Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(431,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.p (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 648) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 431.14 | ||
Character | \(\chi\) | \(=\) | 2592.431 |
Dual form | 2592.2.p.g.2159.14 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.474833 | + | 0.822435i | 0.212352 | + | 0.367804i | 0.952450 | − | 0.304695i | \(-0.0985544\pi\) |
−0.740098 | + | 0.672499i | \(0.765221\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.07898 | − | 2.35500i | −1.54171 | − | 0.890106i | −0.998731 | − | 0.0503587i | \(-0.983964\pi\) |
−0.542978 | − | 0.839747i | \(-0.682703\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.72007 | + | 2.14778i | 1.12164 | + | 0.647581i | 0.941820 | − | 0.336118i | \(-0.109114\pi\) |
0.179823 | + | 0.983699i | \(0.442448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.52349 | + | 2.03429i | −0.977240 | + | 0.564210i | −0.901436 | − | 0.432913i | \(-0.857486\pi\) |
−0.0758039 | + | 0.997123i | \(0.524152\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.19178i | − | 0.289049i | −0.989501 | − | 0.144524i | \(-0.953835\pi\) | ||
0.989501 | − | 0.144524i | \(-0.0461652\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.17693 | 0.728837 | 0.364418 | − | 0.931235i | \(-0.381268\pi\) | ||||
0.364418 | + | 0.931235i | \(0.381268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.375325 | + | 0.650083i | 0.0782608 | + | 0.135552i | 0.902500 | − | 0.430691i | \(-0.141730\pi\) |
−0.824239 | + | 0.566242i | \(0.808397\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.04907 | − | 3.54909i | 0.409813 | − | 0.709818i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.87181 | − | 6.70617i | 0.718977 | − | 1.24530i | −0.242428 | − | 0.970169i | \(-0.577944\pi\) |
0.961405 | − | 0.275136i | \(-0.0887227\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.496917 | + | 0.286895i | −0.0892490 | + | 0.0515279i | −0.543960 | − | 0.839111i | \(-0.683076\pi\) |
0.454711 | + | 0.890639i | \(0.349742\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 4.47293i | − | 0.756062i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.87320i | 0.801148i | 0.916264 | + | 0.400574i | \(0.131189\pi\) | ||||
−0.916264 | + | 0.400574i | \(0.868811\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.45135 | + | 4.87939i | −1.31988 | + | 0.762032i | −0.983709 | − | 0.179769i | \(-0.942465\pi\) |
−0.336170 | + | 0.941801i | \(0.609132\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.65770 | + | 4.60327i | −0.405295 | + | 0.701992i | −0.994356 | − | 0.106097i | \(-0.966165\pi\) |
0.589060 | + | 0.808089i | \(0.299498\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.91012 | + | 8.50458i | −0.716214 | + | 1.24052i | 0.246275 | + | 0.969200i | \(0.420793\pi\) |
−0.962489 | + | 0.271320i | \(0.912540\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.59204 | + | 13.1498i | 1.08458 | + | 1.87854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.877682 | 0.120559 | 0.0602794 | − | 0.998182i | \(-0.480801\pi\) | ||||
0.0602794 | + | 0.998182i | \(0.480801\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.07935i | 0.550060i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.51936 | + | 0.877204i | −0.197804 | + | 0.114202i | −0.595631 | − | 0.803258i | \(-0.703098\pi\) |
0.397827 | + | 0.917461i | \(0.369765\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.59196 | + | 4.96057i | 1.10009 | + | 0.635136i | 0.936244 | − | 0.351350i | \(-0.114277\pi\) |
0.163844 | + | 0.986486i | \(0.447611\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.34614 | − | 1.93189i | −0.415037 | − | 0.239622i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.48335 | + | 9.49744i | 0.669898 | + | 1.16030i | 0.977932 | + | 0.208922i | \(0.0669954\pi\) |
−0.308034 | + | 0.951375i | \(0.599671\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.91048 | 1.17616 | 0.588079 | − | 0.808804i | \(-0.299884\pi\) | ||||
0.588079 | + | 0.808804i | \(0.299884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.74944 | 1.02404 | 0.512022 | − | 0.858972i | \(-0.328897\pi\) | ||||
0.512022 | + | 0.858972i | \(0.328897\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.1160 | − | 17.5215i | −1.15283 | − | 1.99676i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.97571 | + | 2.87273i | 0.559811 | + | 0.323207i | 0.753070 | − | 0.657941i | \(-0.228572\pi\) |
−0.193259 | + | 0.981148i | \(0.561906\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.8283 | + | 6.25173i | 1.18856 | + | 0.686217i | 0.957980 | − | 0.286836i | \(-0.0926034\pi\) |
0.230583 | + | 0.973053i | \(0.425937\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.980161 | − | 0.565896i | 0.106313 | − | 0.0613800i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 10.1440i | − | 1.07527i | −0.843179 | − | 0.537633i | \(-0.819319\pi\) | ||
0.843179 | − | 0.537633i | \(-0.180681\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.1630 | 2.00882 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.50851 | + | 2.61282i | 0.154770 | + | 0.268069i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.91511 | + | 6.78118i | −0.397520 | + | 0.688524i | −0.993419 | − | 0.114535i | \(-0.963462\pi\) |
0.595900 | + | 0.803059i | \(0.296796\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.92656 | + | 15.4613i | −0.888226 | + | 1.53845i | −0.0462544 | + | 0.998930i | \(0.514728\pi\) |
−0.841971 | + | 0.539522i | \(0.818605\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.12533 | − | 1.22706i | 0.209415 | − | 0.120906i | −0.391624 | − | 0.920125i | \(-0.628087\pi\) |
0.601040 | + | 0.799219i | \(0.294753\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.283208i | − | 0.0273788i | −0.999906 | − | 0.0136894i | \(-0.995642\pi\) | ||
0.999906 | − | 0.0136894i | \(-0.00435760\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.74716i | − | 0.933609i | −0.884361 | − | 0.466805i | \(-0.845405\pi\) | ||
0.884361 | − | 0.466805i | \(-0.154595\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.09400 | + | 2.36367i | −0.385131 | + | 0.222356i | −0.680048 | − | 0.733167i | \(-0.738041\pi\) |
0.294917 | + | 0.955523i | \(0.404708\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.356434 | + | 0.617362i | −0.0332376 | + | 0.0575693i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.80664 | + | 4.86124i | −0.257284 | + | 0.445629i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.72594 | + | 6.45351i | 0.338721 | + | 0.586683i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.64019 | 0.772802 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.8042i | 1.22492i | 0.790500 | + | 0.612462i | \(0.209821\pi\) | ||||
−0.790500 | + | 0.612462i | \(0.790179\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.10031 | − | 2.36731i | 0.358245 | − | 0.206833i | −0.310065 | − | 0.950715i | \(-0.600351\pi\) |
0.668311 | + | 0.743882i | \(0.267018\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.9586 | − | 7.48166i | −1.12365 | − | 0.648742i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.4704 | + | 7.77716i | 1.15086 | + | 0.664448i | 0.949096 | − | 0.314987i | \(-0.102000\pi\) |
0.201762 | + | 0.979435i | \(0.435333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.94490 | + | 6.83276i | 0.334602 | + | 0.579547i | 0.983408 | − | 0.181406i | \(-0.0580649\pi\) |
−0.648806 | + | 0.760953i | \(0.724732\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.4768 | −1.46148 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.35385 | 0.610704 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.00344 | + | 13.8624i | 0.655667 | + | 1.13565i | 0.981726 | + | 0.190300i | \(0.0609459\pi\) |
−0.326059 | + | 0.945350i | \(0.605721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.57918 | + | 0.911739i | 0.128512 | + | 0.0741962i | 0.562878 | − | 0.826540i | \(-0.309694\pi\) |
−0.434366 | + | 0.900736i | \(0.643028\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.471905 | − | 0.272455i | −0.0379044 | − | 0.0218841i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.7438 | + | 10.2444i | −1.41611 | + | 0.817589i | −0.995954 | − | 0.0898651i | \(-0.971356\pi\) |
−0.420152 | + | 0.907454i | \(0.638023\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.53556i | − | 0.278641i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.59374 | 0.594787 | 0.297394 | − | 0.954755i | \(-0.403883\pi\) | ||||
0.297394 | + | 0.954755i | \(0.403883\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.80664 | − | 4.86124i | −0.217184 | − | 0.376174i | 0.736762 | − | 0.676152i | \(-0.236354\pi\) |
−0.953946 | + | 0.299978i | \(0.903021\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.77664 | − | 3.07723i | 0.136665 | − | 0.236710i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.31622 | − | 10.9400i | 0.480214 | − | 0.831754i | −0.519529 | − | 0.854453i | \(-0.673892\pi\) |
0.999742 | + | 0.0226986i | \(0.00722582\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.7162 | + | 9.65110i | −1.26363 | + | 0.729555i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 20.5282i | − | 1.53435i | −0.641439 | − | 0.767174i | \(-0.721662\pi\) | ||
0.641439 | − | 0.767174i | \(-0.278338\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.96062i | 0.740367i | 0.928959 | + | 0.370184i | \(0.120705\pi\) | ||||
−0.928959 | + | 0.370184i | \(0.879295\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00789 | + | 2.31395i | −0.294666 | + | 0.170125i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.55968 | − | 4.43350i | 0.187182 | − | 0.324210i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.4999 | − | 19.9185i | 0.832105 | − | 1.44125i | −0.0642603 | − | 0.997933i | \(-0.520469\pi\) |
0.896366 | − | 0.443316i | \(-0.146198\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.500000 | + | 0.866025i | 0.0359908 | + | 0.0623379i | 0.883460 | − | 0.468507i | \(-0.155208\pi\) |
−0.847469 | + | 0.530845i | \(0.821875\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.519639 | 0.0370228 | 0.0185114 | − | 0.999829i | \(-0.494107\pi\) | ||||
0.0185114 | + | 0.999829i | \(0.494107\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 0.630646i | − | 0.0447053i | −0.999750 | − | 0.0223527i | \(-0.992884\pi\) | ||
0.999750 | − | 0.0223527i | \(-0.00711567\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −31.5861 | + | 18.2362i | −2.21691 | + | 1.27993i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.02596 | − | 4.63379i | −0.560557 | − | 0.323638i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.8184 | + | 6.82335i | 0.817495 | + | 0.471981i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.95897 | + | 8.58918i | 0.341389 | + | 0.591304i | 0.984691 | − | 0.174309i | \(-0.0557692\pi\) |
−0.643302 | + | 0.765613i | \(0.722436\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.04785 | −0.344261 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.70255 | 0.183461 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.42442 | + | 4.19922i | 0.163084 | + | 0.282470i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.15507 | − | 3.55363i | −0.412174 | − | 0.237969i | 0.279549 | − | 0.960131i | \(-0.409815\pi\) |
−0.691723 | + | 0.722162i | \(0.743148\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.7925 | − | 6.23105i | −0.716323 | − | 0.413569i | 0.0970749 | − | 0.995277i | \(-0.469051\pi\) |
−0.813398 | + | 0.581708i | \(0.802385\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.45996 | − | 4.88436i | 0.559050 | − | 0.322768i | −0.193714 | − | 0.981058i | \(-0.562053\pi\) |
0.752764 | + | 0.658290i | \(0.228720\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.66388i | − | 0.305541i | −0.988262 | − | 0.152771i | \(-0.951180\pi\) | ||
0.988262 | − | 0.152771i | \(-0.0488196\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.32595 | −0.608358 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.71266 | − | 2.96641i | −0.110783 | − | 0.191881i | 0.805303 | − | 0.592863i | \(-0.202002\pi\) |
−0.916086 | + | 0.400982i | \(0.868669\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.627860 | + | 1.08748i | −0.0404440 | + | 0.0700510i | −0.885539 | − | 0.464565i | \(-0.846211\pi\) |
0.845095 | + | 0.534616i | \(0.179544\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.20990 | + | 12.4879i | −0.460624 | + | 0.797824i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.1939 | + | 6.46278i | −0.712248 | + | 0.411217i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.2340i | 1.27716i | 0.769556 | + | 0.638579i | \(0.220477\pi\) | ||||
−0.769556 | + | 0.638579i | \(0.779523\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.22447i | 0.202721i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.01857 | − | 0.588069i | 0.0635364 | − | 0.0366828i | −0.467895 | − | 0.883784i | \(-0.654988\pi\) |
0.531432 | + | 0.847101i | \(0.321654\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.4764 | − | 19.8777i | 0.713107 | − | 1.23514i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.51217 | − | 6.08325i | 0.216570 | − | 0.375109i | −0.737187 | − | 0.675688i | \(-0.763847\pi\) |
0.953757 | + | 0.300579i | \(0.0971799\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.416752 | + | 0.721836i | 0.0256009 | + | 0.0443420i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.4172 | −0.696119 | −0.348060 | − | 0.937472i | \(-0.613159\pi\) | ||||
−0.348060 | + | 0.937472i | \(0.613159\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 10.9905i | − | 0.667625i | −0.942639 | − | 0.333813i | \(-0.891665\pi\) | ||
0.942639 | − | 0.333813i | \(-0.108335\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.2453 | − | 8.80190i | 0.919328 | − | 0.530775i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.11917 | + | 1.80085i | 0.187413 | + | 0.108203i | 0.590771 | − | 0.806839i | \(-0.298824\pi\) |
−0.403358 | + | 0.915042i | \(0.632157\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.6296 | − | 6.13703i | −0.634111 | − | 0.366104i | 0.148231 | − | 0.988953i | \(-0.452642\pi\) |
−0.782343 | + | 0.622848i | \(0.785975\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.27237 | − | 2.20381i | −0.0756344 | − | 0.131003i | 0.825728 | − | 0.564069i | \(-0.190765\pi\) |
−0.901362 | + | 0.433066i | \(0.857432\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 45.9638 | 2.71316 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.5797 | 0.916451 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.929672 | + | 1.61024i | 0.0543120 | + | 0.0940712i | 0.891903 | − | 0.452226i | \(-0.149370\pi\) |
−0.837591 | + | 0.546298i | \(0.816037\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.44289 | − | 0.833051i | −0.0840081 | − | 0.0485021i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.64491 | − | 1.52704i | −0.152959 | − | 0.0883109i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.6814 | − | 12.5178i | 1.24969 | − | 0.721512i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.42177i | 0.539489i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.0809 | −1.65973 | −0.829867 | − | 0.557961i | \(-0.811584\pi\) | ||||
−0.829867 | + | 0.557961i | \(0.811584\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.36300 | − | 16.2172i | −0.530927 | − | 0.919593i | −0.999349 | − | 0.0360877i | \(-0.988510\pi\) |
0.468421 | − | 0.883505i | \(-0.344823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.31967 | + | 14.4101i | −0.470256 | + | 0.814507i | −0.999421 | − | 0.0340117i | \(-0.989172\pi\) |
0.529166 | + | 0.848519i | \(0.322505\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.55605 | + | 11.3554i | −0.368224 | + | 0.637783i | −0.989288 | − | 0.145977i | \(-0.953368\pi\) |
0.621064 | + | 0.783760i | \(0.286701\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.8068 | − | 16.6316i | 1.61287 | − | 0.931191i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.78619i | − | 0.210669i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.6736i | 0.924883i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 40.0565 | − | 23.1266i | 2.20839 | − | 1.27501i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.3976 | + | 28.4014i | −0.901292 | + | 1.56108i | −0.0754743 | + | 0.997148i | \(0.524047\pi\) |
−0.825818 | + | 0.563937i | \(0.809286\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.20735 | + | 9.01940i | −0.284508 | + | 0.492782i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.1351 | − | 24.4827i | −0.769986 | − | 1.33366i | −0.937570 | − | 0.347798i | \(-0.886930\pi\) |
0.167583 | − | 0.985858i | \(-0.446404\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.46475 | −0.133474 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 38.5470i | − | 2.08134i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.92687 | + | 3.42188i | −0.318171 | + | 0.183696i | −0.650577 | − | 0.759440i | \(-0.725473\pi\) |
0.332406 | + | 0.943136i | \(0.392140\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.5091 | + | 7.22213i | 0.669596 | + | 0.386592i | 0.795924 | − | 0.605397i | \(-0.206986\pi\) |
−0.126327 | + | 0.991989i | \(0.540319\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.7547 | + | 7.94128i | 0.732088 | + | 0.422671i | 0.819186 | − | 0.573528i | \(-0.194426\pi\) |
−0.0870973 | + | 0.996200i | \(0.527759\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.70582 | + | 8.15073i | 0.249759 | + | 0.432596i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.84545 | −0.202955 | −0.101477 | − | 0.994838i | \(-0.532357\pi\) | ||||
−0.101477 | + | 0.994838i | \(0.532357\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.90714 | −0.468797 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.15452 | + | 7.19584i | 0.217458 | + | 0.376648i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.8803 | + | 13.7873i | 1.24654 | + | 0.719692i | 0.970418 | − | 0.241430i | \(-0.0776165\pi\) |
0.276124 | + | 0.961122i | \(0.410950\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.58004 | − | 2.06694i | −0.185867 | − | 0.107310i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.00779 | − | 4.04595i | 0.362849 | − | 0.209491i | −0.307481 | − | 0.951554i | \(-0.599486\pi\) |
0.670330 | + | 0.742063i | \(0.266153\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.5055i | 1.62261i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.9143 | 0.920195 | 0.460098 | − | 0.887868i | \(-0.347814\pi\) | ||||
0.460098 | + | 0.887868i | \(0.347814\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.88757 | − | 5.00142i | −0.147548 | − | 0.255561i | 0.782773 | − | 0.622308i | \(-0.213805\pi\) |
−0.930321 | + | 0.366747i | \(0.880471\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.60687 | − | 16.6396i | 0.489611 | − | 0.848032i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.0163 | − | 19.0807i | 0.558547 | − | 0.967432i | −0.439071 | − | 0.898453i | \(-0.644692\pi\) |
0.997618 | − | 0.0689799i | \(-0.0219744\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.774755 | − | 0.447305i | 0.0391810 | − | 0.0226212i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.45626i | 0.274534i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.3815i | 1.32405i | 0.749481 | + | 0.662026i | \(0.230303\pi\) | ||||
−0.749481 | + | 0.662026i | \(0.769697\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.11822 | − | 0.645607i | 0.0558414 | − | 0.0322401i | −0.471819 | − | 0.881695i | \(-0.656403\pi\) |
0.527661 | + | 0.849455i | \(0.323069\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.16725 | − | 2.02174i | 0.0581451 | − | 0.100710i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.4666 | + | 18.1286i | −0.518808 | + | 0.898602i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.772426 | + | 1.33788i | 0.0381940 | + | 0.0661539i | 0.884490 | − | 0.466558i | \(-0.154506\pi\) |
−0.846297 | + | 0.532712i | \(0.821173\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.26326 | 0.406608 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.8741i | 0.582878i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.9309 | − | 7.46567i | 0.631717 | − | 0.364722i | −0.149700 | − | 0.988732i | \(-0.547831\pi\) |
0.781417 | + | 0.624010i | \(0.214497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.8947 | + | 7.44478i | 0.628451 | + | 0.362836i | 0.780152 | − | 0.625590i | \(-0.215142\pi\) |
−0.151701 | + | 0.988426i | \(0.548475\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.22973 | − | 2.44204i | −0.205172 | − | 0.118456i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.3643 | − | 40.4681i | −1.13068 | − | 1.95839i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.8436 | −1.48568 | −0.742842 | − | 0.669467i | \(-0.766523\pi\) | ||||
−0.742842 | + | 0.669467i | \(0.766523\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.1892 | −1.40275 | −0.701373 | − | 0.712795i | \(-0.747429\pi\) | ||||
−0.701373 | + | 0.712795i | \(0.747429\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.19238 | + | 2.06527i | 0.0570393 | + | 0.0987950i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.08226 | − | 0.624843i | −0.0516535 | − | 0.0298221i | 0.473951 | − | 0.880551i | \(-0.342827\pi\) |
−0.525604 | + | 0.850729i | \(0.676161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.7521 | − | 13.7133i | −1.12850 | − | 0.651538i | −0.184940 | − | 0.982750i | \(-0.559209\pi\) |
−0.943556 | + | 0.331212i | \(0.892542\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.34282 | − | 4.81673i | 0.395487 | − | 0.228335i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 16.2552i | − | 0.767132i | −0.923513 | − | 0.383566i | \(-0.874696\pi\) | ||
0.923513 | − | 0.383566i | \(-0.125304\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −41.9194 | −1.97391 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.09921 | + | 15.7603i | 0.426578 | + | 0.738854i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.44307 | + | 16.3559i | −0.441728 | + | 0.765096i | −0.997818 | − | 0.0660267i | \(-0.978968\pi\) |
0.556090 | + | 0.831122i | \(0.312301\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.65240 | + | 16.7184i | −0.449557 | + | 0.778655i | −0.998357 | − | 0.0572981i | \(-0.981751\pi\) |
0.548800 | + | 0.835954i | \(0.315085\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.02823 | + | 1.17100i | −0.0942598 | + | 0.0544209i | −0.546389 | − | 0.837532i | \(-0.683998\pi\) |
0.452129 | + | 0.891952i | \(0.350665\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 12.2034i | − | 0.564708i | −0.959310 | − | 0.282354i | \(-0.908885\pi\) | ||
0.959310 | − | 0.282354i | \(-0.0911153\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 51.6531i | − | 2.38512i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.7736 | + | 11.4163i | −0.909193 | + | 0.524923i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.50974 | − | 11.2752i | 0.298687 | − | 0.517341i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.7237 | − | 30.6983i | 0.809815 | − | 1.40264i | −0.103177 | − | 0.994663i | \(-0.532901\pi\) |
0.912992 | − | 0.407978i | \(-0.133766\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.91348 | − | 17.1706i | −0.452016 | − | 0.782914i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.43610 | −0.337656 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.7853i | 0.851242i | 0.904902 | + | 0.425621i | \(0.139944\pi\) | ||||
−0.904902 | + | 0.425621i | \(0.860056\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.06466 | + | 0.614681i | −0.0480474 | + | 0.0277402i | −0.523831 | − | 0.851822i | \(-0.675498\pi\) |
0.475784 | + | 0.879562i | \(0.342164\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.99227 | − | 4.61434i | −0.359954 | − | 0.207819i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −40.4246 | − | 23.3392i | −1.81329 | − | 1.04690i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.73661 | − | 3.00789i | −0.0777413 | − | 0.134652i | 0.824534 | − | 0.565813i | \(-0.191437\pi\) |
−0.902275 | + | 0.431161i | \(0.858104\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.5709 | −1.40768 | −0.703838 | − | 0.710360i | \(-0.748532\pi\) | ||||
−0.703838 | + | 0.710360i | \(0.748532\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.9545 | −0.754465 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.7887 | + | 27.3468i | 0.699820 | + | 1.21212i | 0.968529 | + | 0.248902i | \(0.0800698\pi\) |
−0.268709 | + | 0.963222i | \(0.586597\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.6888 | − | 20.6049i | −1.57878 | − | 0.911508i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.01836 | + | 1.16530i | 0.0889394 | + | 0.0513492i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.5319 | + | 21.0917i | −1.60667 | + | 0.927613i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.99232i | 0.393961i | 0.980407 | + | 0.196980i | \(0.0631136\pi\) | ||||
−0.980407 | + | 0.196980i | \(0.936886\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.78978 | −0.121988 | −0.0609942 | − | 0.998138i | \(-0.519427\pi\) | ||||
−0.0609942 | + | 0.998138i | \(0.519427\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.341916 | + | 0.592215i | 0.0148941 | + | 0.0257973i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2183 | − | 19.4306i | 0.487751 | − | 0.844809i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.8521 | − | 34.3849i | 0.859892 | − | 1.48938i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.232920 | − | 0.134477i | 0.0100700 | − | 0.00581393i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 65.2242i | 2.80940i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 38.5456i | − | 1.65721i | −0.559836 | − | 0.828603i | \(-0.689136\pi\) | ||
0.559836 | − | 0.828603i | \(-0.310864\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.01641 | − | 4.62828i | 0.343385 | − | 0.198254i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.8890 | − | 18.8604i | 0.465581 | − | 0.806411i | −0.533646 | − | 0.845708i | \(-0.679179\pi\) |
0.999228 | + | 0.0392972i | \(0.0125119\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.3005 | − | 21.3050i | 0.524017 | − | 0.907624i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.5305 | − | 23.4356i | −0.575377 | − | 0.996582i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.9871 | −0.973995 | −0.486998 | − | 0.873403i | \(-0.661908\pi\) | ||||
−0.486998 | + | 0.873403i | \(0.661908\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 21.6261i | − | 0.914686i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.7358 | − | 20.6321i | 1.50608 | − | 0.869537i | 0.506108 | − | 0.862470i | \(-0.331084\pi\) |
0.999975 | − | 0.00706728i | \(-0.00224960\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.88793 | − | 2.24470i | −0.163567 | − | 0.0944352i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.6609 | − | 14.2380i | −1.03384 | − | 0.596888i | −0.115757 | − | 0.993278i | \(-0.536930\pi\) |
−0.918082 | + | 0.396390i | \(0.870263\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.7603 | − | 30.7617i | −0.743245 | − | 1.28734i | −0.951010 | − | 0.309159i | \(-0.899952\pi\) |
0.207765 | − | 0.978179i | \(-0.433381\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.07627 | 0.128289 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.5676 | −1.27255 | −0.636273 | − | 0.771464i | \(-0.719525\pi\) | ||||
−0.636273 | + | 0.771464i | \(0.719525\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.4457 | − | 51.0014i | −1.22161 | − | 2.11589i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.26504 | + | 1.88507i | 0.135224 | + | 0.0780716i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.1608 | + | 9.33044i | 0.667028 | + | 0.385109i | 0.794949 | − | 0.606676i | \(-0.207497\pi\) |
−0.127922 | + | 0.991784i | \(0.540831\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.57867 | + | 0.911445i | −0.0650479 | + | 0.0375554i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.676531i | 0.0277818i | 0.999904 | + | 0.0138909i | \(0.00442175\pi\) | ||||
−0.999904 | + | 0.0138909i | \(0.995578\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.33074 | −0.218539 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.8685 | + | 32.6813i | 0.770947 | + | 1.33532i | 0.937044 | + | 0.349211i | \(0.113550\pi\) |
−0.166097 | + | 0.986109i | \(0.553116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.5562 | − | 20.0159i | 0.471386 | − | 0.816464i | −0.528078 | − | 0.849196i | \(-0.677087\pi\) |
0.999464 | + | 0.0327315i | \(0.0104206\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.53839 | + | 6.12868i | −0.143856 | + | 0.249166i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.04207 | + | 1.17899i | −0.0828851 | + | 0.0478537i | −0.540870 | − | 0.841106i | \(-0.681905\pi\) |
0.457985 | + | 0.888960i | \(0.348571\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 39.9543i | − | 1.61638i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 23.7808i | − | 0.960497i | −0.877132 | − | 0.480249i | \(-0.840546\pi\) | ||
0.877132 | − | 0.480249i | \(-0.159454\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.17492 | + | 1.83304i | −0.127817 | + | 0.0737954i | −0.562545 | − | 0.826766i | \(-0.690178\pi\) |
0.434728 | + | 0.900562i | \(0.356845\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.79359 | + | 15.2309i | −0.353444 | + | 0.612183i | −0.986850 | − | 0.161636i | \(-0.948323\pi\) |
0.633406 | + | 0.773820i | \(0.281656\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −23.8892 | + | 41.3773i | −0.957101 | + | 1.65775i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.14269 | − | 10.6394i | −0.245708 | − | 0.425578i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.80777 | 0.231571 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.9248i | 0.872811i | 0.899750 | + | 0.436405i | \(0.143749\pi\) | ||||
−0.899750 | + | 0.436405i | \(0.856251\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.3530 | + | 6.55468i | −0.450532 | + | 0.260115i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −53.5009 | − | 30.8888i | −2.11978 | − | 1.22386i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0562 | + | 10.4248i | 0.713178 | + | 0.411754i | 0.812237 | − | 0.583328i | \(-0.198250\pi\) |
−0.0990584 | + | 0.995082i | \(0.531583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.8540 | − | 22.2638i | −0.506914 | − | 0.878000i | −0.999968 | − | 0.00800162i | \(-0.997453\pi\) |
0.493054 | − | 0.869998i | \(-0.335880\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.0025 | 1.02226 | 0.511131 | − | 0.859503i | \(-0.329227\pi\) | ||||
0.511131 | + | 0.859503i | \(0.329227\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.53617 | −0.295821 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.7670 | + | 18.6490i | 0.421346 | + | 0.729792i | 0.996071 | − | 0.0885542i | \(-0.0282246\pi\) |
−0.574726 | + | 0.818346i | \(0.694891\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.89392 | + | 2.24816i | 0.152148 | + | 0.0878428i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.5947 | − | 6.69419i | −0.451665 | − | 0.260769i | 0.256868 | − | 0.966446i | \(-0.417309\pi\) |
−0.708533 | + | 0.705678i | \(0.750643\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.4644 | − | 8.35103i | 0.562600 | − | 0.324818i | −0.191588 | − | 0.981475i | \(-0.561364\pi\) |
0.754189 | + | 0.656658i | \(0.228030\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 14.2102i | − | 0.551046i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.81275 | 0.225071 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.3085 | + | 36.9073i | 0.822604 | + | 1.42479i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.47889 | + | 9.48971i | −0.211196 | + | 0.365802i | −0.952089 | − | 0.305821i | \(-0.901069\pi\) |
0.740893 | + | 0.671623i | \(0.234402\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.2742 | − | 19.5275i | 0.433302 | − | 0.750501i | −0.563853 | − | 0.825875i | \(-0.690682\pi\) |
0.997155 | + | 0.0753738i | \(0.0240150\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.9393 | − | 18.4402i | 1.22572 | − | 0.707669i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.4666i | 1.39536i | 0.716412 | + | 0.697678i | \(0.245783\pi\) | ||||
−0.716412 | + | 0.697678i | \(0.754217\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.7714i | 0.564387i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.09250 | + | 1.78546i | −0.117815 | + | 0.0680205i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.50258 | − | 4.33459i | 0.0952025 | − | 0.164896i | −0.814491 | − | 0.580177i | \(-0.802983\pi\) |
0.909693 | + | 0.415281i | \(0.136317\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.74634 | + | 6.48884i | −0.142107 | + | 0.246136i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.81515 | + | 10.0721i | 0.220265 | + | 0.381509i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.4972 | 0.434243 | 0.217122 | − | 0.976145i | \(-0.430333\pi\) | ||||
0.217122 | + | 0.976145i | \(0.430333\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.4818i | 0.583907i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 72.8225 | − | 42.0441i | 2.73877 | − | 1.58123i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.7367 | + | 17.1685i | 1.11679 | + | 0.644776i | 0.940578 | − | 0.339577i | \(-0.110284\pi\) |
0.176207 | + | 0.984353i | \(0.443617\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.373011 | − | 0.215358i | −0.0139694 | − | 0.00806523i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.29857 | − | 14.3735i | −0.310349 | − | 0.537540i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.5660 | −1.51286 | −0.756429 | − | 0.654076i | \(-0.773058\pi\) | ||||
−0.756429 | + | 0.654076i | \(0.773058\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.5589 | −0.430477 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.8672 | − | 27.4828i | −0.589293 | − | 1.02069i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.7590 | + | 19.4908i | 1.25205 | + | 0.722873i | 0.971517 | − | 0.236971i | \(-0.0761547\pi\) |
0.280535 | + | 0.959844i | \(0.409488\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.48608 | + | 3.16739i | 0.202910 | + | 0.117150i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.5208 | − | 18.1986i | 1.16425 | − | 0.672179i | 0.211930 | − | 0.977285i | \(-0.432025\pi\) |
0.952319 | + | 0.305105i | \(0.0986917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 47.1082i | 1.73525i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.8657 | 0.730770 | 0.365385 | − | 0.930857i | \(-0.380937\pi\) | ||||
0.365385 | + | 0.930857i | \(0.380937\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.13689 | − | 10.6294i | −0.225141 | − | 0.389955i | 0.731221 | − | 0.682141i | \(-0.238951\pi\) |
−0.956362 | + | 0.292186i | \(0.905618\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.60060 | + | 13.1646i | −0.278464 | + | 0.482314i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.666955 | + | 1.15520i | −0.0243700 | + | 0.0422101i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.29326 | + | 2.47872i | −0.156663 | + | 0.0904496i | −0.576282 | − | 0.817251i | \(-0.695497\pi\) |
0.419619 | + | 0.907700i | \(0.362164\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.73169i | 0.0630228i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 0.135856i | − | 0.00493778i | −0.999997 | − | 0.00246889i | \(-0.999214\pi\) | ||
0.999997 | − | 0.00246889i | \(-0.000785872\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.85960 | + | 1.07364i | −0.0674106 | + | 0.0389195i | −0.533326 | − | 0.845910i | \(-0.679058\pi\) |
0.465916 | + | 0.884829i | \(0.345725\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.9546 | + | 39.7585i | −0.831011 | + | 1.43935i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.56897 | − | 6.18164i | 0.128868 | − | 0.223206i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.85585 | + | 11.8747i | 0.247228 | + | 0.428212i | 0.962756 | − | 0.270373i | \(-0.0871469\pi\) |
−0.715527 | + | 0.698585i | \(0.753814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.2269 | 0.763477 | 0.381738 | − | 0.924270i | \(-0.375326\pi\) | ||||
0.381738 | + | 0.924270i | \(0.375326\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.35147i | 0.0844673i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.8493 | + | 15.5015i | −0.961976 | + | 0.555397i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.8677 | + | 21.2856i | 1.31923 | + | 0.761657i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.8506 | − | 9.72872i | −0.601425 | − | 0.347233i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.6033 | + | 18.3654i | 0.377966 | + | 0.654657i | 0.990766 | − | 0.135581i | \(-0.0432902\pi\) |
−0.612800 | + | 0.790238i | \(0.709957\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.2658 | 0.791680 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.3649 | −1.43340 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.6435 | − | 30.5595i | −0.624967 | − | 1.08247i | −0.988547 | − | 0.150911i | \(-0.951779\pi\) |
0.363581 | − | 0.931563i | \(-0.381554\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.1356 | + | 5.85178i | 0.358571 | + | 0.207021i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.5485 | + | 18.7919i | 1.14861 | + | 0.663151i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.90777 | − | 1.67880i | 0.102485 | − | 0.0591700i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.8216i | 0.942996i | 0.881867 | + | 0.471498i | \(0.156286\pi\) | ||||
−0.881867 | + | 0.471498i | \(0.843714\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.68860 | −0.269983 | −0.134992 | − | 0.990847i | \(-0.543101\pi\) | ||||
−0.134992 | + | 0.990847i | \(0.543101\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.60576 | + | 6.24535i | 0.126304 | + | 0.218765i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.44332 | + | 14.6243i | −0.295394 | + | 0.511638i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.3690 | − | 21.4237i | 0.431680 | − | 0.747692i | −0.565338 | − | 0.824859i | \(-0.691254\pi\) |
0.997018 | + | 0.0771675i | \(0.0245876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.2907 | − | 15.7563i | 0.951294 | − | 0.549230i | 0.0578112 | − | 0.998328i | \(-0.481588\pi\) |
0.893483 | + | 0.449098i | \(0.148255\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.9087i | − | 0.553200i | −0.960985 | − | 0.276600i | \(-0.910792\pi\) | ||
0.960985 | − | 0.276600i | \(-0.0892077\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.2678i | 1.39856i | 0.714848 | + | 0.699280i | \(0.246496\pi\) | ||||
−0.714848 | + | 0.699280i | \(0.753504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.6717 | − | 9.04803i | 0.542991 | − | 0.313496i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.66537 | − | 4.61655i | 0.0922389 | − | 0.159762i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.66890 | − | 4.62267i | 0.0921408 | − | 0.159592i | −0.816271 | − | 0.577669i | \(-0.803962\pi\) |
0.908412 | + | 0.418077i | \(0.137296\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.4818 | − | 26.8153i | −0.533856 | − | 0.924666i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.37443 | 0.116084 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 35.0983i | − | 1.20599i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.16798 | + | 1.82903i | −0.108597 | + | 0.0626985i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.1392 | + | 16.2462i | 0.963468 | + | 0.556258i | 0.897239 | − | 0.441546i | \(-0.145570\pi\) |
0.0662290 | + | 0.997804i | \(0.478903\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.1136 | − | 12.1899i | −0.721227 | − | 0.416400i | 0.0939774 | − | 0.995574i | \(-0.470042\pi\) |
−0.815204 | + | 0.579174i | \(0.803375\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.04812 | − | 10.4757i | −0.206359 | − | 0.357425i | 0.744206 | − | 0.667951i | \(-0.232828\pi\) |
−0.950565 | + | 0.310526i | \(0.899495\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.4505 | 1.34291 | 0.671456 | − | 0.741044i | \(-0.265669\pi\) | ||||
0.671456 | + | 0.741044i | \(0.265669\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.9966 | 0.407897 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.3400 | + | 21.3735i | 0.418605 | + | 0.725046i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.6410 | − | 22.3094i | −1.30930 | − | 0.755925i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −35.2431 | − | 20.3476i | −1.19144 | − | 0.687876i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.96635 | − | 3.44467i | 0.201469 | − | 0.116318i | −0.395871 | − | 0.918306i | \(-0.629557\pi\) |
0.597341 | + | 0.801988i | \(0.296224\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 44.3192i | − | 1.49315i | −0.665300 | − | 0.746576i | \(-0.731696\pi\) | ||
0.665300 | − | 0.746576i | \(-0.268304\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.0579 | −1.61728 | −0.808639 | − | 0.588305i | \(-0.799795\pi\) | ||||
−0.808639 | + | 0.588305i | \(0.799795\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.5146 | − | 23.4079i | −0.453775 | − | 0.785961i | 0.544842 | − | 0.838539i | \(-0.316590\pi\) |
−0.998617 | + | 0.0525774i | \(0.983256\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.5088 | − | 56.3070i | 1.09031 | − | 1.88848i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.5991 | + | 27.0184i | −0.522004 | + | 0.904137i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.8831 | − | 9.74746i | 0.564340 | − | 0.325822i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.44322i | 0.148190i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.04600i | − | 0.0348474i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.19196 | + | 4.72963i | −0.272310 | + | 0.157218i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.71996 | − | 4.71111i | 0.0903149 | − | 0.156430i | −0.817329 | − | 0.576172i | \(-0.804546\pi\) |
0.907644 | + | 0.419742i | \(0.137879\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.7758 | + | 34.2528i | −0.655203 | + | 1.13484i | 0.326640 | + | 0.945149i | \(0.394083\pi\) |
−0.981843 | + | 0.189696i | \(0.939250\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.8547 | + | 46.5137i | 0.888762 | + | 1.53938i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.3001 | −0.736414 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.7057i | 0.748991i | 0.927229 | + | 0.374495i | \(0.122184\pi\) | ||||
−0.927229 | + | 0.374495i | \(0.877816\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.9194 | + | 20.1608i | −1.14939 | + | 0.663599i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.2954 | + | 9.98551i | 0.568669 | + | 0.328321i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.0663 | − | 20.8229i | −1.18330 | − | 0.683176i | −0.226521 | − | 0.974006i | \(-0.572735\pi\) |
−0.956775 | + | 0.290830i | \(0.906068\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.1194 | + | 41.7760i | 0.790480 | + | 1.36915i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.86169 | 0.158994 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.4421 | 1.77855 | 0.889274 | − | 0.457376i | \(-0.151211\pi\) | ||||
0.889274 | + | 0.457376i | \(0.151211\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.8217 | + | 37.7963i | 0.711368 | + | 1.23213i | 0.964344 | + | 0.264653i | \(0.0852573\pi\) |
−0.252976 | + | 0.967473i | \(0.581409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.34401 | − | 3.66272i | −0.206589 | − | 0.119274i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.5858 | + | 6.68905i | 0.376487 | + | 0.217365i | 0.676289 | − | 0.736637i | \(-0.263587\pi\) |
−0.299802 | + | 0.954002i | \(0.596920\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.8285 | + | 17.7989i | −1.00074 | + | 0.577775i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 36.5239i | − | 1.18313i | −0.806259 | − | 0.591563i | \(-0.798511\pi\) | ||
0.806259 | − | 0.591563i | \(-0.201489\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.8422 | 0.706796 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36.6304 | − | 63.4458i | −1.18286 | − | 2.04877i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.3354 | + | 26.5617i | −0.494690 | + | 0.856828i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.474833 | + | 0.822435i | −0.0152854 | + | 0.0264751i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.4015 | + | 11.2015i | −0.623911 | + | 0.360215i | −0.778390 | − | 0.627781i | \(-0.783963\pi\) |
0.154479 | + | 0.987996i | \(0.450630\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.7841i | 1.08418i | 0.840320 | + | 0.542091i | \(0.182367\pi\) | ||||
−0.840320 | + | 0.542091i | \(0.817633\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 37.1609i | − | 1.19132i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.6710 | + | 7.31560i | −0.405381 | + | 0.234047i | −0.688803 | − | 0.724948i | \(-0.741864\pi\) |
0.283422 | + | 0.958995i | \(0.408530\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.7872 | − | 37.7365i | 0.696322 | − | 1.20606i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.8379 | − | 32.6283i | 0.600837 | − | 1.04068i | −0.391858 | − | 0.920026i | \(-0.628168\pi\) |
0.992695 | − | 0.120654i | \(-0.0384992\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.246742 | + | 0.427370i | 0.00786185 | + | 0.0136171i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.99001 | −0.126875 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 25.7352i | − | 0.817504i | −0.912645 | − | 0.408752i | \(-0.865964\pi\) | ||
0.912645 | − | 0.408752i | \(-0.134036\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.518666 | − | 0.299452i | 0.0164428 | − | 0.00949326i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.4015 | − | 19.2844i | −1.05784 | − | 0.610743i | −0.133004 | − | 0.991115i | \(-0.542462\pi\) |
−0.924833 | + | 0.380373i | \(0.875796\pi\) | |||||||
\(998\) | 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 | 2592.2.p.g.431.14 | 48 | ||
3.2 | odd | 2 | inner | 2592.2.p.g.431.12 | 48 | ||
4.3 | odd | 2 | 648.2.l.g.107.23 | 48 | |||
8.3 | odd | 2 | inner | 2592.2.p.g.431.11 | 48 | ||
8.5 | even | 2 | 648.2.l.g.107.18 | 48 | |||
9.2 | odd | 6 | 2592.2.f.c.1295.13 | 24 | |||
9.4 | even | 3 | inner | 2592.2.p.g.2159.13 | 48 | ||
9.5 | odd | 6 | inner | 2592.2.p.g.2159.11 | 48 | ||
9.7 | even | 3 | 2592.2.f.c.1295.11 | 24 | |||
12.11 | even | 2 | 648.2.l.g.107.2 | 48 | |||
24.5 | odd | 2 | 648.2.l.g.107.7 | 48 | |||
24.11 | even | 2 | inner | 2592.2.p.g.431.13 | 48 | ||
36.7 | odd | 6 | 648.2.f.c.323.9 | ✓ | 24 | ||
36.11 | even | 6 | 648.2.f.c.323.16 | yes | 24 | ||
36.23 | even | 6 | 648.2.l.g.539.18 | 48 | |||
36.31 | odd | 6 | 648.2.l.g.539.7 | 48 | |||
72.5 | odd | 6 | 648.2.l.g.539.23 | 48 | |||
72.11 | even | 6 | 2592.2.f.c.1295.12 | 24 | |||
72.13 | even | 6 | 648.2.l.g.539.2 | 48 | |||
72.29 | odd | 6 | 648.2.f.c.323.10 | yes | 24 | ||
72.43 | odd | 6 | 2592.2.f.c.1295.14 | 24 | |||
72.59 | even | 6 | inner | 2592.2.p.g.2159.14 | 48 | ||
72.61 | even | 6 | 648.2.f.c.323.15 | yes | 24 | ||
72.67 | odd | 6 | inner | 2592.2.p.g.2159.12 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.2.f.c.323.9 | ✓ | 24 | 36.7 | odd | 6 | ||
648.2.f.c.323.10 | yes | 24 | 72.29 | odd | 6 | ||
648.2.f.c.323.15 | yes | 24 | 72.61 | even | 6 | ||
648.2.f.c.323.16 | yes | 24 | 36.11 | even | 6 | ||
648.2.l.g.107.2 | 48 | 12.11 | even | 2 | |||
648.2.l.g.107.7 | 48 | 24.5 | odd | 2 | |||
648.2.l.g.107.18 | 48 | 8.5 | even | 2 | |||
648.2.l.g.107.23 | 48 | 4.3 | odd | 2 | |||
648.2.l.g.539.2 | 48 | 72.13 | even | 6 | |||
648.2.l.g.539.7 | 48 | 36.31 | odd | 6 | |||
648.2.l.g.539.18 | 48 | 36.23 | even | 6 | |||
648.2.l.g.539.23 | 48 | 72.5 | odd | 6 | |||
2592.2.f.c.1295.11 | 24 | 9.7 | even | 3 | |||
2592.2.f.c.1295.12 | 24 | 72.11 | even | 6 | |||
2592.2.f.c.1295.13 | 24 | 9.2 | odd | 6 | |||
2592.2.f.c.1295.14 | 24 | 72.43 | odd | 6 | |||
2592.2.p.g.431.11 | 48 | 8.3 | odd | 2 | inner | ||
2592.2.p.g.431.12 | 48 | 3.2 | odd | 2 | inner | ||
2592.2.p.g.431.13 | 48 | 24.11 | even | 2 | inner | ||
2592.2.p.g.431.14 | 48 | 1.1 | even | 1 | trivial | ||
2592.2.p.g.2159.11 | 48 | 9.5 | odd | 6 | inner | ||
2592.2.p.g.2159.12 | 48 | 72.67 | odd | 6 | inner | ||
2592.2.p.g.2159.13 | 48 | 9.4 | even | 3 | inner | ||
2592.2.p.g.2159.14 | 48 | 72.59 | even | 6 | inner |