Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(379,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.e (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: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.18 | ||
Character | \(\chi\) | \(=\) | 1368.379 |
Dual form | 1368.2.e.f.379.20 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.26128 | − | 0.639662i | 0.891861 | − | 0.452310i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.18166 | − | 1.61359i | 0.590832 | − | 0.806795i | ||||
\(5\) | 1.96435i | 0.878483i | 0.898369 | + | 0.439242i | \(0.144753\pi\) | ||||
−0.898369 | + | 0.439242i | \(0.855247\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.25539i | − | 0.474491i | −0.971450 | − | 0.237245i | \(-0.923755\pi\) | ||
0.971450 | − | 0.237245i | \(-0.0762446\pi\) | |||||||
\(8\) | 0.458259 | − | 2.79106i | 0.162019 | − | 0.986788i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.25652 | + | 2.47760i | 0.397346 | + | 0.783485i | ||||
\(11\) | 3.11106 | 0.938020 | 0.469010 | − | 0.883193i | \(-0.344611\pi\) | ||||
0.469010 | + | 0.883193i | \(0.344611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.401637 | 0.111394 | 0.0556970 | − | 0.998448i | \(-0.482262\pi\) | ||||
0.0556970 | + | 0.998448i | \(0.482262\pi\) | |||||||
\(14\) | −0.803023 | − | 1.58339i | −0.214617 | − | 0.423180i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.20734 | − | 3.81344i | −0.301835 | − | 0.953360i | ||||
\(17\) | 4.88644 | 1.18514 | 0.592568 | − | 0.805520i | \(-0.298114\pi\) | ||||
0.592568 | + | 0.805520i | \(0.298114\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50466 | + | 3.56744i | −0.574609 | + | 0.818428i | ||||
\(20\) | 3.16965 | + | 2.32120i | 0.708755 | + | 0.519036i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.92392 | − | 1.99003i | 0.836583 | − | 0.424275i | ||||
\(23\) | − | 3.34225i | − | 0.696907i | −0.937326 | − | 0.348454i | \(-0.886707\pi\) | ||
0.937326 | − | 0.348454i | \(-0.113293\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.14134 | 0.228267 | ||||||||
\(26\) | 0.506577 | − | 0.256912i | 0.0993479 | − | 0.0503846i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.02568 | − | 1.48344i | −0.382817 | − | 0.280344i | ||||
\(29\) | 3.79561 | 0.704827 | 0.352414 | − | 0.935844i | \(-0.385361\pi\) | ||||
0.352414 | + | 0.935844i | \(0.385361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.06495 | −0.370876 | −0.185438 | − | 0.982656i | \(-0.559370\pi\) | ||||
−0.185438 | + | 0.982656i | \(0.559370\pi\) | |||||||
\(32\) | −3.96211 | − | 4.03753i | −0.700409 | − | 0.713742i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.16318 | − | 3.12567i | 1.05698 | − | 0.536049i | ||||
\(35\) | 2.46601 | 0.416832 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.55353 | −0.255398 | −0.127699 | − | 0.991813i | \(-0.540759\pi\) | ||||
−0.127699 | + | 0.991813i | \(0.540759\pi\) | |||||||
\(38\) | −0.877128 | + | 6.10169i | −0.142289 | + | 0.989825i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.48261 | + | 0.900181i | 0.866876 | + | 0.142331i | ||||
\(41\) | − | 2.92028i | − | 0.456071i | −0.973653 | − | 0.228035i | \(-0.926770\pi\) | ||
0.973653 | − | 0.228035i | \(-0.0732302\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.08998 | 0.318720 | 0.159360 | − | 0.987221i | \(-0.449057\pi\) | ||||
0.159360 | + | 0.987221i | \(0.449057\pi\) | |||||||
\(44\) | 3.67623 | − | 5.01997i | 0.554212 | − | 0.756789i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.13791 | − | 4.21552i | −0.315218 | − | 0.621545i | ||||
\(47\) | − | 4.59290i | − | 0.669943i | −0.942228 | − | 0.334971i | \(-0.891273\pi\) | ||
0.942228 | − | 0.334971i | \(-0.108727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.42401 | 0.774858 | ||||||||
\(50\) | 1.43955 | − | 0.730070i | 0.203583 | − | 0.103247i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.474600 | − | 0.648077i | 0.0658151 | − | 0.0898720i | ||||
\(53\) | 1.83304 | 0.251787 | 0.125894 | − | 0.992044i | \(-0.459820\pi\) | ||||
0.125894 | + | 0.992044i | \(0.459820\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.11121i | 0.824035i | ||||||||
\(56\) | −3.50385 | − | 0.575292i | −0.468222 | − | 0.0768766i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.78734 | − | 2.42791i | 0.628608 | − | 0.318800i | ||||
\(59\) | − | 7.40388i | − | 0.963903i | −0.876198 | − | 0.481952i | \(-0.839928\pi\) | ||
0.876198 | − | 0.481952i | \(-0.160072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.71150i | 0.219135i | 0.993979 | + | 0.109568i | \(0.0349466\pi\) | ||||
−0.993979 | + | 0.109568i | \(0.965053\pi\) | |||||||
\(62\) | −2.60448 | + | 1.32087i | −0.330770 | + | 0.167751i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.58000 | − | 2.55806i | −0.947500 | − | 0.319757i | ||||
\(65\) | 0.788954i | 0.0978577i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.2314i | 1.24996i | 0.780639 | + | 0.624982i | \(0.214894\pi\) | ||||
−0.780639 | + | 0.624982i | \(0.785106\pi\) | |||||||
\(68\) | 5.77413 | − | 7.88471i | 0.700217 | − | 0.956162i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.11034 | − | 1.57742i | 0.371757 | − | 0.188537i | ||||
\(71\) | −8.84074 | −1.04920 | −0.524601 | − | 0.851348i | \(-0.675786\pi\) | ||||
−0.524601 | + | 0.851348i | \(0.675786\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.14134 | 0.718789 | 0.359395 | − | 0.933186i | \(-0.382983\pi\) | ||||
0.359395 | + | 0.933186i | \(0.382983\pi\) | |||||||
\(74\) | −1.95944 | + | 0.993733i | −0.227780 | + | 0.115519i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.79672 | + | 8.25702i | 0.320805 | + | 0.947145i | ||||
\(77\) | − | 3.90558i | − | 0.445082i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.51739 | 0.170719 | 0.0853597 | − | 0.996350i | \(-0.472796\pi\) | ||||
0.0853597 | + | 0.996350i | \(0.472796\pi\) | |||||||
\(80\) | 7.49093 | − | 2.37164i | 0.837511 | − | 0.265157i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.86799 | − | 3.68330i | −0.206285 | − | 0.406752i | ||||
\(83\) | 3.55077 | 0.389747 | 0.194874 | − | 0.980828i | \(-0.437570\pi\) | ||||
0.194874 | + | 0.980828i | \(0.437570\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.59867i | 1.04112i | ||||||||
\(86\) | 2.63606 | − | 1.33688i | 0.284254 | − | 0.144160i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.42567 | − | 8.68315i | 0.151977 | − | 0.925626i | ||||
\(89\) | − | 5.11730i | − | 0.542433i | −0.962518 | − | 0.271216i | \(-0.912574\pi\) | ||
0.962518 | − | 0.271216i | \(-0.0874259\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.504209i | − | 0.0528554i | ||||||
\(92\) | −5.39302 | − | 3.94942i | −0.562261 | − | 0.411755i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.93790 | − | 5.79294i | −0.303022 | − | 0.597496i | ||||
\(95\) | −7.00770 | − | 4.92003i | −0.718975 | − | 0.504785i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.40618i | 0.955053i | 0.878617 | + | 0.477526i | \(0.158467\pi\) | ||||
−0.878617 | + | 0.477526i | \(0.841533\pi\) | |||||||
\(98\) | 6.84120 | − | 3.46953i | 0.691066 | − | 0.350476i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.34868 | − | 1.84165i | 0.134868 | − | 0.184165i | ||||
\(101\) | 13.2549i | 1.31892i | 0.751742 | + | 0.659458i | \(0.229214\pi\) | ||||
−0.751742 | + | 0.659458i | \(0.770786\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.49863 | −0.837395 | −0.418697 | − | 0.908126i | \(-0.637513\pi\) | ||||
−0.418697 | + | 0.908126i | \(0.637513\pi\) | |||||||
\(104\) | 0.184054 | − | 1.12099i | 0.0180480 | − | 0.109922i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.31198 | − | 1.17252i | 0.224559 | − | 0.113886i | ||||
\(107\) | − | 4.91093i | − | 0.474757i | −0.971417 | − | 0.237379i | \(-0.923712\pi\) | ||
0.971417 | − | 0.237379i | \(-0.0762882\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.1902 | −1.55074 | −0.775372 | − | 0.631505i | \(-0.782438\pi\) | ||||
−0.775372 | + | 0.631505i | \(0.782438\pi\) | |||||||
\(110\) | 3.90911 | + | 7.70795i | 0.372719 | + | 0.734924i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.78734 | + | 1.51568i | −0.452361 | + | 0.143218i | ||||
\(113\) | 8.17825i | 0.769345i | 0.923053 | + | 0.384673i | \(0.125686\pi\) | ||||
−0.923053 | + | 0.384673i | \(0.874314\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.56534 | 0.612222 | ||||||||
\(116\) | 4.48514 | − | 6.12456i | 0.416435 | − | 0.568651i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.73599 | − | 9.33838i | −0.435983 | − | 0.859668i | ||||
\(119\) | − | 6.13437i | − | 0.562337i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.32131 | −0.120119 | ||||||||
\(122\) | 1.09478 | + | 2.15869i | 0.0991170 | + | 0.195438i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.44008 | + | 3.33198i | −0.219125 | + | 0.299221i | ||||
\(125\) | 12.0637i | 1.07901i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.7826 | −1.31175 | −0.655873 | − | 0.754871i | \(-0.727700\pi\) | ||||
−0.655873 | + | 0.754871i | \(0.727700\pi\) | |||||||
\(128\) | −11.1968 | + | 1.62221i | −0.989667 | + | 0.143384i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.504664 | + | 0.995094i | 0.0442620 | + | 0.0872755i | ||||
\(131\) | 15.7897 | 1.37955 | 0.689775 | − | 0.724024i | \(-0.257710\pi\) | ||||
0.689775 | + | 0.724024i | \(0.257710\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.47852 | + | 3.14432i | 0.388337 | + | 0.272647i | ||||
\(134\) | 6.54464 | + | 12.9047i | 0.565371 | + | 1.11479i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.23926 | − | 13.6383i | 0.192015 | − | 1.16948i | ||||
\(137\) | −14.0143 | −1.19732 | −0.598660 | − | 0.801003i | \(-0.704300\pi\) | ||||
−0.598660 | + | 0.801003i | \(0.704300\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.37266 | −0.370884 | −0.185442 | − | 0.982655i | \(-0.559372\pi\) | ||||
−0.185442 | + | 0.982655i | \(0.559372\pi\) | |||||||
\(140\) | 2.91400 | − | 3.97913i | 0.246278 | − | 0.336298i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.1507 | + | 5.65509i | −0.935743 | + | 0.474564i | ||||
\(143\) | 1.24952 | 0.104490 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.45590i | 0.619179i | ||||||||
\(146\) | 7.74596 | − | 3.92838i | 0.641060 | − | 0.325115i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.83575 | + | 2.50676i | −0.150898 | + | 0.206054i | ||||
\(149\) | 6.84807i | 0.561016i | 0.959852 | + | 0.280508i | \(0.0905029\pi\) | ||||
−0.959852 | + | 0.280508i | \(0.909497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3060 | −1.40834 | −0.704171 | − | 0.710031i | \(-0.748681\pi\) | ||||
−0.704171 | + | 0.710031i | \(0.748681\pi\) | |||||||
\(152\) | 8.80915 | + | 8.62548i | 0.714517 | + | 0.699618i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.49825 | − | 4.92604i | −0.201315 | − | 0.396951i | ||||
\(155\) | − | 4.05628i | − | 0.325808i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.8209i | 1.10303i | 0.834164 | + | 0.551516i | \(0.185950\pi\) | ||||
−0.834164 | + | 0.551516i | \(0.814050\pi\) | |||||||
\(158\) | 1.91385 | − | 0.970615i | 0.152258 | − | 0.0772180i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.93112 | − | 7.78296i | 0.627010 | − | 0.615297i | ||||
\(161\) | −4.19581 | −0.330676 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.27334 | 0.0997360 | 0.0498680 | − | 0.998756i | \(-0.484120\pi\) | ||||
0.0498680 | + | 0.998756i | \(0.484120\pi\) | |||||||
\(164\) | −4.71213 | − | 3.45079i | −0.367956 | − | 0.269461i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.47852 | − | 2.27129i | 0.347600 | − | 0.176286i | ||||
\(167\) | −8.84074 | −0.684117 | −0.342058 | − | 0.939679i | \(-0.611124\pi\) | ||||
−0.342058 | + | 0.939679i | \(0.611124\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8387 | −0.987591 | ||||||||
\(170\) | 6.13991 | + | 12.1066i | 0.470910 | + | 0.928537i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.46966 | − | 3.37238i | 0.188310 | − | 0.257141i | ||||
\(173\) | 15.8484 | 1.20493 | 0.602467 | − | 0.798144i | \(-0.294184\pi\) | ||||
0.602467 | + | 0.798144i | \(0.294184\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.43282i | − | 0.108311i | ||||||
\(176\) | −3.75611 | − | 11.8638i | −0.283127 | − | 0.894271i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.27334 | − | 6.45436i | −0.245347 | − | 0.483774i | ||||
\(179\) | − | 11.5916i | − | 0.866393i | −0.901299 | − | 0.433197i | \(-0.857386\pi\) | ||
0.901299 | − | 0.433197i | \(-0.142614\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.3101 | −1.88128 | −0.940641 | − | 0.339402i | \(-0.889775\pi\) | ||||
−0.940641 | + | 0.339402i | \(0.889775\pi\) | |||||||
\(182\) | −0.322523 | − | 0.635949i | −0.0239070 | − | 0.0471397i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.32841 | − | 1.53162i | −0.687700 | − | 0.112912i | ||||
\(185\) | − | 3.05167i | − | 0.224363i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.2020 | 1.11168 | ||||||||
\(188\) | −7.41105 | − | 5.42726i | −0.540506 | − | 0.395824i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.9858 | − | 1.72299i | −0.869545 | − | 0.124998i | ||||
\(191\) | − | 22.6901i | − | 1.64180i | −0.571073 | − | 0.820899i | \(-0.693473\pi\) | ||
0.571073 | − | 0.820899i | \(-0.306527\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 13.0069i | − | 0.936257i | −0.883660 | − | 0.468129i | \(-0.844928\pi\) | ||
0.883660 | − | 0.468129i | \(-0.155072\pi\) | |||||||
\(194\) | 6.01678 | + | 11.8638i | 0.431980 | + | 0.851774i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.40936 | − | 8.75212i | 0.457811 | − | 0.625151i | ||||
\(197\) | 5.77092i | 0.411161i | 0.978640 | + | 0.205580i | \(0.0659082\pi\) | ||||
−0.978640 | + | 0.205580i | \(0.934092\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.4527i | 1.44986i | 0.688825 | + | 0.724928i | \(0.258127\pi\) | ||||
−0.688825 | + | 0.724928i | \(0.741873\pi\) | |||||||
\(200\) | 0.523028 | − | 3.18553i | 0.0369837 | − | 0.225251i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.47869 | + | 16.7182i | 0.596558 | + | 1.17629i | ||||
\(203\) | − | 4.76495i | − | 0.334434i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.73644 | 0.400651 | ||||||||
\(206\) | −10.7192 | + | 5.43625i | −0.746840 | + | 0.378762i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.484912 | − | 1.53162i | −0.0336226 | − | 0.106199i | ||||
\(209\) | −7.79216 | + | 11.0985i | −0.538995 | + | 0.767702i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 12.1817i | − | 0.838621i | −0.907843 | − | 0.419311i | \(-0.862272\pi\) | ||
0.907843 | − | 0.419311i | \(-0.137728\pi\) | |||||||
\(212\) | 2.16603 | − | 2.95777i | 0.148764 | − | 0.203140i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.14134 | − | 6.19407i | −0.214737 | − | 0.423418i | ||||
\(215\) | 4.10546i | 0.279990i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.59231i | 0.175977i | ||||||||
\(218\) | −20.4205 | + | 10.3563i | −1.38305 | + | 0.701416i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.86097 | + | 7.22139i | 0.664827 | + | 0.486866i | ||||
\(221\) | 1.96257 | 0.132017 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.9834 | 1.47212 | 0.736060 | − | 0.676916i | \(-0.236684\pi\) | ||||
0.736060 | + | 0.676916i | \(0.236684\pi\) | |||||||
\(224\) | −5.06866 | + | 4.97397i | −0.338664 | + | 0.332338i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.23132 | + | 10.3151i | 0.347982 | + | 0.686149i | ||||
\(227\) | 20.9715i | 1.39193i | 0.718077 | + | 0.695964i | \(0.245023\pi\) | ||||
−0.718077 | + | 0.695964i | \(0.754977\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 9.59867i | − | 0.634298i | −0.948376 | − | 0.317149i | \(-0.897274\pi\) | ||
0.948376 | − | 0.317149i | \(-0.102726\pi\) | |||||||
\(230\) | 8.28075 | − | 4.19960i | 0.546016 | − | 0.276914i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.73937 | − | 10.5938i | 0.114196 | − | 0.695515i | ||||
\(233\) | −9.81847 | −0.643229 | −0.321615 | − | 0.946871i | \(-0.604226\pi\) | ||||
−0.321615 | + | 0.946871i | \(0.604226\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.02205 | 0.588533 | ||||||||
\(236\) | −11.9468 | − | 8.74890i | −0.777672 | − | 0.569505i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.92392 | − | 7.73717i | −0.254350 | − | 0.501526i | ||||
\(239\) | 5.71955i | 0.369967i | 0.982742 | + | 0.184983i | \(0.0592232\pi\) | ||||
−0.982742 | + | 0.184983i | \(0.940777\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.8705i | 1.15114i | 0.817752 | + | 0.575570i | \(0.195220\pi\) | ||||
−0.817752 | + | 0.575570i | \(0.804780\pi\) | |||||||
\(242\) | −1.66654 | + | 0.845189i | −0.107129 | + | 0.0543308i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.76166 | + | 2.02242i | 0.176797 | + | 0.129472i | ||||
\(245\) | 10.6546i | 0.680700i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.00597 | + | 1.43282i | −0.0640080 | + | 0.0911679i | ||||
\(248\) | −0.946282 | + | 5.76339i | −0.0600890 | + | 0.365976i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.71671 | + | 15.2158i | 0.488048 | + | 0.962329i | ||||
\(251\) | −6.66183 | −0.420491 | −0.210245 | − | 0.977649i | \(-0.567426\pi\) | ||||
−0.210245 | + | 0.977649i | \(0.567426\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 10.3979i | − | 0.653713i | ||||||
\(254\) | −18.6451 | + | 9.45590i | −1.16990 | + | 0.593316i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.0847 | + | 9.20824i | −0.817791 | + | 0.575515i | ||||
\(257\) | 9.82186i | 0.612671i | 0.951924 | + | 0.306335i | \(0.0991029\pi\) | ||||
−0.951924 | + | 0.306335i | \(0.900897\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.95028i | 0.121184i | ||||||||
\(260\) | 1.27305 | + | 0.932279i | 0.0789511 | + | 0.0578175i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.9152 | − | 10.1001i | 1.23037 | − | 0.623983i | ||||
\(263\) | − | 7.49394i | − | 0.462096i | −0.972942 | − | 0.231048i | \(-0.925784\pi\) | ||
0.972942 | − | 0.231048i | \(-0.0742155\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.60072i | 0.221191i | ||||||||
\(266\) | 7.65997 | + | 1.10113i | 0.469663 | + | 0.0675148i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.5093 | + | 12.0901i | 1.00846 | + | 0.738519i | ||||
\(269\) | 25.9387 | 1.58151 | 0.790755 | − | 0.612133i | \(-0.209688\pi\) | ||||
0.790755 | + | 0.612133i | \(0.209688\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.2753i | 1.23164i | 0.787888 | + | 0.615818i | \(0.211175\pi\) | ||||
−0.787888 | + | 0.615818i | \(0.788825\pi\) | |||||||
\(272\) | −5.89960 | − | 18.6342i | −0.357716 | − | 1.12986i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.6760 | + | 8.96441i | −1.06784 | + | 0.541560i | ||||
\(275\) | 3.55077 | 0.214119 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3.31004i | − | 0.198881i | −0.995044 | − | 0.0994405i | \(-0.968295\pi\) | ||
0.995044 | − | 0.0994405i | \(-0.0317053\pi\) | |||||||
\(278\) | −5.51515 | + | 2.79702i | −0.330777 | + | 0.167754i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.13007 | − | 6.88278i | 0.0675348 | − | 0.411325i | ||||
\(281\) | 31.9439i | 1.90562i | 0.303574 | + | 0.952808i | \(0.401820\pi\) | ||||
−0.303574 | + | 0.952808i | \(0.598180\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.1834 | −0.783669 | −0.391835 | − | 0.920036i | \(-0.628159\pi\) | ||||
−0.391835 | + | 0.920036i | \(0.628159\pi\) | |||||||
\(284\) | −10.4468 | + | 14.2653i | −0.619903 | + | 0.846491i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.57599 | − | 0.799268i | 0.0931903 | − | 0.0472617i | ||||
\(287\) | −3.66607 | −0.216402 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.87732 | 0.404548 | ||||||||
\(290\) | 4.76926 | + | 9.40400i | 0.280061 | + | 0.552222i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.25700 | − | 9.90959i | 0.424684 | − | 0.579915i | ||||
\(293\) | −8.25722 | −0.482392 | −0.241196 | − | 0.970476i | \(-0.577540\pi\) | ||||
−0.241196 | + | 0.970476i | \(0.577540\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.5438 | 0.846773 | ||||||||
\(296\) | −0.711919 | + | 4.33598i | −0.0413794 | + | 0.252024i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.38045 | + | 8.63735i | 0.253753 | + | 0.500348i | ||||
\(299\) | − | 1.34237i | − | 0.0776313i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.62374i | − | 0.151230i | ||||||
\(302\) | −21.8277 | + | 11.0700i | −1.25604 | + | 0.637006i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.6282 | + | 5.24427i | 0.953694 | + | 0.300780i | ||||
\(305\) | −3.36199 | −0.192507 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.3166i | 1.10245i | 0.834355 | + | 0.551227i | \(0.185840\pi\) | ||||
−0.834355 | + | 0.551227i | \(0.814160\pi\) | |||||||
\(308\) | −6.30200 | − | 4.61508i | −0.359090 | − | 0.262969i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.59465 | − | 5.11611i | −0.147366 | − | 0.290576i | ||||
\(311\) | − | 19.7891i | − | 1.12213i | −0.827770 | − | 0.561067i | \(-0.810391\pi\) | ||
0.827770 | − | 0.561067i | \(-0.189609\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.385375 | −0.0217827 | −0.0108913 | − | 0.999941i | \(-0.503467\pi\) | ||||
−0.0108913 | + | 0.999941i | \(0.503467\pi\) | |||||||
\(314\) | 8.84074 | + | 17.4321i | 0.498912 | + | 0.983751i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.79304 | − | 2.44844i | 0.100866 | − | 0.137735i | ||||
\(317\) | 17.8110 | 1.00037 | 0.500183 | − | 0.865920i | \(-0.333266\pi\) | ||||
0.500183 | + | 0.865920i | \(0.333266\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.8084 | 0.661142 | ||||||||
\(320\) | 5.02491 | − | 14.8898i | 0.280901 | − | 0.832363i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.29210 | + | 2.68390i | −0.294917 | + | 0.149568i | ||||
\(323\) | −12.2389 | + | 17.4321i | −0.680991 | + | 0.969949i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.458402 | 0.0254276 | ||||||||
\(326\) | 1.60605 | − | 0.814510i | 0.0889506 | − | 0.0451115i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.15066 | − | 1.33825i | −0.450045 | − | 0.0738922i | ||||
\(329\) | −5.76585 | −0.317882 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.504209i | 0.0277138i | 0.999904 | + | 0.0138569i | \(0.00441093\pi\) | ||||
−0.999904 | + | 0.0138569i | \(0.995589\pi\) | |||||||
\(332\) | 4.19581 | − | 5.72948i | 0.230275 | − | 0.314446i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.1507 | + | 5.65509i | −0.610137 | + | 0.309433i | ||||
\(335\) | −20.0980 | −1.09807 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.81387i | 0.371175i | 0.982628 | + | 0.185588i | \(0.0594189\pi\) | ||||
−0.982628 | + | 0.185588i | \(0.940581\pi\) | |||||||
\(338\) | −16.1932 | + | 8.21243i | −0.880794 | + | 0.446697i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 15.4883 | + | 11.3424i | 0.839972 | + | 0.615129i | ||||
\(341\) | −6.42418 | −0.347889 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.5969i | − | 0.842154i | ||||||
\(344\) | 0.957755 | − | 5.83327i | 0.0516387 | − | 0.314509i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.9894 | − | 10.1377i | 1.07463 | − | 0.545004i | ||||
\(347\) | −6.66183 | −0.357626 | −0.178813 | − | 0.983883i | \(-0.557226\pi\) | ||||
−0.178813 | + | 0.983883i | \(0.557226\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 26.8426i | − | 1.43685i | −0.695603 | − | 0.718426i | \(-0.744863\pi\) | ||
0.695603 | − | 0.718426i | \(-0.255137\pi\) | |||||||
\(350\) | −0.916519 | − | 1.80719i | −0.0489900 | − | 0.0965981i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.3264 | − | 12.5610i | −0.656997 | − | 0.669504i | ||||
\(353\) | −23.8328 | −1.26849 | −0.634245 | − | 0.773132i | \(-0.718689\pi\) | ||||
−0.634245 | + | 0.773132i | \(0.718689\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 17.3663i | − | 0.921707i | ||||||
\(356\) | −8.25722 | − | 6.04693i | −0.437632 | − | 0.320487i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.41468 | − | 14.6202i | −0.391878 | − | 0.772702i | ||||
\(359\) | − | 17.8064i | − | 0.939785i | −0.882724 | − | 0.469893i | \(-0.844293\pi\) | ||
0.882724 | − | 0.469893i | \(-0.155707\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.45331 | − | 17.8705i | −0.339648 | − | 0.940553i | ||||
\(362\) | −31.9231 | + | 16.1899i | −1.67784 | + | 0.850922i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.813586 | − | 0.595805i | −0.0426435 | − | 0.0312287i | ||||
\(365\) | 12.0637i | 0.631444i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 23.1409i | − | 1.20795i | −0.797004 | − | 0.603974i | \(-0.793583\pi\) | ||
0.797004 | − | 0.603974i | \(-0.206417\pi\) | |||||||
\(368\) | −12.7455 | + | 4.03523i | −0.664404 | + | 0.210351i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.95204 | − | 3.84902i | −0.101482 | − | 0.200101i | ||||
\(371\) | − | 2.30117i | − | 0.119471i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.4052 | 1.36721 | 0.683605 | − | 0.729852i | \(-0.260411\pi\) | ||||
0.683605 | + | 0.729852i | \(0.260411\pi\) | |||||||
\(374\) | 19.1740 | − | 9.72416i | 0.991465 | − | 0.502824i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.8190 | − | 2.10474i | −0.661091 | − | 0.108544i | ||||
\(377\) | 1.52446 | 0.0785135 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | −16.2197 | + | 5.49373i | −0.832051 | + | 0.281822i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.5140 | − | 28.6186i | −0.742601 | − | 1.46426i | ||||
\(383\) | −2.49903 | −0.127695 | −0.0638473 | − | 0.997960i | \(-0.520337\pi\) | ||||
−0.0638473 | + | 0.997960i | \(0.520337\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.67192 | 0.390997 | ||||||||
\(386\) | −8.32003 | − | 16.4054i | −0.423478 | − | 0.835011i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.1777 | + | 11.1149i | 0.770531 | + | 0.564276i | ||||
\(389\) | 17.0615i | 0.865053i | 0.901621 | + | 0.432526i | \(0.142378\pi\) | ||||
−0.901621 | + | 0.432526i | \(0.857622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 16.3317i | − | 0.825930i | ||||||
\(392\) | 2.48560 | − | 15.1387i | 0.125542 | − | 0.764621i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.69144 | + | 7.27876i | 0.185972 | + | 0.366698i | ||||
\(395\) | 2.98068i | 0.149974i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.9339i | 0.699323i | 0.936876 | + | 0.349662i | \(0.113703\pi\) | ||||
−0.936876 | + | 0.349662i | \(0.886297\pi\) | |||||||
\(398\) | 13.0828 | + | 25.7967i | 0.655784 | + | 1.29307i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.37798 | − | 4.35242i | −0.0688990 | − | 0.217621i | ||||
\(401\) | − | 14.0188i | − | 0.700066i | −0.936737 | − | 0.350033i | \(-0.886170\pi\) | ||
0.936737 | − | 0.350033i | \(-0.113830\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.829359 | −0.0413133 | ||||||||
\(404\) | 21.3880 | + | 15.6629i | 1.06409 | + | 0.779258i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.04796 | − | 6.00995i | −0.151268 | − | 0.298269i | ||||
\(407\) | −4.83312 | −0.239569 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 34.7326i | − | 1.71742i | −0.512465 | − | 0.858708i | \(-0.671268\pi\) | ||
0.512465 | − | 0.858708i | \(-0.328732\pi\) | |||||||
\(410\) | 7.23527 | − | 3.66939i | 0.357325 | − | 0.181218i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.0425 | + | 13.7133i | −0.494760 | + | 0.675606i | ||||
\(413\) | −9.29472 | −0.457363 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.97494i | 0.342386i | ||||||||
\(416\) | −1.59133 | − | 1.62162i | −0.0780213 | − | 0.0795065i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.72880 | + | 18.9827i | −0.133470 | + | 0.928476i | ||||
\(419\) | 18.2557 | 0.891848 | 0.445924 | − | 0.895071i | \(-0.352875\pi\) | ||||
0.445924 | + | 0.895071i | \(0.352875\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.6057 | 0.565626 | 0.282813 | − | 0.959175i | \(-0.408732\pi\) | ||||
0.282813 | + | 0.959175i | \(0.408732\pi\) | |||||||
\(422\) | −7.79216 | − | 15.3645i | −0.379316 | − | 0.747934i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.840006 | − | 5.11611i | 0.0407943 | − | 0.248460i | ||||
\(425\) | 5.57707 | 0.270528 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.14859 | 0.103978 | ||||||||
\(428\) | −7.92422 | − | 5.80307i | −0.383032 | − | 0.280502i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.62611 | + | 5.17814i | 0.126642 | + | 0.249712i | ||||
\(431\) | 4.91559 | 0.236776 | 0.118388 | − | 0.992967i | \(-0.462227\pi\) | ||||
0.118388 | + | 0.992967i | \(0.462227\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.6844i | 1.18626i | 0.805108 | + | 0.593128i | \(0.202107\pi\) | ||||
−0.805108 | + | 0.593128i | \(0.797893\pi\) | |||||||
\(434\) | 1.65820 | + | 3.26963i | 0.0795962 | + | 0.156947i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.1314 | + | 26.1244i | −0.916229 | + | 1.25113i | ||||
\(437\) | 11.9233 | + | 8.37122i | 0.570368 | + | 0.400450i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.4011 | 0.878237 | 0.439119 | − | 0.898429i | \(-0.355291\pi\) | ||||
0.439119 | + | 0.898429i | \(0.355291\pi\) | |||||||
\(440\) | 17.0567 | + | 2.80052i | 0.813147 | + | 0.133509i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.47536 | − | 1.25539i | 0.117741 | − | 0.0597126i | ||||
\(443\) | −6.66183 | −0.316513 | −0.158256 | − | 0.987398i | \(-0.550587\pi\) | ||||
−0.158256 | + | 0.987398i | \(0.550587\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0522 | 0.476518 | ||||||||
\(446\) | 27.7273 | − | 14.0620i | 1.31293 | − | 0.665854i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.21134 | + | 9.51581i | −0.151722 | + | 0.449580i | ||||
\(449\) | − | 2.40339i | − | 0.113423i | −0.998391 | − | 0.0567115i | \(-0.981938\pi\) | ||
0.998391 | − | 0.0567115i | \(-0.0180615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 9.08516i | − | 0.427804i | ||||||
\(452\) | 13.1963 | + | 9.66395i | 0.620704 | + | 0.454554i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.4147 | + | 26.4510i | 0.629582 | + | 1.24141i | ||||
\(455\) | 0.990441 | 0.0464326 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.7746 | −0.644349 | −0.322175 | − | 0.946680i | \(-0.604414\pi\) | ||||
−0.322175 | + | 0.946680i | \(0.604414\pi\) | |||||||
\(458\) | −6.13991 | − | 12.1066i | −0.286899 | − | 0.565706i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.75803 | − | 10.5938i | 0.361720 | − | 0.493937i | ||||
\(461\) | 6.19380i | 0.288474i | 0.989543 | + | 0.144237i | \(0.0460727\pi\) | ||||
−0.989543 | + | 0.144237i | \(0.953927\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 32.6751i | − | 1.51854i | −0.650774 | − | 0.759271i | \(-0.725556\pi\) | ||
0.650774 | − | 0.759271i | \(-0.274444\pi\) | |||||||
\(464\) | −4.58259 | − | 14.4743i | −0.212742 | − | 0.671954i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.3839 | + | 6.28051i | −0.573671 | + | 0.290939i | ||||
\(467\) | −23.5362 | −1.08913 | −0.544564 | − | 0.838720i | \(-0.683305\pi\) | ||||
−0.544564 | + | 0.838720i | \(0.683305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.8444 | 0.593097 | ||||||||
\(470\) | 11.3793 | − | 5.77106i | 0.524890 | − | 0.266199i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −20.6647 | − | 3.39290i | −0.951168 | − | 0.156171i | ||||
\(473\) | 6.50207 | 0.298965 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.85866 | + | 4.07165i | −0.131164 | + | 0.186820i | ||||
\(476\) | −9.89835 | − | 7.24876i | −0.453690 | − | 0.332246i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.65858 | + | 7.21397i | 0.167340 | + | 0.329959i | ||||
\(479\) | 1.31334i | 0.0600081i | 0.999550 | + | 0.0300041i | \(0.00955202\pi\) | ||||
−0.999550 | + | 0.0300041i | \(0.990448\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.623954 | −0.0284498 | ||||||||
\(482\) | 11.4311 | + | 22.5397i | 0.520672 | + | 1.02666i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.56134 | + | 2.13204i | −0.0709700 | + | 0.0969111i | ||||
\(485\) | −18.4770 | −0.838998 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.4413 | −1.19817 | −0.599086 | − | 0.800685i | \(-0.704469\pi\) | ||||
−0.599086 | + | 0.800685i | \(0.704469\pi\) | |||||||
\(488\) | 4.77690 | + | 0.784312i | 0.216240 | + | 0.0355041i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.81537 | + | 13.4385i | 0.307887 | + | 0.607090i | ||||
\(491\) | 25.1228 | 1.13378 | 0.566889 | − | 0.823794i | \(-0.308147\pi\) | ||||
0.566889 | + | 0.823794i | \(0.308147\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.5470 | 0.835317 | ||||||||
\(494\) | −0.352287 | + | 2.45066i | −0.0158501 | + | 0.110261i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.49310 | + | 7.87456i | 0.111943 | + | 0.353578i | ||||
\(497\) | 11.0985i | 0.497837i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.30472 | −0.416536 | −0.208268 | − | 0.978072i | \(-0.566783\pi\) | ||||
−0.208268 | + | 0.978072i | \(0.566783\pi\) | |||||||
\(500\) | 19.4659 | + | 14.2553i | 0.870541 | + | 0.637515i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.40244 | + | 4.26132i | −0.375019 | + | 0.190192i | ||||
\(503\) | 0.887197i | 0.0395582i | 0.999804 | + | 0.0197791i | \(0.00629629\pi\) | ||||
−0.999804 | + | 0.0197791i | \(0.993704\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.0373 | −1.15865 | ||||||||
\(506\) | −6.65117 | − | 13.1147i | −0.295681 | − | 0.583021i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.4681 | + | 23.8531i | −0.775022 | + | 1.05831i | ||||
\(509\) | 17.5519 | 0.777976 | 0.388988 | − | 0.921243i | \(-0.372825\pi\) | ||||
0.388988 | + | 0.921243i | \(0.372825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7.70974i | − | 0.341059i | ||||||
\(512\) | −10.6133 | + | 19.9839i | −0.469045 | + | 0.883174i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.28267 | + | 12.3881i | 0.277117 | + | 0.546417i | ||||
\(515\) | − | 16.6943i | − | 0.735637i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 14.2888i | − | 0.628420i | ||||||
\(518\) | 1.24752 | + | 2.45985i | 0.0548128 | + | 0.108079i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.20202 | + | 0.361546i | 0.0965648 | + | 0.0158548i | ||||
\(521\) | − | 18.4878i | − | 0.809967i | −0.914324 | − | 0.404983i | \(-0.867277\pi\) | ||
0.914324 | − | 0.404983i | \(-0.132723\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.7356i | 0.469436i | 0.972064 | + | 0.234718i | \(0.0754166\pi\) | ||||
−0.972064 | + | 0.234718i | \(0.924583\pi\) | |||||||
\(524\) | 18.6581 | − | 25.4780i | 0.815082 | − | 1.11301i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.79359 | − | 9.45198i | −0.209011 | − | 0.412126i | ||||
\(527\) | −10.0903 | −0.439538 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.8294 | 0.514320 | ||||||||
\(530\) | 2.30325 | + | 4.54153i | 0.100047 | + | 0.197271i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.3657 | − | 3.51096i | 0.449412 | − | 0.152219i | ||||
\(533\) | − | 1.17289i | − | 0.0508036i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.64677 | 0.417066 | ||||||||
\(536\) | 28.5564 | + | 4.68864i | 1.23345 | + | 0.202518i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 32.7160 | − | 16.5920i | 1.41049 | − | 0.715332i | ||||
\(539\) | 16.8744 | 0.726833 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.9269i | 1.63060i | 0.579036 | + | 0.815302i | \(0.303429\pi\) | ||||
−0.579036 | + | 0.815302i | \(0.696571\pi\) | |||||||
\(542\) | 12.9693 | + | 25.5729i | 0.557081 | + | 1.09845i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −19.3606 | − | 19.7292i | −0.830080 | − | 0.845882i | ||||
\(545\) | − | 31.8033i | − | 1.36230i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 37.1871i | − | 1.59000i | −0.606607 | − | 0.795002i | \(-0.707470\pi\) | ||
0.606607 | − | 0.795002i | \(-0.292530\pi\) | |||||||
\(548\) | −16.5602 | + | 22.6133i | −0.707416 | + | 0.965992i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.47852 | − | 2.27129i | 0.190965 | − | 0.0968482i | ||||
\(551\) | −9.50673 | + | 13.5406i | −0.405000 | + | 0.576850i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.90490i | − | 0.0810048i | ||||||
\(554\) | −2.11731 | − | 4.17489i | −0.0899558 | − | 0.177374i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.16701 | + | 7.05567i | −0.219130 | + | 0.299227i | ||||
\(557\) | 6.61994i | 0.280496i | 0.990116 | + | 0.140248i | \(0.0447900\pi\) | ||||
−0.990116 | + | 0.140248i | \(0.955210\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.839414 | 0.0355035 | ||||||||
\(560\) | −2.97732 | − | 9.40400i | −0.125815 | − | 0.397391i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.4333 | + | 40.2903i | 0.861928 | + | 1.69954i | ||||
\(563\) | − | 37.4740i | − | 1.57934i | −0.613532 | − | 0.789670i | \(-0.710252\pi\) | ||
0.613532 | − | 0.789670i | \(-0.289748\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.0649 | −0.675857 | ||||||||
\(566\) | −16.6279 | + | 8.43290i | −0.698924 | + | 0.354461i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.05135 | + | 24.6750i | −0.169991 | + | 1.03534i | ||||
\(569\) | 23.1924i | 0.972276i | 0.873882 | + | 0.486138i | \(0.161595\pi\) | ||||
−0.873882 | + | 0.486138i | \(0.838405\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.6027 | −1.28068 | −0.640341 | − | 0.768091i | \(-0.721207\pi\) | ||||
−0.640341 | + | 0.768091i | \(0.721207\pi\) | |||||||
\(572\) | 1.47651 | − | 2.01621i | 0.0617359 | − | 0.0843018i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.62395 | + | 2.34505i | −0.193000 | + | 0.0978805i | ||||
\(575\) | − | 3.81463i | − | 0.159081i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.2814 | 1.34389 | 0.671945 | − | 0.740601i | \(-0.265459\pi\) | ||||
0.671945 | + | 0.740601i | \(0.265459\pi\) | |||||||
\(578\) | 8.67424 | − | 4.39916i | 0.360801 | − | 0.182981i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.0308 | + | 8.81037i | 0.499550 | + | 0.365831i | ||||
\(581\) | − | 4.45758i | − | 0.184931i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.70269 | 0.236181 | ||||||||
\(584\) | 2.81432 | − | 17.1408i | 0.116458 | − | 0.709292i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.4147 | + | 5.28183i | −0.430226 | + | 0.218190i | ||||
\(587\) | −9.97823 | −0.411845 | −0.205923 | − | 0.978568i | \(-0.566020\pi\) | ||||
−0.205923 | + | 0.978568i | \(0.566020\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.17200 | − | 7.36659i | 0.213109 | − | 0.303535i | ||||
\(590\) | 18.3438 | − | 9.30312i | 0.755204 | − | 0.383004i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.87564 | + | 5.92429i | 0.0770882 | + | 0.243487i | ||||
\(593\) | 21.5721 | 0.885859 | 0.442930 | − | 0.896556i | \(-0.353939\pi\) | ||||
0.442930 | + | 0.896556i | \(0.353939\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0500 | 0.494003 | ||||||||
\(596\) | 11.0500 | + | 8.09212i | 0.452624 | + | 0.331466i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.858664 | − | 1.69311i | −0.0351134 | − | 0.0692363i | ||||
\(599\) | 36.6125 | 1.49595 | 0.747973 | − | 0.663730i | \(-0.231027\pi\) | ||||
0.747973 | + | 0.663730i | \(0.231027\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 46.0890i | − | 1.88001i | −0.341159 | − | 0.940005i | \(-0.610820\pi\) | ||
0.341159 | − | 0.940005i | \(-0.389180\pi\) | |||||||
\(602\) | −1.67830 | − | 3.30927i | −0.0684026 | − | 0.134876i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.4499 | + | 27.9248i | −0.832093 | + | 1.13624i | ||||
\(605\) | − | 2.59550i | − | 0.105522i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.600582 | −0.0243769 | −0.0121884 | − | 0.999926i | \(-0.503880\pi\) | ||||
−0.0121884 | + | 0.999926i | \(0.503880\pi\) | |||||||
\(608\) | 24.3274 | − | 4.02194i | 0.986608 | − | 0.163111i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.24041 | + | 2.15054i | −0.171689 | + | 0.0870726i | ||||
\(611\) | − | 1.84468i | − | 0.0746276i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.5952i | 0.872220i | 0.899893 | + | 0.436110i | \(0.143644\pi\) | ||||
−0.899893 | + | 0.436110i | \(0.856356\pi\) | |||||||
\(614\) | 12.3561 | + | 24.3636i | 0.498651 | + | 0.983236i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.9007 | − | 1.78977i | −0.439201 | − | 0.0721118i | ||||
\(617\) | 16.5945 | 0.668068 | 0.334034 | − | 0.942561i | \(-0.391590\pi\) | ||||
0.334034 | + | 0.942561i | \(0.391590\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.4626 | −1.22440 | −0.612198 | − | 0.790704i | \(-0.709715\pi\) | ||||
−0.612198 | + | 0.790704i | \(0.709715\pi\) | |||||||
\(620\) | −6.54517 | − | 4.79316i | −0.262860 | − | 0.192498i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.6583 | − | 24.9596i | −0.507552 | − | 1.00079i | ||||
\(623\) | −6.42418 | −0.257379 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.9907 | −0.719627 | ||||||||
\(626\) | −0.486067 | + | 0.246510i | −0.0194271 | + | 0.00985252i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.3013 | + | 16.3317i | 0.889920 | + | 0.651706i | ||||
\(629\) | −7.59122 | −0.302682 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.54402i | − | 0.300323i | −0.988661 | − | 0.150161i | \(-0.952021\pi\) | ||
0.988661 | − | 0.150161i | \(-0.0479793\pi\) | |||||||
\(632\) | 0.695357 | − | 4.23511i | 0.0276598 | − | 0.168464i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.4647 | − | 11.3930i | 0.892188 | − | 0.452475i | ||||
\(635\) | − | 29.0382i | − | 1.15235i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.17848 | 0.0863145 | ||||||||
\(638\) | 14.8937 | − | 7.55337i | 0.589647 | − | 0.299041i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.18658 | − | 21.9944i | −0.125961 | − | 0.869406i | ||||
\(641\) | − | 46.0941i | − | 1.82061i | −0.413939 | − | 0.910305i | \(-0.635847\pi\) | ||
0.413939 | − | 0.910305i | \(-0.364153\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.7674 | −0.464059 | −0.232030 | − | 0.972709i | \(-0.574537\pi\) | ||||
−0.232030 | + | 0.972709i | \(0.574537\pi\) | |||||||
\(644\) | −4.95804 | + | 6.77032i | −0.195374 | + | 0.266788i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.28604 | + | 29.8156i | −0.168632 | + | 1.17308i | ||||
\(647\) | 22.2904i | 0.876324i | 0.898896 | + | 0.438162i | \(0.144370\pi\) | ||||
−0.898896 | + | 0.438162i | \(0.855630\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 23.0339i | − | 0.904161i | ||||||
\(650\) | 0.578175 | − | 0.293223i | 0.0226779 | − | 0.0115011i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.50466 | − | 2.05465i | 0.0589272 | − | 0.0804664i | ||||
\(653\) | − | 33.8039i | − | 1.32285i | −0.750011 | − | 0.661425i | \(-0.769952\pi\) | ||
0.750011 | − | 0.661425i | \(-0.230048\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.0164i | 1.21191i | ||||||||
\(656\) | −11.1363 | + | 3.52577i | −0.434800 | + | 0.137658i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.27237 | + | 3.68820i | −0.283506 | + | 0.143781i | ||||
\(659\) | 16.2065i | 0.631317i | 0.948873 | + | 0.315659i | \(0.102225\pi\) | ||||
−0.948873 | + | 0.315659i | \(0.897775\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.564440 | 0.0219542 | 0.0109771 | − | 0.999940i | \(-0.496506\pi\) | ||||
0.0109771 | + | 0.999940i | \(0.496506\pi\) | |||||||
\(662\) | 0.322523 | + | 0.635949i | 0.0125352 | + | 0.0247169i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.62717 | − | 9.91039i | 0.0631465 | − | 0.384598i | ||||
\(665\) | −6.17654 | + | 8.79736i | −0.239516 | + | 0.341147i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 12.6859i | − | 0.491200i | ||||||
\(668\) | −10.4468 | + | 14.2653i | −0.404198 | + | 0.551942i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −25.3493 | + | 12.8560i | −0.979329 | + | 0.496669i | ||||
\(671\) | 5.32459i | 0.205553i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 15.5992i | − | 0.601305i | −0.953734 | − | 0.300653i | \(-0.902796\pi\) | ||
0.953734 | − | 0.300653i | \(-0.0972045\pi\) | |||||||
\(674\) | 4.35858 | + | 8.59421i | 0.167886 | + | 0.331037i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.1710 | + | 20.7164i | −0.583501 | + | 0.796783i | ||||
\(677\) | −3.79561 | −0.145877 | −0.0729386 | − | 0.997336i | \(-0.523238\pi\) | ||||
−0.0729386 | + | 0.997336i | \(0.523238\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.8084 | 0.453164 | ||||||||
\(680\) | 26.7904 | + | 4.39868i | 1.02737 | + | 0.168682i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.10270 | + | 4.10931i | −0.310269 | + | 0.157353i | ||||
\(683\) | 40.6152i | 1.55410i | 0.629440 | + | 0.777049i | \(0.283284\pi\) | ||||
−0.629440 | + | 0.777049i | \(0.716716\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 27.5289i | − | 1.05183i | ||||||
\(686\) | −9.97676 | − | 19.6721i | −0.380914 | − | 0.751085i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.52332 | − | 7.97003i | −0.0962007 | − | 0.303855i | ||||
\(689\) | 0.736215 | 0.0280476 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.90069 | 0.262514 | 0.131257 | − | 0.991348i | \(-0.458099\pi\) | ||||
0.131257 | + | 0.991348i | \(0.458099\pi\) | |||||||
\(692\) | 18.7275 | − | 25.5729i | 0.711914 | − | 0.972135i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.40244 | + | 4.26132i | −0.318952 | + | 0.161757i | ||||
\(695\) | − | 8.58942i | − | 0.325815i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 14.2698i | − | 0.540506i | ||||||
\(698\) | −17.1702 | − | 33.8561i | −0.649902 | − | 1.28147i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.31198 | − | 1.69311i | −0.0873845 | − | 0.0639935i | ||||
\(701\) | − | 42.5932i | − | 1.60872i | −0.594139 | − | 0.804362i | \(-0.702507\pi\) | ||
0.594139 | − | 0.804362i | \(-0.297493\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.89107 | − | 5.54212i | 0.146754 | − | 0.209025i | ||||
\(704\) | −23.5818 | − | 7.95826i | −0.888773 | − | 0.299938i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.0598 | + | 15.2449i | −1.13132 | + | 0.573750i | ||||
\(707\) | 16.6401 | 0.625814 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 34.2854i | − | 1.28761i | −0.765188 | − | 0.643807i | \(-0.777354\pi\) | ||
0.765188 | − | 0.643807i | \(-0.222646\pi\) | |||||||
\(710\) | −11.1086 | − | 21.9038i | −0.416897 | − | 0.822035i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.2827 | − | 2.34505i | −0.535266 | − | 0.0878845i | ||||
\(713\) | 6.90158i | 0.258466i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.45448i | 0.0917925i | ||||||||
\(716\) | −18.7040 | − | 13.6973i | −0.699001 | − | 0.511893i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.3901 | − | 22.4589i | −0.425074 | − | 0.838158i | ||||
\(719\) | 7.09419i | 0.264568i | 0.991212 | + | 0.132284i | \(0.0422312\pi\) | ||||
−0.991212 | + | 0.132284i | \(0.957769\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.6691i | 0.397336i | ||||||||
\(722\) | −19.5705 | − | 18.4118i | −0.728340 | − | 0.685216i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −29.9080 | + | 40.8401i | −1.11152 | + | 1.51781i | ||||
\(725\) | 4.33207 | 0.160889 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.8722i | 1.33043i | 0.746653 | + | 0.665213i | \(0.231659\pi\) | ||||
−0.746653 | + | 0.665213i | \(0.768341\pi\) | |||||||
\(728\) | −1.40728 | − | 0.231058i | −0.0521571 | − | 0.00856359i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.71671 | + | 15.2158i | 0.285608 | + | 0.563160i | ||||
\(731\) | 10.2126 | 0.377726 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 27.6419i | − | 1.02098i | −0.859885 | − | 0.510488i | \(-0.829465\pi\) | ||
0.859885 | − | 0.510488i | \(-0.170535\pi\) | |||||||
\(734\) | −14.8024 | − | 29.1872i | −0.546366 | − | 1.07732i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.4945 | + | 13.2424i | −0.497412 | + | 0.488120i | ||||
\(737\) | 31.8305i | 1.17249i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.7860 | −1.24284 | −0.621419 | − | 0.783478i | \(-0.713444\pi\) | ||||
−0.621419 | + | 0.783478i | \(0.713444\pi\) | |||||||
\(740\) | −4.92414 | − | 3.60605i | −0.181015 | − | 0.132561i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.47197 | − | 2.90242i | −0.0540377 | − | 0.106551i | ||||
\(743\) | −7.67370 | −0.281521 | −0.140760 | − | 0.990044i | \(-0.544955\pi\) | ||||
−0.140760 | + | 0.990044i | \(0.544955\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.4520 | −0.492843 | ||||||||
\(746\) | 33.3044 | − | 16.8904i | 1.21936 | − | 0.618402i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.9637 | − | 24.5298i | 0.656817 | − | 0.896899i | ||||
\(749\) | −6.16511 | −0.225268 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.6688 | 0.754214 | 0.377107 | − | 0.926170i | \(-0.376919\pi\) | ||||
0.377107 | + | 0.926170i | \(0.376919\pi\) | |||||||
\(752\) | −17.5147 | + | 5.54519i | −0.638697 | + | 0.202212i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.92277 | − | 0.975138i | 0.0700232 | − | 0.0355124i | ||||
\(755\) | − | 33.9950i | − | 1.23720i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.7298i | 1.26228i | 0.775671 | + | 0.631138i | \(0.217412\pi\) | ||||
−0.775671 | + | 0.631138i | \(0.782588\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.9434 | + | 17.3042i | −0.614603 | + | 0.627691i | ||||
\(761\) | 41.1634 | 1.49217 | 0.746087 | − | 0.665849i | \(-0.231930\pi\) | ||||
0.746087 | + | 0.665849i | \(0.231930\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.3250i | 0.735814i | ||||||||
\(764\) | −36.6125 | − | 26.8121i | −1.32459 | − | 0.970027i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.15198 | + | 1.59854i | −0.113886 | + | 0.0577575i | ||||
\(767\) | − | 2.97367i | − | 0.107373i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.2466 | 1.12678 | 0.563390 | − | 0.826191i | \(-0.309497\pi\) | ||||
0.563390 | + | 0.826191i | \(0.309497\pi\) | |||||||
\(770\) | 9.67645 | − | 4.90744i | 0.348715 | − | 0.176852i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20.9878 | − | 15.3698i | −0.755367 | − | 0.553171i | ||||
\(773\) | −35.2334 | −1.26726 | −0.633629 | − | 0.773637i | \(-0.718435\pi\) | ||||
−0.633629 | + | 0.773637i | \(0.718435\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.35680 | −0.0846588 | ||||||||
\(776\) | 26.2532 | + | 4.31047i | 0.942434 | + | 0.154737i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.9136 | + | 21.5194i | 0.391272 | + | 0.771507i | ||||
\(779\) | 10.4179 | + | 7.31432i | 0.373261 | + | 0.262063i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.5041 | −0.984173 | ||||||||
\(782\) | −10.4468 | − | 20.5989i | −0.373576 | − | 0.736615i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.54862 | − | 20.6841i | −0.233879 | − | 0.738719i | ||||
\(785\) | −27.1492 | −0.968995 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.9557i | 0.960866i | 0.877032 | + | 0.480433i | \(0.159520\pi\) | ||||
−0.877032 | + | 0.480433i | \(0.840480\pi\) | |||||||
\(788\) | 9.31189 | + | 6.81929i | 0.331722 | + | 0.242927i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.90663 | + | 3.75947i | 0.0678347 | + | 0.133756i | ||||
\(791\) | 10.2669 | 0.365047 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.687402i | 0.0244104i | ||||||||
\(794\) | 8.91300 | + | 17.5746i | 0.316311 | + | 0.623699i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 33.0023 | + | 24.1683i | 1.16974 | + | 0.856621i | ||||
\(797\) | −30.4003 | −1.07683 | −0.538417 | − | 0.842679i | \(-0.680977\pi\) | ||||
−0.538417 | + | 0.842679i | \(0.680977\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 22.4429i | − | 0.793974i | ||||||
\(800\) | −4.52210 | − | 4.60818i | −0.159880 | − | 0.162924i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.96731 | − | 17.6817i | −0.316647 | − | 0.624362i | ||||
\(803\) | 19.1061 | 0.674238 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 8.24204i | − | 0.290494i | ||||||
\(806\) | −1.04606 | + | 0.530510i | −0.0368457 | + | 0.0186864i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 36.9953 | + | 6.07420i | 1.30149 | + | 0.213690i | ||||
\(809\) | 2.71694 | 0.0955225 | 0.0477612 | − | 0.998859i | \(-0.484791\pi\) | ||||
0.0477612 | + | 0.998859i | \(0.484791\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 18.3747i | − | 0.645223i | −0.946531 | − | 0.322612i | \(-0.895439\pi\) | ||
0.946531 | − | 0.322612i | \(-0.104561\pi\) | |||||||
\(812\) | −7.68868 | − | 5.63058i | −0.269820 | − | 0.197594i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.09592 | + | 3.09156i | −0.213662 | + | 0.108359i | ||||
\(815\) | 2.50129i | 0.0876164i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.23471 | + | 7.45590i | −0.183139 | + | 0.260849i | ||||
\(818\) | −22.2171 | − | 43.8076i | −0.776804 | − | 1.53170i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.77855 | − | 9.25627i | 0.236717 | − | 0.323243i | ||||
\(821\) | 7.72021i | 0.269437i | 0.990884 | + | 0.134719i | \(0.0430130\pi\) | ||||
−0.990884 | + | 0.134719i | \(0.956987\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26.3865i | − | 0.919776i | −0.887977 | − | 0.459888i | \(-0.847890\pi\) | ||
0.887977 | − | 0.459888i | \(-0.152110\pi\) | |||||||
\(824\) | −3.89458 | + | 23.7202i | −0.135674 | + | 0.826331i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.7233 | + | 5.94549i | −0.407905 | + | 0.206870i | ||||
\(827\) | 45.4697i | 1.58114i | 0.612373 | + | 0.790569i | \(0.290215\pi\) | ||||
−0.612373 | + | 0.790569i | \(0.709785\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.8307 | 0.584555 | 0.292277 | − | 0.956334i | \(-0.405587\pi\) | ||||
0.292277 | + | 0.956334i | \(0.405587\pi\) | |||||||
\(830\) | 4.46161 | + | 8.79736i | 0.154865 | + | 0.305361i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.04440 | − | 1.02741i | −0.105546 | − | 0.0356190i | ||||
\(833\) | 26.5041 | 0.918313 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 17.3663i | − | 0.600985i | ||||||
\(836\) | 8.70075 | + | 25.6881i | 0.300922 | + | 0.888441i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 23.0256 | − | 11.6775i | 0.795405 | − | 0.403391i | ||||
\(839\) | −45.7123 | −1.57816 | −0.789082 | − | 0.614288i | \(-0.789443\pi\) | ||||
−0.789082 | + | 0.614288i | \(0.789443\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5933 | −0.503218 | ||||||||
\(842\) | 14.6380 | − | 7.42372i | 0.504460 | − | 0.255838i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19.6562 | − | 14.3947i | −0.676595 | − | 0.495484i | ||||
\(845\) | − | 25.2197i | − | 0.867582i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.65875i | 0.0569952i | ||||||||
\(848\) | −2.21310 | − | 6.99018i | −0.0759981 | − | 0.240044i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.03426 | − | 3.56744i | 0.241273 | − | 0.122362i | ||||
\(851\) | 5.19228i | 0.177989i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 36.7727i | − | 1.25907i | −0.776970 | − | 0.629537i | \(-0.783244\pi\) | ||
0.776970 | − | 0.629537i | \(-0.216756\pi\) | |||||||
\(854\) | 2.70998 | − | 1.37437i | 0.0927337 | − | 0.0470301i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.7067 | − | 2.25048i | −0.468485 | − | 0.0769198i | ||||
\(857\) | 6.42314i | 0.219410i | 0.993964 | + | 0.109705i | \(0.0349907\pi\) | ||||
−0.993964 | + | 0.109705i | \(0.965009\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.0500 | 0.888816 | 0.444408 | − | 0.895825i | \(-0.353414\pi\) | ||||
0.444408 | + | 0.895825i | \(0.353414\pi\) | |||||||
\(860\) | 6.62452 | + | 4.85127i | 0.225894 | + | 0.165427i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.19995 | − | 3.14432i | 0.211171 | − | 0.107096i | ||||
\(863\) | 49.3784 | 1.68086 | 0.840430 | − | 0.541921i | \(-0.182303\pi\) | ||||
0.840430 | + | 0.541921i | \(0.182303\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.1319i | 1.05851i | ||||||||
\(866\) | 15.7897 | + | 31.1340i | 0.536555 | + | 1.05797i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.18292 | + | 3.06324i | 0.141977 | + | 0.103973i | ||||
\(869\) | 4.72068 | 0.160138 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.10931i | 0.139239i | ||||||||
\(872\) | −7.41933 | + | 45.1879i | −0.251250 | + | 1.53025i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20.3934 | + | 2.93158i | 0.689817 | + | 0.0991623i | ||||
\(875\) | 15.1446 | 0.511982 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.69536 | 0.259854 | 0.129927 | − | 0.991524i | \(-0.458526\pi\) | ||||
0.129927 | + | 0.991524i | \(0.458526\pi\) | |||||||
\(878\) | 23.2090 | − | 11.7705i | 0.783266 | − | 0.397235i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 23.3047 | − | 7.37830i | 0.785602 | − | 0.248722i | ||||
\(881\) | 23.1421 | 0.779678 | 0.389839 | − | 0.920883i | \(-0.372531\pi\) | ||||
0.389839 | + | 0.920883i | \(0.372531\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.5899 | 1.29865 | 0.649327 | − | 0.760509i | \(-0.275050\pi\) | ||||
0.649327 | + | 0.760509i | \(0.275050\pi\) | |||||||
\(884\) | 2.31910 | − | 3.16679i | 0.0779999 | − | 0.106511i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.40244 | + | 4.26132i | −0.282285 | + | 0.143162i | ||||
\(887\) | 30.4474 | 1.02232 | 0.511161 | − | 0.859485i | \(-0.329215\pi\) | ||||
0.511161 | + | 0.859485i | \(0.329215\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.5579i | 0.622412i | ||||||||
\(890\) | 12.6786 | − | 6.42999i | 0.424988 | − | 0.215534i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 25.9771 | − | 35.4723i | 0.869776 | − | 1.18770i | ||||
\(893\) | 16.3849 | + | 11.5037i | 0.548300 | + | 0.384955i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.7698 | 0.761112 | ||||||||
\(896\) | 2.03650 | + | 14.0563i | 0.0680346 | + | 0.469588i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.53736 | − | 3.03135i | −0.0513023 | − | 0.101158i | ||||
\(899\) | −7.83775 | −0.261403 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.95703 | 0.298402 | ||||||||
\(902\) | −5.81144 | − | 11.4590i | −0.193500 | − | 0.381541i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.8260 | + | 3.74776i | 0.759180 | + | 0.124649i | ||||
\(905\) | − | 49.7178i | − | 1.65268i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 10.0936i | − | 0.335152i | −0.985859 | − | 0.167576i | \(-0.946406\pi\) | ||
0.985859 | − | 0.167576i | \(-0.0535939\pi\) | |||||||
\(908\) | 33.8394 | + | 24.7813i | 1.12300 | + | 0.822395i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.24923 | − | 0.633548i | 0.0414114 | − | 0.0210019i | ||||
\(911\) | 49.1193 | 1.62739 | 0.813697 | − | 0.581289i | \(-0.197451\pi\) | ||||
0.813697 | + | 0.581289i | \(0.197451\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.0466 | 0.365591 | ||||||||
\(914\) | −17.3737 | + | 8.81111i | −0.574670 | + | 0.291445i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.4883 | − | 11.3424i | −0.511748 | − | 0.374764i | ||||
\(917\) | − | 19.8221i | − | 0.654584i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 10.2322i | − | 0.337530i | −0.985656 | − | 0.168765i | \(-0.946022\pi\) | ||
0.985656 | − | 0.168765i | \(-0.0539779\pi\) | |||||||
\(920\) | 3.00863 | − | 18.3242i | 0.0991916 | − | 0.604133i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.96194 | + | 7.81212i | 0.130479 | + | 0.257279i | ||||
\(923\) | −3.55077 | −0.116875 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.77310 | −0.0582991 | ||||||||
\(926\) | −20.9011 | − | 41.2126i | −0.686851 | − | 1.35433i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.0386 | − | 15.3249i | −0.493667 | − | 0.503065i | ||||
\(929\) | 2.58019 | 0.0846532 | 0.0423266 | − | 0.999104i | \(-0.486523\pi\) | ||||
0.0423266 | + | 0.999104i | \(0.486523\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.5853 | + | 19.3498i | −0.445241 | + | 0.634166i | ||||
\(932\) | −11.6021 | + | 15.8430i | −0.380041 | + | 0.518954i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −29.6858 | + | 15.0552i | −0.971350 | + | 0.492623i | ||||
\(935\) | 29.8621i | 0.976594i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.71601 | −0.317408 | −0.158704 | − | 0.987326i | \(-0.550732\pi\) | ||||
−0.158704 | + | 0.987326i | \(0.550732\pi\) | |||||||
\(938\) | 16.2003 | − | 8.21605i | 0.528960 | − | 0.268263i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.6610 | − | 14.5579i | 0.347724 | − | 0.474826i | ||||
\(941\) | −24.7717 | −0.807533 | −0.403766 | − | 0.914862i | \(-0.632299\pi\) | ||||
−0.403766 | + | 0.914862i | \(0.632299\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.76031 | −0.317839 | ||||||||
\(944\) | −28.2343 | + | 8.93900i | −0.918947 | + | 0.290940i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.20094 | − | 4.15913i | 0.266636 | − | 0.135225i | ||||
\(947\) | −43.3785 | −1.40961 | −0.704806 | − | 0.709400i | \(-0.748966\pi\) | ||||
−0.704806 | + | 0.709400i | \(0.748966\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.46659 | 0.0800688 | ||||||||
\(950\) | −1.00110 | + | 6.96408i | −0.0324799 | + | 0.225945i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.1214 | − | 2.81113i | −0.554907 | − | 0.0911093i | ||||
\(953\) | − | 1.09947i | − | 0.0356154i | −0.999841 | − | 0.0178077i | \(-0.994331\pi\) | ||
0.999841 | − | 0.0178077i | \(-0.00566867\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.5713 | 1.44229 | ||||||||
\(956\) | 9.22900 | + | 6.75859i | 0.298487 | + | 0.218588i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.840095 | + | 1.65649i | 0.0271422 | + | 0.0535189i | ||||
\(959\) | 17.5933i | 0.568118i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.7360 | −0.862451 | ||||||||
\(962\) | −0.786981 | + | 0.399120i | −0.0253733 | + | 0.0128681i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 28.8356 | + | 21.1169i | 0.928734 | + | 0.680130i | ||||
\(965\) | 25.5501 | 0.822486 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 18.4508i | − | 0.593339i | −0.954980 | − | 0.296669i | \(-0.904124\pi\) | ||
0.954980 | − | 0.296669i | \(-0.0958760\pi\) | |||||||
\(968\) | −0.605501 | + | 3.68784i | −0.0194615 | + | 0.118532i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.3047 | + | 11.8190i | −0.748269 | + | 0.379487i | ||||
\(971\) | − | 22.0471i | − | 0.707525i | −0.935335 | − | 0.353763i | \(-0.884902\pi\) | ||
0.935335 | − | 0.353763i | \(-0.115098\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.48937i | 0.175981i | ||||||||
\(974\) | −33.3500 | + | 16.9135i | −1.06860 | + | 0.541944i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.52671 | − | 2.06636i | 0.208915 | − | 0.0661427i | ||||
\(977\) | − | 7.59567i | − | 0.243007i | −0.992591 | − | 0.121503i | \(-0.961228\pi\) | ||
0.992591 | − | 0.121503i | \(-0.0387716\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 15.9202i | − | 0.508813i | ||||||
\(980\) | 17.1922 | + | 12.5902i | 0.549185 | + | 0.402179i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 31.6870 | − | 16.0701i | 1.01117 | − | 0.512819i | ||||
\(983\) | 2.75811 | 0.0879699 | 0.0439850 | − | 0.999032i | \(-0.485995\pi\) | ||||
0.0439850 | + | 0.999032i | \(0.485995\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.3361 | −0.361198 | ||||||||
\(986\) | 23.3930 | − | 11.8638i | 0.744986 | − | 0.377822i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.12326 | + | 3.31632i | 0.0357358 | + | 0.105506i | ||||
\(989\) | − | 6.98525i | − | 0.222118i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.8481 | −1.64701 | −0.823504 | − | 0.567310i | \(-0.807984\pi\) | ||||
−0.823504 | + | 0.567310i | \(0.807984\pi\) | |||||||
\(992\) | 8.18156 | + | 8.33730i | 0.259765 | + | 0.264710i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.09931 | + | 13.9984i | 0.225177 | + | 0.444002i | ||||
\(995\) | −40.1763 | −1.27367 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.1940i | 1.24129i | 0.784094 | + | 0.620643i | \(0.213128\pi\) | ||||
−0.784094 | + | 0.620643i | \(0.786872\pi\) | |||||||
\(998\) | −11.7359 | + | 5.95188i | −0.371493 | + | 0.188403i | ||||
\(999\) | 0 | 0 |
(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 | 1368.2.e.f.379.18 | yes | 24 | |
3.2 | odd | 2 | inner | 1368.2.e.f.379.8 | yes | 24 | |
4.3 | odd | 2 | 5472.2.e.f.5167.18 | 24 | |||
8.3 | odd | 2 | inner | 1368.2.e.f.379.5 | ✓ | 24 | |
8.5 | even | 2 | 5472.2.e.f.5167.11 | 24 | |||
12.11 | even | 2 | 5472.2.e.f.5167.19 | 24 | |||
19.18 | odd | 2 | inner | 1368.2.e.f.379.7 | yes | 24 | |
24.5 | odd | 2 | 5472.2.e.f.5167.10 | 24 | |||
24.11 | even | 2 | inner | 1368.2.e.f.379.19 | yes | 24 | |
57.56 | even | 2 | inner | 1368.2.e.f.379.17 | yes | 24 | |
76.75 | even | 2 | 5472.2.e.f.5167.12 | 24 | |||
152.37 | odd | 2 | 5472.2.e.f.5167.17 | 24 | |||
152.75 | even | 2 | inner | 1368.2.e.f.379.20 | yes | 24 | |
228.227 | odd | 2 | 5472.2.e.f.5167.9 | 24 | |||
456.227 | odd | 2 | inner | 1368.2.e.f.379.6 | yes | 24 | |
456.341 | even | 2 | 5472.2.e.f.5167.20 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.e.f.379.5 | ✓ | 24 | 8.3 | odd | 2 | inner | |
1368.2.e.f.379.6 | yes | 24 | 456.227 | odd | 2 | inner | |
1368.2.e.f.379.7 | yes | 24 | 19.18 | odd | 2 | inner | |
1368.2.e.f.379.8 | yes | 24 | 3.2 | odd | 2 | inner | |
1368.2.e.f.379.17 | yes | 24 | 57.56 | even | 2 | inner | |
1368.2.e.f.379.18 | yes | 24 | 1.1 | even | 1 | trivial | |
1368.2.e.f.379.19 | yes | 24 | 24.11 | even | 2 | inner | |
1368.2.e.f.379.20 | yes | 24 | 152.75 | even | 2 | inner | |
5472.2.e.f.5167.9 | 24 | 228.227 | odd | 2 | |||
5472.2.e.f.5167.10 | 24 | 24.5 | odd | 2 | |||
5472.2.e.f.5167.11 | 24 | 8.5 | even | 2 | |||
5472.2.e.f.5167.12 | 24 | 76.75 | even | 2 | |||
5472.2.e.f.5167.17 | 24 | 152.37 | odd | 2 | |||
5472.2.e.f.5167.18 | 24 | 4.3 | odd | 2 | |||
5472.2.e.f.5167.19 | 24 | 12.11 | even | 2 | |||
5472.2.e.f.5167.20 | 24 | 456.341 | even | 2 |