Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2790,2,Mod(559,2790)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2790, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2790.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2790.d (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: | \(22.2782621639\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 930) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 559.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2790.559 |
Dual form | 2790.2.d.i.559.4 |
$q$-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 \(\left(\mathbb{Z}/2790\mathbb{Z}\right)^\times\).
\(n\) | \(1117\) | \(1801\) | \(2171\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | −2.00000 | − | 1.00000i | −0.894427 | − | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.828427i | − | 0.313116i | −0.987669 | − | 0.156558i | \(-0.949960\pi\) | ||
0.987669 | − | 0.156558i | \(-0.0500398\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | + | 2.00000i | −0.316228 | + | 0.632456i | ||||
\(11\) | 0.828427 | 0.249780 | 0.124890 | − | 0.992171i | \(-0.460142\pi\) | ||||
0.124890 | + | 0.992171i | \(0.460142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.82843i | 1.33916i | 0.742738 | + | 0.669582i | \(0.233527\pi\) | ||||
−0.742738 | + | 0.669582i | \(0.766473\pi\) | |||||||
\(14\) | −0.828427 | −0.221406 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.828427i | 0.200923i | 0.994941 | + | 0.100462i | \(0.0320319\pi\) | ||||
−0.994941 | + | 0.100462i | \(0.967968\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 2.00000 | + | 1.00000i | 0.447214 | + | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 0.828427i | − | 0.176621i | ||||||
\(23\) | − | 8.48528i | − | 1.76930i | −0.466252 | − | 0.884652i | \(-0.654396\pi\) | ||
0.466252 | − | 0.884652i | \(-0.345604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | 4.82843 | 0.946932 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.828427i | 0.156558i | ||||||||
\(29\) | 9.65685 | 1.79323 | 0.896616 | − | 0.442808i | \(-0.146018\pi\) | ||||
0.896616 | + | 0.442808i | \(0.146018\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.828427 | 0.142074 | ||||||||
\(35\) | −0.828427 | + | 1.65685i | −0.140030 | + | 0.280059i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.4853i | 1.72377i | 0.507104 | + | 0.861885i | \(0.330716\pi\) | ||||
−0.507104 | + | 0.861885i | \(0.669284\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | − | 2.00000i | 0.158114 | − | 0.316228i | ||||
\(41\) | −7.65685 | −1.19580 | −0.597900 | − | 0.801571i | \(-0.703998\pi\) | ||||
−0.597900 | + | 0.801571i | \(0.703998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.65685i | − | 1.47266i | −0.676625 | − | 0.736328i | \(-0.736558\pi\) | ||
0.676625 | − | 0.736328i | \(-0.263442\pi\) | |||||||
\(44\) | −0.828427 | −0.124890 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.48528 | −1.25109 | ||||||||
\(47\) | − | 5.65685i | − | 0.825137i | −0.910927 | − | 0.412568i | \(-0.864632\pi\) | ||
0.910927 | − | 0.412568i | \(-0.135368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.31371 | 0.901958 | ||||||||
\(50\) | 4.00000 | − | 3.00000i | 0.565685 | − | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4.82843i | − | 0.669582i | ||||||
\(53\) | − | 0.343146i | − | 0.0471347i | −0.999722 | − | 0.0235673i | \(-0.992498\pi\) | ||
0.999722 | − | 0.0235673i | \(-0.00750241\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.65685 | − | 0.828427i | −0.223410 | − | 0.111705i | ||||
\(56\) | 0.828427 | 0.110703 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 9.65685i | − | 1.26801i | ||||||
\(59\) | 3.17157 | 0.412904 | 0.206452 | − | 0.978457i | \(-0.433808\pi\) | ||||
0.206452 | + | 0.978457i | \(0.433808\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.828427 | 0.106069 | 0.0530346 | − | 0.998593i | \(-0.483111\pi\) | ||||
0.0530346 | + | 0.998593i | \(0.483111\pi\) | |||||||
\(62\) | − | 1.00000i | − | 0.127000i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 4.82843 | − | 9.65685i | 0.598893 | − | 1.19779i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.17157i | − | 1.12049i | −0.828328 | − | 0.560243i | \(-0.810708\pi\) | ||
0.828328 | − | 0.560243i | \(-0.189292\pi\) | |||||||
\(68\) | − | 0.828427i | − | 0.100462i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.65685 | + | 0.828427i | 0.198032 | + | 0.0990160i | ||||
\(71\) | 2.82843 | 0.335673 | 0.167836 | − | 0.985815i | \(-0.446322\pi\) | ||||
0.167836 | + | 0.985815i | \(0.446322\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.6569i | − | 1.59841i | −0.601056 | − | 0.799207i | \(-0.705253\pi\) | ||
0.601056 | − | 0.799207i | \(-0.294747\pi\) | |||||||
\(74\) | 10.4853 | 1.21889 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.686292i | − | 0.0782102i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3137 | −1.27289 | −0.636446 | − | 0.771321i | \(-0.719596\pi\) | ||||
−0.636446 | + | 0.771321i | \(0.719596\pi\) | |||||||
\(80\) | −2.00000 | − | 1.00000i | −0.223607 | − | 0.111803i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.65685i | 0.845558i | ||||||||
\(83\) | 1.65685i | 0.181863i | 0.995857 | + | 0.0909317i | \(0.0289845\pi\) | ||||
−0.995857 | + | 0.0909317i | \(0.971016\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.828427 | − | 1.65685i | 0.0898555 | − | 0.179711i | ||||
\(86\) | −9.65685 | −1.04133 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.828427i | 0.0883106i | ||||||||
\(89\) | 4.82843 | 0.511812 | 0.255906 | − | 0.966702i | \(-0.417626\pi\) | ||||
0.255906 | + | 0.966702i | \(0.417626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 8.48528i | 0.884652i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.65685 | −0.583460 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.3137i | 1.14873i | 0.818598 | + | 0.574367i | \(0.194752\pi\) | ||||
−0.818598 | + | 0.574367i | \(0.805248\pi\) | |||||||
\(98\) | − | 6.31371i | − | 0.637781i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | − | 4.00000i | −0.300000 | − | 0.400000i | ||||
\(101\) | −11.3137 | −1.12576 | −0.562878 | − | 0.826540i | \(-0.690306\pi\) | ||||
−0.562878 | + | 0.826540i | \(0.690306\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.51472i | − | 0.149250i | −0.997212 | − | 0.0746248i | \(-0.976224\pi\) | ||
0.997212 | − | 0.0746248i | \(-0.0237759\pi\) | |||||||
\(104\) | −4.82843 | −0.473466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.343146 | −0.0333293 | ||||||||
\(107\) | 4.00000i | 0.386695i | 0.981130 | + | 0.193347i | \(0.0619344\pi\) | ||||
−0.981130 | + | 0.193347i | \(0.938066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.6569 | 1.11652 | 0.558262 | − | 0.829665i | \(-0.311468\pi\) | ||||
0.558262 | + | 0.829665i | \(0.311468\pi\) | |||||||
\(110\) | −0.828427 | + | 1.65685i | −0.0789874 | + | 0.157975i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 0.828427i | − | 0.0782790i | ||||||
\(113\) | − | 14.0000i | − | 1.31701i | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||
0.752577 | − | 0.658505i | \(-0.228811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.48528 | + | 16.9706i | −0.791257 | + | 1.58251i | ||||
\(116\) | −9.65685 | −0.896616 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 3.17157i | − | 0.291967i | ||||||
\(119\) | 0.686292 | 0.0629122 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | − | 0.828427i | − | 0.0750023i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.1421i | − | 1.43238i | −0.697904 | − | 0.716191i | \(-0.745884\pi\) | ||
0.697904 | − | 0.716191i | \(-0.254116\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.65685 | − | 4.82843i | −0.846962 | − | 0.423481i | ||||
\(131\) | −18.4853 | −1.61507 | −0.807533 | − | 0.589822i | \(-0.799198\pi\) | ||||
−0.807533 | + | 0.589822i | \(0.799198\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.17157 | −0.792303 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.828427 | −0.0710370 | ||||||||
\(137\) | − | 6.48528i | − | 0.554075i | −0.960859 | − | 0.277037i | \(-0.910647\pi\) | ||
0.960859 | − | 0.277037i | \(-0.0893526\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1421 | 1.19952 | 0.599760 | − | 0.800180i | \(-0.295263\pi\) | ||||
0.599760 | + | 0.800180i | \(0.295263\pi\) | |||||||
\(140\) | 0.828427 | − | 1.65685i | 0.0700149 | − | 0.140030i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 2.82843i | − | 0.237356i | ||||||
\(143\) | 4.00000i | 0.334497i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.3137 | − | 9.65685i | −1.60392 | − | 0.801958i | ||||
\(146\) | −13.6569 | −1.13025 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 10.4853i | − | 0.861885i | ||||||
\(149\) | −0.686292 | −0.0562232 | −0.0281116 | − | 0.999605i | \(-0.508949\pi\) | ||||
−0.0281116 | + | 0.999605i | \(0.508949\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.6569 | 1.76241 | 0.881205 | − | 0.472735i | \(-0.156733\pi\) | ||||
0.881205 | + | 0.472735i | \(0.156733\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.686292 | −0.0553029 | ||||||||
\(155\) | −2.00000 | − | 1.00000i | −0.160644 | − | 0.0803219i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.3137i | − | 1.38178i | −0.722958 | − | 0.690892i | \(-0.757218\pi\) | ||
0.722958 | − | 0.690892i | \(-0.242782\pi\) | |||||||
\(158\) | 11.3137i | 0.900070i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | + | 2.00000i | −0.0790569 | + | 0.158114i | ||||
\(161\) | −7.02944 | −0.553997 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14.8284i | − | 1.16145i | −0.814099 | − | 0.580726i | \(-0.802769\pi\) | ||
0.814099 | − | 0.580726i | \(-0.197231\pi\) | |||||||
\(164\) | 7.65685 | 0.597900 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.65685 | 0.128597 | ||||||||
\(167\) | − | 0.485281i | − | 0.0375522i | −0.999824 | − | 0.0187761i | \(-0.994023\pi\) | ||
0.999824 | − | 0.0187761i | \(-0.00597697\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.3137 | −0.793362 | ||||||||
\(170\) | −1.65685 | − | 0.828427i | −0.127075 | − | 0.0635375i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.65685i | 0.736328i | ||||||||
\(173\) | 1.31371i | 0.0998794i | 0.998752 | + | 0.0499397i | \(0.0159029\pi\) | ||||
−0.998752 | + | 0.0499397i | \(0.984097\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.31371 | − | 2.48528i | 0.250493 | − | 0.187870i | ||||
\(176\) | 0.828427 | 0.0624450 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 4.82843i | − | 0.361906i | ||||||
\(179\) | −11.1716 | −0.835003 | −0.417501 | − | 0.908676i | \(-0.637094\pi\) | ||||
−0.417501 | + | 0.908676i | \(0.637094\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.8284 | 1.84548 | 0.922741 | − | 0.385420i | \(-0.125943\pi\) | ||||
0.922741 | + | 0.385420i | \(0.125943\pi\) | |||||||
\(182\) | − | 4.00000i | − | 0.296500i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.48528 | 0.625543 | ||||||||
\(185\) | 10.4853 | − | 20.9706i | 0.770893 | − | 1.54179i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.686292i | 0.0501866i | ||||||||
\(188\) | 5.65685i | 0.412568i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.485281 | 0.0351137 | 0.0175569 | − | 0.999846i | \(-0.494411\pi\) | ||||
0.0175569 | + | 0.999846i | \(0.494411\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.3137i | 1.10230i | 0.834405 | + | 0.551152i | \(0.185812\pi\) | ||||
−0.834405 | + | 0.551152i | \(0.814188\pi\) | |||||||
\(194\) | 11.3137 | 0.812277 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.31371 | −0.450979 | ||||||||
\(197\) | − | 26.9706i | − | 1.92157i | −0.277289 | − | 0.960787i | \(-0.589436\pi\) | ||
0.277289 | − | 0.960787i | \(-0.410564\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.6569 | −0.968109 | −0.484054 | − | 0.875038i | \(-0.660836\pi\) | ||||
−0.484054 | + | 0.875038i | \(0.660836\pi\) | |||||||
\(200\) | −4.00000 | + | 3.00000i | −0.282843 | + | 0.212132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.3137i | 0.796030i | ||||||||
\(203\) | − | 8.00000i | − | 0.561490i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.3137 | + | 7.65685i | 1.06956 | + | 0.534778i | ||||
\(206\) | −1.51472 | −0.105535 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.82843i | 0.334791i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3137 | 1.60498 | 0.802491 | − | 0.596664i | \(-0.203508\pi\) | ||||
0.802491 | + | 0.596664i | \(0.203508\pi\) | |||||||
\(212\) | 0.343146i | 0.0235673i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.00000 | 0.273434 | ||||||||
\(215\) | −9.65685 | + | 19.3137i | −0.658592 | + | 1.31718i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.828427i | − | 0.0562373i | ||||||
\(218\) | − | 11.6569i | − | 0.789502i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.65685 | + | 0.828427i | 0.111705 | + | 0.0558525i | ||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 17.7990i | − | 1.19191i | −0.803018 | − | 0.595954i | \(-0.796774\pi\) | ||
0.803018 | − | 0.595954i | \(-0.203226\pi\) | |||||||
\(224\) | −0.828427 | −0.0553516 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | 17.6569i | 1.17193i | 0.810338 | + | 0.585963i | \(0.199284\pi\) | ||||
−0.810338 | + | 0.585963i | \(0.800716\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.4853 | −1.22154 | −0.610771 | − | 0.791807i | \(-0.709140\pi\) | ||||
−0.610771 | + | 0.791807i | \(0.709140\pi\) | |||||||
\(230\) | 16.9706 | + | 8.48528i | 1.11901 | + | 0.559503i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.65685i | 0.634004i | ||||||||
\(233\) | 6.97056i | 0.456657i | 0.973584 | + | 0.228328i | \(0.0733260\pi\) | ||||
−0.973584 | + | 0.228328i | \(0.926674\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.65685 | + | 11.3137i | −0.369012 | + | 0.738025i | ||||
\(236\) | −3.17157 | −0.206452 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 0.686292i | − | 0.0444857i | ||||||
\(239\) | 0.686292 | 0.0443925 | 0.0221963 | − | 0.999754i | \(-0.492934\pi\) | ||||
0.0221963 | + | 0.999754i | \(0.492934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.0000 | 1.41714 | 0.708572 | − | 0.705638i | \(-0.249340\pi\) | ||||
0.708572 | + | 0.705638i | \(0.249340\pi\) | |||||||
\(242\) | 10.3137i | 0.662990i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.828427 | −0.0530346 | ||||||||
\(245\) | −12.6274 | − | 6.31371i | −0.806736 | − | 0.403368i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.00000i | 0.0635001i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.0000 | + | 2.00000i | −0.695701 | + | 0.126491i | ||||
\(251\) | −3.17157 | −0.200188 | −0.100094 | − | 0.994978i | \(-0.531914\pi\) | ||||
−0.100094 | + | 0.994978i | \(0.531914\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.02944i | − | 0.441937i | ||||||
\(254\) | −16.1421 | −1.01285 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 15.6569i | − | 0.976648i | −0.872662 | − | 0.488324i | \(-0.837608\pi\) | ||
0.872662 | − | 0.488324i | \(-0.162392\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.68629 | 0.539740 | ||||||||
\(260\) | −4.82843 | + | 9.65685i | −0.299446 | + | 0.598893i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.4853i | 1.14202i | ||||||||
\(263\) | − | 24.4853i | − | 1.50983i | −0.655824 | − | 0.754914i | \(-0.727679\pi\) | ||
0.655824 | − | 0.754914i | \(-0.272321\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.343146 | + | 0.686292i | −0.0210793 | + | 0.0421586i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.17157i | 0.560243i | ||||||||
\(269\) | −4.97056 | −0.303061 | −0.151530 | − | 0.988453i | \(-0.548420\pi\) | ||||
−0.151530 | + | 0.988453i | \(0.548420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6569 | −0.829595 | −0.414797 | − | 0.909914i | \(-0.636148\pi\) | ||||
−0.414797 | + | 0.909914i | \(0.636148\pi\) | |||||||
\(272\) | 0.828427i | 0.0502308i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.48528 | −0.391790 | ||||||||
\(275\) | 2.48528 | + | 3.31371i | 0.149868 | + | 0.199824i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4.14214i | − | 0.248877i | −0.992227 | − | 0.124438i | \(-0.960287\pi\) | ||
0.992227 | − | 0.124438i | \(-0.0397129\pi\) | |||||||
\(278\) | − | 14.1421i | − | 0.848189i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.65685 | − | 0.828427i | −0.0990160 | − | 0.0495080i | ||||
\(281\) | 21.3137 | 1.27147 | 0.635735 | − | 0.771908i | \(-0.280697\pi\) | ||||
0.635735 | + | 0.771908i | \(0.280697\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 14.8284i | − | 0.881458i | −0.897640 | − | 0.440729i | \(-0.854720\pi\) | ||
0.897640 | − | 0.440729i | \(-0.145280\pi\) | |||||||
\(284\) | −2.82843 | −0.167836 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 6.34315i | 0.374424i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3137 | 0.959630 | ||||||||
\(290\) | −9.65685 | + | 19.3137i | −0.567070 | + | 1.13414i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.6569i | 0.799207i | ||||||||
\(293\) | 2.00000i | 0.116841i | 0.998292 | + | 0.0584206i | \(0.0186065\pi\) | ||||
−0.998292 | + | 0.0584206i | \(0.981394\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.34315 | − | 3.17157i | −0.369312 | − | 0.184656i | ||||
\(296\) | −10.4853 | −0.609445 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.686292i | 0.0397558i | ||||||||
\(299\) | 40.9706 | 2.36939 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | − | 21.6569i | − | 1.24621i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.65685 | − | 0.828427i | −0.0948712 | − | 0.0474356i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.485281i | 0.0276965i | 0.999904 | + | 0.0138482i | \(0.00440817\pi\) | ||||
−0.999904 | + | 0.0138482i | \(0.995592\pi\) | |||||||
\(308\) | 0.686292i | 0.0391051i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.00000 | + | 2.00000i | −0.0567962 | + | 0.113592i | ||||
\(311\) | 16.4853 | 0.934795 | 0.467397 | − | 0.884047i | \(-0.345192\pi\) | ||||
0.467397 | + | 0.884047i | \(0.345192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.970563i | 0.0548595i | 0.999624 | + | 0.0274297i | \(0.00873225\pi\) | ||||
−0.999624 | + | 0.0274297i | \(0.991268\pi\) | |||||||
\(314\) | −17.3137 | −0.977069 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.3137 | 0.636446 | ||||||||
\(317\) | 13.3137i | 0.747772i | 0.927475 | + | 0.373886i | \(0.121975\pi\) | ||||
−0.927475 | + | 0.373886i | \(0.878025\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | 0.447914 | ||||||||
\(320\) | 2.00000 | + | 1.00000i | 0.111803 | + | 0.0559017i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.02944i | 0.391735i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.3137 | + | 14.4853i | −1.07133 | + | 0.803499i | ||||
\(326\) | −14.8284 | −0.821271 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 7.65685i | − | 0.422779i | ||||||
\(329\) | −4.68629 | −0.258364 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4853 | 0.686253 | 0.343127 | − | 0.939289i | \(-0.388514\pi\) | ||||
0.343127 | + | 0.939289i | \(0.388514\pi\) | |||||||
\(332\) | − | 1.65685i | − | 0.0909317i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.485281 | −0.0265534 | ||||||||
\(335\) | −9.17157 | + | 18.3431i | −0.501097 | + | 1.00219i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.65685i | 0.308148i | 0.988059 | + | 0.154074i | \(0.0492395\pi\) | ||||
−0.988059 | + | 0.154074i | \(0.950761\pi\) | |||||||
\(338\) | 10.3137i | 0.560992i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.828427 | + | 1.65685i | −0.0449278 | + | 0.0898555i | ||||
\(341\) | 0.828427 | 0.0448618 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 11.0294i | − | 0.595534i | ||||||
\(344\) | 9.65685 | 0.520663 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.31371 | 0.0706254 | ||||||||
\(347\) | 17.6569i | 0.947870i | 0.880560 | + | 0.473935i | \(0.157167\pi\) | ||||
−0.880560 | + | 0.473935i | \(0.842833\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.3137 | 1.35501 | 0.677506 | − | 0.735517i | \(-0.263061\pi\) | ||||
0.677506 | + | 0.735517i | \(0.263061\pi\) | |||||||
\(350\) | −2.48528 | − | 3.31371i | −0.132844 | − | 0.177125i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 0.828427i | − | 0.0441553i | ||||||
\(353\) | 23.1716i | 1.23330i | 0.787238 | + | 0.616649i | \(0.211510\pi\) | ||||
−0.787238 | + | 0.616649i | \(0.788490\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.65685 | − | 2.82843i | −0.300235 | − | 0.150117i | ||||
\(356\) | −4.82843 | −0.255906 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.1716i | 0.590436i | ||||||||
\(359\) | 10.1421 | 0.535281 | 0.267641 | − | 0.963519i | \(-0.413756\pi\) | ||||
0.267641 | + | 0.963519i | \(0.413756\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | − | 24.8284i | − | 1.30495i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.00000 | −0.209657 | ||||||||
\(365\) | −13.6569 | + | 27.3137i | −0.714832 | + | 1.42966i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.1421i | 1.46901i | 0.678605 | + | 0.734504i | \(0.262585\pi\) | ||||
−0.678605 | + | 0.734504i | \(0.737415\pi\) | |||||||
\(368\) | − | 8.48528i | − | 0.442326i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −20.9706 | − | 10.4853i | −1.09021 | − | 0.545104i | ||||
\(371\) | −0.284271 | −0.0147586 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.343146i | 0.0177674i | 0.999961 | + | 0.00888371i | \(0.00282781\pi\) | ||||
−0.999961 | + | 0.00888371i | \(0.997172\pi\) | |||||||
\(374\) | 0.686292 | 0.0354873 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.65685 | 0.291730 | ||||||||
\(377\) | 46.6274i | 2.40143i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.65685 | 0.496039 | 0.248020 | − | 0.968755i | \(-0.420220\pi\) | ||||
0.248020 | + | 0.968755i | \(0.420220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 0.485281i | − | 0.0248292i | ||||||
\(383\) | − | 11.5147i | − | 0.588375i | −0.955748 | − | 0.294187i | \(-0.904951\pi\) | ||
0.955748 | − | 0.294187i | \(-0.0950490\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.686292 | + | 1.37258i | −0.0349767 | + | 0.0699533i | ||||
\(386\) | 15.3137 | 0.779447 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 11.3137i | − | 0.574367i | ||||||
\(389\) | 12.6863 | 0.643221 | 0.321610 | − | 0.946872i | \(-0.395776\pi\) | ||||
0.321610 | + | 0.946872i | \(0.395776\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.02944 | 0.355494 | ||||||||
\(392\) | 6.31371i | 0.318890i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −26.9706 | −1.35876 | ||||||||
\(395\) | 22.6274 | + | 11.3137i | 1.13851 | + | 0.569254i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 15.6569i | − | 0.785795i | −0.919582 | − | 0.392897i | \(-0.871473\pi\) | ||
0.919582 | − | 0.392897i | \(-0.128527\pi\) | |||||||
\(398\) | 13.6569i | 0.684556i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | −2.48528 | −0.124109 | −0.0620545 | − | 0.998073i | \(-0.519765\pi\) | ||||
−0.0620545 | + | 0.998073i | \(0.519765\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.82843i | 0.240521i | ||||||||
\(404\) | 11.3137 | 0.562878 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.00000 | −0.397033 | ||||||||
\(407\) | 8.68629i | 0.430563i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.3137 | −1.64726 | −0.823628 | − | 0.567130i | \(-0.808054\pi\) | ||||
−0.823628 | + | 0.567130i | \(0.808054\pi\) | |||||||
\(410\) | 7.65685 | − | 15.3137i | 0.378145 | − | 0.756290i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.51472i | 0.0746248i | ||||||||
\(413\) | − | 2.62742i | − | 0.129287i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.65685 | − | 3.31371i | 0.0813318 | − | 0.162664i | ||||
\(416\) | 4.82843 | 0.236733 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.79899 | −0.478712 | −0.239356 | − | 0.970932i | \(-0.576936\pi\) | ||||
−0.239356 | + | 0.970932i | \(0.576936\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | − | 23.3137i | − | 1.13489i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.343146 | 0.0166646 | ||||||||
\(425\) | −3.31371 | + | 2.48528i | −0.160738 | + | 0.120554i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 0.686292i | − | 0.0332120i | ||||||
\(428\) | − | 4.00000i | − | 0.193347i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.3137 | + | 9.65685i | 0.931390 | + | 0.465695i | ||||
\(431\) | 1.17157 | 0.0564327 | 0.0282163 | − | 0.999602i | \(-0.491017\pi\) | ||||
0.0282163 | + | 0.999602i | \(0.491017\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.6569i | − | 0.656307i | −0.944624 | − | 0.328153i | \(-0.893574\pi\) | ||
0.944624 | − | 0.328153i | \(-0.106426\pi\) | |||||||
\(434\) | −0.828427 | −0.0397658 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.6569 | −0.558262 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.970563 | 0.0463224 | 0.0231612 | − | 0.999732i | \(-0.492627\pi\) | ||||
0.0231612 | + | 0.999732i | \(0.492627\pi\) | |||||||
\(440\) | 0.828427 | − | 1.65685i | 0.0394937 | − | 0.0789874i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.00000i | 0.190261i | ||||||||
\(443\) | − | 6.34315i | − | 0.301372i | −0.988582 | − | 0.150686i | \(-0.951852\pi\) | ||
0.988582 | − | 0.150686i | \(-0.0481482\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.65685 | − | 4.82843i | −0.457779 | − | 0.228889i | ||||
\(446\) | −17.7990 | −0.842807 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.828427i | 0.0391395i | ||||||||
\(449\) | −12.1421 | −0.573023 | −0.286511 | − | 0.958077i | \(-0.592496\pi\) | ||||
−0.286511 | + | 0.958077i | \(0.592496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.34315 | −0.298687 | ||||||||
\(452\) | 14.0000i | 0.658505i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.6569 | 0.828677 | ||||||||
\(455\) | −8.00000 | − | 4.00000i | −0.375046 | − | 0.187523i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.3137i | 1.46479i | 0.680878 | + | 0.732397i | \(0.261598\pi\) | ||||
−0.680878 | + | 0.732397i | \(0.738402\pi\) | |||||||
\(458\) | 18.4853i | 0.863760i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.48528 | − | 16.9706i | 0.395628 | − | 0.791257i | ||||
\(461\) | 19.3137 | 0.899529 | 0.449765 | − | 0.893147i | \(-0.351508\pi\) | ||||
0.449765 | + | 0.893147i | \(0.351508\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.17157i | 0.147395i | 0.997281 | + | 0.0736977i | \(0.0234800\pi\) | ||||
−0.997281 | + | 0.0736977i | \(0.976520\pi\) | |||||||
\(464\) | 9.65685 | 0.448308 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.97056 | 0.322905 | ||||||||
\(467\) | 36.0000i | 1.66588i | 0.553362 | + | 0.832941i | \(0.313345\pi\) | ||||
−0.553362 | + | 0.832941i | \(0.686655\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.59798 | −0.350842 | ||||||||
\(470\) | 11.3137 | + | 5.65685i | 0.521862 | + | 0.260931i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.17157i | 0.145983i | ||||||||
\(473\) | − | 8.00000i | − | 0.367840i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.686292 | −0.0314561 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 0.686292i | − | 0.0313902i | ||||||
\(479\) | 21.1716 | 0.967354 | 0.483677 | − | 0.875247i | \(-0.339301\pi\) | ||||
0.483677 | + | 0.875247i | \(0.339301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −50.6274 | −2.30841 | ||||||||
\(482\) | − | 22.0000i | − | 1.00207i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.3137 | 0.468805 | ||||||||
\(485\) | 11.3137 | − | 22.6274i | 0.513729 | − | 1.02746i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 20.1421i | − | 0.912727i | −0.889793 | − | 0.456364i | \(-0.849152\pi\) | ||
0.889793 | − | 0.456364i | \(-0.150848\pi\) | |||||||
\(488\) | 0.828427i | 0.0375011i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.31371 | + | 12.6274i | −0.285224 | + | 0.570449i | ||||
\(491\) | 43.4558 | 1.96113 | 0.980567 | − | 0.196183i | \(-0.0628545\pi\) | ||||
0.980567 | + | 0.196183i | \(0.0628545\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.00000i | 0.360302i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | − | 2.34315i | − | 0.105104i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.1421 | −0.812154 | −0.406077 | − | 0.913839i | \(-0.633103\pi\) | ||||
−0.406077 | + | 0.913839i | \(0.633103\pi\) | |||||||
\(500\) | 2.00000 | + | 11.0000i | 0.0894427 | + | 0.491935i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.17157i | 0.141554i | ||||||||
\(503\) | − | 12.6863i | − | 0.565654i | −0.959171 | − | 0.282827i | \(-0.908728\pi\) | ||
0.959171 | − | 0.282827i | \(-0.0912722\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.6274 | + | 11.3137i | 1.00691 | + | 0.503453i | ||||
\(506\) | −7.02944 | −0.312497 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.1421i | 0.716191i | ||||||||
\(509\) | 20.9706 | 0.929504 | 0.464752 | − | 0.885441i | \(-0.346144\pi\) | ||||
0.464752 | + | 0.885441i | \(0.346144\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3137 | −0.500489 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.6569 | −0.690594 | ||||||||
\(515\) | −1.51472 | + | 3.02944i | −0.0667465 | + | 0.133493i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.68629i | − | 0.206103i | ||||||
\(518\) | − | 8.68629i | − | 0.381654i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.65685 | + | 4.82843i | 0.423481 | + | 0.211741i | ||||
\(521\) | −34.2843 | −1.50202 | −0.751011 | − | 0.660290i | \(-0.770433\pi\) | ||||
−0.751011 | + | 0.660290i | \(0.770433\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.6274i | 0.989428i | 0.869056 | + | 0.494714i | \(0.164727\pi\) | ||||
−0.869056 | + | 0.494714i | \(0.835273\pi\) | |||||||
\(524\) | 18.4853 | 0.807533 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.4853 | −1.06761 | ||||||||
\(527\) | 0.828427i | 0.0360869i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −49.0000 | −2.13043 | ||||||||
\(530\) | 0.686292 | + | 0.343146i | 0.0298106 | + | 0.0149053i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 36.9706i | − | 1.60137i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.00000 | − | 8.00000i | 0.172935 | − | 0.345870i | ||||
\(536\) | 9.17157 | 0.396152 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.97056i | 0.214296i | ||||||||
\(539\) | 5.23045 | 0.225291 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.2843 | 0.958076 | 0.479038 | − | 0.877794i | \(-0.340986\pi\) | ||||
0.479038 | + | 0.877794i | \(0.340986\pi\) | |||||||
\(542\) | 13.6569i | 0.586612i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.828427 | 0.0355185 | ||||||||
\(545\) | −23.3137 | − | 11.6569i | −0.998650 | − | 0.499325i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 9.85786i | − | 0.421492i | −0.977541 | − | 0.210746i | \(-0.932411\pi\) | ||
0.977541 | − | 0.210746i | \(-0.0675893\pi\) | |||||||
\(548\) | 6.48528i | 0.277037i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.31371 | − | 2.48528i | 0.141297 | − | 0.105973i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.37258i | 0.398563i | ||||||||
\(554\) | −4.14214 | −0.175982 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.1421 | −0.599760 | ||||||||
\(557\) | 17.3137i | 0.733605i | 0.930299 | + | 0.366803i | \(0.119548\pi\) | ||||
−0.930299 | + | 0.366803i | \(0.880452\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.6274 | 1.97213 | ||||||||
\(560\) | −0.828427 | + | 1.65685i | −0.0350074 | + | 0.0700149i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 21.3137i | − | 0.899065i | ||||||
\(563\) | − | 4.97056i | − | 0.209484i | −0.994499 | − | 0.104742i | \(-0.966598\pi\) | ||
0.994499 | − | 0.104742i | \(-0.0334017\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.0000 | + | 28.0000i | −0.588984 | + | 1.17797i | ||||
\(566\) | −14.8284 | −0.623285 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.82843i | 0.118678i | ||||||||
\(569\) | −19.1716 | −0.803714 | −0.401857 | − | 0.915702i | \(-0.631635\pi\) | ||||
−0.401857 | + | 0.915702i | \(0.631635\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.1716 | −1.38819 | −0.694094 | − | 0.719885i | \(-0.744195\pi\) | ||||
−0.694094 | + | 0.719885i | \(0.744195\pi\) | |||||||
\(572\) | − | 4.00000i | − | 0.167248i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.34315 | 0.264758 | ||||||||
\(575\) | 33.9411 | − | 25.4558i | 1.41544 | − | 1.06158i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | − | 16.3137i | − | 0.678561i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 19.3137 | + | 9.65685i | 0.801958 | + | 0.400979i | ||||
\(581\) | 1.37258 | 0.0569443 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.284271i | − | 0.0117733i | ||||||
\(584\) | 13.6569 | 0.565125 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.00000 | 0.0826192 | ||||||||
\(587\) | − | 7.31371i | − | 0.301869i | −0.988544 | − | 0.150935i | \(-0.951772\pi\) | ||
0.988544 | − | 0.150935i | \(-0.0482283\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −3.17157 | + | 6.34315i | −0.130572 | + | 0.261143i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.4853i | 0.430942i | ||||||||
\(593\) | 26.9706i | 1.10755i | 0.832667 | + | 0.553774i | \(0.186813\pi\) | ||||
−0.832667 | + | 0.553774i | \(0.813187\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.37258 | − | 0.686292i | −0.0562704 | − | 0.0281352i | ||||
\(596\) | 0.686292 | 0.0281116 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 40.9706i | − | 1.67541i | ||||||
\(599\) | 21.4558 | 0.876662 | 0.438331 | − | 0.898814i | \(-0.355570\pi\) | ||||
0.438331 | + | 0.898814i | \(0.355570\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.0000 | 0.734235 | 0.367118 | − | 0.930175i | \(-0.380345\pi\) | ||||
0.367118 | + | 0.930175i | \(0.380345\pi\) | |||||||
\(602\) | 8.00000i | 0.326056i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21.6569 | −0.881205 | ||||||||
\(605\) | 20.6274 | + | 10.3137i | 0.838624 | + | 0.419312i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.79899i | 0.397729i | 0.980027 | + | 0.198864i | \(0.0637253\pi\) | ||||
−0.980027 | + | 0.198864i | \(0.936275\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.828427 | + | 1.65685i | −0.0335420 | + | 0.0670841i | ||||
\(611\) | 27.3137 | 1.10499 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 49.1127i | − | 1.98364i | −0.127632 | − | 0.991822i | \(-0.540738\pi\) | ||
0.127632 | − | 0.991822i | \(-0.459262\pi\) | |||||||
\(614\) | 0.485281 | 0.0195844 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.686292 | 0.0276515 | ||||||||
\(617\) | 41.5980i | 1.67467i | 0.546689 | + | 0.837336i | \(0.315888\pi\) | ||||
−0.546689 | + | 0.837336i | \(0.684112\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.5147 | 0.623589 | 0.311795 | − | 0.950150i | \(-0.399070\pi\) | ||||
0.311795 | + | 0.950150i | \(0.399070\pi\) | |||||||
\(620\) | 2.00000 | + | 1.00000i | 0.0803219 | + | 0.0401610i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 16.4853i | − | 0.661000i | ||||||
\(623\) | − | 4.00000i | − | 0.160257i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 0.970563 | 0.0387915 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.3137i | 0.690892i | ||||||||
\(629\) | −8.68629 | −0.346345 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.6274 | 0.582308 | 0.291154 | − | 0.956676i | \(-0.405961\pi\) | ||||
0.291154 | + | 0.956676i | \(0.405961\pi\) | |||||||
\(632\) | − | 11.3137i | − | 0.450035i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.3137 | 0.528755 | ||||||||
\(635\) | −16.1421 | + | 32.2843i | −0.640581 | + | 1.28116i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.4853i | 1.20787i | ||||||||
\(638\) | − | 8.00000i | − | 0.316723i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | − | 2.00000i | 0.0395285 | − | 0.0790569i | ||||
\(641\) | 19.4558 | 0.768460 | 0.384230 | − | 0.923237i | \(-0.374467\pi\) | ||||
0.384230 | + | 0.923237i | \(0.374467\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 8.00000i | − | 0.315489i | −0.987480 | − | 0.157745i | \(-0.949578\pi\) | ||
0.987480 | − | 0.157745i | \(-0.0504223\pi\) | |||||||
\(644\) | 7.02944 | 0.276999 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.1421i | 0.713241i | 0.934249 | + | 0.356620i | \(0.116071\pi\) | ||||
−0.934249 | + | 0.356620i | \(0.883929\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.62742 | 0.103135 | ||||||||
\(650\) | 14.4853 | + | 19.3137i | 0.568159 | + | 0.757546i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.8284i | 0.580726i | ||||||||
\(653\) | 14.0000i | 0.547862i | 0.961749 | + | 0.273931i | \(0.0883240\pi\) | ||||
−0.961749 | + | 0.273931i | \(0.911676\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 36.9706 | + | 18.4853i | 1.44456 | + | 0.722280i | ||||
\(656\) | −7.65685 | −0.298950 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.68629i | 0.182691i | ||||||||
\(659\) | −11.1716 | −0.435183 | −0.217591 | − | 0.976040i | \(-0.569820\pi\) | ||||
−0.217591 | + | 0.976040i | \(0.569820\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.6274 | 0.957896 | 0.478948 | − | 0.877843i | \(-0.341018\pi\) | ||||
0.478948 | + | 0.877843i | \(0.341018\pi\) | |||||||
\(662\) | − | 12.4853i | − | 0.485254i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.65685 | −0.0642984 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 81.9411i | − | 3.17277i | ||||||
\(668\) | 0.485281i | 0.0187761i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.3431 | + | 9.17157i | 0.708658 | + | 0.354329i | ||||
\(671\) | 0.686292 | 0.0264940 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.02944i | 0.270965i | 0.990780 | + | 0.135482i | \(0.0432584\pi\) | ||||
−0.990780 | + | 0.135482i | \(0.956742\pi\) | |||||||
\(674\) | 5.65685 | 0.217894 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.3137 | 0.396681 | ||||||||
\(677\) | − | 38.0000i | − | 1.46046i | −0.683202 | − | 0.730229i | \(-0.739413\pi\) | ||
0.683202 | − | 0.730229i | \(-0.260587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.37258 | 0.359687 | ||||||||
\(680\) | 1.65685 | + | 0.828427i | 0.0635375 | + | 0.0317687i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 0.828427i | − | 0.0317221i | ||||||
\(683\) | − | 24.2843i | − | 0.929212i | −0.885518 | − | 0.464606i | \(-0.846196\pi\) | ||
0.885518 | − | 0.464606i | \(-0.153804\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.48528 | + | 12.9706i | −0.247790 | + | 0.495580i | ||||
\(686\) | −11.0294 | −0.421106 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 9.65685i | − | 0.368164i | ||||||
\(689\) | 1.65685 | 0.0631211 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.2843 | −1.68465 | −0.842327 | − | 0.538968i | \(-0.818815\pi\) | ||||
−0.842327 | + | 0.538968i | \(0.818815\pi\) | |||||||
\(692\) | − | 1.31371i | − | 0.0499397i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.6569 | 0.670245 | ||||||||
\(695\) | −28.2843 | − | 14.1421i | −1.07288 | − | 0.536442i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 6.34315i | − | 0.240264i | ||||||
\(698\) | − | 25.3137i | − | 0.958138i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.31371 | + | 2.48528i | −0.125246 | + | 0.0939348i | ||||
\(701\) | −16.0000 | −0.604312 | −0.302156 | − | 0.953259i | \(-0.597706\pi\) | ||||
−0.302156 | + | 0.953259i | \(0.597706\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.828427 | −0.0312225 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.1716 | 0.872074 | ||||||||
\(707\) | 9.37258i | 0.352492i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.8284 | 1.53334 | 0.766672 | − | 0.642039i | \(-0.221911\pi\) | ||||
0.766672 | + | 0.642039i | \(0.221911\pi\) | |||||||
\(710\) | −2.82843 | + | 5.65685i | −0.106149 | + | 0.212298i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.82843i | 0.180953i | ||||||||
\(713\) | − | 8.48528i | − | 0.317776i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | − | 8.00000i | 0.149592 | − | 0.299183i | ||||
\(716\) | 11.1716 | 0.417501 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 10.1421i | − | 0.378501i | ||||||
\(719\) | −35.3137 | −1.31698 | −0.658490 | − | 0.752590i | \(-0.728804\pi\) | ||||
−0.658490 | + | 0.752590i | \(0.728804\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.25483 | −0.0467325 | ||||||||
\(722\) | 19.0000i | 0.707107i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −24.8284 | −0.922741 | ||||||||
\(725\) | 28.9706 | + | 38.6274i | 1.07594 | + | 1.43459i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.5147i | 1.09464i | 0.836923 | + | 0.547320i | \(0.184352\pi\) | ||||
−0.836923 | + | 0.547320i | \(0.815648\pi\) | |||||||
\(728\) | 4.00000i | 0.148250i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 27.3137 | + | 13.6569i | 1.01093 | + | 0.505463i | ||||
\(731\) | 8.00000 | 0.295891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 16.3431i | − | 0.603648i | −0.953364 | − | 0.301824i | \(-0.902405\pi\) | ||
0.953364 | − | 0.301824i | \(-0.0975955\pi\) | |||||||
\(734\) | 28.1421 | 1.03875 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.48528 | −0.312772 | ||||||||
\(737\) | − | 7.59798i | − | 0.279875i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.51472 | 0.129291 | 0.0646455 | − | 0.997908i | \(-0.479408\pi\) | ||||
0.0646455 | + | 0.997908i | \(0.479408\pi\) | |||||||
\(740\) | −10.4853 | + | 20.9706i | −0.385447 | + | 0.770893i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.284271i | 0.0104359i | ||||||||
\(743\) | 21.4558i | 0.787139i | 0.919295 | + | 0.393569i | \(0.128760\pi\) | ||||
−0.919295 | + | 0.393569i | \(0.871240\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.37258 | + | 0.686292i | 0.0502876 | + | 0.0251438i | ||||
\(746\) | 0.343146 | 0.0125635 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 0.686292i | − | 0.0250933i | ||||||
\(749\) | 3.31371 | 0.121080 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.28427 | −0.156335 | −0.0781676 | − | 0.996940i | \(-0.524907\pi\) | ||||
−0.0781676 | + | 0.996940i | \(0.524907\pi\) | |||||||
\(752\) | − | 5.65685i | − | 0.206284i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 46.6274 | 1.69807 | ||||||||
\(755\) | −43.3137 | − | 21.6569i | −1.57635 | − | 0.788174i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.51472i | 0.345818i | 0.984938 | + | 0.172909i | \(0.0553167\pi\) | ||||
−0.984938 | + | 0.172909i | \(0.944683\pi\) | |||||||
\(758\) | − | 9.65685i | − | 0.350753i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.1127 | −1.20033 | −0.600167 | − | 0.799875i | \(-0.704899\pi\) | ||||
−0.600167 | + | 0.799875i | \(0.704899\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 9.65685i | − | 0.349602i | ||||||
\(764\) | −0.485281 | −0.0175569 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.5147 | −0.416044 | ||||||||
\(767\) | 15.3137i | 0.552946i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.00000 | −0.0721218 | −0.0360609 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360609 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(770\) | 1.37258 | + | 0.686292i | 0.0494645 | + | 0.0247322i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 15.3137i | − | 0.551152i | ||||||
\(773\) | 0.343146i | 0.0123421i | 0.999981 | + | 0.00617105i | \(0.00196432\pi\) | ||||
−0.999981 | + | 0.00617105i | \(0.998036\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.00000 | + | 4.00000i | 0.107763 | + | 0.143684i | ||||
\(776\) | −11.3137 | −0.406138 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 12.6863i | − | 0.454826i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.34315 | 0.0838443 | ||||||||
\(782\) | − | 7.02944i | − | 0.251372i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.31371 | 0.225490 | ||||||||
\(785\) | −17.3137 | + | 34.6274i | −0.617953 | + | 1.23591i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.9706i | 0.890104i | 0.895505 | + | 0.445052i | \(0.146815\pi\) | ||||
−0.895505 | + | 0.445052i | \(0.853185\pi\) | |||||||
\(788\) | 26.9706i | 0.960787i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.3137 | − | 22.6274i | 0.402524 | − | 0.805047i | ||||
\(791\) | −11.5980 | −0.412377 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00000i | 0.142044i | ||||||||
\(794\) | −15.6569 | −0.555641 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.6569 | 0.484054 | ||||||||
\(797\) | − | 1.31371i | − | 0.0465339i | −0.999729 | − | 0.0232670i | \(-0.992593\pi\) | ||
0.999729 | − | 0.0232670i | \(-0.00740678\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.68629 | 0.165789 | ||||||||
\(800\) | 4.00000 | − | 3.00000i | 0.141421 | − | 0.106066i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.48528i | 0.0877583i | ||||||||
\(803\) | − | 11.3137i | − | 0.399252i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.0589 | + | 7.02944i | 0.495510 | + | 0.247755i | ||||
\(806\) | 4.82843 | 0.170074 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 11.3137i | − | 0.398015i | ||||||
\(809\) | −18.4853 | −0.649908 | −0.324954 | − | 0.945730i | \(-0.605349\pi\) | ||||
−0.324954 | + | 0.945730i | \(0.605349\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.9706 | −0.736376 | −0.368188 | − | 0.929751i | \(-0.620022\pi\) | ||||
−0.368188 | + | 0.929751i | \(0.620022\pi\) | |||||||
\(812\) | 8.00000i | 0.280745i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.68629 | 0.304454 | ||||||||
\(815\) | −14.8284 | + | 29.6569i | −0.519417 | + | 1.03883i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 33.3137i | 1.16479i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.3137 | − | 7.65685i | −0.534778 | − | 0.267389i | ||||
\(821\) | −25.6569 | −0.895430 | −0.447715 | − | 0.894176i | \(-0.647762\pi\) | ||||
−0.447715 | + | 0.894176i | \(0.647762\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 31.1716i | − | 1.08657i | −0.839547 | − | 0.543286i | \(-0.817180\pi\) | ||
0.839547 | − | 0.543286i | \(-0.182820\pi\) | |||||||
\(824\) | 1.51472 | 0.0527677 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.62742 | −0.0914195 | ||||||||
\(827\) | − | 39.3137i | − | 1.36707i | −0.729917 | − | 0.683536i | \(-0.760441\pi\) | ||
0.729917 | − | 0.683536i | \(-0.239559\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.1716 | −0.665856 | −0.332928 | − | 0.942952i | \(-0.608037\pi\) | ||||
−0.332928 | + | 0.942952i | \(0.608037\pi\) | |||||||
\(830\) | −3.31371 | − | 1.65685i | −0.115021 | − | 0.0575103i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 4.82843i | − | 0.167396i | ||||||
\(833\) | 5.23045i | 0.181224i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.485281 | + | 0.970563i | −0.0167939 | + | 0.0335877i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.79899i | 0.338500i | ||||||||
\(839\) | 40.7696 | 1.40752 | 0.703761 | − | 0.710437i | \(-0.251503\pi\) | ||||
0.703761 | + | 0.710437i | \(0.251503\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.2548 | 2.21568 | ||||||||
\(842\) | − | 14.0000i | − | 0.482472i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.3137 | −0.802491 | ||||||||
\(845\) | 20.6274 | + | 10.3137i | 0.709605 | + | 0.354802i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.54416i | 0.293581i | ||||||||
\(848\) | − | 0.343146i | − | 0.0117837i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.48528 | + | 3.31371i | 0.0852444 | + | 0.113659i | ||||
\(851\) | 88.9706 | 3.04987 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.3137i | 0.729767i | 0.931053 | + | 0.364884i | \(0.118891\pi\) | ||||
−0.931053 | + | 0.364884i | \(0.881109\pi\) | |||||||
\(854\) | −0.686292 | −0.0234844 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | 6.68629i | 0.228399i | 0.993458 | + | 0.114200i | \(0.0364304\pi\) | ||||
−0.993458 | + | 0.114200i | \(0.963570\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.4264 | 1.44757 | 0.723785 | − | 0.690025i | \(-0.242401\pi\) | ||||
0.723785 | + | 0.690025i | \(0.242401\pi\) | |||||||
\(860\) | 9.65685 | − | 19.3137i | 0.329296 | − | 0.658592i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 1.17157i | − | 0.0399039i | ||||||
\(863\) | 3.79899i | 0.129319i | 0.997907 | + | 0.0646596i | \(0.0205961\pi\) | ||||
−0.997907 | + | 0.0646596i | \(0.979404\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.31371 | − | 2.62742i | 0.0446674 | − | 0.0893349i | ||||
\(866\) | −13.6569 | −0.464079 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.828427i | 0.0281186i | ||||||||
\(869\) | −9.37258 | −0.317943 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.2843 | 1.50052 | ||||||||
\(872\) | 11.6569i | 0.394751i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.11270 | + | 1.65685i | −0.308065 | + | 0.0560119i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.6569i | 0.798835i | 0.916769 | + | 0.399418i | \(0.130788\pi\) | ||||
−0.916769 | + | 0.399418i | \(0.869212\pi\) | |||||||
\(878\) | − | 0.970563i | − | 0.0327549i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.65685 | − | 0.828427i | −0.0558525 | − | 0.0279263i | ||||
\(881\) | 36.1421 | 1.21766 | 0.608830 | − | 0.793301i | \(-0.291639\pi\) | ||||
0.608830 | + | 0.793301i | \(0.291639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.970563i | 0.0326620i | 0.999867 | + | 0.0163310i | \(0.00519856\pi\) | ||||
−0.999867 | + | 0.0163310i | \(0.994801\pi\) | |||||||
\(884\) | 4.00000 | 0.134535 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.34315 | −0.213102 | ||||||||
\(887\) | − | 20.0000i | − | 0.671534i | −0.941945 | − | 0.335767i | \(-0.891004\pi\) | ||
0.941945 | − | 0.335767i | \(-0.108996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.3726 | −0.448502 | ||||||||
\(890\) | −4.82843 | + | 9.65685i | −0.161849 | + | 0.323698i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.7990i | 0.595954i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.3431 | + | 11.1716i | 0.746849 | + | 0.373424i | ||||
\(896\) | 0.828427 | 0.0276758 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.1421i | 0.405188i | ||||||||
\(899\) | 9.65685 | 0.322074 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.284271 | 0.00947045 | ||||||||
\(902\) | 6.34315i | 0.211204i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.0000 | 0.465633 | ||||||||
\(905\) | −49.6569 | − | 24.8284i | −1.65065 | − | 0.825325i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 38.1421i | − | 1.26649i | −0.773952 | − | 0.633244i | \(-0.781723\pi\) | ||
0.773952 | − | 0.633244i | \(-0.218277\pi\) | |||||||
\(908\) | − | 17.6569i | − | 0.585963i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.00000 | + | 8.00000i | −0.132599 | + | 0.265197i | ||||
\(911\) | 49.9411 | 1.65462 | 0.827312 | − | 0.561743i | \(-0.189869\pi\) | ||||
0.827312 | + | 0.561743i | \(0.189869\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.37258i | 0.0454259i | ||||||||
\(914\) | 31.3137 | 1.03577 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.4853 | 0.610771 | ||||||||
\(917\) | 15.3137i | 0.505703i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.9706 | 0.559807 | 0.279904 | − | 0.960028i | \(-0.409697\pi\) | ||||
0.279904 | + | 0.960028i | \(0.409697\pi\) | |||||||
\(920\) | −16.9706 | − | 8.48528i | −0.559503 | − | 0.279751i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 19.3137i | − | 0.636063i | ||||||
\(923\) | 13.6569i | 0.449521i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.9411 | + | 31.4558i | −1.37902 | + | 1.03426i | ||||
\(926\) | 3.17157 | 0.104224 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 9.65685i | − | 0.317002i | ||||||
\(929\) | −36.1421 | −1.18579 | −0.592893 | − | 0.805282i | \(-0.702014\pi\) | ||||
−0.592893 | + | 0.805282i | \(0.702014\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 6.97056i | − | 0.228328i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 36.0000 | 1.17796 | ||||||||
\(935\) | 0.686292 | − | 1.37258i | 0.0224441 | − | 0.0448883i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.6274i | 0.739205i | 0.929190 | + | 0.369603i | \(0.120506\pi\) | ||||
−0.929190 | + | 0.369603i | \(0.879494\pi\) | |||||||
\(938\) | 7.59798i | 0.248083i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.65685 | − | 11.3137i | 0.184506 | − | 0.369012i | ||||
\(941\) | 40.0000 | 1.30396 | 0.651981 | − | 0.758235i | \(-0.273938\pi\) | ||||
0.651981 | + | 0.758235i | \(0.273938\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 64.9706i | 2.11573i | ||||||||
\(944\) | 3.17157 | 0.103226 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.00000 | −0.260102 | ||||||||
\(947\) | 54.9117i | 1.78439i | 0.451650 | + | 0.892195i | \(0.350835\pi\) | ||||
−0.451650 | + | 0.892195i | \(0.649165\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 65.9411 | 2.14054 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.686292i | 0.0222428i | ||||||||
\(953\) | − | 5.79899i | − | 0.187848i | −0.995579 | − | 0.0939239i | \(-0.970059\pi\) | ||
0.995579 | − | 0.0939239i | \(-0.0299410\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.970563 | − | 0.485281i | −0.0314067 | − | 0.0157033i | ||||
\(956\) | −0.686292 | −0.0221963 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 21.1716i | − | 0.684022i | ||||||
\(959\) | −5.37258 | −0.173490 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 50.6274i | 1.63229i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.0000 | −0.708572 | ||||||||
\(965\) | 15.3137 | − | 30.6274i | 0.492966 | − | 0.985931i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 7.17157i | − | 0.230622i | −0.993329 | − | 0.115311i | \(-0.963213\pi\) | ||
0.993329 | − | 0.115311i | \(-0.0367865\pi\) | |||||||
\(968\) | − | 10.3137i | − | 0.331495i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.6274 | − | 11.3137i | −0.726523 | − | 0.363261i | ||||
\(971\) | 7.45584 | 0.239269 | 0.119635 | − | 0.992818i | \(-0.461828\pi\) | ||||
0.119635 | + | 0.992818i | \(0.461828\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 11.7157i | − | 0.375589i | ||||||
\(974\) | −20.1421 | −0.645396 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.828427 | 0.0265173 | ||||||||
\(977\) | − | 27.6569i | − | 0.884821i | −0.896813 | − | 0.442411i | \(-0.854123\pi\) | ||
0.896813 | − | 0.442411i | \(-0.145877\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.00000 | 0.127841 | ||||||||
\(980\) | 12.6274 | + | 6.31371i | 0.403368 | + | 0.201684i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 43.4558i | − | 1.38673i | ||||||
\(983\) | − | 36.4853i | − | 1.16370i | −0.813296 | − | 0.581850i | \(-0.802329\pi\) | ||
0.813296 | − | 0.581850i | \(-0.197671\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.9706 | + | 53.9411i | −0.859354 | + | 1.71871i | ||||
\(986\) | 8.00000 | 0.254772 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −81.9411 | −2.60558 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.9411 | −1.07818 | −0.539088 | − | 0.842250i | \(-0.681231\pi\) | ||||
−0.539088 | + | 0.842250i | \(0.681231\pi\) | |||||||
\(992\) | − | 1.00000i | − | 0.0317500i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.34315 | −0.0743201 | ||||||||
\(995\) | 27.3137 | + | 13.6569i | 0.865903 | + | 0.432951i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 10.2843i | − | 0.325706i | −0.986650 | − | 0.162853i | \(-0.947930\pi\) | ||
0.986650 | − | 0.162853i | \(-0.0520697\pi\) | |||||||
\(998\) | 18.1421i | 0.574279i | ||||||||
\(999\) | 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 | 2790.2.d.i.559.1 | 4 | ||
3.2 | odd | 2 | 930.2.d.g.559.3 | yes | 4 | ||
5.4 | even | 2 | inner | 2790.2.d.i.559.4 | 4 | ||
15.2 | even | 4 | 4650.2.a.cc.1.2 | 2 | |||
15.8 | even | 4 | 4650.2.a.cf.1.1 | 2 | |||
15.14 | odd | 2 | 930.2.d.g.559.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.d.g.559.2 | ✓ | 4 | 15.14 | odd | 2 | ||
930.2.d.g.559.3 | yes | 4 | 3.2 | odd | 2 | ||
2790.2.d.i.559.1 | 4 | 1.1 | even | 1 | trivial | ||
2790.2.d.i.559.4 | 4 | 5.4 | even | 2 | inner | ||
4650.2.a.cc.1.2 | 2 | 15.2 | even | 4 | |||
4650.2.a.cf.1.1 | 2 | 15.8 | even | 4 |