Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(529,1008)]
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, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.q (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 | 529.4 | ||
Character | \(\chi\) | \(=\) | 1008.529 |
Dual form | 1008.2.q.l.625.4 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −0.987504 | − | 1.42297i | −0.570136 | − | 0.821550i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.38590 | + | 2.40045i | −0.619793 | + | 1.07351i | 0.369731 | + | 0.929139i | \(0.379450\pi\) |
−0.989523 | + | 0.144373i | \(0.953883\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.74026 | + | 1.99286i | −0.657757 | + | 0.753230i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.04967 | + | 2.81037i | −0.349890 | + | 0.936791i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.71972 | − | 2.97864i | −0.518515 | − | 0.898094i | −0.999769 | − | 0.0215124i | \(-0.993152\pi\) |
0.481254 | − | 0.876581i | \(-0.340181\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.429164 | − | 0.743335i | −0.119029 | − | 0.206164i | 0.800354 | − | 0.599527i | \(-0.204645\pi\) |
−0.919383 | + | 0.393363i | \(0.871311\pi\) | |||||||
\(14\) | 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 | ||||||||
\(21\) | 4.55429 | + | 0.508376i | 0.993827 | + | 0.110937i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.82465 | − | 6.62449i | 0.797495 | − | 1.38130i | −0.123748 | − | 0.992314i | \(-0.539492\pi\) |
0.921243 | − | 0.388988i | \(-0.127175\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.34143 | − | 2.32343i | −0.268286 | − | 0.464685i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.03562 | − | 1.28161i | 0.969106 | − | 0.246646i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.99696 | − | 6.92294i | 0.742217 | − | 1.28556i | −0.209266 | − | 0.977859i | \(-0.567107\pi\) |
0.951484 | − | 0.307700i | \(-0.0995592\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.21156 | 1.29524 | 0.647618 | − | 0.761965i | \(-0.275765\pi\) | ||||
0.647618 | + | 0.761965i | \(0.275765\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.54028 | + | 5.38852i | −0.442205 | + | 0.938021i | ||||
\(34\) | 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 | ||||||||
\(39\) | −0.633939 | + | 1.34473i | −0.101511 | + | 0.215330i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.67577 | + | 2.90251i | 0.261711 | + | 0.453297i | 0.966697 | − | 0.255925i | \(-0.0823800\pi\) |
−0.704986 | + | 0.709221i | \(0.749047\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.20465 | + | 2.08652i | −0.183708 | + | 0.318191i | −0.943140 | − | 0.332395i | \(-0.892143\pi\) |
0.759433 | + | 0.650586i | \(0.225477\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.29141 | − | 6.41457i | −0.788797 | − | 0.956227i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.615039 | 0.0897127 | 0.0448564 | − | 0.998993i | \(-0.485717\pi\) | ||||
0.0448564 | + | 0.998993i | \(0.485717\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.942983 | − | 6.93619i | −0.134712 | − | 0.990885i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.39858 | − | 0.116452i | 0.195840 | − | 0.0163065i | ||||
\(52\) | 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 | ||||||||
\(59\) | −1.46938 | −0.191297 | −0.0956485 | − | 0.995415i | \(-0.530492\pi\) | ||||
−0.0956485 | + | 0.995415i | \(0.530492\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4327 | 1.46381 | 0.731904 | − | 0.681408i | \(-0.238632\pi\) | ||||
0.731904 | + | 0.681408i | \(0.238632\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.77398 | − | 6.98263i | −0.475477 | − | 0.879728i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.37911 | 0.295093 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.2012 | −1.97929 | −0.989647 | − | 0.143522i | \(-0.954157\pi\) | ||||
−0.989647 | + | 0.143522i | \(0.954157\pi\) | |||||||
\(68\) | 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 | ||||||||
\(75\) | −1.98149 | + | 4.20320i | −0.228803 | + | 0.485344i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.92877 | + | 1.75645i | 1.01753 | + | 0.200166i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.75171 | 0.309592 | 0.154796 | − | 0.987946i | \(-0.450528\pi\) | ||||
0.154796 | + | 0.987946i | \(0.450528\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.79639 | − | 5.89993i | −0.755154 | − | 0.655547i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.75814 | − | 9.97340i | 0.632038 | − | 1.09472i | −0.355096 | − | 0.934830i | \(-0.615552\pi\) |
0.987134 | − | 0.159893i | \(-0.0511148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.12294 | − | 1.94500i | −0.121800 | − | 0.210965i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.7981 | + | 1.14889i | −1.47932 | + | 0.123174i | ||||
\(88\) | 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 | ||||||||
\(93\) | −7.12145 | − | 10.2618i | −0.738460 | − | 1.06410i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.15889 | 0.426693 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.82852 | − | 6.63119i | 0.388727 | − | 0.673296i | −0.603551 | − | 0.797324i | \(-0.706248\pi\) |
0.992279 | + | 0.124029i | \(0.0395814\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.1762 | − | 1.70646i | 1.02275 | − | 0.171506i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.84302 | + | 3.19220i | 0.183387 | + | 0.317635i | 0.943032 | − | 0.332703i | \(-0.107961\pi\) |
−0.759645 | + | 0.650338i | \(0.774627\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.06026 | + | 13.9608i | −0.794201 | + | 1.37560i | 0.129145 | + | 0.991626i | \(0.458777\pi\) |
−0.923346 | + | 0.383970i | \(0.874557\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.53211 | + | 10.2278i | −0.735059 | + | 0.998128i | ||||
\(106\) | 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 | 0.991467 | − | 0.130360i | \(-0.0416132\pi\) |
−0.608628 | + | 0.793456i | \(0.708280\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.6012 | + | 18.3617i | 0.988563 | + | 1.71224i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.53953 | − | 0.425856i | 0.234779 | − | 0.0393704i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.693374 | − | 2.02853i | −0.0635615 | − | 0.185955i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.414862 | + | 0.718563i | −0.0377148 | + | 0.0653239i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.47535 | − | 5.25081i | 0.223195 | − | 0.473449i | ||||
\(124\) | 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 | ||||||||
\(129\) | 4.15864 | − | 0.346266i | 0.366148 | − | 0.0304870i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.792752 | − | 1.37309i | 0.0692631 | − | 0.119967i | −0.829314 | − | 0.558783i | \(-0.811269\pi\) |
0.898577 | + | 0.438816i | \(0.144602\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.89511 | + | 0.766240i | 0.337749 | + | 0.0664414i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.90242 | + | 13.8639i | −0.335867 | + | 1.19322i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.46394 | − | 4.26767i | −0.210508 | − | 0.364611i | 0.741365 | − | 0.671102i | \(-0.234179\pi\) |
−0.951874 | + | 0.306490i | \(0.900845\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.12999 | − | 7.15336i | −0.350301 | − | 0.606740i | 0.636001 | − | 0.771688i | \(-0.280588\pi\) |
−0.986302 | + | 0.164949i | \(0.947254\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | −8.93877 | + | 8.19136i | −0.737258 | + | 0.675612i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.95698 | − | 12.0498i | 0.569938 | − | 0.987161i | −0.426634 | − | 0.904425i | \(-0.640301\pi\) |
0.996571 | − | 0.0827368i | \(-0.0263661\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4964 | + | 19.9123i | 0.935561 | + | 1.62044i | 0.773631 | + | 0.633637i | \(0.218439\pi\) |
0.161930 | + | 0.986802i | \(0.448228\pi\) | |||||||
\(152\) | 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 | ||||||||
\(157\) | 18.5804 | 1.48288 | 0.741441 | − | 0.671019i | \(-0.234143\pi\) | ||||
0.741441 | + | 0.671019i | \(0.234143\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.8054 | + | 1.81561i | −1.72928 | + | 0.143987i | ||||
\(160\) | 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 | ||||||||
\(165\) | −9.41430 | − | 13.5657i | −0.732902 | − | 1.05609i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.47493 | + | 9.48286i | 0.423663 | + | 0.733805i | 0.996295 | − | 0.0860073i | \(-0.0274108\pi\) |
−0.572632 | + | 0.819813i | \(0.694077\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.13164 | − | 10.6203i | 0.471664 | − | 0.816947i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.43931 | − | 0.744432i | 0.339482 | − | 0.0569281i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.4054 | −1.01920 | −0.509598 | − | 0.860413i | \(-0.670206\pi\) | ||||
−0.509598 | + | 0.860413i | \(0.670206\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.96470 | + | 1.37008i | 0.526482 | + | 0.103569i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.45102 | + | 2.09088i | 0.109065 | + | 0.157160i | ||||
\(178\) | 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 | ||||||||
\(185\) | −2.54013 | −0.186754 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.78685 | 0.203795 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.20923 | + | 12.2656i | −0.451655 | + | 0.892193i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.6111 | 1.34665 | 0.673325 | − | 0.739347i | \(-0.264866\pi\) | ||||
0.673325 | + | 0.739347i | \(0.264866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.92940 | 0.210863 | 0.105431 | − | 0.994427i | \(-0.466378\pi\) | ||||
0.105431 | + | 0.994427i | \(0.466378\pi\) | |||||||
\(194\) | 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 | ||||||||
\(201\) | 15.9988 | + | 23.0538i | 1.12847 | + | 1.62609i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.84070 | + | 20.0131i | 0.480123 | + | 1.40465i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.28977 | −0.648826 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.6027 | + | 17.7022i | 1.01495 | + | 1.23039i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.58032 | + | 4.46924i | −0.178484 | + | 0.309144i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.3436 | − | 21.3798i | −0.849770 | − | 1.47184i | −0.881414 | − | 0.472345i | \(-0.843408\pi\) |
0.0316443 | − | 0.999499i | \(-0.489926\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.2375 | + | 20.5159i | 0.975539 | + | 1.40573i | ||||
\(214\) | 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 | ||||||||
\(219\) | 14.3918 | − | 1.19832i | 0.972506 | − | 0.0809750i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.695474 | 0.0467826 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.78468 | − | 16.9476i | 0.655231 | − | 1.13489i | −0.326605 | − | 0.945161i | \(-0.605905\pi\) |
0.981836 | − | 0.189732i | \(-0.0607619\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.93775 | − | 1.33109i | 0.529183 | − | 0.0887393i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.32404 | + | 7.48945i | 0.286996 | + | 0.497092i | 0.973091 | − | 0.230420i | \(-0.0740099\pi\) |
−0.686095 | + | 0.727512i | \(0.740677\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.77136 | + | 9.99630i | −0.381382 | + | 0.660574i | −0.991260 | − | 0.131922i | \(-0.957885\pi\) |
0.609878 | + | 0.792496i | \(0.291219\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.31783 | − | 14.4398i | −0.415683 | − | 0.950072i | ||||
\(232\) | 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 | −0.916790 | − | 0.399371i | \(-0.869229\pi\) |
0.112530 | − | 0.993648i | \(-0.464105\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.51814 | + | 16.4859i | 0.613117 | + | 1.06195i | 0.990712 | + | 0.135979i | \(0.0434180\pi\) |
−0.377595 | + | 0.925971i | \(0.623249\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.68394 | + | 15.4972i | −0.108025 | + | 0.994148i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.9568 | + | 7.34928i | 1.14722 | + | 0.469528i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.643931 | + | 1.11532i | −0.0409724 | + | 0.0709662i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.8780 | + | 1.65513i | −1.25972 | + | 0.104889i | ||||
\(250\) | 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 | ||||||||
\(255\) | −1.65875 | + | 3.51861i | −0.103875 | + | 0.220344i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.18362 | + | 3.78215i | −0.136211 | + | 0.235924i | −0.926059 | − | 0.377378i | \(-0.876826\pi\) |
0.789849 | + | 0.613302i | \(0.210159\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.37903 | − | 0.467998i | −0.147826 | − | 0.0290800i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.2606 | + | 18.4998i | 0.944605 | + | 1.14511i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.24212 | − | 10.8117i | −0.384905 | − | 0.666676i | 0.606851 | − | 0.794816i | \(-0.292433\pi\) |
−0.991756 | + | 0.128140i | \(0.959099\pi\) | |||||||
\(264\) | 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 | ||||||||
\(273\) | −1.57665 | − | 3.60354i | −0.0954230 | − | 0.218096i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.61376 | + | 7.99127i | −0.278220 | + | 0.481892i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.980373 | + | 1.69806i | 0.0589049 | + | 0.102026i | 0.893974 | − | 0.448119i | \(-0.147906\pi\) |
−0.835069 | + | 0.550145i | \(0.814572\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.56976 | + | 20.2672i | −0.453190 | + | 1.21336i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.42057 | − | 16.3169i | 0.561984 | − | 0.973385i | −0.435339 | − | 0.900267i | \(-0.643372\pi\) |
0.997323 | − | 0.0731185i | \(-0.0232951\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.4844 | 1.39600 | 0.698002 | − | 0.716095i | \(-0.254072\pi\) | ||||
0.698002 | + | 0.716095i | \(0.254072\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.10692 | − | 5.91796i | −0.243273 | − | 0.350550i | ||||
\(286\) | 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 | ||||||||
\(291\) | −13.2167 | + | 1.10047i | −0.774774 | + | 0.0645109i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.00384 | − | 1.73871i | −0.0586452 | − | 0.101576i | 0.835212 | − | 0.549928i | \(-0.185345\pi\) |
−0.893857 | + | 0.448351i | \(0.852011\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.03641 | − | 3.52717i | 0.118564 | − | 0.205360i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.4773 | − | 12.7953i | −0.724007 | − | 0.742458i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.56561 | −0.379699 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.06173 | − | 6.03179i | −0.118836 | − | 0.347666i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.72240 | − | 5.77486i | 0.156398 | − | 0.331757i | ||||
\(304\) | 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 | ||||||||
\(311\) | 14.0996 | 0.799514 | 0.399757 | − | 0.916621i | \(-0.369094\pi\) | ||||
0.399757 | + | 0.916621i | \(0.369094\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −34.1539 | −1.93049 | −0.965245 | − | 0.261345i | \(-0.915834\pi\) | ||||
−0.965245 | + | 0.261345i | \(0.915834\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 21.9918 | + | 0.617975i | 1.23910 | + | 0.0348189i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.58117 | −0.0888074 | −0.0444037 | − | 0.999014i | \(-0.514139\pi\) | ||||
−0.0444037 | + | 0.999014i | \(0.514139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.4946 | −1.53940 | ||||||||
\(320\) | 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 | ||||||||
\(327\) | −16.8975 | + | 1.40696i | −0.934434 | + | 0.0778049i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.07033 | + | 1.22569i | −0.0590092 | + | 0.0675743i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.7372 | −0.755067 | −0.377533 | − | 0.925996i | \(-0.623228\pi\) | ||||
−0.377533 | + | 0.925996i | \(0.623228\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.71141 | + | 0.454678i | −0.148584 | + | 0.0249162i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.4533 | − | 38.8902i | 1.22675 | − | 2.12480i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.72318 | − | 15.1090i | −0.475182 | − | 0.823039i | 0.524414 | − | 0.851463i | \(-0.324284\pi\) |
−0.999596 | + | 0.0284243i | \(0.990951\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.01144 | − | 12.7517i | 0.326497 | − | 0.692576i | ||||
\(340\) | 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 | ||||||||
\(345\) | 15.6595 | − | 33.2174i | 0.843077 | − | 1.78836i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.83104 | −0.205661 | −0.102830 | − | 0.994699i | \(-0.532790\pi\) | ||||
−0.102830 | + | 0.994699i | \(0.532790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.69984 | − | 2.94421i | 0.0909903 | − | 0.157600i | −0.816938 | − | 0.576726i | \(-0.804330\pi\) |
0.907928 | + | 0.419126i | \(0.137663\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.11377 | − | 3.19313i | −0.166201 | − | 0.170437i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.27841 | − | 10.8745i | −0.334166 | − | 0.578793i | 0.649158 | − | 0.760653i | \(-0.275121\pi\) |
−0.983324 | + | 0.181861i | \(0.941788\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.9815 | − | 34.6089i | 1.06051 | − | 1.83685i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.20182 | + | 2.98983i | −0.116533 | + | 0.158239i | ||||
\(358\) | 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 | ||||||||
\(367\) | −1.01257 | − | 1.75382i | −0.0528557 | − | 0.0915487i | 0.838387 | − | 0.545075i | \(-0.183499\pi\) |
−0.891243 | + | 0.453527i | \(0.850166\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.91615 | + | 1.66285i | −0.516214 | + | 0.0865644i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.8105 | + | 31.6270i | 0.561251 | + | 1.64199i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.8130 | + | 18.7286i | −0.559874 | + | 0.969731i | 0.437632 | + | 0.899154i | \(0.355817\pi\) |
−0.997506 | + | 0.0705766i | \(0.977516\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.34239 | + | 9.13921i | 0.327519 | + | 0.471947i | ||||
\(376\) | 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 | ||||||||
\(381\) | −12.4088 | − | 17.8807i | −0.635722 | − | 0.916058i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.82822 | + | 6.63068i | −0.195613 | + | 0.338812i | −0.947101 | − | 0.320935i | \(-0.896003\pi\) |
0.751488 | + | 0.659747i | \(0.229336\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.5906 | + | 18.9988i | −0.845537 | + | 0.968267i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.59941 | − | 5.57567i | −0.233801 | − | 0.283427i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.5781 | + | 18.3218i | 0.536329 | + | 0.928950i | 0.999098 | + | 0.0424705i | \(0.0135228\pi\) |
−0.462768 | + | 0.886479i | \(0.653144\pi\) | |||||||
\(390\) | 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 | ||||||||
\(399\) | −2.75611 | − | 6.29928i | −0.137978 | − | 0.315359i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.88886 | − | 6.73571i | 0.194201 | − | 0.336365i | −0.752438 | − | 0.658664i | \(-0.771122\pi\) |
0.946638 | + | 0.322298i | \(0.104455\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.09495 | − | 5.36061i | −0.154170 | − | 0.267031i | ||||
\(404\) | 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 | ||||||||
\(409\) | 19.5265 | 0.965526 | 0.482763 | − | 0.875751i | \(-0.339633\pi\) | ||||
0.482763 | + | 0.875751i | \(0.339633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.63960 | + | 7.72044i | −0.179528 | + | 0.380821i | ||||
\(412\) | 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 | ||||||||
\(417\) | −6.10060 | + | 12.9408i | −0.298748 | + | 0.633714i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.5259 | + | 21.6955i | 0.611932 | + | 1.05990i | 0.990915 | + | 0.134493i | \(0.0429406\pi\) |
−0.378983 | + | 0.925404i | \(0.623726\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0746 | − | 31.3061i | 0.880902 | − | 1.52577i | 0.0305620 | − | 0.999533i | \(-0.490270\pi\) |
0.850340 | − | 0.526234i | \(-0.176396\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.645588 | + | 1.72849i | −0.0313896 | + | 0.0840421i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.17383 | 0.105446 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.8959 | + | 22.7838i | −0.962829 | + | 1.10258i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.09567 | − | 0.424287i | 0.246021 | − | 0.0204848i | ||||
\(430\) | 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 | ||||||||
\(437\) | −11.4772 | −0.549031 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.78469 | 0.228361 | 0.114180 | − | 0.993460i | \(-0.463576\pi\) | ||||
0.114180 | + | 0.993460i | \(0.463576\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.4831 | + | 4.63058i | 0.975386 | + | 0.220504i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.26427 | 0.392647 | 0.196324 | − | 0.980539i | \(-0.437100\pi\) | ||||
0.196324 | + | 0.980539i | \(0.437100\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.3497 | 1.34390 | ||||||||
\(446\) | 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 | ||||||||
\(453\) | 16.9818 | − | 36.0224i | 0.797875 | − | 1.69248i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.14028 | + | 4.74124i | −0.194099 | + | 0.222273i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.9644 | −0.840339 | −0.420170 | − | 0.907446i | \(-0.638029\pi\) | ||||
−0.420170 | + | 0.907446i | \(0.638029\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.14077 | + | 4.05277i | −0.0532468 | + | 0.189167i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.03501 | − | 6.98885i | 0.187929 | − | 0.325503i | −0.756630 | − | 0.653843i | \(-0.773156\pi\) |
0.944560 | + | 0.328340i | \(0.106489\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.50704 | + | 4.34232i | 0.116512 | + | 0.201805i | 0.918383 | − | 0.395692i | \(-0.129495\pi\) |
−0.801871 | + | 0.597497i | \(0.796162\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 34.5026 | − | 2.87283i | 1.60002 | − | 0.133224i | ||||
\(466\) | 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 | ||||||||
\(471\) | −18.3483 | − | 26.4394i | −0.845444 | − | 1.21826i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.28665 | 0.381020 | ||||||||
\(474\) | 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 | ||||||||
\(479\) | −12.6222 | − | 21.8623i | −0.576724 | − | 0.998916i | −0.995852 | − | 0.0909886i | \(-0.970997\pi\) |
0.419128 | − | 0.907927i | \(-0.362336\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.393295 | − | 0.681208i | 0.0179327 | − | 0.0310604i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.7863 | − | 28.2255i | 0.945809 | − | 1.28430i | ||||
\(484\) | 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 | 0.963675 | + | 0.267078i | \(0.0860581\pi\) |
−0.250541 | + | 0.968106i | \(0.580609\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.23860 | + | 5.60942i | 0.145859 | + | 0.252635i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.0069 | + | 26.7925i | −0.449779 | + | 1.20423i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.0905 | − | 28.7324i | 1.12546 | − | 1.28883i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.97445 | − | 5.15190i | 0.133155 | − | 0.230631i | −0.791736 | − | 0.610863i | \(-0.790823\pi\) |
0.924891 | + | 0.380232i | \(0.124156\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.08727 | − | 17.1550i | 0.361313 | − | 0.766429i | ||||
\(502\) | 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 | ||||||||
\(507\) | −21.1674 | + | 1.76248i | −0.940075 | + | 0.0782746i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.6443 | + | 32.2928i | −0.826392 | + | 1.43135i | 0.0744581 | + | 0.997224i | \(0.476277\pi\) |
−0.900850 | + | 0.434129i | \(0.857056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.13501 | − | 20.8741i | −0.315634 | − | 0.923418i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.44314 | − | 5.58186i | −0.240320 | − | 0.246445i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.3414 | − | 38.6964i | −0.984480 | − | 1.70517i | ||||
\(516\) | 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 | ||||||||
\(525\) | −4.92809 | − | 11.2635i | −0.215079 | − | 0.491580i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.92164 | + | 5.06043i | −0.127269 | + | 0.220436i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.7559 | − | 30.7541i | −0.771996 | − | 1.33714i | ||||
\(530\) | 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 | ||||||||
\(535\) | 17.5603 | 0.759196 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.9530 | + | 1.91116i | −0.990494 | + | 0.0824727i | ||||
\(538\) | 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 | ||||||||
\(543\) | 10.7825 | + | 15.5373i | 0.462723 | + | 0.666771i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.5673 | + | 23.4993i | 0.581159 | + | 1.00660i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8412 | − | 23.9736i | 0.591805 | − | 1.02504i | −0.402184 | − | 0.915559i | \(-0.631749\pi\) |
0.993989 | − | 0.109478i | \(-0.0349180\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.0006 | + | 32.1301i | −0.512172 | + | 1.37128i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.9943 | −0.510976 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.78870 | + | 5.48378i | −0.203636 | + | 0.233194i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.50839 | + | 3.61453i | 0.106475 | + | 0.153428i | ||||
\(556\) | 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 | ||||||||
\(563\) | −1.91343 | −0.0806414 | −0.0403207 | − | 0.999187i | \(-0.512838\pi\) | ||||
−0.0403207 | + | 0.999187i | \(0.512838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.5604 | −0.949122 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.5852 | − | 3.27684i | 0.990486 | − | 0.137614i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.7628 | −0.618887 | −0.309444 | − | 0.950918i | \(-0.600143\pi\) | ||||
−0.309444 | + | 0.950918i | \(0.600143\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.56417 | −0.107307 | −0.0536535 | − | 0.998560i | \(-0.517087\pi\) | ||||
−0.0536535 | + | 0.998560i | \(0.517087\pi\) | |||||||
\(572\) | 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 | ||||||||
\(579\) | −2.89279 | − | 4.16844i | −0.120220 | − | 0.173234i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.85491 | + | 28.8315i | 0.408851 | + | 1.19613i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −43.4501 | −1.79952 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.49728 | + | 6.68619i | −0.103250 | + | 0.276440i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.7666 | + | 27.3085i | −0.650756 | + | 1.12714i | 0.332183 | + | 0.943215i | \(0.392215\pi\) |
−0.982940 | + | 0.183928i | \(0.941119\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.41022 | − | 9.37078i | −0.222924 | − | 0.386116i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.2738 | + | 26.3320i | 0.751683 | + | 1.08315i | ||||
\(592\) | 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 | ||||||||
\(597\) | 2.74045 | − | 0.228181i | 0.112159 | − | 0.00933883i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.61368 | −0.229369 | −0.114684 | − | 0.993402i | \(-0.536586\pi\) | ||||
−0.114684 | + | 0.993402i | \(0.536586\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.2223 | − | 33.2940i | 0.784094 | − | 1.35809i | −0.145444 | − | 0.989366i | \(-0.546461\pi\) |
0.929539 | − | 0.368725i | \(-0.120205\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.0059 | − | 45.5315i | 0.692535 | − | 1.85418i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.14991 | − | 1.99171i | −0.0467507 | − | 0.0809745i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.17187 | + | 14.1541i | −0.331686 | + | 0.574497i | −0.982843 | − | 0.184446i | \(-0.940951\pi\) |
0.651157 | + | 0.758943i | \(0.274284\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.7228 | − | 29.4971i | 0.880252 | − | 1.19528i | ||||
\(610\) | 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 | 0.885764 | + | 0.464136i | \(0.153635\pi\) |
−0.0409280 | + | 0.999162i | \(0.513031\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.9473 | − | 31.0856i | −0.721361 | − | 1.24943i | −0.960454 | − | 0.278438i | \(-0.910183\pi\) |
0.239093 | − | 0.970997i | \(-0.423150\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.7695 | − | 38.2601i | 0.432164 | − | 1.53533i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.5516 | + | 5.22319i | 1.06377 | + | 0.209263i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6083 | − | 27.0343i | 0.624331 | − | 1.08137i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.90766 | − | 0.741689i | 0.355737 | − | 0.0296202i | ||||
\(628\) | 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 | ||||||||
\(633\) | −18.2333 | + | 38.6772i | −0.724710 | + | 1.53728i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.4149 | + | 30.1636i | −0.691091 | + | 1.19700i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.75122 | + | 3.67772i | −0.188250 | + | 0.145717i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.1338 | − | 40.5191i | 0.598684 | − | 1.60291i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.30132 | + | 12.6463i | 0.288385 | + | 0.499497i | 0.973424 | − | 0.229009i | \(-0.0735485\pi\) |
−0.685040 | + | 0.728506i | \(0.740215\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.96942 | + | 10.3393i | 0.235411 | + | 0.407744i | 0.959392 | − | 0.282076i | \(-0.0910231\pi\) |
−0.723981 | + | 0.689820i | \(0.757690\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | 32.8436 | + | 3.66618i | 1.28724 | + | 0.143689i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.9959 | + | 34.6339i | −0.782501 | + | 1.35533i | 0.147980 | + | 0.988990i | \(0.452723\pi\) |
−0.930481 | + | 0.366340i | \(0.880611\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.19735 | + | 3.80592i | 0.0858575 | + | 0.148710i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.9171 | − | 19.2957i | −0.620986 | − | 0.752796i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.60101 | + | 2.77303i | −0.0623665 | + | 0.108022i | −0.895523 | − | 0.445016i | \(-0.853198\pi\) |
0.833156 | + | 0.553038i | \(0.186531\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.3030 | −1.68429 | −0.842146 | − | 0.539250i | \(-0.818708\pi\) | ||||
−0.842146 | + | 0.539250i | \(0.818708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.686783 | − | 0.989636i | −0.0266725 | − | 0.0384343i | ||||
\(664\) | 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 | ||||||||
\(669\) | −33.7782 | + | 2.81252i | −1.30594 | + | 0.108738i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.6610 | − | 34.0539i | −0.759006 | − | 1.31464i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2936 | − | 21.2931i | 0.473883 | − | 0.820790i | −0.525670 | − | 0.850689i | \(-0.676185\pi\) |
0.999553 | + | 0.0298991i | \(0.00951859\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.73266 | − | 9.98070i | −0.374610 | − | 0.384157i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.4188 | −1.47655 | −0.738276 | − | 0.674498i | \(-0.764360\pi\) | ||||
−0.738276 | + | 0.674498i | \(0.764360\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.55242 | + | 19.1697i | 0.251459 | + | 0.735666i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.38724 | − | 13.5488i | 0.244759 | − | 0.519192i | ||||
\(682\) | 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 | ||||||||
\(689\) | −10.8432 | −0.413093 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.30292 | 0.277816 | 0.138908 | − | 0.990305i | \(-0.455641\pi\) | ||||
0.138908 | + | 0.990305i | \(0.455641\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.3085 | + | 23.2495i | −0.543537 | + | 0.883175i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.8950 | 0.868457 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.71563 | −0.102862 | ||||||||
\(698\) | 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 | ||||||||
\(705\) | 2.94256 | − | 0.245010i | 0.110823 | − | 0.00922760i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.56893 | − | 1.88238i | −0.359877 | − | 0.0707943i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.92274 | 0.109766 | 0.0548828 | − | 0.998493i | \(-0.482521\pi\) | ||||
0.0548828 | + | 0.998493i | \(0.482521\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.88839 | + | 7.73334i | −0.108323 | + | 0.290023i | ||||
\(712\) | 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 | ||||||||
\(717\) | −18.3662 | + | 38.9590i | −0.685898 | + | 1.45495i | ||||
\(718\) | 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 | ||||||||
\(723\) | 14.0597 | − | 29.8239i | 0.522885 | − | 1.10916i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.4466 | −0.796506 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.0486 | + | 34.7252i | −0.743561 | + | 1.28789i | 0.207303 | + | 0.978277i | \(0.433531\pi\) |
−0.950864 | + | 0.309609i | \(0.899802\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.7150 | − | 12.9074i | 0.878332 | − | 0.478052i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.976087 | − | 1.69063i | −0.0361019 | − | 0.0625303i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.56234 | − | 6.17016i | 0.131578 | − | 0.227900i | −0.792707 | − | 0.609603i | \(-0.791329\pi\) |
0.924285 | + | 0.381703i | \(0.124662\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.27468 | − | 32.8094i | −0.268331 | − | 1.21019i | ||||
\(736\) | 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 | 0.864033 | − | 0.503436i | \(-0.167931\pi\) |
−0.868004 | + | 0.496557i | \(0.834598\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.2833 | + | 33.3997i | 0.706487 | + | 1.22367i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.9848 | + | 26.6513i | 0.804382 | + | 0.975120i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.4465 | + | 3.23533i | 0.600942 | + | 0.118216i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.7920 | − | 20.4244i | 0.430297 | − | 0.745296i | −0.566602 | − | 0.823992i | \(-0.691742\pi\) |
0.996899 | + | 0.0786955i | \(0.0250755\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.968182 | − | 1.39512i | −0.0352825 | − | 0.0508412i | ||||
\(754\) | 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 | ||||||||
\(759\) | 25.9805 | + | 37.4372i | 0.943034 | + | 1.35889i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.05699 | − | 15.6872i | 0.328316 | − | 0.568659i | −0.653862 | − | 0.756614i | \(-0.726852\pi\) |
0.982178 | + | 0.187954i | \(0.0601857\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.37727 | + | 24.5085i | 0.303277 | + | 0.887267i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.64489 | − | 1.11429i | 0.240246 | − | 0.0402872i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.630606 | + | 1.09224i | 0.0227699 | + | 0.0394385i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.16710 | + | 5.48558i | 0.114209 | + | 0.197815i | 0.917463 | − | 0.397821i | \(-0.130233\pi\) |
−0.803255 | + | 0.595636i | \(0.796900\pi\) | |||||||
\(770\) | 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 | ||||||||
\(777\) | 1.68336 | + | 3.84743i | 0.0603900 | + | 0.138026i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.51437 | − | 4.35502i | 0.0900867 | − | 0.156035i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.7944 | + | 42.9451i | 0.887212 | + | 1.53670i | ||||
\(782\) | 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 | ||||||||
\(787\) | 19.3183 | 0.688624 | 0.344312 | − | 0.938855i | \(-0.388112\pi\) | ||||
0.344312 | + | 0.938855i | \(0.388112\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.22052 | + | 19.5589i | −0.328259 | + | 0.696315i | ||||
\(790\) | 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 | ||||||||
\(795\) | 25.8618 | − | 54.8590i | 0.917224 | − | 1.94565i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.09519 | − | 8.82513i | −0.180481 | − | 0.312602i | 0.761563 | − | 0.648090i | \(-0.224432\pi\) |
−0.942044 | + | 0.335488i | \(0.891099\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.249172 | + | 0.431579i | −0.00881509 | + | 0.0152682i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 30.2612 | − | 5.07453i | 1.06923 | − | 0.179300i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.6775 | 1.01201 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −55.0412 | − | 10.8276i | −1.93995 | − | 0.381623i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.6277 | + | 2.38366i | −1.00774 | + | 0.0839088i | ||||
\(808\) | 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 | ||||||||
\(815\) | −13.5925 | −0.476126 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.61499 | 0.126473 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.57077 | + | 5.80202i | −0.124773 | + | 0.202739i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 53.6353 | 1.87189 | 0.935943 | − | 0.352152i | \(-0.114550\pi\) | ||||
0.935943 | + | 0.352152i | \(0.114550\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.950384 | 0.0331283 | 0.0165641 | − | 0.999863i | \(-0.494727\pi\) | ||||
0.0165641 | + | 0.999863i | \(0.494727\pi\) | |||||||
\(824\) | 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 | ||||||||
\(831\) | 1.44815 | − | 3.07187i | 0.0502359 | − | 0.106562i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.24923 | + | 2.14838i | 0.181875 | + | 0.0744368i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.3508 | −1.05033 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.3147 | − | 9.24241i | 1.25522 | − | 0.319464i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.7367 | − | 27.2567i | 0.543290 | − | 0.941006i | −0.455422 | − | 0.890276i | \(-0.650512\pi\) |
0.998712 | − | 0.0507305i | \(-0.0161550\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.4514 | − | 30.2268i | −0.601774 | − | 1.04230i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.5213 | + | 2.70786i | −1.12009 | + | 0.0932636i | ||||
\(844\) | 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 | ||||||||
\(849\) | −23.1910 | − | 33.4176i | −0.795913 | − | 1.14689i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.00998 | 0.240299 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.6959 | + | 46.2386i | −0.914049 | + | 1.58318i | −0.105762 | + | 0.994391i | \(0.533728\pi\) |
−0.808287 | + | 0.588788i | \(0.799605\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.36546 | + | 11.6880i | −0.149296 | + | 0.399722i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.8149 | − | 18.7319i | −0.369428 | − | 0.639869i | 0.620048 | − | 0.784564i | \(-0.287113\pi\) |
−0.989476 | + | 0.144695i | \(0.953780\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.2144 | + | 29.8162i | −0.587348 | + | 1.01732i | 0.407230 | + | 0.913326i | \(0.366495\pi\) |
−0.994578 | + | 0.103991i | \(0.966839\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.15636 | + | 14.0708i | 0.209808 | + | 0.479532i | ||||
\(862\) | 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 | ||||||||
\(871\) | 6.95299 | + | 12.0429i | 0.235593 | + | 0.408059i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.6174 | + | 17.7201i | 0.494725 | + | 0.599736i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.1771 | − | 12.7994i | 0.377854 | − | 0.432700i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.2034 | + | 28.0651i | −0.547150 | + | 0.947692i | 0.451318 | + | 0.892363i | \(0.350954\pi\) |
−0.998468 | + | 0.0553291i | \(0.982379\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.48282 | + | 3.14542i | −0.0500144 | + | 0.106092i | ||||
\(880\) | 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 | ||||||||
\(885\) | −7.03001 | + | 0.585348i | −0.236311 | + | 0.0196763i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.9778 | − | 20.7461i | 0.402174 | − | 0.696586i | −0.591814 | − | 0.806074i | \(-0.701588\pi\) |
0.993988 | + | 0.109489i | \(0.0349214\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.8678 | + | 25.0419i | −0.733422 | + | 0.839879i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.88588 | + | 30.3902i | −0.197185 | + | 1.01811i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.461412 | − | 0.799189i | −0.0154406 | − | 0.0267438i | ||||
\(894\) | 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 | ||||||||
\(903\) | −6.54707 | + | 8.89019i | −0.217873 | + | 0.295847i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.1326 | − | 26.2104i | 0.503025 | − | 0.871264i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.35064 | + | 4.07143i | 0.0780517 | + | 0.135190i | 0.902409 | − | 0.430880i | \(-0.141797\pi\) |
−0.824358 | + | 0.566069i | \(0.808463\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.9058 | + | 1.82881i | −0.361723 | + | 0.0606577i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0884 | + | 36.5262i | −0.698689 | + | 1.21017i | 0.270232 | + | 0.962795i | \(0.412900\pi\) |
−0.968921 | + | 0.247370i | \(0.920434\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.6095 | −1.31088 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 54.6979 | − | 4.55438i | 1.80826 | − | 0.150563i | ||||
\(916\) | 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 | ||||||||
\(921\) | 32.3539 | + | 46.6211i | 1.06610 | + | 1.53622i | ||||
\(922\) | 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 | ||||||||
\(927\) | −30.7744 | − | 37.3065i | −1.01076 | − | 1.22531i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.1424 | −0.988938 | −0.494469 | − | 0.869195i | \(-0.664638\pi\) | ||||
−0.494469 | + | 0.869195i | \(0.664638\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.30552 | + | 6.42896i | −0.272203 | + | 0.210701i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.9234 | − | 20.0632i | −0.455832 | − | 0.656841i | ||||
\(934\) | 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 | ||||||||
\(941\) | −3.04326 | −0.0992075 | −0.0496038 | − | 0.998769i | \(-0.515796\pi\) | ||||
−0.0496038 | + | 0.998769i | \(0.515796\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.6369 | 0.834852 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −20.8376 | − | 31.9038i | −0.677848 | − | 1.03783i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.6781 | −0.411983 | −0.205991 | − | 0.978554i | \(-0.566042\pi\) | ||||
−0.205991 | + | 0.978554i | \(0.566042\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.15662 | 0.232314 | ||||||||
\(950\) | 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 | ||||||||
\(957\) | 27.1510 | + | 39.1239i | 0.877669 | + | 1.26470i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.7928 | + | 2.51657i | 0.413100 | + | 0.0812642i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.0067 | 0.677634 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.7443 | − | 3.14325i | 0.604026 | − | 0.101290i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.05985 | + | 7.03187i | −0.130691 | + | 0.226364i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.617767 | + | 1.07000i | 0.0198660 | + | 0.0344090i | 0.875788 | − | 0.482697i | \(-0.160343\pi\) |
−0.855921 | + | 0.517106i | \(0.827009\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.20055 | − | 1.72997i | −0.0385674 | − | 0.0555745i | ||||
\(970\) | 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 | ||||||||
\(975\) | 3.97477 | − | 0.330956i | 0.127295 | − | 0.0105991i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.2603 | 0.712169 | 0.356084 | − | 0.934454i | \(-0.384112\pi\) | ||||
0.356084 | + | 0.934454i | \(0.384112\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | 16.8671 | + | 29.2146i | 0.537976 | + | 0.931801i | 0.999013 | + | 0.0444206i | \(0.0141442\pi\) |
−0.461037 | + | 0.887381i | \(0.652522\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.6461 | − | 44.4203i | 0.817152 | − | 1.41535i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.80107 | + | 0.312671i | 0.0891590 | + | 0.00995243i | ||||
\(988\) | 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 | ||||||||
\(997\) | −18.6283 | − | 32.2651i | −0.589963 | − | 1.02185i | −0.994237 | − | 0.107208i | \(-0.965809\pi\) |
0.404273 | − | 0.914638i | \(-0.367524\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.32452 | + | 3.40924i | 0.105183 | + | 0.107864i |
(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.q.l.529.4 | 22 | ||
3.2 | odd | 2 | 3024.2.q.l.2881.9 | 22 | |||
4.3 | odd | 2 | 504.2.q.c.25.8 | ✓ | 22 | ||
7.2 | even | 3 | 1008.2.t.l.961.10 | 22 | |||
9.4 | even | 3 | 1008.2.t.l.193.10 | 22 | |||
9.5 | odd | 6 | 3024.2.t.k.1873.3 | 22 | |||
12.11 | even | 2 | 1512.2.q.d.1369.9 | 22 | |||
21.2 | odd | 6 | 3024.2.t.k.289.3 | 22 | |||
28.23 | odd | 6 | 504.2.t.c.457.2 | yes | 22 | ||
36.23 | even | 6 | 1512.2.t.c.361.3 | 22 | |||
36.31 | odd | 6 | 504.2.t.c.193.2 | yes | 22 | ||
63.23 | odd | 6 | 3024.2.q.l.2305.9 | 22 | |||
63.58 | even | 3 | inner | 1008.2.q.l.625.4 | 22 | ||
84.23 | even | 6 | 1512.2.t.c.289.3 | 22 | |||
252.23 | even | 6 | 1512.2.q.d.793.9 | 22 | |||
252.247 | odd | 6 | 504.2.q.c.121.8 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.8 | ✓ | 22 | 4.3 | odd | 2 | ||
504.2.q.c.121.8 | yes | 22 | 252.247 | odd | 6 | ||
504.2.t.c.193.2 | yes | 22 | 36.31 | odd | 6 | ||
504.2.t.c.457.2 | yes | 22 | 28.23 | odd | 6 | ||
1008.2.q.l.529.4 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.q.l.625.4 | 22 | 63.58 | even | 3 | inner | ||
1008.2.t.l.193.10 | 22 | 9.4 | even | 3 | |||
1008.2.t.l.961.10 | 22 | 7.2 | even | 3 | |||
1512.2.q.d.793.9 | 22 | 252.23 | even | 6 | |||
1512.2.q.d.1369.9 | 22 | 12.11 | even | 2 | |||
1512.2.t.c.289.3 | 22 | 84.23 | even | 6 | |||
1512.2.t.c.361.3 | 22 | 36.23 | even | 6 | |||
3024.2.q.l.2305.9 | 22 | 63.23 | odd | 6 | |||
3024.2.q.l.2881.9 | 22 | 3.2 | odd | 2 | |||
3024.2.t.k.289.3 | 22 | 21.2 | odd | 6 | |||
3024.2.t.k.1873.3 | 22 | 9.5 | odd | 6 |