Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(440,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.440");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.o (of order \(6\), degree \(2\), not 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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 881.11 | ||
Character | \(\chi\) | \(=\) | 1323.881 |
Dual form | 1323.2.o.e.440.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.105953 | + | 0.0611722i | −0.0749204 | + | 0.0432553i | −0.536992 | − | 0.843587i | \(-0.680440\pi\) |
0.462072 | + | 0.886842i | \(0.347106\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.992516 | + | 1.71909i | −0.496258 | + | 0.859544i | ||||
\(5\) | −0.264715 | + | 0.458500i | −0.118384 | + | 0.205047i | −0.919127 | − | 0.393960i | \(-0.871105\pi\) |
0.800743 | + | 0.599008i | \(0.204438\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 0.487547i | − | 0.172374i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 0.0647728i | − | 0.0204830i | ||||||
\(11\) | 3.64120 | − | 2.10225i | 1.09786 | − | 0.633851i | 0.162204 | − | 0.986757i | \(-0.448140\pi\) |
0.935659 | + | 0.352906i | \(0.114807\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.74714 | + | 1.00871i | 0.484570 | + | 0.279767i | 0.722319 | − | 0.691560i | \(-0.243076\pi\) |
−0.237749 | + | 0.971327i | \(0.576410\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.95521 | − | 3.38652i | −0.488802 | − | 0.846630i | ||||
\(17\) | 4.38762 | 1.06415 | 0.532077 | − | 0.846696i | \(-0.321412\pi\) | ||||
0.532077 | + | 0.846696i | \(0.321412\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.24685i | 1.20371i | 0.798605 | + | 0.601855i | \(0.205572\pi\) | ||||
−0.798605 | + | 0.601855i | \(0.794428\pi\) | |||||||
\(20\) | −0.525467 | − | 0.910136i | −0.117498 | − | 0.203513i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.257198 | + | 0.445480i | −0.0548348 | + | 0.0949767i | ||||
\(23\) | −5.43444 | − | 3.13757i | −1.13316 | − | 0.654230i | −0.188431 | − | 0.982086i | \(-0.560340\pi\) |
−0.944727 | + | 0.327857i | \(0.893674\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.35985 | + | 4.08738i | 0.471970 | + | 0.817477i | ||||
\(26\) | −0.246821 | −0.0484056 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.27689 | − | 4.20131i | 1.35128 | − | 0.780164i | 0.362855 | − | 0.931846i | \(-0.381802\pi\) |
0.988429 | + | 0.151681i | \(0.0484687\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.03204 | − | 0.595849i | −0.185360 | − | 0.107018i | 0.404449 | − | 0.914561i | \(-0.367463\pi\) |
−0.589809 | + | 0.807543i | \(0.700797\pi\) | |||||||
\(32\) | 1.25878 | + | 0.726755i | 0.222522 | + | 0.128473i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.464883 | + | 0.268400i | −0.0797268 | + | 0.0460303i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.23252 | −0.531424 | −0.265712 | − | 0.964053i | \(-0.585607\pi\) | ||||
−0.265712 | + | 0.964053i | \(0.585607\pi\) | |||||||
\(38\) | −0.320962 | − | 0.555922i | −0.0520668 | − | 0.0901824i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.223540 | + | 0.129061i | 0.0353448 | + | 0.0204063i | ||||
\(41\) | −0.0994958 | + | 0.172332i | −0.0155386 | + | 0.0269137i | −0.873690 | − | 0.486483i | \(-0.838280\pi\) |
0.858152 | + | 0.513396i | \(0.171613\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.96309 | + | 6.86427i | 0.604366 | + | 1.04679i | 0.992151 | + | 0.125042i | \(0.0399067\pi\) |
−0.387786 | + | 0.921750i | \(0.626760\pi\) | |||||||
\(44\) | 8.34605i | 1.25821i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.767730 | 0.113196 | ||||||||
\(47\) | 4.98595 | + | 8.63591i | 0.727275 | + | 1.25968i | 0.958031 | + | 0.286665i | \(0.0925468\pi\) |
−0.230756 | + | 0.973012i | \(0.574120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.500069 | − | 0.288715i | −0.0707204 | − | 0.0408304i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.46814 | + | 2.00233i | −0.480944 | + | 0.277673i | ||||
\(53\) | − | 4.21753i | − | 0.579323i | −0.957129 | − | 0.289661i | \(-0.906457\pi\) | ||
0.957129 | − | 0.289661i | \(-0.0935427\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.22598i | 0.300152i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.514008 | + | 0.890287i | −0.0674925 | + | 0.116900i | ||||
\(59\) | −6.71960 | + | 11.6387i | −0.874817 | + | 1.51523i | −0.0178590 | + | 0.999841i | \(0.505685\pi\) |
−0.856958 | + | 0.515387i | \(0.827648\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3564 | + | 6.55662i | −1.45404 | + | 0.839489i | −0.998707 | − | 0.0508335i | \(-0.983812\pi\) |
−0.455330 | + | 0.890323i | \(0.650479\pi\) | |||||||
\(62\) | 0.145798 | 0.0185163 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.64300 | 0.955375 | ||||||||
\(65\) | −0.924990 | + | 0.534043i | −0.114731 | + | 0.0662399i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.29001 | − | 5.69847i | 0.401939 | − | 0.696179i | −0.592021 | − | 0.805923i | \(-0.701670\pi\) |
0.993960 | + | 0.109744i | \(0.0350030\pi\) | |||||||
\(68\) | −4.35478 | + | 7.54270i | −0.528095 | + | 0.914687i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.50587i | 1.00946i | 0.863277 | + | 0.504730i | \(0.168408\pi\) | ||||
−0.863277 | + | 0.504730i | \(0.831592\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.61202i | 0.656837i | 0.944532 | + | 0.328419i | \(0.106516\pi\) | ||||
−0.944532 | + | 0.328419i | \(0.893484\pi\) | |||||||
\(74\) | 0.342497 | − | 0.197741i | 0.0398145 | − | 0.0229869i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.01980 | − | 5.20758i | −1.03464 | − | 0.597351i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.286342 | − | 0.495959i | −0.0322160 | − | 0.0557997i | 0.849468 | − | 0.527640i | \(-0.176923\pi\) |
−0.881684 | + | 0.471841i | \(0.843590\pi\) | |||||||
\(80\) | 2.07029 | 0.231465 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 0.0243455i | − | 0.00268851i | ||||||
\(83\) | 5.42692 | + | 9.39971i | 0.595682 | + | 1.03175i | 0.993450 | + | 0.114266i | \(0.0364516\pi\) |
−0.397768 | + | 0.917486i | \(0.630215\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.16147 | + | 2.01172i | −0.125979 | + | 0.218202i | ||||
\(86\) | −0.839806 | − | 0.484862i | −0.0905586 | − | 0.0522840i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.02494 | − | 1.77525i | −0.109259 | − | 0.189243i | ||||
\(89\) | 12.8738 | 1.36461 | 0.682307 | − | 0.731065i | \(-0.260977\pi\) | ||||
0.682307 | + | 0.731065i | \(0.260977\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.7875 | − | 6.22819i | 1.12468 | − | 0.649333i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.05656 | − | 0.610003i | −0.108975 | − | 0.0629170i | ||||
\(95\) | −2.40568 | − | 1.38892i | −0.246817 | − | 0.142500i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.493773 | + | 0.285080i | −0.0501351 | + | 0.0289455i | −0.524858 | − | 0.851190i | \(-0.675882\pi\) |
0.474723 | + | 0.880135i | \(0.342548\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.36876 | −0.936876 | ||||||||
\(101\) | −5.81552 | − | 10.0728i | −0.578666 | − | 1.00228i | −0.995633 | − | 0.0933576i | \(-0.970240\pi\) |
0.416966 | − | 0.908922i | \(-0.363093\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.54001 | − | 3.19853i | −0.545874 | − | 0.315160i | 0.201582 | − | 0.979472i | \(-0.435392\pi\) |
−0.747456 | + | 0.664311i | \(0.768725\pi\) | |||||||
\(104\) | 0.491795 | − | 0.851814i | 0.0482245 | − | 0.0835272i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.257996 | + | 0.446862i | 0.0250588 | + | 0.0434031i | ||||
\(107\) | 0.253263i | 0.0244839i | 0.999925 | + | 0.0122419i | \(0.00389683\pi\) | ||||
−0.999925 | + | 0.0122419i | \(0.996103\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.9720 | 1.14671 | 0.573357 | − | 0.819306i | \(-0.305641\pi\) | ||||
0.573357 | + | 0.819306i | \(0.305641\pi\) | |||||||
\(110\) | −0.136168 | − | 0.235851i | −0.0129831 | − | 0.0224875i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.28636 | − | 2.47473i | −0.403227 | − | 0.232803i | 0.284648 | − | 0.958632i | \(-0.408123\pi\) |
−0.687875 | + | 0.725829i | \(0.741456\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.87715 | − | 1.66113i | 0.268296 | − | 0.154901i | ||||
\(116\) | 16.6795i | 1.54865i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.64421i | − | 0.151362i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.33888 | − | 5.78311i | 0.303535 | − | 0.525737i | ||||
\(122\) | 0.802166 | − | 1.38939i | 0.0726247 | − | 0.125790i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.04863 | − | 1.18278i | 0.183973 | − | 0.106217i | ||||
\(125\) | −5.14590 | −0.460263 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.68446 | −0.326943 | −0.163472 | − | 0.986548i | \(-0.552269\pi\) | ||||
−0.163472 | + | 0.986548i | \(0.552269\pi\) | |||||||
\(128\) | −3.32736 | + | 1.92105i | −0.294100 | + | 0.169798i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.0653372 | − | 0.113167i | 0.00573045 | − | 0.00992543i | ||||
\(131\) | −2.72837 | + | 4.72567i | −0.238379 | + | 0.412884i | −0.960249 | − | 0.279144i | \(-0.909949\pi\) |
0.721871 | + | 0.692028i | \(0.243283\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.805030i | 0.0695440i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 2.13917i | − | 0.183432i | ||||||
\(137\) | 1.39996 | − | 0.808270i | 0.119607 | − | 0.0690551i | −0.439003 | − | 0.898486i | \(-0.644668\pi\) |
0.558610 | + | 0.829431i | \(0.311335\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.79085 | + | 5.65275i | 0.830449 | + | 0.479460i | 0.854006 | − | 0.520262i | \(-0.174166\pi\) |
−0.0235572 | + | 0.999722i | \(0.507499\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.520323 | − | 0.901226i | −0.0436645 | − | 0.0756292i | ||||
\(143\) | 8.48226 | 0.709322 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.44860i | 0.369436i | ||||||||
\(146\) | −0.343300 | − | 0.594613i | −0.0284117 | − | 0.0492105i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.20833 | − | 5.55699i | 0.263723 | − | 0.456782i | ||||
\(149\) | −4.61426 | − | 2.66404i | −0.378015 | − | 0.218247i | 0.298939 | − | 0.954272i | \(-0.403367\pi\) |
−0.676954 | + | 0.736025i | \(0.736700\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.32132 | + | 2.28859i | 0.107527 | + | 0.186243i | 0.914768 | − | 0.403980i | \(-0.132373\pi\) |
−0.807241 | + | 0.590222i | \(0.799040\pi\) | |||||||
\(152\) | 2.55808 | 0.207488 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.546393 | − | 0.315460i | 0.0438873 | − | 0.0253384i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.3181 | + | 6.53448i | 0.903279 | + | 0.521508i | 0.878263 | − | 0.478179i | \(-0.158703\pi\) |
0.0250163 | + | 0.999687i | \(0.492036\pi\) | |||||||
\(158\) | 0.0606778 | + | 0.0350324i | 0.00482727 | + | 0.00278703i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.666434 | + | 0.384766i | −0.0526862 | + | 0.0304184i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0269 | 1.33365 | 0.666825 | − | 0.745214i | \(-0.267653\pi\) | ||||
0.666825 | + | 0.745214i | \(0.267653\pi\) | |||||||
\(164\) | −0.197502 | − | 0.342084i | −0.0154223 | − | 0.0267123i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.15000 | − | 0.663954i | −0.0892575 | − | 0.0515328i | ||||
\(167\) | 10.6605 | − | 18.4645i | 0.824932 | − | 1.42882i | −0.0770396 | − | 0.997028i | \(-0.524547\pi\) |
0.901971 | − | 0.431796i | \(-0.142120\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.46499 | − | 7.73360i | −0.343461 | − | 0.594892i | ||||
\(170\) | − | 0.284198i | − | 0.0217970i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −15.7337 | −1.19968 | ||||||||
\(173\) | −10.2433 | − | 17.7418i | −0.778781 | − | 1.34889i | −0.932645 | − | 0.360796i | \(-0.882505\pi\) |
0.153864 | − | 0.988092i | \(-0.450828\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.2386 | − | 8.22066i | −1.07327 | − | 0.619655i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.36402 | + | 0.787516i | −0.102237 | + | 0.0590268i | ||||
\(179\) | − | 14.4071i | − | 1.07684i | −0.842676 | − | 0.538420i | \(-0.819021\pi\) | ||
0.842676 | − | 0.538420i | \(-0.180979\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.97309i | 0.518306i | 0.965836 | + | 0.259153i | \(0.0834434\pi\) | ||||
−0.965836 | + | 0.259153i | \(0.916557\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.52971 | + | 2.64954i | −0.112772 | + | 0.195327i | ||||
\(185\) | 0.855697 | − | 1.48211i | 0.0629121 | − | 0.108967i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.9762 | − | 9.22386i | 1.16829 | − | 0.674515i | ||||
\(188\) | −19.7945 | −1.44366 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.339853 | 0.0246555 | ||||||||
\(191\) | 9.38310 | − | 5.41734i | 0.678937 | − | 0.391985i | −0.120517 | − | 0.992711i | \(-0.538455\pi\) |
0.799455 | + | 0.600727i | \(0.205122\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.26223 | + | 9.11444i | −0.378783 | + | 0.656072i | −0.990886 | − | 0.134707i | \(-0.956991\pi\) |
0.612102 | + | 0.790779i | \(0.290324\pi\) | |||||||
\(194\) | 0.0348780 | − | 0.0604104i | 0.00250409 | − | 0.00433722i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.5156i | 1.10544i | 0.833366 | + | 0.552721i | \(0.186410\pi\) | ||||
−0.833366 | + | 0.552721i | \(0.813590\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 12.5479i | − | 0.889495i | −0.895656 | − | 0.444748i | \(-0.853293\pi\) | ||
0.895656 | − | 0.444748i | \(-0.146707\pi\) | |||||||
\(200\) | 1.99279 | − | 1.15054i | 0.140912 | − | 0.0813553i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.23235 | + | 0.711497i | 0.0867078 | + | 0.0500608i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0526760 | − | 0.0912375i | −0.00367905 | − | 0.00637231i | ||||
\(206\) | 0.782644 | 0.0545294 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 7.88898i | − | 0.547002i | ||||||
\(209\) | 11.0302 | + | 19.1048i | 0.762973 | + | 1.32151i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.19765 | + | 2.07438i | −0.0824494 | + | 0.142807i | −0.904302 | − | 0.426894i | \(-0.859608\pi\) |
0.821852 | + | 0.569701i | \(0.192941\pi\) | |||||||
\(212\) | 7.25031 | + | 4.18597i | 0.497953 | + | 0.287493i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.0154927 | − | 0.0268341i | −0.00105906 | − | 0.00183434i | ||||
\(215\) | −4.19636 | −0.286189 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.26848 | + | 0.732357i | −0.0859123 | + | 0.0496015i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.82666 | − | 2.20932i | −0.257993 | − | 0.148953i | ||||
\(221\) | 7.66580 | + | 4.42585i | 0.515657 | + | 0.297715i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.42193 | − | 1.39830i | 0.162184 | − | 0.0936370i | −0.416711 | − | 0.909039i | \(-0.636817\pi\) |
0.578895 | + | 0.815402i | \(0.303484\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.605540 | 0.0402799 | ||||||||
\(227\) | −1.42300 | − | 2.46471i | −0.0944480 | − | 0.163589i | 0.814930 | − | 0.579559i | \(-0.196775\pi\) |
−0.909378 | + | 0.415970i | \(0.863442\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.5460 | + | 11.8623i | 1.35772 | + | 0.783880i | 0.989316 | − | 0.145786i | \(-0.0465711\pi\) |
0.368404 | + | 0.929666i | \(0.379904\pi\) | |||||||
\(230\) | −0.203229 | + | 0.352004i | −0.0134006 | + | 0.0232104i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.04834 | − | 3.54782i | −0.134480 | − | 0.232926i | ||||
\(233\) | − | 18.7298i | − | 1.22703i | −0.789684 | − | 0.613514i | \(-0.789755\pi\) | ||
0.789684 | − | 0.613514i | \(-0.210245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.27942 | −0.344391 | ||||||||
\(236\) | −13.3386 | − | 23.1032i | −0.868270 | − | 1.50389i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.1421 | − | 6.43288i | −0.720721 | − | 0.416109i | 0.0942969 | − | 0.995544i | \(-0.469940\pi\) |
−0.815018 | + | 0.579436i | \(0.803273\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.64082 | + | 2.10203i | −0.234526 | + | 0.135403i | −0.612658 | − | 0.790348i | \(-0.709900\pi\) |
0.378132 | + | 0.925752i | \(0.376566\pi\) | |||||||
\(242\) | 0.816987i | 0.0525179i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 26.0302i | − | 1.66641i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.29257 | + | 9.16700i | −0.336758 | + | 0.583282i | ||||
\(248\) | −0.290504 | + | 0.503168i | −0.0184470 | + | 0.0319512i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.545226 | − | 0.314786i | 0.0344831 | − | 0.0199088i | ||||
\(251\) | −7.50592 | −0.473770 | −0.236885 | − | 0.971538i | \(-0.576126\pi\) | ||||
−0.236885 | + | 0.971538i | \(0.576126\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.3838 | −1.65874 | ||||||||
\(254\) | 0.390381 | − | 0.225387i | 0.0244947 | − | 0.0141420i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.40797 | + | 12.8310i | −0.462998 | + | 0.801936i | ||||
\(257\) | 2.51960 | − | 4.36408i | 0.157169 | − | 0.272224i | −0.776678 | − | 0.629898i | \(-0.783097\pi\) |
0.933847 | + | 0.357674i | \(0.116430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 2.12018i | − | 0.131488i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 0.667601i | − | 0.0412445i | ||||||
\(263\) | −12.2494 | + | 7.07220i | −0.755331 | + | 0.436091i | −0.827617 | − | 0.561293i | \(-0.810304\pi\) |
0.0722856 | + | 0.997384i | \(0.476971\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.93374 | + | 1.11644i | 0.118789 | + | 0.0685826i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.53078 | + | 11.3116i | 0.398931 | + | 0.690969i | ||||
\(269\) | 15.7771 | 0.961948 | 0.480974 | − | 0.876735i | \(-0.340283\pi\) | ||||
0.480974 | + | 0.876735i | \(0.340283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 16.8078i | − | 1.02100i | −0.859877 | − | 0.510501i | \(-0.829460\pi\) | ||
0.859877 | − | 0.510501i | \(-0.170540\pi\) | |||||||
\(272\) | −8.57871 | − | 14.8588i | −0.520160 | − | 0.900944i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.0988873 | + | 0.171278i | −0.00597400 | + | 0.0103473i | ||||
\(275\) | 17.1854 | + | 9.92198i | 1.03632 | + | 0.598318i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.91066 | − | 15.4337i | −0.535390 | − | 0.927322i | −0.999144 | − | 0.0413586i | \(-0.986831\pi\) |
0.463755 | − | 0.885964i | \(-0.346502\pi\) | |||||||
\(278\) | −1.38317 | −0.0829568 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.59774 | + | 4.38656i | −0.453243 | + | 0.261680i | −0.709199 | − | 0.705008i | \(-0.750943\pi\) |
0.255956 | + | 0.966688i | \(0.417610\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.7047 | − | 10.7991i | −1.11188 | − | 0.641942i | −0.172562 | − | 0.984999i | \(-0.555204\pi\) |
−0.939315 | + | 0.343056i | \(0.888538\pi\) | |||||||
\(284\) | −14.6223 | − | 8.44221i | −0.867676 | − | 0.500953i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.898724 | + | 0.518879i | −0.0531427 | + | 0.0306819i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.25120 | 0.132424 | ||||||||
\(290\) | −0.272131 | − | 0.471344i | −0.0159801 | − | 0.0276783i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.64756 | − | 5.57002i | −0.564581 | − | 0.325961i | ||||
\(293\) | 9.79756 | − | 16.9699i | 0.572379 | − | 0.991390i | −0.423942 | − | 0.905690i | \(-0.639354\pi\) |
0.996321 | − | 0.0857006i | \(-0.0273128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.55755 | − | 6.16186i | −0.207129 | − | 0.358758i | ||||
\(296\) | 1.57601i | 0.0916035i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.651862 | 0.0377613 | ||||||||
\(299\) | −6.32983 | − | 10.9636i | −0.366063 | − | 0.634040i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.279996 | − | 0.161656i | −0.0161120 | − | 0.00930224i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 17.7686 | − | 10.2587i | 1.01910 | − | 0.588376i | ||||
\(305\) | − | 6.94254i | − | 0.397529i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.7677i | 1.58478i | 0.610012 | + | 0.792392i | \(0.291165\pi\) | ||||
−0.610012 | + | 0.792392i | \(0.708835\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.0385948 | + | 0.0668482i | −0.00219204 | + | 0.00379672i | ||||
\(311\) | −10.0080 | + | 17.3344i | −0.567501 | + | 0.982941i | 0.429311 | + | 0.903157i | \(0.358756\pi\) |
−0.996812 | + | 0.0797841i | \(0.974577\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.9654 | − | 9.21765i | 0.902420 | − | 0.521012i | 0.0244352 | − | 0.999701i | \(-0.492221\pi\) |
0.877984 | + | 0.478689i | \(0.158888\pi\) | |||||||
\(314\) | −1.59891 | −0.0902320 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.13680 | 0.0639498 | ||||||||
\(317\) | 12.5992 | − | 7.27416i | 0.707642 | − | 0.408558i | −0.102545 | − | 0.994728i | \(-0.532699\pi\) |
0.810187 | + | 0.586171i | \(0.199365\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.6644 | − | 30.5956i | 0.989016 | − | 1.71303i | ||||
\(320\) | −2.02322 | + | 3.50431i | −0.113101 | + | 0.195897i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.0212i | 1.28093i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.52166i | 0.528167i | ||||||||
\(326\) | −1.80406 | + | 1.04157i | −0.0999176 | + | 0.0576874i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.0840197 | + | 0.0485088i | 0.00463921 | + | 0.00267845i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.8446 | + | 25.7115i | 0.815930 | + | 1.41323i | 0.908658 | + | 0.417541i | \(0.137108\pi\) |
−0.0927274 | + | 0.995692i | \(0.529559\pi\) | |||||||
\(332\) | −21.5452 | −1.18245 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.60850i | 0.142731i | ||||||||
\(335\) | 1.74183 | + | 3.01694i | 0.0951664 | + | 0.164833i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.60606 | + | 7.97793i | −0.250908 | + | 0.434586i | −0.963776 | − | 0.266713i | \(-0.914063\pi\) |
0.712868 | + | 0.701298i | \(0.247396\pi\) | |||||||
\(338\) | 0.946163 | + | 0.546267i | 0.0514645 | + | 0.0297130i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.30555 | − | 3.99333i | −0.125036 | − | 0.216569i | ||||
\(341\) | −5.01049 | −0.271333 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.34665 | − | 1.93219i | 0.180439 | − | 0.104177i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.17062 | + | 1.25321i | 0.116693 | + | 0.0673728i | ||||
\(347\) | −15.7313 | − | 9.08247i | −0.844501 | − | 0.487573i | 0.0142910 | − | 0.999898i | \(-0.495451\pi\) |
−0.858791 | + | 0.512325i | \(0.828784\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.70494 | − | 3.29375i | 0.305378 | − | 0.176310i | −0.339478 | − | 0.940614i | \(-0.610250\pi\) |
0.644856 | + | 0.764304i | \(0.276917\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.11128 | 0.325732 | ||||||||
\(353\) | −10.4692 | − | 18.1332i | −0.557221 | − | 0.965135i | −0.997727 | − | 0.0673857i | \(-0.978534\pi\) |
0.440506 | − | 0.897750i | \(-0.354799\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.89994 | − | 2.25163i | −0.206987 | − | 0.119504i | ||||
\(356\) | −12.7774 | + | 22.1311i | −0.677201 | + | 1.17295i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.881317 | + | 1.52649i | 0.0465791 | + | 0.0806773i | ||||
\(359\) | 14.2265i | 0.750845i | 0.926854 | + | 0.375422i | \(0.122502\pi\) | ||||
−0.926854 | + | 0.375422i | \(0.877498\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.52944 | −0.448918 | ||||||||
\(362\) | −0.426560 | − | 0.738823i | −0.0224195 | − | 0.0388317i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.57311 | − | 1.48559i | −0.134683 | − | 0.0777591i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.7237 | + | 6.19136i | −0.559775 | + | 0.323186i | −0.753055 | − | 0.657957i | \(-0.771421\pi\) |
0.193280 | + | 0.981144i | \(0.438087\pi\) | |||||||
\(368\) | 24.5384i | 1.27915i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.209380i | 0.0108851i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.6559 | − | 18.4565i | 0.551740 | − | 0.955642i | −0.446409 | − | 0.894829i | \(-0.647297\pi\) |
0.998149 | − | 0.0608130i | \(-0.0193693\pi\) | |||||||
\(374\) | −1.12849 | + | 1.95460i | −0.0583527 | + | 0.101070i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.21041 | − | 2.43088i | 0.217135 | − | 0.125363i | ||||
\(377\) | 16.9517 | 0.873057 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.6001 | 0.544489 | 0.272244 | − | 0.962228i | \(-0.412234\pi\) | ||||
0.272244 | + | 0.962228i | \(0.412234\pi\) | |||||||
\(380\) | 4.77535 | − | 2.75705i | 0.244970 | − | 0.141434i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.662781 | + | 1.14797i | −0.0339108 | + | 0.0587353i | ||||
\(383\) | 6.32174 | − | 10.9496i | 0.323026 | − | 0.559497i | −0.658085 | − | 0.752944i | \(-0.728633\pi\) |
0.981111 | + | 0.193446i | \(0.0619666\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.28761i | − | 0.0655375i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 1.13179i | − | 0.0574578i | ||||||
\(389\) | −11.4538 | + | 6.61286i | −0.580732 | + | 0.335286i | −0.761424 | − | 0.648254i | \(-0.775499\pi\) |
0.180692 | + | 0.983540i | \(0.442166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.8442 | − | 13.7665i | −1.20586 | − | 0.696201i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.949125 | − | 1.64393i | −0.0478162 | − | 0.0828201i | ||||
\(395\) | 0.303196 | 0.0152554 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 24.7882i | − | 1.24409i | −0.782983 | − | 0.622043i | \(-0.786303\pi\) | ||
0.782983 | − | 0.622043i | \(-0.213697\pi\) | |||||||
\(398\) | 0.767582 | + | 1.32949i | 0.0384754 | + | 0.0666413i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.22800 | − | 15.9834i | 0.461400 | − | 0.799168i | ||||
\(401\) | −3.19615 | − | 1.84530i | −0.159608 | − | 0.0921499i | 0.418068 | − | 0.908416i | \(-0.362707\pi\) |
−0.577677 | + | 0.816266i | \(0.696041\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.20208 | − | 2.08207i | −0.0598800 | − | 0.103715i | ||||
\(404\) | 23.0880 | 1.14867 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.7703 | + | 6.79556i | −0.583430 | + | 0.336843i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0535 | + | 9.26852i | 0.793797 | + | 0.458299i | 0.841297 | − | 0.540573i | \(-0.181792\pi\) |
−0.0475008 | + | 0.998871i | \(0.515126\pi\) | |||||||
\(410\) | 0.0111624 | + | 0.00644462i | 0.000551272 | + | 0.000318277i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.9971 | − | 6.34918i | 0.541788 | − | 0.312802i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.74635 | −0.282077 | ||||||||
\(416\) | 1.46618 | + | 2.53949i | 0.0718852 | + | 0.124509i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.33737 | − | 1.34948i | −0.114324 | − | 0.0660053i | ||||
\(419\) | 1.46994 | − | 2.54600i | 0.0718111 | − | 0.124380i | −0.827884 | − | 0.560899i | \(-0.810455\pi\) |
0.899695 | + | 0.436519i | \(0.143789\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.1081 | − | 24.4359i | −0.687585 | − | 1.19093i | −0.972617 | − | 0.232415i | \(-0.925337\pi\) |
0.285031 | − | 0.958518i | \(-0.407996\pi\) | |||||||
\(422\) | − | 0.293051i | − | 0.0142655i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.05624 | −0.0998600 | ||||||||
\(425\) | 10.3541 | + | 17.9339i | 0.502249 | + | 0.869921i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.435382 | − | 0.251368i | −0.0210450 | − | 0.0121503i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.444618 | − | 0.256700i | 0.0214414 | − | 0.0123792i | ||||
\(431\) | 6.76465i | 0.325842i | 0.986639 | + | 0.162921i | \(0.0520915\pi\) | ||||
−0.986639 | + | 0.162921i | \(0.947908\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 28.3475i | − | 1.36229i | −0.732146 | − | 0.681147i | \(-0.761481\pi\) | ||
0.732146 | − | 0.681147i | \(-0.238519\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.8824 | + | 20.5810i | −0.569066 | + | 0.985651i | ||||
\(437\) | 16.4624 | − | 28.5137i | 0.787503 | − | 1.36399i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.8208 | + | 13.1756i | −1.08918 | + | 0.628837i | −0.933358 | − | 0.358948i | \(-0.883136\pi\) |
−0.155821 | + | 0.987785i | \(0.549802\pi\) | |||||||
\(440\) | 1.08527 | 0.0517382 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.08296 | −0.0515110 | ||||||||
\(443\) | 4.75958 | − | 2.74795i | 0.226135 | − | 0.130559i | −0.382653 | − | 0.923892i | \(-0.624989\pi\) |
0.608788 | + | 0.793333i | \(0.291656\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.40787 | + | 5.90261i | −0.161549 | + | 0.279810i | ||||
\(446\) | −0.171074 | + | 0.296309i | −0.00810060 | + | 0.0140306i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 7.38342i | − | 0.348445i | −0.984706 | − | 0.174223i | \(-0.944259\pi\) | ||
0.984706 | − | 0.174223i | \(-0.0557412\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.836659i | 0.0393967i | ||||||||
\(452\) | 8.50857 | − | 4.91242i | 0.400209 | − | 0.231061i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.301544 | + | 0.174097i | 0.0141522 | + | 0.00817076i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.7109 | − | 35.8724i | −0.968817 | − | 1.67804i | −0.698991 | − | 0.715130i | \(-0.746367\pi\) |
−0.269826 | − | 0.962909i | \(-0.586966\pi\) | |||||||
\(458\) | −2.90256 | −0.135628 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.59477i | 0.307483i | ||||||||
\(461\) | 5.44638 | + | 9.43341i | 0.253663 | + | 0.439357i | 0.964532 | − | 0.263968i | \(-0.0850312\pi\) |
−0.710868 | + | 0.703325i | \(0.751698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.87980 | + | 4.98796i | −0.133836 | + | 0.231810i | −0.925152 | − | 0.379597i | \(-0.876063\pi\) |
0.791316 | + | 0.611407i | \(0.209396\pi\) | |||||||
\(464\) | −28.4557 | − | 16.4289i | −1.32102 | − | 0.762692i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.14574 | + | 1.98448i | 0.0530755 | + | 0.0919294i | ||||
\(467\) | −23.8882 | −1.10541 | −0.552707 | − | 0.833376i | \(-0.686405\pi\) | ||||
−0.552707 | + | 0.833376i | \(0.686405\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.559372 | − | 0.322954i | 0.0258019 | − | 0.0148967i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.67440 | + | 3.27612i | 0.261185 | + | 0.150795i | ||||
\(473\) | 28.8608 | + | 16.6628i | 1.32702 | + | 0.766156i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.4459 | + | 12.3818i | −0.984005 | + | 0.568116i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.57406 | 0.0719956 | ||||||||
\(479\) | 0.947645 | + | 1.64137i | 0.0432990 | + | 0.0749961i | 0.886863 | − | 0.462033i | \(-0.152880\pi\) |
−0.843564 | + | 0.537029i | \(0.819547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.64768 | − | 3.26069i | −0.257512 | − | 0.148675i | ||||
\(482\) | 0.257171 | − | 0.445434i | 0.0117138 | − | 0.0202890i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.62778 | + | 11.4797i | 0.301263 | + | 0.521803i | ||||
\(485\) | − | 0.301860i | − | 0.0137067i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.2248 | 1.27899 | 0.639494 | − | 0.768796i | \(-0.279144\pi\) | ||||
0.639494 | + | 0.768796i | \(0.279144\pi\) | |||||||
\(488\) | 3.19666 | + | 5.53677i | 0.144706 | + | 0.250638i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.30250 | + | 1.32935i | 0.103910 | + | 0.0599927i | 0.551055 | − | 0.834469i | \(-0.314226\pi\) |
−0.447144 | + | 0.894462i | \(0.647559\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.9282 | − | 18.4338i | 1.43797 | − | 0.830215i | ||||
\(494\) | − | 1.29503i | − | 0.0582663i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.66003i | 0.209242i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.27844 | − | 10.8746i | 0.281062 | − | 0.486813i | −0.690585 | − | 0.723251i | \(-0.742647\pi\) |
0.971646 | + | 0.236438i | \(0.0759801\pi\) | |||||||
\(500\) | 5.10739 | − | 8.84625i | 0.228409 | − | 0.395617i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.795278 | − | 0.459154i | 0.0354950 | − | 0.0204930i | ||||
\(503\) | 18.1502 | 0.809278 | 0.404639 | − | 0.914476i | \(-0.367397\pi\) | ||||
0.404639 | + | 0.914476i | \(0.367397\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.15782 | 0.274020 | ||||||||
\(506\) | 2.79546 | − | 1.61396i | 0.124273 | − | 0.0717491i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.65689 | − | 6.33391i | 0.162248 | − | 0.281022i | ||||
\(509\) | 9.33827 | − | 16.1744i | 0.413912 | − | 0.716916i | −0.581402 | − | 0.813617i | \(-0.697496\pi\) |
0.995314 | + | 0.0967005i | \(0.0308289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 9.49685i | − | 0.419705i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.616519i | 0.0271935i | ||||||||
\(515\) | 2.93305 | − | 1.69340i | 0.129245 | − | 0.0746199i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.3096 | + | 20.9634i | 1.59690 | + | 0.921968i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.260371 | + | 0.450975i | 0.0114180 | + | 0.0197766i | ||||
\(521\) | 18.0665 | 0.791508 | 0.395754 | − | 0.918357i | \(-0.370483\pi\) | ||||
0.395754 | + | 0.918357i | \(0.370483\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.1338i | 0.924116i | 0.886850 | + | 0.462058i | \(0.152889\pi\) | ||||
−0.886850 | + | 0.462058i | \(0.847111\pi\) | |||||||
\(524\) | −5.41590 | − | 9.38061i | −0.236595 | − | 0.409794i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.865245 | − | 1.49865i | 0.0377265 | − | 0.0653442i | ||||
\(527\) | −4.52820 | − | 2.61436i | −0.197252 | − | 0.113883i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.18875 | + | 14.1833i | 0.356033 | + | 0.616666i | ||||
\(530\) | −0.273181 | −0.0118662 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.347667 | + | 0.200725i | −0.0150591 | + | 0.00869439i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.116121 | − | 0.0670425i | −0.00502035 | − | 0.00289850i | ||||
\(536\) | −2.77827 | − | 1.60403i | −0.120003 | − | 0.0692837i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.67164 | + | 0.965122i | −0.0720695 | + | 0.0416093i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.7732 | 0.764131 | 0.382065 | − | 0.924135i | \(-0.375213\pi\) | ||||
0.382065 | + | 0.924135i | \(0.375213\pi\) | |||||||
\(542\) | 1.02817 | + | 1.78084i | 0.0441637 | + | 0.0764938i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.52304 | + | 3.18873i | 0.236798 | + | 0.136715i | ||||
\(545\) | −3.16918 | + | 5.48918i | −0.135753 | + | 0.235131i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.1560 | + | 24.5190i | 0.605268 | + | 1.04835i | 0.992009 | + | 0.126166i | \(0.0402673\pi\) |
−0.386741 | + | 0.922188i | \(0.626399\pi\) | |||||||
\(548\) | 3.20888i | 0.137077i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.42780 | −0.103522 | ||||||||
\(551\) | 22.0437 | + | 38.1808i | 0.939092 | + | 1.62655i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.88823 | + | 1.09017i | 0.0802232 | + | 0.0463169i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.4352 | + | 11.2209i | −0.824234 | + | 0.475872i | ||||
\(557\) | − | 11.7214i | − | 0.496651i | −0.968677 | − | 0.248326i | \(-0.920120\pi\) | ||
0.968677 | − | 0.248326i | \(-0.0798803\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.9905i | 0.676326i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.536671 | − | 0.929541i | 0.0226381 | − | 0.0392103i | ||||
\(563\) | −18.3014 | + | 31.6990i | −0.771314 | + | 1.33595i | 0.165529 | + | 0.986205i | \(0.447067\pi\) |
−0.936843 | + | 0.349750i | \(0.886267\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.26933 | − | 1.31020i | 0.0954713 | − | 0.0551204i | ||||
\(566\) | 2.64243 | 0.111070 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.14701 | 0.174005 | ||||||||
\(569\) | −32.6468 | + | 18.8486i | −1.36862 | + | 0.790176i | −0.990752 | − | 0.135682i | \(-0.956677\pi\) |
−0.377872 | + | 0.925858i | \(0.623344\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.1123 | + | 24.4432i | −0.590581 | + | 1.02292i | 0.403574 | + | 0.914947i | \(0.367768\pi\) |
−0.994154 | + | 0.107968i | \(0.965565\pi\) | |||||||
\(572\) | −8.41878 | + | 14.5817i | −0.352007 | + | 0.609694i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 29.6168i | − | 1.23511i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.38512i | 0.390708i | 0.980733 | + | 0.195354i | \(0.0625855\pi\) | ||||
−0.980733 | + | 0.195354i | \(0.937414\pi\) | |||||||
\(578\) | −0.238523 | + | 0.137711i | −0.00992123 | + | 0.00572802i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.64754 | − | 4.41531i | −0.317547 | − | 0.183336i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.86629 | − | 15.3569i | −0.367204 | − | 0.636017i | ||||
\(584\) | 2.73612 | 0.113222 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.39735i | 0.0990338i | ||||||||
\(587\) | −23.1819 | − | 40.1523i | −0.956821 | − | 1.65726i | −0.730146 | − | 0.683291i | \(-0.760548\pi\) |
−0.226675 | − | 0.973971i | \(-0.572785\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.12633 | − | 5.41496i | 0.128818 | − | 0.223120i | ||||
\(590\) | 0.753870 | + | 0.435247i | 0.0310363 | + | 0.0179188i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.32025 | + | 10.9470i | 0.259761 | + | 0.449919i | ||||
\(593\) | −18.1416 | −0.744986 | −0.372493 | − | 0.928035i | \(-0.621497\pi\) | ||||
−0.372493 | + | 0.928035i | \(0.621497\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.15945 | − | 5.28821i | 0.375186 | − | 0.216613i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.34133 | + | 0.774419i | 0.0548512 | + | 0.0316684i | ||||
\(599\) | −6.02771 | − | 3.48010i | −0.246286 | − | 0.142193i | 0.371777 | − | 0.928322i | \(-0.378749\pi\) |
−0.618062 | + | 0.786129i | \(0.712082\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.08865 | + | 1.20588i | −0.0851976 | + | 0.0491889i | −0.541994 | − | 0.840383i | \(-0.682330\pi\) |
0.456796 | + | 0.889572i | \(0.348997\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.24571 | −0.213445 | ||||||||
\(605\) | 1.76770 | + | 3.06175i | 0.0718673 | + | 0.124478i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.0306 | + | 6.36850i | 0.447717 | + | 0.258489i | 0.706865 | − | 0.707348i | \(-0.250109\pi\) |
−0.259149 | + | 0.965837i | \(0.583442\pi\) | |||||||
\(608\) | −3.81318 | + | 6.60462i | −0.154645 | + | 0.267853i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.424690 | + | 0.735585i | 0.0171952 | + | 0.0297830i | ||||
\(611\) | 20.1176i | 0.813870i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.3352 | −0.417436 | −0.208718 | − | 0.977976i | \(-0.566929\pi\) | ||||
−0.208718 | + | 0.977976i | \(0.566929\pi\) | |||||||
\(614\) | −1.69861 | − | 2.94208i | −0.0685503 | − | 0.118733i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.3741 | + | 23.8873i | 1.66566 | + | 0.961668i | 0.969937 | + | 0.243355i | \(0.0782481\pi\) |
0.695721 | + | 0.718313i | \(0.255085\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.2626 | + | 20.3588i | −1.41732 | + | 0.818291i | −0.996063 | − | 0.0886491i | \(-0.971745\pi\) |
−0.421259 | + | 0.906940i | \(0.638412\pi\) | |||||||
\(620\) | 1.25240i | 0.0502975i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 2.44884i | − | 0.0981897i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.4371 | + | 18.0775i | −0.417483 | + | 0.723101i | ||||
\(626\) | −1.12773 | + | 1.95328i | −0.0450731 | + | 0.0780689i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.4667 | + | 12.9711i | −0.896519 | + | 0.517605i | ||||
\(629\) | −14.1831 | −0.565517 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.4782 | 0.456942 | 0.228471 | − | 0.973551i | \(-0.426627\pi\) | ||||
0.228471 | + | 0.973551i | \(0.426627\pi\) | |||||||
\(632\) | −0.241803 | + | 0.139605i | −0.00961841 | + | 0.00555319i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.889953 | + | 1.54144i | −0.0353446 | + | 0.0612186i | ||||
\(635\) | 0.975332 | − | 1.68932i | 0.0387049 | − | 0.0670388i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.32228i | 0.171121i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 2.03412i | − | 0.0804057i | ||||||
\(641\) | 30.5823 | − | 17.6567i | 1.20793 | − | 0.697398i | 0.245622 | − | 0.969366i | \(-0.421008\pi\) |
0.962306 | + | 0.271968i | \(0.0876744\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.09416 | − | 3.51846i | −0.240330 | − | 0.138755i | 0.374998 | − | 0.927025i | \(-0.377643\pi\) |
−0.615328 | + | 0.788271i | \(0.710977\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.40826 | − | 2.43917i | −0.0554071 | − | 0.0959680i | ||||
\(647\) | −14.9942 | −0.589482 | −0.294741 | − | 0.955577i | \(-0.595233\pi\) | ||||
−0.294741 | + | 0.955577i | \(0.595233\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 56.5050i | 2.21801i | ||||||||
\(650\) | −0.582461 | − | 1.00885i | −0.0228460 | − | 0.0395704i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.8995 | + | 29.2708i | −0.661835 | + | 1.14633i | ||||
\(653\) | −4.15597 | − | 2.39945i | −0.162636 | − | 0.0938977i | 0.416473 | − | 0.909148i | \(-0.363266\pi\) |
−0.579109 | + | 0.815250i | \(0.696599\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.44448 | − | 2.50191i | −0.0564405 | − | 0.0977577i | ||||
\(656\) | 0.778140 | 0.0303812 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.4562 | − | 7.76893i | 0.524179 | − | 0.302635i | −0.214464 | − | 0.976732i | \(-0.568800\pi\) |
0.738643 | + | 0.674097i | \(0.235467\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.2131 | − | 10.5154i | −0.708409 | − | 0.409000i | 0.102062 | − | 0.994778i | \(-0.467456\pi\) |
−0.810472 | + | 0.585778i | \(0.800789\pi\) | |||||||
\(662\) | −3.14566 | − | 1.81615i | −0.122260 | − | 0.0705866i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.58280 | − | 2.64588i | 0.177847 | − | 0.102680i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −52.7277 | −2.04163 | ||||||||
\(668\) | 21.1614 | + | 36.6526i | 0.818758 | + | 1.41813i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.369106 | − | 0.213103i | −0.0142598 | − | 0.00823290i | ||||
\(671\) | −27.5673 | + | 47.7479i | −1.06422 | + | 1.84329i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.7194 | + | 18.5665i | 0.413201 | + | 0.715686i | 0.995238 | − | 0.0974770i | \(-0.0310772\pi\) |
−0.582036 | + | 0.813163i | \(0.697744\pi\) | |||||||
\(674\) | − | 1.12705i | − | 0.0434124i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.7263 | 0.681781 | ||||||||
\(677\) | 9.03150 | + | 15.6430i | 0.347109 | + | 0.601210i | 0.985735 | − | 0.168308i | \(-0.0538302\pi\) |
−0.638626 | + | 0.769517i | \(0.720497\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.980808 | + | 0.566270i | 0.0376123 | + | 0.0217155i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.530878 | − | 0.306503i | 0.0203284 | − | 0.0117366i | ||||
\(683\) | − | 45.5647i | − | 1.74349i | −0.489963 | − | 0.871743i | \(-0.662990\pi\) | ||
0.489963 | − | 0.871743i | \(-0.337010\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.855844i | 0.0327001i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15.4973 | − | 26.8422i | 0.590830 | − | 1.02335i | ||||
\(689\) | 4.25428 | − | 7.36863i | 0.162075 | − | 0.280723i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.33627 | + | 1.92620i | −0.126918 | + | 0.0732760i | −0.562115 | − | 0.827059i | \(-0.690012\pi\) |
0.435197 | + | 0.900335i | \(0.356679\pi\) | |||||||
\(692\) | 40.6664 | 1.54590 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.22238 | 0.0843604 | ||||||||
\(695\) | −5.18357 | + | 2.99273i | −0.196624 | + | 0.113521i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.436550 | + | 0.756126i | −0.0165355 | + | 0.0286403i | ||||
\(698\) | −0.402972 | + | 0.697967i | −0.0152527 | + | 0.0264185i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 46.5216i | − | 1.75710i | −0.477653 | − | 0.878549i | \(-0.658512\pi\) | ||
0.477653 | − | 0.878549i | \(-0.341488\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 16.9606i | − | 0.639680i | ||||||
\(704\) | 27.8297 | − | 16.0675i | 1.04887 | − | 0.605566i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.21850 | + | 1.28085i | 0.0834944 | + | 0.0482055i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.6187 | + | 25.3203i | 0.549017 | + | 0.950925i | 0.998342 | + | 0.0575566i | \(0.0183310\pi\) |
−0.449326 | + | 0.893368i | \(0.648336\pi\) | |||||||
\(710\) | 0.550949 | 0.0206767 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 6.27655i | − | 0.235224i | ||||||
\(713\) | 3.73904 | + | 6.47621i | 0.140028 | + | 0.242536i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.24538 | + | 3.88911i | −0.0839724 | + | 0.145445i | ||||
\(716\) | 24.7672 | + | 14.2993i | 0.925592 | + | 0.534391i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.870265 | − | 1.50734i | −0.0324780 | − | 0.0562536i | ||||
\(719\) | 3.37122 | 0.125725 | 0.0628627 | − | 0.998022i | \(-0.479977\pi\) | ||||
0.0628627 | + | 0.998022i | \(0.479977\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.903723 | − | 0.521765i | 0.0336331 | − | 0.0194181i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.9874 | − | 6.92091i | −0.445507 | − | 0.257214i | ||||
\(725\) | 34.3448 | + | 19.8290i | 1.27553 | + | 0.736429i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.34397 | − | 2.50799i | 0.161109 | − | 0.0930164i | −0.417278 | − | 0.908779i | \(-0.637016\pi\) |
0.578387 | + | 0.815763i | \(0.303682\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.363506 | 0.0134540 | ||||||||
\(731\) | 17.3885 | + | 30.1178i | 0.643138 | + | 1.11395i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.6875 | − | 11.3666i | −0.727175 | − | 0.419835i | 0.0902126 | − | 0.995923i | \(-0.471245\pi\) |
−0.817388 | + | 0.576088i | \(0.804579\pi\) | |||||||
\(734\) | 0.757478 | − | 1.31199i | 0.0279590 | − | 0.0484265i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.56050 | − | 7.89901i | −0.168102 | − | 0.291162i | ||||
\(737\) | − | 27.6657i | − | 1.01908i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.39022 | −0.0879256 | −0.0439628 | − | 0.999033i | \(-0.513998\pi\) | ||||
−0.0439628 | + | 0.999033i | \(0.513998\pi\) | |||||||
\(740\) | 1.69859 | + | 2.94204i | 0.0624413 | + | 0.108151i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.1039 | + | 20.8446i | 1.32453 | + | 0.764715i | 0.984447 | − | 0.175682i | \(-0.0562131\pi\) |
0.340078 | + | 0.940397i | \(0.389546\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.44292 | − | 1.41042i | 0.0895018 | − | 0.0516739i | ||||
\(746\) | 2.60737i | 0.0954627i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 36.6193i | 1.33893i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.2710 | + | 22.9861i | −0.484267 | + | 0.838775i | −0.999837 | − | 0.0180728i | \(-0.994247\pi\) |
0.515570 | + | 0.856848i | \(0.327580\pi\) | |||||||
\(752\) | 19.4971 | − | 33.7700i | 0.710987 | − | 1.23147i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.79609 | + | 1.03697i | −0.0654097 | + | 0.0377643i | ||||
\(755\) | −1.39909 | −0.0509180 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.3580 | 0.739923 | 0.369961 | − | 0.929047i | \(-0.379371\pi\) | ||||
0.369961 | + | 0.929047i | \(0.379371\pi\) | |||||||
\(758\) | −1.12311 | + | 0.648430i | −0.0407933 | + | 0.0235520i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.677163 | + | 1.17288i | −0.0245633 | + | 0.0425448i | ||||
\(761\) | −12.9578 | + | 22.4436i | −0.469720 | + | 0.813578i | −0.999401 | − | 0.0346186i | \(-0.988978\pi\) |
0.529681 | + | 0.848197i | \(0.322312\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 21.5072i | 0.778102i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.54686i | 0.0558903i | ||||||||
\(767\) | −23.4802 | + | 13.5563i | −0.847821 | + | 0.489489i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.8269 | − | 10.8697i | −0.678914 | − | 0.391971i | 0.120532 | − | 0.992709i | \(-0.461540\pi\) |
−0.799446 | + | 0.600738i | \(0.794873\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.4457 | − | 18.0925i | −0.375948 | − | 0.651162i | ||||
\(773\) | −20.3213 | −0.730905 | −0.365453 | − | 0.930830i | \(-0.619086\pi\) | ||||
−0.365453 | + | 0.930830i | \(0.619086\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5.62446i | − | 0.202037i | ||||||
\(776\) | 0.138990 | + | 0.240738i | 0.00498945 | + | 0.00864197i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.809047 | − | 1.40131i | 0.0290058 | − | 0.0502394i | ||||
\(779\) | −0.904199 | − | 0.522039i | −0.0323963 | − | 0.0187040i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.8814 | + | 30.9715i | 0.639848 | + | 1.10825i | ||||
\(782\) | 3.36851 | 0.120458 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.99211 | + | 3.45955i | −0.213868 | + | 0.123477i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.4065 | − | 9.47232i | −0.584830 | − | 0.337652i | 0.178221 | − | 0.983991i | \(-0.442966\pi\) |
−0.763051 | + | 0.646339i | \(0.776299\pi\) | |||||||
\(788\) | −26.6727 | − | 15.3995i | −0.950176 | − | 0.548584i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.0321246 | + | 0.0185472i | −0.00114294 | + | 0.000659879i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.4550 | −0.939445 | ||||||||
\(794\) | 1.51635 | + | 2.62640i | 0.0538133 | + | 0.0932074i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.5709 | + | 12.4540i | 0.764560 | + | 0.441419i | ||||
\(797\) | 11.4342 | − | 19.8047i | 0.405022 | − | 0.701518i | −0.589302 | − | 0.807913i | \(-0.700597\pi\) |
0.994324 | + | 0.106394i | \(0.0339306\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.8764 | + | 37.8911i | 0.773932 | + | 1.34049i | ||||
\(800\) | 6.86014i | 0.242543i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.451525 | 0.0159439 | ||||||||
\(803\) | 11.7978 | + | 20.4345i | 0.416337 | + | 0.721117i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.254729 | + | 0.147068i | 0.00897246 | + | 0.00518025i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.91095 | + | 2.83534i | −0.172767 | + | 0.0997469i | ||||
\(809\) | 11.9814i | 0.421245i | 0.977568 | + | 0.210622i | \(0.0675490\pi\) | ||||
−0.977568 | + | 0.210622i | \(0.932451\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.9371i | − | 1.29704i | −0.761199 | − | 0.648519i | \(-0.775389\pi\) | ||
0.761199 | − | 0.648519i | \(-0.224611\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.831399 | − | 1.44003i | 0.0291405 | − | 0.0504729i | ||||
\(815\) | −4.50728 | + | 7.80683i | −0.157883 | + | 0.273461i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.0158 | + | 20.7937i | −1.26003 | + | 0.727481i | ||||
\(818\) | −2.26790 | −0.0792954 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.209127 | 0.00730304 | ||||||||
\(821\) | −32.6907 | + | 18.8740i | −1.14091 | + | 0.658707i | −0.946657 | − | 0.322244i | \(-0.895563\pi\) |
−0.194257 | + | 0.980951i | \(0.562229\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.5082 | − | 18.2008i | 0.366293 | − | 0.634438i | −0.622690 | − | 0.782469i | \(-0.713960\pi\) |
0.988983 | + | 0.148031i | \(0.0472934\pi\) | |||||||
\(824\) | −1.55943 | + | 2.70101i | −0.0543253 | + | 0.0940943i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 23.9104i | − | 0.831447i | −0.909491 | − | 0.415724i | \(-0.863528\pi\) | ||
0.909491 | − | 0.415724i | \(-0.136472\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.0859i | 0.871270i | 0.900123 | + | 0.435635i | \(0.143476\pi\) | ||||
−0.900123 | + | 0.435635i | \(0.856524\pi\) | |||||||
\(830\) | 0.608845 | − | 0.351517i | 0.0211333 | − | 0.0122013i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.3534 | + | 7.70960i | 0.462946 | + | 0.267282i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.64397 | + | 9.77564i | 0.195318 | + | 0.338300i | ||||
\(836\) | −43.7905 | −1.51453 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.359677i | 0.0124248i | ||||||||
\(839\) | 3.72840 | + | 6.45777i | 0.128719 | + | 0.222947i | 0.923180 | − | 0.384367i | \(-0.125580\pi\) |
−0.794462 | + | 0.607314i | \(0.792247\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.8021 | − | 36.0303i | 0.717313 | − | 1.24242i | ||||
\(842\) | 2.98960 | + | 1.72604i | 0.103028 | + | 0.0594834i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.37737 | − | 4.11772i | −0.0818323 | − | 0.141738i | ||||
\(845\) | 4.72780 | 0.162641 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.2828 | + | 8.24615i | −0.490472 | + | 0.283174i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.19411 | − | 1.26677i | −0.0752574 | − | 0.0434499i | ||||
\(851\) | 17.5670 | + | 10.1423i | 0.602187 | + | 0.347673i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.19184 | − | 1.26546i | 0.0750472 | − | 0.0433285i | −0.462007 | − | 0.886876i | \(-0.652870\pi\) |
0.537054 | + | 0.843548i | \(0.319537\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.123478 | 0.00422038 | ||||||||
\(857\) | 9.52098 | + | 16.4908i | 0.325231 | + | 0.563316i | 0.981559 | − | 0.191159i | \(-0.0612247\pi\) |
−0.656328 | + | 0.754475i | \(0.727891\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.88415 | − | 5.12927i | −0.303123 | − | 0.175008i | 0.340722 | − | 0.940164i | \(-0.389329\pi\) |
−0.643845 | + | 0.765156i | \(0.722662\pi\) | |||||||
\(860\) | 4.16495 | − | 7.21390i | 0.142024 | − | 0.245992i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.413809 | − | 0.716738i | −0.0140944 | − | 0.0244122i | ||||
\(863\) | 4.40932i | 0.150095i | 0.997180 | + | 0.0750475i | \(0.0239108\pi\) | ||||
−0.997180 | + | 0.0750475i | \(0.976089\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.8462 | 0.368781 | ||||||||
\(866\) | 1.73408 | + | 3.00352i | 0.0589265 | + | 0.102064i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.08526 | − | 1.20392i | −0.0707375 | − | 0.0408403i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.4962 | − | 6.63736i | 0.389535 | − | 0.224898i | ||||
\(872\) | − | 5.83693i | − | 0.197663i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.02816i | 0.136255i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.0586 | − | 43.4028i | 0.846170 | − | 1.46561i | −0.0384307 | − | 0.999261i | \(-0.512236\pi\) |
0.884601 | − | 0.466349i | \(-0.154431\pi\) | |||||||
\(878\) | 1.61196 | − | 2.79200i | 0.0544011 | − | 0.0942255i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.53833 | − | 4.35226i | 0.254117 | − | 0.146715i | ||||
\(881\) | −42.5809 | −1.43459 | −0.717294 | − | 0.696771i | \(-0.754619\pi\) | ||||
−0.717294 | + | 0.696771i | \(0.754619\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.6590 | −0.526967 | −0.263483 | − | 0.964664i | \(-0.584871\pi\) | ||||
−0.263483 | + | 0.964664i | \(0.584871\pi\) | |||||||
\(884\) | −15.2169 | + | 8.78546i | −0.511798 | + | 0.295487i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.336196 | + | 0.582309i | −0.0112947 | + | 0.0195630i | ||||
\(887\) | 12.3919 | − | 21.4634i | 0.416080 | − | 0.720671i | −0.579461 | − | 0.815000i | \(-0.696737\pi\) |
0.995541 | + | 0.0943286i | \(0.0300704\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 0.833869i | − | 0.0279513i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.55134i | 0.185873i | ||||||||
\(893\) | −45.3113 | + | 26.1605i | −1.51629 | + | 0.875428i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.60567 | + | 3.81379i | 0.220803 | + | 0.127481i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.451660 | + | 0.782299i | 0.0150721 | + | 0.0261056i | ||||
\(899\) | −10.0134 | −0.333965 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 18.5049i | − | 0.616488i | ||||||
\(902\) | −0.0511803 | − | 0.0886468i | −0.00170412 | − | 0.00295162i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.20655 | + | 2.08980i | −0.0401292 | + | 0.0695058i | ||||
\(905\) | −3.19716 | − | 1.84588i | −0.106277 | − | 0.0613592i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0517 | − | 38.1946i | −0.732213 | − | 1.26823i | −0.955935 | − | 0.293577i | \(-0.905154\pi\) |
0.223722 | − | 0.974653i | \(-0.428179\pi\) | |||||||
\(908\) | 5.64941 | 0.187482 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.3259 | + | 12.8899i | −0.739691 | + | 0.427061i | −0.821957 | − | 0.569549i | \(-0.807118\pi\) |
0.0822657 | + | 0.996610i | \(0.473784\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.5210 | + | 22.8175i | 1.30795 | + | 0.755148i | ||||
\(914\) | 4.38879 | + | 2.53387i | 0.145168 | + | 0.0838129i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −40.7845 | + | 23.5470i | −1.34756 | + | 0.778013i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.7102 | 1.73875 | 0.869375 | − | 0.494154i | \(-0.164522\pi\) | ||||
0.869375 | + | 0.494154i | \(0.164522\pi\) | |||||||
\(920\) | −0.809876 | − | 1.40275i | −0.0267008 | − | 0.0462472i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.15412 | − | 0.666334i | −0.0380091 | − | 0.0219446i | ||||
\(923\) | −8.57999 | + | 14.8610i | −0.282414 | + | 0.489155i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.62828 | − | 13.2126i | −0.250816 | − | 0.434426i | ||||
\(926\) | − | 0.704655i | − | 0.0231564i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 12.2133 | 0.400922 | ||||||||
\(929\) | 1.69009 | + | 2.92732i | 0.0554500 | + | 0.0960422i | 0.892418 | − | 0.451210i | \(-0.149007\pi\) |
−0.836968 | + | 0.547252i | \(0.815674\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 32.1981 | + | 18.5896i | 1.05468 | + | 0.608922i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.53103 | − | 1.46129i | 0.0828180 | − | 0.0478150i | ||||
\(935\) | 9.76677i | 0.319407i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.26186i | 0.269903i | 0.990852 | + | 0.134952i | \(0.0430879\pi\) | ||||
−0.990852 | + | 0.134952i | \(0.956912\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.23990 | − | 9.07578i | 0.170907 | − | 0.296019i | ||||
\(941\) | 26.1882 | − | 45.3592i | 0.853710 | − | 1.47867i | −0.0241274 | − | 0.999709i | \(-0.507681\pi\) |
0.877837 | − | 0.478960i | \(-0.158986\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.08141 | − | 0.624351i | 0.0352155 | − | 0.0203317i | ||||
\(944\) | 52.5528 | 1.71045 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.07720 | −0.132561 | ||||||||
\(947\) | 6.53348 | − | 3.77211i | 0.212310 | − | 0.122577i | −0.390075 | − | 0.920783i | \(-0.627551\pi\) |
0.602384 | + | 0.798206i | \(0.294217\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.66092 | + | 9.80500i | −0.183761 | + | 0.318284i | ||||
\(950\) | 1.51484 | − | 2.62379i | 0.0491480 | − | 0.0851269i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 45.2795i | − | 1.46675i | −0.679825 | − | 0.733374i | \(-0.737944\pi\) | ||
0.679825 | − | 0.733374i | \(-0.262056\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.73620i | 0.185619i | ||||||||
\(956\) | 22.1174 | − | 12.7695i | 0.715327 | − | 0.412994i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.200812 | − | 0.115939i | −0.00648795 | − | 0.00374582i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.7899 | − | 25.6169i | −0.477094 | − | 0.826352i | ||||
\(962\) | 0.797855 | 0.0257239 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 8.34518i | − | 0.268780i | ||||||
\(965\) | −2.78598 | − | 4.82546i | −0.0896838 | − | 0.155337i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.82403 | + | 11.8196i | −0.219446 | + | 0.380092i | −0.954639 | − | 0.297766i | \(-0.903758\pi\) |
0.735193 | + | 0.677858i | \(0.237092\pi\) | |||||||
\(968\) | −2.81954 | − | 1.62786i | −0.0906233 | − | 0.0523214i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.0184654 | + | 0.0319831i | 0.000592889 | + | 0.00102691i | ||||
\(971\) | −3.47104 | −0.111391 | −0.0556955 | − | 0.998448i | \(-0.517738\pi\) | ||||
−0.0556955 | + | 0.998448i | \(0.517738\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.99051 | + | 1.72657i | −0.0958222 | + | 0.0553230i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 44.4082 | + | 25.6391i | 1.42147 | + | 0.820688i | ||||
\(977\) | 2.21904 | + | 1.28116i | 0.0709932 | + | 0.0409880i | 0.535076 | − | 0.844804i | \(-0.320283\pi\) |
−0.464083 | + | 0.885792i | \(0.653616\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.8759 | − | 27.0638i | 1.49816 | − | 0.864963i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.325277 | −0.0103800 | ||||||||
\(983\) | −19.5749 | − | 33.9047i | −0.624343 | − | 1.08139i | −0.988668 | − | 0.150122i | \(-0.952033\pi\) |
0.364325 | − | 0.931272i | \(-0.381300\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.11390 | − | 4.10721i | −0.226668 | − | 0.130867i | ||||
\(986\) | −2.25527 | + | 3.90624i | −0.0718224 | + | 0.124400i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.5059 | − | 18.1968i | −0.334238 | − | 0.578917i | ||||
\(989\) | − | 49.7380i | − | 1.58158i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.2067 | −0.514821 | −0.257411 | − | 0.966302i | \(-0.582869\pi\) | ||||
−0.257411 | + | 0.966302i | \(0.582869\pi\) | |||||||
\(992\) | −0.866073 | − | 1.50008i | −0.0274978 | − | 0.0476277i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.75320 | + | 3.32161i | 0.182389 | + | 0.105302i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.5007 | − | 12.4134i | 0.680933 | − | 0.393137i | −0.119273 | − | 0.992861i | \(-0.538057\pi\) |
0.800207 | + | 0.599725i | \(0.204723\pi\) | |||||||
\(998\) | 1.53626i | 0.0486296i | ||||||||
\(999\) | 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 | 1323.2.o.e.881.11 | 48 | ||
3.2 | odd | 2 | 441.2.o.e.293.13 | yes | 48 | ||
7.2 | even | 3 | 1323.2.s.d.962.13 | 48 | |||
7.3 | odd | 6 | 1323.2.i.d.1097.11 | 48 | |||
7.4 | even | 3 | 1323.2.i.d.1097.12 | 48 | |||
7.5 | odd | 6 | 1323.2.s.d.962.14 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.o.e.881.12 | 48 | ||
9.2 | odd | 6 | inner | 1323.2.o.e.440.12 | 48 | ||
9.7 | even | 3 | 441.2.o.e.146.14 | yes | 48 | ||
21.2 | odd | 6 | 441.2.s.d.374.12 | 48 | |||
21.5 | even | 6 | 441.2.s.d.374.11 | 48 | |||
21.11 | odd | 6 | 441.2.i.d.68.13 | 48 | |||
21.17 | even | 6 | 441.2.i.d.68.14 | 48 | |||
21.20 | even | 2 | 441.2.o.e.293.14 | yes | 48 | ||
63.2 | odd | 6 | 1323.2.i.d.521.11 | 48 | |||
63.11 | odd | 6 | 1323.2.s.d.656.14 | 48 | |||
63.16 | even | 3 | 441.2.i.d.227.12 | 48 | |||
63.20 | even | 6 | inner | 1323.2.o.e.440.11 | 48 | ||
63.25 | even | 3 | 441.2.s.d.362.11 | 48 | |||
63.34 | odd | 6 | 441.2.o.e.146.13 | ✓ | 48 | ||
63.38 | even | 6 | 1323.2.s.d.656.13 | 48 | |||
63.47 | even | 6 | 1323.2.i.d.521.12 | 48 | |||
63.52 | odd | 6 | 441.2.s.d.362.12 | 48 | |||
63.61 | odd | 6 | 441.2.i.d.227.11 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.13 | 48 | 21.11 | odd | 6 | |||
441.2.i.d.68.14 | 48 | 21.17 | even | 6 | |||
441.2.i.d.227.11 | 48 | 63.61 | odd | 6 | |||
441.2.i.d.227.12 | 48 | 63.16 | even | 3 | |||
441.2.o.e.146.13 | ✓ | 48 | 63.34 | odd | 6 | ||
441.2.o.e.146.14 | yes | 48 | 9.7 | even | 3 | ||
441.2.o.e.293.13 | yes | 48 | 3.2 | odd | 2 | ||
441.2.o.e.293.14 | yes | 48 | 21.20 | even | 2 | ||
441.2.s.d.362.11 | 48 | 63.25 | even | 3 | |||
441.2.s.d.362.12 | 48 | 63.52 | odd | 6 | |||
441.2.s.d.374.11 | 48 | 21.5 | even | 6 | |||
441.2.s.d.374.12 | 48 | 21.2 | odd | 6 | |||
1323.2.i.d.521.11 | 48 | 63.2 | odd | 6 | |||
1323.2.i.d.521.12 | 48 | 63.47 | even | 6 | |||
1323.2.i.d.1097.11 | 48 | 7.3 | odd | 6 | |||
1323.2.i.d.1097.12 | 48 | 7.4 | even | 3 | |||
1323.2.o.e.440.11 | 48 | 63.20 | even | 6 | inner | ||
1323.2.o.e.440.12 | 48 | 9.2 | odd | 6 | inner | ||
1323.2.o.e.881.11 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.o.e.881.12 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.s.d.656.13 | 48 | 63.38 | even | 6 | |||
1323.2.s.d.656.14 | 48 | 63.11 | odd | 6 | |||
1323.2.s.d.962.13 | 48 | 7.2 | even | 3 | |||
1323.2.s.d.962.14 | 48 | 7.5 | odd | 6 |