Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(185,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.185");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.cx (of order \(6\), degree \(2\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 185.3 | ||
Character | \(\chi\) | \(=\) | 504.185 |
Dual form | 504.2.cx.a.425.3 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.67230 | + | 0.451026i | −0.965501 | + | 0.260400i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.203178 | −0.0908641 | −0.0454320 | − | 0.998967i | \(-0.514466\pi\) | ||||
−0.0454320 | + | 0.998967i | \(0.514466\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.27132 | − | 2.32029i | −0.480515 | − | 0.876987i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.59315 | − | 1.50850i | 0.864383 | − | 0.502833i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.46863i | 1.34734i | 0.739031 | + | 0.673672i | \(0.235284\pi\) | ||||
−0.739031 | + | 0.673672i | \(0.764716\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.25586 | + | 0.725070i | 0.348312 | + | 0.201098i | 0.663942 | − | 0.747784i | \(-0.268882\pi\) |
−0.315629 | + | 0.948883i | \(0.602216\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.339774 | − | 0.0916388i | 0.0877293 | − | 0.0236610i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.60586 | + | 2.78143i | −0.389478 | + | 0.674596i | −0.992379 | − | 0.123220i | \(-0.960678\pi\) |
0.602901 | + | 0.797816i | \(0.294011\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.20156 | + | 3.58047i | −1.42274 | + | 0.821417i | −0.996532 | − | 0.0832106i | \(-0.973483\pi\) |
−0.426203 | + | 0.904627i | \(0.640149\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.17254 | + | 3.30681i | 0.692305 | + | 0.721605i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.26655i | − | 0.264095i | −0.991243 | − | 0.132047i | \(-0.957845\pi\) | ||
0.991243 | − | 0.132047i | \(-0.0421551\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.95872 | −0.991744 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.65614 | + | 3.69224i | −0.703625 | + | 0.710572i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.944433 | + | 0.545269i | −0.175377 | + | 0.101254i | −0.585119 | − | 0.810948i | \(-0.698952\pi\) |
0.409742 | + | 0.912202i | \(0.365619\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.60021 | + | 3.23328i | −1.00583 | + | 0.580715i | −0.909967 | − | 0.414680i | \(-0.863894\pi\) |
−0.0958603 | + | 0.995395i | \(0.530560\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.01547 | − | 7.47288i | −0.350849 | − | 1.30086i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.258305 | + | 0.471432i | 0.0436616 | + | 0.0796866i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.02855 | + | 5.24561i | 0.497891 | + | 0.862373i | 0.999997 | − | 0.00243316i | \(-0.000774500\pi\) |
−0.502106 | + | 0.864806i | \(0.667441\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.42719 | − | 0.646106i | −0.388662 | − | 0.103460i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.370687 | + | 0.642048i | −0.0578915 | + | 0.100271i | −0.893519 | − | 0.449026i | \(-0.851771\pi\) |
0.835627 | + | 0.549297i | \(0.185104\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.69802 | − | 8.13721i | −0.716442 | − | 1.24091i | −0.962401 | − | 0.271633i | \(-0.912436\pi\) |
0.245959 | − | 0.969280i | \(-0.420897\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.526872 | + | 0.306494i | −0.0785414 | + | 0.0456895i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.0465845 | + | 0.0806866i | −0.00679504 | + | 0.0117694i | −0.869403 | − | 0.494104i | \(-0.835496\pi\) |
0.862608 | + | 0.505873i | \(0.168830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.76748 | + | 5.89967i | −0.538211 | + | 0.842810i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.43098 | − | 5.37566i | 0.200377 | − | 0.752744i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.35260 | + | 5.39973i | 1.28468 | + | 0.741710i | 0.977700 | − | 0.210007i | \(-0.0673486\pi\) |
0.306979 | + | 0.951716i | \(0.400682\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.907929i | − | 0.122425i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.75596 | − | 8.78468i | 1.15976 | − | 1.16356i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.16447 | + | 8.94512i | 0.672356 | + | 1.16456i | 0.977234 | + | 0.212164i | \(0.0680511\pi\) |
−0.304878 | + | 0.952392i | \(0.598616\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.34727 | − | 4.24195i | −0.940722 | − | 0.543126i | −0.0505352 | − | 0.998722i | \(-0.516093\pi\) |
−0.890186 | + | 0.455596i | \(0.849426\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.79689 | − | 4.09907i | −0.856327 | − | 0.516434i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.255163 | − | 0.147318i | −0.0316491 | − | 0.0182726i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.02663 | + | 6.97432i | 0.491931 | + | 0.852049i | 0.999957 | − | 0.00929244i | \(-0.00295792\pi\) |
−0.508026 | + | 0.861342i | \(0.669625\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.571249 | + | 2.11805i | 0.0687703 | + | 0.254983i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.6777i | 1.86060i | 0.366802 | + | 0.930299i | \(0.380453\pi\) | ||||
−0.366802 | + | 0.930299i | \(0.619547\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.984428 | + | 0.568360i | 0.115219 | + | 0.0665215i | 0.556502 | − | 0.830846i | \(-0.312143\pi\) |
−0.441283 | + | 0.897368i | \(0.645477\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.29245 | − | 2.23651i | 0.957529 | − | 0.258250i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.3685 | − | 5.68108i | 1.18160 | − | 0.647419i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.86893 | − | 10.1653i | 0.660306 | − | 1.14368i | −0.320229 | − | 0.947340i | \(-0.603760\pi\) |
0.980535 | − | 0.196344i | \(-0.0629068\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.44886 | − | 7.82353i | 0.494317 | − | 0.869281i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.29931 | − | 3.98252i | −0.252382 | − | 0.437139i | 0.711799 | − | 0.702383i | \(-0.247881\pi\) |
−0.964181 | + | 0.265245i | \(0.914547\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.326276 | − | 0.565127i | 0.0353896 | − | 0.0612966i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.33344 | − | 1.33782i | 0.142960 | − | 0.143429i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.52692 | − | 6.10881i | −0.373853 | − | 0.647532i | 0.616302 | − | 0.787510i | \(-0.288630\pi\) |
−0.990155 | + | 0.139978i | \(0.955297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0857700 | − | 3.83575i | 0.00899114 | − | 0.402096i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.90692 | − | 7.93285i | 0.819909 | − | 0.822598i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.26002 | − | 0.727474i | 0.129276 | − | 0.0746373i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.17914 | + | 1.83548i | −0.322793 | + | 0.186365i | −0.652637 | − | 0.757671i | \(-0.726337\pi\) |
0.329844 | + | 0.944036i | \(0.393004\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.74093 | + | 11.5878i | 0.677489 | + | 1.16462i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.1682 | −1.31029 | −0.655143 | − | 0.755505i | \(-0.727391\pi\) | ||||
−0.655143 | + | 0.755505i | \(0.727391\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.5351i | − | 1.33365i | −0.745214 | − | 0.666826i | \(-0.767653\pi\) | ||
0.745214 | − | 0.666826i | \(-0.232347\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.644591 | − | 0.671872i | −0.0629057 | − | 0.0655680i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.0095 | − | 7.51105i | 1.25768 | − | 0.726121i | 0.285056 | − | 0.958511i | \(-0.407988\pi\) |
0.972623 | + | 0.232390i | \(0.0746545\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.72560 | − | 4.72088i | 0.261065 | − | 0.452178i | −0.705460 | − | 0.708750i | \(-0.749260\pi\) |
0.966525 | + | 0.256571i | \(0.0825928\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.43055 | − | 7.40626i | −0.705277 | − | 0.702971i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.03027 | − | 3.48158i | −0.567280 | − | 0.327519i | 0.188782 | − | 0.982019i | \(-0.439546\pi\) |
−0.756062 | + | 0.654500i | \(0.772879\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.257336i | 0.0239967i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.35039 | − | 0.0142461i | 0.402194 | − | 0.00131705i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.49529 | + | 0.189961i | 0.778762 | + | 0.0174137i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.96868 | −0.815335 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.330317 | − | 1.24088i | 0.0297837 | − | 0.111887i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.02340 | 0.180978 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.68718 | 0.238448 | 0.119224 | − | 0.992867i | \(-0.461959\pi\) | ||||
0.119224 | + | 0.992867i | \(0.461959\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.5266 | + | 11.4889i | 1.01486 | + | 1.01154i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.13987 | 0.536443 | 0.268222 | − | 0.963357i | \(-0.413564\pi\) | ||||
0.268222 | + | 0.963357i | \(0.413564\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.1919 | + | 9.83747i | 1.40402 | + | 0.853017i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.742849 | − | 0.750183i | 0.0639342 | − | 0.0645654i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 4.28221i | − | 0.365854i | −0.983127 | − | 0.182927i | \(-0.941443\pi\) | ||
0.983127 | − | 0.182927i | \(-0.0585571\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.43981 | + | 1.98597i | 0.291761 | + | 0.168448i | 0.638736 | − | 0.769426i | \(-0.279458\pi\) |
−0.346975 | + | 0.937874i | \(0.612791\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0415112 | − | 0.155943i | 0.00349587 | − | 0.0131328i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.24007 | + | 5.61197i | −0.270948 | + | 0.469296i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.191888 | − | 0.110787i | 0.0159355 | − | 0.00920034i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.63943 | − | 11.5652i | 0.300175 | − | 0.953884i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.63300i | 0.379550i | 0.981828 | + | 0.189775i | \(0.0607759\pi\) | ||||
−0.981828 | + | 0.189775i | \(0.939224\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.6948 | −1.27722 | −0.638612 | − | 0.769529i | \(-0.720491\pi\) | ||||
−0.638612 | + | 0.769529i | \(0.720491\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0315517 | + | 9.63511i | 0.00255081 | + | 0.778953i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.13784 | − | 0.656933i | 0.0913936 | − | 0.0527661i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.55598 | + | 3.78510i | −0.523224 | + | 0.302084i | −0.738253 | − | 0.674524i | \(-0.764349\pi\) |
0.215029 | + | 0.976608i | \(0.431016\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.0757 | − | 4.81167i | −1.43350 | − | 0.381591i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.93877 | + | 1.61020i | −0.231607 | + | 0.126901i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.97454 | − | 6.88410i | −0.311310 | − | 0.539204i | 0.667337 | − | 0.744756i | \(-0.267434\pi\) |
−0.978646 | + | 0.205552i | \(0.934101\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.409500 | + | 1.51833i | 0.0318795 | + | 0.118202i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.72342 | − | 2.98506i | 0.133363 | − | 0.230991i | −0.791608 | − | 0.611029i | \(-0.790756\pi\) |
0.924971 | + | 0.380038i | \(0.124089\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.44855 | − | 9.43716i | −0.419119 | − | 0.725936i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.6804 | + | 18.6398i | −0.816753 | + | 1.42542i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.21800 | + | 12.5019i | −0.548775 | + | 0.950505i | 0.449584 | + | 0.893238i | \(0.351572\pi\) |
−0.998359 | + | 0.0572675i | \(0.981761\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.30413 | + | 11.5057i | 0.476548 | + | 0.869746i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.6710 | − | 12.6296i | −0.952411 | − | 0.949297i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.7102 | − | 11.3797i | −1.47321 | − | 0.850558i | −0.473665 | − | 0.880705i | \(-0.657069\pi\) |
−0.999545 | + | 0.0301471i | \(0.990402\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.95105i | 0.665326i | 0.943046 | + | 0.332663i | \(0.107947\pi\) | ||||
−0.943046 | + | 0.332663i | \(0.892053\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.2000 | + | 3.77998i | 1.04970 | + | 0.279424i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.615337 | − | 1.06579i | −0.0452404 | − | 0.0783587i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.4292 | − | 7.17600i | −0.908913 | − | 0.524761i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.2152 | + | 3.78928i | 0.961264 | + | 0.275629i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.2572 | + | 12.2729i | 1.53812 | + | 0.888033i | 0.998949 | + | 0.0458359i | \(0.0145951\pi\) |
0.539170 | + | 0.842197i | \(0.318738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.28259 | − | 3.95356i | −0.164305 | − | 0.284584i | 0.772104 | − | 0.635497i | \(-0.219205\pi\) |
−0.936408 | + | 0.350913i | \(0.885871\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.493153 | + | 0.131275i | 0.0353154 | + | 0.00940078i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.1315i | 0.864333i | 0.901794 | + | 0.432166i | \(0.142251\pi\) | ||||
−0.901794 | + | 0.432166i | \(0.857749\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.8273 | + | 7.40587i | 0.909306 | + | 0.524988i | 0.880208 | − | 0.474589i | \(-0.157403\pi\) |
0.0290981 | + | 0.999577i | \(0.490736\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.87932 | − | 9.84702i | −0.696834 | − | 0.694555i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.46586 | + | 1.49814i | 0.173070 | + | 0.105149i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0753154 | − | 0.130450i | 0.00526026 | − | 0.00911104i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.91059 | − | 3.28436i | −0.132796 | − | 0.228279i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.9998 | − | 27.7125i | −1.10673 | − | 1.91691i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.77116 | + | 6.53184i | −0.259617 | + | 0.449670i | −0.966139 | − | 0.258021i | \(-0.916930\pi\) |
0.706522 | + | 0.707691i | \(0.250263\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.07105 | − | 26.2177i | −0.484500 | − | 1.79641i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.954536 | + | 1.65331i | 0.0650988 | + | 0.112754i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.6218 | + | 8.88356i | 0.992594 | + | 0.603055i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.90260 | − | 0.506463i | −0.128566 | − | 0.0342236i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.03346 | + | 2.32872i | −0.271320 | + | 0.156647i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.2846 | − | 14.5980i | 1.69318 | − | 0.977557i | 0.741255 | − | 0.671224i | \(-0.234231\pi\) |
0.951924 | − | 0.306334i | \(-0.0991024\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.8587 | + | 7.48023i | −0.857247 | + | 0.498682i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 29.1575 | 1.93525 | 0.967625 | − | 0.252391i | \(-0.0812169\pi\) | ||||
0.967625 | + | 0.252391i | \(0.0812169\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.4121i | 1.15062i | 0.817934 | + | 0.575312i | \(0.195119\pi\) | ||||
−0.817934 | + | 0.575312i | \(0.804881\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.7769 | + | 14.1769i | −0.972250 | + | 0.932773i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.3517 | − | 8.28596i | 0.940212 | − | 0.542831i | 0.0501850 | − | 0.998740i | \(-0.484019\pi\) |
0.890027 | + | 0.455908i | \(0.150686\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.00946495 | − | 0.0163938i | 0.000617425 | − | 0.00106941i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.22978 | + | 19.6464i | −0.339711 | + | 1.27617i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.45527 | − | 4.88165i | −0.546926 | − | 0.315768i | 0.200955 | − | 0.979600i | \(-0.435595\pi\) |
−0.747881 | + | 0.663833i | \(0.768929\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.8582i | 0.699437i | 0.936855 | + | 0.349719i | \(0.113723\pi\) | ||||
−0.936855 | + | 0.349719i | \(0.886277\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.91119 | + | 15.0898i | −0.250903 | + | 0.968012i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.765469 | − | 1.19869i | 0.0489040 | − | 0.0765812i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.3844 | −0.660741 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.64135 | + | 5.62291i | 0.357506 | + | 0.356337i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.4155 | −1.73045 | −0.865224 | − | 0.501385i | \(-0.832824\pi\) | ||||
−0.865224 | + | 0.501385i | \(0.832824\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.65976 | 0.355826 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.290743 | + | 1.09222i | −0.0182070 | + | 0.0683974i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.3169 | −1.70398 | −0.851989 | − | 0.523559i | \(-0.824604\pi\) | ||||
−0.851989 | + | 0.523559i | \(0.824604\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.32106 | − | 13.6960i | 0.517045 | − | 0.851027i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.62652 | + | 2.83864i | −0.100679 | + | 0.175708i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.8160i | 0.851928i | 0.904740 | + | 0.425964i | \(0.140065\pi\) | ||||
−0.904740 | + | 0.425964i | \(0.859935\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.90025 | − | 1.09711i | −0.116731 | − | 0.0673948i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.65329 | + | 8.62500i | 0.529573 | + | 0.527841i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.7471 | − | 18.6145i | 0.655260 | − | 1.13494i | −0.326568 | − | 0.945174i | \(-0.605892\pi\) |
0.981828 | − | 0.189770i | \(-0.0607744\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.2614 | − | 15.7394i | 1.65601 | − | 0.956101i | 0.681488 | − | 0.731829i | \(-0.261333\pi\) |
0.974527 | − | 0.224271i | \(-0.0720002\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.58659 | + | 6.45319i | 0.0960249 | + | 0.390565i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 22.1587i | − | 1.33622i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8408 | −0.711445 | −0.355722 | − | 0.934592i | \(-0.615765\pi\) | ||||
−0.355722 | + | 0.934592i | \(0.615765\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.64478 | + | 16.8323i | −0.577418 | + | 1.00772i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.4588 | + | 11.2346i | −1.16082 | + | 0.670198i | −0.951500 | − | 0.307650i | \(-0.900457\pi\) |
−0.209317 | + | 0.977848i | \(0.567124\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.17672 | + | 0.679378i | −0.0699486 | + | 0.0403848i | −0.534566 | − | 0.845126i | \(-0.679525\pi\) |
0.464618 | + | 0.885511i | \(0.346192\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.77902 | + | 1.78486i | −0.105380 | + | 0.105726i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.96100 | + | 0.0438493i | 0.115754 | + | 0.00258834i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.34242 | + | 5.78925i | 0.196613 | + | 0.340544i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.48862 | − | 4.50334i | 0.263128 | − | 0.263991i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.10060 | + | 14.0307i | −0.473242 | + | 0.819680i | −0.999531 | − | 0.0306263i | \(-0.990250\pi\) |
0.526289 | + | 0.850306i | \(0.323583\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.04931 | − | 1.81745i | −0.0610931 | − | 0.105816i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.4993 | − | 16.3380i | −0.957384 | − | 0.948025i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.918339 | − | 1.59061i | 0.0531089 | − | 0.0919873i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.9080 | + | 21.2458i | −0.744003 | + | 1.22459i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.0211 | − | 5.93921i | 1.26508 | − | 0.341199i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.49281 | + | 0.861872i | 0.0854778 | + | 0.0493506i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.22930i | 0.526744i | 0.964694 | + | 0.263372i | \(0.0848346\pi\) | ||||
−0.964694 | + | 0.263372i | \(0.915165\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.10468 | + | 22.6347i | 0.347283 | + | 1.28764i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.313334 | − | 0.542711i | −0.0177676 | − | 0.0307743i | 0.857005 | − | 0.515308i | \(-0.172323\pi\) |
−0.874772 | + | 0.484534i | \(0.838989\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.43528 | − | 2.56071i | −0.250697 | − | 0.144740i | 0.369387 | − | 0.929276i | \(-0.379568\pi\) |
−0.620083 | + | 0.784536i | \(0.712901\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.38098 | + | 0.832841i | 0.0778094 | + | 0.0469253i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.62803 | − | 2.09464i | −0.203770 | − | 0.117647i | 0.394643 | − | 0.918835i | \(-0.370868\pi\) |
−0.598413 | + | 0.801188i | \(0.704202\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.43661 | − | 4.22033i | −0.136424 | − | 0.236293i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.3681 | + | 18.4283i | −1.02521 | + | 1.02857i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 22.9990i | − | 1.27970i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.22744 | − | 3.59542i | −0.345436 | − | 0.199438i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.42877 | + | 9.12403i | −0.134311 | + | 0.504560i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.246440 | + | 0.00551057i | 0.0135867 | + | 0.000303808i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9710 | + | 22.4664i | −0.712949 | + | 1.23486i | 0.250797 | + | 0.968040i | \(0.419307\pi\) |
−0.963745 | + | 0.266824i | \(0.914026\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.7665 | + | 9.03408i | 0.863999 | + | 0.495065i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.818123 | − | 1.41703i | −0.0446989 | − | 0.0774207i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.40130 | − | 14.5515i | 0.457648 | − | 0.792669i | −0.541188 | − | 0.840901i | \(-0.682025\pi\) |
0.998836 | + | 0.0482321i | \(0.0153587\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.6547 | + | 3.10242i | 0.632996 | + | 0.168500i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.4484 | − | 25.0253i | −0.782423 | − | 1.35520i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4786 | + | 1.24124i | 0.997752 | + | 0.0670206i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.116065 | − | 0.430342i | −0.00624875 | − | 0.0231688i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.0574 | + | 14.4669i | −1.34515 | + | 0.776624i | −0.987558 | − | 0.157253i | \(-0.949736\pi\) |
−0.357594 | + | 0.933877i | \(0.616403\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.7481 | − | 11.9789i | 1.11062 | − | 0.641217i | 0.171630 | − | 0.985161i | \(-0.445097\pi\) |
0.938990 | + | 0.343944i | \(0.111763\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.26872 | + | 1.98597i | −0.387976 | + | 0.106003i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.5894 | 0.829743 | 0.414871 | − | 0.909880i | \(-0.363827\pi\) | ||||
0.414871 | + | 0.909880i | \(0.363827\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.18536i | − | 0.169062i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.2923 | + | 3.51393i | −0.756430 | + | 0.185977i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.7053 | + | 6.75809i | −0.617785 | + | 0.356678i | −0.776006 | − | 0.630726i | \(-0.782757\pi\) |
0.158221 | + | 0.987404i | \(0.449424\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.1396 | − | 27.9545i | 0.849451 | − | 1.47129i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.9983 | − | 4.04511i | 0.787207 | − | 0.212313i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.200014 | − | 0.115478i | −0.0104692 | − | 0.00604442i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.1785i | 1.00111i | 0.865705 | + | 0.500554i | \(0.166870\pi\) | ||||
−0.865705 | + | 0.500554i | \(0.833130\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.00728320 | + | 2.22411i | 0.000379148 | + | 0.115782i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.638745 | − | 28.5655i | 0.0331620 | − | 1.48305i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.53539 | 0.131278 | 0.0656388 | − | 0.997843i | \(-0.479091\pi\) | ||||
0.0656388 | + | 0.997843i | \(0.479091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.38372 | + | 0.912605i | −0.174734 | + | 0.0471267i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.58143 | −0.0814479 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.11511 | 0.314112 | 0.157056 | − | 0.987590i | \(-0.449800\pi\) | ||||
0.157056 | + | 0.987590i | \(0.449800\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.49375 | + | 1.21199i | −0.230222 | + | 0.0620920i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.67449 | 0.289953 | 0.144976 | − | 0.989435i | \(-0.453689\pi\) | ||||
0.144976 | + | 0.989435i | \(0.453689\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.10666 | + | 1.15427i | −0.107365 | + | 0.0588271i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.4577 | − | 14.0141i | −1.24325 | − | 0.712374i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 7.88653i | − | 0.399863i | −0.979810 | − | 0.199932i | \(-0.935928\pi\) | ||
0.979810 | − | 0.199932i | \(-0.0640720\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.52283 | + | 2.03391i | 0.178157 | + | 0.102859i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.2677 | + | 2.76925i | −0.517936 | + | 0.139690i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.19244 | + | 2.06536i | −0.0599981 | + | 0.103920i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.2548 | − | 5.92061i | 0.514674 | − | 0.297147i | −0.220079 | − | 0.975482i | \(-0.570632\pi\) |
0.734753 | + | 0.678335i | \(0.237298\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −31.5146 | − | 9.14818i | −1.57771 | − | 0.457982i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.1732i | 1.90628i | 0.302534 | + | 0.953139i | \(0.402168\pi\) | ||||
−0.302534 | + | 0.953139i | \(0.597832\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.37742 | −0.467123 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.903911 | + | 1.58957i | −0.0449157 | + | 0.0789865i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.4407 | + | 13.5335i | −1.16191 | + | 0.670831i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.2828 | − | 6.51411i | 0.557897 | − | 0.322102i | −0.194404 | − | 0.980922i | \(-0.562277\pi\) |
0.752301 | + | 0.658820i | \(0.228944\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.93139 | + | 7.16112i | 0.0952684 | + | 0.353232i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.1896 | − | 23.3552i | 0.698222 | − | 1.14923i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.467170 | + | 0.809162i | 0.0229325 | + | 0.0397202i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.64811 | − | 1.76969i | −0.325559 | − | 0.0866622i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.1454 | − | 26.2325i | 0.739899 | − | 1.28154i | −0.212641 | − | 0.977130i | \(-0.568207\pi\) |
0.952540 | − | 0.304412i | \(-0.0984601\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.20295 | − | 5.54767i | −0.156102 | − | 0.270377i | 0.777358 | − | 0.629059i | \(-0.216560\pi\) |
−0.933460 | + | 0.358682i | \(0.883226\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.000915285 | 0.279505i | 4.45027e−5 | 0.0135900i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.96301 | − | 13.7923i | 0.386263 | − | 0.669027i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.501789 | + | 22.4407i | −0.0242833 | + | 1.08598i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.88721 | − | 10.8462i | 0.139396 | − | 0.523661i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.0071 | + | 5.77758i | 0.482023 | + | 0.278296i | 0.721259 | − | 0.692665i | \(-0.243564\pi\) |
−0.239236 | + | 0.970961i | \(0.576897\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.696999i | 0.0334956i | 0.999860 | + | 0.0167478i | \(0.00533125\pi\) | ||||
−0.999860 | + | 0.0167478i | \(0.994669\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.270926 | + | 0.271815i | −0.0129899 | + | 0.0130325i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.53486 | + | 7.85460i | 0.216932 | + | 0.375737i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.4771 | + | 11.8224i | 0.977316 | + | 0.564254i | 0.901459 | − | 0.432865i | \(-0.142497\pi\) |
0.0758575 | + | 0.997119i | \(0.475831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.869976 | + | 20.9820i | −0.0414274 | + | 0.999142i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.3308 | + | 6.54184i | 0.538343 | + | 0.310812i | 0.744407 | − | 0.667726i | \(-0.232732\pi\) |
−0.206064 | + | 0.978538i | \(0.566066\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.716594 | + | 1.24118i | 0.0339698 | + | 0.0588374i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.08961 | − | 7.74775i | −0.0988349 | − | 0.366456i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.5463i | 0.544906i | 0.962169 | + | 0.272453i | \(0.0878348\pi\) | ||||
−0.962169 | + | 0.272453i | \(0.912165\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.86908 | − | 1.65646i | −0.135100 | − | 0.0779998i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.2463 | − | 7.07876i | 1.23316 | − | 0.332589i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0174266 | + | 0.779341i | −0.000816971 | + | 0.0365361i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.51833 | − | 9.55803i | 0.258137 | − | 0.447106i | −0.707606 | − | 0.706607i | \(-0.750225\pi\) |
0.965743 | + | 0.259501i | \(0.0835582\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.39845 | − | 16.0985i | −0.205302 | − | 0.751415i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.69369 | − | 11.5938i | −0.311756 | − | 0.539978i | 0.666986 | − | 0.745070i | \(-0.267584\pi\) |
−0.978743 | + | 0.205092i | \(0.934251\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6622 | − | 18.4675i | 0.495515 | − | 0.858258i | −0.504471 | − | 0.863428i | \(-0.668313\pi\) |
0.999987 | + | 0.00517079i | \(0.00164592\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.60651 | + | 1.61178i | −0.0745003 | + | 0.0747447i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.97308 | + | 13.8098i | 0.368950 | + | 0.639041i | 0.989402 | − | 0.145204i | \(-0.0463839\pi\) |
−0.620451 | + | 0.784245i | \(0.713051\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.0633 | − | 18.2096i | 0.510856 | − | 0.840839i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.25636 | − | 9.28673i | 0.426511 | − | 0.427910i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 36.3622 | − | 20.9937i | 1.67194 | − | 0.965293i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.7518 | − | 17.7546i | 1.41099 | − | 0.814635i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.3982 | − | 0.106093i | 1.48341 | − | 0.00485767i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.7187 | −1.40357 | −0.701787 | − | 0.712387i | \(-0.747614\pi\) | ||||
−0.701787 | + | 0.712387i | \(0.747614\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.78365i | 0.400500i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.18825 | − | 4.01819i | 0.190572 | − | 0.182834i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.645933 | − | 0.372930i | 0.0293303 | − | 0.0169339i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.423250 | − | 0.733091i | 0.0191793 | − | 0.0332195i | −0.856276 | − | 0.516518i | \(-0.827228\pi\) |
0.875456 | + | 0.483298i | \(0.160561\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.75151 | + | 9.71963i | 0.440979 | + | 0.439537i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.78204 | + | 1.02886i | 0.0804225 | + | 0.0464319i | 0.539672 | − | 0.841875i | \(-0.318548\pi\) |
−0.459249 | + | 0.888307i | \(0.651882\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.50250i | − | 0.157745i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.36961 | − | 2.35440i | −0.0615594 | − | 0.105822i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 36.3767 | − | 19.9314i | 1.63172 | − | 0.894045i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −41.1863 | −1.84375 | −0.921877 | − | 0.387483i | \(-0.873345\pi\) | ||||
−0.921877 | + | 0.387483i | \(0.873345\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.53574 | + | 5.76921i | −0.0686116 | + | 0.257749i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.48781 | 0.0663383 | 0.0331692 | − | 0.999450i | \(-0.489440\pi\) | ||||
0.0331692 | + | 0.999450i | \(0.489440\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.67549 | 0.119058 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.3680 | + | 13.3243i | 0.593694 | + | 0.591753i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.7882 | 0.744123 | 0.372062 | − | 0.928208i | \(-0.378651\pi\) | ||||
0.372062 | + | 0.928208i | \(0.378651\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0672325 | − | 3.00673i | 0.00297419 | − | 0.133010i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.45383 | − | 35.9884i | 0.417397 | − | 1.58892i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.75004i | 0.121181i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.360559 | − | 0.208169i | −0.0158574 | − | 0.00915526i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.43193 | − | 24.1625i | 0.282330 | − | 1.06061i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.00777 | − | 1.74551i | 0.0441512 | − | 0.0764722i | −0.843105 | − | 0.537749i | \(-0.819275\pi\) |
0.887257 | + | 0.461276i | \(0.152608\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.4865 | + | 21.6429i | −1.63917 | + | 0.946376i | −0.658052 | + | 0.752973i | \(0.728619\pi\) |
−0.981119 | + | 0.193403i | \(0.938047\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −15.7317 | − | 16.3975i | −0.686589 | − | 0.715647i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 20.7688i | − | 0.904704i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.3958 | 0.930254 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26.8860 | + | 15.4054i | 1.16675 | + | 0.668539i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.931059 | + | 0.537547i | −0.0403286 | + | 0.0232837i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.64325 | + | 1.52608i | −0.114278 | + | 0.0659783i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 38.0939 | + | 10.1404i | 1.64387 | + | 0.437590i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.3635 | − | 16.8355i | −1.13556 | − | 0.725155i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.3502 | + | 21.3912i | 0.530977 | + | 0.919679i | 0.999347 | + | 0.0361463i | \(0.0115082\pi\) |
−0.468370 | + | 0.883533i | \(0.655158\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.03716 | − | 14.9688i | −0.173251 | − | 0.642373i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.553783 | + | 0.959181i | −0.0237215 | + | 0.0410868i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.52320 | − | 9.56646i | −0.236155 | − | 0.409032i | 0.723453 | − | 0.690374i | \(-0.242554\pi\) |
−0.959608 | + | 0.281342i | \(0.909221\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.4516 | + | 0.0833452i | −1.08625 | + | 0.00355709i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.90464 | − | 6.76304i | 0.166343 | − | 0.288115i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.0477 | − | 0.694248i | −1.32028 | − | 0.0295224i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.50973 | + | 1.50479i | 0.0640843 | + | 0.0638748i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.3351 | + | 12.8952i | 0.946369 | + | 0.546386i | 0.891951 | − | 0.452132i | \(-0.149336\pi\) |
0.0544176 | + | 0.998518i | \(0.482670\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.6256i | − | 0.576300i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0219 | + | 6.39450i | 1.01420 | + | 0.269976i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.9859 | − | 32.8846i | −0.800161 | − | 1.38592i | −0.919510 | − | 0.393067i | \(-0.871414\pi\) |
0.119349 | − | 0.992852i | \(-0.461919\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.22522 | + | 0.707381i | 0.0515454 | + | 0.0297597i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.8088 | − | 0.376393i | −0.999875 | − | 0.0158070i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.8834 | + | 11.4797i | 0.833555 | + | 0.481253i | 0.855068 | − | 0.518515i | \(-0.173515\pi\) |
−0.0215131 | + | 0.999769i | \(0.506848\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.91228 | + | 10.2404i | 0.247421 | + | 0.428546i | 0.962810 | − | 0.270181i | \(-0.0870836\pi\) |
−0.715388 | + | 0.698727i | \(0.753750\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −41.0838 | − | 10.9363i | −1.71630 | − | 0.456870i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.28048i | 0.261914i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.4185 | − | 12.9433i | −0.933293 | − | 0.538837i | −0.0454415 | − | 0.998967i | \(-0.514469\pi\) |
−0.887852 | + | 0.460130i | \(0.847803\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.60033 | + | 5.58202i | 0.232742 | + | 0.231981i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.31743 | + | 10.3981i | −0.262091 | + | 0.431387i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.1294 | + | 41.7933i | −0.999338 | + | 1.73090i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.883906 | + | 0.00289449i | −0.0365450 | + | 0.000119672i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.28769 | − | 2.23034i | −0.0531487 | − | 0.0920562i | 0.838227 | − | 0.545321i | \(-0.183592\pi\) |
−0.891376 | + | 0.453265i | \(0.850259\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.1534 | − | 40.1028i | 0.954018 | − | 1.65241i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.47162 | − | 20.2874i | −0.225072 | − | 0.834514i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.0904 | + | 19.2092i | 0.455430 | + | 0.788828i | 0.998713 | − | 0.0507220i | \(-0.0161523\pi\) |
−0.543283 | + | 0.839550i | \(0.682819\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.72606 | − | 0.0385959i | −0.0707615 | − | 0.00158228i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.7914 | − | 6.59934i | −1.01464 | − | 0.270093i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.0096 | + | 12.7072i | −0.899287 | + | 0.519204i | −0.876969 | − | 0.480547i | \(-0.840438\pi\) |
−0.0223184 | + | 0.999751i | \(0.507105\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.04486 | + | 1.75795i | −0.124203 | + | 0.0717084i | −0.560814 | − | 0.827942i | \(-0.689512\pi\) |
0.436612 | + | 0.899650i | \(0.356178\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.9624 | + | 12.0113i | 0.853656 | + | 0.489138i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.82224 | 0.0740847 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 32.7626i | − | 1.32979i | −0.746936 | − | 0.664896i | \(-0.768476\pi\) | ||
0.746936 | − | 0.664896i | \(-0.231524\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.79935 | − | 1.39317i | −0.194480 | − | 0.0564543i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.117007 | + | 0.0675539i | −0.00473359 | + | 0.00273294i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.757167 | + | 1.31145i | −0.0305817 | + | 0.0529691i | −0.880911 | − | 0.473282i | \(-0.843069\pi\) |
0.850329 | + | 0.526251i | \(0.176403\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0671133 | + | 0.252121i | −0.00270627 | + | 0.0101665i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.52621 | − | 3.76791i | −0.262735 | − | 0.151690i | 0.362846 | − | 0.931849i | \(-0.381805\pi\) |
−0.625582 | + | 0.780159i | \(0.715138\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.6456i | 1.31214i | 0.754702 | + | 0.656068i | \(0.227782\pi\) | ||||
−0.754702 | + | 0.656068i | \(0.772218\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.67641 | + | 4.63070i | 0.187658 | + | 0.185823i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.69033 | + | 15.9497i | −0.388235 | + | 0.639013i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.3825 | 0.975299 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 39.2555 | + | 39.1272i | 1.56771 | + | 1.56259i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.4537 | −0.775672 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.79887 | −0.270659 | −0.135329 | − | 0.990801i | \(-0.543209\pi\) | ||||
−0.135329 | + | 0.990801i | \(0.543209\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.36046 | − | 12.6241i | 0.133566 | − | 0.501761i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.545976 | −0.0216664 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.00908 | + | 4.67746i | −0.356953 | + | 0.185328i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.6498 | + | 40.6546i | 0.935570 | + | 1.60827i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.4927i | 1.28338i | 0.766962 | + | 0.641692i | \(0.221767\pi\) | ||||
−0.766962 | + | 0.641692i | \(0.778233\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.5970 | + | 11.8917i | 0.812267 | + | 0.468963i | 0.847742 | − | 0.530408i | \(-0.177961\pi\) |
−0.0354756 | + | 0.999371i | \(0.511295\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.34195 | − | 2.33430i | −0.0922143 | − | 0.0919128i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.1964 | + | 19.3928i | −0.440177 | + | 0.762410i | −0.997702 | − | 0.0677505i | \(-0.978418\pi\) |
0.557525 | + | 0.830160i | \(0.311751\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.9725 | + | 23.0781i | −1.56906 | + | 0.905895i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28.4587 | − | 8.26111i | −1.11539 | − | 0.323778i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.7245i | 1.59367i | 0.604196 | + | 0.796836i | \(0.293494\pi\) | ||||
−0.604196 | + | 0.796836i | \(0.706506\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.24749 | −0.0487434 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.41014 | − | 0.0111671i | 0.133042 | − | 0.000435668i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.8786 | + | 14.3637i | −0.969134 | + | 0.559530i | −0.898972 | − | 0.438006i | \(-0.855685\pi\) |
−0.0701619 | + | 0.997536i | \(0.522352\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.3398 | − | 18.6714i | 1.25787 | − | 0.726234i | 0.285213 | − | 0.958464i | \(-0.407936\pi\) |
0.972661 | + | 0.232230i | \(0.0746023\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.69483 | − | 5.71351i | 0.221169 | − | 0.221894i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.28985 | − | 1.99876i | −0.127575 | − | 0.0775086i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.690612 | + | 1.19617i | 0.0267406 | + | 0.0463161i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −35.6992 | + | 35.8163i | −1.38021 | + | 1.38474i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.9557 | − | 32.8323i | 0.731777 | − | 1.26748i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.5131 | − | 28.6015i | −0.636532 | − | 1.10251i | −0.986188 | − | 0.165628i | \(-0.947035\pi\) |
0.349656 | − | 0.936878i | \(-0.386298\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.1298 | − | 18.3088i | 0.697816 | − | 0.704705i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.4381 | + | 18.0793i | −0.401169 | + | 0.694845i | −0.993867 | − | 0.110580i | \(-0.964729\pi\) |
0.592698 | + | 0.805424i | \(0.298063\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.30056 | + | 5.04304i | 0.318546 | + | 0.193534i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −48.7600 | + | 13.1508i | −1.86849 | + | 0.503940i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.17377 | − | 0.677674i | −0.0449129 | − | 0.0259305i | 0.477375 | − | 0.878699i | \(-0.341588\pi\) |
−0.522288 | + | 0.852769i | \(0.674922\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.870051i | 0.0332430i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.85331 | − | 29.1182i | −0.299623 | − | 1.11093i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.83036 | + | 13.5626i | 0.298313 | + | 0.516693i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.62041 | − | 5.55435i | −0.365978 | − | 0.211297i | 0.305722 | − | 0.952121i | \(-0.401102\pi\) |
−0.671700 | + | 0.740823i | \(0.734436\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.3172 | − | 30.3728i | 0.695814 | − | 1.15377i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.698894 | − | 0.403507i | −0.0265106 | − | 0.0153059i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.19054 | − | 2.06208i | −0.0450950 | − | 0.0781068i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.2631 | + | 20.3296i | −0.766422 | + | 0.768936i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.375966i | 0.0142000i | 0.999975 | + | 0.00710002i | \(0.00226003\pi\) | ||||
−0.999975 | + | 0.00710002i | \(0.997740\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.5635 | − | 21.6873i | −1.41674 | − | 0.817953i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.00843417 | + | 0.0316842i | −0.000317649 | + | 0.00119330i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.7410 | + | 30.5540i | 0.629612 | + | 1.14910i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.94936 | + | 3.37639i | −0.0732098 | + | 0.126803i | −0.900306 | − | 0.435257i | \(-0.856658\pi\) |
0.827097 | + | 0.562060i | \(0.189991\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.115312 | − | 35.2134i | −0.00432453 | − | 1.32061i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.09512 | + | 7.09296i | 0.153364 | + | 0.265634i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.658312 | − | 1.14023i | 0.0246195 | − | 0.0426422i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.3415 | + | 4.35002i | 0.610284 | + | 0.162454i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.4338 | + | 42.3205i | 0.911225 | + | 1.57829i | 0.812336 | + | 0.583190i | \(0.198196\pi\) |
0.0988894 | + | 0.995098i | \(0.468471\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.4053 | + | 17.2075i | −1.16959 | + | 0.640840i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.89733 | − | 18.1581i | −0.182134 | − | 0.675307i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.68318 | − | 2.70384i | 0.173929 | − | 0.100418i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.8420 | + | 6.83700i | −0.439196 | + | 0.253570i | −0.703257 | − | 0.710936i | \(-0.748272\pi\) |
0.264060 | + | 0.964506i | \(0.414938\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.265242 | − | 26.9987i | −0.00982379 | − | 0.999952i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.1775 | 1.11615 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 16.1607i | − | 0.596910i | −0.954424 | − | 0.298455i | \(-0.903529\pi\) | ||
0.954424 | − | 0.298455i | \(-0.0964713\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.739452 | + | 2.34980i | −0.0272751 | + | 0.0866738i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.1657 | + | 17.9935i | −1.14800 | + | 0.662800i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.7914 | + | 27.3515i | −0.580895 | + | 1.00614i | 0.414478 | + | 0.910059i | \(0.363964\pi\) |
−0.995374 | + | 0.0960807i | \(0.969369\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.3657 | − | 4.68362i | 0.637946 | − | 0.172057i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.63924 | − | 4.98787i | −0.316943 | − | 0.182987i | 0.333086 | − | 0.942896i | \(-0.391910\pi\) |
−0.650029 | + | 0.759909i | \(0.725243\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 0.941325i | − | 0.0344875i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.9701 | − | 6.85877i | −0.437963 | − | 0.250949i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33.9671 | − | 20.6369i | −1.24113 | − | 0.754055i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.9066 | −0.762892 | −0.381446 | − | 0.924391i | \(-0.624574\pi\) | ||||
−0.381446 | + | 0.924391i | \(0.624574\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 45.8468 | − | 12.3651i | 1.67075 | − | 0.450609i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.18884 | 0.116054 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −50.5460 | −1.83713 | −0.918563 | − | 0.395274i | \(-0.870650\pi\) | ||||
−0.918563 | + | 0.395274i | \(0.870650\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.46480 | + | 2.55270i | −0.343550 | + | 0.0926572i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.8424 | −0.755535 | −0.377768 | − | 0.925900i | \(-0.623308\pi\) | ||||
−0.377768 | + | 0.925900i | \(0.623308\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.4189 | − | 0.322417i | −0.522000 | − | 0.0116723i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.00641062 | − | 1.95765i | −0.000231777 | − | 0.0707788i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.9784i | 0.540838i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.3167 | + | 14.6166i | 0.912944 | + | 0.527088i | 0.881377 | − | 0.472413i | \(-0.156617\pi\) |
0.0315668 | + | 0.999502i | \(0.489950\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 45.6819 | − | 12.3206i | 1.64519 | − | 0.443716i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.9472 | − | 18.9612i | 0.393745 | − | 0.681986i | −0.599195 | − | 0.800603i | \(-0.704513\pi\) |
0.992940 | + | 0.118617i | \(0.0378459\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.7699 | − | 16.0329i | 0.997523 | − | 0.575920i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.73802 | + | 26.6568i | −0.277600 | + | 0.956306i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 5.30893i | − | 0.190212i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −70.0578 | −2.50686 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.43972 | − | 5.48065i | 0.0514514 | − | 0.195863i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.33203 | − | 0.769050i | 0.0475423 | − | 0.0274486i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.08328 | − | 4.08953i | 0.252492 | − | 0.145776i | −0.368413 | − | 0.929662i | \(-0.620099\pi\) |
0.620905 | + | 0.783886i | \(0.286765\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.23136 | − | 23.1044i | −0.221842 | − | 0.822538i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.411843 | + | 18.4182i | −0.0146435 | + | 0.654875i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.15142 | − | 10.6546i | −0.218443 | − | 0.378355i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.67260 | + | 0.977627i | 0.130254 | + | 0.0346729i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.86546 | − | 8.42722i | 0.172343 | − | 0.298508i | −0.766895 | − | 0.641772i | \(-0.778199\pi\) |
0.939239 | + | 0.343265i | \(0.111533\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.149616 | − | 0.259143i | −0.00529304 | − | 0.00916782i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.3610 | − | 10.5207i | −0.648753 | − | 0.371730i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.53979 | + | 4.39905i | −0.0896273 | + | 0.155239i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.597094 | − | 0.327157i | 0.0210448 | − | 0.0115308i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.57667 | + | 35.9761i | −0.337115 | + | 1.26642i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.2263 | + | 20.9153i | 1.27365 | + | 0.735341i | 0.975673 | − | 0.219232i | \(-0.0703553\pi\) |
0.297976 | + | 0.954574i | \(0.403689\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.7323i | 1.43031i | 0.698968 | + | 0.715153i | \(0.253643\pi\) | ||||
−0.698968 | + | 0.715153i | \(0.746357\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −38.4903 | + | 38.6166i | −1.34991 | + | 1.35434i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.807539 | + | 1.39870i | 0.0282869 | + | 0.0489943i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 58.2701 | + | 33.6423i | 2.03861 | + | 1.17699i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.56381 | − | 10.0761i | −0.194415 | − | 0.352086i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.3422 | + | 11.1672i | 0.675049 | + | 0.389740i | 0.797987 | − | 0.602675i | \(-0.205898\pi\) |
−0.122938 | + | 0.992414i | \(0.539232\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.5308 | + | 23.4360i | 0.471654 | + | 0.816929i | 0.999474 | − | 0.0324276i | \(-0.0103238\pi\) |
−0.527820 | + | 0.849356i | \(0.676991\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.99416 | + | 37.0559i | 0.347952 | + | 1.29012i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 22.1709i | − | 0.770957i | −0.922717 | − | 0.385479i | \(-0.874036\pi\) | ||
0.922717 | − | 0.385479i | \(-0.125964\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.2166 | − | 18.6003i | −1.11893 | − | 0.646013i | −0.177801 | − | 0.984066i | \(-0.556898\pi\) |
−0.941127 | + | 0.338053i | \(0.890232\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.8013 | − | 5.34052i | 0.686901 | − | 0.185260i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.3595 | − | 19.9530i | −0.358935 | − | 0.691331i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.350162 | + | 0.606499i | −0.0121179 | + | 0.0209888i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.53712 | − | 32.4987i | 0.295086 | − | 1.12332i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.96294 | − | 13.7922i | −0.274911 | − | 0.476160i | 0.695202 | − | 0.718815i | \(-0.255315\pi\) |
−0.970113 | + | 0.242655i | \(0.921982\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.9054 | + | 24.0848i | −0.479495 | + | 0.830510i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.4739 | − | 27.5640i | 0.946250 | − | 0.949354i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.10703 | + | 1.91743i | 0.0380829 | + | 0.0659615i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.4021 | + | 20.8099i | 0.391781 | + | 0.715038i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.66140 | − | 1.66685i | 0.0570192 | − | 0.0572062i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.64384 | − | 3.83582i | 0.227748 | − | 0.131490i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.4364 | − | 23.3459i | 1.38451 | − | 0.799350i | 0.391824 | − | 0.920040i | \(-0.371844\pi\) |
0.992690 | + | 0.120690i | \(0.0385107\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.17003 | − | 3.78719i | 0.0742135 | − | 0.129519i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.33848 | −0.182359 | −0.0911795 | − | 0.995834i | \(-0.529064\pi\) | ||||
−0.0911795 | + | 0.995834i | \(0.529064\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.0559i | 0.343102i | 0.985175 | + | 0.171551i | \(0.0548779\pi\) | ||||
−0.985175 | + | 0.171551i | \(0.945122\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.29915 | + | 0.811133i | −0.112435 | + | 0.0276433i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.7144 | − | 18.8877i | 1.11361 | − | 0.642943i | 0.173849 | − | 0.984772i | \(-0.444380\pi\) |
0.939762 | + | 0.341829i | \(0.111046\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.46654 | − | 2.54012i | 0.0498639 | − | 0.0863668i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.20063 | − | 8.17382i | −0.278508 | − | 0.277597i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.4249 | + | 26.2261i | 1.54094 | + | 0.889659i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.6783i | 0.395706i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.47518 | + | 9.55541i | −0.185307 | + | 0.323402i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.57239 | − | 4.69486i | −0.0869626 | − | 0.158715i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.5264 | −1.57109 | −0.785543 | − | 0.618807i | \(-0.787616\pi\) | ||||
−0.785543 | + | 0.618807i | \(0.787616\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.21841 | − | 27.1170i | 0.243471 | − | 0.914634i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.9474 | 1.07633 | 0.538167 | − | 0.842838i | \(-0.319117\pi\) | ||||
0.538167 | + | 0.842838i | \(0.319117\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.2919 | −1.28862 | −0.644312 | − | 0.764763i | \(-0.722856\pi\) | ||||
−0.644312 | + | 0.764763i | \(0.722856\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.57447 | + | 2.56606i | 0.0865400 | + | 0.0862570i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.6168 | 1.36378 | 0.681889 | − | 0.731455i | \(-0.261159\pi\) | ||||
0.681889 | + | 0.731455i | \(0.261159\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.41627 | − | 6.23502i | −0.114578 | − | 0.209116i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 34.9605 | + | 19.8803i | 1.17122 | + | 0.666016i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 0.667177i | − | 0.0223262i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.00469 | + | 2.31211i | 0.133862 | + | 0.0772852i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.818328 | + | 3.07417i | −0.0273232 | + | 0.102643i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.52602 | − | 6.10724i | 0.117599 | − | 0.203688i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.0379 | + | 17.3424i | −1.00071 | + | 0.577760i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.0035 | − | 41.3511i | 0.399453 | − | 1.37608i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.81866i | − | 0.0604543i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.9969 | −0.996030 | −0.498015 | − | 0.867168i | \(-0.665938\pi\) | ||||
−0.498015 | + | 0.867168i | \(0.665938\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −34.1471 | + | 19.8642i | −1.13259 | + | 0.658855i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.2362 | + | 19.7663i | −1.13430 | + | 0.654886i | −0.945012 | − | 0.327036i | \(-0.893950\pi\) |
−0.189284 | + | 0.981922i | \(0.560617\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.7964 | − | 10.2748i | 0.588976 | − | 0.340045i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.88514 | − | 0.768010i | −0.0953798 | − | 0.0253896i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.80576 | − | 14.2463i | −0.257769 | − | 0.470453i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.74272 | + | 16.8749i | 0.321383 | + | 0.556651i | 0.980774 | − | 0.195149i | \(-0.0625191\pi\) |
−0.659391 | + | 0.751800i | \(0.729186\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.16266 | − | 15.4341i | −0.137164 | − | 0.508571i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.3674 | + | 19.6889i | −0.374163 | + | 0.648069i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.0178 | − | 26.0115i | −0.493781 | − | 0.855253i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.4177 | − | 35.0985i | −0.670604 | − | 1.15279i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.93060 | + | 12.0041i | −0.227386 | + | 0.393843i | −0.957032 | − | 0.289981i | \(-0.906351\pi\) |
0.729647 | + | 0.683824i | \(0.239684\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.24061 | − | 50.0765i | 0.0734330 | − | 1.64119i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.768765 | + | 0.766251i | 0.0251682 | + | 0.0250859i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.52534 | + | 1.45801i | 0.0825876 | + | 0.0476819i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.38328i | 0.175864i | 0.996126 | + | 0.0879320i | \(0.0280258\pi\) | ||||
−0.996126 | + | 0.0879320i | \(0.971974\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.57204 | + | 2.28184i | 0.279738 | + | 0.0744649i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.28619 | + | 5.69185i | 0.107127 | + | 0.185549i | 0.914605 | − | 0.404348i | \(-0.132502\pi\) |
−0.807478 | + | 0.589897i | \(0.799168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.813188 | + | 0.469494i | 0.0264810 | + | 0.0152888i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.68504 | − | 0.769899i | −0.0873444 | − | 0.0250448i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.7081 | − | 15.9973i | −0.900392 | − | 0.519841i | −0.0230644 | − | 0.999734i | \(-0.507342\pi\) |
−0.877327 | + | 0.479893i | \(0.840676\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.824201 | + | 1.42756i | 0.0267547 | + | 0.0463405i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.01187 | + | 1.86653i | 0.227376 | + | 0.0605263i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.5312i | 1.66926i | 0.550812 | + | 0.834629i | \(0.314318\pi\) | ||||
−0.550812 | + | 0.834629i | \(0.685682\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.31901 | − | 2.49358i | −0.139760 | − | 0.0806903i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.97821 | + | 5.95866i | 0.193248 | + | 0.192616i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.93595 | + | 5.44407i | −0.320849 | + | 0.175798i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.40825 | − | 9.36736i | 0.174460 | − | 0.302173i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.4052 | − | 39.1022i | 0.721999 | − | 1.26005i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.463773 | + | 0.803278i | 0.0149294 | + | 0.0258584i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.01867 | − | 10.4246i | 0.193547 | − | 0.335234i | −0.752876 | − | 0.658162i | \(-0.771334\pi\) |
0.946423 | + | 0.322929i | \(0.104667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.3731 | + | 38.4611i | 0.333233 | + | 1.23555i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.4783 | + | 40.6656i | 0.753454 | + | 1.30502i | 0.946139 | + | 0.323761i | \(0.104947\pi\) |
−0.192685 | + | 0.981261i | \(0.561719\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.234925 | − | 10.5062i | 0.00753135 | − | 0.336812i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.0358 | + | 3.20386i | 0.385453 | + | 0.102606i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.4083 | + | 16.4015i | −0.908863 | + | 0.524732i | −0.880065 | − | 0.474853i | \(-0.842501\pi\) |
−0.0287976 | + | 0.999585i | \(0.509168\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.2980 | − | 15.7605i | 0.872448 | − | 0.503708i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.0535523 | − | 16.3535i | −0.00170979 | − | 0.522128i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.0145 | 0.957314 | 0.478657 | − | 0.878002i | \(-0.341124\pi\) | ||||
0.478657 | + | 0.878002i | \(0.341124\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2.46485i | − | 0.0785368i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.414606 | + | 0.101936i | −0.0131971 | + | 0.00324465i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.3062 | + | 5.95029i | −0.327718 | + | 0.189208i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.9364 | − | 43.1911i | 0.792131 | − | 1.37201i | −0.132514 | − | 0.991181i | \(-0.542305\pi\) |
0.924645 | − | 0.380831i | \(-0.124362\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.5584 | − | 43.4207i | 0.366794 | − | 1.37791i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.60624 | − | 1.50471i | −0.0826232 | − | 0.0477026i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.48520i | 0.0470368i | 0.999723 | + | 0.0235184i | \(0.00748683\pi\) | ||||
−0.999723 | + | 0.0235184i | \(0.992513\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.4409 | − | 7.99656i | −0.963107 | − | 0.253000i |
(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 | 504.2.cx.a.185.3 | yes | 48 | |
3.2 | odd | 2 | 1512.2.cx.a.17.11 | 48 | |||
4.3 | odd | 2 | 1008.2.df.e.689.22 | 48 | |||
7.5 | odd | 6 | 504.2.bs.a.257.10 | ✓ | 48 | ||
9.2 | odd | 6 | 504.2.bs.a.353.10 | yes | 48 | ||
9.7 | even | 3 | 1512.2.bs.a.521.11 | 48 | |||
12.11 | even | 2 | 3024.2.df.e.17.11 | 48 | |||
21.5 | even | 6 | 1512.2.bs.a.1097.11 | 48 | |||
28.19 | even | 6 | 1008.2.ca.e.257.15 | 48 | |||
36.7 | odd | 6 | 3024.2.ca.e.2033.11 | 48 | |||
36.11 | even | 6 | 1008.2.ca.e.353.15 | 48 | |||
63.47 | even | 6 | inner | 504.2.cx.a.425.3 | yes | 48 | |
63.61 | odd | 6 | 1512.2.cx.a.89.11 | 48 | |||
84.47 | odd | 6 | 3024.2.ca.e.2609.11 | 48 | |||
252.47 | odd | 6 | 1008.2.df.e.929.22 | 48 | |||
252.187 | even | 6 | 3024.2.df.e.1601.11 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.10 | ✓ | 48 | 7.5 | odd | 6 | ||
504.2.bs.a.353.10 | yes | 48 | 9.2 | odd | 6 | ||
504.2.cx.a.185.3 | yes | 48 | 1.1 | even | 1 | trivial | |
504.2.cx.a.425.3 | yes | 48 | 63.47 | even | 6 | inner | |
1008.2.ca.e.257.15 | 48 | 28.19 | even | 6 | |||
1008.2.ca.e.353.15 | 48 | 36.11 | even | 6 | |||
1008.2.df.e.689.22 | 48 | 4.3 | odd | 2 | |||
1008.2.df.e.929.22 | 48 | 252.47 | odd | 6 | |||
1512.2.bs.a.521.11 | 48 | 9.7 | even | 3 | |||
1512.2.bs.a.1097.11 | 48 | 21.5 | even | 6 | |||
1512.2.cx.a.17.11 | 48 | 3.2 | odd | 2 | |||
1512.2.cx.a.89.11 | 48 | 63.61 | odd | 6 | |||
3024.2.ca.e.2033.11 | 48 | 36.7 | odd | 6 | |||
3024.2.ca.e.2609.11 | 48 | 84.47 | odd | 6 | |||
3024.2.df.e.17.11 | 48 | 12.11 | even | 2 | |||
3024.2.df.e.1601.11 | 48 | 252.187 | even | 6 |