Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,3,Mod(319,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.319");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.o (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: | \(15.6948632272\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 319.7 | ||
Root | \(0.186266 - 1.99131i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.319 |
Dual form | 576.3.o.g.511.7 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.67178 | + | 1.36441i | 0.890592 | + | 0.454803i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.07403 | + | 5.32438i | −0.614806 | + | 1.06488i | 0.375612 | + | 0.926777i | \(0.377432\pi\) |
−0.990418 | + | 0.138099i | \(0.955901\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.511543 | − | 0.295340i | 0.0730776 | − | 0.0421914i | −0.463016 | − | 0.886350i | \(-0.653233\pi\) |
0.536094 | + | 0.844159i | \(0.319899\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.27677 | + | 7.29079i | 0.586308 | + | 0.810088i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.1205 | + | 8.72982i | −1.37459 | + | 0.793620i | −0.991502 | − | 0.130092i | \(-0.958473\pi\) |
−0.383088 | + | 0.923712i | \(0.625139\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.892255 | − | 1.54543i | 0.0686350 | − | 0.118879i | −0.829666 | − | 0.558261i | \(-0.811469\pi\) |
0.898301 | + | 0.439381i | \(0.144802\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.4778 | + | 10.0313i | −1.03185 | + | 0.668754i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −16.9171 | −0.995123 | −0.497562 | − | 0.867429i | \(-0.665771\pi\) | ||||
−0.497562 | + | 0.867429i | \(0.665771\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 19.5058i | − | 1.02662i | −0.858203 | − | 0.513310i | \(-0.828419\pi\) | ||
0.858203 | − | 0.513310i | \(-0.171581\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.76969 | − | 0.0911265i | 0.0842711 | − | 0.00433936i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.86778 | − | 3.96511i | −0.298599 | − | 0.172396i | 0.343214 | − | 0.939257i | \(-0.388484\pi\) |
−0.641813 | + | 0.766861i | \(0.721818\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.39933 | − | 11.0840i | −0.255973 | − | 0.443359i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.15071 | + | 26.6790i | 0.153730 | + | 0.988113i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.17517 | − | 5.49956i | −0.109489 | − | 0.189640i | 0.806075 | − | 0.591814i | \(-0.201588\pi\) |
−0.915563 | + | 0.402174i | \(0.868255\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 27.6558 | + | 15.9671i | 0.892124 | + | 0.515068i | 0.874637 | − | 0.484779i | \(-0.161100\pi\) |
0.0174873 | + | 0.999847i | \(0.494433\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −52.3096 | + | 2.69357i | −1.58514 | + | 0.0816233i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.63153i | 0.103758i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −58.2834 | −1.57523 | −0.787614 | − | 0.616169i | \(-0.788684\pi\) | ||||
−0.787614 | + | 0.616169i | \(0.788684\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.49251 | − | 2.91164i | 0.115192 | − | 0.0746575i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.66948 | + | 4.62368i | −0.0651093 | + | 0.112773i | −0.896742 | − | 0.442553i | \(-0.854073\pi\) |
0.831633 | + | 0.555325i | \(0.187406\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 33.9324 | − | 19.5909i | 0.789126 | − | 0.455602i | −0.0505290 | − | 0.998723i | \(-0.516091\pi\) |
0.839655 | + | 0.543121i | \(0.182757\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −55.0399 | + | 5.68339i | −1.22311 | + | 0.126298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.64117 | + | 5.56633i | −0.205131 | + | 0.118433i | −0.599047 | − | 0.800714i | \(-0.704454\pi\) |
0.393915 | + | 0.919147i | \(0.371120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.3255 | + | 42.1331i | −0.496440 | + | 0.859859i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −45.1987 | − | 23.0819i | −0.886249 | − | 0.452585i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −35.8770 | −0.676925 | −0.338462 | − | 0.940980i | \(-0.609907\pi\) | ||||
−0.338462 | + | 0.940980i | \(0.609907\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 107.343i | − | 1.95169i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 26.6139 | − | 52.1151i | 0.466910 | − | 0.914299i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 20.8974 | + | 12.0651i | 0.354194 | + | 0.204494i | 0.666531 | − | 0.745477i | \(-0.267778\pi\) |
−0.312337 | + | 0.949971i | \(0.601112\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 37.9460 | + | 65.7244i | 0.622066 | + | 1.07745i | 0.989100 | + | 0.147243i | \(0.0470398\pi\) |
−0.367034 | + | 0.930207i | \(0.619627\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.85256 | + | 2.17112i | 0.0770247 | + | 0.0344622i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.48564 | + | 9.50141i | 0.0843944 | + | 0.146175i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 31.8200 | + | 18.3713i | 0.474925 | + | 0.274198i | 0.718299 | − | 0.695734i | \(-0.244921\pi\) |
−0.243374 | + | 0.969933i | \(0.578254\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.9391 | − | 19.9644i | −0.187524 | − | 0.289339i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 87.8370i | 1.23714i | 0.785730 | + | 0.618570i | \(0.212288\pi\) | ||||
−0.785730 | + | 0.618570i | \(0.787712\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −60.0423 | −0.822498 | −0.411249 | − | 0.911523i | \(-0.634907\pi\) | ||||
−0.411249 | + | 0.911523i | \(0.634907\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.97450 | − | 38.3452i | −0.0263267 | − | 0.511269i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.15652 | + | 8.93136i | −0.0669678 | + | 0.115992i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 32.1841 | − | 18.5815i | 0.407394 | − | 0.235209i | −0.282275 | − | 0.959333i | \(-0.591089\pi\) |
0.689669 | + | 0.724124i | \(0.257756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −25.3114 | + | 76.9437i | −0.312486 | + | 0.949922i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 66.0281 | − | 38.1214i | 0.795520 | − | 0.459294i | −0.0463824 | − | 0.998924i | \(-0.514769\pi\) |
0.841902 | + | 0.539630i | \(0.181436\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 52.0037 | − | 90.0730i | 0.611808 | − | 1.05968i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.979694 | − | 19.0258i | −0.0112609 | − | 0.218688i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −27.5873 | −0.309969 | −0.154985 | − | 0.987917i | \(-0.549533\pi\) | ||||
−0.154985 | + | 0.987917i | \(0.549533\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.05407i | − | 0.0115832i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 52.1045 | + | 80.3944i | 0.560264 | + | 0.864456i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 103.856 | + | 59.9614i | 1.09322 | + | 0.631172i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0585 | + | 22.6180i | 0.134624 | + | 0.233176i | 0.925454 | − | 0.378861i | \(-0.123684\pi\) |
−0.790830 | + | 0.612036i | \(0.790351\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −143.435 | − | 64.1751i | −1.44883 | − | 0.648234i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.8831 | + | 22.3142i | 0.127556 | + | 0.220933i | 0.922729 | − | 0.385449i | \(-0.125953\pi\) |
−0.795173 | + | 0.606382i | \(0.792620\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.9947 | − | 9.81187i | −0.164997 | − | 0.0952609i | 0.415228 | − | 0.909717i | \(-0.363702\pi\) |
−0.580225 | + | 0.814457i | \(0.697035\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.95490 | + | 9.70264i | −0.0471895 | + | 0.0924061i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 183.200i | 1.71215i | 0.516850 | + | 0.856076i | \(0.327105\pi\) | ||||
−0.516850 | + | 0.856076i | \(0.672895\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −100.841 | −0.925147 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −155.720 | − | 79.5225i | −1.40288 | − | 0.716419i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.12484 | + | 15.8047i | −0.0807508 | + | 0.139865i | −0.903573 | − | 0.428435i | \(-0.859065\pi\) |
0.822822 | + | 0.568299i | \(0.192398\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 42.2235 | − | 24.3778i | 0.367161 | − | 0.211981i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.9756 | − | 1.64964i | 0.136544 | − | 0.0140995i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.65383 | + | 4.99629i | −0.0727212 | + | 0.0419856i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 91.9194 | − | 159.209i | 0.759664 | − | 1.31578i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.4408 | + | 8.71116i | −0.109275 | + | 0.0708224i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −75.0146 | −0.600117 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 164.386i | 1.29438i | 0.762331 | + | 0.647188i | \(0.224055\pi\) | ||||
−0.762331 | + | 0.647188i | \(0.775945\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 117.390 | − | 6.04473i | 0.909998 | − | 0.0468584i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 123.421 | + | 71.2570i | 0.942143 | + | 0.543947i | 0.890631 | − | 0.454726i | \(-0.150263\pi\) |
0.0515116 | + | 0.998672i | \(0.483596\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.76083 | − | 9.97805i | −0.0433145 | − | 0.0750229i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −154.809 | − | 59.9122i | −1.14673 | − | 0.443794i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.08176 | − | 5.33777i | −0.0224946 | − | 0.0389618i | 0.854559 | − | 0.519354i | \(-0.173828\pi\) |
−0.877054 | + | 0.480393i | \(0.840494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −103.168 | − | 59.5642i | −0.742218 | − | 0.428519i | 0.0806575 | − | 0.996742i | \(-0.474298\pi\) |
−0.822875 | + | 0.568222i | \(0.807631\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −33.3538 | + | 1.71748i | −0.236552 | + | 0.0121807i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 31.1569i | 0.217880i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 39.0423 | 0.269257 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −122.479 | + | 79.3801i | −0.833192 | + | 0.540001i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 103.365 | − | 179.034i | 0.693726 | − | 1.20157i | −0.276882 | − | 0.960904i | \(-0.589301\pi\) |
0.970608 | − | 0.240665i | \(-0.0773657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 127.422 | − | 73.5670i | 0.843853 | − | 0.487199i | −0.0147190 | − | 0.999892i | \(-0.504685\pi\) |
0.858572 | + | 0.512693i | \(0.171352\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −89.2676 | − | 123.339i | −0.583449 | − | 0.806138i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −170.030 | + | 98.1668i | −1.09697 | + | 0.633334i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −31.4395 | + | 54.4548i | −0.200251 | + | 0.346846i | −0.948609 | − | 0.316449i | \(-0.897509\pi\) |
0.748358 | + | 0.663295i | \(0.230843\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −95.8554 | − | 48.9510i | −0.602864 | − | 0.307868i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.68422 | −0.0290946 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 143.325i | − | 0.879292i | −0.898171 | − | 0.439646i | \(-0.855104\pi\) | ||
0.898171 | − | 0.439646i | \(-0.144896\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 146.460 | − | 286.796i | 0.887635 | − | 1.73816i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 150.531 | + | 86.9089i | 0.901381 | + | 0.520413i | 0.877648 | − | 0.479306i | \(-0.159111\pi\) |
0.0237332 | + | 0.999718i | \(0.492445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 82.9078 | + | 143.600i | 0.490578 | + | 0.849707i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 142.213 | − | 102.927i | 0.831653 | − | 0.601915i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 125.806 | + | 217.902i | 0.727201 | + | 1.25955i | 0.958062 | + | 0.286562i | \(0.0925125\pi\) |
−0.230861 | + | 0.972987i | \(0.574154\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.54707 | − | 3.77995i | −0.0374118 | − | 0.0215997i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 39.3715 | + | 60.7480i | 0.222438 | + | 0.343209i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 96.0059i | 0.536346i | 0.963371 | + | 0.268173i | \(0.0864199\pi\) | ||||
−0.963371 | + | 0.268173i | \(0.913580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 328.757 | 1.81634 | 0.908170 | − | 0.418603i | \(-0.137480\pi\) | ||||
0.908170 | + | 0.418603i | \(0.137480\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.7082 | + | 227.375i | 0.0639791 | + | 1.24249i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 179.165 | − | 310.323i | 0.968460 | − | 1.67742i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 255.795 | − | 147.683i | 1.36789 | − | 0.789749i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.0027 | + | 12.4216i | 0.0529241 | + | 0.0657229i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.351914 | + | 0.203178i | −0.00184248 | + | 0.00106376i | −0.500921 | − | 0.865493i | \(-0.667005\pi\) |
0.499078 | + | 0.866557i | \(0.333672\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −31.2230 | + | 54.0798i | −0.161777 | + | 0.280206i | −0.935506 | − | 0.353311i | \(-0.885056\pi\) |
0.773729 | + | 0.633517i | \(0.218389\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.69258 | + | 32.8703i | 0.00867992 | + | 0.168566i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 207.861 | 1.05513 | 0.527566 | − | 0.849514i | \(-0.323105\pi\) | ||||
0.527566 | + | 0.849514i | \(0.323105\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 299.128i | − | 1.50316i | −0.659643 | − | 0.751579i | \(-0.729293\pi\) | ||
0.659643 | − | 0.751579i | \(-0.270707\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 59.9499 | + | 92.4995i | 0.298258 | + | 0.460196i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.24848 | − | 1.87551i | −0.0160024 | − | 0.00923896i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.4121 | − | 28.4266i | −0.0800592 | − | 0.138667i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.33086 | − | 70.9946i | −0.0354148 | − | 0.342969i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 170.282 | + | 294.937i | 0.814746 | + | 1.41118i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 141.744 | + | 81.8360i | 0.671773 | + | 0.387848i | 0.796748 | − | 0.604311i | \(-0.206552\pi\) |
−0.124975 | + | 0.992160i | \(0.539885\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −119.846 | + | 234.681i | −0.562656 | + | 1.10179i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 240.892i | 1.12043i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.8629 | 0.0869257 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −160.420 | − | 81.9223i | −0.732510 | − | 0.374075i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.0944 | + | 26.1442i | −0.0683003 | + | 0.118300i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 330.681 | − | 190.919i | 1.48287 | − | 0.856138i | 0.483063 | − | 0.875586i | \(-0.339524\pi\) |
0.999811 | + | 0.0194478i | \(0.00619081\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 47.0431 | − | 105.144i | 0.209081 | − | 0.467306i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 51.5472 | − | 29.7608i | 0.227080 | − | 0.131105i | −0.382144 | − | 0.924103i | \(-0.624814\pi\) |
0.609224 | + | 0.792998i | \(0.291481\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −64.4366 | + | 111.608i | −0.281383 | + | 0.487369i | −0.971726 | − | 0.236113i | \(-0.924126\pi\) |
0.690343 | + | 0.723482i | \(0.257460\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −25.9631 | + | 16.8270i | −0.112394 | + | 0.0728441i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.9939 | 0.0643513 | 0.0321757 | − | 0.999482i | \(-0.489756\pi\) | ||||
0.0321757 | + | 0.999482i | \(0.489756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 68.4443i | − | 0.291252i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 111.342 | − | 5.73329i | 0.469796 | − | 0.0241911i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −315.244 | − | 182.006i | −1.31901 | − | 0.761532i | −0.335442 | − | 0.942061i | \(-0.608886\pi\) |
−0.983570 | + | 0.180529i | \(0.942219\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −40.5235 | − | 70.1888i | −0.168147 | − | 0.291240i | 0.769621 | − | 0.638501i | \(-0.220445\pi\) |
−0.937769 | + | 0.347261i | \(0.887112\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −172.609 | + | 171.041i | −0.710326 | + | 0.703873i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −149.555 | − | 259.037i | −0.610428 | − | 1.05729i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.1448 | − | 17.4041i | −0.122044 | − | 0.0704620i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 228.426 | − | 11.7623i | 0.917372 | − | 0.0472381i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 281.883i | − | 1.12304i | −0.827463 | − | 0.561520i | \(-0.810217\pi\) | ||
0.827463 | − | 0.561520i | \(-0.189783\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 138.459 | 0.547268 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 261.839 | − | 169.701i | 1.02682 | − | 0.665492i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −37.6564 | + | 65.2227i | −0.146523 | + | 0.253785i | −0.929940 | − | 0.367711i | \(-0.880142\pi\) |
0.783417 | + | 0.621496i | \(0.213475\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.8145 | + | 17.2134i | −0.115114 | + | 0.0664610i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 23.3415 | − | 52.1695i | 0.0894311 | − | 0.199883i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −105.914 | + | 61.1497i | −0.402716 | + | 0.232508i | −0.687655 | − | 0.726037i | \(-0.741360\pi\) |
0.284939 | + | 0.958546i | \(0.408027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 110.287 | − | 191.023i | 0.416178 | − | 0.720841i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −73.7070 | − | 37.6403i | −0.276056 | − | 0.140975i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −280.452 | −1.04257 | −0.521287 | − | 0.853382i | \(-0.674548\pi\) | ||||
−0.521287 | + | 0.853382i | \(0.674548\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 81.4468i | − | 0.300542i | −0.988645 | − | 0.150271i | \(-0.951985\pi\) | ||
0.988645 | − | 0.150271i | \(-0.0480146\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.43819 | − | 2.81625i | 0.00526809 | − | 0.0103159i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 193.522 | + | 111.730i | 0.703716 | + | 0.406291i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −224.861 | − | 389.471i | −0.811774 | − | 1.40603i | −0.911622 | − | 0.411031i | \(-0.865169\pi\) |
0.0998479 | − | 0.995003i | \(-0.468164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 29.5206 | + | 285.888i | 0.105809 | + | 1.02469i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −37.8649 | − | 65.5838i | −0.134750 | − | 0.233394i | 0.790752 | − | 0.612137i | \(-0.209690\pi\) |
−0.925502 | + | 0.378743i | \(0.876357\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 322.061 | + | 185.942i | 1.13803 | + | 0.657039i | 0.945941 | − | 0.324339i | \(-0.105142\pi\) |
0.192084 | + | 0.981378i | \(0.438475\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 195.668 | + | 301.906i | 0.686556 | + | 1.05932i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.15361i | 0.0109882i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.81196 | −0.00972996 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.02919 | + | 78.2475i | 0.0138460 | + | 0.268892i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 66.3946 | − | 114.999i | 0.226603 | − | 0.392488i | −0.730196 | − | 0.683237i | \(-0.760571\pi\) |
0.956799 | + | 0.290750i | \(0.0939047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −128.479 | + | 74.1772i | −0.435521 | + | 0.251448i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −295.664 | − | 367.165i | −0.995502 | − | 1.23625i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.2556 | + | 7.07579i | −0.0409887 | + | 0.0236648i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5719 | − | 20.0432i | 0.0384450 | − | 0.0665886i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.97507 | + | 77.1965i | 0.0131190 | + | 0.254774i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −466.589 | −1.52980 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 336.514i | − | 1.09614i | −0.836434 | − | 0.548068i | \(-0.815363\pi\) | ||
0.836434 | − | 0.548068i | \(-0.184637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −32.0185 | − | 49.4028i | −0.103620 | − | 0.159880i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 304.206 | + | 175.634i | 0.978156 | + | 0.564738i | 0.901713 | − | 0.432336i | \(-0.142310\pi\) |
0.0764428 | + | 0.997074i | \(0.475644\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −95.4299 | − | 165.289i | −0.304888 | − | 0.528081i | 0.672349 | − | 0.740235i | \(-0.265286\pi\) |
−0.977236 | + | 0.212154i | \(0.931952\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −26.4768 | + | 19.1628i | −0.0840532 | + | 0.0608342i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 202.797 | + | 351.255i | 0.639738 | + | 1.10806i | 0.985490 | + | 0.169733i | \(0.0542906\pi\) |
−0.345752 | + | 0.938326i | \(0.612376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 96.0203 | + | 55.4374i | 0.301004 | + | 0.173785i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −249.960 | + | 489.470i | −0.778693 | + | 1.52483i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 329.981i | 1.02161i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.8393 | −0.0702749 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −269.424 | − | 137.588i | −0.823928 | − | 0.420760i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.28792 | + | 5.69484i | −0.00999368 | + | 0.0173096i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −384.104 | + | 221.763i | −1.16044 | + | 0.669978i | −0.951408 | − | 0.307932i | \(-0.900363\pi\) |
−0.209027 | + | 0.977910i | \(0.567030\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −307.548 | − | 424.932i | −0.923568 | − | 1.27607i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −195.631 | + | 112.948i | −0.583974 | + | 0.337158i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −254.239 | + | 440.356i | −0.754420 | + | 1.30669i | 0.191243 | + | 0.981543i | \(0.438748\pi\) |
−0.945662 | + | 0.325150i | \(0.894585\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −45.9436 | + | 29.7766i | −0.135527 | + | 0.0878365i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −557.560 | −1.63507 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 57.6805i | 0.168165i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 146.073 | − | 7.52172i | 0.423400 | − | 0.0218021i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −492.773 | − | 284.503i | −1.42010 | − | 0.819893i | −0.423790 | − | 0.905761i | \(-0.639300\pi\) |
−0.996307 | + | 0.0858678i | \(0.972634\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 206.901 | + | 358.363i | 0.592840 | + | 1.02683i | 0.993848 | + | 0.110754i | \(0.0353266\pi\) |
−0.401008 | + | 0.916074i | \(0.631340\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 44.9341 | + | 17.3899i | 0.128017 | + | 0.0495438i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 62.3070 | + | 107.919i | 0.176507 | + | 0.305719i | 0.940682 | − | 0.339290i | \(-0.110187\pi\) |
−0.764175 | + | 0.645009i | \(0.776853\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −467.677 | − | 270.014i | −1.31740 | − | 0.760602i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −29.9381 | + | 1.54160i | −0.0838601 | + | 0.00431820i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 303.196i | − | 0.844557i | −0.906466 | − | 0.422278i | \(-0.861230\pi\) | ||
0.906466 | − | 0.422278i | \(-0.138770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.4752 | −0.0539480 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 462.814 | − | 299.955i | 1.27497 | − | 0.826323i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 184.572 | − | 319.688i | 0.505677 | − | 0.875858i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −615.571 | + | 355.400i | −1.67730 | + | 0.968392i | −0.713936 | + | 0.700211i | \(0.753089\pi\) |
−0.963369 | + | 0.268181i | \(0.913578\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −47.7965 | + | 4.93544i | −0.129530 | + | 0.0133752i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.3527 | + | 10.5959i | −0.0494681 | + | 0.0285604i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −166.740 | + | 288.803i | −0.447025 | + | 0.774271i | −0.998191 | − | 0.0601254i | \(-0.980850\pi\) |
0.551166 | + | 0.834396i | \(0.314183\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −200.422 | − | 102.351i | −0.534459 | − | 0.272935i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.3323 | −0.0300590 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 662.686i | 1.74851i | 0.485465 | + | 0.874256i | \(0.338650\pi\) | ||||
−0.485465 | + | 0.874256i | \(0.661350\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −224.289 | + | 439.202i | −0.588686 | + | 1.15276i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −69.9008 | − | 40.3572i | −0.182509 | − | 0.105371i | 0.405962 | − | 0.913890i | \(-0.366936\pi\) |
−0.588471 | + | 0.808518i | \(0.700270\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.7026 | − | 54.9106i | −0.0823445 | − | 0.142625i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 321.887 | + | 144.018i | 0.831748 | + | 0.372139i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 346.006 | + | 599.301i | 0.889476 | + | 1.54062i | 0.840495 | + | 0.541819i | \(0.182264\pi\) |
0.0489809 | + | 0.998800i | \(0.484403\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 116.183 | + | 67.0782i | 0.297143 | + | 0.171556i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 232.529 | + | 358.779i | 0.591676 | + | 0.912924i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 228.481i | 0.578432i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −657.713 | −1.65671 | −0.828354 | − | 0.560206i | \(-0.810722\pi\) | ||||
−0.828354 | + | 0.560206i | \(0.810722\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.77749 | − | 34.5192i | −0.00445487 | − | 0.0865144i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 296.433 | − | 513.437i | 0.739235 | − | 1.28039i | −0.213606 | − | 0.976920i | \(-0.568521\pi\) |
0.952840 | − | 0.303472i | \(-0.0981459\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 49.3521 | − | 28.4935i | 0.122462 | − | 0.0707034i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −331.869 | − | 371.295i | −0.819431 | − | 0.916777i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 881.274 | − | 508.804i | 2.16529 | − | 1.25013i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −161.594 | + | 279.889i | −0.395095 | + | 0.684325i | −0.993113 | − | 0.117157i | \(-0.962622\pi\) |
0.598018 | + | 0.801483i | \(0.295955\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.950872 | − | 18.4661i | −0.00231356 | − | 0.0449297i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.2533 | 0.0345115 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 468.745i | 1.12951i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −194.372 | − | 299.906i | −0.466121 | − | 0.719199i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 222.744 | + | 128.601i | 0.531608 | + | 0.306924i | 0.741671 | − | 0.670764i | \(-0.234033\pi\) |
−0.210063 | + | 0.977688i | \(0.567367\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −41.9905 | − | 72.7297i | −0.0997400 | − | 0.172755i | 0.811837 | − | 0.583884i | \(-0.198468\pi\) |
−0.911577 | + | 0.411129i | \(0.865134\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −91.4573 | − | 40.9196i | −0.216211 | − | 0.0967365i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 108.258 | + | 187.509i | 0.254725 | + | 0.441197i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 38.8221 | + | 22.4139i | 0.0909182 | + | 0.0524917i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −42.5108 | + | 83.2442i | −0.0990927 | + | 0.194042i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 144.348i | − | 0.334914i | −0.985879 | − | 0.167457i | \(-0.946445\pi\) | ||
0.985879 | − | 0.167457i | \(-0.0535555\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 395.353 | 0.913057 | 0.456528 | − | 0.889709i | \(-0.349093\pi\) | ||||
0.456528 | + | 0.889709i | \(0.349093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 104.312 | + | 53.2697i | 0.239798 | + | 0.122459i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −77.3426 | + | 133.961i | −0.176985 | + | 0.306548i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −194.776 | + | 112.454i | −0.443682 | + | 0.256160i | −0.705158 | − | 0.709050i | \(-0.749124\pi\) |
0.261476 | + | 0.965210i | \(0.415791\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −435.544 | + | 44.9740i | −0.987628 | + | 0.101982i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 369.184 | − | 213.148i | 0.833373 | − | 0.481148i | −0.0216335 | − | 0.999766i | \(-0.506887\pi\) |
0.855006 | + | 0.518618i | \(0.173553\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 84.8041 | − | 146.885i | 0.190571 | − | 0.330079i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 520.444 | − | 337.306i | 1.16430 | − | 0.754599i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −406.744 | −0.905888 | −0.452944 | − | 0.891539i | \(-0.649626\pi\) | ||||
−0.452944 | + | 0.891539i | \(0.649626\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 93.2163i | − | 0.206688i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 440.818 | − | 22.6990i | 0.973108 | − | 0.0501081i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.61228 | + | 3.24025i | 0.0123347 | + | 0.00712144i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −159.600 | − | 276.435i | −0.349234 | − | 0.604891i | 0.636879 | − | 0.770963i | \(-0.280225\pi\) |
−0.986114 | + | 0.166072i | \(0.946892\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −70.2180 | − | 451.332i | −0.152980 | − | 0.983294i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −293.888 | − | 509.029i | −0.637501 | − | 1.10418i | −0.985979 | − | 0.166867i | \(-0.946635\pi\) |
0.348478 | − | 0.937317i | \(-0.386698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 230.088 | + | 132.841i | 0.496950 | + | 0.286914i | 0.727453 | − | 0.686157i | \(-0.240704\pi\) |
−0.230503 | + | 0.973072i | \(0.574037\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −588.221 | + | 30.2892i | −1.26499 | + | 0.0651380i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 794.598i | − | 1.70149i | −0.525575 | − | 0.850747i | \(-0.676150\pi\) | ||
0.525575 | − | 0.850747i | \(-0.323850\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.7031 | 0.0462752 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −158.298 | + | 102.595i | −0.336089 | + | 0.217823i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −342.050 | + | 592.447i | −0.723149 | + | 1.25253i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −216.201 | + | 124.824i | −0.455161 | + | 0.262787i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −189.315 | − | 261.572i | −0.396886 | − | 0.548369i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −572.964 | + | 330.801i | −1.19617 | + | 0.690607i | −0.959698 | − | 0.281033i | \(-0.909323\pi\) |
−0.236468 | + | 0.971639i | \(0.575990\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −52.0037 | + | 90.0730i | −0.108116 | + | 0.187262i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.5152 | − | 6.39120i | −0.0259114 | − | 0.0132323i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −160.569 | −0.331071 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 57.1525i | 0.117356i | 0.998277 | + | 0.0586781i | \(0.0186886\pi\) | ||||
−0.998277 | + | 0.0586781i | \(0.981311\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 195.553 | − | 382.931i | 0.399905 | − | 0.783090i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −48.6600 | − | 28.0939i | −0.0991040 | − | 0.0572177i | 0.449629 | − | 0.893215i | \(-0.351556\pi\) |
−0.548733 | + | 0.835998i | \(0.684890\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 53.7147 | + | 93.0366i | 0.108955 | + | 0.188715i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 782.615 | − | 566.424i | 1.58104 | − | 1.14429i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.9417 | + | 44.9324i | 0.0521967 | + | 0.0904073i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −522.225 | − | 301.507i | −1.04654 | − | 0.604222i | −0.124863 | − | 0.992174i | \(-0.539849\pi\) |
−0.921679 | + | 0.387952i | \(0.873183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 283.605 | + | 437.587i | 0.566077 | + | 0.873427i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 549.354i | − | 1.09216i | −0.837734 | − | 0.546078i | \(-0.816120\pi\) | ||
0.837734 | − | 0.546078i | \(-0.183880\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −158.413 | −0.313688 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.5810 | + | 496.788i | 0.0504557 | + | 0.979859i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 119.464 | − | 206.918i | 0.234704 | − | 0.406519i | −0.724483 | − | 0.689293i | \(-0.757921\pi\) |
0.959187 | + | 0.282774i | \(0.0912547\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.7143 | + | 17.7329i | −0.0601062 | + | 0.0347023i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 520.395 | − | 80.9629i | 1.01442 | − | 0.157822i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 104.484 | − | 60.3240i | 0.202882 | − | 0.117134i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 97.1862 | − | 168.331i | 0.187981 | − | 0.325593i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 38.8171 | + | 753.836i | 0.0747922 | + | 1.45248i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −567.711 | −1.08966 | −0.544828 | − | 0.838548i | \(-0.683405\pi\) | ||||
−0.544828 | + | 0.838548i | \(0.683405\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 941.999i | 1.80114i | 0.434706 | + | 0.900572i | \(0.356852\pi\) | ||||
−0.434706 | + | 0.900572i | \(0.643148\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.3349 | − | 19.0321i | −0.0234950 | − | 0.0362516i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −467.856 | − | 270.117i | −0.887773 | − | 0.512556i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −233.056 | − | 403.664i | −0.440559 | − | 0.763071i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.3065 | + | 216.024i | 0.0420085 | + | 0.406825i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.76372 | + | 8.25100i | 0.00893755 | + | 0.0154803i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −975.428 | − | 563.163i | −1.82323 | − | 1.05264i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −130.991 | + | 256.506i | −0.243932 | + | 0.477665i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 849.430i | − | 1.57594i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 242.245 | 0.447772 | 0.223886 | − | 0.974615i | \(-0.428126\pi\) | ||||
0.223886 | + | 0.974615i | \(0.428126\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 878.366 | + | 448.560i | 1.61762 | + | 0.826077i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 309.988 | − | 536.915i | 0.568786 | − | 0.985166i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 170.503 | − | 98.4402i | 0.311706 | − | 0.179964i | −0.335983 | − | 0.941868i | \(-0.609069\pi\) |
0.647690 | + | 0.761904i | \(0.275735\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −278.951 | + | 623.470i | −0.508107 | + | 1.13565i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −107.273 | + | 61.9342i | −0.194688 | + | 0.112403i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.9757 | − | 19.0105i | 0.0198476 | − | 0.0343770i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 902.096 | − | 584.659i | 1.62540 | − | 1.05344i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −958.121 | −1.72015 | −0.860073 | − | 0.510171i | \(-0.829582\pi\) | ||||
−0.860073 | + | 0.510171i | \(0.829582\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 69.9202i | − | 0.125081i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 884.926 | − | 45.5674i | 1.57741 | − | 0.0812253i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −165.774 | − | 95.7097i | −0.294448 | − | 0.169999i | 0.345498 | − | 0.938419i | \(-0.387710\pi\) |
−0.639946 | + | 0.768420i | \(0.721043\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −56.1001 | − | 97.1682i | −0.0992922 | − | 0.171979i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.77666 | + | 46.8355i | 0.0172428 | + | 0.0826023i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 228.215 | + | 395.280i | 0.401081 | + | 0.694693i | 0.993857 | − | 0.110675i | \(-0.0353012\pi\) |
−0.592775 | + | 0.805368i | \(0.701968\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 842.764 | + | 486.570i | 1.47594 | + | 0.852136i | 0.999632 | − | 0.0271399i | \(-0.00863995\pi\) |
0.476312 | + | 0.879276i | \(0.341973\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.21745 | + | 0.0626902i | −0.00212470 | + | 0.000109407i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 101.496i | 0.176515i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 138.527 | 0.240081 | 0.120040 | − | 0.992769i | \(-0.461698\pi\) | ||||
0.120040 | + | 0.992769i | \(0.461698\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −157.208 | + | 101.888i | −0.271516 | + | 0.175972i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.5175 | − | 39.0015i | 0.0387565 | − | 0.0671282i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 542.478 | − | 313.200i | 0.930494 | − | 0.537221i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −40.3263 | + | 90.1314i | −0.0689339 | + | 0.154071i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −620.808 | + | 358.424i | −1.05759 | + | 0.610602i | −0.924766 | − | 0.380537i | \(-0.875739\pi\) |
−0.132829 | + | 0.991139i | \(0.542406\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 311.451 | − | 539.449i | 0.528779 | − | 0.915872i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 555.358 | + | 283.607i | 0.939691 | + | 0.479877i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 542.129 | 0.914214 | 0.457107 | − | 0.889412i | \(-0.348886\pi\) | ||||
0.457107 | + | 0.889412i | \(0.348886\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 61.4350i | − | 0.103252i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 408.134 | − | 799.204i | 0.683641 | − | 1.33870i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −245.527 | − | 141.755i | −0.409895 | − | 0.236653i | 0.280850 | − | 0.959752i | \(-0.409384\pi\) |
−0.690744 | + | 0.723099i | \(0.742717\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 377.424 | + | 653.717i | 0.627993 | + | 1.08772i | 0.987954 | + | 0.154748i | \(0.0494567\pi\) |
−0.359961 | + | 0.932967i | \(0.617210\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.9656 | + | 328.934i | 0.0563276 | + | 0.545496i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 565.126 | + | 978.827i | 0.934093 | + | 1.61790i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 77.2227 | + | 44.5845i | 0.127220 | + | 0.0734506i | 0.562260 | − | 0.826961i | \(-0.309932\pi\) |
−0.435039 | + | 0.900411i | \(0.643266\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.12024 | − | 9.44320i | −0.0100497 | − | 0.0155061i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.8664i | 0.0325145i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 316.779 | 0.516769 | 0.258385 | − | 0.966042i | \(-0.416810\pi\) | ||||
0.258385 | + | 0.966042i | \(0.416810\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.06393 | − | 98.3425i | −0.00823404 | − | 0.159907i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 534.934 | − | 926.533i | 0.866992 | − | 1.50167i | 0.00193565 | − | 0.999998i | \(-0.499384\pi\) |
0.865056 | − | 0.501675i | \(-0.167283\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −578.542 | + | 334.021i | −0.934640 | + | 0.539615i | −0.888276 | − | 0.459310i | \(-0.848097\pi\) |
−0.0463638 | + | 0.998925i | \(0.514763\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 77.2793 | − | 199.684i | 0.124443 | − | 0.321552i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.1121 | + | 8.14762i | −0.0226518 | + | 0.0130780i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390.580 | − | 676.505i | 0.624929 | − | 1.08241i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 52.5402 | + | 1020.34i | 0.0837961 | + | 1.62734i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 985.986 | 1.56755 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 150.631i | 0.238718i | 0.992851 | + | 0.119359i | \(0.0380839\pi\) | ||||
−0.992851 | + | 0.119359i | \(0.961916\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 267.051 | + | 412.045i | 0.421881 | + | 0.650939i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −875.252 | − | 505.327i | −1.37835 | − | 0.795790i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43.4092 | + | 75.1869i | 0.0681463 | + | 0.118033i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −640.401 | + | 463.496i | −1.00219 | + | 0.725345i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 351.521 | + | 608.852i | 0.548395 | + | 0.949847i | 0.998385 | + | 0.0568139i | \(0.0180942\pi\) |
−0.449990 | + | 0.893034i | \(0.648573\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −742.057 | − | 428.427i | −1.15405 | − | 0.666293i | −0.204182 | − | 0.978933i | \(-0.565454\pi\) |
−0.949872 | + | 0.312639i | \(0.898787\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −328.675 | + | 643.609i | −0.509574 | + | 0.997844i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 156.257i | 0.241510i | 0.992682 | + | 0.120755i | \(0.0385316\pi\) | ||||
−0.992682 | + | 0.120755i | \(0.961468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −421.306 | −0.649162 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 50.3974 | + | 25.7367i | 0.0774154 | + | 0.0395341i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 441.773 | − | 765.173i | 0.676528 | − | 1.17178i | −0.299492 | − | 0.954099i | \(-0.596817\pi\) |
0.976020 | − | 0.217682i | \(-0.0698495\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −758.798 | + | 438.092i | −1.15847 | + | 0.668843i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −316.830 | − | 437.756i | −0.482237 | − | 0.666296i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 379.533 | − | 219.123i | 0.575922 | − | 0.332509i | −0.183589 | − | 0.983003i | \(-0.558772\pi\) |
0.759511 | + | 0.650494i | \(0.225438\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −233.924 | + | 405.168i | −0.353894 | + | 0.612963i | −0.986928 | − | 0.161161i | \(-0.948476\pi\) |
0.633034 | + | 0.774124i | \(0.281809\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −76.0002 | + | 49.2565i | −0.114631 | + | 0.0742934i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 70.8359 | 0.106520 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 50.3597i | 0.0755018i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1144.00 | − | 58.9076i | 1.71001 | − | 0.0880533i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1147.52 | − | 662.524i | −1.71017 | − | 0.987368i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 273.302 | + | 473.372i | 0.406094 | + | 0.703376i | 0.994448 | − | 0.105227i | \(-0.0335571\pi\) |
−0.588354 | + | 0.808604i | \(0.700224\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 269.148 | − | 216.734i | 0.398738 | − | 0.321088i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −227.606 | − | 394.225i | −0.336198 | − | 0.582312i | 0.647516 | − | 0.762052i | \(-0.275808\pi\) |
−0.983714 | + | 0.179740i | \(0.942475\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.3600 | + | 7.71341i | 0.0196760 | + | 0.0113600i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 178.329 | − | 9.18264i | 0.261863 | − | 0.0134841i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 123.214i | − | 0.180400i | −0.995924 | − | 0.0902002i | \(-0.971249\pi\) | ||
0.995924 | − | 0.0902002i | \(-0.0287507\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37.8937 | 0.0553193 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −324.439 | + | 210.272i | −0.472254 | + | 0.306073i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32.0115 | + | 55.4455i | −0.0464607 | + | 0.0804724i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 163.326 | − | 94.2965i | 0.236362 | − | 0.136464i | −0.377141 | − | 0.926156i | \(-0.623093\pi\) |
0.613504 | + | 0.789692i | \(0.289760\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −92.3265 | + | 9.53359i | −0.133227 | + | 0.0137570i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 634.285 | − | 366.204i | 0.912640 | − | 0.526913i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.1599 | − | 78.2192i | 0.0647918 | − | 0.112223i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 40.0602 | + | 20.4578i | 0.0573107 | + | 0.0292672i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 810.064 | 1.15558 | 0.577792 | − | 0.816184i | \(-0.303915\pi\) | ||||
0.577792 | + | 0.816184i | \(0.303915\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1136.86i | 1.61716i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 93.3861 | − | 182.868i | 0.132463 | − | 0.259387i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.1806 | + | 7.60980i | 0.0186429 | + | 0.0107635i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 651.819 | + | 1128.98i | 0.919349 | + | 1.59236i | 0.800406 | + | 0.599459i | \(0.204618\pi\) |
0.118944 | + | 0.992901i | \(0.462049\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 305.302 | + | 136.597i | 0.429398 | + | 0.192120i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −126.623 | − | 219.317i | −0.177592 | − | 0.307598i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −165.891 | − | 95.7772i | −0.232015 | − | 0.133954i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −593.930 | − | 916.401i | −0.828354 | − | 1.27810i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 788.981i | − | 1.09733i | −0.836042 | − | 0.548666i | \(-0.815136\pi\) | ||
0.836042 | − | 0.548666i | \(-0.184864\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.5913 | −0.0160768 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.5035 | − | 242.820i | −0.0172939 | − | 0.335850i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −40.6380 | + | 70.3870i | −0.0560524 | + | 0.0970856i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −232.676 | + | 134.335i | −0.320049 | + | 0.184780i | −0.651414 | − | 0.758722i | \(-0.725824\pi\) |
0.331365 | + | 0.943502i | \(0.392491\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −694.543 | + | 221.474i | −0.952734 | + | 0.303805i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −574.038 | + | 331.421i | −0.785277 | + | 0.453380i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.8343 | − | 63.7989i | 0.0502514 | − | 0.0870380i | −0.839806 | − | 0.542887i | \(-0.817331\pi\) |
0.890057 | + | 0.455849i | \(0.150664\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −46.1449 | − | 896.143i | −0.0627822 | − | 1.21924i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −641.512 | −0.870437 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 448.249i | − | 0.606562i | −0.952901 | − | 0.303281i | \(-0.901918\pi\) | ||
0.952901 | − | 0.303281i | \(-0.0980820\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −56.7939 | − | 87.6298i | −0.0766449 | − | 0.118259i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 656.602 | + | 379.089i | 0.883718 | + | 0.510215i | 0.871882 | − | 0.489715i | \(-0.162899\pi\) |
0.0118352 | + | 0.999930i | \(0.496233\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 635.496 | + | 1100.71i | 0.853015 | + | 1.47746i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 626.350 | + | 280.240i | 0.838488 | + | 0.375154i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 54.1063 | + | 93.7149i | 0.0722381 | + | 0.125120i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1141.58 | + | 659.091i | 1.52008 | + | 0.877618i | 0.999720 | + | 0.0236697i | \(0.00753501\pi\) |
0.520358 | + | 0.853948i | \(0.325798\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 384.604 | − | 753.128i | 0.510762 | − | 1.00017i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 904.589i | 1.19813i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −587.874 | −0.776583 | −0.388292 | − | 0.921537i | \(-0.626935\pi\) | ||||
−0.388292 | + | 0.921537i | \(0.626935\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 369.931 | + | 188.915i | 0.487393 | + | 0.248899i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −188.496 | + | 326.485i | −0.247695 | + | 0.429021i | −0.962886 | − | 0.269908i | \(-0.913007\pi\) |
0.715191 | + | 0.698929i | \(0.246340\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −51.5845 | + | 29.7823i | −0.0676075 | + | 0.0390332i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 931.115 | − | 96.1465i | 1.21714 | − | 0.125682i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.2917 | − | 21.5304i | 0.0486202 | − | 0.0280709i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 643.939 | − | 1115.34i | 0.837372 | − | 1.45037i | −0.0547122 | − | 0.998502i | \(-0.517424\pi\) |
0.892084 | − | 0.451869i | \(-0.149243\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −189.600 | + | 122.882i | −0.245914 | + | 0.159380i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −778.578 | −1.00722 | −0.503608 | − | 0.863932i | \(-0.667994\pi\) | ||||
−0.503608 | + | 0.863932i | \(0.667994\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 408.715i | − | 0.527375i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −103.144 | + | 5.31117i | −0.132746 | + | 0.00683548i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 90.1884 | + | 52.0703i | 0.115775 | + | 0.0668425i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −766.801 | − | 1328.14i | −0.981819 | − | 1.70056i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 133.544 | − | 107.538i | 0.170554 | − | 0.137341i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −193.292 | − | 334.791i | −0.246232 | − | 0.426486i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 390.283 | + | 225.330i | 0.495913 | + | 0.286315i | 0.727024 | − | 0.686612i | \(-0.240903\pi\) |
−0.231111 | + | 0.972927i | \(0.574236\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −366.413 | + | 18.8676i | −0.464402 | + | 0.0239134i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.7797i | 0.0136280i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 135.430 | 0.170782 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 555.296 | − | 359.893i | 0.698485 | − | 0.452696i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 182.891 | − | 316.776i | 0.229474 | − | 0.397461i | −0.728178 | − | 0.685388i | \(-0.759633\pi\) |
0.957652 | + | 0.287927i | \(0.0929661\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 163.101 | − | 94.1662i | 0.204131 | − | 0.117855i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −145.572 | − | 201.133i | −0.181737 | − | 0.251103i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 907.869 | − | 524.158i | 1.13060 | − | 0.652750i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.3994 | − | 24.9406i | 0.0178875 | − | 0.0309821i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −749.305 | − | 382.652i | −0.928507 | − | 0.474166i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1167.70 | 1.44339 | 0.721695 | − | 0.692212i | \(-0.243364\pi\) | ||||
0.721695 | + | 0.692212i | \(0.243364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 810.121i | − | 0.998916i | −0.866338 | − | 0.499458i | \(-0.833533\pi\) | ||
0.866338 | − | 0.499458i | \(-0.166467\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 111.127 | − | 217.608i | 0.136687 | − | 0.267660i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 763.114 | + | 440.584i | 0.936336 | + | 0.540594i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −382.135 | − | 661.878i | −0.467730 | − | 0.810132i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.68503 | − | 5.56210i | 0.00938343 | − | 0.00679134i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 280.513 | + | 485.862i | 0.341672 | + | 0.591793i | 0.984743 | − | 0.174013i | \(-0.0556734\pi\) |
−0.643071 | + | 0.765806i | \(0.722340\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1016.04 | − | 586.612i | −1.23456 | − | 0.712773i | −0.266583 | − | 0.963812i | \(-0.585895\pi\) |
−0.967977 | + | 0.251039i | \(0.919228\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 364.602 | + | 562.561i | 0.441942 | + | 0.681892i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 267.739i | − | 0.323747i | −0.986811 | − | 0.161874i | \(-0.948246\pi\) | ||
0.986811 | − | 0.161874i | \(-0.0517537\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 432.474 | 0.521682 | 0.260841 | − | 0.965382i | \(-0.416000\pi\) | ||||
0.260841 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −69.3806 | − | 1347.38i | −0.0834904 | − | 1.62140i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 411.518 | − | 712.769i | 0.494019 | − | 0.855665i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −925.472 | + | 534.321i | −1.10835 | + | 0.639906i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −311.196 | + | 804.106i | −0.371799 | + | 0.960701i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −459.103 | + | 265.063i | −0.547202 | + | 0.315927i | −0.747993 | − | 0.663707i | \(-0.768982\pi\) |
0.200790 | + | 0.979634i | \(0.435649\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 400.337 | − | 693.403i | 0.476024 | − | 0.824499i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.6831 | − | 226.889i | −0.0138590 | − | 0.269144i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1019.44 | −1.20644 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 108.590i | − | 0.128205i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 606.774 | + | 936.219i | 0.714692 | + | 1.10273i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 400.278 | + | 231.100i | 0.470361 | + | 0.271563i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −88.3868 | − | 153.090i | −0.103619 | − | 0.179473i | 0.809554 | − | 0.587045i | \(-0.199709\pi\) |
−0.913173 | + | 0.407572i | \(0.866376\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 110.859 | + | 1073.60i | 0.129660 | + | 1.25567i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −194.859 | − | 337.505i | −0.227373 | − | 0.393821i | 0.729656 | − | 0.683815i | \(-0.239680\pi\) |
−0.957029 | + | 0.289993i | \(0.906347\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 503.279 | + | 290.568i | 0.585889 | + | 0.338263i | 0.763470 | − | 0.645843i | \(-0.223494\pi\) |
−0.177581 | + | 0.984106i | \(0.556827\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.30282 | + | 8.42575i | −0.00499747 | + | 0.00978601i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 827.326i | − | 0.958663i | −0.877634 | − | 0.479331i | \(-0.840879\pi\) | ||
0.877634 | − | 0.479331i | \(-0.159121\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1546.92 | −1.78835 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.51293 | − | 3.83667i | −0.00866543 | − | 0.00442522i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −324.426 | + | 561.923i | −0.373333 | + | 0.646632i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.7831 | − | 32.7837i | 0.0651930 | − | 0.0376392i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −95.9966 | + | 214.557i | −0.109962 | + | 0.245770i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −38.3732 | + | 22.1548i | −0.0438551 | + | 0.0253198i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 279.815 | − | 484.653i | 0.319059 | − | 0.552626i | −0.661233 | − | 0.750181i | \(-0.729967\pi\) |
0.980292 | + | 0.197554i | \(0.0632999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 334.297 | − | 216.662i | 0.380315 | − | 0.246487i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −957.127 | −1.08641 | −0.543205 | − | 0.839600i | \(-0.682789\pi\) | ||||
−0.543205 | + | 0.839600i | \(0.682789\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 625.252i | 0.708100i | 0.935227 | + | 0.354050i | \(0.115196\pi\) | ||||
−0.935227 | + | 0.354050i | \(0.884804\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −444.475 | + | 22.8873i | −0.502231 | + | 0.0258613i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 921.187 | + | 531.847i | 1.03854 | + | 0.599602i | 0.919420 | − | 0.393277i | \(-0.128659\pi\) |
0.119122 | + | 0.992880i | \(0.461992\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.5496 | + | 84.0904i | 0.0546115 | + | 0.0945899i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −288.984 | − | 1384.39i | −0.324337 | − | 1.55375i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 108.576 | + | 188.059i | 0.121585 | + | 0.210592i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −511.172 | − | 295.125i | −0.571142 | − | 0.329749i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.3985 | + | 2.18322i | −0.0472670 | + | 0.00243391i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 202.793i | − | 0.225577i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 606.935 | 0.673624 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 58.2647 | − | 37.7620i | 0.0645235 | − | 0.0418184i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1010.61 | + | 1750.43i | −1.11670 | + | 1.93418i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −207.207 | + | 119.631i | −0.228453 | + | 0.131898i | −0.609858 | − | 0.792510i | \(-0.708774\pi\) |
0.381405 | + | 0.924408i | \(0.375440\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −94.7072 | + | 211.675i | −0.104188 | + | 0.232866i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 175.804 | − | 101.501i | 0.192980 | − | 0.111417i | −0.400397 | − | 0.916342i | \(-0.631128\pi\) |
0.593377 | + | 0.804925i | \(0.297794\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −665.585 | + | 1152.83i | −0.729009 | + | 1.26268i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1246.62 | − | 636.619i | −1.36243 | − | 0.695758i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 84.1801 | 0.0917994 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 878.708i | − | 0.956156i | −0.878317 | − | 0.478078i | \(-0.841334\pi\) | ||
0.878317 | − | 0.478078i | \(-0.158666\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 459.143 | − | 899.090i | 0.498527 | − | 0.976210i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 135.746 | + | 78.3730i | 0.147070 | + | 0.0849111i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 372.975 | + | 646.011i | 0.403216 | + | 0.698391i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.1406 | − | 175.680i | −0.0195691 | − | 0.189514i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 300.259 | + | 520.064i | 0.323207 | + | 0.559810i | 0.981148 | − | 0.193259i | \(-0.0619058\pi\) |
−0.657941 | + | 0.753069i | \(0.728572\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 821.838 | + | 474.489i | 0.882748 | + | 0.509655i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 573.135 | + | 884.316i | 0.614293 | + | 0.947820i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1815.93i | 1.94217i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −184.325 | −0.196718 | −0.0983589 | − | 0.995151i | \(-0.531359\pi\) | ||||
−0.0983589 | + | 0.995151i | \(0.531359\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.4447 | − | 571.822i | −0.0313575 | − | 0.608969i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 377.587 | − | 653.999i | 0.401261 | − | 0.695005i | −0.592617 | − | 0.805484i | \(-0.701905\pi\) |
0.993878 | + | 0.110479i | \(0.0352386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.6668 | − | 21.1696i | 0.0388831 | − | 0.0224492i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −96.8859 | + | 15.0735i | −0.102525 | + | 0.0159507i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 769.965 | − | 444.539i | 0.813057 | − | 0.469419i | −0.0349595 | − | 0.999389i | \(-0.511130\pi\) |
0.848016 | + | 0.529970i | \(0.177797\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −53.5731 | + | 92.7913i | −0.0564521 | + | 0.0977779i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 62.5727 | + | 1215.17i | 0.0657967 | + | 1.27778i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.5920 | 0.0163610 | 0.00818050 | − | 0.999967i | \(-0.497396\pi\) | ||||
0.00818050 | + | 0.999967i | \(0.497396\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2.49830i | − | 0.00261602i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 180.905 | + | 279.127i | 0.189034 | + | 0.291669i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.15291 | − | 1.82033i | −0.00328770 | − | 0.00189816i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.3970 | + | 50.9172i | 0.0305900 | + | 0.0529835i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1335.68 | + | 966.706i | −1.38699 | + | 1.00385i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −191.961 | − | 332.486i | −0.198923 | − | 0.344545i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 847.921 | + | 489.548i | 0.876858 | + | 0.506254i | 0.869621 | − | 0.493720i | \(-0.164363\pi\) |
0.00723669 | + | 0.999974i | \(0.497696\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −450.229 | + | 881.635i | −0.464633 | + | 0.909840i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 67.3838i | 0.0693963i | 0.999398 | + | 0.0346982i | \(0.0110470\pi\) | ||||
−0.999398 | + | 0.0346982i | \(0.988953\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −70.3667 | −0.0723193 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −61.0216 | − | 31.1622i | −0.0625863 | − | 0.0319613i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 353.710 | − | 612.644i | 0.362037 | − | 0.627067i | −0.626259 | − | 0.779615i | \(-0.715415\pi\) |
0.988296 | + | 0.152549i | \(0.0487480\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 417.133 | − | 240.832i | 0.426081 | − | 0.245998i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −532.115 | − | 735.211i | −0.542421 | − | 0.749451i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −338.829 | + | 195.623i | −0.344689 | + | 0.199006i | −0.662343 | − | 0.749200i | \(-0.730438\pi\) |
0.317655 | + | 0.948206i | \(0.397105\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −638.971 | + | 1106.73i | −0.648701 | + | 1.12358i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.5547 | + | 10.7293i | −0.0167727 | + | 0.0108706i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −310.720 | −0.314176 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 104.988i | − | 0.105941i | −0.998596 | − | 0.0529706i | \(-0.983131\pi\) | ||
0.998596 | − | 0.0529706i | \(-0.0168690\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1328.81 | + | 68.4244i | −1.33818 | + | 0.0689068i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1592.67 | + | 919.530i | 1.60068 | + | 0.924151i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.0028 | + | 67.5547i | 0.0391201 | + | 0.0677580i | 0.884923 | − | 0.465738i | \(-0.154211\pi\) |
−0.845802 | + | 0.533496i | \(0.820878\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −241.918 | − | 1554.95i | −0.242160 | − | 1.55650i |
(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 | 576.3.o.g.319.7 | 16 | ||
3.2 | odd | 2 | 1728.3.o.g.1279.8 | 16 | |||
4.3 | odd | 2 | inner | 576.3.o.g.319.2 | 16 | ||
8.3 | odd | 2 | 36.3.f.c.31.3 | yes | 16 | ||
8.5 | even | 2 | 36.3.f.c.31.4 | yes | 16 | ||
9.2 | odd | 6 | 1728.3.o.g.127.7 | 16 | |||
9.7 | even | 3 | inner | 576.3.o.g.511.2 | 16 | ||
12.11 | even | 2 | 1728.3.o.g.1279.7 | 16 | |||
24.5 | odd | 2 | 108.3.f.c.91.5 | 16 | |||
24.11 | even | 2 | 108.3.f.c.91.6 | 16 | |||
36.7 | odd | 6 | inner | 576.3.o.g.511.7 | 16 | ||
36.11 | even | 6 | 1728.3.o.g.127.8 | 16 | |||
72.5 | odd | 6 | 324.3.d.g.163.1 | 8 | |||
72.11 | even | 6 | 108.3.f.c.19.5 | 16 | |||
72.13 | even | 6 | 324.3.d.i.163.8 | 8 | |||
72.29 | odd | 6 | 108.3.f.c.19.6 | 16 | |||
72.43 | odd | 6 | 36.3.f.c.7.4 | yes | 16 | ||
72.59 | even | 6 | 324.3.d.g.163.2 | 8 | |||
72.61 | even | 6 | 36.3.f.c.7.3 | ✓ | 16 | ||
72.67 | odd | 6 | 324.3.d.i.163.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.3 | ✓ | 16 | 72.61 | even | 6 | ||
36.3.f.c.7.4 | yes | 16 | 72.43 | odd | 6 | ||
36.3.f.c.31.3 | yes | 16 | 8.3 | odd | 2 | ||
36.3.f.c.31.4 | yes | 16 | 8.5 | even | 2 | ||
108.3.f.c.19.5 | 16 | 72.11 | even | 6 | |||
108.3.f.c.19.6 | 16 | 72.29 | odd | 6 | |||
108.3.f.c.91.5 | 16 | 24.5 | odd | 2 | |||
108.3.f.c.91.6 | 16 | 24.11 | even | 2 | |||
324.3.d.g.163.1 | 8 | 72.5 | odd | 6 | |||
324.3.d.g.163.2 | 8 | 72.59 | even | 6 | |||
324.3.d.i.163.7 | 8 | 72.67 | odd | 6 | |||
324.3.d.i.163.8 | 8 | 72.13 | even | 6 | |||
576.3.o.g.319.2 | 16 | 4.3 | odd | 2 | inner | ||
576.3.o.g.319.7 | 16 | 1.1 | even | 1 | trivial | ||
576.3.o.g.511.2 | 16 | 9.7 | even | 3 | inner | ||
576.3.o.g.511.7 | 16 | 36.7 | odd | 6 | inner | ||
1728.3.o.g.127.7 | 16 | 9.2 | odd | 6 | |||
1728.3.o.g.127.8 | 16 | 36.11 | even | 6 | |||
1728.3.o.g.1279.7 | 16 | 12.11 | even | 2 | |||
1728.3.o.g.1279.8 | 16 | 3.2 | odd | 2 |