\) | |||||||
\(420\) | −23.5343 | − | 36.9162i | −1.14836 | − | 1.80132i | ||||
\(421\) | −23.9083 | −1.16522 | −0.582609 | − | 0.812753i | \(-0.697968\pi\) | ||||
−0.582609 | + | 0.812753i | \(0.697968\pi\) | |||||||
\(422\) | − | 3.18217i | − | 0.154905i | ||||||
\(423\) | 16.0189i | 0.778865i | ||||||||
\(424\) | −1.19113 | −0.0578462 | ||||||||
\(425\) | −5.38716 | − | 2.50801i | −0.261316 | − | 0.121656i | ||||
\(426\) | 92.6633 | 4.48955 | ||||||||
\(427\) | − | 25.0060i | − | 1.21013i | ||||||
\(428\) | 8.30227i | 0.401306i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.5791 | − | 41.6923i | −1.28176 | − | 2.01058i | ||||
\(431\) | −7.56383 | −0.364337 | −0.182168 | − | 0.983267i | \(-0.558312\pi\) | ||||
−0.182168 | + | 0.983267i | \(0.558312\pi\) | |||||||
\(432\) | − | 27.7024i | − | 1.33283i | ||||||
\(433\) | 25.6194i | 1.23119i | 0.788063 | + | 0.615595i | \(0.211084\pi\) | ||||
−0.788063 | + | 0.615595i | \(0.788916\pi\) | |||||||
\(434\) | −51.3157 | −2.46323 | ||||||||
\(435\) | 22.8841 | − | 14.5888i | 1.09721 | − | 0.699478i | ||||
\(436\) | −32.2442 | −1.54422 | ||||||||
\(437\) | − | 8.24432i | − | 0.394379i | ||||||
\(438\) | − | 33.6913i | − | 1.60983i | ||||||
\(439\) | 20.4668 | 0.976827 | 0.488413 | − | 0.872612i | \(-0.337576\pi\) | ||||
0.488413 | + | 0.872612i | \(0.337576\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.2037 | 0.866844 | ||||||||
\(442\) | − | 1.55963i | − | 0.0741842i | ||||||
\(443\) | 10.1648i | 0.482946i | 0.970408 | + | 0.241473i | \(0.0776305\pi\) | ||||
−0.970408 | + | 0.241473i | \(0.922369\pi\) | |||||||
\(444\) | −12.5505 | −0.595619 | ||||||||
\(445\) | −10.8182 | − | 16.9696i | −0.512832 | − | 0.804435i | ||||
\(446\) | 6.70509 | 0.317495 | ||||||||
\(447\) | 55.9542i | 2.64654i | ||||||||
\(448\) | 27.9906i | 1.32243i | ||||||||
\(449\) | 14.6995 | 0.693713 | 0.346857 | − | 0.937918i | \(-0.387249\pi\) | ||||
0.346857 | + | 0.937918i | \(0.387249\pi\) | |||||||
\(450\) | 50.3913 | + | 23.4598i | 2.37547 | + | 1.10591i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 21.2006i | 0.997190i | ||||||||
\(453\) | − | 9.59134i | − | 0.450640i | ||||||
\(454\) | 5.74500 | 0.269626 | ||||||||
\(455\) | −2.50421 | − | 3.92813i | −0.117399 | − | 0.184154i | ||||
\(456\) | 1.02286 | 0.0479000 | ||||||||
\(457\) | − | 3.36281i | − | 0.157305i | −0.996902 | − | 0.0786527i | \(-0.974938\pi\) | ||
0.996902 | − | 0.0786527i | \(-0.0250618\pi\) | |||||||
\(458\) | 4.02859i | 0.188243i | ||||||||
\(459\) | −8.64568 | −0.403546 | ||||||||
\(460\) | 17.1953 | − | 10.9621i | 0.801735 | − | 0.511111i | ||||
\(461\) | −1.41424 | −0.0658677 | −0.0329338 | − | 0.999458i | \(-0.510485\pi\) | ||||
−0.0329338 | + | 0.999458i | \(0.510485\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.4595i | − | 0.718465i | −0.933248 | − | 0.359232i | \(-0.883039\pi\) | ||
0.933248 | − | 0.359232i | \(-0.116961\pi\) | |||||||
\(464\) | −15.8566 | −0.736126 | ||||||||
\(465\) | 43.4159 | − | 27.6779i | 2.01336 | − | 1.28353i | ||||
\(466\) | 40.9690 | 1.89785 | ||||||||
\(467\) | − | 18.6908i | − | 0.864905i | −0.901657 | − | 0.432453i | \(-0.857648\pi\) | ||
0.901657 | − | 0.432453i | \(-0.142352\pi\) | |||||||
\(468\) | 7.45793i | 0.344743i | ||||||||
\(469\) | −7.64261 | −0.352903 | ||||||||
\(470\) | 7.08711 | + | 11.1169i | 0.326904 | + | 0.512785i | ||||
\(471\) | −40.8486 | −1.88220 | ||||||||
\(472\) | − | 0.689685i | − | 0.0317453i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 89.9495 | 4.13152 | ||||||||
\(475\) | 3.99045 | − | 8.57142i | 0.183094 | − | 0.393284i | ||||
\(476\) | 7.98317 | 0.365908 | ||||||||
\(477\) | 35.2740i | 1.61508i | ||||||||
\(478\) | − | 3.82504i | − | 0.174953i | ||||||
\(479\) | 29.8765 | 1.36509 | 0.682546 | − | 0.730842i | \(-0.260873\pi\) | ||||
0.682546 | + | 0.730842i | \(0.260873\pi\) | |||||||
\(480\) | −28.2888 | − | 44.3741i | −1.29120 | − | 2.02539i | ||||
\(481\) | −1.33545 | −0.0608915 | ||||||||
\(482\) | 8.10139i | 0.369008i | ||||||||
\(483\) | 40.8087i | 1.85686i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.5430 | − | 18.1963i | 1.29607 | − | 0.826253i | ||||
\(486\) | −16.3379 | −0.741103 | ||||||||
\(487\) | − | 0.934819i | − | 0.0423607i | −0.999776 | − | 0.0211803i | \(-0.993258\pi\) | ||
0.999776 | − | 0.0211803i | \(-0.00674242\pi\) | |||||||
\(488\) | 1.44511i | 0.0654171i | ||||||||
\(489\) | 30.0860 | 1.36053 | ||||||||
\(490\) | 12.6332 | − | 8.05373i | 0.570709 | − | 0.363831i | ||||
\(491\) | −32.8944 | −1.48450 | −0.742251 | − | 0.670121i | \(-0.766242\pi\) | ||||
−0.742251 | + | 0.670121i | \(0.766242\pi\) | |||||||
\(492\) | − | 20.1515i | − | 0.908500i | ||||||
\(493\) | 4.94871i | 0.222879i | ||||||||
\(494\) | 2.48151 | 0.111648 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −30.0833 | −1.35078 | ||||||||
\(497\) | 50.4696i | 2.26387i | ||||||||
\(498\) | − | 62.7139i | − | 2.81028i | ||||||
\(499\) | −8.99158 | −0.402519 | −0.201259 | − | 0.979538i | \(-0.564503\pi\) | ||||
−0.201259 | + | 0.979538i | \(0.564503\pi\) | |||||||
\(500\) | 23.1835 | − | 3.07412i | 1.03680 | − | 0.137479i | ||||
\(501\) | −42.5723 | −1.90199 | ||||||||
\(502\) | 45.9337i | 2.05012i | ||||||||
\(503\) | − | 1.22096i | − | 0.0544400i | −0.999629 | − | 0.0272200i | \(-0.991335\pi\) | ||
0.999629 | − | 0.0272200i | \(-0.00866546\pi\) | |||||||
\(504\) | −3.27523 | −0.145890 | ||||||||
\(505\) | −6.70509 | − | 10.5177i | −0.298373 | − | 0.468031i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 36.6650i | − | 1.62835i | ||||||
\(508\) | − | 34.3946i | − | 1.52601i | ||||||
\(509\) | −24.1953 | −1.07244 | −0.536219 | − | 0.844079i | \(-0.680148\pi\) | ||||
−0.536219 | + | 0.844079i | \(0.680148\pi\) | |||||||
\(510\) | −13.2121 | + | 8.42283i | −0.585043 | + | 0.372969i | ||||
\(511\) | 18.3501 | 0.811763 | ||||||||
\(512\) | 32.1607i | 1.42132i | ||||||||
\(513\) | − | 13.7560i | − | 0.607342i | ||||||
\(514\) | 8.21858 | 0.362506 | ||||||||
\(515\) | 6.00000 | − | 3.82504i | 0.264392 | − | 0.168551i | ||||
\(516\) | −66.6475 | −2.93399 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 13.3715i | − | 0.587512i | ||||||
\(519\) | 6.43691 | 0.282549 | ||||||||
\(520\) | 0.144719 | + | 0.227009i | 0.00634637 | + | 0.00995498i | ||||
\(521\) | −4.85358 | −0.212639 | −0.106320 | − | 0.994332i | \(-0.533907\pi\) | ||||
−0.106320 | + | 0.994332i | \(0.533907\pi\) | |||||||
\(522\) | − | 46.2901i | − | 2.02606i | ||||||
\(523\) | − | 7.33344i | − | 0.320669i | −0.987063 | − | 0.160334i | \(-0.948743\pi\) | ||
0.987063 | − | 0.160334i | \(-0.0512572\pi\) | |||||||
\(524\) | 29.2860 | 1.27936 | ||||||||
\(525\) | −19.7524 | + | 42.4278i | −0.862065 | + | 1.85170i | ||||
\(526\) | −24.8914 | −1.08532 | ||||||||
\(527\) | 9.38873i | 0.408980i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.99158 | 0.173547 | ||||||||
\(530\) | 15.6060 | + | 24.4797i | 0.677881 | + | 1.06333i | ||||
\(531\) | −20.4243 | −0.886338 | ||||||||
\(532\) | 12.7019i | 0.550696i | ||||||||
\(533\) | − | 2.14426i | − | 0.0928781i | ||||||
\(534\) | −53.0638 | −2.29630 | ||||||||
\(535\) | 7.48371 | − | 4.77091i | 0.323549 | − | 0.206264i | ||||
\(536\) | 0.441670 | 0.0190773 | ||||||||
\(537\) | 31.5029i | 1.35945i | ||||||||
\(538\) | 15.5917i | 0.672204i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 28.6911 | − | 18.2908i | 1.23467 | − | 0.787109i | ||||
\(541\) | 28.0803 | 1.20726 | 0.603632 | − | 0.797263i | \(-0.293720\pi\) | ||||
0.603632 | + | 0.797263i | \(0.293720\pi\) | |||||||
\(542\) | 31.5029i | 1.35317i | ||||||||
\(543\) | 9.81391i | 0.421155i | ||||||||
\(544\) | 9.59595 | 0.411423 | ||||||||
\(545\) | 18.5292 | + | 29.0651i | 0.793702 | + | 1.24501i | ||||
\(546\) | −12.2833 | −0.525675 | ||||||||
\(547\) | 23.3628i | 0.998921i | 0.866337 | + | 0.499460i | \(0.166468\pi\) | ||||
−0.866337 | + | 0.499460i | \(0.833532\pi\) | |||||||
\(548\) | − | 28.8065i | − | 1.23055i | ||||||
\(549\) | 42.7954 | 1.82646 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.87382 | −0.335436 | ||||||||
\(552\) | − | 2.35835i | − | 0.100378i | ||||||
\(553\) | 48.9915i | 2.08333i | ||||||||
\(554\) | −41.0691 | −1.74486 | ||||||||
\(555\) | 7.21214 | + | 11.3130i | 0.306138 | + | 0.480212i | ||||
\(556\) | −14.1291 | −0.599209 | ||||||||
\(557\) | 0.0340521i | 0.00144283i | 1.00000 | 0.000721417i | \(0.000229634\pi\) | |||||
−1.00000 | 0.000721417i | \(0.999770\pi\) | ||||||||
\(558\) | − | 87.8219i | − | 3.71780i | ||||||
\(559\) | −7.09174 | −0.299949 | ||||||||
\(560\) | 23.0576 | − | 14.6994i | 0.974361 | − | 0.621161i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 48.9915i | 2.06658i | ||||||||
\(563\) | − | 23.6574i | − | 0.997041i | −0.866878 | − | 0.498520i | \(-0.833877\pi\) | ||
0.866878 | − | 0.498520i | \(-0.166123\pi\) | |||||||
\(564\) | 17.7710 | 0.748295 | ||||||||
\(565\) | 19.1103 | − | 12.1829i | 0.803975 | − | 0.512540i | ||||
\(566\) | −29.2037 | −1.22752 | ||||||||
\(567\) | 15.1455i | 0.636051i | ||||||||
\(568\) | − | 2.91666i | − | 0.122380i | ||||||
\(569\) | −30.7352 | −1.28849 | −0.644244 | − | 0.764820i | \(-0.722828\pi\) | ||||
−0.644244 | + | 0.764820i | \(0.722828\pi\) | |||||||
\(570\) | −13.4014 | − | 21.0216i | −0.561324 | − | 0.880499i | ||||
\(571\) | −28.4768 | −1.19172 | −0.595860 | − | 0.803089i | \(-0.703188\pi\) | ||||
−0.595860 | + | 0.803089i | \(0.703188\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 27.0350i | − | 1.12940i | ||||||
\(574\) | 21.4699 | 0.896135 | ||||||||
\(575\) | −19.7626 | − | 9.20053i | −0.824158 | − | 0.383689i | ||||
\(576\) | −47.9032 | −1.99597 | ||||||||
\(577\) | 38.6132i | 1.60749i | 0.594974 | + | 0.803745i | \(0.297162\pi\) | ||||
−0.594974 | + | 0.803745i | \(0.702838\pi\) | |||||||
\(578\) | 31.5306i | 1.31150i | ||||||||
\(579\) | −14.1742 | −0.589060 | ||||||||
\(580\) | −10.4695 | − | 16.4225i | −0.434722 | − | 0.681909i | ||||
\(581\) | 34.1575 | 1.41709 | ||||||||
\(582\) | − | 89.2539i | − | 3.69969i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.06046 | −0.0438823 | ||||||||
\(585\) | 6.72262 | − | 4.28571i | 0.277946 | − | 0.177192i | ||||
\(586\) | −30.6709 | −1.26700 | ||||||||
\(587\) | − | 14.2818i | − | 0.589474i | −0.955578 | − | 0.294737i | \(-0.904768\pi\) | ||
0.955578 | − | 0.294737i | \(-0.0952320\pi\) | |||||||
\(588\) | − | 20.1948i | − | 0.832821i | ||||||
\(589\) | −14.9383 | −0.615520 | ||||||||
\(590\) | −14.1742 | + | 9.03616i | −0.583543 | + | 0.372013i | ||||
\(591\) | −34.6119 | −1.42374 | ||||||||
\(592\) | − | 7.83893i | − | 0.322178i | ||||||
\(593\) | − | 36.4700i | − | 1.49764i | −0.662771 | − | 0.748822i | \(-0.730620\pi\) | ||
0.662771 | − | 0.748822i | \(-0.269380\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.58754 | − | 7.19606i | −0.188071 | − | 0.295010i | ||||
\(596\) | 40.1550 | 1.64481 | ||||||||
\(597\) | − | 14.5492i | − | 0.595461i | ||||||
\(598\) | − | 5.72146i | − | 0.233968i | ||||||
\(599\) | −30.3410 | −1.23970 | −0.619849 | − | 0.784721i | \(-0.712806\pi\) | ||||
−0.619849 | + | 0.784721i | \(0.712806\pi\) | |||||||
\(600\) | 1.14150 | − | 2.45193i | 0.0466016 | − | 0.100099i | ||||
\(601\) | 37.8224 | 1.54281 | 0.771403 | − | 0.636347i | \(-0.219555\pi\) | ||||
0.771403 | + | 0.636347i | \(0.219555\pi\) | |||||||
\(602\) | − | 71.0077i | − | 2.89406i | ||||||
\(603\) | − | 13.0796i | − | 0.532642i | ||||||
\(604\) | −6.88313 | −0.280071 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −32.8888 | −1.33602 | ||||||||
\(607\) | − | 31.0829i | − | 1.26161i | −0.775940 | − | 0.630807i | \(-0.782724\pi\) | ||
0.775940 | − | 0.630807i | \(-0.217276\pi\) | |||||||
\(608\) | 15.2680i | 0.619198i | ||||||||
\(609\) | 38.9747 | 1.57934 | ||||||||
\(610\) | 29.6995 | − | 18.9336i | 1.20250 | − | 0.766600i | ||||
\(611\) | 1.89096 | 0.0764999 | ||||||||
\(612\) | 13.6624i | 0.552271i | ||||||||
\(613\) | − | 36.2674i | − | 1.46483i | −0.680860 | − | 0.732414i | \(-0.738394\pi\) | ||
0.680860 | − | 0.732414i | \(-0.261606\pi\) | |||||||
\(614\) | 16.2668 | 0.656475 | ||||||||
\(615\) | −18.1647 | + | 11.5801i | −0.732470 | + | 0.466954i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.28079i | 0.0515626i | 0.999668 | + | 0.0257813i | \(0.00820735\pi\) | ||||
−0.999668 | + | 0.0257813i | \(0.991793\pi\) | |||||||
\(618\) | − | 18.7620i | − | 0.754718i | ||||||
\(619\) | −8.24079 | −0.331225 | −0.165613 | − | 0.986191i | \(-0.552960\pi\) | ||||
−0.165613 | + | 0.986191i | \(0.552960\pi\) | |||||||
\(620\) | −19.8628 | − | 31.1570i | −0.797708 | − | 1.25129i | ||||
\(621\) | −31.7163 | −1.27273 | ||||||||
\(622\) | 45.0415i | 1.80600i | ||||||||
\(623\) | − | 28.9015i | − | 1.15791i | ||||||
\(624\) | −7.20094 | −0.288268 | ||||||||
\(625\) | −16.0934 | − | 19.1312i | −0.643738 | − | 0.765246i | ||||
\(626\) | 4.75448 | 0.190027 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 29.3146i | 1.16978i | ||||||||
\(629\) | −2.44646 | −0.0975467 | ||||||||
\(630\) | 42.9117 | + | 67.3117i | 1.70964 | + | 2.68176i | ||||
\(631\) | −12.4074 | −0.493933 | −0.246966 | − | 0.969024i | \(-0.579434\pi\) | ||||
−0.246966 | + | 0.969024i | \(0.579434\pi\) | |||||||
\(632\) | − | 2.83124i | − | 0.112621i | ||||||
\(633\) | 4.58533i | 0.182251i | ||||||||
\(634\) | −36.4577 | −1.44792 | ||||||||
\(635\) | −31.0034 | + | 19.7649i | −1.23033 | + | 0.784346i | ||||
\(636\) | 39.1322 | 1.55169 | ||||||||
\(637\) | − | 2.14887i | − | 0.0851412i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −86.3738 | −3.41689 | ||||||||
\(640\) | −2.79637 | + | 1.78271i | −0.110536 | + | 0.0704677i | ||||
\(641\) | −5.42930 | −0.214444 | −0.107222 | − | 0.994235i | \(-0.534196\pi\) | ||||
−0.107222 | + | 0.994235i | \(0.534196\pi\) | |||||||
\(642\) | − | 23.4015i | − | 0.923585i | ||||||
\(643\) | − | 2.08798i | − | 0.0823420i | −0.999152 | − | 0.0411710i | \(-0.986891\pi\) | ||
0.999152 | − | 0.0411710i | \(-0.0131088\pi\) | |||||||
\(644\) | 29.2860 | 1.15403 | ||||||||
\(645\) | 38.2991 | + | 60.0764i | 1.50802 | + | 2.36550i | ||||
\(646\) | 4.54595 | 0.178858 | ||||||||
\(647\) | 24.7631i | 0.973540i | 0.873530 | + | 0.486770i | \(0.161825\pi\) | ||||
−0.873530 | + | 0.486770i | \(0.838175\pi\) | |||||||
\(648\) | − | 0.875266i | − | 0.0343837i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.76932 | − | 5.94847i | 0.108622 | − | 0.233318i | ||||
\(651\) | 73.9432 | 2.89806 | ||||||||
\(652\) | − | 21.5909i | − | 0.845564i | ||||||
\(653\) | 6.89916i | 0.269985i | 0.990847 | + | 0.134992i | \(0.0431010\pi\) | ||||
−0.990847 | + | 0.134992i | \(0.956899\pi\) | |||||||
\(654\) | 90.8864 | 3.55394 | ||||||||
\(655\) | −16.8292 | − | 26.3985i | −0.657572 | − | 1.03147i | ||||
\(656\) | 12.5865 | 0.491420 | ||||||||
\(657\) | 31.4045i | 1.22521i | ||||||||
\(658\) | 18.9336i | 0.738110i | ||||||||
\(659\) | 12.4567 | 0.485246 | 0.242623 | − | 0.970121i | \(-0.421992\pi\) | ||||
0.242623 | + | 0.970121i | \(0.421992\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.8173 | 0.693012 | 0.346506 | − | 0.938048i | \(-0.387368\pi\) | ||||
0.346506 | + | 0.938048i | \(0.387368\pi\) | |||||||
\(662\) | − | 6.25400i | − | 0.243069i | ||||||
\(663\) | 2.24735i | 0.0872798i | ||||||||
\(664\) | −1.97398 | −0.0766052 | ||||||||
\(665\) | 11.4495 | − | 7.29915i | 0.443994 | − | 0.283049i | ||||
\(666\) | 22.8841 | 0.886741 | ||||||||
\(667\) | 18.1542i | 0.702933i | ||||||||
\(668\) | 30.5516i | 1.18208i | ||||||||
\(669\) | −9.66167 | −0.373542 | ||||||||
\(670\) | −5.78670 | − | 9.07709i | −0.223560 | − | 0.350679i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − | 75.5752i | − | 2.91538i | ||||||
\(673\) | 29.0771i | 1.12084i | 0.828209 | + | 0.560419i | \(0.189360\pi\) | ||||
−0.828209 | + | 0.560419i | \(0.810640\pi\) | |||||||
\(674\) | 72.7113 | 2.80074 | ||||||||
\(675\) | −32.9747 | − | 15.3515i | −1.26920 | − | 0.590879i | ||||
\(676\) | −26.3123 | −1.01201 | ||||||||
\(677\) | − | 40.8682i | − | 1.57069i | −0.619056 | − | 0.785347i | \(-0.712485\pi\) | ||
0.619056 | − | 0.785347i | \(-0.287515\pi\) | |||||||
\(678\) | − | 59.7578i | − | 2.29499i | ||||||
\(679\) | 48.6126 | 1.86558 | ||||||||
\(680\) | 0.265116 | + | 0.415864i | 0.0101667 | + | 0.0159477i | ||||
\(681\) | −8.27824 | −0.317223 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 17.2211i | − | 0.658948i | −0.944165 | − | 0.329474i | \(-0.893129\pi\) | ||
0.944165 | − | 0.329474i | \(-0.106871\pi\) | |||||||
\(684\) | −21.7380 | −0.831175 | ||||||||
\(685\) | −25.9663 | + | 16.5537i | −0.992123 | + | 0.632485i | ||||
\(686\) | −23.9545 | −0.914588 | ||||||||
\(687\) | − | 5.80497i | − | 0.221474i | ||||||
\(688\) | − | 41.6276i | − | 1.58704i | ||||||
\(689\) | 4.16393 | 0.158633 | ||||||||
\(690\) | −48.4683 | + | 30.8988i | −1.84516 | + | 1.17630i | ||||
\(691\) | 20.1406 | 0.766186 | 0.383093 | − | 0.923710i | \(-0.374859\pi\) | ||||
0.383093 | + | 0.923710i | \(0.374859\pi\) | |||||||
\(692\) | − | 4.61938i | − | 0.175603i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.8055 | 0.941603 | ||||||||
\(695\) | 8.11933 | + | 12.7361i | 0.307984 | + | 0.483107i | ||||
\(696\) | −2.25237 | −0.0853759 | ||||||||
\(697\) | − | 3.92813i | − | 0.148789i | ||||||
\(698\) | − | 35.7498i | − | 1.35315i | ||||||
\(699\) | −59.0341 | −2.23287 | ||||||||
\(700\) | 30.4479 | + | 14.1751i | 1.15082 | + | 0.535769i | ||||
\(701\) | 21.1666 | 0.799452 | 0.399726 | − | 0.916635i | \(-0.369105\pi\) | ||||
0.399726 | + | 0.916635i | \(0.369105\pi\) | |||||||
\(702\) | − | 9.54650i | − | 0.360309i | ||||||
\(703\) | − | 3.89252i | − | 0.146809i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.2121 | − | 16.0189i | −0.384611 | − | 0.603306i | ||||
\(706\) | −37.8674 | −1.42516 | ||||||||
\(707\) | − | 17.9131i | − | 0.673690i | ||||||
\(708\) | 22.6583i | 0.851551i | ||||||||
\(709\) | −20.5623 | −0.772233 | −0.386116 | − | 0.922450i | \(-0.626184\pi\) | ||||
−0.386116 | + | 0.922450i | \(0.626184\pi\) | |||||||
\(710\) | −59.9424 | + | 38.2137i | −2.24960 | + | 1.43413i | ||||
\(711\) | −83.8442 | −3.14440 | ||||||||
\(712\) | 1.67023i | 0.0625946i | ||||||||
\(713\) | 34.4422i | 1.28987i | ||||||||
\(714\) | −22.5021 | −0.842119 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.6078 | 0.844892 | ||||||||
\(717\) | 5.51167i | 0.205837i | ||||||||
\(718\) | − | 75.3836i | − | 2.81329i | ||||||
\(719\) | 18.2500 | 0.680609 | 0.340305 | − | 0.940315i | \(-0.389470\pi\) | ||||
0.340305 | + | 0.940315i | \(0.389470\pi\) | |||||||
\(720\) | 25.1565 | + | 39.4608i | 0.937529 | + | 1.47062i | ||||
\(721\) | 10.2188 | 0.380569 | ||||||||
\(722\) | − | 31.2003i | − | 1.16116i | ||||||
\(723\) | − | 11.6737i | − | 0.434148i | ||||||
\(724\) | 7.04286 | 0.261746 | ||||||||
\(725\) | −8.78706 | + | 18.8745i | −0.326343 | + | 0.700980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.218345i | 0.00809798i | 0.999992 | + | 0.00404899i | \(0.00128884\pi\) | ||||
−0.999992 | + | 0.00404899i | \(0.998711\pi\) | |||||||
\(728\) | 0.386627i | 0.0143293i | ||||||||
\(729\) | 37.6911 | 1.39597 | ||||||||
\(730\) | 13.8941 | + | 21.7944i | 0.514242 | + | 0.806646i | ||||
\(731\) | −12.9916 | −0.480511 | ||||||||
\(732\) | − | 47.4764i | − | 1.75478i | ||||||
\(733\) | − | 1.74365i | − | 0.0644033i | −0.999481 | − | 0.0322016i | \(-0.989748\pi\) | ||
0.999481 | − | 0.0322016i | \(-0.0102519\pi\) | |||||||
\(734\) | −36.4081 | −1.34385 | ||||||||
\(735\) | −18.2037 | + | 11.6050i | −0.671454 | + | 0.428057i | ||||
\(736\) | 35.2024 | 1.29758 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 36.7436i | 1.35255i | ||||||||
\(739\) | −30.3837 | −1.11768 | −0.558842 | − | 0.829274i | \(-0.688754\pi\) | ||||
−0.558842 | + | 0.829274i | \(0.688754\pi\) | |||||||
\(740\) | 8.11870 | − | 5.17572i | 0.298449 | − | 0.190263i | ||||
\(741\) | −3.57572 | −0.131357 | ||||||||
\(742\) | 41.6923i | 1.53057i | ||||||||
\(743\) | − | 34.6653i | − | 1.27175i | −0.771794 | − | 0.635873i | \(-0.780640\pi\) | ||
0.771794 | − | 0.635873i | \(-0.219360\pi\) | |||||||
\(744\) | −4.27321 | −0.156664 | ||||||||
\(745\) | −23.0751 | − | 36.1959i | −0.845407 | − | 1.32611i | ||||
\(746\) | −0.409835 | −0.0150051 | ||||||||
\(747\) | 58.4572i | 2.13884i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.7458 | 0.465720 | ||||||||
\(750\) | −65.3471 | + | 8.66499i | −2.38614 | + | 0.316401i | ||||
\(751\) | 9.55888 | 0.348809 | 0.174404 | − | 0.984674i | \(-0.444200\pi\) | ||||
0.174404 | + | 0.984674i | \(0.444200\pi\) | |||||||
\(752\) | 11.0997i | 0.404763i | ||||||||
\(753\) | − | 66.1880i | − | 2.41203i | ||||||
\(754\) | −5.46434 | −0.198999 | ||||||||
\(755\) | 3.95540 | + | 6.20448i | 0.143952 | + | 0.225804i | ||||
\(756\) | 48.8649 | 1.77720 | ||||||||
\(757\) | 6.26124i | 0.227569i | 0.993505 | + | 0.113784i | \(0.0362973\pi\) | ||||
−0.993505 | + | 0.113784i | \(0.963703\pi\) | |||||||
\(758\) | 68.7414i | 2.49680i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.661674 | + | 0.421822i | −0.0240014 | + | 0.0153011i | ||||
\(761\) | 26.6660 | 0.966642 | 0.483321 | − | 0.875443i | \(-0.339430\pi\) | ||||
0.483321 | + | 0.875443i | \(0.339430\pi\) | |||||||
\(762\) | 96.9477i | 3.51205i | ||||||||
\(763\) | 49.5018i | 1.79208i | ||||||||
\(764\) | −19.4014 | −0.701919 | ||||||||
\(765\) | 12.3154 | − | 7.85113i | 0.445263 | − | 0.283858i | ||||
\(766\) | −14.4470 | −0.521990 | ||||||||
\(767\) | 2.41099i | 0.0870560i | ||||||||
\(768\) | − | 42.0678i | − | 1.51799i | ||||||
\(769\) | −42.2399 | −1.52321 | −0.761605 | − | 0.648042i | \(-0.775588\pi\) | ||||
−0.761605 | + | 0.648042i | \(0.775588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.8425 | −0.426498 | ||||||||
\(772\) | 10.1720i | 0.366098i | ||||||||
\(773\) | − | 46.2951i | − | 1.66512i | −0.553937 | − | 0.832559i | \(-0.686875\pi\) | ||
0.553937 | − | 0.832559i | \(-0.313125\pi\) | |||||||
\(774\) | 121.523 | 4.36805 | ||||||||
\(775\) | −16.6709 | + | 35.8088i | −0.598835 | + | 1.28629i | ||||
\(776\) | −2.80935 | −0.100850 | ||||||||
\(777\) | 19.2677i | 0.691224i | ||||||||
\(778\) | − | 26.8362i | − | 0.962124i | ||||||
\(779\) | 6.24998 | 0.223929 | ||||||||
\(780\) | −4.75448 | − | 7.45793i | −0.170238 | − | 0.267037i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 10.4813i | − | 0.374811i | ||||||
\(783\) | 30.2910i | 1.08251i | ||||||||
\(784\) | 12.6136 | 0.450484 | ||||||||
\(785\) | 26.4243 | − | 16.8457i | 0.943123 | − | 0.601247i | ||||
\(786\) | −82.5481 | −2.94439 | ||||||||
\(787\) | 49.1450i | 1.75183i | 0.482465 | + | 0.875915i | \(0.339742\pi\) | ||||
−0.482465 | + | 0.875915i | \(0.660258\pi\) | |||||||
\(788\) | 24.8389i | 0.884848i | ||||||||
\(789\) | 35.8672 | 1.27691 | ||||||||
\(790\) | −58.1869 | + | 37.0945i | −2.07020 | + | 1.31976i | ||||
\(791\) | 32.5474 | 1.15725 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5.05180i | − | 0.179395i | ||||||
\(794\) | −67.8883 | −2.40926 | ||||||||
\(795\) | −22.4874 | − | 35.2740i | −0.797545 | − | 1.25104i | ||||
\(796\) | −10.4411 | −0.370076 | ||||||||
\(797\) | − | 43.6700i | − | 1.54687i | −0.633875 | − | 0.773435i | \(-0.718537\pi\) | ||
0.633875 | − | 0.773435i | \(-0.281463\pi\) | |||||||
\(798\) | − | 35.8027i | − | 1.26740i | ||||||
\(799\) | 3.46410 | 0.122551 | ||||||||
\(800\) | 36.5991 | + | 17.0388i | 1.29397 | + | 0.602413i | ||||
\(801\) | 49.4621 | 1.74766 | ||||||||
\(802\) | 67.9480i | 2.39933i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −14.5102 | −0.511737 | ||||||||
\(805\) | −16.8292 | − | 26.3985i | −0.593152 | − | 0.930425i | ||||
\(806\) | −10.3670 | −0.365161 | ||||||||
\(807\) | − | 22.4667i | − | 0.790866i | ||||||
\(808\) | 1.03520i | 0.0364184i | ||||||||
\(809\) | 39.5048 | 1.38891 | 0.694457 | − | 0.719534i | \(-0.255645\pi\) | ||||
0.694457 | + | 0.719534i | \(0.255645\pi\) | |||||||
\(810\) | −17.9882 | + | 11.4676i | −0.632042 | + | 0.402931i | ||||
\(811\) | 46.5773 | 1.63555 | 0.817775 | − | 0.575538i | \(-0.195207\pi\) | ||||
0.817775 | + | 0.575538i | \(0.195207\pi\) | |||||||
\(812\) | − | 27.9698i | − | 0.981549i | ||||||
\(813\) | − | 45.3940i | − | 1.59204i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.4621 | + | 12.4072i | −0.681728 | + | 0.434606i | ||||
\(816\) | −13.1916 | −0.461799 | ||||||||
\(817\) | − | 20.6707i | − | 0.723176i | ||||||
\(818\) | − | 16.5242i | − | 0.577756i | ||||||
\(819\) | 11.4495 | 0.400079 | ||||||||
\(820\) | 8.31034 | + | 13.0357i | 0.290210 | + | 0.455226i | ||||
\(821\) | 29.2072 | 1.01934 | 0.509669 | − | 0.860371i | \(-0.329768\pi\) | ||||
0.509669 | + | 0.860371i | \(0.329768\pi\) | |||||||
\(822\) | 81.1967i | 2.83206i | ||||||||
\(823\) | 13.8818i | 0.483890i | 0.970290 | + | 0.241945i | \(0.0777854\pi\) | ||||
−0.970290 | + | 0.241945i | \(0.922215\pi\) | |||||||
\(824\) | −0.590551 | −0.0205728 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.1406 | −0.839960 | ||||||||
\(827\) | − | 9.55026i | − | 0.332095i | −0.986118 | − | 0.166048i | \(-0.946899\pi\) | ||
0.986118 | − | 0.166048i | \(-0.0531005\pi\) | |||||||
\(828\) | 50.1201i | 1.74179i | ||||||||
\(829\) | −37.3241 | −1.29632 | −0.648160 | − | 0.761504i | \(-0.724461\pi\) | ||||
−0.648160 | + | 0.761504i | \(0.724461\pi\) | |||||||
\(830\) | 25.8628 | + | 40.5686i | 0.897710 | + | 1.40816i | ||||
\(831\) | 59.1784 | 2.05288 | ||||||||
\(832\) | 5.65476i | 0.196044i | ||||||||
\(833\) | − | 3.93658i | − | 0.136394i | ||||||
\(834\) | 39.8257 | 1.37905 | ||||||||
\(835\) | 27.5393 | − | 17.5565i | 0.953038 | − | 0.607568i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 57.4683i | 1.98640i | ||||||||
\(838\) | − | 39.5112i | − | 1.36489i | ||||||
\(839\) | 1.43270 | 0.0494623 | 0.0247311 | − | 0.999694i | \(-0.492127\pi\) | ||||
0.0247311 | + | 0.999694i | \(0.492127\pi\) | |||||||
\(840\) | 3.27523 | − | 2.08798i | 0.113006 | − | 0.0720422i | ||||
\(841\) | −11.6617 | −0.402127 | ||||||||
\(842\) | − | 48.3618i | − | 1.66666i | ||||||
\(843\) | − | 70.5940i | − | 2.43139i | ||||||
\(844\) | 3.29062 | 0.113268 | ||||||||
\(845\) | 15.1204 | + | 23.7180i | 0.520157 | + | 0.815925i | ||||
\(846\) | −32.4031 | −1.11404 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 24.4417i | 0.839332i | ||||||||
\(849\) | 42.0810 | 1.44422 | ||||||||
\(850\) | 5.07321 | − | 10.8972i | 0.174010 | − | 0.373770i | ||||
\(851\) | −8.97475 | −0.307650 | ||||||||
\(852\) | 95.8213i | 3.28278i | ||||||||
\(853\) | 28.1421i | 0.963569i | 0.876290 | + | 0.481784i | \(0.160011\pi\) | ||||
−0.876290 | + | 0.481784i | \(0.839989\pi\) | |||||||
\(854\) | 50.5823 | 1.73089 | ||||||||
\(855\) | 12.4918 | + | 19.5948i | 0.427210 | + | 0.670127i | ||||
\(856\) | −0.736584 | −0.0251759 | ||||||||
\(857\) | − | 4.04561i | − | 0.138195i | −0.997610 | − | 0.0690977i | \(-0.977988\pi\) | ||
0.997610 | − | 0.0690977i | \(-0.0220120\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.2064 | 1.88362 | 0.941808 | − | 0.336151i | \(-0.109125\pi\) | ||||
0.941808 | + | 0.336151i | \(0.109125\pi\) | |||||||
\(860\) | 43.1132 | − | 27.4850i | 1.47015 | − | 0.937229i | ||||
\(861\) | −30.9369 | −1.05433 | ||||||||
\(862\) | − | 15.3002i | − | 0.521125i | ||||||
\(863\) | 30.1927i | 1.02777i | 0.857859 | + | 0.513885i | \(0.171794\pi\) | ||||
−0.857859 | + | 0.513885i | \(0.828206\pi\) | |||||||
\(864\) | 58.7367 | 1.99826 | ||||||||
\(865\) | −4.16393 | + | 2.65453i | −0.141578 | + | 0.0902568i | ||||
\(866\) | −51.8231 | −1.76102 | ||||||||
\(867\) | − | 45.4338i | − | 1.54301i | ||||||
\(868\) | − | 53.0646i | − | 1.80113i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 29.5102 | + | 46.2901i | 1.00049 | + | 1.56938i | ||||
\(871\) | −1.54399 | −0.0523160 | ||||||||
\(872\) | − | 2.86073i | − | 0.0968766i | ||||||
\(873\) | 83.1958i | 2.81575i | ||||||||
\(874\) | 16.6767 | 0.564096 | ||||||||
\(875\) | −4.71943 | − | 35.5916i | −0.159546 | − | 1.20322i | ||||
\(876\) | 34.8395 | 1.17712 | ||||||||
\(877\) | 30.9398i | 1.04476i | 0.852712 | + | 0.522381i | \(0.174956\pi\) | ||||
−0.852712 | + | 0.522381i | \(0.825044\pi\) | |||||||
\(878\) | 41.4004i | 1.39719i | ||||||||
\(879\) | 44.1951 | 1.49066 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.25840 | −0.278233 | −0.139116 | − | 0.990276i | \(-0.544426\pi\) | ||||
−0.139116 | + | 0.990276i | \(0.544426\pi\) | |||||||
\(882\) | 36.8226i | 1.23988i | ||||||||
\(883\) | 40.0289i | 1.34708i | 0.739152 | + | 0.673539i | \(0.235227\pi\) | ||||
−0.739152 | + | 0.673539i | \(0.764773\pi\) | |||||||
\(884\) | 1.61279 | 0.0542439 | ||||||||
\(885\) | 20.4243 | − | 13.0206i | 0.686555 | − | 0.437683i | ||||
\(886\) | −20.5615 | −0.690777 | ||||||||
\(887\) | − | 37.7350i | − | 1.26702i | −0.773735 | − | 0.633509i | \(-0.781614\pi\) | ||
0.773735 | − | 0.633509i | \(-0.218386\pi\) | |||||||
\(888\) | − | 1.11349i | − | 0.0373662i | ||||||
\(889\) | −52.8031 | −1.77096 | ||||||||
\(890\) | 34.3261 | − | 21.8831i | 1.15062 | − | 0.733525i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.93360i | 0.232154i | ||||||||
\(893\) | 5.51167i | 0.184441i | ||||||||
\(894\) | −113.185 | −3.78546 | ||||||||
\(895\) | −12.9916 | − | 20.3787i | −0.434261 | − | 0.681186i | ||||
\(896\) | −4.76261 | −0.159108 | ||||||||
\(897\) | 8.24432i | 0.275270i | ||||||||
\(898\) | 29.7343i | 0.992245i | ||||||||
\(899\) | 32.8944 | 1.09709 | ||||||||
\(900\) | −24.2593 | + | 52.1087i | −0.808644 | + | 1.73696i | ||||
\(901\) | 7.62803 | 0.254127 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 102.318i | 3.40494i | ||||||||
\(904\) | −1.88093 | −0.0625588 | ||||||||
\(905\) | −4.04719 | − | 6.34846i | −0.134533 | − | 0.211030i | ||||
\(906\) | 19.4014 | 0.644569 | ||||||||
\(907\) | − | 33.5319i | − | 1.11341i | −0.830710 | − | 0.556705i | \(-0.812065\pi\) | ||
0.830710 | − | 0.556705i | \(-0.187935\pi\) | |||||||
\(908\) | 5.94079i | 0.197152i | ||||||||
\(909\) | 30.6565 | 1.01681 | ||||||||
\(910\) | 7.94585 | − | 5.06553i | 0.263402 | − | 0.167921i | ||||
\(911\) | −13.7828 | −0.456646 | −0.228323 | − | 0.973585i | \(-0.573324\pi\) | ||||
−0.228323 | + | 0.973585i | \(0.573324\pi\) | |||||||
\(912\) | − | 20.9890i | − | 0.695014i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 6.80231 | 0.225000 | ||||||||
\(915\) | −42.7954 | + | 27.2823i | −1.41477 | + | 0.901926i | ||||
\(916\) | −4.16588 | −0.137645 | ||||||||
\(917\) | − | 44.9602i | − | 1.48472i | ||||||
\(918\) | − | 17.4885i | − | 0.577207i | ||||||
\(919\) | −41.8128 | −1.37928 | −0.689639 | − | 0.724154i | \(-0.742231\pi\) | ||||
−0.689639 | + | 0.724154i | \(0.742231\pi\) | |||||||
\(920\) | 0.972568 | + | 1.52558i | 0.0320646 | + | 0.0502969i | ||||
\(921\) | −23.4396 | −0.772361 | ||||||||
\(922\) | − | 2.86073i | − | 0.0942131i | ||||||
\(923\) | 10.1960i | 0.335607i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.33084 | − | 4.34399i | −0.306796 | − | 0.142830i | ||||
\(926\) | 31.2716 | 1.02765 | ||||||||
\(927\) | 17.4885i | 0.574399i | ||||||||
\(928\) | − | 33.6204i | − | 1.10364i | ||||||
\(929\) | −13.1028 | −0.429889 | −0.214944 | − | 0.976626i | \(-0.568957\pi\) | ||||
−0.214944 | + | 0.976626i | \(0.568957\pi\) | |||||||
\(930\) | 55.9870 | + | 87.8219i | 1.83589 | + | 2.87979i | ||||
\(931\) | 6.26342 | 0.205275 | ||||||||
\(932\) | 42.3652i | 1.38772i | ||||||||
\(933\) | − | 64.9023i | − | 2.12481i | ||||||
\(934\) | 37.8078 | 1.23711 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.661674 | −0.0216275 | ||||||||
\(937\) | 8.75544i | 0.286028i | 0.989721 | + | 0.143014i | \(0.0456794\pi\) | ||||
−0.989721 | + | 0.143014i | \(0.954321\pi\) | |||||||
\(938\) | − | 15.4595i | − | 0.504771i | ||||||
\(939\) | −6.85095 | −0.223572 | ||||||||
\(940\) | −11.4958 | + | 7.32864i | −0.374951 | + | 0.239034i | ||||
\(941\) | −17.6529 | −0.575468 | −0.287734 | − | 0.957710i | \(-0.592902\pi\) | ||||
−0.287734 | + | 0.957710i | \(0.592902\pi\) | |||||||
\(942\) | − | 82.6287i | − | 2.69219i | ||||||
\(943\) | − | 14.4102i | − | 0.469261i | ||||||
\(944\) | −14.1522 | −0.460615 | ||||||||
\(945\) | −28.0803 | − | 44.0470i | −0.913451 | − | 1.43285i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 56.2415i | − | 1.82760i | −0.406159 | − | 0.913802i | \(-0.633132\pi\) | ||
0.406159 | − | 0.913802i | \(-0.366868\pi\) | |||||||
\(948\) | 93.0150i | 3.02099i | ||||||||
\(949\) | 3.70716 | 0.120340 | ||||||||
\(950\) | 17.3383 | + | 8.07190i | 0.562530 | + | 0.261887i | ||||
\(951\) | 52.5336 | 1.70352 | ||||||||
\(952\) | 0.708273i | 0.0229553i | ||||||||
\(953\) | − | 4.74388i | − | 0.153669i | −0.997044 | − | 0.0768347i | \(-0.975519\pi\) | ||
0.997044 | − | 0.0768347i | \(-0.0244814\pi\) | |||||||
\(954\) | −71.3524 | −2.31012 | ||||||||
\(955\) | 11.1490 | + | 17.4885i | 0.360775 | + | 0.565915i | ||||
\(956\) | 3.95540 | 0.127927 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 60.4344i | 1.95255i | ||||||||
\(959\) | −44.2242 | −1.42807 | ||||||||
\(960\) | 47.9032 | − | 30.5386i | 1.54607 | − | 0.985630i | ||||
\(961\) | 31.4074 | 1.01314 | ||||||||
\(962\) | − | 2.70137i | − | 0.0870955i | ||||||
\(963\) | 21.8132i | 0.702919i | ||||||||
\(964\) | −8.37749 | −0.269821 | ||||||||
\(965\) | 9.16908 | − | 5.84535i | 0.295163 | − | 0.188168i | ||||
\(966\) | −82.5481 | −2.65594 | ||||||||
\(967\) | − | 33.8619i | − | 1.08892i | −0.838785 | − | 0.544462i | \(-0.816734\pi\) | ||
0.838785 | − | 0.544462i | \(-0.183266\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.55047 | −0.210431 | ||||||||
\(970\) | 36.8077 | + | 57.7369i | 1.18182 | + | 1.85382i | ||||
\(971\) | −19.7828 | −0.634862 | −0.317431 | − | 0.948281i | \(-0.602820\pi\) | ||||
−0.317431 | + | 0.948281i | \(0.602820\pi\) | |||||||
\(972\) | − | 16.8947i | − | 0.541898i | ||||||
\(973\) | 21.6913i | 0.695390i | ||||||||
\(974\) | 1.89096 | 0.0605902 | ||||||||
\(975\) | −3.99045 | + | 8.57142i | −0.127797 | + | 0.274505i | ||||
\(976\) | 29.6534 | 0.949182 | ||||||||
\(977\) | 6.66124i | 0.213112i | 0.994307 | + | 0.106556i | \(0.0339823\pi\) | ||||
−0.994307 | + | 0.106556i | \(0.966018\pi\) | |||||||
\(978\) | 60.8581i | 1.94603i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 8.32821 | + | 13.0637i | 0.266035 | + | 0.417305i | ||||
\(981\) | −84.7175 | −2.70482 | ||||||||
\(982\) | − | 66.5390i | − | 2.12334i | ||||||
\(983\) | − | 5.16210i | − | 0.164645i | −0.996606 | − | 0.0823227i | \(-0.973766\pi\) | ||
0.996606 | − | 0.0823227i | \(-0.0262338\pi\) | |||||||
\(984\) | 1.78786 | 0.0569949 | ||||||||
\(985\) | 22.3899 | − | 14.2737i | 0.713400 | − | 0.454797i | ||||
\(986\) | −10.0103 | −0.318792 | ||||||||
\(987\) | − | 27.2823i | − | 0.868407i | ||||||
\(988\) | 2.56608i | 0.0816378i | ||||||||
\(989\) | −47.6592 | −1.51547 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.8830 | −0.758669 | −0.379334 | − | 0.925260i | \(-0.623847\pi\) | ||||
−0.379334 | + | 0.925260i | \(0.623847\pi\) | |||||||
\(992\) | − | 63.7849i | − | 2.02517i | ||||||
\(993\) | 9.01167i | 0.285977i | ||||||||
\(994\) | −102.090 | −3.23810 | ||||||||
\(995\) | 6.00000 | + | 9.41167i | 0.190213 | + | 0.298370i | ||||
\(996\) | 64.8513 | 2.05489 | ||||||||
\(997\) | − | 29.6423i | − | 0.938780i | −0.882991 | − | 0.469390i | \(-0.844474\pi\) | ||
0.882991 | − | 0.469390i | \(-0.155526\pi\) | |||||||
\(998\) | − | 18.1882i | − | 0.575738i | ||||||
\(999\) | −14.9747 | −0.473780 |
(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 | 605.2.b.h.364.9 | yes | 12 | |
5.2 | odd | 4 | 3025.2.a.bo.1.3 | 12 | |||
5.3 | odd | 4 | 3025.2.a.bo.1.10 | 12 | |||
5.4 | even | 2 | inner | 605.2.b.h.364.4 | yes | 12 | |
11.2 | odd | 10 | 605.2.j.k.444.3 | 48 | |||
11.3 | even | 5 | 605.2.j.k.9.10 | 48 | |||
11.4 | even | 5 | 605.2.j.k.269.3 | 48 | |||
11.5 | even | 5 | 605.2.j.k.124.4 | 48 | |||
11.6 | odd | 10 | 605.2.j.k.124.10 | 48 | |||
11.7 | odd | 10 | 605.2.j.k.269.9 | 48 | |||
11.8 | odd | 10 | 605.2.j.k.9.4 | 48 | |||
11.9 | even | 5 | 605.2.j.k.444.9 | 48 | |||
11.10 | odd | 2 | inner | 605.2.b.h.364.3 | ✓ | 12 | |
55.4 | even | 10 | 605.2.j.k.269.10 | 48 | |||
55.9 | even | 10 | 605.2.j.k.444.4 | 48 | |||
55.14 | even | 10 | 605.2.j.k.9.3 | 48 | |||
55.19 | odd | 10 | 605.2.j.k.9.9 | 48 | |||
55.24 | odd | 10 | 605.2.j.k.444.10 | 48 | |||
55.29 | odd | 10 | 605.2.j.k.269.4 | 48 | |||
55.32 | even | 4 | 3025.2.a.bo.1.9 | 12 | |||
55.39 | odd | 10 | 605.2.j.k.124.3 | 48 | |||
55.43 | even | 4 | 3025.2.a.bo.1.4 | 12 | |||
55.49 | even | 10 | 605.2.j.k.124.9 | 48 | |||
55.54 | odd | 2 | inner | 605.2.b.h.364.10 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.h.364.3 | ✓ | 12 | 11.10 | odd | 2 | inner | |
605.2.b.h.364.4 | yes | 12 | 5.4 | even | 2 | inner | |
605.2.b.h.364.9 | yes | 12 | 1.1 | even | 1 | trivial | |
605.2.b.h.364.10 | yes | 12 | 55.54 | odd | 2 | inner | |
605.2.j.k.9.3 | 48 | 55.14 | even | 10 | |||
605.2.j.k.9.4 | 48 | 11.8 | odd | 10 | |||
605.2.j.k.9.9 | 48 | 55.19 | odd | 10 | |||
605.2.j.k.9.10 | 48 | 11.3 | even | 5 | |||
605.2.j.k.124.3 | 48 | 55.39 | odd | 10 | |||
605.2.j.k.124.4 | 48 | 11.5 | even | 5 | |||
605.2.j.k.124.9 | 48 | 55.49 | even | 10 | |||
605.2.j.k.124.10 | 48 | 11.6 | odd | 10 | |||
605.2.j.k.269.3 | 48 | 11.4 | even | 5 | |||
605.2.j.k.269.4 | 48 | 55.29 | odd | 10 | |||
605.2.j.k.269.9 | 48 | 11.7 | odd | 10 | |||
605.2.j.k.269.10 | 48 | 55.4 | even | 10 | |||
605.2.j.k.444.3 | 48 | 11.2 | odd | 10 | |||
605.2.j.k.444.4 | 48 | 55.9 | even | 10 | |||
605.2.j.k.444.9 | 48 | 11.9 | even | 5 | |||
605.2.j.k.444.10 | 48 | 55.24 | odd | 10 | |||
3025.2.a.bo.1.3 | 12 | 5.2 | odd | 4 | |||
3025.2.a.bo.1.4 | 12 | 55.43 | even | 4 | |||
3025.2.a.bo.1.9 | 12 | 55.32 | even | 4 | |||
3025.2.a.bo.1.10 | 12 | 5.3 | odd | 4 |