Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.t (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.7 | ||
Character | \(\chi\) | \(=\) | 1008.193 |
Dual form | 1008.2.t.l.961.7 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.816621 | − | 1.52746i | 0.471476 | − | 0.881879i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.78355 | −0.797627 | −0.398814 | − | 0.917032i | \(-0.630578\pi\) | ||||
−0.398814 | + | 0.917032i | \(0.630578\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.90167 | + | 1.83948i | −0.718762 | + | 0.695256i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.66626 | − | 2.49471i | −0.555421 | − | 0.831570i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.61411 | 1.69272 | 0.846359 | − | 0.532612i | \(-0.178790\pi\) | ||||
0.846359 | + | 0.532612i | \(0.178790\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.14009 | − | 5.43879i | 0.870903 | − | 1.50845i | 0.00983976 | − | 0.999952i | \(-0.496868\pi\) |
0.861064 | − | 0.508497i | \(-0.169799\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.45648 | + | 2.72430i | −0.376062 | + | 0.703410i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.646279 | − | 1.11939i | 0.156746 | − | 0.271491i | −0.776948 | − | 0.629565i | \(-0.783233\pi\) |
0.933693 | + | 0.358074i | \(0.116566\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.559062 | − | 0.968324i | −0.128258 | − | 0.222149i | 0.794744 | − | 0.606945i | \(-0.207605\pi\) |
−0.923002 | + | 0.384796i | \(0.874272\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.25678 | + | 4.40687i | 0.274253 | + | 0.961658i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.61715 | −1.58828 | −0.794142 | − | 0.607732i | \(-0.792080\pi\) | ||||
−0.794142 | + | 0.607732i | \(0.792080\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.81896 | −0.363791 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.17127 | + | 0.507916i | −0.995211 | + | 0.0977485i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.57496 | − | 2.72791i | −0.292462 | − | 0.506560i | 0.681929 | − | 0.731418i | \(-0.261141\pi\) |
−0.974391 | + | 0.224859i | \(0.927808\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.501553 | + | 0.868716i | 0.0900816 | + | 0.156026i | 0.907545 | − | 0.419954i | \(-0.137954\pi\) |
−0.817464 | + | 0.575980i | \(0.804621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.58460 | − | 8.57533i | 0.798076 | − | 1.49277i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.39171 | − | 3.28079i | 0.573304 | − | 0.554555i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.96542 | − | 10.3324i | −0.980708 | − | 1.69864i | −0.659642 | − | 0.751580i | \(-0.729292\pi\) |
−0.321067 | − | 0.947057i | \(-0.604041\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.74327 | − | 9.23778i | −0.919659 | − | 1.47923i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.14160 | − | 7.17347i | 0.646810 | − | 1.12031i | −0.337071 | − | 0.941479i | \(-0.609436\pi\) |
0.983880 | − | 0.178828i | \(-0.0572306\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.34804 | − | 4.06693i | −0.358073 | − | 0.620200i | 0.629566 | − | 0.776947i | \(-0.283233\pi\) |
−0.987639 | + | 0.156747i | \(0.949899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.97186 | + | 4.44943i | 0.443018 | + | 0.663282i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.972001 | + | 1.68356i | −0.141781 | + | 0.245572i | −0.928167 | − | 0.372163i | \(-0.878616\pi\) |
0.786386 | + | 0.617735i | \(0.211950\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.232662 | − | 6.99613i | 0.0332374 | − | 0.999447i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.18205 | − | 1.90128i | −0.165521 | − | 0.266232i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.45992 | + | 7.72481i | −0.612617 | + | 1.06108i | 0.378180 | + | 0.925732i | \(0.376550\pi\) |
−0.990798 | + | 0.135352i | \(0.956783\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.0130 | −1.35016 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.93562 | + | 0.0631911i | −0.256379 | + | 0.00836987i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.19339 | + | 7.26317i | 0.545933 | + | 0.945584i | 0.998548 | + | 0.0538778i | \(0.0171581\pi\) |
−0.452614 | + | 0.891706i | \(0.649509\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.41288 | + | 4.17923i | −0.308937 | + | 0.535095i | −0.978130 | − | 0.207994i | \(-0.933307\pi\) |
0.669193 | + | 0.743089i | \(0.266640\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.75763 | + | 1.67905i | 0.977369 | + | 0.211541i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.60050 | + | 9.70034i | −0.694656 | + | 1.20318i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.27814 | − | 2.21380i | −0.156150 | − | 0.270459i | 0.777327 | − | 0.629096i | \(-0.216575\pi\) |
−0.933477 | + | 0.358637i | \(0.883242\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.22032 | + | 11.6349i | −0.748838 | + | 1.40067i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.86178 | 1.05170 | 0.525850 | − | 0.850577i | \(-0.323747\pi\) | ||||
0.525850 | + | 0.850577i | \(0.323747\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.67598 | − | 9.83109i | 0.664323 | − | 1.15064i | −0.315145 | − | 0.949044i | \(-0.602053\pi\) |
0.979468 | − | 0.201598i | \(-0.0646135\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.48540 | + | 2.77838i | −0.171519 | + | 0.320820i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.6762 | + | 10.3270i | −1.21666 | + | 1.17687i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.72883 | − | 11.6547i | 0.757052 | − | 1.31125i | −0.187295 | − | 0.982304i | \(-0.559972\pi\) |
0.944348 | − | 0.328949i | \(-0.106695\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.44714 | + | 8.31368i | −0.383016 | + | 0.923742i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.60203 | + | 2.77479i | 0.175845 | + | 0.304573i | 0.940453 | − | 0.339922i | \(-0.110401\pi\) |
−0.764608 | + | 0.644495i | \(0.777067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.15267 | + | 1.99648i | −0.125025 | + | 0.216549i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.45291 | + | 0.178018i | −0.584613 | + | 0.0190856i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.404646 | − | 0.700867i | −0.0428924 | − | 0.0742917i | 0.843782 | − | 0.536686i | \(-0.180324\pi\) |
−0.886675 | + | 0.462394i | \(0.846991\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.03312 | + | 16.1189i | 0.422786 | + | 1.68972i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.73651 | − | 0.0566909i | 0.180067 | − | 0.00587857i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.997114 | + | 1.72705i | 0.102302 | + | 0.177192i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.10781 | + | 1.91879i | 0.112481 | + | 0.194823i | 0.916770 | − | 0.399415i | \(-0.130787\pi\) |
−0.804289 | + | 0.594238i | \(0.797454\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.35458 | − | 14.0056i | −0.940171 | − | 1.40761i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.40267 | 0.935601 | 0.467801 | − | 0.883834i | \(-0.345047\pi\) | ||||
0.467801 | + | 0.883834i | \(0.345047\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.52698 | 0.347524 | 0.173762 | − | 0.984788i | \(-0.444408\pi\) | ||||
0.173762 | + | 0.984788i | \(0.444408\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.24153 | − | 7.85986i | −0.218751 | − | 0.767044i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.39276 | + | 5.87644i | 0.327991 | + | 0.568097i | 0.982113 | − | 0.188292i | \(-0.0602951\pi\) |
−0.654122 | + | 0.756389i | \(0.726962\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.681848 | − | 1.18099i | 0.0653092 | − | 0.113119i | −0.831522 | − | 0.555492i | \(-0.812530\pi\) |
0.896831 | + | 0.442373i | \(0.145863\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.6538 | + | 0.674275i | −1.96037 | + | 0.0639993i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.76458 | + | 4.78840i | −0.260070 | + | 0.450455i | −0.966260 | − | 0.257568i | \(-0.917079\pi\) |
0.706190 | + | 0.708022i | \(0.250412\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.5855 | 1.26686 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.8004 | + | 1.22885i | −1.73810 | + | 0.113607i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.830080 | + | 3.31752i | 0.0760933 | + | 0.304116i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.5183 | 1.86530 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.57506 | − | 12.1841i | −0.683020 | − | 1.09861i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1619 | 1.08780 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.8209 | 1.13767 | 0.568837 | − | 0.822450i | \(-0.307394\pi\) | ||||
0.568837 | + | 0.822450i | \(0.307394\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.12952 | + | 0.265401i | −0.715764 | + | 0.0233672i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.81910 | 0.508417 | 0.254208 | − | 0.967149i | \(-0.418185\pi\) | ||||
0.254208 | + | 0.967149i | \(0.418185\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.84436 | + | 0.813047i | 0.246637 | + | 0.0705001i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.22321 | − | 0.905892i | 0.793807 | − | 0.0779668i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.3409 | −1.31066 | −0.655332 | − | 0.755341i | \(-0.727471\pi\) | ||||
−0.655332 | + | 0.755341i | \(0.727471\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.05803 | − | 10.4928i | 0.513835 | − | 0.889988i | −0.486036 | − | 0.873939i | \(-0.661558\pi\) |
0.999871 | − | 0.0160496i | \(-0.00510897\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.77781 | + | 2.85952i | 0.149718 | + | 0.240815i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.6288 | − | 30.5340i | 1.47419 | − | 2.55338i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.80901 | + | 4.86535i | 0.233276 | + | 0.404046i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.4963 | − | 6.06857i | −0.865721 | − | 0.500527i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.73699 | 0.388069 | 0.194035 | − | 0.980995i | \(-0.437843\pi\) | ||||
0.194035 | + | 0.980995i | \(0.437843\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −24.3690 | −1.98312 | −0.991559 | − | 0.129657i | \(-0.958612\pi\) | ||||
−0.991559 | + | 0.129657i | \(0.958612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.86942 | + | 0.252916i | −0.312824 | + | 0.0204470i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.894545 | − | 1.54940i | −0.0718516 | − | 0.124451i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.15229 | + | 5.45993i | 0.251580 | + | 0.435750i | 0.963961 | − | 0.266043i | \(-0.0857165\pi\) |
−0.712381 | + | 0.701793i | \(0.752383\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.15727 | + | 13.1206i | 0.646913 | + | 1.04053i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.4853 | − | 14.0116i | 1.14160 | − | 1.10426i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.350678 | − | 0.607392i | −0.0274672 | − | 0.0475746i | 0.851965 | − | 0.523599i | \(-0.175411\pi\) |
−0.879432 | + | 0.476024i | \(0.842078\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.17686 | + | 15.2945i | −0.636567 | + | 1.19068i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.53822 | + | 6.12839i | −0.273796 | + | 0.474229i | −0.969831 | − | 0.243780i | \(-0.921613\pi\) |
0.696035 | + | 0.718008i | \(0.254946\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.2203 | − | 22.8982i | −1.01695 | − | 1.76140i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.48414 | + | 3.00818i | −0.113495 | + | 0.230041i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.31767 | + | 5.74638i | −0.252238 | + | 0.436889i | −0.964142 | − | 0.265388i | \(-0.914500\pi\) |
0.711904 | + | 0.702277i | \(0.247833\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.45904 | − | 3.34592i | 0.261479 | − | 0.252928i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.5186 | − | 0.473982i | 1.09129 | − | 0.0356267i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.63527 | + | 9.76057i | −0.421200 | + | 0.729539i | −0.996057 | − | 0.0887145i | \(-0.971724\pi\) |
0.574858 | + | 0.818253i | \(0.305057\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.1800 | 1.57430 | 0.787149 | − | 0.616762i | \(-0.211556\pi\) | ||||
0.787149 | + | 0.616762i | \(0.211556\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.41319 | + | 7.09841i | 0.326233 | + | 0.524730i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.6396 | + | 18.4283i | 0.782240 | + | 1.35488i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.62828 | − | 6.28437i | 0.265326 | − | 0.459559i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.89972 | − | 10.4783i | 0.647360 | − | 0.762185i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.72044 | + | 8.17604i | −0.341559 | + | 0.591598i | −0.984722 | − | 0.174131i | \(-0.944288\pi\) |
0.643163 | + | 0.765729i | \(0.277622\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.14021 | + | 5.43900i | 0.226037 | + | 0.391508i | 0.956630 | − | 0.291305i | \(-0.0940896\pi\) |
−0.730593 | + | 0.682813i | \(0.760756\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.2434 | + | 16.4760i | 0.733545 | + | 1.17987i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.4780 | 1.10276 | 0.551382 | − | 0.834253i | \(-0.314101\pi\) | ||||
0.551382 | + | 0.834253i | \(0.314101\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.19477 | + | 3.80145i | −0.155583 | + | 0.269478i | −0.933271 | − | 0.359173i | \(-0.883059\pi\) |
0.777688 | + | 0.628650i | \(0.216392\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.42525 | + | 0.144469i | −0.312133 | + | 0.0101901i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.01296 | + | 2.29047i | 0.562400 | + | 0.160759i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.38675 | + | 12.7942i | −0.515913 | + | 0.893587i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.6922 | + | 19.0026i | 0.882166 | + | 1.32077i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.13864 | − | 5.43628i | −0.217104 | − | 0.376035i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.93101 | + | 13.7369i | −0.545993 | + | 0.945688i | 0.452550 | + | 0.891739i | \(0.350514\pi\) |
−0.998544 | + | 0.0539495i | \(0.982819\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.23671 | − | 13.5360i | 0.495851 | − | 0.927472i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.18784 | + | 7.25356i | 0.285609 | + | 0.494689i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.55177 | − | 0.729412i | −0.173225 | − | 0.0495157i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.3815 | − | 16.6981i | −0.701514 | − | 1.12835i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.05874 | − | 7.02995i | −0.273021 | − | 0.472886i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.99253 | − | 12.1114i | −0.468254 | − | 0.811040i | 0.531088 | − | 0.847317i | \(-0.321784\pi\) |
−0.999342 | + | 0.0362769i | \(0.988450\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.03086 | + | 4.53776i | 0.202057 | + | 0.302518i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.7673 | −0.714650 | −0.357325 | − | 0.933980i | \(-0.616311\pi\) | ||||
−0.357325 | + | 0.933980i | \(0.616311\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.61003 | −0.106394 | −0.0531969 | − | 0.998584i | \(-0.516941\pi\) | ||||
−0.0531969 | + | 0.998584i | \(0.516941\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.05573 | + | 24.7407i | 0.464233 | + | 1.62782i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.510606 | − | 0.884395i | −0.0334509 | − | 0.0579387i | 0.848815 | − | 0.528690i | \(-0.177316\pi\) |
−0.882266 | + | 0.470751i | \(0.843983\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.73361 | − | 3.00270i | 0.113088 | − | 0.195875i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.3071 | − | 19.7955i | −0.799434 | − | 1.28585i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.96428 | − | 12.0625i | 0.450482 | − | 0.780258i | −0.547934 | − | 0.836522i | \(-0.684586\pi\) |
0.998416 | + | 0.0562640i | \(0.0179189\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.5758 | −0.938908 | −0.469454 | − | 0.882957i | \(-0.655549\pi\) | ||||
−0.469454 | + | 0.882957i | \(0.655549\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.88379 | + | 12.0545i | 0.634045 | + | 0.773296i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.414964 | + | 12.4779i | −0.0265111 | + | 0.797186i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.02201 | −0.446800 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.54663 | − | 0.181078i | 0.351503 | − | 0.0114754i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0287 | −1.13796 | −0.568981 | − | 0.822350i | \(-0.692662\pi\) | ||||
−0.568981 | + | 0.822350i | \(0.692662\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −42.7635 | −2.68852 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.10825 | + | 3.39102i | 0.132024 | + | 0.212354i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.9266 | 1.67964 | 0.839818 | − | 0.542869i | \(-0.182662\pi\) | ||||
0.839818 | + | 0.542869i | \(0.182662\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 30.3504 | + | 8.67554i | 1.88588 | + | 0.539072i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.18104 | + | 8.47447i | −0.258800 | + | 0.524556i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.53884 | −0.0948888 | −0.0474444 | − | 0.998874i | \(-0.515108\pi\) | ||||
−0.0474444 | + | 0.998874i | \(0.515108\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.95448 | − | 13.7776i | 0.488640 | − | 0.846349i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.40099 | + | 0.0457374i | −0.0857390 | + | 0.00279908i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.26461 | − | 5.65446i | 0.199047 | − | 0.344759i | −0.749173 | − | 0.662374i | \(-0.769549\pi\) |
0.948220 | + | 0.317616i | \(0.102882\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.64494 | + | 9.77733i | 0.342906 | + | 0.593930i | 0.984971 | − | 0.172720i | \(-0.0552555\pi\) |
−0.642065 | + | 0.766650i | \(0.721922\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 27.9144 | + | 7.00257i | 1.68946 | + | 0.423815i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.2118 | −0.615796 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.81188 | 0.108865 | 0.0544325 | − | 0.998517i | \(-0.482665\pi\) | ||||
0.0544325 | + | 0.998517i | \(0.482665\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.33147 | − | 2.69874i | 0.0797133 | − | 0.161569i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.98798 | − | 5.17533i | −0.178248 | − | 0.308734i | 0.763033 | − | 0.646360i | \(-0.223710\pi\) |
−0.941280 | + | 0.337626i | \(0.890376\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.99760 | − | 17.3163i | −0.594295 | − | 1.02935i | −0.993646 | − | 0.112552i | \(-0.964098\pi\) |
0.399350 | − | 0.916798i | \(-0.369236\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.45227 | − | 0.112704i | 0.204495 | − | 0.00667604i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.31947 | + | 21.2599i | 0.313998 | + | 1.25493i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.66465 | + | 13.2756i | 0.450862 | + | 0.780915i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.83553 | − | 0.125217i | 0.224843 | − | 0.00734033i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.95166 | + | 8.57652i | −0.289279 | + | 0.501046i | −0.973638 | − | 0.228099i | \(-0.926749\pi\) |
0.684359 | + | 0.729145i | \(0.260082\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.47912 | − | 12.9542i | −0.435451 | − | 0.754224i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −29.0321 | + | 2.85150i | −1.68461 | + | 0.165461i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.9185 | + | 41.4281i | −1.38324 | + | 2.39585i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.9462 | + | 3.41477i | 0.688567 | + | 0.196824i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.67842 | − | 14.3622i | 0.441114 | − | 0.825087i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.30348 | − | 7.45385i | 0.246417 | − | 0.426806i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.7122 | 1.35332 | 0.676662 | − | 0.736293i | \(-0.263426\pi\) | ||||
0.676662 | + | 0.736293i | \(0.263426\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.88021 | − | 5.38732i | 0.163849 | − | 0.306474i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.1724 | + | 17.6192i | 0.576826 | + | 0.999092i | 0.995841 | + | 0.0911122i | \(0.0290422\pi\) |
−0.419015 | + | 0.907979i | \(0.637624\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.85936 | + | 8.41665i | −0.274667 | + | 0.475737i | −0.970051 | − | 0.242901i | \(-0.921901\pi\) |
0.695384 | + | 0.718638i | \(0.255234\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −13.8361 | − | 2.99467i | −0.779576 | − | 0.168731i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.66419 | − | 2.88246i | 0.0934703 | − | 0.161895i | −0.815499 | − | 0.578759i | \(-0.803537\pi\) |
0.908969 | + | 0.416863i | \(0.136871\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.84199 | − | 15.3148i | −0.495056 | − | 0.857463i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.7466 | − | 0.383486i | 0.655633 | − | 0.0214041i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.44524 | −0.0804153 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.71168 | + | 9.89292i | −0.316827 | + | 0.548760i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.24711 | − | 2.00592i | −0.0689654 | − | 0.110928i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.24844 | − | 4.98953i | −0.0688286 | − | 0.275082i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.717346 | + | 1.24248i | −0.0394289 | + | 0.0682929i | −0.885066 | − | 0.465465i | \(-0.845887\pi\) |
0.845638 | + | 0.533758i | \(0.179221\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.8364 | + | 32.0985i | −0.867829 | + | 1.75899i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.27962 | + | 3.94843i | 0.124549 | + | 0.215726i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.00257316 | − | 0.00445685i | 0.000140169 | − | 0.000242780i | −0.865955 | − | 0.500121i | \(-0.833289\pi\) |
0.866095 | + | 0.499879i | \(0.166622\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.05647 | + | 8.13309i | 0.274630 | + | 0.441729i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.81578 | + | 4.87707i | 0.152483 | + | 0.264108i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.4268 | + | 13.7323i | 0.670982 | + | 0.741473i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.0942 | − | 20.7514i | 0.597294 | − | 1.11722i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.5536 | + | 20.0114i | 0.620229 | + | 1.07427i | 0.989443 | + | 0.144924i | \(0.0462936\pi\) |
−0.369214 | + | 0.929344i | \(0.620373\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.09723 | + | 10.5607i | 0.326377 | + | 0.565302i | 0.981790 | − | 0.189969i | \(-0.0608387\pi\) |
−0.655413 | + | 0.755271i | \(0.727505\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.4758 | + | 29.7203i | −0.719284 | + | 1.58635i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.7072 | 1.31503 | 0.657515 | − | 0.753441i | \(-0.271608\pi\) | ||||
0.657515 | + | 0.753441i | \(0.271608\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.8054 | −0.838864 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.74523 | + | 1.44124i | 0.304070 | + | 0.0762784i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.20362 | − | 14.2091i | −0.432970 | − | 0.749927i | 0.564157 | − | 0.825667i | \(-0.309201\pi\) |
−0.997128 | + | 0.0757407i | \(0.975868\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.87490 | − | 15.3718i | 0.467100 | − | 0.809041i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.7556 | − | 31.3408i | 0.879443 | − | 1.64497i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.1234 | + | 17.5342i | −0.529882 | + | 0.917783i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.81801 | 0.303698 | 0.151849 | − | 0.988404i | \(-0.451477\pi\) | ||||
0.151849 | + | 0.988404i | \(0.451477\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −24.7967 | + | 1.62078i | −1.29086 | + | 0.0843744i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.72832 | − | 22.8939i | −0.297399 | − | 1.18859i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.84966 | 0.458218 | 0.229109 | − | 0.973401i | \(-0.426419\pi\) | ||||
0.229109 | + | 0.973401i | \(0.426419\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.93169 | − | 18.5769i | 0.512870 | − | 0.959305i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.7820 | −1.01883 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.3300 | −0.890181 | −0.445091 | − | 0.895486i | \(-0.646829\pi\) | ||||
−0.445091 | + | 0.895486i | \(0.646829\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.4698 | − | 19.5834i | 0.536386 | − | 1.00329i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.09090 | −0.362328 | −0.181164 | − | 0.983453i | \(-0.557986\pi\) | ||||
−0.181164 | + | 0.983453i | \(0.557986\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.0415 | − | 18.4187i | 0.970442 | − | 0.938706i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.23335 | + | 12.6342i | −0.316859 | + | 0.642235i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.64240 | 0.336783 | 0.168392 | − | 0.985720i | \(-0.446143\pi\) | ||||
0.168392 | + | 0.985720i | \(0.446143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.92280 | + | 8.52654i | −0.248957 | + | 0.431206i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.75199 | − | 8.88843i | 0.239706 | − | 0.448362i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0012 | + | 20.7867i | −0.603845 | + | 1.04589i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.86340 | + | 13.6198i | 0.394653 | + | 0.683559i | 0.993057 | − | 0.117636i | \(-0.0375315\pi\) |
−0.598404 | + | 0.801195i | \(0.704198\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.56466 | − | 3.68069i | 0.178456 | − | 0.184265i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.96559 | 0.297907 | 0.148954 | − | 0.988844i | \(-0.452409\pi\) | ||||
0.148954 | + | 0.988844i | \(0.452409\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.29968 | 0.313810 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.14815 | − | 14.8278i | 0.305504 | − | 0.736801i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −33.4905 | − | 58.0073i | −1.66006 | − | 2.87531i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.80943 | + | 15.2584i | 0.435598 | + | 0.754478i | 0.997344 | − | 0.0728314i | \(-0.0232035\pi\) |
−0.561746 | + | 0.827310i | \(0.689870\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.5277 | + | 23.4326i | −0.617947 | + | 1.15585i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.3349 | − | 6.09848i | −1.04982 | − | 0.300086i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.85729 | − | 4.94897i | −0.140259 | − | 0.242936i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.0802 | − | 17.8220i | −0.542601 | − | 0.872748i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.62164 | + | 16.6652i | −0.470048 | + | 0.814147i | −0.999413 | − | 0.0342470i | \(-0.989097\pi\) |
0.529365 | + | 0.848394i | \(0.322430\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.77999 | + | 13.4753i | 0.379174 | + | 0.656748i | 0.990942 | − | 0.134289i | \(-0.0428750\pi\) |
−0.611769 | + | 0.791037i | \(0.709542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.81959 | − | 0.380384i | 0.282958 | − | 0.0184949i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.17555 | + | 2.03612i | −0.0570227 | + | 0.0987662i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.09910 | − | 12.3859i | −0.149976 | − | 0.599397i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −32.2434 | − | 51.8620i | −1.55672 | − | 2.50392i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.9779 | − | 29.4067i | 0.817799 | − | 1.41647i | −0.0895020 | − | 0.995987i | \(-0.528528\pi\) |
0.907301 | − | 0.420482i | \(-0.138139\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.8338 | −1.67401 | −0.837004 | − | 0.547197i | \(-0.815695\pi\) | ||||
−0.837004 | + | 0.547197i | \(0.815695\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.72553 | − | 0.317505i | 0.466303 | − | 0.0152232i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.25846 | + | 7.37587i | 0.203710 | + | 0.352835i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.77938 | − | 13.4743i | 0.371290 | − | 0.643093i | −0.618475 | − | 0.785805i | \(-0.712249\pi\) |
0.989764 | + | 0.142712i | \(0.0455824\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.8410 | + | 11.0770i | −0.849571 | + | 0.527474i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.16212 | − | 15.8693i | 0.435305 | − | 0.753971i | −0.562015 | − | 0.827127i | \(-0.689974\pi\) |
0.997321 | + | 0.0731560i | \(0.0233071\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.721705 | + | 1.25003i | 0.0342121 | + | 0.0592571i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.86832 | − | 7.23555i | 0.182965 | − | 0.342230i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.75072 | −0.129815 | −0.0649073 | − | 0.997891i | \(-0.520675\pi\) | ||||
−0.0649073 | + | 0.997891i | \(0.520675\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.2514 | − | 40.2727i | 1.09487 | − | 1.89637i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.9002 | + | 37.2226i | −0.934993 | + | 1.74887i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.19327 | − | 28.7488i | −0.337226 | − | 1.34776i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.3407 | + | 17.9106i | −0.483716 | + | 0.837821i | −0.999825 | − | 0.0187018i | \(-0.994047\pi\) |
0.516109 | + | 0.856523i | \(0.327380\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.77353 | + | 6.11691i | −0.129457 | + | 0.285513i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.40670 | + | 11.0967i | 0.298390 | + | 0.516826i | 0.975768 | − | 0.218809i | \(-0.0702172\pi\) |
−0.677378 | + | 0.735635i | \(0.736884\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.54704 | + | 9.60775i | −0.257793 | + | 0.446510i | −0.965650 | − | 0.259845i | \(-0.916328\pi\) |
0.707858 | + | 0.706355i | \(0.249662\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.09714 | + | 0.101111i | −0.143627 | + | 0.00468891i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.36754 | − | 9.29686i | −0.248380 | − | 0.430207i | 0.714696 | − | 0.699435i | \(-0.246565\pi\) |
−0.963077 | + | 0.269228i | \(0.913232\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.50283 | + | 1.85881i | 0.300273 | + | 0.0858317i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.9140 | − | 0.356305i | 0.502892 | − | 0.0164177i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.1822 | − | 22.8322i | −0.606117 | − | 1.04982i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.01691 | + | 1.76134i | 0.0466590 | + | 0.0808157i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26.7025 | − | 1.74535i | 1.22263 | − | 0.0799141i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.79508 | 0.356166 | 0.178083 | − | 0.984015i | \(-0.443010\pi\) | ||||
0.178083 | + | 0.984015i | \(0.443010\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −74.9277 | −3.41641 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.57311 | − | 33.5678i | −0.435591 | − | 1.52739i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.97583 | − | 3.42225i | −0.0897180 | − | 0.155396i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.9984 | + | 24.2459i | −0.634326 | + | 1.09868i | 0.352331 | + | 0.935875i | \(0.385389\pi\) |
−0.986657 | + | 0.162810i | \(0.947944\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.21414 | + | 0.0396373i | −0.0549052 | + | 0.00179246i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.1227 | − | 20.9971i | 0.547089 | − | 0.947586i | −0.451383 | − | 0.892330i | \(-0.649069\pi\) |
0.998472 | − | 0.0552556i | \(-0.0175974\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.07145 | −0.183369 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.6843 | + | 24.9796i | 0.749906 | + | 1.12275i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.8521 | + | 16.3010i | −0.755922 | + | 0.731201i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.7748 | 1.51197 | 0.755984 | − | 0.654590i | \(-0.227159\pi\) | ||||
0.755984 | + | 0.654590i | \(0.227159\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.47147 | + | 10.4091i | 0.289124 | + | 0.465042i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.09819 | 0.0489661 | 0.0244830 | − | 0.999700i | \(-0.492206\pi\) | ||||
0.0244830 | + | 0.999700i | \(0.492206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.7701 | −0.746261 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −45.7720 | + | 1.49430i | −2.03281 | + | 0.0663641i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.2134 | 0.718648 | 0.359324 | − | 0.933213i | \(-0.383007\pi\) | ||||
0.359324 | + | 0.933213i | \(0.383007\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.29023 | + | 29.1363i | 0.322501 | + | 1.28891i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.38289 | + | 4.72351i | 0.149358 | + | 0.208548i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.29054 | −0.277194 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.45692 | + | 9.45167i | −0.239995 | + | 0.415684i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.06807 | + | 9.76021i | 0.266359 | + | 0.428426i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.1738 | − | 33.2099i | 0.840017 | − | 1.45495i | −0.0498617 | − | 0.998756i | \(-0.515878\pi\) |
0.889879 | − | 0.456197i | \(-0.150789\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.6021 | − | 35.6838i | −0.900865 | − | 1.56034i | −0.826374 | − | 0.563122i | \(-0.809600\pi\) |
−0.0744911 | − | 0.997222i | \(-0.523733\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.28603 | − | 8.01590i | −0.0997707 | − | 0.349843i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.29657 | 0.0564796 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.0209 | 1.52265 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.1322 | − | 22.5636i | 0.483097 | − | 0.979178i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.0100 | − | 45.0506i | −1.12662 | − | 1.95136i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.05116 | − | 10.4809i | −0.261614 | − | 0.453129i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.3070 | + | 16.5783i | 0.444779 | + | 0.715407i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.30619 | − | 39.2771i | 0.0562616 | − | 1.69178i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.09371 | − | 15.7508i | −0.390969 | − | 0.677178i | 0.601609 | − | 0.798791i | \(-0.294527\pi\) |
−0.992578 | + | 0.121613i | \(0.961193\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.2960 | − | 32.3516i | 0.742244 | − | 1.38834i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.21611 | + | 2.10636i | −0.0520924 | + | 0.0902266i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.338699 | − | 0.586644i | −0.0144817 | − | 0.0250831i | 0.858694 | − | 0.512489i | \(-0.171277\pi\) |
−0.873175 | + | 0.487406i | \(0.837943\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.4464 | − | 0.944258i | 0.616559 | − | 0.0403000i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.76100 | + | 3.05014i | −0.0750211 | + | 0.129940i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.64250 | + | 34.5408i | 0.367516 | + | 1.46882i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 36.8371 | − | 1.20260i | 1.56365 | − | 0.0510476i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8659 | − | 25.7484i | 0.629887 | − | 1.09100i | −0.357687 | − | 0.933842i | \(-0.616435\pi\) |
0.987574 | − | 0.157155i | \(-0.0502322\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.4922 | −1.24739 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.63619 | − | 10.6740i | −0.280180 | − | 0.450657i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.6739 | + | 18.4878i | 0.449852 | + | 0.779167i | 0.998376 | − | 0.0569680i | \(-0.0181433\pi\) |
−0.548524 | + | 0.836135i | \(0.684810\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.93077 | − | 8.54034i | 0.207439 | − | 0.359295i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.73749 | − | 22.1508i | −0.366940 | − | 0.930245i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.56212 | − | 13.0980i | 0.317021 | − | 0.549096i | −0.662844 | − | 0.748757i | \(-0.730651\pi\) |
0.979865 | + | 0.199661i | \(0.0639842\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.94314 | + | 17.2220i | 0.416107 | + | 0.720719i | 0.995544 | − | 0.0942981i | \(-0.0300607\pi\) |
−0.579437 | + | 0.815017i | \(0.696727\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.63376 | + | 13.8870i | 0.360681 | + | 0.580138i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.8553 | 0.577804 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.8090 | − | 34.3102i | 0.824661 | − | 1.42835i | −0.0775179 | − | 0.996991i | \(-0.524700\pi\) |
0.902178 | − | 0.431363i | \(-0.141967\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.8722 | − | 0.354940i | 0.451834 | − | 0.0147508i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.15068 | − | 2.32984i | −0.338147 | − | 0.0966579i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.0385 | + | 43.3679i | −1.03699 | + | 1.79612i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 33.5314 | − | 2.19170i | 1.38635 | − | 0.0906158i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.13275 | − | 1.96199i | −0.0467537 | − | 0.0809798i | 0.841701 | − | 0.539943i | \(-0.181554\pi\) |
−0.888455 | + | 0.458963i | \(0.848221\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.560799 | − | 0.971332i | 0.0231073 | − | 0.0400230i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.6397 | − | 23.6421i | 0.519927 | − | 0.972504i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.97295 | + | 10.3454i | 0.245280 | + | 0.424837i | 0.962210 | − | 0.272308i | \(-0.0877869\pi\) |
−0.716931 | + | 0.697145i | \(0.754454\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.48049 | − | 5.91695i | −0.0606941 | − | 0.242571i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.01426 | + | 6.45676i | 0.164293 | + | 0.264257i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.47636 | − | 2.55713i | −0.0603224 | − | 0.104481i | 0.834287 | − | 0.551330i | \(-0.185880\pi\) |
−0.894610 | + | 0.446849i | \(0.852546\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.9751 | + | 27.6697i | 0.651638 | + | 1.12867i | 0.982725 | + | 0.185071i | \(0.0592514\pi\) |
−0.331087 | + | 0.943600i | \(0.607415\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.39308 | + | 6.87736i | −0.138177 | + | 0.280068i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −36.5953 | −1.48781 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.4014 | −0.422179 | −0.211089 | − | 0.977467i | \(-0.567701\pi\) | ||||
−0.211089 | + | 0.977467i | \(0.567701\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.0421 | − | 10.3690i | 0.406928 | − | 0.420174i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.10433 | + | 10.5730i | 0.246955 | + | 0.427739i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.22441 | − | 10.7810i | 0.251402 | − | 0.435441i | −0.712510 | − | 0.701662i | \(-0.752442\pi\) |
0.963912 | + | 0.266221i | \(0.0857751\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.5105 | + | 21.7310i | 0.544795 | + | 0.876278i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.70100 | + | 8.14237i | −0.189255 | + | 0.327799i | −0.945002 | − | 0.327064i | \(-0.893941\pi\) |
0.755747 | + | 0.654864i | \(0.227274\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.1196 | 0.889062 | 0.444531 | − | 0.895763i | \(-0.353370\pi\) | ||||
0.444531 | + | 0.895763i | \(0.353370\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 39.3903 | − | 3.86887i | 1.58068 | − | 0.155252i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.05873 | + | 0.588479i | 0.0824812 | + | 0.0235769i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5966 | −0.503865 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.8668 | + | 0.354762i | −0.433977 | + | 0.0141678i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.4213 | −0.614887 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.3705 | −0.731316 | −0.365658 | − | 0.930749i | \(-0.619156\pi\) | ||||
−0.365658 | + | 0.930749i | \(0.619156\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.5059 | + | 23.3321i | 0.576560 | + | 0.927370i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.8668 | −0.907439 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.3199 | − | 23.2339i | −1.47867 | − | 0.920559i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.7660 | − | 22.1076i | −0.584136 | − | 0.874562i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.7233 | −1.33199 | −0.665995 | − | 0.745956i | \(-0.731993\pi\) | ||||
−0.665995 | + | 0.745956i | \(0.731993\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0635 | + | 17.4306i | −0.396867 | + | 0.687394i | −0.993338 | − | 0.115241i | \(-0.963236\pi\) |
0.596470 | + | 0.802635i | \(0.296569\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.4994 | − | 0.473355i | 0.570913 | − | 0.0186383i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.1891 | − | 19.3800i | 0.439887 | − | 0.761907i | −0.557793 | − | 0.829980i | \(-0.688352\pi\) |
0.997680 | + | 0.0680731i | \(0.0216851\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.5422 | + | 40.7763i | 0.924112 | + | 1.60061i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.19797 | + | 3.30207i | −0.125338 | + | 0.129418i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.6754 | −1.59175 | −0.795875 | − | 0.605460i | \(-0.792989\pi\) | ||||
−0.795875 | + | 0.605460i | \(0.792989\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.3786 | −0.405527 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −33.9834 | + | 2.22124i | −1.32582 | + | 0.0866590i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.69321 | − | 13.3250i | −0.299685 | − | 0.519070i | 0.676379 | − | 0.736554i | \(-0.263548\pi\) |
−0.976064 | + | 0.217484i | \(0.930215\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.5736 | − | 42.5628i | −0.955804 | − | 1.65550i | −0.732518 | − | 0.680747i | \(-0.761655\pi\) |
−0.223285 | − | 0.974753i | \(-0.571678\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.0524 | + | 0.458762i | −0.545751 | + | 0.0178169i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.07305 | − | 1.45011i | −0.196724 | − | 0.0562328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.9967 | + | 20.7789i | 0.464513 | + | 0.804561i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.2099 | + | 0.790370i | −0.936010 | + | 0.0305575i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.5462 | + | 23.4627i | −0.522944 | + | 0.905766i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.99961 | − | 12.1237i | −0.269815 | − | 0.467334i | 0.698999 | − | 0.715123i | \(-0.253629\pi\) |
−0.968814 | + | 0.247789i | \(0.920296\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.40631 | − | 0.923876i | 0.362049 | − | 0.0355600i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.3870 | − | 40.5075i | 0.898836 | − | 1.55683i | 0.0698517 | − | 0.997557i | \(-0.477747\pi\) |
0.828984 | − | 0.559272i | \(-0.188919\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.63624 | − | 1.61110i | −0.216299 | − | 0.0618282i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.79279 | + | 16.4466i | −0.336940 | + | 0.630235i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.6222 | + | 37.4508i | −0.827352 | + | 1.43302i | 0.0727571 | + | 0.997350i | \(0.476820\pi\) |
−0.900109 | + | 0.435665i | \(0.856513\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.3613 | 1.04542 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.31478 | + | 2.45925i | −0.0501621 | + | 0.0938264i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.0091 | + | 48.5131i | 1.06706 | + | 1.84820i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.86072 | + | 10.1511i | −0.222952 | + | 0.386165i | −0.955703 | − | 0.294332i | \(-0.904903\pi\) |
0.732751 | + | 0.680497i | \(0.238236\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 43.5522 | + | 9.42640i | 1.65441 | + | 0.358079i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.8048 | + | 18.7144i | −0.409849 | + | 0.709879i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.35326 | − | 9.27212i | −0.202769 | − | 0.351207i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.76785 | + | 0.0577141i | −0.0668662 | + | 0.00218295i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.0120975 | 0.000456915 | 0.000228458 | − | 1.00000i | \(-0.499927\pi\) | ||||
0.000228458 | 1.00000i | \(0.499927\pi\) | ||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.67008 | + | 11.5529i | −0.251567 | + | 0.435726i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.17080 | − | 5.10009i | −0.119419 | − | 0.192080i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.8807 | + | 17.2960i | −0.672474 | + | 0.650483i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.537388 | + | 0.930783i | −0.0201820 | + | 0.0349563i | −0.875940 | − | 0.482420i | \(-0.839758\pi\) |
0.855758 | + | 0.517376i | \(0.173091\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.2870 | + | 2.63327i | −1.51088 | + | 0.0987552i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.82041 | − | 6.61714i | −0.143075 | − | 0.247814i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.4418 | + | 54.4588i | −1.17586 | + | 2.03664i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.7378 | − | 20.4881i | −0.475701 | − | 0.765143i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.7777 | − | 22.1317i | −0.476529 | − | 0.825372i | 0.523109 | − | 0.852266i | \(-0.324772\pi\) |
−0.999638 | + | 0.0268932i | \(0.991439\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.70714 | + | 6.48779i | −0.249787 | + | 0.241618i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.9029 | + | 22.2639i | −0.442672 | + | 0.828003i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.86478 | + | 4.96194i | 0.106395 | + | 0.184282i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.20522 | − | 10.7478i | −0.230139 | − | 0.398612i | 0.727710 | − | 0.685885i | \(-0.240585\pi\) |
−0.957849 | + | 0.287273i | \(0.907251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.4840 | − | 5.25314i | 0.980890 | − | 0.194561i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.06996 | −0.224505 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.4189 | 1.08661 | 0.543307 | − | 0.839534i | \(-0.317172\pi\) | ||||
0.543307 | + | 0.839534i | \(0.317172\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.7207 | + | 10.8236i | 0.690522 | + | 0.399234i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.17562 | − | 12.4285i | −0.264317 | − | 0.457811i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.75910 | + | 13.4392i | −0.285423 | + | 0.494368i | −0.972712 | − | 0.232017i | \(-0.925468\pi\) |
0.687288 | + | 0.726385i | \(0.258801\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.73432 | + | 10.7258i | −0.210656 | + | 0.394024i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.6333 | − | 23.6136i | 0.500159 | − | 0.866301i | −0.499841 | − | 0.866117i | \(-0.666608\pi\) |
1.00000 | 0.000183414i | \(-5.83824e-5\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.44865 | −0.309534 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.25290 | − | 8.62012i | 0.155606 | − | 0.315394i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.2615 | − | 4.93412i | −0.630720 | − | 0.180289i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.14353 | 0.333652 | 0.166826 | − | 0.985986i | \(-0.446648\pi\) | ||||
0.166826 | + | 0.985986i | \(0.446648\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.7226 | + | 27.5381i | −0.536522 | + | 1.00355i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 43.4632 | 1.58179 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.6307 | −0.749834 | −0.374917 | − | 0.927058i | \(-0.622329\pi\) | ||||
−0.374917 | + | 0.927058i | \(0.622329\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −34.9216 | + | 65.3195i | −1.26757 | + | 2.37095i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.478417 | −0.0173426 | −0.00867130 | − | 0.999962i | \(-0.502760\pi\) | ||||
−0.00867130 | + | 0.999962i | \(0.502760\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.875765 | + | 3.50010i | 0.0317048 | + | 0.126712i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.90129 | − | 0.451087i | 0.249517 | − | 0.0163091i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 52.6705 | 1.90182 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.3518 | + | 23.1261i | −0.481480 | + | 0.833948i | −0.999774 | − | 0.0212548i | \(-0.993234\pi\) |
0.518294 | + | 0.855202i | \(0.326567\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.9888 | − | 41.1293i | 0.791908 | − | 1.48123i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.5143 | + | 23.4074i | −0.486074 | + | 0.841905i | −0.999872 | − | 0.0160062i | \(-0.994905\pi\) |
0.513798 | + | 0.857911i | \(0.328238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.912303 | − | 1.58016i | −0.0327709 | − | 0.0567609i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 38.0363 | − | 39.2744i | 1.36455 | − | 1.40896i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.26165 | −0.331833 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.7510 | 1.78023 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.53008 | + | 13.3068i | 0.340577 | + | 0.475546i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.62226 | − | 9.73804i | −0.200667 | − | 0.347566i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.5915 | + | 42.5937i | 0.876593 | + | 1.51830i | 0.855056 | + | 0.518535i | \(0.173522\pi\) |
0.0215363 | + | 0.999768i | \(0.493144\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.25665 | + | 2.35051i | −0.0447378 | + | 0.0836804i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.55083 | − | 14.1913i | −0.126253 | − | 0.504585i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.1533 | + | 26.2463i | 0.538109 | + | 0.932032i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.5489 | − | 23.4012i | −0.515995 | − | 0.829955i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.1538 | − | 38.3715i | 0.784728 | − | 1.35919i | −0.144434 | − | 0.989514i | \(-0.546136\pi\) |
0.929162 | − | 0.369674i | \(-0.120531\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.25637 | + | 2.17609i | 0.0444471 | + | 0.0769846i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.07421 | + | 2.17730i | −0.0379555 | + | 0.0769311i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.8656 | − | 55.1928i | 1.12451 | − | 1.94771i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.8352 | + | 24.9903i | −0.910570 | + | 0.880792i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.97102 | − | 9.60410i | −0.210190 | − | 0.338080i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.7359 | + | 28.9874i | −0.588402 | + | 1.01914i | 0.406040 | + | 0.913855i | \(0.366909\pi\) |
−0.994442 | + | 0.105286i | \(0.966424\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.7383 | 1.53586 | 0.767929 | − | 0.640535i | \(-0.221287\pi\) | ||||
0.767929 | + | 0.640535i | \(0.221287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.5442 | − | 0.638051i | 0.685446 | − | 0.0223774i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.625451 | + | 1.08331i | 0.0219086 | + | 0.0379468i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.62540 | + | 4.54733i | −0.0918512 | + | 0.159091i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 33.4916 | − | 36.9197i | 1.17029 | − | 1.29008i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.2566 | − | 19.4970i | 0.392857 | − | 0.680449i | −0.599968 | − | 0.800024i | \(-0.704820\pi\) |
0.992825 | + | 0.119575i | \(0.0381533\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.33674 | + | 12.7076i | 0.255743 | + | 0.442959i | 0.965097 | − | 0.261893i | \(-0.0843467\pi\) |
−0.709354 | + | 0.704852i | \(0.751013\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.33919 | + | 15.5981i | −0.290333 | + | 0.543058i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.0520 | −1.56661 | −0.783306 | − | 0.621636i | \(-0.786468\pi\) | ||||
−0.783306 | + | 0.621636i | \(0.786468\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.6688 | − | 35.7993i | 0.717856 | − | 1.24336i | −0.243992 | − | 0.969777i | \(-0.578457\pi\) |
0.961848 | − | 0.273585i | \(-0.0882095\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.47961 | − | 2.76756i | 0.0513273 | − | 0.0960058i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.68102 | − | 4.78189i | −0.266132 | − | 0.165683i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.31059 | − | 10.9303i | 0.218387 | − | 0.378258i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.03490 | − | 4.23762i | −0.104902 | − | 0.146473i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.04477 | − | 3.54164i | −0.0705932 | − | 0.122271i | 0.828568 | − | 0.559888i | \(-0.189156\pi\) |
−0.899161 | + | 0.437617i | \(0.855823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.53902 | − | 16.5221i | 0.328932 | − | 0.569726i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.3451 | + | 0.337733i | −0.356306 | + | 0.0116321i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.5790 | + | 40.8401i | 0.811143 | + | 1.40494i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.0189 | + | 37.7428i | −1.34070 | + | 1.29686i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.6143 | + | 1.13003i | −1.18796 | + | 0.0387827i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.4394 | + | 78.7034i | 1.55764 | + | 2.69792i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.1012 | − | 36.5484i | −0.722491 | − | 1.25139i | −0.959998 | − | 0.280006i | \(-0.909664\pi\) |
0.237507 | − | 0.971386i | \(-0.423670\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.64704 | − | 5.36523i | 0.0905269 | − | 0.183487i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −55.1245 | −1.88302 | −0.941509 | − | 0.336987i | \(-0.890592\pi\) | ||||
−0.941509 | + | 0.336987i | \(0.890592\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.9534 | 1.29495 | 0.647476 | − | 0.762086i | \(-0.275824\pi\) | ||||
0.647476 | + | 0.762086i | \(0.275824\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.8176 | + | 9.23600i | 1.25474 | + | 0.314762i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.27205 | − | 10.8635i | −0.213503 | − | 0.369798i | 0.739305 | − | 0.673370i | \(-0.235154\pi\) |
−0.952809 | + | 0.303572i | \(0.901821\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.91723 | − | 10.2489i | 0.201192 | − | 0.348474i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.5370 | − | 0.866340i | 0.901243 | − | 0.0294224i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.7764 | − | 65.4306i | 1.28148 | − | 2.21958i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.0539 | −0.543965 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.94091 | − | 5.96086i | 0.0995346 | − | 0.201745i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.1279 | + | 22.3716i | −0.781867 | + | 0.756297i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.70673 | 0.327773 | 0.163887 | − | 0.986479i | \(-0.447597\pi\) | ||||
0.163887 | + | 0.986479i | \(0.447597\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.05666 | + | 14.5672i | 0.305474 | + | 0.491340i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.6652 | −0.393012 | −0.196506 | − | 0.980503i | \(-0.562959\pi\) | ||||
−0.196506 | + | 0.980503i | \(0.562959\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.1758 | 0.443401 | 0.221701 | − | 0.975115i | \(-0.428839\pi\) | ||||
0.221701 | + | 0.975115i | \(0.428839\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −25.8946 | + | 0.845370i | −0.870439 | + | 0.0284168i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.830721 | 0.0278929 | 0.0139464 | − | 0.999903i | \(-0.495561\pi\) | ||||
0.0139464 | + | 0.999903i | \(0.495561\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.3811 | + | 23.5838i | −0.817717 | + | 0.790975i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.3527 | + | 46.6739i | −0.648338 | + | 1.56364i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.17364 | 0.0727379 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.0508 | − | 17.4084i | 0.335960 | − | 0.581900i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 43.7473 | + | 70.3655i | 1.46068 | + | 2.34944i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.57985 | − | 2.73638i | 0.0526910 | − | 0.0912634i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.76470 | + | 9.98476i | 0.192050 | + | 0.332641i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.9714 | − | 15.4588i | 0.498218 | − | 0.514435i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −37.7756 | −1.25570 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.3176 | −1.10629 | −0.553146 | − | 0.833084i | \(-0.686573\pi\) | ||||
−0.553146 | + | 0.833084i | \(0.686573\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.6673 | − | 23.4569i | −0.519652 | − | 0.778017i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.1353 | + | 19.2870i | 0.368930 | + | 0.639006i | 0.989399 | − | 0.145226i | \(-0.0463909\pi\) |
−0.620469 | + | 0.784231i | \(0.713058\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.99396 | + | 15.5780i | 0.297657 | + | 0.515556i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.87114 | − | 12.6604i | −0.260212 | − | 0.418539i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.0660 | + | 10.7041i | −0.365431 | + | 0.353480i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.7906 | − | 18.6899i | −0.355949 | − | 0.616522i | 0.631331 | − | 0.775514i | \(-0.282509\pi\) |
−0.987280 | + | 0.158992i | \(0.949176\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.3638 | − | 36.2194i | 0.638060 | − | 1.19347i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.8268 | − | 48.1974i | 0.915929 | − | 1.58644i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.8508 | + | 18.7942i | 0.356773 | + | 0.617949i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.87687 | − | 8.79879i | −0.193022 | − | 0.288990i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.5780 | − | 32.1780i | 0.609523 | − | 1.05572i | −0.381796 | − | 0.924247i | \(-0.624694\pi\) |
0.991319 | − | 0.131478i | \(-0.0419724\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.90460 | + | 3.68598i | −0.226289 | + | 0.120803i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 35.2196 | − | 1.14980i | 1.15304 | − | 0.0376427i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.47122 | + | 11.2085i | −0.211631 | + | 0.366556i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.5238 | 0.703152 | 0.351576 | − | 0.936159i | \(-0.385646\pi\) | ||||
0.351576 | + | 0.936159i | \(0.385646\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.88784 | + | 14.2957i | 0.290044 | + | 0.466522i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.7032 | + | 41.0551i | 0.772702 | + | 1.33836i | 0.936077 | + | 0.351795i | \(0.114429\pi\) |
−0.163375 | + | 0.986564i | \(0.552238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.5472 | + | 54.6413i | −1.02732 | + | 1.77937i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.8731 | + | 18.6886i | −0.516352 | + | 0.607939i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.25059 | + | 2.16608i | −0.0406386 | + | 0.0703881i | −0.885629 | − | 0.464393i | \(-0.846273\pi\) |
0.844991 | + | 0.534781i | \(0.179606\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.6461 | − | 61.7409i | −1.15712 | − | 2.00420i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.04383 | − | 4.89586i | −0.0987031 | − | 0.158759i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.89914 | −0.255878 | −0.127939 | − | 0.991782i | \(-0.540836\pi\) | ||||
−0.127939 | + | 0.991782i | \(0.540836\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.41913 | − | 14.5824i | 0.272437 | − | 0.471874i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −30.6132 | + | 0.999416i | −0.989586 | + | 0.0323065i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.1733 | − | 28.2193i | 0.942055 | − | 0.911247i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.9969 | − | 25.9754i | 0.483771 | − | 0.837915i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.00677 | − | 18.2556i | 0.290239 | − | 0.588280i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.60071 | − | 9.70072i | −0.180293 | − | 0.312277i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.76591 | + | 9.98684i | −0.185419 | + | 0.321155i | −0.943718 | − | 0.330752i | \(-0.892698\pi\) |
0.758299 | + | 0.651907i | \(0.226031\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.18021 | + | 2.20755i | −0.0379139 | + | 0.0709166i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.14669 | + | 15.8425i | 0.293531 | + | 0.508411i | 0.974642 | − | 0.223769i | \(-0.0718362\pi\) |
−0.681111 | + | 0.732180i | \(0.738503\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.78092 | + | 31.0974i | 0.249445 | + | 0.996937i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.4468 | + | 16.8031i | 0.334564 | + | 0.538130i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.9541 | + | 25.9013i | 0.478425 | + | 0.828656i | 0.999694 | − | 0.0247361i | \(-0.00787454\pi\) |
−0.521269 | + | 0.853392i | \(0.674541\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.27173 | − | 3.93475i | −0.0726047 | − | 0.125755i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.08238 | + | 0.266835i | −0.130340 | + | 0.00851939i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.5445 | −0.463897 | −0.231948 | − | 0.972728i | \(-0.574510\pi\) | ||||
−0.231948 | + | 0.972728i | \(0.574510\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.6058 | −0.879594 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.64080 | − | 2.16762i | −0.275040 | − | 0.0689960i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.8854 | + | 30.9784i | 0.568722 | + | 0.985055i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.3753 | − | 24.8987i | 0.456646 | − | 0.790935i | −0.542135 | − | 0.840292i | \(-0.682384\pi\) |
0.998781 | + | 0.0493567i | \(0.0157171\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.31204 | + | 2.11035i | 0.0416363 | + | 0.0669700i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.91447 | − | 6.78007i | 0.124097 | − | 0.214943i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.8938 | 1.13677 | 0.568384 | − | 0.822763i | \(-0.307569\pi\) | ||||
0.568384 | + | 0.822763i | \(0.307569\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36.0968 | + | 50.4017i | 1.14205 | + | 1.59464i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.2.t.l.193.7 | 22 | ||
3.2 | odd | 2 | 3024.2.t.k.1873.8 | 22 | |||
4.3 | odd | 2 | 504.2.t.c.193.5 | yes | 22 | ||
7.2 | even | 3 | 1008.2.q.l.625.8 | 22 | |||
9.2 | odd | 6 | 3024.2.q.l.2881.4 | 22 | |||
9.7 | even | 3 | 1008.2.q.l.529.8 | 22 | |||
12.11 | even | 2 | 1512.2.t.c.361.8 | 22 | |||
21.2 | odd | 6 | 3024.2.q.l.2305.4 | 22 | |||
28.23 | odd | 6 | 504.2.q.c.121.4 | yes | 22 | ||
36.7 | odd | 6 | 504.2.q.c.25.4 | ✓ | 22 | ||
36.11 | even | 6 | 1512.2.q.d.1369.4 | 22 | |||
63.2 | odd | 6 | 3024.2.t.k.289.8 | 22 | |||
63.16 | even | 3 | inner | 1008.2.t.l.961.7 | 22 | ||
84.23 | even | 6 | 1512.2.q.d.793.4 | 22 | |||
252.79 | odd | 6 | 504.2.t.c.457.5 | yes | 22 | ||
252.191 | even | 6 | 1512.2.t.c.289.8 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.4 | ✓ | 22 | 36.7 | odd | 6 | ||
504.2.q.c.121.4 | yes | 22 | 28.23 | odd | 6 | ||
504.2.t.c.193.5 | yes | 22 | 4.3 | odd | 2 | ||
504.2.t.c.457.5 | yes | 22 | 252.79 | odd | 6 | ||
1008.2.q.l.529.8 | 22 | 9.7 | even | 3 | |||
1008.2.q.l.625.8 | 22 | 7.2 | even | 3 | |||
1008.2.t.l.193.7 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.t.l.961.7 | 22 | 63.16 | even | 3 | inner | ||
1512.2.q.d.793.4 | 22 | 84.23 | even | 6 | |||
1512.2.q.d.1369.4 | 22 | 36.11 | even | 6 | |||
1512.2.t.c.289.8 | 22 | 252.191 | even | 6 | |||
1512.2.t.c.361.8 | 22 | 12.11 | even | 2 | |||
3024.2.q.l.2305.4 | 22 | 21.2 | odd | 6 | |||
3024.2.q.l.2881.4 | 22 | 9.2 | odd | 6 | |||
3024.2.t.k.289.8 | 22 | 63.2 | odd | 6 | |||
3024.2.t.k.1873.8 | 22 | 3.2 | odd | 2 |