Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.a (trivial) |
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: | yes |
Analytic conductor: | \(14.6924739719\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −1.61803 | −0.934172 | −0.467086 | − | 0.884212i | \(-0.654696\pi\) | ||||
−0.467086 | + | 0.884212i | \(0.654696\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.618034 | 0.233595 | 0.116797 | − | 0.993156i | \(-0.462737\pi\) | ||||
0.116797 | + | 0.993156i | \(0.462737\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.85410 | 0.860544 | 0.430272 | − | 0.902699i | \(-0.358418\pi\) | ||||
0.430272 | + | 0.902699i | \(0.358418\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.09017 | −1.96646 | −0.983230 | − | 0.182372i | \(-0.941623\pi\) | ||||
−0.983230 | + | 0.182372i | \(0.941623\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.61803 | −0.417775 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.09017 | 1.47708 | 0.738542 | − | 0.674208i | \(-0.235515\pi\) | ||||
0.738542 | + | 0.674208i | \(0.235515\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.85410 | −0.425360 | −0.212680 | − | 0.977122i | \(-0.568219\pi\) | ||||
−0.212680 | + | 0.977122i | \(0.568219\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.47214 | 1.05311 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.23607 | −1.71509 | −0.857547 | − | 0.514405i | \(-0.828013\pi\) | ||||
−0.857547 | + | 0.514405i | \(0.828013\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.09017 | −1.63264 | −0.816321 | − | 0.577598i | \(-0.803990\pi\) | ||||
−0.816321 | + | 0.577598i | \(0.803990\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.61803 | −0.803897 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.618034 | 0.104467 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.47214 | 1.06401 | 0.532006 | − | 0.846740i | \(-0.321438\pi\) | ||||
0.532006 | + | 0.846740i | \(0.321438\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.4721 | 1.83701 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.32624 | 0.519471 | 0.259736 | − | 0.965680i | \(-0.416365\pi\) | ||||
0.259736 | + | 0.965680i | \(0.416365\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.381966 | −0.0569401 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.70820 | 0.540897 | 0.270449 | − | 0.962734i | \(-0.412828\pi\) | ||||
0.270449 | + | 0.962734i | \(0.412828\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.61803 | −0.945433 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.85410 | −1.37985 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.472136 | 0.0648529 | 0.0324264 | − | 0.999474i | \(-0.489677\pi\) | ||||
0.0324264 | + | 0.999474i | \(0.489677\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.85410 | 0.384847 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | 0.397360 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.70820 | −0.222389 | −0.111195 | − | 0.993799i | \(-0.535468\pi\) | ||||
−0.111195 | + | 0.993799i | \(0.535468\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.32624 | −1.19410 | −0.597051 | − | 0.802203i | \(-0.703661\pi\) | ||||
−0.597051 | + | 0.802203i | \(0.703661\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.236068 | −0.0297418 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.09017 | −0.879427 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.4721 | −1.76805 | −0.884026 | − | 0.467437i | \(-0.845177\pi\) | ||||
−0.884026 | + | 0.467437i | \(0.845177\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.61803 | 0.194788 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.09017 | 0.485414 | 0.242707 | − | 0.970100i | \(-0.421965\pi\) | ||||
0.242707 | + | 0.970100i | \(0.421965\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.23607 | 0.378753 | 0.189377 | − | 0.981905i | \(-0.439353\pi\) | ||||
0.189377 | + | 0.981905i | \(0.439353\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.61803 | −0.186834 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.76393 | 0.201019 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.52786 | −0.171898 | −0.0859491 | − | 0.996300i | \(-0.527392\pi\) | ||||
−0.0859491 | + | 0.996300i | \(0.527392\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.94427 | 0.762233 | 0.381116 | − | 0.924527i | \(-0.375540\pi\) | ||||
0.381116 | + | 0.924527i | \(0.375540\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.09017 | 0.660572 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.9443 | 1.60219 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.4721 | −1.11004 | −0.555022 | − | 0.831836i | \(-0.687290\pi\) | ||||
−0.555022 | + | 0.831836i | \(0.687290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.38197 | −0.459355 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.7082 | 1.52517 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.85410 | −0.190227 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3820 | 1.25720 | 0.628599 | − | 0.777730i | \(-0.283629\pi\) | ||||
0.628599 | + | 0.777730i | \(0.283629\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.09017 | −0.109566 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.291796 | −0.0290348 | −0.0145174 | − | 0.999895i | \(-0.504621\pi\) | ||||
−0.0145174 | + | 0.999895i | \(0.504621\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.5623 | −1.63193 | −0.815966 | − | 0.578100i | \(-0.803795\pi\) | ||||
−0.815966 | + | 0.578100i | \(0.803795\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.1803 | −1.75756 | −0.878780 | − | 0.477227i | \(-0.841642\pi\) | ||||
−0.878780 | + | 0.477227i | \(0.841642\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.5623 | −1.10747 | −0.553734 | − | 0.832694i | \(-0.686798\pi\) | ||||
−0.553734 | + | 0.832694i | \(0.686798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.4721 | −0.993971 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.05573 | 0.0993145 | 0.0496573 | − | 0.998766i | \(-0.484187\pi\) | ||||
0.0496573 | + | 0.998766i | \(0.484187\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.70820 | 0.250374 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.76393 | 0.345039 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.85410 | −0.259464 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.38197 | −0.485276 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.1803 | −1.43577 | −0.717886 | − | 0.696160i | \(-0.754890\pi\) | ||||
−0.717886 | + | 0.696160i | \(0.754890\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.94427 | −0.257242 | −0.128621 | − | 0.991694i | \(-0.541055\pi\) | ||||
−0.128621 | + | 0.991694i | \(0.541055\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.14590 | −0.0993620 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.47214 | 0.470966 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3262 | −0.882230 | −0.441115 | − | 0.897451i | \(-0.645417\pi\) | ||||
−0.441115 | + | 0.897451i | \(0.645417\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.7639 | −1.08262 | −0.541311 | − | 0.840822i | \(-0.682072\pi\) | ||||
−0.541311 | + | 0.840822i | \(0.682072\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.2361 | −1.69223 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.23607 | −0.767014 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.7082 | 0.883198 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.85410 | −0.643433 | −0.321717 | − | 0.946836i | \(-0.604260\pi\) | ||||
−0.321717 | + | 0.946836i | \(0.604260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.56231 | 0.208517 | 0.104259 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104259 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.32624 | −0.188065 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.09017 | −0.730140 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.70820 | −0.295947 | −0.147973 | − | 0.988991i | \(-0.547275\pi\) | ||||
−0.147973 | + | 0.988991i | \(0.547275\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.763932 | −0.0605838 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.618034 | −0.0487079 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.38197 | −0.108244 | −0.0541220 | − | 0.998534i | \(-0.517236\pi\) | ||||
−0.0541220 | + | 0.998534i | \(0.517236\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.61803 | −0.359513 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.00000 | 0.619059 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.2705 | 2.86696 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.708204 | 0.0541577 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.43769 | −0.109306 | −0.0546529 | − | 0.998505i | \(-0.517405\pi\) | ||||
−0.0546529 | + | 0.998505i | \(0.517405\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.618034 | 0.0467190 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.76393 | 0.207750 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.18034 | −0.162966 | −0.0814831 | − | 0.996675i | \(-0.525966\pi\) | ||||
−0.0814831 | + | 0.996675i | \(0.525966\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.1459 | −0.902797 | −0.451399 | − | 0.892322i | \(-0.649075\pi\) | ||||
−0.451399 | + | 0.892322i | \(0.649075\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.0902 | 1.11550 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.47214 | 0.475841 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.3820 | 1.27110 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.38197 | 0.246002 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.7082 | 0.991891 | 0.495945 | − | 0.868354i | \(-0.334822\pi\) | ||||
0.495945 | + | 0.868354i | \(0.334822\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.763932 | 0.0549890 | 0.0274945 | − | 0.999622i | \(-0.491247\pi\) | ||||
0.0274945 | + | 0.999622i | \(0.491247\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.4721 | 0.821537 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.5623 | −1.60750 | −0.803749 | − | 0.594969i | \(-0.797164\pi\) | ||||
−0.803749 | + | 0.594969i | \(0.797164\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.00000 | −0.141776 | −0.0708881 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.4164 | 1.65167 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.70820 | −0.400637 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.32624 | 0.232315 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.381966 | 0.0265485 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.29180 | −0.366041 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.0000 | −0.963800 | −0.481900 | − | 0.876226i | \(-0.660053\pi\) | ||||
−0.481900 | + | 0.876226i | \(0.660053\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.61803 | −0.453460 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.61803 | −0.381377 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.23607 | −0.353821 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −43.1803 | −2.90462 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.9443 | 1.40253 | 0.701266 | − | 0.712900i | \(-0.252618\pi\) | ||||
0.701266 | + | 0.712900i | \(0.252618\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.381966 | −0.0254644 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.7639 | 1.24541 | 0.622703 | − | 0.782458i | \(-0.286035\pi\) | ||||
0.622703 | + | 0.782458i | \(0.286035\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.85410 | −0.187786 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.29180 | 0.412189 | 0.206095 | − | 0.978532i | \(-0.433925\pi\) | ||||
0.206095 | + | 0.978532i | \(0.433925\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.70820 | 0.241897 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.47214 | 0.160582 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.3607 | 1.31702 | 0.658511 | − | 0.752571i | \(-0.271186\pi\) | ||||
0.658511 | + | 0.752571i | \(0.271186\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.61803 | −0.422811 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.1459 | 0.836453 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.2361 | −0.712057 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.14590 | −0.387926 | −0.193963 | − | 0.981009i | \(-0.562134\pi\) | ||||
−0.193963 | + | 0.981009i | \(0.562134\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.85410 | −0.179436 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.85410 | −0.617088 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.81966 | −0.487777 | −0.243888 | − | 0.969803i | \(-0.578423\pi\) | ||||
−0.243888 | + | 0.969803i | \(0.578423\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.52786 | 0.218369 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.7426 | −1.27905 | −0.639523 | − | 0.768772i | \(-0.720868\pi\) | ||||
−0.639523 | + | 0.768772i | \(0.720868\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.472136 | 0.0290031 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.9443 | 1.03697 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.1803 | −0.864591 | −0.432295 | − | 0.901732i | \(-0.642296\pi\) | ||||
−0.432295 | + | 0.901732i | \(0.642296\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.3262 | 1.84219 | 0.921094 | − | 0.389341i | \(-0.127297\pi\) | ||||
0.921094 | + | 0.389341i | \(0.127297\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.09017 | 0.429117 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.85410 | 0.172109 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.4164 | 1.76746 | 0.883730 | − | 0.467996i | \(-0.155024\pi\) | ||||
0.883730 | + | 0.467996i | \(0.155024\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.47214 | 0.207871 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.7639 | 1.35798 | 0.678991 | − | 0.734146i | \(-0.262417\pi\) | ||||
0.678991 | + | 0.734146i | \(0.262417\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.9443 | 1.60167 | 0.800835 | − | 0.598885i | \(-0.204389\pi\) | ||||
0.800835 | + | 0.598885i | \(0.204389\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.00000 | 0.177705 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.05573 | 0.121346 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.0902 | 1.18177 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.0344 | −1.17444 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.8885 | −1.16190 | −0.580951 | − | 0.813939i | \(-0.697319\pi\) | ||||
−0.580951 | + | 0.813939i | \(0.697319\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.70820 | −0.0994555 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.6180 | 0.906250 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.09017 | 0.410035 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.472136 | 0.0271235 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.32624 | −0.534019 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.4508 | 1.62378 | 0.811888 | − | 0.583813i | \(-0.198440\pi\) | ||||
0.811888 | + | 0.583813i | \(0.198440\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.7984 | 1.52451 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.00000 | −0.226819 | −0.113410 | − | 0.993548i | \(-0.536177\pi\) | ||||
−0.113410 | + | 0.993548i | \(0.536177\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.7984 | 0.723407 | 0.361703 | − | 0.932293i | \(-0.382195\pi\) | ||||
0.361703 | + | 0.932293i | \(0.382195\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.236068 | −0.0133009 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.0902 | −0.622886 | −0.311443 | − | 0.950265i | \(-0.600812\pi\) | ||||
−0.311443 | + | 0.950265i | \(0.600812\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.3607 | −1.47591 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 29.4164 | 1.64186 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.2918 | −0.628292 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.09017 | −0.393292 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.7082 | 1.03457 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.29180 | 0.126351 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.2361 | −1.05731 | −0.528655 | − | 0.848837i | \(-0.677303\pi\) | ||||
−0.528655 | + | 0.848837i | \(0.677303\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.47214 | −0.135472 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.4721 | −0.790697 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.6738 | 0.744857 | 0.372429 | − | 0.928061i | \(-0.378525\pi\) | ||||
0.372429 | + | 0.928061i | \(0.378525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.70820 | −0.0927769 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.9443 | −1.40496 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.41641 | −0.454443 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.61803 | 0.0871120 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.38197 | 0.342602 | 0.171301 | − | 0.985219i | \(-0.445203\pi\) | ||||
0.171301 | + | 0.985219i | \(0.445203\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −38.7984 | −2.07090 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.0000 | 1.27739 | 0.638696 | − | 0.769460i | \(-0.279474\pi\) | ||||
0.638696 | + | 0.769460i | \(0.279474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.09017 | 0.217084 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.09017 | −0.322326 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.3607 | −1.39126 | −0.695632 | − | 0.718399i | \(-0.744875\pi\) | ||||
−0.695632 | + | 0.718399i | \(0.744875\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.5623 | −0.819069 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.61803 | 0.242384 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.23607 | 0.169384 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.47214 | −0.337843 | −0.168921 | − | 0.985630i | \(-0.554028\pi\) | ||||
−0.168921 | + | 0.985630i | \(0.554028\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.27051 | −0.0661401 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.291796 | 0.0151493 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.1803 | 1.04490 | 0.522449 | − | 0.852670i | \(-0.325018\pi\) | ||||
0.522449 | + | 0.852670i | \(0.325018\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.61803 | −0.0835549 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 65.4853 | 3.37266 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.4508 | 1.15322 | 0.576611 | − | 0.817019i | \(-0.304375\pi\) | ||||
0.576611 | + | 0.817019i | \(0.304375\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.1803 | 1.34126 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.8885 | 0.914062 | 0.457031 | − | 0.889451i | \(-0.348913\pi\) | ||||
0.457031 | + | 0.889451i | \(0.348913\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.76393 | 0.0898983 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.3262 | 1.08128 | 0.540642 | − | 0.841253i | \(-0.318182\pi\) | ||||
0.540642 | + | 0.841253i | \(0.318182\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.09017 | −0.307993 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.76393 | 0.240309 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.52786 | −0.0768752 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.32624 | 0.367693 | 0.183847 | − | 0.982955i | \(-0.441145\pi\) | ||||
0.183847 | + | 0.982955i | \(0.441145\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.85410 | 0.0928212 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.70820 | −0.0853036 | −0.0426518 | − | 0.999090i | \(-0.513581\pi\) | ||||
−0.0426518 | + | 0.999090i | \(0.513581\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 64.4508 | 3.21053 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.70820 | −0.383024 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.4721 | 0.915630 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.2148 | −1.49402 | −0.747012 | − | 0.664810i | \(-0.768512\pi\) | ||||
−0.747012 | + | 0.664810i | \(0.768512\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.7082 | 0.824155 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.05573 | −0.0519490 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.94427 | 0.340881 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.6525 | 1.01136 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.4721 | −0.707010 | −0.353505 | − | 0.935433i | \(-0.615010\pi\) | ||||
−0.353505 | + | 0.935433i | \(0.615010\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7426 | 0.669776 | 0.334888 | − | 0.942258i | \(-0.391302\pi\) | ||||
0.334888 | + | 0.942258i | \(0.391302\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.41641 | −0.0688681 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.09017 | 0.295417 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.76393 | −0.278936 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 32.7426 | 1.58083 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.34752 | −0.161245 | −0.0806223 | − | 0.996745i | \(-0.525691\pi\) | ||||
−0.0806223 | + | 0.996745i | \(0.525691\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.50658 | 0.408800 | 0.204400 | − | 0.978887i | \(-0.434476\pi\) | ||||
0.204400 | + | 0.978887i | \(0.434476\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.9443 | 0.716523 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.85410 | 0.0886937 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.3820 | 0.638686 | 0.319343 | − | 0.947639i | \(-0.396538\pi\) | ||||
0.319343 | + | 0.947639i | \(0.396538\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.52786 | 0.120374 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.0902 | −1.19207 | −0.596035 | − | 0.802958i | \(-0.703258\pi\) | ||||
−0.596035 | + | 0.802958i | \(0.703258\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.4721 | −0.496427 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.7082 | 0.601077 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.56231 | −0.0737298 | −0.0368649 | − | 0.999320i | \(-0.511737\pi\) | ||||
−0.0368649 | + | 0.999320i | \(0.511737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.49342 | 0.447028 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.14590 | −0.194791 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.38197 | −0.205430 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.7771 | −1.76714 | −0.883569 | − | 0.468301i | \(-0.844866\pi\) | ||||
−0.883569 | + | 0.468301i | \(0.844866\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 33.3262 | 1.55554 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.2361 | −1.82741 | −0.913703 | − | 0.406383i | \(-0.866790\pi\) | ||||
−0.913703 | + | 0.406383i | \(0.866790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.00000 | −0.0929479 | −0.0464739 | − | 0.998920i | \(-0.514798\pi\) | ||||
−0.0464739 | + | 0.998920i | \(0.514798\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.7082 | 0.682077 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.1246 | 0.792433 | 0.396216 | − | 0.918157i | \(-0.370323\pi\) | ||||
0.396216 | + | 0.918157i | \(0.370323\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.94427 | −0.413008 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.00000 | 0.276465 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.85410 | −0.0850720 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.180340 | −0.00825720 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.8885 | 1.45702 | 0.728512 | − | 0.685033i | \(-0.240212\pi\) | ||||
0.728512 | + | 0.685033i | \(0.240212\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −45.8885 | −2.09234 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.3820 | 0.562236 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.8197 | 0.898115 | 0.449057 | − | 0.893503i | \(-0.351760\pi\) | ||||
0.449057 | + | 0.893503i | \(0.351760\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.23607 | 0.101118 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.18034 | −0.278915 | −0.139457 | − | 0.990228i | \(-0.544536\pi\) | ||||
−0.139457 | + | 0.990228i | \(0.544536\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −56.2492 | −2.53334 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.09017 | −0.0489995 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.52786 | 0.113390 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.3607 | −0.553340 | −0.276670 | − | 0.960965i | \(-0.589231\pi\) | ||||
−0.276670 | + | 0.960965i | \(0.589231\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.9443 | −0.578307 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.3262 | −1.61971 | −0.809853 | − | 0.586632i | \(-0.800453\pi\) | ||||
−0.809853 | + | 0.586632i | \(0.800453\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.291796 | −0.0129848 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −60.3050 | −2.67824 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.6525 | 1.62459 | 0.812296 | − | 0.583245i | \(-0.198217\pi\) | ||||
0.812296 | + | 0.583245i | \(0.198217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | 0.0884748 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.1459 | −0.447952 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.5623 | −0.729822 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.5836 | 0.465466 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.32624 | 0.102111 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.5279 | −0.680288 | −0.340144 | − | 0.940373i | \(-0.610476\pi\) | ||||
−0.340144 | + | 0.940373i | \(0.610476\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.0000 | 1.13690 | 0.568450 | − | 0.822718i | \(-0.307543\pi\) | ||||
0.568450 | + | 0.822718i | \(0.307543\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −55.3607 | −2.41155 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.652476 | 0.0283150 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.5836 | −1.02152 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.1803 | −0.786005 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.52786 | 0.152239 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.8885 | −0.813587 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.8328 | 0.981659 | 0.490830 | − | 0.871256i | \(-0.336694\pi\) | ||||
0.490830 | + | 0.871256i | \(0.336694\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.6525 | 0.843368 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.5623 | −0.495275 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.9230 | −1.19390 | −0.596950 | − | 0.802278i | \(-0.703621\pi\) | ||||
−0.596950 | + | 0.802278i | \(0.703621\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.56231 | 0.152036 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.1246 | 0.729533 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.944272 | −0.0401545 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.4721 | −0.444517 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.8328 | −0.967457 | −0.483729 | − | 0.875218i | \(-0.660718\pi\) | ||||
−0.483729 | + | 0.875218i | \(0.660718\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.1246 | −1.18742 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.8885 | 0.585332 | 0.292666 | − | 0.956215i | \(-0.405458\pi\) | ||||
0.292666 | + | 0.956215i | \(0.405458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.05573 | 0.0444148 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.76393 | −0.200066 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.00000 | −0.0838444 | −0.0419222 | − | 0.999121i | \(-0.513348\pi\) | ||||
−0.0419222 | + | 0.999121i | \(0.513348\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.9787 | −0.668688 | −0.334344 | − | 0.942451i | \(-0.608515\pi\) | ||||
−0.334344 | + | 0.942451i | \(0.608515\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.1803 | −0.926597 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.52786 | −0.146867 | −0.0734335 | − | 0.997300i | \(-0.523396\pi\) | ||||
−0.0734335 | + | 0.997300i | \(0.523396\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.23607 | −0.0513692 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.29180 | 0.178054 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.34752 | 0.0558087 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.70820 | 0.111970 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.6180 | −0.562076 | −0.281038 | − | 0.959697i | \(-0.590679\pi\) | ||||
−0.281038 | + | 0.959697i | \(0.590679\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.8541 | 0.694461 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.5066 | 1.50168 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.2361 | 1.61123 | 0.805616 | − | 0.592438i | \(-0.201834\pi\) | ||||
0.805616 | + | 0.592438i | \(0.201834\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.76393 | 0.154306 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.23607 | 0.132443 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.3820 | 0.751067 | 0.375533 | − | 0.926809i | \(-0.377460\pi\) | ||||
0.375533 | + | 0.926809i | \(0.377460\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.2705 | −1.35713 | −0.678566 | − | 0.734539i | \(-0.737398\pi\) | ||||
−0.678566 | + | 0.734539i | \(0.737398\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.52786 | 0.225112 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.85410 | −0.116036 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.4721 | −1.07447 | −0.537235 | − | 0.843432i | \(-0.680531\pi\) | ||||
−0.537235 | + | 0.843432i | \(0.680531\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.23607 | 0.374264 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.2918 | −1.06365 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.3050 | 0.779720 | 0.389860 | − | 0.920874i | \(-0.372523\pi\) | ||||
0.389860 | + | 0.920874i | \(0.372523\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.38197 | −0.217022 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0902 | 1.37242 | 0.686209 | − | 0.727404i | \(-0.259273\pi\) | ||||
0.686209 | + | 0.727404i | \(0.259273\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.79837 | 0.112476 | 0.0562381 | − | 0.998417i | \(-0.482089\pi\) | ||||
0.0562381 | + | 0.998417i | \(0.482089\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.47214 | −0.219589 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.47214 | −0.259301 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.56231 | 0.341946 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 39.4164 | 1.57164 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.0689 | −1.67474 | −0.837368 | − | 0.546640i | \(-0.815907\pi\) | ||||
−0.837368 | + | 0.546640i | \(0.815907\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.6525 | 0.900355 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.1803 | −0.642097 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46.9230 | 1.85916 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.56231 | −0.0618039 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.360680 | 0.0142460 | 0.00712300 | − | 0.999975i | \(-0.497733\pi\) | ||||
0.00712300 | + | 0.999975i | \(0.497733\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.29180 | 0.326997 | 0.163498 | − | 0.986544i | \(-0.447722\pi\) | ||||
0.163498 | + | 0.986544i | \(0.447722\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.2492 | 1.42510 | 0.712552 | − | 0.701619i | \(-0.247539\pi\) | ||||
0.712552 | + | 0.701619i | \(0.247539\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.87539 | −0.191376 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.09017 | 0.356272 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.03444 | −0.314412 | −0.157206 | − | 0.987566i | \(-0.550249\pi\) | ||||
−0.157206 | + | 0.987566i | \(0.550249\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.94427 | −0.115042 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.23607 | −0.0482236 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 46.2492 | 1.80161 | 0.900807 | − | 0.434220i | \(-0.142976\pi\) | ||||
0.900807 | + | 0.434220i | \(0.142976\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.6738 | 0.726325 | 0.363163 | − | 0.931726i | \(-0.381697\pi\) | ||||
0.363163 | + | 0.931726i | \(0.381697\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 69.8673 | 2.71342 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.14590 | −0.0444360 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.23607 | 0.357622 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.8885 | −1.31021 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.6180 | −1.02758 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.9443 | −0.421871 | −0.210935 | − | 0.977500i | \(-0.567651\pi\) | ||||
−0.210935 | + | 0.977500i | \(0.567651\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.47214 | 0.210623 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −50.9443 | −1.95795 | −0.978974 | − | 0.203986i | \(-0.934610\pi\) | ||||
−0.978974 | + | 0.203986i | \(0.934610\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.65248 | 0.293675 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.3607 | −1.16342 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.5623 | 1.20770 | 0.603849 | − | 0.797099i | \(-0.293633\pi\) | ||||
0.603849 | + | 0.797099i | \(0.293633\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.3262 | −0.394545 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.1803 | −0.617318 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.34752 | −0.127531 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.2361 | 1.11219 | 0.556096 | − | 0.831118i | \(-0.312299\pi\) | ||||
0.556096 | + | 0.831118i | \(0.312299\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.673762 | −0.0255941 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.7639 | −0.484164 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.2574 | 0.767302 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.1803 | −0.385056 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.3394 | 1.63691 | 0.818453 | − | 0.574573i | \(-0.194832\pi\) | ||||
0.818453 | + | 0.574573i | \(0.194832\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | −0.452589 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | −0.225973 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.180340 | −0.00678238 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.0902 | −0.979837 | −0.489918 | − | 0.871768i | \(-0.662973\pi\) | ||||
−0.489918 | + | 0.871768i | \(0.662973\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.583592 | 0.0218864 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.09017 | 0.340430 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.2361 | −0.756786 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −32.9443 | −1.23033 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.2705 | −1.31537 | −0.657684 | − | 0.753294i | \(-0.728464\pi\) | ||||
−0.657684 | + | 0.753294i | \(0.728464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.2361 | −0.381211 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.23607 | −0.343019 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.2016 | −1.04594 | −0.522970 | − | 0.852351i | \(-0.675176\pi\) | ||||
−0.522970 | + | 0.852351i | \(0.675176\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.4164 | −1.08652 | −0.543260 | − | 0.839565i | \(-0.682810\pi\) | ||||
−0.543260 | + | 0.839565i | \(0.682810\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.7082 | 0.394978 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −41.3050 | −1.52149 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.8885 | 0.510898 | 0.255449 | − | 0.966822i | \(-0.417777\pi\) | ||||
0.255449 | + | 0.966822i | \(0.417777\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.2705 | −0.781392 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.6312 | −1.23381 | −0.616904 | − | 0.787038i | \(-0.711613\pi\) | ||||
−0.616904 | + | 0.787038i | \(0.711613\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.85410 | −0.287752 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.65248 | −0.0970490 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.2361 | −0.410557 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.0132 | 1.71553 | 0.857767 | − | 0.514038i | \(-0.171851\pi\) | ||||
0.857767 | + | 0.514038i | \(0.171851\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.94427 | 0.362389 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.56231 | 0.0932519 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.8885 | −0.650170 | −0.325085 | − | 0.945685i | \(-0.605393\pi\) | ||||
−0.325085 | + | 0.945685i | \(0.605393\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.61803 | 0.167624 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.8673 | 1.69894 | 0.849468 | − | 0.527640i | \(-0.176923\pi\) | ||||
0.849468 | + | 0.527640i | \(0.176923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.14590 | −0.258699 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.32624 | −0.0841053 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.1115 | 0.437319 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.58359 | −0.237410 | −0.118705 | − | 0.992930i | \(-0.537874\pi\) | ||||
−0.118705 | + | 0.992930i | \(0.537874\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.6525 | 0.455668 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.9443 | 1.04105 | 0.520527 | − | 0.853845i | \(-0.325736\pi\) | ||||
0.520527 | + | 0.853845i | \(0.325736\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.09017 | −0.326529 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.47214 | −0.232187 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.16718 | −0.220962 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.6738 | 0.417720 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −50.5410 | −1.80619 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.70820 | −0.132351 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.87539 | 0.102497 | 0.0512483 | − | 0.998686i | \(-0.483680\pi\) | ||||
0.0512483 | + | 0.998686i | \(0.483680\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 33.5623 | 1.19485 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.652476 | 0.0231994 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 66.1246 | 2.34815 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.763932 | −0.0270939 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.7082 | 0.485569 | 0.242785 | − | 0.970080i | \(-0.421939\pi\) | ||||
0.242785 | + | 0.970080i | \(0.421939\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.5836 | 0.798950 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.00000 | 0.141333 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.23607 | 0.325934 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.618034 | −0.0217828 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.9443 | 0.807677 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −46.7426 | −1.64338 | −0.821692 | − | 0.569932i | \(-0.806970\pi\) | ||||
−0.821692 | + | 0.569932i | \(0.806970\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.8197 | −0.766192 | −0.383096 | − | 0.923709i | \(-0.625142\pi\) | ||||
−0.383096 | + | 0.923709i | \(0.625142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −49.0689 | −1.72092 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.38197 | −0.0484082 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.67376 | 0.0584860 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.0557 | −1.15365 | −0.576826 | − | 0.816867i | \(-0.695709\pi\) | ||||
−0.576826 | + | 0.816867i | \(0.695709\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.4164 | −0.885960 | −0.442980 | − | 0.896531i | \(-0.646079\pi\) | ||||
−0.442980 | + | 0.896531i | \(0.646079\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.61803 | −0.160779 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.7082 | −0.754868 | −0.377434 | − | 0.926036i | \(-0.623194\pi\) | ||||
−0.377434 | + | 0.926036i | \(0.623194\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.9443 | 0.657962 | 0.328981 | − | 0.944337i | \(-0.393295\pi\) | ||||
0.328981 | + | 0.944337i | \(0.393295\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −47.5967 | −1.65111 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −40.3050 | −1.39648 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000 | 0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −49.7426 | −1.71936 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.0132 | −1.13974 | −0.569870 | − | 0.821735i | \(-0.693007\pi\) | ||||
−0.569870 | + | 0.821735i | \(0.693007\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 56.3050 | 1.94155 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −36.8328 | −1.26859 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.2705 | 1.28214 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.76393 | −0.0606094 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −43.5967 | −1.49624 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.47214 | −0.221862 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.7984 | −0.369729 | −0.184865 | − | 0.982764i | \(-0.559185\pi\) | ||||
−0.184865 | + | 0.982764i | \(0.559185\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.708204 | 0.0242201 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.58359 | −0.224891 | −0.112446 | − | 0.993658i | \(-0.535868\pi\) | ||||
−0.112446 | + | 0.993658i | \(0.535868\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.0689 | 0.821220 | 0.410610 | − | 0.911811i | \(-0.365316\pi\) | ||||
0.410610 | + | 0.911811i | \(0.365316\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.32624 | −0.113358 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.7639 | −1.11530 | −0.557649 | − | 0.830077i | \(-0.688296\pi\) | ||||
−0.557649 | + | 0.830077i | \(0.688296\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.43769 | −0.0488831 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −32.5066 | −1.10398 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.36068 | −0.147926 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 102.610 | 3.47680 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.72949 | −0.160069 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.618034 | 0.0208934 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.7426 | 0.632894 | 0.316447 | − | 0.948610i | \(-0.397510\pi\) | ||||
0.316447 | + | 0.948610i | \(0.397510\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.1803 | 1.08542 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.58359 | 0.289189 | 0.144594 | − | 0.989491i | \(-0.453812\pi\) | ||||
0.144594 | + | 0.989491i | \(0.453812\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.5623 | −0.523713 | −0.261857 | − | 0.965107i | \(-0.584335\pi\) | ||||
−0.261857 | + | 0.965107i | \(0.584335\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.76393 | 0.0929086 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.16718 | 0.173497 | 0.0867485 | − | 0.996230i | \(-0.472352\pi\) | ||||
0.0867485 | + | 0.996230i | \(0.472352\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.0000 | −0.335389 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.0000 | −0.737028 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.87539 | −0.230076 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.18034 | −0.0728807 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.4721 | −0.383043 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 83.9574 | 2.80014 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.87539 | 0.0957931 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.1459 | −0.403743 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.12461 | −0.236569 | −0.118284 | − | 0.992980i | \(-0.537739\pi\) | ||||
−0.118284 | + | 0.992980i | \(0.537739\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.111456 | 0.00369677 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.0689 | −1.19502 | −0.597508 | − | 0.801863i | \(-0.703842\pi\) | ||||
−0.597508 | + | 0.801863i | \(0.703842\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.8197 | 0.655935 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.0902 | 0.498866 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.81966 | −0.0600905 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.0000 | −1.31948 | −0.659739 | − | 0.751495i | \(-0.729333\pi\) | ||||
−0.659739 | + | 0.751495i | \(0.729333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −46.0344 | −1.51689 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.0000 | −0.954547 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.47214 | 0.212803 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.32624 | 0.207781 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.52786 | −0.115745 | −0.0578727 | − | 0.998324i | \(-0.518432\pi\) | ||||
−0.0578727 | + | 0.998324i | \(0.518432\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.2705 | 0.402150 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.47214 | 0.211888 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.3820 | 0.568451 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.7984 | −1.20215 | −0.601075 | − | 0.799192i | \(-0.705261\pi\) | ||||
−0.601075 | + | 0.799192i | \(0.705261\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.7082 | −0.675787 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.4934 | −0.733265 | −0.366632 | − | 0.930366i | \(-0.619489\pi\) | ||||
−0.366632 | + | 0.930366i | \(0.619489\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.32624 | −0.108317 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.38197 | 0.110015 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.6869 | 1.77709 | 0.888543 | − | 0.458793i | \(-0.151718\pi\) | ||||
0.888543 | + | 0.458793i | \(0.151718\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.9443 | −0.744803 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.9443 | 0.581883 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.79837 | 0.123041 | 0.0615207 | − | 0.998106i | \(-0.480405\pi\) | ||||
0.0615207 | + | 0.998106i | \(0.480405\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.7082 | 0.443587 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 42.6525 | 1.37876 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.38197 | −0.206084 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.6312 | 1.66552 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.94427 | 0.223776 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.763932 | 0.0245918 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.5410 | 0.531923 | 0.265962 | − | 0.963984i | \(-0.414311\pi\) | ||||
0.265962 | + | 0.963984i | \(0.414311\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.2705 | 0.586933 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.2705 | −1.09979 | −0.549896 | − | 0.835233i | \(-0.685333\pi\) | ||||
−0.549896 | + | 0.835233i | \(0.685333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.88854 | −0.252895 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.4721 | 0.367402 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.5623 | −0.753825 | −0.376912 | − | 0.926249i | \(-0.623014\pi\) | ||||
−0.376912 | + | 0.926249i | \(0.623014\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.8885 | −0.955242 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.41641 | 0.141005 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.2705 | 0.455159 | 0.227579 | − | 0.973760i | \(-0.426919\pi\) | ||||
0.227579 | + | 0.973760i | \(0.426919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.5623 | −0.718895 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.70820 | −0.118033 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.5066 | −0.873775 | −0.436888 | − | 0.899516i | \(-0.643919\pi\) | ||||
−0.436888 | + | 0.899516i | \(0.643919\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31.1246 | 0.987710 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.00000 | −0.0634043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.1935 | 1.81134 | 0.905668 | − | 0.423987i | \(-0.139370\pi\) | ||||
0.905668 | + | 0.423987i | \(0.139370\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 35.4164 | 1.12053 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1840.2.a.l.1.1 | 2 | ||
4.3 | odd | 2 | 230.2.a.c.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 9200.2.a.bu.1.2 | 2 | |||
8.3 | odd | 2 | 7360.2.a.bh.1.1 | 2 | |||
8.5 | even | 2 | 7360.2.a.bn.1.2 | 2 | |||
12.11 | even | 2 | 2070.2.a.u.1.1 | 2 | |||
20.3 | even | 4 | 1150.2.b.i.599.2 | 4 | |||
20.7 | even | 4 | 1150.2.b.i.599.3 | 4 | |||
20.19 | odd | 2 | 1150.2.a.j.1.1 | 2 | |||
92.91 | even | 2 | 5290.2.a.o.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.a.c.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
1150.2.a.j.1.1 | 2 | 20.19 | odd | 2 | |||
1150.2.b.i.599.2 | 4 | 20.3 | even | 4 | |||
1150.2.b.i.599.3 | 4 | 20.7 | even | 4 | |||
1840.2.a.l.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2070.2.a.u.1.1 | 2 | 12.11 | even | 2 | |||
5290.2.a.o.1.2 | 2 | 92.91 | even | 2 | |||
7360.2.a.bh.1.1 | 2 | 8.3 | odd | 2 | |||
7360.2.a.bn.1.2 | 2 | 8.5 | even | 2 | |||
9200.2.a.bu.1.2 | 2 | 5.4 | even | 2 |