Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3420,2,Mod(1189,3420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3420, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3420.1189");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3420.bj (of order \(6\), degree \(2\), 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: | \(27.3088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1189.5 | ||
Character | \(\chi\) | \(=\) | 3420.1189 |
Dual form | 3420.2.bj.e.2629.5 |
$q$-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 \(\left(\mathbb{Z}/3420\mathbb{Z}\right)^\times\).
\(n\) | \(1711\) | \(1901\) | \(2737\) | \(3061\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.42631 | + | 1.72210i | −0.637866 | + | 0.770148i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.19629i | 0.830120i | 0.909794 | + | 0.415060i | \(0.136239\pi\) | ||||
−0.909794 | + | 0.415060i | \(0.863761\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.851781 | 0.256821 | 0.128411 | − | 0.991721i | \(-0.459012\pi\) | ||||
0.128411 | + | 0.991721i | \(0.459012\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.197307 | − | 0.113916i | 0.0547233 | − | 0.0315945i | −0.472389 | − | 0.881390i | \(-0.656608\pi\) |
0.527112 | + | 0.849796i | \(0.323275\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.57835 | + | 3.79801i | 1.59548 | + | 0.921153i | 0.992342 | + | 0.123519i | \(0.0394181\pi\) |
0.603142 | + | 0.797634i | \(0.293915\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.93036 | + | 1.88474i | 0.901687 | + | 0.432389i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.46423 | − | 0.845372i | 0.305313 | − | 0.176272i | −0.339514 | − | 0.940601i | \(-0.610263\pi\) |
0.644827 | + | 0.764329i | \(0.276929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.931273 | − | 4.91251i | −0.186255 | − | 0.982502i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.798103 | + | 1.38236i | 0.148204 | + | 0.256697i | 0.930564 | − | 0.366130i | \(-0.119317\pi\) |
−0.782360 | + | 0.622827i | \(0.785984\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.76406 | 1.03526 | 0.517628 | − | 0.855606i | \(-0.326815\pi\) | ||||
0.517628 | + | 0.855606i | \(0.326815\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.78224 | − | 3.13259i | −0.639315 | − | 0.529505i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.94456i | − | 1.47048i | −0.677809 | − | 0.735238i | \(-0.737070\pi\) | ||
0.677809 | − | 0.735238i | \(-0.262930\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.54377 | + | 6.13800i | −0.553445 | + | 0.958594i | 0.444578 | + | 0.895740i | \(0.353354\pi\) |
−0.998023 | + | 0.0628541i | \(0.979980\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.55871 | − | 3.78668i | −1.00019 | − | 0.577463i | −0.0918887 | − | 0.995769i | \(-0.529290\pi\) |
−0.908306 | + | 0.418307i | \(0.862624\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.06032 | − | 2.92158i | 0.738124 | − | 0.426156i | −0.0832628 | − | 0.996528i | \(-0.526534\pi\) |
0.821387 | + | 0.570372i | \(0.193201\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.17631 | 0.310901 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.14208 | + | 2.39143i | −0.568959 | + | 0.328488i | −0.756733 | − | 0.653724i | \(-0.773206\pi\) |
0.187775 | + | 0.982212i | \(0.439873\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.21490 | + | 1.46685i | −0.163818 | + | 0.197790i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.33889 | + | 9.24723i | −0.695065 | + | 1.20389i | 0.275094 | + | 0.961417i | \(0.411291\pi\) |
−0.970159 | + | 0.242470i | \(0.922042\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.17130 | − | 2.02874i | −0.149969 | − | 0.259754i | 0.781247 | − | 0.624222i | \(-0.214584\pi\) |
−0.931216 | + | 0.364468i | \(0.881251\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0852477 | + | 0.502263i | −0.0105737 | + | 0.0622980i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.70127 | − | 2.13693i | 0.452182 | − | 0.261067i | −0.256569 | − | 0.966526i | \(-0.582592\pi\) |
0.708751 | + | 0.705459i | \(0.249259\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.14788 | + | 5.45228i | −0.373584 | + | 0.647067i | −0.990114 | − | 0.140265i | \(-0.955205\pi\) |
0.616530 | + | 0.787332i | \(0.288538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.74621 | + | 4.47228i | 0.906626 | + | 0.523441i | 0.879344 | − | 0.476187i | \(-0.157982\pi\) |
0.0272818 | + | 0.999628i | \(0.491315\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.87076i | 0.213193i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.332949 | + | 0.576685i | −0.0374597 | + | 0.0648822i | −0.884147 | − | 0.467208i | \(-0.845260\pi\) |
0.846688 | + | 0.532090i | \(0.178593\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.71844i | 0.956973i | 0.878095 | + | 0.478487i | \(0.158814\pi\) | ||||
−0.878095 | + | 0.478487i | \(0.841186\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.9233 | + | 5.91144i | −1.72713 | + | 0.641186i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.33889 | + | 9.24723i | 0.565922 | + | 0.980205i | 0.996963 | + | 0.0778729i | \(0.0248128\pi\) |
−0.431042 | + | 0.902332i | \(0.641854\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.250192 | + | 0.433345i | 0.0262272 | + | 0.0454268i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.85164 | + | 4.08026i | −0.908159 | + | 0.418626i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.06614 | + | 4.65699i | 0.818993 | + | 0.472846i | 0.850069 | − | 0.526671i | \(-0.176560\pi\) |
−0.0310763 | + | 0.999517i | \(0.509893\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.03264 | + | 5.25268i | 0.301759 | + | 0.522661i | 0.976534 | − | 0.215362i | \(-0.0690930\pi\) |
−0.674776 | + | 0.738023i | \(0.735760\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.2756i | 1.01248i | 0.862391 | + | 0.506242i | \(0.168966\pi\) | ||||
−0.862391 | + | 0.506242i | \(0.831034\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.21742i | − | 0.601061i | −0.953772 | − | 0.300531i | \(-0.902836\pi\) | ||
0.953772 | − | 0.300531i | \(-0.0971637\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.75405 | + | 3.03811i | −0.168008 | + | 0.290998i | −0.937719 | − | 0.347394i | \(-0.887067\pi\) |
0.769711 | + | 0.638392i | \(0.220400\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 17.9659i | − | 1.69009i | −0.534698 | − | 0.845043i | \(-0.679575\pi\) | ||
0.534698 | − | 0.845043i | \(-0.320425\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.632627 | + | 3.72731i | −0.0589927 | + | 0.347574i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.34154 | + | 14.4480i | −0.764667 | + | 1.32444i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2745 | −0.934043 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.78813 | + | 5.40302i | 0.875477 | + | 0.483261i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.6002 | − | 7.27472i | 1.11809 | − | 0.645527i | 0.177175 | − | 0.984179i | \(-0.443304\pi\) |
0.940912 | + | 0.338652i | \(0.109971\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.18051 | + | 10.7050i | −0.539994 | + | 0.935297i | 0.458910 | + | 0.888483i | \(0.348240\pi\) |
−0.998904 | + | 0.0468142i | \(0.985093\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.13943 | + | 8.63222i | −0.358935 | + | 0.748508i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.5283 | + | 7.23324i | −1.07037 | + | 0.617978i | −0.928282 | − | 0.371877i | \(-0.878714\pi\) |
−0.142086 | + | 0.989854i | \(0.545381\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.71963 | + | 2.97849i | 0.145857 | + | 0.252632i | 0.929692 | − | 0.368337i | \(-0.120073\pi\) |
−0.783835 | + | 0.620969i | \(0.786739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.168063 | − | 0.0970310i | 0.0140541 | − | 0.00811414i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.51890 | − | 0.597254i | −0.292229 | − | 0.0495992i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.0236837 | − | 0.0410214i | 0.00194025 | − | 0.00336060i | −0.865054 | − | 0.501679i | \(-0.832716\pi\) |
0.866994 | + | 0.498319i | \(0.166049\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.94886 | −0.809627 | −0.404813 | − | 0.914399i | \(-0.632664\pi\) | ||||
−0.404813 | + | 0.914399i | \(0.632664\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.22134 | + | 9.92630i | −0.660354 | + | 0.797300i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.6549 | − | 9.03839i | −1.24940 | − | 0.721342i | −0.278411 | − | 0.960462i | \(-0.589808\pi\) |
−0.970990 | + | 0.239120i | \(0.923141\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.85668 | + | 3.21587i | 0.146327 | + | 0.253446i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14.2125i | − | 1.11321i | −0.830777 | − | 0.556605i | \(-0.812104\pi\) | ||
0.830777 | − | 0.556605i | \(-0.187896\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.18567 | + | 1.26190i | −0.169132 | + | 0.0976484i | −0.582177 | − | 0.813062i | \(-0.697799\pi\) |
0.413044 | + | 0.910711i | \(0.364465\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.47405 | + | 11.2134i | −0.498004 | + | 0.862567i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.8605 | + | 6.84768i | 0.901740 | + | 0.520620i | 0.877764 | − | 0.479093i | \(-0.159034\pi\) |
0.0239756 | + | 0.999713i | \(0.492368\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.7893 | − | 2.04535i | 0.815594 | − | 0.154614i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.76670 | −0.132050 | −0.0660248 | − | 0.997818i | \(-0.521032\pi\) | ||||
−0.0660248 | + | 0.997818i | \(0.521032\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.34722 | − | 9.26166i | −0.397456 | − | 0.688414i | 0.595955 | − | 0.803018i | \(-0.296774\pi\) |
−0.993411 | + | 0.114604i | \(0.963440\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.4034 | + | 12.7577i | 1.13248 | + | 0.937966i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.60331 | + | 3.23507i | 0.409755 | + | 0.236572i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.2844 | −1.10594 | −0.552971 | − | 0.833201i | \(-0.686506\pi\) | ||||
−0.552971 | + | 0.833201i | \(0.686506\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.60192 | + | 0.924867i | 0.115309 | + | 0.0665734i | 0.556545 | − | 0.830817i | \(-0.312127\pi\) |
−0.441237 | + | 0.897391i | \(0.645460\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.71391i | − | 0.549594i | −0.961502 | − | 0.274797i | \(-0.911389\pi\) | ||
0.961502 | − | 0.274797i | \(-0.0886106\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.35147 | + | 9.26901i | 0.379355 | + | 0.657063i | 0.990969 | − | 0.134094i | \(-0.0428124\pi\) |
−0.611613 | + | 0.791157i | \(0.709479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.03605 | + | 1.75287i | −0.213089 | + | 0.123027i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.51573 | − | 14.8574i | −0.385236 | − | 1.03769i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.34781 | + | 1.60538i | 0.231573 | + | 0.111047i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.47981 | + | 14.6875i | −0.583774 | + | 1.01113i | 0.411253 | + | 0.911521i | \(0.365091\pi\) |
−0.995027 | + | 0.0996050i | \(0.968242\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.8758 | − | 5.89380i | 1.08272 | − | 0.401954i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.6595i | 0.859386i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.73061 | 0.116413 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.9444 | − | 13.8243i | −1.60344 | − | 0.925745i | −0.990793 | − | 0.135386i | \(-0.956773\pi\) |
−0.612644 | − | 0.790359i | \(-0.709894\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.45083i | 0.428157i | 0.976816 | + | 0.214078i | \(0.0686748\pi\) | ||||
−0.976816 | + | 0.214078i | \(0.931325\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.1452 | 1.13299 | 0.566494 | − | 0.824066i | \(-0.308299\pi\) | ||||
0.566494 | + | 0.824066i | \(0.308299\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.457945 | − | 0.264395i | −0.0300010 | − | 0.0173211i | 0.484924 | − | 0.874556i | \(-0.338847\pi\) |
−0.514925 | + | 0.857235i | \(0.672180\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.18634 | + | 12.8815i | −0.142621 | + | 0.840295i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.81671 | −0.440936 | −0.220468 | − | 0.975394i | \(-0.570758\pi\) | ||||
−0.220468 | + | 0.975394i | \(0.570758\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.93999 | − | 15.4845i | −0.575875 | − | 0.997445i | −0.995946 | − | 0.0899536i | \(-0.971328\pi\) |
0.420071 | − | 0.907491i | \(-0.362005\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.10409 | + | 3.74783i | −0.198313 | + | 0.239440i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.990191 | − | 0.0758562i | 0.0630044 | − | 0.00482662i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.21999 | + | 14.2374i | 0.518841 | + | 0.898659i | 0.999760 | + | 0.0218940i | \(0.00696963\pi\) |
−0.480919 | + | 0.876765i | \(0.659697\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.24720 | − | 0.720072i | 0.0784108 | − | 0.0452705i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.57011 | + | 4.37061i | −0.472211 | + | 0.272631i | −0.717165 | − | 0.696904i | \(-0.754560\pi\) |
0.244954 | + | 0.969535i | \(0.421227\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.6448 | 1.22067 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.0332 | + | 10.9888i | 1.17364 | + | 0.677599i | 0.954534 | − | 0.298103i | \(-0.0963540\pi\) |
0.219102 | + | 0.975702i | \(0.429687\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.78961 | − | 10.5440i | 0.109935 | − | 0.647714i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.17878 | + | 5.50580i | −0.193813 | + | 0.335695i | −0.946511 | − | 0.322672i | \(-0.895419\pi\) |
0.752697 | + | 0.658367i | \(0.228752\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.39590 | − | 12.8101i | 0.449269 | − | 0.778156i | −0.549070 | − | 0.835776i | \(-0.685018\pi\) |
0.998339 | + | 0.0576202i | \(0.0183512\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.793240 | − | 4.18438i | −0.0478342 | − | 0.252328i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.26106i | 0.496359i | 0.968714 | + | 0.248180i | \(0.0798323\pi\) | ||||
−0.968714 | + | 0.248180i | \(0.920168\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.4531 | + | 19.8374i | 0.683235 | + | 1.18340i | 0.973988 | + | 0.226600i | \(0.0727610\pi\) |
−0.290753 | + | 0.956798i | \(0.593906\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.9233 | + | 14.9668i | 1.54098 | + | 0.889684i | 0.998777 | + | 0.0494347i | \(0.0157420\pi\) |
0.542200 | + | 0.840249i | \(0.317591\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.4808 | − | 7.78316i | −0.795748 | − | 0.459425i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.3498 | + | 35.2469i | 1.19705 | + | 2.07335i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 22.4761i | − | 1.31307i | −0.754296 | − | 0.656534i | \(-0.772022\pi\) | ||
0.754296 | − | 0.656534i | \(-0.227978\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.30976 | − | 22.3836i | −0.483813 | − | 1.30322i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.192602 | − | 0.333597i | 0.0111385 | − | 0.0192924i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.31664 | − | 14.4048i | 0.479363 | − | 0.830281i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.16434 | + | 0.876529i | 0.295709 | + | 0.0501899i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.6663 | − | 11.9317i | −1.17949 | − | 0.680979i | −0.223593 | − | 0.974682i | \(-0.571779\pi\) |
−0.955897 | + | 0.293704i | \(0.905112\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.5315 | −0.710598 | −0.355299 | − | 0.934753i | \(-0.615621\pi\) | ||||
−0.355299 | + | 0.934753i | \(0.615621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.44426 | − | 1.98854i | 0.194681 | − | 0.112399i | −0.399491 | − | 0.916737i | \(-0.630813\pi\) |
0.594172 | + | 0.804338i | \(0.297480\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.1149 | − | 10.4587i | 1.01744 | − | 0.587417i | 0.104076 | − | 0.994569i | \(-0.466812\pi\) |
0.913360 | + | 0.407153i | \(0.133478\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.679809 | + | 1.17746i | 0.0380620 | + | 0.0659253i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.6970 | + | 27.3260i | 1.04033 | + | 1.52046i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.743358 | − | 0.863188i | −0.0412341 | − | 0.0478811i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.41663 | + | 11.1139i | 0.353761 | + | 0.612731i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.5367 | −0.744042 | −0.372021 | − | 0.928224i | \(-0.621335\pi\) | ||||
−0.372021 | + | 0.928224i | \(0.621335\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.59915 | + | 9.42189i | −0.0873709 | + | 0.514773i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.3929 | + | 6.57769i | 0.620610 | + | 0.358310i | 0.777107 | − | 0.629369i | \(-0.216687\pi\) |
−0.156496 | + | 0.987679i | \(0.550020\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.90971 | 0.265876 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1538i | 1.08820i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.21363 | − | 0.700688i | −0.0651509 | − | 0.0376149i | 0.467071 | − | 0.884220i | \(-0.345309\pi\) |
−0.532222 | + | 0.846605i | \(0.678643\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.4686 | 0.613899 | 0.306949 | − | 0.951726i | \(-0.400692\pi\) | ||||
0.306949 | + | 0.951726i | \(0.400692\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.17971i | 0.275688i | 0.990454 | + | 0.137844i | \(0.0440173\pi\) | ||||
−0.990454 | + | 0.137844i | \(0.955983\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.89954 | − | 13.1976i | −0.260040 | − | 0.700457i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.29572 | − | 2.24425i | 0.0683853 | − | 0.118447i | −0.829805 | − | 0.558053i | \(-0.811549\pi\) |
0.898191 | + | 0.439606i | \(0.144882\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.8955 | + | 14.8154i | 0.626080 | + | 0.779759i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.7502 | + | 6.96091i | −0.981432 | + | 0.364351i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.3728 | + | 6.56609i | −0.593655 | + | 0.342747i | −0.766541 | − | 0.642195i | \(-0.778024\pi\) |
0.172886 | + | 0.984942i | \(0.444691\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.25228 | − | 9.09721i | −0.272685 | − | 0.472304i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 28.8123i | − | 1.49184i | −0.666035 | − | 0.745921i | \(-0.732010\pi\) | ||
0.666035 | − | 0.745921i | \(-0.267990\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.314944 | + | 0.181833i | 0.0162204 | + | 0.00936486i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.2519 | 1.29710 | 0.648551 | − | 0.761171i | \(-0.275375\pi\) | ||||
0.648551 | + | 0.761171i | \(0.275375\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.4782 | − | 10.6684i | −0.944190 | − | 0.545128i | −0.0529189 | − | 0.998599i | \(-0.516852\pi\) |
−0.891271 | + | 0.453470i | \(0.850186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.22164 | − | 2.66828i | −0.164190 | − | 0.135988i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.2358 | − | 26.3892i | −0.772486 | − | 1.33799i | −0.936196 | − | 0.351477i | \(-0.885680\pi\) |
0.163710 | − | 0.986508i | \(-0.447654\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.8429 | 0.649495 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.518222 | − | 1.39591i | −0.0260746 | − | 0.0702356i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.28442 | − | 2.47361i | −0.215029 | − | 0.124147i | 0.388617 | − | 0.921399i | \(-0.372953\pi\) |
−0.603646 | + | 0.797252i | \(0.706286\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.4584 | − | 26.7747i | 0.771956 | − | 1.33707i | −0.164533 | − | 0.986371i | \(-0.552612\pi\) |
0.936490 | − | 0.350696i | \(-0.114055\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.13729 | − | 0.656616i | 0.0566526 | − | 0.0327084i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7.61880i | − | 0.377650i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.31244 | + | 4.00526i | 0.114343 | + | 0.198047i | 0.917517 | − | 0.397697i | \(-0.130191\pi\) |
−0.803174 | + | 0.595744i | \(0.796857\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.3096 | − | 11.7258i | −0.999371 | − | 0.576987i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.0140 | − | 12.4352i | −0.737011 | − | 0.610420i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.8070 | −1.30961 | −0.654803 | − | 0.755800i | \(-0.727248\pi\) | ||||
−0.654803 | + | 0.755800i | \(0.727248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.1453 | − | 19.3043i | 0.543191 | − | 0.940834i | −0.455528 | − | 0.890222i | \(-0.650549\pi\) |
0.998718 | − | 0.0506123i | \(-0.0161173\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.5315 | − | 35.8532i | 0.607868 | − | 1.73913i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.45571 | − | 2.57251i | 0.215627 | − | 0.124492i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.5079 | − | 25.1283i | −0.698819 | − | 1.21039i | −0.968876 | − | 0.247545i | \(-0.920376\pi\) |
0.270058 | − | 0.962844i | \(-0.412957\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.47132 | − | 3.73622i | 0.310992 | − | 0.179551i | −0.336379 | − | 0.941727i | \(-0.609202\pi\) |
0.647370 | + | 0.762176i | \(0.275869\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.34825 | − | 0.562932i | 0.351515 | − | 0.0269287i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.7675 | + | 18.6499i | −0.513907 | + | 0.890112i | 0.485963 | + | 0.873979i | \(0.338469\pi\) |
−0.999870 | + | 0.0161330i | \(0.994864\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.4833 | + | 17.0222i | −1.40079 | + | 0.808748i | −0.994474 | − | 0.104983i | \(-0.966521\pi\) |
−0.406319 | + | 0.913731i | \(0.633188\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.5396 | − | 3.99531i | −1.11588 | − | 0.189396i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.9505 | 1.74380 | 0.871901 | − | 0.489682i | \(-0.162887\pi\) | ||||
0.871901 | + | 0.489682i | \(0.162887\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.01852 | + | 5.22823i | −0.142136 | + | 0.246188i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.10311 | − | 0.187229i | −0.0517148 | − | 0.00877741i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 30.3030i | − | 1.41752i | −0.705452 | − | 0.708758i | \(-0.749256\pi\) | ||
0.705452 | − | 0.708758i | \(-0.250744\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.18504 | − | 10.7128i | 0.288066 | − | 0.498945i | −0.685282 | − | 0.728278i | \(-0.740321\pi\) |
0.973348 | + | 0.229333i | \(0.0736545\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.3893i | − | 1.17994i | −0.807425 | − | 0.589971i | \(-0.799139\pi\) | ||
0.807425 | − | 0.589971i | \(-0.200861\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.5919i | 1.32307i | 0.749912 | + | 0.661537i | \(0.230096\pi\) | ||||
−0.749912 | + | 0.661537i | \(0.769904\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.69331 | + | 8.12906i | 0.216717 | + | 0.375365i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.58659 | − | 3.22542i | −0.256871 | − | 0.148305i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.59856 | − | 21.0631i | 0.256879 | − | 0.966443i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.22157 | + | 10.7761i | 0.284271 | + | 0.492372i | 0.972432 | − | 0.233186i | \(-0.0749152\pi\) |
−0.688161 | + | 0.725558i | \(0.741582\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.01892 | − | 1.76483i | −0.0464589 | − | 0.0804692i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.5246 | + | 7.24841i | −0.886568 | + | 0.329133i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.2489i | 0.826937i | 0.910518 | + | 0.413469i | \(0.135683\pi\) | ||||
−0.910518 | + | 0.413469i | \(0.864317\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.23347 | + | 15.9928i | −0.416701 | + | 0.721747i | −0.995605 | − | 0.0936485i | \(-0.970147\pi\) |
0.578905 | + | 0.815395i | \(0.303480\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.1248i | 0.546075i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.9748 | − | 6.91365i | −0.537143 | − | 0.310120i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.746715 | − | 1.29335i | 0.0334276 | − | 0.0578982i | −0.848828 | − | 0.528670i | \(-0.822691\pi\) |
0.882255 | + | 0.470771i | \(0.156024\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.34173 | − | 5.39345i | 0.416527 | − | 0.240482i | −0.277063 | − | 0.960852i | \(-0.589361\pi\) |
0.693590 | + | 0.720370i | \(0.256028\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.3711 | − | 2.26945i | −0.595008 | − | 0.100989i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.28888 | − | 3.96446i | −0.101453 | − | 0.175722i | 0.810831 | − | 0.585281i | \(-0.199016\pi\) |
−0.912283 | + | 0.409559i | \(0.865682\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.82242 | + | 17.0129i | −0.434518 | + | 0.752608i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.6956 | − | 14.6562i | −0.779762 | − | 0.645829i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.31028 | − | 2.48854i | 0.189566 | − | 0.109446i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.1613 | 1.27758 | 0.638791 | − | 0.769380i | \(-0.279435\pi\) | ||||
0.638791 | + | 0.769380i | \(0.279435\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.7312 | + | 16.0106i | −1.21260 | + | 0.700097i | −0.963325 | − | 0.268336i | \(-0.913526\pi\) |
−0.249277 | + | 0.968432i | \(0.580193\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 37.9180 | + | 21.8920i | 1.65173 | + | 0.953629i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.0707 | + | 17.4430i | −0.437856 | + | 0.758389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.61476i | 0.0699432i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.7070 | + | 8.86798i | 0.462906 | + | 0.383396i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.85374 | 0.0798462 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.36073 | − | 9.28505i | −0.230476 | − | 0.399196i | 0.727473 | − | 0.686137i | \(-0.240695\pi\) |
−0.957948 | + | 0.286941i | \(0.907362\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.73011 | − | 7.35395i | −0.116945 | − | 0.315009i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.7394 | + | 8.50982i | −0.630213 | + | 0.363854i | −0.780835 | − | 0.624738i | \(-0.785206\pi\) |
0.150622 | + | 0.988591i | \(0.451873\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.531456 | + | 6.93738i | 0.0226408 | + | 0.295542i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.26657 | − | 0.731253i | −0.0538600 | − | 0.0310961i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.3042 | − | 11.1453i | 0.817946 | − | 0.472241i | −0.0317616 | − | 0.999495i | \(-0.510112\pi\) |
0.849708 | + | 0.527254i | \(0.176778\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.72544 | −0.0729785 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 45.7030i | − | 1.92615i | −0.269234 | − | 0.963075i | \(-0.586770\pi\) | ||
0.269234 | − | 0.963075i | \(-0.413230\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.9391 | + | 25.6249i | 1.30162 | + | 1.07805i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.2807 | 0.514835 | 0.257417 | − | 0.966300i | \(-0.417128\pi\) | ||||
0.257417 | + | 0.966300i | \(0.417128\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.5574 | −0.692907 | −0.346453 | − | 0.938067i | \(-0.612614\pi\) | ||||
−0.346453 | + | 0.938067i | \(0.612614\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.51649 | − | 6.40576i | −0.230054 | − | 0.267139i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.0257i | 1.20836i | 0.796849 | + | 0.604179i | \(0.206499\pi\) | ||||
−0.796849 | + | 0.604179i | \(0.793501\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.1482 | −0.794402 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.52814 | + | 2.03698i | −0.146121 | + | 0.0843629i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.69083 | + | 5.01765i | 0.358709 | + | 0.207101i | 0.668514 | − | 0.743699i | \(-0.266931\pi\) |
−0.309805 | + | 0.950800i | \(0.600264\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.6548 | + | 10.8637i | 0.933477 | + | 0.447633i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.2446 | − | 7.64676i | 0.543890 | − | 0.314015i | −0.202764 | − | 0.979228i | \(-0.564993\pi\) |
0.746654 | + | 0.665213i | \(0.231659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.9832 | − | 34.9723i | −0.532261 | − | 1.43372i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.0303 | − | 22.5691i | −0.532402 | − | 0.922147i | −0.999284 | − | 0.0378276i | \(-0.987956\pi\) |
0.466883 | − | 0.884319i | \(-0.345377\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.7129 | 0.640942 | 0.320471 | − | 0.947258i | \(-0.396159\pi\) | ||||
0.320471 | + | 0.947258i | \(0.396159\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.6546 | − | 17.6937i | 0.595794 | − | 0.719351i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.1236i | 1.06032i | 0.847896 | + | 0.530162i | \(0.177869\pi\) | ||||
−0.847896 | + | 0.530162i | \(0.822131\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.665626 | − | 1.15290i | 0.0269284 | − | 0.0466413i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.1549 | + | 19.1420i | 1.33912 | + | 0.773139i | 0.986676 | − | 0.162696i | \(-0.0520190\pi\) |
0.352439 | + | 0.935835i | \(0.385352\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.0154 | + | 8.66916i | −0.604498 | + | 0.349007i | −0.770809 | − | 0.637066i | \(-0.780148\pi\) |
0.166311 | + | 0.986073i | \(0.446814\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.1118 | 1.29068 | 0.645342 | − | 0.763894i | \(-0.276715\pi\) | ||||
0.645342 | + | 0.763894i | \(0.276715\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20.3096 | + | 11.7258i | −0.813687 | + | 0.469783i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.2655 | + | 9.14977i | −0.930618 | + | 0.365991i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.9715 | − | 58.8404i | 1.35453 | − | 2.34612i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.172064 | + | 0.298024i | 0.00684978 | + | 0.0118642i | 0.869430 | − | 0.494056i | \(-0.164486\pi\) |
−0.862580 | + | 0.505920i | \(0.831153\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.44398 | + | 32.0748i | −0.216038 | + | 1.27285i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.429402 | − | 0.247915i | 0.0170135 | − | 0.00982277i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.6410 | − | 27.0909i | 0.617781 | − | 1.07003i | −0.372109 | − | 0.928189i | \(-0.621365\pi\) |
0.989890 | − | 0.141839i | \(-0.0453015\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.11932 | − | 2.95564i | −0.201886 | − | 0.116559i | 0.395649 | − | 0.918402i | \(-0.370520\pi\) |
−0.597535 | + | 0.801843i | \(0.703853\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 19.1643i | − | 0.753425i | −0.926330 | − | 0.376712i | \(-0.877055\pi\) | ||
0.926330 | − | 0.376712i | \(-0.122945\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.54757 | + | 7.87661i | −0.178508 | + | 0.309184i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.5209i | 1.66397i | 0.554799 | + | 0.831985i | \(0.312795\pi\) | ||||
−0.554799 | + | 0.831985i | \(0.687205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.61971 | − | 25.9121i | −0.375873 | − | 1.01247i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.4989 | − | 32.0411i | −0.720616 | − | 1.24814i | −0.960753 | − | 0.277405i | \(-0.910526\pi\) |
0.240137 | − | 0.970739i | \(-0.422808\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.1793 | − | 19.3631i | −0.434824 | − | 0.753137i | 0.562457 | − | 0.826826i | \(-0.309856\pi\) |
−0.997281 | + | 0.0736893i | \(0.976523\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.96144 | − | 19.4408i | −0.347510 | − | 0.753880i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.33721 | + | 1.34939i | 0.0904971 | + | 0.0522485i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.997687 | − | 1.72804i | −0.0385153 | − | 0.0667104i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.94723i | − | 0.190702i | −0.995444 | − | 0.0953508i | \(-0.969603\pi\) | ||
0.995444 | − | 0.0953508i | \(-0.0303973\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.58590i | 0.176250i | 0.996109 | + | 0.0881252i | \(0.0280875\pi\) | ||||
−0.996109 | + | 0.0881252i | \(0.971912\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.2281 | + | 17.7156i | −0.392518 | + | 0.679862i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 26.4117i | − | 1.01062i | −0.862939 | − | 0.505308i | \(-0.831379\pi\) | ||
0.862939 | − | 0.505308i | \(-0.168621\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.41293 | − | 31.8919i | 0.206817 | − | 1.21853i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.544843 | + | 0.943695i | −0.0207568 | + | 0.0359519i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.1599 | −1.64188 | −0.820939 | − | 0.571016i | \(-0.806550\pi\) | ||||
−0.820939 | + | 0.571016i | \(0.806550\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.58199 | − | 1.28687i | −0.287601 | − | 0.0488137i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −46.6244 | + | 26.9186i | −1.76602 | + | 1.01961i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.5715 | − | 23.5065i | 0.512588 | − | 0.887829i | −0.487305 | − | 0.873232i | \(-0.662020\pi\) |
0.999893 | − | 0.0145974i | \(-0.00464665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.8582 | − | 35.1554i | 0.635818 | − | 1.32591i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.5364 | + | 6.66055i | −0.433871 | + | 0.250496i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.3352 | + | 17.9011i | 0.388146 | + | 0.672288i | 0.992200 | − | 0.124655i | \(-0.0397824\pi\) |
−0.604054 | + | 0.796943i | \(0.706449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.43989 | − | 4.87277i | 0.316076 | − | 0.182487i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0726123 | + | 0.427818i | −0.00271555 | + | 0.0159995i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.5398 | − | 26.9157i | 0.579537 | − | 1.00379i | −0.415995 | − | 0.909367i | \(-0.636567\pi\) |
0.995532 | − | 0.0944208i | \(-0.0300999\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.5682 | −0.840483 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.04758 | − | 5.20804i | 0.224601 | − | 0.193422i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.0463 | + | 11.5737i | 0.743475 | + | 0.429246i | 0.823332 | − | 0.567561i | \(-0.192113\pi\) |
−0.0798562 | + | 0.996806i | \(0.525446\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.7637 | − | 49.8202i | −1.06386 | − | 1.84267i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.8489i | 0.659266i | 0.944109 | + | 0.329633i | \(0.106925\pi\) | ||||
−0.944109 | + | 0.329633i | \(0.893075\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.15267 | − | 1.82019i | 0.116130 | − | 0.0670477i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.7079 | + | 30.6710i | −0.651396 | + | 1.12825i | 0.331388 | + | 0.943494i | \(0.392483\pi\) |
−0.982784 | + | 0.184756i | \(0.940850\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.3859 | + | 18.1207i | 1.15144 | + | 0.664782i | 0.949237 | − | 0.314562i | \(-0.101858\pi\) |
0.202200 | + | 0.979344i | \(0.435191\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.0368627 | + | 0.0992951i | 0.00135054 | + | 0.00363789i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.6553 | 0.498953 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.1202 | − | 34.8491i | −0.734195 | − | 1.27166i | −0.955076 | − | 0.296362i | \(-0.904226\pi\) |
0.220881 | − | 0.975301i | \(-0.429107\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.1902 | − | 17.1330i | 0.516433 | − | 0.623532i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.1071 | − | 15.0730i | −0.948880 | − | 0.547836i | −0.0561469 | − | 0.998423i | \(-0.517882\pi\) |
−0.892733 | + | 0.450587i | \(0.851215\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.6964 | −0.568994 | −0.284497 | − | 0.958677i | \(-0.591827\pi\) | ||||
−0.284497 | + | 0.958677i | \(0.591827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.67257 | − | 3.85241i | −0.241563 | − | 0.139467i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.43273i | 0.0878408i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.71335 | + | 16.8240i | 0.350272 | + | 0.606689i | 0.986297 | − | 0.164979i | \(-0.0527557\pi\) |
−0.636025 | + | 0.771669i | \(0.719422\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.5491 | + | 24.5657i | −1.53039 | + | 0.883568i | −0.531042 | + | 0.847346i | \(0.678199\pi\) |
−0.999344 | + | 0.0362225i | \(0.988467\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.36791 | − | 28.3160i | −0.192821 | − | 1.01714i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.4968 | + | 17.4455i | −0.913519 | + | 0.625049i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.68130 | + | 4.64415i | −0.0959445 | + | 0.166181i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 37.8939 | − | 14.0679i | 1.35249 | − | 0.502104i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 24.8250i | − | 0.884917i | −0.896789 | − | 0.442459i | \(-0.854106\pi\) | ||
0.896789 | − | 0.442459i | \(-0.145894\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.4582 | 1.40297 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.462211 | − | 0.266858i | −0.0164136 | − | 0.00947639i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 29.8866i | − | 1.05864i | −0.848423 | − | 0.529319i | \(-0.822447\pi\) | ||
0.848423 | − | 0.529319i | \(-0.177553\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.3848 | 1.57022 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.59807 | + | 3.80940i | 0.232841 | + | 0.134431i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.18626 | − | 1.38943i | −0.288528 | − | 0.0489710i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.8929 | 1.64867 | 0.824333 | − | 0.566105i | \(-0.191550\pi\) | ||||
0.824333 | + | 0.566105i | \(0.191550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.623347 | + | 1.07967i | 0.0218887 | + | 0.0379123i | 0.876762 | − | 0.480924i | \(-0.159699\pi\) |
−0.854874 | + | 0.518836i | \(0.826365\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.4754 | + | 20.2715i | 0.857336 | + | 0.710078i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.6412 | − | 27.2445i | −0.652174 | − | 0.953164i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.101045 | + | 0.175014i | 0.00352648 | + | 0.00610805i | 0.867783 | − | 0.496943i | \(-0.165544\pi\) |
−0.864257 | + | 0.503051i | \(0.832211\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.8967 | + | 7.44589i | −0.449549 | + | 0.259548i | −0.707640 | − | 0.706573i | \(-0.750240\pi\) |
0.258090 | + | 0.966121i | \(0.416907\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.72867 | + | 1.57540i | −0.0948851 | + | 0.0547819i | −0.546692 | − | 0.837334i | \(-0.684113\pi\) |
0.451807 | + | 0.892116i | \(0.350780\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.7012 | 1.41361 | 0.706805 | − | 0.707409i | \(-0.250136\pi\) | ||||
0.706805 | + | 0.707409i | \(0.250136\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.3165 | + | 8.26565i | 0.496038 | + | 0.286388i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.944328 | − | 5.56380i | 0.0326798 | − | 0.192543i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.1206 | + | 22.7255i | −0.452973 | + | 0.784572i | −0.998569 | − | 0.0534763i | \(-0.982970\pi\) |
0.545596 | + | 0.838048i | \(0.316303\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.2261 | − | 22.9082i | 0.456071 | − | 0.789938i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.0766 | − | 27.1427i | −0.346645 | − | 0.933739i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 22.5657i | − | 0.775367i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.56148 | − | 13.0969i | −0.259204 | − | 0.448955i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.85321 | − | 1.64730i | −0.0976919 | − | 0.0564025i | 0.450358 | − | 0.892848i | \(-0.351296\pi\) |
−0.548050 | + | 0.836446i | \(0.684630\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.0460 | − | 10.4188i | −0.616439 | − | 0.355901i | 0.159042 | − | 0.987272i | \(-0.449159\pi\) |
−0.775481 | + | 0.631371i | \(0.782493\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.7172 | + | 25.4910i | 0.502145 | + | 0.869740i | 0.999997 | + | 0.00247823i | \(0.000788846\pi\) |
−0.497852 | + | 0.867262i | \(0.665878\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 49.0615i | − | 1.67007i | −0.550195 | − | 0.835036i | \(-0.685447\pi\) | ||
0.550195 | − | 0.835036i | \(-0.314553\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.7092 | + | 10.6581i | −0.976143 | + | 0.362387i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.283600 | + | 0.491209i | −0.00962047 | + | 0.0166631i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.486859 | − | 0.843264i | 0.0164966 | − | 0.0285729i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.8666 | + | 21.4976i | −0.401164 | + | 0.726750i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.4480 | + | 24.5074i | 1.43337 | + | 0.827556i | 0.997376 | − | 0.0723944i | \(-0.0230640\pi\) |
0.435993 | + | 0.899950i | \(0.356397\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.8746 | 1.47817 | 0.739086 | − | 0.673611i | \(-0.235258\pi\) | ||||
0.739086 | + | 0.673611i | \(0.235258\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.3690 | − | 27.9259i | 1.62775 | − | 0.939780i | 0.642984 | − | 0.765880i | \(-0.277696\pi\) |
0.984763 | − | 0.173900i | \(-0.0556370\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.5390 | + | 11.8582i | −0.689633 | + | 0.398160i | −0.803475 | − | 0.595339i | \(-0.797018\pi\) |
0.113841 | + | 0.993499i | \(0.463684\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.9774 | + | 27.6737i | 0.535865 | + | 0.928145i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.3953 | − | 1.94548i | 0.849822 | − | 0.0651029i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.51987 | − | 3.04244i | 0.0842299 | − | 0.101698i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.60031 | + | 7.96798i | 0.153429 | + | 0.265747i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.3308 | −1.21035 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.5763 | + | 4.00155i | 0.783704 | + | 0.133016i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.7205 | + | 12.5403i | 0.721216 | + | 0.416394i | 0.815200 | − | 0.579179i | \(-0.196627\pi\) |
−0.0939839 | + | 0.995574i | \(0.529960\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.00341 | 0.0995074 | 0.0497537 | − | 0.998762i | \(-0.484156\pi\) | ||||
0.0497537 | + | 0.998762i | \(0.484156\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.42620i | 0.245771i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.5112 | − | 13.5742i | −0.776409 | − | 0.448260i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.5467 | 0.611799 | 0.305899 | − | 0.952064i | \(-0.401043\pi\) | ||||
0.305899 | + | 0.952064i | \(0.401043\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.43437i | 0.0472128i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −43.9402 | + | 8.32982i | −1.44474 | + | 0.273883i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.47449 | + | 7.75005i | −0.146803 | + | 0.254271i | −0.930044 | − | 0.367447i | \(-0.880232\pi\) |
0.783241 | + | 0.621718i | \(0.213565\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.55369 | + | 4.10178i | 0.280336 | + | 0.134430i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.5632 | + | 5.03525i | −0.443564 | + | 0.164670i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.4136 | − | 15.8272i | 0.895563 | − | 0.517054i | 0.0198050 | − | 0.999804i | \(-0.493695\pi\) |
0.875758 | + | 0.482750i | \(0.160362\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.9011 | − | 25.8095i | −0.485763 | − | 0.841366i | 0.514103 | − | 0.857728i | \(-0.328125\pi\) |
−0.999866 | + | 0.0163621i | \(0.994792\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.9832i | 0.390228i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50.1907 | − | 28.9776i | −1.63098 | − | 0.941646i | −0.983792 | − | 0.179314i | \(-0.942612\pi\) |
−0.647187 | − | 0.762332i | \(-0.724055\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.03785 | 0.0661513 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.6329 | + | 15.3765i | 0.862725 | + | 0.498094i | 0.864924 | − | 0.501903i | \(-0.167367\pi\) |
−0.00219907 | + | 0.999998i | \(0.500700\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.8003 | − | 26.3213i | 0.705442 | − | 0.851738i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.8863 | − | 27.5159i | −0.512995 | − | 0.888534i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.22438 | 0.0717541 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.87755 | + | 1.43952i | −0.124823 | + | 0.0463397i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.12068 | − | 1.80172i | −0.100354 | − | 0.0579395i | 0.448983 | − | 0.893540i | \(-0.351786\pi\) |
−0.549337 | + | 0.835601i | \(0.685120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.9543 | − | 27.6337i | 0.511998 | − | 0.886807i | −0.487905 | − | 0.872897i | \(-0.662239\pi\) |
0.999903 | − | 0.0139100i | \(-0.00442783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.54162 | + | 3.77681i | −0.209715 | + | 0.121079i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.9910i | 1.31142i | 0.755014 | + | 0.655709i | \(0.227630\pi\) | ||||
−0.755014 | + | 0.655709i | \(0.772370\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.54757 | + | 7.87661i | 0.145341 | + | 0.251738i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.9335 | − | 23.0556i | −1.27368 | − | 0.735361i | −0.298003 | − | 0.954565i | \(-0.596321\pi\) |
−0.975679 | + | 0.219204i | \(0.929654\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.2842 | + | 11.0024i | 0.423268 | + | 0.350567i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.8046 | −0.407163 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.26185 | − | 2.18559i | 0.0400840 | − | 0.0694276i | −0.845287 | − | 0.534312i | \(-0.820571\pi\) |
0.885371 | + | 0.464884i | \(0.153904\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.5950 | − | 4.00472i | −0.748013 | − | 0.126958i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.194307 | + | 0.112183i | −0.00615376 | + | 0.00355288i | −0.503074 | − | 0.864244i | \(-0.667798\pi\) |
0.496920 | + | 0.867796i | \(0.334464\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3420.2.bj.e.1189.5 | ✓ | 40 | |
3.2 | odd | 2 | inner | 3420.2.bj.e.1189.16 | yes | 40 | |
5.4 | even | 2 | inner | 3420.2.bj.e.1189.9 | yes | 40 | |
15.14 | odd | 2 | inner | 3420.2.bj.e.1189.12 | yes | 40 | |
19.7 | even | 3 | inner | 3420.2.bj.e.2629.9 | yes | 40 | |
57.26 | odd | 6 | inner | 3420.2.bj.e.2629.12 | yes | 40 | |
95.64 | even | 6 | inner | 3420.2.bj.e.2629.5 | yes | 40 | |
285.254 | odd | 6 | inner | 3420.2.bj.e.2629.16 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3420.2.bj.e.1189.5 | ✓ | 40 | 1.1 | even | 1 | trivial | |
3420.2.bj.e.1189.9 | yes | 40 | 5.4 | even | 2 | inner | |
3420.2.bj.e.1189.12 | yes | 40 | 15.14 | odd | 2 | inner | |
3420.2.bj.e.1189.16 | yes | 40 | 3.2 | odd | 2 | inner | |
3420.2.bj.e.2629.5 | yes | 40 | 95.64 | even | 6 | inner | |
3420.2.bj.e.2629.9 | yes | 40 | 19.7 | even | 3 | inner | |
3420.2.bj.e.2629.12 | yes | 40 | 57.26 | odd | 6 | inner | |
3420.2.bj.e.2629.16 | yes | 40 | 285.254 | odd | 6 | inner |