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: | \( x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + 162 x^{7} + 270 x^{6} + 2916 x^{5} - 4374 x^{4} - 729 x^{3} + 19683 \) |
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 | 401.1 | ||
Root | \(0.0786547 + 1.73026i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.401 |
Dual form | 912.2.cc.d.257.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.53778 | + | 0.797015i | −0.887838 | + | 0.460157i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.258510 | + | 0.710252i | 0.115609 | + | 0.317634i | 0.983979 | − | 0.178283i | \(-0.0570542\pi\) |
−0.868370 | + | 0.495917i | \(0.834832\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.777943 | − | 1.34744i | −0.294035 | − | 0.509283i | 0.680725 | − | 0.732539i | \(-0.261665\pi\) |
−0.974760 | + | 0.223256i | \(0.928331\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.72953 | − | 2.45127i | 0.576511 | − | 0.817089i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.832399 | + | 0.480586i | 0.250978 | + | 0.144902i | 0.620212 | − | 0.784434i | \(-0.287047\pi\) |
−0.369234 | + | 0.929336i | \(0.620380\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.416982 | + | 0.496940i | 0.115650 | + | 0.137826i | 0.820763 | − | 0.571268i | \(-0.193548\pi\) |
−0.705113 | + | 0.709095i | \(0.749104\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.963613 | − | 0.886174i | −0.248804 | − | 0.228809i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.73013 | − | 1.18670i | −1.63230 | − | 0.287818i | −0.718968 | − | 0.695043i | \(-0.755385\pi\) |
−0.913328 | + | 0.407226i | \(0.866496\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.14364 | − | 1.35288i | 0.950615 | − | 0.310371i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.27023 | + | 1.45203i | 0.495405 | + | 0.316859i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.400647 | − | 1.10077i | 0.0835407 | − | 0.229526i | −0.890888 | − | 0.454223i | \(-0.849917\pi\) |
0.974429 | + | 0.224697i | \(0.0721392\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.39259 | − | 2.84672i | 0.678519 | − | 0.569345i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.705946 | + | 5.14797i | −0.135859 | + | 0.990728i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.39666 | − | 7.92086i | −0.259354 | − | 1.47087i | −0.784645 | − | 0.619945i | \(-0.787155\pi\) |
0.525292 | − | 0.850922i | \(-0.323956\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.63927 | − | 1.52379i | 0.474028 | − | 0.273680i | −0.243897 | − | 0.969801i | \(-0.578426\pi\) |
0.717924 | + | 0.696121i | \(0.245092\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.66308 | − | 0.0756007i | −0.289505 | − | 0.0131604i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.755913 | − | 0.900862i | 0.127773 | − | 0.152273i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.12648i | 0.678389i | 0.940716 | + | 0.339195i | \(0.110154\pi\) | ||||
−0.940716 | + | 0.339195i | \(0.889846\pi\) | |||||||
\(38\) | 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 | \(-0.140620\pi\) |
−0.264067 | + | 0.964504i | \(0.585064\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.34330 | − | 2.67274i | 1.11984 | − | 0.407589i | 0.285248 | − | 0.958454i | \(-0.407924\pi\) |
0.834595 | + | 0.550865i | \(0.185702\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.18812 | + | 0.594726i | 0.326186 | + | 0.0886566i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.11004 | + | 0.548383i | −0.453646 | + | 0.0799899i | −0.395802 | − | 0.918336i | \(-0.629533\pi\) |
−0.0578432 | + | 0.998326i | \(0.518422\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.28961 | − | 3.96572i | 0.327087 | − | 0.566531i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.2953 | − | 3.53912i | 1.58165 | − | 0.495576i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.6276 | + | 4.96002i | 1.87189 | + | 0.681312i | 0.966462 | + | 0.256809i | \(0.0826711\pi\) |
0.905427 | + | 0.424503i | \(0.139551\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.126153 | + | 0.715449i | −0.0170105 | + | 0.0964711i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.29374 | + | 5.38297i | −0.701173 | + | 0.712991i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.02192 | − | 11.4669i | 0.263231 | − | 1.49286i | −0.510793 | − | 0.859704i | \(-0.670648\pi\) |
0.774024 | − | 0.633156i | \(-0.218241\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1813 | + | 3.70568i | 1.30358 | + | 0.474464i | 0.898161 | − | 0.439667i | \(-0.144903\pi\) |
0.405419 | + | 0.914131i | \(0.367126\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.64841 | − | 0.423492i | −0.585644 | − | 0.0533549i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.245158 | + | 0.424626i | −0.0304081 | + | 0.0526684i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.19012 | − | 1.62047i | 1.12275 | − | 0.197972i | 0.418703 | − | 0.908123i | \(-0.362485\pi\) |
0.704049 | + | 0.710151i | \(0.251374\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.261222 | + | 2.01206i | 0.0314475 | + | 0.242224i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0322101 | − | 0.0117235i | 0.00382263 | − | 0.00139132i | −0.340108 | − | 0.940386i | \(-0.610464\pi\) |
0.343931 | + | 0.938995i | \(0.388241\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.04446 | − | 2.55461i | −0.356327 | − | 0.298994i | 0.446998 | − | 0.894535i | \(-0.352493\pi\) |
−0.803325 | + | 0.595541i | \(0.796938\pi\) | |||||||
\(74\) | 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 | −0.713459 | − | 0.700697i | \(-0.752873\pi\) |
0.813943 | + | 0.580945i | \(0.197317\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.01742 | − | 8.47910i | −0.335269 | − | 0.942122i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.4856 | + | 6.05389i | −1.15095 | + | 0.664500i | −0.949118 | − | 0.314920i | \(-0.898022\pi\) |
−0.201830 | + | 0.979421i | \(0.564689\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.896950 | − | 5.08686i | −0.0972879 | − | 0.551747i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.46081 | + | 11.0674i | 0.907094 | + | 1.18655i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.68075 | + | 3.92762i | −0.496159 | + | 0.416327i | −0.856227 | − | 0.516599i | \(-0.827198\pi\) |
0.360069 | + | 0.932926i | \(0.382753\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.345207 | − | 0.948448i | 0.0361875 | − | 0.0994243i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.84414 | + | 4.44679i | −0.294924 | + | 0.461110i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.03206 | + | 2.59329i | 0.208485 | + | 0.266066i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.54804 | + | 1.68358i | 0.969457 | + | 0.170941i | 0.635885 | − | 0.771784i | \(-0.280635\pi\) |
0.333571 | + | 0.942725i | \(0.391746\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.61771 | − | 1.20924i | 0.263089 | − | 0.121533i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0945 | − | 14.4137i | −1.20345 | − | 1.43422i | −0.871130 | − | 0.491053i | \(-0.836612\pi\) |
−0.332323 | − | 0.943166i | \(-0.607832\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.92876 | − | 5.73237i | −0.978310 | − | 0.564828i | −0.0765505 | − | 0.997066i | \(-0.524391\pi\) |
−0.901759 | + | 0.432238i | \(0.857724\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.444427 | + | 1.98780i | −0.0433716 | + | 0.193990i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.17826 | − | 2.04080i | −0.113906 | − | 0.197292i | 0.803436 | − | 0.595392i | \(-0.203003\pi\) |
−0.917342 | + | 0.398100i | \(0.869670\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.21678 | − | 6.09056i | −0.212329 | − | 0.583370i | 0.787111 | − | 0.616811i | \(-0.211576\pi\) |
−0.999441 | + | 0.0334410i | \(0.989353\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.28887 | − | 6.34562i | −0.312165 | − | 0.602299i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0387 | 0.944358 | 0.472179 | − | 0.881503i | \(-0.343468\pi\) | ||||
0.472179 | + | 0.881503i | \(0.343468\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.885394 | 0.0825635 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.93932 | − | 0.162660i | 0.179290 | − | 0.0150379i | ||||
\(118\) | 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 | ||||||||
\(123\) | −9.04146 | − | 2.02147i | −0.815241 | − | 0.182269i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.17177 | + | 3.56327i | 0.552020 | + | 0.318709i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.95146 | − | 10.6679i | −0.794313 | − | 0.946626i | 0.205171 | − | 0.978726i | \(-0.434225\pi\) |
−0.999485 | + | 0.0321003i | \(0.989780\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.16216 | + | 9.96280i | −0.806683 | + | 0.877176i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.9610 | + | 1.93273i | 0.957671 | + | 0.168863i | 0.630575 | − | 0.776128i | \(-0.282819\pi\) |
0.327096 | + | 0.944991i | \(0.393930\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.04643 | − | 4.53083i | −0.437581 | − | 0.392873i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.83885 | + | 0.829406i | −0.330396 | + | 0.0713839i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.69757 | − | 4.66403i | 0.145033 | − | 0.398475i | −0.845812 | − | 0.533482i | \(-0.820883\pi\) |
0.990845 | + | 0.135007i | \(0.0431056\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.76202 | − | 2.31761i | 0.234272 | − | 0.196577i | −0.518093 | − | 0.855325i | \(-0.673358\pi\) |
0.752364 | + | 0.658747i | \(0.228913\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.34548 | − | 3.32204i | 0.365956 | − | 0.279766i | ||||
\(142\) | 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 | ||||||||
\(147\) | −0.360177 | + | 7.92326i | −0.0297069 | + | 0.653499i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.3170 | + | 14.6788i | −1.00904 | + | 1.20253i | −0.0298610 | + | 0.999554i | \(0.509506\pi\) |
−0.979183 | + | 0.202978i | \(0.934938\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.2624i | 1.56755i | 0.621042 | + | 0.783777i | \(0.286710\pi\) | ||||
−0.621042 | + | 0.783777i | \(0.713290\pi\) | |||||||
\(152\) | 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 | −0.350026 | − | 0.936740i | \(-0.613827\pi\) |
0.333989 | + | 0.942577i | \(0.391605\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −24.9094 | + | 3.23394i | −1.97544 | + | 0.256468i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.79490 | + | 0.316489i | −0.141458 | + | 0.0249428i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.51668 | + | 13.0193i | −0.588752 | + | 1.01975i | 0.405645 | + | 0.914031i | \(0.367047\pi\) |
−0.994396 | + | 0.105717i | \(0.966286\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.376228 | − | 1.20075i | −0.0292893 | − | 0.0934782i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.87982 | − | 3.23199i | −0.687141 | − | 0.250099i | −0.0252305 | − | 0.999682i | \(-0.508032\pi\) |
−0.661911 | + | 0.749583i | \(0.730254\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.18435 | − | 12.3881i | 0.168027 | − | 0.952929i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.85030 | − | 12.4970i | 0.294440 | − | 0.955670i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.33529 | + | 13.2441i | −0.177549 | + | 1.00693i | 0.757612 | + | 0.652705i | \(0.226366\pi\) |
−0.935161 | + | 0.354224i | \(0.884745\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.47502 | − | 2.35672i | −0.489466 | − | 0.178151i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.03000 | + | 19.2450i | 0.453243 | + | 1.44655i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.34644 | − | 14.4565i | 0.623842 | − | 1.08053i | −0.364921 | − | 0.931038i | \(-0.618904\pi\) |
0.988764 | − | 0.149488i | \(-0.0477625\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0398 | + | 1.77029i | −0.746251 | + | 0.131584i | −0.533828 | − | 0.845593i | \(-0.679247\pi\) |
−0.212424 | + | 0.977178i | \(0.568136\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.6101 | + | 2.41611i | −1.37570 | + | 0.178604i | ||||
\(184\) | 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 | −0.837850 | − | 0.545900i | \(-0.816188\pi\) |
0.683098 | + | 0.730327i | \(0.260632\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0385657 | − | 0.848376i | 0.00276175 | − | 0.0607535i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.15098 | + | 2.97392i | −0.366992 | + | 0.211883i | −0.672144 | − | 0.740421i | \(-0.734626\pi\) |
0.305151 | + | 0.952304i | \(0.401293\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.94088 | − | 11.0073i | −0.137585 | − | 0.780286i | −0.973024 | − | 0.230703i | \(-0.925898\pi\) |
0.835439 | − | 0.549583i | \(-0.185214\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.8409 | + | 9.81659i | −0.905724 | + | 0.692409i | ||||
\(202\) | 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 | ||||||||
\(207\) | −2.00535 | − | 2.88591i | −0.139381 | − | 0.200585i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.09933 | + | 0.865240i | 0.283557 | + | 0.0598499i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.9377 | + | 3.69188i | 1.44141 | + | 0.254159i | 0.839045 | − | 0.544063i | \(-0.183115\pi\) |
0.602364 | + | 0.798222i | \(0.294226\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.0401882 | + | 0.0437001i | −0.00275365 | + | 0.00299428i | ||||
\(214\) | 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 | ||||||||
\(219\) | 6.71777 | + | 1.50194i | 0.453945 | + | 0.101492i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.21662 | − | 3.83930i | −0.149106 | − | 0.258259i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.71184 | − | 12.9457i | −0.315528 | − | 0.866907i | −0.991515 | − | 0.129993i | \(-0.958505\pi\) |
0.675987 | − | 0.736914i | \(-0.263718\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.11047 | − | 13.2397i | −0.0740316 | − | 0.882644i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.1886 | 1.07448 | 0.537238 | − | 0.843430i | \(-0.319468\pi\) | ||||
0.537238 | + | 0.843430i | \(0.319468\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.6462 | −1.69475 | −0.847374 | − | 0.530997i | \(-0.821817\pi\) | ||||
−0.847374 | + | 0.530997i | \(0.821817\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.19191 | + | 2.29971i | 0.0784222 | + | 0.151310i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.98107 | − | 10.9379i | −0.260808 | − | 0.716565i | −0.999113 | − | 0.0420981i | \(-0.986596\pi\) |
0.738305 | − | 0.674467i | \(-0.235626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.19347 | − | 2.06715i | −0.0778532 | − | 0.134846i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.525093 | + | 2.34860i | −0.0341085 | + | 0.152558i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.1831 | − | 7.61128i | −0.852746 | − | 0.492333i | 0.00883069 | − | 0.999961i | \(-0.497189\pi\) |
−0.861576 | + | 0.507628i | \(0.830522\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.76016 | + | 11.6317i | 0.628707 | + | 0.749264i | 0.982541 | − | 0.186044i | \(-0.0595666\pi\) |
−0.353834 | + | 0.935308i | \(0.615122\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.3981 | + | 10.6341i | 0.731189 | + | 0.682175i | ||||
\(244\) | 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 | ||||||||
\(249\) | 11.2996 | − | 17.6668i | 0.716081 | − | 1.11958i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.71032 | + | 10.1940i | −0.234193 | + | 0.643441i | 0.765807 | + | 0.643071i | \(0.222340\pi\) |
−1.00000 | 0.000369965i | \(0.999882\pi\) | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.862512 | − | 0.723733i | 0.0542257 | − | 0.0455007i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.43361 | + | 7.10759i | 0.340266 | + | 0.445094i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.00786014 | + | 0.0445771i | 0.000490302 | + | 0.00278064i | 0.985052 | − | 0.172258i | \(-0.0551062\pi\) |
−0.984562 | + | 0.175038i | \(0.943995\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.56017 | − | 3.21017i | 0.345492 | − | 0.199470i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.8317 | − | 10.2758i | −1.35135 | − | 0.636057i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.52577 | + | 4.20185i | −0.217408 | + | 0.259097i | −0.863715 | − | 0.503981i | \(-0.831868\pi\) |
0.646307 | + | 0.763078i | \(0.276313\pi\) | |||||||
\(264\) | 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 | \(-0.296845\pi\) |
−0.687495 | + | 0.726189i | \(0.741290\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.8494 | + | 7.22458i | −1.20576 | + | 0.438862i | −0.865232 | − | 0.501371i | \(-0.832829\pi\) |
−0.340531 | + | 0.940233i | \(0.610607\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.225075 | + | 1.73364i | 0.0136222 | + | 0.104925i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.19208 | − | 0.739177i | 0.252792 | − | 0.0445741i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.91899 | + | 6.78789i | −0.235469 | + | 0.407845i | −0.959409 | − | 0.282018i | \(-0.908996\pi\) |
0.723940 | + | 0.689863i | \(0.242329\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.829509 | − | 9.10501i | 0.0496614 | − | 0.545102i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.0064 | + | 4.00600i | 0.656587 | + | 0.238978i | 0.648762 | − | 0.760991i | \(-0.275287\pi\) |
0.00782495 | + | 0.999969i | \(0.497509\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.21905 | + | 6.91356i | −0.0724648 | + | 0.410968i | 0.926899 | + | 0.375310i | \(0.122464\pi\) |
−0.999364 | + | 0.0356581i | \(0.988647\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.19175 | − | 2.36833i | −0.307533 | − | 0.140288i | ||||
\(286\) | 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 | ||||||||
\(291\) | −16.0246 | + | 5.02096i | −0.939380 | + | 0.294334i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.29095 | − | 2.23599i | 0.0754180 | − | 0.130628i | −0.825850 | − | 0.563890i | \(-0.809304\pi\) |
0.901268 | + | 0.433262i | \(0.142638\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.66705 | − | 1.52824i | 0.504615 | − | 0.0889773i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.06167 | + | 3.94590i | −0.177656 | + | 0.228964i | ||||
\(298\) | 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 | −0.728698 | − | 0.684836i | \(-0.759874\pi\) |
0.800968 | + | 0.598707i | \(0.204318\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.8370 | + | 0.901757i | 1.12849 | + | 0.0512991i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.4909 | − | 12.9851i | 1.27534 | − | 0.736320i | 0.299355 | − | 0.954142i | \(-0.403229\pi\) |
0.975989 | + | 0.217822i | \(0.0698952\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.32842 | − | 13.2051i | −0.131610 | − | 0.746398i | −0.977161 | − | 0.212502i | \(-0.931839\pi\) |
0.845551 | − | 0.533895i | \(-0.179272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.900876 | − | 3.41102i | −0.0507586 | − | 0.192189i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.3056 | − | 19.5557i | 1.30897 | − | 1.09836i | 0.320454 | − | 0.947264i | \(-0.396165\pi\) |
0.988519 | − | 0.151095i | \(-0.0482799\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.64407 | − | 7.26453i | 0.148040 | − | 0.406736i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.43845 | + | 2.19922i | 0.191916 | + | 0.122748i | ||||
\(322\) | 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 | ||||||||
\(327\) | 8.26319 | + | 7.59913i | 0.456956 | + | 0.420233i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.15834 | + | 3.76397i | 0.174125 | + | 0.207514i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.22014 | + | 5.32325i | 0.506785 | + | 0.292592i | 0.731511 | − | 0.681830i | \(-0.238815\pi\) |
−0.224726 | + | 0.974422i | \(0.572149\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.1151 | + | 7.13689i | 0.554304 | + | 0.391099i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.52668 | + | 6.10839i | 0.192683 | + | 0.333737i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.38138 | − | 6.54278i | −0.129722 | − | 0.356408i | 0.857780 | − | 0.514018i | \(-0.171843\pi\) |
−0.987501 | + | 0.157610i | \(0.949621\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.4373 | + | 8.00096i | −0.838436 | + | 0.434553i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.92924 | 0.158627 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0159 | −0.972770 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.36154 | + | 0.705673i | −0.0733029 | + | 0.0379921i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.63081 | − | 26.4604i | −0.517009 | − | 1.42047i | −0.873799 | − | 0.486287i | \(-0.838351\pi\) |
0.356790 | − | 0.934185i | \(-0.383871\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.79155 | + | 16.9595i | 0.524130 | + | 0.907819i | 0.999605 | + | 0.0280904i | \(0.00894261\pi\) |
−0.475476 | + | 0.879729i | \(0.657724\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.85260 | + | 1.79580i | −0.152261 | + | 0.0958527i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.55050 | + | 2.04988i | 0.188974 | + | 0.109104i | 0.591502 | − | 0.806303i | \(-0.298535\pi\) |
−0.402528 | + | 0.915408i | \(0.631868\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0166533 | + | 0.0198466i | 0.000883864 | + | 0.00105335i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −13.5558 | − | 12.4664i | −0.717450 | − | 0.659793i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.52450 | − | 0.974118i | −0.291572 | − | 0.0514120i | 0.0259490 | − | 0.999663i | \(-0.491739\pi\) |
−0.317521 | + | 0.948251i | \(0.602850\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3395 | − | 11.2117i | 0.807340 | − | 0.590087i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.7024 | + | 9.40356i | 0.771674 | + | 0.493559i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.02739 | − | 2.82273i | 0.0537760 | − | 0.147748i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.28539 | − | 1.91767i | 0.119296 | − | 0.100101i | −0.581188 | − | 0.813769i | \(-0.697412\pi\) |
0.700484 | + | 0.713668i | \(0.252967\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.5149 | − | 4.09761i | 0.807674 | − | 0.213313i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.91814 | − | 22.2209i | −0.203420 | − | 1.15365i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.2415 | + | 10.5317i | −0.944510 | + | 0.545313i | −0.891371 | − | 0.453274i | \(-0.850256\pi\) |
−0.0531391 | + | 0.998587i | \(0.516923\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.3308 | − | 0.560536i | −0.636760 | − | 0.0289460i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.35381 | − | 3.99691i | 0.172730 | − | 0.205852i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.54057i | 0.490066i | 0.969515 | + | 0.245033i | \(0.0787988\pi\) | ||||
−0.969515 | + | 0.245033i | \(0.921201\pi\) | |||||||
\(380\) | 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 | \(-0.214072\pi\) |
−0.477665 | + | 0.878542i | \(0.658517\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.06216 | − | 0.386595i | 0.0541328 | − | 0.0197027i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.14888 | − | 22.6230i | 0.312565 | − | 1.14999i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.63724 | + | 1.69931i | −0.488627 | + | 0.0861582i | −0.412533 | − | 0.910942i | \(-0.635356\pi\) |
−0.0760939 | + | 0.997101i | \(0.524245\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00269 | + | 6.93287i | −0.202425 | + | 0.350610i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.3961 | + | 5.76401i | −0.927960 | + | 0.290756i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.986853 | + | 0.359185i | 0.0496539 | + | 0.0180726i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.05329 | + | 11.6448i | −0.103052 | + | 0.584435i | 0.888929 | + | 0.458045i | \(0.151450\pi\) |
−0.991981 | + | 0.126390i | \(0.959661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.3714 | + | 2.94534i | 0.569284 | + | 0.147451i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.59086 | − | 20.3648i | 0.179319 | − | 1.01697i | −0.753720 | − | 0.657195i | \(-0.771743\pi\) |
0.933039 | − | 0.359774i | \(-0.117146\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.85776 | + | 0.676169i | 0.0925416 | + | 0.0336824i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.24226 | − | 4.33507i | 0.260490 | − | 0.215411i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.98313 | + | 3.43488i | −0.0982999 | + | 0.170260i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.39761 | − | 0.599090i | 0.168001 | − | 0.0296231i | −0.0890148 | − | 0.996030i | \(-0.528372\pi\) |
0.257016 | + | 0.966407i | \(0.417261\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.10682 | + | 8.52524i | 0.0545952 | + | 0.420519i | ||||
\(412\) | 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 | 0.0146955 | − | 0.999892i | \(-0.495322\pi\) |
0.982150 | − | 0.188102i | \(-0.0602334\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.03468 | + | 8.57198i | −0.196173 | + | 0.416784i | ||||
\(424\) | 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 | ||||||||
\(429\) | −0.655905 | − | 0.857975i | −0.0316674 | − | 0.0414234i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.2345 | + | 21.1742i | −1.21550 | + | 1.01993i | −0.216455 | + | 0.976293i | \(0.569449\pi\) |
−0.999048 | + | 0.0436350i | \(0.986106\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.46188 | + | 15.0064i | −0.262481 | + | 0.721161i | 0.736517 | + | 0.676419i | \(0.236469\pi\) |
−0.998999 | + | 0.0447423i | \(0.985753\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.67342 | + | 8.87034i | −0.272020 | + | 0.425300i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.170932 | − | 5.10321i | 0.00817679 | − | 0.244120i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.5401 | + | 5.38505i | 1.45760 | + | 0.257014i | 0.845589 | − | 0.533835i | \(-0.179250\pi\) |
0.612011 | + | 0.790849i | \(0.290361\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.76108 | − | 12.4713i | −0.274337 | − | 0.593871i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.5287 | + | 14.9311i | 0.595257 | + | 0.709400i | 0.976607 | − | 0.215031i | \(-0.0689852\pi\) |
−0.381350 | + | 0.924431i | \(0.624541\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.99962 | − | 2.30918i | −0.189600 | − | 0.109466i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.24156 | − | 32.3895i | 0.342514 | − | 1.53197i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.61607 | − | 11.4594i | −0.312232 | − | 0.540801i | 0.666613 | − | 0.745404i | \(-0.267743\pi\) |
−0.978845 | + | 0.204602i | \(0.934410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.75842 | + | 4.83122i | 0.0828007 | + | 0.227493i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.3524 | − | 29.6214i | −0.721321 | − | 1.39173i | ||||
\(454\) | 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 | ||||||||
\(459\) | 10.8602 | − | 33.8088i | 0.506912 | − | 1.57806i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.65076 | + | 15.5253i | 0.263182 | + | 0.723087i | 0.998948 | + | 0.0458511i | \(0.0146000\pi\) |
−0.735766 | + | 0.677236i | \(0.763178\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.69170 | + | 8.12625i | 0.218042 | + | 0.377659i | 0.954209 | − | 0.299140i | \(-0.0966998\pi\) |
−0.736168 | + | 0.676799i | \(0.763366\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.89358 | − | 0.870516i | −0.180560 | − | 0.0403692i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.5458 | + | 10.7074i | 0.858196 | + | 0.495480i | 0.863408 | − | 0.504507i | \(-0.168326\pi\) |
−0.00521153 | + | 0.999986i | \(0.501659\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.33287 | − | 11.1225i | −0.430952 | − | 0.513588i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.250711 | − | 0.272620i | 0.0115522 | − | 0.0125617i | ||||
\(472\) | 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 | ||||||||
\(477\) | 35.7277 | − | 24.8262i | 1.63586 | − | 1.13672i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.4165 | − | 31.3665i | 0.521632 | − | 1.43317i | −0.347071 | − | 0.937839i | \(-0.612824\pi\) |
0.868703 | − | 0.495333i | \(-0.164954\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.05061 | + | 1.72067i | −0.0934998 | + | 0.0784557i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.50791 | − | 1.91725i | 0.114114 | − | 0.0872379i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.27250 | + | 7.21673i | 0.0577815 | + | 0.327695i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.9750 | − | 16.7288i | 1.31298 | − | 0.758052i | 0.330395 | − | 0.943843i | \(-0.392818\pi\) |
0.982589 | + | 0.185791i | \(0.0594846\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.18244 | − | 26.0117i | 0.0534720 | − | 1.17629i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.635055 | − | 0.756829i | 0.0286596 | − | 0.0341552i | −0.751524 | − | 0.659705i | \(-0.770681\pi\) |
0.780184 | + | 0.625550i | \(0.215125\pi\) | |||||||
\(492\) | 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 | −0.248290 | − | 0.968686i | \(-0.579868\pi\) |
0.432458 | + | 0.901654i | \(0.357646\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.2312 | − | 2.10726i | 0.725155 | − | 0.0941454i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.7905 | − | 5.60552i | 1.41747 | − | 0.249938i | 0.588167 | − | 0.808740i | \(-0.299850\pi\) |
0.829301 | + | 0.558802i | \(0.188739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.11080 | − | 12.3163i | 0.316426 | − | 0.548067i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.51443 | + | 20.7911i | 0.289316 | + | 0.923365i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.2608 | − | 7.73831i | −0.942370 | − | 0.342994i | −0.175268 | − | 0.984521i | \(-0.556079\pi\) |
−0.767101 | + | 0.641526i | \(0.778302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.07375 | + | 6.08956i | −0.0475000 | + | 0.269386i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.03939 | + | 22.2864i | 0.178343 | + | 0.983968i | ||||
\(514\) | 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 | ||||||||
\(519\) | −6.96458 | − | 22.2278i | −0.305711 | − | 0.975690i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.86213 | + | 8.42145i | −0.213014 | + | 0.368950i | −0.952656 | − | 0.304049i | \(-0.901661\pi\) |
0.739643 | + | 0.673000i | \(0.234995\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.5671 | + | 5.91879i | −1.46779 | + | 0.258810i | −0.849686 | − | 0.527288i | \(-0.823209\pi\) |
−0.618101 | + | 0.786099i | \(0.712098\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.8355 | − | 1.53658i | 0.516544 | − | 0.0670619i | ||||
\(526\) | 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 | ||||||||
\(537\) | −1.31297 | + | 28.8831i | −0.0566590 | + | 1.24640i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.81174 | − | 2.20071i | 0.164183 | − | 0.0947911i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.180608 | + | 1.02428i | 0.00776495 | + | 0.0440372i | 0.988444 | − | 0.151586i | \(-0.0484381\pi\) |
−0.980679 | + | 0.195623i | \(0.937327\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.0280 | − | 10.7242i | 0.602001 | − | 0.460218i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.75277 | − | 3.14895i | 0.160751 | − | 0.134886i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.86889 | + | 24.3671i | −0.379207 | + | 1.04186i | 0.592480 | + | 0.805586i | \(0.298149\pi\) |
−0.971686 | + | 0.236276i | \(0.924073\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26.6925 | − | 18.5479i | 1.13921 | − | 0.791607i | ||||
\(550\) | 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 | ||||||||
\(555\) | 3.65678 | − | 3.97633i | 0.155222 | − | 0.168786i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.42914 | + | 2.89494i | 0.102926 | + | 0.122662i | 0.815048 | − | 0.579393i | \(-0.196710\pi\) |
−0.712122 | + | 0.702055i | \(0.752266\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.39021 | + | 2.53469i | 0.185686 | + | 0.107206i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.1030 | + | 2.48238i | 0.468770 | + | 0.104806i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.99208 | + | 10.3786i | 0.252536 | + | 0.437406i | 0.964223 | − | 0.265091i | \(-0.0854020\pi\) |
−0.711687 | + | 0.702496i | \(0.752069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.59510 | + | 7.12998i | 0.109177 | + | 0.299960i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.07767 | + | 10.6620i | −0.381226 | + | 0.447764i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.2148 | −0.470147 | −0.235074 | − | 0.971978i | \(-0.575533\pi\) | ||||
−0.235074 | + | 0.971978i | \(0.575533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.2525 | −0.680144 | −0.340072 | − | 0.940399i | \(-0.610452\pi\) | ||||
−0.340072 | + | 0.940399i | \(0.610452\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.61733 | − | 18.5559i | −0.401770 | − | 0.775185i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.77435 | − | 4.87499i | −0.0739956 | − | 0.203301i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.02000 | − | 6.96284i | −0.167355 | − | 0.289867i | 0.770134 | − | 0.637882i | \(-0.220189\pi\) |
−0.937489 | + | 0.348015i | \(0.886856\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.26400 | − | 5.65351i | 0.0525299 | − | 0.234952i | ||||
\(580\) | 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 | ||||||||
\(585\) | 0.616863 | + | 1.33535i | 0.0255041 | + | 0.0552101i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.5628 | − | 3.44945i | −0.807444 | − | 0.142374i | −0.245336 | − | 0.969438i | \(-0.578898\pi\) |
−0.562108 | + | 0.827064i | \(0.690009\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.87470 | − | 9.88463i | 0.365676 | − | 0.407289i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.55081 | − | 8.67864i | 0.228330 | − | 0.356992i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.64203 | − | 20.9963i | 0.313821 | − | 0.862215i | −0.678056 | − | 0.735010i | \(-0.737177\pi\) |
0.991876 | − | 0.127205i | \(-0.0406006\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.15644 | + | 5.16587i | −0.252390 | + | 0.211780i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.7576 | + | 15.3799i | 0.481208 | + | 0.629456i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.89198 | + | 16.4012i | 0.118163 | + | 0.670136i | 0.985135 | + | 0.171780i | \(0.0549517\pi\) |
−0.866972 | + | 0.498356i | \(0.833937\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.9204 | − | 10.3464i | 0.730990 | − | 0.422037i | −0.0877940 | − | 0.996139i | \(-0.527982\pi\) |
0.818784 | + | 0.574101i | \(0.194648\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.9224 | − | 25.3301i | 0.485519 | − | 1.03152i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.89540 | − | 5.83411i | 0.199026 | − | 0.237191i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.3916i | 1.59886i | 0.600761 | + | 0.799428i | \(0.294864\pi\) | ||||
−0.600761 | + | 0.799428i | \(0.705136\pi\) | |||||||
\(608\) | 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 | −0.814794 | − | 0.579750i | \(-0.803150\pi\) |
−0.251512 | + | 0.967854i | \(0.580928\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.901563 | − | 6.94428i | −0.0363545 | − | 0.280020i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.3648 | + | 3.59086i | −0.819854 | + | 0.144562i | −0.567817 | − | 0.823155i | \(-0.692212\pi\) |
−0.252038 | + | 0.967717i | \(0.581101\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.8830 | + | 29.2423i | −0.678586 | + | 1.17535i | 0.296821 | + | 0.954933i | \(0.404074\pi\) |
−0.975407 | + | 0.220412i | \(0.929260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.38390 | + | 2.83960i | 0.216048 | + | 0.113949i | ||||
\(622\) | 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 | ||||||||
\(627\) | −6.99348 | + | 1.93668i | −0.279293 | + | 0.0773435i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.89690 | − | 27.7717i | 0.195252 | − | 1.10733i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.0060 | + | 12.7411i | 1.39357 | + | 0.507217i | 0.926262 | − | 0.376880i | \(-0.123003\pi\) |
0.467304 | + | 0.884096i | \(0.345225\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −35.1400 | + | 11.0103i | −1.39669 | + | 0.437622i | ||||
\(634\) | 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 | ||||||||
\(639\) | 0.0269710 | − | 0.0992317i | 0.00106695 | − | 0.00392554i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.37099 | − | 2.68282i | 0.291137 | − | 0.105965i | −0.192323 | − | 0.981332i | \(-0.561602\pi\) |
0.483460 | + | 0.875367i | \(0.339380\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.9819 | − | 25.1578i | −1.18237 | − | 0.992126i | −0.999960 | − | 0.00890393i | \(-0.997166\pi\) |
−0.182410 | − | 0.983223i | \(-0.558390\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | 8.20435 | + | 0.372955i | 0.321554 | + | 0.0146173i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.3831 | − | 13.5002i | 0.915050 | − | 0.528304i | 0.0329976 | − | 0.999455i | \(-0.489495\pi\) |
0.882053 | + | 0.471151i | \(0.156161\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.46082 | + | 8.28473i | 0.0570790 | + | 0.323711i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.5275 | + | 3.04451i | −0.449731 | + | 0.118778i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.3482 | − | 19.5915i | 0.909517 | − | 0.763176i | −0.0625097 | − | 0.998044i | \(-0.519910\pi\) |
0.972027 | + | 0.234869i | \(0.0754660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.2133 | + | 30.8082i | −0.436146 | + | 1.19830i | 0.505834 | + | 0.862631i | \(0.331185\pi\) |
−0.941980 | + | 0.335670i | \(0.891037\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.46866 | + | 4.13732i | 0.251222 | + | 0.160680i | ||||
\(664\) | 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 | ||||||||
\(669\) | 17.5637 | + | 16.1522i | 0.679051 | + | 0.624480i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.69399 | + | 7.97759i | 0.258419 | + | 0.307971i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.7750 | + | 15.4586i | 1.03210 | + | 0.595884i | 0.917586 | − | 0.397537i | \(-0.130135\pi\) |
0.114516 | + | 0.993421i | \(0.463468\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.2599 | + | 19.4746i | 0.471883 | + | 0.749578i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.6720 | + | 34.0729i | 0.756057 | + | 1.30953i | 0.944847 | + | 0.327511i | \(0.106210\pi\) |
−0.188791 | + | 0.982017i | \(0.560457\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.15932 | − | 14.1751i | −0.197996 | − | 0.543991i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.8945 | + | 12.9026i | −0.953961 | + | 0.494428i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0176 | 0.459840 | 0.229920 | − | 0.973210i | \(-0.426154\pi\) | ||||
0.229920 | + | 0.973210i | \(0.426154\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.75147 | 0.143336 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 39.4382 | − | 20.4404i | 1.50466 | − | 0.779849i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.21761 | + | 8.84031i | 0.122581 | + | 0.336789i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5214 | + | 30.3479i | 0.666544 | + | 1.15449i | 0.978864 | + | 0.204512i | \(0.0655606\pi\) |
−0.312320 | + | 0.949977i | \(0.601106\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.66580 | − | 2.58647i | −0.139252 | − | 0.0982519i | ||||
\(694\) | 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 | ||||||||
\(699\) | 14.8397 | + | 13.6471i | 0.561288 | + | 0.516181i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.95841 | + | 0.521647i | 0.111738 | + | 0.0197023i | 0.229237 | − | 0.973371i | \(-0.426377\pi\) |
−0.117500 | + | 0.993073i | \(0.537488\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.58262 | + | 17.0986i | 0.210552 | + | 0.644887i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.48284 | + | 2.22760i | 0.131171 | + | 0.0838964i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.0127 | + | 27.5097i | −0.376567 | + | 1.03461i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.36012 | − | 1.98037i | 0.0886360 | − | 0.0743744i | −0.597393 | − | 0.801949i | \(-0.703797\pi\) |
0.686029 | + | 0.727574i | \(0.259352\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.06439 | − | 4.03013i | −0.0399178 | − | 0.151142i | ||||
\(712\) | 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 | ||||||||
\(717\) | 26.3391 | + | 1.19733i | 0.983650 | + | 0.0447150i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.13781 | − | 8.50651i | 0.266195 | − | 0.317239i | −0.616345 | − | 0.787476i | \(-0.711387\pi\) |
0.882540 | + | 0.470237i | \(0.155832\pi\) | |||||||
\(720\) | 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 | −0.586179 | − | 0.810182i | \(-0.699368\pi\) |
0.0717355 | + | 0.997424i | \(0.477146\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.0033 | − | 7.26839i | −0.963084 | − | 0.269199i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −52.5931 | + | 9.27357i | −1.94522 | + | 0.342996i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.1447 | + | 31.4276i | −0.670191 | + | 1.16080i | 0.307659 | + | 0.951497i | \(0.400454\pi\) |
−0.977850 | + | 0.209308i | \(0.932879\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.72062 | + | 1.79243i | −0.211008 | + | 0.0661147i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.42862 | + | 3.06777i | 0.310472 | + | 0.113003i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.94942 | − | 16.7270i | 0.108496 | − | 0.615312i | −0.881270 | − | 0.472613i | \(-0.843311\pi\) |
0.989766 | − | 0.142699i | \(-0.0455780\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.88240 | − | 0.386069i | −0.179360 | − | 0.0141826i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.59818 | + | 26.0776i | −0.168691 | + | 0.956693i | 0.776486 | + | 0.630134i | \(0.217000\pi\) |
−0.945177 | + | 0.326559i | \(0.894111\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.6097 | − | 4.95352i | −0.498620 | − | 0.181483i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.29558 | + | 36.1735i | −0.120579 | + | 1.32352i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.83324 | + | 3.17526i | −0.0669850 | + | 0.116021i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.8929 | + | 8.26849i | −1.71115 | + | 0.301722i | −0.941566 | − | 0.336827i | \(-0.890646\pi\) |
−0.769581 | + | 0.638549i | \(0.779535\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.41913 | − | 18.6333i | −0.0881581 | − | 0.679037i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.6812 | + | 4.97954i | −0.497909 | + | 0.181224i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.6519 | − | 10.6162i | −0.459843 | − | 0.385854i | 0.383230 | − | 0.923653i | \(-0.374812\pi\) |
−0.843073 | + | 0.537799i | \(0.819256\pi\) | |||||||
\(758\) | 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 | ||||||||
\(765\) | −14.0206 | − | 6.59923i | −0.506914 | − | 0.238596i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.54145 | − | 3.77671i | 0.236198 | − | 0.136369i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.25863 | − | 29.8231i | −0.189631 | − | 1.07545i | −0.919860 | − | 0.392248i | \(-0.871698\pi\) |
0.730229 | − | 0.683203i | \(-0.239413\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.0476157 | − | 0.0622851i | −0.00171484 | − | 0.00224314i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.9958 | + | 18.4567i | −0.791134 | + | 0.663840i | −0.946026 | − | 0.324091i | \(-0.894942\pi\) |
0.154892 | + | 0.987931i | \(0.450497\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.61619 | − | 12.6829i | 0.165818 | − | 0.455582i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.99177 | + | 9.36807i | −0.214953 | + | 0.336078i | ||||
\(778\) | 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 | ||||||||
\(783\) | 41.7624 | − | 1.59828i | 1.49247 | − | 0.0571177i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.103890 | − | 0.123812i | −0.00370800 | − | 0.00441903i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.1812 | − | 12.8063i | −0.790673 | − | 0.456495i | 0.0495262 | − | 0.998773i | \(-0.484229\pi\) |
−0.840200 | + | 0.542277i | \(0.817562\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.07292 | − | 9.27161i | 0.0737980 | − | 0.330078i | ||||
\(790\) | 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 | ||||||||
\(795\) | −8.73625 | − | 16.8559i | −0.309843 | − | 0.597818i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.4074 | 1.14793 | 0.573965 | − | 0.818880i | \(-0.305405\pi\) | ||||
0.573965 | + | 0.818880i | \(0.305405\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.5817 | 0.763506 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.53212 | + | 18.2667i | 0.0541348 | + | 0.645423i | ||||
\(802\) | 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 | ||||||||
\(807\) | 3.31937 | + | 0.742136i | 0.116847 | + | 0.0261244i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.3938 | + | 17.5479i | 1.06859 | + | 0.616950i | 0.927796 | − | 0.373089i | \(-0.121701\pi\) |
0.140793 | + | 0.990039i | \(0.455035\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.0733 | − | 16.7719i | −0.494181 | − | 0.588942i | 0.460095 | − | 0.887870i | \(-0.347815\pi\) |
−0.954276 | + | 0.298928i | \(0.903371\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.7659 | − | 26.9301i | 0.868577 | − | 0.944479i | ||||
\(814\) | 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 | ||||||||
\(819\) | −1.72785 | − | 2.48657i | −0.0603760 | − | 0.0868877i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.83332 | + | 13.2794i | −0.168684 | + | 0.463455i | −0.995015 | − | 0.0997301i | \(-0.968202\pi\) |
0.826331 | + | 0.563185i | \(0.190424\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.4669 | + | 9.62189i | −0.399712 | + | 0.335398i | −0.820382 | − | 0.571815i | \(-0.806239\pi\) |
0.420670 | + | 0.907214i | \(0.361795\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.85737 | + | 4.47785i | −0.203927 | + | 0.155899i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.63051 | + | 20.5896i | 0.126245 | + | 0.715972i | 0.980561 | + | 0.196217i | \(0.0628657\pi\) |
−0.854315 | + | 0.519755i | \(0.826023\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.1611 | + | 7.02120i | −0.422371 | + | 0.243856i | −0.696091 | − | 0.717953i | \(-0.745079\pi\) |
0.273720 | + | 0.961809i | \(0.411746\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.616494 | − | 13.5618i | 0.0213859 | − | 0.470453i | ||||
\(832\) | 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 | −0.906315 | − | 0.422603i | \(-0.861116\pi\) |
−0.573563 | − | 0.819162i | \(-0.694439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −33.5383 | + | 12.2070i | −1.15649 | + | 0.420929i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.1183 | + | 2.61192i | −0.692910 | + | 0.0899592i | ||||
\(844\) | 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 | ||||||||
\(849\) | −3.63558 | − | 11.6031i | −0.124773 | − | 0.398218i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.54230 | + | 1.65326i | 0.155708 | + | 0.0566731i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.55129 | + | 42.8255i | −0.258551 | + | 1.46632i | 0.528239 | + | 0.849096i | \(0.322853\pi\) |
−0.786790 | + | 0.617221i | \(0.788259\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.87136 | − | 0.495925i | 0.337593 | − | 0.0169603i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.77792 | + | 49.7820i | −0.299848 | + | 1.70052i | 0.346969 | + | 0.937877i | \(0.387211\pi\) |
−0.646817 | + | 0.762645i | \(0.723900\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.3783 | − | 8.50899i | −0.797656 | − | 0.290323i | −0.0891412 | − | 0.996019i | \(-0.528412\pi\) |
−0.708515 | + | 0.705696i | \(0.750634\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.30994 | + | 13.7554i | 0.146883 | + | 0.468782i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.9638 | + | 29.3822i | −0.577455 | + | 1.00018i | 0.418315 | + | 0.908302i | \(0.362621\pi\) |
−0.995770 | + | 0.0918798i | \(0.970712\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0103 | + | 1.76509i | −0.340362 | + | 0.0600149i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −51.0187 | + | 6.62366i | −1.73269 | + | 0.224951i | ||||
\(868\) | 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 | −0.337636 | − | 0.941277i | \(-0.609627\pi\) |
0.985607 | + | 0.169055i | \(0.0540717\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.203078 | + | 4.46736i | −0.00684966 | + | 0.150680i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.59448 | − | 5.53938i | 0.323246 | − | 0.186626i | −0.329592 | − | 0.944123i | \(-0.606911\pi\) |
0.652839 | + | 0.757497i | \(0.273578\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.62988 | − | 54.6138i | −0.324071 | − | 1.83790i | −0.516122 | − | 0.856515i | \(-0.672625\pi\) |
0.192051 | − | 0.981385i | \(-0.438486\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.1100 | + | 9.25786i | −0.407073 | + | 0.311200i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.9548 | − | 16.7441i | 0.670017 | − | 0.562211i | −0.243054 | − | 0.970013i | \(-0.578149\pi\) |
0.913070 | + | 0.407802i | \(0.133705\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.41064 | + | 20.3606i | −0.248545 | + | 0.682871i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.56324 | − | 8.50812i | 0.0523703 | − | 0.285033i | ||||
\(892\) | 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 | ||||||||
\(897\) | −0.890949 | + | 0.968805i | −0.0297479 | + | 0.0323475i | ||||
\(898\) | 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 | ||||||||
\(903\) | 20.5519 | + | 4.59493i | 0.683924 | + | 0.152910i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.85274 | − | 6.67314i | −0.128069 | − | 0.221823i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.92780 | − | 16.2865i | −0.196830 | − | 0.540785i | 0.801535 | − | 0.597947i | \(-0.204017\pi\) |
−0.998365 | + | 0.0571627i | \(0.981795\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −56.2498 | + | 4.71795i | −1.86569 | + | 0.156484i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.0957 | 1.16277 | 0.581386 | − | 0.813628i | \(-0.302511\pi\) | ||||
0.581386 | + | 0.813628i | \(0.302511\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.6376 | −0.385150 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.52694 | − | 12.5932i | −0.215774 | − | 0.416320i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.92284 | − | 16.2729i | −0.195589 | − | 0.537377i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.0221 | + | 26.0190i | 0.495533 | + | 0.858288i | 0.999987 | − | 0.00515052i | \(-0.00163947\pi\) |
−0.504454 | + | 0.863439i | \(0.668306\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.744494 | + | 3.32992i | −0.0245319 | + | 0.109725i | ||||
\(922\) | 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 | ||||||||
\(927\) | −31.2237 | + | 14.4237i | −1.02552 | + | 0.473737i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.1458 | − | 5.66817i | −1.05467 | − | 0.185967i | −0.380680 | − | 0.924707i | \(-0.624310\pi\) |
−0.673990 | + | 0.738740i | \(0.735421\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.12218 | − | 19.5301i | 0.135099 | − | 0.640072i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.2367 | + | 37.8939i | −0.793475 | + | 1.24059i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.69805 | − | 4.66536i | 0.0555322 | − | 0.152573i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.8914 | + | 20.8863i | −0.813165 | + | 0.682327i | −0.951361 | − | 0.308078i | \(-0.900314\pi\) |
0.138196 | + | 0.990405i | \(0.455870\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.1053 | + | 18.4508i | 0.460308 | + | 0.602119i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.50659 | − | 14.2156i | −0.0817126 | − | 0.463415i | −0.998018 | − | 0.0629344i | \(-0.979954\pi\) |
0.916305 | − | 0.400481i | \(-0.131157\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.42639 | − | 3.13293i | 0.176708 | − | 0.102022i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.10398 | + | 4.52738i | 0.133502 | + | 0.147276i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.2988 | + | 33.7252i | −0.919588 | + | 1.09592i | 0.0755210 | + | 0.997144i | \(0.475938\pi\) |
−0.995109 | + | 0.0987786i | \(0.968506\pi\) | |||||||
\(948\) | 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 | \(-0.386223\pi\) |
−0.861808 | + | 0.507234i | \(0.830668\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.57039 | + | 3.11937i | −0.277331 | + | 0.100940i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.72394 | + | 13.2786i | 0.0557270 | + | 0.429237i | ||||
\(958\) | 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 | ||||||||
\(963\) | −7.04039 | − | 0.641413i | −0.226873 | − | 0.0206692i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.37554 | − | 0.864625i | −0.0764713 | − | 0.0278333i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.05922 | − | 40.0348i | 0.227009 | − | 1.28743i | −0.631798 | − | 0.775133i | \(-0.717683\pi\) |
0.858807 | − | 0.512300i | \(-0.171206\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 42.0155 | − | 29.9459i | 1.34973 | − | 0.962003i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.764165 | − | 4.33380i | 0.0245232 | − | 0.139078i | −0.970088 | − | 0.242754i | \(-0.921949\pi\) |
0.994611 | + | 0.103676i | \(0.0330604\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.27154 | − | 1.91868i | −0.168998 | − | 0.0615101i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.74846 | + | 1.48782i | −0.152072 | + | 0.0476485i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.538610 | + | 0.932899i | −0.0172317 | + | 0.0298461i | −0.874513 | − | 0.485003i | \(-0.838819\pi\) |
0.857281 | + | 0.514849i | \(0.172152\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.78381 | + | 1.01984i | −0.184851 | + | 0.0325943i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.7636 | − | 5.09990i | −0.599075 | − | 0.162827i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.78675 | − | 1.74223i | 0.152674 | − | 0.0555687i | −0.264553 | − | 0.964371i | \(-0.585224\pi\) |
0.417227 | + | 0.908803i | \(0.363002\pi\) | |||||||
\(984\) | 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 | −0.629283 | − | 0.777176i | \(-0.716651\pi\) |
0.874643 | + | 0.484768i | \(0.161096\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.4213 | − | 0.837398i | −0.584581 | − | 0.0265740i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.31621 | − | 4.22401i | 0.231939 | − | 0.133910i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.23994 | − | 35.3885i | −0.197621 | − | 1.12076i | −0.908637 | − | 0.417588i | \(-0.862876\pi\) |
0.711016 | − | 0.703176i | \(-0.248235\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.2430 | − | 2.91307i | −0.672099 | − | 0.0921655i |
(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.d.401.1 | 18 | ||
3.2 | odd | 2 | 912.2.cc.c.401.2 | 18 | |||
4.3 | odd | 2 | 114.2.l.a.59.3 | yes | 18 | ||
12.11 | even | 2 | 114.2.l.b.59.2 | yes | 18 | ||
19.10 | odd | 18 | 912.2.cc.c.257.2 | 18 | |||
57.29 | even | 18 | inner | 912.2.cc.d.257.1 | 18 | ||
76.67 | even | 18 | 114.2.l.b.29.2 | yes | 18 | ||
228.143 | odd | 18 | 114.2.l.a.29.3 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.l.a.29.3 | ✓ | 18 | 228.143 | odd | 18 | ||
114.2.l.a.59.3 | yes | 18 | 4.3 | odd | 2 | ||
114.2.l.b.29.2 | yes | 18 | 76.67 | even | 18 | ||
114.2.l.b.59.2 | yes | 18 | 12.11 | even | 2 | ||
912.2.cc.c.257.2 | 18 | 19.10 | odd | 18 | |||
912.2.cc.c.401.2 | 18 | 3.2 | odd | 2 | |||
912.2.cc.d.257.1 | 18 | 57.29 | even | 18 | inner | ||
912.2.cc.d.401.1 | 18 | 1.1 | even | 1 | trivial |