Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5520.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.3 | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.c.1471.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.52302 | −0.575649 | −0.287824 | − | 0.957683i | \(-0.592932\pi\) | ||||
−0.287824 | + | 0.957683i | \(0.592932\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.43261 | −1.93950 | −0.969752 | − | 0.244092i | \(-0.921510\pi\) | ||||
−0.969752 | + | 0.244092i | \(0.921510\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.50229 | −1.24871 | −0.624356 | − | 0.781140i | \(-0.714639\pi\) | ||||
−0.624356 | + | 0.781140i | \(0.714639\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.65230i | − | 0.400743i | −0.979720 | − | 0.200371i | \(-0.935785\pi\) | ||
0.979720 | − | 0.200371i | \(-0.0642148\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.57593 | 1.27921 | 0.639603 | − | 0.768705i | \(-0.279099\pi\) | ||||
0.639603 | + | 0.768705i | \(0.279099\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.52302i | 0.332351i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.99135 | + | 3.74857i | 0.623740 | + | 0.781632i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.30375 | −0.427796 | −0.213898 | − | 0.976856i | \(-0.568616\pi\) | ||||
−0.213898 | + | 0.976856i | \(0.568616\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.77291i | 0.318424i | 0.987244 | + | 0.159212i | \(0.0508953\pi\) | ||||
−0.987244 | + | 0.159212i | \(0.949105\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.43261i | 1.11977i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.52302i | 0.257438i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.43051i | − | 0.892771i | −0.894841 | − | 0.446385i | \(-0.852711\pi\) | ||
0.894841 | − | 0.446385i | \(-0.147289\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.50229i | 0.720944i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.07053 | −0.323362 | −0.161681 | − | 0.986843i | \(-0.551692\pi\) | ||||
−0.161681 | + | 0.986843i | \(0.551692\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.75591 | −0.725270 | −0.362635 | − | 0.931931i | \(-0.618123\pi\) | ||||
−0.362635 | + | 0.931931i | \(0.618123\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.99382i | 0.436693i | 0.975871 | + | 0.218347i | \(0.0700663\pi\) | ||||
−0.975871 | + | 0.218347i | \(0.929934\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.68040 | −0.668628 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.65230 | −0.231369 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.72374i | 0.374134i | 0.982347 | + | 0.187067i | \(0.0598982\pi\) | ||||
−0.982347 | + | 0.187067i | \(0.940102\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.43261i | 0.867373i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.57593i | − | 0.738550i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.99055i | 0.519525i | 0.965673 | + | 0.259763i | \(0.0836443\pi\) | ||||
−0.965673 | + | 0.259763i | \(0.916356\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.74609i | − | 1.24786i | −0.781480 | − | 0.623930i | \(-0.785535\pi\) | ||
0.781480 | − | 0.623930i | \(-0.214465\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.52302 | 0.191883 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.50229i | 0.558441i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.71642 | 0.454033 | 0.227017 | − | 0.973891i | \(-0.427103\pi\) | ||||
0.227017 | + | 0.973891i | \(0.427103\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.74857 | − | 2.99135i | 0.451275 | − | 0.360117i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.39857i | 0.284658i | 0.989819 | + | 0.142329i | \(0.0454591\pi\) | ||||
−0.989819 | + | 0.142329i | \(0.954541\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.23774 | −1.08120 | −0.540598 | − | 0.841281i | \(-0.681802\pi\) | ||||
−0.540598 | + | 0.841281i | \(0.681802\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.79702 | 1.11647 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.4088 | 1.28360 | 0.641798 | − | 0.766874i | \(-0.278189\pi\) | ||||
0.641798 | + | 0.766874i | \(0.278189\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.35972 | 1.02736 | 0.513681 | − | 0.857981i | \(-0.328281\pi\) | ||||
0.513681 | + | 0.857981i | \(0.328281\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.65230 | −0.179218 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.30375i | 0.246988i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.66224i | 0.282197i | 0.989996 | + | 0.141099i | \(0.0450634\pi\) | ||||
−0.989996 | + | 0.141099i | \(0.954937\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.85710 | 0.718820 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.77291 | 0.183842 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 5.57593i | − | 0.572078i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.66759i | 0.880060i | 0.897983 | + | 0.440030i | \(0.145032\pi\) | ||||
−0.897983 | + | 0.440030i | \(0.854968\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.43261 | 0.646501 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.6952 | 1.86024 | 0.930121 | − | 0.367254i | \(-0.119702\pi\) | ||||
0.930121 | + | 0.367254i | \(0.119702\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.63952 | 0.752744 | 0.376372 | − | 0.926469i | \(-0.377171\pi\) | ||||
0.376372 | + | 0.926469i | \(0.377171\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.52302 | 0.148632 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.71244 | 0.648916 | 0.324458 | − | 0.945900i | \(-0.394818\pi\) | ||||
0.324458 | + | 0.945900i | \(0.394818\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.70608i | 0.259196i | 0.991567 | + | 0.129598i | \(0.0413687\pi\) | ||||
−0.991567 | + | 0.129598i | \(0.958631\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.43051 | −0.515441 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 0.212216i | − | 0.0199636i | −0.999950 | − | 0.00998181i | \(-0.996823\pi\) | ||
0.999950 | − | 0.00998181i | \(-0.00317736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.74857 | − | 2.99135i | 0.349556 | − | 0.278945i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.50229 | 0.416237 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.51650i | 0.230687i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.3784 | 2.76168 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.07053i | 0.186693i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.8377i | − | 1.49410i | −0.664767 | − | 0.747051i | \(-0.731469\pi\) | ||
0.664767 | − | 0.747051i | \(-0.268531\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.75591i | 0.418735i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.1242i | 0.971929i | 0.873979 | + | 0.485964i | \(0.161532\pi\) | ||||
−0.873979 | + | 0.485964i | \(0.838468\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.49227 | −0.736374 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.56165i | − | 0.475164i | −0.971368 | − | 0.237582i | \(-0.923645\pi\) | ||
0.971368 | − | 0.237582i | \(-0.0763548\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.63364i | 0.477839i | 0.971039 | + | 0.238920i | \(0.0767932\pi\) | ||||
−0.971039 | + | 0.238920i | \(0.923207\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.99382 | 0.252125 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 28.9615 | 2.42188 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.30375i | 0.191316i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.68040i | 0.386033i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5221i | 0.862001i | 0.902352 | + | 0.431000i | \(0.141839\pi\) | ||||
−0.902352 | + | 0.431000i | \(0.858161\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.5034i | 1.42441i | 0.701972 | + | 0.712205i | \(0.252303\pi\) | ||||
−0.701972 | + | 0.712205i | \(0.747697\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.65230i | 0.133581i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.77291 | 0.142404 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.31873i | − | 0.584098i | −0.956403 | − | 0.292049i | \(-0.905663\pi\) | ||
0.956403 | − | 0.292049i | \(-0.0943371\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.72374 | 0.216007 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.55590 | − | 5.70917i | −0.359055 | − | 0.449946i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 9.06133i | − | 0.709738i | −0.934916 | − | 0.354869i | \(-0.884525\pi\) | ||
0.934916 | − | 0.354869i | \(-0.115475\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.43261 | 0.500778 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.02942i | 0.621335i | 0.950519 | + | 0.310667i | \(0.100553\pi\) | ||||
−0.950519 | + | 0.310667i | \(0.899447\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.27066 | 0.559281 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.57593 | −0.426402 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.927933 | −0.0705495 | −0.0352747 | − | 0.999378i | \(-0.511231\pi\) | ||||
−0.0352747 | + | 0.999378i | \(0.511231\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.52302 | 0.115130 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.99055 | 0.299948 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 25.1922i | − | 1.88295i | −0.337082 | − | 0.941475i | \(-0.609440\pi\) | ||
0.337082 | − | 0.941475i | \(-0.390560\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.69810i | − | 0.126219i | −0.998007 | − | 0.0631095i | \(-0.979898\pi\) | ||
0.998007 | − | 0.0631095i | \(-0.0201017\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.74609 | −0.720452 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.43051 | −0.399259 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.6286i | 0.777242i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.52302i | − | 0.110784i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.0724 | 0.945886 | 0.472943 | − | 0.881093i | \(-0.343192\pi\) | ||||
0.472943 | + | 0.881093i | \(0.343192\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.0209 | 1.15321 | 0.576606 | − | 0.817023i | \(-0.304377\pi\) | ||||
0.576606 | + | 0.817023i | \(0.304377\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.50229 | 0.322416 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.9113 | −0.848647 | −0.424323 | − | 0.905511i | \(-0.639488\pi\) | ||||
−0.424323 | + | 0.905511i | \(0.639488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.54875 | −0.535117 | −0.267558 | − | 0.963542i | \(-0.586217\pi\) | ||||
−0.267558 | + | 0.963542i | \(0.586217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 3.71642i | − | 0.262136i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.50867 | 0.246261 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.07053i | 0.144612i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.99135 | − | 3.74857i | −0.207913 | − | 0.260544i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −35.8678 | −2.48103 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.69539i | − | 0.323244i | −0.986853 | − | 0.161622i | \(-0.948327\pi\) | ||
0.986853 | − | 0.161622i | \(-0.0516726\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.39857 | 0.164347 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.75591i | 0.324351i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.70018i | − | 0.183300i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.23774i | 0.624229i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.43916i | 0.500412i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.1553i | 1.61756i | 0.588110 | + | 0.808781i | \(0.299872\pi\) | ||||
−0.588110 | + | 0.808781i | \(0.700128\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.4903 | 0.829010 | 0.414505 | − | 0.910047i | \(-0.363955\pi\) | ||||
0.414505 | + | 0.910047i | \(0.363955\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 29.8509i | − | 1.97260i | −0.164951 | − | 0.986302i | \(-0.552747\pi\) | ||
0.164951 | − | 0.986302i | \(-0.447253\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 9.79702i | − | 0.644596i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.897082 | −0.0587698 | −0.0293849 | − | 0.999568i | \(-0.509355\pi\) | ||||
−0.0293849 | + | 0.999568i | \(0.509355\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.99382 | 0.195295 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 11.4088i | − | 0.741084i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.9763i | 1.68027i | 0.542381 | + | 0.840133i | \(0.317523\pi\) | ||||
−0.542381 | + | 0.840133i | \(0.682477\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.15296i | 0.525179i | 0.964908 | + | 0.262589i | \(0.0845764\pi\) | ||||
−0.964908 | + | 0.262589i | \(0.915424\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.68040i | 0.299020i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.1045 | −1.59736 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 9.35972i | − | 0.593148i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.31194 | −0.398406 | −0.199203 | − | 0.979958i | \(-0.563835\pi\) | ||||
−0.199203 | + | 0.979958i | \(0.563835\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.2422 | − | 24.1131i | −1.20975 | − | 1.51598i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.65230i | 0.103471i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.8718 | −0.678164 | −0.339082 | − | 0.940757i | \(-0.610116\pi\) | ||||
−0.339082 | + | 0.940757i | \(0.610116\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.27080i | 0.513923i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.30375 | 0.142599 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.5415 | 1.45163 | 0.725814 | − | 0.687891i | \(-0.241463\pi\) | ||||
0.725814 | + | 0.687891i | \(0.241463\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.72374 | 0.167318 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.66224 | 0.162927 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.5049 | 0.823408 | 0.411704 | − | 0.911318i | \(-0.364934\pi\) | ||||
0.411704 | + | 0.911318i | \(0.364934\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 18.2034i | − | 1.10578i | −0.833255 | − | 0.552889i | \(-0.813525\pi\) | ||
0.833255 | − | 0.552889i | \(-0.186475\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 6.85710i | − | 0.415011i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.43261 | 0.387901 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.79569 | −0.588566 | −0.294283 | − | 0.955718i | \(-0.595081\pi\) | ||||
−0.294283 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.77291i | − | 0.106141i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.6935i | 0.637923i | 0.947768 | + | 0.318962i | \(0.103334\pi\) | ||||
−0.947768 | + | 0.318962i | \(0.896666\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.2186 | −1.61797 | −0.808987 | − | 0.587826i | \(-0.799984\pi\) | ||||
−0.808987 | + | 0.587826i | \(0.799984\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.57593 | −0.330290 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.15346 | 0.186143 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.2699 | 0.839405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.66759 | 0.508103 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 23.1769i | − | 1.35401i | −0.735979 | − | 0.677004i | \(-0.763278\pi\) | ||
0.735979 | − | 0.677004i | \(-0.236722\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.99055 | 0.232339 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 6.43261i | − | 0.373258i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.4680 | − | 16.8772i | −0.778872 | − | 0.976033i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.24337 | 0.417501 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 18.6952i | − | 1.07401i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.74609 | −0.558060 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.1278i | 1.31997i | 0.751278 | + | 0.659985i | \(0.229438\pi\) | ||||
−0.751278 | + | 0.659985i | \(0.770562\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 7.63952i | − | 0.434597i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.5382i | 0.881091i | 0.897730 | + | 0.440545i | \(0.145215\pi\) | ||||
−0.897730 | + | 0.440545i | \(0.854785\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.93700i | 0.109486i | 0.998500 | + | 0.0547428i | \(0.0174339\pi\) | ||||
−0.998500 | + | 0.0547428i | \(0.982566\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 1.52302i | − | 0.0858127i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.0281 | −1.12489 | −0.562446 | − | 0.826834i | \(-0.690140\pi\) | ||||
−0.562446 | + | 0.826834i | \(0.690140\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.8191 | 0.829713 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 6.71244i | − | 0.374652i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 9.21313i | − | 0.512632i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.50229 | 0.249742 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.70608 | 0.149647 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 4.55966i | − | 0.251382i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.6804i | 1.08173i | 0.841109 | + | 0.540866i | \(0.181903\pi\) | ||||
−0.841109 | + | 0.540866i | \(0.818097\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.43051i | 0.297590i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 3.71642i | − | 0.203050i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.73958i | − | 0.203708i | −0.994799 | − | 0.101854i | \(-0.967523\pi\) | ||
0.994799 | − | 0.101854i | \(-0.0324774\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.212216 | −0.0115260 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 11.4044i | − | 0.617585i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.7895 | 0.960544 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.99135 | − | 3.74857i | −0.161049 | − | 0.201816i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.8358i | 1.76272i | 0.472449 | + | 0.881358i | \(0.343370\pi\) | ||||
−0.472449 | + | 0.881358i | \(0.656630\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.3391 | 0.928139 | 0.464069 | − | 0.885799i | \(-0.346389\pi\) | ||||
0.464069 | + | 0.885799i | \(0.346389\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.50229i | − | 0.240315i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.90388 | 0.420681 | 0.210340 | − | 0.977628i | \(-0.432543\pi\) | ||||
0.210340 | + | 0.977628i | \(0.432543\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.39857 | 0.127303 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.51650 | 0.133187 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.85014 | 0.361537 | 0.180768 | − | 0.983526i | \(-0.442142\pi\) | ||||
0.180768 | + | 0.983526i | \(0.442142\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.0910 | 0.636368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 30.3784i | − | 1.59446i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.23774i | 0.483526i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.4163 | −1.17012 | −0.585060 | − | 0.810990i | \(-0.698929\pi\) | ||||
−0.585060 | + | 0.810990i | \(0.698929\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.07053 | 0.107787 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4.14832i | − | 0.215370i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 31.4598i | − | 1.62893i | −0.580214 | − | 0.814464i | \(-0.697031\pi\) | ||
0.580214 | − | 0.814464i | \(-0.302969\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.3722 | 0.534195 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.23870 | 0.474560 | 0.237280 | − | 0.971441i | \(-0.423744\pi\) | ||||
0.237280 | + | 0.971441i | \(0.423744\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.8377 | −0.862620 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.2393 | 1.03418 | 0.517089 | − | 0.855932i | \(-0.327016\pi\) | ||||
0.517089 | + | 0.855932i | \(0.327016\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 9.79702i | − | 0.499302i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.75591 | 0.241757 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0549i | 0.763316i | 0.924304 | + | 0.381658i | \(0.124647\pi\) | ||||
−0.924304 | + | 0.381658i | \(0.875353\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.19378 | − | 4.94262i | 0.313233 | − | 0.249959i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.1242 | 0.561143 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 11.4088i | − | 0.574041i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.0861 | 1.50998 | 0.754989 | − | 0.655737i | \(-0.227642\pi\) | ||||
0.754989 | + | 0.655737i | \(0.227642\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.49227i | 0.425145i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.8412i | 1.73989i | 0.493151 | + | 0.869944i | \(0.335845\pi\) | ||||
−0.493151 | + | 0.869944i | \(0.664155\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.98216i | − | 0.397620i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.9324i | 1.73153i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.1224 | 1.24223 | 0.621113 | − | 0.783721i | \(-0.286681\pi\) | ||||
0.621113 | + | 0.783721i | \(0.286681\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.56165 | −0.274336 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.07770i | − | 0.299064i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 9.35972i | − | 0.459451i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.63364 | 0.275881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.1667 | −1.08291 | −0.541456 | − | 0.840729i | \(-0.682127\pi\) | ||||
−0.541456 | + | 0.840729i | \(0.682127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.99216i | 0.389514i | 0.980852 | + | 0.194757i | \(0.0623918\pi\) | ||||
−0.980852 | + | 0.194757i | \(0.937608\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2.99382i | − | 0.145564i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.65230i | 0.0801485i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.8435i | 0.718329i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 28.9615i | − | 1.39827i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.2692 | 1.84336 | 0.921682 | − | 0.387946i | \(-0.126815\pi\) | ||||
0.921682 | + | 0.387946i | \(0.126815\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 22.5291i | − | 1.08268i | −0.840805 | − | 0.541339i | \(-0.817918\pi\) | ||
0.840805 | − | 0.541339i | \(-0.182082\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.30375 | 0.110457 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.6796 | + | 20.9018i | 0.797892 | + | 0.999868i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.6828i | 0.843954i | 0.906606 | + | 0.421977i | \(0.138664\pi\) | ||||
−0.906606 | + | 0.421977i | \(0.861336\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.68040 | 0.222876 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.2484i | 0.676962i | 0.940973 | + | 0.338481i | \(0.109913\pi\) | ||||
−0.940973 | + | 0.338481i | \(0.890087\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.66224 | 0.126202 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.5221 | 0.497676 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.2577 | −1.09760 | −0.548800 | − | 0.835954i | \(-0.684915\pi\) | ||||
−0.548800 | + | 0.835954i | \(0.684915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.3189 | 0.627162 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.5034 | 0.822383 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 6.85710i | − | 0.321466i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.8933i | 0.930569i | 0.885161 | + | 0.465285i | \(0.154048\pi\) | ||||
−0.885161 | + | 0.465285i | \(0.845952\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.65230 | 0.0771230 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.03647 | 0.234572 | 0.117286 | − | 0.993098i | \(-0.462581\pi\) | ||||
0.117286 | + | 0.993098i | \(0.462581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 14.1754i | − | 0.658788i | −0.944193 | − | 0.329394i | \(-0.893156\pi\) | ||
0.944193 | − | 0.329394i | \(-0.106844\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 1.77291i | − | 0.0822167i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.8246 | 0.547176 | 0.273588 | − | 0.961847i | \(-0.411790\pi\) | ||||
0.273588 | + | 0.961847i | \(0.411790\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.66020 | −0.261364 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.31873 | −0.337229 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.5929 | 1.40666 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.57593 | −0.255841 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2.72374i | − | 0.124711i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.6625 | −1.17255 | −0.586276 | − | 0.810112i | \(-0.699406\pi\) | ||||
−0.586276 | + | 0.810112i | \(0.699406\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.4498i | 1.11481i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.70917 | + | 4.55590i | −0.259776 | + | 0.207301i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.66759 | 0.393575 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17.8398i | − | 0.808397i | −0.914671 | − | 0.404199i | \(-0.867550\pi\) | ||
0.914671 | − | 0.404199i | \(-0.132450\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.06133 | −0.409768 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0228i | 0.903616i | 0.892115 | + | 0.451808i | \(0.149221\pi\) | ||||
−0.892115 | + | 0.451808i | \(0.850779\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.80650i | 0.171436i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 6.43261i | − | 0.289124i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 3.65308i | − | 0.163863i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.8428i | 1.11212i | 0.831144 | + | 0.556058i | \(0.187687\pi\) | ||||
−0.831144 | + | 0.556058i | \(0.812313\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.02942 | 0.358728 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.67105 | −0.252860 | −0.126430 | − | 0.991976i | \(-0.540352\pi\) | ||||
−0.126430 | + | 0.991976i | \(0.540352\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 18.6952i | − | 0.831925i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 7.27066i | − | 0.322901i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.8447 | 0.569331 | 0.284666 | − | 0.958627i | \(-0.408117\pi\) | ||||
0.284666 | + | 0.958627i | \(0.408117\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0693 | 0.622389 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.57593i | 0.246183i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 7.63952i | − | 0.336637i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 19.2581i | − | 0.846968i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.927933i | 0.0407317i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 12.9412i | − | 0.566963i | −0.958978 | − | 0.283481i | \(-0.908511\pi\) | ||
0.958978 | − | 0.283481i | \(-0.0914894\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.93781 | −0.128462 | −0.0642308 | − | 0.997935i | \(-0.520459\pi\) | ||||
−0.0642308 | + | 0.997935i | \(0.520459\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.52302i | − | 0.0664702i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.92939 | 0.127606 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.10362 | + | 22.4266i | −0.221897 | + | 0.975070i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 3.99055i | − | 0.173175i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.32212 | 0.403786 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 6.71244i | − | 0.290204i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −25.1922 | −1.08712 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30.1072 | 1.29681 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.0680 | 1.24973 | 0.624865 | − | 0.780733i | \(-0.285154\pi\) | ||||
0.624865 | + | 0.780733i | \(0.285154\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.69810 | −0.0728726 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.70608 | 0.115916 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 35.0271i | − | 1.49765i | −0.662768 | − | 0.748825i | \(-0.730618\pi\) | ||
0.662768 | − | 0.748825i | \(-0.269382\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.74609i | 0.415953i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.8456 | −0.547240 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.3759 | −0.738900 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.43051i | 0.230512i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.5781i | 0.744809i | 0.928071 | + | 0.372404i | \(0.121467\pi\) | ||||
−0.928071 | + | 0.372404i | \(0.878533\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.4125 | 0.905653 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.6286 | 0.448741 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.7102 | −0.830686 | −0.415343 | − | 0.909665i | \(-0.636339\pi\) | ||||
−0.415343 | + | 0.909665i | \(0.636339\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.212216 | −0.00892800 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.52302 | −0.0639610 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.5038i | 1.06918i | 0.845113 | + | 0.534588i | \(0.179533\pi\) | ||||
−0.845113 | + | 0.534588i | \(0.820467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.2420 | −1.85147 | −0.925735 | − | 0.378173i | \(-0.876552\pi\) | ||||
−0.925735 | + | 0.378173i | \(0.876552\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 13.0724i | − | 0.546107i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.99135 | − | 3.74857i | −0.124748 | − | 0.156326i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.3335 | −1.26280 | −0.631400 | − | 0.775457i | \(-0.717519\pi\) | ||||
−0.631400 | + | 0.775457i | \(0.717519\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 16.0209i | − | 0.665807i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.2551 | −0.591400 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 17.5208i | − | 0.725635i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 4.50229i | − | 0.186147i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.0137i | 1.73409i | 0.498230 | + | 0.867045i | \(0.333984\pi\) | ||||
−0.498230 | + | 0.867045i | \(0.666016\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.88562i | 0.407330i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.9113i | 0.489967i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −45.9637 | −1.88750 | −0.943752 | − | 0.330654i | \(-0.892731\pi\) | ||||
−0.943752 | + | 0.330654i | \(0.892731\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.51650 | 0.103166 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.54875i | 0.308950i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 4.06616i | − | 0.166139i | −0.996544 | − | 0.0830694i | \(-0.973528\pi\) | ||
0.996544 | − | 0.0830694i | \(-0.0264723\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.3871 | −1.11714 | −0.558571 | − | 0.829456i | \(-0.688650\pi\) | ||||
−0.558571 | + | 0.829456i | \(0.688650\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.71642 | −0.151344 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 30.3784i | − | 1.23506i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.1569i | 0.980496i | 0.871583 | + | 0.490248i | \(0.163094\pi\) | ||||
−0.871583 | + | 0.490248i | \(0.836906\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 3.50867i | − | 0.142179i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 13.4791i | − | 0.545304i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 21.9152i | − | 0.885147i | −0.896732 | − | 0.442574i | \(-0.854066\pi\) | ||
0.896732 | − | 0.442574i | \(-0.145934\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.07053 | 0.0834917 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.74213i | 0.271428i | 0.990748 | + | 0.135714i | \(0.0433328\pi\) | ||||
−0.990748 | + | 0.135714i | \(0.956667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.3523 | −0.777836 | −0.388918 | − | 0.921272i | \(-0.627151\pi\) | ||||
−0.388918 | + | 0.921272i | \(0.627151\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.74857 | + | 2.99135i | −0.150425 | + | 0.120039i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 4.05466i | − | 0.162446i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 35.8678i | 1.43242i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.97286 | −0.357771 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.1921 | −0.644598 | −0.322299 | − | 0.946638i | \(-0.604456\pi\) | ||||
−0.322299 | + | 0.946638i | \(0.604456\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.69539 | −0.186625 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.8377 | −0.668183 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.0725 | 0.834924 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 2.39857i | − | 0.0948859i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.9194i | 1.02376i | 0.859058 | + | 0.511878i | \(0.171050\pi\) | ||||
−0.859058 | + | 0.511878i | \(0.828950\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.0513 | 0.909055 | 0.454527 | − | 0.890733i | \(-0.349808\pi\) | ||||
0.454527 | + | 0.890733i | \(0.349808\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.75591 | 0.187264 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 38.7579i | − | 1.52373i | −0.647735 | − | 0.761866i | \(-0.724284\pi\) | ||
0.647735 | − | 0.761866i | \(-0.275716\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 25.6696i | − | 1.00762i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.70018 | −0.105829 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.54972 | −0.0997781 | −0.0498891 | − | 0.998755i | \(-0.515887\pi\) | ||||
−0.0498891 | + | 0.998755i | \(0.515887\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.1242 | 0.434660 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.23774 | 0.360399 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.3121 | −1.68720 | −0.843600 | − | 0.536972i | \(-0.819568\pi\) | ||||
−0.843600 | + | 0.536972i | \(0.819568\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.39709i | 0.365504i | 0.983159 | + | 0.182752i | \(0.0585006\pi\) | ||||
−0.983159 | + | 0.182752i | \(0.941499\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.43916 | 0.288913 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.49227i | 0.329316i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.89134 | − | 8.63579i | −0.266834 | − | 0.334379i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.1553 | 0.933900 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 62.6928i | 2.42023i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.72747 | −0.105136 | −0.0525681 | − | 0.998617i | \(-0.516741\pi\) | ||||
−0.0525681 | + | 0.998617i | \(0.516741\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 1.00000i | − | 0.0384900i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.1061i | 0.465276i | 0.972563 | + | 0.232638i | \(0.0747358\pi\) | ||||
−0.972563 | + | 0.232638i | \(0.925264\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13.2009i | − | 0.506606i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 12.4903i | − | 0.478629i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 20.7694i | − | 0.794720i | −0.917663 | − | 0.397360i | \(-0.869926\pi\) | ||
0.917663 | − | 0.397360i | \(-0.130074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.56165 | −0.212500 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.8509 | −1.13888 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 12.2631i | − | 0.467186i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.08978i | 0.231666i | 0.993269 | + | 0.115833i | \(0.0369538\pi\) | ||||
−0.993269 | + | 0.115833i | \(0.963046\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.79702 | −0.372158 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.63364 | 0.213696 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.42114i | 0.129585i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.897082i | 0.0339308i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.6195i | 0.401094i | 0.979684 | + | 0.200547i | \(0.0642720\pi\) | ||||
−0.979684 | + | 0.200547i | \(0.935728\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 30.2802i | − | 1.14204i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 2.99382i | − | 0.112754i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.4732 | −1.07085 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.7363i | 0.928991i | 0.885575 | + | 0.464496i | \(0.153764\pi\) | ||||
−0.885575 | + | 0.464496i | \(0.846236\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.4088 | −0.427865 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.64588 | + | 5.30340i | −0.248890 | + | 0.198614i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 28.9615i | − | 1.08310i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.9763 | 0.970101 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 51.3791i | 1.91612i | 0.286571 | + | 0.958059i | \(0.407485\pi\) | ||||
−0.286571 | + | 0.958059i | \(0.592515\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.6352 | −0.433316 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.15296 | 0.303212 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.30375 | 0.0855593 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.94441 | −0.220466 | −0.110233 | − | 0.993906i | \(-0.535160\pi\) | ||||
−0.110233 | + | 0.993906i | \(0.535160\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.85822i | 0.290647i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 47.7046i | − | 1.76201i | −0.473106 | − | 0.881005i | \(-0.656867\pi\) | ||
0.473106 | − | 0.881005i | \(-0.343133\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.68040 | 0.172639 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.9063 | −0.880599 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 30.6154i | − | 1.12621i | −0.826387 | − | 0.563103i | \(-0.809607\pi\) | ||
0.826387 | − | 0.563103i | \(-0.190393\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.1045i | 0.922236i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.15462 | −0.152418 | −0.0762092 | − | 0.997092i | \(-0.524282\pi\) | ||||
−0.0762092 | + | 0.997092i | \(0.524282\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.5221 | 0.385498 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.35972 | −0.342454 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.2232 | −0.373548 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.49223 | 0.163924 | 0.0819619 | − | 0.996635i | \(-0.473881\pi\) | ||||
0.0819619 | + | 0.996635i | \(0.473881\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.31194i | 0.230020i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.5034 | 0.637015 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.70763i | 0.280138i | 0.990142 | + | 0.140069i | \(0.0447325\pi\) | ||||
−0.990142 | + | 0.140069i | \(0.955267\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24.1131 | + | 19.2422i | −0.875250 | + | 0.698448i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.85989 | −0.103671 | −0.0518355 | − | 0.998656i | \(-0.516507\pi\) | ||||
−0.0518355 | + | 0.998656i | \(0.516507\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 4.12143i | − | 0.149206i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.65230 | 0.0597392 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 17.9666i | − | 0.648737i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.422431i | 0.0152333i | 0.999971 | + | 0.00761663i | \(0.00242447\pi\) | ||||
−0.999971 | + | 0.00761663i | \(0.997576\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.8718i | 0.391538i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.0769i | 0.470342i | 0.971954 | + | 0.235171i | \(0.0755650\pi\) | ||||
−0.971954 | + | 0.235171i | \(0.924435\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.77291i | − | 0.0636848i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.27080 | 0.296713 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.5451 | −0.413647 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 15.4291i | − | 0.552095i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.30375i | − | 0.0823295i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.31873 | −0.261217 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.8315 | 1.59807 | 0.799035 | − | 0.601285i | \(-0.205344\pi\) | ||||
0.799035 | + | 0.601285i | \(0.205344\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 23.5415i | − | 0.838098i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.323210i | 0.0114920i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.8798i | 1.55822i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 2.72374i | − | 0.0966011i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 27.9408i | − | 0.989715i | −0.868974 | − | 0.494858i | \(-0.835220\pi\) | ||
0.868974 | − | 0.494858i | \(-0.164780\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.94670 | 0.175002 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 2.66224i | − | 0.0940657i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 59.4228 | 2.09698 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.70917 | + | 4.55590i | −0.201222 | + | 0.160574i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 13.5049i | − | 0.475395i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.4099 | −0.893364 | −0.446682 | − | 0.894693i | \(-0.647394\pi\) | ||||
−0.446682 | + | 0.894693i | \(0.647394\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.40842i | − | 0.119686i | −0.998208 | − | 0.0598430i | \(-0.980940\pi\) | ||
0.998208 | − | 0.0598430i | \(-0.0190600\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.2034 | −0.638421 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.06133 | −0.317405 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.5186 | −0.927770 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.85710 | −0.239607 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.3534 | 1.23384 | 0.616922 | − | 0.787024i | \(-0.288379\pi\) | ||||
0.616922 | + | 0.787024i | \(0.288379\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 40.5793i | − | 1.41450i | −0.706961 | − | 0.707252i | \(-0.749934\pi\) | ||
0.706961 | − | 0.707252i | \(-0.250066\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6.43261i | − | 0.223955i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0863 | −0.420281 | −0.210141 | − | 0.977671i | \(-0.567392\pi\) | ||||
−0.210141 | + | 0.977671i | \(0.567392\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.2928 | 0.843724 | 0.421862 | − | 0.906660i | \(-0.361377\pi\) | ||||
0.421862 | + | 0.906660i | \(0.361377\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.79569i | 0.339809i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.73344i | 0.267948i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.02942 | 0.277869 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.77291 | −0.0612807 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.0086 | 0.966963 | 0.483482 | − | 0.875354i | \(-0.339372\pi\) | ||||
0.483482 | + | 0.875354i | \(0.339372\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.6927 | −0.816990 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.6935 | 0.368305 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 7.27066i | − | 0.250118i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −46.2671 | −1.58976 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.2186i | 0.934138i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.3567 | − | 16.2446i | 0.697818 | − | 0.556857i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.61457 | −0.123761 | −0.0618803 | − | 0.998084i | \(-0.519710\pi\) | ||||
−0.0618803 | + | 0.998084i | \(0.519710\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.57593i | 0.190693i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.7340 | −0.571622 | −0.285811 | − | 0.958286i | \(-0.592263\pi\) | ||||
−0.285811 | + | 0.958286i | \(0.592263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 15.4101i | − | 0.525786i | −0.964825 | − | 0.262893i | \(-0.915323\pi\) | ||
0.964825 | − | 0.262893i | \(-0.0846767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 3.15346i | − | 0.107470i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 15.7961i | − | 0.537706i | −0.963181 | − | 0.268853i | \(-0.913355\pi\) | ||
0.963181 | − | 0.268853i | \(-0.0866446\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.927933i | 0.0315507i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 14.2699i | − | 0.484631i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −73.3887 | −2.48954 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.7324 | −0.566956 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 8.66759i | − | 0.293353i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 1.52302i | − | 0.0514876i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.5977 | 1.37089 | 0.685444 | − | 0.728125i | \(-0.259608\pi\) | ||||
0.685444 | + | 0.728125i | \(0.259608\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.1769 | −0.781737 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.3114i | 1.72873i | 0.502869 | + | 0.864363i | \(0.332278\pi\) | ||||
−0.502869 | + | 0.864363i | \(0.667722\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.1535i | 0.375346i | 0.982232 | + | 0.187673i | \(0.0600945\pi\) | ||||
−0.982232 | + | 0.187673i | \(0.939906\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 3.99055i | − | 0.134141i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.68530i | 0.291624i | 0.989312 | + | 0.145812i | \(0.0465794\pi\) | ||||
−0.989312 | + | 0.145812i | \(0.953421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.6442i | 0.860078i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.43261 | −0.215500 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.6933i | 0.558621i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.1922 | −0.842081 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.8772 | + | 13.4680i | −0.563513 | + | 0.449682i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 4.08435i | − | 0.136221i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.50045 | 0.149932 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 7.24337i | − | 0.241044i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.69810 | −0.0564468 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.9169 | 1.32542 | 0.662709 | − | 0.748877i | \(-0.269407\pi\) | ||||
0.662709 | + | 0.748877i | \(0.269407\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.6952 | −0.620081 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.43948 | 0.180218 | 0.0901091 | − | 0.995932i | \(-0.471278\pi\) | ||||
0.0901091 | + | 0.995932i | \(0.471278\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −60.2074 | −1.99257 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.74609i | 0.322196i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 16.9425i | − | 0.559490i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.6490 | 1.10998 | 0.554989 | − | 0.831858i | \(-0.312723\pi\) | ||||
0.554989 | + | 0.831858i | \(0.312723\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.1278 | 0.762086 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 10.7991i | − | 0.355455i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.43051i | 0.178554i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.63952 | −0.250915 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.3592 | 1.84909 | 0.924543 | − | 0.381077i | \(-0.124447\pi\) | ||||
0.924543 | + | 0.381077i | \(0.124447\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.0976 | −0.855313 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.5382 | 0.508698 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.6286 | 0.347593 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 0.622601i | − | 0.0203395i | −0.999948 | − | 0.0101697i | \(-0.996763\pi\) | ||
0.999948 | − | 0.0101697i | \(-0.00323718\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.93700 | 0.0632116 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.7044i | 0.577147i | 0.957458 | + | 0.288574i | \(0.0931810\pi\) | ||||
−0.957458 | + | 0.288574i | \(0.906819\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.19368 | − | 7.76153i | −0.201694 | − | 0.252750i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.52302 | −0.0495440 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 0.0434608i | − | 0.00141229i | −1.00000 | 0.000706143i | \(-0.999775\pi\) | |||
1.00000 | 0.000706143i | \(-0.000224772\pi\) | ||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.5910 | 1.35010 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.0281i | 0.649457i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.2160i | 1.75623i | 0.478452 | + | 0.878114i | \(0.341198\pi\) | ||||
−0.478452 | + | 0.878114i | \(0.658802\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 13.0724i | − | 0.423013i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 14.8191i | − | 0.479035i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.47052i | 0.273527i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.8568 | 0.898606 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.71244 | −0.216305 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 16.0209i | − | 0.515732i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.23566i | 0.264841i | 0.991194 | + | 0.132420i | \(0.0422749\pi\) | ||||
−0.991194 | + | 0.132420i | \(0.957725\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.21313 | −0.295968 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.55880 | −0.306756 | −0.153378 | − | 0.988168i | \(-0.549015\pi\) | ||||
−0.153378 | + | 0.988168i | \(0.549015\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 8.58017i | − | 0.275068i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 4.50229i | − | 0.144189i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.3198i | 1.60987i | 0.593361 | + | 0.804936i | \(0.297801\pi\) | ||||
−0.593361 | + | 0.804936i | \(0.702199\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 17.1252i | − | 0.547322i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 2.70608i | − | 0.0863986i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.7966 | −0.599519 | −0.299760 | − | 0.954015i | \(-0.596906\pi\) | ||||
−0.299760 | + | 0.954015i | \(0.596906\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.9113i | 0.379526i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.55966 | −0.145135 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.2266 | − | 17.8279i | −0.452380 | − | 0.566894i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.1729i | 1.02200i | 0.859579 | + | 0.511002i | \(0.170726\pi\) | ||||
−0.859579 | + | 0.511002i | \(0.829274\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.6804 | 0.624538 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.54875i | 0.239311i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.15041 | −0.131445 | −0.0657224 | − | 0.997838i | \(-0.520935\pi\) | ||||
−0.0657224 | + | 0.997838i | \(0.520935\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.43051 | 0.171814 |
(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 | 5520.2.be.c.1471.3 | ✓ | 32 | |
4.3 | odd | 2 | 5520.2.be.d.1471.4 | yes | 32 | ||
23.22 | odd | 2 | 5520.2.be.d.1471.3 | yes | 32 | ||
92.91 | even | 2 | inner | 5520.2.be.c.1471.4 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.c.1471.3 | ✓ | 32 | 1.1 | even | 1 | trivial | |
5520.2.be.c.1471.4 | yes | 32 | 92.91 | even | 2 | inner | |
5520.2.be.d.1471.3 | yes | 32 | 23.22 | odd | 2 | ||
5520.2.be.d.1471.4 | yes | 32 | 4.3 | odd | 2 |