Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(257,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 9, 17]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.cc (of order \(18\), degree \(6\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{18})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 257.2 | ||
Root | \(0.0786547 + 1.73026i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.257 |
Dual form | 912.2.cc.c.401.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.517874 | − | 1.65282i | −0.298995 | − | 0.954255i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.258510 | + | 0.710252i | −0.115609 | + | 0.317634i | −0.983979 | − | 0.178283i | \(-0.942946\pi\) |
0.868370 | + | 0.495917i | \(0.165168\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.777943 | + | 1.34744i | −0.294035 | + | 0.509283i | −0.974760 | − | 0.223256i | \(-0.928331\pi\) |
0.680725 | + | 0.732539i | \(0.261665\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.46361 | + | 1.71190i | −0.821204 | + | 0.570634i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.832399 | + | 0.480586i | −0.250978 | + | 0.144902i | −0.620212 | − | 0.784434i | \(-0.712953\pi\) |
0.369234 | + | 0.929336i | \(0.379620\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.416982 | − | 0.496940i | 0.115650 | − | 0.137826i | −0.705113 | − | 0.709095i | \(-0.749104\pi\) |
0.820763 | + | 0.571268i | \(0.193548\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.30779 | + | 0.0594499i | 0.337671 | + | 0.0153499i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.73013 | − | 1.18670i | 1.63230 | − | 0.287818i | 0.718968 | − | 0.695043i | \(-0.244615\pi\) |
0.913328 | + | 0.407226i | \(0.133504\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.14364 | + | 1.35288i | 0.950615 | + | 0.310371i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.62994 | + | 0.587996i | 0.573901 | + | 0.128311i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.400647 | − | 1.10077i | −0.0835407 | − | 0.229526i | 0.890888 | − | 0.454223i | \(-0.150083\pi\) |
−0.974429 | + | 0.224697i | \(0.927861\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.39259 | + | 2.84672i | 0.678519 | + | 0.569345i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.10530 | + | 3.18535i | 0.790066 | + | 0.613022i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.39666 | − | 7.92086i | 0.259354 | − | 1.47087i | −0.525292 | − | 0.850922i | \(-0.676044\pi\) |
0.784645 | − | 0.619945i | \(-0.212845\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.63927 | + | 1.52379i | 0.474028 | + | 0.273680i | 0.717924 | − | 0.696121i | \(-0.245092\pi\) |
−0.243897 | + | 0.969801i | \(0.578426\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.22540 | + | 1.12692i | 0.213314 | + | 0.196172i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.755913 | − | 0.900862i | −0.127773 | − | 0.152273i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.12648i | − | 0.678389i | −0.940716 | − | 0.339195i | \(-0.889846\pi\) | ||
0.940716 | − | 0.339195i | \(-0.110154\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.03729 | − | 0.431843i | −0.166100 | − | 0.0691502i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.09755 | + | 3.43825i | −0.639929 | + | 0.536964i | −0.903996 | − | 0.427540i | \(-0.859380\pi\) |
0.264067 | + | 0.964504i | \(0.414936\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.34330 | + | 2.67274i | 1.11984 | + | 0.407589i | 0.834595 | − | 0.550865i | \(-0.185702\pi\) |
0.285248 | + | 0.958454i | \(0.407924\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.579012 | − | 2.19233i | −0.0863139 | − | 0.326813i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.11004 | + | 0.548383i | 0.453646 | + | 0.0799899i | 0.395802 | − | 0.918336i | \(-0.370467\pi\) |
0.0578432 | + | 0.998326i | \(0.481578\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.28961 | + | 3.96572i | 0.327087 | + | 0.566531i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.44676 | − | 10.5091i | −0.762699 | − | 1.47157i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.6276 | + | 4.96002i | −1.87189 | + | 0.681312i | −0.905427 | + | 0.424503i | \(0.860449\pi\) |
−0.966462 | + | 0.256809i | \(0.917329\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.126153 | − | 0.715449i | −0.0170105 | − | 0.0964711i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0901766 | − | 7.54930i | 0.0119442 | − | 0.999929i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.02192 | − | 11.4669i | −0.263231 | − | 1.49286i | −0.774024 | − | 0.633156i | \(-0.781759\pi\) |
0.510793 | − | 0.859704i | \(-0.329352\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1813 | − | 3.70568i | 1.30358 | − | 0.474464i | 0.405419 | − | 0.914131i | \(-0.367126\pi\) |
0.898161 | + | 0.439667i | \(0.144903\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.390129 | − | 4.65133i | −0.0491517 | − | 0.586012i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.245158 | + | 0.424626i | 0.0304081 | + | 0.0526684i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.19012 | + | 1.62047i | 1.12275 | + | 0.197972i | 0.704049 | − | 0.710151i | \(-0.251374\pi\) |
0.418703 | + | 0.908123i | \(0.362485\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.61189 | + | 1.23226i | −0.194048 | + | 0.148346i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0322101 | − | 0.0117235i | −0.00382263 | − | 0.00139132i | 0.340108 | − | 0.940386i | \(-0.389536\pi\) |
−0.343931 | + | 0.938995i | \(0.611759\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.04446 | + | 2.55461i | −0.356327 | + | 0.298994i | −0.803325 | − | 0.595541i | \(-0.796938\pi\) |
0.446998 | + | 0.894535i | \(0.352493\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.94818 | − | 7.08158i | 0.340426 | − | 0.817711i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.49547i | − | 0.170425i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.893115 | + | 1.06437i | 0.100483 | + | 0.119751i | 0.813943 | − | 0.580945i | \(-0.197317\pi\) |
−0.713459 | + | 0.700697i | \(0.752873\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.13878 | − | 8.43493i | 0.348753 | − | 0.937215i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.4856 | + | 6.05389i | 1.15095 | + | 0.664500i | 0.949118 | − | 0.314920i | \(-0.101978\pi\) |
0.201830 | + | 0.979421i | \(0.435311\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.896950 | + | 5.08686i | −0.0972879 | + | 0.551747i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.8150 | + | 1.79358i | −1.48113 | + | 0.192292i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.68075 | + | 3.92762i | 0.496159 | + | 0.416327i | 0.856227 | − | 0.516599i | \(-0.172802\pi\) |
−0.360069 | + | 0.932926i | \(0.617247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.345207 | + | 0.948448i | 0.0361875 | + | 0.0994243i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.15173 | − | 5.15137i | 0.119429 | − | 0.534172i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.03206 | + | 2.59329i | −0.208485 | + | 0.266066i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.54804 | − | 1.68358i | 0.969457 | − | 0.170941i | 0.333571 | − | 0.942725i | \(-0.391746\pi\) |
0.635885 | + | 0.771784i | \(0.280635\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.22799 | − | 2.60896i | 0.123418 | − | 0.262211i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0945 | − | 14.4137i | 1.20345 | − | 1.43422i | 0.332323 | − | 0.943166i | \(-0.392168\pi\) |
0.871130 | − | 0.491053i | \(-0.163388\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.92876 | + | 5.73237i | −0.978310 | + | 0.564828i | −0.901759 | − | 0.432238i | \(-0.857724\pi\) |
−0.0765505 | + | 0.997066i | \(0.524391\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.09749 | + | 1.71592i | −0.107104 | + | 0.167457i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.17826 | − | 2.04080i | 0.113906 | − | 0.197292i | −0.803436 | − | 0.595392i | \(-0.796997\pi\) |
0.917342 | + | 0.398100i | \(0.130330\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.21678 | + | 6.09056i | −0.212329 | + | 0.583370i | −0.999441 | − | 0.0334410i | \(-0.989353\pi\) |
0.787111 | + | 0.616811i | \(0.211576\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.82032 | + | 2.13700i | −0.647356 | + | 0.202835i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0387 | −0.944358 | −0.472179 | − | 0.881503i | \(-0.656532\pi\) | ||||
−0.472179 | + | 0.881503i | \(0.656532\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.885394 | 0.0825635 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.176570 | + | 1.93810i | −0.0163239 | + | 0.179177i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.63665 | + | 9.99161i | −0.333371 | + | 0.915929i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.03807 | + | 8.72620i | −0.458007 | + | 0.793291i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.80481 | + | 4.99192i | 0.703736 | + | 0.450106i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.17177 | + | 3.56327i | −0.552020 | + | 0.318709i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.95146 | + | 10.6679i | −0.794313 | + | 0.946626i | −0.999485 | − | 0.0321003i | \(-0.989780\pi\) |
0.205171 | + | 0.978726i | \(0.434225\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.614653 | − | 13.5213i | 0.0541172 | − | 1.19048i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.9610 | + | 1.93273i | −0.957671 | + | 0.168863i | −0.630575 | − | 0.776128i | \(-0.717181\pi\) |
−0.327096 | + | 0.944991i | \(0.606070\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.04643 | + | 4.53083i | −0.437581 | + | 0.392873i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.32367 | + | 2.09235i | −0.286056 | + | 0.180081i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.69757 | − | 4.66403i | −0.145033 | − | 0.398475i | 0.845812 | − | 0.533482i | \(-0.179117\pi\) |
−0.990845 | + | 0.135007i | \(0.956894\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.76202 | + | 2.31761i | 0.234272 | + | 0.196577i | 0.752364 | − | 0.658747i | \(-0.228913\pi\) |
−0.518093 | + | 0.855325i | \(0.673358\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.704229 | − | 5.42432i | −0.0593068 | − | 0.456810i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.108273 | + | 0.614047i | −0.00905425 | + | 0.0513492i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.26475 | + | 3.03961i | 0.437214 | + | 0.252426i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.36888 | − | 5.83805i | 0.442818 | − | 0.481514i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.3170 | + | 14.6788i | 1.00904 | + | 1.20253i | 0.979183 | + | 0.202978i | \(0.0650620\pi\) |
0.0298610 | + | 0.999554i | \(0.490494\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 19.2624i | − | 1.56755i | −0.621042 | − | 0.783777i | \(-0.713290\pi\) | ||
0.621042 | − | 0.783777i | \(-0.286710\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.5489 | + | 14.4449i | −1.17621 | + | 1.16780i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.76455 | + | 1.48063i | −0.141732 | + | 0.118927i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.200940 | − | 0.0731363i | −0.0160368 | − | 0.00583691i | 0.333989 | − | 0.942577i | \(-0.391605\pi\) |
−0.350026 | + | 0.936740i | \(0.613827\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.2554 | + | 19.9552i | 1.20983 | + | 1.58255i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.79490 | + | 0.316489i | 0.141458 | + | 0.0249428i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.51668 | − | 13.0193i | −0.588752 | − | 1.01975i | −0.994396 | − | 0.105717i | \(-0.966286\pi\) |
0.405645 | − | 0.914031i | \(-0.367047\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.11718 | + | 0.579020i | −0.0869720 | + | 0.0450767i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.87982 | − | 3.23199i | 0.687141 | − | 0.250099i | 0.0252305 | − | 0.999682i | \(-0.491968\pi\) |
0.661911 | + | 0.749583i | \(0.269746\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.18435 | + | 12.3881i | 0.168027 | + | 0.952929i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.5243 | + | 3.76054i | −0.957758 | + | 0.287575i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.33529 | + | 13.2441i | 0.177549 | + | 1.00693i | 0.935161 | + | 0.354224i | \(0.115255\pi\) |
−0.757612 | + | 0.652705i | \(0.773634\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.47502 | + | 2.35672i | −0.489466 | + | 0.178151i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.9056 | + | 9.28026i | −1.34586 | + | 0.697547i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.34644 | − | 14.4565i | −0.623842 | − | 1.08053i | −0.988764 | − | 0.149488i | \(-0.952237\pi\) |
0.364921 | − | 0.931038i | \(-0.381096\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0398 | − | 1.77029i | −0.746251 | − | 0.131584i | −0.212424 | − | 0.977178i | \(-0.568136\pi\) |
−0.533828 | + | 0.845593i | \(0.679247\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.3974 | − | 14.9087i | −0.842523 | − | 1.10209i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.93084 | + | 1.06674i | 0.215480 | + | 0.0784281i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.03184 | + | 4.22221i | −0.367964 | + | 0.308759i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.48576 | + | 3.05361i | −0.544509 | + | 0.222118i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0667i | 0.873115i | 0.899676 | + | 0.436558i | \(0.143802\pi\) | ||||
−0.899676 | + | 0.436558i | \(0.856198\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.14990 | − | 2.56215i | −0.154753 | − | 0.184427i | 0.683098 | − | 0.730327i | \(-0.260632\pi\) |
−0.837850 | + | 0.545900i | \(0.816188\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.574869 | − | 0.625104i | 0.0411672 | − | 0.0447647i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.15098 | + | 2.97392i | 0.366992 | + | 0.211883i | 0.672144 | − | 0.740421i | \(-0.265374\pi\) |
−0.305151 | + | 0.952304i | \(0.598707\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.94088 | + | 11.0073i | −0.137585 | + | 0.780286i | 0.835439 | + | 0.549583i | \(0.185214\pi\) |
−0.973024 | + | 0.230703i | \(0.925898\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.08099 | − | 16.0288i | −0.146782 | − | 1.13058i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.58634 | + | 8.04389i | 0.672829 | + | 0.564571i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.38276 | − | 3.79911i | −0.0965764 | − | 0.265342i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.87145 | + | 2.02600i | 0.199579 | + | 0.140817i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.09933 | + | 0.865240i | −0.283557 | + | 0.0598499i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.9377 | − | 3.69188i | 1.44141 | − | 0.254159i | 0.602364 | − | 0.798222i | \(-0.294226\pi\) |
0.839045 | + | 0.544063i | \(0.183115\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.00269607 | + | 0.0593087i | −0.000184731 | + | 0.00406376i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.79664 | + | 4.52466i | −0.258928 | + | 0.308579i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.10641 | + | 2.37084i | −0.278761 | + | 0.160943i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.79895 | + | 3.70898i | 0.391856 | + | 0.250629i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.21662 | − | 3.83930i | 0.149106 | − | 0.258259i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.71184 | + | 12.9457i | −0.315528 | + | 0.866907i | 0.675987 | + | 0.736914i | \(0.263718\pi\) |
−0.991515 | + | 0.129993i | \(0.958505\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.2313 | − | 1.20544i | −0.882090 | − | 0.0803625i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.1886 | −1.07448 | −0.537238 | − | 0.843430i | \(-0.680532\pi\) | ||||
−0.537238 | + | 0.843430i | \(0.680532\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.6462 | −1.69475 | −0.847374 | − | 0.530997i | \(-0.821817\pi\) | ||||
−0.847374 | + | 0.530997i | \(0.821817\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.47174 | + | 0.774466i | −0.162629 | + | 0.0509561i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.98107 | − | 10.9379i | 0.260808 | − | 0.716565i | −0.738305 | − | 0.674467i | \(-0.764374\pi\) |
0.999113 | − | 0.0420981i | \(-0.0134042\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.19347 | + | 2.06715i | −0.0778532 | + | 0.134846i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.29669 | − | 2.02737i | 0.0842293 | − | 0.131692i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.1831 | − | 7.61128i | 0.852746 | − | 0.492333i | −0.00883069 | − | 0.999961i | \(-0.502811\pi\) |
0.861576 | + | 0.507628i | \(0.169478\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.76016 | − | 11.6317i | 0.628707 | − | 0.749264i | −0.353834 | − | 0.935308i | \(-0.615122\pi\) |
0.982541 | + | 0.186044i | \(0.0595666\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5669 | − | 0.819603i | −0.998617 | − | 0.0525776i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.40855 | + | 0.601019i | −0.217764 | + | 0.0383977i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.40012 | − | 1.49501i | 0.152716 | − | 0.0951254i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.57573 | − | 20.4660i | 0.289975 | − | 1.29698i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.71032 | + | 10.1940i | 0.234193 | + | 0.643441i | 1.00000 | 0.000369965i | \(0.000117763\pi\) | |
−0.765807 | + | 0.643071i | \(0.777660\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.862512 | + | 0.723733i | 0.0542257 | + | 0.0455007i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.87216 | − | 1.15186i | 0.555596 | − | 0.0721320i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.00786014 | + | 0.0445771i | −0.000490302 | + | 0.00278064i | −0.985052 | − | 0.172258i | \(-0.944894\pi\) |
0.984562 | + | 0.175038i | \(0.0560049\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.56017 | + | 3.21017i | 0.345492 | + | 0.199470i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.1189 | + | 21.9049i | 0.626345 | + | 1.35588i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.52577 | + | 4.20185i | 0.217408 | + | 0.259097i | 0.863715 | − | 0.503981i | \(-0.168132\pi\) |
−0.646307 | + | 0.763078i | \(0.723687\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10.9612i | − | 0.673342i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.06760 | − | 9.77044i | 0.248933 | − | 0.597941i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.50432 | − | 1.26228i | 0.0917202 | − | 0.0769623i | −0.595775 | − | 0.803152i | \(-0.703155\pi\) |
0.687495 | + | 0.726189i | \(0.258710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.8494 | − | 7.22458i | −1.20576 | − | 0.438862i | −0.340531 | − | 0.940233i | \(-0.610607\pi\) |
−0.865232 | + | 0.501371i | \(0.832829\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.38884 | − | 1.06174i | 0.0840563 | − | 0.0642594i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.19208 | − | 0.739177i | −0.252792 | − | 0.0445741i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.91899 | − | 6.78789i | −0.235469 | − | 0.407845i | 0.723940 | − | 0.689863i | \(-0.242329\pi\) |
−0.959409 | + | 0.282018i | \(0.908996\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.11072 | + | 0.764161i | −0.545445 | + | 0.0457491i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0064 | + | 4.00600i | −0.656587 | + | 0.238978i | −0.648762 | − | 0.760991i | \(-0.724713\pi\) |
−0.00782495 | + | 0.999969i | \(0.502491\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.21905 | − | 6.91356i | −0.0724648 | − | 0.410968i | −0.999364 | − | 0.0356581i | \(-0.988647\pi\) |
0.926899 | − | 0.375310i | \(-0.122464\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.33859 | + | 2.01562i | 0.316231 | + | 0.119395i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.44517 | − | 8.19595i | −0.0853055 | − | 0.483791i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.9116 | − | 10.1590i | 1.64186 | − | 0.597587i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.72733 | − | 14.9093i | −0.452984 | − | 0.873998i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.29095 | − | 2.23599i | −0.0754180 | − | 0.130628i | 0.825850 | − | 0.563890i | \(-0.190696\pi\) |
−0.901268 | + | 0.433262i | \(0.857362\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.66705 | + | 1.52824i | 0.504615 | + | 0.0889773i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.94808 | − | 0.678535i | −0.287117 | − | 0.0393726i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.714078 | − | 0.259903i | −0.0412962 | − | 0.0150306i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.31401 | + | 7.81539i | −0.536851 | + | 0.450471i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −30.0867 | − | 12.5256i | −1.72844 | − | 0.719577i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.18923i | 0.468914i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.26629 | + | 1.50910i | 0.0722709 | + | 0.0861290i | 0.800968 | − | 0.598707i | \(-0.204318\pi\) |
−0.728698 | + | 0.684836i | \(0.759874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.6164 | + | 13.4418i | 0.831499 | + | 0.764677i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.4909 | − | 12.9851i | −1.27534 | − | 0.736320i | −0.299355 | − | 0.954142i | \(-0.596771\pi\) |
−0.975989 | + | 0.217822i | \(0.930105\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.32842 | + | 13.2051i | −0.131610 | + | 0.746398i | 0.845551 | + | 0.533895i | \(0.179272\pi\) |
−0.977161 | + | 0.212502i | \(0.931839\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.40446 | + | 0.925326i | 0.191820 | + | 0.0521362i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.3056 | − | 19.5557i | −1.30897 | − | 1.09836i | −0.988519 | − | 0.151095i | \(-0.951720\pi\) |
−0.320454 | − | 0.947264i | \(-0.603835\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.64407 | + | 7.26453i | 0.148040 | + | 0.406736i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.98326 | − | 0.890567i | −0.222324 | − | 0.0497066i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.4927 | + | 4.18776i | 1.64102 | + | 0.233013i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.82930 | − | 0.498882i | 0.156941 | − | 0.0276730i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.2146 | + | 0.509796i | 0.620169 | + | 0.0281918i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.15834 | + | 3.76397i | −0.174125 | + | 0.207514i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.22014 | − | 5.32325i | 0.506785 | − | 0.292592i | −0.224726 | − | 0.974422i | \(-0.572149\pi\) |
0.731511 | + | 0.681830i | \(0.238815\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.06413 | + | 10.1660i | 0.387112 | + | 0.557096i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.52668 | + | 6.10839i | −0.192683 | + | 0.333737i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.38138 | + | 6.54278i | −0.129722 | + | 0.356408i | −0.987501 | − | 0.157610i | \(-0.949621\pi\) |
0.857780 | + | 0.514018i | \(0.171843\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.19876 | + | 16.5921i | 0.282358 | + | 0.901158i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.92924 | −0.158627 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0159 | −0.972770 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.458523 | − | 1.46340i | −0.0246860 | − | 0.0787866i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.63081 | − | 26.4604i | 0.517009 | − | 1.42047i | −0.356790 | − | 0.934185i | \(-0.616129\pi\) |
0.873799 | − | 0.486287i | \(-0.161649\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.79155 | − | 16.9595i | 0.524130 | − | 0.907819i | −0.475476 | − | 0.879729i | \(-0.657724\pi\) |
0.999605 | − | 0.0280904i | \(-0.00894261\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.29477 | − | 0.711853i | 0.175862 | − | 0.0379959i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.55050 | + | 2.04988i | −0.188974 | + | 0.109104i | −0.591502 | − | 0.806303i | \(-0.701465\pi\) |
0.402528 | + | 0.915408i | \(0.368132\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0166533 | − | 0.0198466i | 0.000883864 | − | 0.00105335i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.3976 | + | 0.836324i | 0.973706 | + | 0.0442629i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.52450 | − | 0.974118i | 0.291572 | − | 0.0514120i | −0.0259490 | − | 0.999663i | \(-0.508261\pi\) |
0.317521 | + | 0.948251i | \(0.397150\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3395 | + | 11.2117i | 0.807340 | + | 0.590087i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.0319 | + | 3.80795i | 0.893943 | + | 0.199865i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.02739 | − | 2.82273i | −0.0537760 | − | 0.147748i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.28539 | + | 1.91767i | 0.119296 | + | 0.100101i | 0.700484 | − | 0.713668i | \(-0.252967\pi\) |
−0.581188 | + | 0.813769i | \(0.697412\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.20882 | − | 15.4851i | 0.219103 | − | 0.806123i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.91814 | − | 22.2209i | 0.203420 | − | 1.15365i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.2415 | − | 10.5317i | −0.944510 | − | 0.545313i | −0.0531391 | − | 0.998587i | \(-0.516923\pi\) |
−0.891371 | + | 0.453274i | \(0.850256\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.08564 | + | 8.35548i | 0.469180 | + | 0.431475i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.35381 | − | 3.99691i | −0.172730 | − | 0.205852i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.54057i | − | 0.490066i | −0.969515 | − | 0.245033i | \(-0.921201\pi\) | ||
0.969515 | − | 0.245033i | \(-0.0787988\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.2679 | + | 9.27048i | 1.14082 | + | 0.474941i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.96084 | + | 5.00173i | −0.304584 | + | 0.255577i | −0.782249 | − | 0.622965i | \(-0.785928\pi\) |
0.477665 | + | 0.878542i | \(0.341483\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.06216 | + | 0.386595i | 0.0541328 | + | 0.0197027i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −22.6665 | + | 5.98640i | −1.15220 | + | 0.304306i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.63724 | + | 1.69931i | 0.488627 | + | 0.0861582i | 0.412533 | − | 0.910942i | \(-0.364644\pi\) |
0.0760939 | + | 0.997101i | \(0.475755\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00269 | − | 6.93287i | −0.202425 | − | 0.350610i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.87089 | + | 17.1157i | 0.447477 | + | 0.863373i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.986853 | + | 0.359185i | −0.0496539 | + | 0.0180726i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.05329 | − | 11.6448i | −0.103052 | − | 0.584435i | −0.991981 | − | 0.126390i | \(-0.959661\pi\) |
0.888929 | − | 0.458045i | \(-0.151450\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.1020 | + | 5.99443i | 0.505735 | + | 0.300097i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.59086 | − | 20.3648i | −0.179319 | − | 1.01697i | −0.933039 | − | 0.359774i | \(-0.882854\pi\) |
0.753720 | − | 0.657195i | \(-0.228257\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.85776 | − | 0.676169i | 0.0925416 | − | 0.0336824i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.17952 | + | 4.40984i | 0.257372 | + | 0.219127i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.98313 | + | 3.43488i | 0.0982999 | + | 0.170260i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.39761 | + | 0.599090i | 0.168001 | + | 0.0296231i | 0.257016 | − | 0.966407i | \(-0.417261\pi\) |
−0.0890148 | + | 0.996030i | \(0.528372\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.82966 | + | 5.22115i | −0.336882 | + | 0.257540i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.0238 | + | 6.19617i | 0.837688 | + | 0.304893i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.01043 | + | 5.88245i | −0.344128 | + | 0.288758i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.40021 | − | 5.76535i | 0.117539 | − | 0.282331i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.3156i | 1.23675i | 0.785884 | + | 0.618374i | \(0.212208\pi\) | ||||
−0.785884 | + | 0.618374i | \(0.787792\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.4536 | + | 24.3756i | 0.996845 | + | 1.18799i | 0.982150 | + | 0.188102i | \(0.0602334\pi\) |
0.0146955 | + | 0.999892i | \(0.495322\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.60071 | + | 3.97307i | −0.418181 | + | 0.193178i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.2108 | + | 15.1328i | 1.27141 | + | 0.734049i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.92728 | + | 16.6014i | −0.141661 | + | 0.803400i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.07098 | − | 0.139043i | 0.0517074 | − | 0.00671308i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.2345 | + | 21.1742i | 1.21550 | + | 1.01993i | 0.999048 | + | 0.0436350i | \(0.0138938\pi\) |
0.216455 | + | 0.976293i | \(0.430551\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.46188 | − | 15.0064i | −0.262481 | − | 0.721161i | −0.998999 | − | 0.0447423i | \(-0.985753\pi\) |
0.736517 | − | 0.676419i | \(-0.236469\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.29744 | − | 10.2758i | 0.110154 | − | 0.492688i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.170932 | − | 5.10321i | −0.00817679 | − | 0.244120i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.5401 | − | 5.38505i | 1.45760 | − | 0.257014i | 0.612011 | − | 0.790849i | \(-0.290361\pi\) |
0.845589 | + | 0.533835i | \(0.179250\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.4296 | − | 5.85041i | −0.591887 | − | 0.278591i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.5287 | + | 14.9311i | −0.595257 | + | 0.709400i | −0.976607 | − | 0.215031i | \(-0.931015\pi\) |
0.381350 | + | 0.924431i | \(0.375459\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.99962 | + | 2.30918i | −0.189600 | + | 0.109466i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.8827 | − | 27.9594i | 0.845823 | − | 1.32244i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.61607 | − | 11.4594i | 0.312232 | − | 0.540801i | −0.666613 | − | 0.745404i | \(-0.732257\pi\) |
0.978845 | + | 0.204602i | \(0.0655901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.75842 | − | 4.83122i | 0.0828007 | − | 0.227493i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −31.8373 | + | 9.97551i | −1.49585 | + | 0.468690i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.762876 | −0.0357642 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.4038 | −0.720559 | −0.360279 | − | 0.932844i | \(-0.617319\pi\) | ||||
−0.360279 | + | 0.932844i | \(0.617319\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 31.4093 | + | 16.5661i | 1.46606 | + | 0.773238i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.65076 | + | 15.5253i | −0.263182 | + | 0.723087i | 0.735766 | + | 0.677236i | \(0.236822\pi\) |
−0.998948 | + | 0.0458511i | \(0.985400\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.69170 | − | 8.12625i | 0.218042 | − | 0.377659i | −0.736168 | − | 0.676799i | \(-0.763366\pi\) |
0.954209 | + | 0.299140i | \(0.0966998\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.36103 | + | 2.14970i | 0.155864 | + | 0.0996899i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.5458 | + | 10.7074i | −0.858196 | + | 0.495480i | −0.863408 | − | 0.504507i | \(-0.831674\pi\) |
0.00521153 | + | 0.999986i | \(0.498341\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.33287 | + | 11.1225i | −0.430952 | + | 0.513588i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0168192 | + | 0.369993i | −0.000774989 | + | 0.0170484i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.39703 | + | 1.30430i | −0.340116 | + | 0.0599716i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.2064 | + | 16.3855i | 0.468302 | + | 0.751820i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.0820 | − | 35.5486i | 1.14842 | − | 1.62766i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.4165 | − | 31.3665i | −0.521632 | − | 1.43317i | −0.868703 | − | 0.495333i | \(-0.835046\pi\) |
0.347071 | − | 0.937839i | \(-0.387176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.05061 | − | 1.72067i | −0.0934998 | − | 0.0784557i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.406432 | − | 3.13054i | −0.0184933 | − | 0.142444i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.27250 | + | 7.21673i | −0.0577815 | + | 0.327695i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.9750 | + | 16.7288i | 1.31298 | + | 0.758052i | 0.982589 | − | 0.185791i | \(-0.0594846\pi\) |
0.330395 | + | 0.943843i | \(0.392818\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.6258 | + | 19.1660i | −0.797066 | + | 0.866718i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.635055 | − | 0.756829i | −0.0286596 | − | 0.0341552i | 0.751524 | − | 0.659705i | \(-0.229319\pi\) |
−0.780184 | + | 0.625550i | \(0.784875\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 54.9658i | − | 2.47554i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.53557 | + | 1.54663i | 0.0690188 | + | 0.0695158i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.0408543 | − | 0.0342808i | 0.00183256 | − | 0.00153770i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.11402 | + | 1.49738i | 0.184169 | + | 0.0670319i | 0.432458 | − | 0.901654i | \(-0.357646\pi\) |
−0.248290 | + | 0.968686i | \(0.579868\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.94052 | − | 13.0030i | −0.444110 | − | 0.580930i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.7905 | − | 5.60552i | −1.41747 | − | 0.249938i | −0.588167 | − | 0.808740i | \(-0.700150\pi\) |
−0.829301 | + | 0.558802i | \(0.811261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.11080 | + | 12.3163i | 0.316426 | + | 0.548067i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.3440 | − | 10.0258i | 0.859097 | − | 0.445261i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.2608 | − | 7.73831i | 0.942370 | − | 0.342994i | 0.175268 | − | 0.984521i | \(-0.443921\pi\) |
0.767101 | + | 0.641526i | \(0.221698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.07375 | − | 6.08956i | −0.0475000 | − | 0.269386i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.7015 | + | 18.7529i | 0.560785 | + | 0.827962i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.50474 | − | 8.53380i | −0.0663067 | − | 0.376044i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.85234 | + | 1.03817i | −0.125446 | + | 0.0456585i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.6807 | − | 10.7186i | 0.907781 | − | 0.470493i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.86213 | + | 8.42145i | 0.213014 | + | 0.368950i | 0.952656 | − | 0.304049i | \(-0.0983388\pi\) |
−0.739643 | + | 0.673000i | \(0.765005\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.5671 | − | 5.91879i | −1.46779 | − | 0.258810i | −0.618101 | − | 0.786099i | \(-0.712098\pi\) |
−0.849686 | + | 0.527288i | \(0.823209\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.24847 | + | 9.48155i | 0.316349 | + | 0.413809i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.5709 | + | 7.12324i | 0.852523 | + | 0.310293i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.5678 | − | 13.9021i | 0.720341 | − | 0.604438i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.6114 | + | 24.7886i | 1.06804 | + | 1.07573i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.46992i | 0.150299i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.14489 | + | 1.36443i | 0.0494980 | + | 0.0589894i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.5715 | + | 21.2818i | −0.844572 | + | 0.918376i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.81174 | − | 2.20071i | −0.164183 | − | 0.0947911i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.180608 | − | 1.02428i | 0.00776495 | − | 0.0440372i | −0.980679 | − | 0.195623i | \(-0.937327\pi\) |
0.988444 | + | 0.151586i | \(0.0484381\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.27338 | + | 17.5107i | 0.0975603 | + | 0.751457i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.75277 | − | 3.14895i | −0.160751 | − | 0.134886i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.86889 | − | 24.3671i | −0.379207 | − | 1.04186i | −0.971686 | − | 0.236276i | \(-0.924073\pi\) |
0.592480 | − | 0.805586i | \(-0.298149\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.7390 | + | 26.5587i | −0.799760 | + | 1.13350i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.5032 | − | 30.9317i | 0.703060 | − | 1.31773i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.12897 | + | 0.375395i | −0.0905330 | + | 0.0159634i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.245319 | − | 5.39658i | 0.0104132 | − | 0.229072i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.42914 | + | 2.89494i | −0.102926 | + | 0.122662i | −0.815048 | − | 0.579393i | \(-0.803290\pi\) |
0.712122 | + | 0.702055i | \(0.247734\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.39021 | − | 2.53469i | 0.185686 | − | 0.107206i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.58440 | + | 6.13013i | 0.404654 | + | 0.258814i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.99208 | + | 10.3786i | −0.252536 | + | 0.437406i | −0.964223 | − | 0.265091i | \(-0.914598\pi\) |
0.711687 | + | 0.702496i | \(0.247931\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.59510 | − | 7.12998i | 0.109177 | − | 0.299960i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.92374 | + | 10.7912i | 0.374762 | + | 0.453188i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.2148 | 0.470147 | 0.235074 | − | 0.971978i | \(-0.424467\pi\) | ||||
0.235074 | + | 0.971978i | \(0.424467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.2525 | −0.680144 | −0.340072 | − | 0.940399i | \(-0.610452\pi\) | ||||
−0.340072 | + | 0.940399i | \(0.610452\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.9440 | − | 6.24902i | 0.833174 | − | 0.261057i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.77435 | − | 4.87499i | 0.0739956 | − | 0.203301i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.02000 | + | 6.96284i | −0.167355 | + | 0.289867i | −0.937489 | − | 0.348015i | \(-0.886856\pi\) |
0.770134 | + | 0.637882i | \(0.220189\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.12138 | + | 4.88025i | −0.129720 | + | 0.202816i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.3145 | + | 9.41916i | −0.676838 | + | 0.390772i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.95984 | − | 10.6779i | 0.371079 | − | 0.442234i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.33089 | − | 0.626428i | −0.0550257 | − | 0.0258996i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.5628 | − | 3.44945i | 0.807444 | − | 0.142374i | 0.245336 | − | 0.969438i | \(-0.421102\pi\) |
0.562108 | + | 0.827064i | \(0.309991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.87470 | + | 9.88463i | 0.365676 | + | 0.407289i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.24779 | − | 10.0537i | 0.0924617 | − | 0.413556i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.64203 | − | 20.9963i | −0.313821 | − | 0.862215i | −0.991876 | − | 0.127205i | \(-0.959399\pi\) |
0.678056 | − | 0.735010i | \(-0.262823\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.15644 | − | 5.16587i | −0.252390 | − | 0.211780i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.1982 | − | 2.49246i | 0.785729 | − | 0.102010i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.89198 | + | 16.4012i | −0.118163 | + | 0.670136i | 0.866972 | + | 0.498356i | \(0.166063\pi\) |
−0.985135 | + | 0.171780i | \(0.945048\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.9204 | + | 10.3464i | 0.730990 | + | 0.422037i | 0.818784 | − | 0.574101i | \(-0.194648\pi\) |
−0.0877940 | + | 0.996139i | \(0.527982\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.4150 | + | 11.7404i | −1.03498 | + | 0.478106i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.89540 | − | 5.83411i | −0.199026 | − | 0.237191i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 39.3916i | − | 1.59886i | −0.600761 | − | 0.799428i | \(-0.705136\pi\) | ||
0.600761 | − | 0.799428i | \(-0.294864\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.33058 | − | 20.0102i | 0.337572 | − | 0.810854i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.56934 | − | 1.31683i | 0.0634888 | − | 0.0532734i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.4005 | − | 9.60900i | −1.06631 | − | 0.388104i | −0.251512 | − | 0.967854i | \(-0.580928\pi\) |
−0.814794 | + | 0.579750i | \(0.803150\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.56314 | + | 4.25292i | −0.224328 | + | 0.171494i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.3648 | + | 3.59086i | 0.819854 | + | 0.144562i | 0.567817 | − | 0.823155i | \(-0.307788\pi\) |
0.252038 | + | 0.967717i | \(0.418899\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.8830 | − | 29.2423i | −0.678586 | − | 1.17535i | −0.975407 | − | 0.220412i | \(-0.929260\pi\) |
0.296821 | − | 0.954933i | \(-0.404074\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.86156 | − | 5.79519i | 0.0747019 | − | 0.232553i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.93358 | + | 3.25156i | −0.357916 | + | 0.130271i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.90984 | + | 16.5025i | 0.116394 | + | 0.660101i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.55302 | + | 6.32736i | 0.141894 | + | 0.252690i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.89690 | − | 27.7717i | −0.195252 | − | 1.10733i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.0060 | − | 12.7411i | 1.39357 | − | 0.507217i | 0.467304 | − | 0.884096i | \(-0.345225\pi\) |
0.926262 | + | 0.376880i | \(0.123003\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.9451 | − | 32.6942i | −0.673506 | − | 1.29948i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.26287 | − | 9.11556i | −0.208851 | − | 0.361740i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.92545 | + | 0.515836i | 0.115911 | + | 0.0204382i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.0994226 | − | 0.0262583i | 0.00393310 | − | 0.00103876i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.37099 | − | 2.68282i | −0.291137 | − | 0.105965i | 0.192323 | − | 0.981332i | \(-0.438398\pi\) |
−0.483460 | + | 0.875367i | \(0.660620\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.9819 | + | 25.1578i | −1.18237 | + | 0.992126i | −0.182410 | + | 0.983223i | \(0.558390\pi\) |
−0.999960 | + | 0.00890393i | \(0.997166\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.44461 | + | 3.93195i | 0.371881 | + | 0.154820i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 6.21339i | − | 0.244274i | −0.992513 | − | 0.122137i | \(-0.961025\pi\) | ||
0.992513 | − | 0.122137i | \(-0.0389747\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.19386 | + | 8.57331i | 0.282384 | + | 0.336532i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.04516 | + | 5.55935i | 0.236929 | + | 0.217888i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.3831 | − | 13.5002i | −0.915050 | − | 0.528304i | −0.0329976 | − | 0.999455i | \(-0.510505\pi\) |
−0.882053 | + | 0.471151i | \(0.843839\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.46082 | − | 8.28473i | 0.0570790 | − | 0.323711i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.12714 | − | 11.5054i | 0.122001 | − | 0.448868i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.3482 | − | 19.5915i | −0.909517 | − | 0.763176i | 0.0625097 | − | 0.998044i | \(-0.480090\pi\) |
−0.972027 | + | 0.234869i | \(0.924534\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.2133 | − | 30.8082i | −0.436146 | − | 1.19830i | −0.941980 | − | 0.335670i | \(-0.891037\pi\) |
0.505834 | − | 0.862631i | \(-0.331185\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.49360 | − | 1.67540i | −0.291027 | − | 0.0650671i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.91347 | − | 4.75550i | −0.0742013 | − | 0.184410i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.27861 | + | 1.63607i | −0.359269 | + | 0.0633489i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.8370 | + | 1.08359i | 0.921591 | + | 0.0418939i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.69399 | + | 7.97759i | −0.258419 | + | 0.307971i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.7750 | − | 15.4586i | 1.03210 | − | 0.595884i | 0.114516 | − | 0.993421i | \(-0.463468\pi\) |
0.917586 | + | 0.397537i | \(0.130135\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.85980 | + | 22.4933i | 0.187054 | + | 0.865766i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.6720 | + | 34.0729i | −0.756057 | + | 1.30953i | 0.188791 | + | 0.982017i | \(0.439543\pi\) |
−0.944847 | + | 0.327511i | \(0.893790\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.15932 | + | 14.1751i | −0.197996 | + | 0.543991i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.38366 | + | 26.7568i | 0.321263 | + | 1.02532i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0176 | −0.459840 | −0.229920 | − | 0.973210i | \(-0.573846\pi\) | ||||
−0.229920 | + | 0.973210i | \(0.573846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.75147 | 0.143336 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.2815 | + | 42.3885i | 0.506720 | + | 1.61722i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.21761 | + | 8.84031i | −0.122581 | + | 0.336789i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5214 | − | 30.3479i | 0.666544 | − | 1.15449i | −0.312320 | − | 0.949977i | \(-0.601106\pi\) |
0.978864 | − | 0.204512i | \(-0.0655606\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.56010 | + | 3.68427i | 0.0972503 | + | 0.139954i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.36010 | + | 1.36260i | −0.0895237 | + | 0.0516865i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.4968 | + | 28.0024i | −0.890006 | + | 1.06067i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.1400 | − | 0.915530i | −0.761766 | − | 0.0346285i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.95841 | + | 0.521647i | −0.111738 | + | 0.0197023i | −0.229237 | − | 0.973371i | \(-0.573623\pi\) |
0.117500 | + | 0.993073i | \(0.462512\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.58262 | − | 17.0986i | 0.210552 | − | 0.644887i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.03468 | + | 0.902063i | 0.151955 | + | 0.0339737i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0127 | + | 27.5097i | 0.376567 | + | 1.03461i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.36012 | + | 1.98037i | 0.0886360 | + | 0.0743744i | 0.686029 | − | 0.727574i | \(-0.259352\pi\) |
−0.597393 | + | 0.801949i | \(0.703797\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.02239 | − | 1.09328i | −0.150852 | − | 0.0410011i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.619918 | − | 3.51573i | 0.0232161 | − | 0.131665i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.408138 | − | 0.235639i | −0.0152635 | − | 0.00881239i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.4073 | − | 17.8476i | −0.724777 | − | 0.666532i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.13781 | − | 8.50651i | −0.266195 | − | 0.317239i | 0.616345 | − | 0.787476i | \(-0.288613\pi\) |
−0.882540 | + | 0.470237i | \(0.844168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 17.8378i | − | 0.664316i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.2796 | − | 10.1080i | −0.902969 | − | 0.375921i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 27.2868 | − | 22.8964i | 1.01341 | − | 0.850349i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.8709 | − | 5.04860i | −0.514444 | − | 0.187242i | 0.0717355 | − | 0.997424i | \(-0.477146\pi\) |
−0.586179 | + | 0.810182i | \(0.699368\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.70703 | + | 26.1537i | 0.248409 | + | 0.968655i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 52.5931 | + | 9.27357i | 1.94522 | + | 0.342996i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.1447 | − | 31.4276i | −0.670191 | − | 1.16080i | −0.977850 | − | 0.209308i | \(-0.932879\pi\) |
0.307659 | − | 0.951497i | \(-0.400454\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.75857 | + | 5.32245i | 0.101751 | + | 0.196322i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.42862 | + | 3.06777i | −0.310472 | + | 0.113003i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.94942 | + | 16.7270i | 0.108496 | + | 0.615312i | 0.989766 | + | 0.142699i | \(0.0455780\pi\) |
−0.881270 | + | 0.472613i | \(0.843311\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.71394 | − | 3.19273i | −0.136435 | − | 0.117288i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.59818 | + | 26.0776i | 0.168691 | + | 0.956693i | 0.945177 | + | 0.326559i | \(0.105889\pi\) |
−0.776486 | + | 0.630134i | \(0.783000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.6097 | + | 4.95352i | −0.498620 | + | 0.181483i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −36.1962 | + | 3.03595i | −1.32435 | + | 0.111080i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.83324 | + | 3.17526i | 0.0669850 | + | 0.116021i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.8929 | − | 8.26849i | −1.71115 | − | 0.301722i | −0.769581 | − | 0.638549i | \(-0.779535\pi\) |
−0.941566 | + | 0.336827i | \(0.890646\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.9274 | − | 11.4117i | 0.543984 | − | 0.415866i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.6812 | + | 4.97954i | 0.497909 | + | 0.181224i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.6519 | + | 10.6162i | −0.459843 | + | 0.385854i | −0.843073 | − | 0.537799i | \(-0.819256\pi\) |
0.383230 | + | 0.923653i | \(0.374812\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.749527 | − | 1.80038i | 0.0272061 | − | 0.0653496i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 19.1974i | − | 0.695906i | −0.937512 | − | 0.347953i | \(-0.886877\pi\) | ||
0.937512 | − | 0.347953i | \(-0.113123\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.48211 | − | 7.72508i | −0.234668 | − | 0.279667i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.49847 | − | 14.0675i | −0.234953 | − | 0.508613i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.54145 | − | 3.77671i | −0.236198 | − | 0.136369i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.25863 | + | 29.8231i | −0.189631 | + | 1.07545i | 0.730229 | + | 0.683203i | \(0.239413\pi\) |
−0.919860 | + | 0.392248i | \(0.871698\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.0777483 | − | 0.0100939i | 0.00280004 | − | 0.000363524i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.9958 | + | 18.4567i | 0.791134 | + | 0.663840i | 0.946026 | − | 0.324091i | \(-0.105058\pi\) |
−0.154892 | + | 0.987931i | \(0.549503\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.61619 | + | 12.6829i | 0.165818 | + | 0.455582i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.42635 | − | 10.8524i | 0.0870449 | − | 0.389328i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.6303 | + | 8.70339i | −0.774985 | + | 0.311831i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0324458 | − | 0.00572106i | 0.00116100 | − | 0.000204716i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.9645 | − | 28.0687i | 1.10658 | − | 1.00309i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.103890 | − | 0.123812i | 0.00370800 | − | 0.00441903i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.1812 | + | 12.8063i | −0.790673 | + | 0.456495i | −0.840200 | − | 0.542277i | \(-0.817562\pi\) |
0.0495262 | + | 0.998773i | \(0.484229\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.11899 | − | 8.00348i | 0.182241 | − | 0.284932i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.80951 | − | 13.5265i | 0.277674 | − | 0.480946i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.40391 | − | 6.60469i | 0.0853653 | − | 0.234539i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.1169 | + | 5.67652i | −0.642540 | + | 0.201326i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.4074 | −1.14793 | −0.573965 | − | 0.818880i | \(-0.694595\pi\) | ||||
−0.573965 | + | 0.818880i | \(0.694595\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.5817 | 0.763506 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.2553 | − | 1.66314i | −0.645018 | − | 0.0587642i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.30650 | − | 3.58957i | 0.0461053 | − | 0.126673i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.688786 | + | 1.19301i | −0.0242765 | + | 0.0420482i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.86536 | − | 1.83267i | −0.100866 | − | 0.0645131i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.3938 | + | 17.5479i | −1.06859 | + | 0.616950i | −0.927796 | − | 0.373089i | \(-0.878299\pi\) |
−0.140793 | + | 0.990039i | \(0.544965\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.0733 | + | 16.7719i | −0.494181 | + | 0.588942i | −0.954276 | − | 0.298928i | \(-0.903371\pi\) |
0.460095 | + | 0.887870i | \(0.347815\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.66144 | + | 36.5488i | −0.0582694 | + | 1.28182i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.1901 | − | 1.97312i | 0.391972 | − | 0.0691152i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.8121 | + | 21.0094i | 0.938035 | + | 0.735027i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.47411 | − | 1.74565i | −0.0864522 | − | 0.0609979i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.83332 | + | 13.2794i | 0.168684 | + | 0.463455i | 0.995015 | − | 0.0997301i | \(-0.0317979\pi\) |
−0.826331 | + | 0.563185i | \(0.809576\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.4669 | − | 9.62189i | −0.399712 | − | 0.335398i | 0.420670 | − | 0.907214i | \(-0.361795\pi\) |
−0.820382 | + | 0.571815i | \(0.806239\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.949245 | + | 7.31155i | 0.0330485 | + | 0.254556i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.63051 | + | 20.5896i | −0.126245 | + | 0.715972i | 0.854315 | + | 0.519755i | \(0.173977\pi\) |
−0.980561 | + | 0.196217i | \(0.937134\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.1611 | − | 7.02120i | −0.422371 | − | 0.243856i | 0.273720 | − | 0.961809i | \(-0.411746\pi\) |
−0.696091 | + | 0.717953i | \(0.745079\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.18960 | + | 9.99265i | −0.318784 | + | 0.346641i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.1155 | + | 23.9727i | 0.696960 | + | 0.830605i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.14241i | 0.247173i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.98122 | + | 14.6626i | 0.206741 | + | 0.506815i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.8654 | − | 35.9683i | 1.47988 | − | 1.24176i | 0.573563 | − | 0.819162i | \(-0.305561\pi\) |
0.906315 | − | 0.422603i | \(-0.138884\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −33.5383 | − | 12.2070i | −1.15649 | − | 0.420929i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.3211 | + | 16.1170i | 0.424362 | + | 0.555098i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.36332 | − | 1.65101i | −0.322108 | − | 0.0567964i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.83867 | − | 13.5770i | −0.269340 | − | 0.466510i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.7955 | + | 5.59521i | −0.370502 | + | 0.192027i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.54230 | + | 1.65326i | −0.155708 | + | 0.0566731i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.55129 | − | 42.8255i | −0.258551 | − | 1.46632i | −0.786790 | − | 0.617221i | \(-0.788259\pi\) |
0.528239 | − | 0.849096i | \(-0.322853\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.566737 | − | 9.86755i | 0.0193820 | − | 0.337463i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.77792 | + | 49.7820i | 0.299848 | + | 1.70052i | 0.646817 | + | 0.762645i | \(0.276100\pi\) |
−0.346969 | + | 0.937877i | \(0.612789\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.3783 | + | 8.50899i | −0.797656 | + | 0.290323i | −0.708515 | − | 0.705696i | \(-0.750634\pi\) |
−0.0891412 | + | 0.996019i | \(0.528412\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.7980 | + | 6.63306i | −0.436154 | + | 0.226054i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.9638 | + | 29.3822i | 0.577455 | + | 1.00018i | 0.995770 | + | 0.0918798i | \(0.0292876\pi\) |
−0.418315 | + | 0.908302i | \(0.637379\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0103 | − | 1.76509i | −0.340362 | − | 0.0600149i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −31.2456 | − | 40.8717i | −1.06116 | − | 1.38807i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.25495 | − | 0.456765i | −0.0425713 | − | 0.0154947i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.63739 | − | 3.89123i | 0.157132 | − | 0.131849i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.6406 | + | 20.4930i | −0.698577 | + | 0.693583i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 11.0881i | − | 0.374846i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.1891 | + | 22.8687i | 0.647971 | + | 0.772222i | 0.985607 | − | 0.169055i | \(-0.0540717\pi\) |
−0.337636 | + | 0.941277i | \(0.609627\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.02713 | + | 3.29166i | −0.102103 | + | 0.111025i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.59448 | − | 5.53938i | −0.323246 | − | 0.186626i | 0.329592 | − | 0.944123i | \(-0.393089\pi\) |
−0.652839 | + | 0.757497i | \(0.726422\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.62988 | + | 54.6138i | −0.324071 | + | 1.83790i | 0.192051 | + | 0.981385i | \(0.438486\pi\) |
−0.516122 | + | 0.856515i | \(0.672625\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.96255 | − | 15.1165i | −0.0659703 | − | 0.508135i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.9548 | − | 16.7441i | −0.670017 | − | 0.562211i | 0.243054 | − | 0.970013i | \(-0.421851\pi\) |
−0.913070 | + | 0.407802i | \(0.866295\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.41064 | − | 20.3606i | −0.248545 | − | 0.682871i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.44099 | + | 8.52968i | 0.0482749 | + | 0.285755i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.1450 | + | 6.47980i | 0.406416 | + | 0.216838i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.4254 | − | 2.19093i | 0.415334 | − | 0.0732346i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0597702 | + | 1.31484i | −0.00199567 | + | 0.0439012i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.7559 | − | 18.7771i | 0.525488 | − | 0.626252i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −85.8291 | + | 49.5535i | −2.85938 | + | 1.65086i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.7409 | + | 11.3470i | 0.590380 | + | 0.377604i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.85274 | − | 6.67314i | 0.128069 | − | 0.221823i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.92780 | + | 16.2865i | −0.196830 | + | 0.540785i | −0.998365 | − | 0.0571627i | \(-0.981795\pi\) |
0.801535 | + | 0.597947i | \(0.204017\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.12141 | + | 56.2145i | −0.169866 | + | 1.86452i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.0957 | −1.16277 | −0.581386 | − | 0.813628i | \(-0.697489\pi\) | ||||
−0.581386 | + | 0.813628i | \(0.697489\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.6376 | −0.385150 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.5353 | − | 4.24099i | 0.447463 | − | 0.140203i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.92284 | − | 16.2729i | 0.195589 | − | 0.537377i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.0221 | − | 26.0190i | 0.495533 | − | 0.858288i | −0.504454 | − | 0.863439i | \(-0.668306\pi\) |
0.999987 | + | 0.00515052i | \(0.00163947\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.83849 | − | 2.87447i | 0.0605805 | − | 0.0947169i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.0192569 | + | 0.0111180i | −0.000633848 | + | 0.000365952i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.7469 | − | 13.9995i | 0.386237 | − | 0.460300i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.6474 | − | 31.1194i | 0.481083 | − | 1.02210i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.1458 | − | 5.66817i | 1.05467 | − | 0.185967i | 0.380680 | − | 0.924707i | \(-0.375690\pi\) |
0.673990 | + | 0.738740i | \(0.264579\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.12218 | + | 19.5301i | 0.135099 | + | 0.640072i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.81461 | + | 43.8981i | −0.321316 | + | 1.43716i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.69805 | − | 4.66536i | −0.0555322 | − | 0.152573i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.8914 | − | 20.8863i | −0.813165 | − | 0.682327i | 0.138196 | − | 0.990405i | \(-0.455870\pi\) |
−0.951361 | + | 0.308078i | \(0.900314\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.0315 | − | 2.99013i | 0.751604 | − | 0.0975794i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.50659 | − | 14.2156i | 0.0817126 | − | 0.463415i | −0.916305 | − | 0.400481i | \(-0.868843\pi\) |
0.998018 | − | 0.0629344i | \(-0.0200459\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.42639 | + | 3.13293i | 0.176708 | + | 0.102022i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.233687 | − | 6.10616i | −0.00760185 | − | 0.198633i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.2988 | + | 33.7252i | 0.919588 | + | 1.09592i | 0.995109 | + | 0.0987786i | \(0.0314936\pi\) |
−0.0755210 | + | 0.997144i | \(0.524062\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.57814i | 0.0836899i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.2527 | + | 48.6473i | −0.656738 | + | 1.57750i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.8037 | − | 13.2609i | 0.511932 | − | 0.429562i | −0.349877 | − | 0.936796i | \(-0.613777\pi\) |
0.861808 | + | 0.507234i | \(0.169332\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.57039 | − | 3.11937i | −0.277331 | − | 0.100940i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.6377 | − | 8.13228i | 0.343866 | − | 0.262879i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.60509 | + | 1.34098i | 0.245581 | + | 0.0433026i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.8562 | − | 18.8034i | −0.350199 | − | 0.606562i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.590883 | + | 7.04481i | 0.0190409 | + | 0.227016i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.37554 | − | 0.864625i | 0.0764713 | − | 0.0278333i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.05922 | + | 40.0348i | 0.227009 | + | 1.28743i | 0.858807 | + | 0.512300i | \(0.171206\pi\) |
−0.631798 | + | 0.775133i | \(0.717683\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.35187 | − | 50.9147i | −0.268301 | − | 1.63562i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.764165 | − | 4.33380i | −0.0245232 | − | 0.139078i | 0.970088 | − | 0.242754i | \(-0.0780507\pi\) |
−0.994611 | + | 0.103676i | \(0.966940\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.27154 | + | 1.91868i | −0.168998 | + | 0.0615101i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.28978 | − | 4.41796i | −0.0733317 | − | 0.141488i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.538610 | + | 0.932899i | 0.0172317 | + | 0.0298461i | 0.874513 | − | 0.485003i | \(-0.161181\pi\) |
−0.857281 | + | 0.514849i | \(0.827848\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.78381 | − | 1.01984i | −0.184851 | − | 0.0325943i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.96515 | − | 18.7997i | −0.158525 | − | 0.600228i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.78675 | − | 1.74223i | −0.152674 | − | 0.0555687i | 0.264553 | − | 0.964371i | \(-0.414776\pi\) |
−0.417227 | + | 0.908803i | \(0.636998\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.44381 | + | 2.88970i | −0.109729 | + | 0.0920736i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.85678 | + | 3.27091i | 0.250084 | + | 0.104114i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 9.15410i | − | 0.291083i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.72397 | + | 9.20507i | 0.245360 | + | 0.292409i | 0.874643 | − | 0.484768i | \(-0.161096\pi\) |
−0.629283 | + | 0.777176i | \(0.716651\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.5732 | − | 12.4824i | −0.430734 | − | 0.396118i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.31621 | − | 4.22401i | −0.231939 | − | 0.133910i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.23994 | + | 35.3885i | −0.197621 | + | 1.12076i | 0.711016 | + | 0.703176i | \(0.248235\pi\) |
−0.908637 | + | 0.417588i | \(0.862876\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.1443 | − | 16.9404i | 0.415867 | − | 0.535972i |
(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 | 912.2.cc.c.257.2 | 18 | ||
3.2 | odd | 2 | 912.2.cc.d.257.1 | 18 | |||
4.3 | odd | 2 | 114.2.l.b.29.2 | yes | 18 | ||
12.11 | even | 2 | 114.2.l.a.29.3 | ✓ | 18 | ||
19.2 | odd | 18 | 912.2.cc.d.401.1 | 18 | |||
57.2 | even | 18 | inner | 912.2.cc.c.401.2 | 18 | ||
76.59 | even | 18 | 114.2.l.a.59.3 | yes | 18 | ||
228.59 | odd | 18 | 114.2.l.b.59.2 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.l.a.29.3 | ✓ | 18 | 12.11 | even | 2 | ||
114.2.l.a.59.3 | yes | 18 | 76.59 | even | 18 | ||
114.2.l.b.29.2 | yes | 18 | 4.3 | odd | 2 | ||
114.2.l.b.59.2 | yes | 18 | 228.59 | odd | 18 | ||
912.2.cc.c.257.2 | 18 | 1.1 | even | 1 | trivial | ||
912.2.cc.c.401.2 | 18 | 57.2 | even | 18 | inner | ||
912.2.cc.d.257.1 | 18 | 3.2 | odd | 2 | |||
912.2.cc.d.401.1 | 18 | 19.2 | odd | 18 |