Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.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: | \(31.6926245622\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.874032\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | 1.14412 | 0.572061 | − | 0.820211i | \(-0.306144\pi\) | ||||
0.572061 | + | 0.820211i | \(0.306144\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | −0.874032 | −0.390879 | −0.195440 | − | 0.980716i | \(-0.562613\pi\) | ||||
−0.195440 | + | 0.980716i | \(0.562613\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.41421 | −0.447214 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.74806 | −0.484826 | −0.242413 | − | 0.970173i | \(-0.577939\pi\) | ||||
−0.242413 | + | 0.970173i | \(0.577939\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 3.16228 | 0.766965 | 0.383482 | − | 0.923548i | \(-0.374725\pi\) | ||||
0.383482 | + | 0.923548i | \(0.374725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.45052 | 1.25044 | 0.625218 | − | 0.780450i | \(-0.285010\pi\) | ||||
0.625218 | + | 0.780450i | \(0.285010\pi\) | |||||||
\(20\) | −0.540182 | −0.120788 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.61803 | 0.344966 | ||||||||
\(23\) | −2.76393 | −0.576320 | −0.288160 | − | 0.957582i | \(-0.593043\pi\) | ||||
−0.288160 | + | 0.957582i | \(0.593043\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.23607 | −0.847214 | ||||||||
\(26\) | −2.82843 | −0.554700 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.23607 | −0.600923 | −0.300461 | − | 0.953794i | \(-0.597141\pi\) | ||||
−0.300461 | + | 0.953794i | \(0.597141\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.333851 | 0.0599613 | 0.0299807 | − | 0.999550i | \(-0.490455\pi\) | ||||
0.0299807 | + | 0.999550i | \(0.490455\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.11667 | 0.877502 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.70820 | 0.445226 | 0.222613 | − | 0.974907i | \(-0.428541\pi\) | ||||
0.222613 | + | 0.974907i | \(0.428541\pi\) | |||||||
\(38\) | 8.81913 | 1.43065 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.95440 | 0.309017 | ||||||||
\(41\) | 10.0270 | 1.56596 | 0.782978 | − | 0.622049i | \(-0.213700\pi\) | ||||
0.782978 | + | 0.622049i | \(0.213700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.9443 | −1.82148 | −0.910742 | − | 0.412975i | \(-0.864490\pi\) | ||||
−0.910742 | + | 0.412975i | \(0.864490\pi\) | |||||||
\(44\) | 0.618034 | 0.0931721 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.47214 | −0.659380 | ||||||||
\(47\) | −12.5216 | −1.82646 | −0.913231 | − | 0.407442i | \(-0.866421\pi\) | ||||
−0.913231 | + | 0.407442i | \(0.866421\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.85410 | −0.969316 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.08036 | −0.149819 | ||||||||
\(53\) | −2.70820 | −0.372000 | −0.186000 | − | 0.982550i | \(-0.559553\pi\) | ||||
−0.186000 | + | 0.982550i | \(0.559553\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.874032 | −0.117854 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.23607 | −0.687529 | ||||||||
\(59\) | −8.15143 | −1.06123 | −0.530613 | − | 0.847614i | \(-0.678038\pi\) | ||||
−0.530613 | + | 0.847614i | \(0.678038\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.1893 | −1.68872 | −0.844358 | − | 0.535780i | \(-0.820018\pi\) | ||||
−0.844358 | + | 0.535780i | \(0.820018\pi\) | |||||||
\(62\) | 0.540182 | 0.0686031 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 1.52786 | 0.189508 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.47214 | −0.912867 | −0.456433 | − | 0.889758i | \(-0.650873\pi\) | ||||
−0.456433 | + | 0.889758i | \(0.650873\pi\) | |||||||
\(68\) | 1.95440 | 0.237005 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.47214 | −0.412067 | −0.206033 | − | 0.978545i | \(-0.566056\pi\) | ||||
−0.206033 | + | 0.978545i | \(0.566056\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.0618 | −1.52876 | −0.764382 | − | 0.644763i | \(-0.776956\pi\) | ||||
−0.764382 | + | 0.644763i | \(0.776956\pi\) | |||||||
\(74\) | 4.38197 | 0.509393 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.36861 | 0.386406 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.2361 | −1.37667 | −0.688333 | − | 0.725395i | \(-0.741657\pi\) | ||||
−0.688333 | + | 0.725395i | \(0.741657\pi\) | |||||||
\(80\) | 4.24264 | 0.474342 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 16.2241 | 1.79165 | ||||||||
\(83\) | 7.19859 | 0.790148 | 0.395074 | − | 0.918649i | \(-0.370719\pi\) | ||||
0.395074 | + | 0.918649i | \(0.370719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.76393 | −0.299791 | ||||||||
\(86\) | −19.3262 | −2.08400 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.23607 | −0.238366 | ||||||||
\(89\) | −6.32456 | −0.670402 | −0.335201 | − | 0.942147i | \(-0.608804\pi\) | ||||
−0.335201 | + | 0.942147i | \(0.608804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.70820 | −0.178093 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −20.2604 | −2.08970 | ||||||||
\(95\) | −4.76393 | −0.488769 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.35931 | 0.950294 | 0.475147 | − | 0.879906i | \(-0.342395\pi\) | ||||
0.475147 | + | 0.879906i | \(0.342395\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.61803 | −0.261803 | ||||||||
\(101\) | 12.3941 | 1.23326 | 0.616628 | − | 0.787255i | \(-0.288498\pi\) | ||||
0.616628 | + | 0.787255i | \(0.288498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0270 | 0.987991 | 0.493996 | − | 0.869464i | \(-0.335536\pi\) | ||||
0.493996 | + | 0.869464i | \(0.335536\pi\) | |||||||
\(104\) | 3.90879 | 0.383288 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.38197 | −0.425614 | ||||||||
\(107\) | −5.94427 | −0.574654 | −0.287327 | − | 0.957832i | \(-0.592767\pi\) | ||||
−0.287327 | + | 0.957832i | \(0.592767\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.94427 | 0.282010 | 0.141005 | − | 0.990009i | \(-0.454967\pi\) | ||||
0.141005 | + | 0.990009i | \(0.454967\pi\) | |||||||
\(110\) | −1.41421 | −0.134840 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.23607 | −0.774784 | −0.387392 | − | 0.921915i | \(-0.626624\pi\) | ||||
−0.387392 | + | 0.921915i | \(0.626624\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.41577 | 0.225271 | ||||||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.1893 | −1.21417 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | −21.3407 | −1.93210 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.206331 | 0.0185291 | ||||||||
\(125\) | 8.07262 | 0.722037 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.6525 | 1.21146 | 0.605731 | − | 0.795670i | \(-0.292881\pi\) | ||||
0.605731 | + | 0.795670i | \(0.292881\pi\) | |||||||
\(128\) | 13.6180 | 1.20368 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.47214 | 0.216821 | ||||||||
\(131\) | −1.87558 | −0.163871 | −0.0819353 | − | 0.996638i | \(-0.526110\pi\) | ||||
−0.0819353 | + | 0.996638i | \(0.526110\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.0902 | −1.04443 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.07107 | −0.606339 | ||||||||
\(137\) | 3.76393 | 0.321574 | 0.160787 | − | 0.986989i | \(-0.448597\pi\) | ||||
0.160787 | + | 0.986989i | \(0.448597\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.206331 | −0.0175008 | −0.00875038 | − | 0.999962i | \(-0.502785\pi\) | ||||
−0.00875038 | + | 0.999962i | \(0.502785\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.61803 | −0.471455 | ||||||||
\(143\) | −1.74806 | −0.146180 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.82843 | 0.234888 | ||||||||
\(146\) | −21.1344 | −1.74909 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.67376 | 0.137582 | ||||||||
\(149\) | −19.4721 | −1.59522 | −0.797610 | − | 0.603174i | \(-0.793903\pi\) | ||||
−0.797610 | + | 0.603174i | \(0.793903\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.29180 | −0.430640 | −0.215320 | − | 0.976544i | \(-0.569079\pi\) | ||||
−0.215320 | + | 0.976544i | \(0.569079\pi\) | |||||||
\(152\) | −12.1877 | −0.988556 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.291796 | −0.0234376 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.16073 | −0.172445 | −0.0862224 | − | 0.996276i | \(-0.527480\pi\) | ||||
−0.0862224 | + | 0.996276i | \(0.527480\pi\) | |||||||
\(158\) | −19.7984 | −1.57507 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.95595 | 0.233688 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.23607 | −0.645099 | −0.322549 | − | 0.946553i | \(-0.604540\pi\) | ||||
−0.322549 | + | 0.946553i | \(0.604540\pi\) | |||||||
\(164\) | 6.19704 | 0.483907 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.6476 | 0.904026 | ||||||||
\(167\) | 8.69161 | 0.672577 | 0.336289 | − | 0.941759i | \(-0.390828\pi\) | ||||
0.336289 | + | 0.941759i | \(0.390828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.94427 | −0.764944 | ||||||||
\(170\) | −4.47214 | −0.342997 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.38197 | −0.562870 | ||||||||
\(173\) | −19.2588 | −1.46422 | −0.732110 | − | 0.681186i | \(-0.761464\pi\) | ||||
−0.732110 | + | 0.681186i | \(0.761464\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.85410 | −0.365892 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.2333 | −0.767022 | ||||||||
\(179\) | 20.3607 | 1.52183 | 0.760914 | − | 0.648852i | \(-0.224751\pi\) | ||||
0.760914 | + | 0.648852i | \(0.224751\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.9613 | 1.70670 | 0.853349 | − | 0.521340i | \(-0.174568\pi\) | ||||
0.853349 | + | 0.521340i | \(0.174568\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.18034 | 0.455621 | ||||||||
\(185\) | −2.36706 | −0.174029 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.16228 | 0.231249 | ||||||||
\(188\) | −7.73877 | −0.564408 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.70820 | −0.559212 | ||||||||
\(191\) | −4.41641 | −0.319560 | −0.159780 | − | 0.987153i | \(-0.551078\pi\) | ||||
−0.159780 | + | 0.987153i | \(0.551078\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.4721 | −1.18569 | −0.592845 | − | 0.805316i | \(-0.701995\pi\) | ||||
−0.592845 | + | 0.805316i | \(0.701995\pi\) | |||||||
\(194\) | 15.1437 | 1.08725 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.4164 | 1.31211 | 0.656057 | − | 0.754711i | \(-0.272223\pi\) | ||||
0.656057 | + | 0.754711i | \(0.272223\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.4412 | −0.811047 | −0.405524 | − | 0.914085i | \(-0.632911\pi\) | ||||
−0.405524 | + | 0.914085i | \(0.632911\pi\) | |||||||
\(200\) | 9.47214 | 0.669781 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.0540 | 1.41100 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.76393 | −0.612100 | ||||||||
\(206\) | 16.2241 | 1.13038 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.48528 | 0.588348 | ||||||||
\(209\) | 5.45052 | 0.377021 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.29180 | −0.226617 | −0.113308 | − | 0.993560i | \(-0.536145\pi\) | ||||
−0.113308 | + | 0.993560i | \(0.536145\pi\) | |||||||
\(212\) | −1.67376 | −0.114954 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.61803 | −0.657475 | ||||||||
\(215\) | 10.4397 | 0.711980 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.76393 | 0.322654 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.540182 | −0.0364190 | ||||||||
\(221\) | −5.52786 | −0.371844 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6476 | 0.779978 | 0.389989 | − | 0.920819i | \(-0.372479\pi\) | ||||
0.389989 | + | 0.920819i | \(0.372479\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.3262 | −0.886448 | ||||||||
\(227\) | 23.0888 | 1.53246 | 0.766228 | − | 0.642568i | \(-0.222131\pi\) | ||||
0.766228 | + | 0.642568i | \(0.222131\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0270 | −0.662604 | −0.331302 | − | 0.943525i | \(-0.607488\pi\) | ||||
−0.331302 | + | 0.943525i | \(0.607488\pi\) | |||||||
\(230\) | 3.90879 | 0.257738 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.23607 | 0.475071 | ||||||||
\(233\) | 22.9443 | 1.50313 | 0.751565 | − | 0.659659i | \(-0.229299\pi\) | ||||
0.751565 | + | 0.659659i | \(0.229299\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.9443 | 0.713926 | ||||||||
\(236\) | −5.03786 | −0.327937 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.9443 | 0.901980 | 0.450990 | − | 0.892529i | \(-0.351071\pi\) | ||||
0.450990 | + | 0.892529i | \(0.351071\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.1089 | −0.780005 | −0.390002 | − | 0.920814i | \(-0.627526\pi\) | ||||
−0.390002 | + | 0.920814i | \(0.627526\pi\) | |||||||
\(242\) | −16.1803 | −1.04011 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.15143 | −0.521842 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.52786 | −0.606243 | ||||||||
\(248\) | −0.746512 | −0.0474036 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.0618 | 0.826099 | ||||||||
\(251\) | −2.70091 | −0.170480 | −0.0852399 | − | 0.996360i | \(-0.527166\pi\) | ||||
−0.0852399 | + | 0.996360i | \(0.527166\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.76393 | −0.173767 | ||||||||
\(254\) | 22.0902 | 1.38606 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 15.8902 | 0.991203 | 0.495602 | − | 0.868550i | \(-0.334948\pi\) | ||||
0.495602 | + | 0.868550i | \(0.334948\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.944272 | 0.0585613 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.03476 | −0.187488 | ||||||||
\(263\) | 14.2361 | 0.877834 | 0.438917 | − | 0.898528i | \(-0.355362\pi\) | ||||
0.438917 | + | 0.898528i | \(0.355362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.36706 | 0.145407 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.61803 | −0.282091 | ||||||||
\(269\) | −21.1344 | −1.28859 | −0.644293 | − | 0.764778i | \(-0.722848\pi\) | ||||
−0.644293 | + | 0.764778i | \(0.722848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.5865 | −1.67576 | −0.837879 | − | 0.545856i | \(-0.816205\pi\) | ||||
−0.837879 | + | 0.545856i | \(0.816205\pi\) | |||||||
\(272\) | −15.3500 | −0.930732 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.09017 | 0.367921 | ||||||||
\(275\) | −4.23607 | −0.255445 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.76393 | 0.346321 | 0.173161 | − | 0.984894i | \(-0.444602\pi\) | ||||
0.173161 | + | 0.984894i | \(0.444602\pi\) | |||||||
\(278\) | −0.333851 | −0.0200230 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.00000 | −0.298275 | −0.149137 | − | 0.988816i | \(-0.547650\pi\) | ||||
−0.149137 | + | 0.988816i | \(0.547650\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1089 | 0.719801 | 0.359901 | − | 0.932991i | \(-0.382811\pi\) | ||||
0.359901 | + | 0.932991i | \(0.382811\pi\) | |||||||
\(284\) | −2.14590 | −0.127336 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.82843 | −0.167248 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 4.57649 | 0.268741 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.07262 | −0.472414 | ||||||||
\(293\) | −14.9374 | −0.872650 | −0.436325 | − | 0.899789i | \(-0.643720\pi\) | ||||
−0.436325 | + | 0.899789i | \(0.643720\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.12461 | 0.414811 | ||||||||
\(296\) | −6.05573 | −0.351982 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −31.5066 | −1.82513 | ||||||||
\(299\) | 4.83153 | 0.279415 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8.56231 | −0.492705 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −26.4574 | −1.51744 | ||||||||
\(305\) | 11.5279 | 0.660084 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.6398 | 1.06383 | 0.531915 | − | 0.846798i | \(-0.321472\pi\) | ||||
0.531915 | + | 0.846798i | \(0.321472\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.472136 | −0.0268155 | ||||||||
\(311\) | −28.4118 | −1.61108 | −0.805542 | − | 0.592538i | \(-0.798126\pi\) | ||||
−0.805542 | + | 0.592538i | \(0.798126\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.3956 | 0.757165 | 0.378583 | − | 0.925567i | \(-0.376412\pi\) | ||||
0.378583 | + | 0.925567i | \(0.376412\pi\) | |||||||
\(314\) | −3.49613 | −0.197298 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.56231 | −0.425413 | ||||||||
\(317\) | 18.8328 | 1.05776 | 0.528878 | − | 0.848698i | \(-0.322613\pi\) | ||||
0.528878 | + | 0.848698i | \(0.322613\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.23607 | −0.181185 | ||||||||
\(320\) | −3.70246 | −0.206974 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.2361 | 0.959040 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.40492 | 0.410751 | ||||||||
\(326\) | −13.3262 | −0.738072 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −22.4211 | −1.23800 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | 0.109930 | 0.0549650 | − | 0.998488i | \(-0.482495\pi\) | ||||
0.0549650 | + | 0.998488i | \(0.482495\pi\) | |||||||
\(332\) | 4.44897 | 0.244169 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.0633 | 0.769511 | ||||||||
\(335\) | 6.53089 | 0.356820 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.1803 | −0.935873 | −0.467936 | − | 0.883762i | \(-0.655002\pi\) | ||||
−0.467936 | + | 0.883762i | \(0.655002\pi\) | |||||||
\(338\) | −16.0902 | −0.875190 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.70820 | −0.0926404 | ||||||||
\(341\) | 0.333851 | 0.0180790 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 26.7082 | 1.44001 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −31.1614 | −1.67525 | ||||||||
\(347\) | 21.9443 | 1.17803 | 0.589015 | − | 0.808122i | \(-0.299516\pi\) | ||||
0.589015 | + | 0.808122i | \(0.299516\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.6668 | −1.53450 | −0.767250 | − | 0.641348i | \(-0.778375\pi\) | ||||
−0.767250 | + | 0.641348i | \(0.778375\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.38197 | −0.180259 | ||||||||
\(353\) | −20.5154 | −1.09192 | −0.545962 | − | 0.837810i | \(-0.683836\pi\) | ||||
−0.545962 | + | 0.837810i | \(0.683836\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.03476 | 0.161068 | ||||||||
\(356\) | −3.90879 | −0.207165 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 32.9443 | 1.74116 | ||||||||
\(359\) | 17.1803 | 0.906744 | 0.453372 | − | 0.891321i | \(-0.350221\pi\) | ||||
0.453372 | + | 0.891321i | \(0.350221\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.7082 | 0.563590 | ||||||||
\(362\) | 37.1521 | 1.95267 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.4164 | 0.597562 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.74806 | 0.0912482 | 0.0456241 | − | 0.998959i | \(-0.485472\pi\) | ||||
0.0456241 | + | 0.998959i | \(0.485472\pi\) | |||||||
\(368\) | 13.4164 | 0.699379 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.82998 | −0.199111 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.18034 | −0.475340 | −0.237670 | − | 0.971346i | \(-0.576384\pi\) | ||||
−0.237670 | + | 0.971346i | \(0.576384\pi\) | |||||||
\(374\) | 5.11667 | 0.264577 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 27.9991 | 1.44394 | ||||||||
\(377\) | 5.65685 | 0.291343 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.6525 | −1.62588 | −0.812939 | − | 0.582349i | \(-0.802134\pi\) | ||||
−0.812939 | + | 0.582349i | \(0.802134\pi\) | |||||||
\(380\) | −2.94427 | −0.151038 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.14590 | −0.365616 | ||||||||
\(383\) | 13.3168 | 0.680457 | 0.340229 | − | 0.940343i | \(-0.389496\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389496\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.6525 | −1.35658 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.78437 | 0.293657 | ||||||||
\(389\) | 10.9443 | 0.554897 | 0.277448 | − | 0.960741i | \(-0.410511\pi\) | ||||
0.277448 | + | 0.960741i | \(0.410511\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.74032 | −0.442017 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 29.7984 | 1.50122 | ||||||||
\(395\) | 10.6947 | 0.538110 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.8245 | −1.44666 | −0.723329 | − | 0.690504i | \(-0.757389\pi\) | ||||
−0.723329 | + | 0.690504i | \(0.757389\pi\) | |||||||
\(398\) | −18.5123 | −0.927938 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 20.5623 | 1.02812 | ||||||||
\(401\) | 37.0689 | 1.85113 | 0.925566 | − | 0.378587i | \(-0.123590\pi\) | ||||
0.925566 | + | 0.378587i | \(0.123590\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.583592 | −0.0290708 | ||||||||
\(404\) | 7.65996 | 0.381097 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.70820 | 0.134241 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.11512 | 0.203480 | 0.101740 | − | 0.994811i | \(-0.467559\pi\) | ||||
0.101740 | + | 0.994811i | \(0.467559\pi\) | |||||||
\(410\) | −14.1803 | −0.700317 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.19704 | 0.305306 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.29180 | −0.308852 | ||||||||
\(416\) | 5.91189 | 0.289854 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.81913 | 0.431358 | ||||||||
\(419\) | 24.4242 | 1.19320 | 0.596600 | − | 0.802539i | \(-0.296518\pi\) | ||||
0.596600 | + | 0.802539i | \(0.296518\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.8885 | 0.725623 | 0.362812 | − | 0.931863i | \(-0.381817\pi\) | ||||
0.362812 | + | 0.931863i | \(0.381817\pi\) | |||||||
\(422\) | −5.32624 | −0.259277 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.05573 | 0.294092 | ||||||||
\(425\) | −13.3956 | −0.649783 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.67376 | −0.177578 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.8918 | 0.814593 | ||||||||
\(431\) | −23.4164 | −1.12793 | −0.563964 | − | 0.825799i | \(-0.690724\pi\) | ||||
−0.563964 | + | 0.825799i | \(0.690724\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.5154 | 0.985907 | 0.492954 | − | 0.870056i | \(-0.335917\pi\) | ||||
0.492954 | + | 0.870056i | \(0.335917\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.81966 | 0.0871459 | ||||||||
\(437\) | −15.0649 | −0.720651 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.6963 | 0.558232 | 0.279116 | − | 0.960257i | \(-0.409959\pi\) | ||||
0.279116 | + | 0.960257i | \(0.409959\pi\) | |||||||
\(440\) | 1.95440 | 0.0931721 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.94427 | −0.425436 | ||||||||
\(443\) | −2.29180 | −0.108887 | −0.0544433 | − | 0.998517i | \(-0.517338\pi\) | ||||
−0.0544433 | + | 0.998517i | \(0.517338\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.52786 | 0.262046 | ||||||||
\(446\) | 18.8461 | 0.892391 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.4721 | 1.48526 | 0.742631 | − | 0.669701i | \(-0.233578\pi\) | ||||
0.742631 | + | 0.669701i | \(0.233578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0270 | 0.472154 | ||||||||
\(452\) | −5.09017 | −0.239421 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 37.3584 | 1.75332 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.8328 | 1.11485 | 0.557426 | − | 0.830227i | \(-0.311789\pi\) | ||||
0.557426 | + | 0.830227i | \(0.311789\pi\) | |||||||
\(458\) | −16.2241 | −0.758100 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.49302 | 0.0696126 | ||||||||
\(461\) | 18.1784 | 0.846655 | 0.423327 | − | 0.905977i | \(-0.360862\pi\) | ||||
0.423327 | + | 0.905977i | \(0.360862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.8885 | −1.71436 | −0.857178 | − | 0.515020i | \(-0.827784\pi\) | ||||
−0.857178 | + | 0.515020i | \(0.827784\pi\) | |||||||
\(464\) | 15.7082 | 0.729235 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 37.1246 | 1.71976 | ||||||||
\(467\) | 40.3144 | 1.86553 | 0.932764 | − | 0.360488i | \(-0.117390\pi\) | ||||
0.932764 | + | 0.360488i | \(0.117390\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 17.7082 | 0.816819 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.2272 | 0.838973 | ||||||||
\(473\) | −11.9443 | −0.549198 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.0888 | −1.05939 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.5623 | 1.03198 | ||||||||
\(479\) | −11.2349 | −0.513336 | −0.256668 | − | 0.966500i | \(-0.582625\pi\) | ||||
−0.256668 | + | 0.966500i | \(0.582625\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.73411 | −0.215857 | ||||||||
\(482\) | −19.5927 | −0.892421 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.18034 | −0.280925 | ||||||||
\(485\) | −8.18034 | −0.371450 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.9443 | −0.631875 | −0.315938 | − | 0.948780i | \(-0.602319\pi\) | ||||
−0.315938 | + | 0.948780i | \(0.602319\pi\) | |||||||
\(488\) | 29.4922 | 1.33505 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.0000 | 0.992846 | 0.496423 | − | 0.868081i | \(-0.334646\pi\) | ||||
0.496423 | + | 0.868081i | \(0.334646\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2333 | −0.460887 | ||||||||
\(494\) | −15.4164 | −0.693617 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.62054 | −0.0727646 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.8885 | −0.621737 | −0.310868 | − | 0.950453i | \(-0.600620\pi\) | ||||
−0.310868 | + | 0.950453i | \(0.600620\pi\) | |||||||
\(500\) | 4.98915 | 0.223122 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.37016 | −0.195050 | ||||||||
\(503\) | −44.4295 | −1.98101 | −0.990507 | − | 0.137463i | \(-0.956105\pi\) | ||||
−0.990507 | + | 0.137463i | \(0.956105\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.8328 | −0.482054 | ||||||||
\(506\) | −4.47214 | −0.198811 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.43769 | 0.374362 | ||||||||
\(509\) | −10.1545 | −0.450092 | −0.225046 | − | 0.974348i | \(-0.572253\pi\) | ||||
−0.225046 | + | 0.974348i | \(0.572253\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 25.7109 | 1.13406 | ||||||||
\(515\) | −8.76393 | −0.386185 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.5216 | −0.550699 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.41641 | −0.149819 | ||||||||
\(521\) | −21.8809 | −0.958620 | −0.479310 | − | 0.877646i | \(-0.659113\pi\) | ||||
−0.479310 | + | 0.877646i | \(0.659113\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.0981 | −0.747647 | −0.373823 | − | 0.927500i | \(-0.621953\pi\) | ||||
−0.373823 | + | 0.927500i | \(0.621953\pi\) | |||||||
\(524\) | −1.15917 | −0.0506388 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.0344 | 1.00435 | ||||||||
\(527\) | 1.05573 | 0.0459882 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3607 | −0.667856 | ||||||||
\(530\) | 3.82998 | 0.166364 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.5279 | −0.759216 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.19548 | 0.224620 | ||||||||
\(536\) | 16.7082 | 0.721684 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −34.1962 | −1.47430 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.5967 | −0.799537 | −0.399768 | − | 0.916616i | \(-0.630909\pi\) | ||||
−0.399768 | + | 0.916616i | \(0.630909\pi\) | |||||||
\(542\) | −44.6358 | −1.91727 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.6947 | −0.458532 | ||||||||
\(545\) | −2.57339 | −0.110232 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.70820 | −0.115794 | −0.0578972 | − | 0.998323i | \(-0.518440\pi\) | ||||
−0.0578972 | + | 0.998323i | \(0.518440\pi\) | |||||||
\(548\) | 2.32624 | 0.0993720 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.85410 | −0.292260 | ||||||||
\(551\) | −17.6383 | −0.751415 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.32624 | 0.396234 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.127520 | −0.00540803 | ||||||||
\(557\) | 20.7082 | 0.877435 | 0.438717 | − | 0.898625i | \(-0.355433\pi\) | ||||
0.438717 | + | 0.898625i | \(0.355433\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.8794 | 0.883103 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.09017 | −0.341263 | ||||||||
\(563\) | 34.2750 | 1.44452 | 0.722259 | − | 0.691623i | \(-0.243104\pi\) | ||||
0.722259 | + | 0.691623i | \(0.243104\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.19859 | 0.302847 | ||||||||
\(566\) | 19.5927 | 0.823541 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.76393 | 0.325767 | ||||||||
\(569\) | −42.4164 | −1.77819 | −0.889094 | − | 0.457724i | \(-0.848665\pi\) | ||||
−0.889094 | + | 0.457724i | \(0.848665\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.1803 | −1.68149 | −0.840747 | − | 0.541427i | \(-0.817884\pi\) | ||||
−0.840747 | + | 0.541427i | \(0.817884\pi\) | |||||||
\(572\) | −1.08036 | −0.0451722 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.7082 | 0.488266 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5216 | 0.521281 | 0.260640 | − | 0.965436i | \(-0.416066\pi\) | ||||
0.260640 | + | 0.965436i | \(0.416066\pi\) | |||||||
\(578\) | −11.3262 | −0.471109 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.74806 | 0.0725844 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.70820 | −0.112162 | ||||||||
\(584\) | 29.2070 | 1.20859 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.1692 | −0.998418 | ||||||||
\(587\) | 2.90724 | 0.119995 | 0.0599973 | − | 0.998199i | \(-0.480891\pi\) | ||||
0.0599973 | + | 0.998199i | \(0.480891\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.81966 | 0.0749778 | ||||||||
\(590\) | 11.5279 | 0.474595 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13.1459 | −0.540293 | ||||||||
\(593\) | 27.9504 | 1.14779 | 0.573893 | − | 0.818930i | \(-0.305432\pi\) | ||||
0.573893 | + | 0.818930i | \(0.305432\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.0344 | −0.492950 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.81758 | 0.319685 | ||||||||
\(599\) | 39.8328 | 1.62752 | 0.813762 | − | 0.581198i | \(-0.197416\pi\) | ||||
0.813762 | + | 0.581198i | \(0.197416\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.9867 | 1.30477 | 0.652383 | − | 0.757889i | \(-0.273769\pi\) | ||||
0.652383 | + | 0.757889i | \(0.273769\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.27051 | −0.133075 | ||||||||
\(605\) | 8.74032 | 0.355345 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.2511 | −1.06550 | −0.532749 | − | 0.846273i | \(-0.678841\pi\) | ||||
−0.532749 | + | 0.846273i | \(0.678841\pi\) | |||||||
\(608\) | −18.4335 | −0.747577 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.6525 | 0.755217 | ||||||||
\(611\) | 21.8885 | 0.885516 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.1803 | 1.58248 | 0.791240 | − | 0.611506i | \(-0.209436\pi\) | ||||
0.791240 | + | 0.611506i | \(0.209436\pi\) | |||||||
\(614\) | 30.1599 | 1.21715 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.4164 | 0.862192 | 0.431096 | − | 0.902306i | \(-0.358127\pi\) | ||||
0.431096 | + | 0.902306i | \(0.358127\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.5617 | 1.42934 | 0.714672 | − | 0.699460i | \(-0.246576\pi\) | ||||
0.714672 | + | 0.699460i | \(0.246576\pi\) | |||||||
\(620\) | −0.180340 | −0.00724262 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −45.9712 | −1.84328 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.1246 | 0.564984 | ||||||||
\(626\) | 21.6746 | 0.866290 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.33540 | −0.0532883 | ||||||||
\(629\) | 8.56409 | 0.341473 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.3475 | −0.451738 | −0.225869 | − | 0.974158i | \(-0.572522\pi\) | ||||
−0.225869 | + | 0.974158i | \(0.572522\pi\) | |||||||
\(632\) | 27.3607 | 1.08835 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.4721 | 1.21020 | ||||||||
\(635\) | −11.9327 | −0.473535 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.23607 | −0.207298 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.9026 | −0.470492 | ||||||||
\(641\) | −12.5279 | −0.494821 | −0.247410 | − | 0.968911i | \(-0.579580\pi\) | ||||
−0.247410 | + | 0.968911i | \(0.579580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.5393 | −1.12548 | −0.562740 | − | 0.826634i | \(-0.690253\pi\) | ||||
−0.562740 | + | 0.826634i | \(0.690253\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 27.8885 | 1.09726 | ||||||||
\(647\) | −29.6684 | −1.16638 | −0.583192 | − | 0.812334i | \(-0.698197\pi\) | ||||
−0.583192 | + | 0.812334i | \(0.698197\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.15143 | −0.319972 | ||||||||
\(650\) | 11.9814 | 0.469950 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.09017 | −0.199346 | ||||||||
\(653\) | 3.29180 | 0.128818 | 0.0644090 | − | 0.997924i | \(-0.479484\pi\) | ||||
0.0644090 | + | 0.997924i | \(0.479484\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.63932 | 0.0640535 | ||||||||
\(656\) | −48.6722 | −1.90033 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.7639 | −0.458258 | −0.229129 | − | 0.973396i | \(-0.573588\pi\) | ||||
−0.229129 | + | 0.973396i | \(0.573588\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.6383 | 0.686049 | 0.343024 | − | 0.939326i | \(-0.388549\pi\) | ||||
0.343024 | + | 0.939326i | \(0.388549\pi\) | |||||||
\(662\) | 3.23607 | 0.125773 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.0965 | −0.624667 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.94427 | 0.346324 | ||||||||
\(668\) | 5.37171 | 0.207838 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.5672 | 0.408246 | ||||||||
\(671\) | −13.1893 | −0.509167 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.65248 | 0.372076 | 0.186038 | − | 0.982543i | \(-0.440435\pi\) | ||||
0.186038 | + | 0.982543i | \(0.440435\pi\) | |||||||
\(674\) | −27.7984 | −1.07075 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.14590 | −0.236381 | ||||||||
\(677\) | 7.07107 | 0.271763 | 0.135882 | − | 0.990725i | \(-0.456613\pi\) | ||||
0.135882 | + | 0.990725i | \(0.456613\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.18034 | 0.237005 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.540182 | 0.0206846 | ||||||||
\(683\) | −17.7639 | −0.679718 | −0.339859 | − | 0.940476i | \(-0.610379\pi\) | ||||
−0.339859 | + | 0.940476i | \(0.610379\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.28980 | −0.125697 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 57.9787 | 2.21042 | ||||||||
\(689\) | 4.73411 | 0.180355 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.7974 | −0.715088 | −0.357544 | − | 0.933896i | \(-0.616386\pi\) | ||||
−0.357544 | + | 0.933896i | \(0.616386\pi\) | |||||||
\(692\) | −11.9026 | −0.452469 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35.5066 | 1.34781 | ||||||||
\(695\) | 0.180340 | 0.00684068 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.7082 | 1.20103 | ||||||||
\(698\) | −46.3839 | −1.75566 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.1803 | −0.497815 | −0.248907 | − | 0.968527i | \(-0.580071\pi\) | ||||
−0.248907 | + | 0.968527i | \(0.580071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.7611 | 0.556727 | ||||||||
\(704\) | 4.23607 | 0.159653 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.1946 | −1.24930 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.65248 | −0.212283 | −0.106142 | − | 0.994351i | \(-0.533850\pi\) | ||||
−0.106142 | + | 0.994351i | \(0.533850\pi\) | |||||||
\(710\) | 4.91034 | 0.184282 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.1421 | 0.529999 | ||||||||
\(713\) | −0.922740 | −0.0345569 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.52786 | 0.0571389 | ||||||||
\(716\) | 12.5836 | 0.470271 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.7984 | 1.03743 | ||||||||
\(719\) | −17.8145 | −0.664368 | −0.332184 | − | 0.943215i | \(-0.607786\pi\) | ||||
−0.332184 | + | 0.943215i | \(0.607786\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17.3262 | 0.644816 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.1908 | 0.527399 | ||||||||
\(725\) | 13.7082 | 0.509110 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.02236 | −0.260445 | −0.130222 | − | 0.991485i | \(-0.541569\pi\) | ||||
−0.130222 | + | 0.991485i | \(0.541569\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18.4721 | 0.683684 | ||||||||
\(731\) | −37.7711 | −1.39701 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.0270 | 0.370356 | 0.185178 | − | 0.982705i | \(-0.440714\pi\) | ||||
0.185178 | + | 0.982705i | \(0.440714\pi\) | |||||||
\(734\) | 2.82843 | 0.104399 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.34752 | 0.344554 | ||||||||
\(737\) | −7.47214 | −0.275240 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.3607 | −1.22719 | −0.613596 | − | 0.789620i | \(-0.710278\pi\) | ||||
−0.613596 | + | 0.789620i | \(0.710278\pi\) | |||||||
\(740\) | −1.46292 | −0.0537781 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.2492 | −1.51329 | −0.756644 | − | 0.653828i | \(-0.773162\pi\) | ||||
−0.756644 | + | 0.653828i | \(0.773162\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.0193 | 0.623538 | ||||||||
\(746\) | −14.8541 | −0.543847 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.95440 | 0.0714598 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.3050 | 1.10584 | 0.552922 | − | 0.833233i | \(-0.313513\pi\) | ||||
0.552922 | + | 0.833233i | \(0.313513\pi\) | |||||||
\(752\) | 60.7811 | 2.21646 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.15298 | 0.333332 | ||||||||
\(755\) | 4.62520 | 0.168328 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.0689 | 0.584034 | 0.292017 | − | 0.956413i | \(-0.405674\pi\) | ||||
0.292017 | + | 0.956413i | \(0.405674\pi\) | |||||||
\(758\) | −51.2148 | −1.86020 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.6525 | 0.386406 | ||||||||
\(761\) | −1.87558 | −0.0679899 | −0.0339949 | − | 0.999422i | \(-0.510823\pi\) | ||||
−0.0339949 | + | 0.999422i | \(0.510823\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.72949 | −0.0987495 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.5471 | 0.778527 | ||||||||
\(767\) | 14.2492 | 0.514510 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 52.2958 | 1.88583 | 0.942917 | − | 0.333027i | \(-0.108070\pi\) | ||||
0.942917 | + | 0.333027i | \(0.108070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.1803 | −0.366398 | ||||||||
\(773\) | 14.3184 | 0.514996 | 0.257498 | − | 0.966279i | \(-0.417102\pi\) | ||||
0.257498 | + | 0.966279i | \(0.417102\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.41421 | −0.0508001 | ||||||||
\(776\) | −20.9281 | −0.751274 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.7082 | 0.634870 | ||||||||
\(779\) | 54.6525 | 1.95813 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.47214 | −0.124243 | ||||||||
\(782\) | −14.1421 | −0.505722 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.88854 | 0.0674050 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.1475 | 1.21723 | 0.608613 | − | 0.793467i | \(-0.291726\pi\) | ||||
0.608613 | + | 0.793467i | \(0.291726\pi\) | |||||||
\(788\) | 11.3820 | 0.405466 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 17.3044 | 0.615663 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.0557 | 0.818733 | ||||||||
\(794\) | −46.6389 | −1.65515 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.07107 | −0.250627 | ||||||||
\(797\) | −27.2039 | −0.963612 | −0.481806 | − | 0.876278i | \(-0.660019\pi\) | ||||
−0.481806 | + | 0.876278i | \(0.660019\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.5967 | −1.40083 | ||||||||
\(800\) | 14.3262 | 0.506509 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 59.9787 | 2.11792 | ||||||||
\(803\) | −13.0618 | −0.460940 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.944272 | −0.0332606 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −27.7140 | −0.974975 | ||||||||
\(809\) | 43.5410 | 1.53082 | 0.765410 | − | 0.643543i | \(-0.222536\pi\) | ||||
0.765410 | + | 0.643543i | \(0.222536\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.5254 | −1.10701 | −0.553503 | − | 0.832847i | \(-0.686709\pi\) | ||||
−0.553503 | + | 0.832847i | \(0.686709\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.38197 | 0.153588 | ||||||||
\(815\) | 7.19859 | 0.252156 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −65.1025 | −2.27765 | ||||||||
\(818\) | 6.65841 | 0.232806 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.41641 | −0.189149 | ||||||||
\(821\) | −33.1803 | −1.15800 | −0.579001 | − | 0.815327i | \(-0.696557\pi\) | ||||
−0.579001 | + | 0.815327i | \(0.696557\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.41641 | −0.328235 | −0.164118 | − | 0.986441i | \(-0.552478\pi\) | ||||
−0.164118 | + | 0.986441i | \(0.552478\pi\) | |||||||
\(824\) | −22.4211 | −0.781076 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.6525 | −0.752930 | −0.376465 | − | 0.926431i | \(-0.622861\pi\) | ||||
−0.376465 | + | 0.926431i | \(0.622861\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.2148 | −0.771550 | −0.385775 | − | 0.922593i | \(-0.626066\pi\) | ||||
−0.385775 | + | 0.922593i | \(0.626066\pi\) | |||||||
\(830\) | −10.1803 | −0.353365 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.40492 | −0.256719 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.59675 | −0.262896 | ||||||||
\(836\) | 3.36861 | 0.116506 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 39.5192 | 1.36517 | ||||||||
\(839\) | 47.4643 | 1.63865 | 0.819324 | − | 0.573330i | \(-0.194349\pi\) | ||||
0.819324 | + | 0.573330i | \(0.194349\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.5279 | −0.638892 | ||||||||
\(842\) | 24.0902 | 0.830202 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.03444 | −0.0700284 | ||||||||
\(845\) | 8.69161 | 0.299001 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 13.1459 | 0.451432 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −21.6746 | −0.743432 | ||||||||
\(851\) | −7.48529 | −0.256592 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.6405 | 1.63118 | 0.815590 | − | 0.578631i | \(-0.196413\pi\) | ||||
0.815590 | + | 0.578631i | \(0.196413\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.2918 | 0.454304 | ||||||||
\(857\) | 26.9675 | 0.921191 | 0.460596 | − | 0.887610i | \(-0.347636\pi\) | ||||
0.460596 | + | 0.887610i | \(0.347636\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.0215 | −1.19492 | −0.597459 | − | 0.801900i | \(-0.703823\pi\) | ||||
−0.597459 | + | 0.801900i | \(0.703823\pi\) | |||||||
\(860\) | 6.45207 | 0.220014 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37.8885 | −1.29049 | ||||||||
\(863\) | −22.3050 | −0.759269 | −0.379635 | − | 0.925136i | \(-0.623950\pi\) | ||||
−0.379635 | + | 0.925136i | \(0.623950\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.8328 | 0.572333 | ||||||||
\(866\) | 33.1946 | 1.12800 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.2361 | −0.415080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.0618 | 0.442581 | ||||||||
\(872\) | −6.58359 | −0.222949 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.3755 | −0.824513 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.76393 | 0.329705 | 0.164852 | − | 0.986318i | \(-0.447285\pi\) | ||||
0.164852 | + | 0.986318i | \(0.447285\pi\) | |||||||
\(878\) | 18.9250 | 0.638686 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.24264 | 0.143019 | ||||||||
\(881\) | 21.7534 | 0.732890 | 0.366445 | − | 0.930440i | \(-0.380575\pi\) | ||||
0.366445 | + | 0.930440i | \(0.380575\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.6525 | 1.40172 | 0.700859 | − | 0.713300i | \(-0.252800\pi\) | ||||
0.700859 | + | 0.713300i | \(0.252800\pi\) | |||||||
\(884\) | −3.41641 | −0.114906 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.70820 | −0.124580 | ||||||||
\(887\) | −14.1421 | −0.474846 | −0.237423 | − | 0.971406i | \(-0.576303\pi\) | ||||
−0.237423 | + | 0.971406i | \(0.576303\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.94427 | 0.299813 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.19859 | 0.241027 | ||||||||
\(893\) | −68.2492 | −2.28387 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.7959 | −0.594851 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 50.9230 | 1.69932 | ||||||||
\(899\) | −1.08036 | −0.0360321 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.56409 | −0.285311 | ||||||||
\(902\) | 16.2241 | 0.540202 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.4164 | 0.612521 | ||||||||
\(905\) | −20.0689 | −0.667112 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.5410 | 0.383213 | 0.191607 | − | 0.981472i | \(-0.438630\pi\) | ||||
0.191607 | + | 0.981472i | \(0.438630\pi\) | |||||||
\(908\) | 14.2697 | 0.473555 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.2492 | −1.33352 | −0.666758 | − | 0.745274i | \(-0.732319\pi\) | ||||
−0.666758 | + | 0.745274i | \(0.732319\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.19859 | 0.238238 | ||||||||
\(914\) | 38.5623 | 1.27553 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.19704 | −0.204756 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.1803 | 0.632701 | 0.316351 | − | 0.948642i | \(-0.397542\pi\) | ||||
0.316351 | + | 0.948642i | \(0.397542\pi\) | |||||||
\(920\) | −5.40182 | −0.178093 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 29.4133 | 0.968677 | ||||||||
\(923\) | 6.06952 | 0.199781 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.4721 | −0.377202 | ||||||||
\(926\) | −59.6869 | −1.96143 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.9443 | 0.359263 | ||||||||
\(929\) | −53.2974 | −1.74863 | −0.874315 | − | 0.485360i | \(-0.838689\pi\) | ||||
−0.874315 | + | 0.485360i | \(0.838689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.1803 | 0.464492 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 65.2301 | 2.13439 | ||||||||
\(935\) | −2.76393 | −0.0903902 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.5440 | 0.638473 | 0.319237 | − | 0.947675i | \(-0.396574\pi\) | ||||
0.319237 | + | 0.947675i | \(0.396574\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.76393 | 0.220615 | ||||||||
\(941\) | 46.5902 | 1.51880 | 0.759399 | − | 0.650625i | \(-0.225493\pi\) | ||||
0.759399 | + | 0.650625i | \(0.225493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.7140 | −0.902492 | ||||||||
\(944\) | 39.5679 | 1.28782 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −19.3262 | −0.628350 | ||||||||
\(947\) | −47.2361 | −1.53497 | −0.767483 | − | 0.641069i | \(-0.778491\pi\) | ||||
−0.767483 | + | 0.641069i | \(0.778491\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.8328 | 0.741185 | ||||||||
\(950\) | −37.3584 | −1.21207 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.5836 | 0.990700 | 0.495350 | − | 0.868694i | \(-0.335040\pi\) | ||||
0.495350 | + | 0.868694i | \(0.335040\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.86008 | 0.124909 | ||||||||
\(956\) | 8.61803 | 0.278727 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.1784 | −0.587319 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8885 | −0.996405 | ||||||||
\(962\) | −7.65996 | −0.246967 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.48373 | −0.241035 | ||||||||
\(965\) | 14.3972 | 0.463461 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.47214 | 0.272446 | 0.136223 | − | 0.990678i | \(-0.456504\pi\) | ||||
0.136223 | + | 0.990678i | \(0.456504\pi\) | |||||||
\(968\) | 22.3607 | 0.718699 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.2361 | −0.424985 | ||||||||
\(971\) | 0.333851 | 0.0107138 | 0.00535689 | − | 0.999986i | \(-0.498295\pi\) | ||||
0.00535689 | + | 0.999986i | \(0.498295\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.5623 | −0.722943 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 64.0222 | 2.04930 | ||||||||
\(977\) | −31.3050 | −1.00153 | −0.500767 | − | 0.865582i | \(-0.666949\pi\) | ||||
−0.500767 | + | 0.865582i | \(0.666949\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.32456 | −0.202134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 35.5967 | 1.13594 | ||||||||
\(983\) | 24.5030 | 0.781524 | 0.390762 | − | 0.920492i | \(-0.372211\pi\) | ||||
0.390762 | + | 0.920492i | \(0.372211\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.0965 | −0.512878 | ||||||||
\(986\) | −16.5579 | −0.527311 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.88854 | −0.187340 | ||||||||
\(989\) | 33.0132 | 1.04976 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.41641 | −0.203824 | −0.101912 | − | 0.994793i | \(-0.532496\pi\) | ||||
−0.101912 | + | 0.994793i | \(0.532496\pi\) | |||||||
\(992\) | −1.12907 | −0.0358480 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0000 | 0.317021 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.1760 | 1.43074 | 0.715369 | − | 0.698746i | \(-0.246258\pi\) | ||||
0.715369 | + | 0.698746i | \(0.246258\pi\) | |||||||
\(998\) | −22.4721 | −0.711343 | ||||||||
\(999\) | 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 | 3969.2.a.y.1.3 | yes | 4 | |
3.2 | odd | 2 | 3969.2.a.r.1.2 | yes | 4 | ||
7.6 | odd | 2 | inner | 3969.2.a.y.1.4 | yes | 4 | |
21.20 | even | 2 | 3969.2.a.r.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3969.2.a.r.1.1 | ✓ | 4 | 21.20 | even | 2 | ||
3969.2.a.r.1.2 | yes | 4 | 3.2 | odd | 2 | ||
3969.2.a.y.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
3969.2.a.y.1.4 | yes | 4 | 7.6 | odd | 2 | inner |