Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1584,2,Mod(17,1584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1584, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 5, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1584.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1584.cd (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.6483036802\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 305.4 | ||
Root | \(0.752864 - 0.902863i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1584.305 |
Dual form | 1584.2.cd.c.161.4 |
$q$-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 \(\left(\mathbb{Z}/1584\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(353\) | \(991\) | \(1189\) |
\(\chi(n)\) | \(e\left(\frac{3}{10}\right)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23109 | − | 3.07083i | 0.997774 | − | 1.37332i | 0.0710932 | − | 0.997470i | \(-0.477351\pi\) |
0.926681 | − | 0.375849i | \(-0.122649\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.349790 | + | 0.113654i | 0.132208 | + | 0.0429571i | 0.374374 | − | 0.927278i | \(-0.377858\pi\) |
−0.242165 | + | 0.970235i | \(0.577858\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.97756 | − | 1.46086i | −0.897769 | − | 0.440467i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.557375 | − | 0.767161i | −0.154588 | − | 0.212772i | 0.724698 | − | 0.689067i | \(-0.241979\pi\) |
−0.879286 | + | 0.476295i | \(0.841979\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.77873 | − | 2.01886i | −0.673940 | − | 0.489646i | 0.197402 | − | 0.980323i | \(-0.436750\pi\) |
−0.871342 | + | 0.490676i | \(0.836750\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.05368 | + | 1.31712i | −0.929979 | + | 0.302168i | −0.734554 | − | 0.678550i | \(-0.762609\pi\) |
−0.195425 | + | 0.980719i | \(0.562609\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.96800i | − | 1.03590i | −0.855411 | − | 0.517950i | \(-0.826695\pi\) | ||
0.855411 | − | 0.517950i | \(-0.173305\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.90717 | − | 8.94734i | −0.581433 | − | 1.78947i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.767418 | − | 2.36187i | 0.142506 | − | 0.438588i | −0.854176 | − | 0.519984i | \(-0.825938\pi\) |
0.996682 | + | 0.0813958i | \(0.0259378\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.84281 | − | 2.06543i | 0.510585 | − | 0.370961i | −0.302461 | − | 0.953162i | \(-0.597808\pi\) |
0.813045 | + | 0.582200i | \(0.197808\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.12943 | − | 0.820576i | 0.190908 | − | 0.138703i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.21947 | + | 6.83082i | −0.364878 | + | 1.12298i | 0.585179 | + | 0.810904i | \(0.301024\pi\) |
−0.950057 | + | 0.312075i | \(0.898976\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.840249 | + | 2.58602i | 0.131225 | + | 0.403869i | 0.994984 | − | 0.100037i | \(-0.0318960\pi\) |
−0.863759 | + | 0.503905i | \(0.831896\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.88749i | − | 0.287839i | −0.989589 | − | 0.143919i | \(-0.954029\pi\) | ||
0.989589 | − | 0.143919i | \(-0.0459706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.0195991 | − | 0.00636813i | 0.00285882 | − | 0.000928888i | −0.307587 | − | 0.951520i | \(-0.599522\pi\) |
0.310446 | + | 0.950591i | \(0.399522\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.55368 | − | 4.03499i | −0.793383 | − | 0.576427i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.25941 | + | 4.48619i | 0.447714 | + | 0.616226i | 0.971905 | − | 0.235375i | \(-0.0756319\pi\) |
−0.524190 | + | 0.851601i | \(0.675632\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.1293 | + | 5.88428i | −1.50067 | + | 0.793436i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.29998 | + | 2.04699i | 0.820187 | + | 0.266495i | 0.688906 | − | 0.724850i | \(-0.258091\pi\) |
0.131281 | + | 0.991345i | \(0.458091\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.73238 | + | 7.88994i | −0.733956 | + | 1.01020i | 0.264988 | + | 0.964252i | \(0.414632\pi\) |
−0.998944 | + | 0.0459514i | \(0.985368\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.59938 | −0.446448 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.46351 | −0.545305 | −0.272652 | − | 0.962113i | \(-0.587901\pi\) | ||||
−0.272652 | + | 0.962113i | \(0.587901\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.06985 | − | 8.35443i | 0.720359 | − | 0.991489i | −0.279153 | − | 0.960247i | \(-0.590054\pi\) |
0.999512 | − | 0.0312420i | \(-0.00994626\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.18072 | − | 1.35840i | −0.489317 | − | 0.158989i | 0.0539588 | − | 0.998543i | \(-0.482816\pi\) |
−0.543275 | + | 0.839555i | \(0.682816\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.875490 | − | 0.849407i | −0.0997714 | − | 0.0967989i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.42867 | − | 8.84831i | −0.723282 | − | 0.995513i | −0.999408 | − | 0.0343911i | \(-0.989051\pi\) |
0.276126 | − | 0.961121i | \(-0.410949\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.42940 | + | 5.39778i | 0.815483 | + | 0.592483i | 0.915415 | − | 0.402511i | \(-0.131863\pi\) |
−0.0999323 | + | 0.994994i | \(0.531863\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.3992 | + | 4.02874i | −1.34488 | + | 0.436978i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.04837i | − | 0.323127i | −0.986862 | − | 0.161563i | \(-0.948346\pi\) | ||
0.986862 | − | 0.161563i | \(-0.0516536\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.107774 | − | 0.331693i | −0.0112978 | − | 0.0347709i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.99948 | + | 15.3868i | −0.512935 | + | 1.57865i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2055 | − | 8.86782i | 1.23928 | − | 0.900391i | 0.241732 | − | 0.970343i | \(-0.422285\pi\) |
0.997550 | + | 0.0699519i | \(0.0222846\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.1253 | − | 10.2626i | 1.40552 | − | 1.02117i | 0.411562 | − | 0.911382i | \(-0.364983\pi\) |
0.993955 | − | 0.109787i | \(-0.0350168\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.87868 | − | 8.85967i | 0.283645 | − | 0.872969i | −0.703157 | − | 0.711035i | \(-0.748227\pi\) |
0.986802 | − | 0.161934i | \(-0.0517733\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.76675 | − | 14.6705i | −0.460819 | − | 1.41825i | −0.864166 | − | 0.503207i | \(-0.832153\pi\) |
0.403347 | − | 0.915047i | \(-0.367847\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.6286i | 1.01803i | 0.860757 | + | 0.509016i | \(0.169991\pi\) | ||||
−0.860757 | + | 0.509016i | \(0.830009\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.995774 | − | 0.323547i | 0.0936746 | − | 0.0304367i | −0.261805 | − | 0.965121i | \(-0.584318\pi\) |
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.2559 | − | 11.0841i | −1.42262 | − | 1.03359i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.742521 | − | 1.02199i | −0.0680668 | − | 0.0936859i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.73176 | + | 8.69962i | 0.611978 | + | 0.790875i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15.9120 | − | 5.17013i | −1.42321 | − | 0.462430i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.3127 | + | 14.1942i | −0.915101 | + | 1.25953i | 0.0502930 | + | 0.998735i | \(0.483984\pi\) |
−0.965394 | + | 0.260794i | \(0.916016\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.8890 | −1.21349 | −0.606744 | − | 0.794897i | \(-0.707525\pi\) | ||||
−0.606744 | + | 0.794897i | \(0.707525\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.56764 | −0.135931 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.609963 | − | 0.839541i | 0.0521126 | − | 0.0717269i | −0.782165 | − | 0.623071i | \(-0.785885\pi\) |
0.834278 | + | 0.551344i | \(0.185885\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.8643 | + | 6.12938i | 1.60005 | + | 0.519887i | 0.967119 | − | 0.254324i | \(-0.0818528\pi\) |
0.632928 | + | 0.774210i | \(0.281853\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.538902 | + | 3.09852i | 0.0450652 | + | 0.259111i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.54073 | − | 7.62616i | −0.460133 | − | 0.633318i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.50125 | − | 4.72344i | −0.532603 | − | 0.386959i | 0.288727 | − | 0.957411i | \(-0.406768\pi\) |
−0.821331 | + | 0.570452i | \(0.806768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.58050 | − | 3.11289i | 0.779650 | − | 0.253324i | 0.107959 | − | 0.994155i | \(-0.465568\pi\) |
0.671691 | + | 0.740832i | \(0.265568\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 13.3380i | − | 1.07133i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.00062 | − | 15.3903i | −0.399093 | − | 1.22828i | −0.925728 | − | 0.378190i | \(-0.876547\pi\) |
0.526635 | − | 0.850091i | \(-0.323453\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.564633 | − | 1.73776i | 0.0444993 | − | 0.136955i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.45923 | − | 2.51328i | 0.270948 | − | 0.196855i | −0.444012 | − | 0.896021i | \(-0.646445\pi\) |
0.714959 | + | 0.699166i | \(0.246445\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.8478 | − | 10.7875i | 1.14896 | − | 0.834765i | 0.160614 | − | 0.987017i | \(-0.448653\pi\) |
0.988342 | + | 0.152252i | \(0.0486526\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.73935 | − | 11.5085i | 0.287642 | − | 0.885272i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.91046 | − | 5.87980i | −0.145250 | − | 0.447033i | 0.851793 | − | 0.523878i | \(-0.175515\pi\) |
−0.997043 | + | 0.0768452i | \(0.975515\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.46010i | − | 0.261559i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.77414 | − | 2.85089i | 0.655810 | − | 0.213086i | 0.0378357 | − | 0.999284i | \(-0.487954\pi\) |
0.617974 | + | 0.786198i | \(0.287954\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.38790 | + | 2.46145i | 0.251821 | + | 0.182958i | 0.706533 | − | 0.707680i | \(-0.250258\pi\) |
−0.454713 | + | 0.890638i | \(0.650258\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.0245 | + | 22.0558i | 1.17814 | + | 1.62157i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.32455 | + | 10.0706i | 0.389370 | + | 0.736438i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.1951 | − | 6.23688i | −1.38891 | − | 0.451285i | −0.483323 | − | 0.875442i | \(-0.660570\pi\) |
−0.905589 | + | 0.424157i | \(0.860570\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.71049 | − | 6.48343i | 0.339068 | − | 0.466687i | −0.605101 | − | 0.796149i | \(-0.706867\pi\) |
0.944169 | + | 0.329462i | \(0.106867\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.1710 | −1.50837 | −0.754187 | − | 0.656659i | \(-0.771969\pi\) | ||||
−0.754187 | + | 0.656659i | \(0.771969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5160 | 0.745457 | 0.372729 | − | 0.927940i | \(-0.378422\pi\) | ||||
0.372729 | + | 0.927940i | \(0.378422\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.536871 | − | 0.738940i | 0.0376810 | − | 0.0518634i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.81591 | + | 3.18938i | 0.685573 | + | 0.222756i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.9942 | + | 2.00007i | 0.968001 | + | 0.138347i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.17376 | + | 2.99193i | 0.149648 | + | 0.205973i | 0.877259 | − | 0.480017i | \(-0.159369\pi\) |
−0.727611 | + | 0.685990i | \(0.759369\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.79615 | − | 4.21115i | −0.395294 | − | 0.287198i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.22913 | − | 0.399369i | 0.0834390 | − | 0.0271110i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.25699i | 0.219089i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.53051 | + | 17.0212i | 0.370351 | + | 1.13982i | 0.946562 | + | 0.322521i | \(0.104530\pi\) |
−0.576212 | + | 0.817301i | \(0.695470\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.37022 | + | 16.5278i | −0.356434 | + | 1.09699i | 0.598740 | + | 0.800944i | \(0.295668\pi\) |
−0.955173 | + | 0.296047i | \(0.904332\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.45989 | + | 2.51375i | −0.228636 | + | 0.166114i | −0.696205 | − | 0.717843i | \(-0.745130\pi\) |
0.467570 | + | 0.883956i | \(0.345130\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.9171 | − | 13.7441i | 1.23930 | − | 0.900404i | 0.241748 | − | 0.970339i | \(-0.422279\pi\) |
0.997552 | + | 0.0699355i | \(0.0222793\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0241719 | − | 0.0743935i | 0.00157680 | − | 0.00485289i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.17902 | + | 19.0171i | 0.399687 | + | 1.23011i | 0.925251 | + | 0.379356i | \(0.123855\pi\) |
−0.525563 | + | 0.850754i | \(0.676145\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.32570i | 0.149811i | 0.997191 | + | 0.0749057i | \(0.0238656\pi\) | ||||
−0.997191 | + | 0.0749057i | \(0.976134\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.7815 | + | 8.05201i | −1.58323 | + | 0.514424i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.26987 | + | 2.37570i | 0.208057 | + | 0.151162i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.88681 | + | 2.59698i | 0.119095 | + | 0.163920i | 0.864402 | − | 0.502801i | \(-0.167697\pi\) |
−0.745307 | + | 0.666721i | \(0.767697\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.25758 | + | 14.7925i | −0.456280 | + | 0.929999i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.1597 | + | 5.57552i | 1.07039 | + | 0.347792i | 0.790641 | − | 0.612281i | \(-0.209748\pi\) |
0.279752 | + | 0.960072i | \(0.409748\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.55270 | + | 2.13710i | −0.0964798 | + | 0.132793i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.05966 | 0.127004 | 0.0635019 | − | 0.997982i | \(-0.479773\pi\) | ||||
0.0635019 | + | 0.997982i | \(0.479773\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.0484 | 1.29299 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.69280 | + | 2.32994i | −0.103212 | + | 0.142059i | −0.857499 | − | 0.514486i | \(-0.827983\pi\) |
0.754287 | + | 0.656545i | \(0.227983\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.67272 | − | 3.14286i | −0.587576 | − | 0.190915i | 0.000115761 | − | 1.00000i | \(-0.499963\pi\) |
−0.587692 | + | 0.809085i | \(0.699963\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.41457 | + | 30.8882i | −0.266208 | + | 1.86263i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.29714 | + | 5.91450i | 0.258190 | + | 0.355368i | 0.918358 | − | 0.395750i | \(-0.129515\pi\) |
−0.660169 | + | 0.751117i | \(0.729515\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.86513 | + | 1.35510i | 0.111264 | + | 0.0808384i | 0.642026 | − | 0.766683i | \(-0.278094\pi\) |
−0.530762 | + | 0.847521i | \(0.678094\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.2370 | + | 7.55016i | −1.38130 | + | 0.448810i | −0.903095 | − | 0.429441i | \(-0.858711\pi\) |
−0.478200 | + | 0.878251i | \(0.658711\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.00006i | 0.0590318i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.60777 | − | 4.94822i | −0.0945749 | − | 0.291072i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.29456 | + | 10.1396i | −0.192470 | + | 0.592362i | 0.807527 | + | 0.589831i | \(0.200806\pi\) |
−0.999997 | + | 0.00253112i | \(0.999194\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.3418 | − | 14.7792i | 1.18434 | − | 0.860476i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.81126 | + | 2.76904i | −0.220411 | + | 0.160138i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.214520 | − | 0.660224i | 0.0123647 | − | 0.0380547i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.4392 | + | 35.2063i | 0.655009 | + | 2.01591i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.56848i | − | 0.260737i | −0.991466 | − | 0.130369i | \(-0.958384\pi\) | ||
0.991466 | − | 0.130369i | \(-0.0416160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.92302 | + | 2.89926i | −0.505978 | + | 0.164402i | −0.550872 | − | 0.834590i | \(-0.685705\pi\) |
0.0448944 | + | 0.998992i | \(0.485705\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.05804 | + | 2.94834i | 0.229374 | + | 0.166650i | 0.696536 | − | 0.717522i | \(-0.254724\pi\) |
−0.467162 | + | 0.884172i | \(0.654724\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.86310 | − | 9.44624i | −0.385470 | − | 0.530554i | 0.571553 | − | 0.820565i | \(-0.306341\pi\) |
−0.957023 | + | 0.290011i | \(0.906341\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.73541 | + | 5.91153i | −0.321121 | + | 0.330982i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.9232 | + | 4.52391i | 0.774706 | + | 0.251717i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.24366 | + | 7.21728i | −0.290866 | + | 0.400343i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.00757934 | 0.000417863 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.0516 | 1.59682 | 0.798411 | − | 0.602113i | \(-0.205674\pi\) | ||||
0.798411 | + | 0.602113i | \(0.205674\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.95850 | + | 13.7067i | −0.544091 | + | 0.748877i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.4668 | + | 8.92451i | 1.49621 | + | 0.486149i | 0.938911 | − | 0.344161i | \(-0.111837\pi\) |
0.557302 | + | 0.830310i | \(0.311837\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.4820 | + | 1.99697i | −0.621783 | + | 0.108142i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.99731 | − | 4.12544i | −0.161840 | − | 0.222753i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.9141 | + | 13.0153i | 0.961678 | + | 0.698700i | 0.953540 | − | 0.301267i | \(-0.0974096\pi\) |
0.00813801 | + | 0.999967i | \(0.497410\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.8959 | + | 4.83997i | −0.797359 | + | 0.259078i | −0.679235 | − | 0.733921i | \(-0.737688\pi\) |
−0.118125 | + | 0.992999i | \(0.537688\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 11.1636i | − | 0.594180i | −0.954850 | − | 0.297090i | \(-0.903984\pi\) | ||
0.954850 | − | 0.297090i | \(-0.0960161\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.1127 | − | 37.2790i | −0.642874 | − | 1.97856i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.11867 | − | 15.7536i | 0.270153 | − | 0.831445i | −0.720308 | − | 0.693654i | \(-0.756000\pi\) |
0.990461 | − | 0.137791i | \(-0.0440002\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.673787 | + | 0.489535i | −0.0354625 | + | 0.0257650i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.4990 | + | 9.80759i | −0.706569 | + | 0.513353i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.03154 | + | 9.33012i | −0.158245 | + | 0.487028i | −0.998475 | − | 0.0552016i | \(-0.982420\pi\) |
0.840230 | + | 0.542230i | \(0.182420\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.630238 | + | 1.93967i | 0.0327203 | + | 0.100703i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 12.6350i | − | 0.654216i | −0.944987 | − | 0.327108i | \(-0.893926\pi\) | ||
0.944987 | − | 0.327108i | \(-0.106074\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.23967 | + | 0.727714i | −0.115349 | + | 0.0374792i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.3981 | + | 20.6325i | 1.45871 | + | 1.05982i | 0.983695 | + | 0.179843i | \(0.0575589\pi\) |
0.475019 | + | 0.879975i | \(0.342441\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.2760 | + | 18.2729i | 0.678374 | + | 0.933701i | 0.999913 | − | 0.0131951i | \(-0.00420024\pi\) |
−0.321539 | + | 0.946896i | \(0.604200\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.56169 | + | 0.793379i | −0.232485 | + | 0.0404344i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.99867 | − | 2.27401i | −0.354847 | − | 0.115297i | 0.126169 | − | 0.992009i | \(-0.459732\pi\) |
−0.481015 | + | 0.876712i | \(0.659732\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.0297 | + | 13.8047i | −0.507225 | + | 0.698135i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −41.5146 | −2.08883 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.7327 | 0.839790 | 0.419895 | − | 0.907573i | \(-0.362067\pi\) | ||||
0.419895 | + | 0.907573i | \(0.362067\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.98209 | − | 4.10449i | 0.148918 | − | 0.204968i | −0.728040 | − | 0.685534i | \(-0.759569\pi\) |
0.876959 | + | 0.480566i | \(0.159569\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.16903 | − | 1.02968i | −0.157860 | − | 0.0512920i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.5875 | − | 17.0968i | 0.822211 | − | 0.847459i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0135 | + | 26.1698i | 0.940156 | + | 1.29401i | 0.955764 | + | 0.294136i | \(0.0950319\pi\) |
−0.0156071 | + | 0.999878i | \(0.504968\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.97102 | + | 1.43203i | 0.0969877 | + | 0.0704657i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.1513 | − | 10.7715i | 1.62734 | − | 0.528753i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 27.9075i | − | 1.36337i | −0.731645 | − | 0.681686i | \(-0.761247\pi\) | ||
0.731645 | − | 0.681686i | \(-0.238753\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.25960 | + | 25.4204i | 0.402549 | + | 1.23892i | 0.922925 | + | 0.384980i | \(0.125792\pi\) |
−0.520376 | + | 0.853937i | \(0.674208\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.98523 | + | 30.7314i | −0.484355 | + | 1.49069i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.90185 | + | 2.10832i | −0.140430 | + | 0.102029i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.579760 | + | 0.421220i | −0.0279260 | + | 0.0202895i | −0.601661 | − | 0.798752i | \(-0.705494\pi\) |
0.573735 | + | 0.819041i | \(0.305494\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.53281 | − | 10.8729i | 0.169776 | − | 0.522517i | −0.829580 | − | 0.558387i | \(-0.811420\pi\) |
0.999356 | + | 0.0358703i | \(0.0114203\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.54346 | + | 20.1387i | 0.313016 | + | 0.963365i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.57525i | − | 0.409274i | −0.978838 | − | 0.204637i | \(-0.934399\pi\) | ||
0.978838 | − | 0.204637i | \(-0.0656015\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.2928 | − | 4.31910i | 0.631561 | − | 0.205207i | 0.0242947 | − | 0.999705i | \(-0.492266\pi\) |
0.607267 | + | 0.794498i | \(0.292266\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.36104 | − | 6.80119i | −0.443756 | − | 0.322407i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.7008 | − | 17.4811i | −0.599388 | − | 0.824986i | 0.396264 | − | 0.918136i | \(-0.370306\pi\) |
−0.995652 | + | 0.0931501i | \(0.970306\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.27593 | − | 8.92753i | 0.0600811 | − | 0.420381i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.25903 | − | 0.409083i | −0.0590241 | − | 0.0191781i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.76327 | − | 7.93246i | 0.269594 | − | 0.371065i | −0.652658 | − | 0.757652i | \(-0.726346\pi\) |
0.922253 | + | 0.386587i | \(0.126346\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.3585 | 0.575595 | 0.287797 | − | 0.957691i | \(-0.407077\pi\) | ||||
0.287797 | + | 0.957691i | \(0.407077\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.8717 | 1.57415 | 0.787076 | − | 0.616856i | \(-0.211594\pi\) | ||||
0.787076 | + | 0.616856i | \(0.211594\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.24994 | − | 12.7315i | 0.428036 | − | 0.589142i | −0.539465 | − | 0.842008i | \(-0.681373\pi\) |
0.967501 | + | 0.252867i | \(0.0813734\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.56129 | − | 0.507295i | −0.0720939 | − | 0.0234247i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.75736 | + | 5.62011i | −0.126783 | + | 0.258413i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.5695 | + | 32.4406i | 1.08144 | + | 1.48848i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.0877 | + | 7.32913i | 0.460918 | + | 0.334877i | 0.793891 | − | 0.608060i | \(-0.208052\pi\) |
−0.332973 | + | 0.942936i | \(0.608052\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.47741 | − | 2.10464i | 0.295344 | − | 0.0959632i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 57.2660i | − | 2.60032i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.14955 | + | 6.61563i | 0.0974054 | + | 0.299783i | 0.987873 | − | 0.155263i | \(-0.0496227\pi\) |
−0.890468 | + | 0.455046i | \(0.849623\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.0932984 | − | 0.287143i | 0.00421050 | − | 0.0129586i | −0.948929 | − | 0.315489i | \(-0.897831\pi\) |
0.953140 | + | 0.302531i | \(0.0978314\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.90074 | + | 5.01368i | −0.310794 | + | 0.225805i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.07269 | − | 2.23244i | 0.137829 | − | 0.100139i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.04468 | + | 6.29287i | −0.0915323 | + | 0.281707i | −0.986334 | − | 0.164755i | \(-0.947317\pi\) |
0.894802 | + | 0.446463i | \(0.147317\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.19188 | − | 9.82361i | −0.142319 | − | 0.438013i | 0.854337 | − | 0.519719i | \(-0.173963\pi\) |
−0.996657 | + | 0.0817056i | \(0.973963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 66.2732i | − | 2.94912i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.3302 | + | 6.28078i | −0.856798 | + | 0.278390i | −0.704291 | − | 0.709912i | \(-0.748735\pi\) |
−0.152507 | + | 0.988302i | \(0.548735\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.30799 | − | 0.950310i | −0.0578621 | − | 0.0420392i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.7840 | − | 28.6067i | −0.915851 | − | 1.26056i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0676605 | − | 0.00967009i | −0.00297571 | − | 0.000425290i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.4110 | − | 3.70764i | −0.499923 | − | 0.162435i | 0.0481915 | − | 0.998838i | \(-0.484654\pi\) |
−0.548115 | + | 0.836403i | \(0.684654\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.2395 | − | 30.6101i | 0.972466 | − | 1.33848i | 0.0316743 | − | 0.999498i | \(-0.489916\pi\) |
0.940791 | − | 0.338986i | \(-0.110084\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.0692 | −0.525743 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.68106 | −0.0730898 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.51556 | − | 2.08599i | 0.0656462 | − | 0.0903542i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −55.6858 | − | 18.0934i | −2.40751 | − | 0.782247i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.6419 | + | 20.1276i | 0.458378 | + | 0.866957i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.6491 | + | 29.7975i | 0.930769 | + | 1.28109i | 0.959559 | + | 0.281508i | \(0.0908345\pi\) |
−0.0287904 | + | 0.999585i | \(0.509166\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 32.6386 | + | 23.7133i | 1.39808 | + | 1.01577i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.8795 | + | 11.3330i | −1.49134 | + | 0.484565i | −0.937478 | − | 0.348044i | \(-0.886846\pi\) |
−0.553860 | + | 0.832610i | \(0.686846\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.5851i | 0.450939i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.24304 | − | 3.82570i | −0.0528596 | − | 0.162685i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.30765 | − | 7.10223i | 0.0977784 | − | 0.300931i | −0.890189 | − | 0.455591i | \(-0.849428\pi\) |
0.987968 | + | 0.154660i | \(0.0494281\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.44800 | + | 1.05204i | −0.0612441 | + | 0.0444964i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.16715 | − | 2.30107i | 0.133479 | − | 0.0969784i | −0.519042 | − | 0.854749i | \(-0.673711\pi\) |
0.652521 | + | 0.757770i | \(0.273711\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.22811 | − | 3.77972i | 0.0516668 | − | 0.159014i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.6410 | − | 35.8274i | −0.488017 | − | 1.50196i | −0.827563 | − | 0.561373i | \(-0.810273\pi\) |
0.339546 | − | 0.940590i | \(-0.389727\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.3411i | 1.26974i | 0.772621 | + | 0.634868i | \(0.218946\pi\) | ||||
−0.772621 | + | 0.634868i | \(0.781054\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −44.4504 | + | 14.4428i | −1.85371 | + | 0.602307i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.68563 | + | 1.95122i | 0.111804 | + | 0.0812305i | 0.642282 | − | 0.766468i | \(-0.277988\pi\) |
−0.530478 | + | 0.847699i | \(0.677988\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.98526 | + | 2.73247i | 0.0823623 | + | 0.113362i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.15138 | − | 18.1195i | −0.130517 | − | 0.750432i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.9053 | − | 12.6411i | −1.60579 | − | 0.521754i | −0.637263 | − | 0.770647i | \(-0.719933\pi\) |
−0.968531 | + | 0.248893i | \(0.919933\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.80345 | + | 12.1169i | −0.362740 | + | 0.499269i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.62924 | −0.190100 | −0.0950500 | − | 0.995472i | \(-0.530301\pi\) | ||||
−0.0950500 | + | 0.995472i | \(0.530301\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.79500 | −0.196576 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.9738 | + | 24.7388i | −0.734390 | + | 1.01080i | 0.264532 | + | 0.964377i | \(0.414782\pi\) |
−0.998922 | + | 0.0464237i | \(0.985218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.7015 | − | 9.65061i | −1.21155 | − | 0.393657i | −0.367552 | − | 0.930003i | \(-0.619804\pi\) |
−0.843998 | + | 0.536346i | \(0.819804\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 41.7343 | − | 1.26245i | 1.69674 | − | 0.0513259i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.0842 | + | 24.8908i | 0.734016 | + | 1.01029i | 0.998941 | + | 0.0460167i | \(0.0146527\pi\) |
−0.264925 | + | 0.964269i | \(0.585347\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0158094 | − | 0.0114862i | −0.000639581 | − | 0.000464683i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.2244 | − | 7.87097i | 0.978413 | − | 0.317906i | 0.224205 | − | 0.974542i | \(-0.428021\pi\) |
0.754207 | + | 0.656636i | \(0.228021\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.20930i | 0.169460i | 0.996404 | + | 0.0847300i | \(0.0270028\pi\) | ||||
−0.996404 | + | 0.0847300i | \(0.972997\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.8981 | − | 36.6187i | −0.478227 | − | 1.47183i | −0.841556 | − | 0.540170i | \(-0.818360\pi\) |
0.363329 | − | 0.931661i | \(-0.381640\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.346459 | − | 1.06629i | 0.0138806 | − | 0.0427200i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.3225 | + | 9.67935i | −0.532899 | + | 0.387174i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.9578 | − | 14.5002i | 0.795769 | − | 0.578160i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.65655 | − | 11.2537i | 0.145565 | − | 0.448003i | −0.851518 | − | 0.524325i | \(-0.824318\pi\) |
0.997083 | + | 0.0763220i | \(0.0243177\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.5794 | + | 63.3370i | 0.816670 | + | 2.51345i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.50957i | 0.257918i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.1810 | + | 11.1061i | −1.35007 | + | 0.438664i | −0.892716 | − | 0.450620i | \(-0.851203\pi\) |
−0.457354 | + | 0.889285i | \(0.651203\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.63357 | + | 1.91340i | 0.103858 | + | 0.0754571i | 0.638502 | − | 0.769620i | \(-0.279554\pi\) |
−0.534644 | + | 0.845077i | \(0.679554\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.14454 | + | 9.83361i | 0.280881 | + | 0.386599i | 0.926025 | − | 0.377461i | \(-0.123203\pi\) |
−0.645145 | + | 0.764060i | \(0.723203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.7682 | − | 15.2984i | −0.618956 | − | 0.600516i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.2713 | + | 7.88623i | 0.949811 | + | 0.308612i | 0.742639 | − | 0.669692i | \(-0.233574\pi\) |
0.207172 | + | 0.978305i | \(0.433574\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.9877 | + | 42.6508i | −1.21079 | + | 1.66651i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.9441 | 1.08855 | 0.544273 | − | 0.838908i | \(-0.316806\pi\) | ||||
0.544273 | + | 0.838908i | \(0.316806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.3798 | −1.06495 | −0.532475 | − | 0.846446i | \(-0.678738\pi\) | ||||
−0.532475 | + | 0.846446i | \(0.678738\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.49754 | + | 4.81395i | −0.135629 | + | 0.186677i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.7338 | − | 3.81254i | −0.454334 | − | 0.147622i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.5946 | − | 15.1186i | 1.10388 | − | 0.583646i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.96377 | − | 10.9612i | −0.306981 | − | 0.422523i | 0.627456 | − | 0.778652i | \(-0.284096\pi\) |
−0.934437 | + | 0.356129i | \(0.884096\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.6885 | + | 21.5700i | 1.14102 | + | 0.829001i | 0.987261 | − | 0.159107i | \(-0.0508616\pi\) |
0.153760 | + | 0.988108i | \(0.450862\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.27723 | − | 1.71468i | 0.202522 | − | 0.0658033i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 30.8347i | − | 1.17986i | −0.807455 | − | 0.589929i | \(-0.799156\pi\) | ||
0.807455 | − | 0.589929i | \(-0.200844\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.21721 | − | 3.74619i | −0.0465072 | − | 0.143134i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.62492 | − | 5.00098i | 0.0619045 | − | 0.190522i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.6062 | + | 28.0491i | −1.46865 | + | 1.06704i | −0.487649 | + | 0.873040i | \(0.662145\pi\) |
−0.981002 | + | 0.193997i | \(0.937855\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 60.9102 | − | 44.2539i | 2.31046 | − | 1.67864i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.88600 | − | 8.88220i | 0.109315 | − | 0.336437i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.34678 | + | 13.3780i | 0.164176 | + | 0.505281i | 0.998975 | − | 0.0452742i | \(-0.0144162\pi\) |
−0.834799 | + | 0.550555i | \(0.814416\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 30.6133i | − | 1.15460i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.10727 | − | 1.98437i | 0.229688 | − | 0.0746300i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.34115 | + | 5.33366i | 0.275703 | + | 0.200310i | 0.717041 | − | 0.697031i | \(-0.245496\pi\) |
−0.441338 | + | 0.897341i | \(0.645496\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.2610 | − | 14.1231i | −0.384279 | − | 0.528915i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.7174 | + | 5.25820i | 0.400807 | + | 0.196645i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.2802 | − | 10.4885i | −1.20385 | − | 0.391155i | −0.362674 | − | 0.931916i | \(-0.618136\pi\) |
−0.841176 | + | 0.540761i | \(0.818136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.01387 | − | 2.77186i | 0.0750005 | − | 0.103229i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.3635 | −0.867697 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.8992 | −1.14599 | −0.572993 | − | 0.819560i | \(-0.694218\pi\) | ||||
−0.572993 | + | 0.819560i | \(0.694218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.81058 | + | 5.24481i | −0.140939 | + | 0.193986i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.5648 | − | 12.8554i | −1.46136 | − | 0.474825i | −0.532876 | − | 0.846194i | \(-0.678889\pi\) |
−0.928485 | + | 0.371369i | \(0.878889\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.2904 | + | 6.52058i | 0.489558 | + | 0.240189i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.44687 | + | 11.6261i | 0.310723 | + | 0.427674i | 0.935607 | − | 0.353044i | \(-0.114854\pi\) |
−0.624883 | + | 0.780718i | \(0.714854\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.8649 | + | 7.89384i | 0.398596 | + | 0.289597i | 0.768969 | − | 0.639286i | \(-0.220770\pi\) |
−0.370373 | + | 0.928883i | \(0.620770\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.0098 | + | 9.42585i | −1.06284 | + | 0.345336i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 5.67337i | − | 0.207301i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.2373 | + | 34.5847i | 0.410054 | + | 1.26202i | 0.916601 | + | 0.399803i | \(0.130922\pi\) |
−0.506547 | + | 0.862212i | \(0.669078\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.8158 | − | 36.3653i | 0.430021 | − | 1.32347i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.2811 | + | 23.4536i | −1.17328 | + | 0.852435i | −0.991397 | − | 0.130887i | \(-0.958218\pi\) |
−0.181878 | + | 0.983321i | \(0.558218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.75887 | + | 2.00443i | −0.100009 | + | 0.0726607i | −0.636666 | − | 0.771140i | \(-0.719687\pi\) |
0.536657 | + | 0.843801i | \(0.319687\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.20798 | + | 3.71777i | −0.0437317 | + | 0.134592i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.94108 | − | 5.97403i | −0.0700884 | − | 0.215710i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.4154i | 0.772260i | 0.922444 | + | 0.386130i | \(0.126188\pi\) | ||||
−0.922444 | + | 0.386130i | \(0.873812\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.1302 | − | 11.0896i | 1.22758 | − | 0.398864i | 0.377741 | − | 0.925911i | \(-0.376701\pi\) |
0.849836 | + | 0.527048i | \(0.176701\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.7446 | − | 19.4311i | −0.960694 | − | 0.697985i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.81221 | − | 9.37620i | −0.244073 | − | 0.335937i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.2780 | + | 16.0086i | −1.08343 | + | 0.572833i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −58.4180 | − | 18.9811i | −2.08503 | − | 0.677466i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.2510 | − | 38.8842i | 1.00704 | − | 1.38607i | 0.0861340 | − | 0.996284i | \(-0.472549\pi\) |
0.920905 | − | 0.389787i | \(-0.127451\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.385085 | 0.0136920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.24793 | 0.328404 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.55363 | + | 4.89115i | −0.125876 | + | 0.173253i | −0.867304 | − | 0.497779i | \(-0.834149\pi\) |
0.741428 | + | 0.671033i | \(0.234149\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.0673169 | − | 0.0218726i | −0.00238150 | − | 0.000773797i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.4639 | + | 10.1522i | 0.369264 | + | 0.358263i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.07663 | − | 5.61099i | −0.143682 | − | 0.197762i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.01444 | + | 4.36974i | 0.211456 | + | 0.153632i | 0.688472 | − | 0.725263i | \(-0.258282\pi\) |
−0.477016 | + | 0.878895i | \(0.658282\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.7357 | + | 9.01188i | −0.973933 | + | 0.316450i | −0.752402 | − | 0.658704i | \(-0.771105\pi\) |
−0.221530 | + | 0.975154i | \(0.571105\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 16.2301i | − | 0.568514i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.48605 | + | 7.65127i | 0.0869758 | + | 0.267684i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.331389 | − | 1.01991i | 0.0115656 | − | 0.0355952i | −0.945107 | − | 0.326760i | \(-0.894043\pi\) |
0.956673 | + | 0.291165i | \(0.0940430\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.23762 | + | 5.25844i | −0.252288 | + | 0.183298i | −0.706740 | − | 0.707473i | \(-0.749835\pi\) |
0.454452 | + | 0.890771i | \(0.349835\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.5608 | + | 20.7507i | −0.993157 | + | 0.721571i | −0.960610 | − | 0.277899i | \(-0.910362\pi\) |
−0.0325471 | + | 0.999470i | \(0.510362\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.36614 | − | 25.7483i | 0.290568 | − | 0.894276i | −0.694106 | − | 0.719873i | \(-0.744200\pi\) |
0.984674 | − | 0.174404i | \(-0.0557998\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.28608 | + | 22.4243i | 0.252448 | + | 0.776954i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 69.6630i | − | 2.41079i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.4106 | + | 11.5056i | −1.22251 | + | 0.397218i | −0.847996 | − | 0.530003i | \(-0.822191\pi\) |
−0.374515 | + | 0.927221i | \(0.622191\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.4720 | + | 13.4207i | 0.636965 | + | 0.462782i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26.9980 | − | 37.1595i | −0.928759 | − | 1.27833i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.36596 | + | 3.80813i | 0.0469349 | + | 0.130849i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.9355 | + | 11.0263i | 1.16329 | + | 0.377977i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.6424 | − | 28.4118i | 0.706782 | − | 0.972802i | −0.293078 | − | 0.956089i | \(-0.594680\pi\) |
0.999860 | − | 0.0167139i | \(-0.00532045\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.9637 | −1.02354 | −0.511770 | − | 0.859122i | \(-0.671010\pi\) | ||||
−0.511770 | + | 0.859122i | \(0.671010\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.2684 | −0.589189 | −0.294595 | − | 0.955622i | \(-0.595185\pi\) | ||||
−0.294595 | + | 0.955622i | \(0.595185\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.4637 | − | 28.1659i | 0.696593 | − | 0.958778i | −0.303389 | − | 0.952867i | \(-0.598118\pi\) |
0.999983 | − | 0.00591175i | \(-0.00188178\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.3183 | − | 7.25166i | −0.758845 | − | 0.246564i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.21560 | + | 35.7378i | 0.210850 | + | 1.21232i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.48785 | + | 3.42423i | 0.0842976 | + | 0.116026i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.97827 | − | 3.61692i | −0.168296 | − | 0.122274i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.88584 | + | 0.612748i | −0.0636804 | + | 0.0206910i | −0.340684 | − | 0.940178i | \(-0.610659\pi\) |
0.277004 | + | 0.960869i | \(0.410659\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 48.9571i | − | 1.64941i | −0.565566 | − | 0.824703i | \(-0.691342\pi\) | ||
0.565566 | − | 0.824703i | \(-0.308658\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.7400 | − | 33.0542i | −0.361429 | − | 1.11236i | −0.952187 | − | 0.305515i | \(-0.901171\pi\) |
0.590758 | − | 0.806848i | \(-0.298829\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.47860 | − | 13.7837i | 0.150377 | − | 0.462812i | −0.847287 | − | 0.531136i | \(-0.821765\pi\) |
0.997663 | + | 0.0683244i | \(0.0217653\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.22049 | + | 3.79291i | −0.175090 | + | 0.127210i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0710609 | + | 0.0516288i | −0.00237796 | + | 0.00172769i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.8213 | − | 33.3045i | 0.361716 | − | 1.11325i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.69664 | − | 8.29941i | −0.0899380 | − | 0.276801i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 19.0462i | − | 0.634521i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.1174 | − | 4.91195i | 0.502520 | − | 0.163279i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.4206 | + | 13.3834i | 0.611647 | + | 0.444387i | 0.849994 | − | 0.526793i | \(-0.176606\pi\) |
−0.238347 | + | 0.971180i | \(0.576606\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.3395 | − | 18.3602i | −0.441956 | − | 0.608300i | 0.528689 | − | 0.848815i | \(-0.322684\pi\) |
−0.970645 | + | 0.240515i | \(0.922684\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.2361 | − | 26.9256i | −0.471146 | − | 0.891106i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.85824 | − | 1.57854i | −0.160433 | − | 0.0521280i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.737746 | − | 1.01542i | 0.0243360 | − | 0.0334956i | −0.796676 | − | 0.604407i | \(-0.793410\pi\) |
0.821012 | + | 0.570911i | \(0.193410\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.79237 | −0.322320 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 67.5699 | 2.22169 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.68995 | − | 2.32602i | 0.0554456 | − | 0.0763143i | −0.780394 | − | 0.625288i | \(-0.784981\pi\) |
0.835839 | + | 0.548974i | \(0.184981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.8274 | + | 9.04168i | 0.912007 | + | 0.296329i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 42.8048 | + | 6.11769i | 1.39987 | + | 0.200070i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.1303 | + | 24.9542i | 0.592291 | + | 0.815219i | 0.994975 | − | 0.100120i | \(-0.0319227\pi\) |
−0.402684 | + | 0.915339i | \(0.631923\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.29167 | − | 3.84462i | −0.172503 | − | 0.125331i | 0.498184 | − | 0.867072i | \(-0.334001\pi\) |
−0.670687 | + | 0.741741i | \(0.734001\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.8474 | − | 4.17436i | 0.418368 | − | 0.135936i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 33.2579i | − | 1.08074i | −0.841429 | − | 0.540368i | \(-0.818285\pi\) | ||
0.841429 | − | 0.540368i | \(-0.181715\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.28812 | + | 3.96442i | 0.0418141 | + | 0.128691i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.9820 | − | 52.2651i | 0.550100 | − | 1.69303i | −0.158445 | − | 0.987368i | \(-0.550648\pi\) |
0.708545 | − | 0.705666i | \(-0.249352\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −61.9785 | + | 45.0300i | −2.00558 | + | 1.45714i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.308776 | − | 0.224339i | 0.00997090 | − | 0.00724428i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.76392 | + | 17.7395i | −0.185933 | + | 0.572242i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.40000 | − | 28.9302i | −0.302597 | − | 0.931297i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 34.0395i | − | 1.09464i | −0.836925 | − | 0.547318i | \(-0.815649\pi\) | ||
0.836925 | − | 0.547318i | \(-0.184351\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.2008 | + | 11.7624i | −1.16174 | + | 0.377472i | −0.825554 | − | 0.564323i | \(-0.809137\pi\) |
−0.336186 | + | 0.941796i | \(0.609137\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.90192 | + | 4.28799i | 0.189207 | + | 0.137467i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.8682 | − | 25.9699i | −0.603648 | − | 0.830850i | 0.392388 | − | 0.919800i | \(-0.371649\pi\) |
−0.996036 | + | 0.0889499i | \(0.971649\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.45325 | + | 9.07671i | −0.142327 | + | 0.290093i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.3816 | − | 6.62238i | −0.650071 | − | 0.211221i | −0.0346258 | − | 0.999400i | \(-0.511024\pi\) |
−0.615446 | + | 0.788179i | \(0.711024\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −47.2345 | + | 65.0128i | −1.50502 | + | 2.07148i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.37704 | −0.298172 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.3068 | 0.930962 | 0.465481 | − | 0.885058i | \(-0.345881\pi\) | ||||
0.465481 | + | 0.885058i | \(0.345881\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.4621 | − | 32.2928i | 0.743798 | − | 1.02375i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.1587 | − | 10.1241i | −0.986807 | − | 0.320633i | −0.229225 | − | 0.973373i | \(-0.573619\pi\) |
−0.757582 | + | 0.652740i | \(0.773619\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1584.2.cd.c.305.4 | 16 | ||
3.2 | odd | 2 | inner | 1584.2.cd.c.305.1 | 16 | ||
4.3 | odd | 2 | 99.2.j.a.8.1 | ✓ | 16 | ||
11.7 | odd | 10 | inner | 1584.2.cd.c.161.1 | 16 | ||
12.11 | even | 2 | 99.2.j.a.8.4 | yes | 16 | ||
33.29 | even | 10 | inner | 1584.2.cd.c.161.4 | 16 | ||
36.7 | odd | 6 | 891.2.u.c.701.4 | 32 | |||
36.11 | even | 6 | 891.2.u.c.701.1 | 32 | |||
36.23 | even | 6 | 891.2.u.c.107.4 | 32 | |||
36.31 | odd | 6 | 891.2.u.c.107.1 | 32 | |||
44.7 | even | 10 | 99.2.j.a.62.4 | yes | 16 | ||
44.31 | odd | 10 | 1089.2.d.g.1088.16 | 16 | |||
44.35 | even | 10 | 1089.2.d.g.1088.2 | 16 | |||
132.35 | odd | 10 | 1089.2.d.g.1088.15 | 16 | |||
132.95 | odd | 10 | 99.2.j.a.62.1 | yes | 16 | ||
132.119 | even | 10 | 1089.2.d.g.1088.1 | 16 | |||
396.7 | even | 30 | 891.2.u.c.458.4 | 32 | |||
396.95 | odd | 30 | 891.2.u.c.755.4 | 32 | |||
396.139 | even | 30 | 891.2.u.c.755.1 | 32 | |||
396.227 | odd | 30 | 891.2.u.c.458.1 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.j.a.8.1 | ✓ | 16 | 4.3 | odd | 2 | ||
99.2.j.a.8.4 | yes | 16 | 12.11 | even | 2 | ||
99.2.j.a.62.1 | yes | 16 | 132.95 | odd | 10 | ||
99.2.j.a.62.4 | yes | 16 | 44.7 | even | 10 | ||
891.2.u.c.107.1 | 32 | 36.31 | odd | 6 | |||
891.2.u.c.107.4 | 32 | 36.23 | even | 6 | |||
891.2.u.c.458.1 | 32 | 396.227 | odd | 30 | |||
891.2.u.c.458.4 | 32 | 396.7 | even | 30 | |||
891.2.u.c.701.1 | 32 | 36.11 | even | 6 | |||
891.2.u.c.701.4 | 32 | 36.7 | odd | 6 | |||
891.2.u.c.755.1 | 32 | 396.139 | even | 30 | |||
891.2.u.c.755.4 | 32 | 396.95 | odd | 30 | |||
1089.2.d.g.1088.1 | 16 | 132.119 | even | 10 | |||
1089.2.d.g.1088.2 | 16 | 44.35 | even | 10 | |||
1089.2.d.g.1088.15 | 16 | 132.35 | odd | 10 | |||
1089.2.d.g.1088.16 | 16 | 44.31 | odd | 10 | |||
1584.2.cd.c.161.1 | 16 | 11.7 | odd | 10 | inner | ||
1584.2.cd.c.161.4 | 16 | 33.29 | even | 10 | inner | ||
1584.2.cd.c.305.1 | 16 | 3.2 | odd | 2 | inner | ||
1584.2.cd.c.305.4 | 16 | 1.1 | even | 1 | trivial |