Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(373,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.373");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.i (of order \(3\), degree \(2\), 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 373.1 | ||
Root | \(0.500000 - 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.373 |
Dual form | 1764.2.i.g.1537.1 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.349814 | − | 1.69636i | −0.201965 | − | 0.979393i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.849814 | + | 1.47192i | 0.380048 | + | 0.658263i | 0.991069 | − | 0.133352i | \(-0.0425740\pi\) |
−0.611020 | + | 0.791615i | \(0.709241\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.75526 | + | 1.18682i | −0.918420 | + | 0.395607i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23855 | + | 2.14523i | −0.373437 | + | 0.646812i | −0.990092 | − | 0.140422i | \(-0.955154\pi\) |
0.616655 | + | 0.787234i | \(0.288487\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.388736 | + | 0.673310i | −0.107816 | + | 0.186743i | −0.914885 | − | 0.403714i | \(-0.867719\pi\) |
0.807069 | + | 0.590457i | \(0.201052\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.19963 | − | 1.95649i | 0.567942 | − | 0.505163i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.40545 | − | 2.43430i | −0.340871 | − | 0.590405i | 0.643724 | − | 0.765258i | \(-0.277389\pi\) |
−0.984595 | + | 0.174852i | \(0.944055\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.49381 | − | 4.31941i | 0.572119 | − | 0.990940i | −0.424229 | − | 0.905555i | \(-0.639455\pi\) |
0.996348 | − | 0.0853846i | \(-0.0272119\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.356004 | − | 0.616617i | −0.0742320 | − | 0.128574i | 0.826520 | − | 0.562907i | \(-0.190317\pi\) |
−0.900752 | + | 0.434334i | \(0.856984\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.05563 | − | 1.82841i | 0.211126 | − | 0.365682i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.97710 | + | 4.25874i | 0.572943 | + | 0.819595i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.25526 | − | 3.90623i | −0.418791 | − | 0.725368i | 0.577027 | − | 0.816725i | \(-0.304213\pi\) |
−0.995818 | + | 0.0913573i | \(0.970879\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.09888 | 0.915787 | 0.457893 | − | 0.889007i | \(-0.348604\pi\) | ||||
0.457893 | + | 0.889007i | \(0.348604\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.07234 | + | 1.35059i | 0.708904 | + | 0.235108i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.43818 | − | 5.95510i | 0.565233 | − | 0.979012i | −0.431795 | − | 0.901972i | \(-0.642120\pi\) |
0.997028 | − | 0.0770405i | \(-0.0245471\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.27816 | + | 0.423902i | 0.204669 | + | 0.0678786i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.93818 | − | 5.08907i | 0.458866 | − | 0.794780i | −0.540035 | − | 0.841643i | \(-0.681589\pi\) |
0.998901 | + | 0.0468628i | \(0.0149223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.32691 | + | 4.03033i | 0.354851 | + | 0.614620i | 0.987092 | − | 0.160151i | \(-0.0511982\pi\) |
−0.632241 | + | 0.774771i | \(0.717865\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.08836 | − | 3.04695i | −0.609457 | − | 0.454212i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.9876 | 1.89444 | 0.947220 | − | 0.320586i | \(-0.103880\pi\) | ||||
0.947220 | + | 0.320586i | \(0.103880\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.63781 | + | 3.23569i | −0.509395 | + | 0.453088i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.944368 | − | 1.63569i | −0.129719 | − | 0.224680i | 0.793849 | − | 0.608115i | \(-0.208074\pi\) |
−0.923568 | + | 0.383436i | \(0.874741\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.21015 | −0.567696 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.19963 | − | 2.71941i | −1.08607 | − | 0.360194i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.2880 | 1.86014 | 0.930069 | − | 0.367385i | \(-0.119747\pi\) | ||||
0.930069 | + | 0.367385i | \(0.119747\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.3090 | 1.83208 | 0.916042 | − | 0.401082i | \(-0.131366\pi\) | ||||
0.916042 | + | 0.401082i | \(0.131366\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.32141 | −0.163901 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.98762 | 0.975843 | 0.487922 | − | 0.872887i | \(-0.337755\pi\) | ||||
0.487922 | + | 0.872887i | \(0.337755\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.921468 | + | 0.819611i | −0.110932 | + | 0.0986696i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2632 | −1.21802 | −0.609011 | − | 0.793162i | \(-0.708433\pi\) | ||||
−0.609011 | + | 0.793162i | \(0.708433\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.49381 | − | 4.31941i | −0.291878 | − | 0.505548i | 0.682376 | − | 0.731002i | \(-0.260947\pi\) |
−0.974254 | + | 0.225454i | \(0.927614\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.47091 | − | 1.15113i | −0.400786 | − | 0.132921i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.21015 | −1.03622 | −0.518111 | − | 0.855313i | \(-0.673365\pi\) | ||||
−0.518111 | + | 0.855313i | \(0.673365\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.18292 | − | 6.53999i | 0.686991 | − | 0.726666i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.40545 | − | 7.63046i | −0.483561 | − | 0.837551i | 0.516261 | − | 0.856431i | \(-0.327323\pi\) |
−0.999822 | + | 0.0188798i | \(0.993990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.38874 | − | 4.13741i | 0.259095 | − | 0.448765i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.83743 | + | 5.19218i | −0.625839 | + | 0.556660i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.82691 | + | 8.36046i | −0.511652 | + | 0.886207i | 0.488257 | + | 0.872700i | \(0.337633\pi\) |
−0.999909 | + | 0.0135071i | \(0.995700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.78366 | − | 8.64953i | −0.184957 | − | 0.896915i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.47710 | 0.869732 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.32072 | − | 7.48371i | −0.438703 | − | 0.759856i | 0.558887 | − | 0.829244i | \(-0.311229\pi\) |
−0.997590 | + | 0.0693880i | \(0.977895\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.866524 | − | 7.38061i | 0.0870890 | − | 0.741779i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.20582 | + | 2.08854i | −0.119983 | + | 0.207817i | −0.919761 | − | 0.392479i | \(-0.871617\pi\) |
0.799777 | + | 0.600297i | \(0.204951\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.16690 | + | 3.75317i | 0.213511 | + | 0.369811i | 0.952811 | − | 0.303565i | \(-0.0981769\pi\) |
−0.739300 | + | 0.673376i | \(0.764844\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.59888 | + | 16.6258i | −0.927959 | + | 1.60727i | −0.141228 | + | 0.989977i | \(0.545105\pi\) |
−0.786732 | + | 0.617295i | \(0.788228\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.48143 | − | 16.4223i | −0.908156 | − | 1.57297i | −0.816623 | − | 0.577171i | \(-0.804157\pi\) |
−0.0915329 | − | 0.995802i | \(-0.529177\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.3047 | − | 3.74920i | −1.07299 | − | 0.355859i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.46472 | + | 11.1972i | −0.608150 | + | 1.05335i | 0.383395 | + | 0.923584i | \(0.374755\pi\) |
−0.991545 | + | 0.129762i | \(0.958579\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.605074 | − | 1.04802i | 0.0564235 | − | 0.0977283i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.271971 | − | 2.31650i | 0.0251437 | − | 0.214161i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.43199 | + | 4.21233i | 0.221090 | + | 0.382939i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.66071 | − | 3.20397i | −0.871077 | − | 0.288892i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0865 | 1.08105 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6291 | 1.56433 | 0.782163 | − | 0.623073i | \(-0.214116\pi\) | ||||
0.782163 | + | 0.623073i | \(0.214116\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.02290 | − | 5.35715i | 0.530287 | − | 0.471670i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.84362 | + | 4.92530i | 0.248449 | + | 0.430326i | 0.963096 | − | 0.269160i | \(-0.0867460\pi\) |
−0.714647 | + | 0.699485i | \(0.753413\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.73855 | + | 8.00119i | −0.321763 | + | 0.688633i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.72617 | − | 16.8462i | 0.830963 | − | 1.43927i | −0.0663128 | − | 0.997799i | \(-0.521124\pi\) |
0.897276 | − | 0.441471i | \(-0.145543\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.49381 | − | 2.58736i | 0.126703 | − | 0.219457i | −0.795694 | − | 0.605699i | \(-0.792894\pi\) |
0.922397 | + | 0.386242i | \(0.126227\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.54325 | − | 22.0317i | −0.382611 | − | 1.85540i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.962937 | − | 1.66786i | −0.0805249 | − | 0.139473i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.83310 | − | 6.63913i | 0.318322 | − | 0.551350i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.04944 | − | 7.01384i | −0.331743 | − | 0.574596i | 0.651111 | − | 0.758983i | \(-0.274303\pi\) |
−0.982854 | + | 0.184387i | \(0.940970\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.43199 | − | 7.67643i | 0.360670 | − | 0.624699i | −0.627401 | − | 0.778696i | \(-0.715881\pi\) |
0.988071 | + | 0.153997i | \(0.0492147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.76145 | + | 5.03913i | 0.546631 | + | 0.407390i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.33310 | + | 7.50516i | 0.348043 | + | 0.602829i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.76509 | −0.699530 | −0.349765 | − | 0.936837i | \(-0.613739\pi\) | ||||
−0.349765 | + | 0.936837i | \(0.613739\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.44437 | + | 2.17417i | −0.193851 | + | 0.172423i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.993810 | − | 1.72133i | 0.0778412 | − | 0.134825i | −0.824477 | − | 0.565895i | \(-0.808531\pi\) |
0.902318 | + | 0.431070i | \(0.141864\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.47277 | + | 7.14192i | 0.114655 | + | 0.555998i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.31089 | + | 2.27053i | −0.101440 | + | 0.175699i | −0.912278 | − | 0.409571i | \(-0.865678\pi\) |
0.810838 | + | 0.585270i | \(0.199012\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.19777 | + | 10.7349i | 0.476751 | + | 0.825758i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.74474 | + | 14.8608i | −0.133424 | + | 1.13643i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.22981 | −0.397615 | −0.198808 | − | 0.980039i | \(-0.563707\pi\) | ||||
−0.198808 | + | 0.980039i | \(0.563707\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.99814 | − | 24.2375i | −0.375683 | − | 1.82181i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.38255 | + | 4.12669i | 0.178080 | + | 0.308443i | 0.941223 | − | 0.337786i | \(-0.109678\pi\) |
−0.763143 | + | 0.646230i | \(0.776345\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4313 | −0.775352 | −0.387676 | − | 0.921796i | \(-0.626722\pi\) | ||||
−0.387676 | + | 0.921796i | \(0.626722\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.00550 | − | 24.2732i | −0.370017 | − | 1.79433i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.6872 | 0.859264 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.96286 | 0.509175 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.3214 | 0.963904 | 0.481952 | − | 0.876198i | \(-0.339928\pi\) | ||||
0.481952 | + | 0.876198i | \(0.339928\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.6414 | −1.05391 | −0.526957 | − | 0.849892i | \(-0.676667\pi\) | ||||
−0.526957 | + | 0.849892i | \(0.676667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.462249 | + | 2.24159i | 0.0331023 | + | 0.160524i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.4858 | −1.31706 | −0.658528 | − | 0.752556i | \(-0.728821\pi\) | ||||
−0.658528 | + | 0.752556i | \(0.728821\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.8083 | − | 20.4527i | −0.837071 | − | 1.44985i | −0.892333 | − | 0.451378i | \(-0.850933\pi\) |
0.0552614 | − | 0.998472i | \(-0.482401\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.79418 | − | 13.5499i | −0.197086 | − | 0.955734i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.98762 | 0.697566 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.71270 | + | 1.27643i | 0.119041 | + | 0.0887178i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.17742 | + | 10.6996i | 0.427301 | + | 0.740107i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.27747 | − | 12.6050i | 0.501002 | − | 0.867761i | −0.498998 | − | 0.866603i | \(-0.666298\pi\) |
0.999999 | − | 0.00115718i | \(-0.000368342\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.59022 | + | 17.4101i | 0.245998 | + | 1.19292i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.95489 | + | 6.85007i | −0.269721 | + | 0.467171i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.45489 | + | 5.74138i | −0.436181 | + | 0.387967i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.18539 | 0.147005 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.72253 | − | 8.17966i | −0.316244 | − | 0.547750i | 0.663457 | − | 0.748214i | \(-0.269088\pi\) |
−0.979701 | + | 0.200464i | \(0.935755\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.738550 | + | 6.29059i | −0.0492367 | + | 0.419372i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.55563 | + | 16.5508i | −0.634230 | + | 1.09852i | 0.352448 | + | 0.935831i | \(0.385349\pi\) |
−0.986678 | + | 0.162687i | \(0.947984\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.72253 | − | 9.91171i | −0.378155 | − | 0.654984i | 0.612639 | − | 0.790363i | \(-0.290108\pi\) |
−0.990794 | + | 0.135379i | \(0.956775\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.595243 | − | 1.03099i | 0.0389956 | − | 0.0675424i | −0.845869 | − | 0.533391i | \(-0.820917\pi\) |
0.884865 | + | 0.465848i | \(0.154251\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.0371 | + | 19.1168i | 0.719979 | + | 1.24704i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.22184 | + | 15.6237i | 0.209281 | + | 1.01487i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.1414 | + | 21.0296i | −0.785365 | + | 1.36029i | 0.143416 | + | 0.989663i | \(0.454191\pi\) |
−0.928781 | + | 0.370630i | \(0.879142\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7095 | − | 18.5493i | 0.689857 | − | 1.19487i | −0.282027 | − | 0.959406i | \(-0.591007\pi\) |
0.971884 | − | 0.235461i | \(-0.0756599\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.2570 | − | 8.20066i | −0.850440 | − | 0.526073i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.93887 | + | 3.35822i | 0.123367 | + | 0.213678i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.4029 | + | 10.1425i | −0.722629 | + | 0.642752i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.67996 | −0.169158 | −0.0845789 | − | 0.996417i | \(-0.526955\pi\) | ||||
−0.0845789 | + | 0.996417i | \(0.526955\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.76371 | 0.110884 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.85414 | − | 2.60483i | −0.491846 | − | 0.163121i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.54256 | + | 9.60000i | 0.345736 | + | 0.598832i | 0.985487 | − | 0.169750i | \(-0.0542961\pi\) |
−0.639752 | + | 0.768582i | \(0.720963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.8498 | + | 8.08608i | 0.671587 | + | 0.500516i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.70396 | + | 11.6116i | −0.413384 | + | 0.716002i | −0.995257 | − | 0.0972776i | \(-0.968987\pi\) |
0.581873 | + | 0.813279i | \(0.302320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.60507 | − | 2.78007i | 0.0985989 | − | 0.170778i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.8709 | + | 5.26357i | 0.971281 | + | 0.322125i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.04511 | − | 3.54224i | −0.124693 | − | 0.215974i | 0.796920 | − | 0.604085i | \(-0.206461\pi\) |
−0.921613 | + | 0.388111i | \(0.873128\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.06182 | + | 5.30323i | −0.185992 | + | 0.322148i | −0.943910 | − | 0.330201i | \(-0.892883\pi\) |
0.757918 | + | 0.652350i | \(0.226217\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.61491 | + | 4.52915i | 0.157685 | + | 0.273118i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.88255 | + | 13.6530i | −0.473616 | + | 0.820327i | −0.999544 | − | 0.0302019i | \(-0.990385\pi\) |
0.525928 | + | 0.850529i | \(0.323718\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.0488 | + | 6.05146i | −0.841077 | + | 0.362291i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.5946 | + | 18.3503i | 0.632018 | + | 1.09469i | 0.987139 | + | 0.159867i | \(0.0511065\pi\) |
−0.355120 | + | 0.934821i | \(0.615560\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.87636 | 0.408757 | 0.204378 | − | 0.978892i | \(-0.434483\pi\) | ||||
0.204378 | + | 0.978892i | \(0.434483\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.96541 | − | 14.3802i | −0.175656 | − | 0.851809i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.54944 | − | 7.87987i | 0.267614 | − | 0.463521i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.1836 | + | 9.94740i | −0.655595 | + | 0.583127i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.7534 | − | 23.8216i | 0.803482 | − | 1.39167i | −0.113829 | − | 0.993500i | \(-0.536311\pi\) |
0.917311 | − | 0.398172i | \(-0.130355\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.1421 | + | 21.0308i | 0.706943 | + | 1.22446i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.8233 | + | 1.11190i | −0.744082 | + | 0.0645192i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.553566 | 0.0320135 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.96472 | + | 1.31490i | 0.227767 | + | 0.0755390i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.1600 | + | 21.0618i | 0.696281 | + | 1.20599i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.5178 | −1.22809 | −0.614043 | − | 0.789273i | \(-0.710458\pi\) | ||||
−0.614043 | + | 0.789273i | \(0.710458\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.60872 | − | 4.98874i | 0.319069 | − | 0.283800i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.3855 | 1.04255 | 0.521273 | − | 0.853390i | \(-0.325457\pi\) | ||||
0.521273 | + | 0.853390i | \(0.325457\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.00137742 | −7.78563e−5 | −3.89281e−5 | − | 1.00000i | \(-0.500012\pi\) | ||||
−3.89281e−5 | 1.00000i | \(0.500012\pi\) | ||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.0989 | 0.791872 | 0.395936 | − | 0.918278i | \(-0.370420\pi\) | ||||
0.395936 | + | 0.918278i | \(0.370420\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.1730 | 0.625568 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.5611 | + | 10.4672i | 1.76157 | + | 0.584223i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.0197 | −0.780075 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.820724 | + | 1.42154i | 0.0455256 | + | 0.0788526i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.5414 | + | 21.8287i | −1.35714 | + | 1.20713i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.9629 | 0.767468 | 0.383734 | − | 0.923444i | \(-0.374638\pi\) | ||||
0.383734 | + | 0.923444i | \(0.374638\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.40545 | + | 20.4883i | −0.131818 | + | 1.12275i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.78799 | + | 11.7571i | 0.370868 | + | 0.642362i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.0982 | + | 20.9547i | −0.659031 | + | 1.14147i | 0.321836 | + | 0.946795i | \(0.395700\pi\) |
−0.980867 | + | 0.194679i | \(0.937633\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.2559 | + | 7.04953i | 1.15446 | + | 0.382878i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.31522 | + | 10.9383i | −0.341988 | + | 0.592341i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.98948 | − | 0.659811i | −0.107110 | − | 0.0355230i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.7156 | −1.75626 | −0.878132 | − | 0.478418i | \(-0.841210\pi\) | ||||
−0.878132 | + | 0.478418i | \(0.841210\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.8887 | + | 20.5919i | 0.636389 | + | 1.10226i | 0.986219 | + | 0.165445i | \(0.0529062\pi\) |
−0.349830 | + | 0.936813i | \(0.613760\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.02476 | + | 0.348986i | −0.214826 | + | 0.0186275i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.0309 | + | 17.3740i | −0.533889 | + | 0.924724i | 0.465327 | + | 0.885139i | \(0.345937\pi\) |
−0.999216 | + | 0.0395847i | \(0.987396\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.72184 | − | 15.1067i | −0.462907 | − | 0.801779i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.15087 | + | 7.18953i | −0.219075 | + | 0.379449i | −0.954525 | − | 0.298130i | \(-0.903637\pi\) |
0.735451 | + | 0.677578i | \(0.236971\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.93818 | − | 5.08907i | −0.154641 | − | 0.267846i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.29487 | − | 5.59905i | 0.330395 | − | 0.293874i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.23855 | − | 7.34138i | 0.221856 | − | 0.384266i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.77197 | + | 9.99735i | −0.301294 | + | 0.521857i | −0.976429 | − | 0.215837i | \(-0.930752\pi\) |
0.675135 | + | 0.737694i | \(0.264085\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.05563 | + | 17.5088i | −0.107012 | + | 0.911472i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.42580 | − | 2.46956i | −0.0738250 | − | 0.127869i | 0.826750 | − | 0.562570i | \(-0.190187\pi\) |
−0.900575 | + | 0.434701i | \(0.856854\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.22803 | − | 20.5030i | −0.218335 | − | 1.05877i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.50680 | 0.180609 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.9519 | 1.84672 | 0.923361 | − | 0.383932i | \(-0.125430\pi\) | ||||
0.923361 | + | 0.383932i | \(0.125430\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.16690 | − | 29.9052i | −0.315940 | − | 1.53209i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.915278 | + | 1.58531i | 0.0467685 | + | 0.0810054i | 0.888462 | − | 0.458950i | \(-0.151774\pi\) |
−0.841694 | + | 0.539956i | \(0.818441\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.1945 | − | 8.34299i | −0.569050 | − | 0.424098i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.69530 | − | 9.86454i | 0.288763 | − | 0.500152i | −0.684752 | − | 0.728776i | \(-0.740089\pi\) |
0.973515 | + | 0.228624i | \(0.0734227\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00069 | + | 1.73324i | −0.0506070 | + | 0.0876539i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.36033 | − | 6.54674i | 0.371280 | − | 0.330240i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.82691 | − | 13.5566i | −0.393815 | − | 0.682107i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.21565 | − | 9.03377i | 0.261766 | − | 0.453392i | −0.704945 | − | 0.709262i | \(-0.749028\pi\) |
0.966711 | + | 0.255870i | \(0.0823618\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.0371 | + | 29.5091i | 0.850790 | + | 1.47361i | 0.880496 | + | 0.474053i | \(0.157210\pi\) |
−0.0297058 | + | 0.999559i | \(0.509457\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.98212 | + | 3.43313i | −0.0987364 | + | 0.171016i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.8807 | + | 3.54299i | 0.739427 | + | 0.176053i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.51671 | + | 14.7514i | 0.422158 | + | 0.731199i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.97524 | 0.196563 | 0.0982815 | − | 0.995159i | \(-0.468665\pi\) | ||||
0.0982815 | + | 0.995159i | \(0.468665\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −31.9796 | − | 10.6060i | −1.57744 | − | 0.523156i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.48762 | − | 12.9689i | 0.367553 | − | 0.636620i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.91164 | − | 1.62894i | −0.240524 | − | 0.0797697i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.72184 | − | 8.17847i | 0.230677 | − | 0.399544i | −0.727331 | − | 0.686287i | \(-0.759239\pi\) |
0.958008 | + | 0.286743i | \(0.0925726\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.16002 | + | 5.47331i | 0.154010 | + | 0.266753i | 0.932698 | − | 0.360658i | \(-0.117448\pi\) |
−0.778688 | + | 0.627411i | \(0.784115\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −35.7843 | + | 15.4140i | −1.73989 | + | 0.749453i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.93454 | −0.287867 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.49243 | + | 2.21693i | −0.120336 | + | 0.107034i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.8770 | + | 24.0357i | 0.668434 | + | 1.15776i | 0.978342 | + | 0.206995i | \(0.0663683\pi\) |
−0.309908 | + | 0.950766i | \(0.600298\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.2473 | 0.540510 | 0.270255 | − | 0.962789i | \(-0.412892\pi\) | ||||
0.270255 | + | 0.962789i | \(0.412892\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.6032 | − | 4.17985i | −0.604278 | − | 0.200409i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.55122 | −0.169878 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.0865 | −0.720040 | −0.360020 | − | 0.932945i | \(-0.617230\pi\) | ||||
−0.360020 | + | 0.932945i | \(0.617230\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.93316 | 0.376916 | 0.188458 | − | 0.982081i | \(-0.439651\pi\) | ||||
0.188458 | + | 0.982081i | \(0.439651\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.4079 | −0.777810 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.4814 | + | 9.32284i | −0.495755 | + | 0.440955i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.5636 | −1.53677 | −0.768386 | − | 0.639987i | \(-0.778940\pi\) | ||||
−0.768386 | + | 0.639987i | \(0.778940\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.27816 | + | 12.6061i | 0.342715 | + | 0.593600i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.5723 | − | 4.83292i | −0.684668 | − | 0.227070i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.4079 | 0.533640 | 0.266820 | − | 0.963746i | \(-0.414027\pi\) | ||||
0.266820 | + | 0.963746i | \(0.414027\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.18292 | − | 13.2326i | 0.288594 | − | 0.617645i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.45853 | − | 4.25830i | −0.114505 | − | 0.198329i | 0.803077 | − | 0.595876i | \(-0.203195\pi\) |
−0.917582 | + | 0.397547i | \(0.869862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.59957 | + | 13.1628i | −0.353182 | + | 0.611729i | −0.986805 | − | 0.161913i | \(-0.948234\pi\) |
0.633623 | + | 0.773642i | \(0.281567\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.2156 | − | 9.97590i | 0.520113 | − | 0.462621i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.8905 | + | 20.5950i | −0.550228 | + | 0.953022i | 0.448030 | + | 0.894018i | \(0.352126\pi\) |
−0.998258 | + | 0.0590037i | \(0.981208\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.06615 | + | 14.8687i | 0.141281 | + | 0.685115i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.5280 | −0.530058 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.26509 | − | 9.11941i | −0.241579 | − | 0.418427i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.54325 | + | 3.38597i | 0.208021 | + | 0.155033i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.02909 | + | 5.24654i | −0.138403 | + | 0.239720i | −0.926892 | − | 0.375328i | \(-0.877530\pi\) |
0.788489 | + | 0.615048i | \(0.210863\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.67309 | + | 4.62992i | 0.121882 | + | 0.211106i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.34362 | − | 12.7195i | 0.333457 | − | 0.577564i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.568012 | − | 0.983825i | −0.0257391 | − | 0.0445814i | 0.852869 | − | 0.522125i | \(-0.174861\pi\) |
−0.878608 | + | 0.477544i | \(0.841527\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.26764 | − | 1.08371i | −0.147768 | − | 0.0490072i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.4382 | − | 28.4718i | 0.741845 | − | 1.28491i | −0.209810 | − | 0.977742i | \(-0.567285\pi\) |
0.951655 | − | 0.307170i | \(-0.0993821\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.33929 | + | 10.9800i | −0.285507 | + | 0.494513i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.6001 | − | 4.99669i | 0.521384 | − | 0.224584i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.0989 | − | 22.6879i | −0.586387 | − | 1.01565i | −0.994701 | − | 0.102810i | \(-0.967217\pi\) |
0.408314 | − | 0.912841i | \(-0.366117\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.31020 | + | 1.42948i | 0.192566 | + | 0.0638644i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.8516 | −1.15267 | −0.576333 | − | 0.817215i | \(-0.695517\pi\) | ||||
−0.576333 | + | 0.817215i | \(0.695517\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.09888 | −0.182398 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.0421 | − | 14.2688i | 0.712454 | − | 0.633701i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.5858 | − | 30.4595i | −0.779478 | − | 1.35009i | −0.932243 | − | 0.361832i | \(-0.882151\pi\) |
0.152766 | − | 0.988262i | \(-0.451182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 25.8196 | − | 2.23881i | 1.13996 | − | 0.0988459i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.68292 | + | 6.37900i | −0.162289 | + | 0.281092i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.0858 | + | 27.8615i | −0.707453 | + | 1.22535i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.82946 | + | 8.87163i | 0.0803045 | + | 0.389421i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.93130 | + | 15.4695i | 0.391287 | + | 0.677730i | 0.992620 | − | 0.121270i | \(-0.0386965\pi\) |
−0.601332 | + | 0.798999i | \(0.705363\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.4320 | − | 19.8008i | 0.499886 | − | 0.865828i | −0.500114 | − | 0.865960i | \(-0.666709\pi\) |
1.00000 | 0.000131698i | \(4.19208e-5\pi\) | ||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.16621 | − | 12.4122i | −0.312165 | − | 0.540685i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2465 | − | 19.4795i | 0.488979 | − | 0.846937i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −39.3671 | + | 16.9573i | −1.70839 | + | 0.735883i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.28435 | + | 3.95661i | 0.0989462 | + | 0.171380i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.6291 | −1.41068 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.16690 | − | 5.48523i | 0.266121 | − | 0.236705i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.1538 | + | 19.3190i | −0.479541 | + | 0.830589i | −0.999725 | − | 0.0234656i | \(-0.992530\pi\) |
0.520184 | + | 0.854054i | \(0.325863\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.64902 | + | 17.6952i | 0.156594 | + | 0.759374i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.1149 | − | 27.9118i | 0.690287 | − | 1.19561i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.8083 | − | 18.7206i | −0.462131 | − | 0.800435i | 0.536936 | − | 0.843623i | \(-0.319582\pi\) |
−0.999067 | + | 0.0431882i | \(0.986249\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −39.4251 | + | 16.9822i | −1.68262 | + | 0.724784i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.4968 | −0.958394 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.08836 | − | 19.8258i | −0.173541 | − | 0.841556i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.58768 | − | 2.74993i | −0.0672720 | − | 0.116518i | 0.830428 | − | 0.557127i | \(-0.188096\pi\) |
−0.897700 | + | 0.440608i | \(0.854763\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.61822 | −0.153034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.43571 | − | 11.8115i | −0.102836 | − | 0.498682i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.7628 | 1.84438 | 0.922190 | − | 0.386737i | \(-0.126398\pi\) | ||||
0.922190 | + | 0.386737i | \(0.126398\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.9752 | −0.924505 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.8626 | −1.00037 | −0.500186 | − | 0.865918i | \(-0.666735\pi\) | ||||
−0.500186 | + | 0.865918i | \(0.666735\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.2212 | 0.427742 | 0.213871 | − | 0.976862i | \(-0.431393\pi\) | ||||
0.213871 | + | 0.976862i | \(0.431393\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.66002 | − | 22.5979i | −0.194675 | − | 0.944040i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.50324 | −0.0626893 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0185 | + | 31.2089i | 0.750120 | + | 1.29925i | 0.947764 | + | 0.318972i | \(0.103337\pi\) |
−0.197645 | + | 0.980274i | \(0.563329\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.12178 | + | 24.8371i | 0.212854 | + | 1.03220i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.67859 | 0.193767 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.64084 | − | 1.56828i | 0.150530 | − | 0.0648403i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.5142 | + | 18.2111i | 0.433966 | + | 0.751651i | 0.997211 | − | 0.0746391i | \(-0.0237805\pi\) |
−0.563245 | + | 0.826290i | \(0.690447\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.7156 | − | 22.0242i | 0.523939 | − | 0.907489i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.46658 | + | 31.3585i | 0.266000 | + | 1.28991i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.5803 | − | 21.7897i | 0.516612 | − | 0.894798i | −0.483202 | − | 0.875509i | \(-0.660526\pi\) |
0.999814 | − | 0.0192889i | \(-0.00614021\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −30.5643 | + | 27.1858i | −1.25091 | + | 1.11264i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.22253 | −0.0908100 | −0.0454050 | − | 0.998969i | \(-0.514458\pi\) | ||||
−0.0454050 | + | 0.998969i | \(0.514458\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0494 | − | 24.3343i | −0.573089 | − | 0.992619i | −0.996246 | − | 0.0865627i | \(-0.972412\pi\) |
0.423158 | − | 0.906056i | \(-0.360922\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.0080 | + | 9.47987i | −0.896234 | + | 0.386050i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.13348 | + | 7.15939i | −0.168050 | + | 0.291071i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.26509 | + | 5.65531i | 0.132526 | + | 0.229542i | 0.924650 | − | 0.380819i | \(-0.124358\pi\) |
−0.792124 | + | 0.610361i | \(0.791025\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.04875 | + | 8.74470i | −0.204251 | + | 0.353773i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.36398 | − | 9.29068i | −0.216649 | − | 0.375247i | 0.737132 | − | 0.675748i | \(-0.236179\pi\) |
−0.953781 | + | 0.300501i | \(0.902846\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.49381 | − | 16.9426i | −0.140884 | − | 0.683191i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.5265 | − | 26.8928i | 0.625075 | − | 1.08266i | −0.363451 | − | 0.931613i | \(-0.618402\pi\) |
0.988526 | − | 0.151049i | \(-0.0482650\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.723217 | − | 1.25265i | 0.0290685 | − | 0.0503482i | −0.851125 | − | 0.524963i | \(-0.824079\pi\) |
0.880194 | + | 0.474615i | \(0.157413\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.56615 | − | 3.35186i | 0.0628475 | − | 0.134505i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.99312 | + | 8.64834i | 0.199725 | + | 0.345934i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.9894 | − | 14.2220i | 0.638555 | − | 0.567971i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.3287 | −0.770686 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.0741250 | 0.00295087 | 0.00147544 | − | 0.999999i | \(-0.499530\pi\) | ||||
0.00147544 | + | 0.999999i | \(0.499530\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.9283 | − | 7.93581i | −0.951063 | − | 0.315420i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.9814 | + | 25.9486i | 0.594520 | + | 1.02974i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.2779 | − | 12.1806i | 1.11866 | − | 0.481857i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.5204 | − | 40.7384i | 0.928998 | − | 1.60907i | 0.143996 | − | 0.989578i | \(-0.454005\pi\) |
0.785002 | − | 0.619494i | \(-0.212662\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.8647 | − | 29.2105i | 0.665077 | − | 1.15195i | −0.314187 | − | 0.949361i | \(-0.601732\pi\) |
0.979264 | − | 0.202587i | \(-0.0649348\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.0036 | + | 4.31266i | 0.512018 | + | 0.169811i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.4814 | − | 38.9390i | −0.883836 | − | 1.53085i | −0.847042 | − | 0.531526i | \(-0.821619\pi\) |
−0.0367945 | − | 0.999323i | \(-0.511715\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.6964 | + | 30.6510i | −0.694644 | + | 1.20316i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.8578 | − | 36.1267i | −0.816228 | − | 1.41375i | −0.908443 | − | 0.418010i | \(-0.862728\pi\) |
0.0922143 | − | 0.995739i | \(-0.470606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.83310 | + | 8.37118i | −0.188845 | + | 0.327089i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.9975 | + | 8.94138i | 0.468065 | + | 0.348837i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.5259 | + | 18.2313i | 0.410029 | + | 0.710191i | 0.994892 | − | 0.100941i | \(-0.0321852\pi\) |
−0.584863 | + | 0.811132i | \(0.698852\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.4437 | 0.872958 | 0.436479 | − | 0.899714i | \(-0.356225\pi\) | ||||
0.436479 | + | 0.899714i | \(0.356225\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.764480 | − | 3.70720i | −0.0296899 | − | 0.143976i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.60576 | + | 2.78126i | −0.0621754 | + | 0.107691i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.2236 | + | 10.8725i | −0.472593 | + | 0.420354i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.7225 | + | 30.6962i | −0.684168 | + | 1.18501i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.83929 | + | 10.1140i | 0.225088 | + | 0.389864i | 0.956346 | − | 0.292237i | \(-0.0943996\pi\) |
−0.731258 | + | 0.682101i | \(0.761066\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.9294 | − | 0.947691i | 0.420674 | − | 0.0364766i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.4684 | 0.402335 | 0.201167 | − | 0.979557i | \(-0.435526\pi\) | ||||
0.201167 | + | 0.979557i | \(0.435526\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.4188 | + | 10.4201i | 1.20397 | + | 0.399297i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.4079 | − | 28.4193i | −0.627832 | − | 1.08744i | −0.987986 | − | 0.154543i | \(-0.950609\pi\) |
0.360154 | − | 0.932893i | \(-0.382724\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.0617 | 1.26322 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.8120 | + | 13.1747i | −0.565113 | + | 0.502647i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.46844 | 0.0559431 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.90112 | 0.224489 | 0.112245 | − | 0.993681i | \(-0.464196\pi\) | ||||
0.112245 | + | 0.993681i | \(0.464196\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.07784 | 0.192614 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.5178 | −0.625656 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.95715 | − | 0.649089i | −0.0740263 | − | 0.0245508i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.3782 | −0.467519 | −0.233759 | − | 0.972294i | \(-0.575103\pi\) | ||||
−0.233759 | + | 0.972294i | \(0.575103\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.1483 | − | 29.7018i | −0.646761 | − | 1.12022i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 28.5679 | − | 25.4101i | 1.07593 | − | 0.957000i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.2829 | −0.498850 | −0.249425 | − | 0.968394i | \(-0.580242\pi\) | ||||
−0.249425 | + | 0.968394i | \(0.580242\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.3764 | − | 10.9308i | 0.951688 | − | 0.409937i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.81522 | − | 3.14406i | −0.0679806 | − | 0.117746i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.63664 | − | 2.83474i | 0.0612067 | − | 0.106013i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 39.9210 | + | 13.2398i | 1.49088 | + | 0.494449i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.1847 | − | 21.1045i | 0.454413 | − | 0.787066i | −0.544242 | − | 0.838929i | \(-0.683183\pi\) |
0.998654 | + | 0.0518628i | \(0.0165158\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −35.2126 | − | 11.6783i | −1.30957 | − | 0.434319i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.52290 | −0.353672 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.99450 | + | 13.8469i | 0.296500 | + | 0.513552i | 0.975333 | − | 0.220740i | \(-0.0708473\pi\) |
−0.678833 | + | 0.734293i | \(0.737514\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.27375 | + | 25.3574i | −0.343472 | + | 0.939163i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.54070 | − | 11.3288i | 0.241917 | − | 0.419012i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.1414 | + | 36.6181i | 0.780877 | + | 1.35252i | 0.931431 | + | 0.363917i | \(0.118561\pi\) |
−0.150554 | + | 0.988602i | \(0.548106\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.89307 | + | 17.1353i | −0.364416 | + | 0.631187i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.54325 | + | 2.67299i | 0.0567695 | + | 0.0983276i | 0.893014 | − | 0.450030i | \(-0.148587\pi\) |
−0.836244 | + | 0.548357i | \(0.815253\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.01849 | − | 4.46376i | 0.184359 | − | 0.163980i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.31522 | + | 5.74213i | −0.121624 | + | 0.210658i | −0.920408 | − | 0.390959i | \(-0.872143\pi\) |
0.798784 | + | 0.601617i | \(0.205477\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.88255 | − | 11.9209i | 0.252157 | − | 0.436749i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.1941 | + | 15.7954i | 0.775453 | + | 0.577924i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.3702 | + | 37.0142i | 0.779808 | + | 1.35067i | 0.932052 | + | 0.362325i | \(0.118017\pi\) |
−0.152243 | + | 0.988343i | \(0.548650\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.937489 | + | 4.54618i | 0.0341640 | + | 0.165672i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.0655 | 0.548288 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.0232 | −1.12756 | −0.563779 | − | 0.825926i | \(-0.690653\pi\) | ||||
−0.563779 | + | 0.825926i | \(0.690653\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.616972 | − | 2.99189i | −0.0223947 | − | 0.108599i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.8182 | − | 20.4697i | −0.428409 | − | 0.742025i | 0.568323 | − | 0.822805i | \(-0.307592\pi\) |
−0.996732 | + | 0.0807799i | \(0.974259\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.67123 | + | 14.2346i | −0.0604233 | + | 0.514655i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.55425 | + | 9.62025i | −0.200553 | + | 0.347367i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.73422 | − | 3.00376i | 0.0625375 | − | 0.108318i | −0.833061 | − | 0.553180i | \(-0.813414\pi\) |
0.895599 | + | 0.444862i | \(0.146747\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.3462 | − | 12.7604i | 0.516665 | − | 0.459554i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.2985 | − | 29.9619i | −0.622184 | − | 1.07765i | −0.989078 | − | 0.147392i | \(-0.952912\pi\) |
0.366894 | − | 0.930263i | \(-0.380421\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.38255 | − | 9.32284i | 0.193347 | − | 0.334886i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.6545 | − | 25.3824i | −0.525053 | − | 0.909418i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.7115 | − | 22.0170i | 0.454854 | − | 0.787831i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.92147 | − | 21.2338i | 0.354564 | − | 0.758834i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.44870 | − | 12.9015i | −0.265855 | − | 0.460475i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.1593 | −0.433431 | −0.216715 | − | 0.976235i | \(-0.569534\pi\) | ||||
−0.216715 | + | 0.976235i | \(0.569534\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.0426 | + | 7.31041i | 0.784736 | + | 0.260258i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.56243 | + | 9.63442i | −0.197528 | + | 0.342128i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.27747 | − | 1.75027i | −0.187173 | − | 0.0620758i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.89493 | + | 5.01416i | −0.102544 | + | 0.177611i | −0.912732 | − | 0.408559i | \(-0.866031\pi\) |
0.810188 | + | 0.586170i | \(0.199365\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.2534 | − | 31.6158i | −0.645759 | − | 1.11849i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.37704 | − | 28.7639i | 0.119322 | − | 1.01632i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.3548 | 0.435993 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.29349 | + | 4.70837i | −0.186340 | + | 0.165742i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.5908 | + | 42.5926i | 0.864568 | + | 1.49748i | 0.867476 | + | 0.497479i | \(0.165741\pi\) |
−0.00290803 | + | 0.999996i | \(0.500926\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.7266 | 1.43010 | 0.715052 | − | 0.699072i | \(-0.246403\pi\) | ||||
0.715052 | + | 0.699072i | \(0.246403\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.0672 | + | 3.33880i | 0.353074 | + | 0.117097i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.37822 | 0.118334 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.2115 | 0.812069 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.0938 | 0.526777 | 0.263388 | − | 0.964690i | \(-0.415160\pi\) | ||||
0.263388 | + | 0.964690i | \(0.415160\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0000 | 0.557725 | 0.278862 | − | 0.960331i | \(-0.410043\pi\) | ||||
0.278862 | + | 0.960331i | \(0.410043\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.76833 | − | 6.02018i | 0.235643 | − | 0.209596i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.2348 | 1.22523 | 0.612616 | − | 0.790381i | \(-0.290117\pi\) | ||||
0.612616 | + | 0.790381i | \(0.290117\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.61745 | + | 2.80151i | 0.0561765 | + | 0.0973006i | 0.892746 | − | 0.450560i | \(-0.148776\pi\) |
−0.836570 | + | 0.547861i | \(0.815442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.9177 | + | 8.59562i | 0.899077 | + | 0.298179i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.45606 | −0.154208 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.1799 | + | 21.7148i | 0.524694 | + | 0.750574i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.5197 | + | 26.8808i | 0.535798 | + | 0.928030i | 0.999124 | + | 0.0418419i | \(0.0133226\pi\) |
−0.463326 | + | 0.886188i | \(0.653344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.32760 | − | 7.49563i | 0.149228 | − | 0.258470i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.4226 | − | 24.3914i | 0.944483 | − | 0.840083i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.5339 | + | 18.2453i | −0.362377 | + | 0.627656i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.40545 | − | 11.6648i | −0.0825547 | − | 0.400334i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.89602 | −0.167833 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.03637 | + | 13.9194i | 0.275160 | + | 0.476591i | 0.970176 | − | 0.242403i | \(-0.0779358\pi\) |
−0.695015 | + | 0.718995i | \(0.744602\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −23.3566 | + | 10.0608i | −0.798779 | + | 0.344072i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.61058 | + | 16.6460i | −0.328291 | + | 0.568617i | −0.982173 | − | 0.187980i | \(-0.939806\pi\) |
0.653882 | + | 0.756597i | \(0.273139\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.40112 | + | 12.8191i | 0.252523 | + | 0.437382i | 0.964220 | − | 0.265104i | \(-0.0854064\pi\) |
−0.711697 | + | 0.702487i | \(0.752073\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.38441 | + | 12.7902i | −0.251368 | + | 0.435382i | −0.963903 | − | 0.266255i | \(-0.914214\pi\) |
0.712535 | + | 0.701637i | \(0.247547\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.44437 | − | 7.69787i | −0.151113 | − | 0.261735i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.9585 | − | 4.96099i | −0.508018 | − | 0.168484i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.4072 | − | 19.7579i | 0.386964 | − | 0.670241i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.10507 | + | 5.37815i | −0.105211 | + | 0.182232i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.7865 | + | 15.4917i | 0.703518 | + | 0.524313i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.1916 | − | 45.3651i | −0.884427 | − | 1.53187i | −0.846369 | − | 0.532597i | \(-0.821216\pi\) |
−0.0380575 | − | 0.999276i | \(-0.512117\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −45.2211 | − | 14.9976i | −1.52527 | − | 0.505855i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.3214 | −1.05525 | −0.527623 | − | 0.849479i | \(-0.676916\pi\) | ||||
−0.527623 | + | 0.849479i | \(0.676916\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.0494 | −1.44873 | −0.724363 | − | 0.689419i | \(-0.757866\pi\) | ||||
−0.724363 | + | 0.689419i | \(0.757866\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 31.4283 | − | 27.9543i | 1.05645 | − | 0.939673i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.48831 | + | 12.9701i | 0.251433 | + | 0.435494i | 0.963921 | − | 0.266190i | \(-0.0857649\pi\) |
−0.712488 | + | 0.701685i | \(0.752432\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.37195 | + | 21.3639i | 0.213468 | + | 0.715718i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32.3887 | − | 56.0988i | 1.08385 | − | 1.87727i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.04944 | + | 7.01384i | −0.135358 | + | 0.234447i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.193645 | − | 0.939046i | −0.00646562 | − | 0.0313538i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.4993 | − | 19.9174i | −0.383524 | − | 0.664282i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.65452 | + | 4.59776i | −0.0884348 | + | 0.153174i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.86467 | − | 15.3541i | −0.294671 | − | 0.510386i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.2280 | + | 26.3756i | −0.505636 | + | 0.875787i | 0.494343 | + | 0.869267i | \(0.335409\pi\) |
−0.999979 | + | 0.00652002i | \(0.997925\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.843624 | − | 7.18555i | 0.0279812 | − | 0.238330i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.97593 | + | 17.2788i | 0.330517 | + | 0.572473i | 0.982613 | − | 0.185664i | \(-0.0594435\pi\) |
−0.652096 | + | 0.758136i | \(0.726110\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.8255 | 0.722317 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.4746 | − | 27.9954i | 1.04052 | − | 0.925501i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.8145 | + | 39.5159i | −0.752582 | + | 1.30351i | 0.193985 | + | 0.981004i | \(0.437859\pi\) |
−0.946567 | + | 0.322506i | \(0.895475\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.52723 | + | 36.5019i | 0.248031 | + | 1.20278i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.98969 | − | 6.91034i | 0.131322 | − | 0.227457i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.25890 | − | 12.5728i | −0.238671 | − | 0.413391i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.4247 | − | 7.76926i | −0.342392 | − | 0.255176i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.3722 | 1.84951 | 0.924755 | − | 0.380562i | \(-0.124270\pi\) | ||||
0.924755 | + | 0.380562i | \(0.124270\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.43151 | − | 31.1884i | −0.210558 | − | 1.02106i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.91714 | + | 10.2488i | 0.193511 | + | 0.335171i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.8530 | −1.20393 | −0.601967 | − | 0.798521i | \(-0.705616\pi\) | ||||
−0.601967 | + | 0.798521i | \(0.705616\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.000481840 | 0.00233659i | 1.57243e−5 | 7.62519e-5i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.76000 | −0.285568 | −0.142784 | − | 0.989754i | \(-0.545605\pi\) | ||||
−0.142784 | + | 0.989754i | \(0.545605\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.18401 | −0.136250 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.6452 | 0.865852 | 0.432926 | − | 0.901430i | \(-0.357481\pi\) | ||||
0.432926 | + | 0.901430i | \(0.357481\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.87773 | 0.125877 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.93199 | − | 23.9168i | −0.159931 | − | 0.775554i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.3039 | 0.787282 | 0.393641 | − | 0.919264i | \(-0.371215\pi\) | ||||
0.393641 | + | 0.919264i | \(0.371215\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.3207 | + | 19.6081i | 0.366330 | + | 0.634502i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.90848 | − | 18.9534i | −0.126343 | − | 0.612677i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.00138 | −0.161335 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.71565 | − | 57.2004i | 0.216409 | − | 1.84326i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.4425 | − | 21.5511i | −0.400539 | − | 0.693753i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.22872 | − | 9.05641i | 0.168144 | − | 0.291234i | −0.769623 | − | 0.638498i | \(-0.779556\pi\) |
0.937767 | + | 0.347264i | \(0.112889\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.90428 | + | 23.7824i | 0.157548 | + | 0.764000i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.8578 | − | 36.1267i | 0.669358 | − | 1.15936i | −0.308726 | − | 0.951151i | \(-0.599902\pi\) |
0.978084 | − | 0.208211i | \(-0.0667642\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.12433 | − | 1.88951i | 0.0680331 | − | 0.0605129i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.89011 | 0.188441 | 0.0942207 | − | 0.995551i | \(-0.469964\pi\) | ||||
0.0942207 | + | 0.995551i | \(0.469964\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.9567 | − | 20.7097i | −0.382139 | − | 0.661885i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.6141 | + | 33.9950i | 1.45635 | + | 1.08538i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.9196 | + | 36.2338i | −0.667232 | + | 1.15568i | 0.311443 | + | 0.950265i | \(0.399188\pi\) |
−0.978675 | + | 0.205415i | \(0.934146\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.7095 | − | 27.2096i | −0.500545 | − | 0.866969i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.65678 | − | 2.86963i | 0.0526826 | − | 0.0912489i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.3578 | + | 47.3851i | 0.869049 | + | 1.50524i | 0.862970 | + | 0.505255i | \(0.168602\pi\) |
0.00607865 | + | 0.999982i | \(0.498065\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.88441 | − | 23.6860i | −0.155002 | − | 0.751653i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.0698 | − | 34.7619i | 0.636255 | − | 1.10203i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.02476 | − | 15.6313i | 0.285817 | − | 0.495050i | −0.686990 | − | 0.726667i | \(-0.741068\pi\) |
0.972807 | + | 0.231617i | \(0.0744017\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 35.5970 | − | 3.08661i | 1.12624 | − | 0.0976561i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))