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: | \(6\) |
Coefficient field: | 6.6.59351616.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 12x^{4} + 21x^{2} - 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 441) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-3.16032\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.69963 | 1.20182 | 0.600909 | − | 0.799317i | \(-0.294805\pi\) | ||||
0.600909 | + | 0.799317i | \(0.294805\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.888736 | 0.444368 | ||||||||
\(5\) | 0.949271 | 0.424527 | 0.212263 | − | 0.977212i | \(-0.431916\pi\) | ||||
0.212263 | + | 0.977212i | \(0.431916\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.88874 | −0.667769 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.61341 | 0.510204 | ||||||||
\(11\) | 0.588364 | 0.177398 | 0.0886992 | − | 0.996058i | \(-0.471729\pi\) | ||||
0.0886992 | + | 0.996058i | \(0.471729\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.01974 | −1.39222 | −0.696112 | − | 0.717933i | \(-0.745088\pi\) | ||||
−0.696112 | + | 0.717933i | \(0.745088\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.98762 | −1.24691 | ||||||||
\(17\) | 7.58242 | 1.83901 | 0.919503 | − | 0.393083i | \(-0.128591\pi\) | ||||
0.919503 | + | 0.393083i | \(0.128591\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.46122 | −1.02347 | −0.511737 | − | 0.859142i | \(-0.670998\pi\) | ||||
−0.511737 | + | 0.859142i | \(0.670998\pi\) | |||||||
\(20\) | 0.843651 | 0.188646 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −2.47710 | −0.516511 | −0.258256 | − | 0.966077i | \(-0.583148\pi\) | ||||
−0.258256 | + | 0.966077i | \(0.583148\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.09888 | −0.819777 | ||||||||
\(26\) | −8.53169 | −1.67320 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.47710 | −1.01707 | −0.508536 | − | 0.861041i | \(-0.669813\pi\) | ||||
−0.508536 | + | 0.861041i | \(0.669813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.07463 | −1.09104 | −0.545518 | − | 0.838099i | \(-0.683667\pi\) | ||||
−0.545518 | + | 0.838099i | \(0.683667\pi\) | |||||||
\(32\) | −4.69963 | −0.830785 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.8873 | 2.21015 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.98762 | −1.14876 | −0.574379 | − | 0.818590i | \(-0.694756\pi\) | ||||
−0.574379 | + | 0.818590i | \(0.694756\pi\) | |||||||
\(38\) | −7.58242 | −1.23003 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.79292 | −0.283486 | ||||||||
\(41\) | 1.05489 | 0.164746 | 0.0823731 | − | 0.996602i | \(-0.473750\pi\) | ||||
0.0823731 | + | 0.996602i | \(0.473750\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.98762 | 1.06560 | 0.532801 | − | 0.846241i | \(-0.321139\pi\) | ||||
0.532801 | + | 0.846241i | \(0.321139\pi\) | |||||||
\(44\) | 0.522900 | 0.0788302 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.21015 | −0.620753 | ||||||||
\(47\) | 7.47680 | 1.09060 | 0.545301 | − | 0.838240i | \(-0.316415\pi\) | ||||
0.545301 | + | 0.838240i | \(0.316415\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.96658 | −0.985223 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.46122 | −0.618660 | ||||||||
\(53\) | −6.92216 | −0.950831 | −0.475416 | − | 0.879761i | \(-0.657702\pi\) | ||||
−0.475416 | + | 0.879761i | \(0.657702\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.558517 | 0.0753104 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.30903 | −1.22234 | ||||||||
\(59\) | −10.4302 | −1.35790 | −0.678950 | − | 0.734184i | \(-0.737565\pi\) | ||||
−0.678950 | + | 0.734184i | \(0.737565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.6529 | 1.49200 | 0.745999 | − | 0.665947i | \(-0.231972\pi\) | ||||
0.745999 | + | 0.665947i | \(0.231972\pi\) | |||||||
\(62\) | −10.3246 | −1.31123 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.98762 | 0.248453 | ||||||||
\(65\) | −4.76509 | −0.591037 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8640 | −1.44942 | −0.724708 | − | 0.689056i | \(-0.758025\pi\) | ||||
−0.724708 | + | 0.689056i | \(0.758025\pi\) | |||||||
\(68\) | 6.73877 | 0.817195 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.30037 | −0.510360 | −0.255180 | − | 0.966894i | \(-0.582135\pi\) | ||||
−0.255180 | + | 0.966894i | \(0.582135\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.46122 | 0.522146 | 0.261073 | − | 0.965319i | \(-0.415924\pi\) | ||||
0.261073 | + | 0.965319i | \(0.415924\pi\) | |||||||
\(74\) | −11.8764 | −1.38060 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.96485 | −0.454799 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.33379 | −0.150063 | −0.0750317 | − | 0.997181i | \(-0.523906\pi\) | ||||
−0.0750317 | + | 0.997181i | \(0.523906\pi\) | |||||||
\(80\) | −4.73460 | −0.529345 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.79292 | 0.197995 | ||||||||
\(83\) | 5.68387 | 0.623886 | 0.311943 | − | 0.950101i | \(-0.399020\pi\) | ||||
0.311943 | + | 0.950101i | \(0.399020\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.19777 | 0.780708 | ||||||||
\(86\) | 11.8764 | 1.28066 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.11126 | −0.118461 | ||||||||
\(89\) | −0.843651 | −0.0894269 | −0.0447134 | − | 0.999000i | \(-0.514237\pi\) | ||||
−0.0447134 | + | 0.999000i | \(0.514237\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.20149 | −0.229521 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.7078 | 1.31071 | ||||||||
\(95\) | −4.23491 | −0.434492 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.40633 | −0.345860 | −0.172930 | − | 0.984934i | \(-0.555324\pi\) | ||||
−0.172930 | + | 0.984934i | \(0.555324\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.64283 | −0.364283 | ||||||||
\(101\) | 9.58658 | 0.953900 | 0.476950 | − | 0.878930i | \(-0.341742\pi\) | ||||
0.476950 | + | 0.878930i | \(0.341742\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.6529 | −1.14819 | −0.574096 | − | 0.818788i | \(-0.694647\pi\) | ||||
−0.574096 | + | 0.818788i | \(0.694647\pi\) | |||||||
\(104\) | 9.48096 | 0.929685 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.7651 | −1.14273 | ||||||||
\(107\) | 3.79851 | 0.367216 | 0.183608 | − | 0.983000i | \(-0.441222\pi\) | ||||
0.183608 | + | 0.983000i | \(0.441222\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.8640 | −1.23215 | −0.616073 | − | 0.787689i | \(-0.711277\pi\) | ||||
−0.616073 | + | 0.787689i | \(0.711277\pi\) | |||||||
\(110\) | 0.949271 | 0.0905094 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.02104 | −0.848628 | −0.424314 | − | 0.905515i | \(-0.639485\pi\) | ||||
−0.424314 | + | 0.905515i | \(0.639485\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.35144 | −0.219273 | ||||||||
\(116\) | −4.86769 | −0.451954 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.7275 | −1.63195 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6538 | −0.968530 | ||||||||
\(122\) | 19.8056 | 1.79311 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.39874 | −0.484821 | ||||||||
\(125\) | −8.63731 | −0.772544 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.43268 | 0.570808 | 0.285404 | − | 0.958407i | \(-0.407872\pi\) | ||||
0.285404 | + | 0.958407i | \(0.407872\pi\) | |||||||
\(128\) | 12.7775 | 1.12938 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.09888 | −0.710319 | ||||||||
\(131\) | −6.63315 | −0.579541 | −0.289770 | − | 0.957096i | \(-0.593579\pi\) | ||||
−0.289770 | + | 0.957096i | \(0.593579\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −20.1643 | −1.74193 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −14.3212 | −1.22803 | ||||||||
\(137\) | −14.0334 | −1.19896 | −0.599478 | − | 0.800391i | \(-0.704625\pi\) | ||||
−0.599478 | + | 0.800391i | \(0.704625\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.80507 | 0.746836 | 0.373418 | − | 0.927663i | \(-0.378186\pi\) | ||||
0.373418 | + | 0.927663i | \(0.378186\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.30903 | −0.613360 | ||||||||
\(143\) | −2.95343 | −0.246978 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.19925 | −0.431774 | ||||||||
\(146\) | 7.58242 | 0.627525 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.21015 | −0.510471 | ||||||||
\(149\) | 4.36584 | 0.357663 | 0.178832 | − | 0.983880i | \(-0.442768\pi\) | ||||
0.178832 | + | 0.983880i | \(0.442768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.6538 | −1.02975 | −0.514877 | − | 0.857264i | \(-0.672162\pi\) | ||||
−0.514877 | + | 0.857264i | \(0.672162\pi\) | |||||||
\(152\) | 8.42607 | 0.683444 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.76647 | −0.463174 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.2739 | 0.899754 | 0.449877 | − | 0.893091i | \(-0.351468\pi\) | ||||
0.449877 | + | 0.893091i | \(0.351468\pi\) | |||||||
\(158\) | −2.26695 | −0.180349 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.46122 | −0.352690 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.66621 | −0.130507 | −0.0652537 | − | 0.997869i | \(-0.520786\pi\) | ||||
−0.0652537 | + | 0.997869i | \(0.520786\pi\) | |||||||
\(164\) | 0.937519 | 0.0732080 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.66047 | 0.749798 | ||||||||
\(167\) | −3.90270 | −0.302000 | −0.151000 | − | 0.988534i | \(-0.548249\pi\) | ||||
−0.151000 | + | 0.988534i | \(0.548249\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1978 | 0.938290 | ||||||||
\(170\) | 12.2335 | 0.938269 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.21015 | 0.473519 | ||||||||
\(173\) | −16.1141 | −1.22513 | −0.612566 | − | 0.790419i | \(-0.709863\pi\) | ||||
−0.612566 | + | 0.790419i | \(0.709863\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.93454 | −0.221199 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.43389 | −0.107475 | ||||||||
\(179\) | −14.2880 | −1.06793 | −0.533967 | − | 0.845505i | \(-0.679299\pi\) | ||||
−0.533967 | + | 0.845505i | \(0.679299\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.8873 | 0.957905 | 0.478952 | − | 0.877841i | \(-0.341017\pi\) | ||||
0.478952 | + | 0.877841i | \(0.341017\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.67859 | 0.344910 | ||||||||
\(185\) | −6.63315 | −0.487679 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.46122 | 0.326237 | ||||||||
\(188\) | 6.64490 | 0.484629 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.19777 | −0.522181 | ||||||||
\(191\) | 2.16435 | 0.156607 | 0.0783034 | − | 0.996930i | \(-0.475050\pi\) | ||||
0.0783034 | + | 0.996930i | \(0.475050\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.4313 | 0.750861 | 0.375431 | − | 0.926850i | \(-0.377495\pi\) | ||||
0.375431 | + | 0.926850i | \(0.377495\pi\) | |||||||
\(194\) | −5.78949 | −0.415661 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.7848 | 1.33836 | 0.669179 | − | 0.743101i | \(-0.266646\pi\) | ||||
0.669179 | + | 0.743101i | \(0.266646\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.42607 | 0.597308 | 0.298654 | − | 0.954361i | \(-0.403462\pi\) | ||||
0.298654 | + | 0.954361i | \(0.403462\pi\) | |||||||
\(200\) | 7.74171 | 0.547422 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.2936 | 1.14642 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00138 | 0.0699392 | ||||||||
\(206\) | −19.8056 | −1.37992 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 25.0365 | 1.73597 | ||||||||
\(209\) | −2.62482 | −0.181563 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.2225 | 0.772591 | 0.386295 | − | 0.922375i | \(-0.373755\pi\) | ||||
0.386295 | + | 0.922375i | \(0.373755\pi\) | |||||||
\(212\) | −6.15197 | −0.422519 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.45606 | 0.441327 | ||||||||
\(215\) | 6.63315 | 0.452377 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −21.8640 | −1.48082 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.496374 | 0.0334655 | ||||||||
\(221\) | −38.0617 | −2.56031 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.7548 | −1.38985 | −0.694923 | − | 0.719084i | \(-0.744562\pi\) | ||||
−0.694923 | + | 0.719084i | \(0.744562\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.3324 | −1.01990 | ||||||||
\(227\) | 10.4302 | 0.692279 | 0.346139 | − | 0.938183i | \(-0.387492\pi\) | ||||
0.346139 | + | 0.938183i | \(0.387492\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.0592 | 0.995141 | 0.497570 | − | 0.867424i | \(-0.334226\pi\) | ||||
0.497570 | + | 0.867424i | \(0.334226\pi\) | |||||||
\(230\) | −3.99657 | −0.263526 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.3448 | 0.679169 | ||||||||
\(233\) | −4.38688 | −0.287394 | −0.143697 | − | 0.989622i | \(-0.545899\pi\) | ||||
−0.143697 | + | 0.989622i | \(0.545899\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.09751 | 0.462990 | ||||||||
\(236\) | −9.26972 | −0.603407 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.55122 | 0.617817 | 0.308909 | − | 0.951092i | \(-0.400036\pi\) | ||||
0.308909 | + | 0.951092i | \(0.400036\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.5358 | 0.678674 | 0.339337 | − | 0.940665i | \(-0.389797\pi\) | ||||
0.339337 | + | 0.940665i | \(0.389797\pi\) | |||||||
\(242\) | −18.1075 | −1.16400 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.3563 | 0.662996 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.3942 | 1.42491 | ||||||||
\(248\) | 11.4734 | 0.728560 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.6802 | −0.928458 | ||||||||
\(251\) | 24.4346 | 1.54230 | 0.771148 | − | 0.636656i | \(-0.219683\pi\) | ||||
0.771148 | + | 0.636656i | \(0.219683\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.45744 | −0.0916282 | ||||||||
\(254\) | 10.9332 | 0.686007 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.7417 | 1.10886 | ||||||||
\(257\) | −4.00832 | −0.250032 | −0.125016 | − | 0.992155i | \(-0.539898\pi\) | ||||
−0.125016 | + | 0.992155i | \(0.539898\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.23491 | −0.262638 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.2739 | −0.696503 | ||||||||
\(263\) | −17.6872 | −1.09064 | −0.545321 | − | 0.838227i | \(-0.683592\pi\) | ||||
−0.545321 | + | 0.838227i | \(0.683592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.57100 | −0.403653 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.5439 | −0.644074 | ||||||||
\(269\) | 14.2273 | 0.867455 | 0.433727 | − | 0.901044i | \(-0.357198\pi\) | ||||
0.433727 | + | 0.901044i | \(0.357198\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.39874 | −0.327950 | −0.163975 | − | 0.986464i | \(-0.552432\pi\) | ||||
−0.163975 | + | 0.986464i | \(0.552432\pi\) | |||||||
\(272\) | −37.8182 | −2.29307 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.8516 | −1.44093 | ||||||||
\(275\) | −2.41164 | −0.145427 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.66621 | 0.460618 | 0.230309 | − | 0.973118i | \(-0.426026\pi\) | ||||
0.230309 | + | 0.973118i | \(0.426026\pi\) | |||||||
\(278\) | 14.9653 | 0.897562 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.6625 | 1.35193 | 0.675965 | − | 0.736933i | \(-0.263727\pi\) | ||||
0.675965 | + | 0.736933i | \(0.263727\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.8492 | −1.89324 | −0.946619 | − | 0.322353i | \(-0.895526\pi\) | ||||
−0.946619 | + | 0.322353i | \(0.895526\pi\) | |||||||
\(284\) | −3.82189 | −0.226788 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.01974 | −0.296823 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.4930 | 2.38194 | ||||||||
\(290\) | −8.83680 | −0.518915 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.96485 | 0.232025 | ||||||||
\(293\) | −27.4936 | −1.60619 | −0.803097 | − | 0.595849i | \(-0.796816\pi\) | ||||
−0.803097 | + | 0.595849i | \(0.796816\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.90112 | −0.576465 | ||||||||
\(296\) | 13.1978 | 0.767105 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.42030 | 0.429846 | ||||||||
\(299\) | 12.4344 | 0.719099 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −21.5068 | −1.23758 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 22.2509 | 1.27618 | ||||||||
\(305\) | 11.0617 | 0.633394 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.8176 | 0.845683 | 0.422841 | − | 0.906204i | \(-0.361033\pi\) | ||||
0.422841 | + | 0.906204i | \(0.361033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.80085 | −0.556651 | ||||||||
\(311\) | −29.0635 | −1.64804 | −0.824021 | − | 0.566559i | \(-0.808274\pi\) | ||||
−0.824021 | + | 0.566559i | \(0.808274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.4780 | −1.38358 | −0.691790 | − | 0.722099i | \(-0.743178\pi\) | ||||
−0.691790 | + | 0.722099i | \(0.743178\pi\) | |||||||
\(314\) | 19.1614 | 1.08134 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.18539 | −0.0666834 | ||||||||
\(317\) | 7.38688 | 0.414888 | 0.207444 | − | 0.978247i | \(-0.433485\pi\) | ||||
0.207444 | + | 0.978247i | \(0.433485\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.22253 | −0.180427 | ||||||||
\(320\) | 1.88679 | 0.105475 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.8268 | −1.88218 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.5753 | 1.14131 | ||||||||
\(326\) | −2.83193 | −0.156846 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.99241 | −0.110012 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0617 | 1.10269 | 0.551347 | − | 0.834276i | \(-0.314114\pi\) | ||||
0.551347 | + | 0.834276i | \(0.314114\pi\) | |||||||
\(332\) | 5.05146 | 0.277235 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.63315 | −0.362950 | ||||||||
\(335\) | −11.2621 | −0.615316 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.40654 | 0.348986 | 0.174493 | − | 0.984658i | \(-0.444171\pi\) | ||||
0.174493 | + | 0.984658i | \(0.444171\pi\) | |||||||
\(338\) | 20.7317 | 1.12765 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.39692 | 0.346921 | ||||||||
\(341\) | −3.57409 | −0.193548 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −13.1978 | −0.711576 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27.3880 | −1.47239 | ||||||||
\(347\) | 29.1927 | 1.56714 | 0.783572 | − | 0.621300i | \(-0.213395\pi\) | ||||
0.783572 | + | 0.621300i | \(0.213395\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.34385 | −0.232521 | −0.116260 | − | 0.993219i | \(-0.537091\pi\) | ||||
−0.116260 | + | 0.993219i | \(0.537091\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.76509 | −0.147380 | ||||||||
\(353\) | −25.7007 | −1.36791 | −0.683955 | − | 0.729525i | \(-0.739741\pi\) | ||||
−0.683955 | + | 0.729525i | \(0.739741\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.08222 | −0.216662 | ||||||||
\(356\) | −0.749783 | −0.0397384 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.2843 | −1.28346 | ||||||||
\(359\) | −20.6872 | −1.09183 | −0.545916 | − | 0.837840i | \(-0.683818\pi\) | ||||
−0.545916 | + | 0.837840i | \(0.683818\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.902493 | 0.0474996 | ||||||||
\(362\) | 21.9036 | 1.15123 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.23491 | 0.221665 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.84781 | −0.148655 | −0.0743273 | − | 0.997234i | \(-0.523681\pi\) | ||||
−0.0743273 | + | 0.997234i | \(0.523681\pi\) | |||||||
\(368\) | 12.3548 | 0.644040 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.2739 | −0.586101 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.4327 | 1.10974 | 0.554871 | − | 0.831936i | \(-0.312768\pi\) | ||||
0.554871 | + | 0.831936i | \(0.312768\pi\) | |||||||
\(374\) | 7.58242 | 0.392077 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.1217 | −0.728271 | ||||||||
\(377\) | 27.4936 | 1.41599 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.0494 | 1.38943 | 0.694716 | − | 0.719284i | \(-0.255530\pi\) | ||||
0.694716 | + | 0.719284i | \(0.255530\pi\) | |||||||
\(380\) | −3.76371 | −0.193074 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.67859 | 0.188213 | ||||||||
\(383\) | 14.4268 | 0.737175 | 0.368588 | − | 0.929593i | \(-0.379841\pi\) | ||||
0.368588 | + | 0.929593i | \(0.379841\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.7293 | 0.902399 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.02733 | −0.153689 | ||||||||
\(389\) | 6.10755 | 0.309665 | 0.154832 | − | 0.987941i | \(-0.450516\pi\) | ||||
0.154832 | + | 0.987941i | \(0.450516\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.7824 | −0.949867 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 31.9271 | 1.60846 | ||||||||
\(395\) | −1.26613 | −0.0637059 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.8873 | −0.646794 | −0.323397 | − | 0.946263i | \(-0.604825\pi\) | ||||
−0.323397 | + | 0.946263i | \(0.604825\pi\) | |||||||
\(398\) | 14.3212 | 0.717856 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 20.4437 | 1.02218 | ||||||||
\(401\) | −8.39060 | −0.419006 | −0.209503 | − | 0.977808i | \(-0.567185\pi\) | ||||
−0.209503 | + | 0.977808i | \(0.567185\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.4930 | 1.51897 | ||||||||
\(404\) | 8.51994 | 0.423883 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.11126 | −0.203788 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.81266 | 0.336864 | 0.168432 | − | 0.985713i | \(-0.446130\pi\) | ||||
0.168432 | + | 0.985713i | \(0.446130\pi\) | |||||||
\(410\) | 1.70197 | 0.0840543 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.3563 | −0.510220 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.39554 | 0.264857 | ||||||||
\(416\) | 23.5909 | 1.15664 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.46122 | −0.218205 | ||||||||
\(419\) | 10.3246 | 0.504390 | 0.252195 | − | 0.967676i | \(-0.418848\pi\) | ||||
0.252195 | + | 0.967676i | \(0.418848\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.13602 | 0.152840 | 0.0764202 | − | 0.997076i | \(-0.475651\pi\) | ||||
0.0764202 | + | 0.997076i | \(0.475651\pi\) | |||||||
\(422\) | 19.0741 | 0.928514 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.0741 | 0.634936 | ||||||||
\(425\) | −31.0795 | −1.50757 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.37587 | 0.163179 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.2739 | 0.543675 | ||||||||
\(431\) | −31.8726 | −1.53525 | −0.767625 | − | 0.640899i | \(-0.778562\pi\) | ||||
−0.767625 | + | 0.640899i | \(0.778562\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.48855 | 0.359877 | 0.179938 | − | 0.983678i | \(-0.442410\pi\) | ||||
0.179938 | + | 0.983678i | \(0.442410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.4327 | −0.547526 | ||||||||
\(437\) | 11.0509 | 0.528636 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.28930 | 0.109262 | 0.0546311 | − | 0.998507i | \(-0.482602\pi\) | ||||
0.0546311 | + | 0.998507i | \(0.482602\pi\) | |||||||
\(440\) | −1.05489 | −0.0502900 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −64.6908 | −3.07703 | ||||||||
\(443\) | −37.3497 | −1.77454 | −0.887270 | − | 0.461251i | \(-0.847401\pi\) | ||||
−0.887270 | + | 0.461251i | \(0.847401\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.800854 | −0.0379641 | ||||||||
\(446\) | −35.2755 | −1.67034 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.20286 | 0.292731 | 0.146366 | − | 0.989231i | \(-0.453242\pi\) | ||||
0.146366 | + | 0.989231i | \(0.453242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.620660 | 0.0292257 | ||||||||
\(452\) | −8.01732 | −0.377103 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.7275 | 0.831993 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.1716 | 0.943589 | 0.471795 | − | 0.881709i | \(-0.343606\pi\) | ||||
0.471795 | + | 0.881709i | \(0.343606\pi\) | |||||||
\(458\) | 25.5951 | 1.19598 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.08981 | −0.0974378 | ||||||||
\(461\) | 22.5360 | 1.04961 | 0.524803 | − | 0.851224i | \(-0.324139\pi\) | ||||
0.524803 | + | 0.851224i | \(0.324139\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.6291 | −1.28403 | −0.642016 | − | 0.766691i | \(-0.721902\pi\) | ||||
−0.642016 | + | 0.766691i | \(0.721902\pi\) | |||||||
\(464\) | 27.3177 | 1.26819 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.45606 | −0.345395 | ||||||||
\(467\) | −20.1224 | −0.931155 | −0.465577 | − | 0.885007i | \(-0.654153\pi\) | ||||
−0.465577 | + | 0.885007i | \(0.654153\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 12.0631 | 0.556430 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 19.6999 | 0.906764 | ||||||||
\(473\) | 4.11126 | 0.189036 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.2860 | 0.839021 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.2335 | 0.742504 | ||||||||
\(479\) | 9.58658 | 0.438022 | 0.219011 | − | 0.975722i | \(-0.429717\pi\) | ||||
0.219011 | + | 0.975722i | \(0.429717\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.0760 | 1.59933 | ||||||||
\(482\) | 17.9070 | 0.815643 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.46844 | −0.430384 | ||||||||
\(485\) | −3.23353 | −0.146827 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.0741 | 0.592445 | 0.296223 | − | 0.955119i | \(-0.404273\pi\) | ||||
0.296223 | + | 0.955119i | \(0.404273\pi\) | |||||||
\(488\) | −22.0092 | −0.996311 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.3411 | −0.692333 | −0.346167 | − | 0.938173i | \(-0.612517\pi\) | ||||
−0.346167 | + | 0.938173i | \(0.612517\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41.5297 | −1.87040 | ||||||||
\(494\) | 38.0617 | 1.71248 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.2979 | 1.36042 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.86535 | 0.217803 | 0.108902 | − | 0.994053i | \(-0.465267\pi\) | ||||
0.108902 | + | 0.994053i | \(0.465267\pi\) | |||||||
\(500\) | −7.67628 | −0.343294 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 41.5297 | 1.85356 | ||||||||
\(503\) | −16.0085 | −0.713783 | −0.356892 | − | 0.934146i | \(-0.616163\pi\) | ||||
−0.356892 | + | 0.934146i | \(0.616163\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.10026 | 0.404956 | ||||||||
\(506\) | −2.47710 | −0.110121 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.71695 | 0.253649 | ||||||||
\(509\) | 31.1851 | 1.38225 | 0.691127 | − | 0.722733i | \(-0.257115\pi\) | ||||
0.691127 | + | 0.722733i | \(0.257115\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4.59937 | 0.203265 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.81266 | −0.300494 | ||||||||
\(515\) | −11.0617 | −0.487439 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.39908 | 0.193471 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.00000 | 0.394676 | ||||||||
\(521\) | −20.9661 | −0.918541 | −0.459270 | − | 0.888297i | \(-0.651889\pi\) | ||||
−0.459270 | + | 0.888297i | \(0.651889\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.5642 | 1.90493 | 0.952465 | − | 0.304647i | \(-0.0985383\pi\) | ||||
0.952465 | + | 0.304647i | \(0.0985383\pi\) | |||||||
\(524\) | −5.89511 | −0.257529 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.0617 | −1.31075 | ||||||||
\(527\) | −46.0604 | −2.00642 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8640 | −0.733216 | ||||||||
\(530\) | −11.1683 | −0.485118 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.29528 | −0.229364 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.60582 | 0.155893 | ||||||||
\(536\) | 22.4079 | 0.967875 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.1811 | 1.04252 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.86535 | 0.424145 | 0.212072 | − | 0.977254i | \(-0.431979\pi\) | ||||
0.212072 | + | 0.977254i | \(0.431979\pi\) | |||||||
\(542\) | −9.17585 | −0.394137 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −35.6345 | −1.52782 | ||||||||
\(545\) | −12.2114 | −0.523079 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.568701 | 0.0243159 | 0.0121579 | − | 0.999926i | \(-0.496130\pi\) | ||||
0.0121579 | + | 0.999926i | \(0.496130\pi\) | |||||||
\(548\) | −12.4720 | −0.532778 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.09888 | −0.174777 | ||||||||
\(551\) | 24.4346 | 1.04095 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13.0297 | 0.553579 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.82538 | 0.331870 | ||||||||
\(557\) | 2.58699 | 0.109614 | 0.0548071 | − | 0.998497i | \(-0.482546\pi\) | ||||
0.0548071 | + | 0.998497i | \(0.482546\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.0760 | −1.48356 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 38.5178 | 1.62478 | ||||||||
\(563\) | 33.2831 | 1.40272 | 0.701358 | − | 0.712809i | \(-0.252578\pi\) | ||||
0.701358 | + | 0.712809i | \(0.252578\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.56341 | −0.360265 | ||||||||
\(566\) | −54.1318 | −2.27533 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.12227 | 0.340803 | ||||||||
\(569\) | 5.35346 | 0.224429 | 0.112214 | − | 0.993684i | \(-0.464206\pi\) | ||||
0.112214 | + | 0.993684i | \(0.464206\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.90112 | 0.205105 | 0.102553 | − | 0.994728i | \(-0.467299\pi\) | ||||
0.102553 | + | 0.994728i | \(0.467299\pi\) | |||||||
\(572\) | −2.62482 | −0.109749 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.1533 | 0.423424 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.0757 | −1.50185 | −0.750925 | − | 0.660387i | \(-0.770392\pi\) | ||||
−0.750925 | + | 0.660387i | \(0.770392\pi\) | |||||||
\(578\) | 68.8231 | 2.86266 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.62076 | −0.191867 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.07275 | −0.168676 | ||||||||
\(584\) | −8.42607 | −0.348673 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −46.7289 | −1.93035 | ||||||||
\(587\) | −1.05489 | −0.0435400 | −0.0217700 | − | 0.999763i | \(-0.506930\pi\) | ||||
−0.0217700 | + | 0.999763i | \(0.506930\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.1003 | 1.11665 | ||||||||
\(590\) | −16.8282 | −0.692807 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 34.8516 | 1.43239 | ||||||||
\(593\) | 15.0710 | 0.618890 | 0.309445 | − | 0.950917i | \(-0.399857\pi\) | ||||
0.309445 | + | 0.950917i | \(0.399857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.88007 | 0.158934 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21.1338 | 0.864227 | ||||||||
\(599\) | −42.0566 | −1.71839 | −0.859194 | − | 0.511650i | \(-0.829035\pi\) | ||||
−0.859194 | + | 0.511650i | \(0.829035\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.8998 | 0.770938 | 0.385469 | − | 0.922721i | \(-0.374040\pi\) | ||||
0.385469 | + | 0.922721i | \(0.374040\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.2459 | −0.457590 | ||||||||
\(605\) | −10.1134 | −0.411167 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.4425 | −1.19504 | −0.597518 | − | 0.801856i | \(-0.703846\pi\) | ||||
−0.597518 | + | 0.801856i | \(0.703846\pi\) | |||||||
\(608\) | 20.9661 | 0.850287 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.8009 | 0.761224 | ||||||||
\(611\) | −37.5316 | −1.51836 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.6676 | −0.471249 | −0.235625 | − | 0.971844i | \(-0.575714\pi\) | ||||
−0.235625 | + | 0.971844i | \(0.575714\pi\) | |||||||
\(614\) | 25.1843 | 1.01636 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.8109 | 1.32092 | 0.660458 | − | 0.750863i | \(-0.270362\pi\) | ||||
0.660458 | + | 0.750863i | \(0.270362\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.1612 | −0.971119 | −0.485560 | − | 0.874204i | \(-0.661384\pi\) | ||||
−0.485560 | + | 0.874204i | \(0.661384\pi\) | |||||||
\(620\) | −5.12487 | −0.205820 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −49.3972 | −1.98065 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.2953 | 0.491811 | ||||||||
\(626\) | −41.6035 | −1.66281 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.0195 | 0.399822 | ||||||||
\(629\) | −52.9830 | −2.11257 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.1003 | −0.441894 | −0.220947 | − | 0.975286i | \(-0.570915\pi\) | ||||
−0.220947 | + | 0.975286i | \(0.570915\pi\) | |||||||
\(632\) | 2.51918 | 0.100208 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.5549 | 0.498620 | ||||||||
\(635\) | 6.10635 | 0.242323 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.47710 | −0.216840 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12.1293 | 0.479452 | ||||||||
\(641\) | −7.30037 | −0.288347 | −0.144174 | − | 0.989552i | \(-0.546052\pi\) | ||||
−0.144174 | + | 0.989552i | \(0.546052\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.2512 | 0.838066 | 0.419033 | − | 0.907971i | \(-0.362369\pi\) | ||||
0.419033 | + | 0.907971i | \(0.362369\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −57.4930 | −2.26203 | ||||||||
\(647\) | −16.9460 | −0.666216 | −0.333108 | − | 0.942889i | \(-0.608097\pi\) | ||||
−0.333108 | + | 0.942889i | \(0.608097\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.13677 | −0.240889 | ||||||||
\(650\) | 34.9704 | 1.37165 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.48082 | −0.0579933 | ||||||||
\(653\) | 3.73305 | 0.146085 | 0.0730427 | − | 0.997329i | \(-0.476729\pi\) | ||||
0.0730427 | + | 0.997329i | \(0.476729\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.29665 | −0.246031 | ||||||||
\(656\) | −5.26140 | −0.205423 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.5984 | 0.919263 | 0.459632 | − | 0.888110i | \(-0.347981\pi\) | ||||
0.459632 | + | 0.888110i | \(0.347981\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.5175 | 1.34258 | 0.671288 | − | 0.741197i | \(-0.265742\pi\) | ||||
0.671288 | + | 0.741197i | \(0.265742\pi\) | |||||||
\(662\) | 34.0975 | 1.32524 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.7353 | −0.416612 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.5673 | 0.525329 | ||||||||
\(668\) | −3.46847 | −0.134199 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −19.1414 | −0.739498 | ||||||||
\(671\) | 6.85614 | 0.264678 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.4574 | −0.942765 | −0.471382 | − | 0.881929i | \(-0.656245\pi\) | ||||
−0.471382 | + | 0.881929i | \(0.656245\pi\) | |||||||
\(674\) | 10.8887 | 0.419418 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.8406 | 0.416946 | ||||||||
\(677\) | 8.32045 | 0.319781 | 0.159890 | − | 0.987135i | \(-0.448886\pi\) | ||||
0.159890 | + | 0.987135i | \(0.448886\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −13.5947 | −0.521332 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.07463 | −0.232610 | ||||||||
\(683\) | 42.4624 | 1.62478 | 0.812389 | − | 0.583116i | \(-0.198167\pi\) | ||||
0.812389 | + | 0.583116i | \(0.198167\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.3215 | −0.508989 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −34.8516 | −1.32870 | ||||||||
\(689\) | 34.7474 | 1.32377 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.3929 | 1.34641 | 0.673204 | − | 0.739456i | \(-0.264917\pi\) | ||||
0.673204 | + | 0.739456i | \(0.264917\pi\) | |||||||
\(692\) | −14.3212 | −0.544410 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 49.6167 | 1.88342 | ||||||||
\(695\) | 8.35840 | 0.317052 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.99862 | 0.302969 | ||||||||
\(698\) | −7.38293 | −0.279448 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.00372 | 0.264527 | 0.132263 | − | 0.991215i | \(-0.457776\pi\) | ||||
0.132263 | + | 0.991215i | \(0.457776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.1733 | 1.17572 | ||||||||
\(704\) | 1.16944 | 0.0440751 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −43.6816 | −1.64398 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.22253 | −0.0834688 | −0.0417344 | − | 0.999129i | \(-0.513288\pi\) | ||||
−0.0417344 | + | 0.999129i | \(0.513288\pi\) | |||||||
\(710\) | −6.93825 | −0.260388 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.59343 | 0.0597165 | ||||||||
\(713\) | 15.0475 | 0.563532 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.80361 | −0.104849 | ||||||||
\(716\) | −12.6983 | −0.474556 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −35.1606 | −1.31218 | ||||||||
\(719\) | −26.0175 | −0.970291 | −0.485145 | − | 0.874434i | \(-0.661233\pi\) | ||||
−0.485145 | + | 0.874434i | \(0.661233\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.53390 | 0.0570859 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.4534 | 0.425662 | ||||||||
\(725\) | 22.4500 | 0.833772 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.37175 | −0.0508754 | −0.0254377 | − | 0.999676i | \(-0.508098\pi\) | ||||
−0.0254377 | + | 0.999676i | \(0.508098\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.19777 | 0.266401 | ||||||||
\(731\) | 52.9830 | 1.95965 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.800174 | −0.0295551 | −0.0147776 | − | 0.999891i | \(-0.504704\pi\) | ||||
−0.0147776 | + | 0.999891i | \(0.504704\pi\) | |||||||
\(734\) | −4.84022 | −0.178656 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.6414 | 0.429109 | ||||||||
\(737\) | −6.98034 | −0.257124 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.37093 | 0.197573 | 0.0987865 | − | 0.995109i | \(-0.468504\pi\) | ||||
0.0987865 | + | 0.995109i | \(0.468504\pi\) | |||||||
\(740\) | −5.89511 | −0.216709 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.2632 | 0.486581 | 0.243290 | − | 0.969953i | \(-0.421773\pi\) | ||||
0.243290 | + | 0.969953i | \(0.421773\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.14436 | 0.151838 | ||||||||
\(746\) | 36.4276 | 1.33371 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.96485 | 0.144969 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.55632 | 0.202753 | 0.101377 | − | 0.994848i | \(-0.467675\pi\) | ||||
0.101377 | + | 0.994848i | \(0.467675\pi\) | |||||||
\(752\) | −37.2914 | −1.35988 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 46.7289 | 1.70177 | ||||||||
\(755\) | −12.0119 | −0.437158 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.3942 | −0.486819 | −0.243410 | − | 0.969924i | \(-0.578266\pi\) | ||||
−0.243410 | + | 0.969924i | \(0.578266\pi\) | |||||||
\(758\) | 45.9739 | 1.66985 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.99862 | 0.290141 | ||||||||
\(761\) | 12.8438 | 0.465588 | 0.232794 | − | 0.972526i | \(-0.425213\pi\) | ||||
0.232794 | + | 0.972526i | \(0.425213\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.92353 | 0.0695910 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.5202 | 0.885951 | ||||||||
\(767\) | 52.3570 | 1.89050 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.96518 | 0.106927 | 0.0534636 | − | 0.998570i | \(-0.482974\pi\) | ||||
0.0534636 | + | 0.998570i | \(0.482974\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.27067 | 0.333659 | ||||||||
\(773\) | 19.2788 | 0.693409 | 0.346705 | − | 0.937974i | \(-0.387301\pi\) | ||||
0.346705 | + | 0.937974i | \(0.387301\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.8992 | 0.894406 | ||||||||
\(776\) | 6.43366 | 0.230955 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.3806 | 0.372161 | ||||||||
\(779\) | −4.70610 | −0.168614 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.53018 | −0.0905371 | ||||||||
\(782\) | −31.9231 | −1.14157 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.7020 | 0.381970 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.6453 | 0.486402 | 0.243201 | − | 0.969976i | \(-0.421803\pi\) | ||||
0.243201 | + | 0.969976i | \(0.421803\pi\) | |||||||
\(788\) | 16.6947 | 0.594724 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.15195 | −0.0765630 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −58.4944 | −2.07720 | ||||||||
\(794\) | −21.9036 | −0.777330 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.48855 | 0.265425 | ||||||||
\(797\) | 22.9585 | 0.813231 | 0.406616 | − | 0.913599i | \(-0.366709\pi\) | ||||
0.406616 | + | 0.913599i | \(0.366709\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 56.6922 | 2.00563 | ||||||||
\(800\) | 19.2632 | 0.681058 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.2609 | −0.503570 | ||||||||
\(803\) | 2.62482 | 0.0926279 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 51.8268 | 1.82552 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18.1065 | −0.636985 | ||||||||
\(809\) | −39.4582 | −1.38728 | −0.693639 | − | 0.720323i | \(-0.743994\pi\) | ||||
−0.693639 | + | 0.720323i | \(0.743994\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.496374 | −0.0174300 | −0.00871502 | − | 0.999962i | \(-0.502774\pi\) | ||||
−0.00871502 | + | 0.999962i | \(0.502774\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.98762 | −0.244916 | ||||||||
\(815\) | −1.58168 | −0.0554039 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.1733 | −1.09062 | ||||||||
\(818\) | 11.5790 | 0.404850 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.889960 | 0.0310788 | ||||||||
\(821\) | −47.1038 | −1.64393 | −0.821967 | − | 0.569534i | \(-0.807124\pi\) | ||||
−0.821967 | + | 0.569534i | \(0.807124\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.19777 | −0.0766094 | −0.0383047 | − | 0.999266i | \(-0.512196\pi\) | ||||
−0.0383047 | + | 0.999266i | \(0.512196\pi\) | |||||||
\(824\) | 22.0092 | 0.766727 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 55.3360 | 1.92422 | 0.962110 | − | 0.272661i | \(-0.0879036\pi\) | ||||
0.962110 | + | 0.272661i | \(0.0879036\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.3206 | −0.705764 | −0.352882 | − | 0.935668i | \(-0.614798\pi\) | ||||
−0.352882 | + | 0.935668i | \(0.614798\pi\) | |||||||
\(830\) | 9.17041 | 0.318310 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.97733 | −0.345902 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.70472 | −0.128207 | ||||||||
\(836\) | −2.33277 | −0.0806806 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17.5480 | 0.606186 | ||||||||
\(839\) | −24.5519 | −0.847627 | −0.423813 | − | 0.905750i | \(-0.639309\pi\) | ||||
−0.423813 | + | 0.905750i | \(0.639309\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.998623 | 0.0344353 | ||||||||
\(842\) | 5.33007 | 0.183686 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.97386 | 0.343315 | ||||||||
\(845\) | 11.5790 | 0.398329 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 34.5251 | 1.18560 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −52.8235 | −1.81183 | ||||||||
\(851\) | 17.3090 | 0.593346 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 53.5416 | 1.83323 | 0.916614 | − | 0.399773i | \(-0.130911\pi\) | ||||
0.916614 | + | 0.399773i | \(0.130911\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.17439 | −0.245215 | ||||||||
\(857\) | −54.1553 | −1.84991 | −0.924955 | − | 0.380076i | \(-0.875898\pi\) | ||||
−0.924955 | + | 0.380076i | \(0.875898\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.79292 | −0.0611737 | −0.0305869 | − | 0.999532i | \(-0.509738\pi\) | ||||
−0.0305869 | + | 0.999532i | \(0.509738\pi\) | |||||||
\(860\) | 5.89511 | 0.201022 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −54.1716 | −1.84509 | ||||||||
\(863\) | 32.5709 | 1.10873 | 0.554363 | − | 0.832275i | \(-0.312962\pi\) | ||||
0.554363 | + | 0.832275i | \(0.312962\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.2967 | −0.520102 | ||||||||
\(866\) | 12.7277 | 0.432506 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.784755 | −0.0266210 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 59.5541 | 2.01791 | ||||||||
\(872\) | 24.2967 | 0.822789 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.7824 | 0.635324 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.7293 | −1.24026 | −0.620131 | − | 0.784499i | \(-0.712920\pi\) | ||||
−0.620131 | + | 0.784499i | \(0.712920\pi\) | |||||||
\(878\) | 3.89095 | 0.131313 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.78567 | −0.0939049 | ||||||||
\(881\) | 25.3721 | 0.854807 | 0.427403 | − | 0.904061i | \(-0.359428\pi\) | ||||
0.427403 | + | 0.904061i | \(0.359428\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.9381 | −0.570012 | −0.285006 | − | 0.958526i | \(-0.591996\pi\) | ||||
−0.285006 | + | 0.958526i | \(0.591996\pi\) | |||||||
\(884\) | −33.8268 | −1.13772 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −63.4807 | −2.13267 | ||||||||
\(887\) | −48.0137 | −1.61214 | −0.806071 | − | 0.591819i | \(-0.798410\pi\) | ||||
−0.806071 | + | 0.591819i | \(0.798410\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.36115 | −0.0456260 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.4456 | −0.617603 | ||||||||
\(893\) | −33.3556 | −1.11620 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.5632 | −0.453367 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.5426 | 0.351810 | ||||||||
\(899\) | 33.2713 | 1.10966 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −52.4867 | −1.74858 | ||||||||
\(902\) | 1.05489 | 0.0351240 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.0384 | 0.566688 | ||||||||
\(905\) | 12.2335 | 0.406656 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.7775 | −0.822722 | −0.411361 | − | 0.911472i | \(-0.634947\pi\) | ||||
−0.411361 | + | 0.911472i | \(0.634947\pi\) | |||||||
\(908\) | 9.26972 | 0.307626 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.5833 | −1.04640 | −0.523200 | − | 0.852210i | \(-0.675262\pi\) | ||||
−0.523200 | + | 0.852210i | \(0.675262\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.34419 | 0.110676 | ||||||||
\(914\) | 34.2843 | 1.13402 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.3837 | 0.442209 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.59208 | 0.0525180 | 0.0262590 | − | 0.999655i | \(-0.491641\pi\) | ||||
0.0262590 | + | 0.999655i | \(0.491641\pi\) | |||||||
\(920\) | 4.44125 | 0.146424 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 38.3028 | 1.26144 | ||||||||
\(923\) | 21.5867 | 0.710536 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.6414 | 0.941725 | ||||||||
\(926\) | −46.9591 | −1.54317 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 25.7403 | 0.844968 | ||||||||
\(929\) | −27.0711 | −0.888175 | −0.444087 | − | 0.895983i | \(-0.646472\pi\) | ||||
−0.444087 | + | 0.895983i | \(0.646472\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.89877 | −0.127709 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34.2006 | −1.11908 | ||||||||
\(935\) | 4.23491 | 0.138496 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.6624 | 1.06704 | 0.533518 | − | 0.845789i | \(-0.320870\pi\) | ||||
0.533518 | + | 0.845789i | \(0.320870\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.30781 | 0.205738 | ||||||||
\(941\) | −4.72285 | −0.153961 | −0.0769803 | − | 0.997033i | \(-0.524528\pi\) | ||||
−0.0769803 | + | 0.997033i | \(0.524528\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.61307 | −0.0850933 | ||||||||
\(944\) | 52.0220 | 1.69317 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.98762 | 0.227187 | ||||||||
\(947\) | −56.7810 | −1.84514 | −0.922568 | − | 0.385835i | \(-0.873913\pi\) | ||||
−0.922568 | + | 0.385835i | \(0.873913\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.3942 | −0.726945 | ||||||||
\(950\) | 31.0795 | 1.00835 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.1693 | 1.52796 | 0.763982 | − | 0.645238i | \(-0.223242\pi\) | ||||
0.763982 | + | 0.645238i | \(0.223242\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.05455 | 0.0664838 | ||||||||
\(956\) | 8.48852 | 0.274538 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.2936 | 0.526423 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.90112 | 0.190359 | ||||||||
\(962\) | 59.6162 | 1.92210 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.36359 | 0.301581 | ||||||||
\(965\) | 9.90213 | 0.318761 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.3969 | 1.52418 | 0.762091 | − | 0.647470i | \(-0.224173\pi\) | ||||
0.762091 | + | 0.647470i | \(0.224173\pi\) | |||||||
\(968\) | 20.1223 | 0.646754 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.49580 | −0.176459 | ||||||||
\(971\) | −22.7473 | −0.729994 | −0.364997 | − | 0.931009i | \(-0.618930\pi\) | ||||
−0.364997 | + | 0.931009i | \(0.618930\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 22.2212 | 0.712012 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −58.1202 | −1.86038 | ||||||||
\(977\) | −35.6849 | −1.14166 | −0.570831 | − | 0.821068i | \(-0.693379\pi\) | ||||
−0.570831 | + | 0.821068i | \(0.693379\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.496374 | −0.0158642 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.0741 | −0.832059 | ||||||||
\(983\) | −24.0134 | −0.765908 | −0.382954 | − | 0.923767i | \(-0.625093\pi\) | ||||
−0.382954 | + | 0.923767i | \(0.625093\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.8318 | 0.568169 | ||||||||
\(986\) | −70.5850 | −2.24788 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 19.9025 | 0.633183 | ||||||||
\(989\) | −17.3090 | −0.550395 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.4189 | −1.41101 | −0.705507 | − | 0.708703i | \(-0.749281\pi\) | ||||
−0.705507 | + | 0.708703i | \(0.749281\pi\) | |||||||
\(992\) | 28.5485 | 0.906416 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.99862 | 0.253573 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.04673 | 0.286513 | 0.143256 | − | 0.989686i | \(-0.454243\pi\) | ||||
0.143256 | + | 0.989686i | \(0.454243\pi\) | |||||||
\(998\) | 8.26929 | 0.261760 | ||||||||
\(999\) | 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.bd.1.6 | 6 | ||
3.2 | odd | 2 | 3969.2.a.be.1.1 | 6 | |||
7.6 | odd | 2 | inner | 3969.2.a.bd.1.5 | 6 | ||
9.2 | odd | 6 | 441.2.f.g.148.6 | yes | 12 | ||
9.4 | even | 3 | 1323.2.f.g.883.1 | 12 | |||
9.5 | odd | 6 | 441.2.f.g.295.6 | yes | 12 | ||
9.7 | even | 3 | 1323.2.f.g.442.1 | 12 | |||
21.20 | even | 2 | 3969.2.a.be.1.2 | 6 | |||
63.2 | odd | 6 | 441.2.g.g.67.5 | 12 | |||
63.4 | even | 3 | 1323.2.g.g.667.2 | 12 | |||
63.5 | even | 6 | 441.2.h.g.214.1 | 12 | |||
63.11 | odd | 6 | 441.2.h.g.373.2 | 12 | |||
63.13 | odd | 6 | 1323.2.f.g.883.2 | 12 | |||
63.16 | even | 3 | 1323.2.g.g.361.2 | 12 | |||
63.20 | even | 6 | 441.2.f.g.148.5 | ✓ | 12 | ||
63.23 | odd | 6 | 441.2.h.g.214.2 | 12 | |||
63.25 | even | 3 | 1323.2.h.g.226.5 | 12 | |||
63.31 | odd | 6 | 1323.2.g.g.667.1 | 12 | |||
63.32 | odd | 6 | 441.2.g.g.79.5 | 12 | |||
63.34 | odd | 6 | 1323.2.f.g.442.2 | 12 | |||
63.38 | even | 6 | 441.2.h.g.373.1 | 12 | |||
63.40 | odd | 6 | 1323.2.h.g.802.6 | 12 | |||
63.41 | even | 6 | 441.2.f.g.295.5 | yes | 12 | ||
63.47 | even | 6 | 441.2.g.g.67.6 | 12 | |||
63.52 | odd | 6 | 1323.2.h.g.226.6 | 12 | |||
63.58 | even | 3 | 1323.2.h.g.802.5 | 12 | |||
63.59 | even | 6 | 441.2.g.g.79.6 | 12 | |||
63.61 | odd | 6 | 1323.2.g.g.361.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.g.148.5 | ✓ | 12 | 63.20 | even | 6 | ||
441.2.f.g.148.6 | yes | 12 | 9.2 | odd | 6 | ||
441.2.f.g.295.5 | yes | 12 | 63.41 | even | 6 | ||
441.2.f.g.295.6 | yes | 12 | 9.5 | odd | 6 | ||
441.2.g.g.67.5 | 12 | 63.2 | odd | 6 | |||
441.2.g.g.67.6 | 12 | 63.47 | even | 6 | |||
441.2.g.g.79.5 | 12 | 63.32 | odd | 6 | |||
441.2.g.g.79.6 | 12 | 63.59 | even | 6 | |||
441.2.h.g.214.1 | 12 | 63.5 | even | 6 | |||
441.2.h.g.214.2 | 12 | 63.23 | odd | 6 | |||
441.2.h.g.373.1 | 12 | 63.38 | even | 6 | |||
441.2.h.g.373.2 | 12 | 63.11 | odd | 6 | |||
1323.2.f.g.442.1 | 12 | 9.7 | even | 3 | |||
1323.2.f.g.442.2 | 12 | 63.34 | odd | 6 | |||
1323.2.f.g.883.1 | 12 | 9.4 | even | 3 | |||
1323.2.f.g.883.2 | 12 | 63.13 | odd | 6 | |||
1323.2.g.g.361.1 | 12 | 63.61 | odd | 6 | |||
1323.2.g.g.361.2 | 12 | 63.16 | even | 3 | |||
1323.2.g.g.667.1 | 12 | 63.31 | odd | 6 | |||
1323.2.g.g.667.2 | 12 | 63.4 | even | 3 | |||
1323.2.h.g.226.5 | 12 | 63.25 | even | 3 | |||
1323.2.h.g.226.6 | 12 | 63.52 | odd | 6 | |||
1323.2.h.g.802.5 | 12 | 63.58 | even | 3 | |||
1323.2.h.g.802.6 | 12 | 63.40 | odd | 6 | |||
3969.2.a.bd.1.5 | 6 | 7.6 | odd | 2 | inner | ||
3969.2.a.bd.1.6 | 6 | 1.1 | even | 1 | trivial | ||
3969.2.a.be.1.1 | 6 | 3.2 | odd | 2 | |||
3969.2.a.be.1.2 | 6 | 21.20 | even | 2 |