Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(589,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.j (of order \(3\), degree \(2\), 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1177.3 | ||
Character | \(\chi\) | \(=\) | 1764.1177 |
Dual form | 1764.2.j.i.589.3 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.47192 | + | 0.912932i | −0.849815 | + | 0.527082i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.94623 | + | 3.37097i | 0.870381 | + | 1.50754i | 0.861603 | + | 0.507583i | \(0.169461\pi\) |
0.00877856 | + | 0.999961i | \(0.497206\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.33311 | − | 2.68753i | 0.444370 | − | 0.895844i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.18778 | + | 3.78935i | −0.659642 | + | 1.14253i | 0.321067 | + | 0.947057i | \(0.395959\pi\) |
−0.980708 | + | 0.195476i | \(0.937375\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.792201 | + | 1.37213i | 0.219717 | + | 0.380561i | 0.954721 | − | 0.297501i | \(-0.0961533\pi\) |
−0.735004 | + | 0.678062i | \(0.762820\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.94217 | − | 3.18503i | −1.53426 | − | 0.822371i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.33356 | 1.29358 | 0.646789 | − | 0.762669i | \(-0.276111\pi\) | ||||
0.646789 | + | 0.762669i | \(0.276111\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.64323 | 1.06523 | 0.532614 | − | 0.846358i | \(-0.321210\pi\) | ||||
0.532614 | + | 0.846358i | \(0.321210\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.183900 | − | 0.318523i | −0.0383457 | − | 0.0664167i | 0.846216 | − | 0.532841i | \(-0.178875\pi\) |
−0.884561 | + | 0.466424i | \(0.845542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.07564 | + | 8.79126i | −1.01513 | + | 1.75825i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.491301 | + | 5.17287i | 0.0945509 | + | 0.995520i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.08750 | + | 8.81180i | −0.944724 | + | 1.63631i | −0.188422 | + | 0.982088i | \(0.560337\pi\) |
−0.756302 | + | 0.654222i | \(0.772996\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.14776 | − | 1.98798i | −0.206144 | − | 0.357052i | 0.744353 | − | 0.667787i | \(-0.232758\pi\) |
−0.950497 | + | 0.310735i | \(0.899425\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.239175 | − | 7.57493i | −0.0416351 | − | 1.31863i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.8803 | 1.78872 | 0.894359 | − | 0.447351i | \(-0.147632\pi\) | ||||
0.894359 | + | 0.447351i | \(0.147632\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.41872 | − | 1.29645i | −0.387305 | − | 0.207597i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.690443 | + | 1.19588i | 0.107829 | + | 0.186766i | 0.914891 | − | 0.403702i | \(-0.132277\pi\) |
−0.807061 | + | 0.590467i | \(0.798943\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.81699 | − | 6.61122i | 0.582086 | − | 1.00820i | −0.413146 | − | 0.910665i | \(-0.635570\pi\) |
0.995232 | − | 0.0975372i | \(-0.0310965\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.6541 | − | 0.736684i | 1.73730 | − | 0.109818i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.80432 | + | 6.58928i | −0.554918 | + | 0.961145i | 0.442992 | + | 0.896525i | \(0.353917\pi\) |
−0.997910 | + | 0.0646200i | \(0.979416\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.85058 | + | 4.86918i | −1.09930 | + | 0.681821i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.925693 | −0.127154 | −0.0635769 | − | 0.997977i | \(-0.520251\pi\) | ||||
−0.0635769 | + | 0.997977i | \(0.520251\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.0317 | −2.29656 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.83447 | + | 4.23895i | −0.905247 | + | 0.561463i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.460475 | − | 0.797565i | −0.0599487 | − | 0.103834i | 0.834493 | − | 0.551018i | \(-0.185760\pi\) |
−0.894442 | + | 0.447184i | \(0.852427\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.27780 | − | 5.67731i | 0.419679 | − | 0.726905i | −0.576228 | − | 0.817289i | \(-0.695476\pi\) |
0.995907 | + | 0.0903836i | \(0.0288093\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.08361 | + | 5.34097i | −0.382475 | + | 0.662466i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.50420 | − | 12.9976i | −0.916783 | − | 1.58792i | −0.804269 | − | 0.594265i | \(-0.797443\pi\) |
−0.112514 | − | 0.993650i | \(-0.535890\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.561476 | + | 0.300954i | 0.0675938 | + | 0.0362306i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.91059 | −0.582780 | −0.291390 | − | 0.956604i | \(-0.594118\pi\) | ||||
−0.291390 | + | 0.956604i | \(0.594118\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.56707 | −0.885658 | −0.442829 | − | 0.896606i | \(-0.646025\pi\) | ||||
−0.442829 | + | 0.896606i | \(0.646025\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.554885 | − | 17.5738i | −0.0640726 | − | 2.02924i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.987715 | + | 1.71077i | −0.111127 | + | 0.192477i | −0.916225 | − | 0.400665i | \(-0.868779\pi\) |
0.805098 | + | 0.593142i | \(0.202113\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.44564 | − | 7.16554i | −0.605071 | − | 0.796171i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.253011 | − | 0.438227i | 0.0277715 | − | 0.0481017i | −0.851806 | − | 0.523858i | \(-0.824492\pi\) |
0.879577 | + | 0.475756i | \(0.157826\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.3803 | + | 17.9793i | 1.12591 | + | 1.95013i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.556181 | − | 17.6148i | −0.0596289 | − | 1.88851i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.2197 | 1.29529 | 0.647645 | − | 0.761942i | \(-0.275754\pi\) | ||||
0.647645 | + | 0.761942i | \(0.275754\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.50431 | + | 1.87833i | 0.363380 | + | 0.194773i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.03679 | + | 15.6522i | 0.927155 | + | 1.60588i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.45315 | + | 7.71308i | −0.452149 | + | 0.783145i | −0.998519 | − | 0.0543987i | \(-0.982676\pi\) |
0.546370 | + | 0.837544i | \(0.316009\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.26745 | + | 10.9314i | 0.730406 | + | 1.09864i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.51180 | − | 9.54672i | 0.548445 | − | 0.949935i | −0.449936 | − | 0.893061i | \(-0.648553\pi\) |
0.998381 | − | 0.0568740i | \(-0.0181133\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.36543 | + | 2.36499i | 0.134540 | + | 0.233029i | 0.925421 | − | 0.378939i | \(-0.123711\pi\) |
−0.790882 | + | 0.611969i | \(0.790378\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.7921 | −1.04331 | −0.521655 | − | 0.853156i | \(-0.674685\pi\) | ||||
−0.521655 | + | 0.853156i | \(0.674685\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.98374 | −0.956269 | −0.478134 | − | 0.878287i | \(-0.658687\pi\) | ||||
−0.478134 | + | 0.878287i | \(0.658687\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.0150 | + | 9.93302i | −1.52008 | + | 0.942800i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.12019 | − | 10.6005i | −0.575739 | − | 0.997209i | −0.995961 | − | 0.0897875i | \(-0.971381\pi\) |
0.420222 | − | 0.907421i | \(-0.361952\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.715822 | − | 1.23984i | 0.0667508 | − | 0.115616i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.74374 | − | 0.299862i | 0.438559 | − | 0.0277223i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.07280 | − | 7.05429i | −0.370254 | − | 0.641299i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.10804 | − | 1.12992i | −0.190075 | − | 0.101881i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −20.0511 | −1.79343 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.2005 | −1.17135 | −0.585677 | − | 0.810544i | \(-0.699171\pi\) | ||||
−0.585677 | + | 0.810544i | \(0.699171\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.417286 | + | 13.2159i | 0.0367399 | + | 1.16359i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.54342 | + | 4.40532i | 0.222219 | + | 0.384895i | 0.955482 | − | 0.295051i | \(-0.0953366\pi\) |
−0.733262 | + | 0.679946i | \(0.762003\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.4814 | + | 11.7238i | −1.41850 | + | 1.00902i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.67208 | + | 11.5564i | −0.570034 | + | 0.987328i | 0.426527 | + | 0.904475i | \(0.359737\pi\) |
−0.996562 | + | 0.0828538i | \(0.973597\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.85642 | + | 8.41157i | 0.411916 | + | 0.713460i | 0.995099 | − | 0.0988809i | \(-0.0315263\pi\) |
−0.583183 | + | 0.812341i | \(0.698193\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.415901 | − | 13.1720i | −0.0350251 | − | 1.10928i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.93265 | −0.579738 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −39.6058 | −3.28908 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.92116 | − | 11.9878i | −0.567004 | − | 0.982079i | −0.996860 | − | 0.0791820i | \(-0.974769\pi\) |
0.429856 | − | 0.902897i | \(-0.358564\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4380 | + | 19.8112i | −0.930809 | + | 1.61221i | −0.148867 | + | 0.988857i | \(0.547563\pi\) |
−0.781942 | + | 0.623352i | \(0.785771\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.11022 | − | 14.3341i | 0.574827 | − | 1.15884i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.46762 | − | 7.73815i | 0.358848 | − | 0.621543i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.78991 | + | 10.0284i | 0.462085 | + | 0.800355i | 0.999065 | − | 0.0432404i | \(-0.0137681\pi\) |
−0.536980 | + | 0.843595i | \(0.680435\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.36255 | − | 0.845095i | 0.108057 | − | 0.0670204i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.41155 | 0.267213 | 0.133607 | − | 0.991034i | \(-0.457344\pi\) | ||||
0.133607 | + | 0.991034i | \(0.457344\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 25.0694 | − | 15.5488i | 1.95165 | − | 1.21047i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.69996 | + | 8.14057i | 0.363694 | + | 0.629936i | 0.988566 | − | 0.150791i | \(-0.0481821\pi\) |
−0.624872 | + | 0.780727i | \(0.714849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.24484 | − | 9.08432i | 0.403449 | − | 0.698794i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.18993 | − | 12.4788i | 0.473355 | − | 0.954278i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.20256 | + | 5.54700i | −0.243486 | + | 0.421730i | −0.961705 | − | 0.274087i | \(-0.911624\pi\) |
0.718219 | + | 0.695817i | \(0.244958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.40591 | + | 0.753572i | 0.105674 | + | 0.0566419i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.0808 | 1.27668 | 0.638338 | − | 0.769756i | \(-0.279622\pi\) | ||||
0.638338 | + | 0.769756i | \(0.279622\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.35988 | −0.101079 | −0.0505395 | − | 0.998722i | \(-0.516094\pi\) | ||||
−0.0505395 | + | 0.998722i | \(0.516094\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.358339 | + | 11.3490i | 0.0264892 | + | 0.838940i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.1757 | + | 36.6773i | 1.55687 | + | 2.69657i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.6687 | + | 20.2107i | −0.853298 | + | 1.47796i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.94048 | − | 15.4854i | 0.646911 | − | 1.12048i | −0.336946 | − | 0.941524i | \(-0.609394\pi\) |
0.983857 | − | 0.178958i | \(-0.0572727\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.50664 | + | 11.2698i | 0.468358 | + | 0.811220i | 0.999346 | − | 0.0361591i | \(-0.0115123\pi\) |
−0.530988 | + | 0.847380i | \(0.678179\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.337110 | − | 10.6766i | −0.0241410 | − | 0.764569i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.36486 | 0.453478 | 0.226739 | − | 0.973956i | \(-0.427194\pi\) | ||||
0.226739 | + | 0.973956i | \(0.427194\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.1529 | −1.64126 | −0.820631 | − | 0.571458i | \(-0.806378\pi\) | ||||
−0.820631 | + | 0.571458i | \(0.806378\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.9116 | + | 12.2807i | 1.61606 | + | 0.866214i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.68753 | + | 4.65493i | −0.187705 | + | 0.325114i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.10120 | + | 0.0696093i | −0.0765387 | + | 0.00483818i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.1584 | + | 17.5948i | −0.702669 | + | 1.21706i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.67737 | − | 9.83349i | −0.390846 | − | 0.676965i | 0.601715 | − | 0.798711i | \(-0.294484\pi\) |
−0.992561 | + | 0.121745i | \(0.961151\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.22801 | − | 4.48304i | 0.495255 | − | 0.307173i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.7150 | 2.02655 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.1381 | − | 6.90822i | 0.752645 | − | 0.466814i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.22525 | + | 7.31835i | 0.284221 | + | 0.492285i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.3206 | − | 23.0719i | 0.892011 | − | 1.54501i | 0.0545504 | − | 0.998511i | \(-0.482627\pi\) |
0.837461 | − | 0.546498i | \(-0.184039\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.8604 | + | 25.3606i | 1.12403 | + | 1.69071i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.30136 | + | 14.3784i | −0.550981 | + | 0.954326i | 0.447224 | + | 0.894422i | \(0.352413\pi\) |
−0.998204 | + | 0.0599042i | \(0.980920\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.25072 | − | 12.5586i | −0.479141 | − | 0.829897i | 0.520573 | − | 0.853817i | \(-0.325718\pi\) |
−0.999714 | + | 0.0239205i | \(0.992385\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.9804 | 1.04691 | 0.523456 | − | 0.852053i | \(-0.324643\pi\) | ||||
0.523456 | + | 0.852053i | \(0.324643\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.6164 | −1.93196 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.107980 | − | 3.41984i | −0.00701407 | − | 0.222143i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.58994 | − | 16.6103i | −0.620322 | − | 1.07443i | −0.989426 | − | 0.145040i | \(-0.953669\pi\) |
0.369104 | − | 0.929388i | \(-0.379665\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.6785 | − | 20.2277i | 0.752276 | − | 1.30298i | −0.194441 | − | 0.980914i | \(-0.562289\pi\) |
0.946717 | − | 0.322067i | \(-0.104377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.5572 | + | 5.57562i | 0.933846 | + | 0.357676i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.67837 | + | 6.37112i | 0.234049 | + | 0.405384i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.0276599 | + | 0.876018i | 0.00175288 | + | 0.0555154i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.4619 | 1.92274 | 0.961371 | − | 0.275257i | \(-0.0887631\pi\) | ||||
0.961371 | + | 0.275257i | \(0.0887631\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.60933 | 0.101178 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −31.6929 | − | 16.9875i | −1.98469 | − | 1.06380i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.40438 | − | 5.89657i | −0.212360 | − | 0.367818i | 0.740093 | − | 0.672505i | \(-0.234782\pi\) |
−0.952453 | + | 0.304687i | \(0.901448\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.8998 | + | 25.4199i | 1.04607 | + | 1.57345i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.30000 | − | 3.98372i | 0.141824 | − | 0.245647i | −0.786359 | − | 0.617769i | \(-0.788037\pi\) |
0.928184 | + | 0.372122i | \(0.121370\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.80161 | − | 3.12049i | −0.110672 | − | 0.191690i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.9865 | + | 11.1558i | −1.10076 | + | 0.682724i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.50179 | 0.518363 | 0.259182 | − | 0.965829i | \(-0.416547\pi\) | ||||
0.259182 | + | 0.965829i | \(0.416547\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.58381 | −0.399938 | −0.199969 | − | 0.979802i | \(-0.564084\pi\) | ||||
−0.199969 | + | 0.979802i | \(0.564084\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −22.2088 | − | 38.4668i | −1.33924 | − | 2.31963i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.63483 | − | 9.75982i | 0.338564 | − | 0.586411i | −0.645599 | − | 0.763677i | \(-0.723392\pi\) |
0.984163 | + | 0.177266i | \(0.0567254\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.87285 | + | 0.434448i | −0.411467 | + | 0.0260097i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.50741 | − | 13.0032i | 0.447854 | − | 0.775707i | −0.550392 | − | 0.834907i | \(-0.685522\pi\) |
0.998246 | + | 0.0592000i | \(0.0188550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.33657 | + | 12.7073i | 0.436114 | + | 0.755371i | 0.997386 | − | 0.0722602i | \(-0.0230212\pi\) |
−0.561272 | + | 0.827631i | \(0.689688\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −27.5908 | − | 14.7888i | −1.63434 | − | 0.876014i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.4469 | 0.673344 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.486833 | − | 15.4185i | −0.0285386 | − | 0.903848i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.38981 | + | 16.2636i | 0.548559 | + | 0.950132i | 0.998374 | + | 0.0570099i | \(0.0181567\pi\) |
−0.449815 | + | 0.893122i | \(0.648510\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.79238 | − | 3.10449i | 0.104356 | − | 0.180751i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −20.6767 | − | 9.45542i | −1.19978 | − | 0.548659i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.291371 | − | 0.504669i | 0.0168504 | − | 0.0291858i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.602568 | + | 19.0839i | 0.0346166 | + | 1.09634i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 25.5174 | 1.46112 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.9425 | 1.65184 | 0.825919 | − | 0.563789i | \(-0.190657\pi\) | ||||
0.825919 | + | 0.563789i | \(0.190657\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.16888 | − | 2.23454i | −0.237159 | − | 0.127118i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.79681 | − | 11.7724i | −0.385412 | − | 0.667553i | 0.606414 | − | 0.795149i | \(-0.292607\pi\) |
−0.991826 | + | 0.127596i | \(0.959274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.93222 | + | 12.0070i | −0.391832 | + | 0.678673i | −0.992691 | − | 0.120682i | \(-0.961492\pi\) |
0.600859 | + | 0.799355i | \(0.294825\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.5428 | + | 19.9927i | −0.648309 | + | 1.12290i | 0.335217 | + | 0.942141i | \(0.391190\pi\) |
−0.983527 | + | 0.180764i | \(0.942143\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.2607 | − | 38.5566i | −1.24636 | − | 2.15876i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.8851 | − | 9.85245i | 0.886621 | − | 0.549910i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.7649 | 1.37796 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.0837 | −0.892163 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.6953 | − | 9.11448i | 0.812651 | − | 0.504032i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.82647 | − | 13.5558i | 0.430182 | − | 0.745097i | −0.566707 | − | 0.823920i | \(-0.691783\pi\) |
0.996889 | + | 0.0788227i | \(0.0251161\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.5047 | − | 29.2413i | 0.794852 | − | 1.60241i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 29.2098 | − | 50.5929i | 1.59590 | − | 2.76418i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.56686 | + | 6.17799i | 0.194299 | + | 0.336537i | 0.946671 | − | 0.322203i | \(-0.104423\pi\) |
−0.752371 | + | 0.658739i | \(0.771090\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.6860 | + | 10.0158i | 1.01488 | + | 0.543981i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.0442 | 0.543925 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0782560 | + | 2.47845i | 0.00421316 | + | 0.133435i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.77827 | − | 4.81211i | −0.149146 | − | 0.258328i | 0.781766 | − | 0.623571i | \(-0.214319\pi\) |
−0.930912 | + | 0.365244i | \(0.880986\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.33296 | − | 9.23696i | 0.285467 | − | 0.494443i | −0.687256 | − | 0.726416i | \(-0.741185\pi\) |
0.972722 | + | 0.231973i | \(0.0745181\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.70866 | + | 4.77208i | −0.358082 | + | 0.254715i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.42132 | + | 11.1221i | −0.341772 | + | 0.591967i | −0.984762 | − | 0.173908i | \(-0.944361\pi\) |
0.642989 | + | 0.765875i | \(0.277694\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.55715 | − | 16.5535i | −0.507241 | − | 0.878567i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.6835 | 1.35552 | 0.677761 | − | 0.735282i | \(-0.262950\pi\) | ||||
0.677761 | + | 0.735282i | \(0.262950\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.55954 | 0.134713 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.4349 | + | 6.66518i | 0.652665 | + | 0.349831i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.7273 | − | 25.5084i | −0.770861 | − | 1.33517i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.49197 | + | 14.7085i | −0.443277 | + | 0.767778i | −0.997930 | − | 0.0643031i | \(-0.979518\pi\) |
0.554653 | + | 0.832082i | \(0.312851\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.13441 | − | 0.261345i | 0.215229 | − | 0.0136051i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.38503 | + | 7.59509i | 0.227048 | + | 0.393259i | 0.956932 | − | 0.290312i | \(-0.0937592\pi\) |
−0.729884 | + | 0.683571i | \(0.760426\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 29.5137 | − | 18.3053i | 1.52408 | − | 0.945283i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.1213 | −0.830288 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7002 | 0.601001 | 0.300500 | − | 0.953782i | \(-0.402846\pi\) | ||||
0.300500 | + | 0.953782i | \(0.402846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.4301 | − | 12.0512i | 0.995434 | − | 0.617400i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.50360 | − | 7.80046i | −0.230123 | − | 0.398585i | 0.727721 | − | 0.685873i | \(-0.240580\pi\) |
−0.957844 | + | 0.287288i | \(0.907246\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.6794 | − | 19.0718i | −0.644530 | − | 0.969472i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.89390 | − | 8.47649i | 0.248131 | − | 0.429775i | −0.714876 | − | 0.699251i | \(-0.753517\pi\) |
0.963007 | + | 0.269476i | \(0.0868504\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.980839 | − | 1.69886i | −0.0496032 | − | 0.0859152i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.76547 | − | 4.16233i | −0.391716 | − | 0.209962i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.68929 | −0.386890 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.9186 | −0.698554 | −0.349277 | − | 0.937020i | \(-0.613573\pi\) | ||||
−0.349277 | + | 0.937020i | \(0.613573\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7414 | + | 20.3367i | 0.586336 | + | 1.01556i | 0.994707 | + | 0.102748i | \(0.0327636\pi\) |
−0.408371 | + | 0.912816i | \(0.633903\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.81852 | − | 3.14976i | 0.0905867 | − | 0.156901i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.5564 | − | 32.3029i | 0.673621 | − | 1.60514i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.8038 | + | 41.2295i | −1.17991 | + | 2.04367i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.81225 | − | 11.7992i | −0.336844 | − | 0.583431i | 0.646993 | − | 0.762496i | \(-0.276026\pi\) |
−0.983837 | + | 0.179064i | \(0.942693\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.729413 | − | 23.1013i | −0.0359793 | − | 1.13950i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.96967 | 0.0966873 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.8275 | − | 7.94759i | −0.726104 | − | 0.389195i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.97733 | + | 6.88894i | 0.194305 | + | 0.336547i | 0.946673 | − | 0.322197i | \(-0.104421\pi\) |
−0.752367 | + | 0.658744i | \(0.771088\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.30584 | − | 2.26178i | 0.0636426 | − | 0.110232i | −0.832448 | − | 0.554102i | \(-0.813062\pi\) |
0.896091 | + | 0.443870i | \(0.146395\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.6373 | + | 19.0085i | 0.614447 | + | 0.924223i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −27.0712 | + | 46.8887i | −1.31315 | + | 2.27444i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.2043 | − | 6.32904i | 0.492670 | − | 0.305569i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.58213 | −0.0762086 | −0.0381043 | − | 0.999274i | \(-0.512132\pi\) | ||||
−0.0381043 | + | 0.999274i | \(0.512132\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.17110 | −0.248507 | −0.124254 | − | 0.992250i | \(-0.539654\pi\) | ||||
−0.124254 | + | 0.992250i | \(0.539654\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 58.2966 | − | 36.1574i | 2.79511 | − | 1.73361i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.853887 | − | 1.47898i | −0.0408470 | − | 0.0707490i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.4806 | + | 21.6170i | −0.595665 | + | 1.03172i | 0.397788 | + | 0.917477i | \(0.369778\pi\) |
−0.993453 | + | 0.114244i | \(0.963555\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.542263 | + | 0.939227i | −0.0257637 | + | 0.0446240i | −0.878620 | − | 0.477522i | \(-0.841535\pi\) |
0.852856 | + | 0.522146i | \(0.174868\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.7825 | + | 41.1924i | 1.12740 | + | 1.95271i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.1315 | + | 11.3266i | 0.999484 | + | 0.535728i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.23372 | 0.199802 | 0.0999008 | − | 0.994997i | \(-0.468147\pi\) | ||||
0.0999008 | + | 0.994997i | \(0.468147\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.04216 | −0.284514 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.25044 | − | 39.6026i | −0.0587506 | − | 1.86069i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.1513 | − | 31.4390i | 0.849083 | − | 1.47065i | −0.0329453 | − | 0.999457i | \(-0.510489\pi\) |
0.882028 | − | 0.471197i | \(-0.156178\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.62038 | + | 27.5898i | 0.122309 | + | 1.28778i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.71236 | − | 2.96589i | 0.0797524 | − | 0.138135i | −0.823391 | − | 0.567475i | \(-0.807920\pi\) |
0.903143 | + | 0.429340i | \(0.141254\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.38499 | + | 4.13092i | 0.110840 | + | 0.191980i | 0.916109 | − | 0.400929i | \(-0.131313\pi\) |
−0.805269 | + | 0.592909i | \(0.797979\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.488414 | + | 15.4686i | 0.0226497 | + | 0.717338i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.0979 | 0.930021 | 0.465010 | − | 0.885305i | \(-0.346051\pi\) | ||||
0.465010 | + | 0.885305i | \(0.346051\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.6776 | − | 9.47525i | −0.814539 | − | 0.436597i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.7015 | + | 28.9279i | 0.767936 | + | 1.33010i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.5673 | + | 40.8198i | −1.08134 | + | 1.87294i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.23405 | + | 2.48783i | −0.0565033 | + | 0.113910i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.42528 | − | 14.5930i | 0.384961 | − | 0.666772i | −0.606803 | − | 0.794852i | \(-0.707548\pi\) |
0.991764 | + | 0.128080i | \(0.0408816\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.61941 | + | 14.9293i | 0.393011 | + | 0.680716i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.6675 | −1.57417 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.9831 | 1.08678 | 0.543389 | − | 0.839481i | \(-0.317141\pi\) | ||||
0.543389 | + | 0.839481i | \(0.317141\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.02153 | + | 3.11451i | −0.227082 | + | 0.140843i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.07281 | − | 1.85816i | −0.0484153 | − | 0.0838577i | 0.840802 | − | 0.541342i | \(-0.182084\pi\) |
−0.889217 | + | 0.457485i | \(0.848750\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.1345 | + | 46.9983i | −1.22207 | + | 2.11670i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −22.7052 | + | 45.7733i | −1.02052 | + | 2.05736i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.8577 | + | 24.0023i | 0.620357 | + | 1.07449i | 0.989419 | + | 0.145085i | \(0.0463455\pi\) |
−0.369062 | + | 0.929405i | \(0.620321\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.3498 | − | 7.69154i | −0.641100 | − | 0.343633i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.4265 | −0.999949 | −0.499974 | − | 0.866040i | \(-0.666657\pi\) | ||||
−0.499974 | + | 0.866040i | \(0.666657\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 42.9090 | 1.90943 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.573382 | + | 18.1596i | 0.0254648 | + | 0.806496i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.6844 | + | 25.4342i | 0.650876 | + | 1.12735i | 0.982911 | + | 0.184083i | \(0.0589316\pi\) |
−0.332034 | + | 0.943267i | \(0.607735\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.28122 | + | 24.0188i | 0.100718 | + | 1.06046i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.31488 | + | 9.20563i | −0.234201 | + | 0.405649i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.6461 | − | 28.8318i | −0.732093 | − | 1.26802i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.350114 | − | 11.0885i | −0.0153683 | − | 0.486730i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.5078 | −0.723219 | −0.361610 | − | 0.932330i | \(-0.617773\pi\) | ||||
−0.361610 | + | 0.932330i | \(0.617773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 44.6952 | 1.95439 | 0.977193 | − | 0.212352i | \(-0.0681122\pi\) | ||||
0.977193 | + | 0.212352i | \(0.0681122\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.12166 | − | 10.6030i | −0.266664 | − | 0.461875i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4324 | − | 19.8014i | 0.497059 | − | 0.860932i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.75734 | + | 0.174298i | −0.119659 | + | 0.00756388i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.09394 | + | 1.89476i | −0.0473838 | + | 0.0820711i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.0039 | − | 36.3798i | −0.908078 | − | 1.57284i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −25.1415 | + | 15.5936i | −1.08494 | + | 0.672912i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0737 | −0.863037 | −0.431519 | − | 0.902104i | \(-0.642022\pi\) | ||||
−0.431519 | + | 0.902104i | \(0.642022\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.00164 | − | 1.24148i | 0.0858985 | − | 0.0532769i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.4307 | − | 33.6549i | −0.832319 | − | 1.44162i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.35012 | − | 10.9987i | 0.271512 | − | 0.470272i | −0.697738 | − | 0.716353i | \(-0.745810\pi\) |
0.969249 | + | 0.246082i | \(0.0791432\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.8883 | − | 16.3777i | −0.464701 | − | 0.698981i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.6224 | + | 40.9152i | −1.00635 | + | 1.74305i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −64.6529 | − | 34.6542i | −2.74436 | − | 1.47099i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.6949 | 0.622642 | 0.311321 | − | 0.950305i | \(-0.399229\pi\) | ||||
0.311321 | + | 0.950305i | \(0.399229\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.0953 | 0.511576 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.27566 | − | 40.4013i | −0.0538583 | − | 1.70575i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.3930 | + | 23.1974i | 0.564448 | + | 0.977653i | 0.997101 | + | 0.0760922i | \(0.0242443\pi\) |
−0.432653 | + | 0.901561i | \(0.642422\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.8226 | − | 41.2620i | 1.00222 | − | 1.73590i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.24168 | + | 5.61475i | −0.135898 | + | 0.235383i | −0.925940 | − | 0.377670i | \(-0.876725\pi\) |
0.790042 | + | 0.613053i | \(0.210059\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.81632 | − | 13.5383i | −0.327103 | − | 0.566559i | 0.654833 | − | 0.755774i | \(-0.272739\pi\) |
−0.981936 | + | 0.189215i | \(0.939406\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.977402 | + | 30.9553i | 0.0408315 | + | 1.29318i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.73363 | 0.155703 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.1600 | 1.21395 | 0.606974 | − | 0.794722i | \(-0.292383\pi\) | ||||
0.606974 | + | 0.794722i | \(0.292383\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.8659 | − | 10.6482i | −0.825597 | − | 0.442524i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.02522 | − | 3.50778i | 0.0838759 | − | 0.145277i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.2432 | + | 15.4074i | 0.423506 | + | 0.637018i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.33110 | − | 4.03758i | 0.0962146 | − | 0.166649i | −0.813900 | − | 0.581005i | \(-0.802660\pi\) |
0.910115 | + | 0.414356i | \(0.135993\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.32932 | − | 9.23065i | −0.219591 | − | 0.380342i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.36858 | + | 5.81069i | −0.385372 | + | 0.239020i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.6644 | −1.30030 | −0.650150 | − | 0.759805i | \(-0.725294\pi\) | ||||
−0.650150 | + | 0.759805i | \(0.725294\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34.0792 | − | 21.1370i | 1.39477 | − | 0.865079i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.15268 | + | 8.92470i | 0.210533 | + | 0.364653i | 0.951881 | − | 0.306467i | \(-0.0991468\pi\) |
−0.741349 | + | 0.671120i | \(0.765813\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.64993 | − | 8.05391i | 0.189674 | − | 0.328526i | −0.755467 | − | 0.655186i | \(-0.772590\pi\) |
0.945142 | + | 0.326661i | \(0.105923\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −44.9355 | + | 2.84047i | −1.82991 | + | 0.115673i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.8532 | − | 27.4586i | 0.644525 | − | 1.11635i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.2484 | + | 17.7507i | 0.415969 | + | 0.720480i | 0.995530 | − | 0.0944495i | \(-0.0301091\pi\) |
−0.579561 | + | 0.814929i | \(0.696776\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0551 | −0.487699 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.3448 | −0.579381 | −0.289691 | − | 0.957120i | \(-0.593552\pi\) | ||||
−0.289691 | + | 0.957120i | \(0.593552\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.293809 | − | 9.30522i | −0.0118475 | − | 0.375223i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.47499 | − | 11.2150i | −0.260673 | − | 0.451499i | 0.705748 | − | 0.708463i | \(-0.250611\pi\) |
−0.966421 | + | 0.256964i | \(0.917278\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.6990 | + | 30.6556i | −0.711383 | + | 1.23215i | 0.252955 | + | 0.967478i | \(0.418598\pi\) |
−0.964338 | + | 0.264674i | \(0.914736\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.55733 | − | 1.10778i | 0.0624936 | − | 0.0444537i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.6460 | − | 23.6355i | −0.545839 | − | 0.945422i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.11055 | − | 35.1721i | −0.0443509 | − | 1.40464i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 58.0310 | 2.31385 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.1936 | 1.32141 | 0.660707 | − | 0.750644i | \(-0.270256\pi\) | ||||
0.660707 | + | 0.750644i | \(0.270256\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.3339 | + | 9.29108i | 0.688963 | + | 0.369287i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.6912 | − | 44.4985i | −1.01952 | − | 1.76587i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.54635 | + | 13.1974i | −0.258970 | + | 0.522080i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.119634 | − | 0.207213i | 0.00472528 | − | 0.00818442i | −0.863653 | − | 0.504087i | \(-0.831829\pi\) |
0.868378 | + | 0.495902i | \(0.165163\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.57211 | + | 7.91913i | 0.180307 | + | 0.312300i | 0.941985 | − | 0.335655i | \(-0.108958\pi\) |
−0.761678 | + | 0.647955i | \(0.775624\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −43.7382 | + | 27.1278i | −1.72219 | + | 1.06816i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.31214 | −0.248156 | −0.124078 | − | 0.992272i | \(-0.539597\pi\) | ||||
−0.124078 | + | 0.992272i | \(0.539597\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.02968 | 0.158179 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.27888 | + | 3.94713i | 0.0891793 | + | 0.154463i | 0.907164 | − | 0.420776i | \(-0.138242\pi\) |
−0.817985 | + | 0.575239i | \(0.804909\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.90015 | + | 17.1476i | −0.386831 | + | 0.670011i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.0877 | + | 20.3367i | −0.393560 | + | 0.793411i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.4631 | + | 28.5149i | −0.641311 | + | 1.11078i | 0.343829 | + | 0.939032i | \(0.388276\pi\) |
−0.985140 | + | 0.171751i | \(0.945058\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.270668 | + | 0.468811i | 0.0105278 | + | 0.0182346i | 0.871241 | − | 0.490855i | \(-0.163316\pi\) |
−0.860714 | + | 0.509090i | \(0.829982\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.9004 | − | 6.91467i | −0.501010 | − | 0.268543i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.74235 | 0.144905 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.45625 | + | 46.1208i | 0.0563017 | + | 1.78313i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.3422 | + | 24.8415i | 0.553676 | + | 0.958994i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.8205 | + | 20.4737i | −0.455647 | + | 0.789204i | −0.998725 | − | 0.0504780i | \(-0.983926\pi\) |
0.543078 | + | 0.839682i | \(0.317259\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −47.9697 | − | 21.9365i | −1.84636 | − | 0.844335i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.36494 | + | 2.36415i | −0.0524591 | + | 0.0908618i | −0.891062 | − | 0.453881i | \(-0.850039\pi\) |
0.838603 | + | 0.544742i | \(0.183373\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.907531 | − | 28.7424i | −0.0347767 | − | 1.10141i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.9279 | −1.22169 | −0.610844 | − | 0.791751i | \(-0.709170\pi\) | ||||
−0.610844 | + | 0.791751i | \(0.709170\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −51.9417 | −1.98459 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.1377 | + | 11.8659i | 0.844605 | + | 0.452712i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.733335 | − | 1.27017i | −0.0279378 | − | 0.0483897i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.19103 | + | 2.06292i | −0.0453089 | + | 0.0784773i | −0.887790 | − | 0.460248i | \(-0.847761\pi\) |
0.842482 | + | 0.538725i | \(0.181094\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.9034 | + | 32.7417i | −0.717048 | + | 1.24196i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.68252 | + | 6.37831i | 0.139485 | + | 0.241596i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.5219 | + | 14.5890i | −0.889680 | + | 0.551808i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.3767 | 1.90270 | 0.951350 | − | 0.308111i | \(-0.0996968\pi\) | ||||
0.951350 | + | 0.308111i | \(0.0996968\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.5199 | 1.90539 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 43.5930 | − | 27.0377i | 1.64181 | − | 1.01830i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.1600 | + | 34.9182i | −0.757126 | + | 1.31138i | 0.187184 | + | 0.982325i | \(0.440064\pi\) |
−0.944310 | + | 0.329056i | \(0.893269\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.28102 | + | 4.93516i | 0.123048 | + | 0.185083i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.422146 | + | 0.731178i | −0.0158095 | + | 0.0273828i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.4926 | − | 23.3698i | −0.504593 | − | 0.873981i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29.2797 | + | 15.6940i | 1.09347 | + | 0.586105i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.0893 | 1.27132 | 0.635658 | − | 0.771971i | \(-0.280729\pi\) | ||||
0.635658 | + | 0.771971i | \(0.280729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.27673 | + | 40.4353i | 0.0474820 | + | 1.50380i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −51.6446 | − | 89.4510i | −1.91803 | − | 3.32213i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.9453 | + | 18.9578i | −0.405938 | + | 0.703105i | −0.994430 | − | 0.105398i | \(-0.966388\pi\) |
0.588492 | + | 0.808503i | \(0.299722\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.5172 | + | 5.08288i | −0.982120 | + | 0.188255i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.3581 | − | 35.2613i | 0.752973 | − | 1.30419i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.34416 | − | 7.52430i | −0.160455 | − | 0.277916i | 0.774577 | − | 0.632480i | \(-0.217963\pi\) |
−0.935032 | + | 0.354563i | \(0.884630\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 65.6702 | 2.41899 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.69385 | 0.246237 | 0.123119 | − | 0.992392i | \(-0.460710\pi\) | ||||
0.123119 | + | 0.992392i | \(0.460710\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.2307 | − | 6.01969i | −0.412569 | − | 0.221139i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.5001 | + | 37.2392i | 0.788761 | + | 1.36617i | 0.926726 | + | 0.375737i | \(0.122611\pi\) |
−0.137965 | + | 0.990437i | \(0.544056\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.9404 | − | 46.6621i | 0.987019 | − | 1.70957i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.840458 | − | 1.26418i | −0.0307508 | − | 0.0462539i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.36369 | + | 14.4863i | 0.305196 | + | 0.528614i | 0.977305 | − | 0.211838i | \(-0.0679448\pi\) |
−0.672109 | + | 0.740452i | \(0.734612\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −44.8376 | + | 27.8097i | −1.63397 | + | 1.01344i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −89.0438 | −3.24064 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.68561 | −0.170301 | −0.0851507 | − | 0.996368i | \(-0.527137\pi\) | ||||
−0.0851507 | + | 0.996368i | \(0.527137\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.36881 | + | 1.46921i | −0.0859823 | + | 0.0533289i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.8242 | − | 44.7288i | −0.936127 | − | 1.62142i | −0.772613 | − | 0.634878i | \(-0.781050\pi\) |
−0.163514 | − | 0.986541i | \(-0.552283\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 62.1580 | − | 3.92915i | 2.24733 | − | 0.142059i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.729576 | − | 1.26366i | 0.0263435 | − | 0.0456282i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.3910 | − | 26.6580i | −0.555014 | − | 0.961313i | −0.997902 | − | 0.0647361i | \(-0.979379\pi\) |
0.442888 | − | 0.896577i | \(-0.353954\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3942 | + | 5.57131i | 0.374336 | + | 0.200646i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.0517 | −0.972982 | −0.486491 | − | 0.873686i | \(-0.661723\pi\) | ||||
−0.486491 | + | 0.873686i | \(0.661723\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.3025 | 0.837050 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.20588 | + | 5.55275i | 0.114863 | + | 0.198948i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.7433 | − | 18.6080i | 0.384426 | − | 0.665845i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −48.0818 | − | 21.9877i | −1.71830 | − | 0.785777i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.5370 | + | 39.0352i | −0.804380 | + | 1.39323i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.5997 | − | 30.4837i | −0.627363 | − | 1.08662i | −0.988079 | − | 0.153949i | \(-0.950801\pi\) |
0.360716 | − | 0.932676i | \(-0.382532\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.251444 | + | 7.96348i | 0.00895163 | + | 0.283507i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.3867 | 0.368842 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.50063 | + | 2.94836i | 0.195087 | + | 0.104568i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.8268 | + | 41.2692i | 0.843988 | + | 1.46183i | 0.886497 | + | 0.462735i | \(0.153132\pi\) |
−0.0425084 | + | 0.999096i | \(0.513535\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.2906 | + | 35.1443i | −0.717829 | + | 1.24332i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.2903 | − | 32.8409i | 0.575588 | − | 1.16038i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.5551 | − | 28.6743i | 0.584217 | − | 1.01189i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.5140 | + | 7.76156i | −0.440513 | + | 0.273220i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.7542 | 0.694521 | 0.347261 | − | 0.937769i | \(-0.387112\pi\) | ||||
0.347261 | + | 0.937769i | \(0.387112\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.2424 | 1.72913 | 0.864567 | − | 0.502518i | \(-0.167593\pi\) | ||||
0.864567 | + | 0.502518i | \(0.167593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.69086 | − | 6.01057i | 0.339873 | − | 0.210800i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.63967 | + | 11.5002i | 0.232577 | + | 0.402836i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.7231 | − | 30.6974i | 0.620054 | − | 1.07397i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.00013 | + | 8.66048i | −0.174506 | + | 0.302253i | −0.939990 | − | 0.341202i | \(-0.889166\pi\) |
0.765484 | + | 0.643455i | \(0.222499\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.5138 | + | 30.3348i | 0.610493 | + | 1.05741i | 0.991157 | + | 0.132692i | \(0.0423621\pi\) |
−0.380664 | + | 0.924713i | \(0.624305\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 67.8072 | + | 36.3449i | 2.36074 | + | 1.26537i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.7079 | −0.789631 | −0.394816 | − | 0.918760i | \(-0.629192\pi\) | ||||
−0.394816 | + | 0.918760i | \(0.629192\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.4417 | 0.432117 | 0.216058 | − | 0.976380i | \(-0.430680\pi\) | ||||
0.216058 | + | 0.976380i | \(0.430680\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.616018 | + | 19.5099i | 0.0213694 | + | 0.676791i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.2944 | + | 31.6869i | −0.633105 | + | 1.09657i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.71968 | − | 6.91392i | 0.335961 | − | 0.238980i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.8249 | − | 23.9455i | 0.477290 | − | 0.826690i | −0.522372 | − | 0.852718i | \(-0.674953\pi\) |
0.999661 | + | 0.0260281i | \(0.00828595\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −37.2652 | − | 64.5453i | −1.28501 | − | 2.22570i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.820733 | + | 25.9935i | 0.0282676 | + | 0.895263i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40.8307 | 1.40462 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.3998 | − | 12.0064i | −0.768758 | − | 0.412058i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.00089 | − | 3.46564i | −0.0685896 | − | 0.118801i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0459 | − | 38.1847i | 0.754839 | − | 1.30742i | −0.190616 | − | 0.981665i | \(-0.561048\pi\) |
0.945454 | − | 0.325754i | \(-0.105618\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 54.1127 | − | 3.42059i | 1.85062 | − | 0.116982i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.3838 | + | 23.1814i | −0.457182 | + | 0.791862i | −0.998811 | − | 0.0487557i | \(-0.984474\pi\) |
0.541629 | + | 0.840618i | \(0.317808\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.0951 | − | 17.4852i | −0.344439 | − | 0.596587i | 0.640812 | − | 0.767698i | \(-0.278598\pi\) |
−0.985252 | + | 0.171111i | \(0.945264\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.49075 | 0.323069 | 0.161534 | − | 0.986867i | \(-0.448356\pi\) | ||||
0.161534 | + | 0.986867i | \(0.448356\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.9317 | −0.847703 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.8489 | + | 10.4502i | −0.572218 | + | 0.354908i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.32182 | − | 7.48560i | −0.146608 | − | 0.253932i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.8897 | − | 20.5935i | 0.402866 | − | 0.697784i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.7926 | + | 22.2504i | 0.500654 | + | 0.753061i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.6227 | − | 25.3273i | −0.493774 | − | 0.855242i | 0.506200 | − | 0.862416i | \(-0.331050\pi\) |
−0.999974 | + | 0.00717380i | \(0.997716\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.6687 | − | 15.3665i | −0.966970 | − | 0.518301i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.2768 | −1.25589 | −0.627944 | − | 0.778259i | \(-0.716103\pi\) | ||||
−0.627944 | + | 0.778259i | \(0.716103\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.9436 | −1.91630 | −0.958152 | − | 0.286260i | \(-0.907588\pi\) | ||||
−0.958152 | + | 0.286260i | \(0.907588\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.195949 | + | 6.20590i | 0.00658674 | + | 0.208609i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.96127 | − | 8.59316i | −0.166583 | − | 0.288530i | 0.770633 | − | 0.637279i | \(-0.219940\pi\) |
−0.937216 | + | 0.348749i | \(0.886607\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 39.0667 | − | 4.95879i | 1.30878 | − | 0.166126i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.6643 | + | 30.5955i | −0.591114 | + | 1.02384i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33.2431 | + | 57.5787i | 1.11119 | + | 1.92465i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0318536 | + | 1.00884i | 0.00106356 | + | 0.0336840i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.3569 | 0.778997 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.93724 | −0.164483 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.64664 | − | 4.58412i | −0.0879774 | − | 0.152381i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.2887 | − | 21.2847i | 0.408040 | − | 0.706747i | −0.586630 | − | 0.809855i | \(-0.699546\pi\) |
0.994670 | + | 0.103109i | \(0.0328789\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.3093 | − | 27.5400i | −0.607280 | − | 0.913443i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.73496 | − | 16.8614i | 0.322534 | − | 0.558645i | −0.658476 | − | 0.752601i | \(-0.728799\pi\) |
0.981010 | + | 0.193957i | \(0.0621321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.10707 | + | 1.91749i | 0.0366385 | + | 0.0634598i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −37.5596 | + | 23.2957i | −1.24168 | + | 0.770131i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.2398 | −0.436742 | −0.218371 | − | 0.975866i | \(-0.570074\pi\) | ||||
−0.218371 | + | 0.975866i | \(0.570074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −42.6012 | + | 26.4226i | −1.40376 | + | 0.870653i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.89017 | − | 6.73798i | −0.128047 | − | 0.221783i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −55.2247 | + | 95.6519i | −1.81578 | + | 3.14502i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.17624 | − | 0.516839i | 0.268543 | − | 0.0169752i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.8682 | − | 27.4845i | 0.520618 | − | 0.901737i | −0.479095 | − | 0.877763i | \(-0.659035\pi\) |
0.999713 | − | 0.0239734i | \(-0.00763170\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.7518 | + | 11.1231i | 0.679384 | + | 0.364153i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −90.8398 | −2.97078 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.5019 | 0.441087 | 0.220543 | − | 0.975377i | \(-0.429217\pi\) | ||||
0.220543 | + | 0.975377i | \(0.429217\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.757852 | − | 24.0020i | −0.0247316 | − | 0.783274i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.8286 | − | 34.3441i | −0.646394 | − | 1.11959i | −0.983978 | − | 0.178291i | \(-0.942943\pi\) |
0.337584 | − | 0.941295i | \(-0.390390\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.253944 | − | 0.439845i | 0.00826957 | − | 0.0143233i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.5172 | − | 52.8573i | 0.991675 | − | 1.71763i | 0.384325 | − | 0.923198i | \(-0.374434\pi\) |
0.607350 | − | 0.794434i | \(-0.292232\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.99464 | − | 10.3830i | −0.194594 | − | 0.337047i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.26190 | − | 39.9656i | −0.0409198 | − | 1.29597i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.22726 | 0.169328 | 0.0846638 | − | 0.996410i | \(-0.473018\pi\) | ||||
0.0846638 | + | 0.996410i | \(0.473018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 69.6010 | 2.25224 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 67.9656 | + | 36.4299i | 2.19702 | + | 1.17761i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.8653 | − | 22.2833i | 0.415009 | − | 0.718817i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.3870 | + | 29.0041i | −0.463616 | + | 0.934643i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.3269 | + | 43.8674i | −0.815301 | + | 1.41214i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.2035 | + | 17.6729i | 0.328121 | + | 0.568323i | 0.982139 | − | 0.188156i | \(-0.0602511\pi\) |
−0.654018 | + | 0.756479i | \(0.726918\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36.4520 | + | 22.6087i | −1.17101 | + | 0.726296i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.17880 | −0.0378296 | −0.0189148 | − | 0.999821i | \(-0.506021\pi\) | ||||
−0.0189148 | + | 0.999821i | \(0.506021\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.6739 | − | 14.6833i | 0.758173 | − | 0.470243i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.10487 | − | 7.10984i | −0.131326 | − | 0.227464i | 0.792862 | − | 0.609402i | \(-0.208590\pi\) |
−0.924188 | + | 0.381938i | \(0.875257\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.7342 | + | 46.3049i | −0.854427 | + | 1.47991i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.3094 | + | 26.8316i | −0.424937 | + | 0.856667i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.753481 | + | 1.30507i | −0.0240323 | + | 0.0416252i | −0.877791 | − | 0.479043i | \(-0.840984\pi\) |
0.853759 | + | 0.520668i | \(0.174317\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.3875 | + | 21.4558i | 0.394698 | + | 0.683638i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.80777 | −0.0892820 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.4459 | 1.03068 | 0.515339 | − | 0.856987i | \(-0.327666\pi\) | ||||
0.515339 | + | 0.856987i | \(0.327666\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.855615 | + | 27.0982i | 0.0271521 | + | 0.859935i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45.0608 | − | 78.0476i | −1.42852 | − | 2.47428i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.26198 | + | 10.8461i | −0.198319 | + | 0.343498i | −0.947983 | − | 0.318320i | \(-0.896881\pi\) |
0.749665 | + | 0.661818i | \(0.230215\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.34552 | + | 56.2826i | 0.169125 | + | 1.78070i |
(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 | 1764.2.j.i.1177.3 | yes | 24 | |
3.2 | odd | 2 | 5292.2.j.i.3529.1 | 24 | |||
7.2 | even | 3 | 1764.2.i.j.1537.6 | 24 | |||
7.3 | odd | 6 | 1764.2.l.j.961.2 | 24 | |||
7.4 | even | 3 | 1764.2.l.j.961.11 | 24 | |||
7.5 | odd | 6 | 1764.2.i.j.1537.7 | 24 | |||
7.6 | odd | 2 | inner | 1764.2.j.i.1177.10 | yes | 24 | |
9.4 | even | 3 | inner | 1764.2.j.i.589.3 | ✓ | 24 | |
9.5 | odd | 6 | 5292.2.j.i.1765.1 | 24 | |||
21.2 | odd | 6 | 5292.2.i.j.2125.1 | 24 | |||
21.5 | even | 6 | 5292.2.i.j.2125.12 | 24 | |||
21.11 | odd | 6 | 5292.2.l.j.3313.12 | 24 | |||
21.17 | even | 6 | 5292.2.l.j.3313.1 | 24 | |||
21.20 | even | 2 | 5292.2.j.i.3529.12 | 24 | |||
63.4 | even | 3 | 1764.2.i.j.373.6 | 24 | |||
63.5 | even | 6 | 5292.2.l.j.361.1 | 24 | |||
63.13 | odd | 6 | inner | 1764.2.j.i.589.10 | yes | 24 | |
63.23 | odd | 6 | 5292.2.l.j.361.12 | 24 | |||
63.31 | odd | 6 | 1764.2.i.j.373.7 | 24 | |||
63.32 | odd | 6 | 5292.2.i.j.1549.1 | 24 | |||
63.40 | odd | 6 | 1764.2.l.j.949.2 | 24 | |||
63.41 | even | 6 | 5292.2.j.i.1765.12 | 24 | |||
63.58 | even | 3 | 1764.2.l.j.949.11 | 24 | |||
63.59 | even | 6 | 5292.2.i.j.1549.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.2.i.j.373.6 | 24 | 63.4 | even | 3 | |||
1764.2.i.j.373.7 | 24 | 63.31 | odd | 6 | |||
1764.2.i.j.1537.6 | 24 | 7.2 | even | 3 | |||
1764.2.i.j.1537.7 | 24 | 7.5 | odd | 6 | |||
1764.2.j.i.589.3 | ✓ | 24 | 9.4 | even | 3 | inner | |
1764.2.j.i.589.10 | yes | 24 | 63.13 | odd | 6 | inner | |
1764.2.j.i.1177.3 | yes | 24 | 1.1 | even | 1 | trivial | |
1764.2.j.i.1177.10 | yes | 24 | 7.6 | odd | 2 | inner | |
1764.2.l.j.949.2 | 24 | 63.40 | odd | 6 | |||
1764.2.l.j.949.11 | 24 | 63.58 | even | 3 | |||
1764.2.l.j.961.2 | 24 | 7.3 | odd | 6 | |||
1764.2.l.j.961.11 | 24 | 7.4 | even | 3 | |||
5292.2.i.j.1549.1 | 24 | 63.32 | odd | 6 | |||
5292.2.i.j.1549.12 | 24 | 63.59 | even | 6 | |||
5292.2.i.j.2125.1 | 24 | 21.2 | odd | 6 | |||
5292.2.i.j.2125.12 | 24 | 21.5 | even | 6 | |||
5292.2.j.i.1765.1 | 24 | 9.5 | odd | 6 | |||
5292.2.j.i.1765.12 | 24 | 63.41 | even | 6 | |||
5292.2.j.i.3529.1 | 24 | 3.2 | odd | 2 | |||
5292.2.j.i.3529.12 | 24 | 21.20 | even | 2 | |||
5292.2.l.j.361.1 | 24 | 63.5 | even | 6 | |||
5292.2.l.j.361.12 | 24 | 63.23 | odd | 6 | |||
5292.2.l.j.3313.1 | 24 | 21.17 | even | 6 | |||
5292.2.l.j.3313.12 | 24 | 21.11 | odd | 6 |