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: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} - 20 x^{18} + 261 x^{16} - 1994 x^{14} + 11074 x^{12} - 39211 x^{10} + 99376 x^{8} - 134299 x^{6} + \cdots + 4096 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1189.7 | ||
Root | \(-2.10552 - 1.21562i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3420.1189 |
Dual form | 3420.2.bj.c.2629.7 |
$q$-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 | ||||||||
\(5\) | 0.896156 | + | 2.04863i | 0.400773 | + | 0.916177i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.663818i | − | 0.250900i | −0.992100 | − | 0.125450i | \(-0.959963\pi\) | ||
0.992100 | − | 0.125450i | \(-0.0400374\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.80905 | 0.545450 | 0.272725 | − | 0.962092i | \(-0.412075\pi\) | ||||
0.272725 | + | 0.962092i | \(0.412075\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.99526 | + | 1.15197i | −0.553386 | + | 0.319498i | −0.750487 | − | 0.660886i | \(-0.770181\pi\) |
0.197100 | + | 0.980383i | \(0.436847\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.77643 | − | 2.18033i | −0.915920 | − | 0.528807i | −0.0335887 | − | 0.999436i | \(-0.510694\pi\) |
−0.882331 | + | 0.470629i | \(0.844027\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.21168 | + | 1.12329i | −0.966225 | + | 0.257699i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.81374 | − | 1.04716i | 0.378191 | − | 0.218349i | −0.298840 | − | 0.954303i | \(-0.596600\pi\) |
0.677031 | + | 0.735955i | \(0.263266\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.39381 | + | 3.67179i | −0.678762 | + | 0.734359i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.974621 | − | 1.68809i | −0.180983 | − | 0.313471i | 0.761233 | − | 0.648479i | \(-0.224594\pi\) |
−0.942215 | + | 0.335008i | \(0.891261\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.52527 | −1.71079 | −0.855394 | − | 0.517977i | \(-0.826685\pi\) | ||||
−0.855394 | + | 0.517977i | \(0.826685\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.35992 | − | 0.594885i | 0.229869 | − | 0.100554i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.97461i | − | 0.489023i | −0.969646 | − | 0.244511i | \(-0.921372\pi\) | ||
0.969646 | − | 0.244511i | \(-0.0786276\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.247657 | − | 0.428954i | 0.0386775 | − | 0.0669914i | −0.846039 | − | 0.533122i | \(-0.821019\pi\) |
0.884716 | + | 0.466130i | \(0.154352\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.81715 | − | 3.93588i | −1.03960 | − | 0.600216i | −0.119884 | − | 0.992788i | \(-0.538252\pi\) |
−0.919721 | + | 0.392572i | \(0.871585\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.69449 | + | 3.28772i | −0.830627 | + | 0.479563i | −0.854067 | − | 0.520163i | \(-0.825871\pi\) |
0.0234403 | + | 0.999725i | \(0.492538\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.55935 | 0.937049 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.99575 | − | 1.15225i | 0.274137 | − | 0.158273i | −0.356629 | − | 0.934246i | \(-0.616074\pi\) |
0.630766 | + | 0.775973i | \(0.282741\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.62119 | + | 3.70609i | 0.218602 | + | 0.499729i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.88559 | + | 6.73003i | −0.505860 | + | 0.876176i | 0.494117 | + | 0.869396i | \(0.335492\pi\) |
−0.999977 | + | 0.00678007i | \(0.997842\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.36021 | − | 9.28415i | −0.686304 | − | 1.18871i | −0.973025 | − | 0.230700i | \(-0.925899\pi\) |
0.286721 | − | 0.958014i | \(-0.407435\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.14802 | − | 3.05522i | −0.514499 | − | 0.378954i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.96984 | + | 2.29199i | −0.484993 | + | 0.280011i | −0.722495 | − | 0.691376i | \(-0.757005\pi\) |
0.237502 | + | 0.971387i | \(0.423671\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.95914 | − | 5.12538i | 0.351185 | − | 0.608270i | −0.635272 | − | 0.772288i | \(-0.719112\pi\) |
0.986457 | + | 0.164018i | \(0.0524455\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.86313 | + | 2.80773i | 0.569187 | + | 0.328620i | 0.756824 | − | 0.653618i | \(-0.226750\pi\) |
−0.187638 | + | 0.982238i | \(0.560083\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.20088i | − | 0.136853i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.99810 | + | 5.19286i | −0.337312 | + | 0.584242i | −0.983926 | − | 0.178575i | \(-0.942851\pi\) |
0.646614 | + | 0.762817i | \(0.276185\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.20090i | 0.680638i | 0.940310 | + | 0.340319i | \(0.110535\pi\) | ||||
−0.940310 | + | 0.340319i | \(0.889465\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.08242 | − | 9.69045i | 0.117404 | − | 1.05108i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.65028 | + | 11.5186i | 0.704928 | + | 1.22097i | 0.966717 | + | 0.255847i | \(0.0823542\pi\) |
−0.261789 | + | 0.965125i | \(0.584312\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.764696 | + | 1.32449i | 0.0801619 | + | 0.138844i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.07552 | − | 7.62155i | −0.623335 | − | 0.781955i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.80695 | − | 5.08470i | −0.894211 | − | 0.516273i | −0.0188932 | − | 0.999822i | \(-0.506014\pi\) |
−0.875317 | + | 0.483549i | \(0.839348\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.48770 | + | 12.9691i | 0.745054 | + | 1.29047i | 0.950170 | + | 0.311733i | \(0.100909\pi\) |
−0.205116 | + | 0.978738i | \(0.565757\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 18.1501i | − | 1.78839i | −0.447681 | − | 0.894193i | \(-0.647750\pi\) | ||
0.447681 | − | 0.894193i | \(-0.352250\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 13.9698i | − | 1.35051i | −0.737584 | − | 0.675256i | \(-0.764033\pi\) | ||
0.737584 | − | 0.675256i | \(-0.235967\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.20544 | + | 15.9443i | −0.881721 | + | 1.52719i | −0.0322945 | + | 0.999478i | \(0.510281\pi\) |
−0.849426 | + | 0.527707i | \(0.823052\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.8946i | − | 1.02487i | −0.858725 | − | 0.512437i | \(-0.828743\pi\) | ||
0.858725 | − | 0.512437i | \(-0.171257\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.77065 | + | 2.77727i | 0.351615 | + | 0.258982i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.44734 | + | 2.50687i | −0.132677 | + | 0.229804i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.72733 | −0.702484 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.5635 | − | 3.66218i | −0.944832 | − | 0.327555i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.86242 | − | 1.65262i | 0.253998 | − | 0.146646i | −0.367595 | − | 0.929986i | \(-0.619819\pi\) |
0.621594 | + | 0.783340i | \(0.286486\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.646627 | − | 1.11999i | 0.0564961 | − | 0.0978541i | −0.836394 | − | 0.548128i | \(-0.815340\pi\) |
0.892890 | + | 0.450274i | \(0.148674\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.745658 | + | 2.79579i | 0.0646567 | + | 0.242426i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.6426 | − | 7.29920i | 1.08013 | − | 0.623613i | 0.149197 | − | 0.988807i | \(-0.452331\pi\) |
0.930931 | + | 0.365195i | \(0.118998\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.87915 | − | 3.25478i | −0.159387 | − | 0.276067i | 0.775261 | − | 0.631641i | \(-0.217618\pi\) |
−0.934648 | + | 0.355575i | \(0.884285\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.60954 | + | 2.08397i | −0.301844 | + | 0.174270i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.58487 | − | 3.50944i | 0.214662 | − | 0.291443i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.83653 | + | 6.64507i | −0.314301 | + | 0.544385i | −0.979289 | − | 0.202469i | \(-0.935103\pi\) |
0.664988 | + | 0.746854i | \(0.268437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.62643 | 0.132357 | 0.0661785 | − | 0.997808i | \(-0.478919\pi\) | ||||
0.0661785 | + | 0.997808i | \(0.478919\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.53613 | − | 19.5138i | −0.685638 | − | 1.56739i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.29893 | − | 1.32729i | −0.183474 | − | 0.105929i | 0.405450 | − | 0.914117i | \(-0.367115\pi\) |
−0.588924 | + | 0.808188i | \(0.700448\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.695126 | − | 1.20399i | −0.0547836 | − | 0.0948880i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 19.8052i | − | 1.55127i | −0.631184 | − | 0.775633i | \(-0.717431\pi\) | ||
0.631184 | − | 0.775633i | \(-0.282569\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.0776925 | − | 0.0448558i | 0.00601203 | − | 0.00347105i | −0.496991 | − | 0.867756i | \(-0.665562\pi\) |
0.503003 | + | 0.864285i | \(0.332228\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.84595 | + | 6.66139i | −0.295842 | + | 0.512414i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.7120 | + | 7.91662i | 1.04250 | + | 0.601889i | 0.920541 | − | 0.390646i | \(-0.127748\pi\) |
0.121962 | + | 0.992535i | \(0.461082\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.43740 | + | 2.25287i | 0.184250 | + | 0.170301i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.5051 | −1.00942 | −0.504709 | − | 0.863290i | \(-0.668400\pi\) | ||||
−0.504709 | + | 0.863290i | \(0.668400\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.78591 | + | 8.28945i | 0.355734 | + | 0.616150i | 0.987243 | − | 0.159219i | \(-0.0508975\pi\) |
−0.631509 | + | 0.775368i | \(0.717564\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.09389 | − | 2.66571i | 0.448032 | − | 0.195987i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.83177 | − | 3.94432i | −0.499588 | − | 0.288438i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.9010 | −1.94649 | −0.973243 | − | 0.229778i | \(-0.926200\pi\) | ||||
−0.973243 | + | 0.229778i | \(0.926200\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.7692 | − | 11.4137i | −1.42302 | − | 0.821579i | −0.426461 | − | 0.904506i | \(-0.640240\pi\) |
−0.996556 | + | 0.0829272i | \(0.973573\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.4172i | 0.742192i | 0.928594 | + | 0.371096i | \(0.121018\pi\) | ||||
−0.928594 | + | 0.371096i | \(0.878982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.782081 | + | 1.35460i | 0.0554403 | + | 0.0960254i | 0.892414 | − | 0.451218i | \(-0.149010\pi\) |
−0.836973 | + | 0.547244i | \(0.815677\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.12059 | + | 0.646971i | −0.0786498 | + | 0.0454085i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.10071 | + | 0.122949i | 0.0768769 | + | 0.00858710i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.61915 | + | 2.03208i | −0.527028 | + | 0.140562i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.4253 | + | 18.0571i | −0.717704 | + | 1.24310i | 0.244203 | + | 0.969724i | \(0.421474\pi\) |
−0.961907 | + | 0.273376i | \(0.911860\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.95396 | − | 17.4930i | 0.133259 | − | 1.19301i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.32305i | 0.429236i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.0466 | 0.675810 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.5472 | − | 11.2856i | −1.30898 | − | 0.755740i | −0.327054 | − | 0.945006i | \(-0.606056\pi\) |
−0.981926 | + | 0.189266i | \(0.939389\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 11.4187i | − | 0.757883i | −0.925421 | − | 0.378941i | \(-0.876288\pi\) | ||
0.925421 | − | 0.378941i | \(-0.123712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8237 | 1.04566 | 0.522829 | − | 0.852438i | \(-0.324877\pi\) | ||||
0.522829 | + | 0.852438i | \(0.324877\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.6621 | − | 6.73314i | −0.764013 | − | 0.441103i | 0.0667219 | − | 0.997772i | \(-0.478746\pi\) |
−0.830735 | + | 0.556669i | \(0.812079\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.8385 | − | 8.71963i | −0.772257 | − | 0.568806i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.7437 | 1.27711 | 0.638557 | − | 0.769574i | \(-0.279532\pi\) | ||||
0.638557 | + | 0.769574i | \(0.279532\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.69793 | + | 4.67295i | 0.173789 | + | 0.301011i | 0.939742 | − | 0.341886i | \(-0.111066\pi\) |
−0.765953 | + | 0.642897i | \(0.777732\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.87820 | + | 13.4377i | 0.375544 | + | 0.858503i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.10942 | − | 7.09296i | 0.452361 | − | 0.451314i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.78646 | − | 3.09424i | −0.112760 | − | 0.195306i | 0.804122 | − | 0.594464i | \(-0.202636\pi\) |
−0.916882 | + | 0.399158i | \(0.869303\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.28115 | − | 1.89437i | 0.206284 | − | 0.119098i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.0500 | + | 9.26649i | −1.00117 | + | 0.578028i | −0.908595 | − | 0.417678i | \(-0.862844\pi\) |
−0.0925780 | + | 0.995705i | \(0.529511\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.97460 | −0.122696 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.30609 | − | 5.37288i | −0.573838 | − | 0.331306i | 0.184843 | − | 0.982768i | \(-0.440822\pi\) |
−0.758681 | + | 0.651462i | \(0.774156\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.14904 | + | 3.05597i | 0.254873 | + | 0.187727i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.05027 | − | 10.4794i | 0.368892 | − | 0.638939i | −0.620501 | − | 0.784206i | \(-0.713071\pi\) |
0.989393 | + | 0.145267i | \(0.0464040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.34472 | − | 16.1855i | 0.567651 | − | 0.983201i | −0.429146 | − | 0.903235i | \(-0.641185\pi\) |
0.996798 | − | 0.0799661i | \(-0.0254812\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.13958 | + | 6.64247i | −0.370231 | + | 0.400556i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.94922i | − | 0.357454i | −0.983899 | − | 0.178727i | \(-0.942802\pi\) | ||
0.983899 | − | 0.178727i | \(-0.0571979\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.78943 | − | 15.2237i | −0.524333 | − | 0.908172i | −0.999599 | − | 0.0283294i | \(-0.990981\pi\) |
0.475265 | − | 0.879843i | \(-0.342352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.2029 | + | 15.7056i | 1.61705 | + | 0.933603i | 0.987679 | + | 0.156495i | \(0.0500196\pi\) |
0.629368 | + | 0.777107i | \(0.283314\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.284748 | − | 0.164399i | −0.0168081 | − | 0.00970418i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00764 | + | 1.74528i | 0.0592727 | + | 0.102663i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.1435i | 1.64416i | 0.569372 | + | 0.822080i | \(0.307186\pi\) | ||||
−0.569372 | + | 0.822080i | \(0.692814\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.2695 | − | 1.92899i | −1.00547 | − | 0.112310i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.41259 | + | 4.17873i | −0.139524 | + | 0.241662i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.61271 | + | 4.52535i | −0.150594 | + | 0.260837i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.2163 | − | 19.3012i | 0.814020 | − | 1.10518i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.3588 | + | 13.4862i | 1.33316 | + | 0.769698i | 0.985782 | − | 0.168028i | \(-0.0537400\pi\) |
0.347374 | + | 0.937727i | \(0.387073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.99721 | 0.283366 | 0.141683 | − | 0.989912i | \(-0.454749\pi\) | ||||
0.141683 | + | 0.989912i | \(0.454749\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.6484 | + | 13.0761i | −1.28017 | + | 0.739104i | −0.976878 | − | 0.213795i | \(-0.931417\pi\) |
−0.303287 | + | 0.952899i | \(0.598084\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.5314 | + | 13.0085i | −1.26549 | + | 0.730632i | −0.974131 | − | 0.225982i | \(-0.927441\pi\) |
−0.291359 | + | 0.956614i | \(0.594108\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.76314 | − | 3.05385i | −0.0987169 | − | 0.170983i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.3543 | + | 4.94081i | 1.02126 | + | 0.274914i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.54176 | − | 11.2357i | 0.140992 | − | 0.623247i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.18245 | + | 3.78011i | 0.120322 | + | 0.208404i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.97402 | 0.438292 | 0.219146 | − | 0.975692i | \(-0.429673\pi\) | ||||
0.219146 | + | 0.975692i | \(0.429673\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.25304 | − | 6.07877i | −0.450912 | − | 0.332119i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.42862 | − | 1.97951i | −0.186769 | − | 0.107831i | 0.403700 | − | 0.914891i | \(-0.367724\pi\) |
−0.590469 | + | 0.807060i | \(0.701057\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.2317 | −0.933150 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.00094i | − | 0.486005i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.16047 | − | 2.40205i | −0.223345 | − | 0.128949i | 0.384153 | − | 0.923269i | \(-0.374494\pi\) |
−0.607498 | + | 0.794321i | \(0.707827\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.02058 | −0.482861 | −0.241430 | − | 0.970418i | \(-0.577617\pi\) | ||||
−0.241430 | + | 0.970418i | \(0.577617\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0910i | 0.962889i | 0.876477 | + | 0.481444i | \(0.159888\pi\) | ||||
−0.876477 | + | 0.481444i | \(0.840112\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.1519 | + | 1.46905i | 0.698029 | + | 0.0779693i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.4849 | + | 30.2848i | −0.922820 | + | 1.59837i | −0.127791 | + | 0.991801i | \(0.540789\pi\) |
−0.795030 | + | 0.606571i | \(0.792545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.4765 | − | 9.46183i | 0.867182 | − | 0.497991i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.39389 | + | 12.4789i | −0.0729595 | + | 0.653178i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.55319 | − | 4.93819i | 0.446473 | − | 0.257771i | −0.259866 | − | 0.965645i | \(-0.583679\pi\) |
0.706339 | + | 0.707873i | \(0.250345\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.764883 | − | 1.32482i | −0.0397107 | − | 0.0687810i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 18.9698i | − | 0.982220i | −0.871098 | − | 0.491110i | \(-0.836591\pi\) | ||
0.871098 | − | 0.491110i | \(-0.163409\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.88925 | + | 2.24546i | 0.200306 | + | 0.115647i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.93773 | −0.459101 | −0.229550 | − | 0.973297i | \(-0.573726\pi\) | ||||
−0.229550 | + | 0.973297i | \(0.573726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.9643 | + | 8.06230i | 0.713543 | + | 0.411964i | 0.812371 | − | 0.583140i | \(-0.198176\pi\) |
−0.0988287 | + | 0.995104i | \(0.531510\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.46017 | − | 1.07618i | 0.125382 | − | 0.0548471i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.0603 | + | 17.4249i | 0.510075 | + | 0.883476i | 0.999932 | + | 0.0116730i | \(0.00371573\pi\) |
−0.489857 | + | 0.871803i | \(0.662951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.13262 | −0.461857 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.3250 | − | 1.48840i | −0.670455 | − | 0.0748894i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.8674 | + | 8.00633i | 0.695983 | + | 0.401826i | 0.805850 | − | 0.592120i | \(-0.201709\pi\) |
−0.109866 | + | 0.993946i | \(0.535042\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.83602 | + | 11.8403i | −0.341375 | + | 0.591278i | −0.984688 | − | 0.174324i | \(-0.944226\pi\) |
0.643313 | + | 0.765603i | \(0.277559\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.0054 | − | 10.9728i | 0.946727 | − | 0.546593i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.38123i | − | 0.266738i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.03518 | + | 5.25709i | 0.150080 | + | 0.259946i | 0.931257 | − | 0.364364i | \(-0.118713\pi\) |
−0.781177 | + | 0.624310i | \(0.785380\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.46752 | + | 2.57932i | 0.219832 | + | 0.126920i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.7034 | + | 5.55698i | −0.623585 | + | 0.272781i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.33985 | −0.309722 | −0.154861 | − | 0.987936i | \(-0.549493\pi\) | ||||
−0.154861 | + | 0.987936i | \(0.549493\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.52768 | − | 6.11011i | 0.171928 | − | 0.297789i | −0.767166 | − | 0.641449i | \(-0.778334\pi\) |
0.939094 | + | 0.343660i | \(0.111667\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.8222 | − | 6.46668i | 1.01002 | − | 0.313680i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.16299 | + | 3.55820i | −0.298248 | + | 0.172194i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.0390 | − | 22.5843i | −0.628069 | − | 1.08785i | −0.987939 | − | 0.154845i | \(-0.950512\pi\) |
0.359870 | − | 0.933002i | \(-0.382821\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.6662 | + | 17.1278i | −1.42567 | + | 0.823109i | −0.996775 | − | 0.0802463i | \(-0.974429\pi\) |
−0.428892 | + | 0.903356i | \(0.641096\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.46262 | + | 6.44766i | −0.309149 | + | 0.308433i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.13427 | − | 5.42872i | 0.149591 | − | 0.259099i | −0.781485 | − | 0.623923i | \(-0.785538\pi\) |
0.931076 | + | 0.364825i | \(0.118871\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.3099 | + | 16.3447i | −1.34504 | + | 0.776561i | −0.987543 | − | 0.157352i | \(-0.949704\pi\) |
−0.357500 | + | 0.933913i | \(0.616371\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.6378 | + | 23.9465i | −0.836110 | + | 1.13517i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.0822 | −1.08932 | −0.544659 | − | 0.838658i | \(-0.683341\pi\) | ||||
−0.544659 | + | 0.838658i | \(0.683341\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.448025 | − | 0.776001i | 0.0210967 | − | 0.0365405i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.02811 | + | 2.75353i | −0.0950794 | + | 0.129088i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.9166i | 0.931661i | 0.884874 | + | 0.465830i | \(0.154244\pi\) | ||||
−0.884874 | + | 0.465830i | \(0.845756\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.2586 | − | 36.8209i | 0.990111 | − | 1.71492i | 0.373562 | − | 0.927605i | \(-0.378136\pi\) |
0.616548 | − | 0.787317i | \(-0.288530\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.2843i | 1.26801i | 0.773329 | + | 0.634005i | \(0.218590\pi\) | ||||
−0.773329 | + | 0.634005i | \(0.781410\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 39.5912i | − | 1.83206i | −0.401107 | − | 0.916031i | \(-0.631375\pi\) | ||
0.401107 | − | 0.916031i | \(-0.368625\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.52146 | + | 2.63525i | 0.0702547 | + | 0.121685i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.3326 | − | 7.12022i | −0.567053 | − | 0.327388i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.1692 | − | 19.2766i | 0.466593 | − | 0.884472i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.7954 | + | 23.8943i | 0.630326 | + | 1.09176i | 0.987485 | + | 0.157713i | \(0.0504121\pi\) |
−0.357159 | + | 0.934044i | \(0.616255\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.42665 | + | 5.93513i | 0.156242 | + | 0.270618i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.52428 | − | 22.5989i | 0.114622 | − | 1.02616i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 29.9289i | − | 1.35621i | −0.734966 | − | 0.678104i | \(-0.762802\pi\) | ||
0.734966 | − | 0.678104i | \(-0.237198\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.23550 | − | 12.5323i | 0.326534 | − | 0.565573i | −0.655288 | − | 0.755379i | \(-0.727453\pi\) |
0.981822 | + | 0.189806i | \(0.0607860\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.49996i | 0.382819i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.40232 | − | 1.96433i | −0.152615 | − | 0.0881122i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.06799 | + | 15.7062i | −0.405939 | + | 0.703107i | −0.994430 | − | 0.105396i | \(-0.966389\pi\) |
0.588491 | + | 0.808504i | \(0.299722\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.7022 | − | 8.48833i | 0.655539 | − | 0.378476i | −0.135036 | − | 0.990841i | \(-0.543115\pi\) |
0.790575 | + | 0.612365i | \(0.209782\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.8587 | + | 26.9619i | −0.883703 | + | 1.19979i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.6888 | + | 28.9058i | 0.739717 | + | 1.28123i | 0.952623 | + | 0.304155i | \(0.0983739\pi\) |
−0.212906 | + | 0.977073i | \(0.568293\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.86382 | − | 3.22824i | 0.0824507 | − | 0.142809i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 37.1830 | − | 16.2654i | 1.63848 | − | 0.716737i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.3016 | + | 5.94765i | −0.453065 | + | 0.261577i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.09359 | −0.0479110 | −0.0239555 | − | 0.999713i | \(-0.507626\pi\) | ||||
−0.0239555 | + | 0.999713i | \(0.507626\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.51597 | − | 2.02994i | 0.153742 | − | 0.0887633i | −0.421155 | − | 0.906989i | \(-0.638375\pi\) |
0.574898 | + | 0.818225i | \(0.305042\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.9715 | + | 20.7682i | 1.56695 | + | 0.904676i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.30690 | + | 16.1200i | −0.404648 | + | 0.700871i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.14117i | 0.0494295i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.6190 | − | 12.5191i | 1.23731 | − | 0.541249i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.8662 | 0.511114 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.65097 | − | 11.5198i | −0.285947 | − | 0.495275i | 0.686891 | − | 0.726760i | \(-0.258975\pi\) |
−0.972838 | + | 0.231485i | \(0.925642\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −40.9135 | − | 4.57001i | −1.75254 | − | 0.195758i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.6808 | + | 17.1362i | −1.26906 | + | 0.732692i | −0.974810 | − | 0.223036i | \(-0.928403\pi\) |
−0.294250 | + | 0.955729i | \(0.595070\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00100 | + | 6.01493i | 0.255651 | + | 0.256244i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.44712 | + | 1.99019i | 0.146586 | + | 0.0846316i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.2047 | − | 20.3255i | 1.49167 | − | 0.861217i | 0.491717 | − | 0.870755i | \(-0.336369\pi\) |
0.999955 | + | 0.00953795i | \(0.00303607\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.1360 | 0.767071 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 20.7137i | − | 0.872980i | −0.899709 | − | 0.436490i | \(-0.856221\pi\) | ||
0.899709 | − | 0.436490i | \(-0.143779\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.3190 | − | 9.76323i | 0.938967 | − | 0.410742i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.0551 | 1.42766 | 0.713831 | − | 0.700318i | \(-0.246958\pi\) | ||||
0.713831 | + | 0.700318i | \(0.246958\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.5413 | 0.775929 | 0.387965 | − | 0.921674i | \(-0.373178\pi\) | ||||
0.387965 | + | 0.921674i | \(0.373178\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.31052 | + | 10.2135i | −0.0963553 | + | 0.425934i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 2.96818i | − | 0.123567i | −0.998090 | − | 0.0617834i | \(-0.980321\pi\) | ||
0.998090 | − | 0.0617834i | \(-0.0196788\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.11627 | 0.170772 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.61042 | − | 2.08448i | 0.149528 | − | 0.0863302i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.9328 | + | 19.0138i | 1.35928 | + | 0.784781i | 0.989527 | − | 0.144348i | \(-0.0461085\pi\) |
0.369754 | + | 0.929130i | \(0.379442\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 40.1174 | − | 10.6996i | 1.65301 | − | 0.440869i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.0060 | − | 21.9428i | 1.56072 | − | 0.901081i | 0.563533 | − | 0.826093i | \(-0.309442\pi\) |
0.997184 | − | 0.0749876i | \(-0.0238917\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.43270 | − | 0.718528i | −0.263715 | − | 0.0294568i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.4883 | + | 30.2906i | 0.714552 | + | 1.23764i | 0.963132 | + | 0.269029i | \(0.0867026\pi\) |
−0.248581 | + | 0.968611i | \(0.579964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.9988 | 1.30526 | 0.652630 | − | 0.757677i | \(-0.273666\pi\) | ||||
0.652630 | + | 0.757677i | \(0.273666\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.92489 | − | 15.8305i | −0.281537 | − | 0.643600i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.10357i | − | 0.0853814i | −0.999088 | − | 0.0426907i | \(-0.986407\pi\) | ||
0.999088 | − | 0.0426907i | \(-0.0135930\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.57467 | − | 13.1197i | 0.306438 | − | 0.530767i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.1598 | + | 17.4127i | 1.21814 | + | 0.703294i | 0.964520 | − | 0.264010i | \(-0.0850450\pi\) |
0.253621 | + | 0.967304i | \(0.418378\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.8782 | + | 9.16726i | −0.639231 | + | 0.369060i | −0.784318 | − | 0.620359i | \(-0.786987\pi\) |
0.145087 | + | 0.989419i | \(0.453654\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.4325 | −1.30357 | −0.651786 | − | 0.758403i | \(-0.725980\pi\) | ||||
−0.651786 | + | 0.758403i | \(0.725980\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.64628 | − | 4.41458i | 0.306342 | − | 0.176866i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.96412 | − | 24.9227i | −0.0785649 | − | 0.996909i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.48562 | + | 11.2334i | −0.258598 | + | 0.447906i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.25551 | − | 12.5669i | −0.288837 | − | 0.500281i | 0.684695 | − | 0.728830i | \(-0.259935\pi\) |
−0.973532 | + | 0.228549i | \(0.926602\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.95078 | + | 4.38304i | 0.236150 | + | 0.173936i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.0876 | + | 7.55614i | −0.518550 | + | 0.299385i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.8849 | + | 24.0494i | −0.548421 | + | 0.949892i | 0.449962 | + | 0.893048i | \(0.351437\pi\) |
−0.998383 | + | 0.0568449i | \(0.981896\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.72615 | + | 5.61539i | 0.383562 | + | 0.221450i | 0.679367 | − | 0.733799i | \(-0.262255\pi\) |
−0.295805 | + | 0.955248i | \(0.595588\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.00223i | 0.0787157i | 0.999225 | + | 0.0393578i | \(0.0125312\pi\) | ||||
−0.999225 | + | 0.0393578i | \(0.987469\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.02923 | + | 12.1750i | −0.275921 | + | 0.477910i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.23945i | 0.126770i | 0.997989 | + | 0.0633848i | \(0.0201895\pi\) | ||||
−0.997989 | + | 0.0633848i | \(0.979810\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.87393 | + | 0.321016i | 0.112294 | + | 0.0125431i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.14745 | + | 5.45154i | 0.122607 | + | 0.212362i | 0.920795 | − | 0.390047i | \(-0.127541\pi\) |
−0.798188 | + | 0.602409i | \(0.794208\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.196536 | − | 0.340410i | −0.00764435 | − | 0.0132404i | 0.862178 | − | 0.506606i | \(-0.169100\pi\) |
−0.869822 | + | 0.493365i | \(0.835767\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.05933 | + | 4.03304i | −0.196192 | + | 0.156395i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.53542 | − | 2.04117i | −0.136892 | − | 0.0790346i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.69690 | − | 16.7955i | −0.374345 | − | 0.648384i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 43.1041i | − | 1.66154i | −0.556616 | − | 0.830770i | \(-0.687900\pi\) | ||
0.556616 | − | 0.830770i | \(-0.312100\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 12.3727i | − | 0.475522i | −0.971324 | − | 0.237761i | \(-0.923587\pi\) | ||
0.971324 | − | 0.237761i | \(-0.0764134\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.37532 | + | 5.84622i | −0.129533 | + | 0.224357i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 32.8415i | − | 1.25664i | −0.777954 | − | 0.628322i | \(-0.783742\pi\) | ||
0.777954 | − | 0.628322i | \(-0.216258\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.2831 | + | 19.3588i | 1.00423 | + | 0.739662i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.65470 | + | 4.59807i | −0.101136 | + | 0.175172i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.6704 | −0.634171 | −0.317085 | − | 0.948397i | \(-0.602704\pi\) | ||||
−0.317085 | + | 0.948397i | \(0.602704\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.98384 | − | 6.76648i | 0.189048 | − | 0.256667i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.87052 | + | 1.07995i | −0.0708510 | + | 0.0409059i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.9399 | − | 27.6087i | 0.602041 | − | 1.04277i | −0.390470 | − | 0.920616i | \(-0.627688\pi\) |
0.992512 | − | 0.122151i | \(-0.0389791\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.34134 | + | 12.5281i | 0.126021 | + | 0.472506i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.60911 | − | 4.97047i | 0.323779 | − | 0.186934i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.99202 | − | 5.18233i | −0.112368 | − | 0.194626i | 0.804357 | − | 0.594147i | \(-0.202510\pi\) |
−0.916724 | + | 0.399520i | \(0.869177\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.2764 | + | 9.97451i | −0.647004 | + | 0.373548i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.50399 | − | 5.52706i | −0.280633 | − | 0.206700i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.345920 | − | 0.599151i | 0.0129006 | − | 0.0223446i | −0.859503 | − | 0.511131i | \(-0.829227\pi\) |
0.872404 | + | 0.488786i | \(0.162560\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0484 | −0.448706 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.50600 | + | 2.15046i | 0.353044 | + | 0.0798660i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.1410 | + | 11.0511i | 0.709902 | + | 0.409862i | 0.811025 | − | 0.585012i | \(-0.198910\pi\) |
−0.101123 | + | 0.994874i | \(0.532244\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.1630 | + | 29.7272i | 0.634796 | + | 1.09950i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.0945i | 0.705271i | 0.935761 | + | 0.352635i | \(0.114714\pi\) | ||||
−0.935761 | + | 0.352635i | \(0.885286\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.18165 | + | 4.14633i | −0.264540 | + | 0.152732i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.05045 | − | 10.4797i | 0.222569 | − | 0.385501i | −0.733018 | − | 0.680209i | \(-0.761889\pi\) |
0.955587 | + | 0.294708i | \(0.0952223\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.6722 | + | 7.89364i | 0.501584 | + | 0.289590i | 0.729368 | − | 0.684122i | \(-0.239814\pi\) |
−0.227783 | + | 0.973712i | \(0.573148\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.0514 | − | 1.90463i | −0.624717 | − | 0.0697804i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.27341 | −0.338843 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.5848 | − | 30.4578i | −0.641678 | − | 1.11142i | −0.985058 | − | 0.172223i | \(-0.944905\pi\) |
0.343380 | − | 0.939197i | \(-0.388428\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.45753 | + | 3.33196i | 0.0530451 | + | 0.121262i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.7465 | + | 7.35917i | 0.463278 | + | 0.267473i | 0.713421 | − | 0.700735i | \(-0.247145\pi\) |
−0.250144 | + | 0.968209i | \(0.580478\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.9486 | 1.44814 | 0.724068 | − | 0.689728i | \(-0.242270\pi\) | ||||
0.724068 | + | 0.689728i | \(0.242270\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.5841 | + | 6.11074i | 0.383170 | + | 0.221224i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 17.9042i | − | 0.646485i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.9729 | + | 43.2544i | 0.900547 | + | 1.55979i | 0.826786 | + | 0.562516i | \(0.190167\pi\) |
0.0737605 | + | 0.997276i | \(0.476500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.1384 | + | 11.6269i | −0.724327 | + | 0.418190i | −0.816343 | − | 0.577567i | \(-0.804002\pi\) |
0.0920165 | + | 0.995757i | \(0.470669\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.3269 | − | 34.9748i | 1.16122 | − | 1.25633i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.561213 | + | 2.08481i | −0.0201075 | + | 0.0746960i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.35324 | − | 9.27208i | 0.191554 | − | 0.331781i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.658928 | − | 5.89912i | 0.0235181 | − | 0.210549i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.5711i | 0.697636i | 0.937191 | + | 0.348818i | \(0.113417\pi\) | ||||
−0.937191 | + | 0.348818i | \(0.886583\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.23201 | −0.257141 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.3900 | + | 12.3495i | 0.759582 | + | 0.438545i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 47.6782i | 1.68885i | 0.535676 | + | 0.844424i | \(0.320057\pi\) | ||||
−0.535676 | + | 0.844424i | \(0.679943\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.6732 | 1.01438 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.79767 | + | 5.07933i | 0.310463 | + | 0.179246i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.84360 | − | 2.50303i | 0.0649784 | − | 0.0882200i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.4485 | −0.859565 | −0.429782 | − | 0.902933i | \(-0.641410\pi\) | ||||
−0.429782 | + | 0.902933i | \(0.641410\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.38004 | + | 9.31850i | 0.188919 | + | 0.327217i | 0.944890 | − | 0.327388i | \(-0.106168\pi\) |
−0.755971 | + | 0.654605i | \(0.772835\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.5737 | − | 17.7486i | 1.42123 | − | 0.621706i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.1327 | + | 8.91906i | 1.15917 | + | 0.312038i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.60434 | − | 6.24289i | −0.125792 | − | 0.217879i | 0.796250 | − | 0.604968i | \(-0.206814\pi\) |
−0.922042 | + | 0.387089i | \(0.873481\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.70433 | + | 3.87075i | −0.233698 | + | 0.134926i | −0.612277 | − | 0.790643i | \(-0.709746\pi\) |
0.378579 | + | 0.925569i | \(0.376413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.0605 | + | 13.3140i | −0.801891 | + | 0.462972i | −0.844132 | − | 0.536136i | \(-0.819884\pi\) |
0.0422411 | + | 0.999107i | \(0.486550\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.1093 | 0.420572 | 0.210286 | − | 0.977640i | \(-0.432561\pi\) | ||||
0.210286 | + | 0.977640i | \(0.432561\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.7709 | − | 14.3015i | −0.858262 | − | 0.495518i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.161518 | + | 0.118966i | 0.00558955 | + | 0.00411698i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.20591 | − | 2.08869i | 0.0416325 | − | 0.0721096i | −0.844458 | − | 0.535621i | \(-0.820077\pi\) |
0.886091 | + | 0.463512i | \(0.153411\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.6002 | − | 21.8242i | 0.434491 | − | 0.752560i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.0933 | − | 1.90931i | −0.588028 | − | 0.0656823i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.12954i | 0.176253i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.11490 | − | 5.39517i | −0.106777 | − | 0.184944i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.9717 | + | 13.8401i | 0.820775 | + | 0.473875i | 0.850684 | − | 0.525678i | \(-0.176188\pi\) |
−0.0299085 | + | 0.999553i | \(0.509522\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.2071 | − | 8.20245i | −0.485304 | − | 0.280190i | 0.237320 | − | 0.971431i | \(-0.423731\pi\) |
−0.722624 | + | 0.691241i | \(0.757064\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.4715 | − | 30.2616i | −0.596121 | − | 1.03251i | −0.993388 | − | 0.114808i | \(-0.963375\pi\) |
0.397267 | − | 0.917703i | \(-0.369959\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.6243i | 0.633979i | 0.948429 | + | 0.316990i | \(0.102672\pi\) | ||||
−0.948429 | + | 0.316990i | \(0.897328\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.93018 | + | 35.1854i | −0.133630 | + | 1.19634i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.42372 | + | 9.39416i | −0.183987 | + | 0.318675i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.28058 | − | 9.14624i | 0.178926 | − | 0.309908i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.43102 | + | 7.01228i | −0.0821835 | + | 0.237058i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.3087 | + | 15.1893i | 0.888381 | + | 0.512907i | 0.873413 | − | 0.486981i | \(-0.161902\pi\) |
0.0149683 | + | 0.999888i | \(0.495235\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.3772 | 0.888670 | 0.444335 | − | 0.895861i | \(-0.353440\pi\) | ||||
0.444335 | + | 0.895861i | \(0.353440\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.2183 | + | 14.5598i | −0.848664 | + | 0.489977i | −0.860200 | − | 0.509957i | \(-0.829661\pi\) |
0.0115356 | + | 0.999933i | \(0.496328\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.3379 | + | 10.0100i | −0.582148 | + | 0.336104i | −0.761987 | − | 0.647593i | \(-0.775776\pi\) |
0.179838 | + | 0.983696i | \(0.442443\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.09704 | − | 1.90012i | −0.0367935 | − | 0.0637281i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.2903 | − | 20.2433i | 0.678990 | − | 0.677418i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.1027 | − | 27.6670i | −0.404547 | − | 0.924805i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.28352 | + | 16.0795i | 0.309623 | + | 0.536283i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0491 | −0.334784 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.6931 | + | 17.2332i | −0.421934 | + | 0.572852i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.50159 | + | 3.75370i | 0.215882 | + | 0.124639i | 0.604042 | − | 0.796952i | \(-0.293556\pi\) |
−0.388160 | + | 0.921592i | \(0.626889\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.3882 | −1.27186 | −0.635929 | − | 0.771748i | \(-0.719383\pi\) | ||||
−0.635929 | + | 0.771748i | \(0.719383\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.2178i | 0.371254i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.743471 | − | 0.429243i | −0.0245516 | − | 0.0141749i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.8811 | 1.24958 | 0.624791 | − | 0.780792i | \(-0.285184\pi\) | ||||
0.624791 | + | 0.780792i | \(0.285184\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.6353i | 0.448811i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.9222 | + | 10.0953i | 0.359118 | + | 0.331930i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.96821 | − | 10.3372i | 0.195811 | − | 0.339154i | −0.751355 | − | 0.659898i | \(-0.770600\pi\) |
0.947166 | + | 0.320744i | \(0.103933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.6258 | + | 7.36802i | −0.905401 | + | 0.241477i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.95815 | − | 17.5305i | 0.0640383 | − | 0.573310i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.7299 | − | 6.77228i | 0.383200 | − | 0.221241i | −0.296010 | − | 0.955185i | \(-0.595656\pi\) |
0.679210 | + | 0.733944i | \(0.262323\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.04614 | + | 12.2043i | 0.229698 | + | 0.397848i | 0.957718 | − | 0.287707i | \(-0.0928929\pi\) |
−0.728021 | + | 0.685555i | \(0.759560\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.03735i | − | 0.0337807i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.58806 | + | 5.53567i | 0.311570 | + | 0.179885i | 0.647629 | − | 0.761956i | \(-0.275761\pi\) |
−0.336059 | + | 0.941841i | \(0.609094\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.9376 | −0.419973 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.40004 | + | 3.69507i | 0.207318 | + | 0.119695i | 0.600064 | − | 0.799952i | \(-0.295142\pi\) |
−0.392747 | + | 0.919647i | \(0.628475\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.1075 | − | 55.1103i | −0.780099 | − | 1.78333i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.84534 | − | 8.39238i | −0.156464 | − | 0.271004i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 59.7307 | 1.92680 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.66632 | − | 50.7283i | 0.182405 | − | 1.63300i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.31785 | − | 0.760861i | −0.0423792 | − | 0.0244676i | 0.478661 | − | 0.878000i | \(-0.341122\pi\) |
−0.521040 | + | 0.853532i | \(0.674456\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.2897 | + | 47.2671i | −0.875768 | + | 1.51687i | −0.0198254 | + | 0.999803i | \(0.506311\pi\) |
−0.855942 | + | 0.517071i | \(0.827022\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.16058 | + | 1.24741i | −0.0692651 | + | 0.0399902i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.0130i | 0.416321i | 0.978095 | + | 0.208161i | \(0.0667477\pi\) | ||||
−0.978095 | + | 0.208161i | \(0.933252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0307 | + | 20.8378i | 0.384503 | + | 0.665979i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.6166 | − | 10.1709i | −0.561882 | − | 0.324402i | 0.192019 | − | 0.981391i | \(-0.438497\pi\) |
−0.753900 | + | 0.656989i | \(0.771830\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.3410 | + | 9.33541i | −0.679980 | + | 0.297451i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.4860 | −0.524225 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.9449 | + | 29.3495i | −0.538274 | + | 0.932318i | 0.460723 | + | 0.887544i | \(0.347590\pi\) |
−0.998997 | + | 0.0447741i | \(0.985743\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.07422 | + | 2.81614i | −0.0657573 | + | 0.0892775i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.05162 | + | 1.76185i | −0.0966458 | + | 0.0557985i | −0.547544 | − | 0.836777i | \(-0.684437\pi\) |
0.450898 | + | 0.892575i | \(0.351104\pi\) | |||||||
\(998\) | 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.c.1189.7 | 20 | ||
3.2 | odd | 2 | 380.2.r.a.49.2 | ✓ | 20 | ||
5.4 | even | 2 | inner | 3420.2.bj.c.1189.1 | 20 | ||
15.2 | even | 4 | 1900.2.i.g.201.2 | 20 | |||
15.8 | even | 4 | 1900.2.i.g.201.9 | 20 | |||
15.14 | odd | 2 | 380.2.r.a.49.9 | yes | 20 | ||
19.7 | even | 3 | inner | 3420.2.bj.c.2629.1 | 20 | ||
57.26 | odd | 6 | 380.2.r.a.349.9 | yes | 20 | ||
95.64 | even | 6 | inner | 3420.2.bj.c.2629.7 | 20 | ||
285.83 | even | 12 | 1900.2.i.g.501.9 | 20 | |||
285.197 | even | 12 | 1900.2.i.g.501.2 | 20 | |||
285.254 | odd | 6 | 380.2.r.a.349.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.r.a.49.2 | ✓ | 20 | 3.2 | odd | 2 | ||
380.2.r.a.49.9 | yes | 20 | 15.14 | odd | 2 | ||
380.2.r.a.349.2 | yes | 20 | 285.254 | odd | 6 | ||
380.2.r.a.349.9 | yes | 20 | 57.26 | odd | 6 | ||
1900.2.i.g.201.2 | 20 | 15.2 | even | 4 | |||
1900.2.i.g.201.9 | 20 | 15.8 | even | 4 | |||
1900.2.i.g.501.2 | 20 | 285.197 | even | 12 | |||
1900.2.i.g.501.9 | 20 | 285.83 | even | 12 | |||
3420.2.bj.c.1189.1 | 20 | 5.4 | even | 2 | inner | ||
3420.2.bj.c.1189.7 | 20 | 1.1 | even | 1 | trivial | ||
3420.2.bj.c.2629.1 | 20 | 19.7 | even | 3 | inner | ||
3420.2.bj.c.2629.7 | 20 | 95.64 | even | 6 | inner |