Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(521,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.521");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.i (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.23 | ||
Character | \(\chi\) | \(=\) | 1323.521 |
Dual form | 1323.2.i.d.1097.23 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.08430i | 1.47383i | 0.675988 | + | 0.736913i | \(0.263717\pi\) | ||||
−0.675988 | + | 0.736913i | \(0.736283\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.34432 | −1.17216 | ||||||||
\(5\) | −1.65233 | + | 2.86191i | −0.738942 | + | 1.27989i | 0.214029 | + | 0.976827i | \(0.431341\pi\) |
−0.952972 | + | 0.303059i | \(0.901992\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 0.717672i | − | 0.253735i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.96509 | − | 3.44395i | −1.88633 | − | 1.08907i | ||||
\(11\) | 2.30482 | − | 1.33069i | 0.694929 | − | 0.401217i | −0.110527 | − | 0.993873i | \(-0.535254\pi\) |
0.805456 | + | 0.592656i | \(0.201921\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.11249 | − | 1.21964i | 0.585899 | − | 0.338269i | −0.177576 | − | 0.984107i | \(-0.556825\pi\) |
0.763474 | + | 0.645839i | \(0.223492\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.19280 | −0.798199 | ||||||||
\(17\) | −3.59017 | + | 6.21836i | −0.870744 | + | 1.50817i | −0.00951656 | + | 0.999955i | \(0.503029\pi\) |
−0.861228 | + | 0.508219i | \(0.830304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.24746 | + | 2.45227i | −0.974433 | + | 0.562589i | −0.900585 | − | 0.434680i | \(-0.856861\pi\) |
−0.0738485 | + | 0.997269i | \(0.523528\pi\) | |||||||
\(20\) | 3.87358 | − | 6.70924i | 0.866160 | − | 1.50023i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.77356 | + | 4.80394i | 0.591324 | + | 1.02420i | ||||
\(23\) | −4.32174 | − | 2.49516i | −0.901145 | − | 0.520276i | −0.0235732 | − | 0.999722i | \(-0.507504\pi\) |
−0.877571 | + | 0.479446i | \(0.840838\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.96036 | − | 5.12749i | −0.592072 | − | 1.02550i | ||||
\(26\) | 2.54211 | + | 4.40306i | 0.498549 | + | 0.863512i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.50701 | − | 3.17947i | −1.02263 | − | 0.590413i | −0.107762 | − | 0.994177i | \(-0.534368\pi\) |
−0.914863 | + | 0.403764i | \(0.867702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.66543i | 0.478725i | 0.970930 | + | 0.239362i | \(0.0769384\pi\) | ||||
−0.970930 | + | 0.239362i | \(0.923062\pi\) | |||||||
\(32\) | − | 8.09010i | − | 1.43014i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.9609 | − | 7.48301i | −2.22278 | − | 1.28333i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.844787 | + | 1.46321i | 0.138882 | + | 0.240551i | 0.927074 | − | 0.374879i | \(-0.122316\pi\) |
−0.788192 | + | 0.615430i | \(0.788982\pi\) | |||||||
\(38\) | −5.11128 | − | 8.85299i | −0.829159 | − | 1.43614i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.05391 | + | 1.18583i | 0.324752 | + | 0.187496i | ||||
\(41\) | −0.553137 | − | 0.958062i | −0.0863855 | − | 0.149624i | 0.819595 | − | 0.572943i | \(-0.194198\pi\) |
−0.905981 | + | 0.423319i | \(0.860865\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.93481 | − | 5.08323i | 0.447554 | − | 0.775186i | −0.550672 | − | 0.834721i | \(-0.685629\pi\) |
0.998226 | + | 0.0595356i | \(0.0189620\pi\) | |||||||
\(44\) | −5.40324 | + | 3.11956i | −0.814568 | + | 0.470291i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.20066 | − | 9.00781i | 0.766796 | − | 1.32813i | ||||
\(47\) | 4.88196 | 0.712107 | 0.356053 | − | 0.934466i | \(-0.384122\pi\) | ||||
0.356053 | + | 0.934466i | \(0.384122\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 10.6873 | − | 6.17029i | 1.51141 | − | 0.872610i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.95235 | + | 2.85924i | −0.686767 | + | 0.396505i | ||||
\(53\) | 8.94013 | + | 5.16159i | 1.22802 | + | 0.708999i | 0.966616 | − | 0.256230i | \(-0.0824806\pi\) |
0.261406 | + | 0.965229i | \(0.415814\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.79491i | 1.18591i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.62698 | − | 11.4783i | 0.870166 | − | 1.50717i | ||||
\(59\) | −5.13640 | −0.668703 | −0.334351 | − | 0.942448i | \(-0.608517\pi\) | ||||
−0.334351 | + | 0.942448i | \(0.608517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.13395i | − | 0.657335i | −0.944446 | − | 0.328668i | \(-0.893400\pi\) | ||
0.944446 | − | 0.328668i | \(-0.106600\pi\) | |||||||
\(62\) | −5.55556 | −0.705556 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 10.4766 | 1.30958 | ||||||||
\(65\) | 8.06100i | 0.999844i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.33088 | 1.01778 | 0.508890 | − | 0.860832i | \(-0.330056\pi\) | ||||
0.508890 | + | 0.860832i | \(0.330056\pi\) | |||||||
\(68\) | 8.41652 | − | 14.5778i | 1.02065 | − | 1.76782i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.07026i | 0.245695i | 0.992426 | + | 0.122848i | \(0.0392026\pi\) | ||||
−0.992426 | + | 0.122848i | \(0.960797\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.94112 | − | 4.00746i | −0.812396 | − | 0.469037i | 0.0353910 | − | 0.999374i | \(-0.488732\pi\) |
−0.847787 | + | 0.530336i | \(0.822066\pi\) | |||||||
\(74\) | −3.04978 | + | 1.76079i | −0.354530 | + | 0.204688i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.95741 | − | 5.74891i | 1.14219 | − | 0.659445i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.01003 | 0.563672 | 0.281836 | − | 0.959463i | \(-0.409057\pi\) | ||||
0.281836 | + | 0.959463i | \(0.409057\pi\) | |||||||
\(80\) | 5.27554 | − | 9.13750i | 0.589823 | − | 1.02160i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.99689 | − | 1.15291i | 0.220520 | − | 0.127317i | ||||
\(83\) | −1.04482 | + | 1.80968i | −0.114684 | + | 0.198638i | −0.917653 | − | 0.397382i | \(-0.869919\pi\) |
0.802970 | + | 0.596020i | \(0.203252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.8643 | − | 20.5495i | −1.28686 | − | 2.22891i | ||||
\(86\) | 10.5950 | + | 6.11703i | 1.14249 | + | 0.659616i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.954997 | − | 1.65410i | −0.101803 | − | 0.176328i | ||||
\(89\) | 0.541267 | + | 0.937501i | 0.0573741 | + | 0.0993749i | 0.893286 | − | 0.449489i | \(-0.148394\pi\) |
−0.835912 | + | 0.548864i | \(0.815061\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.1315 | + | 5.84945i | 1.05629 | + | 0.609847i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.1755i | 1.04952i | ||||||||
\(95\) | − | 16.2078i | − | 1.66288i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.47203 | − | 5.46868i | −0.961739 | − | 0.555260i | −0.0650310 | − | 0.997883i | \(-0.520715\pi\) |
−0.896708 | + | 0.442623i | \(0.854048\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.94004 | + | 12.0205i | 0.694004 | + | 1.20205i | ||||
\(101\) | 0.263957 | + | 0.457188i | 0.0262647 | + | 0.0454919i | 0.878859 | − | 0.477082i | \(-0.158305\pi\) |
−0.852594 | + | 0.522573i | \(0.824972\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.678733 | − | 0.391867i | −0.0668775 | − | 0.0386118i | 0.466188 | − | 0.884685i | \(-0.345627\pi\) |
−0.533066 | + | 0.846074i | \(0.678960\pi\) | |||||||
\(104\) | −0.875305 | − | 1.51607i | −0.0858308 | − | 0.148663i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.7583 | + | 18.6340i | −1.04494 | + | 1.80989i | ||||
\(107\) | 4.63398 | − | 2.67543i | 0.447984 | − | 0.258644i | −0.258994 | − | 0.965879i | \(-0.583391\pi\) |
0.706978 | + | 0.707235i | \(0.250058\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.98261 | + | 5.16603i | −0.285682 | + | 0.494816i | −0.972774 | − | 0.231754i | \(-0.925553\pi\) |
0.687092 | + | 0.726570i | \(0.258887\pi\) | |||||||
\(110\) | −18.3313 | −1.74782 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0024 | + | 5.77487i | −0.940944 | + | 0.543254i | −0.890256 | − | 0.455461i | \(-0.849475\pi\) |
−0.0506876 | + | 0.998715i | \(0.516141\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.2818 | − | 8.24562i | 1.33179 | − | 0.768908i | ||||
\(116\) | 12.9102 | + | 7.45371i | 1.19868 | + | 0.692059i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 10.7058i | − | 0.985551i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.95854 | + | 3.39230i | −0.178049 | + | 0.308391i | ||||
\(122\) | 10.7007 | 0.968797 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 6.24862i | − | 0.561142i | ||||||
\(125\) | 3.04265 | 0.272143 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.0954 | −1.69444 | −0.847221 | − | 0.531241i | \(-0.821726\pi\) | ||||
−0.847221 | + | 0.531241i | \(0.821726\pi\) | |||||||
\(128\) | 5.65629i | 0.499950i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −16.8016 | −1.47360 | ||||||||
\(131\) | −2.07563 | + | 3.59509i | −0.181349 | + | 0.314105i | −0.942340 | − | 0.334657i | \(-0.891380\pi\) |
0.760991 | + | 0.648762i | \(0.224713\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 17.3641i | 1.50003i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.46274 | + | 2.57657i | 0.382677 | + | 0.220939i | ||||
\(137\) | −5.45092 | + | 3.14709i | −0.465704 | + | 0.268874i | −0.714440 | − | 0.699697i | \(-0.753318\pi\) |
0.248736 | + | 0.968571i | \(0.419985\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.32575 | − | 0.765423i | 0.112449 | − | 0.0649223i | −0.442721 | − | 0.896660i | \(-0.645987\pi\) |
0.555170 | + | 0.831737i | \(0.312653\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.31506 | −0.362112 | ||||||||
\(143\) | 3.24593 | − | 5.62212i | 0.271438 | − | 0.470145i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.1987 | − | 10.5070i | 1.51132 | − | 0.872563i | ||||
\(146\) | 8.35276 | − | 14.4674i | 0.691279 | − | 1.19733i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.98045 | − | 3.43025i | −0.162792 | − | 0.281965i | ||||
\(149\) | −4.63163 | − | 2.67407i | −0.379438 | − | 0.219069i | 0.298136 | − | 0.954523i | \(-0.403635\pi\) |
−0.677574 | + | 0.735455i | \(0.736969\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.74384 | − | 9.94862i | −0.467427 | − | 0.809607i | 0.531880 | − | 0.846820i | \(-0.321486\pi\) |
−0.999307 | + | 0.0372121i | \(0.988152\pi\) | |||||||
\(152\) | 1.75993 | + | 3.04828i | 0.142749 | + | 0.247248i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.62821 | − | 4.40415i | −0.612713 | − | 0.353750i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.66542i | 0.531959i | 0.963979 | + | 0.265979i | \(0.0856953\pi\) | ||||
−0.963979 | + | 0.265979i | \(0.914305\pi\) | |||||||
\(158\) | 10.4424i | 0.830754i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 23.1532 | + | 13.3675i | 1.83042 | + | 1.05679i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.5460 | + | 19.9983i | 0.904356 | + | 1.56639i | 0.821779 | + | 0.569807i | \(0.192982\pi\) |
0.0825775 | + | 0.996585i | \(0.473685\pi\) | |||||||
\(164\) | 1.29673 | + | 2.24601i | 0.101258 | + | 0.175384i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.77192 | − | 2.17772i | −0.292757 | − | 0.169024i | ||||
\(167\) | 7.95418 | + | 13.7770i | 0.615513 | + | 1.06610i | 0.990294 | + | 0.138986i | \(0.0443844\pi\) |
−0.374782 | + | 0.927113i | \(0.622282\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.52493 | + | 6.10536i | −0.271149 | + | 0.469643i | ||||
\(170\) | 42.8314 | − | 24.7287i | 3.28502 | − | 1.89661i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.88013 | + | 11.9167i | −0.524605 | + | 0.908643i | ||||
\(173\) | −18.6619 | −1.41884 | −0.709421 | − | 0.704785i | \(-0.751043\pi\) | ||||
−0.709421 | + | 0.704785i | \(0.751043\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.35882 | + | 4.24861i | −0.554692 | + | 0.320251i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.95404 | + | 1.12816i | −0.146461 | + | 0.0845595i | ||||
\(179\) | −19.0792 | − | 11.0154i | −1.42604 | − | 0.823326i | −0.429237 | − | 0.903192i | \(-0.641218\pi\) |
−0.996806 | + | 0.0798653i | \(0.974551\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.6986i | 1.31552i | 0.753226 | + | 0.657762i | \(0.228497\pi\) | ||||
−0.753226 | + | 0.657762i | \(0.771503\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.79070 | + | 3.10159i | −0.132012 | + | 0.228652i | ||||
\(185\) | −5.58346 | −0.410504 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.1096i | 1.39743i | ||||||||
\(188\) | −11.4449 | −0.834704 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 33.7820 | 2.45080 | ||||||||
\(191\) | 15.3242i | 1.10882i | 0.832244 | + | 0.554409i | \(0.187056\pi\) | ||||
−0.832244 | + | 0.554409i | \(0.812944\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.8667 | 1.86192 | 0.930962 | − | 0.365117i | \(-0.118971\pi\) | ||||
0.930962 | + | 0.365117i | \(0.118971\pi\) | |||||||
\(194\) | 11.3984 | − | 19.7426i | 0.818356 | − | 1.41744i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.18301i | − | 0.298027i | −0.988835 | − | 0.149014i | \(-0.952390\pi\) | ||
0.988835 | − | 0.149014i | \(-0.0476098\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.0592 | + | 11.0038i | 1.35107 | + | 0.780041i | 0.988399 | − | 0.151876i | \(-0.0485316\pi\) |
0.362671 | + | 0.931917i | \(0.381865\pi\) | |||||||
\(200\) | −3.67986 | + | 2.12457i | −0.260205 | + | 0.150230i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.952918 | + | 0.550168i | −0.0670471 | + | 0.0387097i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.65585 | 0.255336 | ||||||||
\(206\) | 0.816769 | − | 1.41469i | 0.0569070 | − | 0.0985658i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.74474 | + | 3.89408i | −0.467664 | + | 0.270006i | ||||
\(209\) | −6.52641 | + | 11.3041i | −0.451441 | + | 0.781919i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.2926 | + | 21.2914i | 0.846257 | + | 1.46576i | 0.884525 | + | 0.466493i | \(0.154483\pi\) |
−0.0382677 | + | 0.999268i | \(0.512184\pi\) | |||||||
\(212\) | −20.9586 | − | 12.1004i | −1.43944 | − | 0.831061i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.57641 | + | 9.65863i | 0.381196 | + | 0.660250i | ||||
\(215\) | 9.69851 | + | 16.7983i | 0.661433 | + | 1.14564i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.7676 | − | 6.21666i | −0.729272 | − | 0.421045i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 20.6181i | − | 1.39007i | ||||||
\(221\) | 17.5149i | 1.17818i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.31908 | − | 4.22567i | −0.490122 | − | 0.282972i | 0.234503 | − | 0.972115i | \(-0.424654\pi\) |
−0.724625 | + | 0.689143i | \(0.757987\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.0366 | − | 20.8480i | −0.800662 | − | 1.38679i | ||||
\(227\) | 2.91475 | + | 5.04849i | 0.193458 | + | 0.335080i | 0.946394 | − | 0.323014i | \(-0.104696\pi\) |
−0.752936 | + | 0.658094i | \(0.771363\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.15541 | − | 2.39913i | −0.274597 | − | 0.158539i | 0.356378 | − | 0.934342i | \(-0.384012\pi\) |
−0.630975 | + | 0.775803i | \(0.717345\pi\) | |||||||
\(230\) | 17.1864 | + | 29.7677i | 1.13324 | + | 1.96282i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.28182 | + | 3.95223i | −0.149809 | + | 0.259476i | ||||
\(233\) | −19.9587 | + | 11.5232i | −1.30754 | + | 0.754907i | −0.981685 | − | 0.190513i | \(-0.938985\pi\) |
−0.325853 | + | 0.945420i | \(0.605652\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.06659 | + | 13.9717i | −0.526206 | + | 0.911416i | ||||
\(236\) | 12.0414 | 0.783828 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.91972 | + | 3.41775i | −0.382915 | + | 0.221076i | −0.679086 | − | 0.734059i | \(-0.737624\pi\) |
0.296171 | + | 0.955135i | \(0.404290\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.89112 | − | 2.24654i | 0.250649 | − | 0.144712i | −0.369412 | − | 0.929266i | \(-0.620441\pi\) |
0.620061 | + | 0.784553i | \(0.287108\pi\) | |||||||
\(242\) | −7.07058 | − | 4.08220i | −0.454514 | − | 0.262414i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.0356i | 0.770503i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.98180 | + | 10.3608i | −0.380613 | + | 0.659241i | ||||
\(248\) | 1.91290 | 0.121469 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.34181i | 0.401092i | ||||||||
\(251\) | 0.467438 | 0.0295044 | 0.0147522 | − | 0.999891i | \(-0.495304\pi\) | ||||
0.0147522 | + | 0.999891i | \(0.495304\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.2811 | −0.834975 | ||||||||
\(254\) | − | 39.8006i | − | 2.49731i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.16385 | 0.572741 | ||||||||
\(257\) | 10.7433 | − | 18.6079i | 0.670146 | − | 1.16073i | −0.307716 | − | 0.951478i | \(-0.599565\pi\) |
0.977862 | − | 0.209249i | \(-0.0671020\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 18.8976i | − | 1.17198i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.49327 | − | 4.32624i | −0.462936 | − | 0.267276i | ||||
\(263\) | 9.60394 | − | 5.54484i | 0.592205 | − | 0.341909i | −0.173764 | − | 0.984787i | \(-0.555593\pi\) |
0.765969 | + | 0.642878i | \(0.222260\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.5440 | + | 17.0572i | −1.81487 | + | 1.04782i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −19.5303 | −1.19300 | ||||||||
\(269\) | −11.0288 | + | 19.1024i | −0.672435 | + | 1.16469i | 0.304776 | + | 0.952424i | \(0.401418\pi\) |
−0.977212 | + | 0.212268i | \(0.931915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.10874 | + | 2.37218i | −0.249588 | + | 0.144100i | −0.619576 | − | 0.784937i | \(-0.712695\pi\) |
0.369988 | + | 0.929037i | \(0.379362\pi\) | |||||||
\(272\) | 11.4627 | − | 19.8540i | 0.695028 | − | 1.20382i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.55950 | − | 11.3614i | −0.396274 | − | 0.686366i | ||||
\(275\) | −13.6462 | − | 7.87862i | −0.822895 | − | 0.475099i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.21329 | + | 5.56558i | 0.193068 | + | 0.334404i | 0.946265 | − | 0.323391i | \(-0.104823\pi\) |
−0.753197 | + | 0.657794i | \(0.771490\pi\) | |||||||
\(278\) | 1.59537 | + | 2.76327i | 0.0956842 | + | 0.165730i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.0883 | + | 9.86595i | 1.01940 | + | 0.588553i | 0.913931 | − | 0.405869i | \(-0.133031\pi\) |
0.105473 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.60130i | 0.332963i | 0.986045 | + | 0.166481i | \(0.0532406\pi\) | ||||
−0.986045 | + | 0.166481i | \(0.946759\pi\) | |||||||
\(284\) | − | 4.85336i | − | 0.287994i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.7182 | + | 6.76551i | 0.692912 | + | 0.400053i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.2787 | − | 29.9275i | −1.01639 | − | 1.76044i | ||||
\(290\) | 21.8999 | + | 37.9317i | 1.28600 | + | 2.22743i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.2722 | + | 9.39477i | 0.952260 | + | 0.549787i | ||||
\(293\) | −15.0393 | − | 26.0488i | −0.878603 | − | 1.52178i | −0.852875 | − | 0.522115i | \(-0.825143\pi\) |
−0.0257278 | − | 0.999669i | \(-0.508190\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.48701 | − | 14.6999i | 0.494133 | − | 0.855863i | ||||
\(296\) | 1.05011 | − | 0.606281i | 0.0610363 | − | 0.0352393i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.57358 | − | 9.65373i | 0.322869 | − | 0.559225i | ||||
\(299\) | −12.1728 | −0.703972 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 20.7360 | − | 11.9719i | 1.19322 | − | 0.688906i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 13.5613 | − | 7.82960i | 0.777792 | − | 0.449059i | ||||
\(305\) | 14.6929 | + | 8.48296i | 0.841314 | + | 0.485733i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 23.4497i | − | 1.33835i | −0.743106 | − | 0.669173i | \(-0.766648\pi\) | ||
0.743106 | − | 0.669173i | \(-0.233352\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.17959 | − | 15.8995i | 0.521366 | − | 0.903032i | ||||
\(311\) | 16.7101 | 0.947546 | 0.473773 | − | 0.880647i | \(-0.342892\pi\) | ||||
0.473773 | + | 0.880647i | \(0.342892\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 14.8675i | − | 0.840363i | −0.907440 | − | 0.420182i | \(-0.861966\pi\) | ||
0.907440 | − | 0.420182i | \(-0.138034\pi\) | |||||||
\(314\) | −13.8928 | −0.784014 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.7451 | −0.660715 | ||||||||
\(317\) | 2.27199i | 0.127608i | 0.997962 | + | 0.0638040i | \(0.0203232\pi\) | ||||
−0.997962 | + | 0.0638040i | \(0.979677\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.9235 | −0.947536 | ||||||||
\(320\) | −17.3108 | + | 29.9832i | −0.967704 | + | 1.67611i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 35.2163i | − | 1.95949i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.5074 | − | 7.22117i | −0.693788 | − | 0.400559i | ||||
\(326\) | −41.6826 | + | 24.0655i | −2.30859 | + | 1.33286i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.687575 | + | 0.396971i | −0.0379650 | + | 0.0219191i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.9488 | −0.656765 | −0.328383 | − | 0.944545i | \(-0.606504\pi\) | ||||
−0.328383 | + | 0.944545i | \(0.606504\pi\) | |||||||
\(332\) | 2.44939 | − | 4.24247i | 0.134428 | − | 0.232836i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −28.7155 | + | 16.5789i | −1.57124 | + | 0.907158i | ||||
\(335\) | −13.7653 | + | 23.8423i | −0.752080 | + | 1.30264i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.34636 | + | 4.06402i | 0.127815 | + | 0.221381i | 0.922830 | − | 0.385208i | \(-0.125870\pi\) |
−0.795015 | + | 0.606590i | \(0.792537\pi\) | |||||||
\(338\) | −12.7254 | − | 7.34703i | −0.692172 | − | 0.399626i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 27.8137 | + | 48.1747i | 1.50841 | + | 2.61264i | ||||
\(341\) | 3.54685 | + | 6.14332i | 0.192073 | + | 0.332679i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.64810 | − | 2.10623i | −0.196692 | − | 0.113560i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 38.8972i | − | 2.09112i | ||||||
\(347\) | − | 7.39619i | − | 0.397048i | −0.980096 | − | 0.198524i | \(-0.936385\pi\) | ||
0.980096 | − | 0.198524i | \(-0.0636148\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0496 | + | 10.4209i | 0.966171 | + | 0.557819i | 0.898067 | − | 0.439859i | \(-0.144972\pi\) |
0.0681042 | + | 0.997678i | \(0.478305\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.7654 | − | 18.6462i | −0.573798 | − | 0.993847i | ||||
\(353\) | −3.54953 | − | 6.14797i | −0.188923 | − | 0.327224i | 0.755969 | − | 0.654608i | \(-0.227166\pi\) |
−0.944891 | + | 0.327384i | \(0.893833\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.92491 | − | 3.42075i | −0.314462 | − | 0.181554i | ||||
\(356\) | −1.26890 | − | 2.19780i | −0.0672517 | − | 0.116483i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.9593 | − | 39.7668i | 1.21344 | − | 2.10174i | ||||
\(359\) | −8.56701 | + | 4.94616i | −0.452149 | + | 0.261049i | −0.708737 | − | 0.705472i | \(-0.750735\pi\) |
0.256588 | + | 0.966521i | \(0.417402\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.52726 | − | 4.37734i | 0.133014 | − | 0.230386i | ||||
\(362\) | −36.8892 | −1.93885 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.9380 | − | 13.2432i | 1.20063 | − | 0.693183i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.0321 | + | 15.6070i | −1.41107 | + | 0.814680i | −0.995489 | − | 0.0948779i | \(-0.969754\pi\) |
−0.415578 | + | 0.909558i | \(0.636421\pi\) | |||||||
\(368\) | 13.7984 | + | 7.96653i | 0.719293 | + | 0.415284i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 11.6376i | − | 0.605011i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5232 | + | 25.1549i | −0.751981 | + | 1.30247i | 0.194881 | + | 0.980827i | \(0.437568\pi\) |
−0.946861 | + | 0.321642i | \(0.895765\pi\) | |||||||
\(374\) | −39.8302 | −2.05957 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 3.50365i | − | 0.180687i | ||||||
\(377\) | −15.5113 | −0.798873 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.518354 | −0.0266261 | −0.0133130 | − | 0.999911i | \(-0.504238\pi\) | ||||
−0.0133130 | + | 0.999911i | \(0.504238\pi\) | |||||||
\(380\) | 37.9963i | 1.94917i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −31.9402 | −1.63420 | ||||||||
\(383\) | −6.60511 | + | 11.4404i | −0.337505 | + | 0.584576i | −0.983963 | − | 0.178374i | \(-0.942916\pi\) |
0.646458 | + | 0.762950i | \(0.276250\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 53.9140i | 2.74415i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 22.2055 | + | 12.8203i | 1.12731 | + | 0.650854i | ||||
\(389\) | −29.2921 | + | 16.9118i | −1.48517 | + | 0.857461i | −0.999857 | − | 0.0168815i | \(-0.994626\pi\) |
−0.485309 | + | 0.874343i | \(0.661293\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.0316 | − | 17.9161i | 1.56933 | − | 0.906055i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.71867 | 0.439240 | ||||||||
\(395\) | −8.27820 | + | 14.3383i | −0.416521 | + | 0.721436i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.42483 | − | 4.28673i | 0.372641 | − | 0.215145i | −0.301970 | − | 0.953317i | \(-0.597644\pi\) |
0.674612 | + | 0.738173i | \(0.264311\pi\) | |||||||
\(398\) | −22.9353 | + | 39.7251i | −1.14964 | + | 1.99124i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.45183 | + | 16.3710i | 0.472591 | + | 0.818552i | ||||
\(401\) | 13.9743 | + | 8.06808i | 0.697844 | + | 0.402900i | 0.806544 | − | 0.591174i | \(-0.201335\pi\) |
−0.108700 | + | 0.994075i | \(0.534669\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.25087 | + | 5.63068i | 0.161938 | + | 0.280484i | ||||
\(404\) | −0.618801 | − | 1.07180i | −0.0307865 | − | 0.0533238i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.89416 | + | 2.24830i | 0.193026 | + | 0.111444i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.3233i | 0.807135i | 0.914950 | + | 0.403568i | \(0.132230\pi\) | ||||
−0.914950 | + | 0.403568i | \(0.867770\pi\) | |||||||
\(410\) | 7.61991i | 0.376320i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.59117 | + | 0.918662i | 0.0783913 | + | 0.0452592i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.45276 | − | 5.98035i | −0.169489 | − | 0.293564i | ||||
\(416\) | −9.86706 | − | 17.0902i | −0.483772 | − | 0.837918i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.5611 | − | 13.6030i | −1.15241 | − | 0.665345i | ||||
\(419\) | 0.589031 | + | 1.02023i | 0.0287760 | + | 0.0498415i | 0.880055 | − | 0.474872i | \(-0.157506\pi\) |
−0.851279 | + | 0.524714i | \(0.824172\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.43544 | − | 5.95035i | 0.167433 | − | 0.290002i | −0.770084 | − | 0.637943i | \(-0.779786\pi\) |
0.937517 | + | 0.347941i | \(0.113119\pi\) | |||||||
\(422\) | −44.3777 | + | 25.6215i | −2.16027 | + | 1.24724i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.70433 | − | 6.41609i | 0.179898 | − | 0.311593i | ||||
\(425\) | 42.5128 | 2.06217 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10.8636 | + | 6.27208i | −0.525110 | + | 0.303172i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −35.0128 | + | 20.2146i | −1.68847 | + | 0.974837i | ||||
\(431\) | −0.702488 | − | 0.405582i | −0.0338377 | − | 0.0195362i | 0.482986 | − | 0.875628i | \(-0.339552\pi\) |
−0.516823 | + | 0.856092i | \(0.672886\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.59662i | − | 0.413127i | −0.978433 | − | 0.206564i | \(-0.933772\pi\) | ||
0.978433 | − | 0.206564i | \(-0.0662280\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.99219 | − | 12.1108i | 0.334865 | − | 0.580004i | ||||
\(437\) | 24.4752 | 1.17081 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.5936i | 1.31697i | 0.752593 | + | 0.658486i | \(0.228803\pi\) | ||||
−0.752593 | + | 0.658486i | \(0.771197\pi\) | |||||||
\(440\) | 6.31186 | 0.300906 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −36.5065 | −1.73643 | ||||||||
\(443\) | − | 12.2457i | − | 0.581812i | −0.956752 | − | 0.290906i | \(-0.906043\pi\) | ||
0.956752 | − | 0.290906i | \(-0.0939567\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.57739 | −0.169585 | ||||||||
\(446\) | 8.80759 | − | 15.2552i | 0.417051 | − | 0.722354i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.0163i | − | 1.03901i | −0.854466 | − | 0.519507i | \(-0.826116\pi\) | ||
0.854466 | − | 0.519507i | \(-0.173884\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.54976 | − | 1.47211i | −0.120064 | − | 0.0693187i | ||||
\(452\) | 23.4488 | − | 13.5382i | 1.10294 | − | 0.636781i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.5226 | + | 6.07522i | −0.493849 | + | 0.285124i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.1559 | 1.12997 | 0.564983 | − | 0.825103i | \(-0.308883\pi\) | ||||
0.564983 | + | 0.825103i | \(0.308883\pi\) | |||||||
\(458\) | 5.00051 | − | 8.66114i | 0.233659 | − | 0.404709i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −33.4812 | + | 19.3304i | −1.56107 | + | 0.901284i | ||||
\(461\) | 16.3899 | − | 28.3881i | 0.763352 | − | 1.32216i | −0.177762 | − | 0.984074i | \(-0.556886\pi\) |
0.941114 | − | 0.338091i | \(-0.109781\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.7659 | + | 27.3074i | 0.732704 | + | 1.26908i | 0.955723 | + | 0.294266i | \(0.0950753\pi\) |
−0.223020 | + | 0.974814i | \(0.571591\pi\) | |||||||
\(464\) | 17.5828 | + | 10.1514i | 0.816259 | + | 0.471267i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.0178 | − | 41.6000i | −1.11260 | − | 1.92708i | ||||
\(467\) | 16.5765 | + | 28.7114i | 0.767070 | + | 1.32860i | 0.939145 | + | 0.343521i | \(0.111620\pi\) |
−0.172075 | + | 0.985084i | \(0.555047\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −29.1213 | − | 16.8132i | −1.34327 | − | 0.775536i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.68626i | 0.169674i | ||||||||
\(473\) | − | 15.6212i | − | 0.718265i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.1480 | + | 14.5192i | 1.15387 | + | 0.666187i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.12364 | − | 12.3385i | −0.325828 | − | 0.564350i | ||||
\(479\) | −11.3972 | − | 19.7406i | −0.520754 | − | 0.901972i | −0.999709 | − | 0.0241323i | \(-0.992318\pi\) |
0.478955 | − | 0.877839i | \(-0.341016\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.56921 | + | 2.06068i | 0.162742 | + | 0.0939590i | ||||
\(482\) | 4.68247 | + | 8.11027i | 0.213281 | + | 0.369413i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.59146 | − | 7.95264i | 0.208703 | − | 0.361484i | ||||
\(485\) | 31.3017 | − | 18.0721i | 1.42134 | − | 0.820611i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.36560 | − | 2.36528i | 0.0618811 | − | 0.107181i | −0.833425 | − | 0.552632i | \(-0.813623\pi\) |
0.895306 | + | 0.445451i | \(0.146957\pi\) | |||||||
\(488\) | −3.68449 | −0.166789 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.6775 | + | 12.5155i | −0.978291 | + | 0.564817i | −0.901754 | − | 0.432250i | \(-0.857720\pi\) |
−0.0765375 | + | 0.997067i | \(0.524387\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.5422 | − | 22.8297i | 1.78089 | − | 1.02820i | ||||
\(494\) | −21.5950 | − | 12.4679i | −0.971605 | − | 0.560957i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.51016i | − | 0.382118i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.29981 | + | 7.44749i | −0.192486 | + | 0.333395i | −0.946073 | − | 0.323952i | \(-0.894988\pi\) |
0.753588 | + | 0.657348i | \(0.228322\pi\) | |||||||
\(500\) | −7.13296 | −0.318996 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.974283i | 0.0434844i | ||||||||
\(503\) | 39.0362 | 1.74054 | 0.870269 | − | 0.492577i | \(-0.163945\pi\) | ||||
0.870269 | + | 0.492577i | \(0.163945\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.74457 | −0.0776325 | ||||||||
\(506\) | − | 27.6818i | − | 1.23061i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 44.7657 | 1.98616 | ||||||||
\(509\) | −16.2909 | + | 28.2167i | −0.722083 | + | 1.25068i | 0.238080 | + | 0.971245i | \(0.423482\pi\) |
−0.960163 | + | 0.279439i | \(0.909851\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 30.4128i | 1.34407i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 38.7845 | + | 22.3922i | 1.71071 | + | 0.987679i | ||||
\(515\) | 2.24298 | − | 1.29498i | 0.0988373 | − | 0.0570638i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.2520 | − | 6.49636i | 0.494864 | − | 0.285710i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.78516 | 0.253696 | ||||||||
\(521\) | 3.68456 | − | 6.38185i | 0.161424 | − | 0.279594i | −0.773956 | − | 0.633240i | \(-0.781725\pi\) |
0.935379 | + | 0.353646i | \(0.115058\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.5991 | − | 21.7078i | 1.64409 | − | 0.949217i | 0.664735 | − | 0.747079i | \(-0.268545\pi\) |
0.979357 | − | 0.202138i | \(-0.0647888\pi\) | |||||||
\(524\) | 4.86594 | − | 8.42806i | 0.212570 | − | 0.368181i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.5571 | + | 20.0175i | 0.503915 | + | 0.872806i | ||||
\(527\) | −16.5746 | − | 9.56933i | −0.722000 | − | 0.416847i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.951610 | + | 1.64824i | 0.0413744 | + | 0.0716625i | ||||
\(530\) | −35.5525 | − | 61.5787i | −1.54430 | − | 2.67481i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.33699 | − | 1.34926i | −0.101226 | − | 0.0584430i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.6827i | 0.764491i | ||||||||
\(536\) | − | 5.97884i | − | 0.258247i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −39.8151 | − | 22.9873i | −1.71655 | − | 0.991052i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.8221 | + | 18.7444i | 0.465278 | + | 0.805884i | 0.999214 | − | 0.0396402i | \(-0.0126212\pi\) |
−0.533936 | + | 0.845525i | \(0.679288\pi\) | |||||||
\(542\) | −4.94434 | − | 8.56385i | −0.212378 | − | 0.367849i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 50.3072 | + | 29.0449i | 2.15690 | + | 1.24529i | ||||
\(545\) | −9.85648 | − | 17.0719i | −0.422205 | − | 0.731281i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.9092 | + | 20.6273i | −0.509200 | + | 0.881960i | 0.490743 | + | 0.871304i | \(0.336725\pi\) |
−0.999943 | + | 0.0106561i | \(0.996608\pi\) | |||||||
\(548\) | 12.7787 | − | 7.37780i | 0.545880 | − | 0.315164i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 16.4214 | − | 28.4428i | 0.700213 | − | 1.21280i | ||||
\(551\) | 31.1877 | 1.32864 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −11.6004 | + | 6.69748i | −0.492852 | + | 0.284548i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.10799 | + | 1.79440i | −0.131808 | + | 0.0760994i | ||||
\(557\) | −9.42040 | − | 5.43887i | −0.399155 | − | 0.230452i | 0.286964 | − | 0.957941i | \(-0.407354\pi\) |
−0.686119 | + | 0.727489i | \(0.740687\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 14.3177i | − | 0.605574i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.5636 | + | 35.6173i | −0.867425 | + | 1.50242i | ||||
\(563\) | 13.3552 | 0.562853 | 0.281427 | − | 0.959583i | \(-0.409192\pi\) | ||||
0.281427 | + | 0.959583i | \(0.409192\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 38.1679i | − | 1.60573i | ||||||
\(566\) | −11.6748 | −0.490729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.48577 | 0.0623415 | ||||||||
\(569\) | 9.63862i | 0.404072i | 0.979378 | + | 0.202036i | \(0.0647558\pi\) | ||||
−0.979378 | + | 0.202036i | \(0.935244\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.4062 | −1.43985 | −0.719926 | − | 0.694050i | \(-0.755824\pi\) | ||||
−0.719926 | + | 0.694050i | \(0.755824\pi\) | |||||||
\(572\) | −7.60951 | + | 13.1801i | −0.318170 | + | 0.551086i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.5462i | 1.23216i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.9017 | − | 12.0676i | −0.870149 | − | 0.502381i | −0.00275107 | − | 0.999996i | \(-0.500876\pi\) |
−0.867398 | + | 0.497616i | \(0.834209\pi\) | |||||||
\(578\) | 62.3780 | − | 36.0140i | 2.59458 | − | 1.49798i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −42.6637 | + | 24.6319i | −1.77151 | + | 1.02278i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.4738 | 1.13785 | ||||||||
\(584\) | −2.87604 | + | 4.98145i | −0.119011 | + | 0.206134i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 54.2935 | − | 31.3464i | 2.24284 | − | 1.29491i | ||||
\(587\) | 3.96848 | − | 6.87362i | 0.163797 | − | 0.283704i | −0.772431 | − | 0.635099i | \(-0.780959\pi\) |
0.936227 | + | 0.351395i | \(0.114293\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.53634 | − | 11.3213i | −0.269325 | − | 0.466485i | ||||
\(590\) | 30.6391 | + | 17.6895i | 1.26139 | + | 0.728266i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.69724 | − | 4.67175i | −0.110856 | − | 0.192008i | ||||
\(593\) | −20.9147 | − | 36.2252i | −0.858862 | − | 1.48759i | −0.873015 | − | 0.487693i | \(-0.837839\pi\) |
0.0141532 | − | 0.999900i | \(-0.495495\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.8580 | + | 6.26889i | 0.444763 | + | 0.256784i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 25.3719i | − | 1.03753i | ||||||
\(599\) | 8.74505i | 0.357313i | 0.983911 | + | 0.178657i | \(0.0571751\pi\) | ||||
−0.983911 | + | 0.178657i | \(0.942825\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.6427 | + | 7.29924i | 0.515705 | + | 0.297742i | 0.735176 | − | 0.677877i | \(-0.237100\pi\) |
−0.219471 | + | 0.975619i | \(0.570433\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.4654 | + | 23.3228i | 0.547900 | + | 0.948990i | ||||
\(605\) | −6.47230 | − | 11.2104i | −0.263137 | − | 0.455766i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.51436 | + | 5.49312i | 0.386176 | + | 0.222959i | 0.680502 | − | 0.732746i | \(-0.261762\pi\) |
−0.294326 | + | 0.955705i | \(0.595095\pi\) | |||||||
\(608\) | 19.8391 | + | 34.3624i | 0.804583 | + | 1.39358i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.6811 | + | 30.6245i | −0.715885 | + | 1.23995i | ||||
\(611\) | 10.3131 | − | 5.95426i | 0.417222 | − | 0.240883i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.9068 | + | 20.6231i | −0.480909 | + | 0.832959i | −0.999760 | − | 0.0219056i | \(-0.993027\pi\) |
0.518851 | + | 0.854865i | \(0.326360\pi\) | |||||||
\(614\) | 48.8763 | 1.97249 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.5255 | − | 21.0880i | 1.47046 | − | 0.848971i | 0.471011 | − | 0.882127i | \(-0.343889\pi\) |
0.999450 | + | 0.0331557i | \(0.0105557\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.6532 | + | 13.0789i | −0.910511 | + | 0.525683i | −0.880595 | − | 0.473869i | \(-0.842857\pi\) |
−0.0299151 | + | 0.999552i | \(0.509524\pi\) | |||||||
\(620\) | 17.8830 | + | 10.3247i | 0.718198 | + | 0.414652i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 34.8290i | 1.39652i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.77434 | − | 16.9297i | 0.390974 | − | 0.677186i | ||||
\(626\) | 30.9885 | 1.23855 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 15.6259i | − | 0.623541i | ||||||
\(629\) | −12.1317 | −0.483724 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.2419 | −0.766009 | −0.383004 | − | 0.923746i | \(-0.625111\pi\) | ||||
−0.383004 | + | 0.923746i | \(0.625111\pi\) | |||||||
\(632\) | − | 3.59556i | − | 0.143024i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.73553 | −0.188072 | ||||||||
\(635\) | 31.5518 | − | 54.6493i | 1.25209 | − | 2.16869i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 35.2738i | − | 1.39650i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.1878 | − | 9.34604i | −0.639879 | − | 0.369435i | ||||
\(641\) | 15.2483 | − | 8.80362i | 0.602272 | − | 0.347722i | −0.167663 | − | 0.985844i | \(-0.553622\pi\) |
0.769935 | + | 0.638122i | \(0.220289\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.1158 | + | 24.8929i | −1.70032 | + | 0.981680i | −0.754893 | + | 0.655848i | \(0.772311\pi\) |
−0.945428 | + | 0.325832i | \(0.894355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 73.4014 | 2.88794 | ||||||||
\(647\) | −5.77035 | + | 9.99454i | −0.226856 | + | 0.392926i | −0.956875 | − | 0.290501i | \(-0.906178\pi\) |
0.730019 | + | 0.683427i | \(0.239511\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.8385 | + | 6.83495i | −0.464701 | + | 0.268295i | ||||
\(650\) | 15.0511 | − | 26.0693i | 0.590354 | − | 1.02252i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −27.0677 | − | 46.8826i | −1.06005 | − | 1.83606i | ||||
\(653\) | 18.2249 | + | 10.5222i | 0.713197 | + | 0.411765i | 0.812244 | − | 0.583318i | \(-0.198246\pi\) |
−0.0990464 | + | 0.995083i | \(0.531579\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.85923 | − | 11.8805i | −0.268012 | − | 0.464211i | ||||
\(656\) | 1.76606 | + | 3.05890i | 0.0689529 | + | 0.119430i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.8016 | + | 18.3607i | 1.23881 | + | 0.715230i | 0.968852 | − | 0.247641i | \(-0.0796555\pi\) |
0.269962 | + | 0.962871i | \(0.412989\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.0731i | 0.897439i | 0.893673 | + | 0.448719i | \(0.148120\pi\) | ||||
−0.893673 | + | 0.448719i | \(0.851880\pi\) | |||||||
\(662\) | − | 24.9049i | − | 0.967957i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.29875 | + | 0.749836i | 0.0504015 | + | 0.0290993i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.8666 | + | 27.4817i | 0.614356 | + | 1.06410i | ||||
\(668\) | −18.6472 | − | 32.2978i | −0.721480 | − | 1.24964i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −49.6945 | − | 28.6911i | −1.91987 | − | 1.10844i | ||||
\(671\) | −6.83168 | − | 11.8328i | −0.263734 | − | 0.456801i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.7594 | − | 42.8846i | 0.954406 | − | 1.65308i | 0.218684 | − | 0.975796i | \(-0.429824\pi\) |
0.735722 | − | 0.677284i | \(-0.236843\pi\) | |||||||
\(674\) | −8.47065 | + | 4.89053i | −0.326277 | + | 0.188376i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.26358 | − | 14.3129i | 0.317830 | − | 0.550498i | ||||
\(677\) | −29.8153 | −1.14590 | −0.572948 | − | 0.819592i | \(-0.694200\pi\) | ||||
−0.572948 | + | 0.819592i | \(0.694200\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −14.7478 | + | 8.51465i | −0.565553 | + | 0.326522i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.8045 | + | 7.39271i | −0.490311 | + | 0.283081i | ||||
\(683\) | 26.1841 | + | 15.1174i | 1.00191 | + | 0.578451i | 0.908812 | − | 0.417207i | \(-0.136991\pi\) |
0.0930943 | + | 0.995657i | \(0.470324\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 20.8001i | − | 0.794731i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.37024 | + | 16.2297i | −0.357237 | + | 0.618753i | ||||
\(689\) | 25.1812 | 0.959328 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.8945i | 1.17528i | 0.809121 | + | 0.587642i | \(0.199944\pi\) | ||||
−0.809121 | + | 0.587642i | \(0.800056\pi\) | |||||||
\(692\) | 43.7496 | 1.66311 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.4159 | 0.585180 | ||||||||
\(695\) | 5.05891i | 0.191896i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.94343 | 0.300879 | ||||||||
\(698\) | −21.7204 | + | 37.6208i | −0.822128 | + | 1.42397i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.757329i | 0.0286039i | 0.999898 | + | 0.0143020i | \(0.00455261\pi\) | ||||
−0.999898 | + | 0.0143020i | \(0.995447\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.17640 | − | 4.14329i | −0.270663 | − | 0.156267i | ||||
\(704\) | 24.1467 | − | 13.9411i | 0.910065 | − | 0.525426i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.8142 | − | 7.39831i | 0.482270 | − | 0.278439i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.5087 | −0.807778 | −0.403889 | − | 0.914808i | \(-0.632342\pi\) | ||||
−0.403889 | + | 0.914808i | \(0.632342\pi\) | |||||||
\(710\) | 7.12988 | − | 12.3493i | 0.267580 | − | 0.463461i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.672819 | − | 0.388452i | 0.0252149 | − | 0.0145579i | ||||
\(713\) | 6.65065 | − | 11.5193i | 0.249069 | − | 0.431400i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.7267 | + | 18.5791i | 0.401155 | + | 0.694820i | ||||
\(716\) | 44.7277 | + | 25.8235i | 1.67155 | + | 0.965071i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.3093 | − | 17.8562i | −0.384740 | − | 0.666389i | ||||
\(719\) | −22.1254 | − | 38.3224i | −0.825140 | − | 1.42918i | −0.901813 | − | 0.432127i | \(-0.857763\pi\) |
0.0766729 | − | 0.997056i | \(-0.475570\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.12371 | + | 5.26758i | 0.339549 | + | 0.196039i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 41.4911i | − | 1.54201i | ||||||
\(725\) | 37.6495i | 1.39827i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.95166 | + | 1.70414i | 0.109471 | + | 0.0632031i | 0.553736 | − | 0.832692i | \(-0.313202\pi\) |
−0.444265 | + | 0.895895i | \(0.646535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 27.6029 | + | 47.8097i | 1.02163 | + | 1.76952i | ||||
\(731\) | 21.0729 | + | 36.4994i | 0.779410 | + | 1.34998i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.46407 | − | 3.15468i | −0.201820 | − | 0.116521i | 0.395684 | − | 0.918387i | \(-0.370508\pi\) |
−0.597504 | + | 0.801866i | \(0.703841\pi\) | |||||||
\(734\) | −32.5298 | − | 56.3432i | −1.20070 | − | 2.07967i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.1861 | + | 34.9633i | −0.744069 | + | 1.28876i | ||||
\(737\) | 19.2012 | − | 11.0858i | 0.707284 | − | 0.408351i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.45388 | − | 4.25024i | 0.0902674 | − | 0.156348i | −0.817356 | − | 0.576133i | \(-0.804561\pi\) |
0.907624 | + | 0.419785i | \(0.137895\pi\) | |||||||
\(740\) | 13.0894 | 0.481177 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.1921 | + | 15.1220i | −0.960895 | + | 0.554773i | −0.896448 | − | 0.443148i | \(-0.853862\pi\) |
−0.0644465 | + | 0.997921i | \(0.520528\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.3059 | − | 8.83688i | 0.560766 | − | 0.323758i | ||||
\(746\) | −52.4304 | − | 30.2707i | −1.91961 | − | 1.10829i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 44.7990i | − | 1.63801i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0321 | − | 43.3569i | 0.913435 | − | 1.58212i | 0.104257 | − | 0.994550i | \(-0.466753\pi\) |
0.809177 | − | 0.587565i | \(-0.199913\pi\) | |||||||
\(752\) | −15.5871 | −0.568403 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 32.3303i | − | 1.17740i | ||||||
\(755\) | 37.9628 | 1.38161 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.2695 | 1.35458 | 0.677291 | − | 0.735716i | \(-0.263154\pi\) | ||||
0.677291 | + | 0.735716i | \(0.263154\pi\) | |||||||
\(758\) | − | 1.08041i | − | 0.0392422i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.6319 | −0.421933 | ||||||||
\(761\) | 5.27174 | − | 9.13092i | 0.191100 | − | 0.330996i | −0.754515 | − | 0.656283i | \(-0.772128\pi\) |
0.945615 | + | 0.325287i | \(0.105461\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 35.9248i | − | 1.29971i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.8452 | − | 13.7671i | −0.861563 | − | 0.497424i | ||||
\(767\) | −10.8506 | + | 6.26459i | −0.391792 | + | 0.226201i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.4720 | + | 7.20070i | −0.449751 | + | 0.259664i | −0.707725 | − | 0.706488i | \(-0.750278\pi\) |
0.257974 | + | 0.966152i | \(0.416945\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −60.6398 | −2.18247 | ||||||||
\(773\) | 10.9386 | − | 18.9462i | 0.393433 | − | 0.681446i | −0.599467 | − | 0.800400i | \(-0.704621\pi\) |
0.992900 | + | 0.118954i | \(0.0379541\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.6669 | − | 7.89062i | 0.490931 | − | 0.283439i | ||||
\(776\) | −3.92472 | + | 6.79781i | −0.140889 | + | 0.244027i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.2493 | − | 61.0536i | −1.26375 | − | 2.18888i | ||||
\(779\) | 4.69885 | + | 2.71288i | 0.168354 | + | 0.0971992i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.75487 | + | 4.77158i | 0.0985771 | + | 0.170740i | ||||
\(782\) | 37.3425 | + | 64.6792i | 1.33537 | + | 2.31292i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.0759 | − | 11.0135i | −0.680847 | − | 0.393087i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 27.6901i | − | 0.987046i | −0.869733 | − | 0.493523i | \(-0.835709\pi\) | ||
0.869733 | − | 0.493523i | \(-0.164291\pi\) | |||||||
\(788\) | 9.80633i | 0.349336i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −29.8853 | − | 17.2543i | −1.06327 | − | 0.613880i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.26160 | − | 10.8454i | −0.222356 | − | 0.385132i | ||||
\(794\) | 8.93484 | + | 15.4756i | 0.317086 | + | 0.549208i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −44.6809 | − | 25.7965i | −1.58367 | − | 0.914334i | ||||
\(797\) | −21.3285 | − | 36.9420i | −0.755493 | − | 1.30855i | −0.945129 | − | 0.326697i | \(-0.894064\pi\) |
0.189636 | − | 0.981854i | \(-0.439269\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.5271 | + | 30.3578i | −0.620063 | + | 1.07398i | ||||
\(800\) | −41.4820 | + | 23.9496i | −1.46661 | + | 0.846747i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.8163 | + | 29.1267i | −0.593805 | + | 1.02850i | ||||
\(803\) | −21.3307 | −0.752743 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.7360 | + | 6.77581i | −0.413384 | + | 0.238668i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.328111 | − | 0.189435i | 0.0115429 | − | 0.00666430i | ||||
\(809\) | 30.9391 | + | 17.8627i | 1.08776 | + | 0.628019i | 0.932979 | − | 0.359930i | \(-0.117199\pi\) |
0.154781 | + | 0.987949i | \(0.450533\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.85377i | − | 0.205554i | −0.994704 | − | 0.102777i | \(-0.967227\pi\) | ||
0.994704 | − | 0.102777i | \(-0.0327728\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.68613 | + | 8.11662i | −0.164249 | + | 0.284487i | ||||
\(815\) | −76.3113 | −2.67307 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.7878i | 1.00716i | ||||||||
\(818\) | −34.0227 | −1.18958 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.57050 | −0.299295 | ||||||||
\(821\) | 17.5768i | 0.613436i | 0.951801 | + | 0.306718i | \(0.0992308\pi\) | ||||
−0.951801 | + | 0.306718i | \(0.900769\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.3785 | 1.05893 | 0.529465 | − | 0.848332i | \(-0.322393\pi\) | ||||
0.529465 | + | 0.848332i | \(0.322393\pi\) | |||||||
\(824\) | −0.281232 | + | 0.487108i | −0.00979717 | + | 0.0169692i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.4454i | 0.537089i | 0.963267 | + | 0.268545i | \(0.0865426\pi\) | ||||
−0.963267 | + | 0.268545i | \(0.913457\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.4158 | + | 20.4473i | 1.23004 | + | 0.710164i | 0.967038 | − | 0.254631i | \(-0.0819540\pi\) |
0.263002 | + | 0.964795i | \(0.415287\pi\) | |||||||
\(830\) | 12.4649 | − | 7.19659i | 0.432662 | − | 0.249797i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 22.1318 | − | 12.7778i | 0.767281 | − | 0.442990i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −52.5716 | −1.81931 | ||||||||
\(836\) | 15.3000 | − | 26.5004i | 0.529162 | − | 0.916535i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.12647 | + | 1.22772i | −0.0734577 | + | 0.0424108i | ||||
\(839\) | −16.8620 | + | 29.2058i | −0.582140 | + | 1.00830i | 0.413086 | + | 0.910692i | \(0.364451\pi\) |
−0.995225 | + | 0.0976035i | \(0.968882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.71808 | + | 9.90401i | 0.197175 | + | 0.341517i | ||||
\(842\) | 12.4023 | + | 7.16049i | 0.427413 | + | 0.246767i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28.8178 | − | 49.9139i | −0.991950 | − | 1.71811i | ||||
\(845\) | −11.6487 | − | 20.1761i | −0.400726 | − | 0.694079i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −28.5440 | − | 16.4799i | −0.980206 | − | 0.565922i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 88.6096i | 3.03928i | ||||||||
\(851\) | − | 8.43151i | − | 0.289028i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.6715 | − | 21.7497i | −1.28985 | − | 0.744694i | −0.311221 | − | 0.950337i | \(-0.600738\pi\) |
−0.978627 | + | 0.205643i | \(0.934071\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.92008 | − | 3.32568i | −0.0656271 | − | 0.113669i | ||||
\(857\) | −4.21534 | − | 7.30118i | −0.143993 | − | 0.249404i | 0.785004 | − | 0.619491i | \(-0.212661\pi\) |
−0.928997 | + | 0.370088i | \(0.879328\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.07929 | + | 1.20048i | 0.0709445 | + | 0.0409598i | 0.535053 | − | 0.844819i | \(-0.320292\pi\) |
−0.464108 | + | 0.885779i | \(0.653625\pi\) | |||||||
\(860\) | −22.7364 | − | 39.3807i | −0.775306 | − | 1.34287i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.845356 | − | 1.46420i | 0.0287929 | − | 0.0498708i | ||||
\(863\) | −8.12017 | + | 4.68818i | −0.276414 | + | 0.159588i | −0.631799 | − | 0.775132i | \(-0.717683\pi\) |
0.355385 | + | 0.934720i | \(0.384350\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.8356 | − | 53.4089i | 1.04844 | − | 1.81596i | ||||
\(866\) | 17.9180 | 0.608877 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.5472 | − | 6.66678i | 0.391712 | − | 0.226155i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.5989 | − | 10.1607i | 0.596316 | − | 0.344283i | ||||
\(872\) | 3.70751 | + | 2.14053i | 0.125552 | + | 0.0724877i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 51.0137i | 1.72557i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.71542 | + | 2.97119i | −0.0579256 | + | 0.100330i | −0.893534 | − | 0.448995i | \(-0.851782\pi\) |
0.835608 | + | 0.549326i | \(0.185115\pi\) | |||||||
\(878\) | −57.5135 | −1.94099 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 28.0804i | − | 0.946589i | ||||||
\(881\) | 43.4962 | 1.46542 | 0.732712 | − | 0.680539i | \(-0.238254\pi\) | ||||
0.732712 | + | 0.680539i | \(0.238254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.6074 | 1.66942 | 0.834711 | − | 0.550688i | \(-0.185635\pi\) | ||||
0.834711 | + | 0.550688i | \(0.185635\pi\) | |||||||
\(884\) | − | 41.0607i | − | 1.38102i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.5238 | 0.857489 | ||||||||
\(887\) | −17.5766 | + | 30.4436i | −0.590164 | + | 1.02219i | 0.404045 | + | 0.914739i | \(0.367604\pi\) |
−0.994210 | + | 0.107456i | \(0.965730\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 7.45638i | − | 0.249938i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.1583 | + | 9.90634i | 0.574502 | + | 0.331689i | ||||
\(893\) | −20.7359 | + | 11.9719i | −0.693901 | + | 0.400624i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 63.0500 | − | 36.4019i | 2.10753 | − | 1.21678i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 45.8887 | 1.53132 | ||||||||
\(899\) | 8.47464 | − | 14.6785i | 0.282645 | − | 0.489556i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −64.1932 | + | 37.0620i | −2.13859 | + | 1.23471i | ||||
\(902\) | 3.06832 | − | 5.31448i | 0.102164 | − | 0.176953i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.14446 | + | 7.17842i | 0.137843 | + | 0.238751i | ||||
\(905\) | −50.6517 | − | 29.2438i | −1.68372 | − | 0.972097i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.0816 | − | 33.0504i | −0.633596 | − | 1.09742i | −0.986811 | − | 0.161878i | \(-0.948245\pi\) |
0.353215 | − | 0.935542i | \(-0.385088\pi\) | |||||||
\(908\) | −6.83310 | − | 11.8353i | −0.226765 | − | 0.392768i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.9027 | + | 23.0378i | 1.32203 | + | 0.763277i | 0.984053 | − | 0.177876i | \(-0.0569226\pi\) |
0.337981 | + | 0.941153i | \(0.390256\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.56130i | 0.184052i | ||||||||
\(914\) | 50.3482i | 1.66537i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.74163 | + | 5.62433i | 0.321872 | + | 0.185833i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.27574 | − | 9.13785i | −0.174031 | − | 0.301430i | 0.765795 | − | 0.643085i | \(-0.222346\pi\) |
−0.939825 | + | 0.341655i | \(0.889013\pi\) | |||||||
\(920\) | −5.91765 | − | 10.2497i | −0.195099 | − | 0.337922i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 59.1694 | + | 34.1615i | 1.94864 | + | 1.12505i | ||||
\(923\) | 2.52499 | + | 4.37340i | 0.0831109 | + | 0.143952i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.00175 | − | 8.66328i | 0.164456 | − | 0.284847i | ||||
\(926\) | −56.9168 | + | 32.8609i | −1.87040 | + | 1.07988i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −25.7223 | + | 44.5523i | −0.844375 | + | 1.46250i | ||||
\(929\) | 52.9029 | 1.73569 | 0.867843 | − | 0.496838i | \(-0.165506\pi\) | ||||
0.867843 | + | 0.496838i | \(0.165506\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 46.7896 | − | 27.0140i | 1.53265 | − | 0.884873i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −59.8433 | + | 34.5505i | −1.95813 | + | 1.13053i | ||||
\(935\) | −54.6899 | − | 31.5752i | −1.78855 | − | 1.03262i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.3265i | 0.337353i | 0.985671 | + | 0.168676i | \(0.0539493\pi\) | ||||
−0.985671 | + | 0.168676i | \(0.946051\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18.9107 | − | 32.7543i | 0.616798 | − | 1.06833i | ||||
\(941\) | −1.01067 | −0.0329470 | −0.0164735 | − | 0.999864i | \(-0.505244\pi\) | ||||
−0.0164735 | + | 0.999864i | \(0.505244\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.52066i | 0.179777i | ||||||||
\(944\) | 16.3995 | 0.533758 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.5594 | 1.05860 | ||||||||
\(947\) | 10.8132i | 0.351383i | 0.984445 | + | 0.175692i | \(0.0562162\pi\) | ||||
−0.984445 | + | 0.175692i | \(0.943784\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.5507 | −0.634642 | ||||||||
\(950\) | −30.2624 | + | 52.4161i | −0.981843 | + | 1.70060i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 26.7466i | − | 0.866408i | −0.901296 | − | 0.433204i | \(-0.857383\pi\) | ||
0.901296 | − | 0.433204i | \(-0.142617\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −43.8564 | − | 25.3205i | −1.41916 | − | 0.819353i | ||||
\(956\) | 13.8777 | − | 8.01232i | 0.448838 | − | 0.259137i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 41.1454 | − | 23.7553i | 1.32935 | − | 0.767500i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.8955 | 0.770823 | ||||||||
\(962\) | −4.29509 | + | 7.43931i | −0.138479 | + | 0.239853i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.12204 | + | 5.26661i | −0.293801 | + | 0.169626i | ||||
\(965\) | −42.7402 | + | 74.0281i | −1.37585 | + | 2.38305i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.62313 | + | 2.81134i | 0.0521962 | + | 0.0904065i | 0.890943 | − | 0.454115i | \(-0.150045\pi\) |
−0.838747 | + | 0.544522i | \(0.816711\pi\) | |||||||
\(968\) | 2.43456 | + | 1.40559i | 0.0782497 | + | 0.0451775i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 37.6677 | + | 65.2424i | 1.20944 | + | 2.09481i | ||||
\(971\) | 4.41423 | + | 7.64567i | 0.141659 | + | 0.245361i | 0.928122 | − | 0.372277i | \(-0.121423\pi\) |
−0.786462 | + | 0.617638i | \(0.788090\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.92997 | + | 2.84632i | 0.157966 | + | 0.0912019i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16.3917i | 0.524685i | ||||||||
\(977\) | − | 41.8866i | − | 1.34007i | −0.742330 | − | 0.670035i | \(-0.766279\pi\) | ||
0.742330 | − | 0.670035i | \(-0.233721\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.49504 | + | 1.44051i | 0.0797419 | + | 0.0460390i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.0861 | − | 45.1825i | −0.832441 | − | 1.44183i | ||||
\(983\) | −2.35194 | − | 4.07368i | −0.0750153 | − | 0.129930i | 0.826078 | − | 0.563556i | \(-0.190567\pi\) |
−0.901093 | + | 0.433626i | \(0.857234\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.9714 | + | 6.91170i | 0.381441 | + | 0.220225i | ||||
\(986\) | 47.5840 | + | 82.4179i | 1.51538 | + | 2.62472i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.0233 | − | 24.2890i | 0.446139 | − | 0.772736i | ||||
\(989\) | −25.3669 | + | 14.6456i | −0.806621 | + | 0.465703i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.9327 | + | 32.7924i | −0.601418 | + | 1.04169i | 0.391189 | + | 0.920310i | \(0.372064\pi\) |
−0.992607 | + | 0.121375i | \(0.961269\pi\) | |||||||
\(992\) | 21.5636 | 0.684644 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −62.9840 | + | 36.3638i | −1.99673 | + | 1.15281i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.18336 | − | 1.83791i | 0.100818 | − | 0.0582073i | −0.448743 | − | 0.893661i | \(-0.648128\pi\) |
0.549561 | + | 0.835453i | \(0.314795\pi\) | |||||||
\(998\) | −15.5228 | − | 8.96211i | −0.491367 | − | 0.283691i | ||||
\(999\) | 0 | 0 |
(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 | 1323.2.i.d.521.23 | 48 | ||
3.2 | odd | 2 | 441.2.i.d.227.3 | 48 | |||
7.2 | even | 3 | 1323.2.s.d.656.22 | 48 | |||
7.3 | odd | 6 | 1323.2.o.e.440.4 | 48 | |||
7.4 | even | 3 | 1323.2.o.e.440.3 | 48 | |||
7.5 | odd | 6 | 1323.2.s.d.656.21 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.i.d.521.16 | 48 | ||
9.4 | even | 3 | 441.2.s.d.374.3 | 48 | |||
9.5 | odd | 6 | 1323.2.s.d.962.21 | 48 | |||
21.2 | odd | 6 | 441.2.s.d.362.4 | 48 | |||
21.5 | even | 6 | 441.2.s.d.362.3 | 48 | |||
21.11 | odd | 6 | 441.2.o.e.146.21 | ✓ | 48 | ||
21.17 | even | 6 | 441.2.o.e.146.22 | yes | 48 | ||
21.20 | even | 2 | 441.2.i.d.227.4 | 48 | |||
63.4 | even | 3 | 441.2.o.e.293.22 | yes | 48 | ||
63.5 | even | 6 | inner | 1323.2.i.d.1097.23 | 48 | ||
63.13 | odd | 6 | 441.2.s.d.374.4 | 48 | |||
63.23 | odd | 6 | inner | 1323.2.i.d.1097.16 | 48 | ||
63.31 | odd | 6 | 441.2.o.e.293.21 | yes | 48 | ||
63.32 | odd | 6 | 1323.2.o.e.881.4 | 48 | |||
63.40 | odd | 6 | 441.2.i.d.68.21 | 48 | |||
63.41 | even | 6 | 1323.2.s.d.962.22 | 48 | |||
63.58 | even | 3 | 441.2.i.d.68.22 | 48 | |||
63.59 | even | 6 | 1323.2.o.e.881.3 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.21 | 48 | 63.40 | odd | 6 | |||
441.2.i.d.68.22 | 48 | 63.58 | even | 3 | |||
441.2.i.d.227.3 | 48 | 3.2 | odd | 2 | |||
441.2.i.d.227.4 | 48 | 21.20 | even | 2 | |||
441.2.o.e.146.21 | ✓ | 48 | 21.11 | odd | 6 | ||
441.2.o.e.146.22 | yes | 48 | 21.17 | even | 6 | ||
441.2.o.e.293.21 | yes | 48 | 63.31 | odd | 6 | ||
441.2.o.e.293.22 | yes | 48 | 63.4 | even | 3 | ||
441.2.s.d.362.3 | 48 | 21.5 | even | 6 | |||
441.2.s.d.362.4 | 48 | 21.2 | odd | 6 | |||
441.2.s.d.374.3 | 48 | 9.4 | even | 3 | |||
441.2.s.d.374.4 | 48 | 63.13 | odd | 6 | |||
1323.2.i.d.521.16 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.i.d.521.23 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.i.d.1097.16 | 48 | 63.23 | odd | 6 | inner | ||
1323.2.i.d.1097.23 | 48 | 63.5 | even | 6 | inner | ||
1323.2.o.e.440.3 | 48 | 7.4 | even | 3 | |||
1323.2.o.e.440.4 | 48 | 7.3 | odd | 6 | |||
1323.2.o.e.881.3 | 48 | 63.59 | even | 6 | |||
1323.2.o.e.881.4 | 48 | 63.32 | odd | 6 | |||
1323.2.s.d.656.21 | 48 | 7.5 | odd | 6 | |||
1323.2.s.d.656.22 | 48 | 7.2 | even | 3 | |||
1323.2.s.d.962.21 | 48 | 9.5 | odd | 6 | |||
1323.2.s.d.962.22 | 48 | 63.41 | even | 6 |