Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(49,1500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1500, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.o (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.9775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{14} + 6x^{12} - 20x^{10} - 79x^{8} - 80x^{6} + 96x^{4} + 320x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(-1.41395 + 0.0272949i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1500.649 |
Dual form | 1500.2.o.b.349.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.587785 | + | 0.809017i | −0.339358 | + | 0.467086i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.32440i | − | 1.63447i | −0.576306 | − | 0.817234i | \(-0.695506\pi\) | ||
0.576306 | − | 0.817234i | \(-0.304494\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.180557 | − | 0.555698i | 0.0544401 | − | 0.167549i | −0.920140 | − | 0.391590i | \(-0.871925\pi\) |
0.974580 | + | 0.224041i | \(0.0719250\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.918969 | + | 0.298591i | −0.254876 | + | 0.0828143i | −0.433668 | − | 0.901073i | \(-0.642781\pi\) |
0.178792 | + | 0.983887i | \(0.442781\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.36625 | − | 1.88048i | −0.331363 | − | 0.456082i | 0.610531 | − | 0.791993i | \(-0.290956\pi\) |
−0.941894 | + | 0.335910i | \(0.890956\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.35169 | + | 3.16169i | −0.998346 | + | 0.725341i | −0.961733 | − | 0.273988i | \(-0.911657\pi\) |
−0.0366134 | + | 0.999330i | \(0.511657\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.49851 | + | 2.54182i | 0.763437 | + | 0.554670i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.29166 | − | 0.419687i | −0.269330 | − | 0.0875107i | 0.171238 | − | 0.985230i | \(-0.445223\pi\) |
−0.440569 | + | 0.897719i | \(0.645223\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.951057 | + | 0.309017i | 0.183031 | + | 0.0594703i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.571459 | − | 0.415189i | −0.106117 | − | 0.0770987i | 0.533461 | − | 0.845825i | \(-0.320891\pi\) |
−0.639578 | + | 0.768726i | \(0.720891\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.86707 | + | 4.98922i | −1.23336 | + | 0.896090i | −0.997138 | − | 0.0756084i | \(-0.975910\pi\) |
−0.236225 | + | 0.971698i | \(0.575910\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.343440 | + | 0.472705i | 0.0597853 | + | 0.0822874i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.81960 | + | 1.89090i | −0.956736 | + | 0.310862i | −0.745450 | − | 0.666562i | \(-0.767765\pi\) |
−0.211286 | + | 0.977424i | \(0.567765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.298591 | − | 0.918969i | 0.0478129 | − | 0.147153i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.41820 | + | 10.5201i | 0.533833 | + | 1.64297i | 0.746158 | + | 0.665769i | \(0.231896\pi\) |
−0.212325 | + | 0.977199i | \(0.568104\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.03076i | − | 1.07218i | −0.844161 | − | 0.536090i | \(-0.819901\pi\) | ||
0.844161 | − | 0.536090i | \(-0.180099\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.33081 | + | 7.33723i | −0.777579 | + | 1.07025i | 0.217966 | + | 0.975956i | \(0.430058\pi\) |
−0.995545 | + | 0.0942890i | \(0.969942\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.7004 | −1.67149 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.32440 | 0.325481 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.23465 | − | 7.20487i | 0.719034 | − | 0.989665i | −0.280521 | − | 0.959848i | \(-0.590507\pi\) |
0.999555 | − | 0.0298175i | \(-0.00949262\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.37899i | − | 0.712464i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.25351 | + | 6.93558i | 0.293382 | + | 0.902936i | 0.983760 | + | 0.179487i | \(0.0574439\pi\) |
−0.690379 | + | 0.723448i | \(0.742556\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.48752 | + | 4.57810i | −0.190457 | + | 0.586166i | −1.00000 | 0.000895115i | \(-0.999715\pi\) | |
0.809543 | + | 0.587061i | \(0.199715\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.11275 | + | 1.33631i | −0.518157 | + | 0.168359i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.221011 | − | 0.304195i | −0.0270008 | − | 0.0371634i | 0.795303 | − | 0.606212i | \(-0.207312\pi\) |
−0.822304 | + | 0.569049i | \(0.807312\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.09875 | − | 0.798291i | 0.132274 | − | 0.0961030i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.54359 | − | 6.20729i | −1.01394 | − | 0.736669i | −0.0489067 | − | 0.998803i | \(-0.515574\pi\) |
−0.965031 | + | 0.262134i | \(0.915574\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.202931 | + | 0.0659364i | 0.0237513 | + | 0.00771727i | 0.320869 | − | 0.947124i | \(-0.396025\pi\) |
−0.297117 | + | 0.954841i | \(0.596025\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.40306 | − | 0.780801i | −0.273854 | − | 0.0889806i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.68410 | − | 4.12974i | −0.639511 | − | 0.464632i | 0.220171 | − | 0.975461i | \(-0.429339\pi\) |
−0.859682 | + | 0.510829i | \(0.829339\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.46998 | − | 13.0343i | −1.03946 | − | 1.43070i | −0.897598 | − | 0.440815i | \(-0.854690\pi\) |
−0.141867 | − | 0.989886i | \(-0.545310\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.671790 | − | 0.218278i | 0.0720235 | − | 0.0234018i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.33233 | − | 13.3335i | 0.459226 | − | 1.41335i | −0.406875 | − | 0.913484i | \(-0.633382\pi\) |
0.866101 | − | 0.499869i | \(-0.166618\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.29123 | + | 3.97399i | 0.135357 | + | 0.416587i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 8.48817i | − | 0.880182i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.25880 | + | 12.7436i | −0.940089 | + | 1.29392i | 0.0157030 | + | 0.999877i | \(0.495001\pi\) |
−0.955792 | + | 0.294044i | \(0.904999\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.584296 | −0.0587239 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.14178 | 0.710634 | 0.355317 | − | 0.934746i | \(-0.384373\pi\) | ||||
0.355317 | + | 0.934746i | \(0.384373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.779130 | − | 1.07238i | 0.0767699 | − | 0.105665i | −0.768905 | − | 0.639363i | \(-0.779198\pi\) |
0.845675 | + | 0.533698i | \(0.179198\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 17.6796i | − | 1.70915i | −0.519331 | − | 0.854573i | \(-0.673819\pi\) | ||
0.519331 | − | 0.854573i | \(-0.326181\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.09385 | − | 3.36653i | −0.104772 | − | 0.322455i | 0.884905 | − | 0.465772i | \(-0.154223\pi\) |
−0.989677 | + | 0.143317i | \(0.954223\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.89090 | − | 5.81960i | 0.179476 | − | 0.552372i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.6322 | + | 5.40414i | −1.56463 | + | 0.508379i | −0.958039 | − | 0.286636i | \(-0.907463\pi\) |
−0.606590 | + | 0.795015i | \(0.707463\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.567954 | + | 0.781722i | 0.0525074 | + | 0.0722702i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.13192 | + | 5.90819i | −0.745452 | + | 0.541603i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.62299 | + | 6.26497i | 0.783908 | + | 0.569542i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.5201 | − | 3.41820i | −0.948568 | − | 0.308208i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.6492 | − | 5.40966i | −1.47738 | − | 0.480030i | −0.544051 | − | 0.839052i | \(-0.683110\pi\) |
−0.933329 | + | 0.359022i | \(0.883110\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.68800 | + | 4.13258i | 0.500801 | + | 0.363853i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.2629 | − | 11.0892i | 1.33353 | − | 0.968865i | 0.333872 | − | 0.942618i | \(-0.391645\pi\) |
0.999656 | − | 0.0262465i | \(-0.00835549\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.6724 | + | 18.8184i | 1.18555 | + | 1.63177i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.6023 | − | 4.09472i | 1.07668 | − | 0.349836i | 0.283596 | − | 0.958944i | \(-0.408472\pi\) |
0.793087 | + | 0.609108i | \(0.208472\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.22318 | − | 16.0753i | 0.443024 | − | 1.36349i | −0.441611 | − | 0.897206i | \(-0.645593\pi\) |
0.884636 | − | 0.466283i | \(-0.154407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.80257 | − | 8.62543i | −0.236019 | − | 0.726393i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.564582i | 0.0472128i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.87732 | − | 9.46582i | 0.567232 | − | 0.780728i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.1625 | −0.996388 | −0.498194 | − | 0.867066i | \(-0.666003\pi\) | ||||
−0.498194 | + | 0.867066i | \(0.666003\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.84446 | −0.801131 | −0.400565 | − | 0.916268i | \(-0.631186\pi\) | ||||
−0.400565 | + | 0.916268i | \(0.631186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.36625 | + | 1.88048i | −0.110454 | + | 0.152027i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.4804i | 1.47489i | 0.675405 | + | 0.737447i | \(0.263969\pi\) | ||||
−0.675405 | + | 0.737447i | \(0.736031\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.75202 | + | 8.46984i | 0.218249 | + | 0.671702i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.81489 | + | 5.58566i | −0.143033 | + | 0.440212i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.8253 | − | 4.49212i | 1.08288 | − | 0.351850i | 0.287390 | − | 0.957814i | \(-0.407212\pi\) |
0.795492 | + | 0.605964i | \(0.207212\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.64091 | − | 3.63490i | −0.204360 | − | 0.281277i | 0.694519 | − | 0.719474i | \(-0.255617\pi\) |
−0.898879 | + | 0.438197i | \(0.855617\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.76187 | + | 7.09242i | −0.750913 | + | 0.545570i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.35169 | + | 3.16169i | 0.332782 | + | 0.241780i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.90036 | + | 0.617465i | 0.144482 | + | 0.0469450i | 0.380365 | − | 0.924836i | \(-0.375798\pi\) |
−0.235883 | + | 0.971781i | \(0.575798\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.93558 | − | 2.25351i | −0.521310 | − | 0.169384i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.3095 | + | 8.21683i | 0.845312 | + | 0.614155i | 0.923849 | − | 0.382756i | \(-0.125025\pi\) |
−0.0785376 | + | 0.996911i | \(0.525025\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9524 | + | 7.95740i | −0.814087 | + | 0.591469i | −0.915013 | − | 0.403425i | \(-0.867820\pi\) |
0.100926 | + | 0.994894i | \(0.467820\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.82942 | − | 3.89437i | −0.209157 | − | 0.287880i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.29166 | + | 0.419687i | −0.0944557 | + | 0.0306905i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.33631 | − | 4.11275i | 0.0972024 | − | 0.299158i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.786594 | + | 2.42089i | 0.0569160 | + | 0.175169i | 0.975473 | − | 0.220119i | \(-0.0706446\pi\) |
−0.918557 | + | 0.395288i | \(0.870645\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.60541i | 0.403486i | 0.979438 | + | 0.201743i | \(0.0646606\pi\) | ||||
−0.979438 | + | 0.201743i | \(0.935339\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.61776 | − | 6.35580i | 0.329002 | − | 0.452832i | −0.612187 | − | 0.790713i | \(-0.709710\pi\) |
0.941189 | + | 0.337881i | \(0.109710\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.9970 | −1.20489 | −0.602443 | − | 0.798162i | \(-0.705806\pi\) | ||||
−0.602443 | + | 0.798162i | \(0.705806\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.376006 | 0.0265214 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.79544 | + | 2.47122i | −0.126015 | + | 0.173445i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.35813i | 0.0943969i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.971215 | + | 2.98909i | 0.0671804 | + | 0.206760i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00341 | + | 12.3212i | −0.275606 | + | 0.848229i | 0.713452 | + | 0.700704i | \(0.247131\pi\) |
−0.989058 | + | 0.147525i | \(0.952869\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.0436 | − | 3.26336i | 0.688176 | − | 0.223602i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.5754 | + | 29.6959i | 1.46463 | + | 2.01589i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.172624 | + | 0.125419i | −0.0116648 | + | 0.00847500i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.81703 | + | 1.32015i | 0.122227 | + | 0.0888030i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.0512 | + | 5.86518i | 1.20880 | + | 0.392761i | 0.842990 | − | 0.537930i | \(-0.180793\pi\) |
0.365806 | + | 0.930691i | \(0.380793\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.366260 | + | 0.119005i | 0.0243095 | + | 0.00789865i | 0.321147 | − | 0.947030i | \(-0.395932\pi\) |
−0.296837 | + | 0.954928i | \(0.595932\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.30740 | + | 6.03568i | 0.548968 | + | 0.398849i | 0.827405 | − | 0.561606i | \(-0.189816\pi\) |
−0.278437 | + | 0.960455i | \(0.589816\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.04416 | − | 1.48517i | 0.134496 | − | 0.0977172i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.7185 | + | 17.5055i | 0.833217 | + | 1.14682i | 0.987316 | + | 0.158769i | \(0.0507526\pi\) |
−0.154099 | + | 0.988055i | \(0.549247\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.68206 | − | 2.17113i | 0.434047 | − | 0.141030i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.38438 | − | 7.33836i | 0.154233 | − | 0.474679i | −0.843850 | − | 0.536579i | \(-0.819716\pi\) |
0.998082 | + | 0.0619006i | \(0.0197162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.82629 | − | 24.0868i | −0.504136 | − | 1.55157i | −0.802219 | − | 0.597030i | \(-0.796347\pi\) |
0.298083 | − | 0.954540i | \(-0.403653\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.05502 | − | 4.20487i | 0.194386 | − | 0.267550i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.1113 | 1.02101 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.39913 | −0.151432 | −0.0757160 | − | 0.997129i | \(-0.524124\pi\) | ||||
−0.0757160 | + | 0.997129i | \(0.524124\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.466438 | + | 0.641997i | −0.0293247 | + | 0.0403620i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.3086i | 0.892548i | 0.894896 | + | 0.446274i | \(0.147249\pi\) | ||||
−0.894896 | + | 0.446274i | \(0.852751\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.17701 | + | 25.1662i | 0.508095 | + | 1.56375i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.218278 | + | 0.671790i | −0.0135111 | + | 0.0415828i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.4403 | + | 4.04210i | −0.767103 | + | 0.249247i | −0.666324 | − | 0.745662i | \(-0.732133\pi\) |
−0.100779 | + | 0.994909i | \(0.532133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.24058 | + | 11.3422i | 0.504315 | + | 0.694131i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.8165 | − | 18.0302i | 1.51309 | − | 1.09932i | 0.548306 | − | 0.836278i | \(-0.315273\pi\) |
0.964783 | − | 0.263046i | \(-0.0847270\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.5174 | − | 8.36785i | −0.699629 | − | 0.508310i | 0.180182 | − | 0.983633i | \(-0.442331\pi\) |
−0.879811 | + | 0.475323i | \(0.842331\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.97399 | − | 1.29123i | −0.240517 | − | 0.0781486i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.1454 | − | 6.22072i | −1.15034 | − | 0.373767i | −0.329066 | − | 0.944307i | \(-0.606734\pi\) |
−0.821270 | + | 0.570540i | \(0.806734\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.86707 | + | 4.98922i | 0.411121 | + | 0.298697i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.94172 | − | 5.77000i | 0.473763 | − | 0.344209i | −0.325143 | − | 0.945665i | \(-0.605412\pi\) |
0.798906 | + | 0.601456i | \(0.205412\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.84733 | − | 5.29540i | −0.228700 | − | 0.314779i | 0.679210 | − | 0.733944i | \(-0.262323\pi\) |
−0.907910 | + | 0.419166i | \(0.862323\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 45.4932 | − | 14.7816i | 2.68538 | − | 0.872532i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.58373 | − | 11.0296i | 0.210807 | − | 0.648799i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.86764 | − | 14.9811i | −0.285346 | − | 0.878205i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.869428i | 0.0507925i | 0.999677 | + | 0.0253963i | \(0.00808475\pi\) | ||||
−0.999677 | + | 0.0253963i | \(0.991915\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.343440 | − | 0.472705i | 0.0199284 | − | 0.0274291i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.31231 | 0.0758930 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.4038 | −1.75244 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.19783 | + | 5.77782i | −0.241159 | + | 0.331927i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.7261i | − | 1.23997i | −0.784613 | − | 0.619986i | \(-0.787138\pi\) | ||
0.784613 | − | 0.619986i | \(-0.212862\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.409613 | + | 1.26066i | 0.0233021 | + | 0.0717163i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.86610 | − | 18.0540i | 0.332636 | − | 1.02375i | −0.635239 | − | 0.772316i | \(-0.719098\pi\) |
0.967875 | − | 0.251432i | \(-0.0809016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.78443 | − | 1.87947i | 0.326955 | − | 0.106234i | −0.140940 | − | 0.990018i | \(-0.545012\pi\) |
0.467895 | + | 0.883784i | \(0.345012\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.16274 | + | 1.60038i | 0.0653060 | + | 0.0898860i | 0.840421 | − | 0.541935i | \(-0.182308\pi\) |
−0.775115 | + | 0.631821i | \(0.782308\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.333901 | + | 0.242593i | −0.0186949 | + | 0.0135826i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.3031 | + | 10.3918i | 0.798319 | + | 0.580013i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.8910 | + | 3.86361i | 0.661631 | + | 0.214977i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.36653 | + | 1.09385i | 0.186169 | + | 0.0604901i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 31.7291 | + | 23.0525i | 1.74928 | + | 1.27093i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6230 | − | 7.71805i | 0.583892 | − | 0.424223i | −0.256233 | − | 0.966615i | \(-0.582481\pi\) |
0.840125 | + | 0.542393i | \(0.182481\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.59671 | + | 4.95044i | 0.197098 | + | 0.271283i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.9333 | − | 3.55245i | 0.595576 | − | 0.193514i | 0.00430942 | − | 0.999991i | \(-0.498628\pi\) |
0.591266 | + | 0.806476i | \(0.298628\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.40414 | − | 16.6322i | 0.293513 | − | 0.903339i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.53260 | + | 4.71686i | 0.0829949 | + | 0.255432i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.3264i | 1.09752i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.5028 | + | 24.0905i | −0.939599 | + | 1.29325i | 0.0163966 | + | 0.999866i | \(0.494781\pi\) |
−0.955995 | + | 0.293381i | \(0.905219\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0870 | −0.539946 | −0.269973 | − | 0.962868i | \(-0.587015\pi\) | ||||
−0.269973 | + | 0.962868i | \(0.587015\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.966262 | −0.0515752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.38300 | + | 11.5382i | −0.446182 | + | 0.614117i | −0.971572 | − | 0.236745i | \(-0.923919\pi\) |
0.525390 | + | 0.850862i | \(0.323919\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 10.0516i | − | 0.531988i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.04232 | + | 6.28562i | 0.107790 | + | 0.331742i | 0.990375 | − | 0.138410i | \(-0.0441991\pi\) |
−0.882585 | + | 0.470152i | \(0.844199\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.06962 | − | 9.44731i | 0.161559 | − | 0.497227i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.1369 | + | 3.29369i | −0.532051 | + | 0.172874i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.60900 | + | 7.72012i | 0.292787 | + | 0.402987i | 0.929917 | − | 0.367770i | \(-0.119878\pi\) |
−0.637130 | + | 0.770757i | \(0.719878\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.94895 | − | 6.50180i | 0.465864 | − | 0.338470i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.1567 | − | 22.6367i | −1.61758 | − | 1.17524i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.23959 | − | 0.402767i | −0.0641835 | − | 0.0208545i | 0.276749 | − | 0.960942i | \(-0.410743\pi\) |
−0.340933 | + | 0.940088i | \(0.610743\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.649125 | + | 0.210914i | 0.0334317 | + | 0.0108626i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.6474 | + | 14.2747i | 1.00922 | + | 0.733240i | 0.964045 | − | 0.265739i | \(-0.0856160\pi\) |
0.0451733 | + | 0.998979i | \(0.485616\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.1627 | − | 10.2898i | 0.725576 | − | 0.527162i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.13094 | − | 9.81489i | −0.364374 | − | 0.501518i | 0.586987 | − | 0.809596i | \(-0.300314\pi\) |
−0.951361 | + | 0.308079i | \(0.900314\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.68665 | + | 2.17262i | −0.339901 | + | 0.110441i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.04178 | − | 27.8278i | 0.458437 | − | 1.41092i | −0.408616 | − | 0.912706i | \(-0.633988\pi\) |
0.867053 | − | 0.498217i | \(-0.166012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.975518 | + | 3.00234i | 0.0493341 | + | 0.151835i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.8660i | 0.951664i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.69940 | + | 5.09179i | −0.185668 | + | 0.255550i | −0.891697 | − | 0.452633i | \(-0.850485\pi\) |
0.706029 | + | 0.708183i | \(0.250485\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −23.2609 | −1.16450 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.3064 | 1.51343 | 0.756714 | − | 0.653747i | \(-0.226804\pi\) | ||||
0.756714 | + | 0.653747i | \(0.226804\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.82089 | − | 6.63539i | 0.240146 | − | 0.330532i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.57536i | 0.177224i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.70942 | − | 17.5718i | −0.282313 | − | 0.868870i | −0.987191 | − | 0.159541i | \(-0.948998\pi\) |
0.704878 | − | 0.709328i | \(-0.251002\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.09472 | + | 12.6023i | −0.201978 | + | 0.621623i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.9922 | − | 9.74505i | 1.47582 | − | 0.479523i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.93508 | + | 13.6745i | 0.486523 | + | 0.669641i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.1586 | + | 13.1930i | −0.887108 | + | 0.644522i | −0.935122 | − | 0.354325i | \(-0.884711\pi\) |
0.0480143 | + | 0.998847i | \(0.484711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.05679 | + | 3.67397i | 0.246453 | + | 0.179058i | 0.704153 | − | 0.710048i | \(-0.251327\pi\) |
−0.457700 | + | 0.889106i | \(0.651327\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.62543 | + | 2.80257i | 0.419383 | + | 0.136266i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.7975 | + | 6.43260i | 0.958069 | + | 0.311296i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.456757 | − | 0.331853i | −0.0220524 | − | 0.0160220i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.9850 | + | 20.3323i | −1.34799 | + | 0.979373i | −0.348882 | + | 0.937167i | \(0.613439\pi\) |
−0.999109 | + | 0.0422061i | \(0.986561\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.31081 | + | 3.18056i | 0.111050 | + | 0.152848i | 0.860924 | − | 0.508733i | \(-0.169886\pi\) |
−0.749874 | + | 0.661581i | \(0.769886\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.94784 | − | 2.25749i | 0.332360 | − | 0.107990i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.54170 | + | 4.74487i | −0.0735815 | + | 0.226460i | −0.981083 | − | 0.193589i | \(-0.937987\pi\) |
0.907501 | + | 0.420049i | \(0.137987\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.61562 | + | 11.1277i | 0.172173 | + | 0.529893i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.92754i | 0.471672i | 0.971793 | + | 0.235836i | \(0.0757828\pi\) | ||||
−0.971793 | + | 0.235836i | \(0.924217\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.14892 | − | 9.83964i | 0.338132 | − | 0.465399i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.87365 | −0.465966 | −0.232983 | − | 0.972481i | \(-0.574849\pi\) | ||||
−0.232983 | + | 0.972481i | \(0.574849\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.46320 | 0.304340 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.78643 | − | 7.96433i | 0.271870 | − | 0.374197i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 12.6424i | − | 0.591387i | −0.955283 | − | 0.295693i | \(-0.904449\pi\) | ||
0.955283 | − | 0.295693i | \(-0.0955507\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.718278 | − | 2.21063i | −0.0335263 | − | 0.103183i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.2911 | − | 37.8280i | 0.572452 | − | 1.76183i | −0.0722451 | − | 0.997387i | \(-0.523016\pi\) |
0.644697 | − | 0.764438i | \(-0.276984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.20242 | + | 1.36545i | −0.195303 | + | 0.0634578i | −0.405035 | − | 0.914301i | \(-0.632741\pi\) |
0.209732 | + | 0.977759i | \(0.432741\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.62706 | − | 9.12137i | −0.306664 | − | 0.422086i | 0.627673 | − | 0.778477i | \(-0.284007\pi\) |
−0.934337 | + | 0.356390i | \(0.884007\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.31546 | + | 0.955738i | −0.0607423 | + | 0.0441319i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.9509 | − | 10.8625i | −0.688902 | − | 0.500517i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.90698 | − | 1.26945i | −0.179643 | − | 0.0583696i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.46984 | − | 2.75202i | −0.387807 | − | 0.126006i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.49728 | − | 3.26747i | −0.205486 | − | 0.149294i | 0.480283 | − | 0.877114i | \(-0.340534\pi\) |
−0.685769 | + | 0.727819i | \(0.740534\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.78343 | − | 3.47536i | 0.218105 | − | 0.158463i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.45213 | − | 4.75145i | −0.157077 | − | 0.216198i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.8199 | + | 5.14021i | −0.716870 | + | 0.232925i | −0.644665 | − | 0.764465i | \(-0.723003\pi\) |
−0.0722042 | + | 0.997390i | \(0.523003\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.49212 | + | 13.8253i | −0.203141 | + | 0.625202i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.327326 | + | 1.00741i | 0.0147720 | + | 0.0454636i | 0.958171 | − | 0.286197i | \(-0.0923912\pi\) |
−0.943399 | + | 0.331661i | \(0.892391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.64187i | 0.0739459i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26.8428 | + | 36.9459i | −1.20406 | + | 1.65725i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.9700 | −1.11781 | −0.558906 | − | 0.829231i | \(-0.688779\pi\) | ||||
−0.558906 | + | 0.829231i | \(0.688779\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.49299 | 0.200732 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.37458 | − | 10.1502i | 0.328816 | − | 0.452576i | −0.612317 | − | 0.790612i | \(-0.709762\pi\) |
0.941133 | + | 0.338036i | \(0.109762\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 12.0663i | − | 0.535885i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.76735 | + | 14.6724i | 0.211309 | + | 0.650342i | 0.999395 | + | 0.0347770i | \(0.0110721\pi\) |
−0.788086 | + | 0.615565i | \(0.788928\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.285135 | − | 0.877556i | 0.0126136 | − | 0.0388208i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.11572 | + | 1.66220i | −0.225865 | + | 0.0733878i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.11477 | + | 4.28711i | 0.136987 | + | 0.188547i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.61654 | + | 1.17449i | −0.0709584 | + | 0.0515543i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.6466 | + | 11.3679i | 0.685490 | + | 0.498037i | 0.875174 | − | 0.483808i | \(-0.160747\pi\) |
−0.189685 | + | 0.981845i | \(0.560747\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.61022 | + | 2.14779i | 0.289045 | + | 0.0939163i | 0.449951 | − | 0.893053i | \(-0.351442\pi\) |
−0.160906 | + | 0.986970i | \(0.551442\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.7642 | + | 6.09686i | 0.817382 | + | 0.265583i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.1151 | − | 12.4349i | −0.744136 | − | 0.540647i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.89976 | − | 4.28642i | 0.256028 | − | 0.186015i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.28244 | − | 8.64703i | −0.272123 | − | 0.374545i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.2951 | + | 4.31984i | −0.573727 | + | 0.186415i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.11259 | + | 6.50189i | −0.0909958 | + | 0.280056i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.75145 | + | 5.39040i | 0.0753006 | + | 0.231751i | 0.981621 | − | 0.190839i | \(-0.0611209\pi\) |
−0.906321 | + | 0.422590i | \(0.861121\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 13.5379i | − | 0.580968i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.28835 | + | 10.0315i | −0.311627 | + | 0.428918i | −0.935888 | − | 0.352298i | \(-0.885400\pi\) |
0.624261 | + | 0.781216i | \(0.285400\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.81370 | 0.205444 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.79951 | 0.161865 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.8586 | + | 24.5803i | −0.759427 | + | 1.04526i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 24.8970i | − | 1.05492i | −0.849579 | − | 0.527461i | \(-0.823144\pi\) | ||
0.849579 | − | 0.527461i | \(-0.176856\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.09932 | + | 6.46105i | 0.0887919 | + | 0.273273i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.419687 | − | 1.29166i | 0.0177192 | − | 0.0545340i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.8035 | − | 7.73423i | 1.00320 | − | 0.325959i | 0.239055 | − | 0.971006i | \(-0.423162\pi\) |
0.764143 | + | 0.645047i | \(0.223162\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.54182 | + | 3.49851i | 0.106746 | + | 0.146924i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.69282 | − | 1.22991i | 0.0709669 | − | 0.0515605i | −0.551736 | − | 0.834019i | \(-0.686034\pi\) |
0.622703 | + | 0.782458i | \(0.286034\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.32956 | + | 6.77832i | 0.390430 | + | 0.283664i | 0.765632 | − | 0.643279i | \(-0.222427\pi\) |
−0.375202 | + | 0.926943i | \(0.622427\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.42089 | − | 0.786594i | −0.101134 | − | 0.0328604i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.55908 | + | 1.80625i | 0.231427 | + | 0.0751954i | 0.422435 | − | 0.906393i | \(-0.361175\pi\) |
−0.191007 | + | 0.981589i | \(0.561175\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.53487 | − | 3.29478i | −0.188463 | − | 0.136926i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −56.3655 | + | 40.9519i | −2.33843 | + | 1.69897i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.05858 | − | 4.20978i | −0.126673 | − | 0.174351i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.75234 | + | 2.84381i | −0.361248 | + | 0.117377i | −0.484017 | − | 0.875059i | \(-0.660823\pi\) |
0.122769 | + | 0.992435i | \(0.460823\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.1090 | − | 43.4231i | 0.581352 | − | 1.78922i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.42770 | + | 7.47170i | 0.0998623 | + | 0.307345i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14.9033i | − | 0.612004i | −0.952031 | − | 0.306002i | \(-0.901009\pi\) | ||
0.952031 | − | 0.306002i | \(-0.0989914\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.99060 | − | 13.7509i | 0.408888 | − | 0.562786i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.52244 | 0.307359 | 0.153679 | − | 0.988121i | \(-0.450888\pi\) | ||||
0.153679 | + | 0.988121i | \(0.450888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.6618 | 0.761232 | 0.380616 | − | 0.924733i | \(-0.375712\pi\) | ||||
0.380616 | + | 0.924733i | \(0.375712\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.221011 | + | 0.304195i | −0.00900025 | + | 0.0123878i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 0.810016i | − | 0.0328776i | −0.999865 | − | 0.0164388i | \(-0.994767\pi\) | ||
0.999865 | − | 0.0164388i | \(-0.00523286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.943920 | − | 2.90509i | −0.0382496 | − | 0.117720i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.70802 | − | 8.33443i | 0.109555 | − | 0.337175i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.74678 | + | 1.54232i | −0.191721 | + | 0.0622938i | −0.403304 | − | 0.915066i | \(-0.632138\pi\) |
0.211583 | + | 0.977360i | \(0.432138\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.0455 | − | 34.4722i | −1.00829 | − | 1.38780i | −0.920095 | − | 0.391695i | \(-0.871889\pi\) |
−0.0881990 | − | 0.996103i | \(-0.528111\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.9038 | − | 21.7264i | 1.20193 | − | 0.873257i | 0.207461 | − | 0.978243i | \(-0.433480\pi\) |
0.994474 | + | 0.104987i | \(0.0334800\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.09875 | − | 0.798291i | −0.0440915 | − | 0.0320343i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −57.6595 | − | 18.7347i | −2.31008 | − | 0.750590i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.98909 | − | 0.971215i | −0.119373 | − | 0.0387866i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.5068 | + | 8.36018i | 0.458806 | + | 0.333342i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.8891 | − | 19.5361i | 1.07044 | − | 0.777719i | 0.0944476 | − | 0.995530i | \(-0.469892\pi\) |
0.975991 | + | 0.217811i | \(0.0698915\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.61494 | − | 10.4811i | −0.302667 | − | 0.416585i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.7523 | − | 3.49364i | 0.426022 | − | 0.138423i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.26336 | + | 10.0436i | −0.129097 | + | 0.397319i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.41649 | − | 25.9033i | −0.332431 | − | 1.02312i | −0.967974 | − | 0.251052i | \(-0.919223\pi\) |
0.635542 | − | 0.772066i | \(-0.280777\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 12.8557i | − | 0.506978i | −0.967338 | − | 0.253489i | \(-0.918422\pi\) | ||
0.967338 | − | 0.253489i | \(-0.0815782\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.7155 | + | 25.7597i | −0.735784 | + | 1.01272i | 0.263066 | + | 0.964778i | \(0.415266\pi\) |
−0.998850 | + | 0.0479418i | \(0.984734\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.26098 | 0.167258 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −36.7062 | −1.43863 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.52402 | + | 11.7323i | −0.333571 | + | 0.459121i | −0.942550 | − | 0.334066i | \(-0.891579\pi\) |
0.608979 | + | 0.793186i | \(0.291579\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 0.213375i | − | 0.00832454i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.2713 | − | 31.6118i | −0.400113 | − | 1.23142i | −0.924908 | − | 0.380192i | \(-0.875858\pi\) |
0.524795 | − | 0.851229i | \(-0.324142\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.84316 | + | 30.2941i | −0.382854 | + | 1.17830i | 0.555170 | + | 0.831737i | \(0.312653\pi\) |
−0.938025 | + | 0.346568i | \(0.887347\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.13605 | + | 0.694044i | −0.0829573 | + | 0.0269545i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.563883 | + | 0.776118i | 0.0218336 | + | 0.0300514i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.3552 | + | 11.1562i | −0.593668 | + | 0.431325i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.27546 | + | 1.65322i | 0.0878432 | + | 0.0638218i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.9095 | − | 8.09358i | −0.960190 | − | 0.311985i | −0.213341 | − | 0.976978i | \(-0.568434\pi\) |
−0.746849 | + | 0.664993i | \(0.768434\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.1177 | + | 4.58711i | 0.542586 | + | 0.176297i | 0.567471 | − | 0.823393i | \(-0.307922\pi\) |
−0.0248849 | + | 0.999690i | \(0.507922\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 55.1086 | + | 40.0387i | 2.11487 | + | 1.53655i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.311560 | + | 0.226361i | −0.0119390 | + | 0.00867418i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.30703 | + | 4.55174i | 0.126540 | + | 0.174168i | 0.867586 | − | 0.497286i | \(-0.165670\pi\) |
−0.741046 | + | 0.671454i | \(0.765670\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.76593 | + | 3.17314i | −0.372593 | + | 0.121063i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.65917 | + | 8.18408i | −0.101306 | + | 0.311788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.6330 | + | 32.7249i | 0.404497 | + | 1.24492i | 0.921314 | + | 0.388819i | \(0.127117\pi\) |
−0.516817 | + | 0.856096i | \(0.672883\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.52673i | 0.0959824i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.1128 | − | 20.8009i | 0.572436 | − | 0.787891i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.6380 | −0.818425 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.86294 | 0.334749 | 0.167374 | − | 0.985893i | \(-0.446471\pi\) | ||||
0.167374 | + | 0.985893i | \(0.446471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.3466 | − | 26.6284i | 0.729673 | − | 1.00431i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 30.8839i | − | 1.16151i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.474877 | − | 1.46152i | −0.0178344 | − | 0.0548885i | 0.941743 | − | 0.336333i | \(-0.109187\pi\) |
−0.959578 | + | 0.281444i | \(0.909187\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.17113 | + | 6.68206i | −0.0814239 | + | 0.250597i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.9638 | − | 3.56237i | 0.410599 | − | 0.133412i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.53535 | + | 6.24238i | 0.169376 | + | 0.233126i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.4808 | + | 11.2474i | −0.577335 | + | 0.419459i | −0.837762 | − | 0.546035i | \(-0.816137\pi\) |
0.260427 | + | 0.965493i | \(0.416137\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.63740 | − | 3.36926i | −0.172706 | − | 0.125478i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.0868 | + | 7.82629i | 0.895799 | + | 0.291063i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.5184 | − | 14.4649i | −1.65110 | − | 0.536474i | −0.672119 | − | 0.740443i | \(-0.734616\pi\) |
−0.978977 | + | 0.203970i | \(0.934616\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.2212 | + | 9.60574i | −0.489003 | + | 0.355281i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.9796 | − | 41.2634i | −1.10732 | − | 1.52410i | −0.825303 | − | 0.564690i | \(-0.808996\pi\) |
−0.282019 | − | 0.959409i | \(-0.591004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.208946 | + | 0.0678906i | −0.00769662 | + | 0.00250078i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.08075 | + | 12.5592i | −0.150113 | + | 0.461999i | −0.997633 | − | 0.0687637i | \(-0.978095\pi\) |
0.847520 | + | 0.530763i | \(0.178095\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.60612 | + | 4.94312i | 0.0590022 | + | 0.181590i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.6063i | 0.389107i | 0.980892 | + | 0.194553i | \(0.0623258\pi\) | ||||
−0.980892 | + | 0.194553i | \(0.937674\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.46998 | + | 13.0343i | −0.346488 | + | 0.476900i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −76.4534 | −2.79355 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.2581 | 1.03115 | 0.515577 | − | 0.856843i | \(-0.327578\pi\) | ||||
0.515577 | + | 0.856843i | \(0.327578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.41018 | − | 1.94094i | 0.0513897 | − | 0.0707318i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 27.7474i | − | 1.00849i | −0.863559 | − | 0.504247i | \(-0.831770\pi\) | ||
0.863559 | − | 0.504247i | \(-0.168230\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.245221 | − | 0.754713i | −0.00890096 | − | 0.0273943i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.97988 | + | 15.3265i | −0.180521 | + | 0.555585i | −0.999842 | − | 0.0177487i | \(-0.994350\pi\) |
0.819322 | + | 0.573334i | \(0.194350\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.5582 | + | 4.73024i | −0.527042 | + | 0.171246i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.14181 | − | 5.70071i | −0.149552 | − | 0.205841i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.1081 | + | 20.4217i | −1.01360 | + | 0.736426i | −0.964962 | − | 0.262390i | \(-0.915489\pi\) |
−0.0486417 | + | 0.998816i | \(0.515489\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.5759 | − | 8.41040i | −0.416897 | − | 0.302893i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.3198 | + | 7.25215i | 0.802788 | + | 0.260842i | 0.681540 | − | 0.731781i | \(-0.261310\pi\) |
0.121248 | + | 0.992622i | \(0.461310\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −25.1662 | − | 8.17701i | −0.902834 | − | 0.293349i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −48.1363 | − | 34.9731i | −1.72466 | − | 1.25304i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.99199 | + | 3.62689i | −0.178627 | + | 0.129780i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.415189 | − | 0.571459i | −0.0148377 | − | 0.0204223i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.3677 | + | 7.91755i | −0.868615 | + | 0.282230i | −0.709222 | − | 0.704985i | \(-0.750954\pi\) |
−0.159393 | + | 0.987215i | \(0.550954\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.04210 | − | 12.4403i | 0.143903 | − | 0.442887i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.3696 | + | 71.9244i | 0.830929 | + | 2.55734i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.65129i | − | 0.165172i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.13034 | − | 1.55577i | 0.0400386 | − | 0.0551083i | −0.788528 | − | 0.614998i | \(-0.789157\pi\) |
0.828567 | + | 0.559890i | \(0.189157\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.0807 | 0.745781 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.0197 | −0.495362 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.0732815 | − | 0.100863i | 0.00258605 | − | 0.00355939i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.6749i | 1.07981i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.0321 | + | 43.1862i | 0.493341 | + | 1.51835i | 0.819526 | + | 0.573041i | \(0.194237\pi\) |
−0.326185 | + | 0.945306i | \(0.605763\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.39190 | + | 22.7499i | −0.259565 | + | 0.798858i | 0.733331 | + | 0.679872i | \(0.237965\pi\) |
−0.992896 | + | 0.118987i | \(0.962035\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.5395 | − | 4.39924i | 0.474850 | − | 0.154288i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.2291 | + | 30.5957i | 0.777697 | + | 1.07041i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.38048 | − | 2.45606i | 0.118123 | − | 0.0858217i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.5538 | + | 18.5659i | 0.891834 | + | 0.647955i | 0.936356 | − | 0.351053i | \(-0.114176\pi\) |
−0.0445216 | + | 0.999008i | \(0.514176\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.11491 | + | 2.63669i | 0.282868 | + | 0.0919094i | 0.447015 | − | 0.894527i | \(-0.352487\pi\) |
−0.164147 | + | 0.986436i | \(0.552487\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.9224 | − | 5.49842i | −0.588450 | − | 0.191199i | −0.000367397 | − | 1.00000i | \(-0.500117\pi\) |
−0.588082 | + | 0.808801i | \(0.700117\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.2323 | − | 27.0508i | −1.29313 | − | 0.939515i | −0.293267 | − | 0.956030i | \(-0.594743\pi\) |
−0.999864 | + | 0.0165158i | \(0.994743\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.2861 | − | 11.8325i | 0.564957 | − | 0.410465i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.9856 | + | 22.0023i | 0.553869 | + | 0.762335i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.07273 | + | 2.62299i | −0.279034 | + | 0.0906637i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.312751 | + | 0.962548i | −0.0107974 | + | 0.0332308i | −0.956310 | − | 0.292354i | \(-0.905561\pi\) |
0.945513 | + | 0.325585i | \(0.105561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.80731 | − | 27.1061i | −0.303700 | − | 0.934694i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.81651i | 0.338099i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.0922 | − | 37.2892i | 0.930899 | − | 1.28127i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.54547 | 0.224640 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.31054 | 0.284882 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.76813 | + | 7.93916i | −0.197497 | + | 0.271832i | −0.896267 | − | 0.443515i | \(-0.853731\pi\) |
0.698770 | + | 0.715347i | \(0.253731\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 57.3424i | 1.95878i | 0.201979 | + | 0.979390i | \(0.435263\pi\) | ||||
−0.201979 | + | 0.979390i | \(0.564737\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.31727 | − | 10.2095i | −0.113184 | − | 0.348344i | 0.878380 | − | 0.477963i | \(-0.158625\pi\) |
−0.991564 | + | 0.129619i | \(0.958625\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.7816 | + | 45.4932i | −0.503757 | + | 1.55040i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.16105 | + | 2.97661i | −0.311846 | + | 0.101325i | −0.460759 | − | 0.887525i | \(-0.652423\pi\) |
0.148913 | + | 0.988850i | \(0.452423\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.81665 | + | 9.38232i | 0.231506 | + | 0.318640i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.32120 | + | 2.41299i | −0.112664 | + | 0.0818551i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.293932 | + | 0.213554i | 0.00995951 | + | 0.00723601i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.9811 | + | 4.86764i | 0.507032 | + | 0.164745i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.669370 | + | 0.217491i | 0.0226030 | + | 0.00734416i | 0.320297 | − | 0.947317i | \(-0.396217\pi\) |
−0.297694 | + | 0.954661i | \(0.596217\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.703382 | − | 0.511037i | −0.0237245 | − | 0.0172369i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.03076 | + | 5.83469i | −0.270563 | + | 0.196576i | −0.714791 | − | 0.699338i | \(-0.753478\pi\) |
0.444228 | + | 0.895914i | \(0.353478\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.89850 | − | 13.6241i | −0.333111 | − | 0.458488i | 0.609302 | − | 0.792938i | \(-0.291450\pi\) |
−0.942414 | + | 0.334450i | \(0.891450\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.1212 | − | 14.3358i | 1.48144 | − | 0.481351i | 0.546901 | − | 0.837198i | \(-0.315808\pi\) |
0.934544 | + | 0.355847i | \(0.115808\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.3935 | + | 71.9979i | −0.784594 | + | 2.41473i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.180557 | + | 0.555698i | 0.00604890 | + | 0.0186166i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 48.7837i | − | 1.63249i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.771358 | + | 1.06168i | −0.0257549 | + | 0.0354486i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.99572 | 0.199968 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.7004 | −0.689630 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.8709 | − | 24.5972i | 0.594706 | − | 0.818543i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 28.5101i | − | 0.946662i | −0.880885 | − | 0.473331i | \(-0.843051\pi\) | ||
0.880885 | − | 0.473331i | \(-0.156949\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.20693 | − | 6.79224i | −0.0731993 | − | 0.225284i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.00884 | + | 6.18256i | −0.0665557 | + | 0.204837i | −0.978804 | − | 0.204801i | \(-0.934345\pi\) |
0.912248 | + | 0.409639i | \(0.134345\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.95301 | + | 2.90901i | −0.296301 | + | 0.0962742i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −47.9539 | − | 66.0029i | −1.58358 | − | 2.17961i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.6130 | − | 9.89041i | 0.449051 | − | 0.326255i | −0.340170 | − | 0.940364i | \(-0.610485\pi\) |
0.789221 | + | 0.614109i | \(0.210485\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.5768 | + | 12.7703i | 0.579174 | + | 0.420795i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.70474 | + | 3.15326i | 0.319436 | + | 0.103791i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.26066 | − | 0.409613i | −0.0414054 | − | 0.0134534i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.5979 | − | 18.5979i | −0.839839 | − | 0.610179i | 0.0824866 | − | 0.996592i | \(-0.473714\pi\) |
−0.922326 | + | 0.386413i | \(0.873714\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.9165 | − | 36.9930i | 1.66872 | − | 1.21240i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.1580 | + | 15.3576i | 0.365296 | + | 0.502787i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.23598 | + | 0.726513i | −0.0730462 | + | 0.0237341i | −0.345312 | − | 0.938488i | \(-0.612227\pi\) |
0.272266 | + | 0.962222i | \(0.412227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.87947 | + | 5.78443i | −0.0613343 | + | 0.188768i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.32816 | + | 4.08766i | 0.0432968 | + | 0.133254i | 0.970368 | − | 0.241631i | \(-0.0776823\pi\) |
−0.927071 | + | 0.374885i | \(0.877682\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 15.0230i | − | 0.489217i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.3650 | + | 22.5245i | −0.531791 | + | 0.731948i | −0.987402 | − | 0.158231i | \(-0.949421\pi\) |
0.455611 | + | 0.890179i | \(0.349421\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.206176 | −0.00669275 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.97817 | −0.0641467 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.2275 | + | 36.0991i | −0.849593 | + | 1.16936i | 0.134359 | + | 0.990933i | \(0.457102\pi\) |
−0.983952 | + | 0.178432i | \(0.942898\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.412724i | − | 0.0133415i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.7072 | − | 54.4971i | −0.571795 | − | 1.75980i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.6848 | − | 39.0399i | 0.409188 | − | 1.25935i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.8143 | + | 5.46328i | −0.541832 | + | 0.176052i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.4372 | − | 44.6460i | −1.04311 | − | 1.43572i | −0.894632 | − | 0.446804i | \(-0.852562\pi\) |
−0.148479 | − | 0.988916i | \(-0.547438\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.1151 | + | 7.34902i | −0.324942 | + | 0.236084i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.00915 | + | 3.63936i | 0.160751 | + | 0.116793i | 0.665253 | − | 0.746618i | \(-0.268324\pi\) |
−0.504502 | + | 0.863411i | \(0.668324\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −69.5160 | − | 22.5871i | −2.22858 | − | 0.724109i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.9819 | − | 7.46728i | −0.735257 | − | 0.238900i | −0.0826317 | − | 0.996580i | \(-0.526333\pi\) |
−0.652626 | + | 0.757681i | \(0.726333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.62719 | − | 4.81494i | −0.211806 | − | 0.153886i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.86374 | + | 2.08063i | −0.0914321 | + | 0.0664293i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.59750 | + | 7.70430i | 0.178533 | + | 0.245729i | 0.888899 | − | 0.458103i | \(-0.151471\pi\) |
−0.710367 | + | 0.703832i | \(0.751471\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −37.2998 | + | 12.1194i | −1.18727 | + | 0.385766i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.95072 | + | 9.08137i | −0.0938273 | + | 0.288771i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.21741 | − | 9.90216i | −0.102204 | − | 0.314553i | 0.886860 | − | 0.462039i | \(-0.152882\pi\) |
−0.989064 | + | 0.147486i | \(0.952882\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.1307i | 0.416691i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.9556 | − | 46.7359i | 1.07539 | − | 1.48014i | 0.210883 | − | 0.977511i | \(-0.432366\pi\) |
0.864502 | − | 0.502629i | \(-0.167634\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.11909 | −0.193599 |
(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 | 1500.2.o.b.649.1 | 16 | ||
5.2 | odd | 4 | 300.2.m.b.121.1 | ✓ | 8 | ||
5.3 | odd | 4 | 1500.2.m.a.601.1 | 8 | |||
5.4 | even | 2 | inner | 1500.2.o.b.649.4 | 16 | ||
15.2 | even | 4 | 900.2.n.b.721.2 | 8 | |||
25.6 | even | 5 | inner | 1500.2.o.b.349.3 | 16 | ||
25.8 | odd | 20 | 1500.2.m.a.901.1 | 8 | |||
25.9 | even | 10 | 7500.2.d.c.1249.8 | 8 | |||
25.12 | odd | 20 | 7500.2.a.e.1.4 | 4 | |||
25.13 | odd | 20 | 7500.2.a.f.1.1 | 4 | |||
25.16 | even | 5 | 7500.2.d.c.1249.1 | 8 | |||
25.17 | odd | 20 | 300.2.m.b.181.1 | yes | 8 | ||
25.19 | even | 10 | inner | 1500.2.o.b.349.2 | 16 | ||
75.17 | even | 20 | 900.2.n.b.181.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.m.b.121.1 | ✓ | 8 | 5.2 | odd | 4 | ||
300.2.m.b.181.1 | yes | 8 | 25.17 | odd | 20 | ||
900.2.n.b.181.2 | 8 | 75.17 | even | 20 | |||
900.2.n.b.721.2 | 8 | 15.2 | even | 4 | |||
1500.2.m.a.601.1 | 8 | 5.3 | odd | 4 | |||
1500.2.m.a.901.1 | 8 | 25.8 | odd | 20 | |||
1500.2.o.b.349.2 | 16 | 25.19 | even | 10 | inner | ||
1500.2.o.b.349.3 | 16 | 25.6 | even | 5 | inner | ||
1500.2.o.b.649.1 | 16 | 1.1 | even | 1 | trivial | ||
1500.2.o.b.649.4 | 16 | 5.4 | even | 2 | inner | ||
7500.2.a.e.1.4 | 4 | 25.12 | odd | 20 | |||
7500.2.a.f.1.1 | 4 | 25.13 | odd | 20 | |||
7500.2.d.c.1249.1 | 8 | 25.16 | even | 5 | |||
7500.2.d.c.1249.8 | 8 | 25.9 | even | 10 |