Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4368,2,Mod(337,4368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4368.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4368.h (of order \(2\), degree \(1\), 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: | \(34.8786556029\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} + 8x^{8} + 18x^{7} + 28x^{6} - 48x^{5} + 130x^{4} + 316x^{3} + 324x^{2} + 144x + 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 2184) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.4 | ||
Root | \(-0.535829 + 0.535829i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4368.337 |
Dual form | 4368.2.h.t.337.7 |
$q$-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 \(\left(\mathbb{Z}/4368\mathbb{Z}\right)^\times\).
\(n\) | \(1093\) | \(1249\) | \(1457\) | \(2017\) | \(3823\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.660872i | − | 0.295551i | −0.989021 | − | 0.147775i | \(-0.952789\pi\) | ||
0.989021 | − | 0.147775i | \(-0.0472113\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.393402i | − | 0.118615i | −0.998240 | − | 0.0593077i | \(-0.981111\pi\) | ||
0.998240 | − | 0.0593077i | \(-0.0188893\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.36543 | + | 1.29378i | 0.933403 | + | 0.358829i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.660872i | − | 0.170636i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.29578 | −1.76949 | −0.884743 | − | 0.466079i | \(-0.845666\pi\) | ||||
−0.884743 | + | 0.466079i | \(0.845666\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.32008i | 1.44993i | 0.688788 | + | 0.724963i | \(0.258143\pi\) | ||||
−0.688788 | + | 0.724963i | \(0.741857\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.00000i | − | 0.218218i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.56325 | −1.16002 | −0.580009 | − | 0.814610i | \(-0.696951\pi\) | ||||
−0.580009 | + | 0.814610i | \(0.696951\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.56325 | 0.912650 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.97570 | −0.552573 | −0.276287 | − | 0.961075i | \(-0.589104\pi\) | ||||
−0.276287 | + | 0.961075i | \(0.589104\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.46340i | 1.52007i | 0.649881 | + | 0.760036i | \(0.274819\pi\) | ||||
−0.649881 | + | 0.760036i | \(0.725181\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.393402i | − | 0.0684826i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.660872 | −0.111708 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.7608i | 1.76907i | 0.466473 | + | 0.884536i | \(0.345525\pi\) | ||||
−0.466473 | + | 0.884536i | \(0.654475\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.36543 | + | 1.29378i | 0.538901 | + | 0.207170i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.81167i | 1.06380i | 0.846806 | + | 0.531902i | \(0.178523\pi\) | ||||
−0.846806 | + | 0.531902i | \(0.821477\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.998337 | −0.152245 | −0.0761225 | − | 0.997098i | \(-0.524254\pi\) | ||||
−0.0761225 | + | 0.997098i | \(0.524254\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 0.660872i | − | 0.0985169i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.04736i | − | 0.882098i | −0.897483 | − | 0.441049i | \(-0.854607\pi\) | ||
0.897483 | − | 0.441049i | \(-0.145393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.29578 | −1.02161 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.6159 | 1.59556 | 0.797781 | − | 0.602948i | \(-0.206007\pi\) | ||||
0.797781 | + | 0.602948i | \(0.206007\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.259989 | −0.0350569 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.32008i | 0.837115i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.07166i | 0.139518i | 0.997564 | + | 0.0697591i | \(0.0222230\pi\) | ||||
−0.997564 | + | 0.0697591i | \(0.977777\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.73087 | 0.861799 | 0.430900 | − | 0.902400i | \(-0.358196\pi\) | ||||
0.430900 | + | 0.902400i | \(0.358196\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.855019 | − | 2.22412i | 0.106052 | − | 0.275868i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4709i | 1.52356i | 0.647836 | + | 0.761780i | \(0.275674\pi\) | ||||
−0.647836 | + | 0.761780i | \(0.724326\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.56325 | −0.669736 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.39340i | 0.996114i | 0.867144 | + | 0.498057i | \(0.165953\pi\) | ||||
−0.867144 | + | 0.498057i | \(0.834047\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.39397i | − | 0.865398i | −0.901538 | − | 0.432699i | \(-0.857561\pi\) | ||
0.901538 | − | 0.432699i | \(-0.142439\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.56325 | 0.526919 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.393402 | −0.0448324 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.41993 | 0.609790 | 0.304895 | − | 0.952386i | \(-0.401379\pi\) | ||||
0.304895 | + | 0.952386i | \(0.401379\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.75158i | − | 0.302025i | −0.988532 | − | 0.151012i | \(-0.951747\pi\) | ||
0.988532 | − | 0.151012i | \(-0.0482534\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.82157i | 0.522973i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.97570 | −0.319028 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.84810i | − | 0.619898i | −0.950753 | − | 0.309949i | \(-0.899688\pi\) | ||
0.950753 | − | 0.309949i | \(-0.100312\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.29378 | − | 3.36543i | 0.135624 | − | 0.352793i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.46340i | 0.877614i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.17676 | 0.428527 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.22937i | − | 0.632497i | −0.948676 | − | 0.316249i | \(-0.897577\pi\) | ||
0.948676 | − | 0.316249i | \(-0.102423\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.393402i | − | 0.0395384i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.1174 | 1.60374 | 0.801868 | − | 0.597501i | \(-0.203840\pi\) | ||||
0.801868 | + | 0.597501i | \(0.203840\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.3392 | −1.80702 | −0.903510 | − | 0.428567i | \(-0.859018\pi\) | ||||
−0.903510 | + | 0.428567i | \(0.859018\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.660872 | −0.0644945 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.58755 | −0.443495 | −0.221748 | − | 0.975104i | \(-0.571176\pi\) | ||||
−0.221748 | + | 0.975104i | \(0.571176\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.47088i | − | 0.811363i | −0.914014 | − | 0.405682i | \(-0.867034\pi\) | ||
0.914014 | − | 0.405682i | \(-0.132966\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.7608i | 1.02137i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.46340 | 0.608025 | 0.304013 | − | 0.952668i | \(-0.401673\pi\) | ||||
0.304013 | + | 0.952668i | \(0.401673\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.67659i | 0.342844i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.36543 | + | 1.29378i | 0.311134 | + | 0.119610i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.29578i | 0.668803i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8452 | 0.985930 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.81167i | 0.614188i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 6.32008i | − | 0.565285i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.22189 | −0.552104 | −0.276052 | − | 0.961143i | \(-0.589026\pi\) | ||||
−0.276052 | + | 0.961143i | \(0.589026\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.998337 | −0.0878987 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.12650 | −0.273163 | −0.136582 | − | 0.990629i | \(-0.543612\pi\) | ||||
−0.136582 | + | 0.990629i | \(0.543612\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.32008 | 0.548021 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 0.660872i | − | 0.0568788i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.51990i | 0.813340i | 0.913575 | + | 0.406670i | \(0.133310\pi\) | ||||
−0.913575 | + | 0.406670i | \(0.866690\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.0266 | −1.35936 | −0.679681 | − | 0.733508i | \(-0.737882\pi\) | ||||
−0.679681 | + | 0.733508i | \(0.737882\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 6.04736i | − | 0.509279i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.508974 | − | 1.32397i | 0.0425626 | − | 0.110716i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.96656i | 0.163314i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.57183i | − | 0.128769i | −0.997925 | − | 0.0643846i | \(-0.979492\pi\) | ||
0.997925 | − | 0.0643846i | \(-0.0205084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.12982i | − | 0.417459i | −0.977973 | − | 0.208730i | \(-0.933067\pi\) | ||
0.977973 | − | 0.208730i | \(-0.0669328\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.29578 | −0.589829 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.59322 | 0.449258 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.6628 | 0.850984 | 0.425492 | − | 0.904962i | \(-0.360101\pi\) | ||||
0.425492 | + | 0.904962i | \(0.360101\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.6159 | 0.921198 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.56325i | 0.438445i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.99086i | − | 0.390914i | −0.980712 | − | 0.195457i | \(-0.937381\pi\) | ||
0.980712 | − | 0.195457i | \(-0.0626190\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.259989 | −0.0202401 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.7223i | 1.13924i | 0.821906 | + | 0.569622i | \(0.192911\pi\) | ||||
−0.821906 | + | 0.569622i | \(0.807089\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.65229 | + | 8.70823i | 0.742484 | + | 0.669864i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.32008i | 0.483309i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.52580 | −0.116004 | −0.0580020 | − | 0.998316i | \(-0.518473\pi\) | ||||
−0.0580020 | + | 0.998316i | \(0.518473\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.56325i | − | 0.344949i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.07166i | 0.0805508i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.41079 | 0.628652 | 0.314326 | − | 0.949315i | \(-0.398222\pi\) | ||||
0.314326 | + | 0.949315i | \(0.398222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.02264 | 0.150342 | 0.0751708 | − | 0.997171i | \(-0.476050\pi\) | ||||
0.0751708 | + | 0.997171i | \(0.476050\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.73087 | 0.497560 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.11154 | 0.522850 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.87018i | 0.209888i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.00000i | − | 0.0727393i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.1352 | 1.16750 | 0.583751 | − | 0.811933i | \(-0.301584\pi\) | ||||
0.583751 | + | 0.811933i | \(0.301584\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 7.85336i | − | 0.565297i | −0.959224 | − | 0.282648i | \(-0.908787\pi\) | ||
0.959224 | − | 0.282648i | \(-0.0912130\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.855019 | − | 2.22412i | 0.0612292 | − | 0.159273i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.7013i | 1.26117i | 0.776122 | + | 0.630583i | \(0.217184\pi\) | ||||
−0.776122 | + | 0.630583i | \(0.782816\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.9012 | 1.69431 | 0.847155 | − | 0.531347i | \(-0.178314\pi\) | ||||
0.847155 | + | 0.531347i | \(0.178314\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.4709i | 0.879628i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.97570i | 0.208853i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.50164 | 0.314408 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.56325 | −0.386673 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.48634 | 0.171983 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.7215 | −1.77074 | −0.885372 | − | 0.464884i | \(-0.846096\pi\) | ||||
−0.885372 | + | 0.464884i | \(0.846096\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.39340i | 0.575106i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.659773i | 0.0449961i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.46340 | 0.574533 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 7.39397i | − | 0.499638i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.5535 | − | 9.43910i | −1.65164 | − | 0.634942i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7851i | 1.45884i | 0.684066 | + | 0.729421i | \(0.260210\pi\) | ||||
−0.684066 | + | 0.729421i | \(0.739790\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.56325 | 0.304217 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 14.1948i | − | 0.942144i | −0.882095 | − | 0.471072i | \(-0.843867\pi\) | ||
0.882095 | − | 0.471072i | \(-0.156133\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.1410i | 1.52920i | 0.644504 | + | 0.764601i | \(0.277064\pi\) | ||||
−0.644504 | + | 0.764601i | \(0.722936\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.393402 | −0.0258840 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.84119 | −0.186132 | −0.0930661 | − | 0.995660i | \(-0.529667\pi\) | ||||
−0.0930661 | + | 0.995660i | \(0.529667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.99653 | −0.260705 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.41993 | 0.352062 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.34480i | 0.410411i | 0.978719 | + | 0.205205i | \(0.0657863\pi\) | ||||
−0.978719 | + | 0.205205i | \(0.934214\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.21554i | 0.271547i | 0.990740 | + | 0.135773i | \(0.0433519\pi\) | ||||
−0.990740 | + | 0.135773i | \(0.956648\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.660872i | 0.0422215i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.17676 | + | 21.2698i | −0.520275 | + | 1.35337i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 2.75158i | − | 0.174374i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.1751 | 0.831605 | 0.415802 | − | 0.909455i | \(-0.363501\pi\) | ||||
0.415802 | + | 0.909455i | \(0.363501\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.18860i | 0.137596i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.82157i | 0.301939i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.45592 | −0.527466 | −0.263733 | − | 0.964596i | \(-0.584954\pi\) | ||||
−0.263733 | + | 0.964596i | \(0.584954\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.7608 | 0.668646 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.97570 | −0.184191 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.6685 | −1.82944 | −0.914718 | − | 0.404092i | \(-0.867587\pi\) | ||||
−0.914718 | + | 0.404092i | \(0.867587\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 7.67659i | − | 0.471569i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 5.84810i | − | 0.357898i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.8274 | −1.57472 | −0.787362 | − | 0.616491i | \(-0.788554\pi\) | ||||
−0.787362 | + | 0.616491i | \(0.788554\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.5015i | 1.73134i | 0.500611 | + | 0.865672i | \(0.333109\pi\) | ||||
−0.500611 | + | 0.865672i | \(0.666891\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.29378 | − | 3.36543i | 0.0783028 | − | 0.203685i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.79519i | − | 0.108254i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.52334 | 0.391950 | 0.195975 | − | 0.980609i | \(-0.437213\pi\) | ||||
0.195975 | + | 0.980609i | \(0.437213\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.46340i | 0.506690i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.66654i | − | 0.576658i | −0.957531 | − | 0.288329i | \(-0.906900\pi\) | ||
0.957531 | − | 0.288329i | \(-0.0930996\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.1052 | −0.957356 | −0.478678 | − | 0.877990i | \(-0.658884\pi\) | ||||
−0.478678 | + | 0.877990i | \(0.658884\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.17676 | 0.247410 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.81167 | 0.402080 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.2284 | 2.13108 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 6.22937i | − | 0.365172i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.5004i | − | 0.847122i | −0.905868 | − | 0.423561i | \(-0.860780\pi\) | ||
0.905868 | − | 0.423561i | \(-0.139220\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.708229 | 0.0412347 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.393402i | − | 0.0228275i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.7227 | − | 7.19759i | −1.08276 | − | 0.416248i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.998337i | 0.0575432i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.1174 | 0.925918 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 4.44824i | − | 0.254706i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.124834i | 0.00712467i | 0.999994 | + | 0.00356234i | \(0.00113393\pi\) | ||||
−0.999994 | + | 0.00356234i | \(0.998866\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.3392 | −1.04328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.92680 | 0.279373 | 0.139687 | − | 0.990196i | \(-0.455391\pi\) | ||||
0.139687 | + | 0.990196i | \(0.455391\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.8701 | −1.85793 | −0.928963 | − | 0.370172i | \(-0.879299\pi\) | ||||
−0.928963 | + | 0.370172i | \(0.879299\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.660872 | −0.0372359 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.0302i | 1.40584i | 0.711270 | + | 0.702919i | \(0.248120\pi\) | ||||
−0.711270 | + | 0.702919i | \(0.751880\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.17065i | 0.0655437i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.58755 | −0.256052 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 46.1099i | − | 2.56562i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.3573 | + | 5.90382i | 0.851870 | + | 0.327485i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 8.47088i | − | 0.468441i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.04736 | −0.333402 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 26.0793i | − | 1.43345i | −0.697358 | − | 0.716723i | \(-0.745641\pi\) | ||
0.697358 | − | 0.716723i | \(-0.254359\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.7608i | 0.589690i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.24165 | 0.450290 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.02831 | 0.491803 | 0.245902 | − | 0.969295i | \(-0.420916\pi\) | ||||
0.245902 | + | 0.969295i | \(0.420916\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.46340 | 0.351044 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.32952 | 0.180304 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.67659i | 0.197941i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.1272 | 1.45626 | 0.728132 | − | 0.685437i | \(-0.240389\pi\) | ||||
0.728132 | + | 0.685437i | \(0.240389\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.5205i | 1.20549i | 0.797933 | + | 0.602746i | \(0.205927\pi\) | ||||
−0.797933 | + | 0.602746i | \(0.794073\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.36543 | + | 1.29378i | 0.179634 | + | 0.0690566i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 30.4767i | − | 1.62211i | −0.584970 | − | 0.811055i | \(-0.698894\pi\) | ||
0.584970 | − | 0.811055i | \(-0.301106\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.54696 | 0.294402 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.29578i | 0.386134i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 22.0515i | − | 1.16383i | −0.813248 | − | 0.581917i | \(-0.802303\pi\) | ||
0.813248 | − | 0.581917i | \(-0.197697\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −20.9434 | −1.10229 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.8452 | 0.569227 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.88646 | −0.255769 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.3363 | 1.11374 | 0.556872 | − | 0.830598i | \(-0.312001\pi\) | ||||
0.556872 | + | 0.830598i | \(0.312001\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.81167i | 0.354601i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 11.6159i | − | 0.603065i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.6003 | −1.01486 | −0.507431 | − | 0.861692i | \(-0.669405\pi\) | ||||
−0.507431 | + | 0.861692i | \(0.669405\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 6.32008i | − | 0.326368i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.0145 | − | 3.84988i | −0.515774 | − | 0.198279i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 20.5656i | − | 1.05638i | −0.849125 | − | 0.528192i | \(-0.822870\pi\) | ||
0.849125 | − | 0.528192i | \(-0.177130\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.22189 | −0.318757 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.0259i | 1.17657i | 0.808654 | + | 0.588284i | \(0.200196\pi\) | ||||
−0.808654 | + | 0.588284i | \(0.799804\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.259989i | 0.0132502i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.998337 | −0.0507483 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.967723 | −0.0490655 | −0.0245328 | − | 0.999699i | \(-0.507810\pi\) | ||||
−0.0245328 | + | 0.999699i | \(0.507810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.5882 | 2.05264 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.12650 | −0.157711 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 3.58188i | − | 0.180224i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 32.5274i | − | 1.63250i | −0.577698 | − | 0.816251i | \(-0.696049\pi\) | ||
0.577698 | − | 0.816251i | \(-0.303951\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.32008 | 0.316400 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.1220i | 1.40434i | 0.712007 | + | 0.702172i | \(0.247786\pi\) | ||||
−0.712007 | + | 0.702172i | \(0.752214\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.9497 | + | 28.4830i | −0.545445 | + | 1.41884i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 0.660872i | − | 0.0328390i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.23334 | 0.209839 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 7.87252i | − | 0.389271i | −0.980876 | − | 0.194636i | \(-0.937648\pi\) | ||
0.980876 | − | 0.194636i | \(-0.0623524\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.51990i | 0.469582i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.07166 | 0.0527329 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.81844 | −0.0892637 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.0266 | −0.784828 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.81825 | 0.333093 | 0.166547 | − | 0.986034i | \(-0.446738\pi\) | ||||
0.166547 | + | 0.986034i | \(0.446738\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.7713i | 0.914860i | 0.889246 | + | 0.457430i | \(0.151230\pi\) | ||||
−0.889246 | + | 0.457430i | \(0.848770\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 6.04736i | − | 0.294033i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −33.2925 | −1.61492 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 6.73087i | − | 0.325730i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.508974 | − | 1.32397i | 0.0245735 | − | 0.0639219i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.4668i | 0.648675i | 0.945941 | + | 0.324338i | \(0.105141\pi\) | ||||
−0.945941 | + | 0.324338i | \(0.894859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.3097 | −0.687681 | −0.343841 | − | 0.939028i | \(-0.611728\pi\) | ||||
−0.343841 | + | 0.939028i | \(0.611728\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.96656i | 0.0942891i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 35.1602i | − | 1.68194i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.1126 | −0.864465 | −0.432233 | − | 0.901762i | \(-0.642274\pi\) | ||||
−0.432233 | + | 0.901762i | \(0.642274\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.8662 | −0.896361 | −0.448180 | − | 0.893943i | \(-0.647928\pi\) | ||||
−0.448180 | + | 0.893943i | \(0.647928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.86485 | −0.183211 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1.57183i | − | 0.0743449i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 34.0029i | − | 1.60470i | −0.596856 | − | 0.802348i | \(-0.703584\pi\) | ||
0.596856 | − | 0.802348i | \(-0.296416\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.67973 | 0.126183 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 5.12982i | − | 0.241020i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.22412 | − | 0.855019i | −0.104268 | − | 0.0400839i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.83541i | − | 0.132635i | −0.997799 | − | 0.0663174i | \(-0.978875\pi\) | ||
0.997799 | − | 0.0663174i | \(-0.0211250\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.29578 | −0.340538 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.81935i | − | 0.131310i | −0.997842 | − | 0.0656551i | \(-0.979086\pi\) | ||
0.997842 | − | 0.0656551i | \(-0.0209137\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.8434i | − | 1.06162i | −0.847490 | − | 0.530812i | \(-0.821887\pi\) | ||
0.847490 | − | 0.530812i | \(-0.178113\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.59322 | 0.259379 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.0146 | −1.43519 | −0.717593 | − | 0.696463i | \(-0.754756\pi\) | ||||
−0.717593 | + | 0.696463i | \(0.754756\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.4709 | 0.575852 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.6628 | 0.491316 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.392748i | 0.0180586i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.8401i | 1.32327i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.6159 | 0.531854 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.40387i | 0.155527i | 0.996972 | + | 0.0777634i | \(0.0247779\pi\) | ||||
−0.996972 | + | 0.0777634i | \(0.975222\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.9221 | + | 36.2149i | −0.634793 | + | 1.65126i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.56325i | 0.253137i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.11682 | −0.186935 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.7484i | 1.34803i | 0.738719 | + | 0.674014i | \(0.235431\pi\) | ||||
−0.738719 | + | 0.674014i | \(0.764569\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 4.99086i | − | 0.225694i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.3180 | 1.14258 | 0.571292 | − | 0.820747i | \(-0.306442\pi\) | ||||
0.571292 | + | 0.820747i | \(0.306442\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.7100 | 0.977771 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.259989 | −0.0116856 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.39340 | 0.376496 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.52726i | 0.202668i | 0.994852 | + | 0.101334i | \(0.0323111\pi\) | ||||
−0.994852 | + | 0.101334i | \(0.967689\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.7223i | 0.657743i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.98205 | 0.132963 | 0.0664815 | − | 0.997788i | \(-0.478823\pi\) | ||||
0.0664815 | + | 0.997788i | \(0.478823\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 10.6515i | − | 0.473986i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.65229 | + | 8.70823i | 0.428673 | + | 0.386746i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.2809i | 1.43083i | 0.698702 | + | 0.715413i | \(0.253761\pi\) | ||||
−0.698702 | + | 0.715413i | \(0.746239\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.39397 | −0.327090 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.32008i | 0.279038i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.1199i | 0.534066i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.37905 | −0.104630 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.52580 | −0.0669750 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.8145 | −1.74430 | −0.872152 | − | 0.489235i | \(-0.837276\pi\) | ||||
−0.872152 | + | 0.489235i | \(0.837276\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.77365 | −0.0775564 | −0.0387782 | − | 0.999248i | \(-0.512347\pi\) | ||||
−0.0387782 | + | 0.999248i | \(0.512347\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 4.56325i | − | 0.199156i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 61.7471i | − | 2.68975i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.94973 | 0.345641 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.07166i | 0.0465060i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.81277 | + | 22.9242i | −0.381723 | + | 0.992959i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.03178i | 0.131075i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.41079 | 0.362952 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.393402i | 0.0169450i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0972i | 0.993027i | 0.868029 | + | 0.496513i | \(0.165387\pi\) | ||||
−0.868029 | + | 0.496513i | \(0.834613\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.02264 | 0.0867997 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.59816 | −0.239799 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.5995 | 0.538717 | 0.269359 | − | 0.963040i | \(-0.413188\pi\) | ||||
0.269359 | + | 0.963040i | \(0.413188\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.73087 | 0.287266 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 18.8067i | − | 0.801190i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 5.41993i | − | 0.230479i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.11154 | 0.301868 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 21.0197i | − | 0.890635i | −0.895373 | − | 0.445317i | \(-0.853091\pi\) | ||
0.895373 | − | 0.445317i | \(-0.146909\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.35984 | − | 1.29162i | −0.142106 | − | 0.0546299i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.87018i | 0.121179i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.6818 | 0.787345 | 0.393672 | − | 0.919251i | \(-0.371204\pi\) | ||||
0.393672 | + | 0.919251i | \(0.371204\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 4.27148i | − | 0.179702i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.0469 | 0.546956 | 0.273478 | − | 0.961878i | \(-0.411826\pi\) | ||||
0.273478 | + | 0.961878i | \(0.411826\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.9203 | 0.833640 | 0.416820 | − | 0.908989i | \(-0.363145\pi\) | ||||
0.416820 | + | 0.908989i | \(0.363145\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.1352 | 0.674057 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.3865 | −1.05869 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.0394i | 0.959141i | 0.877503 | + | 0.479570i | \(0.159208\pi\) | ||||
−0.877503 | + | 0.479570i | \(0.840792\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 7.85336i | − | 0.326374i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.75158 | −0.114155 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.56971i | − | 0.189258i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.855019 | − | 2.22412i | 0.0353507 | − | 0.0919561i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.9372i | 0.492700i | 0.969181 | + | 0.246350i | \(0.0792313\pi\) | ||||
−0.969181 | + | 0.246350i | \(0.920769\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −53.4894 | −2.20399 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.7013i | 0.728135i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 43.4795i | 1.78549i | 0.450565 | + | 0.892744i | \(0.351223\pi\) | ||||
−0.450565 | + | 0.892744i | \(0.648777\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.82157 | 0.197665 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.9012 | 0.978210 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.2417 | 1.23564 | 0.617822 | − | 0.786318i | \(-0.288015\pi\) | ||||
0.617822 | + | 0.786318i | \(0.288015\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.8654 | 0.769535 | 0.384767 | − | 0.923014i | \(-0.374282\pi\) | ||||
0.384767 | + | 0.923014i | \(0.374282\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.4709i | 0.507853i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 7.16731i | − | 0.291393i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.67781 | −0.108689 | −0.0543445 | − | 0.998522i | \(-0.517307\pi\) | ||||
−0.0543445 | + | 0.998522i | \(0.517307\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.97570i | 0.120581i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.82392 | − | 20.3520i | 0.316522 | − | 0.823353i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 23.7973i | − | 0.961164i | −0.876950 | − | 0.480582i | \(-0.840425\pi\) | ||
0.876950 | − | 0.480582i | \(-0.159575\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.50164 | 0.181524 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.1250i | 1.01149i | 0.862682 | + | 0.505746i | \(0.168783\pi\) | ||||
−0.862682 | + | 0.505746i | \(0.831217\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.1886i | − | 0.409514i | −0.978813 | − | 0.204757i | \(-0.934360\pi\) | ||
0.978813 | − | 0.204757i | \(-0.0656405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.56325 | −0.223245 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.84810 | −0.234299 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.6395 | 0.745579 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.48634 | 0.0992947 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 78.5087i | − | 3.13035i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.80475i | 0.231084i | 0.993303 | + | 0.115542i | \(0.0368604\pi\) | ||||
−0.993303 | + | 0.115542i | \(0.963140\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.7215 | −1.02234 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.11187i | 0.163175i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.36543 | − | 1.29378i | −0.133343 | − | 0.0512612i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.39340i | 0.332038i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.9398 | −1.10356 | −0.551778 | − | 0.833991i | \(-0.686050\pi\) | ||||
−0.551778 | + | 0.833991i | \(0.686050\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 26.3582i | − | 1.03947i | −0.854329 | − | 0.519733i | \(-0.826031\pi\) | ||
0.854329 | − | 0.519733i | \(-0.173969\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.659773i | 0.0259785i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.8995 | 1.64724 | 0.823619 | − | 0.567143i | \(-0.191951\pi\) | ||||
0.823619 | + | 0.567143i | \(0.191951\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.421593 | 0.0165490 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.46340 | 0.331707 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.9578 | −1.09407 | −0.547036 | − | 0.837109i | \(-0.684244\pi\) | ||||
−0.547036 | + | 0.837109i | \(0.684244\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.06621i | 0.0807336i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 7.39397i | − | 0.288466i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.6362 | −1.42714 | −0.713572 | − | 0.700582i | \(-0.752924\pi\) | ||||
−0.713572 | + | 0.700582i | \(0.752924\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.5721i | 0.683474i | 0.939796 | + | 0.341737i | \(0.111015\pi\) | ||||
−0.939796 | + | 0.341737i | \(0.888985\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24.5535 | − | 9.43910i | −0.953578 | − | 0.366584i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 4.17676i | − | 0.161968i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.5545 | 0.640995 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.7851i | 0.842262i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.64794i | − | 0.102223i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.5167 | 0.713766 | 0.356883 | − | 0.934149i | \(-0.383839\pi\) | ||||
0.356883 | + | 0.934149i | \(0.383839\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.56325 | 0.175640 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.36566 | −0.167786 | −0.0838929 | − | 0.996475i | \(-0.526735\pi\) | ||||
−0.0838929 | + | 0.996475i | \(0.526735\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.22937 | −0.239061 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 14.1948i | − | 0.543947i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 38.9088i | − | 1.48880i | −0.667732 | − | 0.744401i | \(-0.732735\pi\) | ||
0.667732 | − | 0.744401i | \(-0.267265\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.29143 | 0.240383 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.1410i | 0.882885i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39.0924 | + | 15.0283i | 1.48930 | + | 0.572533i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 48.6783i | − | 1.85181i | −0.377757 | − | 0.925905i | \(-0.623304\pi\) | ||
0.377757 | − | 0.925905i | \(-0.376696\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.393402 | −0.0149441 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.5916i | 0.401761i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 49.6964i | − | 1.88239i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.84119 | −0.107464 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.7573 | 1.61492 | 0.807461 | − | 0.589921i | \(-0.200841\pi\) | ||||
0.807461 | + | 0.589921i | \(0.200841\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −68.0094 | −2.56502 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.99653 | −0.150518 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 16.1174i | − | 0.606155i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 34.7608i | − | 1.30547i | −0.757586 | − | 0.652735i | \(-0.773621\pi\) | ||
0.757586 | − | 0.652735i | \(-0.226379\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.41993 | 0.203263 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 47.0840i | − | 1.76331i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.874974 | − | 0.336367i | −0.0327222 | − | 0.0125794i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.34480i | 0.236951i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.151096 | 0.00563494 | 0.00281747 | − | 0.999996i | \(-0.499103\pi\) | ||||
0.00281747 | + | 0.999996i | \(0.499103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.3392i | 0.682989i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.21554i | 0.156778i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.5789 | −0.504306 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.3419 | −0.939879 | −0.469939 | − | 0.882699i | \(-0.655724\pi\) | ||||
−0.469939 | + | 0.882699i | \(0.655724\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.28365 | 0.269395 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.92558i | 0.0711229i | 0.999367 | + | 0.0355615i | \(0.0113219\pi\) | ||||
−0.999367 | + | 0.0355615i | \(0.988678\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.660872i | 0.0243766i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.90607 | 0.180718 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.02953i | 0.221800i | 0.993832 | + | 0.110900i | \(0.0353733\pi\) | ||||
−0.993832 | + | 0.110900i | \(0.964627\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.17676 | + | 21.2698i | −0.300381 | + | 0.781366i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 33.4818i | − | 1.22833i | −0.789178 | − | 0.614164i | \(-0.789493\pi\) | ||
0.789178 | − | 0.614164i | \(-0.210507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.03878 | −0.0380578 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 2.75158i | − | 0.100675i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.58755i | 0.167625i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.5503 | 0.968835 | 0.484418 | − | 0.874837i | \(-0.339031\pi\) | ||||
0.484418 | + | 0.874837i | \(0.339031\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.1751 | 0.480127 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.39015 | −0.123380 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.33289 | −0.230173 | −0.115086 | − | 0.993355i | \(-0.536715\pi\) | ||||
−0.115086 | + | 0.993355i | \(0.536715\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.18860i | 0.0794410i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.7719i | 0.499231i | 0.968345 | + | 0.249616i | \(0.0803043\pi\) | ||||
−0.968345 | + | 0.249616i | \(0.919696\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.47088 | −0.306666 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.82157i | 0.174324i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.38649 | + | 3.60660i | −0.0500631 | + | 0.130227i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 19.1849i | − | 0.691825i | −0.938267 | − | 0.345912i | \(-0.887569\pi\) | ||
0.938267 | − | 0.345912i | \(-0.112431\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.45592 | −0.304532 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 9.89641i | − | 0.355949i | −0.984035 | − | 0.177975i | \(-0.943046\pi\) | ||
0.984035 | − | 0.177975i | \(-0.0569545\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38.6206i | 1.38729i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.7608 | 0.386043 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −43.0503 | −1.54244 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.30199 | 0.118154 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.97570 | −0.106343 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 7.04674i | − | 0.251509i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 21.1383i | − | 0.753500i | −0.926315 | − | 0.376750i | \(-0.877042\pi\) | ||
0.926315 | − | 0.376750i | \(-0.122958\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.6685 | −1.05623 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 6.46340i | − | 0.229812i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.6523 | + | 8.70823i | 0.804406 | + | 0.309238i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 7.67659i | − | 0.272261i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.9845 | −0.778733 | −0.389366 | − | 0.921083i | \(-0.627306\pi\) | ||||
−0.389366 | + | 0.921083i | \(0.627306\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.1202i | 1.56086i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 5.84810i | − | 0.206633i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.90880 | −0.102649 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.67659 | 0.129583 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.8274 | −0.909167 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.1785 | 1.65871 | 0.829353 | − | 0.558725i | \(-0.188709\pi\) | ||||
0.829353 | + | 0.558725i | \(0.188709\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.00631i | 0.105566i | 0.998606 | + | 0.0527830i | \(0.0168091\pi\) | ||||
−0.998606 | + | 0.0527830i | \(0.983191\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.5015i | 0.999592i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.29832 | −0.115535 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.30957i | − | 0.220744i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.29378 | − | 3.36543i | 0.0452082 | − | 0.117598i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 54.3428i | − | 1.89658i | −0.317408 | − | 0.948289i | \(-0.602812\pi\) | ||
0.317408 | − | 0.948289i | \(-0.397188\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 53.1589 | 1.85300 | 0.926501 | − | 0.376293i | \(-0.122801\pi\) | ||||
0.926501 | + | 0.376293i | \(0.122801\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.79519i | − | 0.0625006i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.5064i | 1.19991i | 0.800036 | + | 0.599953i | \(0.204814\pi\) | ||||
−0.800036 | + | 0.599953i | \(0.795186\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.68892 | −0.162853 | −0.0814264 | − | 0.996679i | \(-0.525948\pi\) | ||||
−0.0814264 | + | 0.996679i | \(0.525948\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.52334 | 0.226292 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.29578 | 0.252784 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.72954 | 0.336705 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.46340i | 0.292538i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.21448i | 0.180024i | 0.995941 | + | 0.0900120i | \(0.0286905\pi\) | ||||
−0.995941 | + | 0.0900120i | \(0.971309\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.1452 | −0.694663 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 9.66654i | − | 0.332933i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.75502 | − | 6.37893i | 0.197979 | − | 0.219442i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.8452i | − | 0.372647i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.1052 | −0.552730 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 59.8652i | − | 2.05215i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 36.5276i | − | 1.25068i | −0.780351 | − | 0.625341i | \(-0.784960\pi\) | ||
0.780351 | − | 0.625341i | \(-0.215040\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.17676 | 0.142842 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 54.6394 | 1.86645 | 0.933223 | − | 0.359298i | \(-0.116984\pi\) | ||||
0.933223 | + | 0.359298i | \(0.116984\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.8848 | −0.746700 | −0.373350 | − | 0.927691i | \(-0.621791\pi\) | ||||
−0.373350 | + | 0.927691i | \(0.621791\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.81167 | 0.232141 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.4426i | 0.593752i | 0.954916 | + | 0.296876i | \(0.0959449\pi\) | ||||
−0.954916 | + | 0.296876i | \(0.904055\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.00835i | 0.0342851i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 36.2284 | 1.23038 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.13221i | − | 0.0723304i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.1345 | + | 41.9699i | −0.546697 | + | 1.42210i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6.22937i | − | 0.210832i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.32008 | −0.213658 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.3159i | 0.686020i | 0.939332 | + | 0.343010i | \(0.111446\pi\) | ||||
−0.939332 | + | 0.343010i | \(0.888554\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 14.5004i | − | 0.489086i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.2538 | −0.817131 | −0.408565 | − | 0.912729i | \(-0.633971\pi\) | ||||
−0.408565 | + | 0.912729i | \(0.633971\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.1454 | −0.576988 | −0.288494 | − | 0.957482i | \(-0.593154\pi\) | ||||
−0.288494 | + | 0.957482i | \(0.593154\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.708229 | 0.0238069 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.3223 | −1.32031 | −0.660156 | − | 0.751128i | \(-0.729510\pi\) | ||||
−0.660156 | + | 0.751128i | \(0.729510\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.22189i | 0.208676i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 0.393402i | − | 0.0131795i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38.2198 | 1.27898 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.55845i | − | 0.185799i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.7227 | − | 7.19759i | −0.625134 | − | 0.240321i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 25.1845i | − | 0.839951i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −84.7468 | −2.82332 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.998337i | 0.0332226i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.33670i | − | 0.0444336i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.8783 | 0.560436 | 0.280218 | − | 0.959936i | \(-0.409593\pi\) | ||||
0.280218 | + | 0.959936i | \(0.409593\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.1174 | 0.534579 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.49371 | −0.0494888 | −0.0247444 | − | 0.999694i | \(-0.507877\pi\) | ||||
−0.0247444 | + | 0.999694i | \(0.507877\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.08248 | −0.0358248 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 4.44824i | − | 0.147054i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.12650i | 0.103246i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.7861 | −0.718658 | −0.359329 | − | 0.933211i | \(-0.616994\pi\) | ||||
−0.359329 | + | 0.933211i | \(0.616994\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.124834i | 0.00411343i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.8592 | + | 28.2474i | −0.357434 | + | 0.929776i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49.1044i | 1.61454i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.3392 | −0.602340 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 11.6631i | − | 0.382653i | −0.981526 | − | 0.191326i | \(-0.938721\pi\) | ||
0.981526 | − | 0.191326i | \(-0.0612789\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 6.32008i | − | 0.207132i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.92680 | 0.161296 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.89682 | 0.0620326 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.25784 | 0.106429 | 0.0532144 | − | 0.998583i | \(-0.483053\pi\) | ||||
0.0532144 | + | 0.998583i | \(0.483053\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.8701 | −1.07267 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 42.1411i | − | 1.37376i | −0.726770 | − | 0.686881i | \(-0.758979\pi\) | ||
0.726770 | − | 0.686881i | \(-0.241021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 37.8950i | − | 1.23403i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.660872 | −0.0214982 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.3451i | 0.758615i | 0.925271 | + | 0.379308i | \(0.123838\pi\) | ||||
−0.925271 | + | 0.379308i | \(0.876162\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.56613 | − | 24.8839i | 0.310530 | − | 0.807766i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.0302i | 0.811661i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.0579 | 0.714527 | 0.357263 | − | 0.934004i | \(-0.383710\pi\) | ||||
0.357263 | + | 0.934004i | \(0.383710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 10.6633i | − | 0.345056i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.17065i | 0.0378416i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.51990 | 0.307414 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −40.6291 | −1.31062 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.58755 | −0.147832 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.19006 | −0.167074 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.5178i | − | 0.788439i | −0.919016 | − | 0.394219i | \(-0.871015\pi\) | ||
0.919016 | − | 0.394219i | \(-0.128985\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 46.1099i | − | 1.48126i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.7504 | −1.27565 | −0.637826 | − | 0.770181i | \(-0.720166\pi\) | ||||
−0.637826 | + | 0.770181i | \(0.720166\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.0266i | 0.513791i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.3573 | + | 5.90382i | 0.491828 | + | 0.189073i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.1289i | 1.60376i | 0.597482 | + | 0.801882i | \(0.296168\pi\) | ||||
−0.597482 | + | 0.801882i | \(0.703832\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.30066 | −0.0735293 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 8.47088i | − | 0.270454i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.6425i | 0.722185i | 0.932530 | + | 0.361092i | \(0.117596\pi\) | ||||
−0.932530 | + | 0.361092i | \(0.882404\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.6983 | 0.372739 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.04736 | −0.192490 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.55400 | 0.176607 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.6821 | 0.339329 | 0.169664 | − | 0.985502i | \(-0.445732\pi\) | ||||
0.169664 | + | 0.985502i | \(0.445732\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 26.0793i | − | 0.827600i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 15.7956i | − | 0.500754i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.26400 | −0.0717015 | −0.0358508 | − | 0.999357i | \(-0.511414\pi\) | ||||
−0.0358508 | + | 0.999357i | \(0.511414\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.7608i | 0.340458i |
(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 | 4368.2.h.t.337.4 | 10 | ||
4.3 | odd | 2 | 2184.2.h.e.337.4 | ✓ | 10 | ||
13.12 | even | 2 | inner | 4368.2.h.t.337.7 | 10 | ||
52.51 | odd | 2 | 2184.2.h.e.337.7 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2184.2.h.e.337.4 | ✓ | 10 | 4.3 | odd | 2 | ||
2184.2.h.e.337.7 | yes | 10 | 52.51 | odd | 2 | ||
4368.2.h.t.337.4 | 10 | 1.1 | even | 1 | trivial | ||
4368.2.h.t.337.7 | 10 | 13.12 | even | 2 | inner |