Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(143,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.w (of order \(8\), degree \(4\), 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 431.3 | ||
Character | \(\chi\) | \(=\) | 1152.431 |
Dual form | 1152.2.w.a.719.3 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.65625 | + | 0.686041i | −0.740698 | + | 0.306807i | −0.720940 | − | 0.692998i | \(-0.756290\pi\) |
−0.0197579 | + | 0.999805i | \(0.506290\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.456585 | + | 0.456585i | 0.172573 | + | 0.172573i | 0.788109 | − | 0.615536i | \(-0.211060\pi\) |
−0.615536 | + | 0.788109i | \(0.711060\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.79166 | − | 1.15634i | 0.841718 | − | 0.348651i | 0.0801871 | − | 0.996780i | \(-0.474448\pi\) |
0.761531 | + | 0.648129i | \(0.224448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.29543 | + | 3.12746i | −0.359289 | + | 0.867400i | 0.636111 | + | 0.771597i | \(0.280542\pi\) |
−0.995400 | + | 0.0958031i | \(0.969458\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.55642 | −0.862560 | −0.431280 | − | 0.902218i | \(-0.641938\pi\) | ||||
−0.431280 | + | 0.902218i | \(0.641938\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.61657 | + | 2.32646i | 1.28853 | + | 0.533726i | 0.918547 | − | 0.395313i | \(-0.129364\pi\) |
0.369982 | + | 0.929039i | \(0.379364\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.10130 | − | 4.10130i | −0.855180 | − | 0.855180i | 0.135586 | − | 0.990766i | \(-0.456708\pi\) |
−0.990766 | + | 0.135586i | \(0.956708\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.26302 | + | 1.26302i | −0.252604 | + | 0.252604i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.87699 | + | 4.53146i | −0.348548 | + | 0.841470i | 0.648243 | + | 0.761433i | \(0.275504\pi\) |
−0.996792 | + | 0.0800372i | \(0.974496\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.580857i | 0.104325i | 0.998639 | + | 0.0521625i | \(0.0166114\pi\) | ||||
−0.998639 | + | 0.0521625i | \(0.983389\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.06946 | − | 0.442983i | −0.180771 | − | 0.0748778i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.58037 | + | 6.22957i | 0.424210 | + | 1.02413i | 0.981092 | + | 0.193543i | \(0.0619978\pi\) |
−0.556881 | + | 0.830592i | \(0.688002\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.98306 | + | 2.98306i | −0.465876 | + | 0.465876i | −0.900576 | − | 0.434699i | \(-0.856855\pi\) |
0.434699 | + | 0.900576i | \(0.356855\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.78658 | + | 6.72741i | 0.424950 | + | 1.02592i | 0.980866 | + | 0.194682i | \(0.0623674\pi\) |
−0.555917 | + | 0.831238i | \(0.687633\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.67935i | 1.26601i | 0.774147 | + | 0.633006i | \(0.218179\pi\) | ||||
−0.774147 | + | 0.633006i | \(0.781821\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 6.58306i | − | 0.940437i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.70833 | + | 8.95270i | 0.509378 | + | 1.22975i | 0.944242 | + | 0.329252i | \(0.106797\pi\) |
−0.434864 | + | 0.900496i | \(0.643203\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.83039 | + | 3.83039i | −0.516490 | + | 0.516490i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.77297 | − | 4.28032i | −0.230820 | − | 0.557250i | 0.765454 | − | 0.643491i | \(-0.222515\pi\) |
−0.996274 | + | 0.0862410i | \(0.972515\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.49421 | − | 3.93263i | −1.21561 | − | 0.503522i | −0.319598 | − | 0.947553i | \(-0.603548\pi\) |
−0.896011 | + | 0.444031i | \(0.853548\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 6.06857i | − | 0.752714i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.50440 | + | 8.46037i | −0.428131 | + | 1.03360i | 0.551749 | + | 0.834010i | \(0.313961\pi\) |
−0.979880 | + | 0.199589i | \(0.936039\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.84134 | + | 7.84134i | −0.930596 | + | 0.930596i | −0.997743 | − | 0.0671471i | \(-0.978610\pi\) |
0.0671471 | + | 0.997743i | \(0.478610\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.7396 | + | 10.7396i | 1.25698 | + | 1.25698i | 0.952527 | + | 0.304453i | \(0.0984738\pi\) |
0.304453 | + | 0.952527i | \(0.401526\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.80260 | + | 0.746662i | 0.205425 | + | 0.0850900i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.27177 | 0.593121 | 0.296560 | − | 0.955014i | \(-0.404160\pi\) | ||||
0.296560 | + | 0.955014i | \(0.404160\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.80609 | + | 4.36028i | −0.198244 | + | 0.478603i | −0.991472 | − | 0.130322i | \(-0.958399\pi\) |
0.793228 | + | 0.608925i | \(0.208399\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.89033 | − | 2.43985i | 0.638896 | − | 0.264639i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.4990 | − | 12.4990i | −1.32489 | − | 1.32489i | −0.909764 | − | 0.415125i | \(-0.863738\pi\) |
−0.415125 | − | 0.909764i | \(-0.636262\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.01943 | + | 0.836474i | −0.211693 | + | 0.0876863i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.8985 | −1.11816 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.99452 | 1.01479 | 0.507395 | − | 0.861714i | \(-0.330608\pi\) | ||||
0.507395 | + | 0.861714i | \(0.330608\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.85763 | − | 1.59788i | 0.383849 | − | 0.158995i | −0.182411 | − | 0.983222i | \(-0.558390\pi\) |
0.566259 | + | 0.824227i | \(0.308390\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.59155 | − | 1.59155i | −0.156820 | − | 0.156820i | 0.624336 | − | 0.781156i | \(-0.285370\pi\) |
−0.781156 | + | 0.624336i | \(0.785370\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.1209 | − | 6.67752i | 1.55847 | − | 0.645540i | 0.573648 | − | 0.819102i | \(-0.305528\pi\) |
0.984823 | + | 0.173562i | \(0.0555277\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.94159 | + | 11.9301i | −0.473318 | + | 1.14269i | 0.489369 | + | 0.872077i | \(0.337227\pi\) |
−0.962688 | + | 0.270615i | \(0.912773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.30221 | 0.498790 | 0.249395 | − | 0.968402i | \(-0.419768\pi\) | ||||
0.249395 | + | 0.968402i | \(0.419768\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.60644 | + | 3.97912i | 0.895805 | + | 0.371054i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.62381 | − | 1.62381i | −0.148855 | − | 0.148855i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.32193 | + | 1.32193i | −0.120176 | + | 0.120176i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.65560 | − | 11.2396i | 0.416410 | − | 1.00530i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 22.3469i | − | 1.98297i | −0.130223 | − | 0.991485i | \(-0.541569\pi\) | ||
0.130223 | − | 0.991485i | \(-0.458431\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.42416 | − | 0.589906i | −0.124429 | − | 0.0515403i | 0.319600 | − | 0.947553i | \(-0.396451\pi\) |
−0.444029 | + | 0.896012i | \(0.646451\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.50221 | + | 3.62667i | 0.130259 | + | 0.314472i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.460816 | − | 0.460816i | 0.0393702 | − | 0.0393702i | −0.687148 | − | 0.726518i | \(-0.741137\pi\) |
0.726518 | + | 0.687148i | \(0.241137\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.10753 | − | 19.5733i | −0.687672 | − | 1.66019i | −0.749420 | − | 0.662095i | \(-0.769667\pi\) |
0.0617480 | − | 0.998092i | \(-0.480333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.2288i | 0.855373i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 8.79292i | − | 0.730212i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.69000 | + | 11.3227i | 0.384220 | + | 0.927589i | 0.991139 | + | 0.132826i | \(0.0424051\pi\) |
−0.606919 | + | 0.794764i | \(0.707595\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.98867 | + | 7.98867i | −0.650109 | + | 0.650109i | −0.953019 | − | 0.302910i | \(-0.902042\pi\) |
0.302910 | + | 0.953019i | \(0.402042\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.398492 | − | 0.962044i | −0.0320076 | − | 0.0772732i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.47084 | − | 1.43767i | −0.277003 | − | 0.114739i | 0.239857 | − | 0.970808i | \(-0.422899\pi\) |
−0.516860 | + | 0.856070i | \(0.672899\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.74518i | − | 0.295162i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.897968 | + | 2.16789i | −0.0703343 | + | 0.169802i | −0.955137 | − | 0.296163i | \(-0.904293\pi\) |
0.884803 | + | 0.465965i | \(0.154293\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.17718 | + | 4.17718i | −0.323240 | + | 0.323240i | −0.850009 | − | 0.526769i | \(-0.823403\pi\) |
0.526769 | + | 0.850009i | \(0.323403\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.08956 | + | 1.08956i | 0.0838119 | + | 0.0838119i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.46721 | + | 2.26459i | 0.415664 | + | 0.172174i | 0.580707 | − | 0.814113i | \(-0.302776\pi\) |
−0.165043 | + | 0.986286i | \(0.552776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.15335 | −0.0871854 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.19833 | − | 5.30724i | 0.164311 | − | 0.396681i | −0.820183 | − | 0.572101i | \(-0.806128\pi\) |
0.984494 | + | 0.175420i | \(0.0561283\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.557980 | − | 0.231123i | 0.0414743 | − | 0.0171792i | −0.361850 | − | 0.932236i | \(-0.617855\pi\) |
0.403324 | + | 0.915057i | \(0.367855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.54748 | − | 8.54748i | −0.628423 | − | 0.628423i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.92834 | + | 4.11245i | −0.726032 | + | 0.300732i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.5071 | 1.70091 | 0.850457 | − | 0.526044i | \(-0.176325\pi\) | ||||
0.850457 | + | 0.526044i | \(0.176325\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.17175 | −0.660197 | −0.330098 | − | 0.943946i | \(-0.607082\pi\) | ||||
−0.330098 | + | 0.943946i | \(0.607082\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.13281 | + | 3.36872i | −0.579439 | + | 0.240011i | −0.653100 | − | 0.757272i | \(-0.726532\pi\) |
0.0736610 | + | 0.997283i | \(0.476532\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2257 | − | 13.2257i | −0.937548 | − | 0.937548i | 0.0606129 | − | 0.998161i | \(-0.480694\pi\) |
−0.998161 | + | 0.0606129i | \(0.980694\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.92600 | + | 1.21199i | −0.205365 | + | 0.0850650i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.89419 | − | 6.98720i | 0.202139 | − | 0.488008i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.3697 | 1.27066 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.9447 | + | 8.26135i | 1.37305 | + | 0.568735i | 0.942613 | − | 0.333887i | \(-0.108360\pi\) |
0.430434 | + | 0.902622i | \(0.358360\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.23056 | − | 9.23056i | −0.629519 | − | 0.629519i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.265211 | + | 0.265211i | −0.0180037 | + | 0.0180037i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.60712 | − | 11.1226i | 0.309908 | − | 0.748185i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.8784i | − | 0.929363i | −0.885478 | − | 0.464682i | \(-0.846169\pi\) | ||
0.885478 | − | 0.464682i | \(-0.153831\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.3888 | + | 7.20270i | 1.15414 | + | 0.478060i | 0.875919 | − | 0.482458i | \(-0.160256\pi\) |
0.278219 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.50393 | − | 8.45924i | −0.231546 | − | 0.559002i | 0.764813 | − | 0.644252i | \(-0.222831\pi\) |
−0.996360 | + | 0.0852496i | \(0.972831\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.85253 | + | 5.85253i | −0.383412 | + | 0.383412i | −0.872330 | − | 0.488918i | \(-0.837392\pi\) |
0.488918 | + | 0.872330i | \(0.337392\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.95439 | − | 14.3752i | −0.388422 | − | 0.937733i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.83888i | − | 0.507055i | −0.967328 | − | 0.253527i | \(-0.918409\pi\) | ||
0.967328 | − | 0.253527i | \(-0.0815908\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 29.7873i | − | 1.91877i | −0.282104 | − | 0.959384i | \(-0.591032\pi\) | ||
0.282104 | − | 0.959384i | \(-0.408968\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.51625 | + | 10.9032i | 0.288533 | + | 0.696580i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.5518 | + | 14.5518i | −0.925908 | + | 0.925908i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.558412 | + | 1.34813i | 0.0352466 | + | 0.0850929i | 0.940523 | − | 0.339731i | \(-0.110336\pi\) |
−0.905276 | + | 0.424824i | \(0.860336\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.1919 | − | 6.70692i | −1.01798 | − | 0.421661i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 4.05507i | − | 0.252948i | −0.991970 | − | 0.126474i | \(-0.959634\pi\) | ||
0.991970 | − | 0.126474i | \(-0.0403661\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.66617 | + | 4.02249i | −0.103531 | + | 0.249945i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.79592 | − | 8.79592i | 0.542380 | − | 0.542380i | −0.381846 | − | 0.924226i | \(-0.624712\pi\) |
0.924226 | + | 0.381846i | \(0.124712\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.2838 | − | 12.2838i | −0.754591 | − | 0.754591i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.15796 | − | 0.479643i | −0.0706021 | − | 0.0292443i | 0.347103 | − | 0.937827i | \(-0.387165\pi\) |
−0.417705 | + | 0.908583i | \(0.637165\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.5808 | 1.55392 | 0.776961 | − | 0.629549i | \(-0.216760\pi\) | ||||
0.776961 | + | 0.629549i | \(0.216760\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.06544 | + | 4.98642i | −0.124551 | + | 0.300692i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.32573 | − | 3.03442i | 0.440161 | − | 0.182320i | −0.151587 | − | 0.988444i | \(-0.548438\pi\) |
0.591747 | + | 0.806123i | \(0.298438\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.2794 | + | 15.2794i | 0.911490 | + | 0.911490i | 0.996390 | − | 0.0848997i | \(-0.0270570\pi\) |
−0.0848997 | + | 0.996390i | \(0.527057\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.6335 | − | 4.40456i | 0.632098 | − | 0.261824i | −0.0435461 | − | 0.999051i | \(-0.513866\pi\) |
0.675644 | + | 0.737228i | \(0.263866\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.72405 | −0.160795 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.35184 | −0.255991 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.77403 | + | 3.63432i | −0.512584 | + | 0.212319i | −0.623956 | − | 0.781460i | \(-0.714476\pi\) |
0.111372 | + | 0.993779i | \(0.464476\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.87295 | + | 5.87295i | 0.341936 | + | 0.341936i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.1396 | − | 7.51367i | 1.04904 | − | 0.434527i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.79932 | + | 4.34395i | −0.103711 | + | 0.250381i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.4227 | 1.05488 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.2808 | − | 4.25844i | −0.586755 | − | 0.243042i | 0.0694988 | − | 0.997582i | \(-0.477860\pi\) |
−0.656254 | + | 0.754540i | \(0.727860\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.40680 | − | 1.40680i | −0.0797723 | − | 0.0797723i | 0.666095 | − | 0.745867i | \(-0.267965\pi\) |
−0.745867 | + | 0.666095i | \(0.767965\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.25438 | + | 6.25438i | −0.353518 | + | 0.353518i | −0.861417 | − | 0.507899i | \(-0.830422\pi\) |
0.507899 | + | 0.861417i | \(0.330422\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.54838 | − | 6.15234i | 0.143131 | − | 0.345550i | −0.836015 | − | 0.548707i | \(-0.815120\pi\) |
0.979146 | + | 0.203157i | \(0.0651202\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.8207i | 0.829802i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.9749 | − | 8.27387i | −1.11143 | − | 0.460371i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.31388 | − | 5.58621i | −0.128351 | − | 0.309867i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.96286 | + | 3.96286i | −0.218480 | + | 0.218480i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.67191 | − | 6.45057i | −0.146862 | − | 0.354555i | 0.833281 | − | 0.552850i | \(-0.186460\pi\) |
−0.980142 | + | 0.198295i | \(0.936460\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 16.4167i | − | 0.896938i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.72840i | − | 0.312046i | −0.987753 | − | 0.156023i | \(-0.950133\pi\) | ||
0.987753 | − | 0.156023i | \(-0.0498674\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.671670 | + | 1.62156i | 0.0363730 | + | 0.0878122i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.20182 | − | 6.20182i | 0.334867 | − | 0.334867i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.72462 | − | 21.0631i | −0.468362 | − | 1.13073i | −0.964878 | − | 0.262699i | \(-0.915387\pi\) |
0.496515 | − | 0.868028i | \(-0.334613\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.6969 | − | 9.81557i | −1.26847 | − | 0.525415i | −0.355968 | − | 0.934498i | \(-0.615849\pi\) |
−0.912497 | + | 0.409083i | \(0.865849\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.1720i | 1.02042i | 0.860049 | + | 0.510211i | \(0.170433\pi\) | ||||
−0.860049 | + | 0.510211i | \(0.829567\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.60774 | − | 18.3667i | 0.403777 | − | 0.974804i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.4520 | − | 19.4520i | 1.02664 | − | 1.02664i | 0.0270016 | − | 0.999635i | \(-0.491404\pi\) |
0.999635 | − | 0.0270016i | \(-0.00859591\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.6984 | + | 12.6984i | 0.668336 | + | 0.668336i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.1554 | − | 10.4197i | −1.31669 | − | 0.545392i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.4899 | −1.01737 | −0.508683 | − | 0.860954i | \(-0.669867\pi\) | ||||
−0.508683 | + | 0.860954i | \(0.669867\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.39450 | + | 5.78084i | −0.124316 | + | 0.300126i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.4958 | − | 13.4602i | 1.68257 | − | 0.696943i | 0.683126 | − | 0.730300i | \(-0.260620\pi\) |
0.999443 | + | 0.0333572i | \(0.0106199\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.7404 | − | 11.7404i | −0.604662 | − | 0.604662i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.4703 | + | 4.75115i | −0.589189 | + | 0.244050i | −0.657302 | − | 0.753627i | \(-0.728302\pi\) |
0.0681125 | + | 0.997678i | \(0.478302\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.4414 | 1.09560 | 0.547801 | − | 0.836609i | \(-0.315465\pi\) | ||||
0.547801 | + | 0.836609i | \(0.315465\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.49780 | −0.178264 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.8503 | − | 9.46489i | 1.15855 | − | 0.479889i | 0.281161 | − | 0.959661i | \(-0.409281\pi\) |
0.877393 | + | 0.479772i | \(0.159281\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.5860 | + | 14.5860i | 0.737644 | + | 0.737644i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.73137 | + | 3.61665i | −0.439323 | + | 0.181974i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00126 | − | 4.83148i | 0.100441 | − | 0.242485i | −0.865669 | − | 0.500616i | \(-0.833107\pi\) |
0.966110 | + | 0.258131i | \(0.0831067\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.4805 | −0.822996 | −0.411498 | − | 0.911411i | \(-0.634994\pi\) | ||||
−0.411498 | + | 0.911411i | \(0.634994\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.81660 | − | 0.752462i | −0.0904915 | − | 0.0374828i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.4070 | + | 14.4070i | 0.714131 | + | 0.714131i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.4679 | + | 14.4679i | −0.715393 | + | 0.715393i | −0.967658 | − | 0.252265i | \(-0.918824\pi\) |
0.252265 | + | 0.967658i | \(0.418824\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.14482 | − | 2.76384i | 0.0563329 | − | 0.136000i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.46076i | − | 0.415323i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.2299 | − | 5.48000i | −0.646322 | − | 0.267715i | 0.0353481 | − | 0.999375i | \(-0.488746\pi\) |
−0.681670 | + | 0.731660i | \(0.738746\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.58725 | + | 8.66038i | 0.174832 | + | 0.422081i | 0.986869 | − | 0.161525i | \(-0.0516412\pi\) |
−0.812037 | + | 0.583606i | \(0.801641\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.49184 | − | 4.49184i | 0.217886 | − | 0.217886i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.53933 | − | 6.13050i | −0.122887 | − | 0.296676i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.9638i | 1.44330i | 0.692256 | + | 0.721652i | \(0.256617\pi\) | ||||
−0.692256 | + | 0.721652i | \(0.743383\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.4045i | 1.46115i | 0.682834 | + | 0.730574i | \(0.260747\pi\) | ||||
−0.682834 | + | 0.730574i | \(0.739253\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.4937 | − | 32.5767i | −0.645492 | − | 1.55836i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1550 | − | 10.1550i | 0.484670 | − | 0.484670i | −0.421949 | − | 0.906619i | \(-0.638654\pi\) |
0.906619 | + | 0.421949i | \(0.138654\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0051 | + | 28.9828i | 0.570379 | + | 1.37702i | 0.901233 | + | 0.433335i | \(0.142663\pi\) |
−0.330854 | + | 0.943682i | \(0.607337\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.2763 | + | 12.1266i | 1.38783 | + | 0.574857i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.5653i | 1.06492i | 0.846454 | + | 0.532462i | \(0.178733\pi\) | ||||
−0.846454 | + | 0.532462i | \(0.821267\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.87826 | + | 11.7772i | −0.229708 | + | 0.554564i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.77082 | − | 2.77082i | 0.129898 | − | 0.129898i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.14050 | + | 9.14050i | 0.427575 | + | 0.427575i | 0.887801 | − | 0.460227i | \(-0.152232\pi\) |
−0.460227 | + | 0.887801i | \(0.652232\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.78980 | − | 1.15557i | −0.129934 | − | 0.0538203i | 0.316769 | − | 0.948503i | \(-0.397402\pi\) |
−0.446703 | + | 0.894682i | \(0.647402\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.4593 | 1.55499 | 0.777494 | − | 0.628891i | \(-0.216491\pi\) | ||||
0.777494 | + | 0.628891i | \(0.216491\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.0784 | + | 33.9882i | −0.651470 | + | 1.57279i | 0.159175 | + | 0.987250i | \(0.449117\pi\) |
−0.810645 | + | 0.585538i | \(0.800883\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.46294 | + | 2.26282i | −0.252255 | + | 0.104487i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.5584 | + | 15.5584i | 0.715376 | + | 0.715376i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.0322 | + | 4.15548i | −0.460309 | + | 0.190666i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.68362 | −0.122618 | −0.0613088 | − | 0.998119i | \(-0.519527\pi\) | ||||
−0.0613088 | + | 0.998119i | \(0.519527\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.8254 | −1.04075 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.5534 | + | 6.85666i | −0.751653 | + | 0.311345i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.23834 | − | 2.23834i | −0.101429 | − | 0.101429i | 0.654571 | − | 0.756000i | \(-0.272849\pi\) |
−0.756000 | + | 0.654571i | \(0.772849\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.4388 | + | 5.15233i | −0.561356 | + | 0.232521i | −0.645274 | − | 0.763951i | \(-0.723257\pi\) |
0.0839179 | + | 0.996473i | \(0.473257\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.67538 | − | 16.1158i | 0.300644 | − | 0.725818i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.16048 | −0.321191 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.8865 | − | 10.3083i | −1.11407 | − | 0.461464i | −0.251734 | − | 0.967796i | \(-0.581001\pi\) |
−0.862338 | + | 0.506333i | \(0.831001\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.4779 | − | 22.4779i | −1.00224 | − | 1.00224i | −0.999997 | − | 0.00224387i | \(-0.999286\pi\) |
−0.00224387 | − | 0.999997i | \(-0.500714\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.29299 | + | 5.29299i | −0.235535 | + | 0.235535i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.50936 | + | 13.3008i | −0.244198 | + | 0.589546i | −0.997692 | − | 0.0679092i | \(-0.978367\pi\) |
0.753493 | + | 0.657455i | \(0.228367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.80713i | 0.433842i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.72787 | + | 1.54413i | 0.164269 | + | 0.0680426i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.0363 | + | 24.2298i | 0.441396 | + | 1.06563i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.57998 | + | 5.57998i | −0.244463 | + | 0.244463i | −0.818694 | − | 0.574230i | \(-0.805301\pi\) |
0.574230 | + | 0.818694i | \(0.305301\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.24273 | + | 7.82865i | 0.141795 | + | 0.342323i | 0.978783 | − | 0.204897i | \(-0.0656860\pi\) |
−0.836989 | + | 0.547220i | \(0.815686\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.06577i | − | 0.0899865i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6413i | 0.462665i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.46504 | − | 13.1938i | −0.236717 | − | 0.571485i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.1193 | + | 22.1193i | −0.956300 | + | 0.956300i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.61228 | − | 18.3777i | −0.327884 | − | 0.791583i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.7796 | + | 4.46504i | 0.463450 | + | 0.191967i | 0.602176 | − | 0.798364i | \(-0.294301\pi\) |
−0.138726 | + | 0.990331i | \(0.544301\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 23.1493i | − | 0.991607i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.24172 | − | 5.41200i | 0.0958492 | − | 0.231400i | −0.868682 | − | 0.495371i | \(-0.835032\pi\) |
0.964531 | + | 0.263970i | \(0.0850321\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.0845 | + | 21.0845i | −0.898229 | + | 0.898229i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.40701 | + | 2.40701i | 0.102357 | + | 0.102357i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.25052 | + | 3.83169i | 0.391957 | + | 0.162354i | 0.569953 | − | 0.821677i | \(-0.306961\pi\) |
−0.177996 | + | 0.984031i | \(0.556961\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.6495 | −1.04256 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.82586 | + | 18.8933i | −0.329820 | + | 0.796257i | 0.668785 | + | 0.743456i | \(0.266815\pi\) |
−0.998605 | + | 0.0528009i | \(0.983185\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.78179 | + | 3.63754i | −0.369453 | + | 0.153032i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.2631 | + | 31.2631i | 1.31062 | + | 1.31062i | 0.920959 | + | 0.389659i | \(0.127407\pi\) |
0.389659 | + | 0.920959i | \(0.372593\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.191448 | + | 0.0793005i | −0.00801186 | + | 0.00331862i | −0.386686 | − | 0.922212i | \(-0.626380\pi\) |
0.378674 | + | 0.925530i | \(0.376380\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.3601 | 0.432044 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.6731 | 1.60998 | 0.804991 | − | 0.593287i | \(-0.202170\pi\) | ||||
0.804991 | + | 0.593287i | \(0.202170\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.81547 | + | 1.16621i | −0.116805 | + | 0.0483824i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.7048 | + | 20.7048i | 0.857506 | + | 0.857506i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −43.3422 | + | 17.9529i | −1.78892 | + | 0.740997i | −0.798662 | + | 0.601779i | \(0.794459\pi\) |
−0.990262 | + | 0.139217i | \(0.955541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.35134 | + | 3.26242i | −0.0556809 | + | 0.134426i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.0532 | 0.700290 | 0.350145 | − | 0.936695i | \(-0.386132\pi\) | ||||
0.350145 | + | 0.936695i | \(0.386132\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.80344 | + | 1.57544i | 0.155926 | + | 0.0645866i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.20304 | − | 1.20304i | −0.0491549 | − | 0.0491549i | 0.682102 | − | 0.731257i | \(-0.261066\pi\) |
−0.731257 | + | 0.682102i | \(0.761066\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.21057 | + | 7.21057i | −0.294125 | + | 0.294125i | −0.838707 | − | 0.544582i | \(-0.816688\pi\) |
0.544582 | + | 0.838707i | \(0.316688\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.28255 | − | 3.09635i | 0.0521431 | − | 0.125884i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.4020i | 1.59928i | 0.600480 | + | 0.799640i | \(0.294976\pi\) | ||||
−0.600480 | + | 0.799640i | \(0.705024\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.1443 | − | 11.2435i | −1.09814 | − | 0.454864i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.28364 | − | 10.3416i | −0.173015 | − | 0.417694i | 0.813457 | − | 0.581625i | \(-0.197583\pi\) |
−0.986472 | + | 0.163930i | \(0.947583\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.31416 | − | 3.31416i | 0.133423 | − | 0.133423i | −0.637241 | − | 0.770664i | \(-0.719925\pi\) |
0.770664 | + | 0.637241i | \(0.219925\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.98010 | + | 24.0941i | 0.401134 | + | 0.968423i | 0.987391 | + | 0.158298i | \(0.0506008\pi\) |
−0.586257 | + | 0.810125i | \(0.699399\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 11.4137i | − | 0.457280i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.8786i | 0.515146i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.17690 | − | 22.1550i | −0.365907 | − | 0.883377i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.8296 | − | 13.8296i | 0.550550 | − | 0.550550i | −0.376050 | − | 0.926599i | \(-0.622718\pi\) |
0.926599 | + | 0.376050i | \(0.122718\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.3309 | + | 37.0121i | 0.608389 | + | 1.46878i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.5882 | + | 8.52793i | 0.815736 | + | 0.337889i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.78350i | − | 0.188937i | −0.995528 | − | 0.0944684i | \(-0.969885\pi\) | ||
0.995528 | − | 0.0944684i | \(-0.0301151\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.20578 | − | 10.1536i | 0.165860 | − | 0.400421i | −0.818995 | − | 0.573800i | \(-0.805469\pi\) |
0.984855 | + | 0.173379i | \(0.0554687\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.3311 | − | 11.3311i | 0.445473 | − | 0.445473i | −0.448373 | − | 0.893846i | \(-0.647997\pi\) |
0.893846 | + | 0.448373i | \(0.147997\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.89904 | − | 9.89904i | −0.388571 | − | 0.388571i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.7945 | − | 11.5129i | −1.08768 | − | 0.450533i | −0.234485 | − | 0.972120i | \(-0.575340\pi\) |
−0.853198 | + | 0.521587i | \(0.825340\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.76346 | 0.107977 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.68871 | − | 18.5622i | 0.299510 | − | 0.723080i | −0.700446 | − | 0.713705i | \(-0.747016\pi\) |
0.999956 | − | 0.00937514i | \(-0.00298424\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.39058 | − | 3.06128i | 0.287460 | − | 0.119070i | −0.234294 | − | 0.972166i | \(-0.575278\pi\) |
0.521754 | + | 0.853096i | \(0.325278\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.97609 | − | 4.97609i | −0.192964 | − | 0.192964i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.2830 | − | 10.8868i | 1.01768 | − | 0.421537i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.0521 | −1.19875 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.4300 | 0.517690 | 0.258845 | − | 0.965919i | \(-0.416658\pi\) | ||||
0.258845 | + | 0.965919i | \(0.416658\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.8609 | − | 5.32714i | 0.494283 | − | 0.204739i | −0.121596 | − | 0.992580i | \(-0.538801\pi\) |
0.615879 | + | 0.787841i | \(0.288801\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.56335 | + | 4.56335i | 0.175125 | + | 0.175125i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.117538 | − | 0.0486859i | 0.00449748 | − | 0.00186292i | −0.380434 | − | 0.924808i | \(-0.624225\pi\) |
0.384931 | + | 0.922945i | \(0.374225\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.447088 | + | 1.07937i | −0.0170824 | + | 0.0412405i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32.8031 | −1.24970 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.94322 | + | 4.11862i | 0.378258 | + | 0.156680i | 0.563708 | − | 0.825974i | \(-0.309374\pi\) |
−0.185450 | + | 0.982654i | \(0.559374\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.8562 | + | 26.8562i | 1.01871 | + | 1.01871i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.6090 | − | 10.6090i | 0.401846 | − | 0.401846i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.26297 | − | 10.2917i | 0.161010 | − | 0.388713i | −0.822700 | − | 0.568476i | \(-0.807533\pi\) |
0.983710 | + | 0.179763i | \(0.0575331\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.9919i | 1.54604i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.49091 | + | 1.03177i | 0.0936803 | + | 0.0388036i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.70620 | − | 11.3618i | −0.176745 | − | 0.426700i | 0.810535 | − | 0.585690i | \(-0.199176\pi\) |
−0.987280 | + | 0.158990i | \(0.949176\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.38227 | − | 2.38227i | 0.0892166 | − | 0.0892166i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.01736 | − | 16.9414i | −0.262434 | − | 0.633573i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 31.7208i | − | 1.18299i | −0.806310 | − | 0.591493i | \(-0.798539\pi\) | ||
0.806310 | − | 0.591493i | \(-0.201461\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1.45335i | − | 0.0541257i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.35265 | − | 8.09401i | −0.124514 | − | 0.300604i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.1550 | − | 19.1550i | 0.710421 | − | 0.710421i | −0.256202 | − | 0.966623i | \(-0.582471\pi\) |
0.966623 | + | 0.256202i | \(0.0824714\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.91027 | − | 23.9255i | −0.366545 | − | 0.884917i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.7560 | + | 16.8817i | 1.50536 | + | 0.623539i | 0.974593 | − | 0.223981i | \(-0.0719054\pi\) |
0.530763 | + | 0.847520i | \(0.321905\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.6708i | 1.01927i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.11044 | + | 19.5803i | −0.298348 | + | 0.720275i | 0.701623 | + | 0.712549i | \(0.252459\pi\) |
−0.999970 | + | 0.00772594i | \(0.997541\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.927600 | + | 0.927600i | −0.0340303 | + | 0.0340303i | −0.723917 | − | 0.689887i | \(-0.757660\pi\) |
0.689887 | + | 0.723917i | \(0.257660\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.5356 | − | 15.5356i | −0.569182 | − | 0.569182i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.4094 | + | 4.31173i | 0.380353 | + | 0.157547i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.0488 | −1.13299 | −0.566493 | − | 0.824066i | \(-0.691700\pi\) | ||||
−0.566493 | + | 0.824066i | \(0.691700\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.75068 | − | 18.7118i | 0.282076 | − | 0.680992i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.3806 | + | 9.68456i | −0.849782 | + | 0.351991i | −0.764703 | − | 0.644383i | \(-0.777114\pi\) |
−0.0850792 | + | 0.996374i | \(0.527114\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.78273 | − | 7.78273i | −0.282124 | − | 0.282124i | 0.551832 | − | 0.833956i | \(-0.313929\pi\) |
−0.833956 | + | 0.551832i | \(0.813929\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.70334 | + | 3.19083i | −0.278880 | + | 0.115516i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.6833 | 0.566290 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50.8529 | −1.83380 | −0.916902 | − | 0.399113i | \(-0.869318\pi\) | ||||
−0.916902 | + | 0.399113i | \(0.869318\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.9455 | + | 15.7175i | −1.36480 | + | 0.565320i | −0.940374 | − | 0.340141i | \(-0.889525\pi\) |
−0.424429 | + | 0.905461i | \(0.639525\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.733635 | − | 0.733635i | −0.0263529 | − | 0.0263529i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.6945 | + | 9.81460i | −0.848945 | + | 0.351645i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.8231 | + | 30.9577i | −0.458846 | + | 1.10775i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.73488 | 0.240378 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.7835 | − | 9.02304i | −0.776499 | − | 0.321637i | −0.0409975 | − | 0.999159i | \(-0.513054\pi\) |
−0.735502 | + | 0.677523i | \(0.763054\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.42091 | + | 2.42091i | 0.0860777 | + | 0.0860777i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.5983 | − | 24.5983i | 0.873510 | − | 0.873510i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.4401 | + | 27.6189i | −0.405231 | + | 0.978313i | 0.581144 | + | 0.813800i | \(0.302605\pi\) |
−0.986375 | + | 0.164513i | \(0.947395\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 30.8674i | − | 1.09201i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 42.4002 | + | 17.5627i | 1.49627 | + | 0.619775i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.56935 | + | 6.20296i | 0.0905577 | + | 0.218626i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.79612 | − | 5.79612i | 0.203781 | − | 0.203781i | −0.597837 | − | 0.801618i | \(-0.703973\pi\) |
0.801618 | + | 0.597837i | \(0.203973\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.2750 | + | 46.5341i | 0.676838 | + | 1.63403i | 0.769741 | + | 0.638356i | \(0.220385\pi\) |
−0.0929028 | + | 0.995675i | \(0.529615\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 4.20661i | − | 0.147351i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.2678i | 1.54873i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.7271 | + | 40.3828i | 0.583779 | + | 1.40937i | 0.889363 | + | 0.457202i | \(0.151149\pi\) |
−0.305583 | + | 0.952165i | \(0.598851\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.13069 | − | 8.13069i | 0.283418 | − | 0.283418i | −0.551053 | − | 0.834471i | \(-0.685774\pi\) |
0.834471 | + | 0.551053i | \(0.185774\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.6826 | + | 37.8612i | 0.545339 | + | 1.31656i | 0.920912 | + | 0.389771i | \(0.127446\pi\) |
−0.375573 | + | 0.926793i | \(0.622554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.7729 | − | 6.53333i | −0.547814 | − | 0.226912i | 0.0915711 | − | 0.995799i | \(-0.470811\pi\) |
−0.639385 | + | 0.768886i | \(0.720811\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.4122i | 0.811183i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.05274 | − | 9.78417i | 0.140251 | − | 0.338595i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.63280 | − | 8.63280i | 0.298037 | − | 0.298037i | −0.542207 | − | 0.840245i | \(-0.682411\pi\) |
0.840245 | + | 0.542207i | \(0.182411\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.49509 | + | 3.49509i | 0.120520 | + | 0.120520i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.55206 | − | 1.05710i | −0.0877934 | − | 0.0363652i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.20715 | −0.0414781 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.9664 | − | 36.1322i | 0.513043 | − | 1.23860i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.9586 | + | 8.68133i | −0.717608 | + | 0.297243i | −0.711449 | − | 0.702738i | \(-0.751961\pi\) |
−0.00615957 | + | 0.999981i | \(0.501961\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.1816 | − | 19.1816i | −0.655232 | − | 0.655232i | 0.299016 | − | 0.954248i | \(-0.403342\pi\) |
−0.954248 | + | 0.299016i | \(0.903342\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.8743 | − | 18.1733i | 1.49697 | − | 0.620066i | 0.524151 | − | 0.851625i | \(-0.324383\pi\) |
0.972821 | + | 0.231559i | \(0.0743827\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41.7776 | −1.42212 | −0.711062 | − | 0.703129i | \(-0.751786\pi\) | ||||
−0.711062 | + | 0.703129i | \(0.751786\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.6087 | −0.360706 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.7170 | − | 6.09598i | 0.499240 | − | 0.206792i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.9197 | − | 21.9197i | −0.742722 | − | 0.742722i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.25752 | − | 3.00616i | 0.245349 | − | 0.101627i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.1913 | − | 48.7461i | 0.681811 | − | 1.64604i | −0.0788487 | − | 0.996887i | \(-0.525124\pi\) |
0.760660 | − | 0.649151i | \(-0.224876\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.703923 | −0.0237158 | −0.0118579 | − | 0.999930i | \(-0.503775\pi\) | ||||
−0.0118579 | + | 0.999930i | \(0.503775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.756687 | − | 0.313430i | −0.0254645 | − | 0.0105478i | 0.369915 | − | 0.929066i | \(-0.379387\pi\) |
−0.395379 | + | 0.918518i | \(0.629387\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.2480 | + | 20.2480i | 0.679862 | + | 0.679862i | 0.959969 | − | 0.280106i | \(-0.0903698\pi\) |
−0.280106 | + | 0.959969i | \(0.590370\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.2033 | − | 10.2033i | 0.342207 | − | 0.342207i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.1921 | + | 48.7481i | −0.675704 | + | 1.63129i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.2983i | 0.344233i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.63213 | − | 1.09026i | −0.0877864 | − | 0.0363623i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.1884 | − | 31.8396i | −0.439369 | − | 1.06073i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.765595 | + | 0.765595i | −0.0254492 | + | 0.0254492i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.52443 | + | 6.09451i | 0.0838223 | + | 0.202365i | 0.960233 | − | 0.279199i | \(-0.0900689\pi\) |
−0.876411 | + | 0.481564i | \(0.840069\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 44.3943i | − | 1.47085i | −0.677608 | − | 0.735424i | \(-0.736983\pi\) | ||
0.677608 | − | 0.735424i | \(-0.263017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.2609i | 0.471966i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.380907 | − | 0.919592i | −0.0125787 | − | 0.0303676i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.6702 | − | 13.6702i | 0.450938 | − | 0.450938i | −0.444728 | − | 0.895666i | \(-0.646700\pi\) |
0.895666 | + | 0.444728i | \(0.146700\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.3655 | − | 34.6814i | −0.472846 | − | 1.14155i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.1271 | − | 4.60901i | −0.365858 | − | 0.151543i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 29.8610i | − | 0.979709i | −0.871804 | − | 0.489855i | \(-0.837050\pi\) | ||
0.871804 | − | 0.489855i | \(-0.162950\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.3152 | − | 36.9742i | 0.501936 | − | 1.21178i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.6225 | − | 13.6225i | 0.445503 | − | 0.445503i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.0276 | − | 25.0276i | −0.817617 | − | 0.817617i | 0.168145 | − | 0.985762i | \(-0.446222\pi\) |
−0.985762 | + | 0.168145i | \(0.946222\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.6214 | + | 16.4117i | 1.29162 | + | 0.535007i | 0.919468 | − | 0.393165i | \(-0.128620\pi\) |
0.372152 | + | 0.928172i | \(0.378620\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.4689 | 0.796816 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.0273 | − | 41.1075i | 0.553312 | − | 1.33581i | −0.361665 | − | 0.932308i | \(-0.617792\pi\) |
0.914977 | − | 0.403505i | \(-0.132208\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.5003 | + | 19.6753i | −1.54192 | + | 0.638686i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.7204 | + | 12.7204i | 0.412054 | + | 0.412054i | 0.882454 | − | 0.470400i | \(-0.155890\pi\) |
−0.470400 | + | 0.882454i | \(0.655890\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.9337 | + | 16.1268i | −1.25986 | + | 0.521853i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.420804 | 0.0135885 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.6626 | 0.989116 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.1907 | − | 6.29220i | 0.489006 | − | 0.202553i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.4994 | − | 13.4994i | −0.434112 | − | 0.434112i | 0.455913 | − | 0.890025i | \(-0.349313\pi\) |
−0.890025 | + | 0.455913i | \(0.849313\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.1525 | − | 11.6611i | 0.903457 | − | 0.374224i | 0.117909 | − | 0.993024i | \(-0.462381\pi\) |
0.785548 | + | 0.618800i | \(0.212381\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.23511 | − | 12.6387i | 0.167830 | − | 0.405177i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.5548 | −0.977534 | −0.488767 | − | 0.872414i | \(-0.662553\pi\) | ||||
−0.488767 | + | 0.872414i | \(0.662553\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −49.3461 | − | 20.4398i | −1.57711 | − | 0.653259i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.3548 | + | 30.3548i | 0.968168 | + | 0.968168i | 0.999509 | − | 0.0313409i | \(-0.00997774\pi\) |
−0.0313409 | + | 0.999509i | \(0.509978\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.1589 | − | 11.1589i | 0.355552 | − | 0.355552i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.1625 | − | 39.0197i | 0.513937 | − | 1.24075i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 45.5684i | − | 1.44753i | −0.690048 | − | 0.723764i | \(-0.742411\pi\) | ||
0.690048 | − | 0.723764i | \(-0.257589\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.9786 | + | 12.8317i | 0.982086 | + | 0.406793i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.87805 | − | 11.7767i | −0.154490 | − | 0.372971i | 0.827618 | − | 0.561292i | \(-0.189695\pi\) |
−0.982108 | + | 0.188321i | \(0.939695\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1152.2.w.a.431.3 | 32 | ||
3.2 | odd | 2 | 1152.2.w.b.431.6 | 32 | |||
4.3 | odd | 2 | 288.2.w.b.35.2 | yes | 32 | ||
12.11 | even | 2 | 288.2.w.a.35.7 | ✓ | 32 | ||
32.11 | odd | 8 | 1152.2.w.b.719.6 | 32 | |||
32.21 | even | 8 | 288.2.w.a.107.7 | yes | 32 | ||
96.11 | even | 8 | inner | 1152.2.w.a.719.3 | 32 | ||
96.53 | odd | 8 | 288.2.w.b.107.2 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.w.a.35.7 | ✓ | 32 | 12.11 | even | 2 | ||
288.2.w.a.107.7 | yes | 32 | 32.21 | even | 8 | ||
288.2.w.b.35.2 | yes | 32 | 4.3 | odd | 2 | ||
288.2.w.b.107.2 | yes | 32 | 96.53 | odd | 8 | ||
1152.2.w.a.431.3 | 32 | 1.1 | even | 1 | trivial | ||
1152.2.w.a.719.3 | 32 | 96.11 | even | 8 | inner | ||
1152.2.w.b.431.6 | 32 | 3.2 | odd | 2 | |||
1152.2.w.b.719.6 | 32 | 32.11 | odd | 8 |