Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,3,Mod(15,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.15");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.h (of order \(8\), 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: | \(3.48774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 15.2 | ||
Character | \(\chi\) | \(=\) | 128.15 |
Dual form | 128.3.h.a.111.2 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −2.49683 | + | 1.03422i | −0.832276 | + | 0.344740i | −0.757803 | − | 0.652483i | \(-0.773727\pi\) |
−0.0744725 | + | 0.997223i | \(0.523727\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.452310 | − | 0.187353i | −0.0904620 | − | 0.0374706i | 0.336994 | − | 0.941507i | \(-0.390590\pi\) |
−0.427456 | + | 0.904036i | \(0.640590\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.429965 | + | 0.429965i | −0.0614236 | + | 0.0614236i | −0.737151 | − | 0.675728i | \(-0.763830\pi\) |
0.675728 | + | 0.737151i | \(0.263830\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.19943 | + | 1.19943i | −0.133270 | + | 0.133270i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.3350 | − | 7.18039i | −1.57591 | − | 0.652763i | −0.588149 | − | 0.808752i | \(-0.700143\pi\) |
−0.987759 | + | 0.155990i | \(0.950143\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −19.9596 | + | 8.26755i | −1.53536 | + | 0.635965i | −0.980595 | − | 0.196044i | \(-0.937190\pi\) |
−0.554761 | + | 0.832010i | \(0.687190\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.32310 | 0.0882069 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 13.5961i | − | 0.799770i | −0.916565 | − | 0.399885i | \(-0.869050\pi\) | ||
0.916565 | − | 0.399885i | \(-0.130950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.45810 | + | 8.34859i | 0.182005 | + | 0.439399i | 0.988380 | − | 0.152006i | \(-0.0485733\pi\) |
−0.806374 | + | 0.591405i | \(0.798573\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.628870 | − | 1.51823i | 0.0299462 | − | 0.0722965i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.8850 | + | 16.8850i | 0.734131 | + | 0.734131i | 0.971435 | − | 0.237304i | \(-0.0762639\pi\) |
−0.237304 | + | 0.971435i | \(0.576264\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −17.5082 | − | 17.5082i | −0.700327 | − | 0.700327i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.0623 | − | 26.7067i | 0.409714 | − | 0.989136i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13.8385 | + | 33.4091i | 0.477190 | + | 1.15204i | 0.960921 | + | 0.276821i | \(0.0892810\pi\) |
−0.483732 | + | 0.875216i | \(0.660719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 24.5614i | 0.792305i | 0.918185 | + | 0.396152i | \(0.129655\pi\) | ||||
−0.918185 | + | 0.396152i | \(0.870345\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 50.7086 | 1.53662 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.275033 | − | 0.113922i | 0.00785807 | − | 0.00325492i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.89595 | + | 4.09904i | 0.267458 | + | 0.110785i | 0.512382 | − | 0.858757i | \(-0.328763\pi\) |
−0.244924 | + | 0.969542i | \(0.578763\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 41.2853 | − | 41.2853i | 1.05860 | − | 1.05860i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14.4867 | − | 14.4867i | 0.353334 | − | 0.353334i | −0.508015 | − | 0.861348i | \(-0.669620\pi\) |
0.861348 | + | 0.508015i | \(0.169620\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −17.8494 | − | 7.39348i | −0.415103 | − | 0.171941i | 0.165350 | − | 0.986235i | \(-0.447125\pi\) |
−0.580453 | + | 0.814294i | \(0.697125\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.767229 | − | 0.317796i | 0.0170495 | − | 0.00706214i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −43.6087 | −0.927845 | −0.463922 | − | 0.885876i | \(-0.653558\pi\) | ||||
−0.463922 | + | 0.885876i | \(0.653558\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.6303i | 0.992454i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.0613 | + | 33.9471i | 0.275713 | + | 0.665629i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 28.0630 | − | 67.7501i | 0.529490 | − | 1.27830i | −0.402367 | − | 0.915478i | \(-0.631812\pi\) |
0.931857 | − | 0.362825i | \(-0.118188\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.49552 | + | 6.49552i | 0.118100 | + | 0.118100i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.2685 | − | 17.2685i | −0.302957 | − | 0.302957i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.70130 | + | 4.10730i | −0.0288356 | + | 0.0696153i | −0.937641 | − | 0.347604i | \(-0.886995\pi\) |
0.908806 | + | 0.417219i | \(0.136995\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.53360 | + | 8.53087i | 0.0579279 | + | 0.139850i | 0.950193 | − | 0.311661i | \(-0.100885\pi\) |
−0.892266 | + | 0.451511i | \(0.850885\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.03142i | − | 0.0163718i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.5769 | 0.162721 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.300169 | − | 0.124334i | 0.00448013 | − | 0.00185573i | −0.380442 | − | 0.924805i | \(-0.624228\pi\) |
0.384922 | + | 0.922949i | \(0.374228\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −59.6218 | − | 24.6961i | −0.864084 | − | 0.357915i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 29.0914 | − | 29.0914i | 0.409738 | − | 0.409738i | −0.471909 | − | 0.881647i | \(-0.656435\pi\) |
0.881647 | + | 0.471909i | \(0.156435\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −68.2273 | + | 68.2273i | −0.934620 | + | 0.934620i | −0.997990 | − | 0.0633700i | \(-0.979815\pi\) |
0.0633700 | + | 0.997990i | \(0.479815\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 61.8222 | + | 25.6076i | 0.824296 | + | 0.341435i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.5408 | − | 4.36612i | 0.136893 | − | 0.0567029i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −67.7588 | −0.857706 | −0.428853 | − | 0.903374i | \(-0.641082\pi\) | ||||
−0.428853 | + | 0.903374i | \(0.641082\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 62.8565i | 0.776007i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.4008 | + | 39.5950i | 0.197600 | + | 0.477048i | 0.991358 | − | 0.131186i | \(-0.0418784\pi\) |
−0.793758 | + | 0.608234i | \(0.791878\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.54727 | + | 6.14965i | −0.0299679 | + | 0.0723488i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −69.1047 | − | 69.1047i | −0.794306 | − | 0.794306i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −45.3745 | − | 45.3745i | −0.509825 | − | 0.509825i | 0.404647 | − | 0.914473i | \(-0.367394\pi\) |
−0.914473 | + | 0.404647i | \(0.867394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.02718 | − | 12.1367i | 0.0552438 | − | 0.133370i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −25.4019 | − | 61.3257i | −0.273139 | − | 0.659416i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 4.42403i | − | 0.0465688i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −119.312 | −1.23002 | −0.615012 | − | 0.788518i | \(-0.710849\pi\) | ||||
−0.615012 | + | 0.788518i | \(0.710849\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 29.4044 | − | 12.1797i | 0.297014 | − | 0.123027i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 98.7914 | + | 40.9207i | 0.978133 | + | 0.405156i | 0.813734 | − | 0.581238i | \(-0.197431\pi\) |
0.164399 | + | 0.986394i | \(0.447431\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −127.634 | + | 127.634i | −1.23916 | + | 1.23916i | −0.278817 | + | 0.960344i | \(0.589942\pi\) |
−0.960344 | + | 0.278817i | \(0.910058\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.568888 | + | 0.568888i | −0.00541798 | + | 0.00541798i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −94.9289 | − | 39.3208i | −0.887186 | − | 0.367484i | −0.107906 | − | 0.994161i | \(-0.534415\pi\) |
−0.779279 | + | 0.626677i | \(0.784415\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −27.8610 | + | 11.5404i | −0.255605 | + | 0.105875i | −0.506807 | − | 0.862060i | \(-0.669174\pi\) |
0.251202 | + | 0.967935i | \(0.419174\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −28.9478 | −0.260791 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 140.786i | − | 1.24590i | −0.782263 | − | 0.622948i | \(-0.785935\pi\) | ||
0.782263 | − | 0.622948i | \(-0.214065\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.47380 | − | 10.8007i | −0.0389026 | − | 0.0939193i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.0238 | − | 33.8564i | 0.119861 | − | 0.289371i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.84584 | + | 5.84584i | 0.0491247 | + | 0.0491247i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 163.384 | + | 163.384i | 1.35028 | + | 1.35028i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −21.1883 | + | 51.1532i | −0.172263 | + | 0.415879i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.32274 | + | 22.5071i | 0.0745819 | + | 0.180057i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 163.979i | − | 1.29117i | −0.763687 | − | 0.645587i | \(-0.776613\pi\) | ||
0.763687 | − | 0.645587i | \(-0.223387\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 52.2134 | 0.404755 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2279 | − | 4.65074i | 0.0857090 | − | 0.0355018i | −0.339417 | − | 0.940636i | \(-0.610230\pi\) |
0.425126 | + | 0.905134i | \(0.360230\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.07646 | − | 2.10274i | −0.0381689 | − | 0.0158101i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.0071 | + | 10.0071i | −0.0741270 | + | 0.0741270i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.2983 | − | 21.2983i | 0.155462 | − | 0.155462i | −0.625090 | − | 0.780552i | \(-0.714938\pi\) |
0.780552 | + | 0.625090i | \(0.214938\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 154.836 | + | 64.1351i | 1.11393 | + | 0.461404i | 0.862288 | − | 0.506418i | \(-0.169031\pi\) |
0.251639 | + | 0.967821i | \(0.419031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 108.883 | − | 45.1010i | 0.772223 | − | 0.319865i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 405.364 | 2.83471 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 17.7039i | − | 0.122096i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −50.2944 | − | 121.421i | −0.342139 | − | 0.825996i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −90.9258 | + | 219.514i | −0.610240 | + | 1.47325i | 0.252497 | + | 0.967598i | \(0.418748\pi\) |
−0.862737 | + | 0.505653i | \(0.831252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 82.0484 | + | 82.0484i | 0.543367 | + | 0.543367i | 0.924514 | − | 0.381147i | \(-0.124471\pi\) |
−0.381147 | + | 0.924514i | \(0.624471\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.3075 | + | 16.3075i | 0.106585 | + | 0.106585i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.60166 | − | 11.1094i | 0.0296881 | − | 0.0716735i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −52.8906 | − | 127.689i | −0.336883 | − | 0.813307i | −0.998011 | − | 0.0630341i | \(-0.979922\pi\) |
0.661129 | − | 0.750272i | \(-0.270078\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 198.183i | 1.24644i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.5199 | −0.0901859 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −54.8297 | + | 22.7112i | −0.336379 | + | 0.139333i | −0.544478 | − | 0.838775i | \(-0.683272\pi\) |
0.208099 | + | 0.978108i | \(0.433272\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −22.9360 | − | 9.50040i | −0.139006 | − | 0.0575782i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 98.7296 | − | 98.7296i | 0.591195 | − | 0.591195i | −0.346759 | − | 0.937954i | \(-0.612718\pi\) |
0.937954 | + | 0.346759i | \(0.112718\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 210.533 | − | 210.533i | 1.24576 | − | 1.24576i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.1613 | − | 5.86578i | −0.0828143 | − | 0.0343028i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.09221 | + | 2.52348i | −0.0352151 | + | 0.0145866i | −0.400221 | − | 0.916418i | \(-0.631067\pi\) |
0.365006 | + | 0.931005i | \(0.381067\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.0558 | 0.0860332 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.0147i | − | 0.0678799i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −80.6673 | − | 194.748i | −0.450655 | − | 1.08798i | −0.972073 | − | 0.234677i | \(-0.924597\pi\) |
0.521418 | − | 0.853301i | \(-0.325403\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −59.7464 | + | 144.241i | −0.330091 | + | 0.796910i | 0.668493 | + | 0.743718i | \(0.266939\pi\) |
−0.998584 | + | 0.0531918i | \(0.983061\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.6456 | − | 17.6456i | −0.0964240 | − | 0.0964240i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.70807 | − | 3.70807i | −0.0200436 | − | 0.0200436i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −97.6252 | + | 235.688i | −0.522060 | + | 1.26036i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.72655 | + | 16.2393i | 0.0355902 | + | 0.0859223i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 107.812i | − | 0.564460i | −0.959347 | − | 0.282230i | \(-0.908926\pi\) | ||
0.959347 | − | 0.282230i | \(-0.0910741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −174.830 | −0.905855 | −0.452927 | − | 0.891547i | \(-0.649620\pi\) | ||||
−0.452927 | + | 0.891547i | \(0.649620\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −26.4087 | + | 10.9388i | −0.135429 | + | 0.0560965i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −108.472 | − | 44.9304i | −0.550618 | − | 0.228073i | 0.0899887 | − | 0.995943i | \(-0.471317\pi\) |
−0.640606 | + | 0.767870i | \(0.721317\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −190.347 | + | 190.347i | −0.956516 | + | 0.956516i | −0.999093 | − | 0.0425770i | \(-0.986443\pi\) |
0.0425770 | + | 0.999093i | \(0.486443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.620881 | + | 0.620881i | −0.00308896 | + | 0.00308896i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.3148 | − | 8.41467i | −0.100073 | − | 0.0414516i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.26659 | + | 3.83835i | −0.0452029 | + | 0.0187237i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −40.5047 | −0.195675 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 169.553i | − | 0.811259i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −86.6725 | − | 209.246i | −0.410770 | − | 0.991686i | −0.984932 | − | 0.172944i | \(-0.944672\pi\) |
0.574162 | − | 0.818742i | \(-0.305328\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −42.5493 | + | 102.723i | −0.199762 | + | 0.482269i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.68829 | + | 6.68829i | 0.0311083 | + | 0.0311083i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.5606 | − | 10.5606i | −0.0486662 | − | 0.0486662i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 99.7897 | − | 240.914i | 0.455661 | − | 1.10006i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 112.406 | + | 271.373i | 0.508626 | + | 1.22793i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 103.845i | 0.465671i | 0.972516 | + | 0.232836i | \(0.0748004\pi\) | ||||
−0.972516 | + | 0.232836i | \(0.925200\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 41.9996 | 0.186665 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −106.086 | + | 43.9421i | −0.467338 | + | 0.193578i | −0.603910 | − | 0.797052i | \(-0.706391\pi\) |
0.136572 | + | 0.990630i | \(0.456391\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 46.1162 | + | 19.1019i | 0.201381 | + | 0.0834146i | 0.481094 | − | 0.876669i | \(-0.340240\pi\) |
−0.279714 | + | 0.960083i | \(0.590240\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.8029 | + | 21.8029i | −0.0943849 | + | 0.0943849i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −62.7031 | + | 62.7031i | −0.269112 | + | 0.269112i | −0.828742 | − | 0.559630i | \(-0.810943\pi\) |
0.559630 | + | 0.828742i | \(0.310943\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.7247 | + | 8.17022i | 0.0839347 | + | 0.0347669i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 169.182 | − | 70.0775i | 0.713848 | − | 0.295686i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −306.080 | −1.28067 | −0.640335 | − | 0.768095i | \(-0.721205\pi\) | ||||
−0.640335 | + | 0.768095i | \(0.721205\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 245.242i | 1.01760i | 0.860884 | + | 0.508801i | \(0.169911\pi\) | ||||
−0.860884 | + | 0.508801i | \(0.830089\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 34.5529 | + | 83.4181i | 0.142193 | + | 0.343285i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.11102 | − | 21.9960i | 0.0371878 | − | 0.0897794i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −138.045 | − | 138.045i | −0.558886 | − | 0.558886i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −81.8998 | − | 81.8998i | −0.328915 | − | 0.328915i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −132.845 | + | 320.715i | −0.529261 | + | 1.27775i | 0.402747 | + | 0.915311i | \(0.368056\pi\) |
−0.932008 | + | 0.362438i | \(0.881944\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −171.461 | − | 413.942i | −0.677710 | − | 1.63614i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 17.9890i | − | 0.0705453i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −108.814 | −0.423399 | −0.211700 | − | 0.977335i | \(-0.567900\pi\) | ||||
−0.211700 | + | 0.977335i | \(0.567900\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.01735 | + | 2.49247i | −0.0232330 | + | 0.00962343i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −56.6700 | − | 23.4735i | −0.217126 | − | 0.0899367i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 150.151 | − | 150.151i | 0.570916 | − | 0.570916i | −0.361468 | − | 0.932384i | \(-0.617724\pi\) |
0.932384 | + | 0.361468i | \(0.117724\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.3863 | + | 25.3863i | −0.0957975 | + | 0.0957975i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 160.219 | + | 66.3650i | 0.600072 | + | 0.248558i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −255.485 | + | 105.825i | −0.949758 | + | 0.393403i | −0.803140 | − | 0.595791i | \(-0.796839\pi\) |
−0.146618 | + | 0.989193i | \(0.546839\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 261.648 | 0.965492 | 0.482746 | − | 0.875760i | \(-0.339639\pi\) | ||||
0.482746 | + | 0.875760i | \(0.339639\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 35.5024i | 0.130046i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 177.789 | + | 429.220i | 0.646504 | + | 1.56080i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 120.123 | − | 290.003i | 0.433658 | − | 1.04694i | −0.544440 | − | 0.838799i | \(-0.683258\pi\) |
0.978098 | − | 0.208143i | \(-0.0667420\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −29.4597 | − | 29.4597i | −0.105590 | − | 0.105590i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.7898 | + | 21.7898i | 0.0775437 | + | 0.0775437i | 0.744815 | − | 0.667271i | \(-0.232538\pi\) |
−0.667271 | + | 0.744815i | \(0.732538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 155.937 | − | 376.466i | 0.551016 | − | 1.33027i | −0.365702 | − | 0.930732i | \(-0.619171\pi\) |
0.916717 | − | 0.399537i | \(-0.130829\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.57542 | + | 11.0460i | 0.0160541 | + | 0.0387581i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.4575i | 0.0434060i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 104.146 | 0.360368 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 297.902 | − | 123.395i | 1.02372 | − | 0.424038i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −37.2090 | − | 15.4125i | −0.126993 | − | 0.0526023i | 0.318282 | − | 0.947996i | \(-0.396894\pi\) |
−0.445275 | + | 0.895394i | \(0.646894\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.53903 | − | 1.53903i | 0.00521705 | − | 0.00521705i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −383.529 | + | 383.529i | −1.29134 | + | 1.29134i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −476.616 | − | 197.421i | −1.59403 | − | 0.660271i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.8536 | − | 4.49569i | 0.0360584 | − | 0.0149359i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −288.986 | −0.953750 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 4.52063i | − | 0.0148217i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 101.089 | + | 244.049i | 0.329279 | + | 0.794949i | 0.998646 | + | 0.0520174i | \(0.0165651\pi\) |
−0.669368 | + | 0.742931i | \(0.733435\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 186.678 | − | 450.680i | 0.604136 | − | 1.45851i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 181.395 | + | 181.395i | 0.583264 | + | 0.583264i | 0.935799 | − | 0.352534i | \(-0.114680\pi\) |
−0.352534 | + | 0.935799i | \(0.614680\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 110.963 | + | 110.963i | 0.354513 | + | 0.354513i | 0.861786 | − | 0.507273i | \(-0.169346\pi\) |
−0.507273 | + | 0.861786i | \(0.669346\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.193240 | + | 0.466523i | −0.000613460 | + | 0.00148102i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 134.161 | + | 323.892i | 0.423219 | + | 1.02174i | 0.981392 | + | 0.192017i | \(0.0615028\pi\) |
−0.558172 | + | 0.829725i | \(0.688497\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 678.512i | − | 2.12700i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 277.687 | 0.865070 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 113.508 | − | 47.0166i | 0.351419 | − | 0.145562i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 494.207 | + | 204.707i | 1.52064 | + | 0.629868i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 57.6287 | − | 57.6287i | 0.176235 | − | 0.176235i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.7502 | − | 18.7502i | 0.0569915 | − | 0.0569915i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 580.238 | + | 240.342i | 1.75298 | + | 0.726110i | 0.997479 | + | 0.0709686i | \(0.0226090\pi\) |
0.755506 | + | 0.655141i | \(0.227391\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.7860 | + | 6.95297i | −0.0504083 | + | 0.0208798i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.159064 | −0.000474817 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 130.257i | 0.386519i | 0.981148 | + | 0.193259i | \(0.0619059\pi\) | ||||
−0.981148 | + | 0.193259i | \(0.938094\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 145.604 | + | 351.519i | 0.429510 | + | 1.03693i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 176.361 | − | 425.772i | 0.517187 | − | 1.24860i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −41.9776 | − | 41.9776i | −0.122384 | − | 0.122384i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 22.3406 | + | 22.3406i | 0.0647554 | + | 0.0647554i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 54.6775 | − | 132.003i | 0.157572 | − | 0.380412i | −0.825302 | − | 0.564692i | \(-0.808995\pi\) |
0.982874 | + | 0.184279i | \(0.0589951\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −46.7936 | − | 112.970i | −0.134079 | − | 0.323696i | 0.842553 | − | 0.538613i | \(-0.181052\pi\) |
−0.976632 | + | 0.214918i | \(0.931052\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 624.513i | 1.77924i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 382.113 | 1.08247 | 0.541236 | − | 0.840871i | \(-0.317957\pi\) | ||||
0.541236 | + | 0.840871i | \(0.317957\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.6087 | + | 7.70798i | −0.0524189 | + | 0.0217126i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.6419 | − | 8.55017i | −0.0578206 | − | 0.0239501i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 81.2910 | − | 81.2910i | 0.226437 | − | 0.226437i | −0.584765 | − | 0.811203i | \(-0.698813\pi\) |
0.811203 | + | 0.584765i | \(0.198813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 197.525 | − | 197.525i | 0.547161 | − | 0.547161i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −576.916 | − | 238.967i | −1.58930 | − | 0.658310i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 43.6425 | − | 18.0773i | 0.119568 | − | 0.0495268i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −456.145 | −1.24290 | −0.621452 | − | 0.783453i | \(-0.713457\pi\) | ||||
−0.621452 | + | 0.783453i | \(0.713457\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 34.7514i | 0.0941773i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.0640 | + | 41.1963i | 0.0459947 | + | 0.111041i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −184.108 | + | 444.476i | −0.493588 | + | 1.19163i | 0.459294 | + | 0.888284i | \(0.348102\pi\) |
−0.952882 | + | 0.303342i | \(0.901898\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −46.5545 | − | 46.5545i | −0.124145 | − | 0.124145i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −552.423 | − | 552.423i | −1.46531 | − | 1.46531i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 108.900 | − | 262.908i | 0.287336 | − | 0.693690i | −0.712634 | − | 0.701536i | \(-0.752498\pi\) |
0.999969 | + | 0.00784682i | \(0.00249775\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 169.590 | + | 409.427i | 0.445119 | + | 1.07461i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 476.810i | 1.24493i | 0.782646 | + | 0.622467i | \(0.213869\pi\) | ||||
−0.782646 | + | 0.622467i | \(0.786131\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.58569 | −0.0145083 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 30.2770 | − | 12.5411i | 0.0782352 | − | 0.0324061i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −71.5472 | − | 29.6358i | −0.183926 | − | 0.0761846i | 0.288820 | − | 0.957383i | \(-0.406737\pi\) |
−0.472746 | + | 0.881199i | \(0.656737\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 229.570 | − | 229.570i | 0.587136 | − | 0.587136i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.2242 | + | 23.2242i | −0.0590946 | + | 0.0590946i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.6480 | + | 12.6948i | 0.0775898 | + | 0.0321388i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 120.360 | − | 49.8545i | 0.303173 | − | 0.125578i | −0.225911 | − | 0.974148i | \(-0.572536\pi\) |
0.529084 | + | 0.848570i | \(0.322536\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.8497 | 0.0372174 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 174.015i | 0.433953i | 0.976177 | + | 0.216976i | \(0.0696195\pi\) | ||||
−0.976177 | + | 0.216976i | \(0.930381\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −203.063 | − | 490.237i | −0.503878 | − | 1.21647i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.7764 | − | 28.4306i | 0.0290774 | − | 0.0701991i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −142.114 | − | 142.114i | −0.349173 | − | 0.349173i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −108.736 | − | 108.736i | −0.265857 | − | 0.265857i | 0.561571 | − | 0.827428i | \(-0.310197\pi\) |
−0.827428 | + | 0.561571i | \(0.810197\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −31.1511 | + | 75.2054i | −0.0757934 | + | 0.182981i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.03450 | − | 2.49749i | −0.00250483 | − | 0.00604720i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 20.9819i | − | 0.0505589i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −452.928 | −1.08616 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −370.373 | + | 153.414i | −0.883946 | + | 0.366142i | −0.778026 | − | 0.628232i | \(-0.783779\pi\) |
−0.105920 | + | 0.994375i | \(0.533779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −600.339 | − | 248.669i | −1.42598 | − | 0.590662i | −0.469628 | − | 0.882864i | \(-0.655612\pi\) |
−0.956357 | + | 0.292202i | \(0.905612\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 52.3054 | − | 52.3054i | 0.123654 | − | 0.123654i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −238.043 | + | 238.043i | −0.560101 | + | 0.560101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.18730 | − | 2.14865i | −0.0121482 | − | 0.00503197i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1012.12 | + | 419.236i | −2.35926 | + | 0.977239i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −289.906 | −0.672636 | −0.336318 | − | 0.941749i | \(-0.609182\pi\) | ||||
−0.336318 | + | 0.941749i | \(0.609182\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 314.414i | − | 0.726129i | −0.931764 | − | 0.363064i | \(-0.881731\pi\) | ||
0.931764 | − | 0.363064i | \(-0.118269\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.3098 | + | 44.2037i | 0.0420914 | + | 0.101618i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −82.5760 | + | 199.356i | −0.188961 | + | 0.456192i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 579.455 | + | 579.455i | 1.31994 | + | 1.31994i | 0.913818 | + | 0.406125i | \(0.133120\pi\) |
0.406125 | + | 0.913818i | \(0.366880\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −58.3284 | − | 58.3284i | −0.132264 | − | 0.132264i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −107.736 | + | 260.098i | −0.243197 | + | 0.587130i | −0.997597 | − | 0.0692856i | \(-0.977928\pi\) |
0.754400 | + | 0.656415i | \(0.227928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0223 | + | 29.0244i | 0.0270164 | + | 0.0652233i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 642.127i | − | 1.43652i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 470.997 | 1.04899 | 0.524496 | − | 0.851413i | \(-0.324254\pi\) | ||||
0.524496 | + | 0.851413i | \(0.324254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −355.147 | + | 147.107i | −0.787465 | + | 0.326179i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −289.717 | − | 120.005i | −0.639551 | − | 0.264911i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.54769 | + | 4.54769i | −0.00999493 | + | 0.00999493i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 447.868 | − | 447.868i | 0.980018 | − | 0.980018i | −0.0197861 | − | 0.999804i | \(-0.506299\pi\) |
0.999804 | + | 0.0197861i | \(0.00629852\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −363.106 | − | 150.404i | −0.791082 | − | 0.327677i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 253.222 | − | 104.888i | 0.549288 | − | 0.227523i | −0.0907394 | − | 0.995875i | \(-0.528923\pi\) |
0.640027 | + | 0.768352i | \(0.278923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 653.753 | 1.41199 | 0.705996 | − | 0.708215i | \(-0.250499\pi\) | ||||
0.705996 | + | 0.708215i | \(0.250499\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 32.4973i | 0.0698868i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −39.3875 | − | 95.0899i | −0.0843416 | − | 0.203619i | 0.876082 | − | 0.482162i | \(-0.160148\pi\) |
−0.960424 | + | 0.278544i | \(0.910148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.0756028 | + | 0.182521i | −0.000161200 | + | 0.000389171i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 264.117 | + | 264.117i | 0.560758 | + | 0.560758i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 256.332 | + | 256.332i | 0.541927 | + | 0.541927i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 85.6236 | − | 206.714i | 0.180260 | − | 0.435187i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 47.6017 | + | 114.921i | 0.0997940 | + | 0.240924i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 857.713i | 1.79063i | 0.445432 | + | 0.895316i | \(0.353050\pi\) | ||||
−0.445432 | + | 0.895316i | \(0.646950\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −231.408 | −0.481099 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 36.2537 | − | 15.0168i | 0.0750595 | − | 0.0310907i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 53.9661 | + | 22.3535i | 0.111270 | + | 0.0460897i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.5467 | + | 12.5467i | −0.0257633 | + | 0.0257633i | −0.719871 | − | 0.694108i | \(-0.755799\pi\) |
0.694108 | + | 0.719871i | \(0.255799\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 113.412 | − | 113.412i | 0.231926 | − | 0.231926i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −91.7015 | − | 37.9840i | −0.186765 | − | 0.0773605i | 0.287341 | − | 0.957828i | \(-0.407229\pi\) |
−0.474106 | + | 0.880468i | \(0.657229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 454.233 | − | 188.149i | 0.921365 | − | 0.381642i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.5818 | −0.0314784 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.0166i | 0.0503352i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −193.677 | − | 467.577i | −0.388130 | − | 0.937029i | −0.990336 | − | 0.138688i | \(-0.955711\pi\) |
0.602206 | − | 0.798341i | \(-0.294289\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −144.403 | + | 348.619i | −0.288229 | + | 0.695846i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −659.583 | − | 659.583i | −1.31130 | − | 1.31130i | −0.920459 | − | 0.390840i | \(-0.872184\pi\) |
−0.390840 | − | 0.920459i | \(-0.627816\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −37.0177 | − | 37.0177i | −0.0733024 | − | 0.0733024i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −307.928 | + | 743.403i | −0.607353 | + | 1.46628i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −133.178 | − | 321.521i | −0.261647 | − | 0.631671i | 0.737394 | − | 0.675463i | \(-0.236056\pi\) |
−0.999041 | + | 0.0437918i | \(0.986056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 58.6707i | − | 0.114815i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 261.217 | 0.509196 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 81.6425 | − | 33.8174i | 0.158529 | − | 0.0656649i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 755.957 | + | 313.127i | 1.46220 | + | 0.605662i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.6014 | − | 12.6014i | 0.0242801 | − | 0.0242801i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 71.2918 | − | 71.2918i | 0.136837 | − | 0.136837i | −0.635371 | − | 0.772207i | \(-0.719153\pi\) |
0.772207 | + | 0.635371i | \(0.219153\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 376.338 | + | 155.884i | 0.719576 | + | 0.298058i | 0.712261 | − | 0.701915i | \(-0.247671\pi\) |
0.00731529 | + | 0.999973i | \(0.497671\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −37.5918 | + | 15.5710i | −0.0716033 | + | 0.0296591i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 333.940 | 0.633662 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.2074i | 0.0778968i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.88582 | − | 6.96699i | −0.00543469 | − | 0.0131205i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −169.379 | + | 408.918i | −0.317785 | + | 0.767201i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.5704 | + | 35.5704i | 0.0664867 | + | 0.0664867i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 402.825 | + | 402.825i | 0.750139 | + | 0.750139i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 349.184 | − | 843.005i | 0.647837 | − | 1.56402i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −131.242 | − | 316.846i | −0.242591 | − | 0.585667i | 0.754948 | − | 0.655785i | \(-0.227662\pi\) |
−0.997539 | + | 0.0701185i | \(0.977662\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 421.935i | − | 0.777044i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.7639 | 0.0270898 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 57.6667 | − | 23.8863i | 0.105424 | − | 0.0436679i | −0.329348 | − | 0.944209i | \(-0.606829\pi\) |
0.434772 | + | 0.900541i | \(0.356829\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.4705 | − | 5.99386i | −0.0263578 | − | 0.0109178i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −231.064 | + | 231.064i | −0.419354 | + | 0.419354i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.1339 | − | 29.1339i | 0.0526834 | − | 0.0526834i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.0934 | + | 5.42345i | 0.0235917 | + | 0.00977198i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 403.952 | − | 167.322i | 0.725228 | − | 0.300399i | 0.0106383 | − | 0.999943i | \(-0.496614\pi\) |
0.714589 | + | 0.699544i | \(0.246614\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 417.394 | 0.746680 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 689.438i | − | 1.22895i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.60893 | − | 6.29851i | −0.00463398 | − | 0.0111874i | 0.921546 | − | 0.388270i | \(-0.126927\pi\) |
−0.926180 | + | 0.377083i | \(0.876927\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.3767 | + | 63.6791i | −0.0466845 | + | 0.112706i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −27.0261 | − | 27.0261i | −0.0476651 | − | 0.0476651i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 225.325 | + | 225.325i | 0.396002 | + | 0.396002i | 0.876820 | − | 0.480818i | \(-0.159660\pi\) |
−0.480818 | + | 0.876820i | \(0.659660\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −203.081 | + | 490.280i | −0.355658 | + | 0.858634i | 0.640242 | + | 0.768173i | \(0.278834\pi\) |
−0.995900 | + | 0.0904608i | \(0.971166\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 111.501 | + | 269.187i | 0.194592 | + | 0.469786i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 591.252i | − | 1.02826i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1017.81 | −1.76396 | −0.881980 | − | 0.471286i | \(-0.843790\pi\) | ||||
−0.881980 | + | 0.471286i | \(0.843790\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 436.520 | − | 180.813i | 0.753921 | − | 0.312284i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0762 | − | 9.97270i | −0.0414393 | − | 0.0171647i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −972.943 | + | 972.943i | −1.66886 | + | 1.66886i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.6862 | + | 12.6862i | −0.0216858 | + | 0.0216858i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 721.215 | + | 298.737i | 1.22865 | + | 0.508922i | 0.900149 | − | 0.435583i | \(-0.143458\pi\) |
0.328498 | + | 0.944505i | \(0.393458\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −205.053 | + | 84.9359i | −0.348138 | + | 0.144204i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 317.303 | 0.536892 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 525.499i | − | 0.886170i | −0.896479 | − | 0.443085i | \(-0.853884\pi\) | ||
0.896479 | − | 0.443085i | \(-0.146116\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.54890 | − | 3.73937i | −0.00260319 | − | 0.00628465i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 278.403 | − | 672.123i | 0.466336 | − | 1.12583i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 359.176 | + | 359.176i | 0.599626 | + | 0.599626i | 0.940213 | − | 0.340587i | \(-0.110626\pi\) |
−0.340587 | + | 0.940213i | \(0.610626\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 163.858 | + | 163.858i | 0.272642 | + | 0.272642i | 0.830163 | − | 0.557521i | \(-0.188247\pi\) |
−0.557521 | + | 0.830163i | \(0.688247\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.210901 | + | 0.509160i | −0.000349753 | + | 0.000844378i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −43.2897 | − | 104.511i | −0.0715533 | − | 0.172745i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 208.191i | − | 0.342984i | −0.985186 | − | 0.171492i | \(-0.945141\pi\) | ||
0.985186 | − | 0.171492i | \(-0.0548587\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 59.4252 | 0.0975783 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 870.414 | − | 360.537i | 1.42457 | − | 0.590077i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 643.217 | + | 266.429i | 1.04929 | + | 0.434632i | 0.839640 | − | 0.543144i | \(-0.182766\pi\) |
0.209654 | + | 0.977776i | \(0.432766\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.1674 | − | 19.1674i | 0.0311665 | − | 0.0311665i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −526.767 | + | 526.767i | −0.853755 | + | 0.853755i | −0.990593 | − | 0.136838i | \(-0.956306\pi\) |
0.136838 | + | 0.990593i | \(0.456306\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 316.799 | + | 131.222i | 0.511791 | + | 0.211991i | 0.623607 | − | 0.781738i | \(-0.285667\pi\) |
−0.111816 | + | 0.993729i | \(0.535667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 637.729 | − | 264.156i | 1.02694 | − | 0.425372i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39.0188 | 0.0626306 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 607.081i | 0.971330i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 175.355 | + | 423.345i | 0.279673 | + | 0.675191i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 55.7309 | − | 134.546i | 0.0886024 | − | 0.213905i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −515.138 | − | 515.138i | −0.816383 | − | 0.816383i | 0.169199 | − | 0.985582i | \(-0.445882\pi\) |
−0.985582 | + | 0.169199i | \(0.945882\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 432.812 | + | 432.812i | 0.683748 | + | 0.683748i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.7220 | + | 74.1694i | −0.0483810 | + | 0.116802i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −402.053 | − | 970.642i | −0.631167 | − | 1.52377i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 69.7861i | 0.109211i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −827.282 | −1.29061 | −0.645306 | − | 0.763925i | \(-0.723270\pi\) | ||||
−0.645306 | + | 0.763925i | \(0.723270\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −300.259 | + | 124.371i | −0.466965 | + | 0.193423i | −0.603744 | − | 0.797178i | \(-0.706325\pi\) |
0.136779 | + | 0.990602i | \(0.456325\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.6166 | − | 9.78234i | −0.0366150 | − | 0.0151664i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 182.325 | − | 182.325i | 0.281800 | − | 0.281800i | −0.552027 | − | 0.833827i | \(-0.686145\pi\) |
0.833827 | + | 0.552027i | \(0.186145\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 58.9840 | − | 58.9840i | 0.0908845 | − | 0.0908845i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.2898 | + | 15.4460i | 0.0572808 | + | 0.0237265i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −83.4520 | + | 34.5670i | −0.127798 | + | 0.0529356i | −0.445666 | − | 0.895199i | \(-0.647033\pi\) |
0.317868 | + | 0.948135i | \(0.397033\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.94981 | −0.00908368 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 163.667i | − | 0.249113i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.4182 | − | 87.9213i | −0.0552628 | − | 0.133416i | 0.893837 | − | 0.448393i | \(-0.148003\pi\) |
−0.949099 | + | 0.314976i | \(0.898003\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −420.501 | + | 1015.18i | −0.636159 | + | 1.53582i | 0.195597 | + | 0.980684i | \(0.437335\pi\) |
−0.831757 | + | 0.555140i | \(0.812665\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −561.319 | − | 561.319i | −0.846634 | − | 0.846634i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.90218 | + | 1.90218i | 0.00286042 | + | 0.00286042i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −330.450 | + | 797.776i | −0.495427 | + | 1.19607i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −107.398 | − | 259.282i | −0.160535 | − | 0.387567i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 173.255i | − | 0.258205i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 80.3370 | 0.119372 | 0.0596858 | − | 0.998217i | \(-0.480990\pi\) | ||||
0.0596858 | + | 0.998217i | \(0.480990\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −661.266 | + | 273.905i | −0.979653 | + | 0.405785i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −944.061 | − | 391.043i | −1.39448 | − | 0.577611i | −0.446165 | − | 0.894951i | \(-0.647211\pi\) |
−0.948312 | + | 0.317339i | \(0.897211\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 51.3001 | − | 51.3001i | 0.0755524 | − | 0.0755524i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 219.432 | − | 219.432i | 0.322220 | − | 0.322220i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 173.921 | + | 72.0404i | 0.254643 | + | 0.105476i | 0.506353 | − | 0.862326i | \(-0.330993\pi\) |
−0.251711 | + | 0.967803i | \(0.580993\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.6237 | + | 5.64314i | −0.0198887 | + | 0.00823816i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −134.900 | −0.196361 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1584.28i | 2.29939i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −185.902 | − | 448.807i | −0.269033 | − | 0.649503i | 0.730405 | − | 0.683014i | \(-0.239331\pi\) |
−0.999438 | + | 0.0335109i | \(0.989331\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.40601 | + | 17.8797i | −0.0106869 | + | 0.0258004i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −58.0179 | − | 58.0179i | −0.0834790 | − | 0.0834790i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −196.962 | − | 196.962i | −0.282586 | − | 0.282586i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 91.7099 | − | 221.407i | 0.131202 | − | 0.316749i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −150.886 | − | 364.271i | −0.215244 | − | 0.519645i | 0.778970 | − | 0.627061i | \(-0.215742\pi\) |
−0.994214 | + | 0.107416i | \(0.965742\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 96.7921i | 0.137684i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −57.6989 | −0.0818423 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −60.0713 | + | 24.8824i | −0.0849665 | + | 0.0351943i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −457.191 | − | 189.375i | −0.644839 | − | 0.267101i | 0.0362043 | − | 0.999344i | \(-0.488473\pi\) |
−0.681043 | + | 0.732243i | \(0.738473\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 81.2717 | − | 81.2717i | 0.114306 | − | 0.114306i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −414.720 | + | 414.720i | −0.581656 | + | 0.581656i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −183.350 | − | 75.9462i | −0.256434 | − | 0.106218i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 764.230 | − | 316.554i | 1.06587 | − | 0.441498i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1277.00 | −1.77608 | −0.888039 | − | 0.459768i | \(-0.847932\pi\) | ||||
−0.888039 | + | 0.459768i | \(0.847932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 109.756i | − | 0.152227i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −253.634 | − | 612.327i | −0.350808 | − | 0.846925i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 342.646 | − | 827.219i | 0.472614 | − | 1.14099i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −470.863 | − | 470.863i | −0.647679 | − | 0.647679i | 0.304753 | − | 0.952432i | \(-0.401426\pi\) |
−0.952432 | + | 0.304753i | \(0.901426\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −572.562 | − | 572.562i | −0.785407 | − | 0.785407i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −100.522 | + | 242.683i | −0.137514 | + | 0.331987i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 364.452 | + | 879.866i | 0.497206 | + | 1.20036i | 0.950982 | + | 0.309246i | \(0.100077\pi\) |
−0.453776 | + | 0.891116i | \(0.649923\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 64.3429i | 0.0875413i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.09619 | −0.00827163 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1146.65 | + | 474.958i | −1.55162 | + | 0.642704i | −0.983609 | − | 0.180314i | \(-0.942289\pi\) |
−0.568016 | + | 0.823018i | \(0.692289\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 487.442 | + | 201.905i | 0.657817 | + | 0.272477i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −512.021 | + | 512.021i | −0.689126 | + | 0.689126i | −0.962039 | − | 0.272913i | \(-0.912013\pi\) |
0.272913 | + | 0.962039i | \(0.412013\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 82.2533 | − | 82.2533i | 0.110407 | − | 0.110407i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −67.1628 | − | 27.8197i | −0.0899101 | − | 0.0372420i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 57.7227 | − | 23.9095i | 0.0770663 | − | 0.0319219i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −335.629 | −0.446910 | −0.223455 | − | 0.974714i | \(-0.571734\pi\) | ||||
−0.223455 | + | 0.974714i | \(0.571734\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 938.161i | − | 1.24590i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.7393 | − | 52.4833i | −0.0287938 | − | 0.0695143i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −139.805 | + | 337.518i | −0.184682 | + | 0.445863i | −0.988921 | − | 0.148444i | \(-0.952573\pi\) |
0.804238 | + | 0.594307i | \(0.202573\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 856.215 | + | 856.215i | 1.12808 | + | 1.12808i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 495.581 | + | 495.581i | 0.651223 | + | 0.651223i | 0.953288 | − | 0.302064i | \(-0.0976758\pi\) |
−0.302064 | + | 0.953288i | \(0.597676\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.01728 | − | 16.9412i | 0.00919696 | − | 0.0222034i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.32079 | − | 10.4313i | −0.00564809 | − | 0.0136357i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 96.0458i | − | 0.125223i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 372.267 | 0.484092 | 0.242046 | − | 0.970265i | \(-0.422181\pi\) | ||||
0.242046 | + | 0.970265i | \(0.422181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 271.689 | − | 112.537i | 0.352385 | − | 0.145963i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −534.778 | − | 221.512i | −0.691822 | − | 0.286562i | 0.00893708 | − | 0.999960i | \(-0.497155\pi\) |
−0.700759 | + | 0.713398i | \(0.747155\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 430.026 | − | 430.026i | 0.554873 | − | 0.554873i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.4465 | − | 12.4465i | 0.0160187 | − | 0.0160187i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 171.040 | + | 70.8470i | 0.219563 | + | 0.0909461i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −713.187 | + | 295.412i | −0.913172 | + | 0.378248i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1045.33 | 1.33503 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 67.6643i | 0.0861965i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 280.233 | + | 676.541i | 0.356077 | + | 0.859646i | 0.995844 | + | 0.0910769i | \(0.0290309\pi\) |
−0.639767 | + | 0.768569i | \(0.720969\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −219.612 | + | 530.190i | −0.278342 | + | 0.671978i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 60.5332 | + | 60.5332i | 0.0765274 | + | 0.0765274i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −141.059 | − | 141.059i | −0.177880 | − | 0.177880i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 37.1303 | − | 89.6404i | 0.0467047 | − | 0.112755i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 92.5205 | + | 223.364i | 0.116086 | + | 0.280256i | 0.971234 | − | 0.238128i | \(-0.0765337\pi\) |
−0.855148 | + | 0.518384i | \(0.826534\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 592.908i | 0.742063i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 108.847 | 0.135888 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1672.62 | − | 692.821i | 2.08296 | − | 0.862790i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.56751 | + | 2.72035i | 0.00815839 | + | 0.00337932i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 528.455 | − | 528.455i | 0.654839 | − | 0.654839i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 977.291 | − | 977.291i | 1.20802 | − | 1.20802i | 0.236358 | − | 0.971666i | \(-0.424046\pi\) |
0.971666 | − | 0.236358i | \(-0.0759538\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −553.320 | − | 229.193i | −0.682269 | − | 0.282605i | 0.0145062 | − | 0.999895i | \(-0.495382\pi\) |
−0.696775 | + | 0.717290i | \(0.745382\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −653.290 | + | 270.602i | −0.803555 | + | 0.332843i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29.0550 | 0.0356503 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 174.585i | − | 0.213690i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.52734 | + | 20.5868i | 0.0104119 | + | 0.0251365i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 390.123 | − | 941.839i | 0.475180 | − | 1.14719i | −0.486665 | − | 0.873589i | \(-0.661787\pi\) |
0.961844 | − | 0.273597i | \(-0.0882134\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 692.747 | + | 692.747i | 0.841734 | + | 0.841734i | 0.989084 | − | 0.147350i | \(-0.0470744\pi\) |
−0.147350 | + | 0.989084i | \(0.547074\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −887.815 | − | 887.815i | −1.07614 | − | 1.07614i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 401.669 | − | 969.714i | 0.485694 | − | 1.17257i | −0.471173 | − | 0.882041i | \(-0.656169\pi\) |
0.956867 | − | 0.290528i | \(-0.0938309\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 562.011 | + | 1356.81i | 0.677938 | + | 1.63669i | 0.767766 | + | 0.640730i | \(0.221368\pi\) |
−0.0898281 | + | 0.995957i | \(0.528632\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 848.321i | 1.02084i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 661.182 | 0.793735 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −63.1537 | + | 26.1591i | −0.0756331 | + | 0.0313283i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 655.955 | + | 271.705i | 0.783697 | + | 0.324618i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 708.611 | − | 708.611i | 0.844590 | − | 0.844590i | −0.144862 | − | 0.989452i | \(-0.546274\pi\) |
0.989452 | + | 0.144862i | \(0.0462737\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −329.986 | + | 329.986i | −0.392374 | + | 0.392374i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −76.9407 | − | 31.8699i | −0.0912701 | − | 0.0378053i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −134.670 | + | 55.7823i | −0.159373 | + | 0.0660146i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −140.499 | −0.165878 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1101.24i | 1.29711i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 97.8810 | + | 236.306i | 0.115019 | + | 0.277680i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −178.189 | + | 430.187i | −0.208897 | + | 0.504322i | −0.993250 | − | 0.115992i | \(-0.962995\pi\) |
0.784353 | + | 0.620315i | \(0.212995\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.30630 | + | 5.30630i | 0.00620620 | + | 0.00620620i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −195.982 | − | 195.982i | −0.228683 | − | 0.228683i | 0.583459 | − | 0.812142i | \(-0.301699\pi\) |
−0.812142 | + | 0.583459i | \(0.801699\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 155.060 | − | 374.347i | 0.180512 | − | 0.435794i | −0.807560 | − | 0.589785i | \(-0.799213\pi\) |
0.988072 | + | 0.153991i | \(0.0492126\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.8838 | − | 31.1043i | −0.0149638 | − | 0.0361258i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 63.9126i | 0.0740586i | 0.999314 | + | 0.0370293i | \(0.0117895\pi\) | ||||
−0.999314 | + | 0.0370293i | \(0.988211\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.22835 | 0.00373219 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −260.035 | + | 107.710i | −0.299925 | + | 0.124233i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1174.60 | + | 486.534i | 1.35167 | + | 0.559879i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.96332 | + | 4.96332i | −0.00569842 | + | 0.00569842i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 143.106 | − | 143.106i | 0.163925 | − | 0.163925i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.6857 | − | 5.66881i | −0.0156408 | − | 0.00647864i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.2590 | + | 14.1905i | −0.0390638 | + | 0.0161808i | −0.402130 | − | 0.915583i | \(-0.631730\pi\) |
0.363066 | + | 0.931763i | \(0.381730\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 108.844 | 0.123827 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1126.03i | − | 1.27812i | −0.769155 | − | 0.639062i | \(-0.779323\pi\) | ||
0.769155 | − | 0.639062i | \(-0.220677\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 114.384 | + | 276.148i | 0.129540 | + | 0.312738i | 0.975321 | − | 0.220793i | \(-0.0708646\pi\) |
−0.845780 | + | 0.533531i | \(0.820865\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.25100 | + | 5.43439i | −0.00254350 | + | 0.00614055i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −65.1075 | − | 65.1075i | −0.0734020 | − | 0.0734020i | 0.669453 | − | 0.742855i | \(-0.266529\pi\) |
−0.742855 | + | 0.669453i | \(0.766529\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 70.5052 | + | 70.5052i | 0.0793085 | + | 0.0793085i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 451.334 | − | 1089.62i | 0.506548 | − | 1.22292i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −150.803 | − | 364.071i | −0.168873 | − | 0.407694i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 103.200i | 0.115307i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1394.21 | 1.55430 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −820.576 | + | 339.894i | −0.912765 | + | 0.378080i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −921.136 | − | 381.547i | −1.02235 | − | 0.423471i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −22.4499 | + | 22.4499i | −0.0248615 | + | 0.0248615i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 54.0478 | − | 54.0478i | 0.0597213 | − | 0.0597213i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1085.79 | − | 449.751i | −1.19713 | − | 0.495866i | −0.307058 | − | 0.951691i | \(-0.599344\pi\) |
−0.890070 | + | 0.455825i | \(0.849344\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −167.574 | + | 69.4116i | −0.184350 | + | 0.0763604i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.8649 | 0.0415641 | 0.0207821 | − | 0.999784i | \(-0.493384\pi\) | ||||
0.0207821 | + | 0.999784i | \(0.493384\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 804.143i | − | 0.880770i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.67532 | + | 11.2872i | 0.00510964 | + | 0.0123358i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.82794 | + | 6.82725i | −0.00308390 | + | 0.00744520i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1205.51 | + | 1205.51i | 1.31176 | + | 1.31176i | 0.920119 | + | 0.391640i | \(0.128092\pi\) |
0.391640 | + | 0.920119i | \(0.371908\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −504.801 | − | 504.801i | −0.548101 | − | 0.548101i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −340.139 | + | 821.169i | −0.368515 | + | 0.889674i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −101.493 | − | 245.027i | −0.109723 | − | 0.264894i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 306.174i | − | 0.330285i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1384.29 | 1.49009 | 0.745045 | − | 0.667014i | \(-0.232428\pi\) | ||||
0.745045 | + | 0.667014i | \(0.232428\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −405.994 | + | 168.168i | −0.436084 | + | 0.180632i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −640.515 | − | 265.310i | −0.686511 | − | 0.284362i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 88.3137 | − | 88.3137i | 0.0944532 | − | 0.0944532i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −500.748 | + | 500.748i | −0.534416 | + | 0.534416i | −0.921883 | − | 0.387467i | \(-0.873350\pi\) |
0.387467 | + | 0.921883i | \(0.373350\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −391.814 | − | 162.295i | −0.417267 | − | 0.172838i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1312.74 | + | 543.756i | −1.39505 | + | 0.577849i | −0.948462 | − | 0.316891i | \(-0.897361\pi\) |
−0.446588 | + | 0.894740i | \(0.647361\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 489.216 | 0.518787 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 8.60544i | − | 0.00910629i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 256.726 | + | 619.792i | 0.271094 | + | 0.654480i | 0.999531 | − | 0.0306337i | \(-0.00975255\pi\) |
−0.728436 | + | 0.685114i | \(0.759753\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 797.719 | − | 1925.86i | 0.840589 | − | 2.02936i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −669.951 | − | 669.951i | −0.704470 | − | 0.704470i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 948.406 | + | 948.406i | 0.995179 | + | 0.995179i | 0.999988 | − | 0.00480927i | \(-0.00153084\pi\) |
−0.00480927 | + | 0.999988i | \(0.501531\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.1989 | + | 48.7643i | −0.0211506 | + | 0.0510621i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 701.730 | + | 1694.13i | 0.733260 | + | 1.77025i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.3151i | 0.0190981i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 357.735 | 0.372253 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 161.023 | − | 66.6978i | 0.167209 | − | 0.0692604i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 79.0773 | + | 32.7549i | 0.0819454 | + | 0.0339429i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.79422 | − | 5.79422i | 0.00599196 | − | 0.00599196i | −0.704104 | − | 0.710096i | \(-0.748651\pi\) |
0.710096 | + | 0.704104i | \(0.248651\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −234.785 | + | 234.785i | −0.242296 | + | 0.242296i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1644.17 | − | 681.037i | −1.69327 | − | 0.701377i | −0.693457 | − | 0.720498i | \(-0.743913\pi\) |
−0.999817 | + | 0.0191210i | \(0.993913\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −94.1498 | + | 38.9981i | −0.0967624 | + | 0.0400803i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1445.66 | −1.48273 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 538.935i | 0.551623i | 0.961212 | + | 0.275811i | \(0.0889465\pi\) | ||||
−0.961212 | + | 0.275811i | \(0.911054\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 460.760 | + | 1112.37i | 0.470643 | + | 1.13623i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.5753 | − | 47.2590i | 0.0199545 | − | 0.0481744i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −171.371 | − | 171.371i | −0.174335 | − | 0.174335i | 0.614546 | − | 0.788881i | \(-0.289339\pi\) |
−0.788881 | + | 0.614546i | \(0.789339\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40.6450 | + | 40.6450i | 0.0412639 | + | 0.0412639i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.4242 | + | 66.2079i | −0.0277854 | + | 0.0670799i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −176.549 | − | 426.227i | −0.178513 | − | 0.430967i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1670.67i | − | 1.68584i | −0.538038 | − | 0.842921i | \(-0.680834\pi\) | ||
0.538038 | − | 0.842921i | \(-0.319166\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1697.32 | −1.70929 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 121.758 | − | 50.4337i | 0.122370 | − | 0.0506871i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1252.59 | + | 518.840i | 1.25636 | + | 0.520402i | 0.908791 | − | 0.417252i | \(-0.137007\pi\) |
0.347570 | + | 0.937654i | \(0.387007\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 218.943 | − | 218.943i | 0.219162 | − | 0.219162i |
(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 | 128.3.h.a.15.2 | 28 | ||
4.3 | odd | 2 | 32.3.h.a.27.3 | yes | 28 | ||
8.3 | odd | 2 | 256.3.h.b.31.2 | 28 | |||
8.5 | even | 2 | 256.3.h.a.31.6 | 28 | |||
12.11 | even | 2 | 288.3.u.a.91.5 | 28 | |||
32.3 | odd | 8 | 256.3.h.a.223.6 | 28 | |||
32.13 | even | 8 | 32.3.h.a.19.3 | ✓ | 28 | ||
32.19 | odd | 8 | inner | 128.3.h.a.111.2 | 28 | ||
32.29 | even | 8 | 256.3.h.b.223.2 | 28 | |||
96.77 | odd | 8 | 288.3.u.a.19.5 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.19.3 | ✓ | 28 | 32.13 | even | 8 | ||
32.3.h.a.27.3 | yes | 28 | 4.3 | odd | 2 | ||
128.3.h.a.15.2 | 28 | 1.1 | even | 1 | trivial | ||
128.3.h.a.111.2 | 28 | 32.19 | odd | 8 | inner | ||
256.3.h.a.31.6 | 28 | 8.5 | even | 2 | |||
256.3.h.a.223.6 | 28 | 32.3 | odd | 8 | |||
256.3.h.b.31.2 | 28 | 8.3 | odd | 2 | |||
256.3.h.b.223.2 | 28 | 32.29 | even | 8 | |||
288.3.u.a.19.5 | 28 | 96.77 | odd | 8 | |||
288.3.u.a.91.5 | 28 | 12.11 | even | 2 |