Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2156,2,Mod(901,2156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2156, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2156.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2156.q (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: | \(17.2157466758\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 17x^{12} - 343x^{10} + 490x^{8} - 16807x^{6} - 40817x^{4} + 235298x^{2} + 5764801 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | no (minimal twist has level 308) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.1 | ||
Root | \(2.64407 - 0.0942693i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2156.901 |
Dual form | 2156.2.q.c.2089.1 |
$q$-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 \(\left(\mathbb{Z}/2156\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1079\) | \(1277\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −2.37157 | + | 1.36923i | −1.36923 | + | 0.790524i | −0.990829 | − | 0.135118i | \(-0.956859\pi\) |
−0.378399 | + | 0.925643i | \(0.623525\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.316246 | − | 0.182585i | −0.141429 | − | 0.0816543i | 0.427616 | − | 0.903961i | \(-0.359354\pi\) |
−0.569045 | + | 0.822306i | \(0.692687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.24957 | − | 3.89637i | 0.749857 | − | 1.29879i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.70717 | + | 1.91604i | −0.816243 | + | 0.577709i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.51413 | 1.25199 | 0.625997 | − | 0.779826i | \(-0.284692\pi\) | ||||
0.625997 | + | 0.779826i | \(0.284692\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.66183 | − | 2.87837i | −0.403052 | − | 0.698107i | 0.591040 | − | 0.806642i | \(-0.298717\pi\) |
−0.994093 | + | 0.108535i | \(0.965384\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.66183 | + | 2.87837i | −0.381249 | + | 0.660343i | −0.991241 | − | 0.132064i | \(-0.957839\pi\) |
0.609992 | + | 0.792408i | \(0.291173\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.55533 | + | 4.42596i | −0.532822 | + | 0.922876i | 0.466443 | + | 0.884551i | \(0.345535\pi\) |
−0.999265 | + | 0.0383243i | \(0.987798\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.43333 | − | 4.21464i | −0.486665 | − | 0.842929i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.10534i | 0.790073i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.32202i | − | 0.988274i | −0.869384 | − | 0.494137i | \(-0.835484\pi\) | ||
0.869384 | − | 0.494137i | \(-0.164516\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.37714 | − | 2.52714i | 0.786158 | − | 0.453888i | −0.0524503 | − | 0.998624i | \(-0.516703\pi\) |
0.838608 | + | 0.544735i | \(0.183370\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.79676 | − | 8.25077i | 0.660930 | − | 1.43627i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.305755 | + | 0.529584i | −0.0502659 | + | 0.0870630i | −0.890064 | − | 0.455836i | \(-0.849340\pi\) |
0.839798 | + | 0.542899i | \(0.182674\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.7056 | + | 6.18087i | −1.71427 | + | 0.989731i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.51413 | −0.704988 | −0.352494 | − | 0.935814i | \(-0.614666\pi\) | ||||
−0.352494 | + | 0.935814i | \(0.614666\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.03973i | − | 1.07355i | −0.843726 | − | 0.536774i | \(-0.819643\pi\) | ||
0.843726 | − | 0.536774i | \(-0.180357\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.42284 | + | 0.821474i | −0.212104 | + | 0.122458i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.505569 | − | 0.291890i | −0.0737448 | − | 0.0425766i | 0.462674 | − | 0.886528i | \(-0.346890\pi\) |
−0.536419 | + | 0.843952i | \(0.680223\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.88229 | + | 4.55084i | 1.10374 | + | 0.637245i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.87072 | + | 11.9004i | 0.943765 | + | 1.63465i | 0.758204 | + | 0.652017i | \(0.226077\pi\) |
0.185561 | + | 0.982633i | \(0.440590\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.20597 | − | 0.111652i | 0.162613 | − | 0.0150552i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 9.10169i | − | 1.20555i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.95431 | − | 1.70567i | 0.384618 | − | 0.222059i | −0.295208 | − | 0.955433i | \(-0.595389\pi\) |
0.679826 | + | 0.733374i | \(0.262055\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.72010 | − | 9.90750i | 0.732384 | − | 1.26853i | −0.223478 | − | 0.974709i | \(-0.571741\pi\) |
0.955862 | − | 0.293817i | \(-0.0949256\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.42757 | − | 0.824210i | −0.177069 | − | 0.102231i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.43739 | − | 9.41784i | −0.664283 | − | 1.15057i | −0.979479 | − | 0.201545i | \(-0.935404\pi\) |
0.315196 | − | 0.949027i | \(-0.397930\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 13.9953i | − | 1.68484i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.37564 | −1.11268 | −0.556342 | − | 0.830954i | \(-0.687795\pi\) | ||||
−0.556342 | + | 0.830954i | \(0.687795\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.56695 | − | 2.71404i | −0.183398 | − | 0.317655i | 0.759637 | − | 0.650347i | \(-0.225376\pi\) |
−0.943036 | + | 0.332692i | \(0.892043\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.5416 | + | 6.66356i | 1.33271 | + | 0.769441i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3291 | + | 5.96351i | 1.16211 | + | 0.670947i | 0.951810 | − | 0.306689i | \(-0.0992210\pi\) |
0.210305 | + | 0.977636i | \(0.432554\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.12757 | + | 1.95301i | 0.125286 | + | 0.217001i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.7639 | 1.62054 | 0.810272 | − | 0.586054i | \(-0.199319\pi\) | ||||
0.810272 | + | 0.586054i | \(0.199319\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.21370i | 0.131644i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.28705 | + | 12.6215i | 0.781254 | + | 1.35317i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.38527 | − | 4.26389i | −0.782837 | − | 0.451971i | 0.0545977 | − | 0.998508i | \(-0.482612\pi\) |
−0.837435 | + | 0.546537i | \(0.815946\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.92047 | + | 11.9866i | −0.717620 | + | 1.24295i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.05109 | − | 0.606848i | 0.107840 | − | 0.0622613i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.15963i | 0.930019i | 0.885306 | + | 0.465010i | \(0.153949\pi\) | ||||
−0.885306 | + | 0.465010i | \(0.846051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.37564 | + | 14.8584i | 0.138257 | + | 1.49333i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.69182 | + | 11.5906i | 0.665861 | + | 1.15330i | 0.979051 | + | 0.203614i | \(0.0652689\pi\) |
−0.313190 | + | 0.949690i | \(0.601398\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.92284 | + | 3.41955i | 0.583594 | + | 0.336938i | 0.762561 | − | 0.646917i | \(-0.223942\pi\) |
−0.178966 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.65449 | + | 5.57402i | 0.933335 | + | 0.538861i | 0.887865 | − | 0.460105i | \(-0.152188\pi\) |
0.0454701 | + | 0.998966i | \(0.485521\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.65449 | − | 5.57402i | 0.924732 | − | 0.533895i | 0.0395907 | − | 0.999216i | \(-0.487395\pi\) |
0.885142 | + | 0.465321i | \(0.154061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.67460i | − | 0.158946i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.84567 | 0.832131 | 0.416065 | − | 0.909335i | \(-0.363409\pi\) | ||||
0.416065 | + | 0.909335i | \(0.363409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.61622 | − | 0.933127i | 0.150714 | − | 0.0870145i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.1549 | − | 17.5887i | 0.938817 | − | 1.62608i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.65756 | − | 10.3741i | 0.332506 | − | 0.943101i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.7056 | − | 6.18087i | 0.965290 | − | 0.557310i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.60300i | 0.322262i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.03973i | 0.624675i | 0.949971 | + | 0.312337i | \(0.101112\pi\) | ||||
−0.949971 | + | 0.312337i | \(0.898888\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.63899 | + | 16.6952i | 0.848666 | + | 1.46993i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.43475 | + | 7.68122i | −0.387466 | + | 0.671111i | −0.992108 | − | 0.125386i | \(-0.959983\pi\) |
0.604642 | + | 0.796498i | \(0.293316\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.749572 | − | 1.29830i | 0.0645128 | − | 0.111740i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.28798 | − | 7.42700i | −0.366347 | − | 0.634532i | 0.622644 | − | 0.782505i | \(-0.286058\pi\) |
−0.988991 | + | 0.147973i | \(0.952725\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.8204 | 1.08741 | 0.543707 | − | 0.839275i | \(-0.317020\pi\) | ||||
0.543707 | + | 0.839275i | \(0.317020\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.59866 | 0.134631 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.2205 | + | 8.64926i | −1.02193 | + | 0.723288i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.971718 | + | 1.68307i | −0.0806968 | + | 0.139771i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.5879 | + | 10.7317i | 1.52278 | + | 0.879176i | 0.999637 | + | 0.0269298i | \(0.00857307\pi\) |
0.523141 | + | 0.852246i | \(0.324760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.05109 | + | 0.606848i | −0.0855367 | + | 0.0493846i | −0.542158 | − | 0.840276i | \(-0.682393\pi\) |
0.456622 | + | 0.889661i | \(0.349059\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.9536 | −1.20893 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.84567 | −0.148248 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.8949 | + | 8.02223i | −1.10893 | + | 0.640243i | −0.938553 | − | 0.345135i | \(-0.887833\pi\) |
−0.170381 | + | 0.985378i | \(0.554500\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −32.5888 | − | 18.8152i | −2.58446 | − | 1.49214i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.61878 | − | 16.6602i | 0.753401 | − | 1.30493i | −0.192764 | − | 0.981245i | \(-0.561745\pi\) |
0.946165 | − | 0.323684i | \(-0.104921\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.70717 | + | 1.91604i | −0.210753 | + | 0.149164i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.189746 | −0.0146830 | −0.00734151 | − | 0.999973i | \(-0.502337\pi\) | ||||
−0.00734151 | + | 0.999973i | \(0.502337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.37735 | 0.567489 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.47680 | + | 12.9502i | 0.571765 | + | 0.990326i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.3008 | − | 19.5736i | 0.859185 | − | 1.48815i | −0.0135217 | − | 0.999909i | \(-0.504304\pi\) |
0.872707 | − | 0.488244i | \(-0.162362\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.67090 | + | 8.09024i | −0.351086 | + | 0.608100i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.44231 | + | 5.96226i | 0.257290 | + | 0.445640i | 0.965515 | − | 0.260347i | \(-0.0838370\pi\) |
−0.708225 | + | 0.705987i | \(0.750504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.3397i | 1.51184i | 0.654664 | + | 0.755920i | \(0.272810\pi\) | ||||
−0.654664 | + | 0.755920i | \(0.727190\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 31.3285i | 2.31587i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.193388 | − | 0.111652i | 0.0142181 | − | 0.00820885i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0139 | + | 4.60811i | 0.732291 | + | 0.336978i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.50000 | + | 2.59808i | −0.108536 | + | 0.187990i | −0.915177 | − | 0.403051i | \(-0.867950\pi\) |
0.806641 | + | 0.591041i | \(0.201283\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.4623 | − | 12.9686i | 1.61687 | − | 0.933500i | 0.629145 | − | 0.777288i | \(-0.283405\pi\) |
0.987724 | − | 0.156212i | \(-0.0499282\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.51413 | 0.323263 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 15.7067i | − | 1.11906i | −0.828812 | − | 0.559528i | \(-0.810983\pi\) | ||
0.828812 | − | 0.559528i | \(-0.189017\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.63099 | − | 0.941651i | 0.115618 | − | 0.0667519i | −0.441076 | − | 0.897470i | \(-0.645403\pi\) |
0.556694 | + | 0.830718i | \(0.312070\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 25.7903 | + | 14.8901i | 1.81911 | + | 1.05026i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.42757 | + | 0.824210i | 0.0997061 | + | 0.0575653i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.4968 | + | 19.9130i | 0.799082 | + | 1.38405i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.01623 | − | 10.9764i | −0.0702938 | − | 0.759252i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 11.5135i | − | 0.792621i | −0.918117 | − | 0.396310i | \(-0.870290\pi\) | ||
0.918117 | − | 0.396310i | \(-0.129710\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.2350 | − | 12.8374i | 1.52352 | − | 0.879603i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.28535 | + | 2.22628i | −0.0876598 | + | 0.151831i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.43229 | + | 4.29104i | 0.502228 | + | 0.289961i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.50170 | − | 12.9933i | −0.504619 | − | 0.874026i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.120749i | − | 0.00808595i | −0.999992 | − | 0.00404298i | \(-0.998713\pi\) | ||
0.999992 | − | 0.00404298i | \(-0.00128692\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.8958 | −1.45972 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.595236 | + | 1.03098i | 0.0395072 | + | 0.0684285i | 0.885103 | − | 0.465395i | \(-0.154088\pi\) |
−0.845596 | + | 0.533824i | \(0.820755\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.8401 | + | 7.99058i | 0.914579 | + | 0.528032i | 0.881902 | − | 0.471434i | \(-0.156263\pi\) |
0.0326773 | + | 0.999466i | \(0.489597\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.14767 | − | 4.12671i | −0.468260 | − | 0.270350i | 0.247251 | − | 0.968951i | \(-0.420473\pi\) |
−0.715511 | + | 0.698602i | \(0.753806\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.106589 | + | 0.184618i | 0.00695313 | + | 0.0120432i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −32.6616 | −2.12160 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.89462i | 0.187238i | 0.995608 | + | 0.0936188i | \(0.0298435\pi\) | ||||
−0.995608 | + | 0.0936188i | \(0.970157\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.376482 | + | 0.652086i | 0.0242513 | + | 0.0420045i | 0.877896 | − | 0.478851i | \(-0.158946\pi\) |
−0.853645 | + | 0.520855i | \(0.825613\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.0142 | − | 9.24581i | −1.02731 | − | 0.593119i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.50170 | + | 12.9933i | −0.477322 | + | 0.826746i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −35.0136 | + | 20.2151i | −2.21889 | + | 1.28108i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.66515i | − | 0.231342i | −0.993288 | − | 0.115671i | \(-0.963098\pi\) | ||
0.993288 | − | 0.115671i | \(-0.0369018\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.56261 | − | 16.8779i | −0.0982404 | − | 1.06111i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.66183 | − | 2.87837i | −0.104068 | − | 0.180251i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.51220 | + | 2.02777i | 0.219085 | + | 0.126489i | 0.605527 | − | 0.795825i | \(-0.292963\pi\) |
−0.386441 | + | 0.922314i | \(0.626296\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.7366 | − | 11.9723i | −1.28356 | − | 0.741064i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.88229 | − | 4.55084i | 0.486043 | − | 0.280617i | −0.236888 | − | 0.971537i | \(-0.576128\pi\) |
0.722931 | + | 0.690920i | \(0.242794\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.01795i | − | 0.308250i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.3529 | 1.42918 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.64213 | + | 3.25748i | −0.344006 | + | 0.198612i | −0.662042 | − | 0.749466i | \(-0.730310\pi\) |
0.318036 | + | 0.948079i | \(0.396977\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.01376 | − | 6.95204i | 0.243819 | − | 0.422307i | −0.717980 | − | 0.696064i | \(-0.754933\pi\) |
0.961799 | + | 0.273757i | \(0.0882664\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.6629 | + | 6.74741i | 0.884204 | + | 0.406884i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.84572 | − | 1.06562i | 0.110898 | − | 0.0640272i | −0.443525 | − | 0.896262i | \(-0.646272\pi\) |
0.554423 | + | 0.832235i | \(0.312939\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 22.7400i | − | 1.36141i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4.54304i | − | 0.271015i | −0.990776 | − | 0.135508i | \(-0.956733\pi\) | ||
0.990776 | − | 0.135508i | \(-0.0432665\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.9098 | − | 27.5566i | −0.945741 | − | 1.63807i | −0.754261 | − | 0.656574i | \(-0.772005\pi\) |
−0.191479 | − | 0.981497i | \(-0.561328\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.66183 | + | 2.87837i | −0.0984382 | + | 0.170500i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.97666 | − | 5.15572i | 0.175097 | − | 0.303278i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.5416 | − | 21.7227i | −0.735203 | − | 1.27341i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.3263 | 0.836954 | 0.418477 | − | 0.908227i | \(-0.362564\pi\) | ||||
0.418477 | + | 0.908227i | \(0.362564\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.24572 | −0.0725284 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.86600 | − | 11.1139i | −0.456432 | − | 0.644891i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.5351 | + | 19.9793i | −0.667090 | + | 1.15543i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −31.7403 | − | 18.3253i | −1.82343 | − | 1.05276i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.61792 | + | 2.08880i | −0.207161 | + | 0.119605i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.9253 | 1.47963 | 0.739817 | − | 0.672808i | \(-0.234912\pi\) | ||||
0.739817 | + | 0.672808i | \(0.234912\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.7286 | −1.06543 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.9162 | − | 12.0760i | 1.18605 | − | 0.684766i | 0.228643 | − | 0.973510i | \(-0.426571\pi\) |
0.957406 | + | 0.288745i | \(0.0932379\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.8345 | − | 13.7609i | −1.34721 | − | 0.777810i | −0.359354 | − | 0.933201i | \(-0.617003\pi\) |
−0.987853 | + | 0.155391i | \(0.950336\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.28798 | − | 12.6232i | 0.409334 | − | 0.708987i | −0.585481 | − | 0.810686i | \(-0.699094\pi\) |
0.994815 | + | 0.101699i | \(0.0324278\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.1972 | + | 14.4076i | 0.570934 | + | 0.806672i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.5284 | −1.70393 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.0467 | 0.614654 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.9843 | − | 19.0254i | −0.609302 | − | 1.05534i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.2642 | + | 26.4384i | −0.844113 | + | 1.46205i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.2414 | + | 21.2028i | −0.672850 | + | 1.16541i | 0.304242 | + | 0.952595i | \(0.401597\pi\) |
−0.977092 | + | 0.212816i | \(0.931737\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.37564 | + | 2.38267i | 0.0753845 | + | 0.130570i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.97114i | 0.216966i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.14510i | 0.225798i | 0.993606 | + | 0.112899i | \(0.0360137\pi\) | ||||
−0.993606 | + | 0.112899i | \(0.963986\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.9782 | + | 12.1117i | −1.13938 | + | 0.657819i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.00756 | + | 15.2282i | −0.379481 | + | 0.824653i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.55533 | + | 4.42596i | −0.137574 | + | 0.238285i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.6535 | + | 8.46019i | −0.786640 | + | 0.454167i | −0.838778 | − | 0.544473i | \(-0.816730\pi\) |
0.0521382 | + | 0.998640i | \(0.483396\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.0882 | 1.02177 | 0.510885 | − | 0.859649i | \(-0.329318\pi\) | ||||
0.510885 | + | 0.859649i | \(0.329318\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.5320i | 0.989166i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.5015 | − | 11.2592i | 1.03796 | − | 0.599266i | 0.118705 | − | 0.992930i | \(-0.462126\pi\) |
0.919255 | + | 0.393663i | \(0.128792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.96501 | + | 1.71185i | 0.157366 | + | 0.0908554i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.4247 | − | 12.3695i | −1.13075 | − | 0.652839i | −0.186627 | − | 0.982431i | \(-0.559756\pi\) |
−0.944124 | + | 0.329591i | \(0.893089\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.97666 | + | 6.88777i | 0.209298 | + | 0.362514i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.53035 | + | 29.6110i | 0.290268 | + | 1.55417i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.14441i | 0.0599010i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.50706 | + | 3.75685i | −0.339666 | + | 0.196106i | −0.660124 | − | 0.751156i | \(-0.729496\pi\) |
0.320458 | + | 0.947263i | \(0.396163\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.1549 | + | 17.5887i | −0.528641 | + | 0.915632i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.29253 | − | 2.47829i | −0.222259 | − | 0.128321i | 0.384737 | − | 0.923026i | \(-0.374292\pi\) |
−0.606996 | + | 0.794705i | \(0.707625\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.93333 | − | 8.54477i | −0.254756 | − | 0.441250i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 24.0243i | − | 1.23731i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.3080 | −1.60818 | −0.804091 | − | 0.594506i | \(-0.797348\pi\) | ||||
−0.804091 | + | 0.594506i | \(0.797348\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.63899 | − | 16.6952i | −0.493820 | − | 0.855322i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.1421 | + | 8.16495i | 0.722628 | + | 0.417210i | 0.815719 | − | 0.578448i | \(-0.196341\pi\) |
−0.0930910 | + | 0.995658i | \(0.529675\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.4294 | − | 15.8364i | −1.39431 | − | 0.805008i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.74465 | − | 15.1462i | −0.443371 | − | 0.767942i | 0.554566 | − | 0.832140i | \(-0.312884\pi\) |
−0.997937 | + | 0.0641981i | \(0.979551\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.9861 | 0.859022 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 24.2888i | − | 1.22521i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.17769 | − | 3.77187i | −0.109571 | − | 0.189783i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.3203 | − | 11.1546i | −0.969658 | − | 0.559832i | −0.0705261 | − | 0.997510i | \(-0.522468\pi\) |
−0.899132 | + | 0.437678i | \(0.855801\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.4179 | + | 26.7046i | −0.769933 | + | 1.33356i | 0.167665 | + | 0.985844i | \(0.446377\pi\) |
−0.937599 | + | 0.347720i | \(0.886956\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.7590 | − | 11.4079i | 0.984265 | − | 0.568266i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 0.823508i | − | 0.0409204i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.186973 | − | 2.01951i | −0.00926789 | − | 0.100104i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.6845 | − | 25.4343i | −0.726101 | − | 1.25764i | −0.958519 | − | 0.285028i | \(-0.907997\pi\) |
0.232418 | − | 0.972616i | \(-0.425336\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.3385 | + | 11.7425i | 1.00323 | + | 0.579212i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.66901 | − | 2.69565i | −0.229193 | − | 0.132324i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.4046 | + | 17.5541i | −1.48892 | + | 0.859627i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.2447i | 1.72181i | 0.508762 | + | 0.860907i | \(0.330103\pi\) | ||||
−0.508762 | + | 0.860907i | \(0.669897\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.47173 | −0.461624 | −0.230812 | − | 0.972998i | \(-0.574138\pi\) | ||||
−0.230812 | + | 0.972998i | \(0.574138\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.27463 | + | 1.31326i | −0.110596 | + | 0.0638527i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.08754 | + | 14.0080i | −0.392303 | + | 0.679489i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.1390 | − | 37.2450i | 0.827481 | − | 1.79821i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.9123 | + | 13.2284i | −1.10364 | + | 0.637189i | −0.937176 | − | 0.348857i | \(-0.886570\pi\) |
−0.166469 | + | 0.986047i | \(0.553236\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 23.5184i | − | 1.13022i | −0.825015 | − | 0.565110i | \(-0.808834\pi\) | ||
0.825015 | − | 0.565110i | \(-0.191166\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 5.32202i | − | 0.255171i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.49303 | − | 14.7104i | −0.406277 | − | 0.703692i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.5862 | + | 21.7999i | −0.600705 | + | 1.04045i | 0.392010 | + | 0.919961i | \(0.371780\pi\) |
−0.992715 | + | 0.120490i | \(0.961553\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.2936 | − | 21.2931i | 0.584084 | − | 1.01166i | −0.410905 | − | 0.911678i | \(-0.634787\pi\) |
0.994989 | − | 0.0999853i | \(-0.0318796\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.55704 | + | 2.69687i | 0.0738108 | + | 0.127844i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −58.7767 | −2.78004 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.8474 | 0.889462 | 0.444731 | − | 0.895664i | \(-0.353299\pi\) | ||||
0.444731 | + | 0.895664i | \(0.353299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.2205 | − | 8.64926i | 0.575442 | − | 0.407278i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.66183 | − | 2.87837i | 0.0780795 | − | 0.135238i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.661101 | + | 0.381687i | 0.0309250 | + | 0.0178546i | 0.515383 | − | 0.856960i | \(-0.327650\pi\) |
−0.484458 | + | 0.874815i | \(0.660983\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.8167 | − | 6.82236i | 0.551555 | − | 0.318441i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0034 | −0.559055 | −0.279527 | − | 0.960138i | \(-0.590178\pi\) | ||||
−0.279527 | + | 0.960138i | \(0.590178\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.8940 | 1.06398 | 0.531988 | − | 0.846752i | \(-0.321445\pi\) | ||||
0.531988 | + | 0.846752i | \(0.321445\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.37714 | − | 2.52714i | 0.202985 | − | 0.117193i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.7736 | − | 18.3445i | −1.47031 | − | 0.848883i | −0.470863 | − | 0.882206i | \(-0.656058\pi\) |
−0.999445 | + | 0.0333234i | \(0.989391\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.9685 | − | 38.0506i | 1.01226 | − | 1.75328i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.4884 | + | 19.0578i | 0.620198 | + | 0.876276i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.1751 | 0.742163 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 61.8247 | 2.83076 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.72668 | − | 11.6510i | −0.307350 | − | 0.532346i | 0.670432 | − | 0.741971i | \(-0.266109\pi\) |
−0.977782 | + | 0.209625i | \(0.932776\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.38022 | + | 2.39061i | −0.0629326 | + | 0.109002i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.67241 | − | 2.89669i | 0.0759401 | − | 0.131532i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.2863 | + | 26.4766i | 0.692687 | + | 1.19977i | 0.970954 | + | 0.239265i | \(0.0769066\pi\) |
−0.278267 | + | 0.960504i | \(0.589760\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 52.6812i | 2.38233i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 40.4514i | − | 1.82554i | −0.408469 | − | 0.912772i | \(-0.633937\pi\) | ||
0.408469 | − | 0.912772i | \(-0.366063\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.3187 | + | 8.84427i | −0.689921 | + | 0.398326i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.27788 | − | 4.95009i | 0.102383 | − | 0.222490i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.03061 | + | 13.9094i | −0.359500 | + | 0.622672i | −0.987877 | − | 0.155237i | \(-0.950386\pi\) |
0.628378 | + | 0.777908i | \(0.283719\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.449997 | − | 0.259806i | 0.0201044 | − | 0.0116073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.2531 | −0.992219 | −0.496109 | − | 0.868260i | \(-0.665238\pi\) | ||||
−0.496109 | + | 0.868260i | \(0.665238\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 4.88729i | − | 0.217482i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.4959 | + | 10.1013i | −0.777021 | + | 0.448613i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.4284 | + | 12.9490i | 0.994121 | + | 0.573956i | 0.906504 | − | 0.422198i | \(-0.138741\pi\) |
0.0876175 | + | 0.996154i | \(0.472075\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.8167 | − | 6.82236i | −0.521719 | − | 0.301215i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.24871 | − | 2.16284i | −0.0550249 | − | 0.0953060i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.92794 | − | 0.178494i | 0.0847906 | − | 0.00785016i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 61.8936i | 2.71683i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.9066 | + | 11.4931i | −0.872122 | + | 0.503520i | −0.868053 | − | 0.496472i | \(-0.834629\pi\) |
−0.00406920 | + | 0.999992i | \(0.501295\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.49961 | − | 16.4538i | 0.415389 | − | 0.719475i | −0.580080 | − | 0.814559i | \(-0.696979\pi\) |
0.995469 | + | 0.0950845i | \(0.0303121\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.5481 | − | 8.39936i | −0.633726 | − | 0.365882i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.55939 | − | 2.70095i | −0.0677996 | − | 0.117432i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 15.3481i | − | 0.666051i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.3774 | −0.882641 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.03546 | − | 3.52552i | −0.0880007 | − | 0.152422i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.3274 | − | 9.42662i | −0.704579 | − | 0.406789i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.358135 | − | 0.206769i | −0.0153974 | − | 0.00888970i | 0.492282 | − | 0.870436i | \(-0.336163\pi\) |
−0.507679 | + | 0.861546i | \(0.669496\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −27.8497 | − | 48.2371i | −1.19515 | − | 2.07005i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.07092 | −0.174379 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.64842i | − | 0.0704814i | −0.999379 | − | 0.0352407i | \(-0.988780\pi\) | ||
0.999379 | − | 0.0352407i | \(-0.0112198\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.7355 | − | 44.5753i | −1.09837 | − | 1.90243i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.3187 | + | 8.84427i | 0.652600 | + | 0.376779i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.305755 | + | 0.529584i | −0.0129786 | + | 0.0224796i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.0905 | − | 16.2181i | 1.19023 | − | 0.687181i | 0.231873 | − | 0.972746i | \(-0.425515\pi\) |
0.958359 | + | 0.285565i | \(0.0921812\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 31.7782i | − | 1.34408i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −30.0583 | + | 2.78289i | −1.26906 | + | 0.117494i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.9781 | + | 22.4788i | 0.546964 | + | 0.947369i | 0.998480 | + | 0.0551062i | \(0.0175497\pi\) |
−0.451517 | + | 0.892263i | \(0.649117\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.79741 | − | 1.61508i | −0.117688 | − | 0.0679471i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.0464 | + | 17.3473i | 1.25961 | + | 0.727237i | 0.972999 | − | 0.230810i | \(-0.0741374\pi\) |
0.286613 | + | 0.958047i | \(0.407471\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.9681 | − | 17.3021i | 1.25412 | − | 0.724069i | 0.282199 | − | 0.959356i | \(-0.408936\pi\) |
0.971926 | + | 0.235287i | \(0.0756030\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 8.21537i | − | 0.343202i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.8718 | 1.03722 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.406054 | + | 0.234435i | −0.0169042 | + | 0.00975966i | −0.508428 | − | 0.861104i | \(-0.669773\pi\) |
0.491524 | + | 0.870864i | \(0.336440\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −35.5139 | + | 61.5119i | −1.47591 | + | 2.55635i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −41.4019 | − | 19.0519i | −1.71469 | − | 0.789050i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.42286 | + | 3.70824i | −0.265553 | + | 0.153317i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 44.9718i | − | 1.85618i | −0.372352 | − | 0.928091i | \(-0.621449\pi\) | ||
0.372352 | − | 0.928091i | \(-0.378551\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.7987i | 0.692179i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.5060 | + | 37.2496i | 0.884640 | + | 1.53224i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.75841 | − | 13.4380i | 0.318600 | − | 0.551831i | −0.661596 | − | 0.749860i | \(-0.730121\pi\) |
0.980196 | + | 0.198029i | \(0.0634541\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.57867 | + | 4.46639i | −0.105538 | + | 0.182797i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.44231 | − | 7.69431i | −0.181508 | − | 0.314381i | 0.760886 | − | 0.648885i | \(-0.224764\pi\) |
−0.942394 | + | 0.334504i | \(0.891431\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.2497 | −0.418095 | −0.209048 | − | 0.977905i | \(-0.567036\pi\) | ||||
−0.209048 | + | 0.977905i | \(0.567036\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −48.9272 | −1.99247 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.05084 | + | 2.61296i | −0.124034 | + | 0.106232i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5505 | − | 37.3266i | 0.874710 | − | 1.51504i | 0.0176380 | − | 0.999844i | \(-0.494385\pi\) |
0.857072 | − | 0.515197i | \(-0.172281\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.28220 | − | 1.31763i | −0.0923281 | − | 0.0533056i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.0830 | − | 6.97610i | 0.488026 | − | 0.281762i | −0.235729 | − | 0.971819i | \(-0.575748\pi\) |
0.723755 | + | 0.690057i | \(0.242415\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.51413 | −0.182027 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.7915 | −0.555226 | −0.277613 | − | 0.960693i | \(-0.589543\pi\) | ||||
−0.277613 | + | 0.960693i | \(0.589543\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.0553 | − | 17.3524i | 1.20803 | − | 0.697454i | 0.245698 | − | 0.969347i | \(-0.420983\pi\) |
0.962328 | + | 0.271893i | \(0.0876496\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.1700 | − | 10.4905i | −0.729139 | − | 0.420968i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.5088 | + | 19.9338i | −0.460351 | + | 0.797351i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.4392 | + | 24.6398i | 0.696455 | + | 0.984020i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.03245 | 0.0810391 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.9790 | −0.437067 | −0.218533 | − | 0.975829i | \(-0.570127\pi\) | ||||
−0.218533 | + | 0.975829i | \(0.570127\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.7646 | + | 27.3051i | 0.626586 | + | 1.08528i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.28535 | − | 2.22628i | 0.0510074 | − | 0.0883474i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −21.0912 | + | 36.5310i | −0.834354 | + | 1.44514i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.85401 | − | 11.8715i | −0.270717 | − | 0.468896i | 0.698329 | − | 0.715777i | \(-0.253927\pi\) |
−0.969046 | + | 0.246882i | \(0.920594\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.7909i | 0.425553i | 0.977101 | + | 0.212777i | \(0.0682507\pi\) | ||||
−0.977101 | + | 0.212777i | \(0.931749\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 7.03973i | − | 0.277189i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.193388 | + | 0.111652i | −0.00760286 | + | 0.00438951i | −0.503797 | − | 0.863822i | \(-0.668064\pi\) |
0.496194 | + | 0.868212i | \(0.334731\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.72968 | + | 10.2781i | −0.185656 | + | 0.403451i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.8497 | + | 20.5243i | −0.463716 | + | 0.803180i | −0.999143 | − | 0.0414022i | \(-0.986818\pi\) |
0.535427 | + | 0.844582i | \(0.320151\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.80494 | − | 1.61944i | 0.109598 | − | 0.0632766i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.0999 | −0.550090 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.3521i | 1.26026i | 0.776490 | + | 0.630130i | \(0.216998\pi\) | ||||
−0.776490 | + | 0.630130i | \(0.783002\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.9690 | − | 20.7667i | 1.39903 | − | 0.807732i | 0.404742 | − | 0.914431i | \(-0.367361\pi\) |
0.994291 | + | 0.106699i | \(0.0340281\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 35.5817 | + | 20.5431i | 1.38188 | + | 0.797827i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.5550 | + | 13.5995i | 0.912054 | + | 0.526574i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.165333 | + | 0.286365i | 0.00639214 | + | 0.0110715i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.49790 | + | 37.7813i | 0.135035 | + | 1.45853i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.8621i | 0.958362i | 0.877716 | + | 0.479181i | \(0.159066\pi\) | ||||
−0.877716 | + | 0.479181i | \(0.840934\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.3025 | − | 9.98962i | 0.665975 | − | 0.384501i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.6335 | + | 21.8819i | −0.485546 | + | 0.840990i | −0.999862 | − | 0.0166108i | \(-0.994712\pi\) |
0.514316 | + | 0.857601i | \(0.328046\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.82329 | − | 1.63003i | −0.108189 | − | 0.0624628i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.64769 | + | 8.05004i | 0.177839 | + | 0.308026i | 0.941140 | − | 0.338017i | \(-0.109756\pi\) |
−0.763301 | + | 0.646043i | \(0.776423\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.13168i | 0.119655i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −43.7637 | −1.66969 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 31.0153 | + | 53.7201i | 1.18159 | + | 2.04657i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.1609 | − | 8.17577i | −0.538704 | − | 0.311021i | 0.205849 | − | 0.978584i | \(-0.434004\pi\) |
−0.744554 | + | 0.667563i | \(0.767338\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.05440 | − | 2.34081i | −0.153792 | − | 0.0887920i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.50170 | + | 12.9933i | 0.284147 | + | 0.492157i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.6016 | 0.854872 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.9480i | 1.62213i | 0.584959 | + | 0.811063i | \(0.301110\pi\) | ||||
−0.584959 | + | 0.811063i | \(0.698890\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.01623 | − | 1.76015i | −0.0383277 | − | 0.0663855i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.505569 | − | 0.291890i | −0.0190408 | − | 0.0109932i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.39812 | + | 4.15367i | −0.0900634 | + | 0.155994i | −0.907538 | − | 0.419971i | \(-0.862040\pi\) |
0.817474 | + | 0.575965i | \(0.195374\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 46.4721 | − | 26.8307i | 1.74284 | − | 1.00623i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.8307i | 0.967368i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.44391 | − | 0.504013i | 0.203591 | − | 0.0188490i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.96340 | − | 6.86481i | −0.148016 | − | 0.256371i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.29184 | − | 1.32319i | −0.0854711 | − | 0.0493468i | 0.456655 | − | 0.889644i | \(-0.349047\pi\) |
−0.542126 | + | 0.840297i | \(0.682381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.78571 | − | 1.03098i | −0.0664112 | − | 0.0383425i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.4304 | + | 12.9502i | −0.833044 | + | 0.480958i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 17.1118i | − | 0.634642i | −0.948318 | − | 0.317321i | \(-0.897217\pi\) | ||
0.948318 | − | 0.317321i | \(-0.102783\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.8731 | 1.62493 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.2629 | + | 11.6988i | −0.749452 | + | 0.432696i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.17596 | + | 10.6971i | −0.228114 | + | 0.395105i | −0.957249 | − | 0.289265i | \(-0.906589\pi\) |
0.729135 | + | 0.684370i | \(0.239923\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.7649 | + | 15.0774i | 1.20691 | + | 0.555384i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.4903 | − | 10.0980i | 0.643390 | − | 0.371462i | −0.142529 | − | 0.989791i | \(-0.545523\pi\) |
0.785919 | + | 0.618329i | \(0.212190\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 41.0862i | − | 1.50934i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.44593i | 0.346538i | 0.984875 | + | 0.173269i | \(0.0554330\pi\) | ||||
−0.984875 | + | 0.173269i | \(0.944567\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.91889 | − | 6.78772i | −0.143577 | − | 0.248683i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 33.2123 | − | 57.5255i | 1.21518 | − | 2.10475i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.592367 | − | 1.02601i | 0.0216158 | − | 0.0374397i | −0.855015 | − | 0.518603i | \(-0.826452\pi\) |
0.876631 | + | 0.481163i | \(0.159786\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.01842 | + | 8.69216i | 0.182881 | + | 0.316760i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.443205 | 0.0161299 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.1275 | 1.42211 | 0.711057 | − | 0.703134i | \(-0.248217\pi\) | ||||
0.711057 | + | 0.703134i | \(0.248217\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 26.8156 | + | 37.8877i | 0.973344 | + | 1.37524i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.17769 | − | 3.77187i | 0.0789412 | − | 0.136730i | −0.823852 | − | 0.566805i | \(-0.808179\pi\) |
0.902793 | + | 0.430075i | \(0.141513\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.72901 | + | 2.73030i | 0.170978 | + | 0.0987141i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.3361 | − | 7.69961i | 0.481539 | − | 0.278017i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.5312 | 0.776434 | 0.388217 | − | 0.921568i | \(-0.373091\pi\) | ||||
0.388217 | + | 0.921568i | \(0.373091\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.1059 | −0.399970 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.31569 | + | 4.22372i | −0.263127 | + | 0.151917i | −0.625760 | − | 0.780015i | \(-0.715211\pi\) |
0.362633 | + | 0.931932i | \(0.381878\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.3020 | − | 12.2987i | −0.765191 | − | 0.441783i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.50170 | − | 12.9933i | 0.268776 | − | 0.465534i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.3815 | − | 17.9641i | 0.908220 | − | 0.642807i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.8487 | 0.780808 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.85894 | 0.209115 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.65351 | − | 8.06011i | −0.165880 | − | 0.287312i | 0.771088 | − | 0.636729i | \(-0.219713\pi\) |
−0.936967 | + | 0.349417i | \(0.886380\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.4623 | + | 21.5853i | −0.443669 | + | 0.768457i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.8213 | − | 44.7237i | 0.916940 | − | 1.58819i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.87072 | + | 11.9004i | 0.243679 | + | 0.422065i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.1607i | 0.466175i | 0.972456 | + | 0.233088i | \(0.0748829\pi\) | ||||
−0.972456 | + | 0.233088i | \(0.925117\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.94029i | 0.0686424i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.2274 | + | 19.1838i | −1.17403 | + | 0.677828i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.44224 | + | 4.34504i | 0.333209 | + | 0.153333i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.92047 | − | 15.4507i | 0.314016 | − | 0.543891i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.9081 | + | 17.2674i | −1.05151 | + | 0.607090i | −0.923072 | − | 0.384627i | \(-0.874330\pi\) |
−0.128439 | + | 0.991717i | \(0.540997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.6941 | 0.515980 | 0.257990 | − | 0.966148i | \(-0.416940\pi\) | ||||
0.257990 | + | 0.966148i | \(0.416940\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.9830i | 0.770979i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.08380 | + | 3.51248i | −0.213106 | + | 0.123037i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.2629 | + | 11.6988i | 0.708910 | + | 0.409290i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.2742 | − | 16.3241i | −0.986777 | − | 0.569716i | −0.0824677 | − | 0.996594i | \(-0.526280\pi\) |
−0.904309 | + | 0.426878i | \(0.859613\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.99507 | − | 15.5799i | −0.313548 | − | 0.543082i | 0.665580 | − | 0.746327i | \(-0.268184\pi\) |
−0.979128 | + | 0.203245i | \(0.934851\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −44.0128 | + | 4.07484i | −1.53233 | + | 0.141868i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 46.5793i | − | 1.61972i | −0.586623 | − | 0.809860i | \(-0.699543\pi\) | ||
0.586623 | − | 0.809860i | \(-0.300457\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.4802 | − | 12.9789i | 0.780769 | − | 0.450777i | −0.0559338 | − | 0.998434i | \(-0.517814\pi\) |
0.836703 | + | 0.547657i | \(0.184480\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.91817 | + | 5.05441i | −0.101230 | + | 0.175336i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.0600065 | + | 0.0346448i | 0.00207661 | + | 0.00119893i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.3748 | + | 17.9696i | 0.358605 | + | 0.621122i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.9653i | 0.585707i | 0.956157 | + | 0.292854i | \(0.0946049\pi\) | ||||
−0.956157 | + | 0.292854i | \(0.905395\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.676145 | 0.0233154 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.22046 | + | 10.7742i | 0.214244 | + | 0.371082i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.33306 | − | 1.34699i | −0.0802596 | − | 0.0463379i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 75.4626 | + | 43.5683i | 2.58987 | + | 1.49526i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.56261 | − | 2.70652i | −0.0535656 | − | 0.0927783i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.5342 | −0.360684 | −0.180342 | − | 0.983604i | \(-0.557720\pi\) | ||||
−0.180342 | + | 0.983604i | \(0.557720\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 5.46060i | − | 0.186748i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.5122 | + | 33.7962i | 0.666525 | + | 1.15446i | 0.978869 | + | 0.204487i | \(0.0655525\pi\) |
−0.312344 | + | 0.949969i | \(0.601114\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.84673 | + | 4.53031i | 0.267727 | + | 0.154572i | 0.627854 | − | 0.778331i | \(-0.283933\pi\) |
−0.360127 | + | 0.932903i | \(0.617267\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.4590 | − | 23.3117i | 0.458150 | − | 0.793540i | −0.540713 | − | 0.841207i | \(-0.681845\pi\) |
0.998863 | + | 0.0476675i | \(0.0151788\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.14767 | + | 4.12671i | −0.243028 | + | 0.140312i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.3029i | 0.553675i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.3890 | + | 3.64675i | −1.33618 | + | 0.123708i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.5451 | − | 42.5133i | −0.831678 | − | 1.44051i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.6893 | + | 20.6052i | 1.20790 | + | 0.697382i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.1411 | − | 9.31905i | −0.545045 | − | 0.314682i | 0.202076 | − | 0.979370i | \(-0.435231\pi\) |
−0.747121 | + | 0.664688i | \(0.768564\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −33.9760 | + | 19.6160i | −1.14598 | + | 0.661633i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 17.4946i | − | 0.589408i | −0.955589 | − | 0.294704i | \(-0.904779\pi\) | ||
0.955589 | − | 0.294704i | \(-0.0952211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.8846 | 0.938392 | 0.469196 | − | 0.883094i | \(-0.344544\pi\) | ||||
0.469196 | + | 0.883094i | \(0.344544\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.95431 | − | 1.70567i | 0.0993079 | − | 0.0573355i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.3947 | − | 28.3964i | 0.550480 | − | 0.953459i | −0.447760 | − | 0.894154i | \(-0.647778\pi\) |
0.998240 | − | 0.0593050i | \(-0.0188885\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.79458 | − | 3.12666i | −0.227627 | − | 0.104747i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.68034 | − | 0.970143i | 0.0562304 | − | 0.0324646i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.51405i | − | 0.0840355i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 63.1766i | − | 2.10940i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.4495 | − | 23.2952i | −0.448566 | − | 0.776939i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.8359 | − | 39.5529i | 0.760774 | − | 1.31770i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.71372 | − | 6.43235i | 0.123448 | − | 0.213819i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.27698 | − | 5.67589i | −0.108810 | − | 0.188465i | 0.806478 | − | 0.591264i | \(-0.201371\pi\) |
−0.915289 | + | 0.402799i | \(0.868037\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 60.2149 | 1.99720 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.4216 | −1.07418 | −0.537088 | − | 0.843526i | \(-0.680476\pi\) | ||||
−0.537088 | + | 0.843526i | \(0.680476\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.9683 | + | 28.2882i | −1.32276 | + | 0.936202i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.72010 | − | 9.90750i | 0.189101 | − | 0.327532i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.04549 | + | 2.91301i | 0.166435 | + | 0.0960915i | 0.580904 | − | 0.813972i | \(-0.302699\pi\) |
−0.414469 | + | 0.910064i | \(0.636033\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −61.4837 | + | 35.4976i | −2.02596 | + | 1.16969i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −42.3228 | −1.39307 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.97601 | 0.0978506 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.6477 | − | 15.3850i | 0.875225 | − | 0.505311i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.6675 | − | 8.46828i | −0.481225 | − | 0.277835i | 0.239702 | − | 0.970847i | \(-0.422950\pi\) |
−0.720927 | + | 0.693011i | \(0.756284\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33.0695 | + | 57.2781i | −1.08265 | + | 1.87520i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.32549 | − | 3.28569i | −0.0760518 | − | 0.107453i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.52101 | −0.278369 | −0.139185 | − | 0.990266i | \(-0.544448\pi\) | ||||
−0.139185 | + | 0.990266i | \(0.544448\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 75.3671 | 2.45951 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.94717 | + | 5.10465i | 0.0960751 | + | 0.166407i | 0.910057 | − | 0.414484i | \(-0.136038\pi\) |
−0.813982 | + | 0.580891i | \(0.802704\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.5351 | − | 19.9793i | 0.375634 | − | 0.650617i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.16363 | + | 3.74752i | −0.0703085 | + | 0.121778i | −0.899037 | − | 0.437874i | \(-0.855732\pi\) |
0.828728 | + | 0.559652i | \(0.189065\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.07343 | − | 12.2515i | −0.229613 | − | 0.397702i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39.9156i | 1.29435i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 42.1267i | − | 1.36462i | −0.731064 | − | 0.682309i | \(-0.760976\pi\) | ||
0.731064 | − | 0.682309i | \(-0.239024\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.948737 | − | 0.547754i | 0.0307004 | − | 0.0177249i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −43.9107 | − | 20.2064i | −1.41943 | − | 0.653180i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.72709 | + | 4.72345i | −0.0879705 | + | 0.152369i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 43.4369 | − | 25.0783i | 1.39974 | − | 0.808138i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.47146 | −0.304897 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.74288i | − | 0.120363i | −0.998187 | − | 0.0601815i | \(-0.980832\pi\) | ||
0.998187 | − | 0.0601815i | \(-0.0191680\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −26.1980 | + | 15.1254i | −0.841602 | + | 0.485899i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.7126 | − | 19.4640i | −1.08189 | − | 0.624630i | −0.150485 | − | 0.988612i | \(-0.548083\pi\) |
−0.931406 | + | 0.363983i | \(0.881417\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 52.1003 | + | 30.0801i | 1.66855 | + | 0.963336i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.2664 | − | 24.7100i | −0.456421 | − | 0.790544i | 0.542348 | − | 0.840154i | \(-0.317536\pi\) |
−0.998769 | + | 0.0496097i | \(0.984202\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.1630 | − | 2.60741i | 0.900093 | − | 0.0833333i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 50.1567i | − | 1.60138i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.0264 | + | 10.9849i | −0.606848 | + | 0.350364i | −0.771731 | − | 0.635949i | \(-0.780609\pi\) |
0.164883 | + | 0.986313i | \(0.447275\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.86780 | + | 4.96717i | −0.0913757 | + | 0.158267i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.1575 | + | 17.9888i | 0.990751 | + | 0.572011i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.9739 | − | 24.2035i | −0.443895 | − | 0.768849i | 0.554079 | − | 0.832464i | \(-0.313070\pi\) |
−0.997975 | + | 0.0636148i | \(0.979737\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 67.0453i | − | 2.12762i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.687724 | −0.0218023 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.7410 | − | 39.3886i | −0.720215 | − | 1.24745i | −0.960913 | − | 0.276849i | \(-0.910710\pi\) |
0.240698 | − | 0.970600i | \(-0.422624\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.17412 | − | 1.25523i | −0.0687861 | − | 0.0397137i |
(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 | 2156.2.q.c.901.1 | 16 | ||
7.2 | even | 3 | 2156.2.c.c.1077.1 | 16 | |||
7.3 | odd | 6 | inner | 2156.2.q.c.2089.2 | 16 | ||
7.4 | even | 3 | 308.2.q.a.241.7 | ✓ | 16 | ||
7.5 | odd | 6 | 2156.2.c.c.1077.15 | 16 | |||
7.6 | odd | 2 | 308.2.q.a.285.8 | yes | 16 | ||
11.10 | odd | 2 | inner | 2156.2.q.c.901.2 | 16 | ||
21.11 | odd | 6 | 2772.2.cs.a.2089.3 | 16 | |||
21.20 | even | 2 | 2772.2.cs.a.901.4 | 16 | |||
28.11 | odd | 6 | 1232.2.bn.c.241.2 | 16 | |||
28.27 | even | 2 | 1232.2.bn.c.593.1 | 16 | |||
77.10 | even | 6 | inner | 2156.2.q.c.2089.1 | 16 | ||
77.32 | odd | 6 | 308.2.q.a.241.8 | yes | 16 | ||
77.54 | even | 6 | 2156.2.c.c.1077.16 | 16 | |||
77.65 | odd | 6 | 2156.2.c.c.1077.2 | 16 | |||
77.76 | even | 2 | 308.2.q.a.285.7 | yes | 16 | ||
231.32 | even | 6 | 2772.2.cs.a.2089.4 | 16 | |||
231.230 | odd | 2 | 2772.2.cs.a.901.3 | 16 | |||
308.263 | even | 6 | 1232.2.bn.c.241.1 | 16 | |||
308.307 | odd | 2 | 1232.2.bn.c.593.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
308.2.q.a.241.7 | ✓ | 16 | 7.4 | even | 3 | ||
308.2.q.a.241.8 | yes | 16 | 77.32 | odd | 6 | ||
308.2.q.a.285.7 | yes | 16 | 77.76 | even | 2 | ||
308.2.q.a.285.8 | yes | 16 | 7.6 | odd | 2 | ||
1232.2.bn.c.241.1 | 16 | 308.263 | even | 6 | |||
1232.2.bn.c.241.2 | 16 | 28.11 | odd | 6 | |||
1232.2.bn.c.593.1 | 16 | 28.27 | even | 2 | |||
1232.2.bn.c.593.2 | 16 | 308.307 | odd | 2 | |||
2156.2.c.c.1077.1 | 16 | 7.2 | even | 3 | |||
2156.2.c.c.1077.2 | 16 | 77.65 | odd | 6 | |||
2156.2.c.c.1077.15 | 16 | 7.5 | odd | 6 | |||
2156.2.c.c.1077.16 | 16 | 77.54 | even | 6 | |||
2156.2.q.c.901.1 | 16 | 1.1 | even | 1 | trivial | ||
2156.2.q.c.901.2 | 16 | 11.10 | odd | 2 | inner | ||
2156.2.q.c.2089.1 | 16 | 77.10 | even | 6 | inner | ||
2156.2.q.c.2089.2 | 16 | 7.3 | odd | 6 | inner | ||
2772.2.cs.a.901.3 | 16 | 231.230 | odd | 2 | |||
2772.2.cs.a.901.4 | 16 | 21.20 | even | 2 | |||
2772.2.cs.a.2089.3 | 16 | 21.11 | odd | 6 | |||
2772.2.cs.a.2089.4 | 16 | 231.32 | even | 6 |