Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(109,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.v (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 109.4 | ||
Character | \(\chi\) | \(=\) | 864.109 |
Dual form | 864.2.v.b.325.4 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.23997 | + | 0.680049i | −0.876793 | + | 0.480867i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.07507 | − | 1.68649i | 0.537533 | − | 0.843243i | ||||
\(5\) | 1.02237 | − | 0.423478i | 0.457217 | − | 0.189385i | −0.142175 | − | 0.989842i | \(-0.545409\pi\) |
0.599391 | + | 0.800456i | \(0.295409\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.485592 | − | 0.485592i | 0.183537 | − | 0.183537i | −0.609358 | − | 0.792895i | \(-0.708573\pi\) |
0.792895 | + | 0.609358i | \(0.208573\pi\) | |||||||
\(8\) | −0.186159 | + | 2.82229i | −0.0658172 | + | 0.997832i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.979722 | + | 1.22036i | −0.309815 | + | 0.385912i | ||||
\(11\) | 1.70905 | + | 4.12601i | 0.515298 | + | 1.24404i | 0.940763 | + | 0.339064i | \(0.110110\pi\) |
−0.425465 | + | 0.904975i | \(0.639890\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.03122 | − | 0.841358i | −0.563358 | − | 0.233351i | 0.0827840 | − | 0.996568i | \(-0.473619\pi\) |
−0.646142 | + | 0.763217i | \(0.723619\pi\) | |||||||
\(14\) | −0.271894 | + | 0.932347i | −0.0726668 | + | 0.249180i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.68847 | − | 3.62617i | −0.422117 | − | 0.906541i | ||||
\(17\) | 4.47838i | 1.08617i | 0.839679 | + | 0.543083i | \(0.182743\pi\) | ||||
−0.839679 | + | 0.543083i | \(0.817257\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.51262 | + | 1.04076i | 0.576434 | + | 0.238767i | 0.651802 | − | 0.758389i | \(-0.274013\pi\) |
−0.0753681 | + | 0.997156i | \(0.524013\pi\) | |||||||
\(20\) | 0.384922 | − | 2.17947i | 0.0860711 | − | 0.487345i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.92507 | − | 3.95390i | −1.05003 | − | 0.842975i | ||||
\(23\) | −1.15719 | − | 1.15719i | −0.241291 | − | 0.241291i | 0.576093 | − | 0.817384i | \(-0.304577\pi\) |
−0.817384 | + | 0.576093i | \(0.804577\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.66963 | + | 2.66963i | −0.533927 | + | 0.533927i | ||||
\(26\) | 3.09082 | − | 0.338067i | 0.606160 | − | 0.0663004i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.296901 | − | 1.34099i | −0.0561089 | − | 0.253423i | ||||
\(29\) | −1.62983 | + | 3.93476i | −0.302652 | + | 0.730667i | 0.697252 | + | 0.716826i | \(0.254406\pi\) |
−0.999904 | + | 0.0138407i | \(0.995594\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.62389 | 1.18969 | 0.594843 | − | 0.803842i | \(-0.297214\pi\) | ||||
0.594843 | + | 0.803842i | \(0.297214\pi\) | |||||||
\(32\) | 4.55963 | + | 3.34811i | 0.806035 | + | 0.591867i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.04552 | − | 5.55306i | −0.522302 | − | 0.952343i | ||||
\(35\) | 0.290816 | − | 0.702091i | 0.0491568 | − | 0.118675i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.60845 | − | 3.97995i | 1.57962 | − | 0.654300i | 0.591266 | − | 0.806477i | \(-0.298628\pi\) |
0.988353 | + | 0.152177i | \(0.0486284\pi\) | |||||||
\(38\) | −3.82335 | + | 0.418190i | −0.620229 | + | 0.0678393i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00486 | + | 2.96426i | 0.158882 | + | 0.468690i | ||||
\(41\) | 3.06238 | + | 3.06238i | 0.478263 | + | 0.478263i | 0.904576 | − | 0.426313i | \(-0.140188\pi\) |
−0.426313 | + | 0.904576i | \(0.640188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.15582 | − | 5.20462i | −0.328760 | − | 0.793696i | −0.998685 | − | 0.0512678i | \(-0.983674\pi\) |
0.669925 | − | 0.742429i | \(-0.266326\pi\) | |||||||
\(44\) | 8.79580 | + | 1.55345i | 1.32602 | + | 0.234191i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.22184 | + | 0.647940i | 0.327592 | + | 0.0955335i | ||||
\(47\) | − | 8.66512i | − | 1.26394i | −0.774994 | − | 0.631969i | \(-0.782247\pi\) | ||
0.774994 | − | 0.631969i | \(-0.217753\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.52840i | 0.932629i | ||||||||
\(50\) | 1.49479 | − | 5.12575i | 0.211395 | − | 0.724891i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.60263 | + | 2.52110i | −0.499595 | + | 0.349614i | ||||
\(53\) | 2.26817 | + | 5.47584i | 0.311557 | + | 0.752165i | 0.999648 | + | 0.0265403i | \(0.00844902\pi\) |
−0.688091 | + | 0.725625i | \(0.741551\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.49455 | + | 3.49455i | 0.471205 | + | 0.471205i | ||||
\(56\) | 1.28009 | + | 1.46088i | 0.171059 | + | 0.195218i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.654885 | − | 5.98736i | −0.0859906 | − | 0.786179i | ||||
\(59\) | 7.36470 | − | 3.05056i | 0.958802 | − | 0.397149i | 0.152270 | − | 0.988339i | \(-0.451342\pi\) |
0.806532 | + | 0.591190i | \(0.201342\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.16848 | + | 2.82095i | −0.149608 | + | 0.361186i | −0.980861 | − | 0.194708i | \(-0.937624\pi\) |
0.831253 | + | 0.555894i | \(0.187624\pi\) | |||||||
\(62\) | −8.21344 | + | 4.50457i | −1.04311 | + | 0.572081i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.93069 | − | 1.05079i | −0.991336 | − | 0.131349i | ||||
\(65\) | −2.43295 | −0.301770 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.63065 | + | 3.93673i | −0.199215 | + | 0.480948i | −0.991642 | − | 0.129019i | \(-0.958817\pi\) |
0.792427 | + | 0.609967i | \(0.208817\pi\) | |||||||
\(68\) | 7.55272 | + | 4.81455i | 0.915901 | + | 0.583850i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.116853 | + | 1.06834i | 0.0139666 | + | 0.127691i | ||||
\(71\) | −2.11730 | + | 2.11730i | −0.251277 | + | 0.251277i | −0.821494 | − | 0.570217i | \(-0.806859\pi\) |
0.570217 | + | 0.821494i | \(0.306859\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.06373 | + | 6.06373i | 0.709706 | + | 0.709706i | 0.966473 | − | 0.256767i | \(-0.0826573\pi\) |
−0.256767 | + | 0.966473i | \(0.582657\pi\) | |||||||
\(74\) | −9.20765 | + | 11.4692i | −1.07037 | + | 1.33327i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.45646 | − | 3.11861i | 0.511191 | − | 0.357729i | ||||
\(77\) | 2.83346 | + | 1.17366i | 0.322903 | + | 0.133751i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.65785i | 0.636558i | 0.947997 | + | 0.318279i | \(0.103105\pi\) | ||||
−0.947997 | + | 0.318279i | \(0.896895\pi\) | |||||||
\(80\) | −3.26184 | − | 2.99224i | −0.364684 | − | 0.334543i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.87983 | − | 1.71470i | −0.649319 | − | 0.189357i | ||||
\(83\) | −1.59099 | − | 0.659009i | −0.174634 | − | 0.0723356i | 0.293654 | − | 0.955912i | \(-0.405129\pi\) |
−0.468287 | + | 0.883576i | \(0.655129\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.89650 | + | 4.57854i | 0.205704 | + | 0.496613i | ||||
\(86\) | 6.21256 | + | 4.98752i | 0.669917 | + | 0.537818i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11.9630 | + | 4.05535i | −1.27526 | + | 0.432301i | ||||
\(89\) | 0.998730 | − | 0.998730i | 0.105865 | − | 0.105865i | −0.652190 | − | 0.758055i | \(-0.726150\pi\) |
0.758055 | + | 0.652190i | \(0.226150\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.39490 | + | 0.577786i | −0.146225 | + | 0.0605685i | ||||
\(92\) | −3.19565 | + | 0.707531i | −0.333169 | + | 0.0737652i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.89271 | + | 10.7445i | 0.607787 | + | 1.10821i | ||||
\(95\) | 3.00956 | 0.308774 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.78679 | 0.993698 | 0.496849 | − | 0.867837i | \(-0.334490\pi\) | ||||
0.496849 | + | 0.867837i | \(0.334490\pi\) | |||||||
\(98\) | −4.43963 | − | 8.09504i | −0.448471 | − | 0.817723i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.63227 | + | 7.37233i | 0.163227 | + | 0.737233i | ||||
\(101\) | −9.75718 | + | 4.04156i | −0.970876 | + | 0.402150i | −0.811038 | − | 0.584993i | \(-0.801097\pi\) |
−0.159838 | + | 0.987143i | \(0.551097\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.84442 | + | 6.84442i | −0.674400 | + | 0.674400i | −0.958727 | − | 0.284327i | \(-0.908230\pi\) |
0.284327 | + | 0.958727i | \(0.408230\pi\) | |||||||
\(104\) | 2.75269 | − | 5.57607i | 0.269923 | − | 0.546778i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.53631 | − | 5.24743i | −0.634863 | − | 0.509675i | ||||
\(107\) | −7.22263 | − | 17.4370i | −0.698238 | − | 1.68570i | −0.727485 | − | 0.686123i | \(-0.759311\pi\) |
0.0292471 | − | 0.999572i | \(-0.490689\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.61835 | + | 1.08456i | 0.250793 | + | 0.103882i | 0.504539 | − | 0.863389i | \(-0.331663\pi\) |
−0.253746 | + | 0.967271i | \(0.581663\pi\) | |||||||
\(110\) | −6.70962 | − | 1.95668i | −0.639737 | − | 0.186562i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.58074 | − | 0.940931i | −0.243857 | − | 0.0889096i | ||||
\(113\) | 9.73367i | 0.915667i | 0.889038 | + | 0.457833i | \(0.151374\pi\) | ||||
−0.889038 | + | 0.457833i | \(0.848626\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.67312 | − | 0.693030i | −0.156019 | − | 0.0646254i | ||||
\(116\) | 4.88374 | + | 6.97881i | 0.453444 | + | 0.647966i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.05750 | + | 8.79097i | −0.649695 | + | 0.809274i | ||||
\(119\) | 2.17466 | + | 2.17466i | 0.199351 | + | 0.199351i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.32494 | + | 6.32494i | −0.574994 | + | 0.574994i | ||||
\(122\) | −0.469507 | − | 4.29252i | −0.0425072 | − | 0.388627i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.12112 | − | 11.1711i | 0.639495 | − | 1.00319i | ||||
\(125\) | −3.71621 | + | 8.97171i | −0.332388 | + | 0.802454i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.1424 | 1.34367 | 0.671834 | − | 0.740702i | \(-0.265507\pi\) | ||||
0.671834 | + | 0.740702i | \(0.265507\pi\) | |||||||
\(128\) | 10.5484 | − | 4.09031i | 0.932358 | − | 0.361535i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.01679 | − | 1.65452i | 0.264590 | − | 0.145111i | ||||
\(131\) | 1.28871 | − | 3.11121i | 0.112595 | − | 0.271828i | −0.857530 | − | 0.514434i | \(-0.828002\pi\) |
0.970125 | + | 0.242606i | \(0.0780021\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.72549 | − | 0.714722i | 0.149619 | − | 0.0619743i | ||||
\(134\) | −0.655213 | − | 5.99036i | −0.0566018 | − | 0.517488i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.6393 | − | 0.833690i | −1.08381 | − | 0.0714884i | ||||
\(137\) | −6.62181 | − | 6.62181i | −0.565739 | − | 0.565739i | 0.365193 | − | 0.930932i | \(-0.381003\pi\) |
−0.930932 | + | 0.365193i | \(0.881003\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.72217 | + | 11.4003i | 0.400529 | + | 0.966963i | 0.987538 | + | 0.157382i | \(0.0503054\pi\) |
−0.587009 | + | 0.809581i | \(0.699695\pi\) | |||||||
\(140\) | −0.871420 | − | 1.24525i | −0.0736485 | − | 0.105243i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.18552 | − | 4.06525i | 0.0994869 | − | 0.341149i | ||||
\(143\) | − | 9.81875i | − | 0.821085i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.71297i | 0.391391i | ||||||||
\(146\) | −11.6425 | − | 3.39523i | −0.963540 | − | 0.280991i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.61759 | − | 20.4832i | 0.297364 | − | 1.68371i | ||||
\(149\) | 5.42967 | + | 13.1084i | 0.444816 | + | 1.07388i | 0.974238 | + | 0.225522i | \(0.0724086\pi\) |
−0.529423 | + | 0.848358i | \(0.677591\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.50713 | + | 7.50713i | 0.610921 | + | 0.610921i | 0.943186 | − | 0.332265i | \(-0.107813\pi\) |
−0.332265 | + | 0.943186i | \(0.607813\pi\) | |||||||
\(152\) | −3.40508 | + | 6.89760i | −0.276188 | + | 0.559469i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.31156 | + | 0.471589i | −0.347435 | + | 0.0380017i | ||||
\(155\) | 6.77205 | − | 2.80507i | 0.543944 | − | 0.225309i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.85968 | − | 18.9749i | 0.627270 | − | 1.51436i | −0.215731 | − | 0.976453i | \(-0.569213\pi\) |
0.843001 | − | 0.537912i | \(-0.180787\pi\) | |||||||
\(158\) | −3.84762 | − | 7.01558i | −0.306100 | − | 0.558130i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.07946 | + | 1.49209i | 0.480624 | + | 0.117960i | ||||
\(161\) | −1.12385 | −0.0885716 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.90975 | − | 11.8532i | 0.384561 | − | 0.928413i | −0.606510 | − | 0.795076i | \(-0.707431\pi\) |
0.991071 | − | 0.133337i | \(-0.0425692\pi\) | |||||||
\(164\) | 8.45691 | − | 1.87240i | 0.660374 | − | 0.146210i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.42094 | − | 0.264797i | 0.187901 | − | 0.0205523i | ||||
\(167\) | 6.25647 | − | 6.25647i | 0.484140 | − | 0.484140i | −0.422311 | − | 0.906451i | \(-0.638781\pi\) |
0.906451 | + | 0.422311i | \(0.138781\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.77443 | − | 5.77443i | −0.444187 | − | 0.444187i | ||||
\(170\) | −5.46524 | − | 4.38756i | −0.419165 | − | 0.336511i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.0952 | − | 1.95954i | −0.845998 | − | 0.149414i | ||||
\(173\) | −19.6250 | − | 8.12896i | −1.49206 | − | 0.618033i | −0.520300 | − | 0.853984i | \(-0.674180\pi\) |
−0.971765 | + | 0.235950i | \(0.924180\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.59270i | 0.195990i | ||||||||
\(176\) | 12.0759 | − | 13.1639i | 0.910257 | − | 0.992269i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.559212 | + | 1.91758i | −0.0419147 | + | 0.143729i | ||||
\(179\) | −17.6010 | − | 7.29058i | −1.31556 | − | 0.544923i | −0.389059 | − | 0.921213i | \(-0.627200\pi\) |
−0.926502 | + | 0.376289i | \(0.877200\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.96863 | − | 14.4095i | −0.443644 | − | 1.07105i | −0.974660 | − | 0.223691i | \(-0.928189\pi\) |
0.531016 | − | 0.847362i | \(-0.321811\pi\) | |||||||
\(182\) | 1.33671 | − | 1.66504i | 0.0990839 | − | 0.123421i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.48136 | − | 3.05052i | 0.256649 | − | 0.224887i | ||||
\(185\) | 8.13794 | − | 8.13794i | 0.598313 | − | 0.598313i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.4778 | + | 7.65377i | −1.35123 | + | 0.559699i | ||||
\(188\) | −14.6136 | − | 9.31557i | −1.06581 | − | 0.679408i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.73177 | + | 2.04665i | −0.270731 | + | 0.148479i | ||||
\(191\) | −1.13157 | −0.0818774 | −0.0409387 | − | 0.999162i | \(-0.513035\pi\) | ||||
−0.0409387 | + | 0.999162i | \(0.513035\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.9180 | −1.79363 | −0.896817 | − | 0.442401i | \(-0.854127\pi\) | ||||
−0.896817 | + | 0.442401i | \(0.854127\pi\) | |||||||
\(194\) | −12.1354 | + | 6.65550i | −0.871268 | + | 0.477837i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.0101 | + | 7.01846i | 0.786432 | + | 0.501319i | ||||
\(197\) | 13.0772 | − | 5.41675i | 0.931711 | − | 0.385927i | 0.135384 | − | 0.990793i | \(-0.456773\pi\) |
0.796327 | + | 0.604866i | \(0.206773\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.5340 | − | 13.5340i | 0.959398 | − | 0.959398i | −0.0398095 | − | 0.999207i | \(-0.512675\pi\) |
0.999207 | + | 0.0398095i | \(0.0126751\pi\) | |||||||
\(200\) | −7.03751 | − | 8.03147i | −0.497627 | − | 0.567910i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.35018 | − | 11.6468i | 0.657877 | − | 0.819465i | ||||
\(203\) | 1.11926 | + | 2.70212i | 0.0785563 | + | 0.189652i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.42772 | + | 1.83402i | 0.309246 | + | 0.128094i | ||||
\(206\) | 3.83235 | − | 13.1414i | 0.267013 | − | 0.915607i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.378741 | + | 8.78614i | 0.0262610 | + | 0.609209i | ||||
\(209\) | 12.1458i | 0.840143i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.1970 | − | 9.19431i | −1.52811 | − | 0.632962i | −0.548910 | − | 0.835881i | \(-0.684957\pi\) |
−0.979196 | + | 0.202919i | \(0.934957\pi\) | |||||||
\(212\) | 11.6734 | + | 2.06166i | 0.801730 | + | 0.141595i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20.8139 | + | 16.7096i | 1.42281 | + | 1.14225i | ||||
\(215\) | −4.40808 | − | 4.40808i | −0.300629 | − | 0.300629i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.21651 | − | 3.21651i | 0.218351 | − | 0.218351i | ||||
\(218\) | −3.98424 | + | 0.435788i | −0.269847 | + | 0.0295153i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.65039 | − | 2.13664i | 0.650629 | − | 0.144052i | ||||
\(221\) | 3.76792 | − | 9.09656i | 0.253458 | − | 0.611901i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.4842 | 0.769038 | 0.384519 | − | 0.923117i | \(-0.374367\pi\) | ||||
0.384519 | + | 0.923117i | \(0.374367\pi\) | |||||||
\(224\) | 3.83993 | − | 0.588304i | 0.256566 | − | 0.0393077i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.61938 | − | 12.0695i | −0.440314 | − | 0.802850i | ||||
\(227\) | 1.61220 | − | 3.89220i | 0.107006 | − | 0.258335i | −0.861303 | − | 0.508092i | \(-0.830351\pi\) |
0.968308 | + | 0.249758i | \(0.0803509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.52685 | − | 2.28930i | 0.365225 | − | 0.151281i | −0.192521 | − | 0.981293i | \(-0.561666\pi\) |
0.557746 | + | 0.830012i | \(0.311666\pi\) | |||||||
\(230\) | 2.54592 | − | 0.278467i | 0.167873 | − | 0.0183616i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.8016 | − | 5.33235i | −0.709163 | − | 0.350086i | ||||
\(233\) | 16.1535 | + | 16.1535i | 1.05825 | + | 1.05825i | 0.998195 | + | 0.0600537i | \(0.0191272\pi\) |
0.0600537 | + | 0.998195i | \(0.480873\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.66949 | − | 8.85893i | −0.239371 | − | 0.577893i | ||||
\(236\) | 2.77281 | − | 15.7000i | 0.180495 | − | 1.02198i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.17540 | − | 1.21765i | −0.270651 | − | 0.0789282i | ||||
\(239\) | − | 26.7053i | − | 1.72742i | −0.503985 | − | 0.863712i | \(-0.668133\pi\) | ||
0.503985 | − | 0.863712i | \(-0.331867\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7649i | 0.951088i | 0.879692 | + | 0.475544i | \(0.157749\pi\) | ||||
−0.879692 | + | 0.475544i | \(0.842251\pi\) | |||||||
\(242\) | 3.54148 | − | 12.1440i | 0.227655 | − | 0.780647i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.50130 | + | 5.00332i | 0.224148 | + | 0.320305i | ||||
\(245\) | 2.76464 | + | 6.67442i | 0.176626 | + | 0.426413i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.22802 | − | 4.22802i | −0.269023 | − | 0.269023i | ||||
\(248\) | −1.23310 | + | 18.6946i | −0.0783018 | + | 1.18711i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.49321 | − | 13.6519i | −0.0944391 | − | 0.863421i | ||||
\(251\) | 16.6808 | − | 6.90939i | 1.05288 | − | 0.436117i | 0.211961 | − | 0.977278i | \(-0.432015\pi\) |
0.840919 | + | 0.541161i | \(0.182015\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.79689 | − | 6.75229i | 0.175839 | − | 0.424513i | ||||
\(254\) | −18.7761 | + | 10.2976i | −1.17812 | + | 0.646126i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.2982 | + | 12.2453i | −0.643635 | + | 0.765333i | ||||
\(257\) | −18.9756 | −1.18367 | −0.591833 | − | 0.806061i | \(-0.701595\pi\) | ||||
−0.591833 | + | 0.806061i | \(0.701595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.73315 | − | 6.59842i | 0.169830 | − | 0.410006i | ||||
\(260\) | −2.61558 | + | 4.10313i | −0.162211 | + | 0.254465i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.517817 | + | 4.73421i | 0.0319909 | + | 0.292480i | ||||
\(263\) | −0.267788 | + | 0.267788i | −0.0165125 | + | 0.0165125i | −0.715315 | − | 0.698802i | \(-0.753717\pi\) |
0.698802 | + | 0.715315i | \(0.253717\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.63780 | + | 4.63780i | 0.284898 | + | 0.284898i | ||||
\(266\) | −1.65352 | + | 2.05966i | −0.101384 | + | 0.126286i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.88619 | + | 6.98231i | 0.298471 | + | 0.426512i | ||||
\(269\) | −11.2094 | − | 4.64308i | −0.683449 | − | 0.283094i | 0.0138189 | − | 0.999905i | \(-0.495601\pi\) |
−0.697268 | + | 0.716811i | \(0.745601\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.73779i | 0.409292i | 0.978836 | + | 0.204646i | \(0.0656043\pi\) | ||||
−0.978836 | + | 0.204646i | \(0.934396\pi\) | |||||||
\(272\) | 16.2393 | − | 7.56159i | 0.984654 | − | 0.458489i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.7140 | + | 3.70771i | 0.768082 | + | 0.223991i | ||||
\(275\) | −15.5775 | − | 6.45240i | −0.939357 | − | 0.389094i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.41073 | − | 10.6484i | −0.265015 | − | 0.639803i | 0.734220 | − | 0.678912i | \(-0.237548\pi\) |
−0.999235 | + | 0.0391089i | \(0.987548\pi\) | |||||||
\(278\) | −13.6081 | − | 10.9248i | −0.816162 | − | 0.655225i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.92737 | + | 0.951468i | 0.115182 | + | 0.0568611i | ||||
\(281\) | −2.44614 | + | 2.44614i | −0.145925 | + | 0.145925i | −0.776295 | − | 0.630370i | \(-0.782903\pi\) |
0.630370 | + | 0.776295i | \(0.282903\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.00045 | + | 2.48547i | −0.356690 | + | 0.147746i | −0.553831 | − | 0.832629i | \(-0.686834\pi\) |
0.197141 | + | 0.980375i | \(0.436834\pi\) | |||||||
\(284\) | 1.29456 | + | 5.84702i | 0.0768178 | + | 0.346957i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.67723 | + | 12.1750i | 0.394833 | + | 0.719922i | ||||
\(287\) | 2.97413 | 0.175557 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.05585 | −0.179756 | ||||||||
\(290\) | −3.20505 | − | 5.84395i | −0.188207 | − | 0.343169i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.7453 | − | 3.70749i | 0.979945 | − | 0.216964i | ||||
\(293\) | −1.19634 | + | 0.495540i | −0.0698909 | + | 0.0289498i | −0.417355 | − | 0.908744i | \(-0.637043\pi\) |
0.347464 | + | 0.937693i | \(0.387043\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.23758 | − | 6.23758i | 0.363166 | − | 0.363166i | ||||
\(296\) | 9.44389 | + | 27.8588i | 0.548915 | + | 1.61926i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.6470 | − | 12.5616i | −0.906405 | − | 0.727673i | ||||
\(299\) | 1.37690 | + | 3.32412i | 0.0796280 | + | 0.192239i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.57417 | − | 1.48047i | −0.206012 | − | 0.0853328i | ||||
\(302\) | −14.4138 | − | 4.20342i | −0.829424 | − | 0.241879i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.468503 | − | 10.8685i | −0.0268705 | − | 0.623349i | ||||
\(305\) | 3.37887i | 0.193474i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.8795 | − | 11.1339i | −1.53410 | − | 0.635444i | −0.553742 | − | 0.832688i | \(-0.686801\pi\) |
−0.980354 | + | 0.197245i | \(0.936801\pi\) | |||||||
\(308\) | 5.02551 | − | 3.51683i | 0.286355 | − | 0.200390i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.48957 | + | 8.08354i | −0.368583 | + | 0.459114i | ||||
\(311\) | 11.0006 | + | 11.0006i | 0.623786 | + | 0.623786i | 0.946497 | − | 0.322711i | \(-0.104594\pi\) |
−0.322711 | + | 0.946497i | \(0.604594\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.444422 | + | 0.444422i | −0.0251202 | + | 0.0251202i | −0.719555 | − | 0.694435i | \(-0.755654\pi\) |
0.694435 | + | 0.719555i | \(0.255654\pi\) | |||||||
\(314\) | 3.15811 | + | 28.8734i | 0.178222 | + | 1.62942i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.54189 | + | 6.08256i | 0.536773 | + | 0.342171i | ||||
\(317\) | 7.05034 | − | 17.0210i | 0.395986 | − | 0.955995i | −0.592622 | − | 0.805481i | \(-0.701907\pi\) |
0.988608 | − | 0.150514i | \(-0.0480930\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.0203 | −1.06493 | ||||||||
\(320\) | −8.55306 | + | 2.28418i | −0.478131 | + | 0.127690i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.39354 | − | 0.764272i | 0.0776590 | − | 0.0425912i | ||||
\(323\) | −4.66092 | + | 11.2525i | −0.259340 | + | 0.626103i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.66872 | − | 3.17649i | 0.425384 | − | 0.176200i | ||||
\(326\) | 1.97279 | + | 18.0365i | 0.109263 | + | 0.998949i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.21302 | + | 8.07284i | −0.508704 | + | 0.445748i | ||||
\(329\) | −4.20771 | − | 4.20771i | −0.231979 | − | 0.231979i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.72879 | − | 23.4874i | −0.534743 | − | 1.29098i | −0.928351 | − | 0.371705i | \(-0.878773\pi\) |
0.393608 | − | 0.919278i | \(-0.371227\pi\) | |||||||
\(332\) | −2.82183 | + | 1.97470i | −0.154868 | + | 0.108376i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.50315 | + | 12.0126i | −0.191684 | + | 0.657298i | ||||
\(335\) | 4.71533i | 0.257626i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.5844i | 1.61157i | 0.592210 | + | 0.805784i | \(0.298256\pi\) | ||||
−0.592210 | + | 0.805784i | \(0.701744\pi\) | |||||||
\(338\) | 11.0870 | + | 3.23324i | 0.603055 | + | 0.175865i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.76051 | + | 1.72382i | 0.529338 | + | 0.0934875i | ||||
\(341\) | 11.3206 | + | 27.3302i | 0.613042 | + | 1.48002i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.56928 | + | 6.56928i | 0.354708 | + | 0.354708i | ||||
\(344\) | 15.0903 | − | 5.11548i | 0.813614 | − | 0.275808i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 29.8626 | − | 3.26631i | 1.60542 | − | 0.175598i | ||||
\(347\) | 2.09304 | − | 0.866967i | 0.112360 | − | 0.0465412i | −0.325795 | − | 0.945440i | \(-0.605632\pi\) |
0.438155 | + | 0.898899i | \(0.355632\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.65875 | − | 4.00459i | 0.0887910 | − | 0.214361i | −0.873246 | − | 0.487280i | \(-0.837989\pi\) |
0.962037 | + | 0.272919i | \(0.0879892\pi\) | |||||||
\(350\) | −1.76317 | − | 3.21488i | −0.0942453 | − | 0.171843i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.02170 | + | 24.5351i | −0.320958 | + | 1.30773i | ||||
\(353\) | −35.4920 | −1.88905 | −0.944524 | − | 0.328444i | \(-0.893476\pi\) | ||||
−0.944524 | + | 0.328444i | \(0.893476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.26802 | + | 3.06128i | −0.0672998 | + | 0.162476i | ||||
\(356\) | −0.610643 | − | 2.75804i | −0.0323640 | − | 0.146176i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 26.7827 | − | 2.92944i | 1.41551 | − | 0.154826i | ||||
\(359\) | −20.6647 | + | 20.6647i | −1.09064 | + | 1.09064i | −0.0951815 | + | 0.995460i | \(0.530343\pi\) |
−0.995460 | + | 0.0951815i | \(0.969657\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.20496 | − | 8.20496i | −0.431840 | − | 0.431840i | ||||
\(362\) | 17.2001 | + | 13.8085i | 0.904019 | + | 0.725757i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.525181 | + | 2.97364i | −0.0275269 | + | 0.155861i | ||||
\(365\) | 8.76722 | + | 3.63150i | 0.458897 | + | 0.190081i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.73373i | 0.508096i | 0.967192 | + | 0.254048i | \(0.0817622\pi\) | ||||
−0.967192 | + | 0.254048i | \(0.918238\pi\) | |||||||
\(368\) | −2.24229 | + | 6.15006i | −0.116888 | + | 0.320594i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.55662 | + | 15.6250i | −0.236888 | + | 0.812306i | ||||
\(371\) | 3.76043 | + | 1.55762i | 0.195232 | + | 0.0808676i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.81708 | − | 23.7005i | −0.508309 | − | 1.22717i | −0.944856 | − | 0.327486i | \(-0.893799\pi\) |
0.436547 | − | 0.899681i | \(-0.356201\pi\) | |||||||
\(374\) | 17.7071 | − | 22.0563i | 0.915611 | − | 1.14050i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.4555 | + | 1.61309i | 1.26120 | + | 0.0831888i | ||||
\(377\) | 6.62108 | − | 6.62108i | 0.341003 | − | 0.341003i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.55314 | − | 3.12861i | 0.387979 | − | 0.160706i | −0.180163 | − | 0.983637i | \(-0.557663\pi\) |
0.568142 | + | 0.822931i | \(0.307663\pi\) | |||||||
\(380\) | 3.23547 | − | 5.07558i | 0.165976 | − | 0.260372i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.40311 | − | 0.769522i | 0.0717895 | − | 0.0393722i | ||||
\(383\) | −37.2848 | −1.90516 | −0.952582 | − | 0.304283i | \(-0.901583\pi\) | ||||
−0.952582 | + | 0.304283i | \(0.901583\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.39385 | 0.172967 | ||||||||
\(386\) | 30.8976 | − | 16.9454i | 1.57265 | − | 0.862501i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.5214 | − | 16.5053i | 0.534145 | − | 0.837929i | ||||
\(389\) | 18.9989 | − | 7.86962i | 0.963284 | − | 0.399005i | 0.155076 | − | 0.987903i | \(-0.450438\pi\) |
0.808208 | + | 0.588897i | \(0.200438\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.18234 | − | 5.18234i | 0.262082 | − | 0.262082i | ||||
\(392\) | −18.4251 | − | 1.21532i | −0.930606 | − | 0.0613830i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.5317 | + | 15.6098i | −0.631338 | + | 0.786408i | ||||
\(395\) | 2.39598 | + | 5.78440i | 0.120555 | + | 0.291045i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.456018 | − | 0.188889i | −0.0228869 | − | 0.00948006i | 0.371211 | − | 0.928549i | \(-0.378943\pi\) |
−0.394098 | + | 0.919069i | \(0.628943\pi\) | |||||||
\(398\) | −7.57799 | + | 25.9855i | −0.379850 | + | 1.30254i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.1881 | + | 5.17294i | 0.709406 | + | 0.258647i | ||||
\(401\) | 34.6938i | 1.73252i | 0.499590 | + | 0.866262i | \(0.333484\pi\) | ||||
−0.499590 | + | 0.866262i | \(0.666516\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.4546 | − | 5.57306i | −0.670219 | − | 0.277614i | ||||
\(404\) | −3.67358 | + | 20.8003i | −0.182768 | + | 1.03485i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.22542 | − | 2.58941i | −0.160075 | − | 0.128510i | ||||
\(407\) | 32.8426 | + | 32.8426i | 1.62795 | + | 1.62795i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.3301 | + | 26.3301i | −1.30194 | + | 1.30194i | −0.374860 | + | 0.927081i | \(0.622309\pi\) |
−0.927081 | + | 0.374860i | \(0.877691\pi\) | |||||||
\(410\) | −6.73748 | + | 0.736931i | −0.332741 | + | 0.0363944i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.18481 | + | 18.9012i | 0.206171 | + | 0.931196i | ||||
\(413\) | 2.09491 | − | 5.05756i | 0.103084 | − | 0.248866i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.90565 | −0.0935447 | ||||||||
\(416\) | −6.44464 | − | 10.6370i | −0.315974 | − | 0.521522i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.25975 | − | 15.0605i | −0.403997 | − | 0.736632i | ||||
\(419\) | −2.41226 | + | 5.82370i | −0.117846 | + | 0.284506i | −0.971785 | − | 0.235867i | \(-0.924207\pi\) |
0.853939 | + | 0.520373i | \(0.174207\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.8254 | + | 12.3541i | −1.45360 | + | 0.602101i | −0.963053 | − | 0.269314i | \(-0.913203\pi\) |
−0.490547 | + | 0.871414i | \(0.663203\pi\) | |||||||
\(422\) | 33.7763 | − | 3.69438i | 1.64420 | − | 0.179839i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.8767 | + | 5.38206i | −0.771040 | + | 0.261376i | ||||
\(425\) | −11.9556 | − | 11.9556i | −0.579933 | − | 0.579933i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.802428 | + | 1.93723i | 0.0388322 | + | 0.0937493i | ||||
\(428\) | −37.1720 | − | 6.56503i | −1.79678 | − | 0.317333i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.46362 | + | 2.46819i | 0.408152 | + | 0.119027i | ||||
\(431\) | − | 34.6034i | − | 1.66679i | −0.552680 | − | 0.833394i | \(-0.686395\pi\) | ||
0.552680 | − | 0.833394i | \(-0.313605\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.1909i | − | 0.730027i | −0.931002 | − | 0.365013i | \(-0.881064\pi\) | ||
0.931002 | − | 0.365013i | \(-0.118936\pi\) | |||||||
\(434\) | −1.80100 | + | 6.17577i | −0.0864507 | + | 0.296446i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.64400 | − | 3.24985i | 0.222407 | − | 0.155639i | ||||
\(437\) | −1.70322 | − | 4.11195i | −0.0814762 | − | 0.196701i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.6561 | + | 25.6561i | 1.22450 | + | 1.22450i | 0.966015 | + | 0.258486i | \(0.0832235\pi\) |
0.258486 | + | 0.966015i | \(0.416776\pi\) | |||||||
\(440\) | −10.5132 | + | 9.21211i | −0.501197 | + | 0.439170i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.51399 | + | 13.8419i | 0.0720133 | + | 0.658390i | ||||
\(443\) | 32.9101 | − | 13.6318i | 1.56361 | − | 0.647667i | 0.577896 | − | 0.816110i | \(-0.303874\pi\) |
0.985711 | + | 0.168443i | \(0.0538739\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.598128 | − | 1.44401i | 0.0283540 | − | 0.0684526i | ||||
\(446\) | −14.2401 | + | 7.80981i | −0.674287 | + | 0.369805i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.36134 | + | 3.34082i | −0.206054 | + | 0.157839i | ||||
\(449\) | 27.6838 | 1.30648 | 0.653240 | − | 0.757151i | \(-0.273409\pi\) | ||||
0.653240 | + | 0.757151i | \(0.273409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.40164 | + | 17.8691i | −0.348530 | + | 0.841425i | ||||
\(452\) | 16.4157 | + | 10.4643i | 0.772129 | + | 0.492201i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.647802 | + | 5.92260i | 0.0304028 | + | 0.277962i | ||||
\(455\) | −1.18142 | + | 1.18142i | −0.0553858 | + | 0.0553858i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.63136 | − | 1.63136i | −0.0763119 | − | 0.0763119i | 0.667921 | − | 0.744233i | \(-0.267185\pi\) |
−0.744233 | + | 0.667921i | \(0.767185\pi\) | |||||||
\(458\) | −5.29631 | + | 6.59720i | −0.247481 | + | 0.308267i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.96750 | + | 2.07664i | −0.138360 | + | 0.0968240i | ||||
\(461\) | −9.64566 | − | 3.99536i | −0.449243 | − | 0.186083i | 0.146579 | − | 0.989199i | \(-0.453174\pi\) |
−0.595822 | + | 0.803116i | \(0.703174\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 27.9841i | − | 1.30053i | −0.759707 | − | 0.650266i | \(-0.774658\pi\) | ||
0.759707 | − | 0.650266i | \(-0.225342\pi\) | |||||||
\(464\) | 17.0200 | − | 0.733675i | 0.790134 | − | 0.0340600i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −31.0150 | − | 9.04471i | −1.43674 | − | 0.418988i | ||||
\(467\) | −0.710835 | − | 0.294438i | −0.0328935 | − | 0.0136250i | 0.366176 | − | 0.930546i | \(-0.380667\pi\) |
−0.399070 | + | 0.916921i | \(0.630667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.11982 | + | 2.70347i | 0.0517083 | + | 0.124835i | ||||
\(470\) | 10.5746 | + | 8.48940i | 0.487769 | + | 0.391587i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.23857 | + | 21.3532i | 0.333182 | + | 0.982862i | ||||
\(473\) | 17.7899 | − | 17.7899i | 0.817980 | − | 0.817980i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.48622 | + | 3.92932i | −0.435258 | + | 0.180290i | ||||
\(476\) | 6.00544 | − | 1.32963i | 0.275259 | − | 0.0609436i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.1609 | + | 33.1139i | 0.830662 | + | 1.51459i | ||||
\(479\) | 39.4950 | 1.80457 | 0.902285 | − | 0.431139i | \(-0.141888\pi\) | ||||
0.902285 | + | 0.431139i | \(0.141888\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.8654 | −1.04257 | ||||||||
\(482\) | −10.0408 | − | 18.3080i | −0.457347 | − | 0.833908i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.86719 | + | 17.4666i | 0.175781 | + | 0.793938i | ||||
\(485\) | 10.0057 | − | 4.14449i | 0.454335 | − | 0.188192i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.03654 | − | 1.03654i | 0.0469700 | − | 0.0469700i | −0.683232 | − | 0.730202i | \(-0.739426\pi\) |
0.730202 | + | 0.683232i | \(0.239426\pi\) | |||||||
\(488\) | −7.74403 | − | 3.82293i | −0.350556 | − | 0.173056i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.96701 | − | 6.39601i | −0.359913 | − | 0.288942i | ||||
\(491\) | 8.81350 | + | 21.2777i | 0.397748 | + | 0.960248i | 0.988199 | + | 0.153174i | \(0.0489497\pi\) |
−0.590452 | + | 0.807073i | \(0.701050\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.6213 | − | 7.29900i | −0.793625 | − | 0.328730i | ||||
\(494\) | 8.11790 | + | 2.36737i | 0.365242 | + | 0.106513i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.1842 | − | 24.0193i | −0.502186 | − | 1.07850i | ||||
\(497\) | 2.05628i | 0.0922369i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.2067 | + | 12.9263i | 1.39701 | + | 0.578659i | 0.948973 | − | 0.315359i | \(-0.102125\pi\) |
0.448033 | + | 0.894017i | \(0.352125\pi\) | |||||||
\(500\) | 11.1355 | + | 15.9125i | 0.497995 | + | 0.711629i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.9850 | + | 19.9112i | −0.713443 | + | 0.888680i | ||||
\(503\) | −1.63550 | − | 1.63550i | −0.0729233 | − | 0.0729233i | 0.669704 | − | 0.742628i | \(-0.266421\pi\) |
−0.742628 | + | 0.669704i | \(0.766421\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.26391 | + | 8.26391i | −0.367739 | + | 0.367739i | ||||
\(506\) | 1.12382 | + | 10.2747i | 0.0499600 | + | 0.456765i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.2790 | − | 25.5374i | 0.722266 | − | 1.13304i | ||||
\(509\) | −7.48659 | + | 18.0742i | −0.331837 | + | 0.801126i | 0.666609 | + | 0.745407i | \(0.267745\pi\) |
−0.998447 | + | 0.0557188i | \(0.982255\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.88900 | 0.260514 | ||||||||
\(512\) | 4.44201 | − | 22.1871i | 0.196311 | − | 0.980542i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 23.5292 | − | 12.9043i | 1.03783 | − | 0.569186i | ||||
\(515\) | −4.09904 | + | 9.89597i | −0.180626 | + | 0.436069i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.7524 | − | 14.8091i | 1.57239 | − | 0.651304i | ||||
\(518\) | 1.09821 | + | 10.0405i | 0.0482527 | + | 0.441156i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.452915 | − | 6.86649i | 0.0198617 | − | 0.301116i | ||||
\(521\) | 3.96008 | + | 3.96008i | 0.173494 | + | 0.173494i | 0.788513 | − | 0.615018i | \(-0.210851\pi\) |
−0.615018 | + | 0.788513i | \(0.710851\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.21965 | − | 19.8440i | −0.359420 | − | 0.867717i | −0.995382 | − | 0.0959961i | \(-0.969396\pi\) |
0.635962 | − | 0.771721i | \(-0.280604\pi\) | |||||||
\(524\) | −3.86157 | − | 5.51815i | −0.168694 | − | 0.241061i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.149941 | − | 0.514158i | 0.00653772 | − | 0.0224184i | ||||
\(527\) | 29.6643i | 1.29220i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 20.3218i | − | 0.883557i | ||||||
\(530\) | −8.90468 | − | 2.59681i | −0.386795 | − | 0.112798i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.649649 | − | 3.67839i | 0.0281659 | − | 0.159479i | ||||
\(533\) | −3.64380 | − | 8.79691i | −0.157830 | − | 0.381036i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.7684 | − | 14.7684i | −0.638492 | − | 0.638492i | ||||
\(536\) | −10.8071 | − | 5.33503i | −0.466794 | − | 0.230438i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.0569 | − | 1.86564i | 0.735374 | − | 0.0804336i | ||||
\(539\) | −26.9363 | + | 11.1574i | −1.16023 | + | 0.480582i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.31469 | − | 15.2450i | 0.271490 | − | 0.655435i | −0.728058 | − | 0.685516i | \(-0.759577\pi\) |
0.999547 | + | 0.0300814i | \(0.00957665\pi\) | |||||||
\(542\) | −4.58203 | − | 8.35468i | −0.196815 | − | 0.358864i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.9941 | + | 20.4197i | −0.642866 | + | 0.875488i | ||||
\(545\) | 3.13621 | 0.134340 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.21894 | − | 2.94279i | 0.0521182 | − | 0.125825i | −0.895676 | − | 0.444707i | \(-0.853308\pi\) |
0.947794 | + | 0.318883i | \(0.103308\pi\) | |||||||
\(548\) | −18.2865 | + | 4.04871i | −0.781159 | + | 0.172952i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 23.7036 | − | 2.59265i | 1.01072 | − | 0.110551i | ||||
\(551\) | −8.19029 | + | 8.19029i | −0.348918 | + | 0.348918i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.74741 | + | 2.74741i | 0.116832 | + | 0.116832i | ||||
\(554\) | 12.7106 | + | 10.2043i | 0.540024 | + | 0.433538i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 24.3031 | + | 4.29223i | 1.03068 | + | 0.182031i | ||||
\(557\) | −30.1821 | − | 12.5018i | −1.27886 | − | 0.529719i | −0.363211 | − | 0.931707i | \(-0.618319\pi\) |
−0.915645 | + | 0.401988i | \(0.868319\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.3855i | 0.523852i | ||||||||
\(560\) | −3.03693 | + | 0.130912i | −0.128334 | + | 0.00553204i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.36965 | − | 4.69665i | 0.0577753 | − | 0.198116i | ||||
\(563\) | −35.5009 | − | 14.7050i | −1.49618 | − | 0.619740i | −0.523532 | − | 0.852006i | \(-0.675386\pi\) |
−0.972652 | + | 0.232266i | \(0.925386\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.12200 | + | 9.95138i | 0.173414 | + | 0.418658i | ||||
\(566\) | 5.75016 | − | 7.16252i | 0.241697 | − | 0.301063i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.58148 | − | 6.36978i | −0.234194 | − | 0.267270i | ||||
\(569\) | 25.8368 | − | 25.8368i | 1.08313 | − | 1.08313i | 0.0869193 | − | 0.996215i | \(-0.472298\pi\) |
0.996215 | − | 0.0869193i | \(-0.0277022\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.57652 | + | 1.06723i | −0.107824 | + | 0.0446621i | −0.435943 | − | 0.899974i | \(-0.643585\pi\) |
0.328119 | + | 0.944636i | \(0.393585\pi\) | |||||||
\(572\) | −16.5592 | − | 10.5558i | −0.692374 | − | 0.441360i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.68784 | + | 2.02256i | −0.153928 | + | 0.0844198i | ||||
\(575\) | 6.17856 | 0.257664 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.8404 | 0.576184 | 0.288092 | − | 0.957603i | \(-0.406979\pi\) | ||||
0.288092 | + | 0.957603i | \(0.406979\pi\) | |||||||
\(578\) | 3.78917 | − | 2.07813i | 0.157609 | − | 0.0864387i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.94835 | + | 5.06675i | 0.330037 | + | 0.210385i | ||||
\(581\) | −1.09258 | + | 0.452562i | −0.0453279 | + | 0.0187754i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.7170 | + | 18.7170i | −0.775178 | + | 0.775178i | ||||
\(584\) | −18.2425 | + | 15.9848i | −0.754878 | + | 0.661456i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.14644 | − | 1.42803i | 0.0473589 | − | 0.0589912i | ||||
\(587\) | 16.7762 | + | 40.5013i | 0.692427 | + | 1.67167i | 0.739832 | + | 0.672791i | \(0.234905\pi\) |
−0.0474052 | + | 0.998876i | \(0.515095\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.6433 | + | 6.89388i | 0.685776 | + | 0.284058i | ||||
\(590\) | −3.49257 | + | 11.9763i | −0.143787 | + | 0.493056i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −30.6555 | − | 28.1218i | −1.25993 | − | 1.15580i | ||||
\(593\) | − | 14.3003i | − | 0.587243i | −0.955922 | − | 0.293621i | \(-0.905139\pi\) | ||
0.955922 | − | 0.293621i | \(-0.0948605\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.14423 | + | 1.30238i | 0.128901 | + | 0.0533924i | ||||
\(596\) | 27.9443 | + | 4.93531i | 1.14464 | + | 0.202158i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.96788 | − | 3.18547i | −0.162259 | − | 0.130263i | ||||
\(599\) | 5.98650 | + | 5.98650i | 0.244602 | + | 0.244602i | 0.818751 | − | 0.574149i | \(-0.194667\pi\) |
−0.574149 | + | 0.818751i | \(0.694667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.6645 | − | 14.6645i | 0.598179 | − | 0.598179i | −0.341649 | − | 0.939828i | \(-0.610985\pi\) |
0.939828 | + | 0.341649i | \(0.110985\pi\) | |||||||
\(602\) | 5.43867 | − | 0.594870i | 0.221663 | − | 0.0242451i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.7313 | − | 4.59001i | 0.843545 | − | 0.186765i | ||||
\(605\) | −3.78794 | + | 9.14489i | −0.154001 | + | 0.371792i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.96144 | −0.241967 | −0.120984 | − | 0.992654i | \(-0.538605\pi\) | ||||
−0.120984 | + | 0.992654i | \(0.538605\pi\) | |||||||
\(608\) | 7.97202 | + | 13.1580i | 0.323308 | + | 0.533627i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.29780 | − | 4.18971i | −0.0930352 | − | 0.169636i | ||||
\(611\) | −7.29047 | + | 17.6007i | −0.294941 | + | 0.712050i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.23798 | + | 2.16964i | −0.211560 | + | 0.0876310i | −0.485947 | − | 0.873988i | \(-0.661525\pi\) |
0.274387 | + | 0.961619i | \(0.411525\pi\) | |||||||
\(614\) | 40.9015 | − | 4.47372i | 1.65065 | − | 0.180544i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.83988 | + | 7.77837i | −0.154713 | + | 0.313399i | ||||
\(617\) | −9.39267 | − | 9.39267i | −0.378135 | − | 0.378135i | 0.492294 | − | 0.870429i | \(-0.336158\pi\) |
−0.870429 | + | 0.492294i | \(0.836158\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.90970 | − | 19.0957i | −0.317918 | − | 0.767521i | −0.999364 | − | 0.0356533i | \(-0.988649\pi\) |
0.681447 | − | 0.731868i | \(-0.261351\pi\) | |||||||
\(620\) | 2.54968 | − | 14.4366i | 0.102398 | − | 0.579788i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.1214 | − | 6.15949i | −0.846890 | − | 0.246973i | ||||
\(623\) | − | 0.969950i | − | 0.0388602i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 8.13104i | − | 0.325242i | ||||||
\(626\) | 0.248843 | − | 0.853301i | 0.00994575 | − | 0.0341048i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −23.5513 | − | 33.6545i | −0.939799 | − | 1.34296i | ||||
\(629\) | 17.8237 | + | 43.0302i | 0.710678 | + | 1.71573i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.71198 | − | 7.71198i | −0.307009 | − | 0.307009i | 0.536739 | − | 0.843748i | \(-0.319656\pi\) |
−0.843748 | + | 0.536739i | \(0.819656\pi\) | |||||||
\(632\) | −15.9681 | − | 1.05326i | −0.635178 | − | 0.0418965i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.83291 | + | 25.9002i | 0.112509 | + | 1.02863i | ||||
\(635\) | 15.4811 | − | 6.41247i | 0.614347 | − | 0.254471i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.49272 | − | 13.2606i | 0.217630 | − | 0.525404i | ||||
\(638\) | 23.5847 | − | 12.9348i | 0.933727 | − | 0.512092i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.05221 | − | 8.64883i | 0.357820 | − | 0.341875i | ||||
\(641\) | 12.0769 | 0.477008 | 0.238504 | − | 0.971141i | \(-0.423343\pi\) | ||||
0.238504 | + | 0.971141i | \(0.423343\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.69996 | + | 11.3467i | −0.185348 | + | 0.447470i | −0.989054 | − | 0.147557i | \(-0.952859\pi\) |
0.803705 | + | 0.595028i | \(0.202859\pi\) | |||||||
\(644\) | −1.20821 | + | 1.89535i | −0.0476101 | + | 0.0746873i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.87281 | − | 17.1224i | −0.0736847 | − | 0.673671i | ||||
\(647\) | −25.6699 | + | 25.6699i | −1.00919 | + | 1.00919i | −0.00923049 | + | 0.999957i | \(0.502938\pi\) |
−0.999957 | + | 0.00923049i | \(0.997062\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.1733 | + | 25.1733i | 0.988137 | + | 0.988137i | ||||
\(650\) | −7.34884 | + | 9.15387i | −0.288245 | + | 0.359044i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.7119 | − | 21.0232i | −0.576163 | − | 0.823331i | ||||
\(653\) | −44.9438 | − | 18.6163i | −1.75879 | − | 0.728513i | −0.996712 | − | 0.0810226i | \(-0.974181\pi\) |
−0.762074 | − | 0.647490i | \(-0.775819\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3.72654i | − | 0.145608i | ||||||
\(656\) | 5.93396 | − | 16.2754i | 0.231682 | − | 0.635448i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.07890 | + | 2.35600i | 0.314948 | + | 0.0918464i | ||||
\(659\) | −19.3749 | − | 8.02536i | −0.754740 | − | 0.312623i | −0.0280660 | − | 0.999606i | \(-0.508935\pi\) |
−0.726674 | + | 0.686983i | \(0.758935\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.55430 | − | 6.16663i | −0.0993509 | − | 0.239854i | 0.866387 | − | 0.499373i | \(-0.166436\pi\) |
−0.965738 | + | 0.259518i | \(0.916436\pi\) | |||||||
\(662\) | 28.0360 | + | 22.5077i | 1.08965 | + | 0.874785i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.15609 | − | 4.36756i | 0.0836727 | − | 0.169494i | ||||
\(665\) | 1.46142 | − | 1.46142i | 0.0566713 | − | 0.0566713i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.43931 | − | 2.66725i | 0.249331 | − | 0.103276i | ||||
\(668\) | −3.82533 | − | 17.2776i | −0.148006 | − | 0.668489i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.20666 | − | 5.84688i | −0.123884 | − | 0.225885i | ||||
\(671\) | −13.6363 | −0.526422 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.63737 | −0.217305 | −0.108652 | − | 0.994080i | \(-0.534654\pi\) | ||||
−0.108652 | + | 0.994080i | \(0.534654\pi\) | |||||||
\(674\) | −20.1189 | − | 36.6839i | −0.774950 | − | 1.41301i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.9464 | + | 3.53060i | −0.613322 | + | 0.135792i | ||||
\(677\) | −0.110383 | + | 0.0457221i | −0.00424236 | + | 0.00175724i | −0.384804 | − | 0.922998i | \(-0.625731\pi\) |
0.380561 | + | 0.924756i | \(0.375731\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.75239 | − | 4.75239i | 0.182380 | − | 0.182380i | ||||
\(680\) | −13.2750 | + | 4.50013i | −0.509075 | + | 0.172572i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −32.6231 | − | 26.1902i | −1.24920 | − | 1.00288i | ||||
\(683\) | −10.5093 | − | 25.3717i | −0.402127 | − | 0.970820i | −0.987149 | − | 0.159803i | \(-0.948914\pi\) |
0.585022 | − | 0.811017i | \(-0.301086\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.57412 | − | 3.96573i | −0.365808 | − | 0.151523i | ||||
\(686\) | −12.6132 | − | 3.67830i | −0.481573 | − | 0.140438i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15.2328 | + | 16.6052i | −0.580744 | + | 0.633067i | ||||
\(689\) | − | 13.0310i | − | 0.496440i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.2220 | − | 14.5894i | −1.33991 | − | 0.555008i | −0.406443 | − | 0.913676i | \(-0.633231\pi\) |
−0.933465 | + | 0.358668i | \(0.883231\pi\) | |||||||
\(692\) | −34.8076 | + | 24.3582i | −1.32319 | + | 0.925959i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.00574 | + | 2.49839i | −0.0761367 | + | 0.0948375i | ||||
\(695\) | 9.65558 | + | 9.65558i | 0.366257 | + | 0.366257i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.7145 | + | 13.7145i | −0.519473 | + | 0.519473i | ||||
\(698\) | 0.666506 | + | 6.09361i | 0.0252276 | + | 0.230647i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.37256 | + | 2.78733i | 0.165267 | + | 0.105351i | ||||
\(701\) | 14.7113 | − | 35.5162i | 0.555638 | − | 1.34143i | −0.357552 | − | 0.933893i | \(-0.616388\pi\) |
0.913190 | − | 0.407535i | \(-0.133612\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.2845 | 1.06677 | ||||||||
\(704\) | −9.21836 | − | 34.5180i | −0.347430 | − | 1.30094i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 44.0091 | − | 24.1363i | 1.65630 | − | 0.908381i | ||||
\(707\) | −2.77546 | + | 6.70056i | −0.104382 | + | 0.252000i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.3798 | − | 5.12787i | 0.464932 | − | 0.192581i | −0.137905 | − | 0.990445i | \(-0.544037\pi\) |
0.602837 | + | 0.797864i | \(0.294037\pi\) | |||||||
\(710\) | −0.509507 | − | 4.65823i | −0.0191214 | − | 0.174820i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.63279 | + | 3.00463i | 0.0986678 | + | 0.112603i | ||||
\(713\) | −7.66512 | − | 7.66512i | −0.287061 | − | 0.287061i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.15803 | − | 10.0384i | −0.155501 | − | 0.375414i | ||||
\(716\) | −31.2177 | + | 21.8460i | −1.16666 | + | 0.816423i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11.5707 | − | 39.6767i | 0.431813 | − | 1.48072i | ||||
\(719\) | − | 32.5496i | − | 1.21390i | −0.794741 | − | 0.606948i | \(-0.792393\pi\) | ||
0.794741 | − | 0.606948i | \(-0.207607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.64719i | 0.247554i | ||||||||
\(722\) | 15.7537 | + | 4.59415i | 0.586292 | + | 0.170977i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −30.7181 | − | 5.42520i | −1.14163 | − | 0.201626i | ||||
\(725\) | −6.15332 | − | 14.8554i | −0.228528 | − | 0.551716i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.49561 | + | 7.49561i | 0.277997 | + | 0.277997i | 0.832309 | − | 0.554312i | \(-0.187019\pi\) |
−0.554312 | + | 0.832309i | \(0.687019\pi\) | |||||||
\(728\) | −1.37101 | − | 4.04438i | −0.0508130 | − | 0.149895i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −13.3407 | + | 1.45918i | −0.493762 | + | 0.0540066i | ||||
\(731\) | 23.3082 | − | 9.65458i | 0.862086 | − | 0.357088i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.16287 | − | 14.8785i | 0.227631 | − | 0.549550i | −0.768257 | − | 0.640141i | \(-0.778876\pi\) |
0.995888 | + | 0.0905917i | \(0.0288758\pi\) | |||||||
\(734\) | −6.61942 | − | 12.0696i | −0.244327 | − | 0.445496i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.40196 | − | 9.15077i | −0.0516770 | − | 0.337302i | ||||
\(737\) | −19.0299 | −0.700974 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.76773 | + | 4.26769i | −0.0650272 | + | 0.156989i | −0.953053 | − | 0.302805i | \(-0.902077\pi\) |
0.888025 | + | 0.459794i | \(0.152077\pi\) | |||||||
\(740\) | −4.97570 | − | 22.4733i | −0.182910 | − | 0.826136i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.72209 | + | 0.625870i | −0.210065 | + | 0.0229764i | ||||
\(743\) | −9.36119 | + | 9.36119i | −0.343429 | + | 0.343429i | −0.857655 | − | 0.514226i | \(-0.828079\pi\) |
0.514226 | + | 0.857655i | \(0.328079\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.1022 | + | 11.1022i | 0.406754 | + | 0.406754i | ||||
\(746\) | 28.2904 | + | 22.7119i | 1.03579 | + | 0.831542i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.95691 | + | 39.3909i | −0.254370 | + | 1.44027i | ||||
\(749\) | −11.9745 | − | 4.96000i | −0.437539 | − | 0.181235i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.39834i | 0.0510263i | 0.999674 | + | 0.0255131i | \(0.00812196\pi\) | ||||
−0.999674 | + | 0.0255131i | \(0.991878\pi\) | |||||||
\(752\) | −31.4212 | + | 14.6308i | −1.14581 | + | 0.533529i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.70730 | + | 12.7126i | −0.135012 | + | 0.462967i | ||||
\(755\) | 10.8541 | + | 4.49593i | 0.395023 | + | 0.163624i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.78917 | + | 21.2189i | 0.319448 | + | 0.771216i | 0.999283 | + | 0.0378509i | \(0.0120512\pi\) |
−0.679835 | + | 0.733365i | \(0.737949\pi\) | |||||||
\(758\) | −7.23808 | + | 9.01590i | −0.262899 | + | 0.327472i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.560257 | + | 8.49386i | −0.0203227 | + | 0.308105i | ||||
\(761\) | 29.1747 | − | 29.1747i | 1.05758 | − | 1.05758i | 0.0593461 | − | 0.998237i | \(-0.481098\pi\) |
0.998237 | − | 0.0593461i | \(-0.0189015\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.79810 | − | 0.744799i | 0.0650958 | − | 0.0269635i | ||||
\(764\) | −1.21651 | + | 1.90837i | −0.0440118 | + | 0.0690425i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 46.2321 | − | 25.3555i | 1.67043 | − | 0.916131i | ||||
\(767\) | −17.5259 | −0.632824 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.4734 | 1.17102 | 0.585509 | − | 0.810666i | \(-0.300894\pi\) | ||||
0.585509 | + | 0.810666i | \(0.300894\pi\) | |||||||
\(770\) | −4.20829 | + | 2.30799i | −0.151656 | + | 0.0831741i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −26.7885 | + | 42.0238i | −0.964138 | + | 1.51247i | ||||
\(773\) | 46.7641 | − | 19.3703i | 1.68199 | − | 0.696702i | 0.682570 | − | 0.730820i | \(-0.260862\pi\) |
0.999418 | + | 0.0341178i | \(0.0108621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.6834 | + | 17.6834i | −0.635205 | + | 0.635205i | ||||
\(776\) | −1.82190 | + | 27.6212i | −0.0654024 | + | 0.991543i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.2064 | + | 22.6783i | −0.652732 | + | 0.813057i | ||||
\(779\) | 4.50738 | + | 10.8818i | 0.161494 | + | 0.389880i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.3545 | − | 5.11742i | −0.442080 | − | 0.183116i | ||||
\(782\) | −2.90172 | + | 9.95022i | −0.103765 | + | 0.355819i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23.6731 | − | 11.0230i | 0.845467 | − | 0.393678i | ||||
\(785\) | − | 22.7278i | − | 0.811188i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.0612 | + | 20.7360i | 1.78449 | + | 0.739160i | 0.991529 | + | 0.129886i | \(0.0414612\pi\) |
0.792960 | + | 0.609273i | \(0.208539\pi\) | |||||||
\(788\) | 4.92357 | − | 27.8779i | 0.175395 | − | 0.993108i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.90463 | − | 5.54312i | −0.245656 | − | 0.197215i | ||||
\(791\) | 4.72659 | + | 4.72659i | 0.168058 | + | 0.168058i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.74686 | − | 4.74686i | 0.168566 | − | 0.168566i | ||||
\(794\) | 0.693904 | − | 0.0758977i | 0.0246257 | − | 0.00269351i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.27494 | − | 37.3748i | −0.293297 | − | 1.32471i | ||||
\(797\) | 17.7292 | − | 42.8021i | 0.628002 | − | 1.51613i | −0.214100 | − | 0.976812i | \(-0.568682\pi\) |
0.842102 | − | 0.539318i | \(-0.181318\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.8057 | 1.37285 | ||||||||
\(800\) | −21.1107 | + | 3.23431i | −0.746377 | + | 0.114350i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.5935 | − | 43.0193i | −0.833114 | − | 1.51907i | ||||
\(803\) | −14.6558 | + | 35.3822i | −0.517192 | + | 1.24861i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.14898 | + | 0.475925i | −0.0404964 | + | 0.0167742i | ||||
\(806\) | 20.4732 | − | 2.23932i | 0.721139 | − | 0.0788767i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.59007 | − | 28.2900i | −0.337378 | − | 0.995239i | ||||
\(809\) | −4.15956 | − | 4.15956i | −0.146242 | − | 0.146242i | 0.630195 | − | 0.776437i | \(-0.282975\pi\) |
−0.776437 | + | 0.630195i | \(0.782975\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.3981 | + | 37.1743i | 0.540701 | + | 1.30537i | 0.924229 | + | 0.381838i | \(0.124709\pi\) |
−0.383529 | + | 0.923529i | \(0.625291\pi\) | |||||||
\(812\) | 5.76036 | + | 1.01735i | 0.202149 | + | 0.0357020i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −63.0586 | − | 18.3894i | −2.21020 | − | 0.644547i | ||||
\(815\) | − | 14.1975i | − | 0.497316i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 15.3209i | − | 0.536011i | ||||||
\(818\) | 14.7429 | − | 50.5544i | 0.515472 | − | 1.76759i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.85315 | − | 5.49560i | 0.274244 | − | 0.191915i | ||||
\(821\) | −6.35947 | − | 15.3531i | −0.221947 | − | 0.535828i | 0.773207 | − | 0.634153i | \(-0.218651\pi\) |
−0.995154 | + | 0.0983258i | \(0.968651\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.14531 | + | 9.14531i | 0.318785 | + | 0.318785i | 0.848301 | − | 0.529515i | \(-0.177626\pi\) |
−0.529515 | + | 0.848301i | \(0.677626\pi\) | |||||||
\(824\) | −18.0428 | − | 20.5911i | −0.628551 | − | 0.717325i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.841759 | + | 7.69589i | 0.0292886 | + | 0.267774i | ||||
\(827\) | 21.0420 | − | 8.71588i | 0.731702 | − | 0.303081i | 0.0144505 | − | 0.999896i | \(-0.495400\pi\) |
0.717251 | + | 0.696815i | \(0.245400\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.11975 | + | 22.0170i | −0.316742 | + | 0.764683i | 0.682681 | + | 0.730717i | \(0.260814\pi\) |
−0.999423 | + | 0.0339663i | \(0.989186\pi\) | |||||||
\(830\) | 2.36295 | − | 1.29594i | 0.0820193 | − | 0.0449826i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15.2249 | + | 8.80694i | 0.527827 | + | 0.305326i | ||||
\(833\) | −29.2366 | −1.01299 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.74693 | − | 9.04589i | 0.129668 | − | 0.313046i | ||||
\(836\) | 20.4837 | + | 13.0575i | 0.708444 | + | 0.451604i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.969272 | − | 8.86169i | −0.0334830 | − | 0.306122i | ||||
\(839\) | −1.52555 | + | 1.52555i | −0.0526679 | + | 0.0526679i | −0.732950 | − | 0.680282i | \(-0.761857\pi\) |
0.680282 | + | 0.732950i | \(0.261857\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.68011 | + | 7.68011i | 0.264831 | + | 0.264831i | ||||
\(842\) | 28.5813 | − | 35.6014i | 0.984976 | − | 1.22691i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −39.3693 | + | 27.5505i | −1.35515 | + | 0.948326i | ||||
\(845\) | −8.34893 | − | 3.45824i | −0.287212 | − | 0.118967i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.14268i | 0.211065i | ||||||||
\(848\) | 16.0266 | − | 17.4705i | 0.550355 | − | 0.599941i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 22.9551 | + | 6.69423i | 0.787352 | + | 0.229610i | ||||
\(851\) | −15.7244 | − | 6.51326i | −0.539025 | − | 0.223272i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.9713 | + | 40.9724i | 0.581087 | + | 1.40287i | 0.891829 | + | 0.452373i | \(0.149423\pi\) |
−0.310742 | + | 0.950494i | \(0.600577\pi\) | |||||||
\(854\) | −2.31240 | − | 1.85643i | −0.0791288 | − | 0.0635256i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 50.5568 | − | 17.1383i | 1.72800 | − | 0.585776i | ||||
\(857\) | 25.3444 | − | 25.3444i | 0.865748 | − | 0.865748i | −0.126250 | − | 0.991998i | \(-0.540294\pi\) |
0.991998 | + | 0.126250i | \(0.0402941\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.74139 | − | 2.79237i | 0.230013 | − | 0.0952746i | −0.264700 | − | 0.964331i | \(-0.585273\pi\) |
0.494713 | + | 0.869056i | \(0.335273\pi\) | |||||||
\(860\) | −12.1732 | + | 2.69519i | −0.415101 | + | 0.0919052i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 23.5320 | + | 42.9073i | 0.801504 | + | 1.46143i | ||||
\(863\) | −8.92208 | −0.303711 | −0.151856 | − | 0.988403i | \(-0.548525\pi\) | ||||
−0.151856 | + | 0.988403i | \(0.548525\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.5064 | −0.799243 | ||||||||
\(866\) | 10.3305 | + | 18.8363i | 0.351046 | + | 0.640083i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.96664 | − | 8.88255i | −0.0667520 | − | 0.301493i | ||||
\(869\) | −23.3444 | + | 9.66955i | −0.791903 | + | 0.328017i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.62440 | − | 6.62440i | 0.224459 | − | 0.224459i | ||||
\(872\) | −3.54837 | + | 7.18787i | −0.120163 | + | 0.243412i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.90828 | + | 3.94043i | 0.166025 | + | 0.133287i | ||||
\(875\) | 2.55203 | + | 6.16115i | 0.0862744 | + | 0.208285i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.5784 | + | 13.0802i | 1.06633 | + | 0.441688i | 0.845694 | − | 0.533669i | \(-0.179187\pi\) |
0.220635 | + | 0.975356i | \(0.429187\pi\) | |||||||
\(878\) | −49.2604 | − | 14.3655i | −1.66246 | − | 0.484811i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.77139 | − | 18.5723i | 0.228264 | − | 0.626071i | ||||
\(881\) | − | 12.9945i | − | 0.437797i | −0.975748 | − | 0.218898i | \(-0.929754\pi\) | ||
0.975748 | − | 0.218898i | \(-0.0702463\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.87442 | + | 3.67591i | 0.298648 | + | 0.123704i | 0.526976 | − | 0.849880i | \(-0.323326\pi\) |
−0.228328 | + | 0.973584i | \(0.573326\pi\) | |||||||
\(884\) | −11.2905 | − | 16.1339i | −0.379739 | − | 0.542643i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.5374 | + | 39.2836i | −1.05952 | + | 1.31976i | ||||
\(887\) | 12.8751 | + | 12.8751i | 0.432305 | + | 0.432305i | 0.889412 | − | 0.457107i | \(-0.151114\pi\) |
−0.457107 | + | 0.889412i | \(0.651114\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.35302 | − | 7.35302i | 0.246612 | − | 0.246612i | ||||
\(890\) | 0.240335 | + | 2.19729i | 0.00805604 | + | 0.0736533i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.3463 | − | 19.3679i | 0.413383 | − | 0.648486i | ||||
\(893\) | 9.01832 | − | 21.7721i | 0.301786 | − | 0.728577i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.0821 | −0.704697 | ||||||||
\(896\) | 3.13601 | − | 7.10845i | 0.104767 | − | 0.237477i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −34.3272 | + | 18.8264i | −1.14551 | + | 0.628244i | ||||
\(899\) | −10.7958 | + | 26.0634i | −0.360061 | + | 0.869263i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.5229 | + | 10.1577i | −0.816976 | + | 0.338402i | ||||
\(902\) | −2.97406 | − | 27.1907i | −0.0990255 | − | 0.905353i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −27.4713 | − | 1.81201i | −0.913681 | − | 0.0602666i | ||||
\(905\) | −12.2043 | − | 12.2043i | −0.405683 | − | 0.405683i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.6075 | + | 35.2657i | 0.485036 | + | 1.17098i | 0.957189 | + | 0.289463i | \(0.0934768\pi\) |
−0.472153 | + | 0.881516i | \(0.656523\pi\) | |||||||
\(908\) | −4.83092 | − | 6.90333i | −0.160320 | − | 0.229095i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.661505 | − | 2.26835i | 0.0219287 | − | 0.0751951i | ||||
\(911\) | − | 16.2958i | − | 0.539903i | −0.962874 | − | 0.269951i | \(-0.912992\pi\) | ||
0.962874 | − | 0.269951i | \(-0.0870076\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 7.69071i | − | 0.254525i | ||||||
\(914\) | 3.13225 | + | 0.913438i | 0.103606 | + | 0.0302138i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.08086 | − | 11.7821i | 0.0687537 | − | 0.389292i | ||||
\(917\) | −0.884995 | − | 2.13657i | −0.0292251 | − | 0.0705557i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.15448 | + | 8.15448i | 0.268991 | + | 0.268991i | 0.828694 | − | 0.559702i | \(-0.189085\pi\) |
−0.559702 | + | 0.828694i | \(0.689085\pi\) | |||||||
\(920\) | 2.26740 | − | 4.59303i | 0.0747540 | − | 0.151428i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.6774 | − | 1.60538i | 0.483374 | − | 0.0528705i | ||||
\(923\) | 6.08209 | − | 2.51928i | 0.200194 | − | 0.0829233i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.0260 | + | 36.2760i | −0.494053 | + | 1.19275i | ||||
\(926\) | 19.0306 | + | 34.6995i | 0.625383 | + | 1.14030i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20.6054 | + | 12.4842i | −0.676406 | + | 0.409813i | ||||
\(929\) | −36.3461 | −1.19248 | −0.596239 | − | 0.802807i | \(-0.703339\pi\) | ||||
−0.596239 | + | 0.802807i | \(0.703339\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.79450 | + | 16.4034i | −0.222681 | + | 0.537599i | ||||
\(932\) | 44.6086 | − | 9.87655i | 1.46120 | − | 0.323517i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.08165 | − | 0.118308i | 0.0353926 | − | 0.00387117i | ||||
\(935\) | −15.6499 | + | 15.6499i | −0.511807 | + | 0.511807i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.8090 | − | 16.8090i | −0.549127 | − | 0.549127i | 0.377061 | − | 0.926188i | \(-0.376935\pi\) |
−0.926188 | + | 0.377061i | \(0.876935\pi\) | |||||||
\(938\) | −3.22704 | − | 2.59071i | −0.105367 | − | 0.0845895i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.8854 | − | 3.33539i | −0.615974 | − | 0.108789i | ||||
\(941\) | 40.9660 | + | 16.9687i | 1.33545 | + | 0.553163i | 0.932206 | − | 0.361928i | \(-0.117881\pi\) |
0.403248 | + | 0.915091i | \(0.367881\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 7.08752i | − | 0.230801i | ||||||
\(944\) | −23.4969 | − | 21.5548i | −0.764758 | − | 0.701551i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.96098 | + | 34.1570i | −0.323859 | + | 1.11054i | ||||
\(947\) | 19.2307 | + | 7.96563i | 0.624915 | + | 0.258848i | 0.672591 | − | 0.740015i | \(-0.265181\pi\) |
−0.0476758 | + | 0.998863i | \(0.515181\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.21499 | − | 17.4185i | −0.234209 | − | 0.565429i | ||||
\(950\) | 9.09052 | − | 11.3233i | 0.294936 | − | 0.367378i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.54237 | + | 5.73271i | −0.212040 | + | 0.185798i | ||||
\(953\) | −14.1277 | + | 14.1277i | −0.457640 | + | 0.457640i | −0.897880 | − | 0.440240i | \(-0.854893\pi\) |
0.440240 | + | 0.897880i | \(0.354893\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.15688 | + | 0.479194i | −0.0374357 | + | 0.0155064i | ||||
\(956\) | −45.0382 | − | 28.7100i | −1.45664 | − | 0.928547i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −48.9727 | + | 26.8585i | −1.58224 | + | 0.867759i | ||||
\(959\) | −6.43100 | −0.207668 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.8759 | 0.415352 | ||||||||
\(962\) | 28.3525 | − | 15.5496i | 0.914121 | − | 0.501340i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.9007 | + | 15.8732i | 0.801998 | + | 0.511241i | ||||
\(965\) | −25.4753 | + | 10.5522i | −0.820079 | + | 0.339688i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.2594 | − | 21.2594i | 0.683657 | − | 0.683657i | −0.277165 | − | 0.960822i | \(-0.589395\pi\) |
0.960822 | + | 0.277165i | \(0.0893949\pi\) | |||||||
\(968\) | −16.6734 | − | 19.0283i | −0.535903 | − | 0.611592i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.58833 | + | 11.9434i | −0.307863 | + | 0.383480i | ||||
\(971\) | −3.11646 | − | 7.52380i | −0.100012 | − | 0.241450i | 0.865952 | − | 0.500127i | \(-0.166713\pi\) |
−0.965964 | + | 0.258677i | \(0.916713\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.82895 | + | 3.24286i | 0.250985 | + | 0.103961i | ||||
\(974\) | −0.580382 | + | 1.99018i | −0.0185966 | + | 0.0637694i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.2022 | − | 0.525994i | 0.390582 | − | 0.0168367i | ||||
\(977\) | 55.2830i | 1.76866i | 0.466864 | + | 0.884329i | \(0.345384\pi\) | ||||
−0.466864 | + | 0.884329i | \(0.654616\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.82765 | + | 2.41389i | 0.186252 | + | 0.0771483i | ||||
\(980\) | 14.2285 | + | 2.51292i | 0.454512 | + | 0.0802724i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25.3984 | − | 20.3901i | −0.810494 | − | 0.650675i | ||||
\(983\) | −14.9227 | − | 14.9227i | −0.475962 | − | 0.475962i | 0.427876 | − | 0.903837i | \(-0.359262\pi\) |
−0.903837 | + | 0.427876i | \(0.859262\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.0758 | − | 11.0758i | 0.352905 | − | 0.352905i | ||||
\(986\) | 26.8137 | − | 2.93282i | 0.853921 | − | 0.0934000i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.6759 | + | 2.58510i | −0.371460 | + | 0.0822429i | ||||
\(989\) | −3.52804 | + | 8.51745i | −0.112185 | + | 0.270839i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.7647 | −1.32670 | −0.663350 | − | 0.748310i | \(-0.730866\pi\) | ||||
−0.663350 | + | 0.748310i | \(0.730866\pi\) | |||||||
\(992\) | 30.2024 | + | 22.1775i | 0.958929 | + | 0.704136i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.39837 | − | 2.54974i | −0.0443537 | − | 0.0808727i | ||||
\(995\) | 8.10535 | − | 19.5680i | 0.256957 | − | 0.620348i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.4885 | + | 16.7709i | −1.28228 | + | 0.531139i | −0.916676 | − | 0.399631i | \(-0.869138\pi\) |
−0.365606 | + | 0.930770i | \(0.619138\pi\) | |||||||
\(998\) | −47.4860 | + | 5.19392i | −1.50314 | + | 0.164411i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 864.2.v.b.109.4 | ✓ | 128 | |
3.2 | odd | 2 | inner | 864.2.v.b.109.29 | yes | 128 | |
32.5 | even | 8 | inner | 864.2.v.b.325.4 | yes | 128 | |
96.5 | odd | 8 | inner | 864.2.v.b.325.29 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.v.b.109.4 | ✓ | 128 | 1.1 | even | 1 | trivial | |
864.2.v.b.109.29 | yes | 128 | 3.2 | odd | 2 | inner | |
864.2.v.b.325.4 | yes | 128 | 32.5 | even | 8 | inner | |
864.2.v.b.325.29 | yes | 128 | 96.5 | odd | 8 | inner |