Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(19,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([20, 27]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.y (of order \(30\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(224\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{30})\) |
Twist minimal: | no (minimal twist has level 225) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{30}]$ |
Embedding invariants
Embedding label | 469.9 | ||
Character | \(\chi\) | \(=\) | 675.469 |
Dual form | 675.2.y.a.154.9 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{9}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.894901 | − | 0.805773i | −0.632791 | − | 0.569767i | 0.289061 | − | 0.957311i | \(-0.406657\pi\) |
−0.921851 | + | 0.387543i | \(0.873324\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.0574783 | − | 0.546869i | −0.0287391 | − | 0.273435i | ||||
\(5\) | −2.23444 | + | 0.0854168i | −0.999270 | + | 0.0381996i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.32094 | + | 1.33999i | −0.877233 | + | 0.506470i | −0.869745 | − | 0.493501i | \(-0.835717\pi\) |
−0.00748764 | + | 0.999972i | \(0.502383\pi\) | |||||||
\(8\) | −1.80485 | + | 2.48416i | −0.638110 | + | 0.878283i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.06843 | + | 1.72401i | 0.654094 | + | 0.545179i | ||||
\(11\) | 0.941029 | − | 1.04512i | 0.283731 | − | 0.315115i | −0.584385 | − | 0.811476i | \(-0.698664\pi\) |
0.868116 | + | 0.496361i | \(0.165331\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.120849 | + | 0.108813i | −0.0335175 | + | 0.0301793i | −0.685719 | − | 0.727866i | \(-0.740512\pi\) |
0.652202 | + | 0.758045i | \(0.273846\pi\) | |||||||
\(14\) | 3.15674 | + | 0.670987i | 0.843675 | + | 0.179329i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.54110 | − | 0.540127i | 0.635274 | − | 0.135032i | ||||
\(17\) | −0.113531 | + | 0.156262i | −0.0275354 | + | 0.0378992i | −0.822563 | − | 0.568674i | \(-0.807456\pi\) |
0.795027 | + | 0.606574i | \(0.207456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.07397 | + | 4.41300i | 1.39346 | + | 1.01241i | 0.995475 | + | 0.0950213i | \(0.0302919\pi\) |
0.397989 | + | 0.917390i | \(0.369708\pi\) | |||||||
\(20\) | 0.175143 | + | 1.21703i | 0.0391632 | + | 0.272137i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.68426 | + | 0.177022i | −0.359085 | + | 0.0377413i | ||||
\(23\) | 1.22650 | − | 5.77024i | 0.255743 | − | 1.20318i | −0.643403 | − | 0.765528i | \(-0.722478\pi\) |
0.899146 | − | 0.437649i | \(-0.144189\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.98541 | − | 0.381717i | 0.997082 | − | 0.0763434i | ||||
\(26\) | 0.195827 | 0.0384048 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.866205 | + | 1.19223i | 0.163697 | + | 0.225310i | ||||
\(29\) | 5.56680 | + | 2.47850i | 1.03373 | + | 0.460245i | 0.852242 | − | 0.523148i | \(-0.175243\pi\) |
0.181486 | + | 0.983393i | \(0.441909\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.549855 | + | 0.244811i | −0.0987568 | + | 0.0439694i | −0.455520 | − | 0.890225i | \(-0.650547\pi\) |
0.356764 | + | 0.934195i | \(0.383880\pi\) | |||||||
\(32\) | 2.60917 | + | 1.50640i | 0.461240 | + | 0.266297i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.227511 | − | 0.0483590i | 0.0390178 | − | 0.00829350i | ||||
\(35\) | 5.07153 | − | 3.19238i | 0.857245 | − | 0.539611i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.888903 | + | 0.288822i | 0.146135 | + | 0.0474821i | 0.381171 | − | 0.924505i | \(-0.375521\pi\) |
−0.235036 | + | 0.971987i | \(0.575521\pi\) | |||||||
\(38\) | −1.87973 | − | 8.84344i | −0.304933 | − | 1.43460i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.82063 | − | 5.70486i | 0.604094 | − | 0.902017i | ||||
\(41\) | −3.78427 | − | 4.20285i | −0.591003 | − | 0.656376i | 0.371249 | − | 0.928533i | \(-0.378929\pi\) |
−0.962253 | + | 0.272158i | \(0.912263\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.91893 | + | 3.41730i | −0.902629 | + | 0.521133i | −0.878052 | − | 0.478565i | \(-0.841157\pi\) |
−0.0245768 | + | 0.999698i | \(0.507824\pi\) | |||||||
\(44\) | −0.625632 | − | 0.454548i | −0.0943175 | − | 0.0685257i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.74710 | + | 4.17551i | −0.847363 | + | 0.615645i | ||||
\(47\) | −0.0890280 | + | 0.199960i | −0.0129861 | + | 0.0291672i | −0.919922 | − | 0.392101i | \(-0.871748\pi\) |
0.906936 | + | 0.421268i | \(0.138415\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0911727 | − | 0.157916i | 0.0130247 | − | 0.0225594i | ||||
\(50\) | −4.76903 | − | 3.67551i | −0.674442 | − | 0.519795i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0664527 | + | 0.0598343i | 0.00921534 | + | 0.00829753i | ||||
\(53\) | 7.64631 | + | 10.5242i | 1.05030 | + | 1.44562i | 0.888547 | + | 0.458785i | \(0.151715\pi\) |
0.161754 | + | 0.986831i | \(0.448285\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.01340 | + | 2.41563i | −0.271486 | + | 0.325723i | ||||
\(56\) | 0.860180 | − | 8.18407i | 0.114946 | − | 1.09364i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.98463 | − | 6.70358i | −0.391901 | − | 0.880224i | ||||
\(59\) | 3.97717 | + | 4.41709i | 0.517783 | + | 0.575057i | 0.944159 | − | 0.329489i | \(-0.106877\pi\) |
−0.426376 | + | 0.904546i | \(0.640210\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.43845 | − | 10.4825i | 1.20847 | − | 1.34214i | 0.284972 | − | 0.958536i | \(-0.408016\pi\) |
0.923497 | − | 0.383606i | \(-0.125318\pi\) | |||||||
\(62\) | 0.689328 | + | 0.223976i | 0.0875447 | + | 0.0284450i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.72670 | − | 8.39191i | −0.340837 | − | 1.04899i | ||||
\(65\) | 0.260735 | − | 0.253458i | 0.0323402 | − | 0.0314377i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.62723 | + | 5.90086i | 0.320967 | + | 0.720904i | 0.999912 | − | 0.0132854i | \(-0.00422899\pi\) |
−0.678945 | + | 0.734190i | \(0.737562\pi\) | |||||||
\(68\) | 0.0919806 | + | 0.0531050i | 0.0111543 | + | 0.00643993i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.11085 | − | 1.22964i | −0.849910 | − | 0.146970i | ||||
\(71\) | −2.90460 | + | 2.11032i | −0.344713 | + | 0.250449i | −0.746648 | − | 0.665220i | \(-0.768338\pi\) |
0.401935 | + | 0.915668i | \(0.368338\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0652 | + | 3.59530i | −1.29508 | + | 0.420798i | −0.873868 | − | 0.486163i | \(-0.838396\pi\) |
−0.421215 | + | 0.906961i | \(0.638396\pi\) | |||||||
\(74\) | −0.562756 | − | 0.974721i | −0.0654190 | − | 0.113309i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.06421 | − | 3.57532i | 0.236781 | − | 0.410117i | ||||
\(77\) | −0.783617 | + | 3.68663i | −0.0893015 | + | 0.420130i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.4249 | + | 5.53192i | 1.39791 | + | 0.622390i | 0.960857 | − | 0.277046i | \(-0.0893554\pi\) |
0.437053 | + | 0.899436i | \(0.356022\pi\) | |||||||
\(80\) | −5.63178 | + | 1.42393i | −0.629653 | + | 0.159200i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.81040i | 0.752083i | ||||||||
\(83\) | 14.5730 | + | 1.53168i | 1.59959 | + | 0.168124i | 0.861922 | − | 0.507040i | \(-0.169260\pi\) |
0.737668 | + | 0.675164i | \(0.235927\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.240331 | − | 0.358856i | 0.0260675 | − | 0.0389234i | ||||
\(86\) | 8.05043 | + | 1.71117i | 0.868100 | + | 0.184520i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.897827 | + | 4.22394i | 0.0957087 | + | 0.450274i | ||||
\(89\) | 3.38521 | + | 10.4186i | 0.358831 | + | 1.10437i | 0.953754 | + | 0.300587i | \(0.0971825\pi\) |
−0.594923 | + | 0.803783i | \(0.702817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.134675 | − | 0.414486i | 0.0141177 | − | 0.0434499i | ||||
\(92\) | −3.22606 | − | 0.339073i | −0.336340 | − | 0.0353508i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.240794 | − | 0.107208i | 0.0248360 | − | 0.0110577i | ||||
\(95\) | −13.9488 | − | 9.34174i | −1.43112 | − | 0.958443i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.26033 | + | 2.83075i | −0.127967 | + | 0.287419i | −0.966155 | − | 0.257963i | \(-0.916949\pi\) |
0.838188 | + | 0.545382i | \(0.183615\pi\) | |||||||
\(98\) | −0.208835 | + | 0.0678546i | −0.0210955 | + | 0.00685435i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.495302 | − | 2.70443i | −0.0495302 | − | 0.270443i | ||||
\(101\) | −4.01857 | − | 6.96037i | −0.399863 | − | 0.692583i | 0.593846 | − | 0.804579i | \(-0.297609\pi\) |
−0.993709 | + | 0.111996i | \(0.964276\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.536843 | + | 0.0564245i | −0.0528968 | + | 0.00555967i | −0.130940 | − | 0.991390i | \(-0.541799\pi\) |
0.0780431 | + | 0.996950i | \(0.475133\pi\) | |||||||
\(104\) | −0.0521947 | − | 0.496600i | −0.00511811 | − | 0.0486956i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.63746 | − | 15.5794i | 0.159044 | − | 1.51320i | ||||
\(107\) | 0.671621i | 0.0649281i | 0.999473 | + | 0.0324640i | \(0.0103354\pi\) | ||||
−0.999473 | + | 0.0324640i | \(0.989665\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.32136 | − | 13.2998i | 0.413911 | − | 1.27389i | −0.499310 | − | 0.866423i | \(-0.666413\pi\) |
0.913221 | − | 0.407464i | \(-0.133587\pi\) | |||||||
\(110\) | 3.74824 | − | 0.539409i | 0.357381 | − | 0.0514306i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.17397 | + | 4.65866i | −0.488894 | + | 0.440202i | ||||
\(113\) | 2.75193 | − | 2.47785i | 0.258880 | − | 0.233097i | −0.529462 | − | 0.848333i | \(-0.677606\pi\) |
0.788342 | + | 0.615237i | \(0.210940\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.24766 | + | 12.9980i | −0.209596 | + | 1.21207i | ||||
\(116\) | 1.03544 | − | 3.18677i | 0.0961386 | − | 0.295884i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 7.15756i | − | 0.658907i | ||||||
\(119\) | 0.0541083 | − | 0.514807i | 0.00496010 | − | 0.0471922i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.943076 | + | 8.97277i | 0.0857342 | + | 0.815706i | ||||
\(122\) | −16.8930 | + | 1.77552i | −1.52942 | + | 0.160748i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.165484 | + | 0.286627i | 0.0148609 | + | 0.0257399i | ||||
\(125\) | −11.1070 | + | 1.27876i | −0.993438 | + | 0.114376i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.6104 | − | 4.42230i | 1.20773 | − | 0.392416i | 0.365132 | − | 0.930956i | \(-0.381024\pi\) |
0.842600 | + | 0.538540i | \(0.181024\pi\) | |||||||
\(128\) | −1.87101 | + | 4.20237i | −0.165376 | + | 0.371440i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.437562 | + | 0.0167269i | −0.0383768 | + | 0.00146705i | ||||
\(131\) | −10.6971 | + | 4.76265i | −0.934608 | + | 0.416114i | −0.816799 | − | 0.576922i | \(-0.804254\pi\) |
−0.117809 | + | 0.993036i | \(0.537587\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.0107 | − | 2.10321i | −1.73515 | − | 0.182372i | ||||
\(134\) | 2.40364 | − | 7.39763i | 0.207643 | − | 0.639058i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.183274 | − | 0.564059i | −0.0157156 | − | 0.0483677i | ||||
\(137\) | 4.27866 | + | 20.1295i | 0.365550 | + | 1.71978i | 0.648997 | + | 0.760791i | \(0.275189\pi\) |
−0.283447 | + | 0.958988i | \(0.591478\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.891271 | + | 0.189445i | 0.0755966 | + | 0.0160686i | 0.245555 | − | 0.969383i | \(-0.421030\pi\) |
−0.169958 | + | 0.985451i | \(0.554363\pi\) | |||||||
\(140\) | −2.03732 | − | 2.58997i | −0.172185 | − | 0.218893i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.29977 | + | 0.451924i | 0.360829 | + | 0.0379246i | ||||
\(143\) | 0.228698i | 0.0191247i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.6504 | − | 5.06254i | −1.05055 | − | 0.420421i | ||||
\(146\) | 12.7993 | + | 5.69860i | 1.05927 | + | 0.471619i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.106855 | − | 0.502715i | 0.00878345 | − | 0.0413229i | ||||
\(149\) | −10.6085 | + | 18.3745i | −0.869083 | + | 1.50530i | −0.00614869 | + | 0.999981i | \(0.501957\pi\) |
−0.862935 | + | 0.505315i | \(0.831376\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.66528 | − | 4.61641i | −0.216898 | − | 0.375678i | 0.736960 | − | 0.675936i | \(-0.236260\pi\) |
−0.953858 | + | 0.300258i | \(0.902927\pi\) | |||||||
\(152\) | −21.9252 | + | 7.12392i | −1.77837 | + | 0.577826i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.67185 | − | 2.66775i | 0.295886 | − | 0.214974i | ||||
\(155\) | 1.20770 | − | 0.593982i | 0.0970051 | − | 0.0477098i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.4979 | − | 6.06096i | −0.837823 | − | 0.483717i | 0.0187007 | − | 0.999825i | \(-0.494047\pi\) |
−0.856524 | + | 0.516108i | \(0.827380\pi\) | |||||||
\(158\) | −6.66159 | − | 14.9622i | −0.529967 | − | 1.19033i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.95868 | − | 3.14309i | −0.471075 | − | 0.248483i | ||||
\(161\) | 4.88545 | + | 15.0359i | 0.385027 | + | 1.18499i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.508454 | − | 0.165207i | −0.0398252 | − | 0.0129400i | 0.289037 | − | 0.957318i | \(-0.406665\pi\) |
−0.328862 | + | 0.944378i | \(0.606665\pi\) | |||||||
\(164\) | −2.08090 | + | 2.31107i | −0.162491 | + | 0.180464i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.8072 | − | 13.1132i | −0.916415 | − | 1.01778i | ||||
\(167\) | 4.43413 | + | 9.95922i | 0.343123 | + | 0.770668i | 0.999863 | + | 0.0165503i | \(0.00526835\pi\) |
−0.656740 | + | 0.754117i | \(0.728065\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.35611 | + | 12.9025i | −0.104316 | + | 0.992499i | ||||
\(170\) | −0.504228 | + | 0.127488i | −0.0386726 | + | 0.00977791i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.20903 | + | 3.04046i | 0.168437 | + | 0.231833i | ||||
\(173\) | −7.80136 | − | 7.02437i | −0.593126 | − | 0.534053i | 0.316978 | − | 0.948433i | \(-0.397332\pi\) |
−0.910104 | + | 0.414380i | \(0.863999\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.0593 | + | 7.56636i | −0.836007 | + | 0.571963i | ||||
\(176\) | 1.82675 | − | 3.16402i | 0.137696 | − | 0.238497i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.36560 | − | 12.0513i | 0.402169 | − | 0.903285i | ||||
\(179\) | 11.1491 | − | 8.10027i | 0.833321 | − | 0.605443i | −0.0871761 | − | 0.996193i | \(-0.527784\pi\) |
0.920497 | + | 0.390750i | \(0.127784\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.95243 | − | 4.32469i | −0.442441 | − | 0.321452i | 0.344163 | − | 0.938910i | \(-0.388163\pi\) |
−0.786604 | + | 0.617458i | \(0.788163\pi\) | |||||||
\(182\) | −0.454502 | + | 0.262407i | −0.0336899 | + | 0.0194509i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.1205 | + | 13.4612i | 0.893538 | + | 0.992374i | ||||
\(185\) | −2.01087 | − | 0.569427i | −0.147842 | − | 0.0418651i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0564765 | + | 0.265701i | 0.00412997 | + | 0.0194300i | ||||
\(188\) | 0.114469 | + | 0.0371933i | 0.00834852 | + | 0.00271260i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.95552 | + | 19.5995i | 0.359511 | + | 1.42190i | ||||
\(191\) | 1.09062 | − | 0.231818i | 0.0789142 | − | 0.0167737i | −0.168285 | − | 0.985738i | \(-0.553823\pi\) |
0.247200 | + | 0.968965i | \(0.420490\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.9469 | + | 12.6711i | 1.57977 | + | 0.912083i | 0.994890 | + | 0.100966i | \(0.0321934\pi\) |
0.584884 | + | 0.811117i | \(0.301140\pi\) | |||||||
\(194\) | 3.40881 | − | 1.51770i | 0.244738 | − | 0.108965i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0915997 | − | 0.0407828i | −0.00654284 | − | 0.00291306i | ||||
\(197\) | −9.37839 | − | 12.9082i | −0.668182 | − | 0.919674i | 0.331535 | − | 0.943443i | \(-0.392433\pi\) |
−0.999717 | + | 0.0237688i | \(0.992433\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.2943 | −1.36774 | −0.683868 | − | 0.729606i | \(-0.739704\pi\) | ||||
−0.683868 | + | 0.729606i | \(0.739704\pi\) | |||||||
\(200\) | −8.04965 | + | 13.0735i | −0.569196 | + | 0.924435i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.01225 | + | 9.46690i | −0.141582 | + | 0.666089i | ||||
\(203\) | −16.2414 | + | 1.70704i | −1.13992 | + | 0.119810i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.81470 | + | 9.06777i | 0.615645 | + | 0.633320i | ||||
\(206\) | 0.525887 | + | 0.382080i | 0.0366403 | + | 0.0266207i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.248317 | + | 0.341779i | −0.0172177 | + | 0.0236981i | ||||
\(209\) | 10.3279 | − | 2.19526i | 0.714395 | − | 0.151849i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.96507 | − | 0.630245i | −0.204124 | − | 0.0433879i | 0.104715 | − | 0.994502i | \(-0.466607\pi\) |
−0.308839 | + | 0.951114i | \(0.599940\pi\) | |||||||
\(212\) | 5.31589 | − | 4.78645i | 0.365097 | − | 0.328735i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.541174 | − | 0.601035i | 0.0369939 | − | 0.0410859i | ||||
\(215\) | 12.9336 | − | 8.14131i | 0.882063 | − | 0.555233i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.948134 | − | 1.30499i | 0.0643635 | − | 0.0885888i | ||||
\(218\) | −14.5838 | + | 8.41995i | −0.987738 | + | 0.570271i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.43676 | + | 0.962219i | 0.0968663 | + | 0.0648728i | ||||
\(221\) | −0.00328323 | − | 0.0312379i | −0.000220854 | − | 0.00210129i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.5387 | − | 12.1903i | −0.906616 | − | 0.816321i | 0.0769189 | − | 0.997037i | \(-0.475492\pi\) |
−0.983535 | + | 0.180716i | \(0.942158\pi\) | |||||||
\(224\) | −8.07429 | −0.539486 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.45929 | −0.296628 | ||||||||
\(227\) | 6.28780 | + | 5.66156i | 0.417336 | + | 0.375771i | 0.850879 | − | 0.525362i | \(-0.176070\pi\) |
−0.433543 | + | 0.901133i | \(0.642737\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.02248 | + | 9.72823i | 0.0675673 | + | 0.642860i | 0.974930 | + | 0.222511i | \(0.0714255\pi\) |
−0.907363 | + | 0.420348i | \(0.861908\pi\) | |||||||
\(230\) | 12.4849 | − | 9.82081i | 0.823227 | − | 0.647565i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.2042 | + | 9.35550i | −1.06386 | + | 0.614218i | ||||
\(233\) | 1.49631 | − | 2.05949i | 0.0980263 | − | 0.134922i | −0.757186 | − | 0.653199i | \(-0.773427\pi\) |
0.855213 | + | 0.518277i | \(0.173427\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.181847 | − | 0.454403i | 0.0118624 | − | 0.0296420i | ||||
\(236\) | 2.18697 | − | 2.42888i | 0.142360 | − | 0.158107i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.463239 | + | 0.417102i | −0.0300273 | + | 0.0270367i | ||||
\(239\) | 10.3206 | + | 2.19372i | 0.667586 | + | 0.141900i | 0.529224 | − | 0.848482i | \(-0.322483\pi\) |
0.138362 | + | 0.990382i | \(0.455816\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.00671 | − | 0.639097i | 0.193680 | − | 0.0411679i | −0.110050 | − | 0.993926i | \(-0.535101\pi\) |
0.303730 | + | 0.952758i | \(0.401768\pi\) | |||||||
\(242\) | 6.38605 | − | 8.78965i | 0.410511 | − | 0.565020i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.27504 | − | 4.55908i | −0.401718 | − | 0.291865i | ||||
\(245\) | −0.190231 | + | 0.360640i | −0.0121534 | + | 0.0230405i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.21423 | + | 0.127620i | −0.0772594 | + | 0.00812029i | ||||
\(248\) | 0.384254 | − | 1.80777i | 0.0244002 | − | 0.114794i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.9700 | + | 7.80533i | 0.693806 | + | 0.493652i | ||||
\(251\) | 23.8819 | 1.50741 | 0.753707 | − | 0.657211i | \(-0.228264\pi\) | ||||
0.753707 | + | 0.657211i | \(0.228264\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.87640 | − | 6.71180i | −0.306577 | − | 0.421967i | ||||
\(254\) | −15.7434 | − | 7.00940i | −0.987827 | − | 0.439809i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.0613 | + | 4.92482i | −0.691333 | + | 0.307801i | ||||
\(257\) | −4.15137 | − | 2.39680i | −0.258955 | − | 0.149508i | 0.364903 | − | 0.931046i | \(-0.381102\pi\) |
−0.623858 | + | 0.781538i | \(0.714436\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.45011 | + | 0.520787i | −0.152242 | + | 0.0323601i | ||||
\(260\) | −0.153595 | − | 0.128020i | −0.00952557 | − | 0.00793945i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.4104 | + | 4.35732i | 0.828500 | + | 0.269196i | ||||
\(263\) | −4.83640 | − | 22.7535i | −0.298225 | − | 1.40304i | −0.830760 | − | 0.556631i | \(-0.812094\pi\) |
0.532535 | − | 0.846408i | \(-0.321239\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.9841 | − | 22.8626i | −1.10476 | − | 1.40444i | ||||
\(266\) | 16.2129 | + | 18.0063i | 0.994077 | + | 1.10403i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.07599 | − | 1.77592i | 0.187896 | − | 0.108482i | ||||
\(269\) | −6.79619 | − | 4.93772i | −0.414371 | − | 0.301058i | 0.360998 | − | 0.932567i | \(-0.382436\pi\) |
−0.775369 | + | 0.631508i | \(0.782436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4715 | − | 11.9673i | 1.00058 | − | 0.726960i | 0.0383636 | − | 0.999264i | \(-0.487785\pi\) |
0.962211 | + | 0.272304i | \(0.0877855\pi\) | |||||||
\(272\) | −0.204092 | + | 0.458399i | −0.0123749 | + | 0.0277945i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.3908 | − | 21.4615i | 0.748557 | − | 1.29654i | ||||
\(275\) | 4.29247 | − | 5.56955i | 0.258846 | − | 0.335856i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.58456 | − | 6.82917i | −0.455712 | − | 0.410325i | 0.409046 | − | 0.912514i | \(-0.365862\pi\) |
−0.864758 | + | 0.502189i | \(0.832528\pi\) | |||||||
\(278\) | −0.644950 | − | 0.887697i | −0.0386815 | − | 0.0532405i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.22296 | + | 18.3602i | −0.0730859 | + | 1.09723i | ||||
\(281\) | 2.45064 | − | 23.3163i | 0.146193 | − | 1.39093i | −0.637818 | − | 0.770187i | \(-0.720163\pi\) |
0.784011 | − | 0.620747i | \(-0.213171\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.59912 | + | 14.8219i | 0.392277 | + | 0.881069i | 0.996448 | + | 0.0842137i | \(0.0268378\pi\) |
−0.604171 | + | 0.796855i | \(0.706495\pi\) | |||||||
\(284\) | 1.32102 | + | 1.46714i | 0.0783881 | + | 0.0870588i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.184279 | − | 0.204662i | 0.0108966 | − | 0.0121019i | ||||
\(287\) | 14.4149 | + | 4.68367i | 0.850882 | + | 0.276468i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.24176 | + | 16.1325i | 0.308339 | + | 0.948969i | ||||
\(290\) | 7.24156 | + | 14.7238i | 0.425239 | + | 0.864611i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.60217 | + | 5.84456i | 0.152280 | + | 0.342027i | ||||
\(293\) | −2.77885 | − | 1.60437i | −0.162342 | − | 0.0937283i | 0.416628 | − | 0.909077i | \(-0.363212\pi\) |
−0.578970 | + | 0.815349i | \(0.696545\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.26402 | − | 9.53000i | −0.539372 | − | 0.554858i | ||||
\(296\) | −2.32181 | + | 1.68690i | −0.134953 | + | 0.0980489i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 24.2992 | − | 7.89530i | 1.40762 | − | 0.457363i | ||||
\(299\) | 0.479656 | + | 0.830788i | 0.0277392 | + | 0.0480457i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.15833 | − | 15.8627i | 0.527877 | − | 0.914310i | ||||
\(302\) | −1.33461 | + | 6.27884i | −0.0767981 | + | 0.361307i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 17.8181 | + | 7.93314i | 1.02194 | + | 0.454997i | ||||
\(305\) | −20.1942 | + | 24.2286i | −1.15632 | + | 1.38732i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.5271i | − | 0.943250i | −0.881799 | − | 0.471625i | \(-0.843668\pi\) | ||
0.881799 | − | 0.471625i | \(-0.156332\pi\) | |||||||
\(308\) | 2.06115 | + | 0.216635i | 0.117445 | + | 0.0123439i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.55939 | − | 0.441580i | −0.0885674 | − | 0.0250801i | ||||
\(311\) | 18.3936 | + | 3.90968i | 1.04301 | + | 0.221698i | 0.697400 | − | 0.716682i | \(-0.254340\pi\) |
0.345606 | + | 0.938380i | \(0.387673\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.657406 | + | 3.09285i | 0.0371588 | + | 0.174818i | 0.992814 | − | 0.119671i | \(-0.0381839\pi\) |
−0.955655 | + | 0.294489i | \(0.904851\pi\) | |||||||
\(314\) | 4.51082 | + | 13.8829i | 0.254560 | + | 0.783456i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.31108 | − | 7.11276i | 0.130008 | − | 0.400124i | ||||
\(317\) | −0.398908 | − | 0.0419269i | −0.0224049 | − | 0.00235485i | 0.0933194 | − | 0.995636i | \(-0.470252\pi\) |
−0.115724 | + | 0.993281i | \(0.536919\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.82884 | − | 3.48562i | 0.438331 | − | 0.195157i | ||||
\(320\) | 6.80944 | + | 18.5183i | 0.380659 | + | 1.03520i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.74350 | − | 17.3922i | 0.431528 | − | 0.969229i | ||||
\(323\) | −1.37917 | + | 0.448120i | −0.0767391 | + | 0.0249340i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.560947 | + | 0.588608i | −0.0311157 | + | 0.0326501i | ||||
\(326\) | 0.321897 | + | 0.557543i | 0.0178282 | + | 0.0308794i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 17.2706 | − | 1.81521i | 0.953608 | − | 0.100228i | ||||
\(329\) | −0.0613170 | − | 0.583392i | −0.00338052 | − | 0.0321635i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.52674 | + | 24.0403i | −0.138882 | + | 1.32138i | 0.673906 | + | 0.738817i | \(0.264615\pi\) |
−0.812789 | + | 0.582559i | \(0.802052\pi\) | |||||||
\(332\) | − | 8.05754i | − | 0.442215i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.05676 | − | 12.4854i | 0.221976 | − | 0.683172i | ||||
\(335\) | −6.37441 | − | 12.9607i | −0.348271 | − | 0.708117i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.8166 | − | 22.3450i | 1.35185 | − | 1.21721i | 0.397830 | − | 0.917459i | \(-0.369763\pi\) |
0.954018 | − | 0.299750i | \(-0.0969032\pi\) | |||||||
\(338\) | 11.6101 | − | 10.4537i | 0.631504 | − | 0.568608i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.210061 | − | 0.110803i | −0.0113921 | − | 0.00600914i | ||||
\(341\) | −0.261573 | + | 0.805038i | −0.0141649 | + | 0.0435952i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.2712i | − | 0.986554i | ||||||
\(344\) | 2.19366 | − | 20.8713i | 0.118274 | − | 1.12530i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.32140 | + | 12.5722i | 0.0710387 | + | 0.675888i | ||||
\(347\) | 3.72354 | − | 0.391360i | 0.199890 | − | 0.0210093i | −0.00405417 | − | 0.999992i | \(-0.501290\pi\) |
0.203944 | + | 0.978982i | \(0.434624\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.67752 | − | 15.0299i | −0.464497 | − | 0.804532i | 0.534682 | − | 0.845053i | \(-0.320431\pi\) |
−0.999179 | + | 0.0405213i | \(0.987098\pi\) | |||||||
\(350\) | 15.9938 | + | 2.14016i | 0.854904 | + | 0.114396i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.02967 | − | 1.30932i | 0.214782 | − | 0.0697869i | ||||
\(353\) | 2.24699 | − | 5.04682i | 0.119595 | − | 0.268615i | −0.843821 | − | 0.536624i | \(-0.819699\pi\) |
0.963416 | + | 0.268009i | \(0.0863659\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.30990 | − | 4.96347i | 0.334895 | − | 0.263434i | ||||
\(356\) | 5.50304 | − | 2.45011i | 0.291660 | − | 0.129856i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.5043 | − | 1.73467i | −0.872279 | − | 0.0916803i | ||||
\(359\) | 4.30244 | − | 13.2416i | 0.227074 | − | 0.698863i | −0.771000 | − | 0.636835i | \(-0.780243\pi\) |
0.998074 | − | 0.0620276i | \(-0.0197567\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.5473 | + | 35.5388i | 0.607750 | + | 1.87046i | ||||
\(362\) | 1.84212 | + | 8.66648i | 0.0968196 | + | 0.455500i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.234410 | − | 0.0498255i | −0.0122864 | − | 0.00261156i | ||||
\(365\) | 24.4174 | − | 8.97862i | 1.27806 | − | 0.469963i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.4865 | + | 3.83489i | 1.90458 | + | 0.200179i | 0.982427 | − | 0.186645i | \(-0.0597615\pi\) |
0.922153 | + | 0.386825i | \(0.126428\pi\) | |||||||
\(368\) | − | 15.3252i | − | 0.798881i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.34070 | + | 2.12988i | 0.0696996 | + | 0.110727i | ||||
\(371\) | −31.8491 | − | 14.1801i | −1.65352 | − | 0.736195i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.88898 | + | 18.2962i | −0.201364 | + | 0.947342i | 0.755127 | + | 0.655579i | \(0.227575\pi\) |
−0.956491 | + | 0.291763i | \(0.905758\pi\) | |||||||
\(374\) | 0.163554 | − | 0.283283i | 0.00845716 | − | 0.0146482i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.336051 | − | 0.582057i | −0.0173305 | − | 0.0300173i | ||||
\(377\) | −0.942436 | + | 0.306216i | −0.0485379 | + | 0.0157709i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.54812 | − | 1.12477i | 0.0795216 | − | 0.0577758i | −0.547314 | − | 0.836927i | \(-0.684350\pi\) |
0.626836 | + | 0.779151i | \(0.284350\pi\) | |||||||
\(380\) | −4.30696 | + | 8.16514i | −0.220942 | + | 0.418863i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.16279 | − | 0.671335i | −0.0594933 | − | 0.0343485i | ||||
\(383\) | 3.92887 | + | 8.82440i | 0.200756 | + | 0.450906i | 0.985667 | − | 0.168703i | \(-0.0539579\pi\) |
−0.784911 | + | 0.619609i | \(0.787291\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.43604 | − | 8.30447i | 0.0731875 | − | 0.423235i | ||||
\(386\) | −9.43034 | − | 29.0236i | −0.479991 | − | 1.47726i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.62049 | + | 0.526529i | 0.0822680 | + | 0.0267305i | ||||
\(389\) | −15.2919 | + | 16.9834i | −0.775332 | + | 0.861093i | −0.993384 | − | 0.114844i | \(-0.963363\pi\) |
0.218052 | + | 0.975937i | \(0.430030\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.762424 | + | 0.846758i | 0.0385574 | + | 0.0428224i | ||||
\(392\) | 0.227735 | + | 0.511501i | 0.0115024 | + | 0.0258347i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.00838 | + | 19.1085i | −0.101181 | + | 0.962670i | ||||
\(395\) | −28.2352 | − | 11.2994i | −1.42066 | − | 0.568536i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.64077 | + | 7.76385i | 0.283102 | + | 0.389657i | 0.926758 | − | 0.375658i | \(-0.122583\pi\) |
−0.643656 | + | 0.765315i | \(0.722583\pi\) | |||||||
\(398\) | 17.2665 | + | 15.5468i | 0.865491 | + | 0.779291i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.4622 | − | 3.66273i | 0.623112 | − | 0.183137i | ||||
\(401\) | 3.09035 | − | 5.35264i | 0.154325 | − | 0.267298i | −0.778488 | − | 0.627659i | \(-0.784013\pi\) |
0.932813 | + | 0.360361i | \(0.117347\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0398109 | − | 0.0894166i | 0.00198312 | − | 0.00445416i | ||||
\(404\) | −3.57543 | + | 2.59770i | −0.177884 | + | 0.129241i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.9099 | + | 11.5592i | 0.789595 | + | 0.573675i | ||||
\(407\) | 1.13834 | − | 0.657219i | 0.0564252 | − | 0.0325771i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.96923 | − | 2.18705i | −0.0973722 | − | 0.108143i | 0.692489 | − | 0.721428i | \(-0.256514\pi\) |
−0.789861 | + | 0.613286i | \(0.789847\pi\) | |||||||
\(410\) | −0.581723 | − | 15.2174i | −0.0287292 | − | 0.751534i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.0617137 | + | 0.290340i | 0.00304041 | + | 0.0143040i | ||||
\(413\) | −15.1497 | − | 4.92242i | −0.745466 | − | 0.242216i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −32.6932 | − | 2.17766i | −1.60484 | − | 0.106897i | ||||
\(416\) | −0.479232 | + | 0.101864i | −0.0234963 | + | 0.00499429i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.0113 | − | 6.35739i | −0.538581 | − | 0.310950i | ||||
\(419\) | −5.57816 | + | 2.48356i | −0.272511 | + | 0.121330i | −0.538443 | − | 0.842662i | \(-0.680987\pi\) |
0.265932 | + | 0.963992i | \(0.414320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.22140 | + | 0.543804i | 0.0595276 | + | 0.0265034i | 0.436285 | − | 0.899809i | \(-0.356294\pi\) |
−0.376757 | + | 0.926312i | \(0.622961\pi\) | |||||||
\(422\) | 2.14561 | + | 2.95318i | 0.104447 | + | 0.143759i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −39.9443 | −1.93987 | ||||||||
\(425\) | −0.506351 | + | 0.822368i | −0.0245617 | + | 0.0398907i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.85962 | + | 36.9766i | −0.380354 | + | 1.78942i | ||||
\(428\) | 0.367289 | − | 0.0386036i | 0.0177536 | − | 0.00186598i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.1343 | − | 3.13586i | −0.874515 | − | 0.151225i | ||||
\(431\) | 26.8953 | + | 19.5406i | 1.29550 | + | 0.941237i | 0.999901 | − | 0.0140751i | \(-0.00448038\pi\) |
0.295600 | + | 0.955312i | \(0.404480\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.84957 | + | 9.42763i | −0.329169 | + | 0.453063i | −0.941239 | − | 0.337741i | \(-0.890337\pi\) |
0.612070 | + | 0.790804i | \(0.290337\pi\) | |||||||
\(434\) | −1.90002 | + | 0.403861i | −0.0912037 | + | 0.0193859i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.52162 | − | 1.59877i | −0.360220 | − | 0.0765672i | ||||
\(437\) | 32.9138 | − | 29.6357i | 1.57448 | − | 1.41767i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.8478 | + | 16.4901i | −0.708646 | + | 0.787031i | −0.984727 | − | 0.174103i | \(-0.944297\pi\) |
0.276081 | + | 0.961134i | \(0.410964\pi\) | |||||||
\(440\) | −2.36693 | − | 9.36144i | −0.112839 | − | 0.446289i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0222324 | + | 0.0306003i | −0.00105749 | + | 0.00145551i | ||||
\(443\) | 6.90522 | − | 3.98673i | 0.328077 | − | 0.189415i | −0.326910 | − | 0.945055i | \(-0.606007\pi\) |
0.654987 | + | 0.755640i | \(0.272674\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.45396 | − | 22.9905i | −0.400756 | − | 1.08986i | ||||
\(446\) | 2.29318 | + | 21.8182i | 0.108585 | + | 1.03312i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17.5736 | + | 15.8234i | 0.830276 | + | 0.747583i | ||||
\(449\) | −19.4821 | −0.919419 | −0.459710 | − | 0.888069i | \(-0.652047\pi\) | ||||
−0.459710 | + | 0.888069i | \(0.652047\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.95358 | −0.374520 | ||||||||
\(452\) | −1.51324 | − | 1.36252i | −0.0711767 | − | 0.0640878i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.06503 | − | 10.1331i | −0.0499843 | − | 0.475569i | ||||
\(455\) | −0.265518 | + | 0.937646i | −0.0124477 | + | 0.0439575i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0307 | + | 8.67800i | −0.703108 | + | 0.405940i | −0.808504 | − | 0.588491i | \(-0.799722\pi\) |
0.105396 | + | 0.994430i | \(0.466389\pi\) | |||||||
\(458\) | 6.92373 | − | 9.52970i | 0.323525 | − | 0.445293i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.23739 | + | 0.482076i | 0.337445 | + | 0.0224769i | ||||
\(461\) | −19.9699 | + | 22.1788i | −0.930089 | + | 1.03297i | 0.0692850 | + | 0.997597i | \(0.477928\pi\) |
−0.999374 | + | 0.0353718i | \(0.988738\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.67871 | − | 7.81435i | 0.403334 | − | 0.363163i | −0.442355 | − | 0.896840i | \(-0.645857\pi\) |
0.845689 | + | 0.533677i | \(0.179190\pi\) | |||||||
\(464\) | 15.4845 | + | 3.29133i | 0.718849 | + | 0.152796i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.99853 | + | 0.637357i | −0.138904 | + | 0.0295250i | ||||
\(467\) | 8.44207 | − | 11.6195i | 0.390652 | − | 0.537687i | −0.567715 | − | 0.823225i | \(-0.692172\pi\) |
0.958367 | + | 0.285538i | \(0.0921724\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0048 | − | 10.1751i | −0.646680 | − | 0.469840i | ||||
\(470\) | −0.528881 | + | 0.260118i | −0.0243954 | + | 0.0119983i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.1509 | + | 1.90774i | −0.835465 | + | 0.0878109i | ||||
\(473\) | −1.99841 | + | 9.40176i | −0.0918868 | + | 0.432293i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.9657 | + | 19.6821i | 1.46669 | + | 0.903075i | ||||
\(476\) | −0.284642 | −0.0130465 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.46831 | − | 10.2792i | −0.341592 | − | 0.470162i | ||||
\(479\) | −4.69795 | − | 2.09166i | −0.214655 | − | 0.0955705i | 0.296592 | − | 0.955004i | \(-0.404150\pi\) |
−0.511247 | + | 0.859434i | \(0.670816\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.138851 | + | 0.0618204i | −0.00633105 | + | 0.00281877i | ||||
\(482\) | −3.20568 | − | 1.85080i | −0.146015 | − | 0.0843016i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.85272 | − | 1.03148i | 0.220578 | − | 0.0468854i | ||||
\(485\) | 2.57433 | − | 6.43278i | 0.116895 | − | 0.292098i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.7356 | + | 12.5860i | 1.75528 | + | 0.570324i | 0.996694 | − | 0.0812511i | \(-0.0258916\pi\) |
0.758584 | + | 0.651575i | \(0.225892\pi\) | |||||||
\(488\) | 9.00514 | + | 42.3658i | 0.407643 | + | 1.91781i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.460832 | − | 0.169455i | 0.0208183 | − | 0.00765518i | ||||
\(491\) | −26.8216 | − | 29.7884i | −1.21044 | − | 1.34433i | −0.922171 | − | 0.386783i | \(-0.873586\pi\) |
−0.288271 | − | 0.957549i | \(-0.593080\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.01930 | + | 0.588493i | −0.0459070 | + | 0.0265044i | ||||
\(494\) | 1.18945 | + | 0.864183i | 0.0535157 | + | 0.0388814i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.26501 | + | 0.919080i | −0.0568004 | + | 0.0412679i | ||||
\(497\) | 3.91359 | − | 8.79008i | 0.175549 | − | 0.394289i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.6136 | − | 25.3114i | 0.654193 | − | 1.13310i | −0.327903 | − | 0.944712i | \(-0.606342\pi\) |
0.982096 | − | 0.188384i | \(-0.0603249\pi\) | |||||||
\(500\) | 1.33772 | + | 6.00056i | 0.0598248 | + | 0.268353i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21.3720 | − | 19.2434i | −0.953878 | − | 0.858875i | ||||
\(503\) | −4.96862 | − | 6.83872i | −0.221540 | − | 0.304923i | 0.683751 | − | 0.729715i | \(-0.260347\pi\) |
−0.905291 | + | 0.424792i | \(0.860347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.57377 | + | 15.2092i | 0.426027 | + | 0.676803i | ||||
\(506\) | −1.04428 | + | 9.93567i | −0.0464240 | + | 0.441694i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.20072 | − | 7.18895i | −0.142009 | − | 0.318958i | ||||
\(509\) | −8.40814 | − | 9.33819i | −0.372684 | − | 0.413908i | 0.527404 | − | 0.849614i | \(-0.323165\pi\) |
−0.900089 | + | 0.435706i | \(0.856499\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.8640 | − | 23.1718i | 0.922968 | − | 1.02506i | ||||
\(512\) | 22.6169 | + | 7.34868i | 0.999536 | + | 0.324769i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.78380 | + | 5.48996i | 0.0786799 | + | 0.242152i | ||||
\(515\) | 1.19472 | − | 0.171932i | 0.0526458 | − | 0.00757625i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.125204 | + | 0.281213i | 0.00550647 | + | 0.0123677i | ||||
\(518\) | 2.61224 | + | 1.50818i | 0.114775 | + | 0.0662656i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.159044 | + | 1.10516i | 0.00697453 | + | 0.0484646i | ||||
\(521\) | −15.5846 | + | 11.3229i | −0.682773 | + | 0.496063i | −0.874276 | − | 0.485429i | \(-0.838664\pi\) |
0.191504 | + | 0.981492i | \(0.438664\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.3250 | − | 7.90367i | 1.06366 | − | 0.345604i | 0.275644 | − | 0.961260i | \(-0.411109\pi\) |
0.788015 | + | 0.615656i | \(0.211109\pi\) | |||||||
\(524\) | 3.21939 | + | 5.57615i | 0.140640 | + | 0.243595i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.0060 | + | 24.2591i | −0.610692 | + | 1.05775i | ||||
\(527\) | 0.0241709 | − | 0.113715i | 0.00105290 | − | 0.00495352i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.7798 | − | 4.79946i | −0.468685 | − | 0.208672i | ||||
\(530\) | −2.32805 | + | 34.9509i | −0.101124 | + | 1.51817i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.0641i | 0.479691i | ||||||||
\(533\) | 0.914651 | + | 0.0961337i | 0.0396179 | + | 0.00416401i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.0573678 | − | 1.50069i | −0.00248022 | − | 0.0648807i | ||||
\(536\) | −19.4004 | − | 4.12368i | −0.837970 | − | 0.178116i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.10324 | + | 9.89496i | 0.0906771 | + | 0.426602i | ||||
\(539\) | −0.0792445 | − | 0.243890i | −0.00341330 | − | 0.0105051i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.8581 | + | 36.4956i | −0.509821 | + | 1.56907i | 0.282690 | + | 0.959211i | \(0.408773\pi\) |
−0.792511 | + | 0.609858i | \(0.791227\pi\) | |||||||
\(542\) | −24.3833 | − | 2.56279i | −1.04735 | − | 0.110081i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.531616 | + | 0.236690i | −0.0227928 | + | 0.0101480i | ||||
\(545\) | −8.51977 | + | 30.0866i | −0.364947 | + | 1.28877i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.7170 | − | 28.5628i | 0.543739 | − | 1.22126i | −0.407613 | − | 0.913155i | \(-0.633639\pi\) |
0.951353 | − | 0.308104i | \(-0.0996944\pi\) | |||||||
\(548\) | 10.7623 | − | 3.49687i | 0.459741 | − | 0.149379i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.32913 | + | 1.52544i | −0.355155 | + | 0.0650449i | ||||
\(551\) | 22.8750 | + | 39.6206i | 0.974506 | + | 1.68789i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36.2502 | + | 3.81005i | −1.54151 | + | 0.162020i | ||||
\(554\) | 1.28468 | + | 12.2229i | 0.0545806 | + | 0.519300i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.0523732 | − | 0.498298i | 0.00222112 | − | 0.0211325i | ||||
\(557\) | − | 24.3166i | − | 1.03033i | −0.857091 | − | 0.515165i | \(-0.827731\pi\) | ||
0.857091 | − | 0.515165i | \(-0.172269\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.343452 | − | 1.05704i | 0.0145265 | − | 0.0447078i | ||||
\(560\) | 11.1630 | − | 10.8514i | 0.471721 | − | 0.458556i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.9807 | + | 18.8911i | −0.885019 | + | 0.796874i | ||||
\(563\) | −12.1037 | + | 10.8982i | −0.510109 | + | 0.459304i | −0.883541 | − | 0.468353i | \(-0.844847\pi\) |
0.373432 | + | 0.927657i | \(0.378181\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.93737 | + | 5.77166i | −0.249787 | + | 0.242816i | ||||
\(566\) | 6.03750 | − | 18.5815i | 0.253775 | − | 0.781039i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 11.0243i | − | 0.462569i | ||||||
\(569\) | −2.00198 | + | 19.0476i | −0.0839276 | + | 0.798517i | 0.868896 | + | 0.494994i | \(0.164830\pi\) |
−0.952824 | + | 0.303523i | \(0.901837\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.480995 | − | 4.57636i | −0.0201290 | − | 0.191515i | 0.979837 | − | 0.199800i | \(-0.0640293\pi\) |
−0.999966 | + | 0.00828549i | \(0.997363\pi\) | |||||||
\(572\) | 0.125068 | − | 0.0131452i | 0.00522935 | − | 0.000549627i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.12590 | − | 15.8065i | −0.380908 | − | 0.659752i | ||||
\(575\) | 3.91201 | − | 29.2352i | 0.163142 | − | 1.21919i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.5521 | + | 11.8765i | −1.52168 | + | 0.494425i | −0.946253 | − | 0.323427i | \(-0.895165\pi\) |
−0.575429 | + | 0.817852i | \(0.695165\pi\) | |||||||
\(578\) | 8.30826 | − | 18.6606i | 0.345578 | − | 0.776181i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.04143 | + | 7.20907i | −0.0847657 | + | 0.299341i | ||||
\(581\) | −35.8754 | + | 15.9728i | −1.48836 | + | 0.662662i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.1945 | + | 1.91232i | 0.753538 | + | 0.0792001i | ||||
\(584\) | 11.0397 | − | 33.9767i | 0.456826 | − | 1.40597i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.19404 | + | 3.67487i | 0.0493253 | + | 0.151808i | ||||
\(587\) | −5.40305 | − | 25.4193i | −0.223008 | − | 1.04917i | −0.937085 | − | 0.349102i | \(-0.886487\pi\) |
0.714077 | − | 0.700067i | \(-0.246847\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.42015 | − | 0.939533i | −0.182129 | − | 0.0387128i | ||||
\(590\) | 0.611376 | + | 15.9931i | 0.0251700 | + | 0.658426i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.41479 | + | 0.253805i | 0.0992472 | + | 0.0104313i | ||||
\(593\) | 32.5216i | 1.33550i | 0.744385 | + | 0.667750i | \(0.232743\pi\) | ||||
−0.744385 | + | 0.667750i | \(0.767257\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0769285 | + | 1.15492i | −0.00315376 | + | 0.0473473i | ||||
\(596\) | 10.6582 | + | 4.74534i | 0.436577 | + | 0.194377i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.240182 | − | 1.12997i | 0.00982176 | − | 0.0462078i | ||||
\(599\) | −5.00962 | + | 8.67692i | −0.204688 | + | 0.354529i | −0.950033 | − | 0.312149i | \(-0.898951\pi\) |
0.745346 | + | 0.666678i | \(0.232285\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.09862 | + | 10.5631i | 0.248768 | + | 0.430878i | 0.963184 | − | 0.268842i | \(-0.0866411\pi\) |
−0.714416 | + | 0.699721i | \(0.753308\pi\) | |||||||
\(602\) | −20.9775 | + | 6.81601i | −0.854980 | + | 0.277800i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.37137 | + | 1.72290i | −0.0964899 | + | 0.0701040i | ||||
\(605\) | −2.87367 | − | 19.9685i | −0.116831 | − | 0.811836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.1063 | − | 10.4537i | −0.734910 | − | 0.424301i | 0.0853054 | − | 0.996355i | \(-0.472813\pi\) |
−0.820216 | + | 0.572054i | \(0.806147\pi\) | |||||||
\(608\) | 9.20024 | + | 20.6641i | 0.373119 | + | 0.838039i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 37.5946 | − | 5.41023i | 1.52216 | − | 0.219054i | ||||
\(611\) | −0.0109993 | − | 0.0338524i | −0.000444985 | − | 0.00136952i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.43863 | − | 1.11728i | −0.138885 | − | 0.0451265i | 0.238750 | − | 0.971081i | \(-0.423262\pi\) |
−0.377635 | + | 0.925955i | \(0.623262\pi\) | |||||||
\(614\) | −13.3171 | + | 14.7901i | −0.537433 | + | 0.596880i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.74386 | − | 8.60043i | −0.312009 | − | 0.346521i | ||||
\(617\) | 2.39310 | + | 5.37500i | 0.0963427 | + | 0.216389i | 0.955287 | − | 0.295679i | \(-0.0955460\pi\) |
−0.858945 | + | 0.512069i | \(0.828879\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.88523 | − | 27.4512i | 0.115967 | − | 1.10336i | −0.769498 | − | 0.638649i | \(-0.779493\pi\) |
0.885465 | − | 0.464706i | \(-0.153840\pi\) | |||||||
\(620\) | −0.394247 | − | 0.626315i | −0.0158333 | − | 0.0251534i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.3102 | − | 18.3199i | −0.533689 | − | 0.734559i | ||||
\(623\) | −21.8177 | − | 19.6448i | −0.874109 | − | 0.787051i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7086 | − | 3.80603i | 0.988343 | − | 0.152241i | ||||
\(626\) | 1.90382 | − | 3.29752i | 0.0760921 | − | 0.131795i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.71115 | + | 6.08935i | −0.108187 | + | 0.242991i | ||||
\(629\) | −0.146050 | + | 0.106112i | −0.00582340 | + | 0.00423095i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.50355 | − | 3.99857i | −0.219093 | − | 0.159180i | 0.472825 | − | 0.881156i | \(-0.343234\pi\) |
−0.691918 | + | 0.721976i | \(0.743234\pi\) | |||||||
\(632\) | −36.1672 | + | 20.8811i | −1.43865 | + | 0.830607i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.323200 | + | 0.358950i | 0.0128359 | + | 0.0142557i | ||||
\(635\) | −30.0339 | + | 11.0439i | −1.19186 | + | 0.438264i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.00616516 | + | 0.0290048i | 0.000244272 | + | 0.00114921i | ||||
\(638\) | −9.81466 | − | 3.18898i | −0.388566 | − | 0.126253i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.82171 | − | 9.54974i | 0.151066 | − | 0.377486i | ||||
\(641\) | 1.85596 | − | 0.394497i | 0.0733060 | − | 0.0155817i | −0.171113 | − | 0.985251i | \(-0.554736\pi\) |
0.244419 | + | 0.969670i | \(0.421403\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.7142 | + | 7.91791i | 0.540836 | + | 0.312252i | 0.745418 | − | 0.666598i | \(-0.232250\pi\) |
−0.204581 | + | 0.978850i | \(0.565583\pi\) | |||||||
\(644\) | 7.94185 | − | 3.53594i | 0.312953 | − | 0.139335i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.59530 | + | 0.710275i | 0.0627664 | + | 0.0279454i | ||||
\(647\) | 1.30998 | + | 1.80303i | 0.0515007 | + | 0.0708846i | 0.833991 | − | 0.551779i | \(-0.186051\pi\) |
−0.782490 | + | 0.622663i | \(0.786051\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.35902 | 0.328120 | ||||||||
\(650\) | 0.976276 | − | 0.0747504i | 0.0382927 | − | 0.00293195i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.0611215 | + | 0.287554i | −0.00239370 | + | 0.0112615i | ||||
\(653\) | 1.00426 | − | 0.105552i | 0.0392999 | − | 0.00413058i | −0.0848581 | − | 0.996393i | \(-0.527044\pi\) |
0.124158 | + | 0.992262i | \(0.460377\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.4951 | − | 11.5555i | 0.918030 | − | 0.451512i | ||||
\(656\) | −11.8863 | − | 8.63588i | −0.464081 | − | 0.337174i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.415209 | + | 0.571486i | −0.0161865 | + | 0.0222788i | ||||
\(659\) | 14.3529 | − | 3.05080i | 0.559109 | − | 0.118842i | 0.0803150 | − | 0.996770i | \(-0.474407\pi\) |
0.478794 | + | 0.877927i | \(0.341074\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.9764 | − | 6.58425i | −1.20484 | − | 0.256098i | −0.438621 | − | 0.898672i | \(-0.644533\pi\) |
−0.766223 | + | 0.642575i | \(0.777866\pi\) | |||||||
\(662\) | 21.6322 | − | 19.4777i | 0.840760 | − | 0.757024i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −30.1069 | + | 33.4371i | −1.16837 | + | 1.29761i | ||||
\(665\) | 44.8923 | + | 2.99024i | 1.74085 | + | 0.115956i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.1292 | − | 29.0818i | 0.818126 | − | 1.12605i | ||||
\(668\) | 5.19152 | − | 2.99733i | 0.200866 | − | 0.115970i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.73889 | + | 16.7349i | −0.183079 | + | 0.646524i | ||||
\(671\) | −2.07356 | − | 19.7286i | −0.0800488 | − | 0.761614i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.0916 | − | 27.0946i | −1.15995 | − | 1.04442i | −0.998342 | − | 0.0575650i | \(-0.981666\pi\) |
−0.161605 | − | 0.986856i | \(-0.551667\pi\) | |||||||
\(674\) | −40.2134 | −1.54896 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.13392 | 0.274381 | ||||||||
\(677\) | −1.87592 | − | 1.68909i | −0.0720975 | − | 0.0649169i | 0.632294 | − | 0.774728i | \(-0.282113\pi\) |
−0.704392 | + | 0.709812i | \(0.748780\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.868038 | − | 8.25883i | −0.0333123 | − | 0.316945i | ||||
\(680\) | 0.457694 | + | 1.24470i | 0.0175518 | + | 0.0477320i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.882759 | − | 0.509661i | 0.0338026 | − | 0.0195159i | ||||
\(683\) | −12.8169 | + | 17.6409i | −0.490425 | + | 0.675012i | −0.980466 | − | 0.196687i | \(-0.936982\pi\) |
0.490042 | + | 0.871699i | \(0.336982\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.2798 | − | 44.6126i | −0.430978 | − | 1.70456i | ||||
\(686\) | −14.7225 | + | 16.3510i | −0.562107 | + | 0.624283i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13.1948 | + | 11.8807i | −0.503048 | + | 0.452946i | ||||
\(689\) | −2.06923 | − | 0.439828i | −0.0788312 | − | 0.0167561i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.5345 | + | 2.66428i | −0.476833 | + | 0.101354i | −0.440058 | − | 0.897969i | \(-0.645042\pi\) |
−0.0367757 | + | 0.999324i | \(0.511709\pi\) | |||||||
\(692\) | −3.39301 | + | 4.67007i | −0.128983 | + | 0.177529i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.64755 | − | 2.65010i | −0.138459 | − | 0.100596i | ||||
\(695\) | −2.00767 | − | 0.347174i | −0.0761552 | − | 0.0131691i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.08638 | − | 0.114183i | 0.0411496 | − | 0.00432500i | ||||
\(698\) | −4.34516 | + | 20.4424i | −0.164467 | + | 0.773756i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.77348 | + | 5.61311i | 0.180421 | + | 0.212155i | ||||
\(701\) | −48.5879 | −1.83514 | −0.917569 | − | 0.397577i | \(-0.869851\pi\) | ||||
−0.917569 | + | 0.397577i | \(0.869851\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.12460 | + | 5.67702i | 0.155562 | + | 0.214113i | ||||
\(704\) | −11.3364 | − | 5.04731i | −0.427258 | − | 0.190228i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.07742 | + | 2.70584i | −0.228727 | + | 0.101836i | ||||
\(707\) | 18.6537 | + | 10.7697i | 0.701545 | + | 0.405037i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.36006 | − | 1.56443i | 0.276413 | − | 0.0587533i | −0.0676195 | − | 0.997711i | \(-0.521540\pi\) |
0.344032 | + | 0.938958i | \(0.388207\pi\) | |||||||
\(710\) | −9.64617 | − | 0.642523i | −0.362014 | − | 0.0241135i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −31.9912 | − | 10.3946i | −1.19892 | − | 0.389554i | ||||
\(713\) | 0.738220 | + | 3.47305i | 0.0276466 | + | 0.130067i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0195347 | − | 0.511011i | −0.000730555 | − | 0.0191107i | ||||
\(716\) | −5.07062 | − | 5.63149i | −0.189498 | − | 0.210459i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.5199 | + | 8.38310i | −0.541880 | + | 0.312854i | ||||
\(719\) | 35.5528 | + | 25.8307i | 1.32590 | + | 0.963321i | 0.999839 | + | 0.0179714i | \(0.00572079\pi\) |
0.326059 | + | 0.945349i | \(0.394279\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.17037 | − | 0.850325i | 0.0435869 | − | 0.0316678i | ||||
\(722\) | 18.3025 | − | 41.1082i | 0.681150 | − | 1.52989i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.02291 | + | 3.50378i | −0.0751807 | + | 0.130217i | ||||
\(725\) | 28.6988 | + | 10.2314i | 1.06585 | + | 0.379984i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.6361 | − | 24.8837i | −1.02497 | − | 0.922884i | −0.0279140 | − | 0.999610i | \(-0.508886\pi\) |
−0.997052 | + | 0.0767266i | \(0.975553\pi\) | |||||||
\(728\) | 0.786582 | + | 1.08264i | 0.0291527 | + | 0.0401252i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −29.0859 | − | 11.6399i | −1.07652 | − | 0.430811i | ||||
\(731\) | 0.137989 | − | 1.31288i | 0.00510370 | − | 0.0485585i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.24663 | + | 5.04602i | 0.0829813 | + | 0.186379i | 0.950271 | − | 0.311425i | \(-0.100806\pi\) |
−0.867289 | + | 0.497804i | \(0.834140\pi\) | |||||||
\(734\) | −29.5618 | − | 32.8317i | −1.09115 | − | 1.21184i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.8924 | − | 13.2079i | 0.438361 | − | 0.486849i | ||||
\(737\) | 8.63939 | + | 2.80711i | 0.318236 | + | 0.103401i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.0729 | + | 40.2342i | 0.480894 | + | 1.48004i | 0.837840 | + | 0.545915i | \(0.183818\pi\) |
−0.356946 | + | 0.934125i | \(0.616182\pi\) | |||||||
\(740\) | −0.195821 | + | 1.13241i | −0.00719852 | + | 0.0416282i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.0758 | + | 38.3529i | 0.626873 | + | 1.40798i | ||||
\(743\) | 16.0074 | + | 9.24189i | 0.587256 | + | 0.339052i | 0.764012 | − | 0.645203i | \(-0.223227\pi\) |
−0.176756 | + | 0.984255i | \(0.556560\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.1346 | − | 41.9628i | 0.810947 | − | 1.53740i | ||||
\(746\) | 18.2228 | − | 13.2397i | 0.667186 | − | 0.484739i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.142057 | − | 0.0461573i | 0.00519413 | − | 0.00168768i | ||||
\(749\) | −0.899969 | − | 1.55879i | −0.0328841 | − | 0.0569570i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.6388 | − | 21.8911i | 0.461197 | − | 0.798816i | −0.537824 | − | 0.843057i | \(-0.680754\pi\) |
0.999021 | + | 0.0442409i | \(0.0140869\pi\) | |||||||
\(752\) | −0.118225 | + | 0.556205i | −0.00431122 | + | 0.0202827i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.09013 | + | 0.485356i | 0.0397001 | + | 0.0176756i | ||||
\(755\) | 6.34972 | + | 10.0874i | 0.231090 | + | 0.367118i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 14.6646i | − | 0.532993i | −0.963836 | − | 0.266497i | \(-0.914134\pi\) | ||
0.963836 | − | 0.266497i | \(-0.0858661\pi\) | |||||||
\(758\) | −2.29173 | − | 0.240870i | −0.0832393 | − | 0.00874880i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 48.3819 | − | 17.7907i | 1.75500 | − | 0.645338i | ||||
\(761\) | 9.76945 | + | 2.07656i | 0.354142 | + | 0.0752752i | 0.381548 | − | 0.924349i | \(-0.375391\pi\) |
−0.0274055 | + | 0.999624i | \(0.508725\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.79202 | + | 36.6586i | 0.282090 | + | 1.32713i | ||||
\(764\) | −0.189461 | − | 0.583100i | −0.00685444 | − | 0.0210958i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.59450 | − | 11.0627i | 0.129875 | − | 0.399713i | ||||
\(767\) | −0.961275 | − | 0.101034i | −0.0347096 | − | 0.00364813i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.8890 | + | 7.51947i | −0.609033 | + | 0.271159i | −0.687991 | − | 0.725719i | \(-0.741507\pi\) |
0.0789582 | + | 0.996878i | \(0.474841\pi\) | |||||||
\(770\) | −7.97663 | + | 6.27456i | −0.287458 | + | 0.226119i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.66794 | − | 12.7304i | 0.203994 | − | 0.458177i | ||||
\(773\) | −3.41227 | + | 1.10871i | −0.122731 | + | 0.0398777i | −0.369739 | − | 0.929136i | \(-0.620553\pi\) |
0.247008 | + | 0.969014i | \(0.420553\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.64780 | + | 1.43037i | −0.0951119 | + | 0.0513805i | ||||
\(776\) | −4.75733 | − | 8.23993i | −0.170778 | − | 0.295796i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.3695 | − | 2.87666i | 0.981246 | − | 0.103133i | ||||
\(779\) | −4.43834 | − | 42.2280i | −0.159020 | − | 1.51297i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.527784 | + | 5.02153i | −0.0188856 | + | 0.179684i | ||||
\(782\) | − | 1.37211i | − | 0.0490664i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.146384 | − | 0.450524i | 0.00522801 | − | 0.0160902i | ||||
\(785\) | 23.9746 | + | 12.6461i | 0.855689 | + | 0.451360i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.0214 | − | 10.8241i | 0.428517 | − | 0.385839i | −0.426458 | − | 0.904507i | \(-0.640239\pi\) |
0.854975 | + | 0.518669i | \(0.173572\pi\) | |||||||
\(788\) | −6.52007 | + | 5.87069i | −0.232268 | + | 0.209135i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16.1629 | + | 32.8630i | 0.575050 | + | 1.16921i | ||||
\(791\) | −3.06676 | + | 9.43852i | −0.109041 | + | 0.335595i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.29382i | 0.0814561i | ||||||||
\(794\) | 1.20797 | − | 11.4931i | 0.0428692 | − | 0.407874i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.10900 | + | 10.5514i | 0.0393075 | + | 0.373986i | ||||
\(797\) | −18.9150 | + | 1.98804i | −0.670003 | + | 0.0704202i | −0.433421 | − | 0.901191i | \(-0.642694\pi\) |
−0.236582 | + | 0.971612i | \(0.576027\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.0211388 | − | 0.0366134i | −0.000747836 | − | 0.00129529i | ||||
\(800\) | 13.5828 | + | 6.51407i | 0.480224 | + | 0.230307i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.07857 | + | 2.29997i | −0.249953 | + | 0.0812146i | ||||
\(803\) | −6.65515 | + | 14.9477i | −0.234855 | + | 0.527494i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.2005 | − | 33.1794i | −0.430013 | − | 1.16942i | ||||
\(806\) | −0.107676 | + | 0.0479406i | −0.00379274 | + | 0.00168863i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 24.5436 | + | 2.57963i | 0.863440 | + | 0.0907512i | ||||
\(809\) | −3.06508 | + | 9.43335i | −0.107763 | + | 0.331659i | −0.990369 | − | 0.138454i | \(-0.955787\pi\) |
0.882606 | + | 0.470113i | \(0.155787\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.46694 | + | 26.0585i | 0.297314 | + | 0.915039i | 0.982434 | + | 0.186609i | \(0.0597498\pi\) |
−0.685120 | + | 0.728430i | \(0.740250\pi\) | |||||||
\(812\) | 1.86705 | + | 8.78379i | 0.0655207 | + | 0.308250i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.54827 | − | 0.329094i | −0.0542668 | − | 0.0115348i | ||||
\(815\) | 1.15022 | + | 0.325714i | 0.0402905 | + | 0.0114092i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −51.0320 | − | 5.36368i | −1.78538 | − | 0.187651i | ||||
\(818\) | 3.54395i | 0.123911i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.45223 | − | 5.34169i | 0.155479 | − | 0.186540i | ||||
\(821\) | 8.76982 | + | 3.90458i | 0.306069 | + | 0.136271i | 0.554024 | − | 0.832501i | \(-0.313092\pi\) |
−0.247955 | + | 0.968772i | \(0.579758\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.15784 | + | 33.6750i | −0.249507 | + | 1.17384i | 0.657742 | + | 0.753243i | \(0.271512\pi\) |
−0.907249 | + | 0.420594i | \(0.861822\pi\) | |||||||
\(824\) | 0.828753 | − | 1.43544i | 0.0288710 | − | 0.0500060i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.59109 | + | 16.6123i | 0.333717 | + | 0.578014i | ||||
\(827\) | −25.3249 | + | 8.22855i | −0.880632 | + | 0.286135i | −0.714220 | − | 0.699922i | \(-0.753218\pi\) |
−0.166412 | + | 0.986056i | \(0.553218\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.0528 | − | 20.3815i | 0.974314 | − | 0.707880i | 0.0178831 | − | 0.999840i | \(-0.494307\pi\) |
0.956431 | + | 0.291960i | \(0.0943073\pi\) | |||||||
\(830\) | 27.5025 | + | 28.2921i | 0.954625 | + | 0.982032i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.24267 | + | 0.717456i | 0.0430818 | + | 0.0248733i | ||||
\(833\) | 0.0143253 | + | 0.0321752i | 0.000496344 | + | 0.00111481i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.7585 | − | 21.8745i | −0.372312 | − | 0.756998i | ||||
\(836\) | −1.79415 | − | 5.52182i | −0.0620519 | − | 0.190976i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.99309 | + | 2.27219i | 0.241572 | + | 0.0784916i | ||||
\(839\) | −3.14488 | + | 3.49274i | −0.108573 | + | 0.120583i | −0.794982 | − | 0.606633i | \(-0.792520\pi\) |
0.686408 | + | 0.727216i | \(0.259186\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.44148 | + | 6.04337i | 0.187637 | + | 0.208392i | ||||
\(842\) | −0.654854 | − | 1.47083i | −0.0225677 | − | 0.0506880i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.174235 | + | 1.65773i | −0.00599740 | + | 0.0570614i | ||||
\(845\) | 1.92804 | − | 28.9456i | 0.0663267 | − | 0.995759i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.2123 | − | 19.5615i | −0.488340 | − | 0.672142i | ||||
\(848\) | 25.1144 | + | 22.6132i | 0.862434 | + | 0.776539i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.11578 | − | 0.327934i | 0.0382708 | − | 0.0112480i | ||||
\(851\) | 2.75681 | − | 4.77494i | 0.0945023 | − | 0.163683i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.63819 | + | 17.1556i | −0.261527 | + | 0.587398i | −0.995810 | − | 0.0914446i | \(-0.970852\pi\) |
0.734284 | + | 0.678843i | \(0.237518\pi\) | |||||||
\(854\) | 36.8283 | − | 26.7574i | 1.26024 | − | 0.915618i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.66841 | − | 1.21217i | −0.0570252 | − | 0.0414312i | ||||
\(857\) | 28.3893 | − | 16.3906i | 0.969759 | − | 0.559891i | 0.0705962 | − | 0.997505i | \(-0.477510\pi\) |
0.899163 | + | 0.437614i | \(0.144176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.34105 | + | 7.04245i | 0.216354 | + | 0.240285i | 0.841546 | − | 0.540186i | \(-0.181646\pi\) |
−0.625192 | + | 0.780471i | \(0.714979\pi\) | |||||||
\(860\) | −5.19563 | − | 6.60503i | −0.177170 | − | 0.225230i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.32337 | − | 39.1584i | −0.283495 | − | 1.33374i | ||||
\(863\) | 32.4083 | + | 10.5301i | 1.10319 | + | 0.358449i | 0.803330 | − | 0.595534i | \(-0.203059\pi\) |
0.299862 | + | 0.953983i | \(0.403059\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.0316 | + | 15.0291i | 0.613094 | + | 0.511006i | ||||
\(866\) | 13.7262 | − | 2.91760i | 0.466436 | − | 0.0991440i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.768158 | − | 0.443496i | −0.0260730 | − | 0.0150532i | ||||
\(869\) | 17.4737 | − | 7.77979i | 0.592754 | − | 0.263911i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.959589 | − | 0.427237i | −0.0325144 | − | 0.0144764i | ||||
\(872\) | 25.2394 | + | 34.7390i | 0.854712 | + | 1.17641i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −53.3342 | −1.80406 | ||||||||
\(875\) | 24.0651 | − | 17.8512i | 0.813548 | − | 0.603481i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.61830 | − | 26.4320i | 0.189716 | − | 0.892546i | −0.775552 | − | 0.631284i | \(-0.782528\pi\) |
0.965268 | − | 0.261262i | \(-0.0841385\pi\) | |||||||
\(878\) | 26.5746 | − | 2.79310i | 0.896849 | − | 0.0942627i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.81149 | + | 7.22584i | −0.128485 | + | 0.243583i | ||||
\(881\) | −44.5745 | − | 32.3853i | −1.50175 | − | 1.09109i | −0.969676 | − | 0.244393i | \(-0.921411\pi\) |
−0.532078 | − | 0.846695i | \(-0.678589\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.9914 | − | 33.0214i | 0.807376 | − | 1.11126i | −0.184347 | − | 0.982861i | \(-0.559017\pi\) |
0.991723 | − | 0.128396i | \(-0.0409829\pi\) | |||||||
\(884\) | −0.0168943 | + | 0.00359100i | −0.000568217 | + | 0.000120778i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.39189 | − | 1.99631i | −0.315527 | − | 0.0670673i | ||||
\(887\) | −21.7243 | + | 19.5606i | −0.729430 | + | 0.656782i | −0.947720 | − | 0.319102i | \(-0.896619\pi\) |
0.218290 | + | 0.975884i | \(0.429952\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.6632 | + | 28.5018i | −0.860714 | + | 0.955920i | ||||
\(890\) | −10.9597 | + | 27.3862i | −0.367370 | + | 0.917989i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.88831 | + | 8.10456i | −0.197155 | + | 0.271361i | ||||
\(893\) | −1.42318 | + | 0.821672i | −0.0476248 | + | 0.0274962i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.2200 | + | 19.0519i | −0.809585 | + | 0.636834i | ||||
\(896\) | −1.28864 | − | 12.2606i | −0.0430504 | − | 0.409598i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.4346 | + | 15.6982i | 0.581800 | + | 0.523855i | ||||
\(899\) | −3.66769 | −0.122324 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.51264 | −0.0837081 | ||||||||
\(902\) | 7.11767 | + | 6.40878i | 0.236993 | + | 0.213389i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.18856 | + | 11.3084i | 0.0395309 | + | 0.376111i | ||||
\(905\) | 13.6697 | + | 9.15482i | 0.454397 | + | 0.304316i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.5281 | + | 15.3160i | −0.880851 | + | 0.508560i | −0.870939 | − | 0.491391i | \(-0.836489\pi\) |
−0.00991216 | + | 0.999951i | \(0.503155\pi\) | |||||||
\(908\) | 2.73472 | − | 3.76402i | 0.0907548 | − | 0.124913i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.993142 | − | 0.625153i | 0.0329223 | − | 0.0207236i | ||||
\(911\) | 6.81616 | − | 7.57012i | 0.225830 | − | 0.250809i | −0.619573 | − | 0.784939i | \(-0.712694\pi\) |
0.845402 | + | 0.534130i | \(0.179361\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.3144 | − | 13.7891i | 0.506831 | − | 0.456353i | ||||
\(914\) | 20.4435 | + | 4.34541i | 0.676212 | + | 0.143733i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.26130 | − | 1.11832i | 0.173838 | − | 0.0369505i | ||||
\(917\) | 18.4453 | − | 25.3878i | 0.609119 | − | 0.838380i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.8946 | + | 15.9074i | 0.722236 | + | 0.524735i | 0.887098 | − | 0.461581i | \(-0.152718\pi\) |
−0.164862 | + | 0.986317i | \(0.552718\pi\) | |||||||
\(920\) | −28.2324 | − | 29.0429i | −0.930794 | − | 0.957517i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 35.7421 | − | 3.75665i | 1.17710 | − | 0.123719i | ||||
\(923\) | 0.121389 | − | 0.571089i | 0.00399556 | − | 0.0187976i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.54179 | + | 1.10059i | 0.149333 | + | 0.0361871i | ||||
\(926\) | −14.0632 | −0.462145 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.7911 | + | 14.8526i | 0.354234 | + | 0.487562i | ||||
\(929\) | 18.6446 | + | 8.30111i | 0.611709 | + | 0.272351i | 0.689118 | − | 0.724649i | \(-0.257998\pi\) |
−0.0774089 | + | 0.996999i | \(0.524665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.25066 | − | 0.556831i | 0.0409888 | − | 0.0182494i | ||||
\(932\) | −1.21228 | − | 0.699908i | −0.0397094 | − | 0.0229262i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.9175 | + | 3.59593i | −0.553558 | + | 0.117662i | ||||
\(935\) | −0.148888 | − | 0.588867i | −0.00486917 | − | 0.0192580i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.4195 | + | 6.30978i | 0.634408 | + | 0.206132i | 0.608527 | − | 0.793533i | \(-0.291761\pi\) |
0.0258811 | + | 0.999665i | \(0.491761\pi\) | |||||||
\(938\) | 4.33410 | + | 20.3903i | 0.141513 | + | 0.665768i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.258951 | − | 0.0733284i | −0.00844605 | − | 0.00239171i | ||||
\(941\) | 0.394588 | + | 0.438234i | 0.0128632 | + | 0.0142860i | 0.749542 | − | 0.661957i | \(-0.230274\pi\) |
−0.736679 | + | 0.676243i | \(0.763607\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.8929 | + | 16.6813i | −0.940881 | + | 0.543218i | ||||
\(944\) | 12.4922 | + | 9.07609i | 0.406585 | + | 0.295402i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.36406 | − | 6.80339i | 0.304452 | − | 0.221197i | ||||
\(947\) | 10.9735 | − | 24.6470i | 0.356592 | − | 0.800919i | −0.642799 | − | 0.766035i | \(-0.722227\pi\) |
0.999391 | − | 0.0348845i | \(-0.0111063\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.946005 | − | 1.63853i | 0.0307086 | − | 0.0531889i | ||||
\(950\) | −12.7469 | − | 43.3706i | −0.413565 | − | 1.40713i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.18120 | + | 1.06356i | 0.0382830 | + | 0.0344702i | ||||
\(953\) | 10.0812 | + | 13.8756i | 0.326563 | + | 0.449475i | 0.940457 | − | 0.339913i | \(-0.110398\pi\) |
−0.613894 | + | 0.789388i | \(0.710398\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.41711 | + | 0.611139i | −0.0782159 | + | 0.0197760i | ||||
\(956\) | 0.606465 | − | 5.77012i | 0.0196145 | − | 0.186619i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.51880 | + | 5.65731i | 0.0813786 | + | 0.182779i | ||||
\(959\) | −36.9039 | − | 40.9860i | −1.19169 | − | 1.32351i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.5006 | + | 22.7683i | −0.661311 | + | 0.734460i | ||||
\(962\) | 0.174071 | + | 0.0565591i | 0.00561227 | + | 0.00182354i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.522323 | − | 1.60755i | −0.0168229 | − | 0.0517756i | ||||
\(965\) | −50.1213 | − | 26.4380i | −1.61346 | − | 0.851071i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.46728 | + | 12.2797i | 0.175816 | + | 0.394889i | 0.979861 | − | 0.199679i | \(-0.0639898\pi\) |
−0.804045 | + | 0.594568i | \(0.797323\pi\) | |||||||
\(968\) | −23.9919 | − | 13.8517i | −0.771129 | − | 0.445211i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.48714 | + | 3.68238i | −0.240397 | + | 0.118234i | ||||
\(971\) | 17.9377 | − | 13.0325i | 0.575648 | − | 0.418232i | −0.261505 | − | 0.965202i | \(-0.584219\pi\) |
0.837152 | + | 0.546970i | \(0.184219\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.32244 | + | 0.754607i | −0.0744541 | + | 0.0241916i | ||||
\(974\) | −24.5231 | − | 42.4753i | −0.785771 | − | 1.36100i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.3222 | − | 31.7349i | 0.586478 | − | 1.01581i | ||||
\(977\) | 4.34346 | − | 20.4344i | 0.138960 | − | 0.653753i | −0.852434 | − | 0.522835i | \(-0.824874\pi\) |
0.991393 | − | 0.130918i | \(-0.0417924\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.0742 | + | 6.26626i | 0.449815 | + | 0.200271i | ||||
\(980\) | 0.208157 | + | 0.0833025i | 0.00664934 | + | 0.00266100i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 48.2698i | 1.54035i | ||||||||
\(983\) | −27.2383 | − | 2.86286i | −0.868767 | − | 0.0913111i | −0.340353 | − | 0.940298i | \(-0.610547\pi\) |
−0.528414 | + | 0.848987i | \(0.677213\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.0580 | + | 28.0416i | 0.702826 | + | 0.893479i | ||||
\(986\) | 1.38637 | + | 0.294681i | 0.0441509 | + | 0.00938456i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.139583 | + | 0.656688i | 0.00444074 | + | 0.0208920i | ||||
\(989\) | 12.4590 | + | 38.3450i | 0.396174 | + | 1.21930i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.58088 | + | 14.0985i | −0.145516 | + | 0.447854i | −0.997077 | − | 0.0764026i | \(-0.975657\pi\) |
0.851561 | + | 0.524256i | \(0.175657\pi\) | |||||||
\(992\) | −1.80345 | − | 0.189550i | −0.0572595 | − | 0.00601821i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.5851 | + | 4.71278i | −0.335739 | + | 0.149480i | ||||
\(995\) | 43.1118 | − | 1.64806i | 1.36674 | − | 0.0522469i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.842806 | − | 1.89297i | 0.0266919 | − | 0.0599510i | −0.899708 | − | 0.436493i | \(-0.856220\pi\) |
0.926400 | + | 0.376542i | \(0.122887\pi\) | |||||||
\(998\) | −33.4730 | + | 10.8760i | −1.05957 | + | 0.344275i | ||||
\(999\) | 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 | 675.2.y.a.469.9 | 224 | ||
3.2 | odd | 2 | 225.2.u.a.94.20 | yes | 224 | ||
9.2 | odd | 6 | 225.2.u.a.169.20 | yes | 224 | ||
9.7 | even | 3 | inner | 675.2.y.a.19.9 | 224 | ||
25.4 | even | 10 | inner | 675.2.y.a.604.9 | 224 | ||
75.29 | odd | 10 | 225.2.u.a.4.20 | ✓ | 224 | ||
225.29 | odd | 30 | 225.2.u.a.79.20 | yes | 224 | ||
225.79 | even | 30 | inner | 675.2.y.a.154.9 | 224 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.u.a.4.20 | ✓ | 224 | 75.29 | odd | 10 | ||
225.2.u.a.79.20 | yes | 224 | 225.29 | odd | 30 | ||
225.2.u.a.94.20 | yes | 224 | 3.2 | odd | 2 | ||
225.2.u.a.169.20 | yes | 224 | 9.2 | odd | 6 | ||
675.2.y.a.19.9 | 224 | 9.7 | even | 3 | inner | ||
675.2.y.a.154.9 | 224 | 225.79 | even | 30 | inner | ||
675.2.y.a.469.9 | 224 | 1.1 | even | 1 | trivial | ||
675.2.y.a.604.9 | 224 | 25.4 | even | 10 | inner |