Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(881,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("4410.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.b (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: | \(35.2140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.3 | ||
Root | \(0.382683 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4410.881 |
Dual form | 4410.2.b.d.881.6 |
$q$-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 \(\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(2647\) | \(3431\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 1.00000i | − 0.316228i | ||||||||
\(11\) | − 1.23463i | − 0.372256i | −0.982526 | − | 0.186128i | \(-0.940406\pi\) | ||||
0.982526 | − | 0.186128i | \(-0.0595939\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.33182i | − 1.20143i | −0.799463 | − | 0.600716i | \(-0.794882\pi\) | ||||
0.799463 | − | 0.600716i | \(-0.205118\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.12906 | 1.00145 | 0.500723 | − | 0.865608i | \(-0.333068\pi\) | ||||
0.500723 | + | 0.865608i | \(0.333068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.28130i | − 0.523367i | −0.965154 | − | 0.261684i | \(-0.915722\pi\) | ||||
0.965154 | − | 0.261684i | \(-0.0842777\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.23463 | −0.263225 | ||||||||
\(23\) | − 2.26038i | − 0.471322i | −0.971835 | − | 0.235661i | \(-0.924275\pi\) | ||||
0.971835 | − | 0.235661i | \(-0.0757255\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.33182 | −0.849540 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.511402i | 0.0949649i | 0.998872 | + | 0.0474825i | \(0.0151198\pi\) | ||||
−0.998872 | + | 0.0474825i | \(0.984880\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.89828i | 0.700151i | 0.936721 | + | 0.350076i | \(0.113844\pi\) | ||||
−0.936721 | + | 0.350076i | \(0.886156\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 4.12906i | − 0.708129i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.39488 | −0.722514 | −0.361257 | − | 0.932466i | \(-0.617652\pi\) | ||||
−0.361257 | + | 0.932466i | \(0.617652\pi\) | |||||||
\(38\) | −2.28130 | −0.370076 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | 7.08239 | 1.10608 | 0.553042 | − | 0.833153i | \(-0.313467\pi\) | ||||
0.553042 | + | 0.833153i | \(0.313467\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.1837 | 1.55301 | 0.776503 | − | 0.630113i | \(-0.216992\pi\) | ||||
0.776503 | + | 0.630113i | \(0.216992\pi\) | |||||||
\(44\) | 1.23463i | 0.186128i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.26038 | −0.333275 | ||||||||
\(47\) | −7.51594 | −1.09631 | −0.548156 | − | 0.836376i | \(-0.684670\pi\) | ||||
−0.548156 | + | 0.836376i | \(0.684670\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.33182i | 0.600716i | ||||||||
\(53\) | − 8.83259i | − 1.21325i | −0.794988 | − | 0.606625i | \(-0.792523\pi\) | ||||
0.794988 | − | 0.606625i | \(-0.207477\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.23463i | − 0.166478i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.511402 | 0.0671503 | ||||||||
\(59\) | −8.33598 | −1.08525 | −0.542626 | − | 0.839974i | \(-0.682570\pi\) | ||||
−0.542626 | + | 0.839974i | \(0.682570\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 0.890268i | − 0.113987i | −0.998375 | − | 0.0569936i | \(-0.981849\pi\) | ||||
0.998375 | − | 0.0569936i | \(-0.0181515\pi\) | |||||||
\(62\) | 3.89828 | 0.495082 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − 4.33182i | − 0.537296i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.24105 | −0.640296 | −0.320148 | − | 0.947368i | \(-0.603733\pi\) | ||||
−0.320148 | + | 0.947368i | \(0.603733\pi\) | |||||||
\(68\) | −4.12906 | −0.500723 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.818827i | 0.0971769i | 0.998819 | + | 0.0485884i | \(0.0154723\pi\) | ||||
−0.998819 | + | 0.0485884i | \(0.984528\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6610i | 1.36482i | 0.730970 | + | 0.682409i | \(0.239068\pi\) | ||||
−0.730970 | + | 0.682409i | \(0.760932\pi\) | |||||||
\(74\) | 4.39488i | 0.510895i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.28130i | 0.261684i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.65685 | 0.636446 | 0.318223 | − | 0.948016i | \(-0.396914\pi\) | ||||
0.318223 | + | 0.948016i | \(0.396914\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 7.08239i | − 0.782119i | ||||||||
\(83\) | −0.164784 | −0.0180874 | −0.00904372 | − | 0.999959i | \(-0.502879\pi\) | ||||
−0.00904372 | + | 0.999959i | \(0.502879\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.12906 | 0.447860 | ||||||||
\(86\) | − 10.1837i | − 1.09814i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.23463 | 0.131612 | ||||||||
\(89\) | −4.49886 | −0.476878 | −0.238439 | − | 0.971157i | \(-0.576636\pi\) | ||||
−0.238439 | + | 0.971157i | \(0.576636\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.26038i | 0.235661i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.51594i | 0.775210i | ||||||||
\(95\) | − 2.28130i | − 0.234057i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 9.06147i | − 0.920053i | −0.887905 | − | 0.460026i | \(-0.847840\pi\) | ||||
0.887905 | − | 0.460026i | \(-0.152160\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −3.88348 | −0.386421 | −0.193210 | − | 0.981157i | \(-0.561890\pi\) | ||||
−0.193210 | + | 0.981157i | \(0.561890\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.56767i | 0.745665i | 0.927899 | + | 0.372833i | \(0.121613\pi\) | ||||
−0.927899 | + | 0.372833i | \(0.878387\pi\) | |||||||
\(104\) | 4.33182 | 0.424770 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.83259 | −0.857897 | ||||||||
\(107\) | − 13.7679i | − 1.33100i | −0.746399 | − | 0.665498i | \(-0.768219\pi\) | ||||
0.746399 | − | 0.665498i | \(-0.231781\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.810688 | 0.0776498 | 0.0388249 | − | 0.999246i | \(-0.487639\pi\) | ||||
0.0388249 | + | 0.999246i | \(0.487639\pi\) | |||||||
\(110\) | −1.23463 | −0.117718 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 11.0866i | − 1.04294i | −0.853271 | − | 0.521468i | \(-0.825385\pi\) | ||||
0.853271 | − | 0.521468i | \(-0.174615\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.26038i | − 0.210782i | ||||||||
\(116\) | − 0.511402i | − 0.0474825i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.33598i | 0.767389i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.47568 | 0.861426 | ||||||||
\(122\) | −0.890268 | −0.0806011 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 3.89828i | − 0.350076i | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.12612 | 0.721077 | 0.360538 | − | 0.932744i | \(-0.382593\pi\) | ||||
0.360538 | + | 0.932744i | \(0.382593\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.33182 | −0.379926 | ||||||||
\(131\) | −0.391410 | −0.0341976 | −0.0170988 | − | 0.999854i | \(-0.505443\pi\) | ||||
−0.0170988 | + | 0.999854i | \(0.505443\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.24105i | 0.452758i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.12906i | 0.354064i | ||||||||
\(137\) | − 21.5832i | − 1.84397i | −0.387221 | − | 0.921987i | \(-0.626565\pi\) | ||||
0.387221 | − | 0.921987i | \(-0.373435\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 22.9700i | − 1.94829i | −0.225918 | − | 0.974146i | \(-0.572538\pi\) | ||||
0.225918 | − | 0.974146i | \(-0.427462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.818827 | 0.0687144 | ||||||||
\(143\) | −5.34821 | −0.447240 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.511402i | 0.0424696i | ||||||||
\(146\) | 11.6610 | 0.965073 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.39488 | 0.361257 | ||||||||
\(149\) | − 22.8033i | − 1.86812i | −0.357119 | − | 0.934059i | \(-0.616241\pi\) | ||||
0.357119 | − | 0.934059i | \(-0.383759\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.2905 | −1.73260 | −0.866299 | − | 0.499525i | \(-0.833508\pi\) | ||||
−0.866299 | + | 0.499525i | \(0.833508\pi\) | |||||||
\(152\) | 2.28130 | 0.185038 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.89828i | 0.313117i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 6.60127i | − 0.526839i | −0.964681 | − | 0.263419i | \(-0.915150\pi\) | ||||
0.964681 | − | 0.263419i | \(-0.0848503\pi\) | |||||||
\(158\) | − 5.65685i | − 0.450035i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 1.00000i | − 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.4286 | −1.28679 | −0.643395 | − | 0.765534i | \(-0.722475\pi\) | ||||
−0.643395 | + | 0.765534i | \(0.722475\pi\) | |||||||
\(164\) | −7.08239 | −0.553042 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.164784i | 0.0127897i | ||||||||
\(167\) | 0.834556 | 0.0645799 | 0.0322899 | − | 0.999479i | \(-0.489720\pi\) | ||||
0.0322899 | + | 0.999479i | \(0.489720\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.76468 | −0.443437 | ||||||||
\(170\) | − 4.12906i | − 0.316685i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.1837 | −0.776503 | ||||||||
\(173\) | 3.54675 | 0.269654 | 0.134827 | − | 0.990869i | \(-0.456952\pi\) | ||||
0.134827 | + | 0.990869i | \(0.456952\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 1.23463i | − 0.0930640i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.49886i | 0.337204i | ||||||||
\(179\) | − 16.6685i | − 1.24586i | −0.782277 | − | 0.622931i | \(-0.785942\pi\) | ||||
0.782277 | − | 0.622931i | \(-0.214058\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.53036i | 0.188080i | 0.995568 | + | 0.0940401i | \(0.0299782\pi\) | ||||
−0.995568 | + | 0.0940401i | \(0.970022\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.26038 | 0.166637 | ||||||||
\(185\) | −4.39488 | −0.323118 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 5.09788i | − 0.372794i | ||||||||
\(188\) | 7.51594 | 0.548156 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.28130 | −0.165503 | ||||||||
\(191\) | 5.15158i | 0.372755i | 0.982478 | + | 0.186378i | \(0.0596748\pi\) | ||||
−0.982478 | + | 0.186378i | \(0.940325\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.50793 | 0.324488 | 0.162244 | − | 0.986751i | \(-0.448127\pi\) | ||||
0.162244 | + | 0.986751i | \(0.448127\pi\) | |||||||
\(194\) | −9.06147 | −0.650575 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.14476i | 0.224055i | 0.993705 | + | 0.112028i | \(0.0357345\pi\) | ||||
−0.993705 | + | 0.112028i | \(0.964266\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.28343i | 0.232756i | 0.993205 | + | 0.116378i | \(0.0371284\pi\) | ||||
−0.993205 | + | 0.116378i | \(0.962872\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.88348i | 0.273241i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.08239 | 0.494656 | ||||||||
\(206\) | 7.56767 | 0.527265 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 4.33182i | − 0.300358i | ||||||||
\(209\) | −2.81657 | −0.194827 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.0907 | 1.72732 | 0.863658 | − | 0.504078i | \(-0.168168\pi\) | ||||
0.863658 | + | 0.504078i | \(0.168168\pi\) | |||||||
\(212\) | 8.83259i | 0.606625i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.7679 | −0.941157 | ||||||||
\(215\) | 10.1837 | 0.694525 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 0.810688i | − 0.0549067i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.23463i | 0.0832389i | ||||||||
\(221\) | − 17.8864i | − 1.20317i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.21440i | 0.215252i | 0.994191 | + | 0.107626i | \(0.0343249\pi\) | ||||
−0.994191 | + | 0.107626i | \(0.965675\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.0866 | −0.737467 | ||||||||
\(227\) | 7.15800 | 0.475093 | 0.237546 | − | 0.971376i | \(-0.423657\pi\) | ||||
0.237546 | + | 0.971376i | \(0.423657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.0156i | 1.12443i | 0.826993 | + | 0.562213i | \(0.190050\pi\) | ||||
−0.826993 | + | 0.562213i | \(0.809950\pi\) | |||||||
\(230\) | −2.26038 | −0.149045 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.511402 | −0.0335752 | ||||||||
\(233\) | − 8.18080i | − 0.535942i | −0.963427 | − | 0.267971i | \(-0.913647\pi\) | ||||
0.963427 | − | 0.267971i | \(-0.0863531\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.51594 | −0.490286 | ||||||||
\(236\) | 8.33598 | 0.542626 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 22.3224i | − 1.44392i | −0.691937 | − | 0.721958i | \(-0.743242\pi\) | ||||
0.691937 | − | 0.721958i | \(-0.256758\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5525i | 0.808578i | 0.914631 | + | 0.404289i | \(0.132481\pi\) | ||||
−0.914631 | + | 0.404289i | \(0.867519\pi\) | |||||||
\(242\) | − 9.47568i | − 0.609120i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.890268i | 0.0569936i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.88220 | −0.628790 | ||||||||
\(248\) | −3.89828 | −0.247541 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 1.00000i | − 0.0632456i | ||||||||
\(251\) | 6.05468 | 0.382168 | 0.191084 | − | 0.981574i | \(-0.438800\pi\) | ||||
0.191084 | + | 0.981574i | \(0.438800\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.79074 | −0.175452 | ||||||||
\(254\) | − 8.12612i | − 0.509878i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.9298 | 0.993672 | 0.496836 | − | 0.867844i | \(-0.334495\pi\) | ||||
0.496836 | + | 0.867844i | \(0.334495\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.33182i | 0.268648i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.391410i | 0.0241814i | ||||||||
\(263\) | 8.09560i | 0.499196i | 0.968350 | + | 0.249598i | \(0.0802984\pi\) | ||||
−0.968350 | + | 0.249598i | \(0.919702\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 8.83259i | − 0.542582i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.24105 | 0.320148 | ||||||||
\(269\) | −31.7070 | −1.93321 | −0.966606 | − | 0.256268i | \(-0.917507\pi\) | ||||
−0.966606 | + | 0.256268i | \(0.917507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.2571i | 1.83799i | 0.394272 | + | 0.918994i | \(0.370997\pi\) | ||||
−0.394272 | + | 0.918994i | \(0.629003\pi\) | |||||||
\(272\) | 4.12906 | 0.250361 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.5832 | −1.30389 | ||||||||
\(275\) | − 1.23463i | − 0.0744512i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.07626 | 0.184835 | 0.0924174 | − | 0.995720i | \(-0.470541\pi\) | ||||
0.0924174 | + | 0.995720i | \(0.470541\pi\) | |||||||
\(278\) | −22.9700 | −1.37765 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 23.4167i | − 1.39692i | −0.715649 | − | 0.698460i | \(-0.753869\pi\) | ||||
0.715649 | − | 0.698460i | \(-0.246131\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.4152i | 1.15411i | 0.816704 | + | 0.577057i | \(0.195799\pi\) | ||||
−0.816704 | + | 0.577057i | \(0.804201\pi\) | |||||||
\(284\) | − 0.818827i | − 0.0485884i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.34821i | 0.316246i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.0491665 | 0.00289215 | ||||||||
\(290\) | 0.511402 | 0.0300305 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 11.6610i | − 0.682409i | ||||||||
\(293\) | 26.1609 | 1.52833 | 0.764167 | − | 0.645019i | \(-0.223151\pi\) | ||||
0.764167 | + | 0.645019i | \(0.223151\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.33598 | −0.485340 | ||||||||
\(296\) | − 4.39488i | − 0.255447i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.8033 | −1.32096 | ||||||||
\(299\) | −9.79156 | −0.566261 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 21.2905i | 1.22513i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 2.28130i | − 0.130842i | ||||||||
\(305\) | − 0.890268i | − 0.0509766i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 7.86481i | − 0.448868i | −0.974489 | − | 0.224434i | \(-0.927947\pi\) | ||||
0.974489 | − | 0.224434i | \(-0.0720534\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.89828 | 0.221407 | ||||||||
\(311\) | −14.4170 | −0.817515 | −0.408757 | − | 0.912643i | \(-0.634038\pi\) | ||||
−0.408757 | + | 0.912643i | \(0.634038\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 8.40649i | − 0.475163i | −0.971368 | − | 0.237582i | \(-0.923645\pi\) | ||||
0.971368 | − | 0.237582i | \(-0.0763547\pi\) | |||||||
\(314\) | −6.60127 | −0.372531 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.65685 | −0.318223 | ||||||||
\(317\) | 11.0420i | 0.620181i | 0.950707 | + | 0.310090i | \(0.100359\pi\) | ||||
−0.950707 | + | 0.310090i | \(0.899641\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.631394 | 0.0353513 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 9.41965i | − 0.524123i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4.33182i | − 0.240286i | ||||||||
\(326\) | 16.4286i | 0.909898i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.08239i | 0.391060i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.1667 | −1.16343 | −0.581713 | − | 0.813394i | \(-0.697617\pi\) | ||||
−0.581713 | + | 0.813394i | \(0.697617\pi\) | |||||||
\(332\) | 0.164784 | 0.00904372 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 0.834556i | − 0.0456649i | ||||||||
\(335\) | −5.24105 | −0.286349 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.2992 | 1.10577 | 0.552885 | − | 0.833258i | \(-0.313527\pi\) | ||||
0.552885 | + | 0.833258i | \(0.313527\pi\) | |||||||
\(338\) | 5.76468i | 0.313557i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.12906 | −0.223930 | ||||||||
\(341\) | 4.81294 | 0.260635 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.1837i | 0.549071i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 3.54675i | − 0.190674i | ||||||||
\(347\) | − 28.6912i | − 1.54022i | −0.637910 | − | 0.770111i | \(-0.720201\pi\) | ||||
0.637910 | − | 0.770111i | \(-0.279799\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 23.5191i | − 1.25895i | −0.777022 | − | 0.629473i | \(-0.783271\pi\) | ||||
0.777022 | − | 0.629473i | \(-0.216729\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.23463 | −0.0658062 | ||||||||
\(353\) | −8.98390 | −0.478165 | −0.239082 | − | 0.970999i | \(-0.576847\pi\) | ||||
−0.239082 | + | 0.970999i | \(0.576847\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.818827i | 0.0434588i | ||||||||
\(356\) | 4.49886 | 0.238439 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.6685 | −0.880957 | ||||||||
\(359\) | 10.2872i | 0.542937i | 0.962447 | + | 0.271469i | \(0.0875093\pi\) | ||||
−0.962447 | + | 0.271469i | \(0.912491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.7956 | 0.726087 | ||||||||
\(362\) | 2.53036 | 0.132993 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.6610i | 0.610365i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.39104i | 0.177011i | 0.996076 | + | 0.0885053i | \(0.0282090\pi\) | ||||
−0.996076 | + | 0.0885053i | \(0.971791\pi\) | |||||||
\(368\) | − 2.26038i | − 0.117830i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.39488i | 0.228479i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.4460 | −1.42110 | −0.710549 | − | 0.703648i | \(-0.751553\pi\) | ||||
−0.710549 | + | 0.703648i | \(0.751553\pi\) | |||||||
\(374\) | −5.09788 | −0.263605 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 7.51594i | − 0.387605i | ||||||||
\(377\) | 2.21530 | 0.114094 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.0933 | −1.75126 | −0.875629 | − | 0.482985i | \(-0.839553\pi\) | ||||
−0.875629 | + | 0.482985i | \(0.839553\pi\) | |||||||
\(380\) | 2.28130i | 0.117028i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.15158 | 0.263578 | ||||||||
\(383\) | −5.25290 | −0.268411 | −0.134205 | − | 0.990954i | \(-0.542848\pi\) | ||||
−0.134205 | + | 0.990954i | \(0.542848\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 4.50793i | − 0.229448i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.06147i | 0.460026i | ||||||||
\(389\) | 19.8428i | 1.00607i | 0.864265 | + | 0.503036i | \(0.167784\pi\) | ||||
−0.864265 | + | 0.503036i | \(0.832216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 9.33325i | − 0.472003i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.14476 | 0.158431 | ||||||||
\(395\) | 5.65685 | 0.284627 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.84339i | − 0.243083i | −0.992586 | − | 0.121541i | \(-0.961216\pi\) | ||||
0.992586 | − | 0.121541i | \(-0.0387837\pi\) | |||||||
\(398\) | 3.28343 | 0.164583 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | − 6.14161i | − 0.306697i | −0.988172 | − | 0.153349i | \(-0.950994\pi\) | ||||
0.988172 | − | 0.153349i | \(-0.0490057\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.8866 | 0.841183 | ||||||||
\(404\) | 3.88348 | 0.193210 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.42607i | 0.268960i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 27.2071i | − 1.34530i | −0.739959 | − | 0.672652i | \(-0.765155\pi\) | ||||
0.739959 | − | 0.672652i | \(-0.234845\pi\) | |||||||
\(410\) | − 7.08239i | − 0.349774i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 7.56767i | − 0.372833i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.164784 | −0.00808895 | ||||||||
\(416\) | −4.33182 | −0.212385 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.81657i | 0.137763i | ||||||||
\(419\) | −37.6098 | −1.83736 | −0.918678 | − | 0.395007i | \(-0.870742\pi\) | ||||
−0.918678 | + | 0.395007i | \(0.870742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.2049 | 0.887253 | 0.443627 | − | 0.896212i | \(-0.353692\pi\) | ||||
0.443627 | + | 0.896212i | \(0.353692\pi\) | |||||||
\(422\) | − 25.0907i | − 1.22140i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.83259 | 0.428948 | ||||||||
\(425\) | 4.12906 | 0.200289 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.7679i | 0.665498i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 10.1837i | − 0.491104i | ||||||||
\(431\) | − 14.4266i | − 0.694906i | −0.937697 | − | 0.347453i | \(-0.887047\pi\) | ||||
0.937697 | − | 0.347453i | \(-0.112953\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.5560i | 1.56454i | 0.622939 | + | 0.782270i | \(0.285938\pi\) | ||||
−0.622939 | + | 0.782270i | \(0.714062\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.810688 | −0.0388249 | ||||||||
\(437\) | −5.15661 | −0.246674 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.4300i | 1.21371i | 0.794814 | + | 0.606854i | \(0.207569\pi\) | ||||
−0.794814 | + | 0.606854i | \(0.792431\pi\) | |||||||
\(440\) | 1.23463 | 0.0588588 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.8864 | −0.850768 | ||||||||
\(443\) | 22.0115i | 1.04580i | 0.852395 | + | 0.522899i | \(0.175150\pi\) | ||||
−0.852395 | + | 0.522899i | \(0.824850\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.49886 | −0.213266 | ||||||||
\(446\) | 3.21440 | 0.152206 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.5223i | 1.58201i | 0.611808 | + | 0.791006i | \(0.290443\pi\) | ||||
−0.611808 | + | 0.791006i | \(0.709557\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 8.74416i | − 0.411746i | ||||||||
\(452\) | 11.0866i | 0.521468i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 7.15800i | − 0.335941i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.2136 | −0.945551 | −0.472776 | − | 0.881183i | \(-0.656748\pi\) | ||||
−0.472776 | + | 0.881183i | \(0.656748\pi\) | |||||||
\(458\) | 17.0156 | 0.795089 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.26038i | 0.105391i | ||||||||
\(461\) | −10.1557 | −0.472999 | −0.236499 | − | 0.971632i | \(-0.576000\pi\) | ||||
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.0606 | 0.839346 | 0.419673 | − | 0.907675i | \(-0.362145\pi\) | ||||
0.419673 | + | 0.907675i | \(0.362145\pi\) | |||||||
\(464\) | 0.511402i | 0.0237412i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.18080 | −0.378968 | ||||||||
\(467\) | 7.84805 | 0.363164 | 0.181582 | − | 0.983376i | \(-0.441878\pi\) | ||||
0.181582 | + | 0.983376i | \(0.441878\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.51594i | 0.346684i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 8.33598i | − 0.383695i | ||||||||
\(473\) | − 12.5732i | − 0.578116i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 2.28130i | − 0.104673i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −22.3224 | −1.02100 | ||||||||
\(479\) | −16.0502 | −0.733351 | −0.366676 | − | 0.930349i | \(-0.619504\pi\) | ||||
−0.366676 | + | 0.930349i | \(0.619504\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.0378i | 0.868051i | ||||||||
\(482\) | 12.5525 | 0.571751 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.47568 | −0.430713 | ||||||||
\(485\) | − 9.06147i | − 0.411460i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.9509 | −0.722806 | −0.361403 | − | 0.932410i | \(-0.617702\pi\) | ||||
−0.361403 | + | 0.932410i | \(0.617702\pi\) | |||||||
\(488\) | 0.890268 | 0.0403006 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.45991i | 0.291532i | 0.989319 | + | 0.145766i | \(0.0465646\pi\) | ||||
−0.989319 | + | 0.145766i | \(0.953435\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.11161i | 0.0951022i | ||||||||
\(494\) | 9.88220i | 0.444621i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.89828i | 0.175038i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.9934 | 0.984558 | 0.492279 | − | 0.870437i | \(-0.336164\pi\) | ||||
0.492279 | + | 0.870437i | \(0.336164\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 6.05468i | − 0.270234i | ||||||||
\(503\) | 43.2100 | 1.92664 | 0.963318 | − | 0.268361i | \(-0.0864819\pi\) | ||||
0.963318 | + | 0.268361i | \(0.0864819\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.88348 | −0.172813 | ||||||||
\(506\) | 2.79074i | 0.124064i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.12612 | −0.360538 | ||||||||
\(509\) | −18.5792 | −0.823506 | −0.411753 | − | 0.911295i | \(-0.635083\pi\) | ||||
−0.411753 | + | 0.911295i | \(0.635083\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 15.9298i | − 0.702632i | ||||||||
\(515\) | 7.56767i | 0.333472i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.27943i | 0.408109i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.33182 | 0.189963 | ||||||||
\(521\) | −5.77390 | −0.252959 | −0.126480 | − | 0.991969i | \(-0.540368\pi\) | ||||
−0.126480 | + | 0.991969i | \(0.540368\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 9.73569i | − 0.425712i | −0.977084 | − | 0.212856i | \(-0.931723\pi\) | ||||
0.977084 | − | 0.212856i | \(-0.0682765\pi\) | |||||||
\(524\) | 0.391410 | 0.0170988 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.09560 | 0.352985 | ||||||||
\(527\) | 16.0962i | 0.701163i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.8907 | 0.777856 | ||||||||
\(530\) | −8.83259 | −0.383663 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 30.6797i | − 1.32888i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 13.7679i | − 0.595240i | ||||||||
\(536\) | − 5.24105i | − 0.226379i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.7070i | 1.36699i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.37420 | 0.360035 | 0.180017 | − | 0.983663i | \(-0.442385\pi\) | ||||
0.180017 | + | 0.983663i | \(0.442385\pi\) | |||||||
\(542\) | 30.2571 | 1.29965 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 4.12906i | − 0.177032i | ||||||||
\(545\) | 0.810688 | 0.0347261 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.3099 | 1.12493 | 0.562464 | − | 0.826822i | \(-0.309853\pi\) | ||||
0.562464 | + | 0.826822i | \(0.309853\pi\) | |||||||
\(548\) | 21.5832i | 0.921987i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.23463 | −0.0526449 | ||||||||
\(551\) | 1.16666 | 0.0497015 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 3.07626i | − 0.130698i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.9700i | 0.974146i | ||||||||
\(557\) | − 18.8671i | − 0.799424i | −0.916641 | − | 0.399712i | \(-0.869110\pi\) | ||||
0.916641 | − | 0.399712i | \(-0.130890\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 44.1142i | − 1.86583i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.4167 | −0.987772 | ||||||||
\(563\) | 25.2513 | 1.06422 | 0.532109 | − | 0.846676i | \(-0.321400\pi\) | ||||
0.532109 | + | 0.846676i | \(0.321400\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 11.0866i | − 0.466415i | ||||||||
\(566\) | 19.4152 | 0.816081 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.818827 | −0.0343572 | ||||||||
\(569\) | 13.4780i | 0.565026i | 0.959264 | + | 0.282513i | \(0.0911680\pi\) | ||||
−0.959264 | + | 0.282513i | \(0.908832\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.7981 | 1.37256 | 0.686279 | − | 0.727339i | \(-0.259243\pi\) | ||||
0.686279 | + | 0.727339i | \(0.259243\pi\) | |||||||
\(572\) | 5.34821 | 0.223620 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 2.26038i | − 0.0942644i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 44.5364i | − 1.85408i | −0.374967 | − | 0.927038i | \(-0.622346\pi\) | ||||
0.374967 | − | 0.927038i | \(-0.377654\pi\) | |||||||
\(578\) | − 0.0491665i | − 0.00204506i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 0.511402i | − 0.0212348i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.9050 | −0.451639 | ||||||||
\(584\) | −11.6610 | −0.482536 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 26.1609i | − 1.08069i | ||||||||
\(587\) | −38.5483 | −1.59106 | −0.795529 | − | 0.605916i | \(-0.792807\pi\) | ||||
−0.795529 | + | 0.605916i | \(0.792807\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.89315 | 0.366436 | ||||||||
\(590\) | 8.33598i | 0.343187i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.39488 | −0.180629 | ||||||||
\(593\) | 33.1728 | 1.36224 | 0.681122 | − | 0.732170i | \(-0.261492\pi\) | ||||
0.681122 | + | 0.732170i | \(0.261492\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.8033i | 0.934059i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.79156i | 0.400407i | ||||||||
\(599\) | 27.0509i | 1.10527i | 0.833424 | + | 0.552634i | \(0.186377\pi\) | ||||
−0.833424 | + | 0.552634i | \(0.813623\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.7601i | 1.74422i | 0.489309 | + | 0.872111i | \(0.337249\pi\) | ||||
−0.489309 | + | 0.872111i | \(0.662751\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21.2905 | 0.866299 | ||||||||
\(605\) | 9.47568 | 0.385241 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.6190i | 1.16161i | 0.814043 | + | 0.580805i | \(0.197262\pi\) | ||||
−0.814043 | + | 0.580805i | \(0.802738\pi\) | |||||||
\(608\) | −2.28130 | −0.0925191 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.890268 | −0.0360459 | ||||||||
\(611\) | 32.5577i | 1.31714i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.9971 | 1.65586 | 0.827929 | − | 0.560833i | \(-0.189519\pi\) | ||||
0.827929 | + | 0.560833i | \(0.189519\pi\) | |||||||
\(614\) | −7.86481 | −0.317398 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.66277i | 0.348750i | 0.984679 | + | 0.174375i | \(0.0557905\pi\) | ||||
−0.984679 | + | 0.174375i | \(0.944209\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.3620i | 0.456676i | 0.973582 | + | 0.228338i | \(0.0733292\pi\) | ||||
−0.973582 | + | 0.228338i | \(0.926671\pi\) | |||||||
\(620\) | − 3.89828i | − 0.156559i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.4170i | 0.578070i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −8.40649 | −0.335991 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.60127i | 0.263419i | ||||||||
\(629\) | −18.1467 | −0.723558 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.2837 | −1.12596 | −0.562979 | − | 0.826471i | \(-0.690345\pi\) | ||||
−0.562979 | + | 0.826471i | \(0.690345\pi\) | |||||||
\(632\) | 5.65685i | 0.225018i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.0420 | 0.438534 | ||||||||
\(635\) | 8.12612 | 0.322475 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 0.631394i | − 0.0249971i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 17.0146i | 0.672036i | 0.941856 | + | 0.336018i | \(0.109080\pi\) | ||||
−0.941856 | + | 0.336018i | \(0.890920\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 28.9046i | − 1.13988i | −0.821685 | − | 0.569942i | \(-0.806966\pi\) | ||||
0.821685 | − | 0.569942i | \(-0.193034\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.41965 | −0.370611 | ||||||||
\(647\) | 35.6085 | 1.39992 | 0.699958 | − | 0.714184i | \(-0.253202\pi\) | ||||
0.699958 | + | 0.714184i | \(0.253202\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.2919i | 0.403992i | ||||||||
\(650\) | −4.33182 | −0.169908 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.4286 | 0.643395 | ||||||||
\(653\) | − 1.79205i | − 0.0701282i | −0.999385 | − | 0.0350641i | \(-0.988836\pi\) | ||||
0.999385 | − | 0.0350641i | \(-0.0111635\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.391410 | −0.0152937 | ||||||||
\(656\) | 7.08239 | 0.276521 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.64709i | 0.375797i | 0.982188 | + | 0.187899i | \(0.0601677\pi\) | ||||
−0.982188 | + | 0.187899i | \(0.939832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 16.8868i | − 0.656821i | −0.944535 | − | 0.328411i | \(-0.893487\pi\) | ||||
0.944535 | − | 0.328411i | \(-0.106513\pi\) | |||||||
\(662\) | 21.1667i | 0.822666i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 0.164784i | − 0.00639487i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.15596 | 0.0447590 | ||||||||
\(668\) | −0.834556 | −0.0322899 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.24105i | 0.202479i | ||||||||
\(671\) | −1.09915 | −0.0424324 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.4010 | 0.478024 | 0.239012 | − | 0.971017i | \(-0.423177\pi\) | ||||
0.239012 | + | 0.971017i | \(0.423177\pi\) | |||||||
\(674\) | − 20.2992i | − 0.781897i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.76468 | 0.221718 | ||||||||
\(677\) | −1.57184 | −0.0604106 | −0.0302053 | − | 0.999544i | \(-0.509616\pi\) | ||||
−0.0302053 | + | 0.999544i | \(0.509616\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.12906i | 0.158342i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 4.81294i | − 0.184297i | ||||||||
\(683\) | 35.8613i | 1.37219i | 0.727510 | + | 0.686097i | \(0.240677\pi\) | ||||
−0.727510 | + | 0.686097i | \(0.759323\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 21.5832i | − 0.824650i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.1837 | 0.388252 | ||||||||
\(689\) | −38.2612 | −1.45764 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.40105i | 0.319591i | 0.987150 | + | 0.159796i | \(0.0510835\pi\) | ||||
−0.987150 | + | 0.159796i | \(0.948916\pi\) | |||||||
\(692\) | −3.54675 | −0.134827 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.6912 | −1.08910 | ||||||||
\(695\) | − 22.9700i | − 0.871303i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.2436 | 1.10768 | ||||||||
\(698\) | −23.5191 | −0.890210 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 5.58154i | − 0.210812i | −0.994429 | − | 0.105406i | \(-0.966386\pi\) | ||||
0.994429 | − | 0.105406i | \(-0.0336142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0261i | 0.378140i | ||||||||
\(704\) | 1.23463i | 0.0465320i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.98390i | 0.338113i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.5415 | 1.78546 | 0.892729 | − | 0.450594i | \(-0.148788\pi\) | ||||
0.892729 | + | 0.450594i | \(0.148788\pi\) | |||||||
\(710\) | 0.818827 | 0.0307300 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 4.49886i | − 0.168602i | ||||||||
\(713\) | 8.81158 | 0.329996 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.34821 | −0.200012 | ||||||||
\(716\) | 16.6685i | 0.622931i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.2872 | 0.383915 | ||||||||
\(719\) | 39.6210 | 1.47762 | 0.738808 | − | 0.673916i | \(-0.235389\pi\) | ||||
0.738808 | + | 0.673916i | \(0.235389\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 13.7956i | − 0.513421i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 2.53036i | − 0.0940401i | ||||||||
\(725\) | 0.511402i | 0.0189930i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.9137i | 0.775645i | 0.921734 | + | 0.387823i | \(0.126773\pi\) | ||||
−0.921734 | + | 0.387823i | \(0.873227\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.6610 | 0.431594 | ||||||||
\(731\) | 42.0493 | 1.55525 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.2326i | 0.414886i | 0.978247 | + | 0.207443i | \(0.0665142\pi\) | ||||
−0.978247 | + | 0.207443i | \(0.933486\pi\) | |||||||
\(734\) | 3.39104 | 0.125165 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.26038 | −0.0833187 | ||||||||
\(737\) | 6.47077i | 0.238354i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.2983 | −1.88704 | −0.943520 | − | 0.331316i | \(-0.892507\pi\) | ||||
−0.943520 | + | 0.331316i | \(0.892507\pi\) | |||||||
\(740\) | 4.39488 | 0.161559 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 20.5208i | − 0.752834i | −0.926450 | − | 0.376417i | \(-0.877156\pi\) | ||||
0.926450 | − | 0.376417i | \(-0.122844\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 22.8033i | − 0.835448i | ||||||||
\(746\) | 27.4460i | 1.00487i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.09788i | 0.186397i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.0794 | −0.915160 | −0.457580 | − | 0.889168i | \(-0.651284\pi\) | ||||
−0.457580 | + | 0.889168i | \(0.651284\pi\) | |||||||
\(752\) | −7.51594 | −0.274078 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 2.21530i | − 0.0806765i | ||||||||
\(755\) | −21.2905 | −0.774842 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.2316 | −0.989751 | −0.494875 | − | 0.868964i | \(-0.664786\pi\) | ||||
−0.494875 | + | 0.868964i | \(0.664786\pi\) | |||||||
\(758\) | 34.0933i | 1.23833i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.28130 | 0.0827516 | ||||||||
\(761\) | −45.3792 | −1.64499 | −0.822496 | − | 0.568770i | \(-0.807419\pi\) | ||||
−0.822496 | + | 0.568770i | \(0.807419\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 5.15158i | − 0.186378i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.25290i | 0.189795i | ||||||||
\(767\) | 36.1100i | 1.30386i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 34.0610i | − 1.22827i | −0.789201 | − | 0.614135i | \(-0.789505\pi\) | ||||
0.789201 | − | 0.614135i | \(-0.210495\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.50793 | −0.162244 | ||||||||
\(773\) | −19.5924 | −0.704688 | −0.352344 | − | 0.935871i | \(-0.614615\pi\) | ||||
−0.352344 | + | 0.935871i | \(0.614615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.89828i | 0.140030i | ||||||||
\(776\) | 9.06147 | 0.325288 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.8428 | 0.711401 | ||||||||
\(779\) | − 16.1571i | − 0.578888i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.01095 | 0.0361747 | ||||||||
\(782\) | −9.33325 | −0.333756 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 6.60127i | − 0.235610i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.5398i | 0.625227i | 0.949880 | + | 0.312613i | \(0.101204\pi\) | ||||
−0.949880 | + | 0.312613i | \(0.898796\pi\) | |||||||
\(788\) | − 3.14476i | − 0.112028i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 5.65685i | − 0.201262i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.85648 | −0.136948 | ||||||||
\(794\) | −4.84339 | −0.171885 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 3.28343i | − 0.116378i | ||||||||
\(797\) | 19.7785 | 0.700589 | 0.350295 | − | 0.936640i | \(-0.386081\pi\) | ||||
0.350295 | + | 0.936640i | \(0.386081\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.0338 | −1.09790 | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.14161 | −0.216868 | ||||||||
\(803\) | 14.3971 | 0.508062 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 16.8866i | − 0.594806i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 3.88348i | − 0.136620i | ||||||||
\(809\) | 20.1357i | 0.707934i | 0.935258 | + | 0.353967i | \(0.115168\pi\) | ||||
−0.935258 | + | 0.353967i | \(0.884832\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.7335i | 1.43035i | 0.698946 | + | 0.715174i | \(0.253653\pi\) | ||||
−0.698946 | + | 0.715174i | \(0.746347\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.42607 | 0.190184 | ||||||||
\(815\) | −16.4286 | −0.575470 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 23.2322i | − 0.812792i | ||||||||
\(818\) | −27.2071 | −0.951273 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.08239 | −0.247328 | ||||||||
\(821\) | 1.57950i | 0.0551250i | 0.999620 | + | 0.0275625i | \(0.00877453\pi\) | ||||
−0.999620 | + | 0.0275625i | \(0.991225\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.4028 | 0.955202 | 0.477601 | − | 0.878577i | \(-0.341506\pi\) | ||||
0.477601 | + | 0.878577i | \(0.341506\pi\) | |||||||
\(824\) | −7.56767 | −0.263632 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.7182i | 0.685668i | 0.939396 | + | 0.342834i | \(0.111387\pi\) | ||||
−0.939396 | + | 0.342834i | \(0.888613\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 28.9250i | − 1.00461i | −0.864691 | − | 0.502303i | \(-0.832486\pi\) | ||||
0.864691 | − | 0.502303i | \(-0.167514\pi\) | |||||||
\(830\) | 0.164784i | 0.00571975i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.33182i | 0.150179i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.834556 | 0.0288810 | ||||||||
\(836\) | 2.81657 | 0.0974133 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 37.6098i | 1.29921i | ||||||||
\(839\) | −50.5905 | −1.74658 | −0.873289 | − | 0.487203i | \(-0.838017\pi\) | ||||
−0.873289 | + | 0.487203i | \(0.838017\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.7385 | 0.990982 | ||||||||
\(842\) | − 18.2049i | − 0.627383i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.0907 | −0.863658 | ||||||||
\(845\) | −5.76468 | −0.198311 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 8.83259i | − 0.303312i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 4.12906i | − 0.141626i | ||||||||
\(851\) | 9.93410i | 0.340537i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.1746i | 1.68371i | 0.539706 | + | 0.841854i | \(0.318536\pi\) | ||||
−0.539706 | + | 0.841854i | \(0.681464\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.7679 | 0.470578 | ||||||||
\(857\) | 44.8289 | 1.53133 | 0.765663 | − | 0.643242i | \(-0.222411\pi\) | ||||
0.765663 | + | 0.643242i | \(0.222411\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 14.5032i | − 0.494843i | −0.968908 | − | 0.247422i | \(-0.920417\pi\) | ||||
0.968908 | − | 0.247422i | \(-0.0795832\pi\) | |||||||
\(860\) | −10.1837 | −0.347263 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.4266 | −0.491373 | ||||||||
\(863\) | 43.4906i | 1.48044i | 0.672367 | + | 0.740218i | \(0.265278\pi\) | ||||
−0.672367 | + | 0.740218i | \(0.734722\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.54675 | 0.120593 | ||||||||
\(866\) | 32.5560 | 1.10630 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 6.98414i | − 0.236921i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.7033i | 0.769271i | ||||||||
\(872\) | 0.810688i | 0.0274534i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.15661i | 0.174425i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.8913 | 1.88732 | 0.943658 | − | 0.330922i | \(-0.107360\pi\) | ||||
0.943658 | + | 0.330922i | \(0.107360\pi\) | |||||||
\(878\) | 25.4300 | 0.858220 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 1.23463i | − 0.0416195i | ||||||||
\(881\) | −24.0647 | −0.810761 | −0.405381 | − | 0.914148i | \(-0.632861\pi\) | ||||
−0.405381 | + | 0.914148i | \(0.632861\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.8242 | 1.20558 | 0.602790 | − | 0.797900i | \(-0.294056\pi\) | ||||
0.602790 | + | 0.797900i | \(0.294056\pi\) | |||||||
\(884\) | 17.8864i | 0.601584i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.0115 | 0.739491 | ||||||||
\(887\) | 47.7182 | 1.60222 | 0.801111 | − | 0.598516i | \(-0.204243\pi\) | ||||
0.801111 | + | 0.598516i | \(0.204243\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.49886i | 0.150802i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 3.21440i | − 0.107626i | ||||||||
\(893\) | 17.1461i | 0.573774i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 16.6685i | − 0.557166i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 33.5223 | 1.11865 | ||||||||
\(899\) | −1.99359 | −0.0664898 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 36.4703i | − 1.21500i | ||||||||
\(902\) | −8.74416 | −0.291149 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.0866 | 0.368733 | ||||||||
\(905\) | 2.53036i | 0.0841120i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.0550 | −0.898346 | −0.449173 | − | 0.893445i | \(-0.648281\pi\) | ||||
−0.449173 | + | 0.893445i | \(0.648281\pi\) | |||||||
\(908\) | −7.15800 | −0.237546 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 10.6210i | − 0.351890i | −0.984400 | − | 0.175945i | \(-0.943702\pi\) | ||||
0.984400 | − | 0.175945i | \(-0.0562980\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.203448i | 0.00673316i | ||||||||
\(914\) | 20.2136i | 0.668606i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 17.0156i | − 0.562213i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.7502 | 0.651497 | 0.325749 | − | 0.945456i | \(-0.394384\pi\) | ||||
0.325749 | + | 0.945456i | \(0.394384\pi\) | |||||||
\(920\) | 2.26038 | 0.0745225 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.1557i | 0.334461i | ||||||||
\(923\) | 3.54701 | 0.116751 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.39488 | −0.144503 | ||||||||
\(926\) | − 18.0606i | − 0.593507i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.511402 | 0.0167876 | ||||||||
\(929\) | 6.94442 | 0.227839 | 0.113919 | − | 0.993490i | \(-0.463659\pi\) | ||||
0.113919 | + | 0.993490i | \(0.463659\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.18080i | 0.267971i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 7.84805i | − 0.256796i | ||||||||
\(935\) | − 5.09788i | − 0.166718i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.7945i | 1.23469i | 0.786692 | + | 0.617346i | \(0.211792\pi\) | ||||
−0.786692 | + | 0.617346i | \(0.788208\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.51594 | 0.245143 | ||||||||
\(941\) | 57.4570 | 1.87304 | 0.936522 | − | 0.350608i | \(-0.114025\pi\) | ||||
0.936522 | + | 0.350608i | \(0.114025\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 16.0089i | − 0.521321i | ||||||||
\(944\) | −8.33598 | −0.271313 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.5732 | −0.408790 | ||||||||
\(947\) | − 7.80522i | − 0.253636i | −0.991926 | − | 0.126818i | \(-0.959524\pi\) | ||||
0.991926 | − | 0.126818i | \(-0.0404763\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.5134 | 1.63974 | ||||||||
\(950\) | −2.28130 | −0.0740153 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 33.4531i | − 1.08365i | −0.840491 | − | 0.541826i | \(-0.817733\pi\) | ||||
0.840491 | − | 0.541826i | \(-0.182267\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.15158i | 0.166701i | ||||||||
\(956\) | 22.3224i | 0.721958i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.0502i | 0.518558i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.8034 | 0.509789 | ||||||||
\(962\) | 19.0378 | 0.613805 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 12.5525i | − 0.404289i | ||||||||
\(965\) | 4.50793 | 0.145115 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.1290 | 1.25830 | 0.629152 | − | 0.777283i | \(-0.283402\pi\) | ||||
0.629152 | + | 0.777283i | \(0.283402\pi\) | |||||||
\(968\) | 9.47568i | 0.304560i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.06147 | −0.290946 | ||||||||
\(971\) | −35.7937 | −1.14868 | −0.574338 | − | 0.818618i | \(-0.694740\pi\) | ||||
−0.574338 | + | 0.818618i | \(0.694740\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 15.9509i | 0.511101i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 0.890268i | − 0.0284968i | ||||||||
\(977\) | − 6.01733i | − 0.192512i | −0.995357 | − | 0.0962558i | \(-0.969313\pi\) | ||||
0.995357 | − | 0.0962558i | \(-0.0306867\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.55444i | 0.177521i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.45991 | 0.206144 | ||||||||
\(983\) | 58.9136 | 1.87905 | 0.939526 | − | 0.342479i | \(-0.111266\pi\) | ||||
0.939526 | + | 0.342479i | \(0.111266\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.14476i | 0.100200i | ||||||||
\(986\) | 2.11161 | 0.0672474 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.88220 | 0.314395 | ||||||||
\(989\) | − 23.0191i | − 0.731966i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.4659 | −1.03131 | −0.515657 | − | 0.856795i | \(-0.672452\pi\) | ||||
−0.515657 | + | 0.856795i | \(0.672452\pi\) | |||||||
\(992\) | 3.89828 | 0.123770 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.28343i | 0.104092i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 0.389500i | − 0.0123356i | −0.999981 | − | 0.00616780i | \(-0.998037\pi\) | ||||
0.999981 | − | 0.00616780i | \(-0.00196328\pi\) | |||||||
\(998\) | − 21.9934i | − 0.696188i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4410.2.b.d.881.3 | yes | 8 | |
3.2 | odd | 2 | 4410.2.b.a.881.6 | yes | 8 | ||
7.6 | odd | 2 | 4410.2.b.a.881.3 | ✓ | 8 | ||
21.20 | even | 2 | inner | 4410.2.b.d.881.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4410.2.b.a.881.3 | ✓ | 8 | 7.6 | odd | 2 | ||
4410.2.b.a.881.6 | yes | 8 | 3.2 | odd | 2 | ||
4410.2.b.d.881.3 | yes | 8 | 1.1 | even | 1 | trivial | |
4410.2.b.d.881.6 | yes | 8 | 21.20 | even | 2 | inner |