Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [88,2,Mod(9,88)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(88, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("88.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 88 = 2^{3} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 88.i (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.702683537787\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.682515625.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 81.2 | ||
Root | \(0.581882 - 1.79085i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 88.81 |
Dual form | 88.2.i.b.25.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/88\mathbb{Z}\right)^\times\).
\(n\) | \(23\) | \(45\) | \(57\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.941506 | − | 2.89766i | 0.543578 | − | 1.67296i | −0.180767 | − | 0.983526i | \(-0.557858\pi\) |
0.724346 | − | 0.689437i | \(-0.242142\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.44151 | + | 1.04732i | −0.644661 | + | 0.468374i | −0.861448 | − | 0.507845i | \(-0.830442\pi\) |
0.216787 | + | 0.976219i | \(0.430442\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.109101 | + | 0.335777i | 0.0412361 | + | 0.126912i | 0.969555 | − | 0.244873i | \(-0.0787461\pi\) |
−0.928319 | + | 0.371784i | \(0.878746\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.08293 | − | 3.69296i | −1.69431 | − | 1.23099i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.91429 | + | 1.58333i | 0.878691 | + | 0.477391i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.48828 | + | 3.26093i | 1.24483 | + | 0.904419i | 0.997910 | − | 0.0646185i | \(-0.0205831\pi\) |
0.246915 | + | 0.969037i | \(0.420583\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.67757 | + | 5.16304i | 0.433148 | + | 1.33309i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.08462 | + | 2.24111i | −0.748130 | + | 0.543548i | −0.895247 | − | 0.445571i | \(-0.853001\pi\) |
0.147117 | + | 0.989119i | \(0.453001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.42705 | − | 4.39201i | 0.327388 | − | 1.00760i | −0.642963 | − | 0.765897i | \(-0.722295\pi\) |
0.970351 | − | 0.241699i | \(-0.0777048\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.07569 | 0.234734 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.00209 | −1.46004 | −0.730018 | − | 0.683428i | \(-0.760489\pi\) | ||||
−0.730018 | + | 0.683428i | \(0.760489\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.564016 | + | 1.73586i | −0.112803 | + | 0.347172i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.09186 | + | 5.87908i | −1.55728 | + | 1.13143i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.654831 | + | 2.01536i | 0.121599 | + | 0.374244i | 0.993266 | − | 0.115855i | \(-0.0369608\pi\) |
−0.871667 | + | 0.490099i | \(0.836961\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.79456 | − | 2.03037i | −0.501918 | − | 0.364665i | 0.307831 | − | 0.951441i | \(-0.400397\pi\) |
−0.809749 | + | 0.586776i | \(0.800397\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.33176 | − | 6.95389i | 1.27630 | − | 1.21052i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.508933 | − | 0.369762i | −0.0860254 | − | 0.0625011i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.537843 | − | 1.65531i | −0.0884208 | − | 0.272131i | 0.897063 | − | 0.441904i | \(-0.145697\pi\) |
−0.985483 | + | 0.169773i | \(0.945697\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.6748 | − | 9.93532i | 2.18972 | − | 1.59092i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.458327 | + | 1.41059i | −0.0715787 | + | 0.220297i | −0.980446 | − | 0.196789i | \(-0.936949\pi\) |
0.908867 | + | 0.417086i | \(0.136949\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.92979 | −0.599287 | −0.299643 | − | 0.954051i | \(-0.596868\pi\) | ||||
−0.299643 | + | 0.954051i | \(0.596868\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.1948 | 1.66882 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.374078 | + | 1.15129i | −0.0545648 | + | 0.167933i | −0.974625 | − | 0.223844i | \(-0.928140\pi\) |
0.920060 | + | 0.391777i | \(0.128140\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.56228 | − | 4.04123i | 0.794611 | − | 0.577319i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.58977 | + | 11.0482i | 0.502668 | + | 1.54705i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.41260 | − | 4.65902i | −0.880838 | − | 0.639966i | 0.0526352 | − | 0.998614i | \(-0.483238\pi\) |
−0.933473 | + | 0.358648i | \(0.883238\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.85921 | + | 0.769801i | −0.790055 | + | 0.103800i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.3830 | − | 8.27021i | −1.50771 | − | 1.09542i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.954915 | − | 2.93893i | −0.124319 | − | 0.382616i | 0.869457 | − | 0.494008i | \(-0.164469\pi\) |
−0.993776 | + | 0.111393i | \(0.964469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.15309 | − | 4.47048i | 0.787823 | − | 0.572387i | −0.119494 | − | 0.992835i | \(-0.538127\pi\) |
0.907317 | + | 0.420448i | \(0.138127\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.685462 | − | 2.10963i | 0.0863601 | − | 0.265789i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.88510 | −1.22610 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.17352 | 0.143368 | 0.0716839 | − | 0.997427i | \(-0.477163\pi\) | ||||
0.0716839 | + | 0.997427i | \(0.477163\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.59251 | + | 20.2896i | −0.793645 | + | 2.44259i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.91702 | − | 1.39280i | 0.227509 | − | 0.165295i | −0.468191 | − | 0.883627i | \(-0.655094\pi\) |
0.695700 | + | 0.718332i | \(0.255094\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.20648 | + | 3.71317i | 0.141208 | + | 0.434594i | 0.996504 | − | 0.0835461i | \(-0.0266246\pi\) |
−0.855296 | + | 0.518140i | \(0.826625\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.49891 | + | 3.26865i | 0.519489 | + | 0.377431i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.213695 | + | 1.15129i | −0.0243528 | + | 0.131202i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.32452 | − | 2.41540i | −0.374037 | − | 0.271754i | 0.384846 | − | 0.922981i | \(-0.374255\pi\) |
−0.758883 | + | 0.651227i | \(0.774255\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.59251 | + | 11.0566i | 0.399167 | + | 1.22851i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.662074 | + | 0.481025i | −0.0726720 | + | 0.0527993i | −0.623528 | − | 0.781801i | \(-0.714301\pi\) |
0.550856 | + | 0.834600i | \(0.314301\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.09935 | − | 6.46114i | 0.227706 | − | 0.700809i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.45636 | 0.692194 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.92979 | −0.204557 | −0.102279 | − | 0.994756i | \(-0.532613\pi\) | ||||
−0.102279 | + | 0.994756i | \(0.532613\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.605270 | + | 1.86283i | −0.0634496 | + | 0.195278i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.51441 | + | 6.18608i | −0.882903 | + | 0.641466i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.54272 | + | 7.82568i | 0.260877 | + | 0.802898i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.66755 | + | 5.57080i | 0.778521 | + | 0.565629i | 0.904535 | − | 0.426400i | \(-0.140218\pi\) |
−0.126014 | + | 0.992029i | \(0.540218\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.96594 | − | 18.8103i | −0.901111 | − | 1.89051i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6541 | + | 8.46723i | 1.15963 | + | 0.842520i | 0.989731 | − | 0.142941i | \(-0.0456559\pi\) |
0.169899 | + | 0.985462i | \(0.445656\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.48002 | + | 7.63273i | 0.244364 | + | 0.752075i | 0.995740 | + | 0.0922013i | \(0.0293903\pi\) |
−0.751376 | + | 0.659874i | \(0.770610\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.55061 | + | 1.12658i | −0.151324 | + | 0.109943i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.41364 | − | 4.35074i | 0.136662 | − | 0.420602i | −0.859183 | − | 0.511669i | \(-0.829028\pi\) |
0.995845 | + | 0.0910665i | \(0.0290276\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.6592 | −1.97880 | −0.989398 | − | 0.145228i | \(-0.953608\pi\) | ||||
−0.989398 | + | 0.145228i | \(0.953608\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.30290 | −0.503329 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.72094 | − | 8.37418i | 0.255964 | − | 0.787777i | −0.737674 | − | 0.675157i | \(-0.764076\pi\) |
0.993638 | − | 0.112620i | \(-0.0359242\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.0936 | − | 7.33339i | 0.941229 | − | 0.683843i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.7711 | − | 33.1501i | −0.995791 | − | 3.06473i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.08905 | − | 0.791238i | −0.0998327 | − | 0.0725327i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.98614 | + | 9.22855i | 0.544195 | + | 0.838959i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.65588 | + | 2.65615i | 0.329639 | + | 0.239497i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.75799 | − | 11.5659i | −0.336125 | − | 1.03449i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.3946 | + | 10.4583i | −1.27732 | + | 0.928025i | −0.999468 | − | 0.0325998i | \(-0.989621\pi\) |
−0.277849 | + | 0.960625i | \(0.589621\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.69992 | + | 11.3872i | −0.325759 | + | 1.00258i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.3585 | 1.60399 | 0.801996 | − | 0.597329i | \(-0.203771\pi\) | ||||
0.801996 | + | 0.597329i | \(0.203771\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.63043 | 0.141376 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.50721 | − | 16.9495i | 0.473985 | − | 1.45878i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.9036 | − | 7.92194i | 0.931559 | − | 0.676817i | −0.0148153 | − | 0.999890i | \(-0.504716\pi\) |
0.946374 | + | 0.323073i | \(0.104716\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.40981 | + | 13.5720i | 0.374035 | + | 1.15116i | 0.944127 | + | 0.329581i | \(0.106908\pi\) |
−0.570092 | + | 0.821581i | \(0.693092\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.98385 | + | 2.16790i | 0.251286 | + | 0.182570i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.91702 | + | 16.6097i | 0.662055 | + | 1.38897i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.05466 | − | 2.21934i | −0.253676 | − | 0.184306i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.47318 | − | 19.9224i | −0.533899 | − | 1.64317i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.25430 | − | 5.99710i | 0.676219 | − | 0.491302i | −0.195882 | − | 0.980627i | \(-0.562757\pi\) |
0.872101 | + | 0.489326i | \(0.162757\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.35621 | − | 4.17399i | 0.110367 | − | 0.339674i | −0.880586 | − | 0.473887i | \(-0.842851\pi\) |
0.990953 | + | 0.134213i | \(0.0428505\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 23.9552 | 1.93666 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.15481 | 0.494366 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.85433 | − | 21.0955i | 0.547035 | − | 1.68360i | −0.169066 | − | 0.985605i | \(-0.554075\pi\) |
0.716101 | − | 0.697996i | \(-0.245925\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.5377 | + | 14.1950i | −1.54944 | + | 1.12574i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.763932 | − | 2.35114i | −0.0602063 | − | 0.185296i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.9621 | − | 11.5971i | −1.25025 | − | 0.908356i | −0.252009 | − | 0.967725i | \(-0.581091\pi\) |
−0.998236 | + | 0.0593688i | \(0.981091\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.28586 | + | 17.7027i | −0.255804 | + | 1.37816i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.800035 | + | 0.581259i | 0.0619085 | + | 0.0449792i | 0.618309 | − | 0.785935i | \(-0.287818\pi\) |
−0.556401 | + | 0.830914i | \(0.687818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.49380 | + | 16.9082i | 0.422600 | + | 1.30063i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23.4731 | + | 17.0542i | −1.79504 | + | 1.30417i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.40772 | + | 16.6433i | −0.411141 | + | 1.26536i | 0.504516 | + | 0.863403i | \(0.331671\pi\) |
−0.915657 | + | 0.401961i | \(0.868329\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.644397 | −0.0487118 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.41506 | −0.707679 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.881320 | + | 2.71242i | −0.0658730 | + | 0.202736i | −0.978575 | − | 0.205889i | \(-0.933992\pi\) |
0.912702 | + | 0.408625i | \(0.133992\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.70101 | − | 1.23586i | 0.126435 | − | 0.0918605i | −0.522770 | − | 0.852474i | \(-0.675102\pi\) |
0.649206 | + | 0.760613i | \(0.275102\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.16075 | − | 22.0385i | −0.529338 | − | 1.62913i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.50893 | + | 1.82285i | 0.184460 | + | 0.134018i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.5379 | + | 1.64726i | −0.916860 | + | 0.120460i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.85689 | − | 2.07565i | −0.207808 | − | 0.150981i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.29073 | − | 16.2832i | −0.382824 | − | 1.17821i | −0.938047 | − | 0.346509i | \(-0.887367\pi\) |
0.555223 | − | 0.831702i | \(-0.312633\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.2846 | + | 11.8314i | −1.17219 | + | 0.851645i | −0.991269 | − | 0.131853i | \(-0.957907\pi\) |
−0.180919 | + | 0.983498i | \(0.557907\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.30688 | + | 28.6436i | −0.666479 | + | 2.05121i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.5589 | 0.894786 | 0.447393 | − | 0.894337i | \(-0.352352\pi\) | ||||
0.447393 | + | 0.894337i | \(0.352352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.32962 | −0.236031 | −0.118015 | − | 0.993012i | \(-0.537653\pi\) | ||||
−0.118015 | + | 0.993012i | \(0.537653\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.10487 | − | 3.40044i | 0.0779316 | − | 0.239849i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.605270 | + | 0.439755i | −0.0424817 | + | 0.0308647i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.816647 | − | 2.51338i | −0.0570371 | − | 0.175542i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 35.5911 | + | 25.8585i | 2.47375 | + | 1.79729i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.1128 | − | 10.5401i | 0.768691 | − | 0.729073i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.4927 | + | 14.1623i | 1.34194 | + | 0.974973i | 0.999370 | + | 0.0354791i | \(0.0112957\pi\) |
0.342565 | + | 0.939494i | \(0.388704\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.23096 | − | 6.86620i | −0.152863 | − | 0.470464i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.66481 | − | 4.11573i | 0.386337 | − | 0.280690i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.376863 | − | 1.15986i | 0.0255831 | − | 0.0787367i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.8954 | 0.803817 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.1527 | −1.42289 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.163537 | − | 0.503315i | 0.0109512 | − | 0.0337044i | −0.945432 | − | 0.325821i | \(-0.894359\pi\) |
0.956383 | + | 0.292116i | \(0.0943594\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.27732 | − | 6.74037i | 0.618488 | − | 0.449358i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.91835 | − | 12.0594i | −0.260070 | − | 0.800412i | −0.992788 | − | 0.119881i | \(-0.961749\pi\) |
0.732719 | − | 0.680532i | \(-0.238251\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.93708 | + | 3.58700i | 0.326251 | + | 0.237035i | 0.738838 | − | 0.673883i | \(-0.235375\pi\) |
−0.412587 | + | 0.910918i | \(0.635375\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.13486 | + | 1.70316i | 0.206258 | + | 0.112060i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.01513 | + | 1.46408i | 0.132016 | + | 0.0959149i | 0.651833 | − | 0.758362i | \(-0.274000\pi\) |
−0.519818 | + | 0.854277i | \(0.674000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.666531 | − | 2.05137i | −0.0434797 | − | 0.133817i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.1291 | + | 7.35919i | −0.657953 | + | 0.478031i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.91215 | − | 21.2734i | 0.447110 | − | 1.37606i | −0.433044 | − | 0.901373i | \(-0.642560\pi\) |
0.880153 | − | 0.474689i | \(-0.157440\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.1025 | −1.55258 | −0.776288 | − | 0.630378i | \(-0.782900\pi\) | ||||
−0.776288 | + | 0.630378i | \(0.782900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.41432 | 0.347329 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.78561 | + | 11.6509i | −0.241854 | + | 0.744349i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.7270 | − | 15.0591i | 1.31883 | − | 0.958186i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.770498 | + | 2.37135i | 0.0488283 | + | 0.150278i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.60736 | + | 4.07399i | 0.353933 | + | 0.257148i | 0.750517 | − | 0.660851i | \(-0.229804\pi\) |
−0.396584 | + | 0.917999i | \(0.629804\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.4061 | − | 11.0866i | −1.28292 | − | 0.697009i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.7456 | − | 12.1664i | −1.04865 | − | 0.761889i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.52799 | − | 13.9357i | −0.282448 | − | 0.869286i | −0.987152 | − | 0.159784i | \(-0.948920\pi\) |
0.704704 | − | 0.709501i | \(-0.251080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.497136 | − | 0.361190i | 0.0308905 | − | 0.0224433i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.11420 | − | 12.6622i | 0.254663 | − | 0.783772i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.9868 | −1.41742 | −0.708712 | − | 0.705497i | \(-0.750724\pi\) | ||||
−0.708712 | + | 0.705497i | \(0.750724\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.1233 | 0.867585 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.81691 | + | 5.59186i | −0.111193 | + | 0.342216i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.48828 | − | 3.26093i | 0.273655 | − | 0.198822i | −0.442490 | − | 0.896773i | \(-0.645905\pi\) |
0.716145 | + | 0.697951i | \(0.245905\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.18270 | − | 12.8730i | −0.254081 | − | 0.781980i | −0.994009 | − | 0.109295i | \(-0.965141\pi\) |
0.739929 | − | 0.672685i | \(-0.234859\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.82798 | + | 3.50773i | 0.292203 | + | 0.212298i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.39214 | + | 4.16578i | −0.264856 | + | 0.251206i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.39473 | + | 1.73987i | 0.143885 | + | 0.104539i | 0.657399 | − | 0.753542i | \(-0.271657\pi\) |
−0.513514 | + | 0.858081i | \(0.671657\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.70648 | + | 20.6404i | 0.401507 | + | 1.23571i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.25120 | − | 5.26830i | 0.432570 | − | 0.314281i | −0.350106 | − | 0.936710i | \(-0.613854\pi\) |
0.782676 | + | 0.622430i | \(0.213854\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.57487 | − | 17.1577i | 0.331392 | − | 1.01992i | −0.637081 | − | 0.770797i | \(-0.719858\pi\) |
0.968472 | − | 0.249121i | \(-0.0801417\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 25.0701 | 1.48503 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.523646 | −0.0309099 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.760976 | + | 2.34204i | −0.0447633 | + | 0.137767i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.3613 | − | 16.9730i | 1.36946 | − | 0.994973i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.54122 | + | 26.2872i | 0.498984 | + | 1.53571i | 0.810655 | + | 0.585524i | \(0.199111\pi\) |
−0.311671 | + | 0.950190i | \(0.600889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.45450 | + | 3.23638i | 0.259351 | + | 0.188429i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −32.8905 | + | 4.32126i | −1.90850 | + | 0.250745i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.4274 | − | 22.8333i | −1.81749 | − | 1.32048i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.428742 | − | 1.31953i | −0.0247123 | − | 0.0760566i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 35.5075 | − | 25.7977i | 2.03986 | − | 1.48204i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.18771 | + | 12.8885i | −0.239788 | + | 0.737991i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.662166 | 0.0377918 | 0.0188959 | − | 0.999821i | \(-0.493985\pi\) | ||||
0.0188959 | + | 0.999821i | \(0.493985\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.4520 | 1.39102 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.03889 | + | 12.4304i | −0.229024 | + | 0.704864i | 0.768834 | + | 0.639449i | \(0.220837\pi\) |
−0.997858 | + | 0.0654157i | \(0.979163\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.0289 | + | 11.6457i | −0.906006 | + | 0.658252i | −0.940002 | − | 0.341170i | \(-0.889177\pi\) |
0.0339952 | + | 0.999422i | \(0.489177\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.22136 | + | 3.75894i | 0.0688156 | + | 0.211793i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.9693 | + | 11.6024i | 0.896924 | + | 0.651653i | 0.937674 | − | 0.347516i | \(-0.112975\pi\) |
−0.0407503 | + | 0.999169i | \(0.512975\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.28262 | + | 6.91016i | −0.0718127 | + | 0.386895i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.2760 | − | 8.19249i | −0.629365 | − | 0.457260i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.44106 | + | 16.7459i | 0.302749 | + | 0.931764i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.19198 | + | 5.95182i | −0.454409 | + | 0.330148i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.4508 | + | 59.8634i | −1.07563 | + | 3.31045i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.427390 | −0.0235628 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.0860 | 1.15899 | 0.579494 | − | 0.814976i | \(-0.303250\pi\) | ||||
0.579494 | + | 0.814976i | \(0.303250\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.37918 | + | 10.4000i | −0.185178 | + | 0.569919i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.69163 | + | 1.22904i | −0.0924236 | + | 0.0671496i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.428343 | − | 1.31830i | −0.0233333 | − | 0.0718126i | 0.938712 | − | 0.344703i | \(-0.112020\pi\) |
−0.962045 | + | 0.272890i | \(0.912020\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.7037 | − | 15.7687i | −1.17878 | − | 0.856437i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.92942 | − | 10.3418i | −0.266943 | − | 0.560039i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.96320 | + | 2.87944i | 0.213993 | + | 0.155475i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.7465 | − | 36.1521i | −0.632411 | − | 1.94636i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.4653 | + | 11.2362i | −0.830220 | + | 0.603190i | −0.919622 | − | 0.392805i | \(-0.871505\pi\) |
0.0894013 | + | 0.995996i | \(0.471505\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.40170 | − | 19.7024i | 0.342675 | − | 1.05464i | −0.620142 | − | 0.784490i | \(-0.712925\pi\) |
0.962817 | − | 0.270155i | \(-0.0870750\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −55.4898 | −2.96183 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.09091 | 0.270962 | 0.135481 | − | 0.990780i | \(-0.456742\pi\) | ||||
0.135481 | + | 0.990780i | \(0.456742\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.30470 | + | 4.01546i | −0.0692463 | + | 0.213118i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.31808 | + | 2.41073i | −0.175611 | + | 0.127589i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.27450 | − | 3.92251i | −0.0672655 | − | 0.207022i | 0.911774 | − | 0.410692i | \(-0.134713\pi\) |
−0.979040 | + | 0.203670i | \(0.934713\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.88197 | − | 1.36733i | −0.0990508 | − | 0.0719646i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 32.3771 | − | 8.65705i | 1.69936 | − | 0.454377i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.62801 | − | 4.08899i | −0.294584 | − | 0.214028i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2797 | + | 34.7153i | 0.588795 | + | 1.81212i | 0.583464 | + | 0.812139i | \(0.301697\pi\) |
0.00533096 | + | 0.999986i | \(0.498303\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.53889 | − | 5.47732i | 0.392459 | − | 0.285138i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.864775 | − | 2.66150i | 0.0448969 | − | 0.138178i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.01741 | −0.259792 | −0.129896 | − | 0.991528i | \(-0.541464\pi\) | ||||
−0.129896 | + | 0.991528i | \(0.541464\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −37.0522 | −1.91337 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.63289 | + | 11.1809i | −0.187103 | + | 0.575845i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.3812 | + | 11.9017i | −0.841447 | + | 0.611347i | −0.922774 | − | 0.385340i | \(-0.874084\pi\) |
0.0813276 | + | 0.996687i | \(0.474084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.7520 | + | 51.5573i | 0.858229 | + | 2.64136i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.60736 | + | 5.52707i | 0.388718 | + | 0.282420i | 0.764930 | − | 0.644113i | \(-0.222774\pi\) |
−0.376212 | + | 0.926534i | \(0.622774\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.897724 | − | 1.88340i | −0.0457522 | − | 0.0959870i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19.9748 | + | 14.5126i | 1.01538 | + | 0.737715i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.09040 | + | 6.43358i | 0.105987 | + | 0.326196i | 0.989961 | − | 0.141341i | \(-0.0451415\pi\) |
−0.883974 | + | 0.467537i | \(0.845141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.5988 | − | 15.6924i | 1.09230 | − | 0.793600i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.2847 | − | 53.1967i | 0.871896 | − | 2.68342i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.32200 | 0.368410 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.18919 | −0.260438 | −0.130219 | − | 0.991485i | \(-0.541568\pi\) | ||||
−0.130219 | + | 0.991485i | \(0.541568\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.53506 | − | 4.72442i | 0.0768490 | − | 0.236517i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.76448 | + | 3.46160i | −0.237927 | + | 0.172864i | −0.700359 | − | 0.713791i | \(-0.746977\pi\) |
0.462432 | + | 0.886655i | \(0.346977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.92190 | − | 18.2257i | −0.294991 | − | 0.907888i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.7584 | − | 12.1757i | −0.832730 | − | 0.605014i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.05347 | − | 5.67563i | 0.0522186 | − | 0.281330i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.9425 | + | 20.3014i | 1.38167 | + | 1.00384i | 0.996722 | + | 0.0808983i | \(0.0257789\pi\) |
0.384943 | + | 0.922940i | \(0.374221\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.6892 | − | 39.0535i | −0.625914 | − | 1.92637i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.882642 | − | 0.641277i | 0.0434320 | − | 0.0315552i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.450599 | − | 1.38680i | 0.0221190 | − | 0.0680753i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 43.4789 | 2.12917 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.32141 | −0.357674 | −0.178837 | − | 0.983879i | \(-0.557233\pi\) | ||||
−0.178837 | + | 0.983879i | \(0.557233\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.1601 | − | 31.2694i | 0.495171 | − | 1.52398i | −0.321519 | − | 0.946903i | \(-0.604194\pi\) |
0.816690 | − | 0.577076i | \(-0.195806\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.15309 | − | 4.47048i | 0.299174 | − | 0.217362i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.15048 | − | 6.61849i | −0.104313 | − | 0.321044i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.17239 | + | 1.57833i | 0.105129 | + | 0.0763810i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 55.5831 | − | 7.30268i | 2.68358 | − | 0.352577i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.21992 | + | 3.06595i | 0.203267 | + | 0.147682i | 0.684762 | − | 0.728767i | \(-0.259906\pi\) |
−0.481495 | + | 0.876449i | \(0.659906\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.40789 | + | 10.4884i | 0.163773 | + | 0.504041i | 0.998944 | − | 0.0459495i | \(-0.0146313\pi\) |
−0.835171 | + | 0.549990i | \(0.814631\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.30688 | + | 6.76184i | −0.446231 | + | 0.324206i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.99234 | + | 30.7533i | −0.477998 | + | 1.47113i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.5808 | 1.07772 | 0.538862 | − | 0.842394i | \(-0.318855\pi\) | ||||
0.538862 | + | 0.842394i | \(0.318855\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −43.1968 | −2.05699 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.9139 | + | 33.5895i | −0.518534 | + | 1.59589i | 0.258223 | + | 0.966085i | \(0.416863\pi\) |
−0.776758 | + | 0.629800i | \(0.783137\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.78180 | − | 2.02110i | 0.131870 | − | 0.0958091i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.60607 | − | 29.5644i | −0.454351 | − | 1.39835i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.9820 | − | 21.7832i | −1.41494 | − | 1.02801i | −0.992581 | − | 0.121584i | \(-0.961203\pi\) |
−0.422358 | − | 0.906429i | \(-0.638797\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.56912 | + | 3.38517i | −0.168063 | + | 0.159401i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.8179 | − | 7.85967i | −0.508269 | − | 0.369279i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.07847 | − | 3.31919i | −0.0505595 | − | 0.155606i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.285580 | + | 0.207486i | −0.0133589 | + | 0.00970579i | −0.594445 | − | 0.804137i | \(-0.702628\pi\) |
0.581086 | + | 0.813842i | \(0.302628\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.7847 | − | 36.2694i | 0.550061 | − | 1.69291i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.2449 | 0.570303 | 0.285151 | − | 0.958482i | \(-0.407956\pi\) | ||||
0.285151 | + | 0.958482i | \(0.407956\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.9578 | 0.973992 | 0.486996 | − | 0.873404i | \(-0.338093\pi\) | ||||
0.486996 | + | 0.873404i | \(0.338093\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.79479 | − | 17.8345i | 0.268727 | − | 0.827057i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.9281 | + | 17.3848i | −1.10726 | + | 0.804473i | −0.982230 | − | 0.187680i | \(-0.939903\pi\) |
−0.125031 | + | 0.992153i | \(0.539903\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.128031 | + | 0.394039i | 0.00591193 | + | 0.0181951i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −54.6740 | − | 39.7230i | −2.51924 | − | 1.83034i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.4525 | − | 6.22214i | −0.526588 | − | 0.286094i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.81904 | + | 4.95433i | 0.312879 | + | 0.227320i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.3892 | + | 47.3630i | 0.704621 | + | 2.16860i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.71340 | − | 3.42449i | 0.215361 | − | 0.156469i | −0.474875 | − | 0.880053i | \(-0.657507\pi\) |
0.690236 | + | 0.723584i | \(0.257507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.98385 | − | 9.18336i | 0.136052 | − | 0.418725i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.53204 | −0.342720 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.8872 | −0.766808 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.56462 | − | 29.4369i | 0.433414 | − | 1.33391i | −0.461288 | − | 0.887250i | \(-0.652613\pi\) |
0.894703 | − | 0.446662i | \(-0.147387\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −48.6328 | + | 35.3338i | −2.19925 | + | 1.59785i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.30431 | + | 10.1696i | 0.149122 | + | 0.458949i | 0.997518 | − | 0.0704125i | \(-0.0224316\pi\) |
−0.848396 | + | 0.529361i | \(0.822432\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.53655 | − | 4.74908i | −0.294391 | − | 0.213888i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 32.6248 | + | 17.7250i | 1.46637 | + | 0.796679i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.676818 | + | 0.491737i | 0.0303595 | + | 0.0220574i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.93548 | + | 24.4229i | 0.355241 | + | 1.09332i | 0.955870 | + | 0.293791i | \(0.0949169\pi\) |
−0.600629 | + | 0.799528i | \(0.705083\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.43753 | − | 1.77097i | 0.108901 | − | 0.0791210i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.33277 | + | 16.4126i | −0.237777 | + | 0.731801i | 0.758964 | + | 0.651132i | \(0.225706\pi\) |
−0.996741 | + | 0.0806690i | \(0.974294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.6674 | −1.14218 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 54.1666 | 2.40562 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.7918 | − | 33.2137i | 0.478337 | − | 1.47217i | −0.363067 | − | 0.931763i | \(-0.618270\pi\) |
0.841404 | − | 0.540407i | \(-0.181730\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.11517 | + | 0.810218i | −0.0493322 | + | 0.0358419i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.2735 | + | 43.9293i | 0.630190 | + | 1.93953i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.5688 | − | 8.40526i | −0.509784 | − | 0.370380i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.91304 | + | 2.76291i | −0.128116 | + | 0.121513i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 43.1350 | + | 31.3394i | 1.89342 | + | 1.37565i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.46282 | − | 7.57979i | −0.107898 | − | 0.332076i | 0.882502 | − | 0.470310i | \(-0.155858\pi\) |
−0.990400 | + | 0.138233i | \(0.955858\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.4741 | + | 13.4223i | −0.807818 | + | 0.586914i | −0.913197 | − | 0.407518i | \(-0.866394\pi\) |
0.105379 | + | 0.994432i | \(0.466394\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.606703 | + | 1.86724i | −0.0264787 | + | 0.0814931i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.1704 | 0.573713 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 26.0293 | 1.13171 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.99958 | + | 18.4648i | −0.260360 | + | 0.801305i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.65692 | + | 4.83654i | −0.288343 | + | 0.209494i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.51882 | + | 7.75215i | 0.108898 | + | 0.335154i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.02991 | + | 5.10753i | 0.303363 | + | 0.220406i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.6087 | − | 2.97040i | 0.973824 | − | 0.127944i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.3265 | − | 23.4866i | −1.38983 | − | 1.00977i | −0.995885 | − | 0.0906312i | \(-0.971112\pi\) |
−0.393941 | − | 0.919136i | \(-0.628888\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.97958 | − | 6.09251i | −0.0849517 | − | 0.261455i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.7804 | − | 21.6367i | 1.27565 | − | 0.926816i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.14156 | + | 15.8241i | −0.219837 | + | 0.676590i | 0.778937 | + | 0.627102i | \(0.215759\pi\) |
−0.998775 | + | 0.0494881i | \(0.984241\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −47.7850 | −2.03942 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.78598 | 0.416897 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.448330 | − | 1.37982i | 0.0190649 | − | 0.0586758i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.64416 | − | 5.55381i | 0.324476 | − | 0.235746i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.10617 | − | 18.7929i | −0.258727 | − | 0.796280i | −0.993072 | − | 0.117504i | \(-0.962511\pi\) |
0.734346 | − | 0.678776i | \(-0.237489\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.6380 | − | 12.8148i | −0.746008 | − | 0.542006i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.03127 | + | 37.8814i | −0.296860 | + | 1.59935i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.6319 | − | 14.2634i | −0.827385 | − | 0.601130i | 0.0914334 | − | 0.995811i | \(-0.470855\pi\) |
−0.918818 | + | 0.394681i | \(0.870855\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.84816 | + | 14.9211i | 0.203964 | + | 0.627736i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.32061 | + | 2.41256i | −0.139452 | + | 0.101318i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.79195 | + | 27.0588i | −0.368578 | + | 1.13437i | 0.579133 | + | 0.815233i | \(0.303391\pi\) |
−0.947710 | + | 0.319132i | \(0.896609\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.9485 | −1.12776 | −0.563879 | − | 0.825858i | \(-0.690692\pi\) | ||||
−0.563879 | + | 0.825858i | \(0.690692\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −52.1644 | −2.17920 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.94929 | − | 12.1547i | 0.164697 | − | 0.506884i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.80048 | + | 6.39392i | −0.366369 | + | 0.266183i | −0.755704 | − | 0.654914i | \(-0.772705\pi\) |
0.389335 | + | 0.921096i | \(0.372705\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.9514 | + | 58.3264i | 0.787594 | + | 2.42396i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.233750 | − | 0.169829i | −0.00969757 | − | 0.00704570i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.3114 | − | 23.7310i | −0.468470 | − | 0.982837i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 50.2453 | + | 36.5053i | 2.07739 | + | 1.50931i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.35893 | − | 25.7261i | −0.345010 | − | 1.06183i | −0.961579 | − | 0.274530i | \(-0.911478\pi\) |
0.616569 | − | 0.787301i | \(-0.288522\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.9054 | + | 9.37631i | −0.531757 | + | 0.386344i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.8243 | − | 36.3914i | 0.486387 | − | 1.49694i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.72088 | 0.275993 | 0.137997 | − | 0.990433i | \(-0.455934\pi\) | ||||
0.137997 | + | 0.990433i | \(0.455934\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.39854 | 0.0983306 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.13486 | + | 9.64809i | −0.128301 | + | 0.394870i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.6797 | + | 16.4777i | −0.926666 | + | 0.673262i | −0.945174 | − | 0.326566i | \(-0.894108\pi\) |
0.0185083 | + | 0.999829i | \(0.494108\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.29192 | − | 16.2868i | −0.215862 | − | 0.664354i | −0.999091 | − | 0.0426217i | \(-0.986429\pi\) |
0.783229 | − | 0.621733i | \(-0.213571\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.96489 | − | 4.33375i | −0.242909 | − | 0.176484i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.2943 | − | 7.03363i | −0.743767 | − | 0.285958i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.3423 | − | 22.0450i | −1.23156 | − | 0.894777i | −0.234550 | − | 0.972104i | \(-0.575362\pi\) |
−0.997006 | + | 0.0773268i | \(0.975362\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.704392 | + | 2.16790i | 0.0285434 | + | 0.0878476i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.43325 | + | 3.94749i | −0.219806 | + | 0.159698i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.22609 | − | 25.3173i | 0.332249 | − | 1.02256i | −0.635813 | − | 0.771843i | \(-0.719335\pi\) |
0.968061 | − | 0.250713i | \(-0.0806650\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.05179 | −0.324680 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.8616 | 0.558047 | 0.279024 | − | 0.960284i | \(-0.409989\pi\) | ||||
0.279024 | + | 0.960284i | \(0.409989\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.53801 | − | 7.81120i | 0.102011 | − | 0.313959i | −0.887006 | − | 0.461758i | \(-0.847219\pi\) |
0.989017 | + | 0.147799i | \(0.0472189\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 56.6599 | − | 41.1659i | 2.27369 | − | 1.65193i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.210541 | − | 0.647978i | −0.00843514 | − | 0.0259607i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.1473 | + | 7.37242i | 0.405891 | + | 0.294897i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.0788 | − | 42.1247i | −0.801869 | − | 1.68230i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.36876 | + | 3.90064i | 0.214067 | + | 0.155529i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.1950 | + | 37.5323i | 0.485475 | + | 1.49414i | 0.831292 | + | 0.555836i | \(0.187602\pi\) |
−0.345817 | + | 0.938302i | \(0.612398\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 59.3900 | − | 43.1494i | 2.36054 | − | 1.71503i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.79679 | − | 30.1514i | 0.388774 | − | 1.19652i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38.1432 | 1.51129 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.8876 | −0.588946 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.1686 | + | 34.3735i | −0.441134 | + | 1.35767i | 0.445534 | + | 0.895265i | \(0.353014\pi\) |
−0.886668 | + | 0.462406i | \(0.846986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.4047 | − | 14.0983i | 0.765245 | − | 0.555983i | −0.135270 | − | 0.990809i | \(-0.543190\pi\) |
0.900515 | + | 0.434826i | \(0.143190\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.59251 | − | 20.2896i | −0.259580 | − | 0.798904i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.6307 | + | 24.4341i | 1.32216 | + | 0.960605i | 0.999903 | + | 0.0139526i | \(0.00444138\pi\) |
0.322257 | + | 0.946652i | \(0.395559\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.87039 | − | 10.0768i | 0.0734192 | − | 0.395550i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.00607 | − | 2.18404i | −0.117817 | − | 0.0855992i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.28600 | + | 28.5794i | 0.363389 | + | 1.11840i | 0.950984 | + | 0.309241i | \(0.100075\pi\) |
−0.587594 | + | 0.809156i | \(0.699925\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.4639 | + | 19.2272i | −1.03403 | + | 0.751267i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.58014 | − | 23.3293i | 0.295730 | − | 0.910162i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.2450 | 0.983405 | 0.491702 | − | 0.870763i | \(-0.336375\pi\) | ||||
0.491702 | + | 0.870763i | \(0.336375\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.51852 | 0.370227 | 0.185114 | − | 0.982717i | \(-0.440735\pi\) | ||||
0.185114 | + | 0.982717i | \(0.440735\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.9154 | + | 61.2933i | −0.773450 | + | 2.38044i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.35027 | + | 1.70757i | −0.0911396 | + | 0.0662168i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.58519 | − | 14.1118i | −0.177539 | − | 0.546410i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.30446 | − | 0.947747i | −0.0504334 | − | 0.0366420i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.0101 | − | 3.28591i | 0.965505 | − | 0.126851i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.13567 | − | 6.63745i | −0.352154 | − | 0.255855i | 0.397618 | − | 0.917551i | \(-0.369837\pi\) |
−0.749772 | + | 0.661696i | \(0.769837\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.64133 | − | 17.3622i | −0.217135 | − | 0.668273i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.7064 | − | 20.8564i | 1.10328 | − | 0.801577i | 0.121684 | − | 0.992569i | \(-0.461170\pi\) |
0.981592 | + | 0.190992i | \(0.0611704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.03401 | + | 3.18236i | −0.0396818 | + | 0.122128i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −38.6332 | −1.48043 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.8947 | 0.952569 | 0.476284 | − | 0.879291i | \(-0.341983\pi\) | ||||
0.476284 | + | 0.879291i | \(0.341983\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.42085 | + | 22.8390i | −0.283536 | + | 0.872635i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.0422 | − | 10.9288i | 0.573895 | − | 0.416959i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.5888 | − | 41.8220i | −0.517692 | − | 1.59329i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.513361 | + | 0.372978i | 0.0195292 | + | 0.0141888i | 0.597507 | − | 0.801864i | \(-0.296158\pi\) |
−0.577978 | + | 0.816052i | \(0.696158\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.33788 | − | 5.06277i | 0.202769 | − | 0.192319i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.5709 | − | 14.9457i | −0.780300 | − | 0.566921i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.74751 | − | 5.37828i | −0.0661916 | − | 0.203717i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.13965 | − | 4.46072i | 0.232223 | − | 0.168720i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.39612 | − | 16.6076i | 0.203809 | − | 0.627259i | −0.795951 | − | 0.605361i | \(-0.793029\pi\) |
0.999760 | − | 0.0218985i | \(-0.00697107\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.03767 | −0.303146 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.57171 | −0.247505 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.57163 | + | 4.83697i | −0.0591071 | + | 0.181913i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.3781 | + | 19.1648i | −0.990651 | + | 0.719750i | −0.960064 | − | 0.279782i | \(-0.909738\pi\) |
−0.0305874 | + | 0.999532i | \(0.509738\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.97828 | + | 24.5546i | 0.299209 | + | 0.920871i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.5678 | + | 14.2168i | 0.732819 | + | 0.532424i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.8080 | − | 15.6514i | −1.07736 | − | 0.585328i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −55.1352 | − | 40.0581i | −2.05906 | − | 1.49600i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.8109 | − | 33.2726i | −0.403180 | − | 1.24086i | −0.922405 | − | 0.386223i | \(-0.873780\pi\) |
0.519226 | − | 0.854637i | \(-0.326220\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.29232 | + | 1.66547i | −0.0853706 | + | 0.0620254i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.6926 | + | 69.8407i | −0.843947 | + | 2.59740i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.86773 | −0.143644 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.2644 | −0.603214 | −0.301607 | − | 0.953432i | \(-0.597523\pi\) | ||||
−0.301607 | + | 0.953432i | \(0.597523\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.67991 | + | 17.4810i | −0.210367 | + | 0.647443i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.1219 | − | 8.80707i | 0.448344 | − | 0.325741i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.9308 | + | 42.8746i | 0.514546 | + | 1.58361i | 0.784106 | + | 0.620627i | \(0.213122\pi\) |
−0.269560 | + | 0.962984i | \(0.586878\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 30.1962 | + | 21.9388i | 1.11380 | + | 0.809225i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.41996 | + | 1.85806i | 0.125976 | + | 0.0684425i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.8506 | + | 8.60999i | 0.435933 | + | 0.316724i | 0.784017 | − | 0.620740i | \(-0.213168\pi\) |
−0.348084 | + | 0.937463i | \(0.613168\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.1214 | − | 74.2380i | −0.886122 | − | 2.72720i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.42499 | + | 2.48840i | −0.125651 | + | 0.0912906i | −0.648836 | − | 0.760929i | \(-0.724744\pi\) |
0.523185 | + | 0.852219i | \(0.324744\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.61777 | + | 17.2897i | −0.205819 | + | 0.633446i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.14168 | 0.188124 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.61511 | 0.0590148 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.05755 | + | 21.7209i | −0.257534 | + | 0.792607i | 0.735786 | + | 0.677214i | \(0.236813\pi\) |
−0.993320 | + | 0.115393i | \(0.963187\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.0844 | − | 12.4125i | 0.622589 | − | 0.452337i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.41649 | + | 7.43721i | 0.0879453 | + | 0.270668i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.0773 | + | 18.2197i | 0.911450 | + | 0.662207i | 0.941381 | − | 0.337345i | \(-0.109529\pi\) |
−0.0299310 | + | 0.999552i | \(0.509529\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −51.3376 | + | 48.6918i | −1.86344 | + | 1.76740i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.3917 | + | 16.9951i | 0.847948 | + | 0.616071i | 0.924580 | − | 0.380989i | \(-0.124416\pi\) |
−0.0766312 | + | 0.997060i | \(0.524416\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.25393 | − | 6.93690i | −0.0815979 | − | 0.251133i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −34.5316 | + | 25.0887i | −1.24849 | + | 0.907082i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.29770 | − | 16.3046i | 0.191289 | − | 0.588726i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.37741 | 0.193914 | 0.0969571 | − | 0.995289i | \(-0.469089\pi\) | ||||
0.0969571 | + | 0.995289i | \(0.469089\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.6440 | −1.60782 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.7820 | − | 42.4167i | 0.495705 | − | 1.52562i | −0.320150 | − | 0.947367i | \(-0.603733\pi\) |
0.815855 | − | 0.578256i | \(-0.196267\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.10062 | − | 3.70581i | 0.183220 | − | 0.133117i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.578549 | − | 1.78059i | −0.0207553 | − | 0.0638784i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.54125 | + | 4.02596i | 0.198536 | + | 0.144245i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.79202 | − | 1.02374i | 0.278820 | − | 0.0366323i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.1473 | − | 12.4582i | −0.612794 | − | 0.445221i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.2130 | + | 37.5879i | 0.435902 | + | 1.34157i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.6779 | − | 24.4684i | 1.20049 | − | 0.872206i | 0.206156 | − | 0.978519i | \(-0.433905\pi\) |
0.994333 | + | 0.106313i | \(0.0339047\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.6422 | + | 66.6078i | −0.770482 | + | 2.37130i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.10871 | 0.110533 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.1947 | 1.49838 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.2971 | − | 40.9244i | 0.471601 | − | 1.45144i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.07959 | − | 2.96400i | 0.144507 | − | 0.104990i | −0.513183 | − | 0.858279i | \(-0.671534\pi\) |
0.657690 | + | 0.753289i | \(0.271534\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.42628 | − | 4.38965i | −0.0504583 | − | 0.155295i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.80897 | + | 7.12663i | 0.346583 | + | 0.251807i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.36313 | + | 12.7315i | −0.0833932 | + | 0.449285i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.56360 | + | 2.58911i | 0.125600 | + | 0.0912540i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.22330 | − | 16.0757i | −0.183869 | − | 0.565891i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.6592 | + | 16.4628i | −0.796654 | + | 0.578803i | −0.909931 | − | 0.414761i | \(-0.863865\pi\) |
0.113277 | + | 0.993563i | \(0.463865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.3208 | + | 31.7642i | −0.362413 | + | 1.11539i | 0.589172 | + | 0.808008i | \(0.299454\pi\) |
−0.951585 | + | 0.307386i | \(0.900546\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −41.2396 | −1.44634 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 35.1552 | 1.23143 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.60801 | + | 17.2597i | −0.196199 | + | 0.603839i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.95591 | − | 7.23339i | 0.347888 | − | 0.252755i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.37955 | + | 28.8673i | 0.327349 | + | 1.00748i | 0.970369 | + | 0.241627i | \(0.0776809\pi\) |
−0.643021 | + | 0.765849i | \(0.722319\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.46823 | − | 3.97290i | −0.190610 | − | 0.138487i | 0.488387 | − | 0.872627i | \(-0.337585\pi\) |
−0.678998 | + | 0.734140i | \(0.737585\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.93576 | + | 16.6490i | 0.276288 | + | 0.579645i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.5609 | + | 19.2976i | 0.923614 | + | 0.671045i | 0.944421 | − | 0.328739i | \(-0.106623\pi\) |
−0.0208068 | + | 0.999784i | \(0.506623\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.77520 | + | 14.6966i | 0.165850 | + | 0.510433i | 0.999098 | − | 0.0424663i | \(-0.0135215\pi\) |
−0.833248 | + | 0.552899i | \(0.813522\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.29620 | − | 5.30100i | 0.253103 | − | 0.183890i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.10067 | + | 24.9313i | −0.280672 | + | 0.863819i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.76202 | −0.0609771 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.5499 | 1.19422 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.63951 | − | 26.5897i | 0.298269 | − | 0.917978i | −0.683835 | − | 0.729637i | \(-0.739689\pi\) |
0.982104 | − | 0.188341i | \(-0.0603109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.8286 | − | 14.4063i | 0.683745 | − | 0.496770i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.43869 | − | 25.9716i | −0.290644 | − | 0.894510i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.6275 | − | 18.6195i | −0.881614 | − | 0.640530i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.44564 | + | 3.01685i | −0.0840333 | + | 0.103660i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −44.4683 | − | 32.3081i | −1.52615 | − | 1.10881i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.76602 | + | 11.5906i | 0.129098 | + | 0.397321i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.3899 | + | 8.27524i | −0.389983 | + | 0.283339i | −0.765448 | − | 0.643497i | \(-0.777483\pi\) |
0.375466 | + | 0.926836i | \(0.377483\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.9755 | − | 49.1675i | 0.546351 | − | 1.68149i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.4776 | 0.904457 | 0.452228 | − | 0.891902i | \(-0.350629\pi\) | ||||
0.452228 | + | 0.891902i | \(0.350629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.5614 | −1.62277 | −0.811387 | − | 0.584510i | \(-0.801287\pi\) | ||||
−0.811387 | + | 0.584510i | \(0.801287\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.493016 | + | 1.51735i | −0.0168019 | + | 0.0517110i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.1250 | + | 25.5198i | −1.19567 | + | 0.868704i | −0.993852 | − | 0.110720i | \(-0.964684\pi\) |
−0.201817 | + | 0.979423i | \(0.564684\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.63547 | − | 29.6549i | −0.327616 | − | 1.00830i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.06997 | + | 4.41009i | 0.206147 | + | 0.149775i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.86422 | − | 12.3030i | −0.198930 | − | 0.417350i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.26707 | + | 3.82675i | 0.178468 | + | 0.129664i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.4008 | − | 56.6319i | −0.622774 | − | 1.91670i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.47357 | − | 2.52370i | 0.117428 | − | 0.0853165i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.05884 | − | 12.4918i | 0.137057 | − | 0.421819i | −0.858847 | − | 0.512232i | \(-0.828819\pi\) |
0.995904 | + | 0.0904129i | \(0.0288187\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 84.2128 | 2.84043 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.3388 | −1.22429 | −0.612143 | − | 0.790747i | \(-0.709692\pi\) | ||||
−0.612143 | + | 0.790747i | \(0.709692\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.3944 | − | 31.9907i | 0.349800 | − | 1.07657i | −0.609163 | − | 0.793045i | \(-0.708495\pi\) |
0.958964 | − | 0.283529i | \(-0.0915054\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.5719 | − | 9.86053i | 0.456213 | − | 0.331458i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.8199 | − | 33.3001i | −0.363295 | − | 1.11811i | −0.951042 | − | 0.309062i | \(-0.899985\pi\) |
0.587747 | − | 0.809045i | \(-0.300015\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.08212 | − | 3.69238i | −0.170449 | − | 0.123838i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.03663 | + | 37.9102i | −0.235736 | + | 1.27004i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.52266 | + | 3.28591i | 0.151345 | + | 0.109959i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.57034 | − | 4.83299i | −0.0524905 | − | 0.161549i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −95.7521 | + | 69.5680i | −3.19707 | + | 2.32281i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.26196 | − | 6.96161i | 0.0754407 | − | 0.232183i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.2218 | 1.00683 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.22721 | −0.140673 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.15768 | + | 3.56299i | −0.0384827 | + | 0.118438i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.9407 | + | 30.4717i | −1.39262 | + | 1.01180i | −0.397046 | + | 0.917799i | \(0.629965\pi\) |
−0.995572 | + | 0.0939979i | \(0.970035\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.9680 | − | 86.0766i | −0.927639 | − | 2.85498i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.9715 | + | 17.4163i | 0.794212 | + | 0.577029i | 0.909210 | − | 0.416337i | \(-0.136686\pi\) |
−0.114998 | + | 0.993366i | \(0.536686\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.69109 | + | 0.353564i | −0.0890622 | + | 0.0117013i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 33.4035 | + | 24.2691i | 1.10429 | + | 0.802312i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.00293 | + | 6.16437i | 0.0661424 | + | 0.203566i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.3567 | − | 17.6962i | 0.803454 | − | 0.583743i | −0.108472 | − | 0.994100i | \(-0.534596\pi\) |
0.911925 | + | 0.410356i | \(0.134596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.623433 | − | 1.91873i | 0.0205428 | − | 0.0632243i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.1460 | 0.432704 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.17674 | 0.104451 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.5816 | − | 47.9553i | 0.511767 | − | 1.57506i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.3186 | − | 30.0197i | 1.35562 | − | 0.984914i | 0.356908 | − | 0.934140i | \(-0.383831\pi\) |
0.998710 | − | 0.0507745i | \(-0.0161690\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.81148 | − | 30.1966i | −0.321558 | − | 0.989654i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.2164 | + | 23.4066i | 1.05472 | + | 0.766298i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.3482 | − | 15.5056i | 0.534644 | − | 0.507089i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.75635 | + | 4.90878i | 0.220720 | + | 0.160363i | 0.692651 | − | 0.721273i | \(-0.256443\pi\) |
−0.471931 | + | 0.881636i | \(0.656443\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.6539 | + | 57.4107i | 0.608746 | + | 1.87353i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.1964 | + | 31.3840i | −1.40816 | + | 1.02309i | −0.414576 | + | 0.910015i | \(0.636070\pi\) |
−0.993586 | + | 0.113075i | \(0.963930\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.20925 | − | 9.87705i | 0.104508 | − | 0.321641i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.29208 | 0.204681 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.2532 | −0.625646 | −0.312823 | − | 0.949811i | \(-0.601275\pi\) | ||||
−0.312823 | + | 0.949811i | \(0.601275\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.69335 | + | 20.6000i | −0.217275 | + | 0.668705i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.6548 | − | 35.3498i | 1.57774 | − | 1.14630i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.3253 | − | 34.8556i | −0.366862 | − | 1.12908i | −0.948807 | − | 0.315857i | \(-0.897708\pi\) |
0.581945 | − | 0.813228i | \(-0.302292\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.6803 | + | 17.9313i | 0.798634 | + | 0.580242i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.8157 | + | 10.2225i | 0.608225 | + | 0.330448i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.84960 | + | 2.79689i | 0.124310 | + | 0.0903164i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.89234 | − | 18.1348i | −0.190076 | − | 0.584993i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.2526 | + | 16.8940i | −0.749303 | + | 0.544401i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.0831 | − | 34.1101i | 0.356776 | − | 1.09804i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.6501 | −1.46801 | −0.734004 | − | 0.679146i | \(-0.762351\pi\) | ||||
−0.734004 | + | 0.679146i | \(0.762351\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 53.6465 | 1.72337 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.2715 | − | 43.9232i | 0.457995 | − | 1.40956i | −0.409588 | − | 0.912270i | \(-0.634328\pi\) |
0.867583 | − | 0.497292i | \(-0.165672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.07605 | + | 2.96143i | −0.130672 | + | 0.0949390i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.53354 | + | 29.3412i | 0.305318 | + | 0.939671i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.1572 | − | 31.3555i | −1.38072 | − | 1.00315i | −0.996812 | − | 0.0797806i | \(-0.974578\pi\) |
−0.383908 | − | 0.923371i | \(-0.625422\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.62395 | − | 3.05549i | −0.179742 | − | 0.0976538i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 105.009 | + | 76.2938i | 3.35269 | + | 2.43587i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.73470 | + | 11.4942i | 0.119118 | + | 0.366609i | 0.992784 | − | 0.119919i | \(-0.0382634\pi\) |
−0.873665 | + | 0.486527i | \(0.838263\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.1038 | + | 13.1532i | −0.576834 | + | 0.419094i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.402390 | + | 1.23843i | −0.0128082 | + | 0.0394196i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.5167 | 0.874981 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.0620 | −1.14555 | −0.572774 | − | 0.819714i | \(-0.694133\pi\) | ||||
−0.572774 | + | 0.819714i | \(0.694133\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.8525 | − | 61.0998i | 0.630001 | − | 1.93894i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.79967 | − | 3.48716i | 0.152160 | − | 0.110550i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.88069 | − | 8.86586i | −0.0912325 | − | 0.280785i | 0.895021 | − | 0.446024i | \(-0.147160\pi\) |
−0.986254 | + | 0.165239i | \(0.947160\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.0838 | + | 10.2325i | 0.445593 | + | 0.323742i |
(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 | 88.2.i.b.81.2 | yes | 8 | |
3.2 | odd | 2 | 792.2.r.g.433.2 | 8 | |||
4.3 | odd | 2 | 176.2.m.d.81.1 | 8 | |||
8.3 | odd | 2 | 704.2.m.i.257.2 | 8 | |||
8.5 | even | 2 | 704.2.m.l.257.1 | 8 | |||
11.2 | odd | 10 | 968.2.i.t.753.1 | 8 | |||
11.3 | even | 5 | inner | 88.2.i.b.25.2 | ✓ | 8 | |
11.4 | even | 5 | 968.2.i.s.9.1 | 8 | |||
11.5 | even | 5 | 968.2.a.n.1.4 | 4 | |||
11.6 | odd | 10 | 968.2.a.m.1.4 | 4 | |||
11.7 | odd | 10 | 968.2.i.t.9.1 | 8 | |||
11.8 | odd | 10 | 968.2.i.p.729.2 | 8 | |||
11.9 | even | 5 | 968.2.i.s.753.1 | 8 | |||
11.10 | odd | 2 | 968.2.i.p.81.2 | 8 | |||
33.5 | odd | 10 | 8712.2.a.ce.1.2 | 4 | |||
33.14 | odd | 10 | 792.2.r.g.289.2 | 8 | |||
33.17 | even | 10 | 8712.2.a.cd.1.2 | 4 | |||
44.3 | odd | 10 | 176.2.m.d.113.1 | 8 | |||
44.27 | odd | 10 | 1936.2.a.bb.1.1 | 4 | |||
44.39 | even | 10 | 1936.2.a.bc.1.1 | 4 | |||
88.3 | odd | 10 | 704.2.m.i.641.2 | 8 | |||
88.5 | even | 10 | 7744.2.a.di.1.1 | 4 | |||
88.27 | odd | 10 | 7744.2.a.dr.1.4 | 4 | |||
88.61 | odd | 10 | 7744.2.a.dh.1.1 | 4 | |||
88.69 | even | 10 | 704.2.m.l.641.1 | 8 | |||
88.83 | even | 10 | 7744.2.a.ds.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
88.2.i.b.25.2 | ✓ | 8 | 11.3 | even | 5 | inner | |
88.2.i.b.81.2 | yes | 8 | 1.1 | even | 1 | trivial | |
176.2.m.d.81.1 | 8 | 4.3 | odd | 2 | |||
176.2.m.d.113.1 | 8 | 44.3 | odd | 10 | |||
704.2.m.i.257.2 | 8 | 8.3 | odd | 2 | |||
704.2.m.i.641.2 | 8 | 88.3 | odd | 10 | |||
704.2.m.l.257.1 | 8 | 8.5 | even | 2 | |||
704.2.m.l.641.1 | 8 | 88.69 | even | 10 | |||
792.2.r.g.289.2 | 8 | 33.14 | odd | 10 | |||
792.2.r.g.433.2 | 8 | 3.2 | odd | 2 | |||
968.2.a.m.1.4 | 4 | 11.6 | odd | 10 | |||
968.2.a.n.1.4 | 4 | 11.5 | even | 5 | |||
968.2.i.p.81.2 | 8 | 11.10 | odd | 2 | |||
968.2.i.p.729.2 | 8 | 11.8 | odd | 10 | |||
968.2.i.s.9.1 | 8 | 11.4 | even | 5 | |||
968.2.i.s.753.1 | 8 | 11.9 | even | 5 | |||
968.2.i.t.9.1 | 8 | 11.7 | odd | 10 | |||
968.2.i.t.753.1 | 8 | 11.2 | odd | 10 | |||
1936.2.a.bb.1.1 | 4 | 44.27 | odd | 10 | |||
1936.2.a.bc.1.1 | 4 | 44.39 | even | 10 | |||
7744.2.a.dh.1.1 | 4 | 88.61 | odd | 10 | |||
7744.2.a.di.1.1 | 4 | 88.5 | even | 10 | |||
7744.2.a.dr.1.4 | 4 | 88.27 | odd | 10 | |||
7744.2.a.ds.1.4 | 4 | 88.83 | even | 10 | |||
8712.2.a.cd.1.2 | 4 | 33.17 | even | 10 | |||
8712.2.a.ce.1.2 | 4 | 33.5 | odd | 10 |