Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(881,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 8x^{12} + 80x^{10} + 1189x^{8} - 2028x^{6} + 1800x^{4} + 1080x^{2} + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.13 | ||
Root | \(-1.12256 - 0.464978i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.881 |
Dual form | 1386.2.g.a.881.5 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.929956 | 0.415889 | 0.207944 | − | 0.978141i | \(-0.433323\pi\) | ||||
0.207944 | + | 0.978141i | \(0.433323\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.07739 | − | 1.63843i | −0.785181 | − | 0.619267i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.929956i | 0.294078i | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 1.63843 | − | 2.07739i | 0.437888 | − | 0.555207i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.34690 | −0.569206 | −0.284603 | − | 0.958645i | \(-0.591862\pi\) | ||||
−0.284603 | + | 0.958645i | \(0.591862\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.87928i | 1.57822i | 0.614255 | + | 0.789108i | \(0.289457\pi\) | ||||
−0.614255 | + | 0.789108i | \(0.710543\pi\) | |||||||
\(20\) | −0.929956 | −0.207944 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | − | 3.04733i | − | 0.635412i | −0.948189 | − | 0.317706i | \(-0.897088\pi\) | ||
0.948189 | − | 0.317706i | \(-0.102912\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.13518 | −0.827036 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.07739 | + | 1.63843i | 0.392590 | + | 0.309633i | ||||
\(29\) | − | 6.39743i | − | 1.18797i | −0.804475 | − | 0.593986i | \(-0.797553\pi\) | ||
0.804475 | − | 0.593986i | \(-0.202447\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 10.0122i | − | 1.79824i | −0.437700 | − | 0.899121i | \(-0.644207\pi\) | ||
0.437700 | − | 0.899121i | \(-0.355793\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.34690i | − | 0.402489i | ||||||
\(35\) | −1.93188 | − | 1.52366i | −0.326548 | − | 0.257546i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.04733 | −0.829775 | −0.414888 | − | 0.909873i | \(-0.636179\pi\) | ||||
−0.414888 | + | 0.909873i | \(0.636179\pi\) | |||||||
\(38\) | −6.87928 | −1.11597 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 0.929956i | − | 0.147039i | ||||||
\(41\) | −10.1561 | −1.58612 | −0.793061 | − | 0.609143i | \(-0.791514\pi\) | ||||
−0.793061 | + | 0.609143i | \(0.791514\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.15479 | 0.938596 | 0.469298 | − | 0.883040i | \(-0.344507\pi\) | ||||
0.469298 | + | 0.883040i | \(0.344507\pi\) | |||||||
\(44\) | 1.00000i | 0.150756i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.04733 | 0.449304 | ||||||||
\(47\) | −12.0160 | −1.75272 | −0.876360 | − | 0.481657i | \(-0.840035\pi\) | ||||
−0.876360 | + | 0.481657i | \(0.840035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.63112 | + | 6.80731i | 0.233017 | + | 0.972473i | ||||
\(50\) | − | 4.13518i | − | 0.584803i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.2021i | − | 1.53873i | −0.638810 | − | 0.769364i | \(-0.720573\pi\) | ||
0.638810 | − | 0.769364i | \(-0.279427\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.929956i | − | 0.125395i | ||||||
\(56\) | −1.63843 | + | 2.07739i | −0.218944 | + | 0.277603i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.39743 | 0.840023 | ||||||||
\(59\) | 1.85991 | 0.242140 | 0.121070 | − | 0.992644i | \(-0.461367\pi\) | ||||
0.121070 | + | 0.992644i | \(0.461367\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.2735i | − | 1.31539i | −0.753284 | − | 0.657695i | \(-0.771532\pi\) | ||
0.753284 | − | 0.657695i | \(-0.228468\pi\) | |||||||
\(62\) | 10.0122 | 1.27155 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0878550 | −0.0107332 | −0.00536660 | − | 0.999986i | \(-0.501708\pi\) | ||||
−0.00536660 | + | 0.999986i | \(0.501708\pi\) | |||||||
\(68\) | 2.34690 | 0.284603 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.52366 | − | 1.93188i | 0.182113 | − | 0.230904i | ||||
\(71\) | − | 11.5326i | − | 1.36867i | −0.729168 | − | 0.684334i | \(-0.760093\pi\) | ||
0.729168 | − | 0.684334i | \(-0.239907\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0160i | 1.40637i | 0.711006 | + | 0.703186i | \(0.248240\pi\) | ||||
−0.711006 | + | 0.703186i | \(0.751760\pi\) | |||||||
\(74\) | − | 5.04733i | − | 0.586740i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 6.87928i | − | 0.789108i | ||||||
\(77\) | −1.63843 | + | 2.07739i | −0.186716 | + | 0.236741i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.5995 | 1.53007 | 0.765034 | − | 0.643990i | \(-0.222722\pi\) | ||||
0.765034 | + | 0.643990i | \(0.222722\pi\) | |||||||
\(80\) | 0.929956 | 0.103972 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 10.1561i | − | 1.12156i | ||||||
\(83\) | 4.06286 | 0.445957 | 0.222979 | − | 0.974823i | \(-0.428422\pi\) | ||||
0.222979 | + | 0.974823i | \(0.428422\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.18251 | −0.236726 | ||||||||
\(86\) | 6.15479i | 0.663688i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −17.0354 | −1.80575 | −0.902875 | − | 0.429903i | \(-0.858548\pi\) | ||||
−0.902875 | + | 0.429903i | \(0.858548\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.04733i | 0.317706i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 12.0160i | − | 1.23936i | ||||||
\(95\) | 6.39743i | 0.656362i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.6185i | 1.58582i | 0.609342 | + | 0.792908i | \(0.291434\pi\) | ||||
−0.609342 | + | 0.792908i | \(0.708566\pi\) | |||||||
\(98\) | −6.80731 | + | 1.63112i | −0.687642 | + | 0.164768i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.13518 | 0.413518 | ||||||||
\(101\) | 4.54985 | 0.452727 | 0.226363 | − | 0.974043i | \(-0.427316\pi\) | ||||
0.226363 | + | 0.974043i | \(0.427316\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.06286i | 0.400326i | 0.979763 | + | 0.200163i | \(0.0641471\pi\) | ||||
−0.979763 | + | 0.200163i | \(0.935853\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.2021 | 1.08805 | ||||||||
\(107\) | − | 5.57182i | − | 0.538648i | −0.963050 | − | 0.269324i | \(-0.913200\pi\) | ||
0.963050 | − | 0.269324i | \(-0.0868002\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.6597 | −1.49992 | −0.749962 | − | 0.661481i | \(-0.769928\pi\) | ||||
−0.749962 | + | 0.661481i | \(0.769928\pi\) | |||||||
\(110\) | 0.929956 | 0.0886678 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.07739 | − | 1.63843i | −0.196295 | − | 0.154817i | ||||
\(113\) | − | 13.6874i | − | 1.28760i | −0.765193 | − | 0.643801i | \(-0.777357\pi\) | ||
0.765193 | − | 0.643801i | \(-0.222643\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.83388i | − | 0.264261i | ||||||
\(116\) | 6.39743i | 0.593986i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.85991i | 0.171219i | ||||||||
\(119\) | 4.87542 | + | 3.84521i | 0.446929 | + | 0.352490i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 10.2735 | 0.930121 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.0122i | 0.899121i | ||||||||
\(125\) | −8.49532 | −0.759844 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.98040 | 0.441939 | 0.220969 | − | 0.975281i | \(-0.429078\pi\) | ||||
0.220969 | + | 0.975281i | \(0.429078\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.7992 | 1.81724 | 0.908619 | − | 0.417625i | \(-0.137138\pi\) | ||||
0.908619 | + | 0.417625i | \(0.137138\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.2712 | − | 14.2910i | 0.977336 | − | 1.23918i | ||||
\(134\) | − | 0.0878550i | − | 0.00758951i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.34690i | 0.201245i | ||||||||
\(137\) | 0.330496i | 0.0282362i | 0.999900 | + | 0.0141181i | \(0.00449407\pi\) | ||||
−0.999900 | + | 0.0141181i | \(0.995506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 19.0944i | − | 1.61957i | −0.586728 | − | 0.809784i | \(-0.699584\pi\) | ||
0.586728 | − | 0.809784i | \(-0.300416\pi\) | |||||||
\(140\) | 1.93188 | + | 1.52366i | 0.163274 | + | 0.128773i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.5326 | 0.967795 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 5.94932i | − | 0.494064i | ||||||
\(146\) | −12.0160 | −0.994455 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.04733 | 0.414888 | ||||||||
\(149\) | 1.26224i | 0.103407i | 0.998662 | + | 0.0517035i | \(0.0164651\pi\) | ||||
−0.998662 | + | 0.0517035i | \(0.983535\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3778 | −1.41419 | −0.707094 | − | 0.707120i | \(-0.749994\pi\) | ||||
−0.707094 | + | 0.707120i | \(0.749994\pi\) | |||||||
\(152\) | 6.87928 | 0.557983 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.07739 | − | 1.63843i | −0.167401 | − | 0.132028i | ||||
\(155\) | − | 9.31089i | − | 0.747869i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0199i | 1.11891i | 0.828861 | + | 0.559455i | \(0.188989\pi\) | ||||
−0.828861 | + | 0.559455i | \(0.811011\pi\) | |||||||
\(158\) | 13.5995i | 1.08192i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.929956i | 0.0735195i | ||||||||
\(161\) | −4.99282 | + | 6.33050i | −0.393489 | + | 0.498913i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.8422 | −1.08420 | −0.542102 | − | 0.840313i | \(-0.682371\pi\) | ||||
−0.542102 | + | 0.840313i | \(0.682371\pi\) | |||||||
\(164\) | 10.1561 | 0.793061 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.06286i | 0.315339i | ||||||||
\(167\) | 6.69765 | 0.518279 | 0.259140 | − | 0.965840i | \(-0.416561\pi\) | ||||
0.259140 | + | 0.965840i | \(0.416561\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | − | 2.18251i | − | 0.167391i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.15479 | −0.469298 | ||||||||
\(173\) | 5.20100 | 0.395425 | 0.197712 | − | 0.980260i | \(-0.436649\pi\) | ||||
0.197712 | + | 0.980260i | \(0.436649\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.59040 | + | 6.77519i | 0.649373 | + | 0.512156i | ||||
\(176\) | − | 1.00000i | − | 0.0753778i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 17.0354i | − | 1.27686i | ||||||
\(179\) | − | 3.91215i | − | 0.292407i | −0.989255 | − | 0.146204i | \(-0.953294\pi\) | ||
0.989255 | − | 0.146204i | \(-0.0467055\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.768549i | − | 0.0571258i | −0.999592 | − | 0.0285629i | \(-0.990907\pi\) | ||
0.999592 | − | 0.0285629i | \(-0.00909309\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.04733 | −0.224652 | ||||||||
\(185\) | −4.69379 | −0.345094 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.34690i | 0.171622i | ||||||||
\(188\) | 12.0160 | 0.876360 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.39743 | −0.464118 | ||||||||
\(191\) | 20.1518i | 1.45813i | 0.684445 | + | 0.729065i | \(0.260045\pi\) | ||||
−0.684445 | + | 0.729065i | \(0.739955\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.17571 | −0.444537 | −0.222269 | − | 0.974985i | \(-0.571346\pi\) | ||||
−0.222269 | + | 0.974985i | \(0.571346\pi\) | |||||||
\(194\) | −15.6185 | −1.12134 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.63112 | − | 6.80731i | −0.116509 | − | 0.486236i | ||||
\(197\) | 14.2772i | 1.01721i | 0.861001 | + | 0.508603i | \(0.169838\pi\) | ||||
−0.861001 | + | 0.508603i | \(0.830162\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 7.46620i | − | 0.529265i | −0.964349 | − | 0.264632i | \(-0.914749\pi\) | ||
0.964349 | − | 0.264632i | \(-0.0852506\pi\) | |||||||
\(200\) | 4.13518i | 0.292402i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.54985i | 0.320126i | ||||||||
\(203\) | −10.4817 | + | 13.2900i | −0.735672 | + | 0.932773i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.44475 | −0.659650 | ||||||||
\(206\) | −4.06286 | −0.283073 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.87928 | 0.475850 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.4252 | 1.13075 | 0.565377 | − | 0.824833i | \(-0.308731\pi\) | ||||
0.565377 | + | 0.824833i | \(0.308731\pi\) | |||||||
\(212\) | 11.2021i | 0.769364i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.57182 | 0.380881 | ||||||||
\(215\) | 5.72368 | 0.390352 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.4042 | + | 20.7992i | −1.11359 | + | 1.41194i | ||||
\(218\) | − | 15.6597i | − | 1.06061i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.929956i | 0.0626976i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.81504i | − | 0.456369i | −0.973618 | − | 0.228184i | \(-0.926721\pi\) | ||
0.973618 | − | 0.228184i | \(-0.0732789\pi\) | |||||||
\(224\) | 1.63843 | − | 2.07739i | 0.109472 | − | 0.138802i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.6874 | 0.910472 | ||||||||
\(227\) | 0.0265489 | 0.00176211 | 0.000881055 | − | 1.00000i | \(-0.499720\pi\) | ||||
0.000881055 | 1.00000i | \(0.499720\pi\) | ||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.69570i | 0.640710i | 0.947298 | + | 0.320355i | \(0.103802\pi\) | ||||
−0.947298 | + | 0.320355i | \(0.896198\pi\) | |||||||
\(230\) | 2.83388 | 0.186860 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.39743 | −0.420012 | ||||||||
\(233\) | − | 2.48528i | − | 0.162816i | −0.996681 | − | 0.0814081i | \(-0.974058\pi\) | ||
0.996681 | − | 0.0814081i | \(-0.0259417\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.1744 | −0.728937 | ||||||||
\(236\) | −1.85991 | −0.121070 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.84521 | + | 4.87542i | −0.249248 | + | 0.316027i | ||||
\(239\) | − | 11.4380i | − | 0.739860i | −0.929060 | − | 0.369930i | \(-0.879382\pi\) | ||
0.929060 | − | 0.369930i | \(-0.120618\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 7.69184i | − | 0.495475i | −0.968827 | − | 0.247738i | \(-0.920313\pi\) | ||
0.968827 | − | 0.247738i | \(-0.0796871\pi\) | |||||||
\(242\) | − | 1.00000i | − | 0.0642824i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.2735i | 0.657695i | ||||||||
\(245\) | 1.51687 | + | 6.33050i | 0.0969094 | + | 0.404441i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.0122 | −0.635775 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 8.49532i | − | 0.537291i | ||||||
\(251\) | −8.41361 | −0.531063 | −0.265531 | − | 0.964102i | \(-0.585547\pi\) | ||||
−0.265531 | + | 0.964102i | \(0.585547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.04733 | −0.191584 | ||||||||
\(254\) | 4.98040i | 0.312498i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.0354 | 1.06264 | 0.531320 | − | 0.847171i | \(-0.321696\pi\) | ||||
0.531320 | + | 0.847171i | \(0.321696\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.4853 | + | 8.26967i | 0.651524 | + | 0.513852i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 20.7992i | 1.28498i | ||||||||
\(263\) | 31.2869i | 1.92923i | 0.263653 | + | 0.964617i | \(0.415072\pi\) | ||||
−0.263653 | + | 0.964617i | \(0.584928\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10.4175i | − | 0.639940i | ||||||
\(266\) | 14.2910 | + | 11.2712i | 0.876235 | + | 0.691081i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.0878550 | 0.00536660 | ||||||||
\(269\) | −3.68213 | −0.224504 | −0.112252 | − | 0.993680i | \(-0.535806\pi\) | ||||
−0.112252 | + | 0.993680i | \(0.535806\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.2442i | 1.10825i | 0.832432 | + | 0.554127i | \(0.186948\pi\) | ||||
−0.832432 | + | 0.554127i | \(0.813052\pi\) | |||||||
\(272\) | −2.34690 | −0.142301 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.330496 | −0.0199660 | ||||||||
\(275\) | 4.13518i | 0.249361i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.8354 | −0.951456 | −0.475728 | − | 0.879592i | \(-0.657815\pi\) | ||||
−0.475728 | + | 0.879592i | \(0.657815\pi\) | |||||||
\(278\) | 19.0944 | 1.14521 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.52366 | + | 1.93188i | −0.0910563 | + | 0.115452i | ||||
\(281\) | − | 10.9706i | − | 0.654449i | −0.944947 | − | 0.327224i | \(-0.893887\pi\) | ||
0.944947 | − | 0.327224i | \(-0.106113\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.6625i | 0.931038i | 0.885038 | + | 0.465519i | \(0.154132\pi\) | ||||
−0.885038 | + | 0.465519i | \(0.845868\pi\) | |||||||
\(284\) | 11.5326i | 0.684334i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.0983 | + | 16.6401i | 1.24539 | + | 0.982232i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.4921 | −0.676005 | ||||||||
\(290\) | 5.94932 | 0.349356 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 12.0160i | − | 0.703186i | ||||||
\(293\) | 11.7547 | 0.686717 | 0.343359 | − | 0.939204i | \(-0.388435\pi\) | ||||
0.343359 | + | 0.939204i | \(0.388435\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.72964 | 0.100703 | ||||||||
\(296\) | 5.04733i | 0.293370i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.26224 | −0.0731198 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.7859 | − | 10.0842i | −0.736967 | − | 0.581241i | ||||
\(302\) | − | 17.3778i | − | 0.999981i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.87928i | 0.394554i | ||||||||
\(305\) | − | 9.55393i | − | 0.547056i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.5327i | 1.28601i | 0.765863 | + | 0.643004i | \(0.222312\pi\) | ||||
−0.765863 | + | 0.643004i | \(0.777688\pi\) | |||||||
\(308\) | 1.63843 | − | 2.07739i | 0.0933580 | − | 0.118370i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.31089 | 0.528823 | ||||||||
\(311\) | 6.06672 | 0.344012 | 0.172006 | − | 0.985096i | \(-0.444975\pi\) | ||||
0.172006 | + | 0.985096i | \(0.444975\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.48889i | 0.310250i | 0.987895 | + | 0.155125i | \(0.0495781\pi\) | ||||
−0.987895 | + | 0.155125i | \(0.950422\pi\) | |||||||
\(314\) | −14.0199 | −0.791189 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.5995 | −0.765034 | ||||||||
\(317\) | − | 34.2119i | − | 1.92153i | −0.277362 | − | 0.960765i | \(-0.589460\pi\) | ||
0.277362 | − | 0.960765i | \(-0.410540\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.39743 | −0.358187 | ||||||||
\(320\) | −0.929956 | −0.0519861 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.33050 | − | 4.99282i | −0.352785 | − | 0.278239i | ||||
\(323\) | − | 16.1450i | − | 0.898329i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 13.8422i | − | 0.766647i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.1561i | 0.560779i | ||||||||
\(329\) | 24.9620 | + | 19.6874i | 1.37620 | + | 1.08540i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.8017 | 0.813572 | 0.406786 | − | 0.913523i | \(-0.366649\pi\) | ||||
0.406786 | + | 0.913523i | \(0.366649\pi\) | |||||||
\(332\) | −4.06286 | −0.222979 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.69765i | 0.366479i | ||||||||
\(335\) | −0.0817013 | −0.00446382 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.4042 | −0.675701 | −0.337851 | − | 0.941200i | \(-0.609700\pi\) | ||||
−0.337851 | + | 0.941200i | \(0.609700\pi\) | |||||||
\(338\) | 13.0000i | 0.707107i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.18251 | 0.118363 | ||||||||
\(341\) | −10.0122 | −0.542190 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.76479 | − | 16.8139i | 0.419259 | − | 0.907867i | ||||
\(344\) | − | 6.15479i | − | 0.331844i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.20100i | 0.279608i | ||||||||
\(347\) | 20.0179i | 1.07462i | 0.843386 | + | 0.537308i | \(0.180559\pi\) | ||||
−0.843386 | + | 0.537308i | \(0.819441\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0464i | 0.751889i | 0.926642 | + | 0.375945i | \(0.122682\pi\) | ||||
−0.926642 | + | 0.375945i | \(0.877318\pi\) | |||||||
\(350\) | −6.77519 | + | 8.59040i | −0.362149 | + | 0.459176i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −24.4751 | −1.30268 | −0.651338 | − | 0.758788i | \(-0.725792\pi\) | ||||
−0.651338 | + | 0.758788i | \(0.725792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 10.7248i | − | 0.569214i | ||||||
\(356\) | 17.0354 | 0.902875 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.91215 | 0.206763 | ||||||||
\(359\) | − | 5.04053i | − | 0.266029i | −0.991114 | − | 0.133014i | \(-0.957534\pi\) | ||
0.991114 | − | 0.133014i | \(-0.0424657\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −28.3245 | −1.49076 | ||||||||
\(362\) | 0.768549 | 0.0403940 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.1744i | 0.584894i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 6.21066i | − | 0.324194i | −0.986775 | − | 0.162097i | \(-0.948174\pi\) | ||
0.986775 | − | 0.162097i | \(-0.0518257\pi\) | |||||||
\(368\) | − | 3.04733i | − | 0.158853i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 4.69379i | − | 0.244019i | ||||||
\(371\) | −18.3538 | + | 23.2712i | −0.952883 | + | 1.20818i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.78508 | 0.506652 | 0.253326 | − | 0.967381i | \(-0.418475\pi\) | ||||
0.253326 | + | 0.967381i | \(0.418475\pi\) | |||||||
\(374\) | −2.34690 | −0.121355 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.0160i | 0.619680i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.8422 | −0.916491 | −0.458246 | − | 0.888826i | \(-0.651522\pi\) | ||||
−0.458246 | + | 0.888826i | \(0.651522\pi\) | |||||||
\(380\) | − | 6.39743i | − | 0.328181i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.1518 | −1.03105 | ||||||||
\(383\) | −34.2699 | −1.75111 | −0.875556 | − | 0.483118i | \(-0.839504\pi\) | ||||
−0.875556 | + | 0.483118i | \(0.839504\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.52366 | + | 1.93188i | −0.0776531 | + | 0.0984579i | ||||
\(386\) | − | 6.17571i | − | 0.314335i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 15.6185i | − | 0.792908i | ||||||
\(389\) | 13.5927i | 0.689179i | 0.938753 | + | 0.344590i | \(0.111982\pi\) | ||||
−0.938753 | + | 0.344590i | \(0.888018\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.15176i | 0.361680i | ||||||||
\(392\) | 6.80731 | − | 1.63112i | 0.343821 | − | 0.0823841i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.2772 | −0.719273 | ||||||||
\(395\) | 12.6470 | 0.636338 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.1741i | 0.962322i | 0.876632 | + | 0.481161i | \(0.159785\pi\) | ||||
−0.876632 | + | 0.481161i | \(0.840215\pi\) | |||||||
\(398\) | 7.46620 | 0.374247 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.13518 | −0.206759 | ||||||||
\(401\) | − | 14.8550i | − | 0.741823i | −0.928668 | − | 0.370911i | \(-0.879045\pi\) | ||
0.928668 | − | 0.370911i | \(-0.120955\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −4.54985 | −0.226363 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.2900 | − | 10.4817i | −0.659570 | − | 0.520198i | ||||
\(407\) | 5.04733i | 0.250187i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.40395i | 0.366102i | 0.983103 | + | 0.183051i | \(0.0585973\pi\) | ||||
−0.983103 | + | 0.183051i | \(0.941403\pi\) | |||||||
\(410\) | − | 9.44475i | − | 0.466443i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 4.06286i | − | 0.200163i | ||||||
\(413\) | −3.86377 | − | 3.04733i | −0.190124 | − | 0.149949i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.77828 | 0.185469 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.87928i | 0.336477i | ||||||||
\(419\) | −19.3383 | −0.944738 | −0.472369 | − | 0.881401i | \(-0.656601\pi\) | ||||
−0.472369 | + | 0.881401i | \(0.656601\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0179 | 1.65793 | 0.828965 | − | 0.559300i | \(-0.188930\pi\) | ||||
0.828965 | + | 0.559300i | \(0.188930\pi\) | |||||||
\(422\) | 16.4252i | 0.799564i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.2021 | −0.544023 | ||||||||
\(425\) | 9.70484 | 0.470754 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.8324 | + | 21.3422i | −0.814577 | + | 1.03282i | ||||
\(428\) | 5.57182i | 0.269324i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.72368i | 0.276020i | ||||||||
\(431\) | 2.92191i | 0.140744i | 0.997521 | + | 0.0703718i | \(0.0224186\pi\) | ||||
−0.997521 | + | 0.0703718i | \(0.977581\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.60690i | − | 0.461678i | −0.972992 | − | 0.230839i | \(-0.925853\pi\) | ||
0.972992 | − | 0.230839i | \(-0.0741471\pi\) | |||||||
\(434\) | −20.7992 | − | 16.4042i | −0.998396 | − | 0.787428i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.6597 | 0.749962 | ||||||||
\(437\) | 20.9634 | 1.00282 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 36.6616i | − | 1.74976i | −0.484338 | − | 0.874881i | \(-0.660939\pi\) | ||
0.484338 | − | 0.874881i | \(-0.339061\pi\) | |||||||
\(440\) | −0.929956 | −0.0443339 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 28.7624i | − | 1.36655i | −0.730163 | − | 0.683273i | \(-0.760556\pi\) | ||
0.730163 | − | 0.683273i | \(-0.239444\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.8422 | −0.750991 | ||||||||
\(446\) | 6.81504 | 0.322702 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.07739 | + | 1.63843i | 0.0981476 | + | 0.0774083i | ||||
\(449\) | − | 24.0916i | − | 1.13695i | −0.822699 | − | 0.568477i | \(-0.807533\pi\) | ||
0.822699 | − | 0.568477i | \(-0.192467\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.1561i | 0.478234i | ||||||||
\(452\) | 13.6874i | 0.643801i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.0265489i | 0.00124600i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.4853 | −0.490481 | −0.245240 | − | 0.969462i | \(-0.578867\pi\) | ||||
−0.245240 | + | 0.969462i | \(0.578867\pi\) | |||||||
\(458\) | −9.69570 | −0.453050 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.83388i | 0.132130i | ||||||||
\(461\) | 20.4562 | 0.952741 | 0.476370 | − | 0.879245i | \(-0.341952\pi\) | ||||
0.476370 | + | 0.879245i | \(0.341952\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.4989 | 1.69625 | 0.848123 | − | 0.529799i | \(-0.177733\pi\) | ||||
0.848123 | + | 0.529799i | \(0.177733\pi\) | |||||||
\(464\) | − | 6.39743i | − | 0.296993i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.48528 | 0.115128 | ||||||||
\(467\) | 16.9557 | 0.784616 | 0.392308 | − | 0.919834i | \(-0.371677\pi\) | ||||
0.392308 | + | 0.919834i | \(0.371677\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.182509 | + | 0.143944i | 0.00842750 | + | 0.00664671i | ||||
\(470\) | − | 11.1744i | − | 0.515436i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 1.85991i | − | 0.0856094i | ||||||
\(473\) | − | 6.15479i | − | 0.282997i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 28.4471i | − | 1.30524i | ||||||
\(476\) | −4.87542 | − | 3.84521i | −0.223465 | − | 0.176245i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.4380 | 0.523160 | ||||||||
\(479\) | 31.9385 | 1.45931 | 0.729653 | − | 0.683817i | \(-0.239681\pi\) | ||||
0.729653 | + | 0.683817i | \(0.239681\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 7.69184 | 0.350354 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 14.5245i | 0.659523i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.57994 | 0.298165 | 0.149083 | − | 0.988825i | \(-0.452368\pi\) | ||||
0.149083 | + | 0.988825i | \(0.452368\pi\) | |||||||
\(488\) | −10.2735 | −0.465061 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.33050 | + | 1.51687i | −0.285983 | + | 0.0685253i | ||||
\(491\) | 9.14198i | 0.412572i | 0.978492 | + | 0.206286i | \(0.0661377\pi\) | ||||
−0.978492 | + | 0.206286i | \(0.933862\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.0141i | 0.676201i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 10.0122i | − | 0.449560i | ||||||
\(497\) | −18.8953 | + | 23.9578i | −0.847571 | + | 1.07465i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.47848 | −0.290017 | −0.145008 | − | 0.989430i | \(-0.546321\pi\) | ||||
−0.145008 | + | 0.989430i | \(0.546321\pi\) | |||||||
\(500\) | 8.49532 | 0.379922 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 8.41361i | − | 0.375518i | ||||||
\(503\) | −2.97782 | −0.132775 | −0.0663873 | − | 0.997794i | \(-0.521147\pi\) | ||||
−0.0663873 | + | 0.997794i | \(0.521147\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.23116 | 0.188284 | ||||||||
\(506\) | − | 3.04733i | − | 0.135470i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.98040 | −0.220969 | ||||||||
\(509\) | −7.40196 | −0.328086 | −0.164043 | − | 0.986453i | \(-0.552454\pi\) | ||||
−0.164043 | + | 0.986453i | \(0.552454\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.6874 | − | 24.9620i | 0.870919 | − | 1.10426i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.0354i | 0.751400i | ||||||||
\(515\) | 3.77828i | 0.166491i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0160i | 0.528465i | ||||||||
\(518\) | −8.26967 | + | 10.4853i | −0.363348 | + | 0.460697i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.02271 | −0.263860 | −0.131930 | − | 0.991259i | \(-0.542117\pi\) | ||||
−0.131930 | + | 0.991259i | \(0.542117\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 21.2422i | − | 0.928857i | −0.885611 | − | 0.464429i | \(-0.846260\pi\) | ||
0.885611 | − | 0.464429i | \(-0.153740\pi\) | |||||||
\(524\) | −20.7992 | −0.908619 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −31.2869 | −1.36418 | ||||||||
\(527\) | 23.4976i | 1.02357i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.7138 | 0.596252 | ||||||||
\(530\) | 10.4175 | 0.452506 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.2712 | + | 14.2910i | −0.488668 | + | 0.619592i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 5.18154i | − | 0.224018i | ||||||
\(536\) | 0.0878550i | 0.00379476i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 3.68213i | − | 0.158748i | ||||||
\(539\) | 6.80731 | − | 1.63112i | 0.293212 | − | 0.0702574i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.0947 | 1.12190 | 0.560948 | − | 0.827851i | \(-0.310437\pi\) | ||||
0.560948 | + | 0.827851i | \(0.310437\pi\) | |||||||
\(542\) | −18.2442 | −0.783654 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 2.34690i | − | 0.100622i | ||||||
\(545\) | −14.5628 | −0.623802 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.42515 | −0.189206 | −0.0946029 | − | 0.995515i | \(-0.530158\pi\) | ||||
−0.0946029 | + | 0.995515i | \(0.530158\pi\) | |||||||
\(548\) | − | 0.330496i | − | 0.0141181i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.13518 | −0.176325 | ||||||||
\(551\) | 44.0097 | 1.87488 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.2516 | − | 22.2818i | −1.20138 | − | 0.947520i | ||||
\(554\) | − | 15.8354i | − | 0.672781i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.0944i | 0.809784i | ||||||||
\(557\) | 14.2772i | 0.604943i | 0.953158 | + | 0.302471i | \(0.0978117\pi\) | ||||
−0.953158 | + | 0.302471i | \(0.902188\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.93188 | − | 1.52366i | −0.0816370 | − | 0.0643865i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.9706 | 0.462765 | ||||||||
\(563\) | −7.08746 | −0.298701 | −0.149350 | − | 0.988784i | \(-0.547718\pi\) | ||||
−0.149350 | + | 0.988784i | \(0.547718\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 12.7287i | − | 0.535499i | ||||||
\(566\) | −15.6625 | −0.658343 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.5326 | −0.483898 | ||||||||
\(569\) | − | 14.4853i | − | 0.607255i | −0.952791 | − | 0.303627i | \(-0.901802\pi\) | ||
0.952791 | − | 0.303627i | \(-0.0981978\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.1095 | 1.67853 | 0.839265 | − | 0.543722i | \(-0.182985\pi\) | ||||
0.839265 | + | 0.543722i | \(0.182985\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.6401 | + | 21.0983i | −0.694543 | + | 0.880625i | ||||
\(575\) | 12.6013i | 0.525509i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.98168i | 0.207390i | 0.994609 | + | 0.103695i | \(0.0330666\pi\) | ||||
−0.994609 | + | 0.103695i | \(0.966933\pi\) | |||||||
\(578\) | − | 11.4921i | − | 0.478008i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.94932i | 0.247032i | ||||||||
\(581\) | −8.44016 | − | 6.65670i | −0.350157 | − | 0.276166i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.2021 | −0.463944 | ||||||||
\(584\) | 12.0160 | 0.497227 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.7547i | 0.485582i | ||||||||
\(587\) | 39.6855 | 1.63800 | 0.818998 | − | 0.573797i | \(-0.194530\pi\) | ||||
0.818998 | + | 0.573797i | \(0.194530\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 68.8766 | 2.83801 | ||||||||
\(590\) | 1.72964i | 0.0712080i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.04733 | −0.207444 | ||||||||
\(593\) | −10.5194 | −0.431980 | −0.215990 | − | 0.976396i | \(-0.569298\pi\) | ||||
−0.215990 | + | 0.976396i | \(0.569298\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.53393 | + | 3.57588i | 0.185873 | + | 0.146597i | ||||
\(596\) | − | 1.26224i | − | 0.0517035i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.85802i | 0.116775i | 0.998294 | + | 0.0583877i | \(0.0185960\pi\) | ||||
−0.998294 | + | 0.0583877i | \(0.981404\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.5307i | 1.36775i | 0.729600 | + | 0.683874i | \(0.239706\pi\) | ||||
−0.729600 | + | 0.683874i | \(0.760294\pi\) | |||||||
\(602\) | 10.0842 | − | 12.7859i | 0.411000 | − | 0.521115i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.3778 | 0.707094 | ||||||||
\(605\) | −0.929956 | −0.0378081 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 22.9030i | − | 0.929605i | −0.885414 | − | 0.464803i | \(-0.846125\pi\) | ||
0.885414 | − | 0.464803i | \(-0.153875\pi\) | |||||||
\(608\) | −6.87928 | −0.278992 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.55393 | 0.386827 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.9885 | −1.89785 | −0.948923 | − | 0.315508i | \(-0.897825\pi\) | ||||
−0.948923 | + | 0.315508i | \(0.897825\pi\) | |||||||
\(614\) | −22.5327 | −0.909345 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.07739 | + | 1.63843i | 0.0837005 | + | 0.0660141i | ||||
\(617\) | − | 33.3471i | − | 1.34250i | −0.741230 | − | 0.671251i | \(-0.765757\pi\) | ||
0.741230 | − | 0.671251i | \(-0.234243\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.7259i | − | 1.15459i | −0.816535 | − | 0.577295i | \(-0.804108\pi\) | ||
0.816535 | − | 0.577295i | \(-0.195892\pi\) | |||||||
\(620\) | 9.31089i | 0.373934i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.06672i | 0.243253i | ||||||||
\(623\) | 35.3892 | + | 27.9113i | 1.41784 | + | 1.11824i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.7756 | 0.511026 | ||||||||
\(626\) | −5.48889 | −0.219380 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 14.0199i | − | 0.559455i | ||||||
\(629\) | 11.8456 | 0.472313 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.1599 | 1.47931 | 0.739656 | − | 0.672986i | \(-0.234988\pi\) | ||||
0.739656 | + | 0.672986i | \(0.234988\pi\) | |||||||
\(632\) | − | 13.5995i | − | 0.540961i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 34.2119 | 1.35873 | ||||||||
\(635\) | 4.63155 | 0.183797 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 6.39743i | − | 0.253277i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 0.929956i | − | 0.0367597i | ||||||
\(641\) | 24.8618i | 0.981981i | 0.871165 | + | 0.490991i | \(0.163365\pi\) | ||||
−0.871165 | + | 0.490991i | \(0.836635\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.8233i | 0.900064i | 0.893012 | + | 0.450032i | \(0.148587\pi\) | ||||
−0.893012 | + | 0.450032i | \(0.851413\pi\) | |||||||
\(644\) | 4.99282 | − | 6.33050i | 0.196745 | − | 0.249456i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.1450 | 0.635215 | ||||||||
\(647\) | −38.9637 | −1.53182 | −0.765911 | − | 0.642947i | \(-0.777712\pi\) | ||||
−0.765911 | + | 0.642947i | \(0.777712\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.85991i | − | 0.0730079i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.8422 | 0.542102 | ||||||||
\(653\) | − | 29.4306i | − | 1.15171i | −0.817552 | − | 0.575855i | \(-0.804669\pi\) | ||
0.817552 | − | 0.575855i | \(-0.195331\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.3424 | 0.755769 | ||||||||
\(656\) | −10.1561 | −0.396530 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −19.6874 | + | 24.9620i | −0.767495 | + | 0.973122i | ||||
\(659\) | − | 7.74588i | − | 0.301736i | −0.988554 | − | 0.150868i | \(-0.951793\pi\) | ||
0.988554 | − | 0.150868i | \(-0.0482069\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 31.2167i | − | 1.21419i | −0.794629 | − | 0.607095i | \(-0.792335\pi\) | ||
0.794629 | − | 0.607095i | \(-0.207665\pi\) | |||||||
\(662\) | 14.8017i | 0.575283i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 4.06286i | − | 0.157670i | ||||||
\(665\) | 10.4817 | − | 13.2900i | 0.406463 | − | 0.515363i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.4951 | −0.754851 | ||||||||
\(668\) | −6.69765 | −0.259140 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 0.0817013i | − | 0.00315639i | ||||||
\(671\) | −10.2735 | −0.396605 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.5603 | 1.56348 | 0.781742 | − | 0.623602i | \(-0.214332\pi\) | ||||
0.781742 | + | 0.623602i | \(0.214332\pi\) | |||||||
\(674\) | − | 12.4042i | − | 0.477793i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | −42.7038 | −1.64124 | −0.820619 | − | 0.571475i | \(-0.806371\pi\) | ||||
−0.820619 | + | 0.571475i | \(0.806371\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.5897 | − | 32.4457i | 0.982043 | − | 1.24515i | ||||
\(680\) | 2.18251i | 0.0836954i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 10.0122i | − | 0.383386i | ||||||
\(683\) | − | 24.4529i | − | 0.935663i | −0.883818 | − | 0.467832i | \(-0.845035\pi\) | ||
0.883818 | − | 0.467832i | \(-0.154965\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.307346i | 0.0117431i | ||||||||
\(686\) | 16.8139 | + | 7.76479i | 0.641959 | + | 0.296461i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.15479 | 0.234649 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.95461i | − | 0.150441i | −0.997167 | − | 0.0752203i | \(-0.976034\pi\) | ||
0.997167 | − | 0.0752203i | \(-0.0239660\pi\) | |||||||
\(692\) | −5.20100 | −0.197712 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.0179 | −0.759869 | ||||||||
\(695\) | − | 17.7570i | − | 0.673560i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.8354 | 0.902829 | ||||||||
\(698\) | −14.0464 | −0.531666 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.59040 | − | 6.77519i | −0.324687 | − | 0.256078i | ||||
\(701\) | − | 9.37479i | − | 0.354081i | −0.984204 | − | 0.177040i | \(-0.943348\pi\) | ||
0.984204 | − | 0.177040i | \(-0.0566523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 34.7220i | − | 1.30956i | ||||||
\(704\) | 1.00000i | 0.0376889i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 24.4751i | − | 0.921131i | ||||||
\(707\) | −9.45182 | − | 7.45459i | −0.355472 | − | 0.280359i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.4461 | −0.617645 | −0.308823 | − | 0.951120i | \(-0.599935\pi\) | ||||
−0.308823 | + | 0.951120i | \(0.599935\pi\) | |||||||
\(710\) | 10.7248 | 0.402495 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17.0354i | 0.638429i | ||||||||
\(713\) | −30.5104 | −1.14262 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.91215i | 0.146204i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.04053 | 0.188111 | ||||||||
\(719\) | −3.80861 | −0.142037 | −0.0710187 | − | 0.997475i | \(-0.522625\pi\) | ||||
−0.0710187 | + | 0.997475i | \(0.522625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.65670 | − | 8.44016i | 0.247908 | − | 0.314328i | ||||
\(722\) | − | 28.3245i | − | 1.05413i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.768549i | 0.0285629i | ||||||||
\(725\) | 26.4545i | 0.982496i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 44.3709i | − | 1.64563i | −0.568313 | − | 0.822813i | \(-0.692404\pi\) | ||
0.568313 | − | 0.822813i | \(-0.307596\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.1744 | −0.413583 | ||||||||
\(731\) | −14.4446 | −0.534254 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 16.8272i | − | 0.621528i | −0.950487 | − | 0.310764i | \(-0.899415\pi\) | ||
0.950487 | − | 0.310764i | \(-0.100585\pi\) | |||||||
\(734\) | 6.21066 | 0.229240 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.04733 | 0.112326 | ||||||||
\(737\) | 0.0878550i | 0.00323618i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.97908 | 0.219944 | 0.109972 | − | 0.993935i | \(-0.464924\pi\) | ||||
0.109972 | + | 0.993935i | \(0.464924\pi\) | |||||||
\(740\) | 4.69379 | 0.172547 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23.2712 | − | 18.3538i | −0.854312 | − | 0.673790i | ||||
\(743\) | 2.38634i | 0.0875462i | 0.999041 | + | 0.0437731i | \(0.0139379\pi\) | ||||
−0.999041 | + | 0.0437731i | \(0.986062\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.17383i | 0.0430059i | ||||||||
\(746\) | 9.78508i | 0.358257i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 2.34690i | − | 0.0858110i | ||||||
\(749\) | −9.12901 | + | 11.5748i | −0.333567 | + | 0.422936i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.2187 | 0.409378 | 0.204689 | − | 0.978827i | \(-0.434382\pi\) | ||||
0.204689 | + | 0.978827i | \(0.434382\pi\) | |||||||
\(752\) | −12.0160 | −0.438180 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.1606 | −0.588145 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.0315 | −1.09151 | −0.545757 | − | 0.837944i | \(-0.683758\pi\) | ||||
−0.545757 | + | 0.837944i | \(0.683758\pi\) | |||||||
\(758\) | − | 17.8422i | − | 0.648057i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.39743 | 0.232059 | ||||||||
\(761\) | −2.71648 | −0.0984725 | −0.0492362 | − | 0.998787i | \(-0.515679\pi\) | ||||
−0.0492362 | + | 0.998787i | \(0.515679\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.5313 | + | 25.6572i | 1.17771 | + | 0.928853i | ||||
\(764\) | − | 20.1518i | − | 0.729065i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 34.2699i | − | 1.23822i | ||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.4424i | − | 1.13384i | −0.823773 | − | 0.566920i | \(-0.808135\pi\) | ||
0.823773 | − | 0.566920i | \(-0.191865\pi\) | |||||||
\(770\) | −1.93188 | − | 1.52366i | −0.0696203 | − | 0.0549090i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.17571 | 0.222269 | ||||||||
\(773\) | 9.42527 | 0.339003 | 0.169502 | − | 0.985530i | \(-0.445784\pi\) | ||||
0.169502 | + | 0.985530i | \(0.445784\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 41.4022i | 1.48721i | ||||||||
\(776\) | 15.6185 | 0.560670 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.5927 | −0.487323 | ||||||||
\(779\) | − | 69.8669i | − | 2.50324i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.5326 | −0.412669 | ||||||||
\(782\) | −7.15176 | −0.255746 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.63112 | + | 6.80731i | 0.0582544 | + | 0.243118i | ||||
\(785\) | 13.0379i | 0.465342i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 16.6301i | − | 0.592800i | −0.955064 | − | 0.296400i | \(-0.904214\pi\) | ||
0.955064 | − | 0.296400i | \(-0.0957862\pi\) | |||||||
\(788\) | − | 14.2772i | − | 0.508603i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.6470i | 0.449959i | ||||||||
\(791\) | −22.4258 | + | 28.4341i | −0.797369 | + | 1.01100i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −19.1741 | −0.680464 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.46620i | 0.264632i | ||||||||
\(797\) | −20.5847 | −0.729149 | −0.364574 | − | 0.931174i | \(-0.618786\pi\) | ||||
−0.364574 | + | 0.931174i | \(0.618786\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.2004 | 0.997658 | ||||||||
\(800\) | − | 4.13518i | − | 0.146201i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.8550 | 0.524548 | ||||||||
\(803\) | 12.0160 | 0.424037 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.64310 | + | 5.88708i | −0.163648 | + | 0.207492i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 4.54985i | − | 0.160063i | ||||||
\(809\) | − | 5.39446i | − | 0.189659i | −0.995494 | − | 0.0948295i | \(-0.969769\pi\) | ||
0.995494 | − | 0.0948295i | \(-0.0302306\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12.5407i | − | 0.440364i | −0.975459 | − | 0.220182i | \(-0.929335\pi\) | ||
0.975459 | − | 0.220182i | \(-0.0706651\pi\) | |||||||
\(812\) | 10.4817 | − | 13.2900i | 0.367836 | − | 0.466386i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.04733 | −0.176909 | ||||||||
\(815\) | −12.8726 | −0.450908 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42.3405i | 1.48131i | ||||||||
\(818\) | −7.40395 | −0.258873 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.44475 | 0.329825 | ||||||||
\(821\) | − | 16.2149i | − | 0.565905i | −0.959134 | − | 0.282952i | \(-0.908686\pi\) | ||
0.959134 | − | 0.282952i | \(-0.0913138\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.9706 | 1.28871 | 0.644356 | − | 0.764725i | \(-0.277125\pi\) | ||||
0.644356 | + | 0.764725i | \(0.277125\pi\) | |||||||
\(824\) | 4.06286 | 0.141537 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.04733 | − | 3.86377i | 0.106030 | − | 0.134438i | ||||
\(827\) | 25.9232i | 0.901439i | 0.892666 | + | 0.450720i | \(0.148833\pi\) | ||||
−0.892666 | + | 0.450720i | \(0.851167\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.1717i | 0.735322i | 0.929960 | + | 0.367661i | \(0.119841\pi\) | ||||
−0.929960 | + | 0.367661i | \(0.880159\pi\) | |||||||
\(830\) | 3.77828i | 0.131146i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.82807 | − | 15.9760i | −0.132635 | − | 0.553537i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.22852 | 0.215547 | ||||||||
\(836\) | −6.87928 | −0.237925 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 19.3383i | − | 0.668030i | ||||||
\(839\) | −8.05511 | −0.278093 | −0.139047 | − | 0.990286i | \(-0.544404\pi\) | ||||
−0.139047 | + | 0.990286i | \(0.544404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.9271 | −0.411278 | ||||||||
\(842\) | 34.0179i | 1.17233i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.4252 | −0.565377 | ||||||||
\(845\) | 12.0894 | 0.415889 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.07739 | + | 1.63843i | 0.0713801 | + | 0.0562970i | ||||
\(848\) | − | 11.2021i | − | 0.384682i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.70484i | 0.332873i | ||||||||
\(851\) | 15.3809i | 0.527249i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 41.9618i | − | 1.43674i | −0.695660 | − | 0.718372i | \(-0.744888\pi\) | ||
0.695660 | − | 0.718372i | \(-0.255112\pi\) | |||||||
\(854\) | −21.3422 | − | 16.8324i | −0.730313 | − | 0.575993i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.57182 | −0.190441 | ||||||||
\(857\) | 42.8834 | 1.46487 | 0.732434 | − | 0.680838i | \(-0.238384\pi\) | ||||
0.732434 | + | 0.680838i | \(0.238384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 45.3532i | − | 1.54743i | −0.633532 | − | 0.773716i | \(-0.718396\pi\) | ||
0.633532 | − | 0.773716i | \(-0.281604\pi\) | |||||||
\(860\) | −5.72368 | −0.195176 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.92191 | −0.0995208 | ||||||||
\(863\) | − | 10.0768i | − | 0.343017i | −0.985183 | − | 0.171509i | \(-0.945136\pi\) | ||
0.985183 | − | 0.171509i | \(-0.0548641\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.83670 | 0.164453 | ||||||||
\(866\) | 9.60690 | 0.326456 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.4042 | − | 20.7992i | 0.556796 | − | 0.705972i | ||||
\(869\) | − | 13.5995i | − | 0.461333i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 15.6597i | 0.530303i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20.9634i | 0.709098i | ||||||||
\(875\) | 17.6481 | + | 13.9189i | 0.596615 | + | 0.470546i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.9339 | −0.639351 | −0.319676 | − | 0.947527i | \(-0.603574\pi\) | ||||
−0.319676 | + | 0.947527i | \(0.603574\pi\) | |||||||
\(878\) | 36.6616 | 1.23727 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 0.929956i | − | 0.0313488i | ||||||
\(881\) | 53.5991 | 1.80580 | 0.902900 | − | 0.429850i | \(-0.141434\pi\) | ||||
0.902900 | + | 0.429850i | \(0.141434\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.1774 | 0.544412 | 0.272206 | − | 0.962239i | \(-0.412247\pi\) | ||||
0.272206 | + | 0.962239i | \(0.412247\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.7624 | 0.966293 | ||||||||
\(887\) | −4.64069 | −0.155819 | −0.0779096 | − | 0.996960i | \(-0.524825\pi\) | ||||
−0.0779096 | + | 0.996960i | \(0.524825\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.3462 | − | 8.16001i | −0.347002 | − | 0.273678i | ||||
\(890\) | − | 15.8422i | − | 0.531031i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.81504i | 0.228184i | ||||||||
\(893\) | − | 82.6617i | − | 2.76617i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.63812i | − | 0.121609i | ||||||
\(896\) | −1.63843 | + | 2.07739i | −0.0547360 | + | 0.0694008i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.0916 | 0.803948 | ||||||||
\(899\) | −64.0522 | −2.13626 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.2902i | 0.875853i | ||||||||
\(902\) | −10.1561 | −0.338162 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.6874 | −0.455236 | ||||||||
\(905\) | − | 0.714716i | − | 0.0237580i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.1407 | −0.602351 | −0.301175 | − | 0.953569i | \(-0.597379\pi\) | ||||
−0.301175 | + | 0.953569i | \(0.597379\pi\) | |||||||
\(908\) | −0.0265489 | −0.000881055 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 10.7378i | − | 0.355758i | −0.984052 | − | 0.177879i | \(-0.943076\pi\) | ||
0.984052 | − | 0.177879i | \(-0.0569235\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 4.06286i | − | 0.134461i | ||||||
\(914\) | − | 10.4853i | − | 0.346822i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 9.69570i | − | 0.320355i | ||||||
\(917\) | −43.2082 | − | 34.0780i | −1.42686 | − | 1.12536i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.40343 | −0.112269 | −0.0561344 | − | 0.998423i | \(-0.517878\pi\) | ||||
−0.0561344 | + | 0.998423i | \(0.517878\pi\) | |||||||
\(920\) | −2.83388 | −0.0934302 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.4562i | 0.673689i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.8716 | 0.686255 | ||||||||
\(926\) | 36.4989i | 1.19943i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.39743 | 0.210006 | ||||||||
\(929\) | −19.1301 | −0.627639 | −0.313819 | − | 0.949483i | \(-0.601609\pi\) | ||||
−0.313819 | + | 0.949483i | \(0.601609\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −46.8294 | + | 11.2209i | −1.53477 | + | 0.367752i | ||||
\(932\) | 2.48528i | 0.0814081i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.9557i | 0.554808i | ||||||||
\(935\) | 2.18251i | 0.0713757i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.6672i | 0.413819i | 0.978360 | + | 0.206910i | \(0.0663406\pi\) | ||||
−0.978360 | + | 0.206910i | \(0.933659\pi\) | |||||||
\(938\) | −0.143944 | + | 0.182509i | −0.00469993 | + | 0.00595914i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.1744 | 0.364468 | ||||||||
\(941\) | −8.32277 | −0.271314 | −0.135657 | − | 0.990756i | \(-0.543315\pi\) | ||||
−0.135657 | + | 0.990756i | \(0.543315\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.9491i | 1.00784i | ||||||||
\(944\) | 1.85991 | 0.0605350 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.15479 | 0.200109 | ||||||||
\(947\) | 51.0021i | 1.65734i | 0.559735 | + | 0.828672i | \(0.310903\pi\) | ||||
−0.559735 | + | 0.828672i | \(0.689097\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 28.4471 | 0.922945 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.84521 | − | 4.87542i | 0.124624 | − | 0.158013i | ||||
\(953\) | 38.6191i | 1.25100i | 0.780225 | + | 0.625498i | \(0.215104\pi\) | ||||
−0.780225 | + | 0.625498i | \(0.784896\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.7402i | 0.606420i | ||||||||
\(956\) | 11.4380i | 0.369930i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 31.9385i | 1.03189i | ||||||||
\(959\) | 0.541493 | − | 0.686569i | 0.0174857 | − | 0.0221705i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −69.2439 | −2.23367 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.69184i | 0.247738i | ||||||||
\(965\) | −5.74314 | −0.184878 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.2456 | −0.683213 | −0.341606 | − | 0.939843i | \(-0.610971\pi\) | ||||
−0.341606 | + | 0.939843i | \(0.610971\pi\) | |||||||
\(968\) | 1.00000i | 0.0321412i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.5245 | −0.466353 | ||||||||
\(971\) | 28.5665 | 0.916742 | 0.458371 | − | 0.888761i | \(-0.348433\pi\) | ||||
0.458371 | + | 0.888761i | \(0.348433\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.2848 | + | 39.6666i | −1.00294 | + | 1.27165i | ||||
\(974\) | 6.57994i | 0.210835i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 10.2735i | − | 0.328848i | ||||||
\(977\) | 2.65294i | 0.0848749i | 0.999099 | + | 0.0424375i | \(0.0135123\pi\) | ||||
−0.999099 | + | 0.0424375i | \(0.986488\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.0354i | 0.544454i | ||||||||
\(980\) | −1.51687 | − | 6.33050i | −0.0484547 | − | 0.202220i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.14198 | −0.291732 | ||||||||
\(983\) | 14.5620 | 0.464457 | 0.232228 | − | 0.972661i | \(-0.425398\pi\) | ||||
0.232228 | + | 0.972661i | \(0.425398\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.2771i | 0.423045i | ||||||||
\(986\) | −15.0141 | −0.478146 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 18.7556i | − | 0.596395i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.254124 | −0.00807252 | −0.00403626 | − | 0.999992i | \(-0.501285\pi\) | ||||
−0.00403626 | + | 0.999992i | \(0.501285\pi\) | |||||||
\(992\) | 10.0122 | 0.317887 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −23.9578 | − | 18.8953i | −0.759894 | − | 0.599323i | ||||
\(995\) | − | 6.94323i | − | 0.220115i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 9.01167i | − | 0.285402i | −0.989766 | − | 0.142701i | \(-0.954421\pi\) | ||
0.989766 | − | 0.142701i | \(-0.0455788\pi\) | |||||||
\(998\) | − | 6.47848i | − | 0.205073i | ||||||
\(999\) | 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 | 1386.2.g.a.881.13 | yes | 16 | |
3.2 | odd | 2 | inner | 1386.2.g.a.881.4 | ✓ | 16 | |
7.6 | odd | 2 | inner | 1386.2.g.a.881.12 | yes | 16 | |
21.20 | even | 2 | inner | 1386.2.g.a.881.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.g.a.881.4 | ✓ | 16 | 3.2 | odd | 2 | inner | |
1386.2.g.a.881.5 | yes | 16 | 21.20 | even | 2 | inner | |
1386.2.g.a.881.12 | yes | 16 | 7.6 | odd | 2 | inner | |
1386.2.g.a.881.13 | yes | 16 | 1.1 | even | 1 | trivial |