Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(241,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1232.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.bn (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: | \(9.83756952902\) |
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: | \( 7 \) |
Twist minimal: | no (minimal twist has level 308) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 241.2 | ||
Root | \(2.64407 + 0.0942693i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.241 |
Dual form | 1232.2.bn.c.593.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.37157 | − | 1.36923i | −1.36923 | − | 0.790524i | −0.378399 | − | 0.925643i | \(-0.623525\pi\) |
−0.990829 | + | 0.135118i | \(0.956859\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.316246 | − | 0.182585i | 0.141429 | − | 0.0816543i | −0.427616 | − | 0.903961i | \(-0.640646\pi\) |
0.569045 | + | 0.822306i | \(0.307313\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64407 | − | 0.0942693i | 0.999365 | − | 0.0356305i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.24957 | + | 3.89637i | 0.749857 | + | 1.29879i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.01293 | − | 1.38646i | −0.908432 | − | 0.418033i | ||||
\(12\) | 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 | −0.994093 | − | 0.108535i | \(-0.965384\pi\) |
0.591040 | + | 0.806642i | \(0.298717\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.66183 | + | 2.87837i | 0.381249 | + | 0.660343i | 0.991241 | − | 0.132064i | \(-0.0421606\pi\) |
−0.609992 | + | 0.792408i | \(0.708827\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.39968 | − | 3.39677i | −1.39653 | − | 0.741236i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.55533 | + | 4.42596i | 0.532822 | + | 0.922876i | 0.999265 | + | 0.0383243i | \(0.0122020\pi\) |
−0.466443 | + | 0.884551i | \(0.654465\pi\) | |||||||
\(24\) | 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 | 0.838608 | − | 0.544735i | \(-0.183370\pi\) |
−0.0524503 | + | 0.998624i | \(0.516703\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.24700 | + | 7.41347i | 0.913385 | + | 1.29052i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.818964 | − | 0.512579i | 0.138430 | − | 0.0866417i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.305755 | − | 0.529584i | −0.0502659 | − | 0.0870630i | 0.839798 | − | 0.542899i | \(-0.182674\pi\) |
−0.890064 | + | 0.455836i | \(0.849340\pi\) | |||||||
\(38\) | 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 | \(0.180357\pi\) | ||||
−0.843726 | + | 0.536774i | \(0.819643\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.42284 | + | 0.821474i | 0.212104 | + | 0.122458i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.505569 | + | 0.291890i | −0.0737448 | + | 0.0425766i | −0.536419 | − | 0.843952i | \(-0.680223\pi\) |
0.462674 | + | 0.886528i | \(0.346890\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98223 | − | 0.498510i | 0.997461 | − | 0.0712157i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.88229 | − | 4.55084i | 1.10374 | − | 0.637245i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.87072 | − | 11.9004i | 0.943765 | − | 1.63465i | 0.185561 | − | 0.982633i | \(-0.440590\pi\) |
0.758204 | − | 0.652017i | \(-0.226077\pi\) | |||||||
\(54\) | 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 | 0.679826 | − | 0.733374i | \(-0.262055\pi\) |
−0.295208 | + | 0.955433i | \(0.595389\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.72010 | + | 9.90750i | 0.732384 | + | 1.26853i | 0.955862 | + | 0.293817i | \(0.0949256\pi\) |
−0.223478 | + | 0.974709i | \(0.571741\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.31534 | + | 10.0902i | 0.795658 | + | 1.27125i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.42757 | − | 0.824210i | 0.177069 | − | 0.102231i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.43739 | − | 9.41784i | 0.664283 | − | 1.15057i | −0.315196 | − | 0.949027i | \(-0.602070\pi\) |
0.979479 | − | 0.201545i | \(-0.0645963\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 13.9953i | − | 1.68484i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.37564 | 1.11268 | 0.556342 | − | 0.830954i | \(-0.312205\pi\) | ||||
0.556342 | + | 0.830954i | \(0.312205\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.56695 | + | 2.71404i | −0.183398 | + | 0.317655i | −0.943036 | − | 0.332692i | \(-0.892043\pi\) |
0.759637 | + | 0.650347i | \(0.225376\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.5416 | − | 6.66356i | 1.33271 | − | 0.769441i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.09710 | − | 3.38187i | −0.922750 | − | 0.385400i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3291 | − | 5.96351i | 1.16211 | − | 0.670947i | 0.210305 | − | 0.977636i | \(-0.432554\pi\) |
0.951810 | + | 0.306689i | \(0.0992210\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.12757 | − | 1.95301i | 0.125286 | − | 0.217001i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.7639 | −1.62054 | −0.810272 | − | 0.586054i | \(-0.800681\pi\) | ||||
−0.810272 | + | 0.586054i | \(0.800681\pi\) | |||||||
\(84\) | 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 | \(-0.517388\pi\) |
0.837435 | + | 0.546537i | \(0.184054\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.9357 | − | 0.425544i | 1.25120 | − | 0.0446091i | ||||
\(92\) | 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 | −0.313190 | − | 0.949690i | \(-0.601398\pi\) |
0.979051 | − | 0.203614i | \(-0.0652689\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.92284 | − | 3.41955i | 0.583594 | − | 0.336938i | −0.178966 | − | 0.983855i | \(-0.557275\pi\) |
0.762561 | + | 0.646917i | \(0.223942\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.64407 | + | 0.0942693i | −0.258035 | + | 0.00919974i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.65449 | − | 5.57402i | 0.933335 | − | 0.538861i | 0.0454701 | − | 0.998966i | \(-0.485521\pi\) |
0.887865 | + | 0.460105i | \(0.152188\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.65449 | − | 5.57402i | −0.924732 | − | 0.533895i | −0.0395907 | − | 0.999216i | \(-0.512605\pi\) |
−0.885142 | + | 0.465321i | \(0.845939\pi\) | |||||||
\(110\) | 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 | ||||||||
\(119\) | −4.12265 | + | 7.76727i | −0.377923 | + | 0.712025i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.15546 | + | 8.35460i | 0.650497 | + | 0.759509i | ||||
\(122\) | 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 | \(-0.898888\pi\) | ||
0.949971 | − | 0.312337i | \(-0.101112\pi\) | |||||||
\(128\) | 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 | \(-0.0400170\pi\) |
−0.604642 | + | 0.796498i | \(0.706684\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.66533 | + | 7.45396i | 0.404536 | + | 0.646340i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.749572 | − | 1.29830i | −0.0645128 | − | 0.111740i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.28798 | + | 7.42700i | −0.366347 | + | 0.634532i | −0.988991 | − | 0.147973i | \(-0.952725\pi\) |
0.622644 | + | 0.782505i | \(0.286058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.8204 | −1.08741 | −0.543707 | − | 0.839275i | \(-0.682980\pi\) | ||||
−0.543707 | + | 0.839275i | \(0.682980\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.59866 | 0.134631 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.6007 | − | 6.25865i | −1.13735 | − | 0.523375i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.971718 | − | 1.68307i | −0.0806968 | − | 0.139771i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.2414 | − | 8.37801i | −1.42205 | − | 0.691007i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.5879 | + | 10.7317i | −1.52278 | + | 0.879176i | −0.523141 | + | 0.852246i | \(0.675240\pi\) |
−0.999637 | + | 0.0269298i | \(0.991427\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.05109 | − | 0.606848i | −0.0855367 | − | 0.0493846i | 0.456622 | − | 0.889661i | \(-0.349059\pi\) |
−0.542158 | + | 0.840276i | \(0.682393\pi\) | |||||||
\(152\) | 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 | \(-0.112167\pi\) |
0.170381 | + | 0.985378i | \(0.445500\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −32.5888 | + | 18.8152i | −2.58446 | + | 1.49214i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.17370 | + | 11.4617i | 0.565367 | + | 0.903305i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.61878 | − | 16.6602i | −0.753401 | − | 1.30493i | −0.946165 | − | 0.323684i | \(-0.895079\pi\) |
0.192764 | − | 0.981245i | \(-0.438255\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.01293 | + | 1.38646i | 0.234556 | + | 0.107936i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.189746 | 0.0146830 | 0.00734151 | − | 0.999973i | \(-0.497663\pi\) | ||||
0.00734151 | + | 0.999973i | \(0.497663\pi\) | |||||||
\(168\) | 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 | 0.872707 | + | 0.488244i | \(0.162362\pi\) |
−0.0135217 | + | 0.999909i | \(0.504304\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.03658 | + | 11.3732i | −0.456322 | + | 0.859734i | ||||
\(176\) | 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 | \(-0.916163\pi\) |
0.708225 | + | 0.705987i | \(0.249496\pi\) | |||||||
\(180\) | 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 | ||||||||
\(187\) | 8.99771 | − | 6.36826i | 0.657978 | − | 0.465694i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.387007 | − | 10.8548i | −0.0281506 | − | 0.789571i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.50000 | + | 2.59808i | 0.108536 | + | 0.187990i | 0.915177 | − | 0.403051i | \(-0.132050\pi\) |
−0.806641 | + | 0.591041i | \(0.798717\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.4623 | − | 12.9686i | −1.61687 | − | 0.933500i | −0.987724 | − | 0.156212i | \(-0.950072\pi\) |
−0.629145 | − | 0.777288i | \(-0.716595\pi\) | |||||||
\(194\) | 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 | 0.556694 | − | 0.830718i | \(-0.312070\pi\) |
−0.441076 | + | 0.897470i | \(0.645403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −25.7903 | + | 14.8901i | −1.81911 | + | 1.05026i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.501703 | − | 14.0718i | −0.0352126 | − | 0.987646i | ||||
\(204\) | 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 | \(0.129710\pi\) | ||||
−0.918117 | + | 0.396310i | \(0.870290\pi\) | |||||||
\(212\) | 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 | ||||||||
\(217\) | 11.8117 | + | 6.26932i | 0.801831 | + | 0.425589i | ||||
\(218\) | 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 | \(0.00128692\pi\) | ||||
−0.999992 | + | 0.00404298i | \(0.998713\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.8958 | −1.45972 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.595236 | + | 1.03098i | −0.0395072 | + | 0.0684285i | −0.885103 | − | 0.465395i | \(-0.845912\pi\) |
0.845596 | + | 0.533824i | \(0.179245\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.8401 | + | 7.99058i | −0.914579 | + | 0.528032i | −0.881902 | − | 0.471434i | \(-0.843737\pi\) |
−0.0326773 | + | 0.999466i | \(0.510403\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.5723 | + | 19.1071i | 0.958787 | + | 1.25716i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.14767 | − | 4.12671i | 0.468260 | − | 0.270350i | −0.247251 | − | 0.968951i | \(-0.579527\pi\) |
0.715511 | + | 0.698602i | \(0.246194\pi\) | |||||||
\(234\) | 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 | \(-0.970157\pi\) | ||
0.995608 | − | 0.0936188i | \(-0.0298435\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.376482 | − | 0.652086i | 0.0242513 | − | 0.0420045i | −0.853645 | − | 0.520855i | \(-0.825613\pi\) |
0.877896 | + | 0.478851i | \(0.158946\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.0142 | + | 9.24581i | −1.02731 | + | 0.593119i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.11708 | − | 1.43250i | 0.135255 | − | 0.0915190i | ||||
\(246\) | 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 | \(0.0369018\pi\) | ||||
−0.993288 | + | 0.115671i | \(0.963098\pi\) | |||||||
\(252\) | 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 | \(-0.707037\pi\) |
0.386441 | + | 0.922314i | \(0.373704\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.858363 | − | 1.37143i | −0.0533361 | − | 0.0852168i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.7366 | − | 11.9723i | 1.28356 | − | 0.741064i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.88229 | + | 4.55084i | 0.486043 | + | 0.280617i | 0.722931 | − | 0.690920i | \(-0.242794\pi\) |
−0.236888 | + | 0.971537i | \(0.576128\pi\) | |||||||
\(264\) | 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 | \(-0.269690\pi\) |
−0.318036 | + | 0.948079i | \(0.603023\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.01376 | − | 6.95204i | −0.243819 | − | 0.422307i | 0.717980 | − | 0.696064i | \(-0.245067\pi\) |
−0.961799 | + | 0.273757i | \(0.911734\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −28.8890 | − | 15.3335i | −1.74844 | − | 0.928023i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.1749 | − | 9.32471i | 0.794474 | − | 0.562301i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.84572 | − | 1.06562i | −0.110898 | − | 0.0640272i | 0.443525 | − | 0.896262i | \(-0.353728\pi\) |
−0.554423 | + | 0.832235i | \(0.687061\pi\) | |||||||
\(278\) | 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 | 0.191479 | − | 0.981497i | \(-0.438672\pi\) |
0.754261 | − | 0.656574i | \(-0.227995\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.66183 | − | 2.87837i | −0.0984382 | − | 0.170500i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.9357 | + | 0.425544i | −0.704541 | + | 0.0251191i | ||||
\(288\) | 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 | ||||||||
\(297\) | −5.69188 | + | 12.3691i | −0.330276 | + | 0.717727i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.5351 | + | 19.9793i | 0.667090 | + | 1.15543i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.663630 | + | 18.6135i | 0.0382510 | + | 1.07287i | ||||
\(302\) | 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 | \(-0.765088\pi\) | ||||
−0.739817 | + | 0.672808i | \(0.765088\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.7286 | −1.06543 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.9162 | + | 12.0760i | 1.18605 | + | 0.684766i | 0.957406 | − | 0.288745i | \(-0.0932379\pi\) |
0.228643 | + | 0.973510i | \(0.426571\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.8345 | − | 13.7609i | 1.34721 | − | 0.777810i | 0.359354 | − | 0.933201i | \(-0.382997\pi\) |
0.987853 | + | 0.155391i | \(0.0496638\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.83952 | + | 2.03791i | 0.216332 | + | 0.114823i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.28798 | + | 12.6232i | 0.409334 | + | 0.708987i | 0.994815 | − | 0.101699i | \(-0.0324278\pi\) |
−0.585481 | + | 0.810686i | \(0.699094\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.37876 | + | 16.0348i | −0.413131 | + | 0.897779i | ||||
\(320\) | 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 | ||||||||
\(329\) | −1.30924 | + | 0.819439i | −0.0721810 | + | 0.0451771i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.2414 | + | 21.2028i | 0.672850 | + | 1.16541i | 0.977092 | + | 0.212816i | \(0.0682634\pi\) |
−0.304242 | + | 0.952595i | \(0.598403\pi\) | |||||||
\(332\) | 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 | ||||||||
\(341\) | −9.68423 | − | 13.6828i | −0.524430 | − | 0.740967i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4145 | − | 1.97630i | 0.994290 | − | 0.106710i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.55533 | − | 4.42596i | −0.137574 | − | 0.238285i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.6535 | − | 8.46019i | −0.786640 | − | 0.454167i | 0.0521382 | − | 0.998640i | \(-0.483396\pi\) |
−0.838778 | + | 0.544473i | \(0.816730\pi\) | |||||||
\(348\) | 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 | \(-0.537874\pi\) |
−0.919255 | + | 0.393663i | \(0.871208\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.96501 | − | 1.71185i | 0.157366 | − | 0.0908554i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 20.4123 | − | 12.7758i | 1.08034 | − | 0.676168i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.4247 | + | 12.3695i | −1.13075 | + | 0.652839i | −0.944124 | − | 0.329591i | \(-0.893089\pi\) |
−0.186627 | + | 0.982431i | \(0.559756\pi\) | |||||||
\(360\) | 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 | 0.320458 | − | 0.947263i | \(-0.396163\pi\) |
−0.660124 | + | 0.751156i | \(0.729496\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.1549 | − | 17.5887i | −0.528641 | − | 0.915632i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.0448 | − | 32.1133i | 0.884923 | − | 1.66724i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.29253 | − | 2.47829i | 0.222259 | − | 0.128321i | −0.384737 | − | 0.923026i | \(-0.625708\pi\) |
0.606996 | + | 0.794705i | \(0.292375\pi\) | |||||||
\(374\) | 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 | \(-0.202652\pi\) | ||||
0.804091 | + | 0.594506i | \(0.202652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.63899 | + | 16.6952i | −0.493820 | + | 0.855322i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.1421 | − | 8.16495i | 0.722628 | − | 0.417210i | −0.0930910 | − | 0.995658i | \(-0.529675\pi\) |
0.815719 | + | 0.578448i | \(0.196341\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.17815 | + | 0.408903i | −0.161974 | + | 0.0208396i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.4294 | + | 15.8364i | −1.39431 | + | 0.805008i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.74465 | + | 15.1462i | −0.443371 | + | 0.767942i | −0.997937 | − | 0.0641981i | \(-0.979551\pi\) |
0.554566 | + | 0.832140i | \(0.312884\pi\) | |||||||
\(390\) | 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 | \(-0.477532\pi\) |
0.899132 | + | 0.437678i | \(0.144199\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.858010 | − | 24.0655i | −0.0429542 | − | 1.20478i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.4179 | − | 26.7046i | −0.769933 | − | 1.33356i | −0.937599 | − | 0.347720i | \(-0.886956\pi\) |
0.167665 | − | 0.985844i | \(-0.446377\pi\) | |||||||
\(402\) | 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 | 0.232418 | + | 0.972616i | \(0.425336\pi\) |
−0.958519 | + | 0.285028i | \(0.907997\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.3385 | − | 11.7425i | 1.00323 | − | 0.579212i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.97219 | + | 4.23141i | 0.392286 | + | 0.208214i | ||||
\(414\) | 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 | \(-0.669897\pi\) | ||
0.508762 | − | 0.860907i | \(-0.330103\pi\) | |||||||
\(420\) | 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 | ||||||||
\(427\) | 16.0583 | + | 25.6569i | 0.777117 | + | 1.24163i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 23.6856 | + | 33.4654i | 1.14355 | + | 1.61572i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.9123 | − | 13.2284i | −1.10364 | − | 0.637189i | −0.166469 | − | 0.986047i | \(-0.553236\pi\) |
−0.937176 | + | 0.348857i | \(0.886570\pi\) | |||||||
\(432\) | 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 | 0.992715 | + | 0.120490i | \(0.0384466\pi\) |
−0.392010 | + | 0.919961i | \(0.628220\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.6494 | + | 26.0839i | 0.840447 | + | 1.24209i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.2936 | − | 21.2931i | −0.584084 | − | 1.01166i | −0.994989 | − | 0.0999853i | \(-0.968120\pi\) |
0.410905 | − | 0.911678i | \(-0.365213\pi\) | |||||||
\(444\) | 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 | ||||||||
\(451\) | 13.6007 | + | 6.25865i | 0.640434 | + | 0.294708i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.66183 | + | 2.87837i | 0.0780795 | + | 0.135238i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.69691 | − | 2.31385i | 0.173314 | − | 0.108475i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.661101 | + | 0.381687i | −0.0309250 | + | 0.0178546i | −0.515383 | − | 0.856960i | \(-0.672350\pi\) |
0.484458 | + | 0.874815i | \(0.339017\pi\) | |||||||
\(458\) | 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 | \(-0.678555\pi\) | ||||
−0.531988 | + | 0.846752i | \(0.678555\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.37714 | − | 2.52714i | −0.202985 | − | 0.117193i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.7736 | + | 18.3445i | −1.47031 | + | 0.848883i | −0.999445 | − | 0.0333234i | \(-0.989391\pi\) |
−0.470863 | + | 0.882206i | \(0.656058\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4890 | − | 25.4140i | 0.622866 | − | 1.17351i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.9685 | − | 38.0506i | −1.01226 | − | 1.75328i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.76029 | − | 21.2102i | 0.448779 | − | 0.975245i | ||||
\(474\) | 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 | \(-0.733891\pi\) |
0.977782 | + | 0.209625i | \(0.0672244\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.38022 | − | 2.39061i | −0.0629326 | − | 0.109002i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.31933 | − | 37.0046i | −0.0600315 | − | 1.68377i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.67241 | + | 2.89669i | 0.0759401 | + | 0.131532i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.2863 | + | 26.4766i | −0.692687 | + | 1.19977i | 0.278267 | + | 0.960504i | \(0.410240\pi\) |
−0.970954 | + | 0.239265i | \(0.923093\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 52.6812i | 2.38233i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.4514i | 1.82554i | 0.408469 | + | 0.912772i | \(0.366063\pi\) | ||||
−0.408469 | + | 0.912772i | \(0.633937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.3187 | + | 8.84427i | 0.689921 | + | 0.398326i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.14796 | − | 4.44774i | −0.141490 | − | 0.199911i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.7899 | − | 0.883835i | 1.11198 | − | 0.0396454i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.03061 | + | 13.9094i | 0.359500 | + | 0.622672i | 0.987877 | − | 0.155237i | \(-0.0496140\pi\) |
−0.628378 | + | 0.777908i | \(0.716281\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.449997 | − | 0.259806i | −0.0201044 | − | 0.0116073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.2531 | 0.992219 | 0.496109 | − | 0.868260i | \(-0.334762\pi\) | ||||
0.496109 | + | 0.868260i | \(0.334762\pi\) | |||||||
\(504\) | 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 | \(-0.861259\pi\) |
−0.0876175 | + | 0.996154i | \(0.527925\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.88729 | + | 7.32384i | −0.171964 | + | 0.323988i | ||||
\(512\) | 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 | \(-0.165371\pi\) |
0.00406920 | + | 0.999992i | \(0.498705\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.49961 | − | 16.4538i | −0.415389 | − | 0.719475i | 0.580080 | − | 0.814559i | \(-0.303021\pi\) |
−0.995469 | + | 0.0950845i | \(0.969688\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 29.8887 | − | 18.7069i | 1.30445 | − | 0.816438i | ||||
\(526\) | 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 | ||||||||
\(539\) | −21.7281 | − | 8.17860i | −0.935896 | − | 0.352277i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.358135 | − | 0.206769i | 0.0153974 | − | 0.00888970i | −0.492282 | − | 0.870436i | \(-0.663837\pi\) |
0.507679 | + | 0.861546i | \(0.330504\pi\) | |||||||
\(542\) | 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 | \(0.0112198\pi\) | ||||
−0.999379 | + | 0.0352407i | \(0.988780\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | 26.7487 | − | 16.7417i | 1.13747 | − | 0.711928i | ||||
\(554\) | 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 | \(-0.574485\pi\) |
−0.958359 | + | 0.285565i | \(0.907819\pi\) | |||||||
\(558\) | 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 | 0.451517 | + | 0.892263i | \(0.350883\pi\) |
−0.998480 | + | 0.0551062i | \(0.982450\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.79741 | − | 1.61508i | 0.117688 | − | 0.0679471i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.79727 | − | 5.27019i | 0.117474 | − | 0.221327i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.0464 | + | 17.3473i | −1.25961 | + | 0.727237i | −0.972999 | − | 0.230810i | \(-0.925863\pi\) |
−0.286613 | + | 0.958047i | \(0.592529\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.9681 | + | 17.3021i | 1.25412 | + | 0.724069i | 0.971926 | − | 0.235287i | \(-0.0756030\pi\) |
0.282199 | + | 0.959356i | \(0.408936\pi\) | |||||||
\(572\) | 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 | \(-0.330227\pi\) |
−0.491524 | + | 0.870864i | \(0.663560\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 35.5139 | + | 61.5119i | 1.47591 | + | 2.55635i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.0367 | + | 1.39178i | −1.61951 | + | 0.0577407i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.2004 | + | 26.3292i | −1.54068 | + | 1.09044i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.42286 | + | 3.70824i | 0.265553 | + | 0.153317i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.9718i | 1.85618i | 0.372352 | + | 0.928091i | \(0.378551\pi\) | ||||
−0.372352 | + | 0.928091i | \(0.621449\pi\) | |||||||
\(588\) | 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 | 0.980196 | − | 0.198029i | \(-0.0634541\pi\) |
−0.661596 | + | 0.749860i | \(0.730121\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.114414 | + | 3.20910i | 0.00469053 | + | 0.131560i | ||||
\(596\) | 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 | \(-0.775236\pi\) |
0.942394 | + | 0.334504i | \(0.108569\pi\) | |||||||
\(600\) | 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 | ||||||||
\(605\) | 3.78831 | + | 1.33563i | 0.154017 | + | 0.0543011i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.5505 | − | 37.3266i | −0.874710 | − | 1.51504i | −0.857072 | − | 0.515197i | \(-0.827719\pi\) |
−0.0176380 | − | 0.999844i | \(-0.505615\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.0777 | + | 34.0592i | −0.732544 | + | 1.38015i | ||||
\(610\) | 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 | \(-0.424252\pi\) |
−0.723755 | + | 0.690057i | \(0.757585\pi\) | |||||||
\(614\) | 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 | 0.962328 | − | 0.271893i | \(-0.0876496\pi\) |
0.245698 | + | 0.969347i | \(0.420983\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.1700 | − | 10.4905i | 0.729139 | − | 0.420968i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.1252 | − | 11.9702i | 0.766236 | − | 0.479577i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.5088 | − | 19.9338i | −0.460351 | − | 0.797351i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.6191 | + | 27.4227i | −0.503959 | + | 1.09516i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.03245 | 0.0810391 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.9790 | 0.437067 | 0.218533 | − | 0.975829i | \(-0.429873\pi\) | ||||
0.218533 | + | 0.975829i | \(0.429873\pi\) | |||||||
\(632\) | 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 | ||||||||
\(637\) | 31.5187 | − | 2.25034i | 1.24881 | − | 0.0891616i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.0912 | + | 36.5310i | 0.834354 | + | 1.44514i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.85401 | + | 11.8715i | −0.270717 | + | 0.468896i | −0.969046 | − | 0.246882i | \(-0.920594\pi\) |
0.698329 | + | 0.715777i | \(0.253927\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 10.7909i | − | 0.425553i | −0.977101 | − | 0.212777i | \(-0.931749\pi\) | ||
0.977101 | − | 0.212777i | \(-0.0682507\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 7.03973i | − | 0.277189i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.193388 | − | 0.111652i | −0.00760286 | − | 0.00438951i | 0.496194 | − | 0.868212i | \(-0.334731\pi\) |
−0.503797 | + | 0.863822i | \(0.668064\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.53627 | − | 9.23508i | −0.256571 | − | 0.362509i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.4282 | − | 31.0411i | −0.761451 | − | 1.21660i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.8497 | − | 20.5243i | −0.463716 | − | 0.803180i | 0.535427 | − | 0.844582i | \(-0.320151\pi\) |
−0.999143 | + | 0.0414022i | \(0.986818\pi\) | |||||||
\(654\) | 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 | \(-0.783002\pi\) | ||
0.776490 | − | 0.630130i | \(-0.216998\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.9690 | − | 20.7667i | −1.39903 | − | 0.807732i | −0.404742 | − | 0.914431i | \(-0.632639\pi\) |
−0.994291 | + | 0.106699i | \(0.965972\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 35.5817 | − | 20.5431i | 1.38188 | − | 0.797827i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.83637 | + | 1.50546i | 0.109990 | + | 0.0583794i | ||||
\(666\) | 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 | 0.514316 | − | 0.857601i | \(-0.328046\pi\) |
−0.999862 | + | 0.0166108i | \(0.994712\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.863472 | + | 24.2187i | 0.0331370 | + | 0.929429i | ||||
\(680\) | 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 | \(-0.890244\pi\) |
0.763301 | + | 0.646043i | \(0.223577\pi\) | |||||||
\(684\) | 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 | −0.744554 | − | 0.667563i | \(-0.767338\pi\) |
0.205849 | + | 0.978584i | \(0.434004\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.03798 | − | 39.1571i | −0.191377 | − | 1.48745i | ||||
\(694\) | 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 | ||||||||
\(707\) | 16.6010 | − | 31.2771i | 0.624345 | − | 1.17630i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.39812 | − | 4.15367i | −0.0900634 | − | 0.155994i | 0.817474 | − | 0.575965i | \(-0.195374\pi\) |
−0.907538 | + | 0.419971i | \(0.862040\pi\) | |||||||
\(710\) | 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 | −0.542126 | − | 0.840297i | \(-0.682381\pi\) |
0.456655 | + | 0.889644i | \(0.349047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3380 | − | 9.59988i | 0.571218 | − | 0.357518i | ||||
\(722\) | 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 | \(0.102783\pi\) | ||||
−0.948318 | + | 0.317321i | \(0.897217\pi\) | |||||||
\(728\) | 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 | 0.729135 | − | 0.684370i | \(-0.239923\pi\) |
−0.957249 | + | 0.289265i | \(0.906589\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.98223 | + | 0.498510i | −0.257543 | + | 0.0183878i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.4399 | + | 20.8365i | −1.08443 | + | 0.767524i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.4903 | + | 10.0980i | 0.643390 | + | 0.371462i | 0.785919 | − | 0.618329i | \(-0.212190\pi\) |
−0.142529 | + | 0.989791i | \(0.545523\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 41.0862i | − | 1.50934i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 9.44593i | − | 0.346538i | −0.984875 | − | 0.173269i | \(-0.944567\pi\) | ||
0.984875 | − | 0.173269i | \(-0.0554330\pi\) | |||||||
\(744\) | 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 | ||||||||
\(749\) | 25.0017 | − | 15.6482i | 0.913542 | − | 0.571774i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.592367 | − | 1.02601i | −0.0216158 | − | 0.0374397i | 0.855015 | − | 0.518603i | \(-0.173548\pi\) |
−0.876631 | + | 0.481163i | \(0.840214\pi\) | |||||||
\(752\) | 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 | ||||||||
\(759\) | −19.4039 | + | 42.1668i | −0.704317 | + | 1.53056i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.17769 | + | 3.77187i | 0.0789412 | + | 0.136730i | 0.902793 | − | 0.430075i | \(-0.141513\pi\) |
−0.823852 | + | 0.566805i | \(0.808179\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.0526 | − | 13.8280i | −0.943168 | − | 0.500607i | ||||
\(764\) | 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 | \(-0.284789\pi\) |
−0.362633 | + | 0.931932i | \(0.618122\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.3020 | + | 12.2987i | −0.765191 | + | 0.441783i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.157863 | + | 4.42775i | 0.00566330 | + | 0.158845i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.50170 | − | 12.9933i | −0.268776 | − | 0.465534i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.2481 | − | 12.9989i | −1.01080 | − | 0.465138i | ||||
\(782\) | 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 | \(-0.780287\pi\) |
0.936967 | + | 0.349417i | \(0.113620\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.4623 | − | 21.5853i | −0.443669 | − | 0.768457i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.3886 | − | 0.833875i | 0.831602 | − | 0.0296492i | ||||
\(792\) | 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 | ||||||||
\(803\) | 8.48403 | − | 6.00470i | 0.299395 | − | 0.211901i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.36137 | + | 2.31489i | 0.153718 | + | 0.0815893i | ||||
\(806\) | 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 | \(-0.125670\pi\) |
0.128439 | + | 0.991717i | \(0.459003\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.6941 | −0.515980 | −0.257990 | − | 0.966148i | \(-0.583060\pi\) | ||||
−0.257990 | + | 0.966148i | \(0.583060\pi\) | |||||||
\(812\) | 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 | ||||||||
\(819\) | 28.5082 | + | 45.5485i | 0.996158 | + | 1.59160i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.2742 | − | 16.3241i | 0.986777 | − | 0.569716i | 0.0824677 | − | 0.996594i | \(-0.473720\pi\) |
0.904309 | + | 0.426878i | \(0.140387\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.99507 | − | 15.5799i | 0.313548 | − | 0.543082i | −0.665580 | − | 0.746327i | \(-0.731816\pi\) |
0.979128 | + | 0.203245i | \(0.0651489\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −44.0128 | + | 4.07484i | −1.53233 | + | 0.141868i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.5793i | 1.61972i | 0.586623 | + | 0.809860i | \(0.300457\pi\) | ||||
−0.586623 | + | 0.809860i | \(0.699543\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.4802 | − | 12.9789i | −0.780769 | − | 0.450777i | 0.0559338 | − | 0.998434i | \(-0.482186\pi\) |
−0.836703 | + | 0.547657i | \(0.815520\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.91817 | + | 5.05441i | 0.101230 | + | 0.175336i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.1684 | + | 20.9259i | −0.352313 | + | 0.725038i | ||||
\(834\) | 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 | \(-0.905395\pi\) | ||
0.956157 | − | 0.292854i | \(-0.0946049\pi\) | |||||||
\(840\) | 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 | ||||||||
\(847\) | 19.7071 | + | 21.4156i | 0.677145 | + | 0.735849i | ||||
\(848\) | 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 | −0.312344 | − | 0.949969i | \(-0.601114\pi\) |
0.978869 | − | 0.204487i | \(-0.0655525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.84673 | − | 4.53031i | 0.267727 | − | 0.154572i | −0.360127 | − | 0.932903i | \(-0.617267\pi\) |
0.627854 | + | 0.778331i | \(0.283933\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 28.8890 | + | 15.3335i | 0.984534 | + | 0.522563i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.4590 | − | 23.3117i | −0.458150 | − | 0.793540i | 0.540713 | − | 0.841207i | \(-0.318155\pi\) |
−0.998863 | + | 0.0476675i | \(0.984821\pi\) | |||||||
\(864\) | 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 | ||||||||
\(875\) | 0.339652 | + | 9.52658i | 0.0114823 | + | 0.322057i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.1411 | − | 9.31905i | 0.545045 | − | 0.314682i | −0.202076 | − | 0.979370i | \(-0.564769\pi\) |
0.747121 | + | 0.664688i | \(0.231436\pi\) | |||||||
\(878\) | 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 | \(-0.655456\pi\) | ||||
−0.469196 | + | 0.883094i | \(0.655456\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.95431 | − | 1.70567i | −0.0993079 | − | 0.0573355i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.3947 | − | 28.3964i | −0.550480 | − | 0.953459i | −0.998240 | − | 0.0593050i | \(-0.981112\pi\) |
0.447760 | − | 0.894154i | \(-0.352222\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.663630 | − | 18.6135i | −0.0222574 | − | 0.624278i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.10505 | + | 4.32095i | −0.204527 | + | 0.144757i | ||||
\(892\) | 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 | ||||||||
\(903\) | 23.9123 | − | 45.0520i | 0.795753 | − | 1.49924i | ||||
\(904\) | 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 | \(-0.798629\pi\) |
0.915289 | + | 0.402799i | \(0.131963\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 60.2149 | 1.99720 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.4216 | 1.07418 | 0.537088 | − | 0.843526i | \(-0.319524\pi\) | ||||
0.537088 | + | 0.843526i | \(0.319524\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.4824 | + | 20.4695i | 1.47215 | + | 0.677441i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.72010 | − | 9.90750i | −0.189101 | − | 0.327532i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.4499 | + | 19.8916i | 0.411132 | + | 0.656880i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.04549 | − | 2.91301i | 0.166435 | − | 0.0960915i | −0.414469 | − | 0.910064i | \(-0.636033\pi\) |
0.580904 | + | 0.813972i | \(0.302699\pi\) | |||||||
\(920\) | 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 | \(-0.577050\pi\) |
0.720927 | + | 0.693011i | \(0.243716\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.0382 | + | 19.2690i | 0.427308 | + | 0.631516i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33.0695 | − | 57.2781i | −1.08265 | − | 1.87520i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.68274 | − | 3.65678i | 0.0550315 | − | 0.119589i | ||||
\(936\) | 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 | −0.813982 | − | 0.580891i | \(-0.802704\pi\) |
0.910057 | + | 0.414484i | \(0.136038\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.5351 | − | 19.9793i | −0.375634 | − | 0.650617i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.10431 | − | 3.36213i | −0.0684532 | − | 0.109370i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.16363 | + | 3.74752i | 0.0703085 | + | 0.121778i | 0.899037 | − | 0.437874i | \(-0.144268\pi\) |
−0.828728 | + | 0.559652i | \(0.810935\pi\) | |||||||
\(948\) | 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 | ||||||||
\(957\) | 39.4546 | − | 27.9246i | 1.27539 | − | 0.902674i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.6376 | + | 20.0417i | −0.343506 | + | 0.647182i | ||||
\(960\) | 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 | \(0.0191680\pi\) | ||||
−0.998187 | + | 0.0601815i | \(0.980832\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 26.1980 | + | 15.1254i | 0.841602 | + | 0.485899i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.7126 | + | 19.4640i | −1.08189 | + | 0.624630i | −0.931406 | − | 0.363983i | \(-0.881417\pi\) |
−0.150485 | + | 0.988612i | \(0.548083\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.8981 | + | 1.20857i | −1.08672 | + | 0.0387450i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 52.1003 | − | 30.0801i | 1.66855 | − | 0.963336i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.2664 | + | 24.7100i | −0.456421 | + | 0.790544i | −0.998769 | − | 0.0496097i | \(-0.984202\pi\) |
0.542348 | + | 0.840154i | \(0.317536\pi\) | |||||||
\(978\) | 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 | 0.164883 | − | 0.986313i | \(-0.447275\pi\) |
−0.771731 | + | 0.635949i | \(0.780609\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.86780 | − | 4.96717i | −0.0913757 | − | 0.158267i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.22697 | − | 0.150704i | 0.134546 | − | 0.00479698i | ||||
\(988\) | 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 | \(-0.686930\pi\) |
0.997975 | + | 0.0636148i | \(0.0202629\pi\) | |||||||
\(992\) | 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 | 0.240698 | + | 0.970600i | \(0.422624\pi\) |
−0.960913 | + | 0.276849i | \(0.910710\pi\) | |||||||
\(998\) | 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 | 1232.2.bn.c.241.2 | 16 | ||
4.3 | odd | 2 | 308.2.q.a.241.7 | ✓ | 16 | ||
7.5 | odd | 6 | inner | 1232.2.bn.c.593.1 | 16 | ||
11.10 | odd | 2 | inner | 1232.2.bn.c.241.1 | 16 | ||
12.11 | even | 2 | 2772.2.cs.a.2089.3 | 16 | |||
28.3 | even | 6 | 2156.2.c.c.1077.15 | 16 | |||
28.11 | odd | 6 | 2156.2.c.c.1077.1 | 16 | |||
28.19 | even | 6 | 308.2.q.a.285.8 | yes | 16 | ||
28.23 | odd | 6 | 2156.2.q.c.901.1 | 16 | |||
28.27 | even | 2 | 2156.2.q.c.2089.2 | 16 | |||
44.43 | even | 2 | 308.2.q.a.241.8 | yes | 16 | ||
77.54 | even | 6 | inner | 1232.2.bn.c.593.2 | 16 | ||
84.47 | odd | 6 | 2772.2.cs.a.901.4 | 16 | |||
132.131 | odd | 2 | 2772.2.cs.a.2089.4 | 16 | |||
308.87 | odd | 6 | 2156.2.c.c.1077.16 | 16 | |||
308.131 | odd | 6 | 308.2.q.a.285.7 | yes | 16 | ||
308.219 | even | 6 | 2156.2.q.c.901.2 | 16 | |||
308.263 | even | 6 | 2156.2.c.c.1077.2 | 16 | |||
308.307 | odd | 2 | 2156.2.q.c.2089.1 | 16 | |||
924.131 | even | 6 | 2772.2.cs.a.901.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
308.2.q.a.241.7 | ✓ | 16 | 4.3 | odd | 2 | ||
308.2.q.a.241.8 | yes | 16 | 44.43 | even | 2 | ||
308.2.q.a.285.7 | yes | 16 | 308.131 | odd | 6 | ||
308.2.q.a.285.8 | yes | 16 | 28.19 | even | 6 | ||
1232.2.bn.c.241.1 | 16 | 11.10 | odd | 2 | inner | ||
1232.2.bn.c.241.2 | 16 | 1.1 | even | 1 | trivial | ||
1232.2.bn.c.593.1 | 16 | 7.5 | odd | 6 | inner | ||
1232.2.bn.c.593.2 | 16 | 77.54 | even | 6 | inner | ||
2156.2.c.c.1077.1 | 16 | 28.11 | odd | 6 | |||
2156.2.c.c.1077.2 | 16 | 308.263 | even | 6 | |||
2156.2.c.c.1077.15 | 16 | 28.3 | even | 6 | |||
2156.2.c.c.1077.16 | 16 | 308.87 | odd | 6 | |||
2156.2.q.c.901.1 | 16 | 28.23 | odd | 6 | |||
2156.2.q.c.901.2 | 16 | 308.219 | even | 6 | |||
2156.2.q.c.2089.1 | 16 | 308.307 | odd | 2 | |||
2156.2.q.c.2089.2 | 16 | 28.27 | even | 2 | |||
2772.2.cs.a.901.3 | 16 | 924.131 | even | 6 | |||
2772.2.cs.a.901.4 | 16 | 84.47 | odd | 6 | |||
2772.2.cs.a.2089.3 | 16 | 12.11 | even | 2 | |||
2772.2.cs.a.2089.4 | 16 | 132.131 | odd | 2 |