Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1040,2,Mod(641,1040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1040, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1040.641");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1040 = 2^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1040.da (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.30444181021\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 641.2 | ||
Root | \(-1.27597 - 0.609843i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1040.641 |
Dual form | 1040.2.da.b.881.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(417\) | \(561\) | \(911\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.800098 | + | 1.38581i | −0.461937 | + | 0.800098i | −0.999057 | − | 0.0434075i | \(-0.986179\pi\) |
0.537121 | + | 0.843505i | \(0.319512\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.287734 | − | 0.166123i | 0.108753 | − | 0.0627887i | −0.444637 | − | 0.895711i | \(-0.646667\pi\) |
0.553390 | + | 0.832922i | \(0.313334\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.219687 | + | 0.380509i | 0.0732290 | + | 0.126836i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.65213 | − | 2.68591i | −1.40267 | − | 0.809832i | −0.408004 | − | 0.912980i | \(-0.633775\pi\) |
−0.994666 | + | 0.103149i | \(0.967108\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.55193 | + | 0.619491i | −0.985129 | + | 0.171816i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.38581 | − | 0.800098i | −0.357815 | − | 0.206584i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.53215 | − | 4.38581i | −0.614136 | − | 1.06372i | −0.990535 | − | 0.137258i | \(-0.956171\pi\) |
0.376399 | − | 0.926458i | \(-0.377162\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.96410 | − | 1.13397i | 0.450596 | − | 0.260152i | −0.257486 | − | 0.966282i | \(-0.582894\pi\) |
0.708082 | + | 0.706130i | \(0.249561\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.531659i | 0.116018i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.41959 | − | 2.45880i | 0.296005 | − | 0.512695i | −0.679213 | − | 0.733941i | \(-0.737679\pi\) |
0.975218 | + | 0.221246i | \(0.0710122\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.50367 | −1.05918 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.45174 | − | 2.51448i | 0.269581 | − | 0.466928i | −0.699173 | − | 0.714953i | \(-0.746448\pi\) |
0.968754 | + | 0.248025i | \(0.0797815\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46410i | 0.981382i | 0.871334 | + | 0.490691i | \(0.163256\pi\) | ||||
−0.871334 | + | 0.490691i | \(0.836744\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.44432 | − | 4.29798i | 1.29589 | − | 0.748182i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.166123 | + | 0.287734i | 0.0280800 | + | 0.0486359i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.17191 | − | 2.98601i | −0.850257 | − | 0.490896i | 0.0104803 | − | 0.999945i | \(-0.496664\pi\) |
−0.860738 | + | 0.509049i | \(0.829997\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.98340 | − | 5.41796i | 0.317598 | − | 0.867568i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.23205 | + | 1.86603i | 0.504762 | + | 0.291424i | 0.730678 | − | 0.682723i | \(-0.239204\pi\) |
−0.225916 | + | 0.974147i | \(0.572538\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.53215 | + | 4.38581i | 0.386149 | + | 0.668830i | 0.991928 | − | 0.126803i | \(-0.0404717\pi\) |
−0.605779 | + | 0.795633i | \(0.707138\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.380509 | + | 0.219687i | −0.0567229 | + | 0.0327490i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.34285i | − | 1.21693i | −0.793581 | − | 0.608465i | \(-0.791786\pi\) | ||
0.793581 | − | 0.608465i | \(-0.208214\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.44481 | + | 5.96658i | −0.492115 | + | 0.852368i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.10387 | 1.13477 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.56063 | −0.214369 | −0.107184 | − | 0.994239i | \(-0.534183\pi\) | ||||
−0.107184 | + | 0.994239i | \(0.534183\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.68591 | − | 4.65213i | 0.362168 | − | 0.627293i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.62916i | 0.480694i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.34461 | + | 1.35366i | −0.305242 | + | 0.176232i | −0.644795 | − | 0.764355i | \(-0.723057\pi\) |
0.339553 | + | 0.940587i | \(0.389724\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.05193 | − | 12.2143i | −0.902908 | − | 1.56388i | −0.823702 | − | 0.567023i | \(-0.808095\pi\) |
−0.0792059 | − | 0.996858i | \(-0.525238\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.126423 | + | 0.0729902i | 0.0159278 | + | 0.00919590i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.619491 | − | 3.55193i | −0.0768384 | − | 0.440563i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.94799 | − | 5.16612i | −1.09317 | − | 0.631142i | −0.158752 | − | 0.987319i | \(-0.550747\pi\) |
−0.934419 | + | 0.356176i | \(0.884080\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.27162 | + | 3.93456i | 0.273471 | + | 0.473666i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.0828 | − | 6.39866i | 1.31529 | − | 0.759382i | 0.332321 | − | 0.943166i | \(-0.392168\pi\) |
0.982967 | + | 0.183785i | \(0.0588349\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.68922i | − | 1.13404i | −0.823705 | − | 0.567019i | \(-0.808097\pi\) | ||
0.823705 | − | 0.567019i | \(-0.191903\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.800098 | − | 1.38581i | 0.0923873 | − | 0.160020i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.78477 | −0.203393 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.51851 | −0.508372 | −0.254186 | − | 0.967155i | \(-0.581808\pi\) | ||||
−0.254186 | + | 0.967155i | \(0.581808\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.74441 | − | 6.48552i | 0.416046 | − | 0.720613i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.26371i | − | 0.468003i | −0.972236 | − | 0.234001i | \(-0.924818\pi\) | ||
0.972236 | − | 0.234001i | \(-0.0751821\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.38581 | − | 2.53215i | 0.475708 | − | 0.274650i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.32306 | + | 4.02367i | 0.249059 | + | 0.431382i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.79366 | − | 1.61292i | −0.296127 | − | 0.170969i | 0.344575 | − | 0.938759i | \(-0.388023\pi\) |
−0.640702 | + | 0.767790i | \(0.721356\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.919100 | + | 0.768307i | −0.0963478 | + | 0.0805405i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.57221 | − | 4.37182i | −0.785201 | − | 0.453336i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.13397 | + | 1.96410i | 0.116343 | + | 0.201513i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.17191 | − | 1.25396i | 0.220524 | − | 0.127320i | −0.385669 | − | 0.922637i | \(-0.626029\pi\) |
0.606193 | + | 0.795318i | \(0.292696\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.36023i | − | 0.237213i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.22336 | − | 10.7792i | 0.619247 | − | 1.07257i | −0.370376 | − | 0.928882i | \(-0.620771\pi\) |
0.989623 | − | 0.143686i | \(-0.0458955\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0247 | −1.48043 | −0.740215 | − | 0.672370i | \(-0.765276\pi\) | ||||
−0.740215 | + | 0.672370i | \(0.765276\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.531659 | −0.0518846 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.53215 | + | 11.3140i | −0.631487 | + | 1.09377i | 0.355761 | + | 0.934577i | \(0.384222\pi\) |
−0.987248 | + | 0.159190i | \(0.949112\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.2325i | 1.07587i | 0.842985 | + | 0.537937i | \(0.180796\pi\) | ||||
−0.842985 | + | 0.537937i | \(0.819204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.27607 | − | 4.77819i | 0.785530 | − | 0.453526i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.17191 | + | 15.8862i | 0.862821 | + | 1.49445i | 0.869195 | + | 0.494470i | \(0.164638\pi\) |
−0.00637349 | + | 0.999980i | \(0.502029\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.45880 | + | 1.41959i | 0.229284 | + | 0.132377i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.01603 | − | 1.21545i | −0.0939325 | − | 0.112368i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.45717 | − | 0.841298i | −0.133579 | − | 0.0771216i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.92820 | + | 15.4641i | 0.811655 | + | 1.40583i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.17191 | + | 2.98601i | −0.466336 | + | 0.269239i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.61998 | + | 2.80589i | −0.143750 | + | 0.248982i | −0.928906 | − | 0.370316i | \(-0.879249\pi\) |
0.785156 | + | 0.619298i | \(0.212583\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.10387 | −0.713506 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.175664 | −0.0153478 | −0.00767390 | − | 0.999971i | \(-0.502443\pi\) | ||||
−0.00767390 | + | 0.999971i | \(0.502443\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.376759 | − | 0.652566i | 0.0326692 | − | 0.0565846i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 5.50367i | − | 0.473681i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.5736 | + | 8.99144i | −1.33054 | + | 0.768190i | −0.985383 | − | 0.170353i | \(-0.945509\pi\) |
−0.345162 | + | 0.938543i | \(0.612176\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.99307 | + | 10.3803i | 0.508325 | + | 0.880445i | 0.999954 | + | 0.00964021i | \(0.00306862\pi\) |
−0.491628 | + | 0.870805i | \(0.663598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.5616 | + | 6.67510i | 0.973663 | + | 0.562144i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.1879 | + | 6.65821i | 1.52095 | + | 0.556788i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.51448 | + | 1.45174i | 0.208816 | + | 0.120560i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.51236 | − | 9.54769i | −0.454652 | − | 0.787481i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.95350 | − | 1.70520i | 0.241960 | − | 0.139696i | −0.374117 | − | 0.927381i | \(-0.622054\pi\) |
0.616077 | + | 0.787686i | \(0.288721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.96141i | − | 0.647890i | −0.946076 | − | 0.323945i | \(-0.894991\pi\) | ||
0.946076 | − | 0.323945i | \(-0.105009\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.11256 | − | 1.92701i | 0.0899451 | − | 0.155790i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.46410 | −0.438887 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.4329 | −1.31148 | −0.655742 | − | 0.754985i | \(-0.727644\pi\) | ||||
−0.655742 | + | 0.754985i | \(0.727644\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.24865 | − | 2.16273i | 0.0990247 | − | 0.171516i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 0.943307i | − | 0.0743430i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.4215 | + | 8.90361i | −1.20791 | + | 0.697384i | −0.962301 | − | 0.271986i | \(-0.912320\pi\) |
−0.245604 | + | 0.969370i | \(0.578986\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.29798 | + | 7.44432i | 0.334597 | + | 0.579539i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.45047 | − | 3.14683i | −0.421770 | − | 0.243509i | 0.274064 | − | 0.961711i | \(-0.411632\pi\) |
−0.695834 | + | 0.718202i | \(0.744965\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.2325 | − | 4.40078i | 0.940959 | − | 0.338522i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.862975 | + | 0.498239i | 0.0659933 | + | 0.0381013i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.98756 | + | 13.8349i | 0.607283 | + | 1.05184i | 0.991686 | + | 0.128679i | \(0.0410738\pi\) |
−0.384404 | + | 0.923165i | \(0.625593\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.287734 | + | 0.166123i | −0.0217506 | + | 0.0125577i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 4.33225i | − | 0.325632i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.8087 | + | 20.4533i | −0.882625 | + | 1.52875i | −0.0342123 | + | 0.999415i | \(0.510892\pi\) |
−0.848412 | + | 0.529336i | \(0.822441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.62590 | 0.195182 | 0.0975909 | − | 0.995227i | \(-0.468886\pi\) | ||||
0.0975909 | + | 0.995227i | \(0.468886\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.5689 | 1.66834 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.98601 | − | 5.17191i | 0.219536 | − | 0.380247i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.2045i | 1.98939i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.58359 | + | 0.914288i | −0.115189 | + | 0.0665046i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.00791 | − | 1.74575i | −0.0729298 | − | 0.126318i | 0.827254 | − | 0.561828i | \(-0.189902\pi\) |
−0.900184 | + | 0.435509i | \(0.856568\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.7636 | − | 11.4105i | −1.42262 | − | 0.821348i | −0.426095 | − | 0.904678i | \(-0.640111\pi\) |
−0.996522 | + | 0.0833298i | \(0.973445\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.41796 | + | 1.98340i | 0.387988 | + | 0.142034i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.556877 | − | 0.321513i | −0.0396758 | − | 0.0229068i | 0.480031 | − | 0.877252i | \(-0.340625\pi\) |
−0.519707 | + | 0.854345i | \(0.673959\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.53342 | − | 2.65596i | −0.108701 | − | 0.188276i | 0.806543 | − | 0.591175i | \(-0.201336\pi\) |
−0.915244 | + | 0.402899i | \(0.868003\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.3185 | − | 8.26681i | 1.00995 | − | 0.583096i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 0.964670i | − | 0.0677065i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.86603 | + | 3.23205i | −0.130329 | + | 0.225736i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.24746 | 0.0867045 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.1830 | −0.842716 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.10020 | + | 7.10175i | −0.282269 | + | 0.488904i | −0.971943 | − | 0.235215i | \(-0.924420\pi\) |
0.689674 | + | 0.724120i | \(0.257754\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.4782i | 1.40314i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.38581 | + | 2.53215i | −0.299110 | + | 0.172691i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.907714 | + | 1.57221i | 0.0616197 | + | 0.106728i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.4274 | + | 7.75232i | 0.907341 | + | 0.523854i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.7110 | + | 14.0095i | 0.787767 | + | 0.942378i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.87174 | − | 5.12210i | −0.594095 | − | 0.343001i | 0.172620 | − | 0.984989i | \(-0.444777\pi\) |
−0.766715 | + | 0.641987i | \(0.778110\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.219687 | − | 0.380509i | −0.0146458 | − | 0.0253673i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.10012 | − | 3.52190i | 0.404879 | − | 0.233757i | −0.283708 | − | 0.958911i | \(-0.591565\pi\) |
0.688587 | + | 0.725154i | \(0.258231\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.32899i | 0.0878219i | 0.999035 | + | 0.0439109i | \(0.0139818\pi\) | ||||
−0.999035 | + | 0.0439109i | \(0.986018\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.42799 | − | 2.47335i | 0.0939547 | − | 0.162734i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.24746 | 0.0817238 | 0.0408619 | − | 0.999165i | \(-0.486990\pi\) | ||||
0.0408619 | + | 0.999165i | \(0.486990\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.34285 | 0.544227 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.61525 | − | 6.26180i | 0.234836 | − | 0.406748i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.94207i | − | 0.643099i | −0.946893 | − | 0.321549i | \(-0.895796\pi\) | ||
0.946893 | − | 0.321549i | \(-0.104204\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.5608 | + | 11.2934i | −1.26002 | + | 0.727475i | −0.973079 | − | 0.230472i | \(-0.925973\pi\) |
−0.286944 | + | 0.957947i | \(0.592640\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.26371 | − | 3.92086i | −0.145217 | − | 0.251523i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.96658 | − | 3.44481i | −0.381191 | − | 0.220081i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.27387 | + | 5.24455i | −0.399197 | + | 0.333702i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.90869 | + | 3.41139i | 0.374448 | + | 0.216188i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.38418 | + | 5.86157i | 0.213608 | + | 0.369979i | 0.952841 | − | 0.303470i | \(-0.0981453\pi\) |
−0.739233 | + | 0.673449i | \(0.764812\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.2082 | + | 7.62577i | −0.830394 | + | 0.479428i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.10387i | 0.507484i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.12691 | + | 8.88007i | −0.319808 | + | 0.553924i | −0.980448 | − | 0.196779i | \(-0.936952\pi\) |
0.660640 | + | 0.750703i | \(0.270285\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.98418 | −0.123291 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.27571 | 0.0789645 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.32850 | − | 16.1574i | 0.575220 | − | 0.996310i | −0.420798 | − | 0.907154i | \(-0.638250\pi\) |
0.996018 | − | 0.0891555i | \(-0.0284168\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.56063i | − | 0.0958685i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.47040 | − | 2.58098i | 0.273584 | − | 0.157954i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.97894 | − | 15.5520i | −0.547456 | − | 0.948221i | −0.998448 | − | 0.0556934i | \(-0.982263\pi\) |
0.450992 | − | 0.892528i | \(-0.351070\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.7582 | + | 15.4488i | 1.62544 | + | 0.938450i | 0.985429 | + | 0.170086i | \(0.0544047\pi\) |
0.640014 | + | 0.768363i | \(0.278929\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.329358 | − | 1.88842i | −0.0199337 | − | 0.114292i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.65213 | + | 2.68591i | 0.280534 | + | 0.161966i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.2522 | + | 22.9536i | 0.796250 | + | 1.37915i | 0.922042 | + | 0.387089i | \(0.126519\pi\) |
−0.125792 | + | 0.992057i | \(0.540147\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.07914 | + | 1.20039i | −0.124475 | + | 0.0718656i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.97766i | 0.296942i | 0.988917 | + | 0.148471i | \(0.0474352\pi\) | ||||
−0.988917 | + | 0.148471i | \(0.952565\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.29317 | − | 10.9001i | 0.374090 | − | 0.647943i | −0.616100 | − | 0.787668i | \(-0.711288\pi\) |
0.990190 | + | 0.139725i | \(0.0446218\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.62916 | −0.214973 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.23996 | 0.0731926 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.32355 | + | 7.48861i | −0.254327 | + | 0.440507i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.01315i | 0.235255i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.6511 | − | 8.45880i | 0.855925 | − | 0.494168i | −0.00672072 | − | 0.999977i | \(-0.502139\pi\) |
0.862645 | + | 0.505809i | \(0.168806\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.35366 | − | 2.34461i | −0.0788132 | − | 0.136508i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25.6038 | + | 14.7824i | 1.48568 | + | 0.857759i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.51908 | + | 9.61292i | −0.203514 | + | 0.555929i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.45717 | + | 0.841298i | 0.0839899 | + | 0.0484916i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.95859 | + | 17.2488i | 0.572106 | + | 0.990917i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.2143 | − | 7.05193i | 0.699389 | − | 0.403793i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.30426i | 0.245657i | 0.992428 | + | 0.122828i | \(0.0391965\pi\) | ||||
−0.992428 | + | 0.122828i | \(0.960803\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.0213 | − | 20.8214i | 0.683865 | − | 1.18449i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.22512 | −0.126175 | −0.0630875 | − | 0.998008i | \(-0.520095\pi\) | ||||
−0.0630875 | + | 0.998008i | \(0.520095\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.20887 | 0.407469 | 0.203735 | − | 0.979026i | \(-0.434692\pi\) | ||||
0.203735 | + | 0.979026i | \(0.434692\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0729902 | + | 0.126423i | −0.00411253 | + | 0.00712311i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.321644i | 0.0180653i | 0.999959 | + | 0.00903266i | \(0.00287522\pi\) | ||||
−0.999959 | + | 0.00903266i | \(0.997125\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.5073 | + | 7.79847i | −0.756266 | + | 0.436630i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.4527 | − | 18.1046i | −0.583414 | − | 1.01050i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.94679 | − | 5.74278i | −0.553454 | − | 0.319537i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.55193 | − | 0.619491i | 0.197026 | − | 0.0343632i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.5661 | − | 8.98707i | −0.860805 | − | 0.496986i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.38594 | − | 2.40052i | −0.0764094 | − | 0.132345i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4037 | − | 8.31600i | 0.791701 | − | 0.457089i | −0.0488600 | − | 0.998806i | \(-0.515559\pi\) |
0.840561 | + | 0.541717i | \(0.182225\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.62395i | − | 0.143791i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.16612 | − | 8.94799i | 0.282255 | − | 0.488881i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.2186 | −1.31927 | −0.659636 | − | 0.751586i | \(-0.729289\pi\) | ||||
−0.659636 | + | 0.751586i | \(0.729289\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −29.3537 | −1.59427 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.6761 | − | 25.4197i | 0.794754 | − | 1.37655i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.61478i | 0.249174i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.93456 | + | 2.27162i | −0.211830 | + | 0.122300i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.13680 | − | 5.43309i | −0.168392 | − | 0.291664i | 0.769463 | − | 0.638692i | \(-0.220524\pi\) |
−0.937855 | + | 0.347028i | \(0.887191\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.12275 | − | 3.53497i | −0.327743 | − | 0.189223i | 0.327095 | − | 0.944991i | \(-0.393930\pi\) |
−0.654839 | + | 0.755769i | \(0.727263\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.5487 | − | 3.40948i | 1.04343 | − | 0.181984i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.8705 | − | 10.8949i | −1.00438 | − | 0.579878i | −0.0948371 | − | 0.995493i | \(-0.530233\pi\) |
−0.909541 | + | 0.415615i | \(0.863566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.39866 | + | 11.0828i | 0.339606 | + | 0.588214i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.33176 | − | 1.34624i | 0.123410 | − | 0.0712506i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 23.9737i | − | 1.26528i | −0.774444 | − | 0.632642i | \(-0.781971\pi\) | ||
0.774444 | − | 0.632642i | \(-0.218029\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.92820 | + | 12.0000i | −0.364642 | + | 0.631579i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −28.5737 | −1.49973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.68922 | 0.507157 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.19566 | − | 5.53505i | 0.166812 | − | 0.288927i | −0.770485 | − | 0.637458i | \(-0.779986\pi\) |
0.937297 | + | 0.348531i | \(0.113319\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.63977i | 0.0853628i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.449045 | + | 0.259256i | −0.0233133 | + | 0.0134599i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0401 | + | 17.3899i | 0.519855 | + | 0.900414i | 0.999734 | + | 0.0230798i | \(0.00734719\pi\) |
−0.479879 | + | 0.877335i | \(0.659319\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.38581 | + | 0.800098i | 0.0715629 | + | 0.0413169i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.59878 | + | 9.83062i | −0.185346 | + | 0.506302i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.73007 | + | 2.73091i | 0.242968 | + | 0.140277i | 0.616540 | − | 0.787324i | \(-0.288534\pi\) |
−0.373572 | + | 0.927601i | \(0.621867\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.59229 | − | 4.48997i | −0.132807 | − | 0.230028i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.90842 | + | 2.83388i | −0.250808 | + | 0.144804i | −0.620134 | − | 0.784496i | \(-0.712922\pi\) |
0.369326 | + | 0.929300i | \(0.379589\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 1.78477i | − | 0.0909602i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.11256 | + | 1.92701i | −0.0565546 | + | 0.0979554i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.6174 | −0.538325 | −0.269162 | − | 0.963095i | \(-0.586747\pi\) | ||||
−0.269162 | + | 0.963095i | \(0.586747\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.3784 | −0.727149 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.140548 | − | 0.243436i | 0.00708971 | − | 0.0122797i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 4.51851i | − | 0.227351i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.2780 | − | 14.0169i | 1.21848 | − | 0.703487i | 0.253884 | − | 0.967235i | \(-0.418292\pi\) |
0.964592 | + | 0.263748i | \(0.0849586\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.602888 | + | 1.04423i | 0.0301822 | + | 0.0522770i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.4979 | + | 11.2571i | 0.973680 | + | 0.562155i | 0.900356 | − | 0.435154i | \(-0.143306\pi\) |
0.0733241 | + | 0.997308i | \(0.476639\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.38496 | − | 19.4081i | −0.168617 | − | 0.966788i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.48552 | + | 3.74441i | 0.322268 | + | 0.186061i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.0403 | + | 27.7826i | 0.795087 | + | 1.37713i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.71328 | + | 2.14386i | −0.183610 | + | 0.106007i | −0.588988 | − | 0.808142i | \(-0.700473\pi\) |
0.405378 | + | 0.914149i | \(0.367140\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 28.7761i | − | 1.41942i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.449749 | + | 0.778989i | −0.0221307 | + | 0.0383315i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.26371 | 0.209297 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.1802 | −0.939257 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.85578 | − | 15.3387i | 0.432633 | − | 0.749343i | −0.564466 | − | 0.825456i | \(-0.690918\pi\) |
0.997099 | + | 0.0761137i | \(0.0242512\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.8787i | − | 0.627672i | −0.949477 | − | 0.313836i | \(-0.898386\pi\) | ||
0.949477 | − | 0.313836i | \(-0.101614\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.17453 | − | 1.83281i | 0.154351 | − | 0.0891145i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.53215 | + | 4.38581i | 0.122827 | + | 0.212743i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.05816 | − | 2.34298i | −0.196388 | − | 0.113385i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −23.7792 | + | 19.8778i | −1.14807 | + | 0.959710i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.22590 | − | 4.74923i | −0.396228 | − | 0.228762i | 0.288627 | − | 0.957442i | \(-0.406801\pi\) |
−0.684855 | + | 0.728679i | \(0.740134\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.698141 | − | 1.20922i | −0.0335505 | − | 0.0581112i | 0.848763 | − | 0.528774i | \(-0.177348\pi\) |
−0.882313 | + | 0.470663i | \(0.844015\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.02367 | + | 2.32306i | −0.192920 | + | 0.111382i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.43911i | − | 0.308024i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.08090 | + | 3.60422i | −0.0993159 | + | 0.172020i | −0.911402 | − | 0.411518i | \(-0.864999\pi\) |
0.812086 | + | 0.583538i | \(0.198332\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.02711 | −0.144148 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.54563 | −0.453526 | −0.226763 | − | 0.973950i | \(-0.572814\pi\) | ||||
−0.226763 | + | 0.973950i | \(0.572814\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.61292 | − | 2.79366i | 0.0764596 | − | 0.132432i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.45732i | 0.258122i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.8075 | − | 10.8585i | 0.887582 | − | 0.512446i | 0.0144310 | − | 0.999896i | \(-0.495406\pi\) |
0.873151 | + | 0.487450i | \(0.162073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0239 | − | 17.3620i | −0.472009 | − | 0.817544i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.0330 | + | 6.36991i | 0.518376 | + | 0.299284i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.768307 | − | 0.919100i | −0.0360188 | − | 0.0430881i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.08989 | + | 2.36130i | 0.191317 | + | 0.110457i | 0.592599 | − | 0.805498i | \(-0.298102\pi\) |
−0.401282 | + | 0.915955i | \(0.631435\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.9361 | + | 24.1381i | 0.650482 | + | 1.12667i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.54283 | − | 0.890753i | 0.0718568 | − | 0.0414865i | −0.463641 | − | 0.886023i | \(-0.653457\pi\) |
0.535498 | + | 0.844537i | \(0.320124\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.80200i | − | 0.316116i | −0.987430 | − | 0.158058i | \(-0.949477\pi\) | ||
0.987430 | − | 0.158058i | \(-0.0505232\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.37182 | − | 7.57221i | 0.202738 | − | 0.351153i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.2374 | 0.843927 | 0.421963 | − | 0.906613i | \(-0.361341\pi\) | ||||
0.421963 | + | 0.906613i | \(0.361341\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.43285 | −0.158514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.1479 | − | 22.7728i | 0.605823 | − | 1.04932i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 27.2045i | − | 1.25086i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.96410 | + | 1.13397i | −0.0901192 | + | 0.0520303i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.342849 | − | 0.593832i | −0.0156980 | − | 0.0271897i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.4674 | − | 17.5904i | −1.39209 | − | 0.803724i | −0.398544 | − | 0.917149i | \(-0.630485\pi\) |
−0.993547 | + | 0.113425i | \(0.963818\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.2201 | + | 7.40214i | 0.921957 | + | 0.337508i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.30724 | + | 0.754738i | 0.0594817 | + | 0.0343418i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.25396 | + | 2.17191i | 0.0569392 | + | 0.0986215i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.92352 | + | 5.15200i | −0.404363 | + | 0.233459i | −0.688365 | − | 0.725364i | \(-0.741671\pi\) |
0.284002 | + | 0.958824i | \(0.408338\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 28.4950i | − | 1.28859i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.66599 | + | 8.08174i | −0.210573 | + | 0.364724i | −0.951894 | − | 0.306427i | \(-0.900866\pi\) |
0.741321 | + | 0.671151i | \(0.234200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.7041 | −0.662238 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.36023 | 0.106085 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.12593 | − | 3.68222i | 0.0953611 | − | 0.165170i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.9421i | 1.07179i | 0.844283 | + | 0.535897i | \(0.180026\pi\) | ||||
−0.844283 | + | 0.535897i | \(0.819974\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.72181 | − | 5.03554i | 0.389662 | − | 0.224971i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.0721 | + | 36.4980i | 0.939560 | + | 1.62737i | 0.766294 | + | 0.642490i | \(0.222099\pi\) |
0.173266 | + | 0.984875i | \(0.444568\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.7792 | + | 6.22336i | 0.479667 | + | 0.276936i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.68852 | + | 20.4729i | −0.163813 | + | 0.909235i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.0640 | − | 16.7801i | −1.28824 | − | 0.743765i | −0.309899 | − | 0.950770i | \(-0.600295\pi\) |
−0.978340 | + | 0.207005i | \(0.933629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.60960 | − | 2.78792i | −0.0712047 | − | 0.123330i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.8098 | + | 6.24102i | −0.477263 | + | 0.275548i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 15.0247i | − | 0.662069i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.4081 | + | 38.8120i | −0.985508 | + | 1.70695i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.5633 | −1.12210 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.4649 | 0.546098 | 0.273049 | − | 0.962000i | \(-0.411968\pi\) | ||||
0.273049 | + | 0.962000i | \(0.411968\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.82978 | + | 4.90132i | −0.123738 | + | 0.214320i | −0.921239 | − | 0.388998i | \(-0.872821\pi\) |
0.797501 | + | 0.603317i | \(0.206155\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 0.531659i | − | 0.0232035i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.9645 | − | 13.8359i | 1.04391 | − | 0.602702i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.46953 | + | 12.9376i | 0.324762 | + | 0.562505i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.03016 | − | 0.594763i | −0.0447051 | − | 0.0258105i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.6360 | − | 4.62577i | −0.547327 | − | 0.200364i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.3140 | − | 6.53215i | −0.489147 | − | 0.282409i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.8963 | − | 32.7293i | −0.815433 | − | 1.41237i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.0514 | − | 18.5049i | 1.38055 | − | 0.797061i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 15.4750i | − | 0.665321i | −0.943047 | − | 0.332660i | \(-0.892054\pi\) | ||
0.943047 | − | 0.332660i | \(-0.107946\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.10098 | + | 3.63900i | −0.0901616 | + | 0.156165i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.2325 | −0.481146 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.1765 | −1.07647 | −0.538234 | − | 0.842795i | \(-0.680908\pi\) | ||||
−0.538234 | + | 0.842795i | \(0.680908\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.09843 | − | 5.36665i | 0.132238 | − | 0.229043i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.58493i | − | 0.280528i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.30013 | + | 0.750630i | −0.0552871 | + | 0.0319200i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.77819 | + | 8.27607i | 0.202823 | + | 0.351300i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.6752 | − | 21.1744i | −1.55398 | − | 0.897190i | −0.997812 | − | 0.0661194i | \(-0.978938\pi\) |
−0.556167 | − | 0.831071i | \(-0.687728\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.7110 | − | 14.0095i | −0.495322 | − | 0.592537i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.7002 | − | 21.7662i | −1.59171 | − | 0.918971i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.8953 | − | 20.6032i | −0.501326 | − | 0.868322i | −0.999999 | − | 0.00153173i | \(-0.999512\pi\) |
0.498673 | − | 0.866790i | \(-0.333821\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.8862 | + | 9.17191i | −0.668338 | + | 0.385865i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.48814i | − | 0.104492i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.3710 | + | 23.1593i | −0.560543 | + | 0.970889i | 0.436906 | + | 0.899507i | \(0.356074\pi\) |
−0.997449 | + | 0.0713817i | \(0.977259\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.7159 | −0.699539 | −0.349769 | − | 0.936836i | \(-0.613740\pi\) | ||||
−0.349769 | + | 0.936836i | \(0.613740\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.22571 | 0.134756 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.41959 | + | 2.45880i | −0.0592010 | + | 0.102539i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.6768i | 0.860786i | 0.902642 | + | 0.430393i | \(0.141625\pi\) | ||||
−0.902642 | + | 0.430393i | \(0.858375\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 31.6257 | − | 18.2591i | 1.31432 | − | 0.758822i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.708301 | − | 1.22681i | −0.0293853 | − | 0.0508968i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.26023 | + | 4.19170i | 0.300688 | + | 0.173602i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.21545 | − | 1.01603i | 0.0502526 | − | 0.0420079i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.0109 | − | 10.3986i | −0.743388 | − | 0.429196i | 0.0799116 | − | 0.996802i | \(-0.474536\pi\) |
−0.823300 | + | 0.567606i | \(0.807870\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.19615 | + | 10.7321i | 0.255308 | + | 0.442206i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.891111 | − | 0.514483i | 0.0366554 | − | 0.0211630i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 21.8475i | − | 0.897169i | −0.893740 | − | 0.448585i | \(-0.851928\pi\) | ||
0.893740 | − | 0.448585i | \(-0.148072\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.841298 | − | 1.45717i | 0.0344898 | − | 0.0597381i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.90755 | 0.200853 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.58040 | 0.146291 | 0.0731456 | − | 0.997321i | \(-0.476696\pi\) | ||||
0.0731456 | + | 0.997321i | \(0.476696\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.6743 | + | 18.4885i | −0.435414 | + | 0.754160i | −0.997329 | − | 0.0730352i | \(-0.976731\pi\) |
0.561915 | + | 0.827195i | \(0.310065\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 4.53972i | − | 0.184872i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.4641 | + | 8.92820i | −0.628705 | + | 0.362983i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.64988 | − | 2.85767i | −0.0669665 | − | 0.115989i | 0.830598 | − | 0.556872i | \(-0.187999\pi\) |
−0.897565 | + | 0.440883i | \(0.854665\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.33685 | + | 0.771830i | 0.0541718 | + | 0.0312761i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.16832 | + | 29.6332i | 0.209088 | + | 1.19883i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.56183 | + | 4.94318i | 0.345809 | + | 0.199653i | 0.662838 | − | 0.748763i | \(-0.269352\pi\) |
−0.317029 | + | 0.948416i | \(0.602685\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.98601 | − | 5.17191i | −0.120407 | − | 0.208552i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.5920 | − | 22.8584i | 1.59391 | − | 0.920246i | 0.601287 | − | 0.799033i | \(-0.294655\pi\) |
0.992626 | − | 0.121213i | \(-0.0386785\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 19.9143i | − | 0.800425i | −0.916422 | − | 0.400212i | \(-0.868936\pi\) | ||
0.916422 | − | 0.400212i | \(-0.131064\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.81295 | + | 13.5324i | −0.313523 | + | 0.543038i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.07177 | −0.0429397 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.74760 | − | 16.8833i | 0.389282 | − | 0.674255i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.2440i | 1.20591i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.6403 | + | 7.29790i | −0.503204 | + | 0.290525i | −0.730036 | − | 0.683409i | \(-0.760497\pi\) |
0.226832 | + | 0.973934i | \(0.427163\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.56112 | − | 11.3642i | −0.260781 | − | 0.451686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.80589 | − | 1.61998i | −0.111348 | − | 0.0642870i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.53948 | − | 23.3269i | 0.338346 | − | 0.924246i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.86950 | + | 2.81140i | 0.192634 | + | 0.111217i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.08183 | − | 12.2661i | −0.279716 | − | 0.484482i | 0.691598 | − | 0.722282i | \(-0.256907\pi\) |
−0.971314 | + | 0.237801i | \(0.923573\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.5246 | − | 8.38581i | 0.572796 | − | 0.330704i | −0.185469 | − | 0.982650i | \(-0.559380\pi\) |
0.758265 | + | 0.651946i | \(0.226047\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 8.10387i | − | 0.319089i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.49584 | − | 2.59087i | 0.0588075 | − | 0.101858i | −0.835123 | − | 0.550063i | \(-0.814604\pi\) |
0.893930 | + | 0.448206i | \(0.147937\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.5432 | 0.570872 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.90504 | −0.113858 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.83217 | − | 10.1016i | 0.228230 | − | 0.395307i | −0.729053 | − | 0.684457i | \(-0.760039\pi\) |
0.957284 | + | 0.289150i | \(0.0933727\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 0.175664i | − | 0.00686374i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.68683 | − | 2.12859i | 0.143837 | − | 0.0830444i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.905237 | − | 1.56792i | −0.0352630 | − | 0.0610773i | 0.847855 | − | 0.530228i | \(-0.177894\pi\) |
−0.883118 | + | 0.469150i | \(0.844560\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.6872 | + | 6.17028i | 0.415686 | + | 0.239996i | 0.693230 | − | 0.720717i | \(-0.256187\pi\) |
−0.277544 | + | 0.960713i | \(0.589520\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −28.7844 | + | 5.02027i | −1.11789 | + | 0.194971i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.652566 | + | 0.376759i | 0.0253054 | + | 0.0146101i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.12174 | − | 7.13907i | −0.159594 | − | 0.276426i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.1965 | − | 8.19636i | 0.548869 | − | 0.316890i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 75.7634i | 2.92481i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.63313 | − | 8.02481i | 0.178594 | − | 0.309334i | −0.762805 | − | 0.646628i | \(-0.776178\pi\) |
0.941399 | + | 0.337295i | \(0.109512\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.50367 | 0.211836 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.8984 | 0.534158 | 0.267079 | − | 0.963675i | \(-0.413941\pi\) | ||||
0.267079 | + | 0.963675i | \(0.413941\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.416622 | − | 0.721611i | 0.0159885 | − | 0.0276929i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.2715i | 0.431924i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.6935 | − | 18.8756i | 1.25098 | − | 0.722255i | 0.279678 | − | 0.960094i | \(-0.409772\pi\) |
0.971305 | + | 0.237838i | \(0.0764388\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.99144 | − | 15.5736i | −0.343545 | − | 0.595038i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.84172 | − | 1.06332i | −0.0702661 | − | 0.0405681i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.54324 | − | 0.966794i | 0.211181 | − | 0.0368319i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.43146 | + | 0.826456i | 0.0544554 | + | 0.0314399i | 0.526981 | − | 0.849877i | \(-0.323324\pi\) |
−0.472525 | + | 0.881317i | \(0.656657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.392090 | − | 0.679120i | −0.0148943 | − | 0.0257976i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.3803 | + | 5.99307i | −0.393747 | + | 0.227330i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 18.9002i | − | 0.715897i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.998090 | + | 1.72874i | −0.0377512 | + | 0.0653871i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.4819 | −0.773590 | −0.386795 | − | 0.922166i | \(-0.626418\pi\) | ||||
−0.386795 | + | 0.922166i | \(0.626418\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.5442 | −0.510830 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.67510 | + | 11.5616i | −0.251399 | + | 0.435435i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.13538i | − | 0.155527i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.0021 | − | 10.9709i | 0.713639 | − | 0.412020i | −0.0987679 | − | 0.995110i | \(-0.531490\pi\) |
0.812407 | + | 0.583091i | \(0.198157\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.992658 | − | 1.71933i | −0.0372276 | − | 0.0644801i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.4351 | + | 7.75678i | 0.503150 | + | 0.290494i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.65821 | + | 18.1879i | −0.249003 | + | 0.680191i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.7778 | + | 7.95463i | 0.514542 | + | 0.297071i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.4237 | − | 33.6429i | −0.724384 | − | 1.25467i | −0.959227 | − | 0.282636i | \(-0.908791\pi\) |
0.234844 | − | 0.972033i | \(-0.424542\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.32312 | + | 2.49596i | −0.161002 | + | 0.0929543i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 36.1434i | − | 1.34419i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.45174 | + | 2.51448i | −0.0539162 | + | 0.0933856i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.6598 | −1.13711 | −0.568555 | − | 0.822645i | \(-0.692497\pi\) | ||||
−0.568555 | + | 0.822645i | \(0.692497\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7112 | 1.10042 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.8236 | − | 22.2110i | 0.474296 | − | 0.821505i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 24.3858i | − | 0.900709i | −0.892850 | − | 0.450355i | \(-0.851298\pi\) | ||
0.892850 | − | 0.450355i | \(-0.148702\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.54769 | − | 5.51236i | 0.352172 | − | 0.203327i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.7515 | + | 48.0669i | 1.02224 | + | 1.77057i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.1504 | + | 19.1394i | 1.21946 | + | 0.704054i | 0.964802 | − | 0.262977i | \(-0.0847044\pi\) |
0.254656 | + | 0.967032i | \(0.418038\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.24823 | − | 12.8905i | −0.0825909 | − | 0.473546i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.6479 | + | 20.0040i | 1.27111 | + | 0.733874i | 0.975196 | − | 0.221342i | \(-0.0710437\pi\) |
0.295910 | + | 0.955216i | \(0.404377\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.70520 | + | 2.95350i | 0.0624738 | + | 0.108208i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.62238 | − | 0.936681i | 0.0593598 | − | 0.0342714i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.34057i | 0.158601i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.8010 | + | 22.1720i | −0.467115 | + | 0.809067i | −0.999294 | − | 0.0375648i | \(-0.988040\pi\) |
0.532179 | + | 0.846632i | \(0.321373\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.8307 | −0.394693 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.96141 | 0.289745 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.924239 | − | 1.60083i | 0.0335920 | − | 0.0581831i | −0.848741 | − | 0.528809i | \(-0.822639\pi\) |
0.882333 | + | 0.470626i | \(0.155972\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 24.4055i | − | 0.885862i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.7006 | − | 13.1062i | 0.822896 | − | 0.475099i | −0.0285179 | − | 0.999593i | \(-0.509079\pi\) |
0.851414 | + | 0.524494i | \(0.175745\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.86597 | + | 3.23196i | 0.0675528 | + | 0.117005i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.92701 | + | 1.11256i | 0.0696712 | + | 0.0402247i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.48932 | − | 6.26058i | 0.270424 | − | 0.226056i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.4078 | − | 22.1747i | −1.38502 | − | 0.799641i | −0.392271 | − | 0.919850i | \(-0.628310\pi\) |
−0.992749 | + | 0.120208i | \(0.961644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.20406 | − | 14.2099i | −0.295462 | − | 0.511755i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.1471 | − | 11.6319i | 0.724640 | − | 0.418371i | −0.0918181 | − | 0.995776i | \(-0.529268\pi\) |
0.816458 | + | 0.577405i | \(0.195935\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5.46410i | − | 0.196276i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.58754 | − | 2.74970i | 0.0569526 | − | 0.0986448i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.46410 | 0.303258 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −68.7449 | −2.45989 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.98989 | + | 13.8389i | −0.285535 | + | 0.494562i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 16.4329i | − | 0.586514i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.4942 | − | 23.9567i | 1.47911 | − | 0.853963i | 0.479387 | − | 0.877604i | \(-0.340859\pi\) |
0.999721 | + | 0.0236408i | \(0.00752582\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.9274 | + | 25.8551i | 0.531430 | + | 0.920464i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.27814 | + | 3.04734i | 0.187669 | + | 0.108351i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.6147 | + | 39.0158i | 1.15818 | + | 1.38549i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.16273 | + | 1.24865i | 0.0767042 | + | 0.0442852i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.3476 | − | 17.9225i | −0.366530 | − | 0.634849i | 0.622490 | − | 0.782627i | \(-0.286121\pi\) |
−0.989020 | + | 0.147779i | \(0.952788\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.5902 | + | 21.1253i | −1.29447 | + | 0.747361i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1.41735i | − | 0.0500795i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.0244 | + | 45.0755i | −0.918380 | + | 1.59068i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.943307 | 0.0332472 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.7361 | 1.01156 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.94574 | + | 13.7624i | −0.279357 | + | 0.483861i | −0.971225 | − | 0.238163i | \(-0.923455\pi\) |
0.691868 | + | 0.722024i | \(0.256788\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23.8796i | − | 0.838525i | −0.907865 | − | 0.419263i | \(-0.862289\pi\) | ||
0.907865 | − | 0.419263i | \(-0.137711\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −42.8183 | + | 24.7212i | −1.50170 | + | 0.867009i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.90361 | − | 15.4215i | −0.311880 | − | 0.540192i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.94679 | + | 5.74278i | 0.347994 | + | 0.200915i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.494262 | − | 0.180939i | −0.0172709 | − | 0.00632250i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.7782 | + | 7.95484i | 0.480862 | + | 0.277626i | 0.720776 | − | 0.693169i | \(-0.243786\pi\) |
−0.239914 | + | 0.970794i | \(0.577119\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.40573 | + | 12.8271i | 0.258147 | + | 0.447124i | 0.965746 | − | 0.259491i | \(-0.0835547\pi\) |
−0.707598 | + | 0.706615i | \(0.750221\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.44432 | + | 4.29798i | −0.259178 | + | 0.149636i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 33.9498i | − | 1.18055i | −0.807202 | − | 0.590275i | \(-0.799019\pi\) | ||
0.807202 | − | 0.590275i | \(-0.200981\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.6573 | − | 20.1910i | 0.404875 | − | 0.701264i | −0.589432 | − | 0.807818i | \(-0.700648\pi\) |
0.994307 | + | 0.106554i | \(0.0339818\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.4124 | −1.47127 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.8910 | 1.20890 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.14683 | − | 5.45047i | 0.108900 | − | 0.188621i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 30.0726i | − | 1.03946i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.8111 | − | 7.39649i | 0.442288 | − | 0.255355i | −0.262280 | − | 0.964992i | \(-0.584474\pi\) |
0.704568 | + | 0.709637i | \(0.251141\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.2849 | + | 17.8140i | 0.354652 | + | 0.614276i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.89809 | − | 3.98261i | −0.237583 | − | 0.137169i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.40078 | + | 12.2325i | 0.151392 | + | 0.420809i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.13789 | + | 2.96636i | 0.176540 | + | 0.101925i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.0703 | + | 17.4423i | 0.345612 | + | 0.598617i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.6840 | + | 8.47780i | −0.503360 | + | 0.290615i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 16.3452i | − | 0.559650i | −0.960051 | − | 0.279825i | \(-0.909724\pi\) | ||
0.960051 | − | 0.279825i | \(-0.0902765\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.498239 | + | 0.862975i | −0.0170394 | + | 0.0295131i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.1418 | 1.16626 | 0.583132 | − | 0.812378i | \(-0.301827\pi\) | ||||
0.583132 | + | 0.812378i | \(0.301827\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.1996 | 1.54219 | 0.771096 | − | 0.636719i | \(-0.219709\pi\) | ||||
0.771096 | + | 0.636719i | \(0.219709\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.992090 | + | 1.71835i | −0.0338103 | + | 0.0585612i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.75058i | 0.161712i | 0.996726 | + | 0.0808559i | \(0.0257653\pi\) | ||||
−0.996726 | + | 0.0808559i | \(0.974235\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.8349 | + | 7.98756i | −0.470399 | + | 0.271585i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.91853 | − | 11.9832i | −0.234966 | − | 0.406972i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.0207 | + | 12.1363i | 0.713079 | + | 0.411696i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.9830 | + | 12.8065i | 1.18535 | + | 0.433933i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.954282 | + | 0.550955i | 0.0322975 | + | 0.0186470i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.166123 | − | 0.287734i | −0.00561599 | − | 0.00972718i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.95294 | + | 1.12753i | −0.0659462 | + | 0.0380741i | −0.532611 | − | 0.846360i | \(-0.678789\pi\) |
0.466664 | + | 0.884434i | \(0.345456\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.0715i | 0.913098i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.49152 | + | 2.58339i | −0.0502507 | + | 0.0870367i | −0.890057 | − | 0.455850i | \(-0.849335\pi\) |
0.839806 | + | 0.542887i | \(0.182669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.2874 | 0.951947 | 0.475973 | − | 0.879460i | \(-0.342096\pi\) | ||||
0.475973 | + | 0.879460i | \(0.342096\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.33225 | 0.145627 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.9908 | + | 24.2328i | −0.469766 | + | 0.813658i | −0.999402 | − | 0.0345665i | \(-0.988995\pi\) |
0.529637 | + | 0.848225i | \(0.322328\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.07647i | 0.0361035i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.8390 | + | 20.1143i | −1.16715 | + | 0.673855i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.46058 | − | 16.3862i | −0.316586 | − | 0.548343i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.4533 | − | 11.8087i | −0.683678 | − | 0.394722i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.5061 | − | 12.5681i | −0.350787 | − | 0.419635i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.7394 | + | 7.93244i | 0.458234 | + | 0.264562i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.95174 | + | 6.84461i | 0.131651 | + | 0.228027i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.33176 | + | 1.34624i | −0.0775960 | + | 0.0448001i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.62590i | 0.0872879i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.27600 | + | 14.3344i | −0.274800 | + | 0.475967i | −0.970085 | − | 0.242767i | \(-0.921945\pi\) |
0.695285 | + | 0.718734i | \(0.255278\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.46876 | 0.181387 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.04863 | −0.233532 | −0.116766 | − | 0.993159i | \(-0.537253\pi\) | ||||
−0.116766 | + | 0.993159i | \(0.537253\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.4519 | + | 19.8353i | −0.379004 | + | 0.656454i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.5689i | 0.746106i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.0505443 | + | 0.0291818i | −0.00166912 | + | 0.000963668i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.27188 | + | 14.3273i | 0.272864 | + | 0.472615i | 0.969594 | − | 0.244719i | \(-0.0786957\pi\) |
−0.696730 | + | 0.717334i | \(0.745362\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.96488 | − | 3.44383i | −0.196550 | − | 0.113478i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.4015 | + | 29.5933i | −1.16525 | + | 0.974076i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.17191 | + | 2.98601i | 0.170051 | + | 0.0981793i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.30074 | − | 5.71704i | −0.108410 | − | 0.187772i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.3035 | + | 16.9184i | −0.961416 | + | 0.555074i | −0.896609 | − | 0.442824i | \(-0.853977\pi\) |
−0.0648073 | + | 0.997898i | \(0.520643\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.6253i | 0.512098i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.78031 | − | 3.08359i | 0.0582848 | − | 0.100952i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −27.2045 | −0.889681 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.4606 | −0.995104 | −0.497552 | − | 0.867434i | \(-0.665768\pi\) | ||||
−0.497552 | + | 0.867434i | \(0.665768\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.76780 | + | 9.99012i | −0.188225 | + | 0.326015i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.2101i | 1.24561i | 0.782375 | + | 0.622807i | \(0.214008\pi\) | ||||
−0.782375 | + | 0.622807i | \(0.785992\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.17637 | − | 5.29798i | 0.298824 | − | 0.172526i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.914288 | − | 1.58359i | −0.0297418 | − | 0.0515143i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.4215 | + | 26.2241i | 1.47600 | + | 0.852169i | 0.999633 | − | 0.0270773i | \(-0.00862003\pi\) |
0.476367 | + | 0.879247i | \(0.341953\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00239 | + | 34.4155i | 0.194846 | + | 1.11717i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.445737 | − | 0.257347i | −0.0144540 | − | 0.00834504i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.8750 | + | 34.4245i | 0.643814 | + | 1.11512i | 0.984574 | + | 0.174969i | \(0.0559824\pi\) |
−0.340760 | + | 0.940150i | \(0.610684\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.74575 | − | 1.00791i | 0.0564912 | − | 0.0326152i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 24.9581i | − | 0.806782i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.98737 | + | 5.17428i | −0.0964673 | + | 0.167086i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.14359 | 0.0368901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.74011 | −0.184972 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.4105 | − | 19.7636i | 0.367318 | − | 0.636214i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.7857i | 0.829214i | 0.910001 | + | 0.414607i | \(0.136081\pi\) | ||||
−0.910001 | + | 0.414607i | \(0.863919\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.9168 | − | 9.18958i | 0.511322 | − | 0.295212i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.7626 | − | 48.0863i | −0.890945 | − | 1.54316i | −0.838744 | − | 0.544525i | \(-0.816710\pi\) |
−0.0522005 | − | 0.998637i | \(-0.516623\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.44882 | + | 1.99118i | 0.110564 | + | 0.0638342i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.98340 | + | 5.41796i | −0.0635195 | + | 0.173514i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.0879 | − | 20.2580i | −1.12256 | − | 0.648112i | −0.180509 | − | 0.983573i | \(-0.557774\pi\) |
−0.942054 | + | 0.335461i | \(0.891108\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.66430 | + | 15.0070i | 0.276912 | + | 0.479626i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.27405 | + | 2.46762i | −0.136460 | + | 0.0787852i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 34.8059i | − | 1.11014i | −0.831805 | − | 0.555068i | \(-0.812692\pi\) | ||
0.831805 | − | 0.555068i | \(-0.187308\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.321513 | − | 0.556877i | 0.0102443 | − | 0.0177436i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.43555 | 0.141185 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.3784 | 0.457208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.9427 | − | 38.0059i | 0.697034 | − | 1.20730i | −0.272456 | − | 0.962168i | \(-0.587836\pi\) |
0.969490 | − | 0.245130i | \(-0.0788307\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.6145i | 0.844584i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.65596 | − | 1.53342i | 0.0841997 | − | 0.0486127i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.74569 | + | 4.75567i | 0.0869568 | + | 0.150614i | 0.906223 | − | 0.422799i | \(-0.138952\pi\) |
−0.819267 | + | 0.573413i | \(0.805619\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.4645 | + | 16.4340i | 0.900577 | + | 0.519949i |
(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 | 1040.2.da.b.641.2 | 8 | ||
4.3 | odd | 2 | 65.2.m.a.56.2 | yes | 8 | ||
12.11 | even | 2 | 585.2.bu.c.316.3 | 8 | |||
13.10 | even | 6 | inner | 1040.2.da.b.881.2 | 8 | ||
20.3 | even | 4 | 325.2.m.c.199.2 | 8 | |||
20.7 | even | 4 | 325.2.m.b.199.3 | 8 | |||
20.19 | odd | 2 | 325.2.n.d.251.3 | 8 | |||
52.3 | odd | 6 | 845.2.m.g.361.3 | 8 | |||
52.7 | even | 12 | 845.2.a.m.1.2 | 4 | |||
52.11 | even | 12 | 845.2.e.m.146.3 | 8 | |||
52.15 | even | 12 | 845.2.e.n.146.2 | 8 | |||
52.19 | even | 12 | 845.2.a.l.1.3 | 4 | |||
52.23 | odd | 6 | 65.2.m.a.36.2 | ✓ | 8 | ||
52.31 | even | 4 | 845.2.e.n.191.2 | 8 | |||
52.35 | odd | 6 | 845.2.c.g.506.5 | 8 | |||
52.43 | odd | 6 | 845.2.c.g.506.4 | 8 | |||
52.47 | even | 4 | 845.2.e.m.191.3 | 8 | |||
52.51 | odd | 2 | 845.2.m.g.316.3 | 8 | |||
156.23 | even | 6 | 585.2.bu.c.361.3 | 8 | |||
156.59 | odd | 12 | 7605.2.a.cf.1.3 | 4 | |||
156.71 | odd | 12 | 7605.2.a.cj.1.2 | 4 | |||
260.19 | even | 12 | 4225.2.a.bl.1.2 | 4 | |||
260.23 | even | 12 | 325.2.m.b.49.3 | 8 | |||
260.59 | even | 12 | 4225.2.a.bi.1.3 | 4 | |||
260.127 | even | 12 | 325.2.m.c.49.2 | 8 | |||
260.179 | odd | 6 | 325.2.n.d.101.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.2 | ✓ | 8 | 52.23 | odd | 6 | ||
65.2.m.a.56.2 | yes | 8 | 4.3 | odd | 2 | ||
325.2.m.b.49.3 | 8 | 260.23 | even | 12 | |||
325.2.m.b.199.3 | 8 | 20.7 | even | 4 | |||
325.2.m.c.49.2 | 8 | 260.127 | even | 12 | |||
325.2.m.c.199.2 | 8 | 20.3 | even | 4 | |||
325.2.n.d.101.3 | 8 | 260.179 | odd | 6 | |||
325.2.n.d.251.3 | 8 | 20.19 | odd | 2 | |||
585.2.bu.c.316.3 | 8 | 12.11 | even | 2 | |||
585.2.bu.c.361.3 | 8 | 156.23 | even | 6 | |||
845.2.a.l.1.3 | 4 | 52.19 | even | 12 | |||
845.2.a.m.1.2 | 4 | 52.7 | even | 12 | |||
845.2.c.g.506.4 | 8 | 52.43 | odd | 6 | |||
845.2.c.g.506.5 | 8 | 52.35 | odd | 6 | |||
845.2.e.m.146.3 | 8 | 52.11 | even | 12 | |||
845.2.e.m.191.3 | 8 | 52.47 | even | 4 | |||
845.2.e.n.146.2 | 8 | 52.15 | even | 12 | |||
845.2.e.n.191.2 | 8 | 52.31 | even | 4 | |||
845.2.m.g.316.3 | 8 | 52.51 | odd | 2 | |||
845.2.m.g.361.3 | 8 | 52.3 | odd | 6 | |||
1040.2.da.b.641.2 | 8 | 1.1 | even | 1 | trivial | ||
1040.2.da.b.881.2 | 8 | 13.10 | even | 6 | inner | ||
4225.2.a.bi.1.3 | 4 | 260.59 | even | 12 | |||
4225.2.a.bl.1.2 | 4 | 260.19 | even | 12 | |||
7605.2.a.cf.1.3 | 4 | 156.59 | odd | 12 | |||
7605.2.a.cj.1.2 | 4 | 156.71 | odd | 12 |