Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(609,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1520.609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.d (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: | \(12.1372611072\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 760) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 609.3 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.609 |
Dual form | 1520.2.d.d.609.2 |
$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.414214i | 0.239146i | 0.992825 | + | 0.119573i | \(0.0381526\pi\) | ||||
−0.992825 | + | 0.119573i | \(0.961847\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.12132 | + | 0.707107i | −0.948683 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.414214i | 0.156558i | 0.996931 | + | 0.0782790i | \(0.0249425\pi\) | ||||
−0.996931 | + | 0.0782790i | \(0.975058\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41421 | 0.426401 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.82843i | − | 1.06181i | −0.847430 | − | 0.530907i | \(-0.821851\pi\) | ||
0.847430 | − | 0.530907i | \(-0.178149\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.292893 | − | 0.878680i | −0.0756247 | − | 0.226874i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.00000i | − | 0.242536i | −0.992620 | − | 0.121268i | \(-0.961304\pi\) | ||
0.992620 | − | 0.121268i | \(-0.0386960\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.171573 | −0.0374403 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.24264i | 0.676137i | 0.941121 | + | 0.338069i | \(0.109774\pi\) | ||||
−0.941121 | + | 0.338069i | \(0.890226\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | − | 3.00000i | 0.800000 | − | 0.600000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.41421i | 0.464616i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.82843 | 0.339530 | 0.169765 | − | 0.985485i | \(-0.445699\pi\) | ||||
0.169765 | + | 0.985485i | \(0.445699\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.585786 | −0.105210 | −0.0526052 | − | 0.998615i | \(-0.516752\pi\) | ||||
−0.0526052 | + | 0.998615i | \(0.516752\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.585786i | 0.101972i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.292893 | − | 0.878680i | −0.0495080 | − | 0.148524i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.8284i | − | 1.78018i | −0.455782 | − | 0.890091i | \(-0.650640\pi\) | ||
0.455782 | − | 0.890091i | \(-0.349360\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.58579 | 0.253929 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.07107 | 1.10432 | 0.552158 | − | 0.833740i | \(-0.313805\pi\) | ||||
0.552158 | + | 0.833740i | \(0.313805\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.24264i | 0.951994i | 0.879447 | + | 0.475997i | \(0.157913\pi\) | ||||
−0.879447 | + | 0.475997i | \(0.842087\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.00000 | + | 2.00000i | −0.894427 | + | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000i | 1.16692i | 0.812142 | + | 0.583460i | \(0.198301\pi\) | ||||
−0.812142 | + | 0.583460i | \(0.801699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.82843 | 0.975490 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.414214 | 0.0580015 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.82843i | 0.525875i | 0.964813 | + | 0.262937i | \(0.0846913\pi\) | ||||
−0.964813 | + | 0.262937i | \(0.915309\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | + | 1.00000i | −0.404520 | + | 0.134840i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.414214i | − | 0.0548639i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.5858 | 1.50834 | 0.754170 | − | 0.656679i | \(-0.228039\pi\) | ||||
0.754170 | + | 0.656679i | \(0.228039\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.585786 | 0.0750023 | 0.0375011 | − | 0.999297i | \(-0.488060\pi\) | ||||
0.0375011 | + | 0.999297i | \(0.488060\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.17157i | 0.147604i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.70711 | + | 8.12132i | 0.335775 | + | 1.00733i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.07107i | 0.986038i | 0.870019 | + | 0.493019i | \(0.164107\pi\) | ||||
−0.870019 | + | 0.493019i | \(0.835893\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.34315 | −0.161696 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.0711 | 1.31389 | 0.656947 | − | 0.753937i | \(-0.271848\pi\) | ||||
0.656947 | + | 0.753937i | \(0.271848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.17157i | 0.956410i | 0.878248 | + | 0.478205i | \(0.158712\pi\) | ||||
−0.878248 | + | 0.478205i | \(0.841288\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.24264 | + | 1.65685i | 0.143488 | + | 0.191317i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.585786i | 0.0667566i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.82843 | 0.543240 | 0.271620 | − | 0.962405i | \(-0.412441\pi\) | ||||
0.271620 | + | 0.962405i | \(0.412441\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 14.4853i | − | 1.58997i | −0.606632 | − | 0.794983i | \(-0.707480\pi\) | ||
0.606632 | − | 0.794983i | \(-0.292520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.707107 | + | 2.12132i | 0.0766965 | + | 0.230089i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.757359i | 0.0811974i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.2426 | 1.29772 | 0.648859 | − | 0.760909i | \(-0.275247\pi\) | ||||
0.648859 | + | 0.760909i | \(0.275247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.58579 | 0.166236 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 0.242641i | − | 0.0251607i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.12132 | − | 0.707107i | 0.217643 | − | 0.0725476i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.65685i | 0.371297i | 0.982616 | + | 0.185649i | \(0.0594386\pi\) | ||||
−0.982616 | + | 0.185649i | \(0.940561\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.89949 | −0.388014 | −0.194007 | − | 0.981000i | \(-0.562148\pi\) | ||||
−0.194007 | + | 0.981000i | \(0.562148\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.89949i | − | 0.975426i | −0.873004 | − | 0.487713i | \(-0.837831\pi\) | ||
0.873004 | − | 0.487713i | \(-0.162169\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.363961 | − | 0.121320i | 0.0355190 | − | 0.0118397i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.414214i | 0.0400435i | 0.999800 | + | 0.0200218i | \(0.00637355\pi\) | ||||
−0.999800 | + | 0.0200218i | \(0.993626\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.48528 | 0.425724 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.07107i | 0.100758i | 0.998730 | + | 0.0503788i | \(0.0160429\pi\) | ||||
−0.998730 | + | 0.0503788i | \(0.983957\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.29289 | − | 6.87868i | −0.213813 | − | 0.641440i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 10.8284i | − | 1.00109i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.414214 | 0.0379709 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.92893i | 0.264093i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.36396 | + | 9.19239i | −0.569210 | + | 0.822192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.8284i | 1.49328i | 0.665228 | + | 0.746641i | \(0.268335\pi\) | ||||
−0.665228 | + | 0.746641i | \(0.731665\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.58579 | −0.227666 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3431 | −0.903685 | −0.451842 | − | 0.892098i | \(-0.649233\pi\) | ||||
−0.451842 | + | 0.892098i | \(0.649233\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.414214i | − | 0.0359169i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.70711 | − | 5.12132i | −0.146924 | − | 0.440773i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.31371i | 0.539417i | 0.962942 | + | 0.269708i | \(0.0869273\pi\) | ||||
−0.962942 | + | 0.269708i | \(0.913073\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.31371 | −0.279065 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 5.41421i | − | 0.452759i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.87868 | + | 1.29289i | −0.322107 | + | 0.107369i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.82843i | 0.233285i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.34315 | 0.519651 | 0.259825 | − | 0.965656i | \(-0.416335\pi\) | ||||
0.259825 | + | 0.965656i | \(0.416335\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.8284 | −1.36948 | −0.684739 | − | 0.728788i | \(-0.740084\pi\) | ||||
−0.684739 | + | 0.728788i | \(0.740084\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.82843i | − | 0.228665i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.24264 | − | 0.414214i | 0.0998113 | − | 0.0332704i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 11.6569i | − | 0.930318i | −0.885227 | − | 0.465159i | \(-0.845997\pi\) | ||
0.885227 | − | 0.465159i | \(-0.154003\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.58579 | −0.125761 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.34315 | −0.105855 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17.0711i | − | 1.33711i | −0.743663 | − | 0.668555i | \(-0.766913\pi\) | ||
0.743663 | − | 0.668555i | \(-0.233087\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.414214 | − | 1.24264i | −0.0322465 | − | 0.0967394i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 19.2132i | − | 1.48676i | −0.668868 | − | 0.743381i | \(-0.733221\pi\) | ||
0.668868 | − | 0.743381i | \(-0.266779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.65685 | −0.127450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.1716i | 1.00142i | 0.865616 | + | 0.500708i | \(0.166927\pi\) | ||||
−0.865616 | + | 0.500708i | \(0.833073\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.24264 | + | 1.65685i | 0.0939348 | + | 0.125246i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.79899i | 0.360714i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.9706 | 0.819978 | 0.409989 | − | 0.912090i | \(-0.365532\pi\) | ||||
0.409989 | + | 0.912090i | \(0.365532\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.4853 | −1.22534 | −0.612671 | − | 0.790338i | \(-0.709905\pi\) | ||||
−0.612671 | + | 0.790338i | \(0.709905\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.242641i | 0.0179365i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.65685 | + | 22.9706i | 0.562943 | + | 1.68883i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.41421i | − | 0.103418i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.75736 | 0.199516 | 0.0997578 | − | 0.995012i | \(-0.468193\pi\) | ||||
0.0997578 | + | 0.995012i | \(0.468193\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 3.65685i | − | 0.263226i | −0.991301 | − | 0.131613i | \(-0.957984\pi\) | ||
0.991301 | − | 0.131613i | \(-0.0420156\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.36396 | + | 1.12132i | −0.240898 | + | 0.0802994i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.72792i | 0.336850i | 0.985714 | + | 0.168425i | \(0.0538682\pi\) | ||||
−0.985714 | + | 0.168425i | \(0.946132\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.92893 | 0.136738 | 0.0683692 | − | 0.997660i | \(-0.478220\pi\) | ||||
0.0683692 | + | 0.997660i | \(0.478220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.34315 | −0.235807 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.757359i | 0.0531562i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.0000 | + | 5.00000i | −1.04765 | + | 0.349215i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.17157i | 0.637468i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.41421 | −0.0978232 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.10051 | 0.351133 | 0.175567 | − | 0.984468i | \(-0.443824\pi\) | ||||
0.175567 | + | 0.984468i | \(0.443824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.58579i | 0.314213i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.41421 | − | 13.2426i | −0.301047 | − | 0.903141i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.242641i | − | 0.0164715i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.38478 | −0.228722 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.82843 | −0.257528 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.82843i | − | 0.591195i | −0.955313 | − | 0.295598i | \(-0.904481\pi\) | ||
0.955313 | − | 0.295598i | \(-0.0955188\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.3137 | − | 8.48528i | 0.754247 | − | 0.565685i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 8.75736i | − | 0.581246i | −0.956838 | − | 0.290623i | \(-0.906137\pi\) | ||
0.956838 | − | 0.290623i | \(-0.0938626\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.97056 | −0.460628 | −0.230314 | − | 0.973116i | \(-0.573975\pi\) | ||||
−0.230314 | + | 0.973116i | \(0.573975\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.242641 | −0.0159646 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.6569i | − | 0.894690i | −0.894361 | − | 0.447345i | \(-0.852370\pi\) | ||
0.894361 | − | 0.447345i | \(-0.147630\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.65685 | − | 16.9706i | −0.369012 | − | 1.10704i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.00000i | 0.129914i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.7279 | 1.79357 | 0.896785 | − | 0.442466i | \(-0.145896\pi\) | ||||
0.896785 | + | 0.442466i | \(0.145896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.65685 | −0.364390 | −0.182195 | − | 0.983262i | \(-0.558320\pi\) | ||||
−0.182195 | + | 0.983262i | \(0.558320\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.3431i | 0.663513i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.4853 | + | 4.82843i | −0.925431 | + | 0.308477i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.82843i | 0.243597i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.55635 | −0.224475 | −0.112237 | − | 0.993681i | \(-0.535802\pi\) | ||||
−0.112237 | + | 0.993681i | \(0.535802\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.58579i | 0.288306i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.878680 | + | 0.292893i | −0.0550251 | + | 0.0183417i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 28.7279i | − | 1.79200i | −0.444056 | − | 0.895999i | \(-0.646461\pi\) | ||
0.444056 | − | 0.895999i | \(-0.353539\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.48528 | 0.278702 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.17157 | 0.320112 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.6569i | 0.965443i | 0.875774 | + | 0.482721i | \(0.160352\pi\) | ||||
−0.875774 | + | 0.482721i | \(0.839648\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.70711 | − | 8.12132i | −0.166296 | − | 0.498889i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.07107i | 0.310344i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.3848 | −0.934559 | −0.467279 | − | 0.884110i | \(-0.654766\pi\) | ||||
−0.467279 | + | 0.884110i | \(0.654766\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.656854i | 0.0397546i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.65685 | − | 4.24264i | 0.341121 | − | 0.255841i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.31371i | 0.199101i | 0.995032 | + | 0.0995507i | \(0.0317406\pi\) | ||||
−0.995032 | + | 0.0995507i | \(0.968259\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.65685 | −0.0991933 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.75736 | −0.224145 | −0.112073 | − | 0.993700i | \(-0.535749\pi\) | ||||
−0.112073 | + | 0.993700i | \(0.535749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 9.51472i | − | 0.565591i | −0.959180 | − | 0.282796i | \(-0.908738\pi\) | ||
0.959180 | − | 0.282796i | \(-0.0912618\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.292893 | + | 0.878680i | 0.0173495 | + | 0.0520485i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.92893i | 0.172889i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0000 | 0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.51472 | −0.0887944 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.7990i | 0.630884i | 0.948945 | + | 0.315442i | \(0.102153\pi\) | ||||
−0.948945 | + | 0.315442i | \(0.897847\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.5772 | + | 8.19239i | −1.43094 | + | 0.476979i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.41421i | 0.198113i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.4142 | 0.717933 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.58579 | −0.149042 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1.61522i | − | 0.0927922i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.24264 | + | 0.414214i | −0.0711534 | + | 0.0237178i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.2843i | 1.84256i | 0.388899 | + | 0.921280i | \(0.372855\pi\) | ||||
−0.388899 | + | 0.921280i | \(0.627145\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.10051 | 0.233270 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.2426 | −1.31797 | −0.658985 | − | 0.752156i | \(-0.729014\pi\) | ||||
−0.658985 | + | 0.752156i | \(0.729014\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.65685i | 0.376268i | 0.982143 | + | 0.188134i | \(0.0602439\pi\) | ||||
−0.982143 | + | 0.188134i | \(0.939756\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.828427 | − | 2.48528i | −0.0466766 | − | 0.140030i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 6.79899i | − | 0.381869i | −0.981603 | − | 0.190935i | \(-0.938848\pi\) | ||
0.981603 | − | 0.190935i | \(-0.0611519\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.58579 | 0.144776 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.171573 | −0.00957626 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.00000i | 0.0556415i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.4853 | − | 15.3137i | −0.637089 | − | 0.849452i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.07107i | 0.114530i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.31371 | −0.182691 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.3848 | −1.06548 | −0.532742 | − | 0.846278i | \(-0.678838\pi\) | ||||
−0.532742 | + | 0.846278i | \(0.678838\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 30.6274i | − | 1.67837i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.70711 | − | 17.1213i | −0.311813 | − | 0.935438i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 12.7279i | − | 0.693334i | −0.937988 | − | 0.346667i | \(-0.887313\pi\) | ||
0.937988 | − | 0.346667i | \(-0.112687\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.443651 | −0.0240958 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.828427 | −0.0448618 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.72792i | 0.309279i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.84924 | − | 0.949747i | 0.153398 | − | 0.0511327i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.1716i | 0.814453i | 0.913327 | + | 0.407226i | \(0.133504\pi\) | ||||
−0.913327 | + | 0.407226i | \(0.866496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.6274 | −1.53239 | −0.766195 | − | 0.642608i | \(-0.777852\pi\) | ||||
−0.766195 | + | 0.642608i | \(0.777852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.24264 | 0.493336 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 36.1127i | 1.92208i | 0.276401 | + | 0.961042i | \(0.410858\pi\) | ||||
−0.276401 | + | 0.961042i | \(0.589142\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.4853 | + | 7.82843i | −1.24647 | + | 0.415490i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.171573i | 0.00908060i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.07107 | −0.320419 | −0.160209 | − | 0.987083i | \(-0.551217\pi\) | ||||
−0.160209 | + | 0.987083i | \(0.551217\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.72792i | − | 0.195665i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.77817 | − | 17.3345i | −0.302443 | − | 0.907330i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 33.4558i | − | 1.74638i | −0.487379 | − | 0.873190i | \(-0.662047\pi\) | ||
0.487379 | − | 0.873190i | \(-0.337953\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.0000 | 1.04116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.58579 | −0.0823299 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 27.9706i | − | 1.44826i | −0.689663 | − | 0.724130i | \(-0.742241\pi\) | ||
0.689663 | − | 0.724130i | \(-0.257759\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.80761 | − | 2.63604i | −0.196624 | − | 0.136124i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.00000i | − | 0.360518i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.38478 | −0.173864 | −0.0869321 | − | 0.996214i | \(-0.527706\pi\) | ||||
−0.0869321 | + | 0.996214i | \(0.527706\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.97056 | −0.357113 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.7279i | 1.05915i | 0.848264 | + | 0.529574i | \(0.177648\pi\) | ||||
−0.848264 | + | 0.529574i | \(0.822352\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.414214 | − | 1.24264i | −0.0211103 | − | 0.0633308i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.6569i | 0.897548i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.89949 | −0.400520 | −0.200260 | − | 0.979743i | \(-0.564179\pi\) | ||||
−0.200260 | + | 0.979743i | \(0.564179\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.24264 | 0.163987 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.28427i | − | 0.216113i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.2426 | + | 3.41421i | −0.515363 | + | 0.171788i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 22.6274i | − | 1.13564i | −0.823154 | − | 0.567819i | \(-0.807787\pi\) | ||
0.823154 | − | 0.567819i | \(-0.192213\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.171573 | 0.00858939 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.10051 | −0.304645 | −0.152322 | − | 0.988331i | \(-0.548675\pi\) | ||||
−0.152322 | + | 0.988331i | \(0.548675\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.24264i | 0.111714i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.8787 | + | 5.29289i | −0.789018 | + | 0.263006i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 15.3137i | − | 0.759072i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.58579 | −0.127859 | −0.0639295 | − | 0.997954i | \(-0.520363\pi\) | ||||
−0.0639295 | + | 0.997954i | \(0.520363\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.61522 | −0.128999 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.79899i | 0.236143i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.2426 | + | 30.7279i | 0.502791 | + | 1.50837i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.65685i | − | 0.0811365i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.2132 | −1.32945 | −0.664726 | − | 0.747087i | \(-0.731452\pi\) | ||||
−0.664726 | + | 0.747087i | \(0.731452\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.1421 | 0.640508 | 0.320254 | − | 0.947332i | \(-0.396232\pi\) | ||||
0.320254 | + | 0.947332i | \(0.396232\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.6274i | 1.10018i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.00000 | − | 4.00000i | −0.145521 | − | 0.194029i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.242641i | 0.0117422i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.24264 | 0.108276 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.41421 | 0.260793 | 0.130397 | − | 0.991462i | \(-0.458375\pi\) | ||||
0.130397 | + | 0.991462i | \(0.458375\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.07107i | 0.243700i | 0.992549 | + | 0.121850i | \(0.0388827\pi\) | ||||
−0.992549 | + | 0.121850i | \(0.961117\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.535534 | − | 1.60660i | −0.0256769 | − | 0.0770307i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 3.24264i | − | 0.155117i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.7279 | −1.46656 | −0.733282 | − | 0.679925i | \(-0.762012\pi\) | ||||
−0.733282 | + | 0.679925i | \(0.762012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.3137 | 0.919700 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 15.5563i | − | 0.739104i | −0.929210 | − | 0.369552i | \(-0.879511\pi\) | ||
0.929210 | − | 0.369552i | \(-0.120489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.9706 | + | 8.65685i | −1.23112 | + | 0.410374i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.62742i | 0.124273i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.9411 | 1.69617 | 0.848083 | − | 0.529863i | \(-0.177757\pi\) | ||||
0.848083 | + | 0.529863i | \(0.177757\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0000 | 0.470882 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 6.97056i | − | 0.327506i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.36396 | + | 1.12132i | −0.157705 | + | 0.0525683i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 16.3137i | − | 0.763123i | −0.924343 | − | 0.381562i | \(-0.875386\pi\) | ||
0.924343 | − | 0.381562i | \(-0.124614\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.41421 | 0.112686 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.27208 | −0.338694 | −0.169347 | − | 0.985556i | \(-0.554166\pi\) | ||||
−0.169347 | + | 0.985556i | \(0.554166\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.1421i | − | 1.02903i | −0.857481 | − | 0.514516i | \(-0.827972\pi\) | ||
0.857481 | − | 0.514516i | \(-0.172028\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.171573 | + | 0.514719i | 0.00795650 | + | 0.0238695i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 21.8995i | − | 1.01339i | −0.862126 | − | 0.506694i | \(-0.830867\pi\) | ||
0.862126 | − | 0.506694i | \(-0.169133\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.34315 | −0.154372 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.82843 | 0.222482 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.82843i | 0.405932i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | + | 3.00000i | −0.183533 | + | 0.137649i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.8284i | 0.495800i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.4558 | 1.52864 | 0.764318 | − | 0.644839i | \(-0.223076\pi\) | ||||
0.764318 | + | 0.644839i | \(0.223076\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.4558 | −1.89022 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 0.556349i | − | 0.0253148i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.58579 | − | 7.75736i | −0.117415 | − | 0.352244i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.17157i | 0.324975i | 0.986711 | + | 0.162487i | \(0.0519517\pi\) | ||||
−0.986711 | + | 0.162487i | \(0.948048\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.07107 | 0.319765 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.7574 | −0.801378 | −0.400689 | − | 0.916214i | \(-0.631229\pi\) | ||||
−0.400689 | + | 0.916214i | \(0.631229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.82843i | − | 0.0823482i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.48528 | + | 2.82843i | −0.381385 | + | 0.127128i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.58579i | 0.205701i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.9289 | 0.847375 | 0.423688 | − | 0.905808i | \(-0.360735\pi\) | ||||
0.423688 | + | 0.905808i | \(0.360735\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.95837 | 0.355554 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 32.8995i | − | 1.46692i | −0.679735 | − | 0.733458i | \(-0.737905\pi\) | ||
0.679735 | − | 0.733458i | \(-0.262095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.27208 | − | 2.75736i | 0.368103 | − | 0.122701i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 0.686292i | − | 0.0304793i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.65685 | −0.428033 | −0.214016 | − | 0.976830i | \(-0.568655\pi\) | ||||
−0.214016 | + | 0.976830i | \(0.568655\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.38478 | −0.149734 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 2.41421i | − | 0.106590i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.00000 | + | 21.0000i | 0.308457 | + | 0.925371i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.3137i | 0.497576i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.45584 | −0.239485 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.0000 | −1.22670 | −0.613351 | − | 0.789810i | \(-0.710179\pi\) | ||||
−0.613351 | + | 0.789810i | \(0.710179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.2132i | 0.883862i | 0.897049 | + | 0.441931i | \(0.145706\pi\) | ||||
−0.897049 | + | 0.441931i | \(0.854294\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.686292 | + | 0.514719i | −0.0299522 | + | 0.0224642i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.585786i | 0.0255173i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.4853 | 0.542838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32.7696 | 1.42208 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 27.0711i | − | 1.17258i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.292893 | − | 0.878680i | −0.0126629 | − | 0.0379886i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.54416i | 0.196095i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.65685 | 0.415950 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0416 | 1.29159 | 0.645795 | − | 0.763511i | \(-0.276526\pi\) | ||||
0.645795 | + | 0.763511i | \(0.276526\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 6.82843i | − | 0.293036i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.6066 | + | 3.53553i | −0.454337 | + | 0.151446i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 23.9411i | − | 1.02365i | −0.859090 | − | 0.511824i | \(-0.828970\pi\) | ||
0.859090 | − | 0.511824i | \(-0.171030\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.65685 | 0.0707128 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.82843 | −0.0778936 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.00000i | 0.0850487i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.51472 | + | 3.17157i | −0.403877 | + | 0.134626i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.3137i | 1.83526i | 0.397435 | + | 0.917630i | \(0.369900\pi\) | ||||
−0.397435 | + | 0.917630i | \(0.630100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.8995 | 1.01084 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.585786 | 0.0247319 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 44.9706i | 1.89528i | 0.319336 | + | 0.947642i | \(0.396540\pi\) | ||||
−0.319336 | + | 0.947642i | \(0.603460\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.757359 | − | 2.27208i | −0.0318623 | − | 0.0955870i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.10051i | 0.130209i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.97056 | 0.376066 | 0.188033 | − | 0.982163i | \(-0.439789\pi\) | ||||
0.188033 | + | 0.982163i | \(0.439789\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −47.6985 | −1.99612 | −0.998060 | − | 0.0622637i | \(-0.980168\pi\) | ||||
−0.998060 | + | 0.0622637i | \(0.980168\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.14214i | 0.0477134i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.72792 | + | 12.9706i | 0.405682 | + | 0.540910i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.0000i | 1.04076i | 0.853934 | + | 0.520382i | \(0.174210\pi\) | ||||
−0.853934 | + | 0.520382i | \(0.825790\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.51472 | 0.0629496 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | 0.248922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.41421i | 0.224234i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.65685 | + | 22.9706i | 0.316572 | + | 0.949716i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 32.3848i | − | 1.33666i | −0.743864 | − | 0.668331i | \(-0.767009\pi\) | ||
0.743864 | − | 0.668331i | \(-0.232991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.585786 | 0.0241369 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.95837 | −0.0805566 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 42.0000i | − | 1.72473i | −0.506284 | − | 0.862367i | \(-0.668981\pi\) | ||
0.506284 | − | 0.862367i | \(-0.331019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.878680 | + | 0.292893i | −0.0360224 | + | 0.0120075i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.798990i | 0.0327005i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.5563 | −1.37108 | −0.685538 | − | 0.728037i | \(-0.740433\pi\) | ||||
−0.685538 | + | 0.728037i | \(0.740433\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.443651 | 0.0180969 | 0.00904845 | − | 0.999959i | \(-0.497120\pi\) | ||||
0.00904845 | + | 0.999959i | \(0.497120\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.8284i | 0.929645i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.0919 | − | 6.36396i | 0.776195 | − | 0.258732i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.4853i | 1.23736i | 0.785643 | + | 0.618680i | \(0.212332\pi\) | ||||
−0.785643 | + | 0.618680i | \(0.787668\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.313708 | −0.0127121 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.6274 | 1.23905 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 2.72792i | − | 0.110180i | −0.998481 | − | 0.0550899i | \(-0.982455\pi\) | ||
0.998481 | − | 0.0550899i | \(-0.0175445\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.07107 | − | 6.21320i | −0.0835135 | − | 0.250541i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.7990i | 1.28018i | 0.768300 | + | 0.640090i | \(0.221103\pi\) | ||||
−0.768300 | + | 0.640090i | \(0.778897\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.38478 | 0.256626 | 0.128313 | − | 0.991734i | \(-0.459044\pi\) | ||||
0.128313 | + | 0.991734i | \(0.459044\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.82843 | −0.314144 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.07107i | 0.203168i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.00000 | − | 24.0000i | 0.280000 | − | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 0.585786i | − | 0.0233941i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.8284 | −0.431758 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.02944 | 0.200219 | 0.100109 | − | 0.994976i | \(-0.468081\pi\) | ||||
0.100109 | + | 0.994976i | \(0.468081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.11270i | 0.0839722i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.8995 | − | 35.6985i | −0.472217 | − | 1.41665i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 26.1421i | − | 1.03579i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 31.3137 | 1.23875 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.21320 | 0.126914 | 0.0634570 | − | 0.997985i | \(-0.479787\pi\) | ||||
0.0634570 | + | 0.997985i | \(0.479787\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 36.8284i | − | 1.45237i | −0.687499 | − | 0.726186i | \(-0.741291\pi\) | ||
0.687499 | − | 0.726186i | \(-0.258709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.48528 | − | 1.82843i | 0.215983 | − | 0.0719942i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 2.07107i | − | 0.0814221i | −0.999171 | − | 0.0407110i | \(-0.987038\pi\) | ||
0.999171 | − | 0.0407110i | \(-0.0129623\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.3848 | 0.643159 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.100505 | 0.00393910 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.2843i | 0.950317i | 0.879900 | + | 0.475158i | \(0.157609\pi\) | ||||
−0.879900 | + | 0.475158i | \(0.842391\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.9411 | − | 7.31371i | 0.857311 | − | 0.285770i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.1127i | 0.901712i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.8995 | 0.424584 | 0.212292 | − | 0.977206i | \(-0.431907\pi\) | ||||
0.212292 | + | 0.977206i | \(0.431907\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.5147 | 1.03130 | 0.515652 | − | 0.856798i | \(-0.327550\pi\) | ||||
0.515652 | + | 0.856798i | \(0.327550\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1.58579i | − | 0.0615868i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.292893 | + | 0.878680i | 0.0113579 | + | 0.0340737i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.92893i | 0.229569i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.65685 | 0.141382 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.828427 | 0.0319811 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.0000i | 1.07932i | 0.841883 | + | 0.539660i | \(0.181447\pi\) | ||||
−0.841883 | + | 0.539660i | \(0.818553\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.24264 | + | 9.65685i | 0.278769 | + | 0.371692i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.6569i | 1.25510i | 0.778574 | + | 0.627552i | \(0.215943\pi\) | ||||
−0.778574 | + | 0.627552i | \(0.784057\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.51472 | −0.0581296 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.62742 | 0.139003 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 0.686292i | − | 0.0262602i | −0.999914 | − | 0.0131301i | \(-0.995820\pi\) | ||
0.999914 | − | 0.0131301i | \(-0.00417956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.46447 | − | 13.3934i | −0.170578 | − | 0.511735i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2.88730i | − | 0.110157i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.6569 | 0.558382 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.4558 | 1.65314 | 0.826569 | − | 0.562835i | \(-0.190289\pi\) | ||||
0.826569 | + | 0.562835i | \(0.190289\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.65685i | 0.0629387i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.48528 | − | 2.82843i | 0.321865 | − | 0.107288i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 7.07107i | − | 0.267836i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.65685 | 0.213962 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.970563 | −0.0366576 | −0.0183288 | − | 0.999832i | \(-0.505835\pi\) | ||||
−0.0183288 | + | 0.999832i | \(0.505835\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.8284i | 0.408402i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.02944 | − | 2.34315i | 0.264744 | − | 0.0882480i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.61522i | − | 0.0607467i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.3137 | −1.25112 | −0.625561 | − | 0.780175i | \(-0.715130\pi\) | ||||
−0.625561 | + | 0.780175i | \(0.715130\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.6569 | 0.512172 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.89949i | − | 0.0711366i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.82843 | + | 11.4853i | 0.143175 | + | 0.429525i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.4853i | 0.428926i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.5858 | 1.02878 | 0.514388 | − | 0.857557i | \(-0.328019\pi\) | ||||
0.514388 | + | 0.857557i | \(0.328019\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.10051 | 0.152711 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 2.34315i | − | 0.0871425i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.31371 | − | 5.48528i | 0.271624 | − | 0.203718i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 44.2132i | − | 1.63978i | −0.572523 | − | 0.819888i | \(-0.694035\pi\) | ||
0.572523 | − | 0.819888i | \(-0.305965\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.1716 | 0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.24264 | 0.230892 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.6274i | 1.27899i | 0.768794 | + | 0.639496i | \(0.220857\pi\) | ||||
−0.768794 | + | 0.639496i | \(0.779143\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.00000 | − | 6.00000i | −0.0737711 | − | 0.221313i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.4142i | 0.420448i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.58579 | 0.168691 | 0.0843454 | − | 0.996437i | \(-0.473120\pi\) | ||||
0.0843454 | + | 0.996437i | \(0.473120\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.58579 | −0.0582553 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5.75736i | − | 0.211217i | −0.994408 | − | 0.105609i | \(-0.966321\pi\) | ||
0.994408 | − | 0.105609i | \(-0.0336790\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.4558 | + | 4.48528i | −0.492984 | + | 0.164328i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 40.9706i | − | 1.49903i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.171573 | −0.00626914 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.2426 | −1.39549 | −0.697747 | − | 0.716344i | \(-0.745814\pi\) | ||||
−0.697747 | + | 0.716344i | \(0.745814\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.47309i | − | 0.0536823i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 35.6985 | − | 11.8995i | 1.29920 | − | 0.433067i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.6569i | 1.00521i | 0.864517 | + | 0.502603i | \(0.167624\pi\) | ||||
−0.864517 | + | 0.502603i | \(0.832376\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.89949 | −0.0689473 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.9706 | −1.37643 | −0.688216 | − | 0.725506i | \(-0.741606\pi\) | ||||
−0.688216 | + | 0.725506i | \(0.741606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.07107i | 0.0749777i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.00000 | + | 6.00000i | 0.0723102 | + | 0.216930i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 44.3553i | − | 1.60158i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.79899 | −0.317300 | −0.158650 | − | 0.987335i | \(-0.550714\pi\) | ||||
−0.158650 | + | 0.987335i | \(0.550714\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.8995 | 0.428550 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.00000i | 0.323708i | 0.986815 | + | 0.161854i | \(0.0517473\pi\) | ||||
−0.986815 | + | 0.161854i | \(0.948253\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.34315 | + | 1.75736i | −0.0841683 | + | 0.0631262i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.85786i | 0.0666505i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.07107 | −0.253347 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.6569 | 0.560246 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.41421i | 0.157751i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.24264 | + | 24.7279i | 0.294192 | + | 0.882577i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 31.2426i | − | 1.11368i | −0.830620 | − | 0.556840i | \(-0.812014\pi\) | ||
0.830620 | − | 0.556840i | \(-0.187986\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.48528 | −0.230882 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.443651 | −0.0157744 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.24264i | − | 0.0796385i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.36396 | − | 1.12132i | 0.119307 | − | 0.0397691i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 6.85786i | − | 0.242918i | −0.992596 | − | 0.121459i | \(-0.961243\pi\) | ||
0.992596 | − | 0.121459i | \(-0.0387573\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | 0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.6274 | 1.22350 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.5563i | 0.407815i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.84924 | − | 0.949747i | 0.100423 | − | 0.0334742i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.14214i | 0.145810i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.4853 | 0.896015 | 0.448007 | − | 0.894030i | \(-0.352134\pi\) | ||||
0.448007 | + | 0.894030i | \(0.352134\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.0122 | −1.40502 | −0.702509 | − | 0.711675i | \(-0.747937\pi\) | ||||
−0.702509 | + | 0.711675i | \(0.747937\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 6.37258i | − | 0.223496i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.0711 | + | 36.2132i | 0.422831 | + | 1.26849i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.24264i | − | 0.218402i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.48528 | 0.156728 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.5980 | 0.963176 | 0.481588 | − | 0.876398i | \(-0.340060\pi\) | ||||
0.481588 | + | 0.876398i | \(0.340060\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 17.5269i | − | 0.610950i | −0.952200 | − | 0.305475i | \(-0.901185\pi\) | ||
0.952200 | − | 0.305475i | \(-0.0988152\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.75736 | + | 2.34315i | 0.0611834 | + | 0.0815779i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.8701i | 0.690950i | 0.938428 | + | 0.345475i | \(0.112282\pi\) | ||||
−0.938428 | + | 0.345475i | \(0.887718\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.7696 | 1.65911 | 0.829553 | − | 0.558429i | \(-0.188596\pi\) | ||||
0.829553 | + | 0.558429i | \(0.188596\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.37258 | −0.0476144 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 6.82843i | − | 0.236591i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.5858 | + | 40.7574i | 0.470156 | + | 1.41047i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 1.41421i | − | 0.0488824i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.9411 | 0.619396 | 0.309698 | − | 0.950835i | \(-0.399772\pi\) | ||||
0.309698 | + | 0.950835i | \(0.399772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.6569 | −0.884719 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1.55635i | − | 0.0536035i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.51472 | − | 1.17157i | 0.120910 | − | 0.0403033i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3.72792i | − | 0.128093i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.94113 | 0.135259 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.1127 | 1.20365 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.9411i | 1.64147i | 0.571307 | + | 0.820736i | \(0.306437\pi\) | ||||
−0.571307 | + | 0.820736i | \(0.693563\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | − | 2.00000i | 0.205196 | − | 0.0683986i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 16.0000i | − | 0.546550i | −0.961936 | − | 0.273275i | \(-0.911893\pi\) | ||
0.961936 | − | 0.273275i | \(-0.0881068\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.2132 | −1.26970 | −0.634849 | − | 0.772636i | \(-0.718938\pi\) | ||||
−0.634849 | + | 0.772636i | \(0.718938\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.21320 | −0.0413459 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.9289i | 0.712429i | 0.934404 | + | 0.356215i | \(0.115933\pi\) | ||||
−0.934404 | + | 0.356215i | \(0.884067\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.31371 | − | 27.9411i | −0.316676 | − | 0.950027i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.62742i | 0.225079i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.82843 | 0.231639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.8995 | 1.04699 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.3431i | 0.350062i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.80761 | − | 2.63604i | −0.128721 | − | 0.0891144i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.5147i | 0.422592i | 0.977422 | + | 0.211296i | \(0.0677684\pi\) | ||||
−0.977422 | + | 0.211296i | \(0.932232\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.47309 | −0.150874 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.2843 | −1.49198 | −0.745988 | − | 0.665960i | \(-0.768022\pi\) | ||||
−0.745988 | + | 0.665960i | \(0.768022\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.4558i | 1.19318i | 0.802545 | + | 0.596592i | \(0.203479\pi\) | ||||
−0.802545 | + | 0.596592i | \(0.796521\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.39340 | − | 10.1802i | −0.114068 | − | 0.342204i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.0711i | 0.506037i | 0.967461 | + | 0.253018i | \(0.0814233\pi\) | ||||
−0.967461 | + | 0.253018i | \(0.918577\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.97056 | −0.233785 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.5858 | 0.354637 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 8.00000i | − | 0.267710i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.2721 | + | 7.75736i | −0.777900 | + | 0.259300i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.14214i | 0.171691i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.07107 | −0.0357221 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.82843 | 0.127543 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.07107i | − | 0.0356429i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 34.9706 | − | 11.6569i | 1.16246 | − | 0.387487i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 22.5563i | − | 0.748971i | −0.927233 | − | 0.374486i | \(-0.877819\pi\) | ||
0.927233 | − | 0.374486i | \(-0.122181\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.0294 | −0.365823 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.65685 | −0.0548940 | −0.0274470 | − | 0.999623i | \(-0.508738\pi\) | ||||
−0.0274470 | + | 0.999623i | \(0.508738\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 20.4853i | − | 0.677964i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.171573 | − | 0.514719i | −0.00567202 | − | 0.0170161i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 4.28427i | − | 0.141479i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.8406 | −1.34721 | −0.673604 | − | 0.739093i | \(-0.735255\pi\) | ||||
−0.673604 | + | 0.739093i | \(0.735255\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.3726 | −0.440642 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 42.3848i | − | 1.39511i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.4853 | − | 43.3137i | −1.06811 | − | 1.42415i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 28.0000i | − | 0.919641i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.51472 | −0.279359 | −0.139679 | − | 0.990197i | \(-0.544607\pi\) | ||||
−0.139679 | + | 0.990197i | \(0.544607\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.82843 | −0.223793 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 9.62742i | − | 0.315187i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.00000 | + | 3.00000i | 0.0327035 | + | 0.0981105i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.313708i | 0.0102484i | 0.999987 | + | 0.00512420i | \(0.00163109\pi\) | ||||
−0.999987 | + | 0.00512420i | \(0.998369\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.75736 | −0.0899830 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.8579 | 0.940739 | 0.470370 | − | 0.882469i | \(-0.344121\pi\) | ||||
0.470370 | + | 0.882469i | \(0.344121\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.9289i | 0.746669i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.12132 | − | 0.707107i | 0.0690066 | − | 0.0230022i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49.2548i | 1.60057i | 0.599622 | + | 0.800284i | \(0.295318\pi\) | ||||
−0.599622 | + | 0.800284i | \(0.704682\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.2843 | 1.01553 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.81623 | 0.0913226 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 23.2132i | − | 0.751949i | −0.926630 | − | 0.375975i | \(-0.877308\pi\) | ||
0.926630 | − | 0.375975i | \(-0.122692\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.84924 | + | 1.94975i | −0.189277 | + | 0.0630923i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.07107i | 0.0346227i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.61522 | −0.0844500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6569 | −0.988931 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.17157i | 0.0377534i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.58579 | + | 7.75736i | 0.0832394 | + | 0.249718i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.8579i | 0.702902i | 0.936206 | + | 0.351451i | \(0.114312\pi\) | ||||
−0.936206 | + | 0.351451i | \(0.885688\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.414214 | −0.0133065 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.5980 | −1.39913 | −0.699563 | − | 0.714571i | \(-0.746622\pi\) | ||||
−0.699563 | + | 0.714571i | \(0.746622\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.65685i | − | 0.0531163i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.34315 | − | 4.75736i | 0.203143 | − | 0.152357i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.3848i | 1.22804i | 0.789291 | + | 0.614019i | \(0.210448\pi\) | ||||
−0.789291 | + | 0.614019i | \(0.789552\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.3137 | 0.553349 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.1421 | 0.451524 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.2010i | 0.452942i | 0.974018 | + | 0.226471i | \(0.0727188\pi\) | ||||
−0.974018 | + | 0.226471i | \(0.927281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.34315 | − | 10.0294i | −0.106521 | − | 0.319564i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1.37258i | − | 0.0436898i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.2426 | −0.643679 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.5269 | 1.73210 | 0.866052 | − | 0.499954i | \(-0.166650\pi\) | ||||
0.866052 | + | 0.499954i | \(0.166650\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.02944i | − | 0.254806i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.09188 | + | 1.36396i | −0.129721 | + | 0.0432405i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.55635i | 0.112631i | 0.998413 | + | 0.0563154i | \(0.0179352\pi\) | ||||
−0.998413 | + | 0.0563154i | \(0.982065\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26.1421 | 0.827101 |
(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 | 1520.2.d.d.609.3 | 4 | ||
4.3 | odd | 2 | 760.2.d.c.609.2 | ✓ | 4 | ||
5.2 | odd | 4 | 7600.2.a.x.1.2 | 2 | |||
5.3 | odd | 4 | 7600.2.a.bc.1.1 | 2 | |||
5.4 | even | 2 | inner | 1520.2.d.d.609.2 | 4 | ||
20.3 | even | 4 | 3800.2.a.l.1.2 | 2 | |||
20.7 | even | 4 | 3800.2.a.p.1.1 | 2 | |||
20.19 | odd | 2 | 760.2.d.c.609.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.d.c.609.2 | ✓ | 4 | 4.3 | odd | 2 | ||
760.2.d.c.609.3 | yes | 4 | 20.19 | odd | 2 | ||
1520.2.d.d.609.2 | 4 | 5.4 | even | 2 | inner | ||
1520.2.d.d.609.3 | 4 | 1.1 | even | 1 | trivial | ||
3800.2.a.l.1.2 | 2 | 20.3 | even | 4 | |||
3800.2.a.p.1.1 | 2 | 20.7 | even | 4 | |||
7600.2.a.x.1.2 | 2 | 5.2 | odd | 4 | |||
7600.2.a.bc.1.1 | 2 | 5.3 | odd | 4 |