Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, 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("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.527896576.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 2x^{5} + 7x^{4} - 10x^{3} + 8x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 115) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.3 | ||
Root | \(-0.199724 + 0.199724i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.d.369.6 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 1.39945i | − | 0.807971i | −0.914765 | − | 0.403986i | \(-0.867625\pi\) | ||
0.914765 | − | 0.403986i | \(-0.132375\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.19972 | + | 1.88697i | −0.536533 | + | 0.843879i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.60747i | 1.74146i | 0.491762 | + | 0.870730i | \(0.336353\pi\) | ||||
−0.491762 | + | 0.870730i | \(0.663647\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.04155 | 0.347182 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.56592 | −0.472143 | −0.236072 | − | 0.971736i | \(-0.575860\pi\) | ||||
−0.236072 | + | 0.971736i | \(0.575860\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.60055i | 0.721264i | 0.932708 | + | 0.360632i | \(0.117439\pi\) | ||||
−0.932708 | + | 0.360632i | \(0.882561\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.64072 | + | 1.67895i | 0.681830 | + | 0.433503i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.559006i | − | 0.135579i | −0.997700 | − | 0.0677894i | \(-0.978405\pi\) | ||
0.997700 | − | 0.0677894i | \(-0.0215946\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.16647 | −0.267608 | −0.133804 | − | 0.991008i | \(-0.542719\pi\) | ||||
−0.133804 | + | 0.991008i | \(0.542719\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.44791 | 1.40705 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.12133 | − | 4.52769i | −0.424265 | − | 0.905538i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.65593i | − | 1.08848i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.17339 | 0.589284 | 0.294642 | − | 0.955608i | \(-0.404800\pi\) | ||||
0.294642 | + | 0.955608i | \(0.404800\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.0554 | −1.80600 | −0.903000 | − | 0.429641i | \(-0.858640\pi\) | ||||
−0.903000 | + | 0.429641i | \(0.858640\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.19143i | 0.381478i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.69416 | − | 5.52769i | −1.46958 | − | 0.934350i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.07341i | − | 0.834064i | −0.908892 | − | 0.417032i | \(-0.863070\pi\) | ||
0.908892 | − | 0.417032i | \(-0.136930\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.63934 | 0.582760 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.8127 | −1.84484 | −0.922419 | − | 0.386190i | \(-0.873791\pi\) | ||||
−0.922419 | + | 0.386190i | \(0.873791\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.76426i | 0.421546i | 0.977535 | + | 0.210773i | \(0.0675982\pi\) | ||||
−0.977535 | + | 0.210773i | \(0.932402\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.24957 | + | 1.96537i | −0.186275 | + | 0.292980i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.32298i | 1.35990i | 0.733260 | + | 0.679948i | \(0.237998\pi\) | ||||
−0.733260 | + | 0.679948i | \(0.762002\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.2288 | −2.03268 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.782299 | −0.109544 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.54789i | − | 0.762061i | −0.924562 | − | 0.381030i | \(-0.875569\pi\) | ||
0.924562 | − | 0.381030i | \(-0.124431\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.87867 | − | 2.95485i | 0.253320 | − | 0.398432i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.63242i | 0.216219i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.84044 | 0.499983 | 0.249991 | − | 0.968248i | \(-0.419572\pi\) | ||||
0.249991 | + | 0.968248i | \(0.419572\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.29832 | −0.550343 | −0.275172 | − | 0.961395i | \(-0.588735\pi\) | ||||
−0.275172 | + | 0.961395i | \(0.588735\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.79889i | 0.604604i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.90717 | − | 3.11994i | −0.608659 | − | 0.386981i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.60747i | 0.318553i | 0.987234 | + | 0.159277i | \(0.0509161\pi\) | ||||
−0.987234 | + | 0.159277i | \(0.949084\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.39945 | 0.168474 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.89582 | −0.937062 | −0.468531 | − | 0.883447i | \(-0.655217\pi\) | ||||
−0.468531 | + | 0.883447i | \(0.655217\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.90579i | 1.15938i | 0.814835 | + | 0.579692i | \(0.196827\pi\) | ||||
−0.814835 | + | 0.579692i | \(0.803173\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.33626 | + | 2.96868i | −0.731649 | + | 0.342794i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 7.21494i | − | 0.822219i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0485 | 1.35556 | 0.677779 | − | 0.735266i | \(-0.262943\pi\) | ||||
0.677779 | + | 0.735266i | \(0.262943\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.79054 | −0.532282 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 13.3856i | − | 1.46926i | −0.678470 | − | 0.734628i | \(-0.737357\pi\) | ||
0.678470 | − | 0.734628i | \(-0.262643\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.05483 | + | 0.670652i | 0.114412 | + | 0.0727425i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 4.44099i | − | 0.476125i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.71551 | 0.817843 | 0.408921 | − | 0.912570i | \(-0.365905\pi\) | ||||
0.408921 | + | 0.912570i | \(0.365905\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.9820 | −1.25605 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.0720i | 1.45920i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.39945 | − | 2.20111i | 0.143580 | − | 0.225829i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.62130i | 0.266153i | 0.991106 | + | 0.133076i | \(0.0424856\pi\) | ||||
−0.991106 | + | 0.133076i | \(0.957514\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.63098 | −0.163920 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.88199 | −0.883791 | −0.441895 | − | 0.897067i | \(-0.645694\pi\) | ||||
−0.441895 | + | 0.897067i | \(0.645694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.65593i | 0.852894i | 0.904512 | + | 0.426447i | \(0.140235\pi\) | ||||
−0.904512 | + | 0.426447i | \(0.859765\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.73571 | + | 12.1670i | −0.754928 | + | 1.18738i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.91662i | − | 0.668655i | −0.942457 | − | 0.334327i | \(-0.891491\pi\) | ||
0.942457 | − | 0.334327i | \(-0.108509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.84736 | 0.655858 | 0.327929 | − | 0.944702i | \(-0.393649\pi\) | ||||
0.327929 | + | 0.944702i | \(0.393649\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.09998 | −0.673900 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.60747i | − | 0.433434i | −0.976234 | − | 0.216717i | \(-0.930465\pi\) | ||
0.976234 | − | 0.216717i | \(-0.0695349\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.88697 | − | 1.19972i | −0.175961 | − | 0.111875i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.70860i | 0.250410i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.57560 | 0.236105 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.54789 | −0.777081 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.5313i | 1.49058i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0886 | + | 1.42909i | 0.991797 | + | 0.127822i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.5324i | 1.02334i | 0.859182 | + | 0.511669i | \(0.170973\pi\) | ||||
−0.859182 | + | 0.511669i | \(0.829027\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.86844 | 0.340597 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.9639 | 1.13266 | 0.566332 | − | 0.824177i | \(-0.308362\pi\) | ||||
0.566332 | + | 0.824177i | \(0.308362\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.37450i | − | 0.466028i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.6726 | + | 6.78556i | 0.918550 | + | 0.584008i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.1457i | 1.46485i | 0.680846 | + | 0.732427i | \(0.261612\pi\) | ||||
−0.680846 | + | 0.732427i | \(0.738388\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.4798 | −1.65225 | −0.826127 | − | 0.563485i | \(-0.809460\pi\) | ||||
−0.826127 | + | 0.563485i | \(0.809460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.0470 | 1.09876 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.07226i | − | 0.340540i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.80719 | + | 5.98810i | −0.316170 | + | 0.497285i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.9124i | 1.64235i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.2288 | −1.08374 | −0.541872 | − | 0.840461i | \(-0.682284\pi\) | ||||
−0.541872 | + | 0.840461i | \(0.682284\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.50749 | 0.204057 | 0.102028 | − | 0.994781i | \(-0.467467\pi\) | ||||
0.102028 | + | 0.994781i | \(0.467467\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.582231i | − | 0.0470706i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.0637 | − | 18.9742i | 0.968978 | − | 1.52405i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.52824i | 0.680628i | 0.940312 | + | 0.340314i | \(0.110533\pi\) | ||||
−0.940312 | + | 0.340314i | \(0.889467\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.76398 | −0.615723 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.60747 | −0.363119 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.73240i | 0.605648i | 0.953046 | + | 0.302824i | \(0.0979294\pi\) | ||||
−0.953046 | + | 0.302824i | \(0.902071\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.13516 | − | 2.62911i | −0.321922 | − | 0.204676i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 14.3064i | − | 1.10706i | −0.832829 | − | 0.553531i | \(-0.813280\pi\) | ||
0.832829 | − | 0.553531i | \(-0.186720\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.23713 | 0.479779 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.21494 | −0.0929086 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.4714i | 1.17627i | 0.808763 | + | 0.588135i | \(0.200138\pi\) | ||||
−0.808763 | + | 0.588135i | \(0.799862\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.8612 | − | 9.77394i | 1.57696 | − | 0.738841i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.37450i | − | 0.403972i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.98612 | 0.447424 | 0.223712 | − | 0.974655i | \(-0.428183\pi\) | ||||
0.223712 | + | 0.974655i | \(0.428183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.69892 | −0.423597 | −0.211799 | − | 0.977313i | \(-0.567932\pi\) | ||||
−0.211799 | + | 0.977313i | \(0.567932\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.01527i | 0.444662i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.57339 | + | 6.08670i | 0.703850 | + | 0.447503i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.875359i | 0.0640126i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 26.0595 | 1.89555 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.34402 | 0.603752 | 0.301876 | − | 0.953347i | \(-0.402387\pi\) | ||||
0.301876 | + | 0.953347i | \(0.402387\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.0250i | 1.15350i | 0.816920 | + | 0.576751i | \(0.195680\pi\) | ||||
−0.816920 | + | 0.576751i | \(0.804320\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.36620 | + | 6.86733i | −0.312670 | + | 0.491779i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.78893i | − | 0.412444i | −0.978505 | − | 0.206222i | \(-0.933883\pi\) | ||
0.978505 | − | 0.206222i | \(-0.0661169\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.8085 | −1.33330 | −0.666651 | − | 0.745370i | \(-0.732273\pi\) | ||||
−0.666651 | + | 0.745370i | \(0.732273\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.64902 | 0.257382 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.6213i | 1.02621i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.1720 | − | 22.2903i | 0.989816 | − | 1.55682i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.04155i | 0.0723925i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.82661 | 0.126349 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.88199 | 0.336090 | 0.168045 | − | 0.985779i | \(-0.446255\pi\) | ||||
0.168045 | + | 0.985779i | \(0.446255\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.0498i | 0.757119i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.21609 | − | 3.31635i | −0.355734 | − | 0.226173i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 46.3299i | − | 3.14508i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.8626 | 0.936750 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.45372 | 0.0977880 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.4786i | 0.902596i | 0.892373 | + | 0.451298i | \(0.149039\pi\) | ||||
−0.892373 | + | 0.451298i | \(0.850961\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.20946 | − | 4.71580i | −0.147297 | − | 0.314387i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.6894i | 0.908598i | 0.890849 | + | 0.454299i | \(0.150110\pi\) | ||||
−0.890849 | + | 0.454299i | \(0.849890\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.3964 | −1.81040 | −0.905202 | − | 0.424981i | \(-0.860281\pi\) | ||||
−0.905202 | + | 0.424981i | \(0.860281\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.0969 | −0.664329 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 0.0387841i | − | 0.00254083i | −0.999999 | − | 0.00127041i | \(-0.999596\pi\) | ||
0.999999 | − | 0.00127041i | \(-0.000404386\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.5922 | − | 11.1850i | −1.14759 | − | 0.729629i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 16.8612i | − | 1.09525i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.9030 | −0.899312 | −0.449656 | − | 0.893202i | \(-0.648453\pi\) | ||||
−0.449656 | + | 0.893202i | \(0.648453\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.9972 | −0.772810 | −0.386405 | − | 0.922329i | \(-0.626283\pi\) | ||||
−0.386405 | + | 0.922329i | \(0.626283\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 10.2637i | − | 0.658416i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.0706 | − | 26.8493i | 1.09060 | − | 1.71534i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.03348i | − | 0.193016i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.7324 | −1.18712 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.7806 | 1.12230 | 0.561150 | − | 0.827714i | \(-0.310359\pi\) | ||||
0.561150 | + | 0.827714i | \(0.310359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.56592i | − | 0.0984487i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.938543 | − | 1.47618i | 0.0587738 | − | 0.0924418i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 10.2315i | − | 0.638226i | −0.947717 | − | 0.319113i | \(-0.896615\pi\) | ||
0.947717 | − | 0.319113i | \(-0.103385\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.3756 | 1.45249 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.30524 | 0.204589 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.99856i | 0.246562i | 0.992372 | + | 0.123281i | \(0.0393416\pi\) | ||||
−0.992372 | + | 0.123281i | \(0.960658\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.4687 | + | 6.65593i | 0.643088 | + | 0.408871i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 10.7975i | − | 0.660794i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.88084 | 0.175648 | 0.0878239 | − | 0.996136i | \(-0.472009\pi\) | ||||
0.0878239 | + | 0.996136i | \(0.472009\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.1944 | −0.862250 | −0.431125 | − | 0.902292i | \(-0.641883\pi\) | ||||
−0.431125 | + | 0.902292i | \(0.641883\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.7681i | 1.01485i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.32183 | + | 7.09001i | 0.200314 | + | 0.427544i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 9.13576i | − | 0.548915i | −0.961599 | − | 0.274457i | \(-0.911502\pi\) | ||
0.961599 | − | 0.274457i | \(-0.0884982\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.4731 | −0.627011 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.8640 | 0.886709 | 0.443355 | − | 0.896346i | \(-0.353788\pi\) | ||||
0.443355 | + | 0.896346i | \(0.353788\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.03878i | − | 0.180637i | −0.995913 | − | 0.0903185i | \(-0.971212\pi\) | ||
0.995913 | − | 0.0903185i | \(-0.0287885\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.08033 | − | 1.95845i | −0.182463 | − | 0.116009i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 54.4268i | − | 3.21271i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6875 | 0.981618 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.66837 | 0.215044 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 19.2288i | − | 1.12336i | −0.827356 | − | 0.561678i | \(-0.810156\pi\) | ||
0.827356 | − | 0.561678i | \(-0.189844\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.60747 | + | 7.24681i | −0.268257 | + | 0.421925i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.85675i | 0.513921i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.60055 | −0.150394 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.7363 | −0.734106 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.4299i | 0.714078i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.15680 | − | 8.11081i | 0.295277 | − | 0.464423i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.5395i | − | 1.17225i | −0.810220 | − | 0.586127i | \(-0.800652\pi\) | ||
0.810220 | − | 0.586127i | \(-0.199348\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.1135 | 0.689114 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.83929 | 0.557935 | 0.278967 | − | 0.960301i | \(-0.410008\pi\) | ||||
0.278967 | + | 0.960301i | \(0.410008\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.4659i | 1.26985i | 0.772574 | + | 0.634925i | \(0.218969\pi\) | ||||
−0.772574 | + | 0.634925i | \(0.781031\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.05538 | − | 5.75735i | −0.510213 | − | 0.324390i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.8404i | 1.00202i | 0.865442 | + | 0.501010i | \(0.167038\pi\) | ||||
−0.865442 | + | 0.501010i | \(0.832962\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.96928 | −0.278226 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.67944 | −0.540254 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.652066i | 0.0362819i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.7745 | − | 5.51662i | 0.653132 | − | 0.306007i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 9.58252i | − | 0.529914i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −42.9554 | −2.36821 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.3130 | −0.731750 | −0.365875 | − | 0.930664i | \(-0.619230\pi\) | ||||
−0.365875 | + | 0.930664i | \(0.619230\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 5.28420i | − | 0.289572i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.92022 | − | 3.12824i | −0.268820 | − | 0.170914i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.08338i | − | 0.167962i | −0.996467 | − | 0.0839812i | \(-0.973236\pi\) | ||
0.996467 | − | 0.0839812i | \(-0.0267636\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.44791 | −0.350202 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.7459 | 0.852691 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 33.3063i | − | 1.79837i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.67895 | + | 2.64072i | −0.0903916 | + | 0.142171i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.5617i | 0.620666i | 0.950628 | + | 0.310333i | \(0.100441\pi\) | ||||
−0.950628 | + | 0.310333i | \(0.899559\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.4980 | 0.883117 | 0.441558 | − | 0.897232i | \(-0.354426\pi\) | ||||
0.441558 | + | 0.897232i | \(0.354426\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.7085 | 0.785084 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.7252i | 0.730518i | 0.930906 | + | 0.365259i | \(0.119020\pi\) | ||||
−0.930906 | + | 0.365259i | \(0.880980\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.47280 | − | 14.8992i | 0.502764 | − | 0.790767i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 3.60442i | − | 0.190766i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.1442 | 0.799282 | 0.399641 | − | 0.916672i | \(-0.369135\pi\) | ||||
0.399641 | + | 0.916672i | \(0.369135\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6393 | −0.928386 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.9623i | 0.627859i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.6919 | − | 11.8842i | −0.978381 | − | 0.622048i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2719i | 0.588390i | 0.955745 | + | 0.294195i | \(0.0950515\pi\) | ||||
−0.955745 | + | 0.294195i | \(0.904949\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.3035 | −0.640495 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.5617 | 1.32710 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 35.3296i | − | 1.82930i | −0.404252 | − | 0.914648i | \(-0.632468\pi\) | ||
0.404252 | − | 0.914648i | \(-0.367532\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.99994 | − | 15.5180i | 0.103277 | − | 0.801344i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.25257i | 0.425029i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.8598 | −1.89336 | −0.946679 | − | 0.322178i | \(-0.895585\pi\) | ||||
−0.946679 | + | 0.322178i | \(0.895585\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.1390 | 0.826828 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.27065i | 0.218220i | 0.994030 | + | 0.109110i | \(0.0348001\pi\) | ||||
−0.994030 | + | 0.109110i | \(0.965200\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.6144 | + | 8.65593i | 0.693853 | + | 0.441147i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.87911i | 0.146353i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.42988 | 0.326008 | 0.163004 | − | 0.986625i | \(-0.447882\pi\) | ||||
0.163004 | + | 0.986625i | \(0.447882\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.559006 | 0.0282701 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 18.1423i | − | 0.915160i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.4548 | + | 22.7351i | −0.727301 | + | 1.14393i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.9539i | 1.70410i | 0.523462 | + | 0.852049i | \(0.324640\pi\) | ||||
−0.523462 | + | 0.852049i | \(0.675360\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.52133 | −0.376537 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.6421 | 1.38038 | 0.690189 | − | 0.723629i | \(-0.257527\pi\) | ||||
0.690189 | + | 0.723629i | \(0.257527\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 26.1495i | − | 1.30260i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.74732 | − | 9.03961i | 0.285587 | − | 0.449182i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.94457i | 0.393798i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.2161 | 0.653494 | 0.326747 | − | 0.945112i | \(-0.394048\pi\) | ||||
0.326747 | + | 0.945112i | \(0.394048\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.9945 | 1.18356 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.6947i | 0.870700i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.2582 | + | 16.0590i | 1.23988 | + | 0.788304i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.2609i | 1.33497i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.4772 | 1.14694 | 0.573468 | − | 0.819228i | \(-0.305598\pi\) | ||||
0.573468 | + | 0.819228i | \(0.305598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.1138 | 1.12650 | 0.563249 | − | 0.826287i | \(-0.309551\pi\) | ||||
0.563249 | + | 0.826287i | \(0.309551\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.71032i | 0.472132i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.53100 | + | 1.18583i | −0.122772 | + | 0.0575214i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 19.8044i | − | 0.958401i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.69892 | −0.275146 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.52709 | 0.458904 | 0.229452 | − | 0.973320i | \(-0.426307\pi\) | ||||
0.229452 | + | 0.973320i | \(0.426307\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.79445i | 0.134293i | 0.997743 | + | 0.0671464i | \(0.0213895\pi\) | ||||
−0.997743 | + | 0.0671464i | \(0.978611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.38003 | + | 5.32797i | 0.401792 | + | 0.255456i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.16647i | − | 0.0558001i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.09578 | 0.100026 | 0.0500129 | − | 0.998749i | \(-0.484074\pi\) | ||||
0.0500129 | + | 0.998749i | \(0.484074\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.8199 | −0.705711 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.0870i | 1.28694i | 0.765471 | + | 0.643470i | \(0.222506\pi\) | ||||
−0.765471 | + | 0.643470i | \(0.777494\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.25648 | + | 14.5590i | −0.438799 | + | 0.690161i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.5130i | 0.875633i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.470272 | 0.0221935 | 0.0110967 | − | 0.999938i | \(-0.496468\pi\) | ||||
0.0110967 | + | 0.999938i | \(0.496468\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.4978 | 0.871028 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 3.50910i | − | 0.164872i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.3750 | − | 22.6096i | 0.673913 | − | 1.05996i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 5.83768i | − | 0.273075i | −0.990635 | − | 0.136538i | \(-0.956403\pi\) | ||
0.990635 | − | 0.136538i | \(-0.0435974\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.16170 | −0.147575 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.8487 | 0.505277 | 0.252638 | − | 0.967561i | \(-0.418702\pi\) | ||||
0.252638 | + | 0.967561i | \(0.418702\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.06258i | − | 0.0493825i | −0.999695 | − | 0.0246912i | \(-0.992140\pi\) | ||
0.999695 | − | 0.0246912i | \(-0.00786026\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −26.5534 | − | 16.8825i | −1.23139 | − | 0.782906i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 4.99885i | − | 0.231319i | −0.993289 | − | 0.115660i | \(-0.963102\pi\) | ||
0.993289 | − | 0.115660i | \(-0.0368982\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.0138 | −0.554747 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.9348 | 0.549928 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 4.32862i | − | 0.199030i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.47447 | + | 5.28144i | 0.113537 | + | 0.242329i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 5.77838i | − | 0.264574i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.4283 | 1.52738 | 0.763688 | − | 0.645585i | \(-0.223387\pi\) | ||||
0.763688 | + | 0.645585i | \(0.223387\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.1937 | 0.601580 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.44791i | 0.293390i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.94632 | − | 3.14484i | −0.224601 | − | 0.142800i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.7901i | − | 0.488945i | −0.969656 | − | 0.244473i | \(-0.921385\pi\) | ||
0.969656 | − | 0.244473i | \(-0.0786148\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.8211 | 0.489346 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.8127 | −0.713618 | −0.356809 | − | 0.934177i | \(-0.616135\pi\) | ||||
−0.356809 | + | 0.934177i | \(0.616135\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.77394i | − | 0.0798944i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.95673 | − | 3.07762i | 0.0879483 | − | 0.138329i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 36.3798i | − | 1.63185i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.9711 | 0.580668 | 0.290334 | − | 0.956925i | \(-0.406234\pi\) | ||||
0.290334 | + | 0.956925i | \(0.406234\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.0210 | −0.894474 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.998849i | 0.0445365i | 0.999752 | + | 0.0222682i | \(0.00708878\pi\) | ||||
−0.999752 | + | 0.0222682i | \(0.992911\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.6559 | − | 16.7601i | 0.474183 | − | 0.745813i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 8.72853i | − | 0.387648i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.6936 | 0.917228 | 0.458614 | − | 0.888636i | \(-0.348346\pi\) | ||||
0.458614 | + | 0.888636i | \(0.348346\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −45.6406 | −2.01902 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.59750i | 0.291287i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.3335 | − | 10.3847i | −0.719740 | − | 0.457606i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 14.5991i | − | 0.642066i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.6514 | 0.950393 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.2620 | 1.72010 | 0.860049 | − | 0.510212i | \(-0.170433\pi\) | ||||
0.860049 | + | 0.510212i | \(0.170433\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.74162i | 0.0761556i | 0.999275 | + | 0.0380778i | \(0.0121235\pi\) | ||||
−0.999275 | + | 0.0380778i | \(0.987877\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.6781 | − | 29.1941i | −0.596962 | − | 1.27414i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.62101i | 0.244855i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 30.7196i | − | 1.33061i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.0515 | + | 8.29803i | 0.564264 | + | 0.358755i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 8.37726i | − | 0.361505i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.2811 | 0.959717 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.18117 | −0.351736 | −0.175868 | − | 0.984414i | \(-0.556273\pi\) | ||||
−0.175868 | + | 0.984414i | \(0.556273\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.97534i | 0.342254i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.21494 | + | 12.9208i | −0.351889 | + | 0.553465i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 24.2470i | − | 1.03673i | −0.855160 | − | 0.518364i | \(-0.826541\pi\) | ||
0.855160 | − | 0.518364i | \(-0.173459\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.47690 | −0.191069 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.70168 | −0.157697 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 55.5129i | 2.36065i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.51801 | − | 13.3975i | 0.361569 | − | 0.568690i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.0966i | 1.48709i | 0.668685 | + | 0.743546i | \(0.266858\pi\) | ||||
−0.668685 | + | 0.743546i | \(0.733142\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.18862 | −0.304046 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.22502 | 0.0517204 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.98179i | 0.294247i | 0.989118 | + | 0.147124i | \(0.0470016\pi\) | ||||
−0.989118 | + | 0.147124i | \(0.952998\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.69416 | + | 5.52769i | 0.365766 | + | 0.232552i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 22.0723i | − | 0.926948i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.7280 | −0.910886 | −0.455443 | − | 0.890265i | \(-0.650519\pi\) | ||||
−0.455443 | + | 0.890265i | \(0.650519\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.71016 | 0.197114 | 0.0985570 | − | 0.995131i | \(-0.468577\pi\) | ||||
0.0985570 | + | 0.995131i | \(0.468577\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 11.6770i | − | 0.487814i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.52769 | − | 2.12133i | 0.188818 | − | 0.0884654i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.49085i | 0.395109i | 0.980292 | + | 0.197555i | \(0.0633000\pi\) | ||||
−0.980292 | + | 0.197555i | \(0.936700\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.4261 | 0.931996 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 61.6736 | 2.55865 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.68756i | 0.359802i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.11105 | − | 3.24957i | −0.211316 | − | 0.134353i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.4952i | 0.433184i | 0.976262 | + | 0.216592i | \(0.0694942\pi\) | ||||
−0.976262 | + | 0.216592i | \(0.930506\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.7293 | 0.483299 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.10130 | −0.333243 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 18.2138i | − | 0.747951i | −0.927439 | − | 0.373975i | \(-0.877994\pi\) | ||
0.927439 | − | 0.373975i | \(-0.122006\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.09001 | + | 4.86009i | −0.126678 | + | 0.199244i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.3215i | 1.07727i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.8055 | −0.850091 | −0.425045 | − | 0.905172i | \(-0.639742\pi\) | ||||
−0.425045 | + | 0.905172i | \(0.639742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −47.4004 | −1.93350 | −0.966752 | − | 0.255716i | \(-0.917689\pi\) | ||||
−0.966752 | + | 0.255716i | \(0.917689\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.71580i | 0.110596i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.2551 | − | 16.1296i | 0.416929 | − | 0.655762i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 5.77118i | − | 0.234245i | −0.993117 | − | 0.117123i | \(-0.962633\pi\) | ||
0.993117 | − | 0.117123i | \(-0.0373670\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.4617 | 0.829152 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.2449 | −0.980844 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.9329i | 1.57248i | 0.617919 | + | 0.786242i | \(0.287976\pi\) | ||||
−0.617919 | + | 0.786242i | \(0.712024\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −31.1941 | − | 19.8330i | −1.25787 | − | 0.799743i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 10.1653i | − | 0.409241i | −0.978841 | − | 0.204620i | \(-0.934404\pi\) | ||
0.978841 | − | 0.204620i | \(-0.0655959\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.09923 | 0.0843752 | 0.0421876 | − | 0.999110i | \(-0.486567\pi\) | ||||
0.0421876 | + | 0.999110i | \(0.486567\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.65593 | 0.226965 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.5490i | 1.42424i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.0000 | + | 19.2094i | −0.639998 | + | 0.768377i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 2.55624i | − | 0.102087i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.83607 | −0.113081 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.3066 | 1.28611 | 0.643053 | − | 0.765821i | \(-0.277667\pi\) | ||||
0.643053 | + | 0.765821i | \(0.277667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6.83209i | − | 0.271551i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.7614 | − | 13.8357i | −0.863575 | − | 0.549055i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 37.0027i | − | 1.46610i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.22387 | −0.325331 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.5758 | 0.575711 | 0.287856 | − | 0.957674i | \(-0.407058\pi\) | ||||
0.287856 | + | 0.957674i | \(0.407058\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.5090i | 1.67639i | 0.545369 | + | 0.838196i | \(0.316389\pi\) | ||||
−0.545369 | + | 0.838196i | \(0.683611\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.64106 | + | 7.29964i | −0.182742 | + | 0.287423i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 3.04979i | − | 0.119900i | −0.998201 | − | 0.0599498i | \(-0.980906\pi\) | ||
0.998201 | − | 0.0599498i | \(-0.0190940\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.01383 | −0.236064 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −64.8362 | −2.54113 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.9600i | 0.702830i | 0.936220 | + | 0.351415i | \(0.114299\pi\) | ||||
−0.936220 | + | 0.351415i | \(0.885701\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.5531 | + | 24.4626i | −0.607711 | + | 0.955832i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.3173i | 0.402518i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 46.3411 | 1.80519 | 0.902597 | − | 0.430486i | \(-0.141658\pi\) | ||||
0.902597 | + | 0.430486i | \(0.141658\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.23165 | 0.0479056 | 0.0239528 | − | 0.999713i | \(-0.492375\pi\) | ||||
0.0239528 | + | 0.999713i | \(0.492375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 2.03441i | − | 0.0790099i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.1415 | + | 6.44791i | 0.393271 | + | 0.250039i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.17339i | 0.122874i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.8626 | 0.729271 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.73083 | 0.259841 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.4664i | 1.63696i | 0.574537 | + | 0.818479i | \(0.305182\pi\) | ||||
−0.574537 | + | 0.818479i | \(0.694818\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.6083 | + | 11.9981i | −0.985664 | + | 0.461806i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.41777i | − | 0.0544893i | −0.999629 | − | 0.0272447i | \(-0.991327\pi\) | ||
0.999629 | − | 0.0272447i | \(-0.00867332\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0776 | −0.463495 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.1576 | 0.734121 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 4.60886i | − | 0.176353i | −0.996105 | − | 0.0881766i | \(-0.971896\pi\) | ||
0.996105 | − | 0.0881766i | \(-0.0281040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.3534 | − | 20.5701i | −1.23616 | − | 0.785942i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38.3398i | 1.46276i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.4276 | 0.549647 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.8903 | 0.642537 | 0.321269 | − | 0.946988i | \(-0.395891\pi\) | ||||
0.321269 | + | 0.946988i | \(0.395891\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 7.51470i | − | 0.285460i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.3704 | − | 36.7578i | 0.886488 | − | 1.39430i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.60338i | 0.250121i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.0542763 | −0.00205292 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.9543 | −0.451508 | −0.225754 | − | 0.974184i | \(-0.572484\pi\) | ||||
−0.225754 | + | 0.974184i | \(0.572484\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.91801i | 0.223202i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.6528 | + | 24.6194i | −0.589519 | + | 0.927219i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 40.9235i | − | 1.53909i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.6755 | 0.476040 | 0.238020 | − | 0.971260i | \(-0.423502\pi\) | ||||
0.238020 | + | 0.971260i | \(0.423502\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.5490 | 0.470626 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 10.0554i | − | 0.376577i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.68425 | + | 4.88559i | 0.287375 | + | 0.182711i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.4566i | 0.726618i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.7351 | −1.29540 | −0.647700 | − | 0.761896i | \(-0.724269\pi\) | ||||
−0.647700 | + | 0.761896i | \(0.724269\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.8819 | −1.48528 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.7895i | 0.624408i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.73180 | − | 14.3681i | −0.250013 | − | 0.533619i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.6631i | 1.02597i | 0.858398 | + | 0.512984i | \(0.171460\pi\) | ||||
−0.858398 | + | 0.512984i | \(0.828540\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.7351 | −1.06426 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.54524 | 0.0571528 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 2.14239i | − | 0.0791309i | −0.999217 | − | 0.0395654i | \(-0.987403\pi\) | ||
0.999217 | − | 0.0395654i | \(-0.0125974\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −37.5742 | − | 23.8894i | −1.38594 | − | 0.881174i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.08309i | − | 0.150403i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.6249 | −1.56798 | −0.783991 | − | 0.620772i | \(-0.786819\pi\) | ||||
−0.783991 | + | 0.620772i | \(0.786819\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.24519 | −0.155951 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 23.4687i | − | 0.860982i | −0.902595 | − | 0.430491i | \(-0.858340\pi\) | ||
0.902595 | − | 0.430491i | \(-0.141660\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.8709 | − | 24.9623i | 0.581464 | − | 0.914549i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 13.9417i | − | 0.510100i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.8681 | 1.16444 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.2579 | 0.994654 | 0.497327 | − | 0.867563i | \(-0.334315\pi\) | ||||
0.497327 | + | 0.867563i | \(0.334315\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 24.8830i | − | 0.906786i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.00830 | + | 4.73157i | −0.109483 | + | 0.172199i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.7382i | 0.462976i | 0.972838 | + | 0.231488i | \(0.0743595\pi\) | ||||
−0.972838 | + | 0.231488i | \(0.925641\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.19143 | −0.0795437 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.61715 | 0.239871 | 0.119936 | − | 0.992782i | \(-0.461731\pi\) | ||||
0.119936 | + | 0.992782i | \(0.461731\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.5490i | 1.14215i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.09865 | + | 0.698516i | 0.0397219 | + | 0.0252549i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.98727i | 0.360619i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.2116 | 0.981275 | 0.490638 | − | 0.871364i | \(-0.336764\pi\) | ||||
0.490638 | + | 0.871364i | \(0.336764\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.3185 | −0.515668 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.9249i | 0.824552i | 0.911059 | + | 0.412276i | \(0.135266\pi\) | ||||
−0.911059 | + | 0.412276i | \(0.864734\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.3307 | + | 45.5276i | 0.766223 | + | 1.63540i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 32.7129i | − | 1.17357i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.7792 | 0.493693 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.3642 | 0.442427 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 17.9485i | − | 0.641427i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.0926 | − | 10.2315i | −0.574368 | − | 0.365179i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.0620i | 0.465610i | 0.972523 | + | 0.232805i | \(0.0747904\pi\) | ||||
−0.972523 | + | 0.232805i | \(0.925210\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.59578 | 0.199215 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.2288 | 0.754808 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 11.1780i | − | 0.396943i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.31463 | − | 14.6504i | 0.330356 | − | 0.519596i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 20.9305i | − | 0.741395i | −0.928754 | − | 0.370697i | \(-0.879119\pi\) | ||
0.928754 | − | 0.370697i | \(-0.120881\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.21160 | 0.184373 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.03607 | 0.283941 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 15.5117i | − | 0.547396i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.52769 | − | 8.69416i | 0.194825 | − | 0.306429i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 4.03158i | − | 0.141918i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.0664 | −0.635180 | −0.317590 | − | 0.948228i | \(-0.602874\pi\) | ||||
−0.317590 | + | 0.948228i | \(0.602874\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.8658 | −1.22430 | −0.612152 | − | 0.790740i | \(-0.709696\pi\) | ||||
−0.612152 | + | 0.790740i | \(0.709696\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.8644i | 0.696673i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.5908 | − | 9.27674i | −0.511094 | − | 0.324950i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.22444i | − | 0.112809i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.4798 | −0.436079 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.5989 | 0.509507 | 0.254753 | − | 0.967006i | \(-0.418006\pi\) | ||||
0.254753 | + | 0.967006i | \(0.418006\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 25.8126i | − | 0.899771i | −0.893086 | − | 0.449886i | \(-0.851465\pi\) | ||
0.893086 | − | 0.449886i | \(-0.148535\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.92210 | − | 4.64873i | 0.345443 | − | 0.161848i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.9097i | 1.90940i | 0.297577 | + | 0.954698i | \(0.403822\pi\) | ||||
−0.297577 | + | 0.954698i | \(0.596178\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.4809 | 0.954452 | 0.477226 | − | 0.878781i | \(-0.341642\pi\) | ||||
0.477226 | + | 0.878781i | \(0.341642\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.7850 | −0.443507 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.95396i | 0.275589i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.9958 | + | 17.1637i | 0.934226 | + | 0.593975i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 56.8725i | 1.96580i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.46577 | −0.0506041 | −0.0253020 | − | 0.999680i | \(-0.508055\pi\) | ||||
−0.0253020 | + | 0.999680i | \(0.508055\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9296 | −0.652744 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 20.8013i | − | 0.716436i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.48283 | + | 11.7693i | −0.257417 | + | 0.404876i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 39.3841i | − | 1.35325i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.25262 | −0.145949 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.07341 | 0.173914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.8044i | 1.22592i | 0.790115 | + | 0.612959i | \(0.210021\pi\) | ||||
−0.790115 | + | 0.612959i | \(0.789979\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.45759 | − | 2.29255i | 0.0498485 | − | 0.0784037i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 28.1663i | − | 0.962141i | −0.876682 | − | 0.481070i | \(-0.840248\pi\) | ||
0.876682 | − | 0.481070i | \(-0.159752\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.3185 | 0.693258 | 0.346629 | − | 0.938002i | \(-0.387326\pi\) | ||||
0.346629 | + | 0.938002i | \(0.387326\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −76.1674 | −2.59578 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.1357i | 0.515224i | 0.966248 | + | 0.257612i | \(0.0829356\pi\) | ||||
−0.966248 | + | 0.257612i | \(0.917064\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29.1941 | − | 18.5614i | −0.992631 | − | 0.631108i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 23.3533i | − | 0.793120i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.8670 | −0.640018 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.78086 | −0.229761 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.73021i | 0.0924036i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.58451 | + | 51.0905i | −0.222597 | + | 1.72717i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 12.9668i | − | 0.437856i | −0.975741 | − | 0.218928i | \(-0.929744\pi\) | ||
0.975741 | − | 0.218928i | \(-0.0702560\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.9097 | −0.907640 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.3573 | −1.15753 | −0.578763 | − | 0.815496i | \(-0.696464\pi\) | ||||
−0.578763 | + | 0.815496i | \(0.696464\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.7201i | 0.495372i | 0.968840 | + | 0.247686i | \(0.0796701\pi\) | ||||
−0.968840 | + | 0.247686i | \(0.920330\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.1415 | + | 6.44791i | 0.340904 | + | 0.216744i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.9401i | 0.703101i | 0.936169 | + | 0.351550i | \(0.114345\pi\) | ||||
−0.936169 | + | 0.351550i | \(0.885655\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −53.1354 | −1.78210 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.50161 | 0.251313 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 10.8750i | − | 0.363919i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.18169 | + | 11.2956i | −0.240057 | + | 0.377572i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.63934i | 0.121514i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.9097 | −1.06425 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.10130 | −0.103319 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.8237i | 0.593137i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.83713 | − | 10.7537i | 0.227274 | − | 0.357465i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 40.2008i | − | 1.33485i | −0.744679 | − | 0.667423i | \(-0.767397\pi\) | ||
0.744679 | − | 0.667423i | \(-0.232603\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.25101 | −0.306837 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.6058 | −1.80917 | −0.904586 | − | 0.426292i | \(-0.859820\pi\) | ||||
−0.904586 | + | 0.426292i | \(0.859820\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.9608i | 0.693700i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.3506 | − | 7.21666i | −0.375241 | − | 0.238576i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 59.7309i | 1.97249i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.8019 | 0.455284 | 0.227642 | − | 0.973745i | \(-0.426898\pi\) | ||||
0.227642 | + | 0.973745i | \(0.426898\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.7440 | −0.947147 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 20.5335i | − | 0.675868i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.9708 | + | 10.7624i | −0.755277 | + | 0.353864i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.01556i | 0.296110i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.2775 | −0.632475 | −0.316237 | − | 0.948680i | \(-0.602420\pi\) | ||||
−0.316237 | + | 0.948680i | \(0.602420\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.5975 | 0.543961 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 13.7696i | − | 0.450795i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.65178 | − | 1.05019i | −0.0540189 | − | 0.0343449i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 48.0855i | − | 1.57089i | −0.618934 | − | 0.785443i | \(-0.712435\pi\) | ||
0.618934 | − | 0.785443i | \(-0.287565\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.4399 | 1.02600 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.6853 | −1.00031 | −0.500156 | − | 0.865935i | \(-0.666724\pi\) | ||||
−0.500156 | + | 0.865935i | \(0.666724\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 11.8127i | − | 0.384675i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −31.2642 | + | 49.1736i | −1.01703 | + | 1.59962i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 12.9280i | − | 0.420103i | −0.977690 | − | 0.210051i | \(-0.932637\pi\) | ||
0.977690 | − | 0.210051i | \(-0.0673631\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.7605 | −0.836222 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.9668 | 0.809603 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 6.38285i | − | 0.206761i | −0.994642 | − | 0.103380i | \(-0.967034\pi\) | ||
0.994642 | − | 0.103380i | \(-0.0329659\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.0105 | + | 15.7449i | −0.323933 | + | 0.509494i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.95425i | 0.224799i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −78.9982 | −2.55098 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 70.1107 | 2.26163 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 7.20398i | − | 0.232145i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30.2386 | − | 19.2255i | −0.973416 | − | 0.618891i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 38.6028i | − | 1.24138i | −0.784056 | − | 0.620691i | \(-0.786852\pi\) | ||
0.784056 | − | 0.620691i | \(-0.213148\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.912532 | 0.0293148 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0216 | 0.770889 | 0.385444 | − | 0.922731i | \(-0.374048\pi\) | ||||
0.385444 | + | 0.922731i | \(0.374048\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 89.7525i | − | 2.87733i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.72022 | − | 16.4778i | −0.247245 | − | 0.527712i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 45.5558i | − | 1.45746i | −0.684801 | − | 0.728730i | \(-0.740111\pi\) | ||
0.684801 | − | 0.728730i | \(-0.259889\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0819 | −0.386139 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.13184 | 0.227702 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.1396i | 0.929408i | 0.885466 | + | 0.464704i | \(0.153839\pi\) | ||||
−0.885466 | + | 0.464704i | \(0.846161\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.9235 | + | 6.94511i | 0.348053 | + | 0.221290i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 60.1138i | 1.91344i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.76426 | −0.0878985 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0415 | 0.636639 | 0.318320 | − | 0.947983i | \(-0.396881\pi\) | ||||
0.318320 | + | 0.947983i | \(0.396881\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.6309i | 0.591233i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.5650 | − | 35.4912i | 0.715360 | − | 1.12515i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 0.340153i | − | 0.0107728i | −0.999985 | − | 0.00538638i | \(-0.998285\pi\) | ||
0.999985 | − | 0.00538638i | \(-0.00171455\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.6949 | −0.907866 |
(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 | 1840.2.e.d.369.3 | 8 | ||
4.3 | odd | 2 | 115.2.b.b.24.7 | yes | 8 | ||
5.2 | odd | 4 | 9200.2.a.ck.1.2 | 4 | |||
5.3 | odd | 4 | 9200.2.a.cq.1.3 | 4 | |||
5.4 | even | 2 | inner | 1840.2.e.d.369.6 | 8 | ||
12.11 | even | 2 | 1035.2.b.e.829.2 | 8 | |||
20.3 | even | 4 | 575.2.a.i.1.4 | 4 | |||
20.7 | even | 4 | 575.2.a.j.1.1 | 4 | |||
20.19 | odd | 2 | 115.2.b.b.24.2 | ✓ | 8 | ||
60.23 | odd | 4 | 5175.2.a.bv.1.1 | 4 | |||
60.47 | odd | 4 | 5175.2.a.bw.1.4 | 4 | |||
60.59 | even | 2 | 1035.2.b.e.829.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.b.b.24.2 | ✓ | 8 | 20.19 | odd | 2 | ||
115.2.b.b.24.7 | yes | 8 | 4.3 | odd | 2 | ||
575.2.a.i.1.4 | 4 | 20.3 | even | 4 | |||
575.2.a.j.1.1 | 4 | 20.7 | even | 4 | |||
1035.2.b.e.829.2 | 8 | 12.11 | even | 2 | |||
1035.2.b.e.829.7 | 8 | 60.59 | even | 2 | |||
1840.2.e.d.369.3 | 8 | 1.1 | even | 1 | trivial | ||
1840.2.e.d.369.6 | 8 | 5.4 | even | 2 | inner | ||
5175.2.a.bv.1.1 | 4 | 60.23 | odd | 4 | |||
5175.2.a.bw.1.4 | 4 | 60.47 | odd | 4 | |||
9200.2.a.ck.1.2 | 4 | 5.2 | odd | 4 | |||
9200.2.a.cq.1.3 | 4 | 5.3 | odd | 4 |