Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.t (of order \(3\), 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.10 | ||
Character | \(\chi\) | \(=\) | 1008.193 |
Dual form | 1008.2.t.l.961.10 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 1.72608 | + | 0.143720i | 0.996551 | + | 0.0829771i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.77180 | 1.23959 | 0.619793 | − | 0.784766i | \(-0.287217\pi\) | ||||
0.619793 | + | 0.784766i | \(0.287217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.855737 | − | 2.50354i | −0.323438 | − | 0.946249i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.95869 | + | 0.496145i | 0.986230 | + | 0.165382i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.43944 | 1.03703 | 0.518515 | − | 0.855069i | \(-0.326485\pi\) | ||||
0.518515 | + | 0.855069i | \(0.326485\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.429164 | + | 0.743335i | −0.119029 | + | 0.206164i | −0.919383 | − | 0.393363i | \(-0.871311\pi\) |
0.800354 | + | 0.599527i | \(0.204645\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.78434 | + | 0.398364i | 1.23531 | + | 0.102857i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.405132 | + | 0.701710i | −0.0982590 | + | 0.170190i | −0.910964 | − | 0.412486i | \(-0.864661\pi\) |
0.812705 | + | 0.582675i | \(0.197994\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.750215 | − | 1.29941i | −0.172111 | − | 0.298105i | 0.767047 | − | 0.641591i | \(-0.221725\pi\) |
−0.939158 | + | 0.343486i | \(0.888392\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.11726 | − | 4.44429i | −0.243806 | − | 0.969824i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.64930 | −1.59499 | −0.797495 | − | 0.603326i | \(-0.793842\pi\) | ||||
−0.797495 | + | 0.603326i | \(0.793842\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.68286 | 0.536572 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.03562 | + | 1.28161i | 0.969106 | + | 0.246646i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.99696 | + | 6.92294i | 0.742217 | + | 1.28556i | 0.951484 | + | 0.307700i | \(0.0995592\pi\) |
−0.209266 | + | 0.977859i | \(0.567107\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.60578 | − | 6.24540i | −0.647618 | − | 1.12171i | −0.983690 | − | 0.179871i | \(-0.942432\pi\) |
0.336073 | − | 0.941836i | \(-0.390901\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.93674 | + | 0.494317i | 1.03345 | + | 0.0860496i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.37193 | − | 6.93931i | −0.400929 | − | 1.17296i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.458211 | + | 0.793644i | 0.0753294 | + | 0.130474i | 0.901229 | − | 0.433342i | \(-0.142666\pi\) |
−0.825900 | + | 0.563817i | \(0.809333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.847604 | + | 1.22137i | −0.135725 | + | 0.195576i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.67577 | − | 2.90251i | 0.261711 | − | 0.453297i | −0.704986 | − | 0.709221i | \(-0.749047\pi\) |
0.966697 | + | 0.255925i | \(0.0823800\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.20465 | − | 2.08652i | −0.183708 | − | 0.318191i | 0.759433 | − | 0.650586i | \(-0.225477\pi\) |
−0.943140 | + | 0.332395i | \(0.892143\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.20089 | + | 1.37521i | 1.22252 | + | 0.205005i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.307520 | + | 0.532640i | −0.0448564 | + | 0.0776935i | −0.887582 | − | 0.460650i | \(-0.847616\pi\) |
0.842726 | + | 0.538343i | \(0.180950\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.53543 | + | 4.28474i | −0.790775 | + | 0.612106i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.800140 | + | 1.15298i | −0.112042 | + | 0.161449i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.31646 | − | 10.9404i | 0.867633 | − | 1.50278i | 0.00322332 | − | 0.999995i | \(-0.498974\pi\) |
0.864409 | − | 0.502789i | \(-0.167693\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.53342 | 1.28549 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.10818 | − | 2.35070i | −0.146782 | − | 0.311358i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.734690 | + | 1.27252i | 0.0956485 | + | 0.165668i | 0.909879 | − | 0.414874i | \(-0.136174\pi\) |
−0.814231 | + | 0.580542i | \(0.802841\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.71635 | + | 9.90101i | −0.731904 | + | 1.26769i | 0.224165 | + | 0.974551i | \(0.428035\pi\) |
−0.956069 | + | 0.293143i | \(0.905299\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.28974 | − | 7.83177i | −0.162492 | − | 0.986710i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.18956 | + | 2.06037i | −0.147546 | + | 0.255558i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.10061 | + | 14.0307i | 0.989647 | + | 1.71412i | 0.619117 | + | 0.785299i | \(0.287491\pi\) |
0.370530 | + | 0.928820i | \(0.379176\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.2033 | − | 1.09936i | −1.58949 | − | 0.132348i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.4177 | −1.71106 | −0.855532 | − | 0.517749i | \(-0.826770\pi\) | ||||
−0.855532 | + | 0.517749i | \(0.826770\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.16893 | + | 7.22079i | −0.487936 | + | 0.845130i | −0.999904 | − | 0.0138749i | \(-0.995583\pi\) |
0.511968 | + | 0.859005i | \(0.328917\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.63083 | + | 0.385582i | 0.534722 | + | 0.0445232i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.94325 | − | 8.61077i | −0.335415 | − | 0.981288i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.37586 | + | 2.38305i | −0.154796 | + | 0.268115i | −0.932985 | − | 0.359916i | \(-0.882805\pi\) |
0.778189 | + | 0.628031i | \(0.216139\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.50768 | + | 2.93588i | 0.945298 | + | 0.326209i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.75814 | + | 9.97340i | 0.632038 | + | 1.09472i | 0.987134 | + | 0.159893i | \(0.0511148\pi\) |
−0.355096 | + | 0.934830i | \(0.615552\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.12294 | + | 1.94500i | −0.121800 | + | 0.210965i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.90410 | + | 12.5240i | 0.632986 | + | 1.34271i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.11395 | − | 8.85763i | −0.542078 | − | 0.938907i | −0.998785 | − | 0.0492892i | \(-0.984304\pi\) |
0.456707 | − | 0.889617i | \(-0.349029\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.22822 | + | 0.438331i | 0.233581 | + | 0.0459496i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.32627 | − | 11.2983i | −0.552308 | − | 1.17158i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.07944 | − | 3.60170i | −0.213346 | − | 0.369527i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.82852 | + | 6.63119i | 0.388727 | + | 0.673296i | 0.992279 | − | 0.124029i | \(-0.0395814\pi\) |
−0.603551 | + | 0.797324i | \(0.706248\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.1762 | + | 1.70646i | 1.02275 | + | 0.171506i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.68603 | −0.366774 | −0.183387 | − | 0.983041i | \(-0.558706\pi\) | ||||
−0.183387 | + | 0.983041i | \(0.558706\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.1205 | 1.58840 | 0.794201 | − | 0.607656i | \(-0.207890\pi\) | ||||
0.794201 | + | 0.607656i | \(0.207890\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.09681 | − | 12.3187i | −0.302218 | − | 1.20218i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.16767 | − | 5.48656i | −0.306230 | − | 0.530405i | 0.671305 | − | 0.741182i | \(-0.265734\pi\) |
−0.977534 | + | 0.210776i | \(0.932401\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.89477 | − | 8.47799i | 0.468834 | − | 0.812044i | −0.530532 | − | 0.847665i | \(-0.678008\pi\) |
0.999365 | + | 0.0356213i | \(0.0113410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.676844 | + | 1.43575i | 0.0642432 | + | 0.136275i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.06963 | − | 7.04881i | 0.382839 | − | 0.663096i | −0.608628 | − | 0.793456i | \(-0.708280\pi\) |
0.991467 | + | 0.130360i | \(0.0416132\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.2023 | −1.97713 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.63857 | + | 1.98637i | −0.151485 | + | 0.183640i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.10345 | + | 0.413786i | 0.192823 | + | 0.0379317i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.829725 | 0.0754295 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.30966 | − | 4.76912i | 0.298422 | − | 0.430017i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.42264 | −0.574459 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.5658 | 1.11504 | 0.557518 | − | 0.830165i | \(-0.311754\pi\) | ||||
0.557518 | + | 0.830165i | \(0.311754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.77945 | − | 3.77463i | −0.156672 | − | 0.332337i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.58550 | −0.138526 | −0.0692631 | − | 0.997598i | \(-0.522065\pi\) | ||||
−0.0692631 | + | 0.997598i | \(0.522065\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.61114 | + | 2.99015i | −0.226415 | + | 0.259279i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.9577 | + | 3.55236i | 1.20129 | + | 0.305739i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.92788 | 0.421017 | 0.210508 | − | 0.977592i | \(-0.432488\pi\) | ||||
0.210508 | + | 0.977592i | \(0.432488\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.12999 | + | 7.15336i | −0.350301 | + | 0.606740i | −0.986302 | − | 0.164949i | \(-0.947254\pi\) |
0.636001 | + | 0.771688i | \(0.280588\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.607354 | + | 0.875181i | −0.0511485 | + | 0.0737035i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.47608 | + | 2.55665i | −0.123436 | + | 0.213798i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.0788 | + | 19.1890i | 0.920042 | + | 1.59356i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.1704 | + | 6.60025i | −0.838839 | + | 0.544379i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.9140 | −1.13988 | −0.569938 | − | 0.821688i | \(-0.693033\pi\) | ||||
−0.569938 | + | 0.821688i | \(0.693033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.9927 | −1.87112 | −0.935561 | − | 0.353166i | \(-0.885105\pi\) | ||||
−0.935561 | + | 0.353166i | \(0.885105\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.54681 | + | 1.87514i | −0.125052 | + | 0.151596i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.99450 | − | 17.3110i | −0.802777 | − | 1.39045i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.29022 | − | 16.0911i | −0.741441 | − | 1.28421i | −0.951839 | − | 0.306597i | \(-0.900810\pi\) |
0.210399 | − | 0.977616i | \(-0.432524\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.4751 | − | 17.9762i | 0.989337 | − | 1.42561i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.54579 | + | 19.1503i | 0.515880 | + | 1.50926i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.45194 | + | 4.24688i | 0.192050 | + | 0.332641i | 0.945930 | − | 0.324372i | \(-0.105153\pi\) |
−0.753879 | + | 0.657013i | \(0.771820\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16.4554 | + | 1.37015i | 1.28105 | + | 0.106666i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.47493 | − | 9.48286i | 0.423663 | − | 0.733805i | −0.572632 | − | 0.819813i | \(-0.694077\pi\) |
0.996295 | + | 0.0860073i | \(0.0274108\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.13164 | + | 10.6203i | 0.471664 | + | 0.816947i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.57496 | − | 4.21677i | −0.120440 | − | 0.322464i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.70271 | − | 11.6094i | 0.509598 | − | 0.882649i | −0.490340 | − | 0.871531i | \(-0.663127\pi\) |
0.999938 | − | 0.0111184i | \(-0.00353917\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.29582 | − | 6.71665i | −0.173548 | − | 0.507731i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.08524 | + | 2.30206i | 0.0815720 | + | 0.173033i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.64888 | − | 11.5162i | 0.496961 | − | 0.860761i | −0.503033 | − | 0.864267i | \(-0.667783\pi\) |
0.999994 | + | 0.00350600i | \(0.00111600\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9190 | −0.811601 | −0.405801 | − | 0.913962i | \(-0.633007\pi\) | ||||
−0.405801 | + | 0.913962i | \(0.633007\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.2898 | + | 16.2684i | −0.834569 | + | 1.20259i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.27007 | + | 2.19982i | 0.0933772 | + | 0.161734i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.39343 | + | 2.41349i | −0.101897 | + | 0.176492i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.10061 | − | 13.7036i | −0.0800573 | − | 0.996790i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.30553 | + | 16.1177i | −0.673325 | + | 1.16623i | 0.303631 | + | 0.952790i | \(0.401801\pi\) |
−0.976956 | + | 0.213443i | \(0.931532\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.46470 | − | 2.53693i | −0.105431 | − | 0.182613i | 0.808483 | − | 0.588520i | \(-0.200289\pi\) |
−0.913914 | + | 0.405907i | \(0.866956\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.34939 | + | 3.38540i | −0.168243 | + | 0.242434i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.5050 | −1.31843 | −0.659214 | − | 0.751956i | \(-0.729111\pi\) | ||||
−0.659214 | + | 0.751956i | \(0.729111\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.793836 | + | 1.37496i | −0.0562736 | + | 0.0974687i | −0.892790 | − | 0.450473i | \(-0.851255\pi\) |
0.836516 | + | 0.547942i | \(0.184589\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.9658 | + | 25.3823i | 0.844002 | + | 1.79033i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.9115 | − | 15.9308i | 0.976397 | − | 1.11812i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.64489 | − | 8.04518i | 0.324413 | − | 0.561900i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −22.6319 | − | 3.79517i | −1.57303 | − | 0.263782i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.58032 | − | 4.46924i | −0.178484 | − | 0.309144i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.3436 | + | 21.3798i | −0.849770 | + | 1.47184i | 0.0316443 | + | 0.999499i | \(0.489926\pi\) |
−0.881414 | + | 0.472345i | \(0.843408\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.8860 | − | 2.07212i | −1.70516 | − | 0.141979i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.33905 | − | 5.78340i | −0.227721 | − | 0.394425i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.5500 | + | 14.3716i | −0.851950 | + | 0.975611i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.23367 | + | 11.8645i | −0.556380 | + | 0.801728i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.347737 | − | 0.602298i | −0.0233913 | − | 0.0405149i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.78468 | + | 16.9476i | 0.655231 | + | 1.13489i | 0.981836 | + | 0.189732i | \(0.0607619\pi\) |
−0.326605 | + | 0.945161i | \(0.605905\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.93775 | + | 1.33109i | 0.529183 | + | 0.0887393i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.64808 | −0.573993 | −0.286996 | − | 0.957932i | \(-0.592657\pi\) | ||||
−0.286996 | + | 0.957932i | \(0.592657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.5427 | 0.762765 | 0.381382 | − | 0.924417i | \(-0.375448\pi\) | ||||
0.381382 | + | 0.924417i | \(0.375448\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.84274 | − | 15.2859i | −0.252834 | − | 1.00574i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.12745 | − | 14.0772i | −0.532447 | − | 0.922225i | −0.999282 | − | 0.0378811i | \(-0.987939\pi\) |
0.466835 | − | 0.884344i | \(-0.345394\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.852382 | + | 1.47637i | −0.0556033 | + | 0.0963077i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.71733 | + | 3.91560i | −0.176510 | + | 0.254345i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.4336 | + | 21.5355i | −0.804260 | + | 1.39302i | 0.112530 | + | 0.993648i | \(0.464105\pi\) |
−0.916790 | + | 0.399371i | \(0.869229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.0363 | −1.22623 | −0.613117 | − | 0.789992i | \(-0.710085\pi\) | ||||
−0.613117 | + | 0.789992i | \(0.710085\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.2630 | + | 6.29028i | 0.914970 | + | 0.403522i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.3431 | + | 11.8764i | −0.980234 | + | 0.758758i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.28786 | 0.0819447 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.50562 | + | 18.0424i | 0.539022 | + | 1.14339i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.980433 | 0.0618844 | 0.0309422 | − | 0.999521i | \(-0.490149\pi\) | ||||
0.0309422 | + | 0.999521i | \(0.490149\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.3093 | −1.65405 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.21783 | + | 3.19583i | −0.138886 | + | 0.200130i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.36725 | 0.272421 | 0.136211 | − | 0.990680i | \(-0.456508\pi\) | ||||
0.136211 | + | 0.990680i | \(0.456508\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.59481 | − | 1.82630i | 0.0990968 | − | 0.113481i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.39098 | + | 22.4659i | 0.519389 | + | 1.39060i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.4842 | 0.769811 | 0.384905 | − | 0.922956i | \(-0.374234\pi\) | ||||
0.384905 | + | 0.922956i | \(0.374234\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.5079 | − | 30.3247i | 1.07550 | − | 1.86283i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.55406 | − | 16.0239i | −0.462301 | − | 0.980649i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.29270 | − | 14.3634i | 0.505615 | − | 0.875750i | −0.494364 | − | 0.869255i | \(-0.664599\pi\) |
0.999979 | − | 0.00649532i | \(-0.00206754\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.9814 | − | 22.4845i | −0.788566 | − | 1.36584i | −0.926845 | − | 0.375444i | \(-0.877490\pi\) |
0.138279 | − | 0.990393i | \(-0.455843\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.78308 | + | 1.07684i | 0.228963 | + | 0.0651730i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.22753 | 0.556441 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.96075 | −0.117810 | −0.0589049 | − | 0.998264i | \(-0.518761\pi\) | ||||
−0.0589049 | + | 0.998264i | \(0.518761\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.56976 | − | 20.2672i | −0.453190 | − | 1.21336i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.42057 | + | 16.3169i | 0.561984 | + | 0.973385i | 0.997323 | + | 0.0731185i | \(0.0232951\pi\) |
−0.435339 | + | 0.900267i | \(0.643372\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.7422 | − | 20.3381i | −0.698002 | − | 1.20898i | −0.969158 | − | 0.246440i | \(-0.920739\pi\) |
0.271156 | − | 0.962536i | \(-0.412594\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.07164 | − | 6.51568i | −0.181948 | − | 0.385955i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.70058 | − | 1.71156i | −0.513579 | − | 0.101030i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.17174 | + | 14.1539i | 0.480690 | + | 0.832580i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.65529 | + | 11.9962i | 0.331519 | + | 0.703229i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.00384 | + | 1.73871i | −0.0586452 | + | 0.101576i | −0.893857 | − | 0.448351i | \(-0.852011\pi\) |
0.835212 | + | 0.549928i | \(0.185345\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.03641 | + | 3.52717i | 0.118564 | + | 0.205360i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.3197 | + | 4.40802i | 1.00499 | + | 0.255779i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.28281 | − | 5.68599i | 0.189850 | − | 0.328829i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.19282 | + | 4.80140i | −0.241670 | + | 0.276748i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.36237 | − | 0.529758i | −0.365509 | − | 0.0304338i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.8446 | + | 27.4436i | −0.907257 | + | 1.57142i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.7633 | −1.86990 | −0.934951 | − | 0.354777i | \(-0.884557\pi\) | ||||
−0.934951 | + | 0.354777i | \(0.884557\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.8253 | + | 2.31685i | 1.58292 | + | 0.131801i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.04979 | − | 12.2106i | −0.399757 | − | 0.692400i | 0.593939 | − | 0.804510i | \(-0.297572\pi\) |
−0.993696 | + | 0.112111i | \(0.964239\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.0769 | − | 29.5781i | 0.965245 | − | 1.67185i | 0.256291 | − | 0.966600i | \(-0.417499\pi\) |
0.708954 | − | 0.705255i | \(-0.249167\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.57490 | − | 21.7081i | −0.201423 | − | 1.22311i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.790586 | − | 1.36933i | 0.0444037 | − | 0.0769095i | −0.842969 | − | 0.537962i | \(-0.819195\pi\) |
0.887373 | + | 0.461052i | \(0.152528\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.7473 | + | 23.8110i | 0.769701 | + | 1.33316i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.67911 | − | 9.92548i | −0.261162 | − | 0.553986i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.21575 | 0.0676459 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.15139 | + | 1.99426i | −0.0638675 | + | 0.110622i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.66721 | − | 13.9302i | 0.534598 | − | 0.770341i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.59664 | + | 0.314088i | 0.0880257 | + | 0.0173163i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.86862 | − | 11.8968i | 0.377533 | − | 0.653907i | −0.613169 | − | 0.789951i | \(-0.710106\pi\) |
0.990703 | + | 0.136044i | \(0.0434390\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.961940 | + | 2.57549i | 0.0527140 | + | 0.141136i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.4533 | + | 38.8902i | 1.22675 | + | 2.12480i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.72318 | + | 15.1090i | −0.475182 | + | 0.823039i | −0.999596 | − | 0.0284243i | \(-0.990951\pi\) |
0.524414 | + | 0.851463i | \(0.324284\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.03756 | − | 11.5819i | 0.436540 | − | 0.629042i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.4019 | − | 21.4807i | −0.671598 | − | 1.16324i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4639 | + | 10.1916i | 0.834972 | + | 0.550292i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −36.5968 | − | 3.04721i | −1.97031 | − | 0.164056i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.91552 | + | 3.31778i | 0.102830 | + | 0.178108i | 0.912850 | − | 0.408296i | \(-0.133877\pi\) |
−0.810019 | + | 0.586403i | \(0.800543\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.69984 | + | 2.94421i | 0.0909903 | + | 0.157600i | 0.907928 | − | 0.419126i | \(-0.137663\pi\) |
−0.816938 | + | 0.576726i | \(0.804330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.11377 | + | 3.19313i | −0.166201 | + | 0.170437i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.5568 | 0.668332 | 0.334166 | − | 0.942514i | \(-0.391545\pi\) | ||||
0.334166 | + | 0.942514i | \(0.391545\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −39.9629 | −2.12101 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.57124 | + | 1.01654i | 0.189010 | + | 0.0538008i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.02209 | + | 10.4306i | 0.317834 | + | 0.550504i | 0.980036 | − | 0.198821i | \(-0.0637113\pi\) |
−0.662202 | + | 0.749325i | \(0.730378\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.37435 | − | 14.5048i | 0.440756 | − | 0.763411i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.43217 | + | 0.119248i | 0.0751694 | + | 0.00625892i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.5554 | + | 20.0146i | −0.604838 | + | 1.04761i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.02514 | 0.105711 | 0.0528557 | − | 0.998602i | \(-0.483168\pi\) | ||||
0.0528557 | + | 0.998602i | \(0.483168\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.39814 | − | 7.75621i | 0.333074 | − | 0.403772i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −32.7950 | − | 6.45138i | −1.70263 | − | 0.334939i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.6259 | 1.11975 | 0.559874 | − | 0.828578i | \(-0.310849\pi\) | ||||
0.559874 | + | 0.828578i | \(0.310849\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.0860 | − | 0.923065i | −0.572477 | − | 0.0476669i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.86142 | −0.353381 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.76701 | 0.347598 | 0.173799 | − | 0.984781i | \(-0.444396\pi\) | ||||
0.173799 | + | 0.984781i | \(0.444396\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.6896 | + | 1.80597i | 1.11119 | + | 0.0925224i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.65645 | 0.391226 | 0.195613 | − | 0.980681i | \(-0.437330\pi\) | ||||
0.195613 | + | 0.980681i | \(0.437330\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.15810 | − | 23.8673i | −0.415775 | − | 1.21639i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.52897 | − | 6.77104i | −0.128555 | − | 0.344191i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.1561 | −1.07266 | −0.536329 | − | 0.844009i | \(-0.680189\pi\) | ||||
−0.536329 | + | 0.844009i | \(0.680189\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.09898 | − | 5.36759i | 0.156722 | − | 0.271451i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.73670 | − | 0.227869i | −0.138048 | − | 0.0114945i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.81360 | + | 6.60534i | −0.191883 | + | 0.332351i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.02642 | + | 6.97396i | 0.202080 | + | 0.350013i | 0.949199 | − | 0.314678i | \(-0.101896\pi\) |
−0.747118 | + | 0.664691i | \(0.768563\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.93678 | + | 4.78595i | −0.247148 | + | 0.239597i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.77773 | −0.388401 | −0.194201 | − | 0.980962i | \(-0.562211\pi\) | ||||
−0.194201 | + | 0.980962i | \(0.562211\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.18989 | 0.308341 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 23.5816 | + | 8.13766i | 1.17178 | + | 0.404364i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.57599 | + | 2.72969i | 0.0781188 | + | 0.135306i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.76327 | − | 16.9105i | −0.482763 | − | 0.836170i | 0.517041 | − | 0.855960i | \(-0.327033\pi\) |
−0.999804 | + | 0.0197907i | \(0.993700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.50590 | + | 0.708237i | 0.419565 | + | 0.0349347i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.55710 | − | 2.92827i | 0.125827 | − | 0.144091i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.9604 | + | 27.6442i | 0.783466 | + | 1.35700i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.15677 | + | 11.7537i | −0.399439 | + | 0.575580i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.5259 | − | 21.6955i | 0.611932 | − | 1.05990i | −0.378983 | − | 0.925404i | \(-0.623726\pi\) |
0.990915 | − | 0.134493i | \(-0.0429406\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0746 | + | 31.3061i | 0.880902 | + | 1.52577i | 0.850340 | + | 0.526234i | \(0.176396\pi\) |
0.0305620 | + | 0.999533i | \(0.490270\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.17412 | + | 1.42334i | −0.0570878 | + | 0.0692052i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.08691 | + | 1.88259i | −0.0527231 | + | 0.0913190i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.6793 | + | 5.83845i | 1.43628 | + | 0.282543i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.91528 | + | 4.20084i | −0.140751 | + | 0.202818i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.95636 | − | 3.38852i | 0.0942346 | − | 0.163219i | −0.815054 | − | 0.579385i | \(-0.803293\pi\) |
0.909289 | + | 0.416165i | \(0.136626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.2929 | −0.686872 | −0.343436 | − | 0.939176i | \(-0.611591\pi\) | ||||
−0.343436 | + | 0.939176i | \(0.611591\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.3650 | + | 34.7139i | 0.784640 | + | 1.66441i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.73862 | + | 9.93958i | 0.274515 | + | 0.475475i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.39235 | + | 4.14367i | −0.114180 | + | 0.197766i | −0.917452 | − | 0.397847i | \(-0.869758\pi\) |
0.803271 | + | 0.595613i | \(0.203091\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.5035 | + | 9.93085i | −0.881117 | + | 0.472898i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.13213 | + | 7.15707i | −0.196324 | + | 0.340042i | −0.947334 | − | 0.320248i | \(-0.896234\pi\) |
0.751010 | + | 0.660291i | \(0.229567\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.1748 | − | 24.5515i | −0.671952 | − | 1.16385i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.0166 | − | 1.99972i | −1.13594 | − | 0.0945835i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.6036 | −0.972346 | −0.486173 | − | 0.873863i | \(-0.661608\pi\) | ||||
−0.486173 | + | 0.873863i | \(0.661608\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.76370 | − | 9.98301i | 0.271402 | − | 0.470082i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −39.6872 | − | 3.30453i | −1.86467 | − | 0.155260i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.17617 | + | 1.21497i | 0.289543 | + | 0.0569585i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.98220 | − | 15.5576i | 0.420170 | − | 0.727755i | −0.575786 | − | 0.817600i | \(-0.695304\pi\) |
0.995956 | + | 0.0898451i | \(0.0286372\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.93941 | + | 3.01432i | −0.137200 | + | 0.140697i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.03501 | + | 6.98885i | 0.187929 | + | 0.325503i | 0.944560 | − | 0.328340i | \(-0.106489\pi\) |
−0.756630 | + | 0.653843i | \(0.773156\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.50704 | − | 4.34232i | 0.116512 | − | 0.201805i | −0.801871 | − | 0.597497i | \(-0.796162\pi\) |
0.918383 | + | 0.395692i | \(0.129495\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.7633 | − | 31.3165i | −0.684633 | − | 1.45227i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.1673 | + | 22.8063i | 0.609308 | + | 1.05535i | 0.991355 | + | 0.131209i | \(0.0418859\pi\) |
−0.382047 | + | 0.924143i | \(0.624781\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.1944 | − | 32.2868i | 1.30189 | − | 1.49086i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.7230 | − | 29.1098i | −0.632323 | − | 1.34131i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.14332 | − | 7.17645i | −0.190510 | − | 0.329973i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.01272 | − | 3.48614i | −0.0923500 | − | 0.159955i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.1165 | − | 29.2354i | 1.10422 | − | 1.33860i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.2445 | 1.15345 | 0.576724 | − | 0.816939i | \(-0.304331\pi\) | ||||
0.576724 | + | 0.816939i | \(0.304331\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.786591 | −0.0358655 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.54625 | + | 33.9957i | 0.388868 | + | 1.54686i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.6119 | + | 18.3803i | 0.481861 | + | 0.834608i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.36124 | + | 2.35774i | −0.0616837 | + | 0.106839i | −0.895218 | − | 0.445628i | \(-0.852980\pi\) |
0.833534 | + | 0.552468i | \(0.186314\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.62187 | + | 7.68283i | 0.163787 | + | 0.347430i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.8020 | − | 27.3698i | 0.713134 | − | 1.23518i | −0.250541 | − | 0.968106i | \(-0.580609\pi\) |
0.963675 | − | 0.267078i | \(-0.0860581\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.47720 | −0.291718 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 28.2064 | + | 4.72996i | 1.26778 | + | 0.212596i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.3377 | + | 36.0953i | 0.553424 | + | 1.61909i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.94890 | −0.266309 | −0.133155 | − | 0.991095i | \(-0.542511\pi\) | ||||
−0.133155 | + | 0.991095i | \(0.542511\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.8130 | − | 15.5813i | 0.483091 | − | 0.696121i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.6905 | 1.23466 | 0.617329 | − | 0.786705i | \(-0.288215\pi\) | ||||
0.617329 | + | 0.786705i | \(0.288215\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.2169 | −0.454647 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.05732 | + | 19.2127i | 0.402250 | + | 0.853267i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.2885 | 1.65278 | 0.826392 | − | 0.563095i | \(-0.190389\pi\) | ||||
0.826392 | + | 0.563095i | \(0.190389\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.6450 | + | 4.25798i | 0.957521 | + | 0.188362i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.11246 | − | 7.50482i | −0.0932674 | − | 0.331346i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 44.6828 | 1.96896 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.05769 | + | 1.83198i | −0.0465174 | + | 0.0805704i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.2379 | − | 19.0755i | 0.581080 | − | 0.837321i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.1271 | − | 31.3971i | 0.794163 | − | 1.37553i | −0.129207 | − | 0.991618i | \(-0.541243\pi\) |
0.923370 | − | 0.383912i | \(-0.125423\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.2931 | − | 17.8282i | −0.450086 | − | 0.779572i | 0.548305 | − | 0.836278i | \(-0.315273\pi\) |
−0.998391 | + | 0.0567068i | \(0.981940\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.99745 | − | 11.9234i | −0.130819 | − | 0.520380i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.84328 | 0.254537 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.5118 | 1.54399 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.54236 | + | 4.12951i | 0.0669329 | + | 0.179205i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.43836 | + | 2.49131i | 0.0623023 | + | 0.107911i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.78013 | − | 15.2076i | −0.379598 | − | 0.657483i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.1316 | − | 18.9223i | 0.566670 | − | 0.816556i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.0388 | + | 14.7371i | −0.820057 | + | 0.634772i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.649192 | − | 1.12443i | −0.0279109 | − | 0.0483432i | 0.851733 | − | 0.523977i | \(-0.175552\pi\) |
−0.879643 | + | 0.475634i | \(0.842219\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.8470 | − | 1.56928i | −0.808802 | − | 0.0673443i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.5673 | − | 23.4993i | 0.581159 | − | 1.00660i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8412 | + | 23.9736i | 0.591805 | + | 1.02504i | 0.993989 | + | 0.109478i | \(0.0349180\pi\) |
−0.402184 | + | 0.915559i | \(0.631749\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.8252 | + | 26.4579i | −0.931479 | + | 1.12919i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.99716 | − | 10.3874i | 0.255488 | − | 0.442518i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.14344 | + | 1.40525i | 0.303770 | + | 0.0597571i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.87608 | + | 3.97960i | 0.0796350 | + | 0.168924i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.72089 | + | 13.3730i | −0.327145 | + | 0.566631i | −0.981944 | − | 0.189172i | \(-0.939420\pi\) |
0.654799 | + | 0.755803i | \(0.272753\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.06797 | 0.0874660 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.75203 | + | 3.96560i | −0.116191 | + | 0.167428i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.956715 | + | 1.65708i | 0.0403207 | + | 0.0698375i | 0.885482 | − | 0.464675i | \(-0.153829\pi\) |
−0.845161 | + | 0.534512i | \(0.820495\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.2802 | − | 19.5379i | 0.474561 | − | 0.821964i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.0697573 | − | 23.8117i | 0.00292953 | − | 0.999996i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.38138 | − | 12.7849i | 0.309444 | − | 0.535972i | −0.668797 | − | 0.743445i | \(-0.733191\pi\) |
0.978241 | + | 0.207473i | \(0.0665239\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.28208 | + | 2.22063i | 0.0536535 | + | 0.0929306i | 0.891605 | − | 0.452814i | \(-0.149580\pi\) |
−0.837951 | + | 0.545745i | \(0.816247\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.3785 | + | 26.4829i | −0.767773 | + | 1.10634i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.5220 | −0.855827 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.01283 | − | 12.1466i | 0.291948 | − | 0.505669i | −0.682322 | − | 0.731052i | \(-0.739030\pi\) |
0.974270 | + | 0.225383i | \(0.0723632\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.16358 | − | 4.58945i | −0.0899151 | − | 0.190731i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.0413 | − | 22.9504i | 0.831455 | − | 0.952141i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.7251 | − | 37.6289i | 0.899760 | − | 1.55843i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.54177 | + | 5.50581i | −0.187779 | + | 0.227637i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.7666 | − | 27.3085i | −0.650756 | − | 1.12714i | −0.982940 | − | 0.183928i | \(-0.941119\pi\) |
0.332183 | − | 0.943215i | \(-0.392215\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.41022 | + | 9.37078i | −0.222924 | + | 0.386116i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −31.9411 | − | 2.65955i | −1.31388 | − | 0.109399i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.72311 | − | 9.91272i | −0.235020 | − | 0.407067i | 0.724258 | − | 0.689529i | \(-0.242182\pi\) |
−0.959279 | + | 0.282462i | \(0.908849\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.83033 | + | 1.14693i | 0.239020 | + | 0.0470196i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.56783 | + | 2.25921i | −0.0641672 | + | 0.0924631i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.80684 | + | 4.86159i | 0.114684 | + | 0.198639i | 0.917654 | − | 0.397381i | \(-0.130081\pi\) |
−0.802969 | + | 0.596021i | \(0.796748\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.2223 | + | 33.2940i | 0.784094 | + | 1.35809i | 0.929539 | + | 0.368725i | \(0.120205\pi\) |
−0.145444 | + | 0.989366i | \(0.546461\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.0059 | + | 45.5315i | 0.692535 | + | 1.85418i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.29983 | 0.0935013 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.3437 | 0.663372 | 0.331686 | − | 0.943390i | \(-0.392383\pi\) | ||||
0.331686 | + | 0.943390i | \(0.392383\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 26.3019 | − | 25.4984i | 1.06581 | − | 1.03325i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.263953 | − | 0.457180i | −0.0106784 | − | 0.0184955i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.19332 | + | 10.7272i | −0.250146 | + | 0.433266i | −0.963566 | − | 0.267471i | \(-0.913812\pi\) |
0.713420 | + | 0.700737i | \(0.247145\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.17369 | − | 13.2190i | 0.369919 | − | 0.533043i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.9853 | − | 36.3476i | 0.844836 | − | 1.46330i | −0.0409280 | − | 0.999162i | \(-0.513031\pi\) |
0.885764 | − | 0.464136i | \(-0.153635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.8945 | 1.44272 | 0.721361 | − | 0.692559i | \(-0.243517\pi\) | ||||
0.721361 | + | 0.692559i | \(0.243517\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −38.5190 | − | 9.80342i | −1.54571 | − | 0.393398i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.7992 | + | 20.3828i | −0.713111 | + | 0.816619i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2166 | −1.24866 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.81151 | − | 8.08510i | −0.152217 | − | 0.322888i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.742544 | −0.0296072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.5519 | 0.778349 | 0.389175 | − | 0.921164i | \(-0.372760\pi\) | ||||
0.389175 | + | 0.921164i | \(0.372760\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.3788 | + | 35.1291i | −0.968968 | + | 1.39626i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 34.8299 | 1.38218 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.809390 | − | 5.95353i | −0.0320692 | − | 0.235888i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −42.6574 | − | 7.15327i | −1.68750 | − | 0.282979i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.6026 | −0.576769 | −0.288385 | − | 0.957515i | \(-0.593118\pi\) | ||||
−0.288385 | + | 0.957515i | \(0.593118\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.96942 | − | 10.3393i | 0.235411 | − | 0.407744i | −0.723981 | − | 0.689820i | \(-0.757690\pi\) |
0.959392 | + | 0.282076i | \(0.0910231\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.93227 | − | 10.4625i | −0.194208 | − | 0.411960i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.92060 | − | 3.32658i | 0.0755067 | − | 0.130781i | −0.825800 | − | 0.563963i | \(-0.809276\pi\) |
0.901306 | + | 0.433182i | \(0.142609\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.52692 | + | 4.37675i | 0.0991903 | + | 0.171803i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.7278 | + | 23.0029i | −0.929965 | + | 0.901554i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.9918 | 1.56500 | 0.782501 | − | 0.622650i | \(-0.213944\pi\) | ||||
0.782501 | + | 0.622650i | \(0.213944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.39469 | −0.171715 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.9171 | + | 19.2957i | −0.620986 | + | 0.752796i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.60101 | − | 2.77303i | −0.0623665 | − | 0.108022i | 0.833156 | − | 0.553038i | \(-0.186531\pi\) |
−0.895523 | + | 0.445016i | \(0.853198\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.6515 | + | 37.5015i | 0.842146 | + | 1.45864i | 0.888077 | + | 0.459695i | \(0.152041\pi\) |
−0.0459311 | + | 0.998945i | \(0.514625\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.513658 | − | 1.08959i | −0.0199488 | − | 0.0423162i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.23755 | + | 8.28808i | −0.280660 | + | 0.321398i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.5740 | − | 52.9557i | −1.18383 | − | 2.05045i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.4534 | + | 30.6591i | 0.558801 | + | 1.18535i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.6610 | + | 34.0539i | −0.759006 | + | 1.31464i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2936 | + | 21.2931i | 0.473883 | + | 0.820790i | 0.999553 | − | 0.0298991i | \(-0.00951859\pi\) |
−0.525670 | + | 0.850689i | \(0.676185\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.5099 | + | 3.43838i | 0.519995 | + | 0.132343i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.2094 | − | 33.2716i | 0.738276 | − | 1.27873i | −0.214994 | − | 0.976615i | \(-0.568973\pi\) |
0.953271 | − | 0.302117i | \(-0.0976933\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.3253 | − | 15.2594i | 0.511376 | − | 0.585603i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.9273 | − | 1.24291i | −0.572013 | − | 0.0476282i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.122464 | − | 0.212113i | 0.00468594 | − | 0.00811629i | −0.863673 | − | 0.504053i | \(-0.831842\pi\) |
0.868359 | + | 0.495936i | \(0.165175\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.6591 | 0.521886 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.9236 | + | 1.65893i | 0.760135 | + | 0.0632920i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.42160 | + | 9.39049i | 0.206547 | + | 0.357749i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.65146 | + | 6.32452i | −0.138908 | + | 0.240596i | −0.927084 | − | 0.374855i | \(-0.877693\pi\) |
0.788175 | + | 0.615451i | \(0.211026\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.43598 | − | 26.9369i | −0.168509 | − | 1.02325i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.4475 | + | 19.8277i | −0.434229 | + | 0.752106i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.35782 | + | 2.35181i | 0.0514309 | + | 0.0890810i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.0054 | − | 25.4664i | −0.454087 | − | 0.963226i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.3889 | 1.22331 | 0.611656 | − | 0.791124i | \(-0.290504\pi\) | ||||
0.611656 | + | 0.791124i | \(0.290504\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.687513 | − | 1.19081i | 0.0259301 | − | 0.0449122i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.68346 | + | 2.42582i | −0.0634029 | + | 0.0913618i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.15427 | + | 9.22813i | 0.118629 | + | 0.347059i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.46137 | + | 2.53116i | −0.0548828 | + | 0.0950599i | −0.892162 | − | 0.451716i | \(-0.850812\pi\) |
0.837279 | + | 0.546776i | \(0.184145\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.25307 | + | 6.36809i | −0.197006 | + | 0.238822i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.5817 | + | 47.7729i | 1.03294 | + | 1.78911i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.09141 | + | 7.08652i | −0.153010 | + | 0.265021i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.5564 | + | 35.3851i | −0.917075 | + | 1.32148i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.78527 | − | 15.2165i | −0.327635 | − | 0.567481i | 0.654407 | − | 0.756143i | \(-0.272918\pi\) |
−0.982042 | + | 0.188662i | \(0.939585\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.7949 | − | 40.3584i | −0.513750 | − | 1.50302i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −32.8581 | − | 2.73590i | −1.22201 | − | 0.101749i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.7233 | + | 18.5733i | 0.398253 | + | 0.689795i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.0486 | − | 34.7252i | −0.743561 | − | 1.28789i | −0.950864 | − | 0.309609i | \(-0.899802\pi\) |
0.207303 | − | 0.978277i | \(-0.433531\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.7150 | + | 12.9074i | 0.878332 | + | 0.478052i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.95217 | 0.0722037 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.12469 | −0.263156 | −0.131578 | − | 0.991306i | \(-0.542004\pi\) | ||||
−0.131578 | + | 0.991306i | \(0.542004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −28.1902 | + | 18.2945i | −1.03981 | + | 0.674805i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.8615 | + | 48.2576i | 1.02629 | + | 1.77759i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.13570 | − | 3.69914i | 0.0785631 | − | 0.136075i | −0.824067 | − | 0.566492i | \(-0.808300\pi\) |
0.902630 | + | 0.430417i | \(0.141633\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.22295 | + | 0.185092i | 0.0816621 | + | 0.00679953i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.108257 | + | 0.187507i | −0.00397157 | + | 0.00687896i | −0.868004 | − | 0.496557i | \(-0.834598\pi\) |
0.864033 | + | 0.503436i | \(0.167931\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.5667 | −1.41297 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0883 | + | 32.3651i | 0.442288 | + | 1.18418i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.0251 | + | 12.6254i | −0.402849 | + | 0.461323i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.5840 | −0.860594 | −0.430297 | − | 0.902687i | \(-0.641591\pi\) | ||||
−0.430297 | + | 0.902687i | \(0.641591\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.69230 | + | 0.140908i | 0.0616710 | + | 0.00513499i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −63.7312 | −2.31942 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0176 | −0.800242 | −0.400121 | − | 0.916462i | \(-0.631032\pi\) | ||||
−0.400121 | + | 0.916462i | \(0.631032\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −45.4119 | − | 3.78118i | −1.64835 | − | 0.137248i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.1140 | −0.656631 | −0.328316 | − | 0.944568i | \(-0.606481\pi\) | ||||
−0.328316 | + | 0.944568i | \(0.606481\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.4136 | − | 4.99932i | −0.920035 | − | 0.180988i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.28745 | + | 5.19750i | −0.155013 | + | 0.187916i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.26121 | −0.0455397 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.16710 | − | 5.48558i | 0.114209 | − | 0.197815i | −0.803255 | − | 0.595636i | \(-0.796900\pi\) |
0.917463 | + | 0.397821i | \(0.130233\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.53821 | + | 0.627663i | 0.271482 | + | 0.0226047i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.10740 | − | 5.38218i | 0.111765 | − | 0.193584i | −0.804717 | − | 0.593659i | \(-0.797683\pi\) |
0.916482 | + | 0.400076i | \(0.131016\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.67381 | − | 16.7555i | −0.347494 | − | 0.601876i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.01525 | − | 2.92313i | 0.108171 | − | 0.104867i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.02874 | −0.180173 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −49.5887 | −1.77442 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.2547 | + | 39.9839i | 0.402209 | + | 1.42891i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.7506 | − | 44.6014i | −0.919079 | − | 1.59189i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.65916 | − | 16.7302i | −0.344312 | − | 0.596366i | 0.640917 | − | 0.767611i | \(-0.278554\pi\) |
−0.985229 | + | 0.171245i | \(0.945221\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.5488 | + | 1.79424i | 0.767156 | + | 0.0638766i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.1295 | − | 4.15656i | −0.751279 | − | 0.147790i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.90651 | − | 8.49832i | −0.174235 | − | 0.301784i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 34.5784 | − | 49.8265i | 1.22637 | − | 1.76716i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.09519 | + | 8.82513i | −0.180481 | + | 0.312602i | −0.942044 | − | 0.335488i | \(-0.891099\pi\) |
0.761563 | + | 0.648090i | \(0.224432\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.249172 | − | 0.431579i | −0.00881509 | − | 0.0152682i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.7359 | − | 28.7442i | −0.379335 | − | 1.01563i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.3388 | + | 24.8355i | −0.506004 | + | 0.876424i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.1436 | + | 53.0808i | 0.639478 | + | 1.87085i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.3781 | − | 23.6005i | 0.576538 | − | 0.830776i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.7068 | + | 41.0613i | −0.833485 | + | 1.44364i | 0.0617729 | + | 0.998090i | \(0.480325\pi\) |
−0.895258 | + | 0.445548i | \(0.853009\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.4177 | −1.66506 | −0.832531 | − | 0.553979i | \(-0.813109\pi\) | ||||
−0.832531 | + | 0.553979i | \(0.813109\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.1755 | − | 40.6757i | −0.672514 | − | 1.42656i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.79627 | + | 11.7715i | 0.238063 | + | 0.412337i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.80750 | + | 3.13067i | −0.0632363 | + | 0.109528i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.37513 | + | 2.40241i | 0.222765 | + | 0.0839469i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.8177 | + | 46.4495i | −0.935943 | + | 1.62110i | −0.162998 | + | 0.986626i | \(0.552117\pi\) |
−0.772944 | + | 0.634474i | \(0.781217\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.475192 | − | 0.823057i | −0.0165641 | − | 0.0286899i | 0.857625 | − | 0.514276i | \(-0.171939\pi\) |
−0.874189 | + | 0.485586i | \(0.838606\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.9274 | + | 1.32618i | 0.554522 | + | 0.0461718i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.7813 | −0.722636 | −0.361318 | − | 0.932443i | \(-0.617673\pi\) | ||||
−0.361318 | + | 0.932443i | \(0.617673\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.1615 | − | 21.0644i | 0.422387 | − | 0.731596i | −0.573785 | − | 0.819006i | \(-0.694526\pi\) |
0.996172 | + | 0.0874096i | \(0.0278589\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.38440 | − | 0.281799i | −0.117403 | − | 0.00977551i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.764066 | − | 5.62015i | −0.0264733 | − | 0.194727i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.1754 | − | 26.2846i | 0.525166 | − | 0.909615i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.1532 | − | 36.0707i | −0.350946 | − | 1.24678i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.7367 | + | 27.2567i | 0.543290 | + | 0.941006i | 0.998712 | + | 0.0507305i | \(0.0161550\pi\) |
−0.455422 | + | 0.890276i | \(0.650512\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.4514 | + | 30.2268i | −0.601774 | + | 1.04230i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.9156 | + | 29.5182i | 0.479277 | + | 1.01666i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.9957 | + | 29.4373i | 0.584668 | + | 1.01268i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.710026 | − | 2.07725i | −0.0243968 | − | 0.0713751i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.3450 | − | 36.7928i | −0.595278 | − | 1.26272i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.50499 | − | 6.07082i | −0.120150 | − | 0.208105i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.6959 | − | 46.2386i | −0.914049 | − | 1.58318i | −0.808287 | − | 0.588788i | \(-0.799605\pi\) |
−0.105762 | − | 0.994391i | \(-0.533728\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.36546 | − | 11.6880i | −0.149296 | − | 0.399722i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.6297 | 0.738857 | 0.369428 | − | 0.929259i | \(-0.379554\pi\) | ||||
0.369428 | + | 0.929259i | \(0.379554\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.4288 | 1.17470 | 0.587348 | − | 0.809334i | \(-0.300172\pi\) | ||||
0.587348 | + | 0.809334i | \(0.300172\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.7719 | − | 4.20474i | −0.503425 | − | 0.143297i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.4262 | + | 23.2548i | 0.457033 | + | 0.791604i | 0.998803 | − | 0.0489229i | \(-0.0155789\pi\) |
−0.541770 | + | 0.840527i | \(0.682246\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.5786 | − | 32.1790i | 0.631690 | − | 1.09412i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.0709 | + | 25.6051i | 0.409948 | + | 0.869595i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.73217 | + | 8.19636i | −0.160528 | + | 0.278043i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.9060 | −0.471186 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.03737 | + | 21.5191i | 0.272024 | + | 0.728313i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.49609 | + | 16.0793i | 0.185802 | + | 0.543581i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.4068 | 1.09430 | 0.547150 | − | 0.837034i | \(-0.315713\pi\) | ||||
0.547150 | + | 0.837034i | \(0.315713\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.98260 | + | 2.85687i | −0.0668715 | + | 0.0963599i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.0404 | −1.31530 | −0.657652 | − | 0.753322i | \(-0.728450\pi\) | ||||
−0.657652 | + | 0.753322i | \(0.728450\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.8079 | 0.464672 | 0.232336 | − | 0.972636i | \(-0.425363\pi\) | ||||
0.232336 | + | 0.972636i | \(0.425363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.00808 | + | 6.38084i | 0.101115 | + | 0.214490i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.9555 | −0.804348 | −0.402174 | − | 0.915563i | \(-0.631745\pi\) | ||||
−0.402174 | + | 0.915563i | \(0.631745\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.7530 | − | 31.4590i | −0.360645 | − | 1.05510i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.2616 | + | 10.0978i | 0.980301 | + | 0.338288i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.922824 | 0.0308811 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.4293 | − | 31.9206i | 0.616025 | − | 1.06699i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.48357 | − | 9.34265i | 0.216480 | − | 0.311942i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.8244 | − | 49.9253i | 0.961346 | − | 1.66510i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.11801 | + | 8.86465i | 0.170505 | + | 0.295324i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.92719 | + | 7.68500i | −0.263800 | + | 0.255741i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.2652 | −1.00605 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.70128 | −0.156103 | −0.0780517 | − | 0.996949i | \(-0.524870\pi\) | ||||
−0.0780517 | + | 0.996949i | \(0.524870\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.9058 | − | 1.82881i | −0.361723 | − | 0.0606577i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0884 | − | 36.5262i | −0.698689 | − | 1.21017i | −0.968921 | − | 0.247370i | \(-0.920434\pi\) |
0.270232 | − | 0.962795i | \(-0.412900\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.8048 | + | 34.3029i | 0.655442 | + | 1.13526i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −31.2932 | + | 45.0926i | −1.03452 | + | 1.49071i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.35677 | + | 3.96937i | 0.0448046 | + | 0.131080i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.1071 | + | 34.8265i | 0.663271 | + | 1.14882i | 0.979751 | + | 0.200220i | \(0.0641656\pi\) |
−0.316480 | + | 0.948599i | \(0.602501\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −56.5521 | − | 4.70876i | −1.86345 | − | 0.155159i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.18756 | − | 10.7172i | 0.203666 | − | 0.352760i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.22932 | + | 2.12924i | 0.0404196 | + | 0.0700089i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 47.6956 | + | 7.99812i | 1.56653 | + | 0.262693i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.0712 | − | 26.1040i | 0.494469 | − | 0.856446i | −0.505510 | − | 0.862820i | \(-0.668696\pi\) |
0.999980 | + | 0.00637464i | \(0.00202912\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.72040 | + | 3.97831i | 0.318573 | + | 0.130384i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.4136 | − | 22.0896i | −0.340925 | − | 0.723183i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.86230 | + | 6.68970i | −0.126311 | + | 0.218776i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.1550 | 1.14846 | 0.574231 | − | 0.818693i | \(-0.305301\pi\) | ||||
0.574231 | + | 0.818693i | \(0.305301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.7271 | − | 48.5998i | 1.10064 | − | 1.58600i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.52163 | + | 2.63554i | 0.0496038 | + | 0.0859162i | 0.889761 | − | 0.456426i | \(-0.150871\pi\) |
−0.840157 | + | 0.542343i | \(0.817537\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.8184 | + | 22.2022i | −0.417426 | + | 0.723003i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.05066 | − | 37.9836i | −0.0992378 | − | 1.23561i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.33905 | − | 10.9796i | 0.205991 | − | 0.356788i | −0.744457 | − | 0.667671i | \(-0.767291\pi\) |
0.950448 | + | 0.310883i | \(0.100625\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.57831 | − | 6.19781i | −0.116157 | − | 0.201190i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.56141 | − | 2.24996i | 0.0506323 | − | 0.0729598i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.0052 | 0.745212 | 0.372606 | − | 0.927990i | \(-0.378464\pi\) | ||||
0.372606 | + | 0.927990i | \(0.378464\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.7930 | + | 44.6749i | −0.834643 | + | 1.44564i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.3068 | + | 43.0755i | 0.656425 | + | 1.39243i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.21697 | − | 12.3371i | −0.136173 | − | 0.398387i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.5033 | + | 18.1923i | −0.338817 | + | 0.586849i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.65001 | − | 17.8046i | −0.214293 | − | 0.573746i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.05985 | − | 7.03187i | −0.130691 | − | 0.226364i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.617767 | − | 1.07000i | 0.0198660 | − | 0.0344090i | −0.855921 | − | 0.517106i | \(-0.827009\pi\) |
0.875788 | + | 0.482697i | \(0.160343\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.09847 | + | 0.174728i | 0.0674126 | + | 0.00561306i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.01657 | + | 12.1530i | 0.225172 | + | 0.390010i | 0.956371 | − | 0.292155i | \(-0.0943722\pi\) |
−0.731199 | + | 0.682164i | \(0.761039\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.4429 | + | 4.21821i | 0.687428 | + | 0.135230i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.27400 | + | 3.27677i | −0.0728263 | + | 0.104941i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.1301 | − | 19.2780i | −0.356084 | − | 0.616756i | 0.631218 | − | 0.775605i | \(-0.282555\pi\) |
−0.987303 | + | 0.158849i | \(0.949222\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.5891 | − | 30.4652i | −0.562151 | − | 0.973673i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.6884 | − | 22.6552i | 0.596675 | − | 0.723325i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.7341 | −1.07595 | −0.537976 | − | 0.842960i | \(-0.680811\pi\) | ||||
−0.537976 | + | 0.842960i | \(0.680811\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −51.2921 | −1.63430 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.71079 | + | 0.771611i | 0.0862853 | + | 0.0245607i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.21474 | + | 15.9604i | 0.293012 | + | 0.507511i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.87364 | + | 11.9055i | −0.218348 | + | 0.378191i | −0.954303 | − | 0.298840i | \(-0.903400\pi\) |
0.735955 | + | 0.677031i | \(0.236734\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.5656 | − | 19.5476i | 0.430491 | − | 0.620325i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.20035 | + | 3.81112i | −0.0697559 | + | 0.120821i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.2565 | 1.17993 | 0.589963 | − | 0.807430i | \(-0.299142\pi\) | ||||
0.589963 | + | 0.807430i | \(0.299142\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.29023 | + | 4.58374i | 0.0408212 | + | 0.145023i |
(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 | 1008.2.t.l.193.10 | 22 | ||
3.2 | odd | 2 | 3024.2.t.k.1873.3 | 22 | |||
4.3 | odd | 2 | 504.2.t.c.193.2 | yes | 22 | ||
7.2 | even | 3 | 1008.2.q.l.625.4 | 22 | |||
9.2 | odd | 6 | 3024.2.q.l.2881.9 | 22 | |||
9.7 | even | 3 | 1008.2.q.l.529.4 | 22 | |||
12.11 | even | 2 | 1512.2.t.c.361.3 | 22 | |||
21.2 | odd | 6 | 3024.2.q.l.2305.9 | 22 | |||
28.23 | odd | 6 | 504.2.q.c.121.8 | yes | 22 | ||
36.7 | odd | 6 | 504.2.q.c.25.8 | ✓ | 22 | ||
36.11 | even | 6 | 1512.2.q.d.1369.9 | 22 | |||
63.2 | odd | 6 | 3024.2.t.k.289.3 | 22 | |||
63.16 | even | 3 | inner | 1008.2.t.l.961.10 | 22 | ||
84.23 | even | 6 | 1512.2.q.d.793.9 | 22 | |||
252.79 | odd | 6 | 504.2.t.c.457.2 | yes | 22 | ||
252.191 | even | 6 | 1512.2.t.c.289.3 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.8 | ✓ | 22 | 36.7 | odd | 6 | ||
504.2.q.c.121.8 | yes | 22 | 28.23 | odd | 6 | ||
504.2.t.c.193.2 | yes | 22 | 4.3 | odd | 2 | ||
504.2.t.c.457.2 | yes | 22 | 252.79 | odd | 6 | ||
1008.2.q.l.529.4 | 22 | 9.7 | even | 3 | |||
1008.2.q.l.625.4 | 22 | 7.2 | even | 3 | |||
1008.2.t.l.193.10 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.t.l.961.10 | 22 | 63.16 | even | 3 | inner | ||
1512.2.q.d.793.9 | 22 | 84.23 | even | 6 | |||
1512.2.q.d.1369.9 | 22 | 36.11 | even | 6 | |||
1512.2.t.c.289.3 | 22 | 252.191 | even | 6 | |||
1512.2.t.c.361.3 | 22 | 12.11 | even | 2 | |||
3024.2.q.l.2305.9 | 22 | 21.2 | odd | 6 | |||
3024.2.q.l.2881.9 | 22 | 9.2 | odd | 6 | |||
3024.2.t.k.289.3 | 22 | 63.2 | odd | 6 | |||
3024.2.t.k.1873.3 | 22 | 3.2 | odd | 2 |