Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(289,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.s (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 802.6 | ||
Root | \(-0.181721 - 0.314749i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.802 |
Dual form | 819.2.s.d.289.6 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.38804 | 1.68860 | 0.844299 | − | 0.535873i | \(-0.180017\pi\) | ||||
0.844299 | + | 0.535873i | \(0.180017\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.70272 | 1.85136 | ||||||||
\(5\) | 0.491140 | + | 0.850679i | 0.219644 | + | 0.380435i | 0.954699 | − | 0.297572i | \(-0.0961769\pi\) |
−0.735055 | + | 0.678008i | \(0.762844\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.911766 | + | 2.48368i | −0.344615 | + | 0.938744i | ||||
\(8\) | 4.06616 | 1.43761 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.17286 | + | 2.03145i | 0.370891 | + | 0.642402i | ||||
\(11\) | −0.293901 | − | 0.509052i | −0.0886146 | − | 0.153485i | 0.818311 | − | 0.574775i | \(-0.194911\pi\) |
−0.906926 | + | 0.421291i | \(0.861577\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.39227 | + | 2.69760i | 0.663496 | + | 0.748179i | ||||
\(14\) | −2.17733 | + | 5.93113i | −0.581916 | + | 1.58516i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.30470 | 0.576176 | ||||||||
\(17\) | 6.45420 | 1.56537 | 0.782687 | − | 0.622416i | \(-0.213849\pi\) | ||||
0.782687 | + | 0.622416i | \(0.213849\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.91345 | − | 3.31419i | 0.438975 | − | 0.760327i | −0.558636 | − | 0.829413i | \(-0.688675\pi\) |
0.997611 | + | 0.0690863i | \(0.0220084\pi\) | |||||||
\(20\) | 1.81855 | + | 3.14983i | 0.406641 | + | 0.704323i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.701847 | − | 1.21563i | −0.149634 | − | 0.259174i | ||||
\(23\) | −8.26001 | −1.72233 | −0.861166 | − | 0.508324i | \(-0.830265\pi\) | ||||
−0.861166 | + | 0.508324i | \(0.830265\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.01756 | − | 3.49452i | 0.403513 | − | 0.698904i | ||||
\(26\) | 5.71283 | + | 6.44197i | 1.12038 | + | 1.26337i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.37601 | + | 9.19639i | −0.638007 | + | 1.73795i | ||||
\(29\) | −1.98009 | + | 3.42962i | −0.367694 | + | 0.636864i | −0.989205 | − | 0.146541i | \(-0.953186\pi\) |
0.621511 | + | 0.783406i | \(0.286519\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.49436 | − | 2.58831i | 0.268395 | − | 0.464874i | −0.700053 | − | 0.714091i | \(-0.746840\pi\) |
0.968448 | + | 0.249218i | \(0.0801734\pi\) | |||||||
\(32\) | −2.62861 | −0.464676 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15.4129 | 2.64329 | ||||||||
\(35\) | −2.56062 | + | 0.444216i | −0.432824 | + | 0.0750862i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.75588 | 0.288665 | 0.144333 | − | 0.989529i | \(-0.453896\pi\) | ||||
0.144333 | + | 0.989529i | \(0.453896\pi\) | |||||||
\(38\) | 4.56938 | − | 7.91440i | 0.741252 | − | 1.28389i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.99705 | + | 3.45900i | 0.315762 | + | 0.546916i | ||||
\(41\) | 1.83584 | − | 3.17977i | 0.286710 | − | 0.496597i | −0.686312 | − | 0.727307i | \(-0.740772\pi\) |
0.973023 | + | 0.230710i | \(0.0741049\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.19042 | − | 5.52598i | −0.486535 | − | 0.842703i | 0.513345 | − | 0.858182i | \(-0.328406\pi\) |
−0.999880 | + | 0.0154788i | \(0.995073\pi\) | |||||||
\(44\) | −1.08823 | − | 1.88488i | −0.164058 | − | 0.284156i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −19.7252 | −2.90832 | ||||||||
\(47\) | −2.17030 | − | 3.75906i | −0.316570 | − | 0.548316i | 0.663200 | − | 0.748442i | \(-0.269198\pi\) |
−0.979770 | + | 0.200127i | \(0.935865\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.33737 | − | 4.52907i | −0.762481 | − | 0.647011i | ||||
\(50\) | 4.81802 | − | 8.34505i | 0.681370 | − | 1.18017i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.85791 | + | 9.98846i | 1.22837 | + | 1.38515i | ||||
\(53\) | 0.212770 | − | 0.368529i | 0.0292263 | − | 0.0506214i | −0.851042 | − | 0.525097i | \(-0.824029\pi\) |
0.880269 | + | 0.474476i | \(0.157362\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.288693 | − | 0.500031i | 0.0389274 | − | 0.0674242i | ||||
\(56\) | −3.70739 | + | 10.0991i | −0.495420 | + | 1.34954i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.72853 | + | 8.19006i | −0.620887 | + | 1.07541i | ||||
\(59\) | −6.00863 | −0.782256 | −0.391128 | − | 0.920336i | \(-0.627915\pi\) | ||||
−0.391128 | + | 0.920336i | \(0.627915\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.10337 | + | 1.91109i | −0.141272 | + | 0.244691i | −0.927976 | − | 0.372640i | \(-0.878453\pi\) |
0.786704 | + | 0.617331i | \(0.211786\pi\) | |||||||
\(62\) | 3.56859 | − | 6.18097i | 0.453211 | − | 0.784985i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.8866 | −1.36083 | ||||||||
\(65\) | −1.11985 | + | 3.35995i | −0.138901 | + | 0.416751i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.50651 | − | 6.07346i | −0.428389 | − | 0.741991i | 0.568341 | − | 0.822793i | \(-0.307585\pi\) |
−0.996730 | + | 0.0808015i | \(0.974252\pi\) | |||||||
\(68\) | 23.8981 | 2.89807 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.11486 | + | 1.06080i | −0.730866 | + | 0.126790i | ||||
\(71\) | 1.80127 | + | 3.11988i | 0.213771 | + | 0.370262i | 0.952892 | − | 0.303311i | \(-0.0980920\pi\) |
−0.739121 | + | 0.673573i | \(0.764759\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.46714 | + | 4.27321i | −0.288756 | + | 0.500141i | −0.973513 | − | 0.228631i | \(-0.926575\pi\) |
0.684757 | + | 0.728772i | \(0.259908\pi\) | |||||||
\(74\) | 4.19311 | 0.487439 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.08496 | − | 12.2715i | 0.812701 | − | 1.40764i | ||||
\(77\) | 1.53229 | − | 0.265822i | 0.174621 | − | 0.0302932i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.39270 | − | 2.41223i | −0.156691 | − | 0.271397i | 0.776982 | − | 0.629522i | \(-0.216749\pi\) |
−0.933674 | + | 0.358125i | \(0.883416\pi\) | |||||||
\(80\) | 1.13193 | + | 1.96056i | 0.126554 | + | 0.219198i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.38406 | − | 7.59342i | 0.484138 | − | 0.838552i | ||||
\(83\) | 2.86819 | 0.314825 | 0.157412 | − | 0.987533i | \(-0.449685\pi\) | ||||
0.157412 | + | 0.987533i | \(0.449685\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.16992 | + | 5.49045i | 0.343826 | + | 0.595523i | ||||
\(86\) | −7.61885 | − | 13.1962i | −0.821562 | − | 1.42299i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.19505 | − | 2.06989i | −0.127393 | − | 0.220651i | ||||
\(89\) | 2.09311 | 0.221870 | 0.110935 | − | 0.993828i | \(-0.464616\pi\) | ||||
0.110935 | + | 0.993828i | \(0.464616\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.88117 | + | 3.48206i | −0.931000 | + | 0.365020i | ||||
\(92\) | −30.5845 | −3.18866 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.18275 | − | 8.97679i | −0.534560 | − | 0.925885i | ||||
\(95\) | 3.75908 | 0.385674 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.84852 | − | 6.66584i | −0.390758 | − | 0.676813i | 0.601791 | − | 0.798653i | \(-0.294454\pi\) |
−0.992550 | + | 0.121840i | \(0.961120\pi\) | |||||||
\(98\) | −12.7458 | − | 10.8156i | −1.28752 | − | 1.09254i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.47047 | − | 12.9392i | 0.747047 | − | 1.29392i | ||||
\(101\) | −1.31866 | − | 2.28399i | −0.131212 | − | 0.227265i | 0.792932 | − | 0.609310i | \(-0.208553\pi\) |
−0.924144 | + | 0.382045i | \(0.875220\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.43095 | + | 9.40669i | 0.535128 | + | 0.926868i | 0.999157 | + | 0.0410486i | \(0.0130699\pi\) |
−0.464029 | + | 0.885820i | \(0.653597\pi\) | |||||||
\(104\) | 9.72736 | + | 10.9689i | 0.953846 | + | 1.07559i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.508103 | − | 0.880061i | 0.0493514 | − | 0.0854791i | ||||
\(107\) | 15.9805 | 1.54489 | 0.772446 | − | 0.635080i | \(-0.219033\pi\) | ||||
0.772446 | + | 0.635080i | \(0.219033\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.61738 | + | 7.99754i | −0.442265 | + | 0.766026i | −0.997857 | − | 0.0654294i | \(-0.979158\pi\) |
0.555592 | + | 0.831455i | \(0.312492\pi\) | |||||||
\(110\) | 0.689410 | − | 1.19409i | 0.0657327 | − | 0.113852i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.10135 | + | 5.72416i | −0.198559 | + | 0.540882i | ||||
\(113\) | 5.09012 | + | 8.81635i | 0.478838 | + | 0.829372i | 0.999706 | − | 0.0242655i | \(-0.00772470\pi\) |
−0.520867 | + | 0.853638i | \(0.674391\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.05682 | − | 7.02662i | −0.378301 | − | 0.655236i | ||||
\(116\) | −7.33173 | + | 12.6989i | −0.680734 | + | 1.17907i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −14.3488 | −1.32092 | ||||||||
\(119\) | −5.88472 | + | 16.0302i | −0.539451 | + | 1.46949i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.32724 | − | 9.22706i | 0.484295 | − | 0.838823i | ||||
\(122\) | −2.63489 | + | 4.56376i | −0.238552 | + | 0.413184i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.53320 | − | 9.58378i | 0.496896 | − | 0.860649i | ||||
\(125\) | 8.87502 | 0.793806 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.12513 | + | 3.68083i | −0.188575 | + | 0.326621i | −0.944775 | − | 0.327719i | \(-0.893720\pi\) |
0.756201 | + | 0.654340i | \(0.227053\pi\) | |||||||
\(128\) | −20.7404 | −1.83321 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.67425 | + | 8.02369i | −0.234547 | + | 0.703725i | ||||
\(131\) | −1.08478 | − | 1.87890i | −0.0947779 | − | 0.164160i | 0.814738 | − | 0.579829i | \(-0.196881\pi\) |
−0.909516 | + | 0.415669i | \(0.863547\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.48678 | + | 7.77416i | 0.562475 | + | 0.674105i | ||||
\(134\) | −8.37369 | − | 14.5037i | −0.723376 | − | 1.25292i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 26.2438 | 2.25039 | ||||||||
\(137\) | −8.36316 | −0.714513 | −0.357257 | − | 0.934006i | \(-0.616288\pi\) | ||||
−0.357257 | + | 0.934006i | \(0.616288\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.288457 | + | 0.499622i | 0.0244666 | + | 0.0423774i | 0.877999 | − | 0.478662i | \(-0.158878\pi\) |
−0.853533 | + | 0.521039i | \(0.825545\pi\) | |||||||
\(140\) | −9.48127 | + | 1.64481i | −0.801314 | + | 0.139012i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.30149 | + | 7.45040i | 0.360973 | + | 0.625224i | ||||
\(143\) | 0.670127 | − | 2.01062i | 0.0560388 | − | 0.168136i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.89001 | −0.323048 | ||||||||
\(146\) | −5.89161 | + | 10.2046i | −0.487593 | + | 0.844537i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.50154 | 0.534423 | ||||||||
\(149\) | 1.40331 | − | 2.43061i | 0.114964 | − | 0.199123i | −0.802801 | − | 0.596246i | \(-0.796658\pi\) |
0.917765 | + | 0.397123i | \(0.129991\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5054 | − | 19.9280i | 0.936300 | − | 1.62172i | 0.164000 | − | 0.986460i | \(-0.447560\pi\) |
0.772300 | − | 0.635258i | \(-0.219106\pi\) | |||||||
\(152\) | 7.78039 | − | 13.4760i | 0.631073 | − | 1.09305i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.65917 | − | 0.634792i | 0.294864 | − | 0.0511530i | ||||
\(155\) | 2.93576 | 0.235806 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.2880 | + | 19.5513i | −0.900879 | + | 1.56037i | −0.0745227 | + | 0.997219i | \(0.523743\pi\) |
−0.826356 | + | 0.563148i | \(0.809590\pi\) | |||||||
\(158\) | −3.32583 | − | 5.76050i | −0.264588 | − | 0.458281i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.29101 | − | 2.23610i | −0.102064 | − | 0.176779i | ||||
\(161\) | 7.53119 | − | 20.5153i | 0.593541 | − | 1.61683i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.08857 | + | 7.08161i | −0.320242 | + | 0.554675i | −0.980538 | − | 0.196331i | \(-0.937097\pi\) |
0.660296 | + | 0.751005i | \(0.270431\pi\) | |||||||
\(164\) | 6.79761 | − | 11.7738i | 0.530804 | − | 0.919380i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.84934 | 0.531612 | ||||||||
\(167\) | −1.16386 | + | 2.01586i | −0.0900619 | + | 0.155992i | −0.907537 | − | 0.419972i | \(-0.862040\pi\) |
0.817475 | + | 0.575964i | \(0.195373\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.55408 | + | 12.9068i | −0.119545 | + | 0.992829i | ||||
\(170\) | 7.56988 | + | 13.1114i | 0.580583 | + | 1.00560i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.8133 | − | 20.4611i | −0.900752 | − | 1.56015i | ||||
\(173\) | −4.06686 | + | 7.04401i | −0.309198 | + | 0.535546i | −0.978187 | − | 0.207726i | \(-0.933394\pi\) |
0.668989 | + | 0.743272i | \(0.266727\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.83974 | + | 8.19717i | 0.517036 | + | 0.619648i | ||||
\(176\) | −0.677355 | − | 1.17321i | −0.0510576 | − | 0.0884343i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.99843 | 0.374648 | ||||||||
\(179\) | −10.4963 | − | 18.1801i | −0.784528 | − | 1.35884i | −0.929281 | − | 0.369375i | \(-0.879572\pi\) |
0.144752 | − | 0.989468i | \(-0.453761\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.60807 | −0.119527 | −0.0597635 | − | 0.998213i | \(-0.519035\pi\) | ||||
−0.0597635 | + | 0.998213i | \(0.519035\pi\) | |||||||
\(182\) | −21.2086 | + | 8.31530i | −1.57208 | + | 0.616371i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −33.5865 | −2.47603 | ||||||||
\(185\) | 0.862384 | + | 1.49369i | 0.0634037 | + | 0.109818i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.89690 | − | 3.28552i | −0.138715 | − | 0.240261i | ||||
\(188\) | −8.03601 | − | 13.9188i | −0.586086 | − | 1.01513i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.97683 | 0.651247 | ||||||||
\(191\) | −5.78111 | + | 10.0132i | −0.418307 | + | 0.724529i | −0.995769 | − | 0.0918886i | \(-0.970710\pi\) |
0.577463 | + | 0.816417i | \(0.304043\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7894 | − | 20.4199i | −0.848621 | − | 1.46985i | −0.882439 | − | 0.470427i | \(-0.844100\pi\) |
0.0338178 | − | 0.999428i | \(-0.489233\pi\) | |||||||
\(194\) | −9.19041 | − | 15.9183i | −0.659833 | − | 1.14286i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.7628 | − | 16.7699i | −1.41163 | − | 1.19785i | ||||
\(197\) | −0.735472 | + | 1.27387i | −0.0524002 | + | 0.0907598i | −0.891036 | − | 0.453933i | \(-0.850020\pi\) |
0.838636 | + | 0.544693i | \(0.183354\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.39399 | 0.665922 | 0.332961 | − | 0.942941i | \(-0.391952\pi\) | ||||
0.332961 | + | 0.942941i | \(0.391952\pi\) | |||||||
\(200\) | 8.20374 | − | 14.2093i | 0.580092 | − | 1.00475i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.14901 | − | 5.45425i | −0.221564 | − | 0.383760i | ||||
\(203\) | −6.71271 | − | 8.04493i | −0.471140 | − | 0.564643i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.60662 | 0.251897 | ||||||||
\(206\) | 12.9693 | + | 22.4635i | 0.903615 | + | 1.56511i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.51348 | + | 6.21717i | 0.382291 | + | 0.431083i | ||||
\(209\) | −2.24946 | −0.155598 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.47109 | − | 7.74416i | 0.307803 | − | 0.533130i | −0.670079 | − | 0.742290i | \(-0.733740\pi\) |
0.977881 | + | 0.209160i | \(0.0670730\pi\) | |||||||
\(212\) | 0.787829 | − | 1.36456i | 0.0541083 | − | 0.0937184i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 38.1620 | 2.60870 | ||||||||
\(215\) | 3.13389 | − | 5.42805i | 0.213729 | − | 0.370190i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.06603 | + | 6.07145i | 0.343905 | + | 0.412157i | ||||
\(218\) | −11.0265 | + | 19.0984i | −0.746808 | + | 1.29351i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.06895 | − | 1.85148i | 0.0720686 | − | 0.124827i | ||||
\(221\) | 15.4402 | + | 17.4108i | 1.03862 | + | 1.17118i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.9098 | + | 18.8963i | −0.730574 | + | 1.26539i | 0.226064 | + | 0.974112i | \(0.427414\pi\) |
−0.956638 | + | 0.291279i | \(0.905919\pi\) | |||||||
\(224\) | 2.39667 | − | 6.52862i | 0.160134 | − | 0.436212i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.1554 | + | 21.0538i | 0.808565 | + | 1.40048i | ||||
\(227\) | 18.5525 | 1.23137 | 0.615687 | − | 0.787990i | \(-0.288878\pi\) | ||||
0.615687 | + | 0.787990i | \(0.288878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.67525 | − | 16.7580i | −0.639359 | − | 1.10740i | −0.985574 | − | 0.169247i | \(-0.945867\pi\) |
0.346215 | − | 0.938155i | \(-0.387467\pi\) | |||||||
\(230\) | −9.68784 | − | 16.7798i | −0.638797 | − | 1.10643i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.05137 | + | 13.9454i | −0.528599 | + | 0.915560i | ||||
\(233\) | 8.08170 | + | 13.9979i | 0.529450 | + | 0.917034i | 0.999410 | + | 0.0343462i | \(0.0109349\pi\) |
−0.469960 | + | 0.882688i | \(0.655732\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.13184 | − | 3.69245i | 0.139066 | − | 0.240869i | ||||
\(236\) | −22.2483 | −1.44824 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.0529 | + | 38.2807i | −0.910916 | + | 2.48137i | ||||
\(239\) | −16.1037 | −1.04166 | −0.520831 | − | 0.853660i | \(-0.674378\pi\) | ||||
−0.520831 | + | 0.853660i | \(0.674378\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.00600 | −0.258049 | −0.129025 | − | 0.991641i | \(-0.541185\pi\) | ||||
−0.129025 | + | 0.991641i | \(0.541185\pi\) | |||||||
\(242\) | 12.7217 | − | 22.0346i | 0.817779 | − | 1.41643i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.08548 | + | 7.07625i | −0.261546 | + | 0.453011i | ||||
\(245\) | 1.23140 | − | 6.76480i | 0.0786710 | − | 0.432187i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.5178 | − | 2.76672i | 0.860119 | − | 0.176042i | ||||
\(248\) | 6.07631 | − | 10.5245i | 0.385846 | − | 0.668305i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 21.1939 | 1.34042 | ||||||||
\(251\) | 1.62344 | + | 2.81188i | 0.102471 | + | 0.177484i | 0.912702 | − | 0.408626i | \(-0.133992\pi\) |
−0.810231 | + | 0.586110i | \(0.800659\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.42763 | + | 4.20477i | 0.152624 | + | 0.264352i | ||||
\(254\) | −5.07489 | + | 8.78996i | −0.318427 | + | 0.551531i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −27.7557 | −1.73473 | ||||||||
\(257\) | 26.8924 | 1.67750 | 0.838751 | − | 0.544516i | \(-0.183287\pi\) | ||||
0.838751 | + | 0.544516i | \(0.183287\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.60095 | + | 4.36106i | −0.0994784 | + | 0.270983i | ||||
\(260\) | −4.14650 | + | 12.4410i | −0.257155 | + | 0.771556i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.59050 | − | 4.48688i | −0.160042 | − | 0.277200i | ||||
\(263\) | −1.90353 | − | 3.29701i | −0.117377 | − | 0.203302i | 0.801351 | − | 0.598195i | \(-0.204115\pi\) |
−0.918727 | + | 0.394893i | \(0.870782\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.418000 | 0.0256775 | ||||||||
\(266\) | 15.4907 | + | 18.5650i | 0.949794 | + | 1.13829i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.9836 | − | 22.4883i | −0.793102 | − | 1.37369i | ||||
\(269\) | 23.8381 | 1.45343 | 0.726716 | − | 0.686938i | \(-0.241046\pi\) | ||||
0.726716 | + | 0.686938i | \(0.241046\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.90135 | 0.601464 | 0.300732 | − | 0.953709i | \(-0.402769\pi\) | ||||
0.300732 | + | 0.953709i | \(0.402769\pi\) | |||||||
\(272\) | 14.8750 | 0.901931 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.9715 | −1.20653 | ||||||||
\(275\) | −2.37186 | −0.143028 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.7858 | 0.708139 | 0.354069 | − | 0.935219i | \(-0.384798\pi\) | ||||
0.354069 | + | 0.935219i | \(0.384798\pi\) | |||||||
\(278\) | 0.688846 | + | 1.19312i | 0.0413142 | + | 0.0715584i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.4119 | + | 1.80625i | −0.622231 | + | 0.107944i | ||||
\(281\) | −12.9976 | −0.775372 | −0.387686 | − | 0.921791i | \(-0.626726\pi\) | ||||
−0.387686 | + | 0.921791i | \(0.626726\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.40249 | + | 14.5535i | 0.499476 | + | 0.865118i | 1.00000 | 0.000604910i | \(-0.000192549\pi\) | |
−0.500524 | + | 0.865723i | \(0.666859\pi\) | |||||||
\(284\) | 6.66959 | + | 11.5521i | 0.395767 | + | 0.685489i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.60029 | − | 4.80143i | 0.0946270 | − | 0.283914i | ||||
\(287\) | 6.22369 | + | 7.45886i | 0.367373 | + | 0.440283i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.6567 | 1.45039 | ||||||||
\(290\) | −9.28948 | −0.545497 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.13512 | + | 15.8225i | −0.534592 | + | 0.925941i | ||||
\(293\) | −7.04782 | − | 12.2072i | −0.411738 | − | 0.713151i | 0.583342 | − | 0.812227i | \(-0.301745\pi\) |
−0.995080 | + | 0.0990757i | \(0.968411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.95108 | − | 5.11141i | −0.171818 | − | 0.297598i | ||||
\(296\) | 7.13970 | 0.414987 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.35116 | − | 5.80438i | 0.194128 | − | 0.336239i | ||||
\(299\) | −19.7602 | − | 22.2822i | −1.14276 | − | 1.28861i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.6337 | − | 2.88561i | 0.958750 | − | 0.166324i | ||||
\(302\) | 27.4754 | − | 47.5888i | 1.58103 | − | 2.73843i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.40993 | − | 7.63822i | 0.252927 | − | 0.438082i | ||||
\(305\) | −2.16764 | −0.124119 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.8786 | 0.906240 | 0.453120 | − | 0.891450i | \(-0.350311\pi\) | ||||
0.453120 | + | 0.891450i | \(0.350311\pi\) | |||||||
\(308\) | 5.67365 | − | 0.984264i | 0.323286 | − | 0.0560836i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.01070 | 0.398181 | ||||||||
\(311\) | −14.3017 | + | 24.7713i | −0.810975 | + | 1.40465i | 0.101208 | + | 0.994865i | \(0.467729\pi\) |
−0.912183 | + | 0.409784i | \(0.865604\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.28962 | + | 16.0901i | 0.525080 | + | 0.909465i | 0.999573 | + | 0.0292063i | \(0.00929798\pi\) |
−0.474493 | + | 0.880259i | \(0.657369\pi\) | |||||||
\(314\) | −26.9561 | + | 46.6893i | −1.52122 | + | 2.63483i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.15679 | − | 8.93182i | −0.290092 | − | 0.502454i | ||||
\(317\) | 15.3223 | + | 26.5389i | 0.860584 | + | 1.49057i | 0.871366 | + | 0.490633i | \(0.163234\pi\) |
−0.0107826 | + | 0.999942i | \(0.503432\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.32781 | 0.130332 | ||||||||
\(320\) | −5.34685 | − | 9.26102i | −0.298898 | − | 0.517707i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 17.9848 | − | 48.9912i | 1.00225 | − | 2.73017i | ||||
\(323\) | 12.3498 | − | 21.3904i | 0.687160 | − | 1.19020i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.2534 | − | 2.91727i | 0.790635 | − | 0.161821i | ||||
\(326\) | −9.76366 | + | 16.9112i | −0.540759 | + | 0.936622i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.46483 | − | 12.9295i | 0.412177 | − | 0.713911i | ||||
\(329\) | 11.3151 | − | 1.96295i | 0.623823 | − | 0.108221i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.6138 | + | 23.5799i | −0.748284 | + | 1.29607i | 0.200360 | + | 0.979722i | \(0.435789\pi\) |
−0.948644 | + | 0.316344i | \(0.897545\pi\) | |||||||
\(332\) | 10.6201 | 0.582854 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.77933 | + | 4.81395i | −0.152078 | + | 0.263407i | ||||
\(335\) | 3.44438 | − | 5.96584i | 0.188187 | − | 0.325949i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.3160 | −0.670898 | −0.335449 | − | 0.942058i | \(-0.608888\pi\) | ||||
−0.335449 | + | 0.942058i | \(0.608888\pi\) | |||||||
\(338\) | −3.71121 | + | 30.8219i | −0.201863 | + | 1.67649i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.7373 | + | 20.3296i | 0.636545 | + | 1.10253i | ||||
\(341\) | −1.75678 | −0.0951348 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.1152 | − | 9.12688i | 0.870140 | − | 0.492805i | ||||
\(344\) | −12.9728 | − | 22.4695i | −0.699445 | − | 1.21148i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.71182 | + | 16.8214i | −0.522111 | + | 0.904322i | ||||
\(347\) | −6.14506 | −0.329884 | −0.164942 | − | 0.986303i | \(-0.552744\pi\) | ||||
−0.164942 | + | 0.986303i | \(0.552744\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.51563 | + | 11.2854i | −0.348774 | + | 0.604094i | −0.986032 | − | 0.166557i | \(-0.946735\pi\) |
0.637258 | + | 0.770650i | \(0.280068\pi\) | |||||||
\(350\) | 16.3336 | + | 19.5752i | 0.873065 | + | 1.04634i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.772550 | + | 1.33810i | 0.0411771 | + | 0.0713208i | ||||
\(353\) | 15.8332 | + | 27.4240i | 0.842718 | + | 1.45963i | 0.887589 | + | 0.460637i | \(0.152379\pi\) |
−0.0448710 | + | 0.998993i | \(0.514288\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.76935 | + | 3.06460i | −0.0939072 | + | 0.162652i | ||||
\(356\) | 7.75021 | 0.410761 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −25.0655 | − | 43.4147i | −1.32475 | − | 2.29454i | ||||
\(359\) | 9.96610 | + | 17.2618i | 0.525991 | + | 0.911043i | 0.999542 | + | 0.0302764i | \(0.00963874\pi\) |
−0.473551 | + | 0.880767i | \(0.657028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.17744 | + | 3.77144i | 0.114602 | + | 0.198497i | ||||
\(362\) | −3.84014 | −0.201833 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −32.8845 | + | 12.8931i | −1.72362 | + | 0.675783i | ||||
\(365\) | −4.84684 | −0.253695 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.85950 | − | 17.0772i | −0.514662 | − | 0.891420i | −0.999855 | − | 0.0170133i | \(-0.994584\pi\) |
0.485194 | − | 0.874407i | \(-0.338749\pi\) | |||||||
\(368\) | −19.0369 | −0.992366 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.05940 | + | 3.56699i | 0.107063 | + | 0.185439i | ||||
\(371\) | 0.721313 | + | 0.864466i | 0.0374487 | + | 0.0448808i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.77345 | + | 15.1961i | −0.454272 | + | 0.786823i | −0.998646 | − | 0.0520202i | \(-0.983434\pi\) |
0.544374 | + | 0.838843i | \(0.316767\pi\) | |||||||
\(374\) | −4.52986 | − | 7.84595i | −0.234234 | − | 0.405704i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.82478 | − | 15.2850i | −0.455103 | − | 0.788262i | ||||
\(377\) | −13.9887 | + | 2.86308i | −0.720452 | + | 0.147456i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.85068 | − | 10.1337i | 0.300529 | − | 0.520532i | −0.675727 | − | 0.737152i | \(-0.736170\pi\) |
0.976256 | + | 0.216620i | \(0.0695034\pi\) | |||||||
\(380\) | 13.9188 | 0.714021 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.8055 | + | 23.9119i | −0.706352 | + | 1.22344i | ||||
\(383\) | −10.7644 | + | 18.6445i | −0.550036 | + | 0.952690i | 0.448235 | + | 0.893916i | \(0.352053\pi\) |
−0.998271 | + | 0.0587748i | \(0.981281\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.978699 | + | 1.17293i | 0.0498791 | + | 0.0597783i | ||||
\(386\) | −28.1536 | − | 48.7634i | −1.43298 | − | 2.48199i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.2500 | − | 24.6817i | −0.723435 | − | 1.25303i | ||||
\(389\) | 13.2455 | − | 22.9419i | 0.671574 | − | 1.16320i | −0.305884 | − | 0.952069i | \(-0.598952\pi\) |
0.977458 | − | 0.211131i | \(-0.0677147\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −53.3118 | −2.69609 | ||||||||
\(392\) | −21.7026 | − | 18.4160i | −1.09615 | − | 0.930146i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.75633 | + | 3.04206i | −0.0884828 | + | 0.153257i | ||||
\(395\) | 1.36802 | − | 2.36949i | 0.0688327 | − | 0.119222i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.8995 | − | 29.2707i | 0.848160 | − | 1.46906i | −0.0346887 | − | 0.999398i | \(-0.511044\pi\) |
0.882849 | − | 0.469658i | \(-0.155623\pi\) | |||||||
\(398\) | 22.4332 | 1.12447 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.64989 | − | 8.05384i | 0.232494 | − | 0.402692i | ||||
\(401\) | −21.6119 | −1.07925 | −0.539623 | − | 0.841907i | \(-0.681433\pi\) | ||||
−0.539623 | + | 0.841907i | \(0.681433\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.5571 | − | 2.16075i | 0.525888 | − | 0.107635i | ||||
\(404\) | −4.88264 | − | 8.45697i | −0.242920 | − | 0.420750i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.0302 | − | 19.2116i | −0.795565 | − | 0.953455i | ||||
\(407\) | −0.516056 | − | 0.893835i | −0.0255799 | − | 0.0443058i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.74217 | 0.382826 | 0.191413 | − | 0.981510i | \(-0.438693\pi\) | ||||
0.191413 | + | 0.981510i | \(0.438693\pi\) | |||||||
\(410\) | 8.61275 | 0.425353 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 20.1093 | + | 34.8303i | 0.990714 | + | 1.71597i | ||||
\(413\) | 5.47846 | − | 14.9235i | 0.269577 | − | 0.734339i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.40868 | + | 2.43991i | 0.0691495 | + | 0.119770i | ||||
\(416\) | −6.28834 | − | 7.09092i | −0.308311 | − | 0.347661i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.37179 | −0.262743 | ||||||||
\(419\) | −4.05097 | + | 7.01649i | −0.197903 | + | 0.342778i | −0.947848 | − | 0.318722i | \(-0.896746\pi\) |
0.749945 | + | 0.661500i | \(0.230080\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.1124 | −1.56506 | −0.782530 | − | 0.622612i | \(-0.786071\pi\) | ||||
−0.782530 | + | 0.622612i | \(0.786071\pi\) | |||||||
\(422\) | 10.6771 | − | 18.4933i | 0.519755 | − | 0.900242i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.865159 | − | 1.49850i | 0.0420158 | − | 0.0727735i | ||||
\(425\) | 13.0218 | − | 22.5543i | 0.631648 | − | 1.09405i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.74054 | − | 4.48289i | −0.181017 | − | 0.216942i | ||||
\(428\) | 59.1713 | 2.86015 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.48384 | − | 12.9624i | 0.360903 | − | 0.625102i | ||||
\(431\) | −14.7640 | − | 25.5721i | −0.711159 | − | 1.23176i | −0.964422 | − | 0.264366i | \(-0.914837\pi\) |
0.253263 | − | 0.967397i | \(-0.418496\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.0455 | − | 19.1314i | −0.530813 | − | 0.919395i | −0.999353 | − | 0.0359531i | \(-0.988553\pi\) |
0.468540 | − | 0.883442i | \(-0.344780\pi\) | |||||||
\(434\) | 12.0979 | + | 14.4988i | 0.580716 | + | 0.695967i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.0969 | + | 29.6127i | −0.818792 | + | 1.41819i | ||||
\(437\) | −15.8051 | + | 27.3752i | −0.756060 | + | 1.30953i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.35580 | −0.303346 | −0.151673 | − | 0.988431i | \(-0.548466\pi\) | ||||
−0.151673 | + | 0.988431i | \(0.548466\pi\) | |||||||
\(440\) | 1.17387 | − | 2.03321i | 0.0559622 | − | 0.0969294i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 36.8718 | + | 41.5777i | 1.75381 | + | 1.97765i | ||||
\(443\) | −6.78135 | − | 11.7456i | −0.322192 | − | 0.558052i | 0.658748 | − | 0.752363i | \(-0.271086\pi\) |
−0.980940 | + | 0.194311i | \(0.937753\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.02801 | + | 1.78057i | 0.0487324 | + | 0.0844070i | ||||
\(446\) | −26.0530 | + | 45.1251i | −1.23365 | + | 2.13674i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.92604 | − | 27.0389i | 0.468961 | − | 1.27747i | ||||
\(449\) | 10.9559 | + | 18.9762i | 0.517041 | + | 0.895541i | 0.999804 | + | 0.0197900i | \(0.00629977\pi\) |
−0.482763 | + | 0.875751i | \(0.660367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.15823 | −0.101627 | ||||||||
\(452\) | 18.8473 | + | 32.6445i | 0.886502 | + | 1.53547i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 44.3041 | 2.07930 | ||||||||
\(455\) | −7.32402 | − | 5.84485i | −0.343355 | − | 0.274011i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.2146 | 0.711710 | 0.355855 | − | 0.934541i | \(-0.384190\pi\) | ||||
0.355855 | + | 0.934541i | \(0.384190\pi\) | |||||||
\(458\) | −23.1049 | − | 40.0188i | −1.07962 | − | 1.86996i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.0213 | − | 26.0176i | −0.700371 | − | 1.21308i | ||||
\(461\) | −8.10813 | − | 14.0437i | −0.377633 | − | 0.654080i | 0.613084 | − | 0.790018i | \(-0.289929\pi\) |
−0.990717 | + | 0.135937i | \(0.956595\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.44769 | −0.0672799 | −0.0336400 | − | 0.999434i | \(-0.510710\pi\) | ||||
−0.0336400 | + | 0.999434i | \(0.510710\pi\) | |||||||
\(464\) | −4.56353 | + | 7.90426i | −0.211856 | + | 0.366946i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.2994 | + | 33.4275i | 0.894027 | + | 1.54850i | ||||
\(467\) | 7.00337 | + | 12.1302i | 0.324078 | + | 0.561319i | 0.981325 | − | 0.192356i | \(-0.0616128\pi\) |
−0.657248 | + | 0.753675i | \(0.728279\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.2817 | − | 3.17150i | 0.844169 | − | 0.146446i | ||||
\(470\) | 5.09091 | − | 8.81772i | 0.234826 | − | 0.406731i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −24.4320 | −1.12458 | ||||||||
\(473\) | −1.87534 | + | 3.24818i | −0.0862282 | + | 0.149352i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.72100 | − | 13.3732i | −0.354264 | − | 0.613603i | ||||
\(476\) | −21.7895 | + | 59.3553i | −0.998719 | + | 2.72055i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −38.4562 | −1.75895 | ||||||||
\(479\) | −15.0122 | − | 26.0018i | −0.685923 | − | 1.18805i | −0.973146 | − | 0.230189i | \(-0.926065\pi\) |
0.287223 | − | 0.957864i | \(-0.407268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.20055 | + | 4.73667i | 0.191528 | + | 0.215973i | ||||
\(482\) | −9.56649 | −0.435742 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.7253 | − | 34.1652i | 0.896605 | − | 1.55296i | ||||
\(485\) | 3.78033 | − | 6.54772i | 0.171656 | − | 0.297317i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.4903 | −1.29102 | −0.645510 | − | 0.763752i | \(-0.723355\pi\) | ||||
−0.645510 | + | 0.763752i | \(0.723355\pi\) | |||||||
\(488\) | −4.48649 | + | 7.77082i | −0.203094 | + | 0.351769i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.94062 | − | 16.1546i | 0.132844 | − | 0.729790i | ||||
\(491\) | −14.2339 | + | 24.6538i | −0.642365 | + | 1.11261i | 0.342539 | + | 0.939504i | \(0.388713\pi\) |
−0.984903 | + | 0.173105i | \(0.944620\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.7799 | + | 22.1354i | −0.575578 | + | 0.996930i | ||||
\(494\) | 32.2811 | − | 6.60703i | 1.45239 | − | 0.297264i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.44406 | − | 5.96528i | 0.154643 | − | 0.267849i | ||||
\(497\) | −9.39114 | + | 1.62917i | −0.421250 | + | 0.0730783i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.1164 | + | 22.7183i | 0.587172 | + | 1.01701i | 0.994601 | + | 0.103775i | \(0.0330921\pi\) |
−0.407429 | + | 0.913237i | \(0.633575\pi\) | |||||||
\(500\) | 32.8617 | 1.46962 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.87684 | + | 6.71488i | 0.173032 | + | 0.299700i | ||||
\(503\) | 4.26588 | + | 7.38872i | 0.190206 | + | 0.329447i | 0.945318 | − | 0.326149i | \(-0.105751\pi\) |
−0.755112 | + | 0.655595i | \(0.772418\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.29529 | − | 2.24352i | 0.0576398 | − | 0.0998351i | ||||
\(506\) | 5.79726 | + | 10.0412i | 0.257720 | + | 0.446384i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.86876 | + | 13.6291i | −0.349120 | + | 0.604693i | ||||
\(509\) | 13.0260 | 0.577366 | 0.288683 | − | 0.957425i | \(-0.406783\pi\) | ||||
0.288683 | + | 0.957425i | \(0.406783\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.36384 | − | 10.0237i | −0.369995 | − | 0.443425i | ||||
\(512\) | −24.8008 | −1.09605 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 64.2200 | 2.83262 | ||||||||
\(515\) | −5.33472 | + | 9.24000i | −0.235076 | + | 0.407163i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.27571 | + | 2.20959i | −0.0561055 | + | 0.0971775i | ||||
\(518\) | −3.82313 | + | 10.4144i | −0.167979 | + | 0.457581i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.55350 | + | 13.6621i | −0.199684 | + | 0.599124i | ||||
\(521\) | 2.23285 | − | 3.86741i | 0.0978230 | − | 0.169434i | −0.812960 | − | 0.582319i | \(-0.802145\pi\) |
0.910783 | + | 0.412885i | \(0.135479\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.90811 | −0.127163 | −0.0635815 | − | 0.997977i | \(-0.520252\pi\) | ||||
−0.0635815 | + | 0.997977i | \(0.520252\pi\) | |||||||
\(524\) | −4.01665 | − | 6.95704i | −0.175468 | − | 0.303920i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.54570 | − | 7.87339i | −0.198202 | − | 0.343296i | ||||
\(527\) | 9.64490 | − | 16.7055i | 0.420138 | − | 0.727701i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 45.2278 | 1.96643 | ||||||||
\(530\) | 0.998200 | 0.0433590 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 24.0187 | + | 28.7855i | 1.04134 | + | 1.24801i | ||||
\(533\) | 12.9696 | − | 2.65451i | 0.561775 | − | 0.114980i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.84866 | + | 13.5943i | 0.339327 | + | 0.587732i | ||||
\(536\) | −14.2581 | − | 24.6957i | −0.615854 | − | 1.06669i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 56.9262 | 2.45426 | ||||||||
\(539\) | −0.736875 | + | 4.04810i | −0.0317394 | + | 0.174364i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.23193 | + | 15.9902i | 0.396912 | + | 0.687471i | 0.993343 | − | 0.115193i | \(-0.0367486\pi\) |
−0.596431 | + | 0.802664i | \(0.703415\pi\) | |||||||
\(542\) | 23.6448 | 1.01563 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16.9655 | −0.727392 | ||||||||
\(545\) | −9.07112 | −0.388564 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.9817 | 1.49571 | 0.747856 | − | 0.663861i | \(-0.231083\pi\) | ||||
0.747856 | + | 0.663861i | \(0.231083\pi\) | |||||||
\(548\) | −30.9665 | −1.32282 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.66408 | −0.241517 | ||||||||
\(551\) | 7.57760 | + | 13.1248i | 0.322817 | + | 0.559135i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.26104 | − | 1.25964i | 0.308771 | − | 0.0535655i | ||||
\(554\) | 28.1449 | 1.19576 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.06808 | + | 1.84996i | 0.0452965 | + | 0.0784559i | ||||
\(557\) | 0.0265706 | + | 0.0460217i | 0.00112583 | + | 0.00195000i | 0.866588 | − | 0.499025i | \(-0.166308\pi\) |
−0.865462 | + | 0.500975i | \(0.832975\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.27451 | − | 21.8261i | 0.307679 | − | 0.923146i | ||||
\(560\) | −5.90148 | + | 1.02379i | −0.249383 | + | 0.0432629i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31.0388 | −1.30929 | ||||||||
\(563\) | −7.98506 | −0.336530 | −0.168265 | − | 0.985742i | \(-0.553816\pi\) | ||||
−0.168265 | + | 0.985742i | \(0.553816\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.99992 | + | 8.66012i | −0.210348 | + | 0.364334i | ||||
\(566\) | 20.0655 | + | 34.7544i | 0.843414 | + | 1.46084i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.32424 | + | 12.6860i | 0.307318 | + | 0.532291i | ||||
\(569\) | 26.7241 | 1.12033 | 0.560167 | − | 0.828380i | \(-0.310737\pi\) | ||||
0.560167 | + | 0.828380i | \(0.310737\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.74647 | + | 11.6852i | −0.282331 | + | 0.489012i | −0.971958 | − | 0.235153i | \(-0.924441\pi\) |
0.689627 | + | 0.724164i | \(0.257774\pi\) | |||||||
\(572\) | 2.48129 | − | 7.44476i | 0.103748 | − | 0.311281i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.8624 | + | 17.8120i | 0.620345 | + | 0.743460i | ||||
\(575\) | −16.6651 | + | 28.8648i | −0.694982 | + | 1.20374i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.00662 | + | 10.4038i | −0.250059 | + | 0.433115i | −0.963542 | − | 0.267558i | \(-0.913783\pi\) |
0.713483 | + | 0.700673i | \(0.247117\pi\) | |||||||
\(578\) | 58.8811 | 2.44913 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −14.4036 | −0.598078 | ||||||||
\(581\) | −2.61512 | + | 7.12367i | −0.108493 | + | 0.295540i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.250134 | −0.0103595 | ||||||||
\(584\) | −10.0318 | + | 17.3756i | −0.415118 | + | 0.719005i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.8305 | − | 29.1512i | −0.695260 | − | 1.20422i | ||||
\(587\) | 5.21177 | − | 9.02705i | 0.215113 | − | 0.372586i | −0.738195 | − | 0.674588i | \(-0.764321\pi\) |
0.953307 | + | 0.302002i | \(0.0976548\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.71876 | − | 9.90518i | −0.235637 | − | 0.408136i | ||||
\(590\) | −7.04728 | − | 12.2062i | −0.290132 | − | 0.502523i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.04679 | 0.166322 | ||||||||
\(593\) | −11.1751 | − | 19.3558i | −0.458905 | − | 0.794847i | 0.539998 | − | 0.841666i | \(-0.318425\pi\) |
−0.998903 | + | 0.0468194i | \(0.985091\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.5268 | + | 2.86706i | −0.677532 | + | 0.117538i | ||||
\(596\) | 5.19607 | − | 8.99986i | 0.212839 | − | 0.368649i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −47.1880 | − | 53.2107i | −1.92966 | − | 2.17595i | ||||
\(599\) | 0.579463 | − | 1.00366i | 0.0236762 | − | 0.0410084i | −0.853945 | − | 0.520364i | \(-0.825796\pi\) |
0.877621 | + | 0.479356i | \(0.159130\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.0907 | + | 36.5301i | −0.860306 | + | 1.49009i | 0.0113271 | + | 0.999936i | \(0.496394\pi\) |
−0.871633 | + | 0.490158i | \(0.836939\pi\) | |||||||
\(602\) | 39.7219 | − | 6.89094i | 1.61894 | − | 0.280854i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 42.6014 | − | 73.7879i | 1.73343 | − | 3.00239i | ||||
\(605\) | 10.4657 | 0.425491 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.07844 | − | 15.7243i | 0.368482 | − | 0.638230i | −0.620846 | − | 0.783932i | \(-0.713211\pi\) |
0.989328 | + | 0.145702i | \(0.0465441\pi\) | |||||||
\(608\) | −5.02970 | + | 8.71169i | −0.203981 | + | 0.353306i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.17640 | −0.209586 | ||||||||
\(611\) | 4.94851 | − | 14.8473i | 0.200195 | − | 0.600657i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.451323 | + | 0.781714i | 0.0182288 | + | 0.0315731i | 0.874996 | − | 0.484130i | \(-0.160864\pi\) |
−0.856767 | + | 0.515703i | \(0.827531\pi\) | |||||||
\(614\) | 37.9187 | 1.53027 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.23055 | − | 1.08087i | 0.251036 | − | 0.0435497i | ||||
\(617\) | −13.0218 | − | 22.5544i | −0.524238 | − | 0.908008i | −0.999602 | − | 0.0282180i | \(-0.991017\pi\) |
0.475363 | − | 0.879790i | \(-0.342317\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.4171 | + | 23.2390i | −0.539277 | + | 0.934056i | 0.459666 | + | 0.888092i | \(0.347969\pi\) |
−0.998943 | + | 0.0459638i | \(0.985364\pi\) | |||||||
\(620\) | 10.8703 | 0.436562 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −34.1530 | + | 59.1547i | −1.36941 | + | 2.37189i | ||||
\(623\) | −1.90843 | + | 5.19863i | −0.0764596 | + | 0.208279i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.72894 | − | 9.92281i | −0.229158 | − | 0.396912i | ||||
\(626\) | 22.1839 | + | 38.4237i | 0.886649 | + | 1.53572i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −41.7962 | + | 72.3932i | −1.66785 | + | 2.88880i | ||||
\(629\) | 11.3328 | 0.451869 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.8061 | + | 29.1089i | 0.669039 | + | 1.15881i | 0.978173 | + | 0.207791i | \(0.0666273\pi\) |
−0.309135 | + | 0.951018i | \(0.600039\pi\) | |||||||
\(632\) | −5.66296 | − | 9.80853i | −0.225260 | − | 0.390162i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 36.5901 | + | 63.3760i | 1.45318 | + | 2.51698i | ||||
\(635\) | −4.17494 | −0.165678 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.550800 | − | 25.2328i | −0.0218235 | − | 0.999762i | ||||
\(638\) | 5.55889 | 0.220078 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.1865 | − | 17.6435i | −0.402655 | − | 0.697419i | ||||
\(641\) | −21.1841 | −0.836722 | −0.418361 | − | 0.908281i | \(-0.637395\pi\) | ||||
−0.418361 | + | 0.908281i | \(0.637395\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.330770 | − | 0.572910i | −0.0130443 | − | 0.0225933i | 0.859430 | − | 0.511254i | \(-0.170819\pi\) |
−0.872474 | + | 0.488661i | \(0.837486\pi\) | |||||||
\(644\) | 27.8859 | − | 75.9623i | 1.09886 | − | 2.99333i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 29.4917 | − | 51.0811i | 1.16034 | − | 2.00976i | ||||
\(647\) | −20.0162 | − | 34.6690i | −0.786916 | − | 1.36298i | −0.927848 | − | 0.372960i | \(-0.878343\pi\) |
0.140931 | − | 0.990019i | \(-0.454990\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.76594 | + | 3.05870i | 0.0693193 | + | 0.120065i | ||||
\(650\) | 34.0376 | − | 6.96654i | 1.33506 | − | 0.273250i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.1388 | + | 26.2212i | −0.592883 | + | 1.02690i | ||||
\(653\) | −12.7120 | −0.497460 | −0.248730 | − | 0.968573i | \(-0.580013\pi\) | ||||
−0.248730 | + | 0.968573i | \(0.580013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.06556 | − | 1.84560i | 0.0416349 | − | 0.0721138i | ||||
\(656\) | 4.23107 | − | 7.32844i | 0.165196 | − | 0.286127i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 27.0209 | − | 4.68759i | 1.05339 | − | 0.182741i | ||||
\(659\) | −7.09522 | − | 12.2893i | −0.276391 | − | 0.478723i | 0.694094 | − | 0.719884i | \(-0.255805\pi\) |
−0.970485 | + | 0.241161i | \(0.922472\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.0890 | − | 43.4554i | −0.975848 | − | 1.69022i | −0.677106 | − | 0.735885i | \(-0.736766\pi\) |
−0.298742 | − | 0.954334i | \(-0.596567\pi\) | |||||||
\(662\) | −32.5104 | + | 56.3096i | −1.26355 | + | 2.18853i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.6625 | 0.452594 | ||||||||
\(665\) | −3.42740 | + | 9.33637i | −0.132909 | + | 0.362049i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.3556 | − | 28.3287i | 0.633290 | − | 1.09689i | ||||
\(668\) | −4.30944 | + | 7.46417i | −0.166737 | + | 0.288797i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.22530 | − | 14.2466i | 0.317771 | − | 0.550396i | ||||
\(671\) | 1.29713 | 0.0500751 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.937137 | − | 1.62317i | 0.0361240 | − | 0.0625685i | −0.847398 | − | 0.530958i | \(-0.821832\pi\) |
0.883522 | + | 0.468389i | \(0.155166\pi\) | |||||||
\(674\) | −29.4112 | −1.13288 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.75433 | + | 47.7902i | −0.221321 | + | 1.83808i | ||||
\(677\) | −1.00439 | − | 1.73966i | −0.0386020 | − | 0.0668607i | 0.846079 | − | 0.533058i | \(-0.178957\pi\) |
−0.884681 | + | 0.466197i | \(0.845624\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.0648 | − | 3.48083i | 0.770015 | − | 0.133582i | ||||
\(680\) | 12.8894 | + | 22.3251i | 0.494286 | + | 0.856128i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.19525 | −0.160644 | ||||||||
\(683\) | 14.1012 | 0.539568 | 0.269784 | − | 0.962921i | \(-0.413048\pi\) | ||||
0.269784 | + | 0.962921i | \(0.413048\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.10748 | − | 7.11437i | −0.156939 | − | 0.271826i | ||||
\(686\) | 38.4837 | − | 21.7953i | 1.46932 | − | 0.832149i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.35298 | − | 12.7357i | −0.280330 | − | 0.485546i | ||||
\(689\) | 1.50315 | − | 0.307652i | 0.0572654 | − | 0.0117206i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.6920 | −1.35779 | −0.678895 | − | 0.734236i | \(-0.737541\pi\) | ||||
−0.678895 | + | 0.734236i | \(0.737541\pi\) | |||||||
\(692\) | −15.0585 | + | 26.0820i | −0.572437 | + | 0.991489i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.6746 | −0.557041 | ||||||||
\(695\) | −0.283346 | + | 0.490769i | −0.0107479 | + | 0.0186159i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.8489 | − | 20.5229i | 0.448809 | − | 0.777360i | ||||
\(698\) | −15.5596 | + | 26.9500i | −0.588938 | + | 1.02007i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 25.3257 | + | 30.3518i | 0.957220 | + | 1.14719i | ||||
\(701\) | 6.15865 | 0.232609 | 0.116305 | − | 0.993214i | \(-0.462895\pi\) | ||||
0.116305 | + | 0.993214i | \(0.462895\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.35979 | − | 5.81932i | 0.126717 | − | 0.219480i | ||||
\(704\) | 3.19959 | + | 5.54185i | 0.120589 | + | 0.208866i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 37.8103 | + | 65.4894i | 1.42301 | + | 2.46473i | ||||
\(707\) | 6.87501 | − | 1.19268i | 0.258561 | − | 0.0448552i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0185 | + | 29.4770i | −0.639144 | + | 1.10703i | 0.346477 | + | 0.938059i | \(0.387378\pi\) |
−0.985621 | + | 0.168972i | \(0.945955\pi\) | |||||||
\(710\) | −4.22527 | + | 7.31838i | −0.158571 | + | 0.274654i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.51094 | 0.318961 | ||||||||
\(713\) | −12.3434 | + | 21.3794i | −0.462265 | + | 0.800667i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.03952 | − | 0.417432i | 0.0762736 | − | 0.0156111i | ||||
\(716\) | −38.8648 | − | 67.3158i | −1.45244 | − | 2.51571i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 23.7994 | + | 41.2218i | 0.888187 | + | 1.53838i | ||||
\(719\) | −11.4824 | + | 19.8881i | −0.428222 | + | 0.741702i | −0.996715 | − | 0.0809859i | \(-0.974193\pi\) |
0.568493 | + | 0.822688i | \(0.307526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.3150 | + | 4.91208i | −1.05451 | + | 0.182935i | ||||
\(722\) | 5.19981 | + | 9.00633i | 0.193517 | + | 0.335181i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.95424 | −0.221288 | ||||||||
\(725\) | 7.98992 | + | 13.8389i | 0.296738 | + | 0.513966i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.06558 | 0.0395203 | 0.0197601 | − | 0.999805i | \(-0.493710\pi\) | ||||
0.0197601 | + | 0.999805i | \(0.493710\pi\) | |||||||
\(728\) | −36.1123 | + | 14.1586i | −1.33841 | + | 0.524754i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.5744 | −0.428389 | ||||||||
\(731\) | −20.5916 | − | 35.6658i | −0.761609 | − | 1.31915i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.1689 | + | 22.8092i | 0.486404 | + | 0.842476i | 0.999878 | − | 0.0156289i | \(-0.00497504\pi\) |
−0.513474 | + | 0.858105i | \(0.671642\pi\) | |||||||
\(734\) | −23.5448 | − | 40.7809i | −0.869056 | − | 1.50525i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.7123 | 0.800326 | ||||||||
\(737\) | −2.06114 | + | 3.57000i | −0.0759230 | + | 0.131502i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.1075 | − | 29.6310i | −0.629308 | − | 1.08999i | −0.987691 | − | 0.156419i | \(-0.950005\pi\) |
0.358383 | − | 0.933575i | \(-0.383328\pi\) | |||||||
\(740\) | 3.19317 | + | 5.53073i | 0.117383 | + | 0.203314i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.72252 | + | 2.06438i | 0.0632358 | + | 0.0757857i | ||||
\(743\) | 11.2391 | − | 19.4667i | 0.412322 | − | 0.714163i | −0.582821 | − | 0.812600i | \(-0.698051\pi\) |
0.995143 | + | 0.0984379i | \(0.0313846\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.75689 | 0.101005 | ||||||||
\(746\) | −20.9513 | + | 36.2888i | −0.767083 | + | 1.32863i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.02368 | − | 12.1654i | −0.256811 | − | 0.444810i | ||||
\(749\) | −14.5705 | + | 39.6905i | −0.532393 | + | 1.45026i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.5424 | −1.55239 | −0.776197 | − | 0.630491i | \(-0.782854\pi\) | ||||
−0.776197 | + | 0.630491i | \(0.782854\pi\) | |||||||
\(752\) | −5.00189 | − | 8.66353i | −0.182400 | − | 0.315927i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −33.4054 | + | 6.83715i | −1.21655 | + | 0.248994i | ||||
\(755\) | 22.6031 | 0.822612 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.61902 | − | 9.73243i | 0.204227 | − | 0.353731i | −0.745659 | − | 0.666327i | \(-0.767865\pi\) |
0.949886 | + | 0.312596i | \(0.101199\pi\) | |||||||
\(758\) | 13.9716 | − | 24.1996i | 0.507473 | − | 0.878969i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 15.2850 | 0.554447 | ||||||||
\(761\) | 6.40422 | − | 11.0924i | 0.232153 | − | 0.402101i | −0.726289 | − | 0.687390i | \(-0.758756\pi\) |
0.958441 | + | 0.285289i | \(0.0920897\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.6534 | − | 18.7600i | −0.566691 | − | 0.679158i | ||||
\(764\) | −21.4059 | + | 37.0760i | −0.774437 | + | 1.34136i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.7058 | + | 44.5238i | −0.928789 | + | 1.60871i | ||||
\(767\) | −14.3743 | − | 16.2089i | −0.519024 | − | 0.585268i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.6759 | − | 44.4719i | 0.925895 | − | 1.60370i | 0.135780 | − | 0.990739i | \(-0.456646\pi\) |
0.790115 | − | 0.612958i | \(-0.210021\pi\) | |||||||
\(770\) | 2.33717 | + | 2.80101i | 0.0842258 | + | 0.100941i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −43.6529 | − | 75.6091i | −1.57110 | − | 2.72123i | ||||
\(773\) | −20.0046 | −0.719517 | −0.359759 | − | 0.933045i | \(-0.617141\pi\) | ||||
−0.359759 | + | 0.933045i | \(0.617141\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.02993 | − | 10.4441i | −0.216602 | − | 0.375165i | ||||
\(776\) | −15.6487 | − | 27.1044i | −0.561756 | − | 0.972990i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.6308 | − | 54.7861i | 1.13402 | − | 1.96418i | ||||
\(779\) | −7.02558 | − | 12.1687i | −0.251717 | − | 0.435987i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.05879 | − | 1.83388i | 0.0378864 | − | 0.0656212i | ||||
\(782\) | −127.310 | −4.55261 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.3011 | − | 10.4382i | −0.439323 | − | 0.372792i | ||||
\(785\) | −22.1759 | −0.791492 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.3192 | 1.04512 | 0.522558 | − | 0.852604i | \(-0.324978\pi\) | ||||
0.522558 | + | 0.852604i | \(0.324978\pi\) | |||||||
\(788\) | −2.72325 | + | 4.71680i | −0.0970117 | + | 0.168029i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.26689 | − | 5.65842i | 0.116231 | − | 0.201318i | ||||
\(791\) | −26.5380 | + | 4.60381i | −0.943583 | + | 0.163693i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.79493 | + | 1.59540i | −0.276806 | + | 0.0566544i | ||||
\(794\) | 40.3566 | − | 69.8996i | 1.43220 | − | 2.48064i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 34.7833 | 1.23286 | ||||||||
\(797\) | 1.55050 | + | 2.68554i | 0.0549215 | + | 0.0951269i | 0.892179 | − | 0.451682i | \(-0.149176\pi\) |
−0.837258 | + | 0.546809i | \(0.815842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.0075 | − | 24.2618i | −0.495551 | − | 0.858319i | ||||
\(800\) | −5.30338 | + | 9.18572i | −0.187503 | + | 0.324764i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −51.6100 | −1.82241 | ||||||||
\(803\) | 2.90038 | 0.102352 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.1508 | − | 3.66923i | 0.745467 | − | 0.129323i | ||||
\(806\) | 25.2108 | − | 5.15995i | 0.888013 | − | 0.181751i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.36189 | − | 9.28707i | −0.188631 | − | 0.326718i | ||||
\(809\) | 3.99501 | + | 6.91957i | 0.140457 | + | 0.243279i | 0.927669 | − | 0.373404i | \(-0.121809\pi\) |
−0.787212 | + | 0.616683i | \(0.788476\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.2554 | −1.69448 | −0.847239 | − | 0.531213i | \(-0.821737\pi\) | ||||
−0.847239 | + | 0.531213i | \(0.821737\pi\) | |||||||
\(812\) | −24.8553 | − | 29.7881i | −0.872250 | − | 1.04536i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.23236 | − | 2.13451i | −0.0431942 | − | 0.0748146i | ||||
\(815\) | −8.03224 | −0.281357 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.4188 | −0.854307 | ||||||||
\(818\) | 18.4886 | 0.646439 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.3543 | 0.466353 | ||||||||
\(821\) | 27.5519 | 0.961569 | 0.480785 | − | 0.876839i | \(-0.340352\pi\) | ||||
0.480785 | + | 0.876839i | \(0.340352\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.4274 | 0.712056 | 0.356028 | − | 0.934475i | \(-0.384131\pi\) | ||||
0.356028 | + | 0.934475i | \(0.384131\pi\) | |||||||
\(824\) | 22.0831 | + | 38.2491i | 0.769303 | + | 1.33247i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.0828 | − | 35.6379i | 0.455207 | − | 1.24000i | ||||
\(827\) | 27.7142 | 0.963719 | 0.481859 | − | 0.876249i | \(-0.339962\pi\) | ||||
0.481859 | + | 0.876249i | \(0.339962\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.62832 | − | 8.01648i | −0.160748 | − | 0.278424i | 0.774389 | − | 0.632710i | \(-0.218057\pi\) |
−0.935137 | + | 0.354286i | \(0.884724\pi\) | |||||||
\(830\) | 3.36398 | + | 5.82659i | 0.116766 | + | 0.202244i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −26.0437 | − | 29.3677i | −0.902904 | − | 1.01814i | ||||
\(833\) | −34.4484 | − | 29.2315i | −1.19357 | − | 1.01281i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.28647 | −0.0791264 | ||||||||
\(836\) | −8.32912 | −0.288069 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.67387 | + | 16.7556i | −0.334178 | + | 0.578814i | ||||
\(839\) | −15.1870 | − | 26.3046i | −0.524312 | − | 0.908135i | −0.999599 | − | 0.0283045i | \(-0.990989\pi\) |
0.475287 | − | 0.879831i | \(-0.342344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.65848 | + | 11.5328i | 0.229603 | + | 0.397683i | ||||
\(842\) | −76.6855 | −2.64276 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.5552 | − | 28.6745i | 0.569854 | − | 0.987016i | ||||
\(845\) | −11.7428 | + | 5.01701i | −0.403965 | + | 0.172590i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.0599 | + | 21.6441i | 0.620545 | + | 0.743700i | ||||
\(848\) | 0.490373 | − | 0.849350i | 0.0168395 | − | 0.0291668i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 31.0964 | − | 53.8606i | 1.06660 | − | 1.84740i | ||||
\(851\) | −14.5036 | −0.497177 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.30773 | −0.181733 | −0.0908666 | − | 0.995863i | \(-0.528964\pi\) | ||||
−0.0908666 | + | 0.995863i | \(0.528964\pi\) | |||||||
\(854\) | −8.93254 | − | 10.7053i | −0.305665 | − | 0.366328i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 64.9793 | 2.22095 | ||||||||
\(857\) | −8.31857 | + | 14.4082i | −0.284157 | + | 0.492175i | −0.972404 | − | 0.233302i | \(-0.925047\pi\) |
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.29426 | + | 9.16993i | 0.180638 | + | 0.312874i | 0.942098 | − | 0.335338i | \(-0.108850\pi\) |
−0.761460 | + | 0.648212i | \(0.775517\pi\) | |||||||
\(860\) | 11.6039 | − | 20.0986i | 0.395690 | − | 0.685356i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −35.2571 | − | 61.0671i | −1.20086 | − | 2.07995i | ||||
\(863\) | −28.0316 | − | 48.5522i | −0.954207 | − | 1.65273i | −0.736173 | − | 0.676793i | \(-0.763369\pi\) |
−0.218033 | − | 0.975941i | \(-0.569964\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.98959 | −0.271654 | ||||||||
\(866\) | −26.3771 | − | 45.6864i | −0.896329 | − | 1.55249i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.7581 | + | 22.4809i | 0.636691 | + | 0.763051i | ||||
\(869\) | −0.818634 | + | 1.41792i | −0.0277703 | + | 0.0480995i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.99523 | − | 23.9885i | 0.270908 | − | 0.812820i | ||||
\(872\) | −18.7750 | + | 32.5193i | −0.635803 | + | 1.10124i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −37.7432 | + | 65.3731i | −1.27668 | + | 2.21128i | ||||
\(875\) | −8.09194 | + | 22.0427i | −0.273558 | + | 0.745181i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.83026 | − | 3.17010i | 0.0618033 | − | 0.107047i | −0.833468 | − | 0.552567i | \(-0.813648\pi\) |
0.895272 | + | 0.445521i | \(0.146982\pi\) | |||||||
\(878\) | −15.1779 | −0.512229 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.665353 | − | 1.15242i | 0.0224290 | − | 0.0388482i | ||||
\(881\) | 5.11493 | − | 8.85932i | 0.172326 | − | 0.298478i | −0.766906 | − | 0.641759i | \(-0.778205\pi\) |
0.939233 | + | 0.343281i | \(0.111538\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.98979 | −0.134267 | −0.0671335 | − | 0.997744i | \(-0.521385\pi\) | ||||
−0.0671335 | + | 0.997744i | \(0.521385\pi\) | |||||||
\(884\) | 57.1707 | + | 64.4675i | 1.92286 | + | 2.16828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.1941 | − | 28.0490i | −0.544052 | − | 0.942325i | ||||
\(887\) | 14.2208 | 0.477487 | 0.238743 | − | 0.971083i | \(-0.423265\pi\) | ||||
0.238743 | + | 0.971083i | \(0.423265\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.20440 | − | 8.63420i | −0.241628 | − | 0.289582i | ||||
\(890\) | 2.45493 | + | 4.25206i | 0.0822894 | + | 0.142529i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −40.3960 | + | 69.9678i | −1.35256 | + | 2.34270i | ||||
\(893\) | −16.6110 | −0.555866 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.3103 | − | 17.8579i | 0.344635 | − | 0.596924i | ||||
\(896\) | 18.9104 | − | 51.5127i | 0.631753 | − | 1.72092i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.1631 | + | 45.3158i | 0.873074 | + | 1.51221i | ||||
\(899\) | 5.91794 | + | 10.2502i | 0.197374 | + | 0.341862i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.37326 | − | 2.37856i | 0.0457500 | − | 0.0792413i | ||||
\(902\) | −5.15392 | −0.171607 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.6973 | + | 35.8487i | 0.688381 | + | 1.19231i | ||||
\(905\) | −0.789789 | − | 1.36795i | −0.0262535 | − | 0.0454723i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.7126 | − | 37.6074i | −0.720956 | − | 1.24873i | −0.960617 | − | 0.277876i | \(-0.910370\pi\) |
0.239661 | − | 0.970857i | \(-0.422964\pi\) | |||||||
\(908\) | 68.6949 | 2.27972 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −17.4900 | − | 13.9577i | −0.579789 | − | 0.462694i | ||||
\(911\) | −24.8617 | −0.823706 | −0.411853 | − | 0.911250i | \(-0.635118\pi\) | ||||
−0.411853 | + | 0.911250i | \(0.635118\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.842964 | − | 1.46006i | −0.0278980 | − | 0.0483208i | ||||
\(914\) | 36.3331 | 1.20179 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −35.8248 | − | 62.0503i | −1.18368 | − | 2.05020i | ||||
\(917\) | 5.65566 | − | 0.981142i | 0.186766 | − | 0.0324002i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.831637 | − | 1.44044i | 0.0274332 | − | 0.0475157i | −0.851983 | − | 0.523570i | \(-0.824600\pi\) |
0.879416 | + | 0.476054i | \(0.157933\pi\) | |||||||
\(920\) | −16.4957 | − | 28.5714i | −0.543847 | − | 0.941971i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.3625 | − | 33.5369i | −0.637671 | − | 1.10448i | ||||
\(923\) | −4.10708 | + | 12.3227i | −0.135186 | + | 0.405607i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.54260 | − | 6.13597i | 0.116480 | − | 0.201749i | ||||
\(926\) | −3.45714 | −0.113609 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.20488 | − | 9.01512i | 0.170859 | − | 0.295936i | ||||
\(929\) | 4.74761 | − | 8.22310i | 0.155764 | − | 0.269791i | −0.777573 | − | 0.628793i | \(-0.783549\pi\) |
0.933337 | + | 0.359002i | \(0.116883\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.2230 | + | 9.02289i | −0.826649 | + | 0.295713i | ||||
\(932\) | 29.9243 | + | 51.8304i | 0.980202 | + | 1.69776i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.7243 | + | 28.9674i | 0.547236 | + | 0.947841i | ||||
\(935\) | 1.86328 | − | 3.22730i | 0.0609359 | − | 0.105544i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.41678 | −0.209627 | −0.104813 | − | 0.994492i | \(-0.533425\pi\) | ||||
−0.104813 | + | 0.994492i | \(0.533425\pi\) | |||||||
\(938\) | 43.6573 | − | 7.57366i | 1.42546 | − | 0.247289i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.89361 | − | 13.6721i | 0.257461 | − | 0.445936i | ||||
\(941\) | −25.7593 | + | 44.6164i | −0.839730 | + | 1.45445i | 0.0503911 | + | 0.998730i | \(0.483953\pi\) |
−0.890121 | + | 0.455725i | \(0.849380\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.1641 | + | 26.2650i | −0.493810 | + | 0.855305i | ||||
\(944\) | −13.8481 | −0.450717 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.47838 | + | 7.75678i | −0.145605 | + | 0.252195i | ||||
\(947\) | 8.40219 | 0.273034 | 0.136517 | − | 0.990638i | \(-0.456409\pi\) | ||||
0.136517 | + | 0.990638i | \(0.456409\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.4295 | + | 3.56732i | −0.565784 | + | 0.115800i | ||||
\(950\) | −18.4380 | − | 31.9356i | −0.598209 | − | 1.03613i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −23.9282 | + | 65.1814i | −0.775518 | + | 2.11254i | ||||
\(953\) | −18.0455 | − | 31.2558i | −0.584552 | − | 1.01247i | −0.994931 | − | 0.100559i | \(-0.967937\pi\) |
0.410379 | − | 0.911915i | \(-0.365396\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.3573 | −0.367515 | ||||||||
\(956\) | −59.6275 | −1.92849 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −35.8496 | − | 62.0933i | −1.15825 | − | 2.00614i | ||||
\(959\) | 7.62524 | − | 20.7715i | 0.246232 | − | 0.670745i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0338 | + | 19.1111i | 0.355928 | + | 0.616486i | ||||
\(962\) | 10.0311 | + | 11.3113i | 0.323414 | + | 0.364692i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.8331 | −0.477743 | ||||||||
\(965\) | 11.5805 | − | 20.0580i | 0.372790 | − | 0.645691i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.18338 | 0.102371 | 0.0511853 | − | 0.998689i | \(-0.483700\pi\) | ||||
0.0511853 | + | 0.998689i | \(0.483700\pi\) | |||||||
\(968\) | 21.6614 | − | 37.5187i | 0.696225 | − | 1.20590i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.02756 | − | 15.6362i | 0.289857 | − | 0.502048i | ||||
\(971\) | 18.8738 | − | 32.6904i | 0.605690 | − | 1.04909i | −0.386253 | − | 0.922393i | \(-0.626231\pi\) |
0.991942 | − | 0.126692i | \(-0.0404360\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.50391 | + | 0.260898i | −0.0482131 | + | 0.00836399i | ||||
\(974\) | −68.0359 | −2.18001 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.54294 | + | 4.40451i | −0.0813977 | + | 0.140985i | ||||
\(977\) | −10.6538 | − | 18.4530i | −0.340846 | − | 0.590363i | 0.643744 | − | 0.765241i | \(-0.277380\pi\) |
−0.984590 | + | 0.174878i | \(0.944047\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.615168 | − | 1.06550i | −0.0196609 | − | 0.0340536i | ||||
\(980\) | 4.55951 | − | 25.0482i | 0.145648 | − | 0.800134i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −33.9910 | + | 58.8741i | −1.08470 | + | 1.87875i | ||||
\(983\) | −11.0158 | + | 19.0799i | −0.351350 | + | 0.608556i | −0.986486 | − | 0.163844i | \(-0.947611\pi\) |
0.635136 | + | 0.772400i | \(0.280944\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.44488 | −0.0460377 | ||||||||
\(986\) | −30.5189 | + | 52.8603i | −0.971919 | + | 1.68341i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 50.0528 | − | 10.2444i | 1.59239 | − | 0.325918i | ||||
\(989\) | 26.3529 | + | 45.6446i | 0.837975 | + | 1.45141i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.0129 | + | 19.0750i | 0.349838 | + | 0.605937i | 0.986220 | − | 0.165437i | \(-0.0529033\pi\) |
−0.636383 | + | 0.771374i | \(0.719570\pi\) | |||||||
\(992\) | −3.92808 | + | 6.80364i | −0.124717 | + | 0.216016i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22.4264 | + | 3.89052i | −0.711322 | + | 0.123400i | ||||
\(995\) | 4.61376 | + | 7.99127i | 0.146266 | + | 0.253340i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.0820 | 0.319301 | 0.159651 | − | 0.987174i | \(-0.448963\pi\) | ||||
0.159651 | + | 0.987174i | \(0.448963\pi\) | |||||||
\(998\) | 31.3225 | + | 54.2522i | 0.991497 | + | 1.71732i | ||||
\(999\) | 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 | 819.2.s.d.802.6 | 12 | ||
3.2 | odd | 2 | 91.2.h.b.74.1 | yes | 12 | ||
7.2 | even | 3 | 819.2.n.d.100.1 | 12 | |||
13.3 | even | 3 | 819.2.n.d.172.1 | 12 | |||
21.2 | odd | 6 | 91.2.g.b.9.6 | ✓ | 12 | ||
21.5 | even | 6 | 637.2.g.l.373.6 | 12 | |||
21.11 | odd | 6 | 637.2.f.k.295.6 | 12 | |||
21.17 | even | 6 | 637.2.f.j.295.6 | 12 | |||
21.20 | even | 2 | 637.2.h.l.165.1 | 12 | |||
39.17 | odd | 6 | 1183.2.e.g.508.1 | 12 | |||
39.29 | odd | 6 | 91.2.g.b.81.6 | yes | 12 | ||
39.35 | odd | 6 | 1183.2.e.h.508.6 | 12 | |||
91.16 | even | 3 | inner | 819.2.s.d.289.6 | 12 | ||
273.17 | even | 6 | 8281.2.a.cf.1.6 | 6 | |||
273.68 | even | 6 | 637.2.h.l.471.1 | 12 | |||
273.74 | odd | 6 | 8281.2.a.bz.1.1 | 6 | |||
273.95 | odd | 6 | 8281.2.a.ce.1.6 | 6 | |||
273.107 | odd | 6 | 91.2.h.b.16.1 | yes | 12 | ||
273.146 | even | 6 | 637.2.g.l.263.6 | 12 | |||
273.185 | even | 6 | 637.2.f.j.393.6 | 12 | |||
273.191 | odd | 6 | 1183.2.e.h.170.6 | 12 | |||
273.212 | odd | 6 | 1183.2.e.g.170.1 | 12 | |||
273.263 | odd | 6 | 637.2.f.k.393.6 | 12 | |||
273.269 | even | 6 | 8281.2.a.ca.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.6 | ✓ | 12 | 21.2 | odd | 6 | ||
91.2.g.b.81.6 | yes | 12 | 39.29 | odd | 6 | ||
91.2.h.b.16.1 | yes | 12 | 273.107 | odd | 6 | ||
91.2.h.b.74.1 | yes | 12 | 3.2 | odd | 2 | ||
637.2.f.j.295.6 | 12 | 21.17 | even | 6 | |||
637.2.f.j.393.6 | 12 | 273.185 | even | 6 | |||
637.2.f.k.295.6 | 12 | 21.11 | odd | 6 | |||
637.2.f.k.393.6 | 12 | 273.263 | odd | 6 | |||
637.2.g.l.263.6 | 12 | 273.146 | even | 6 | |||
637.2.g.l.373.6 | 12 | 21.5 | even | 6 | |||
637.2.h.l.165.1 | 12 | 21.20 | even | 2 | |||
637.2.h.l.471.1 | 12 | 273.68 | even | 6 | |||
819.2.n.d.100.1 | 12 | 7.2 | even | 3 | |||
819.2.n.d.172.1 | 12 | 13.3 | even | 3 | |||
819.2.s.d.289.6 | 12 | 91.16 | even | 3 | inner | ||
819.2.s.d.802.6 | 12 | 1.1 | even | 1 | trivial | ||
1183.2.e.g.170.1 | 12 | 273.212 | odd | 6 | |||
1183.2.e.g.508.1 | 12 | 39.17 | odd | 6 | |||
1183.2.e.h.170.6 | 12 | 273.191 | odd | 6 | |||
1183.2.e.h.508.6 | 12 | 39.35 | odd | 6 | |||
8281.2.a.bz.1.1 | 6 | 273.74 | odd | 6 | |||
8281.2.a.ca.1.1 | 6 | 273.269 | even | 6 | |||
8281.2.a.ce.1.6 | 6 | 273.95 | odd | 6 | |||
8281.2.a.cf.1.6 | 6 | 273.17 | even | 6 |