Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(95,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.o (of order \(8\), degree \(4\), 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: | \(6.13251087523\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 95.6 | ||
Character | \(\chi\) | \(=\) | 768.95 |
Dual form | 768.2.o.b.671.6 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) |
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 | ||||||||
\(3\) | −0.602068 | − | 1.62404i | −0.347604 | − | 0.937641i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.378520 | + | 0.156788i | −0.169279 | + | 0.0701179i | −0.465714 | − | 0.884935i | \(-0.654202\pi\) |
0.296434 | + | 0.955053i | \(0.404202\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.01144 | + | 2.01144i | 0.760253 | + | 0.760253i | 0.976368 | − | 0.216115i | \(-0.0693386\pi\) |
−0.216115 | + | 0.976368i | \(0.569339\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.27503 | + | 1.95557i | −0.758343 | + | 0.651856i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.709852 | + | 0.294030i | −0.214028 | + | 0.0886534i | −0.487122 | − | 0.873334i | \(-0.661953\pi\) |
0.273093 | + | 0.961988i | \(0.411953\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.08393 | + | 5.03104i | −0.577977 | + | 1.39536i | 0.316648 | + | 0.948543i | \(0.397443\pi\) |
−0.894625 | + | 0.446817i | \(0.852557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.482526 | + | 0.520336i | 0.124588 | + | 0.134350i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.33777 | −1.53714 | −0.768568 | − | 0.639768i | \(-0.779030\pi\) | ||||
−0.768568 | + | 0.639768i | \(0.779030\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.646487 | − | 0.267784i | −0.148314 | − | 0.0614338i | 0.307291 | − | 0.951615i | \(-0.400577\pi\) |
−0.455606 | + | 0.890182i | \(0.650577\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.05564 | − | 4.47769i | 0.448577 | − | 0.977112i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.61798 | + | 1.61798i | 0.337371 | + | 0.337371i | 0.855377 | − | 0.518006i | \(-0.173325\pi\) |
−0.518006 | + | 0.855377i | \(0.673325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.41684 | + | 3.41684i | −0.683368 | + | 0.683368i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.54565 | + | 2.51736i | 0.874810 | + | 0.484465i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.04571 | + | 4.93879i | −0.379879 | + | 0.917110i | 0.612108 | + | 0.790774i | \(0.290322\pi\) |
−0.991988 | + | 0.126336i | \(0.959678\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.75464i | − | 1.03356i | −0.856117 | − | 0.516782i | \(-0.827130\pi\) | ||
0.856117 | − | 0.516782i | \(-0.172870\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.904897 | + | 0.975803i | 0.157522 | + | 0.169866i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.07674 | − | 0.446001i | −0.182002 | − | 0.0753879i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50232 | + | 6.04113i | 0.411379 | + | 0.993156i | 0.984768 | + | 0.173873i | \(0.0556282\pi\) |
−0.573389 | + | 0.819283i | \(0.694372\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.42529 | + | 0.355354i | 1.50925 | + | 0.0569021i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.52228 | − | 5.52228i | 0.862435 | − | 0.862435i | −0.129185 | − | 0.991620i | \(-0.541236\pi\) |
0.991620 | + | 0.129185i | \(0.0412361\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.406593 | + | 0.981601i | 0.0620048 | + | 0.149693i | 0.951845 | − | 0.306579i | \(-0.0991844\pi\) |
−0.889840 | + | 0.456272i | \(0.849184\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.554534 | − | 1.09692i | 0.0826651 | − | 0.163519i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4826i | 1.52904i | 0.644597 | + | 0.764522i | \(0.277025\pi\) | ||||
−0.644597 | + | 0.764522i | \(0.722975\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.09178i | 0.155969i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.81577 | + | 10.2928i | 0.534315 | + | 1.44128i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.674566 | − | 1.62855i | −0.0926588 | − | 0.223698i | 0.870755 | − | 0.491718i | \(-0.163631\pi\) |
−0.963413 | + | 0.268020i | \(0.913631\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.222593 | − | 0.222593i | 0.0300144 | − | 0.0300144i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0456628 | + | 1.21115i | −0.00604819 | + | 0.160420i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.35082 | + | 8.08960i | 0.436240 | + | 1.05318i | 0.977237 | + | 0.212152i | \(0.0680472\pi\) |
−0.540997 | + | 0.841025i | \(0.681953\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.14715 | − | 1.71781i | −0.530988 | − | 0.219943i | 0.101048 | − | 0.994882i | \(-0.467781\pi\) |
−0.632036 | + | 0.774939i | \(0.717781\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.50959 | − | 0.642573i | −1.07211 | − | 0.0809566i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.23109i | − | 0.276732i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.65183 | − | 6.40208i | 0.323972 | − | 0.782138i | −0.675043 | − | 0.737778i | \(-0.735875\pi\) |
0.999016 | − | 0.0443601i | \(-0.0141249\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.65353 | − | 3.60179i | 0.199061 | − | 0.433605i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.97014 | + | 1.97014i | −0.233813 | + | 0.233813i | −0.814282 | − | 0.580469i | \(-0.802869\pi\) |
0.580469 | + | 0.814282i | \(0.302869\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.48914 | + | 9.48914i | 1.11062 | + | 1.11062i | 0.993067 | + | 0.117554i | \(0.0375052\pi\) |
0.117554 | + | 0.993067i | \(0.462495\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.60626 | + | 3.49192i | 0.878295 | + | 0.403212i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.01925 | − | 0.836400i | −0.230115 | − | 0.0953166i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.75751 | −0.985297 | −0.492649 | − | 0.870228i | \(-0.663971\pi\) | ||||
−0.492649 | + | 0.870228i | \(0.663971\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.35150 | − | 8.89795i | 0.150167 | − | 0.988661i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.60293 | − | 15.9409i | 0.724766 | − | 1.74974i | 0.0654719 | − | 0.997854i | \(-0.479145\pi\) |
0.659294 | − | 0.751885i | \(-0.270855\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.39898 | − | 0.993689i | 0.260206 | − | 0.107781i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.25246 | + | 0.348838i | 0.991968 | + | 0.0373993i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.11535 | + | 6.11535i | 0.648226 | + | 0.648226i | 0.952564 | − | 0.304338i | \(-0.0984353\pi\) |
−0.304338 | + | 0.952564i | \(0.598435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.3113 | + | 5.92795i | −1.50024 | + | 0.621418i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.34579 | + | 3.46469i | −0.969113 | + | 0.359271i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.286694 | 0.0294142 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.09195 | −0.517009 | −0.258505 | − | 0.966010i | \(-0.583230\pi\) | ||||
−0.258505 | + | 0.966010i | \(0.583230\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.03994 | − | 2.05709i | 0.104518 | − | 0.206745i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.33659 | + | 0.967847i | −0.232499 | + | 0.0963044i | −0.495892 | − | 0.868384i | \(-0.665159\pi\) |
0.263392 | + | 0.964689i | \(0.415159\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.15411 | − | 6.15411i | −0.606383 | − | 0.606383i | 0.335616 | − | 0.941999i | \(-0.391055\pi\) |
−0.941999 | + | 0.335616i | \(0.891055\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0760526 | + | 2.01720i | −0.00742198 | + | 0.196858i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.19264 | − | 0.494009i | 0.115297 | − | 0.0477576i | −0.324289 | − | 0.945958i | \(-0.605125\pi\) |
0.439586 | + | 0.898200i | \(0.355125\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.933827 | − | 2.25446i | 0.0894444 | − | 0.215938i | −0.872827 | − | 0.488030i | \(-0.837716\pi\) |
0.962271 | + | 0.272092i | \(0.0877156\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.30449 | − | 7.70104i | 0.788227 | − | 0.730951i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.02329 | −0.660696 | −0.330348 | − | 0.943859i | \(-0.607166\pi\) | ||||
−0.330348 | + | 0.943859i | \(0.607166\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.866116 | − | 0.358757i | −0.0807657 | − | 0.0334543i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.09756 | − | 15.5210i | −0.471270 | − | 1.43492i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.7481 | − | 12.7481i | −1.16861 | − | 1.16861i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.36074 | + | 7.36074i | −0.669158 | + | 0.669158i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.2932 | − | 5.64363i | −1.10844 | − | 0.508869i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.54156 | − | 3.72167i | 0.137882 | − | 0.332876i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.12307i | 0.454599i | 0.973825 | + | 0.227299i | \(0.0729896\pi\) | ||||
−0.973825 | + | 0.227299i | \(0.927010\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.34937 | − | 1.25131i | 0.118805 | − | 0.110172i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.0406 | − | 5.40161i | −1.13937 | − | 0.471941i | −0.268412 | − | 0.963304i | \(-0.586499\pi\) |
−0.870955 | + | 0.491363i | \(0.836499\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.761739 | − | 1.83900i | −0.0660512 | − | 0.159462i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.11531 | − | 0.240166i | −0.182057 | − | 0.0206702i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.19191 | − | 5.19191i | 0.443575 | − | 0.443575i | −0.449637 | − | 0.893211i | \(-0.648447\pi\) |
0.893211 | + | 0.449637i | \(0.148447\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.91660 | − | 7.04129i | −0.247383 | − | 0.597234i | 0.750598 | − | 0.660759i | \(-0.229766\pi\) |
−0.997980 | + | 0.0635252i | \(0.979766\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.0242 | − | 6.31124i | 1.43370 | − | 0.531502i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.18403i | − | 0.349886i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.19018i | − | 0.181884i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.77310 | − | 0.657327i | 0.146243 | − | 0.0542154i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.55828 | + | 18.2473i | 0.619199 | + | 1.49488i | 0.852636 | + | 0.522506i | \(0.175003\pi\) |
−0.233437 | + | 0.972372i | \(0.574997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.19627 | + | 8.19627i | −0.667003 | + | 0.667003i | −0.957021 | − | 0.290018i | \(-0.906339\pi\) |
0.290018 | + | 0.957021i | \(0.406339\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.4186 | − | 12.3940i | 1.16568 | − | 1.00199i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.902261 | + | 2.17825i | 0.0724713 | + | 0.174961i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.42476 | + | 0.590154i | 0.113708 | + | 0.0470994i | 0.438812 | − | 0.898579i | \(-0.355399\pi\) |
−0.325104 | + | 0.945678i | \(0.605399\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.23869 | + | 2.07602i | −0.177540 | + | 0.164639i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.50892i | 0.512975i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.927085 | + | 2.23818i | −0.0726149 | + | 0.175308i | −0.956019 | − | 0.293303i | \(-0.905245\pi\) |
0.883405 | + | 0.468611i | \(0.155245\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.495516 | − | 0.227484i | −0.0385759 | − | 0.0177096i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.4441 | − | 13.4441i | 1.04033 | − | 1.04033i | 0.0411813 | − | 0.999152i | \(-0.486888\pi\) |
0.999152 | − | 0.0411813i | \(-0.0131121\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7763 | − | 11.7763i | −0.905866 | − | 0.905866i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.99445 | − | 0.655035i | 0.152519 | − | 0.0500918i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.11484 | − | 2.11864i | −0.388874 | − | 0.161077i | 0.179675 | − | 0.983726i | \(-0.442495\pi\) |
−0.568550 | + | 0.822649i | \(0.692495\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.7455 | −1.03906 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.1204 | − | 10.3124i | 0.835863 | − | 0.775125i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.02160 | + | 4.88057i | −0.151101 | + | 0.364791i | −0.981247 | − | 0.192756i | \(-0.938257\pi\) |
0.830145 | + | 0.557547i | \(0.188257\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.06344 | + | 3.33999i | −0.599351 | + | 0.248259i | −0.661668 | − | 0.749797i | \(-0.730151\pi\) |
0.0623171 | + | 0.998056i | \(0.480151\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.292922 | + | 7.76939i | −0.0216535 | + | 0.574330i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.89436 | − | 1.89436i | −0.139276 | − | 0.139276i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.49888 | − | 1.86350i | 0.328991 | − | 0.136272i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.07979 | + | 14.2068i | 0.296761 | + | 1.03339i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.8066 | 0.781940 | 0.390970 | − | 0.920404i | \(-0.372140\pi\) | ||||
0.390970 | + | 0.920404i | \(0.372140\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.82359 | −0.419192 | −0.209596 | − | 0.977788i | \(-0.567215\pi\) | ||||
−0.209596 | + | 0.977788i | \(0.567215\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.62338 | + | 1.34327i | −0.259476 | + | 0.0961933i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.4552 | − | 8.05861i | 1.38613 | − | 0.574152i | 0.440014 | − | 0.897991i | \(-0.354974\pi\) |
0.946112 | + | 0.323839i | \(0.104974\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.63519 | + | 1.63519i | 0.115916 | + | 0.115916i | 0.762685 | − | 0.646770i | \(-0.223880\pi\) |
−0.646770 | + | 0.762685i | \(0.723880\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.9938 | − | 0.452193i | −0.845979 | − | 0.0318952i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.0489 | + | 5.81925i | −0.986040 | + | 0.408431i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.22447 | + | 2.95612i | −0.0855205 | + | 0.206465i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.84500 | − | 0.516877i | −0.475760 | − | 0.0359254i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.537647 | 0.0371898 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4379 | − | 5.56618i | −0.925106 | − | 0.383192i | −0.131286 | − | 0.991344i | \(-0.541911\pi\) |
−0.793820 | + | 0.608153i | \(0.791911\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.38575 | + | 2.01343i | 0.300507 | + | 0.137958i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.307807 | − | 0.307807i | −0.0209923 | − | 0.0209923i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.5751 | − | 11.5751i | 0.785771 | − | 0.785771i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.69766 | − | 21.1239i | 0.655307 | − | 1.42742i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.2075 | − | 31.8856i | 0.888430 | − | 2.14486i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.106627i | 0.00714024i | 0.999994 | + | 0.00357012i | \(0.00113641\pi\) | ||||
−0.999994 | + | 0.00357012i | \(0.998864\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.09154 | − | 14.4553i | 0.0727694 | − | 0.963684i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.0312 | + | 8.71141i | 1.39589 | + | 0.578196i | 0.948681 | − | 0.316233i | \(-0.102418\pi\) |
0.447208 | + | 0.894430i | \(0.352418\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.56199 | + | 3.77098i | 0.103219 | + | 0.249193i | 0.967049 | − | 0.254591i | \(-0.0819407\pi\) |
−0.863830 | + | 0.503784i | \(0.831941\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.142624 | + | 3.78291i | −0.00938397 | + | 0.248898i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.47635 | − | 4.47635i | 0.293255 | − | 0.293255i | −0.545110 | − | 0.838365i | \(-0.683512\pi\) |
0.838365 | + | 0.545110i | \(0.183512\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.64355 | − | 3.96788i | −0.107213 | − | 0.258836i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.27262 | + | 14.2226i | 0.342493 | + | 0.923855i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.68031i | − | 0.561483i | −0.959783 | − | 0.280741i | \(-0.909420\pi\) | ||
0.959783 | − | 0.280741i | \(-0.0905803\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.55656i | 0.293514i | 0.989173 | + | 0.146757i | \(0.0468835\pi\) | ||||
−0.989173 | + | 0.146757i | \(0.953117\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2643 | + | 3.16227i | −0.979208 | + | 0.202860i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.171179 | − | 0.413262i | −0.0109362 | − | 0.0264023i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.69446 | − | 2.69446i | 0.171445 | − | 0.171445i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −29.8641 | − | 1.12594i | −1.89256 | − | 0.0713536i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.750992 | − | 1.81305i | −0.0474022 | − | 0.114439i | 0.898405 | − | 0.439168i | \(-0.144727\pi\) |
−0.945807 | + | 0.324729i | \(0.894727\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.62426 | − | 0.672789i | −0.102116 | − | 0.0422979i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.05814 | − | 3.29777i | −0.191508 | − | 0.206515i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.4127i | 0.836663i | 0.908294 | + | 0.418332i | \(0.137385\pi\) | ||||
−0.908294 | + | 0.418332i | \(0.862615\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.11811 | + | 17.1846i | −0.442298 | + | 1.06780i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.00409 | − | 15.2364i | −0.309745 | − | 0.943110i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.7027 | + | 18.7027i | −1.15326 | + | 1.15326i | −0.167359 | + | 0.985896i | \(0.553524\pi\) |
−0.985896 | + | 0.167359i | \(0.946476\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.510674 | + | 0.510674i | 0.0313705 | + | 0.0313705i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.24973 | − | 13.6134i | 0.382477 | − | 0.833130i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.20132 | − | 2.56867i | −0.378101 | − | 0.156615i | 0.185535 | − | 0.982638i | \(-0.440598\pi\) |
−0.563636 | + | 0.826023i | \(0.690598\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.4006 | 1.60372 | 0.801860 | − | 0.597512i | \(-0.203844\pi\) | ||||
0.801860 | + | 0.597512i | \(0.203844\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.2436 | + | 19.6732i | 1.10416 | + | 1.19068i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.42079 | − | 3.43010i | 0.0856772 | − | 0.206843i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.8110 | − | 4.89227i | 0.709654 | − | 0.293948i | 0.00149230 | − | 0.999999i | \(-0.499525\pi\) |
0.708161 | + | 0.706051i | \(0.249525\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.2536 | + | 13.0920i | 0.673736 | + | 0.783796i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.9033 | + | 10.9033i | 0.650433 | + | 0.650433i | 0.953097 | − | 0.302664i | \(-0.0978760\pi\) |
−0.302664 | + | 0.953097i | \(0.597876\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.86260 | − | 3.67101i | 0.526827 | − | 0.218219i | −0.103386 | − | 0.994641i | \(-0.532968\pi\) |
0.630213 | + | 0.776423i | \(0.282968\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.172609 | − | 0.465603i | −0.0102245 | − | 0.0275800i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.2155 | 1.31134 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.1674 | 1.36279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.06570 | + | 8.26954i | 0.179715 | + | 0.484769i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.0666 | + | 8.31184i | −1.17230 | + | 0.485583i | −0.881952 | − | 0.471338i | \(-0.843771\pi\) |
−0.290348 | + | 0.956921i | \(0.593771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.53671 | − | 2.53671i | −0.147693 | − | 0.147693i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.96691 | − | 0.450392i | −0.230184 | − | 0.0261344i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.5118 | + | 4.76836i | −0.665747 | + | 0.275761i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.15660 | + | 2.79227i | −0.0666650 | + | 0.160944i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.97861 | + | 3.21201i | 0.171117 | + | 0.184525i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.83911 | 0.105307 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.548682 | − | 0.227272i | −0.0313149 | − | 0.0129711i | 0.366971 | − | 0.930232i | \(-0.380395\pi\) |
−0.398286 | + | 0.917261i | \(0.630395\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.28934 | + | 13.6997i | −0.357788 | + | 0.779351i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.31914 | − | 8.31914i | −0.471735 | − | 0.471735i | 0.430741 | − | 0.902476i | \(-0.358252\pi\) |
−0.902476 | + | 0.430741i | \(0.858252\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.90243 | − | 5.90243i | 0.333625 | − | 0.333625i | −0.520336 | − | 0.853961i | \(-0.674193\pi\) |
0.853961 | + | 0.520336i | \(0.174193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.32180 | − | 1.09098i | 0.187162 | − | 0.0614696i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.432895 | − | 1.04510i | 0.0243138 | − | 0.0586987i | −0.911256 | − | 0.411840i | \(-0.864886\pi\) |
0.935570 | + | 0.353141i | \(0.114886\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.10731i | − | 0.229965i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.52034 | − | 1.63948i | −0.0848573 | − | 0.0915066i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.09729 | + | 1.69715i | 0.227979 | + | 0.0944321i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.0698 | − | 24.3107i | −0.558573 | − | 1.34852i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.22356 | − | 0.159237i | −0.233564 | − | 0.00880584i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.0851 | + | 21.0851i | −1.16246 | + | 1.16246i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.16978 | + | 14.8952i | 0.339122 | + | 0.818713i | 0.997801 | + | 0.0662882i | \(0.0211157\pi\) |
−0.658679 | + | 0.752424i | \(0.728884\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.5067 | − | 8.85029i | −0.959361 | − | 0.484993i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.83909i | 0.155116i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.2474i | 0.939527i | 0.882792 | + | 0.469763i | \(0.155661\pi\) | ||||
−0.882792 | + | 0.469763i | \(0.844339\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.22850 | + | 11.4061i | 0.229661 | + | 0.619496i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.69204 | + | 4.08494i | 0.0916291 | + | 0.221212i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.8840 | − | 11.8840i | 0.641677 | − | 0.641677i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0611757 | + | 1.62261i | −0.00329359 | + | 0.0873581i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.34246 | + | 8.06942i | 0.179433 | + | 0.433189i | 0.987848 | − | 0.155424i | \(-0.0496743\pi\) |
−0.808415 | + | 0.588613i | \(0.799674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.7745 | + | 9.43351i | 1.21909 | + | 0.504964i | 0.897121 | − | 0.441785i | \(-0.145655\pi\) |
0.321971 | + | 0.946750i | \(0.395655\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.1377 | + | 17.6234i | −1.18162 | + | 0.940666i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 7.05617i | − | 0.375562i | −0.982211 | − | 0.187781i | \(-0.939870\pi\) | ||
0.982211 | − | 0.187781i | \(-0.0601295\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.436843 | − | 1.05463i | 0.0231852 | − | 0.0559741i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −13.0282 | + | 28.3786i | −0.689525 | + | 1.50195i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.9832 | + | 17.9832i | −0.949116 | + | 0.949116i | −0.998767 | − | 0.0496509i | \(-0.984189\pi\) |
0.0496509 | + | 0.998767i | \(0.484189\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0888 | − | 13.0888i | −0.688884 | − | 0.688884i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.3858 | + | 7.52249i | 0.860032 | + | 0.394828i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.07962 | − | 2.10405i | −0.265879 | − | 0.110131i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.28729 | 0.484792 | 0.242396 | − | 0.970177i | \(-0.422067\pi\) | ||||
0.242396 | + | 0.970177i | \(0.422067\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.76414 | + | 23.3625i | −0.0918376 | + | 1.21621i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.91887 | − | 4.63257i | 0.0996230 | − | 0.240511i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.7209 | + | 13.1392i | −1.64244 | + | 0.680323i | −0.996541 | − | 0.0830975i | \(-0.973519\pi\) |
−0.645902 | + | 0.763420i | \(0.723519\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.97227 | − | 0.262869i | −0.360046 | − | 0.0135745i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.5841 | − | 20.5841i | −1.06014 | − | 1.06014i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0588 | − | 11.6223i | 1.44128 | − | 0.596999i | 0.481174 | − | 0.876625i | \(-0.340211\pi\) |
0.960109 | + | 0.279626i | \(0.0902105\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.32008 | − | 3.08444i | 0.426251 | − | 0.158021i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.32676 | 0.272185 | 0.136092 | − | 0.990696i | \(-0.456546\pi\) | ||||
0.136092 | + | 0.990696i | \(0.456546\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.895464 | 0.0456371 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.84460 | − | 1.43805i | −0.144599 | − | 0.0731002i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.0435 | + | 8.30227i | −1.01624 | + | 0.420942i | −0.827729 | − | 0.561128i | \(-0.810367\pi\) |
−0.188515 | + | 0.982070i | \(0.560367\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.2544 | − | 10.2544i | −0.518585 | − | 0.518585i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.921090 | + | 24.4307i | −0.0464628 | + | 1.23237i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.31490 | − | 1.37308i | 0.166791 | − | 0.0690869i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.65193 | − | 6.40233i | 0.133097 | − | 0.321323i | −0.843255 | − | 0.537514i | \(-0.819363\pi\) |
0.976351 | + | 0.216191i | \(0.0693634\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.52800 | + | 2.34430i | −0.126558 | + | 0.117362i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.61080 | −0.280190 | −0.140095 | − | 0.990138i | \(-0.544741\pi\) | ||||
−0.140095 | + | 0.990138i | \(0.544741\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.9519 | + | 11.9923i | 1.44220 | + | 0.597377i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.883522 | + | 3.57995i | 0.0439026 | + | 0.177889i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.55255 | − | 3.55255i | −0.176093 | − | 0.176093i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.683364 | + | 0.683364i | −0.0337902 | + | 0.0337902i | −0.723800 | − | 0.690010i | \(-0.757606\pi\) |
0.690010 | + | 0.723800i | \(0.257606\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.5578 | − | 5.30600i | −0.570102 | − | 0.261725i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.53177 | + | 23.0117i | −0.469028 | + | 1.13233i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.06921i | 0.347014i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.67936 | + | 8.97601i | −0.474000 | + | 0.439557i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.8772 | + | 6.99075i | 0.824503 | + | 0.341521i | 0.754724 | − | 0.656042i | \(-0.227771\pi\) |
0.0697790 | + | 0.997562i | \(0.477771\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.36473 | + | 17.7800i | 0.358935 | + | 0.866546i | 0.995450 | + | 0.0952818i | \(0.0303752\pi\) |
−0.636515 | + | 0.771264i | \(0.719625\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.4994 | − | 23.8482i | −0.996717 | − | 1.15954i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.6552 | − | 21.6552i | 1.05043 | − | 1.05043i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.88648 | − | 11.7970i | −0.236473 | − | 0.570897i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.79505 | + | 2.51907i | −0.328068 | + | 0.121622i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 18.7398i | − | 0.902664i | −0.892356 | − | 0.451332i | \(-0.850949\pi\) | ||
0.892356 | − | 0.451332i | \(-0.149051\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.88137i | − | 0.138470i | −0.997600 | − | 0.0692349i | \(-0.977944\pi\) | ||
0.997600 | − | 0.0692349i | \(-0.0220558\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.55694 | + | 1.31864i | −0.170542 | + | 0.0632237i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.612733 | − | 1.47927i | −0.0293110 | − | 0.0707630i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.54440 | − | 6.54440i | 0.312347 | − | 0.312347i | −0.533471 | − | 0.845818i | \(-0.679113\pi\) |
0.845818 | + | 0.533471i | \(0.179113\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.13505 | − | 2.48383i | −0.101669 | − | 0.118278i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.97491 | − | 14.4247i | −0.283877 | − | 0.685339i | 0.716042 | − | 0.698057i | \(-0.245952\pi\) |
−0.999919 | + | 0.0127177i | \(0.995952\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.27360 | − | 1.35597i | −0.155184 | − | 0.0642791i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.0838 | − | 23.2611i | 1.18642 | − | 1.10021i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.52116i | 0.118981i | 0.998229 | + | 0.0594905i | \(0.0189476\pi\) | ||||
−0.998229 | + | 0.0594905i | \(0.981052\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.29628 | + | 5.54372i | −0.108128 | + | 0.261043i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.2458 | + | 8.37638i | 0.857263 | + | 0.393557i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.48770 | − | 4.48770i | 0.210387 | − | 0.210387i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.6180 | + | 26.6180i | 1.24514 | + | 1.24514i | 0.957842 | + | 0.287295i | \(0.0927560\pi\) |
0.287295 | + | 0.957842i | \(0.407244\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −28.8093 | − | 15.9544i | −1.34470 | − | 0.744689i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.9365 | − | 7.01532i | −0.788810 | − | 0.326736i | −0.0483450 | − | 0.998831i | \(-0.515395\pi\) |
−0.740465 | + | 0.672095i | \(0.765395\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.1078 | 1.02744 | 0.513719 | − | 0.857959i | \(-0.328268\pi\) | ||||
0.513719 | + | 0.857959i | \(0.328268\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.99435 | − | 2.77677i | 0.138860 | − | 0.128769i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.0935 | + | 26.7822i | −0.513348 | + | 1.23933i | 0.428577 | + | 0.903505i | \(0.359015\pi\) |
−0.941924 | + | 0.335825i | \(0.890985\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.2114 | − | 7.54340i | 0.840923 | − | 0.348322i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.100634 | − | 2.66918i | 0.00463696 | − | 0.122989i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.577241 | − | 0.577241i | −0.0265416 | − | 0.0265416i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.12392 | − | 1.29397i | 0.143335 | − | 0.0593714i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.71939 | + | 2.38583i | 0.216086 | + | 0.109240i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.5288 | −0.526765 | −0.263382 | − | 0.964692i | \(-0.584838\pi\) | ||||
−0.263382 | + | 0.964692i | \(0.584838\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −35.6078 | −1.62358 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.5708 | − | 3.91881i | 0.480986 | − | 0.178312i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.92741 | − | 0.798358i | 0.0875190 | − | 0.0362516i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.3533 | + | 24.3533i | 1.10355 | + | 1.10355i | 0.993979 | + | 0.109575i | \(0.0349489\pi\) |
0.109575 | + | 0.993979i | \(0.465051\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.19307 | + | 0.158088i | 0.189617 | + | 0.00714897i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.2408 | + | 5.48453i | −0.597550 | + | 0.247513i | −0.660895 | − | 0.750478i | \(-0.729823\pi\) |
0.0633450 | + | 0.997992i | \(0.479823\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.9653 | − | 31.3009i | 0.583926 | − | 1.40972i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0711093 | + | 0.941700i | −0.00319613 | + | 0.0423263i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.92564 | −0.355513 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.79930 | + | 2.81636i | 0.304378 | + | 0.126078i | 0.529645 | − | 0.848220i | \(-0.322325\pi\) |
−0.225266 | + | 0.974297i | \(0.572325\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.9280 | − | 13.7395i | −1.33708 | − | 0.613835i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.7317 | + | 20.7317i | 0.924383 | + | 0.924383i | 0.997335 | − | 0.0729527i | \(-0.0232422\pi\) |
−0.0729527 | + | 0.997335i | \(0.523242\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.732700 | − | 0.732700i | 0.0326047 | − | 0.0326047i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.0350 | + | 26.2153i | −0.534495 | + | 1.16426i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.27710 | − | 17.5685i | 0.322552 | − | 0.778708i | −0.676553 | − | 0.736394i | \(-0.736527\pi\) |
0.999104 | − | 0.0423143i | \(-0.0134731\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.1737i | 1.68870i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.26460 | − | 2.84469i | −0.0999844 | − | 0.125596i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.29435 | + | 1.36456i | 0.145166 | + | 0.0601299i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.08220 | − | 7.44109i | −0.135555 | − | 0.327259i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.361273 | + | 9.58229i | −0.0158581 | + | 0.420616i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.9964 | + | 12.9964i | −0.569382 | + | 0.569382i | −0.931955 | − | 0.362573i | \(-0.881898\pi\) |
0.362573 | + | 0.931955i | \(0.381898\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.8611 | + | 33.4638i | 0.606105 | + | 1.46327i | 0.867203 | + | 0.497955i | \(0.165916\pi\) |
−0.261097 | + | 0.965313i | \(0.584084\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.27575 | + | 22.3233i | 0.361183 | + | 0.974270i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 36.4716i | 1.58873i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 17.7643i | − | 0.772361i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.4430 | − | 11.8513i | −1.01734 | − | 0.514303i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.2748 | + | 39.2909i | 0.704940 | + | 1.70188i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.373985 | + | 0.373985i | −0.0161688 | + | 0.0161688i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.14339 | + | 0.344725i | 0.394566 | + | 0.0148760i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.321017 | − | 0.775003i | −0.0138272 | − | 0.0333817i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.814609 | − | 0.337422i | −0.0350228 | − | 0.0145069i | 0.365103 | − | 0.930967i | \(-0.381034\pi\) |
−0.400126 | + | 0.916460i | \(0.631034\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.2790 | + | 11.0845i | 0.441115 | + | 0.475680i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.999771i | 0.0428255i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.6045 | − | 28.0158i | 0.496173 | − | 1.19787i | −0.455356 | − | 0.890310i | \(-0.650488\pi\) |
0.951529 | − | 0.307559i | \(-0.0995121\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.7942 | − | 4.20198i | 0.546042 | − | 0.179336i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.64506 | − | 2.64506i | 0.112683 | − | 0.112683i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.6152 | − | 17.6152i | −0.749075 | − | 0.749075i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.93598 | + | 4.21705i | −0.0821780 | + | 0.179004i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.67547 | + | 4.00771i | 0.409963 | + | 0.169812i | 0.578127 | − | 0.815947i | \(-0.303784\pi\) |
−0.168164 | + | 0.985759i | \(0.553784\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.78579 | −0.244713 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.73503 | − | 6.18442i | −0.242133 | − | 0.261106i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.67115 | − | 18.5198i | 0.323300 | − | 0.780516i | −0.675758 | − | 0.737124i | \(-0.736183\pi\) |
0.999058 | − | 0.0433923i | \(-0.0138165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.65846 | − | 1.10117i | 0.111842 | − | 0.0463266i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20.6162 | − | 15.1792i | 0.865797 | − | 0.637467i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.36174 | + | 3.36174i | 0.140932 | + | 0.140932i | 0.774053 | − | 0.633121i | \(-0.218227\pi\) |
−0.633121 | + | 0.774053i | \(0.718227\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.6718 | + | 6.07726i | −0.613996 | + | 0.254325i | −0.667936 | − | 0.744219i | \(-0.732822\pi\) |
0.0539402 | + | 0.998544i | \(0.482822\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.50632 | − | 17.5504i | −0.271806 | − | 0.733179i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.0567 | −0.461097 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.1656 | 0.464830 | 0.232415 | − | 0.972617i | \(-0.425337\pi\) | ||||
0.232415 | + | 0.972617i | \(0.425337\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.50620 | + | 9.45777i | 0.145713 | + | 0.393051i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 45.3455 | − | 18.7827i | 1.88125 | − | 0.779239i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.957684 | + | 0.957684i | 0.0396632 | + | 0.0396632i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.36305 | + | 5.07579i | 0.180390 | + | 0.209858i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.3098 | − | 12.9689i | 1.29229 | − | 0.535286i | 0.372625 | − | 0.927982i | \(-0.378458\pi\) |
0.919668 | + | 0.392696i | \(0.128458\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.54100 | + | 3.72030i | −0.0634958 | + | 0.153292i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.8009 | − | 26.7442i | −1.02017 | − | 1.10011i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.0070 | 0.862656 | 0.431328 | − | 0.902195i | \(-0.358045\pi\) | ||||
0.431328 | + | 0.902195i | \(0.358045\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.82414 | + | 2.82665i | 0.279763 | + | 0.115881i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.67113 | − | 3.64012i | 0.0683947 | − | 0.148980i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.73031 | + | 4.73031i | 0.193275 | + | 0.193275i | 0.797110 | − | 0.603835i | \(-0.206361\pi\) |
−0.603835 | + | 0.797110i | \(0.706361\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.8135 | − | 22.8135i | 0.930581 | − | 0.930581i | −0.0671615 | − | 0.997742i | \(-0.521394\pi\) |
0.997742 | + | 0.0671615i | \(0.0213943\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.48672 | + | 19.7507i | 0.264160 | + | 0.804312i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.63211 | − | 3.94027i | 0.0663548 | − | 0.160195i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 20.5708i | − | 0.834943i | −0.908690 | − | 0.417472i | \(-0.862916\pi\) | ||
0.908690 | − | 0.417472i | \(-0.137084\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.9091 | + | 19.3124i | 0.725714 | + | 0.782579i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −52.7384 | − | 21.8450i | −2.13357 | − | 0.883753i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.90289 | + | 4.59399i | 0.0768571 | + | 0.185550i | 0.957638 | − | 0.287974i | \(-0.0929818\pi\) |
−0.880781 | + | 0.473524i | \(0.842982\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.53808 | + | 0.208798i | 0.223317 | + | 0.00841953i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.85391 | − | 2.85391i | 0.114894 | − | 0.114894i | −0.647322 | − | 0.762216i | \(-0.724111\pi\) |
0.762216 | + | 0.647322i | \(0.224111\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.0551 | − | 29.1035i | −0.484534 | − | 1.16977i | −0.957434 | − | 0.288652i | \(-0.906793\pi\) |
0.472901 | − | 0.881116i | \(-0.343207\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.28173 | + | 11.4278i | 0.131691 | + | 0.458580i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.6013i | 0.985631i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 22.5103i | − | 0.900411i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.323700 | − | 0.873161i | −0.0129273 | − | 0.0348707i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.8591 | − | 38.2873i | −0.632345 | − | 1.52662i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.3014 | + | 27.3014i | −1.08685 | + | 1.08685i | −0.0910003 | + | 0.995851i | \(0.529006\pi\) |
−0.995851 | + | 0.0910003i | \(0.970994\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.949152 | + | 25.1750i | −0.0377254 | + | 1.00062i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.803237 | − | 1.93919i | −0.0318755 | − | 0.0769543i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.49280 | − | 2.27519i | −0.217633 | − | 0.0901464i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.629379 | − | 8.33487i | 0.0248979 | − | 0.329722i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 34.3968i | − | 1.35859i | −0.733865 | − | 0.679295i | \(-0.762286\pi\) | ||
0.733865 | − | 0.679295i | \(-0.237714\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.4779 | − | 25.2960i | 0.413210 | − | 0.997576i | −0.571061 | − | 0.820908i | \(-0.693468\pi\) |
0.984270 | − | 0.176669i | \(-0.0565321\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.314571 | + | 0.685213i | −0.0123862 | + | 0.0269802i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.7097 | − | 26.7097i | 1.05007 | − | 1.05007i | 0.0513899 | − | 0.998679i | \(-0.483635\pi\) |
0.998679 | − | 0.0513899i | \(-0.0163651\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.75718 | − | 4.75718i | −0.186735 | − | 0.186735i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.7675 | − | 11.8295i | −1.00991 | − | 0.463634i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.0093 | + | 16.5724i | 1.56569 | + | 0.648528i | 0.986065 | − | 0.166358i | \(-0.0532008\pi\) |
0.579620 | + | 0.814887i | \(0.303201\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.78306 | 0.225963 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −40.1447 | − | 3.03139i | −1.56620 | − | 0.118266i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.33558 | − | 15.2955i | 0.246799 | − | 0.595826i | −0.751129 | − | 0.660155i | \(-0.770491\pi\) |
0.997929 | + | 0.0643286i | \(0.0204906\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.2351 | − | 5.48218i | 0.514787 | − | 0.213232i | −0.110138 | − | 0.993916i | \(-0.535129\pi\) |
0.624926 | + | 0.780684i | \(0.285129\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −59.7354 | − | 2.25215i | −2.31993 | − | 0.0874663i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.576668 | + | 0.576668i | 0.0223622 | + | 0.0223622i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.3007 | + | 4.68092i | −0.437567 | + | 0.181246i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.173166 | − | 0.0641964i | 0.00669499 | − | 0.00248198i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.44895 | 0.133145 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.2651 | 0.781160 | 0.390580 | − | 0.920569i | \(-0.372274\pi\) | ||||
0.390580 | + | 0.920569i | \(0.372274\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −24.1331 | + | 6.93035i | −0.928885 | + | 0.266749i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.6561 | + | 15.1834i | −1.40881 | + | 0.583547i | −0.952022 | − | 0.306030i | \(-0.900999\pi\) |
−0.456785 | + | 0.889577i | \(0.650999\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.2422 | − | 10.2422i | −0.393058 | − | 0.393058i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.48548 | − | 39.4004i | 0.0569237 | − | 1.50983i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.0996 | − | 9.98236i | 0.922144 | − | 0.381965i | 0.129451 | − | 0.991586i | \(-0.458678\pi\) |
0.792693 | + | 0.609621i | \(0.208678\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.15121 | + | 2.77927i | −0.0439856 | + | 0.106191i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.18381 | − | 4.80713i | 0.197775 | − | 0.183403i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.59903 | 0.365694 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.6860 | − | 5.66894i | −0.520641 | − | 0.215657i | 0.106857 | − | 0.994274i | \(-0.465921\pi\) |
−0.627499 | + | 0.778618i | \(0.715921\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.22948 | − | 2.04595i | 0.236638 | − | 0.0777190i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.20798 | + | 2.20798i | 0.0837536 | + | 0.0837536i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34.9990 | + | 34.9990i | −1.32568 | + | 1.32568i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.96484 | − | 4.57471i | −0.376905 | − | 0.173031i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.2498 | + | 36.8163i | −0.575977 | + | 1.39053i | 0.320419 | + | 0.947276i | \(0.396176\pi\) |
−0.896396 | + | 0.443255i | \(0.853824\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.57559i | − | 0.172572i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.45447 | + | 5.05813i | −0.205427 | + | 0.190500i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.64668 | − | 2.75314i | −0.249974 | − | 0.103543i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.6037 | − | 28.0139i | −0.435788 | − | 1.05209i | −0.977389 | − | 0.211449i | \(-0.932182\pi\) |
0.541601 | − | 0.840636i | \(-0.317818\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.9236 | − | 17.1259i | 0.747193 | − | 0.642272i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.31087 | − | 9.31087i | 0.348695 | − | 0.348695i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.656007 | + | 1.58374i | 0.0245333 | + | 0.0592286i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.0972 | + | 5.22614i | −0.526469 | + | 0.195174i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 44.6170i | − | 1.66393i | −0.554826 | − | 0.831967i | \(-0.687215\pi\) | ||
0.554826 | − | 0.831967i | \(-0.312785\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 24.7573i | − | 0.922008i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.40004 | − | 2.74336i | 0.275211 | − | 0.102027i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.88517 | − | 23.8649i | −0.367126 | − | 0.886321i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.5081 | − | 15.5081i | 0.575162 | − | 0.575162i | −0.358405 | − | 0.933566i | \(-0.616679\pi\) |
0.933566 | + | 0.358405i | \(0.116679\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.3258 | + | 22.8860i | 0.530587 | + | 0.847631i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.57689 | − | 6.22117i | −0.0953098 | − | 0.230098i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.3401 | − | 17.9520i | −1.60080 | − | 0.663074i | −0.609273 | − | 0.792961i | \(-0.708538\pi\) |
−0.991529 | + | 0.129887i | \(0.958538\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.568093 | + | 0.526813i | −0.0209544 | + | 0.0194318i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.32424i | 0.196121i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.0170 | + | 43.4968i | −0.662765 | + | 1.60006i | 0.130686 | + | 0.991424i | \(0.458282\pi\) |
−0.793452 | + | 0.608633i | \(0.791718\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.99817 | − | 2.75367i | −0.220348 | − | 0.101159i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.20365 | + | 3.20365i | −0.117530 | + | 0.117530i | −0.763426 | − | 0.645895i | \(-0.776484\pi\) |
0.645895 | + | 0.763426i | \(0.276484\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.72193 | − | 5.72193i | −0.209635 | − | 0.209635i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.1516 | + | 49.1784i | 0.590958 | + | 1.79935i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.39260 | + | 1.40526i | 0.123963 | + | 0.0513471i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −53.3838 | −1.94800 | −0.974001 | − | 0.226542i | \(-0.927258\pi\) | ||||
−0.974001 | + | 0.226542i | \(0.927258\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.49233 | + | 2.31123i | −0.0908255 | + | 0.0842257i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.81738 | − | 4.38754i | 0.0661411 | − | 0.159679i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.7929 | − | 16.8970i | 1.48264 | − | 0.614130i | 0.512941 | − | 0.858424i | \(-0.328556\pi\) |
0.969701 | + | 0.244294i | \(0.0785560\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.114725 | + | 3.04293i | −0.00416425 | + | 0.110451i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.82203 | − | 2.82203i | −0.102299 | − | 0.102299i | 0.654105 | − | 0.756404i | \(-0.273045\pi\) |
−0.756404 | + | 0.654105i | \(0.773045\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.41304 | − | 2.65637i | 0.232168 | − | 0.0961670i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.51451 | + | 6.95203i | −0.127067 | + | 0.251351i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −47.6820 | −1.72170 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.4430 | 0.412645 | 0.206322 | − | 0.978484i | \(-0.433850\pi\) | ||||
0.206322 | + | 0.978484i | \(0.433850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.7828 | − | 8.07538i | 0.784490 | − | 0.290828i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.4059 | − | 7.20975i | 0.626046 | − | 0.259317i | −0.0470263 | − | 0.998894i | \(-0.514974\pi\) |
0.673072 | + | 0.739577i | \(0.264974\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.6627 | + | 19.6627i | 0.706305 | + | 0.706305i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.1942 | + | 1.21379i | 1.15496 | + | 0.0435444i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.04886 | + | 2.09131i | −0.180894 | + | 0.0749289i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.819227 | − | 1.97779i | 0.0293142 | − | 0.0707708i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.7318 | + | 17.3002i | −0.776631 | + | 0.618259i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.631829 | −0.0225509 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.6913 | − | 11.0559i | −0.951441 | − | 0.394100i | −0.147669 | − | 0.989037i | \(-0.547177\pi\) |
−0.803772 | + | 0.594937i | \(0.797177\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 41.6342 | + | 19.1136i | 1.48222 | + | 0.680463i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.1269 | − | 14.1269i | −0.502296 | − | 0.502296i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.2847 | − | 17.2847i | 0.613798 | − | 0.613798i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.521896 | − | 1.13682i | 0.0185097 | − | 0.0403187i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.1728 | + | 43.8730i | −0.643714 | + | 1.55406i | 0.177919 | + | 0.984045i | \(0.443064\pi\) |
−0.821633 | + | 0.570017i | \(0.806936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 66.4364i | − | 2.35035i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.8716 | − | 1.95361i | −0.914128 | − | 0.0690272i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.52598 | − | 3.94579i | −0.336164 | − | 0.139244i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.02052 | − | 2.46376i | −0.0359687 | − | 0.0868361i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.438013 | + | 11.6177i | −0.0154188 | + | 0.408963i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.4387 | + | 10.4387i | −0.367006 | + | 0.367006i | −0.866384 | − | 0.499378i | \(-0.833562\pi\) |
0.499378 | + | 0.866384i | \(0.333562\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.74617 | + | 13.8725i | 0.201775 | + | 0.487129i | 0.992083 | − | 0.125581i | \(-0.0400794\pi\) |
−0.790308 | + | 0.612710i | \(0.790079\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.8949 | − | 42.8756i | −0.557460 | − | 1.50371i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 0.992553i | − | 0.0347676i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 0.743472i | − | 0.0260108i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.9662 | − | 41.4730i | 0.732617 | − | 1.44919i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.81831 | − | 4.38979i | −0.0634594 | − | 0.153205i | 0.888969 | − | 0.457968i | \(-0.151423\pi\) |
−0.952428 | + | 0.304763i | \(0.901423\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.63123 | − | 6.63123i | 0.231150 | − | 0.231150i | −0.582023 | − | 0.813173i | \(-0.697738\pi\) |
0.813173 | + | 0.582023i | \(0.197738\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.42605 | − | 0.242276i | −0.223726 | − | 0.00843496i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.53700 | + | 10.9533i | 0.157767 | + | 0.380883i | 0.982922 | − | 0.184023i | \(-0.0589122\pi\) |
−0.825155 | + | 0.564907i | \(0.808912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.9460 | + | 9.91877i | 0.831680 | + | 0.344493i | 0.757568 | − | 0.652757i | \(-0.226388\pi\) |
0.0741124 | + | 0.997250i | \(0.476388\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.0563 | − | 16.2361i | −0.522296 | − | 0.563223i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 6.91947i | − | 0.239745i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.98098 | + | 7.19672i | −0.103161 | + | 0.249053i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.4865 | − | 26.1586i | 0.500726 | − | 0.904173i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.4190 | − | 20.4190i | 0.704940 | − | 0.704940i | −0.260526 | − | 0.965467i | \(-0.583896\pi\) |
0.965467 | + | 0.260526i | \(0.0838961\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.299407 | + | 0.299407i | 0.0103244 | + | 0.0103244i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.1428 | − | 24.2718i | 0.383780 | − | 0.835967i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.30393 | + | 2.61117i | 0.216862 | + | 0.0898271i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.6114 | −1.01746 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.2978 | − | 12.1830i | −0.387738 | − | 0.418121i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.72571 | + | 13.8231i | −0.196275 | + | 0.473849i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.7580 | − | 6.52717i | 0.539543 | − | 0.223486i | −0.0962340 | − | 0.995359i | \(-0.530680\pi\) |
0.635777 | + | 0.771873i | \(0.280680\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.652237 | + | 0.560650i | −0.0223060 | + | 0.0191738i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.0421 | + | 33.0421i | 1.12870 | + | 1.12870i | 0.990389 | + | 0.138307i | \(0.0441662\pi\) |
0.138307 | + | 0.990389i | \(0.455834\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.6597 | + | 12.2854i | −1.01198 | + | 0.419174i | −0.826175 | − | 0.563413i | \(-0.809488\pi\) |
−0.185801 | + | 0.982587i | \(0.559488\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.3752 | − | 36.0789i | −0.455827 | − | 1.22956i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.6539 | −1.24771 | −0.623856 | − | 0.781539i | \(-0.714435\pi\) | ||||
−0.623856 | + | 0.781539i | \(0.714435\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.26825 | 0.0771228 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.9483 | − | 37.6248i | −0.473711 | − | 1.27781i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.21654 | − | 2.57497i | 0.210882 | − | 0.0873500i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.6829 | + | 26.6829i | 0.904116 | + | 0.904116i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.5843 | − | 9.95766i | 0.392070 | − | 0.337016i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.5867 | − | 4.38514i | 0.357895 | − | 0.148245i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.7546 | + | 42.8634i | −0.599531 | + | 1.44740i | 0.274529 | + | 0.961579i | \(0.411478\pi\) |
−0.874060 | + | 0.485817i | \(0.838522\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.5802 | + | 27.5846i | 0.862799 | + | 0.930407i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.9787 | 1.04370 | 0.521850 | − | 0.853038i | \(-0.325242\pi\) | ||||
0.521850 | + | 0.853038i | \(0.325242\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.3679 | + | 11.3361i | 0.921002 | + | 0.381492i | 0.792258 | − | 0.610186i | \(-0.208905\pi\) |
0.128744 | + | 0.991678i | \(0.458905\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.59245 | + | 5.64700i | −0.0871443 | + | 0.189822i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.37216 | + | 2.37216i | 0.0796492 | + | 0.0796492i | 0.745809 | − | 0.666160i | \(-0.232063\pi\) |
−0.666160 | + | 0.745809i | \(0.732063\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.3047 | + | 10.3047i | −0.345610 | + | 0.345610i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.65690 | + | 6.71360i | 0.0555082 | + | 0.224914i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.80707 | − | 6.77687i | 0.0939350 | − | 0.226779i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.16436i | − | 0.0723465i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.6749 | + | 15.8248i | 0.489982 | + | 0.528376i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.4210 | + | 11.7724i | 0.947893 | + | 0.392630i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.27525 | + | 10.3214i | 0.142429 | + | 0.343854i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.23111 | + | 0.197224i | 0.174080 | + | 0.00656321i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.52850 | − | 2.52850i | 0.0840503 | − | 0.0840503i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.3336 | + | 32.1901i | 0.442734 | + | 1.06885i | 0.974986 | + | 0.222268i | \(0.0713459\pi\) |
−0.532252 | + | 0.846586i | \(0.678654\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.42312 | − | 6.77124i | 0.113538 | − | 0.224588i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.2111i | 0.371441i | 0.982603 | + | 0.185721i | \(0.0594620\pi\) | ||||
−0.982603 | + | 0.185721i | \(0.940538\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.2571i | 0.438747i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.10727 | − | 2.98680i | −0.0366053 | − | 0.0987405i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.3655 | − | 37.0955i | −0.507412 | − | 1.22500i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.86384 | + | 9.86384i | −0.325378 | + | 0.325378i | −0.850826 | − | 0.525448i | \(-0.823898\pi\) |
0.525448 | + | 0.850826i | \(0.323898\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.0387546 | + | 1.02792i | −0.00127701 | + | 0.0338710i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.80623 | − | 14.0175i | −0.191115 | − | 0.461391i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.1916 | − | 12.0916i | −0.959814 | − | 0.397568i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.0356 | + | 1.96599i | 0.855120 | + | 0.0645715i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 6.97392i | − | 0.228807i | −0.993434 | − | 0.114403i | \(-0.963504\pi\) | ||
0.993434 | − | 0.114403i | \(-0.0364956\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.292361 | − | 0.705823i | 0.00958176 | − | 0.0231324i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.50194 | + | 18.5193i | −0.278341 | + | 0.606295i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.41074 | + | 1.41074i | −0.0461362 | + | 0.0461362i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.9019 | + | 32.9019i | 1.07486 | + | 1.07486i | 0.996961 | + | 0.0778973i | \(0.0248206\pi\) |
0.0778973 | + | 0.996961i | \(0.475179\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.1395 | − | 6.03213i | −0.428790 | − | 0.196851i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.67400 | − | 0.693394i | −0.0545709 | − | 0.0226040i | 0.355231 | − | 0.934779i | \(-0.384402\pi\) |
−0.409802 | + | 0.912175i | \(0.634402\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.8698 | 0.581922 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.77174 | − | 4.73790i | −0.122695 | − | 0.154124i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.82625 | + | 14.0658i | −0.189328 | + | 0.457078i | −0.989831 | − | 0.142251i | \(-0.954566\pi\) |
0.800503 | + | 0.599329i | \(0.204566\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −67.5150 | + | 27.9656i | −2.19163 | + | 0.907802i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.95792 | − | 0.0738178i | −0.0634899 | − | 0.00239371i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.1975 | − | 30.1975i | −0.978193 | − | 0.978193i | 0.0215739 | − | 0.999767i | \(-0.493132\pi\) |
−0.999767 | + | 0.0215739i | \(0.993132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.09053 | + | 1.69435i | −0.132366 | + | 0.0548279i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.67044 | + | 2.47288i | −0.215625 | + | 0.0799369i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.8864 | 0.674458 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.11594 | −0.0682560 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.74723 | + | 3.45618i | −0.0563036 | + | 0.111374i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.20435 | − | 0.913071i | 0.0709605 | − | 0.0293928i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.7575 | − | 19.7575i | −0.635360 | − | 0.635360i | 0.314047 | − | 0.949407i | \(-0.398315\pi\) |
−0.949407 | + | 0.314047i | \(0.898315\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.289401 | − | 7.67598i | 0.00929689 | − | 0.246588i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.7822 | − | 5.29454i | 0.410199 | − | 0.169910i | −0.168035 | − | 0.985781i | \(-0.553742\pi\) |
0.578234 | + | 0.815871i | \(0.303742\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.29657 | − | 20.0297i | 0.265976 | − | 0.642122i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −33.4189 | + | 30.9905i | −1.07026 | + | 0.992491i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.6385 | −1.23615 | −0.618077 | − | 0.786117i | \(-0.712088\pi\) | ||||
−0.618077 | + | 0.786117i | \(0.712088\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.13909 | − | 2.54289i | −0.196206 | − | 0.0812713i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.28426 | + | 6.95512i | 0.0729309 | + | 0.222060i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.6692 | + | 20.6692i | 0.659244 | + | 0.659244i | 0.955201 | − | 0.295957i | \(-0.0956386\pi\) |
−0.295957 | + | 0.955201i | \(0.595639\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.10069 | + | 6.10069i | −0.194384 | + | 0.194384i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 46.9378 | + | 21.5485i | 1.49405 | + | 0.685895i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.930350 | + | 2.24606i | −0.0295834 | + | 0.0714206i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.7543i | 1.19931i | 0.800260 | + | 0.599653i | \(0.204695\pi\) | ||||
−0.800260 | + | 0.599653i | \(0.795305\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.4758 | − | 18.9879i | 0.649779 | − | 0.602563i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.875334 | − | 0.362575i | −0.0277499 | − | 0.0114944i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.1744 | + | 26.9773i | 0.353896 | + | 0.854381i | 0.996132 | + | 0.0878737i | \(0.0280072\pi\) |
−0.642235 | + | 0.766507i | \(0.721993\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.83302 | + | 33.7601i | −0.121271 | + | 1.06812i |
(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 | 768.2.o.b.95.6 | 56 | ||
3.2 | odd | 2 | inner | 768.2.o.b.95.12 | 56 | ||
4.3 | odd | 2 | 768.2.o.a.95.9 | 56 | |||
8.3 | odd | 2 | 384.2.o.a.47.6 | 56 | |||
8.5 | even | 2 | 96.2.o.a.35.4 | yes | 56 | ||
12.11 | even | 2 | 768.2.o.a.95.3 | 56 | |||
24.5 | odd | 2 | 96.2.o.a.35.11 | yes | 56 | ||
24.11 | even | 2 | 384.2.o.a.47.12 | 56 | |||
32.5 | even | 8 | 384.2.o.a.335.12 | 56 | |||
32.11 | odd | 8 | inner | 768.2.o.b.671.12 | 56 | ||
32.21 | even | 8 | 768.2.o.a.671.3 | 56 | |||
32.27 | odd | 8 | 96.2.o.a.11.11 | yes | 56 | ||
96.5 | odd | 8 | 384.2.o.a.335.6 | 56 | |||
96.11 | even | 8 | inner | 768.2.o.b.671.6 | 56 | ||
96.53 | odd | 8 | 768.2.o.a.671.9 | 56 | |||
96.59 | even | 8 | 96.2.o.a.11.4 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.2.o.a.11.4 | ✓ | 56 | 96.59 | even | 8 | ||
96.2.o.a.11.11 | yes | 56 | 32.27 | odd | 8 | ||
96.2.o.a.35.4 | yes | 56 | 8.5 | even | 2 | ||
96.2.o.a.35.11 | yes | 56 | 24.5 | odd | 2 | ||
384.2.o.a.47.6 | 56 | 8.3 | odd | 2 | |||
384.2.o.a.47.12 | 56 | 24.11 | even | 2 | |||
384.2.o.a.335.6 | 56 | 96.5 | odd | 8 | |||
384.2.o.a.335.12 | 56 | 32.5 | even | 8 | |||
768.2.o.a.95.3 | 56 | 12.11 | even | 2 | |||
768.2.o.a.95.9 | 56 | 4.3 | odd | 2 | |||
768.2.o.a.671.3 | 56 | 32.21 | even | 8 | |||
768.2.o.a.671.9 | 56 | 96.53 | odd | 8 | |||
768.2.o.b.95.6 | 56 | 1.1 | even | 1 | trivial | ||
768.2.o.b.95.12 | 56 | 3.2 | odd | 2 | inner | ||
768.2.o.b.671.6 | 56 | 96.11 | even | 8 | inner | ||
768.2.o.b.671.12 | 56 | 32.11 | odd | 8 | inner |