Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [512,2,Mod(17,512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(512, base_ring=CyclotomicField(32))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("512.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 512 = 2^{9} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 512.k (of order \(32\), degree \(16\), 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: | \(4.08834058349\) |
Analytic rank: | \(0\) |
Dimension: | \(240\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{32})\) |
Twist minimal: | no (minimal twist has level 128) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{32}]$ |
Embedding invariants
Embedding label | 497.2 | ||
Character | \(\chi\) | \(=\) | 512.497 |
Dual form | 512.2.k.a.273.2 |
$q$-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 \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{9}{32}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.34878 | + | 1.25545i | −1.35607 | + | 0.724835i | −0.979479 | − | 0.201545i | \(-0.935404\pi\) |
−0.376591 | + | 0.926380i | \(0.622904\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.35055 | − | 2.86416i | −1.05120 | − | 1.28089i | −0.958468 | − | 0.285200i | \(-0.907940\pi\) |
−0.0927320 | − | 0.995691i | \(-0.529560\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.77512 | − | 1.18610i | 0.670932 | − | 0.448302i | −0.172879 | − | 0.984943i | \(-0.555307\pi\) |
0.843811 | + | 0.536641i | \(0.180307\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.27391 | − | 3.40315i | 0.757971 | − | 1.13438i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00424 | + | 0.911326i | −0.905812 | + | 0.274775i | −0.708621 | − | 0.705590i | \(-0.750682\pi\) |
−0.197192 | + | 0.980365i | \(0.563182\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.40033 | + | 3.61126i | 1.22043 | + | 1.00158i | 0.999655 | + | 0.0262590i | \(0.00835946\pi\) |
0.220777 | + | 0.975324i | \(0.429141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.11675 | + | 3.77628i | 2.35394 | + | 0.975032i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.12200 | + | 0.878960i | −0.514660 | + | 0.213179i | −0.624869 | − | 0.780729i | \(-0.714848\pi\) |
0.110210 | + | 0.993908i | \(0.464848\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.222958 | + | 2.26373i | 0.0511500 | + | 0.519334i | 0.986286 | + | 0.165045i | \(0.0527771\pi\) |
−0.935136 | + | 0.354289i | \(0.884723\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.68028 | + | 5.01446i | −0.584886 | + | 1.09424i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.14830 | + | 0.825148i | −0.864981 | + | 0.172055i | −0.607589 | − | 0.794252i | \(-0.707863\pi\) |
−0.257392 | + | 0.966307i | \(0.582863\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.70285 | + | 8.56080i | −0.340570 | + | 1.71216i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.285305 | + | 2.89675i | −0.0549069 | + | 0.557480i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.05879 | + | 3.49035i | −0.196612 | + | 0.648142i | 0.802090 | + | 0.597203i | \(0.203721\pi\) |
−0.998702 | + | 0.0509386i | \(0.983779\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.733820 | + | 0.733820i | 0.131798 | + | 0.131798i | 0.769928 | − | 0.638130i | \(-0.220292\pi\) |
−0.638130 | + | 0.769928i | \(0.720292\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.91218 | − | 5.91218i | 1.02918 | − | 1.02918i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.56968 | − | 2.29624i | −1.27951 | − | 0.388135i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.40268 | + | 0.138152i | 0.230600 | + | 0.0227121i | 0.212657 | − | 0.977127i | \(-0.431788\pi\) |
0.0179429 | + | 0.999839i | \(0.494288\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.8692 | − | 2.95766i | −2.38097 | − | 0.473605i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.67780 | + | 8.43488i | 0.262028 | + | 1.31731i | 0.857730 | + | 0.514100i | \(0.171874\pi\) |
−0.595702 | + | 0.803206i | \(0.703126\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.27833 | + | 1.21779i | 0.347442 | + | 0.185711i | 0.635882 | − | 0.771787i | \(-0.280637\pi\) |
−0.288440 | + | 0.957498i | \(0.593137\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −15.0921 | + | 1.48644i | −2.24980 | + | 0.221586i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.22422 | + | 10.1982i | 0.616166 | + | 1.48756i | 0.856123 | + | 0.516772i | \(0.172867\pi\) |
−0.239957 | + | 0.970783i | \(0.577133\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.934561 | + | 2.25623i | −0.133509 | + | 0.322319i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.88062 | − | 4.72855i | 0.543395 | − | 0.662129i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.810406 | − | 2.67155i | −0.111318 | − | 0.366966i | 0.883526 | − | 0.468381i | \(-0.155163\pi\) |
−0.994844 | + | 0.101416i | \(0.967663\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.67181 | + | 6.46250i | 1.30415 | + | 0.871403i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.36567 | − | 5.03709i | −0.445794 | − | 0.667179i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.48788 | − | 5.32446i | 0.844650 | − | 0.693186i | −0.109021 | − | 0.994039i | \(-0.534771\pi\) |
0.953670 | + | 0.300853i | \(0.0972715\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.18727 | + | 7.83384i | 0.536125 | + | 1.00302i | 0.993509 | + | 0.113751i | \(0.0362866\pi\) |
−0.457384 | + | 0.889269i | \(0.651213\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 8.73808i | − | 1.10089i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 21.0917i | − | 2.61611i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.02445 | − | 1.91661i | −0.125157 | − | 0.234152i | 0.811537 | − | 0.584300i | \(-0.198631\pi\) |
−0.936694 | + | 0.350149i | \(0.886131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.70752 | − | 7.14608i | 1.04826 | − | 0.860287i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.85914 | + | 7.27222i | 0.576674 | + | 0.863053i | 0.999059 | − | 0.0433628i | \(-0.0138071\pi\) |
−0.422386 | + | 0.906416i | \(0.638807\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.35312 | − | 6.24955i | −1.09470 | − | 0.731455i | −0.129137 | − | 0.991627i | \(-0.541221\pi\) |
−0.965562 | + | 0.260172i | \(0.916221\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.74804 | − | 22.2453i | −0.779196 | − | 2.56867i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.25196 | + | 5.18103i | −0.484556 | + | 0.590433i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50619 | − | 3.63626i | 0.169459 | − | 0.409111i | −0.816220 | − | 0.577741i | \(-0.803934\pi\) |
0.985679 | + | 0.168630i | \(0.0539343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.73229 | + | 4.18212i | 0.192477 | + | 0.464680i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.375929 | − | 0.0370258i | 0.0412636 | − | 0.00406411i | −0.0773643 | − | 0.997003i | \(-0.524650\pi\) |
0.118628 | + | 0.992939i | \(0.462150\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.50535 | + | 4.01169i | 0.814070 | + | 0.435129i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.89510 | − | 9.52732i | −0.203176 | − | 1.02144i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.47983 | + | 1.09001i | 0.580861 | + | 0.115540i | 0.476771 | − | 0.879028i | \(-0.341807\pi\) |
0.104090 | + | 0.994568i | \(0.466807\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0944 | + | 1.19120i | 1.26784 | + | 0.124871i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.64486 | − | 0.802308i | −0.274259 | − | 0.0831955i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.95960 | − | 5.95960i | 0.611442 | − | 0.611442i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.20900 | − | 4.20900i | −0.427359 | − | 0.427359i | 0.460369 | − | 0.887728i | \(-0.347717\pi\) |
−0.887728 | + | 0.460369i | \(0.847717\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.73000 | + | 12.2962i | −0.374879 | + | 1.23581i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.26435 | + | 12.8372i | −0.125808 | + | 1.27735i | 0.700306 | + | 0.713843i | \(0.253047\pi\) |
−0.826114 | + | 0.563503i | \(0.809453\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.03672 | − | 5.21196i | 0.102151 | − | 0.513550i | −0.895500 | − | 0.445061i | \(-0.853182\pi\) |
0.997652 | − | 0.0684892i | \(-0.0218179\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 20.6624 | − | 4.11000i | 2.01644 | − | 0.401095i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.69560 | + | 14.3975i | −0.743962 | + | 1.39185i | 0.169749 | + | 0.985487i | \(0.445704\pi\) |
−0.913710 | + | 0.406367i | \(0.866796\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.12768 | − | 11.4495i | −0.108012 | − | 1.09666i | −0.884503 | − | 0.466535i | \(-0.845502\pi\) |
0.776491 | − | 0.630129i | \(-0.216998\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.46805 | + | 1.43651i | −0.329172 | + | 0.136348i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.2154 | − | 5.88823i | −1.33728 | − | 0.553918i | −0.404554 | − | 0.914514i | \(-0.632573\pi\) |
−0.932722 | + | 0.360596i | \(0.882573\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.1142 | + | 9.94184i | 1.12965 | + | 0.927081i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 22.2956 | − | 6.76331i | 2.06123 | − | 0.625268i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.72427 | + | 4.07715i | −0.249733 | + | 0.373752i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.951224 | + | 0.635587i | −0.0864749 | + | 0.0577807i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.5304 | − | 17.7053i | −1.31016 | − | 1.59643i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1837 | − | 6.51230i | 1.08974 | − | 0.582478i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.24212 | −0.465163 | −0.232582 | − | 0.972577i | \(-0.574717\pi\) | ||||
−0.232582 | + | 0.972577i | \(0.574717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.88017 | −0.605765 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.27431 | − | 1.75016i | 0.286078 | − | 0.152912i | −0.322116 | − | 0.946700i | \(-0.604394\pi\) |
0.608194 | + | 0.793788i | \(0.291894\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.08077 | + | 3.75393i | 0.267137 | + | 0.325507i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.96738 | − | 5.99181i | 0.771789 | − | 0.515693i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.16098 | − | 6.22734i | 0.355496 | − | 0.532038i | −0.610018 | − | 0.792388i | \(-0.708838\pi\) |
0.965514 | + | 0.260350i | \(0.0838378\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.39432 | + | 1.63635i | −0.457541 | + | 0.138793i | −0.510638 | − | 0.859796i | \(-0.670591\pi\) |
0.0530972 | + | 0.998589i | \(0.483091\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.7251 | − | 18.6500i | −1.91380 | − | 1.57061i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.5107 | − | 6.83895i | −1.38069 | − | 0.571902i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.4856 | − | 5.17173i | 1.03688 | − | 0.429488i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.637504 | − | 6.47269i | −0.0525805 | − | 0.533858i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.95792 | − | 9.27561i | 0.406168 | − | 0.759887i | −0.592798 | − | 0.805351i | \(-0.701977\pi\) |
0.998966 | + | 0.0454640i | \(0.0144766\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0126 | + | 3.18511i | −1.30309 | + | 0.259200i | −0.797366 | − | 0.603496i | \(-0.793774\pi\) |
−0.505722 | + | 0.862697i | \(0.668774\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.83400 | + | 9.22015i | −0.148270 | + | 0.745405i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.376893 | − | 3.82666i | 0.0302728 | − | 0.307365i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.96267 | + | 9.76661i | −0.236447 | + | 0.779461i | 0.755759 | + | 0.654850i | \(0.227268\pi\) |
−0.992206 | + | 0.124611i | \(0.960232\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.25746 | + | 5.25746i | 0.416944 | + | 0.416944i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.38502 | + | 6.38502i | −0.503210 | + | 0.503210i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.5566 | − | 4.71903i | −1.21848 | − | 0.369623i | −0.385390 | − | 0.922754i | \(-0.625933\pi\) |
−0.833095 | + | 0.553131i | \(0.813433\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −30.8303 | − | 3.03652i | −2.40014 | − | 0.236393i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.4273 | + | 3.46651i | 1.34857 | + | 0.268246i | 0.815956 | − | 0.578115i | \(-0.196211\pi\) |
0.532610 | + | 0.846361i | \(0.321211\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.78556 | + | 19.0313i | 0.291197 | + | 1.46394i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.21079 | + | 4.38876i | 0.627895 | + | 0.335617i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.62158 | + | 0.455186i | −0.351372 | + | 0.0346072i | −0.272164 | − | 0.962251i | \(-0.587739\pi\) |
−0.0792085 | + | 0.996858i | \(0.525239\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.13118 | + | 17.2162i | 0.539066 | + | 1.30142i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.55401 | + | 20.6512i | −0.642959 | + | 1.55224i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.15470 | + | 5.06252i | −0.310537 | + | 0.378391i | −0.904769 | − | 0.425903i | \(-0.859956\pi\) |
0.594231 | + | 0.804294i | \(0.297456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.19266 | − | 3.93167i | −0.0886497 | − | 0.292239i | 0.901394 | − | 0.433000i | \(-0.142545\pi\) |
−0.990044 | + | 0.140761i | \(0.955045\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.6700 | − | 13.1431i | −1.45405 | − | 0.971563i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.90140 | − | 4.34225i | −0.213315 | − | 0.319248i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.57397 | − | 4.57444i | 0.407609 | − | 0.334516i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.92937 | + | 5.48047i | 0.213081 | + | 0.398646i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 16.4545i | − | 1.19061i | −0.803500 | − | 0.595304i | \(-0.797032\pi\) | ||
0.803500 | − | 0.595304i | \(-0.202968\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0562i | 0.939805i | 0.882718 | + | 0.469903i | \(0.155711\pi\) | ||||
−0.882718 | + | 0.469903i | \(0.844289\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 26.4796 | + | 49.5399i | 1.89624 | + | 3.54762i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.7091 | − | 9.60941i | 0.834239 | − | 0.684642i | −0.116988 | − | 0.993133i | \(-0.537324\pi\) |
0.951227 | + | 0.308491i | \(0.0998239\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.43353 | + | 5.13863i | 0.243396 | + | 0.364268i | 0.932974 | − | 0.359943i | \(-0.117204\pi\) |
−0.689578 | + | 0.724211i | \(0.742204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.81243 | + | 3.21556i | 0.339442 | + | 0.226808i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.26042 | + | 7.45161i | 0.158650 | + | 0.523000i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.2151 | − | 24.6321i | 1.41188 | − | 1.72038i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.62477 | + | 15.9936i | −0.460453 | + | 1.11163i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.73281 | − | 6.59759i | −0.189032 | − | 0.456365i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.5935 | + | 1.73281i | −1.21119 | + | 0.119291i | −0.683373 | − | 0.730069i | \(-0.739488\pi\) |
−0.527813 | + | 0.849361i | \(0.676988\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.5430 | − | 10.9804i | −1.40758 | − | 0.752368i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.86738 | − | 9.38797i | −0.127355 | − | 0.640255i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.17300 | + | 0.432236i | 0.147513 | + | 0.0293421i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 29.8144 | + | 2.93647i | 2.01467 | + | 0.198428i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.5116 | − | 3.79537i | −0.841624 | − | 0.255304i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.16002 | + | 2.16002i | −0.144646 | + | 0.144646i | −0.775721 | − | 0.631076i | \(-0.782614\pi\) |
0.631076 | + | 0.775721i | \(0.282614\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 25.2616 | + | 25.2616i | 1.68410 | + | 1.68410i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.185477 | − | 0.611434i | 0.0123105 | − | 0.0405823i | −0.950570 | − | 0.310511i | \(-0.899500\pi\) |
0.962880 | + | 0.269928i | \(0.0870000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.56897 | + | 15.9300i | −0.103680 | + | 1.05268i | 0.792765 | + | 0.609528i | \(0.208641\pi\) |
−0.896445 | + | 0.443155i | \(0.853859\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.48241 | − | 17.5072i | 0.229126 | − | 1.15189i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.7807 | + | 3.33790i | −1.09934 | + | 0.218673i | −0.711244 | − | 0.702945i | \(-0.751868\pi\) |
−0.388098 | + | 0.921618i | \(0.626868\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.2799 | − | 36.0702i | 1.25768 | − | 2.35296i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.02744 | + | 10.4317i | 0.0667391 | + | 0.677614i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.5753 | − | 6.03728i | 0.942796 | − | 0.390519i | 0.142277 | − | 0.989827i | \(-0.454557\pi\) |
0.800519 | + | 0.599308i | \(0.204557\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.4975 | + | 9.73297i | 1.51361 | + | 0.626956i | 0.976298 | − | 0.216430i | \(-0.0694415\pi\) |
0.537307 | + | 0.843386i | \(0.319441\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.0694 | − | 13.1878i | −1.03085 | − | 0.845997i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.65894 | − | 2.62666i | 0.553199 | − | 0.167811i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.19381 | + | 10.7663i | −0.457731 | + | 0.685044i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.836491 | + | 0.558926i | −0.0530105 | + | 0.0354205i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.7570 | + | 19.1999i | 0.994571 | + | 1.21189i | 0.977261 | + | 0.212038i | \(0.0680101\pi\) |
0.0173097 | + | 0.999850i | \(0.494490\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.7105 | − | 6.25940i | 0.736234 | − | 0.393525i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −22.6649 | −1.41933 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.8743 | −1.61399 | −0.806996 | − | 0.590556i | \(-0.798908\pi\) | ||||
−0.806996 | + | 0.590556i | \(0.798908\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.65380 | − | 1.41848i | 0.164899 | − | 0.0881402i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.47060 | + | 11.5400i | 0.586215 | + | 0.714305i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.21468 | − | 2.81616i | 0.259889 | − | 0.173652i | −0.418799 | − | 0.908079i | \(-0.637549\pi\) |
0.678688 | + | 0.734427i | \(0.262549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.74684 | + | 8.60075i | −0.353026 | + | 0.528340i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.2394 | + | 4.31947i | −0.871436 | + | 0.264347i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.4268 | + | 16.7639i | 1.24545 | + | 1.02211i | 0.998591 | + | 0.0530576i | \(0.0168967\pi\) |
0.246854 | + | 0.969053i | \(0.420603\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.58713 | + | 3.14269i | 0.460885 | + | 0.190905i | 0.601031 | − | 0.799226i | \(-0.294757\pi\) |
−0.140145 | + | 0.990131i | \(0.544757\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −29.9026 | + | 12.3861i | −1.80979 | + | 0.749640i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.68591 | − | 27.2705i | −0.161967 | − | 1.64448i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.99602 | − | 16.8304i | 0.540519 | − | 1.01124i | −0.452329 | − | 0.891851i | \(-0.649407\pi\) |
0.992848 | − | 0.119388i | \(-0.0380933\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.16594 | − | 0.828657i | 0.249408 | − | 0.0496104i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.19188 | − | 11.0193i | 0.130756 | − | 0.657357i | −0.858694 | − | 0.512488i | \(-0.828724\pi\) |
0.989451 | − | 0.144869i | \(-0.0462761\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.99934 | + | 30.4528i | −0.178292 | + | 1.81023i | 0.324567 | + | 0.945863i | \(0.394781\pi\) |
−0.502859 | + | 0.864368i | \(0.667719\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.51582 | + | 21.4798i | −0.385964 | + | 1.27235i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.9829 | + | 12.9829i | 0.766355 | + | 0.766355i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.29052 | + | 8.29052i | −0.487677 | + | 0.487677i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.1702 | + | 4.60183i | 0.889293 | + | 0.269764i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.03820 | + | 0.693202i | 0.411176 | + | 0.0404973i | 0.301491 | − | 0.953469i | \(-0.402516\pi\) |
0.109685 | + | 0.993966i | \(0.465016\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.5002 | − | 6.06687i | −1.77579 | − | 0.353227i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.78276 | − | 8.96253i | −0.103446 | − | 0.520059i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.2337 | − | 11.3497i | −1.22798 | − | 0.656368i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.48872 | − | 0.540592i | 0.316365 | − | 0.0311592i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.1467 | − | 31.7390i | −0.755261 | − | 1.82336i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.5949 | − | 30.4069i | 0.721184 | − | 1.74109i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.52850 | − | 11.6105i | 0.543820 | − | 0.662647i | −0.426495 | − | 0.904490i | \(-0.640252\pi\) |
0.970315 | + | 0.241843i | \(0.0777519\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.10832 | + | 13.5433i | 0.233714 | + | 0.770452i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.42437 | + | 1.61991i | 0.137473 | + | 0.0918568i | 0.622405 | − | 0.782695i | \(-0.286156\pi\) |
−0.484932 | + | 0.874552i | \(0.661156\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.9231 | − | 22.3340i | −0.843503 | − | 1.26239i | −0.962985 | − | 0.269555i | \(-0.913123\pi\) |
0.119482 | − | 0.992836i | \(-0.461877\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −25.0272 | + | 20.5393i | −1.41013 | + | 1.15726i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.12714 | − | 5.85047i | −0.175638 | − | 0.328595i | 0.778663 | − | 0.627442i | \(-0.215898\pi\) |
−0.954301 | + | 0.298847i | \(0.903398\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 11.4507i | − | 0.641119i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 43.4779i | − | 2.42670i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.46284 | − | 4.60765i | −0.137036 | − | 0.256376i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −38.4084 | + | 31.5209i | −2.13051 | + | 1.74847i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.0230 | + | 25.4767i | 0.941372 | + | 1.40886i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.5945 | + | 13.0926i | 1.08028 | + | 0.721820i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.42723 | + | 24.4843i | 0.408238 | + | 1.34578i | 0.884526 | + | 0.466490i | \(0.154482\pi\) |
−0.476289 | + | 0.879289i | \(0.658018\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.65974 | − | 4.45940i | 0.200552 | − | 0.244374i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.08146 | + | 7.43930i | −0.168358 | + | 0.406452i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.24956 | + | 15.0878i | 0.340435 | + | 0.821884i | 0.997672 | + | 0.0681991i | \(0.0217253\pi\) |
−0.657236 | + | 0.753684i | \(0.728275\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 40.7814 | − | 4.01661i | 2.21494 | − | 0.218152i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.87332 | − | 1.53582i | −0.155599 | − | 0.0831694i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.93266 | + | 19.7708i | 0.212344 | + | 1.06752i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −40.9350 | − | 8.14248i | −2.20387 | − | 0.438377i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.4576 | − | 2.21188i | −1.20559 | − | 0.118740i | −0.524804 | − | 0.851223i | \(-0.675861\pi\) |
−0.680785 | + | 0.732483i | \(0.738361\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.54990 | + | 1.68354i | 0.297079 | + | 0.0901180i | 0.435306 | − | 0.900283i | \(-0.356640\pi\) |
−0.138227 | + | 0.990401i | \(0.544140\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.7163 | + | 11.7163i | −0.625372 | + | 0.625372i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.26290 | − | 2.26290i | −0.120442 | − | 0.120442i | 0.644317 | − | 0.764759i | \(-0.277142\pi\) |
−0.764759 | + | 0.644317i | \(0.777142\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.40711 | − | 31.0111i | 0.499278 | − | 1.64590i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.28005 | − | 12.9965i | 0.0677472 | − | 0.687849i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.26954 | + | 16.4371i | −0.172560 | + | 0.867517i | 0.793375 | + | 0.608733i | \(0.208322\pi\) |
−0.965935 | + | 0.258784i | \(0.916678\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.5602 | − | 2.69729i | 0.713693 | − | 0.141962i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.43627 | − | 2.68707i | 0.0753846 | − | 0.141035i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.08530 | + | 41.4787i | 0.213834 | + | 2.17110i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.44587 | − | 1.01311i | 0.127673 | − | 0.0528840i | −0.317932 | − | 0.948113i | \(-0.602988\pi\) |
0.445606 | + | 0.895229i | \(0.352988\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 32.5203 | + | 13.4704i | 1.69294 | + | 0.701239i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.60728 | − | 3.78110i | −0.239198 | − | 0.196305i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.70150 | + | 2.63957i | −0.450546 | + | 0.136672i | −0.507400 | − | 0.861711i | \(-0.669393\pi\) |
0.0568534 | + | 0.998383i | \(0.481893\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −20.4409 | + | 30.5919i | −1.05556 | + | 1.57976i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.2636 | + | 11.5351i | −0.889119 | + | 0.594090i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.32849 | + | 11.3668i | 0.479172 | + | 0.583873i | 0.955350 | − | 0.295476i | \(-0.0954782\pi\) |
−0.476178 | + | 0.879349i | \(0.657978\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.3126 | − | 6.58123i | 0.630794 | − | 0.337166i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.03046 | −0.154849 | −0.0774246 | − | 0.996998i | \(-0.524670\pi\) | ||||
−0.0774246 | + | 0.996998i | \(0.524670\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 24.8338 | 1.26565 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.32504 | − | 4.98434i | 0.474019 | − | 0.253368i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.09026 | − | 2.54698i | −0.105980 | − | 0.129137i | 0.717319 | − | 0.696745i | \(-0.245369\pi\) |
−0.823299 | + | 0.567608i | \(0.807869\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.07741 | − | 5.39715i | 0.408492 | − | 0.272946i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.49341 | + | 8.22148i | −0.277106 | + | 0.414719i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.9552 | + | 4.23327i | −0.702163 | + | 0.212999i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.0553 | − | 14.8176i | −0.906171 | − | 0.743675i | 0.0609102 | − | 0.998143i | \(-0.480600\pi\) |
−0.967081 | + | 0.254468i | \(0.918100\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.9489 | − | 4.94942i | −0.598195 | − | 0.247781i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.6903 | + | 7.74178i | −0.933349 | + | 0.386606i | −0.796948 | − | 0.604048i | \(-0.793554\pi\) |
−0.136401 | + | 0.990654i | \(0.543554\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.579037 | + | 5.87906i | 0.0288439 | + | 0.292857i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.90641 | − | 14.7918i | 0.392872 | − | 0.735013i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.33990 | + | 0.863261i | −0.215121 | + | 0.0427902i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.61481 | + | 23.2002i | −0.228188 | + | 1.14718i | 0.681479 | + | 0.731838i | \(0.261337\pi\) |
−0.909666 | + | 0.415340i | \(0.863663\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.95511 | + | 19.8506i | −0.0964385 | + | 0.979157i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.20143 | − | 17.1468i | 0.255945 | − | 0.843739i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.989689 | − | 0.989689i | −0.0485819 | − | 0.0485819i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.6157 | − | 10.6157i | 0.519855 | − | 0.519855i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.3546 | − | 10.1180i | −1.62948 | − | 0.494297i | −0.662480 | − | 0.749080i | \(-0.730496\pi\) |
−0.966998 | + | 0.254783i | \(0.917996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.9772 | − | 2.65702i | −1.31479 | − | 0.129495i | −0.583806 | − | 0.811893i | \(-0.698437\pi\) |
−0.730981 | + | 0.682398i | \(0.760937\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 44.3114 | + | 8.81409i | 2.15449 | + | 0.428556i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.91116 | − | 19.6627i | −0.189719 | − | 0.953782i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.7246 | + | 8.93949i | 0.809360 | + | 0.432612i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 47.3660 | − | 4.66514i | 2.28685 | − | 0.225235i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.26076 | − | 22.3575i | −0.446075 | − | 1.07692i | −0.973780 | − | 0.227493i | \(-0.926947\pi\) |
0.527705 | − | 0.849428i | \(-0.323053\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.6385 | − | 32.9264i | 0.655427 | − | 1.58234i | −0.149365 | − | 0.988782i | \(-0.547723\pi\) |
0.804792 | − | 0.593557i | \(-0.202277\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.8332 | + | 27.8224i | −1.09477 | + | 1.33398i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.79280 | − | 9.20664i | −0.133598 | − | 0.440413i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.7610 | + | 11.8675i | 0.847687 | + | 0.566406i | 0.901812 | − | 0.432128i | \(-0.142237\pi\) |
−0.0541255 | + | 0.998534i | \(0.517237\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.55318 | + | 8.31092i | 0.264437 | + | 0.395758i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.16430 | − | 1.77619i | 0.102829 | − | 0.0843895i | −0.581574 | − | 0.813493i | \(-0.697563\pi\) |
0.684403 | + | 0.729104i | \(0.260063\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.75869 | − | 18.2572i | −0.462606 | − | 0.865475i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.0108i | 1.32487i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.25127i | − | 0.295016i | −0.989061 | − | 0.147508i | \(-0.952875\pi\) | ||
0.989061 | − | 0.147508i | \(-0.0471252\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.7274 | − | 23.8114i | −0.599312 | − | 1.12123i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.6114 | − | 27.5842i | 1.57920 | − | 1.29602i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25.0168 | − | 37.4403i | −1.17281 | − | 1.75523i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.13911 | − | 3.43384i | −0.240397 | − | 0.160628i | 0.429536 | − | 0.903050i | \(-0.358677\pi\) |
−0.669933 | + | 0.742421i | \(0.733677\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.94071 | − | 6.39766i | −0.0905846 | − | 0.298617i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.29080 | + | 5.22836i | −0.199843 | + | 0.243509i | −0.863283 | − | 0.504720i | \(-0.831596\pi\) |
0.663440 | + | 0.748229i | \(0.269096\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.69113 | + | 8.91117i | −0.171541 | + | 0.414137i | −0.986146 | − | 0.165879i | \(-0.946954\pi\) |
0.814605 | + | 0.580016i | \(0.196954\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.91894 | + | 9.46116i | 0.181737 | + | 0.438751i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 39.4447 | − | 3.88497i | 1.82529 | − | 0.179775i | 0.873558 | − | 0.486720i | \(-0.161807\pi\) |
0.951727 | + | 0.306945i | \(0.0993068\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.09181 | − | 2.18712i | −0.188942 | − | 0.100992i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.30283 | − | 26.6591i | −0.244342 | − | 1.22839i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.95444 | − | 1.58224i | −0.365746 | − | 0.0727514i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.7590 | − | 1.94609i | −0.906604 | − | 0.0892927i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.9345 | − | 3.31694i | −0.500655 | − | 0.151872i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.7076 | − | 25.7076i | 1.17461 | − | 1.17461i | 0.193512 | − | 0.981098i | \(-0.438012\pi\) |
0.981098 | − | 0.193512i | \(-0.0619878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.67338 | + | 5.67338i | 0.258684 | + | 0.258684i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.98095 | − | 23.0131i | 0.317644 | − | 1.04713i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.16176 | + | 21.9487i | −0.0981604 | + | 0.996640i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.68891 | − | 28.6001i | 0.257789 | − | 1.29599i | −0.607340 | − | 0.794442i | \(-0.707763\pi\) |
0.865129 | − | 0.501550i | \(-0.167237\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 42.4635 | − | 8.44652i | 1.92027 | − | 0.381965i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.827745 | − | 1.54860i | 0.0373556 | − | 0.0698874i | −0.862551 | − | 0.505970i | \(-0.831135\pi\) |
0.899907 | + | 0.436083i | \(0.143635\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.821137 | − | 8.33714i | −0.0369821 | − | 0.375486i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 43.9857 | − | 18.2195i | 1.97701 | − | 0.818905i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.2511 | + | 7.14564i | 0.773818 | + | 0.320526i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.7153 | − | 16.1799i | −0.882577 | − | 0.724312i | 0.0795743 | − | 0.996829i | \(-0.474644\pi\) |
−0.962151 | + | 0.272517i | \(0.912144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −45.2850 | + | 13.7370i | −2.02318 | + | 0.613726i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.2925 | − | 22.8869i | 0.681861 | − | 1.02048i | −0.315575 | − | 0.948901i | \(-0.602197\pi\) |
0.997435 | − | 0.0715757i | \(-0.0228028\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.7396 | − | 26.5532i | 1.76839 | − | 1.18160i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.7843 | − | 39.9478i | −1.45600 | − | 1.77414i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.6838 | + | 8.38317i | −0.695173 | + | 0.371578i | −0.780827 | − | 0.624747i | \(-0.785202\pi\) |
0.0856542 | + | 0.996325i | \(0.472702\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.0155 | −1.06238 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.62106 | −0.292327 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.3648 | + | 9.28166i | −0.765183 | + | 0.408999i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.9844 | − | 26.7881i | −0.966874 | − | 1.17814i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.2836 | − | 6.87130i | 0.451401 | − | 0.301617i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.31872 | − | 12.4499i | 0.364450 | − | 0.545438i | −0.603247 | − | 0.797554i | \(-0.706127\pi\) |
0.967697 | + | 0.252117i | \(0.0811267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.67447 | − | 2.02468i | 0.291854 | − | 0.0885330i | −0.140963 | − | 0.990015i | \(-0.545020\pi\) |
0.432817 | + | 0.901482i | \(0.357520\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −38.3636 | − | 31.4842i | −1.67433 | − | 1.37408i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.20216 | − | 0.912165i | −0.0959276 | − | 0.0397345i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.72170 | + | 1.95579i | −0.205291 | + | 0.0850344i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.36708 | − | 34.1866i | −0.146119 | − | 1.48357i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.0776 | + | 43.1752i | −0.999604 | + | 1.87013i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 59.3255 | − | 11.8006i | 2.56487 | − | 0.510184i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.40275 | − | 17.1068i | 0.146840 | − | 0.738212i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.751484 | − | 7.62995i | 0.0323687 | − | 0.328645i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.97559 | − | 16.4023i | 0.213917 | − | 0.705190i | −0.782655 | − | 0.622456i | \(-0.786135\pi\) |
0.996572 | − | 0.0827339i | \(-0.0263652\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.73732 | + | 7.73732i | 0.332040 | + | 0.332040i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30.1425 | + | 30.1425i | −1.29116 | + | 1.29116i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.8558 | + | 8.14662i | 1.14827 | + | 0.348324i | 0.806370 | − | 0.591412i | \(-0.201429\pi\) |
0.341901 | + | 0.939736i | \(0.388929\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.1812 | + | 3.56354i | 1.54418 | + | 0.152088i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.13726 | − | 1.61860i | −0.346659 | − | 0.0689547i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.63929 | − | 8.24128i | −0.0697098 | − | 0.350455i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.2662 | + | 6.55644i | 0.520672 | + | 0.278305i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.9648 | − | 1.27692i | 0.549337 | − | 0.0541050i | 0.180458 | − | 0.983583i | \(-0.442242\pi\) |
0.368878 | + | 0.929478i | \(0.379742\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.62764 | + | 13.5863i | 0.238024 | + | 0.574640i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.34906 | + | 17.7422i | −0.310278 | + | 0.749076i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.7436 | + | 33.8057i | −1.16925 | + | 1.42474i | −0.284504 | + | 0.958675i | \(0.591829\pi\) |
−0.884750 | + | 0.466066i | \(0.845671\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.5493 | + | 54.5559i | 0.696236 | + | 2.29518i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.03541 | + | 5.36909i | 0.337456 | + | 0.225481i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.71604 | + | 5.56145i | 0.155785 | + | 0.233148i | 0.901149 | − | 0.433509i | \(-0.142725\pi\) |
−0.745365 | + | 0.666657i | \(0.767725\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.9215 | − | 13.0665i | 0.666296 | − | 0.546815i | −0.239306 | − | 0.970944i | \(-0.576920\pi\) |
0.905602 | + | 0.424129i | \(0.139420\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.6578 | + | 38.6481i | 0.862994 | + | 1.61455i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 36.9179i | − | 1.53958i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.28283i | 0.0950356i | 0.998870 | + | 0.0475178i | \(0.0151311\pi\) | ||||
−0.998870 | + | 0.0475178i | \(0.984869\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.3914 | − | 30.6662i | −0.681203 | − | 1.27444i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.623402 | − | 0.511613i | 0.0258631 | − | 0.0212253i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.86931 | + | 7.28743i | 0.201666 | + | 0.301815i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −71.7783 | − | 47.9607i | −2.96767 | − | 1.98293i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.20450 | − | 23.7501i | −0.297362 | − | 0.980270i | −0.970570 | − | 0.240818i | \(-0.922584\pi\) |
0.673209 | − | 0.739453i | \(-0.264916\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.49756 | + | 1.82478i | −0.0617057 | + | 0.0751886i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.4380 | + | 37.2706i | −0.635034 | + | 1.53311i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.96953 | + | 4.75487i | 0.0808789 | + | 0.195259i | 0.959146 | − | 0.282911i | \(-0.0913002\pi\) |
−0.878267 | + | 0.478170i | \(0.841300\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.0811 | − | 1.78084i | 0.741255 | − | 0.0730072i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.5159 | − | 7.75891i | −0.594097 | − | 0.317551i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.42145 | + | 12.1734i | 0.0989376 | + | 0.497393i | 0.998199 | + | 0.0599823i | \(0.0191044\pi\) |
−0.899262 | + | 0.437411i | \(0.855896\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6453 | + | 2.31639i | 0.475021 | + | 0.0944875i | 0.426794 | − | 0.904349i | \(-0.359643\pi\) |
0.0482267 | + | 0.998836i | \(0.484643\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.85204 | − | 0.871849i | −0.360483 | − | 0.0355045i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.05633 | + | 1.23047i | 0.164913 | + | 0.0500259i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.9482 | + | 31.9482i | −1.29674 | + | 1.29674i | −0.366202 | + | 0.930535i | \(0.619342\pi\) |
−0.930535 | + | 0.366202i | \(0.880658\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.6644 | − | 14.6644i | −0.594230 | − | 0.594230i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.2403 | + | 60.1301i | −0.737922 | + | 2.43260i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.117361 | − | 1.19159i | 0.00474017 | − | 0.0481277i | −0.992524 | − | 0.122052i | \(-0.961052\pi\) |
0.997264 | + | 0.0739246i | \(0.0235524\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.5564 | + | 83.2345i | −0.667617 | + | 3.35634i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.36091 | − | 0.270701i | 0.0547880 | − | 0.0108980i | −0.167620 | − | 0.985852i | \(-0.553608\pi\) |
0.222408 | + | 0.974954i | \(0.428608\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.74430 | + | 18.2303i | −0.391656 | + | 0.732737i | −0.998050 | − | 0.0624275i | \(-0.980116\pi\) |
0.606393 | + | 0.795165i | \(0.292616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.20672 | − | 12.2520i | −0.0484239 | − | 0.491656i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.0202 | − | 4.56472i | 0.441515 | − | 0.182882i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.97013 | − | 2.88712i | −0.278805 | − | 0.115485i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.7017 | + | 12.0654i | 0.587130 | + | 0.481845i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.09792 | + | 0.939745i | −0.123522 | + | 0.0374701i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.39374 | − | 8.07230i | 0.214721 | − | 0.321353i | −0.708436 | − | 0.705775i | \(-0.750599\pi\) |
0.923158 | + | 0.384422i | \(0.125599\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 39.1478 | − | 26.1578i | 1.55599 | − | 1.03968i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.3219 | + | 15.0143i | 0.488980 | + | 0.595823i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.2602 | + | 6.55322i | −0.485767 | + | 0.259648i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 35.7977 | 1.41614 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.5260 | 1.79817 | 0.899084 | − | 0.437776i | \(-0.144234\pi\) | ||||
0.899084 | + | 0.437776i | \(0.144234\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.69364 | + | 4.64685i | −0.342844 | + | 0.183254i | −0.633828 | − | 0.773474i | \(-0.718517\pi\) |
0.290984 | + | 0.956728i | \(0.406017\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.1722 | + | 19.7059i | 0.636780 | + | 0.775919i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.48460 | − | 1.66016i | 0.0976798 | − | 0.0652675i | −0.505771 | − | 0.862668i | \(-0.668792\pi\) |
0.603451 | + | 0.797400i | \(0.293792\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.6388 | + | 21.9085i | −0.574624 | + | 0.859985i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.64655 | + | 1.71286i | −0.221306 | + | 0.0671324i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.1963 | + | 23.9607i | 1.14254 | + | 0.937656i | 0.998650 | − | 0.0519377i | \(-0.0165397\pi\) |
0.143887 | + | 0.989594i | \(0.454040\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.7092 | − | 5.26432i | −0.496589 | − | 0.205694i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −42.5363 | + | 17.6191i | −1.65950 | + | 0.687388i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.713561 | + | 7.24490i | 0.0277964 | + | 0.282221i | 0.999028 | + | 0.0440838i | \(0.0140369\pi\) |
−0.971231 | + | 0.238137i | \(0.923463\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.6445 | − | 21.7854i | 0.452920 | − | 0.847354i | −0.547027 | − | 0.837115i | \(-0.684241\pi\) |
0.999948 | − | 0.0102393i | \(-0.00325932\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 34.1520 | − | 6.79326i | 1.32635 | − | 0.263828i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.51034 | − | 17.6477i | 0.136125 | − | 0.684347i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.51211 | − | 15.3527i | 0.0585490 | − | 0.594458i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.36162 | − | 7.78522i | 0.0913055 | − | 0.300994i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.7188 | − | 19.7188i | −0.761234 | − | 0.761234i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.6942 | − | 25.6942i | 0.990440 | − | 0.990440i | −0.00951435 | − | 0.999955i | \(-0.503029\pi\) |
0.999955 | + | 0.00951435i | \(0.00302856\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −24.3127 | − | 7.37516i | −0.935795 | − | 0.283870i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.56047 | + | 0.744641i | 0.290572 | + | 0.0286189i | 0.242253 | − | 0.970213i | \(-0.422114\pi\) |
0.0483192 | + | 0.998832i | \(0.484614\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.4637 | − | 2.47919i | −0.478315 | − | 0.0951427i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.331981 | + | 1.66898i | 0.0127215 | + | 0.0639555i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.9055 | − | 9.03616i | −0.646870 | − | 0.345759i | 0.115117 | − | 0.993352i | \(-0.463276\pi\) |
−0.761987 | + | 0.647593i | \(0.775776\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.6167 | + | 2.72001i | −1.05518 | + | 0.103926i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.3141 | − | 39.3858i | −0.622423 | − | 1.50266i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.08160 | − | 14.6823i | 0.231691 | − | 0.559351i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.8155 | + | 13.1788i | −0.411443 | + | 0.501344i | −0.936959 | − | 0.349439i | \(-0.886372\pi\) |
0.525516 | + | 0.850783i | \(0.323872\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.96324 | + | 26.2513i | 0.302498 | + | 0.997204i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.3664 | + | 11.6039i | 0.658746 | + | 0.440160i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.9742 | − | 16.4241i | −0.415678 | − | 0.622106i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.2237 | − | 28.9074i | 1.33228 | − | 1.09338i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.8768 | + | 25.9616i | 0.524119 | + | 0.980557i | 0.995143 | + | 0.0984370i | \(0.0313843\pi\) |
−0.471025 | + | 0.882120i | \(0.656116\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.20610i | 0.120920i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 108.926i | 4.10239i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.9818 | + | 24.2871i | 0.488229 | + | 0.913412i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.6625 | + | 8.75053i | −0.400440 | + | 0.328633i | −0.812964 | − | 0.582314i | \(-0.802147\pi\) |
0.412524 | + | 0.910947i | \(0.364647\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.94980 | − | 13.3943i | −0.335644 | − | 0.502326i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.64961 | − | 2.43859i | −0.136679 | − | 0.0913261i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.2214 | + | 63.3646i | 0.718841 | + | 2.36970i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.6546 | + | 32.4788i | −0.995436 | + | 1.21294i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.82739 | + | 16.4828i | −0.254619 | + | 0.614704i | −0.998566 | − | 0.0535346i | \(-0.982951\pi\) |
0.743947 | + | 0.668238i | \(0.232951\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.34158 | − | 10.4815i | −0.161689 | − | 0.390352i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −67.4097 | + | 6.63928i | −2.50699 | + | 0.246917i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.0772 | − | 15.0076i | −1.04276 | − | 0.557368i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.41470 | − | 7.11218i | −0.0524683 | − | 0.263776i | 0.945643 | − | 0.325206i | \(-0.105434\pi\) |
−0.998111 | + | 0.0614304i | \(0.980434\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 40.9809 | + | 8.15161i | 1.51781 | + | 0.301912i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.90499 | − | 0.581591i | −0.218404 | − | 0.0215109i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.7665 | + | 4.47938i | 0.545415 | + | 0.165450i | 0.550955 | − | 0.834535i | \(-0.314264\pi\) |
−0.00554040 | + | 0.999985i | \(0.501764\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.0403 | + | 17.0403i | −0.628542 | + | 0.628542i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.82436 | + | 4.82436i | 0.177707 | + | 0.177707i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.853799 | + | 2.81460i | −0.0314075 | + | 0.103537i | −0.971243 | − | 0.238091i | \(-0.923478\pi\) |
0.939835 | + | 0.341628i | \(0.110978\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.38014 | − | 34.3192i | 0.124173 | − | 1.26075i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.59498 | + | 8.01851i | −0.0585142 | + | 0.294171i | −0.998951 | − | 0.0457987i | \(-0.985417\pi\) |
0.940437 | + | 0.339969i | \(0.110417\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.2207 | + | 7.60256i | −1.40030 | + | 0.278536i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.728825 | − | 1.36354i | 0.0266663 | − | 0.0498892i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.41617 | + | 34.6849i | 0.124824 | + | 1.26736i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.5276 | + | 18.8581i | −1.66132 | + | 0.688143i | −0.998178 | − | 0.0603455i | \(-0.980780\pi\) |
−0.663147 | + | 0.748489i | \(0.730780\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −61.1142 | − | 25.3143i | −2.22713 | − | 0.922506i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 46.7612 | + | 38.3759i | 1.70181 | + | 1.39664i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.1867 | − | 4.60685i | 0.551971 | − | 0.167439i | −0.00196446 | − | 0.999998i | \(-0.500625\pi\) |
0.553936 | + | 0.832559i | \(0.313125\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.6471 | + | 29.4039i | −0.713144 | + | 1.06730i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.11658 | − | 4.75515i | 0.257976 | − | 0.172374i | −0.419856 | − | 0.907591i | \(-0.637920\pi\) |
0.677832 | + | 0.735217i | \(0.262920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.5820 | − | 18.9867i | −0.564106 | − | 0.687365i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 30.7189 | − | 16.4196i | 1.11064 | − | 0.593652i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47.7768 | 1.72512 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.7650 | −1.90276 | −0.951378 | − | 0.308026i | \(-0.900332\pi\) | ||||
−0.951378 | + | 0.308026i | \(0.900332\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.7730 | − | 32.4839i | 2.18869 | − | 1.16988i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.0801 | − | 32.9972i | −0.974003 | − | 1.18683i | −0.982386 | − | 0.186861i | \(-0.940169\pi\) |
0.00838378 | − | 0.999965i | \(-0.497331\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.53167 | + | 5.03250i | −0.270545 | + | 0.180773i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.45235 | + | 6.66342i | −0.159727 | + | 0.239049i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.7202 | + | 5.67870i | −0.670720 | + | 0.203461i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.2254 | − | 17.4192i | −0.759504 | − | 0.623309i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.80859 | − | 4.06285i | −0.350530 | − | 0.145194i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 34.9371 | − | 14.4714i | 1.24696 | − | 0.516506i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.162474 | − | 1.64963i | −0.00579158 | − | 0.0588029i | 0.991855 | − | 0.127376i | \(-0.0406554\pi\) |
−0.997646 | + | 0.0685729i | \(0.978155\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.36383 | + | 11.9059i | −0.226558 | + | 0.423861i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.2181 | + | 6.40858i | −1.14554 | + | 0.227863i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.86463 | + | 49.5928i | −0.350303 | + | 1.76109i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.70026 | − | 27.4162i | 0.0957683 | − | 0.972351i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.5311 | − | 41.3094i | 0.443873 | − | 1.46325i | −0.394876 | − | 0.918734i | \(-0.629213\pi\) |
0.838749 | − | 0.544518i | \(-0.183287\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.9276 | − | 17.9276i | −0.634232 | − | 0.634232i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.1701 | − | 16.1701i | 0.571343 | − | 0.571343i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.7944 | + | 10.2514i | 1.19258 | + | 0.361765i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 33.2961 | + | 3.27938i | 1.17353 | + | 0.115583i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −69.0243 | − | 13.7298i | −2.42977 | − | 0.483312i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.99285 | − | 15.0461i | −0.105223 | − | 0.528992i | −0.997059 | − | 0.0766334i | \(-0.975583\pi\) |
0.891836 | − | 0.452358i | \(-0.149417\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.70107 | + | 5.18533i | 0.340650 | + | 0.182081i | 0.632847 | − | 0.774277i | \(-0.281886\pi\) |
−0.292197 | + | 0.956358i | \(0.594386\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.7660 | + | 2.14377i | −0.763367 | + | 0.0751851i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.0505 | + | 55.6488i | 0.807424 | + | 1.94929i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.24877 | + | 5.42902i | −0.0786747 | + | 0.189937i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 31.5555 | − | 38.4505i | 1.10264 | − | 1.34357i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.8632 | + | 42.4044i | 0.448930 | + | 1.47992i | 0.831252 | + | 0.555896i | \(0.187625\pi\) |
−0.382322 | + | 0.924029i | \(0.624875\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.6861 | − | 27.1856i | −1.41823 | − | 0.947629i | −0.999214 | − | 0.0396490i | \(-0.987376\pi\) |
−0.419013 | − | 0.907980i | \(-0.637624\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 40.5454 | + | 60.6806i | 1.41161 | + | 2.11263i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.1801 | − | 28.0509i | 1.18856 | − | 0.975425i | 0.188581 | − | 0.982058i | \(-0.439611\pi\) |
0.999978 | + | 0.00663288i | \(0.00211133\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.5280 | − | 47.7596i | −0.886626 | − | 1.65876i | −0.743170 | − | 0.669103i | \(-0.766678\pi\) |
−0.143456 | − | 0.989657i | \(-0.545822\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 50.8250i | 1.76310i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5.60916i | − | 0.194346i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.0352 | − | 58.0628i | −1.07402 | − | 2.00935i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.33505 | + | 1.91633i | −0.0807112 | + | 0.0662380i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.6160 | + | 32.3506i | 0.746267 | + | 1.11687i | 0.989164 | + | 0.146816i | \(0.0469024\pi\) |
−0.242897 | + | 0.970052i | \(0.578098\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0511 | + | 8.72047i | 0.450038 | + | 0.300706i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.68595 | + | 28.6338i | 0.299160 | + | 0.986199i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 45.6105 | − | 55.5765i | 1.56905 | − | 1.91189i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.934667 | + | 2.25649i | −0.0321156 | + | 0.0775338i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.1872 | − | 75.2925i | −1.07034 | − | 2.58403i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.93276 | + | 0.584325i | −0.203372 | + | 0.0200304i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.6328 | + | 19.0461i | 1.22004 | + | 0.652126i | 0.950459 | − | 0.310851i | \(-0.100614\pi\) |
0.269584 | + | 0.962977i | \(0.413114\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.72980 | − | 33.8330i | −0.230154 | − | 1.15706i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.4994 | + | 5.07215i | 0.871044 | + | 0.173261i | 0.610323 | − | 0.792153i | \(-0.291040\pi\) |
0.260721 | + | 0.965414i | \(0.416040\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.2440 | + | 1.59989i | 0.554236 | + | 0.0545875i | 0.371259 | − | 0.928530i | \(-0.378926\pi\) |
0.182978 | + | 0.983117i | \(0.441426\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −46.7933 | − | 14.1946i | −1.59471 | − | 0.483750i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.2495 | − | 10.2495i | 0.348897 | − | 0.348897i | −0.510802 | − | 0.859699i | \(-0.670651\pi\) |
0.859699 | + | 0.510802i | \(0.170651\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.1670 | + | 12.1670i | 0.413691 | + | 0.413691i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.06429 | − | 29.8809i | 0.307839 | − | 1.01481i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.21113 | + | 12.2968i | −0.0410848 | + | 0.417141i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.41346 | − | 12.1333i | 0.0817770 | − | 0.411121i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.8947 | + | 4.75296i | −0.808714 | + | 0.160863i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.9032 | − | 26.0111i | 0.470015 | − | 0.879336i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.64214 | + | 16.6729i | 0.0554512 | + | 0.563005i | 0.982267 | + | 0.187489i | \(0.0600348\pi\) |
−0.926816 | + | 0.375517i | \(0.877465\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.4015 | + | 7.20793i | −0.586937 | + | 0.243117i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.2814 | + | 10.4719i | 0.851751 | + | 0.352807i | 0.765476 | − | 0.643465i | \(-0.222504\pi\) |
0.0862749 | + | 0.996271i | \(0.472504\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.8236 | + | 13.8067i | 0.566158 | + | 0.464634i | 0.873404 | − | 0.486996i | \(-0.161907\pi\) |
−0.307246 | + | 0.951630i | \(0.599407\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 79.2550 | − | 24.0418i | 2.66413 | − | 0.808155i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.4637 | − | 17.1566i | 0.384912 | − | 0.576062i | −0.587531 | − | 0.809202i | \(-0.699900\pi\) |
0.972443 | + | 0.233140i | \(0.0748999\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.30539 | + | 6.21767i | −0.312093 | + | 0.208534i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.01548 | − | 10.9854i | −0.302030 | − | 0.368025i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.1440 | + | 11.8362i | −0.741022 | + | 0.396084i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.2657 | 0.811114 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 64.1224 | 2.14098 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.33824 | + | 1.78433i | −0.111337 | + | 0.0595107i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.06786 | + | 4.95671i | 0.135520 | + | 0.165132i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.2131 | + | 8.16055i | −0.406427 | + | 0.271566i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.45753 | + | 12.6576i | −0.281138 | + | 0.420752i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.8824 | + | 9.06472i | −0.992228 | + | 0.300989i | −0.744341 | − | 0.667800i | \(-0.767236\pi\) |
−0.247887 | + | 0.968789i | \(0.579736\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 40.8118 | + | 33.4934i | 1.35364 | + | 1.11091i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.5842 | + | 9.76890i | 0.781380 | + | 0.323658i | 0.737472 | − | 0.675378i | \(-0.236019\pi\) |
0.0439074 | + | 0.999036i | \(0.486019\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.09564 | + | 0.453828i | −0.0362603 | + | 0.0150195i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.59155 | + | 87.2315i | 0.284028 | + | 2.88378i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.73644 | − | 6.99039i | 0.123388 | − | 0.230843i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.2229 | − | 9.98996i | 1.65670 | − | 0.329538i | 0.723894 | − | 0.689912i | \(-0.242351\pi\) |
0.932808 | + | 0.360373i | \(0.117351\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.80395 | + | 39.2331i | −0.257149 | + | 1.29277i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.88003 | + | 49.5478i | −0.160628 | + | 1.63089i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.57126 | + | 11.7729i | −0.117422 | + | 0.387089i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.3797 | − | 15.3797i | −0.505135 | − | 0.505135i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.41129 | + | 5.41129i | −0.177539 | + | 0.177539i | −0.790282 | − | 0.612743i | \(-0.790066\pi\) |
0.612743 | + | 0.790282i | \(0.290066\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.31585 | − | 1.61255i | −0.174220 | − | 0.0528491i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.72804 | − | 0.761145i | −0.253005 | − | 0.0249188i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −26.2038 | − | 5.21227i | −0.856957 | − | 0.170459i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.344820 | − | 1.73353i | −0.0112648 | − | 0.0566319i | 0.974744 | − | 0.223325i | \(-0.0716911\pi\) |
−0.986009 | + | 0.166693i | \(0.946691\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 63.0903 | + | 33.7225i | 2.05887 | + | 1.10049i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −57.1654 | + | 5.63030i | −1.86354 | + | 0.183543i | −0.966199 | − | 0.257797i | \(-0.917003\pi\) |
−0.897340 | + | 0.441340i | \(0.854503\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.9200 | − | 33.6060i | −0.453299 | − | 1.09436i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.81130 | − | 21.2723i | 0.286631 | − | 0.691990i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.3082 | + | 23.5271i | −0.627433 | + | 0.764530i | −0.985594 | − | 0.169131i | \(-0.945904\pi\) |
0.358161 | + | 0.933660i | \(0.383404\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.5881 | − | 61.2766i | −0.603394 | − | 1.98912i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.6900 | + | 9.81552i | 0.476355 | + | 0.318290i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.8785 | + | 38.7299i | 0.838286 | + | 1.25458i | 0.964896 | + | 0.262631i | \(0.0845901\pi\) |
−0.126611 | + | 0.991952i | \(0.540410\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −47.1284 | + | 38.6773i | −1.52504 | + | 1.25157i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.3758 | + | 26.8953i | 0.464705 | + | 0.869402i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 15.9896i | − | 0.516331i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 29.9230i | − | 0.965259i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.4976 | + | 58.9278i | 1.01500 | + | 1.89892i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.3950 | − | 30.6893i | 1.20379 | − | 0.987923i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.0598 | + | 16.5521i | 0.355659 | + | 0.532281i | 0.965555 | − | 0.260201i | \(-0.0837887\pi\) |
−0.609896 | + | 0.792482i | \(0.708789\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.5693 | + | 7.73039i | 0.371661 | + | 0.248336i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.8031 | − | 52.0957i | −0.507145 | − | 1.67183i | −0.719383 | − | 0.694614i | \(-0.755575\pi\) |
0.212238 | − | 0.977218i | \(-0.431925\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.63470 | + | 9.30291i | −0.244757 | + | 0.298238i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 50.6399 | − | 122.256i | 1.62178 | − | 3.91531i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.4388 | + | 32.4441i | 0.429945 | + | 1.03798i | 0.979305 | + | 0.202392i | \(0.0648716\pi\) |
−0.549360 | + | 0.835586i | \(0.685128\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.4561 | + | 1.71927i | −0.557898 | + | 0.0549482i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −41.5286 | − | 22.1975i | −1.32591 | − | 0.708712i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.32816 | − | 6.67710i | −0.0423617 | − | 0.212966i | 0.953807 | − | 0.300420i | \(-0.0971269\pi\) |
−0.996169 | + | 0.0874539i | \(0.972127\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −55.0458 | − | 10.9493i | −1.75390 | − | 0.348873i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −62.4604 | − | 6.15181i | −1.98814 | − | 0.195814i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.4560 | − | 3.17181i | −0.332483 | − | 0.100858i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.4332 | − | 11.4332i | 0.363189 | − | 0.363189i | −0.501797 | − | 0.864985i | \(-0.667328\pi\) |
0.864985 | + | 0.501797i | \(0.167328\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −48.1838 | − | 48.1838i | −1.52907 | − | 1.52907i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.64718 | − | 21.9128i | 0.210730 | − | 0.694683i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.43791 | + | 14.5993i | −0.0455390 | + | 0.462365i | 0.945191 | + | 0.326519i | \(0.105876\pi\) |
−0.990730 | + | 0.135847i | \(0.956624\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.800386 | + | 4.02381i | −0.0253231 | + | 0.127308i |
(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 | 512.2.k.a.497.2 | 240 | ||
4.3 | odd | 2 | 128.2.k.a.101.7 | ✓ | 240 | ||
128.19 | odd | 32 | 128.2.k.a.109.7 | yes | 240 | ||
128.109 | even | 32 | inner | 512.2.k.a.273.2 | 240 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.2.k.a.101.7 | ✓ | 240 | 4.3 | odd | 2 | ||
128.2.k.a.109.7 | yes | 240 | 128.19 | odd | 32 | ||
512.2.k.a.273.2 | 240 | 128.109 | even | 32 | inner | ||
512.2.k.a.497.2 | 240 | 1.1 | even | 1 | trivial |