Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4005,2,Mod(1,4005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4005 = 3^{2} \cdot 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4005.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: | \(31.9800860095\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 8x^{5} + 6x^{4} + 19x^{3} - 10x^{2} - 12x + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 445) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.26266\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.11962 | −1.49880 | −0.749399 | − | 0.662119i | \(-0.769657\pi\) | ||||
−0.749399 | + | 0.662119i | \(0.769657\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.49279 | 1.24639 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.83304 | −1.82672 | −0.913358 | − | 0.407157i | \(-0.866520\pi\) | ||||
−0.913358 | + | 0.407157i | \(0.866520\pi\) | |||||||
\(8\) | −1.04452 | −0.369294 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.11962 | 0.670283 | ||||||||
\(11\) | 2.21586 | 0.668106 | 0.334053 | − | 0.942554i | \(-0.391583\pi\) | ||||
0.334053 | + | 0.942554i | \(0.391583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.26162 | −0.627261 | −0.313631 | − | 0.949545i | \(-0.601545\pi\) | ||||
−0.313631 | + | 0.949545i | \(0.601545\pi\) | |||||||
\(14\) | 10.2442 | 2.73788 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.77159 | −0.692896 | ||||||||
\(17\) | 3.10920 | 0.754092 | 0.377046 | − | 0.926194i | \(-0.376940\pi\) | ||||
0.377046 | + | 0.926194i | \(0.376940\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.93952 | −1.36262 | −0.681309 | − | 0.731996i | \(-0.738589\pi\) | ||||
−0.681309 | + | 0.731996i | \(0.738589\pi\) | |||||||
\(20\) | −2.49279 | −0.557404 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.69678 | −1.00136 | ||||||||
\(23\) | −5.79416 | −1.20817 | −0.604083 | − | 0.796921i | \(-0.706460\pi\) | ||||
−0.604083 | + | 0.796921i | \(0.706460\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.79378 | 0.940138 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −12.0477 | −2.27681 | ||||||||
\(29\) | −2.32757 | −0.432220 | −0.216110 | − | 0.976369i | \(-0.569337\pi\) | ||||
−0.216110 | + | 0.976369i | \(0.569337\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.47624 | 0.803956 | 0.401978 | − | 0.915649i | \(-0.368323\pi\) | ||||
0.401978 | + | 0.915649i | \(0.368323\pi\) | |||||||
\(32\) | 7.96375 | 1.40781 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.59033 | −1.13023 | ||||||||
\(35\) | 4.83304 | 0.816932 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.23124 | −1.35321 | −0.676604 | − | 0.736347i | \(-0.736549\pi\) | ||||
−0.676604 | + | 0.736347i | \(0.736549\pi\) | |||||||
\(38\) | 12.5895 | 2.04229 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.04452 | 0.165153 | ||||||||
\(41\) | 0.278075 | 0.0434281 | 0.0217140 | − | 0.999764i | \(-0.493088\pi\) | ||||
0.0217140 | + | 0.999764i | \(0.493088\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.176109 | −0.0268564 | −0.0134282 | − | 0.999910i | \(-0.504274\pi\) | ||||
−0.0134282 | + | 0.999910i | \(0.504274\pi\) | |||||||
\(44\) | 5.52366 | 0.832724 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.2814 | 1.81080 | ||||||||
\(47\) | −1.91855 | −0.279850 | −0.139925 | − | 0.990162i | \(-0.544686\pi\) | ||||
−0.139925 | + | 0.990162i | \(0.544686\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.3583 | 2.33689 | ||||||||
\(50\) | −2.11962 | −0.299759 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.63775 | −0.781815 | ||||||||
\(53\) | −8.65904 | −1.18941 | −0.594706 | − | 0.803944i | \(-0.702731\pi\) | ||||
−0.594706 | + | 0.803944i | \(0.702731\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.21586 | −0.298786 | ||||||||
\(56\) | 5.04821 | 0.674596 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.93357 | 0.647810 | ||||||||
\(59\) | −5.39666 | −0.702585 | −0.351292 | − | 0.936266i | \(-0.614258\pi\) | ||||
−0.351292 | + | 0.936266i | \(0.614258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.69150 | −1.24087 | −0.620434 | − | 0.784258i | \(-0.713044\pi\) | ||||
−0.620434 | + | 0.784258i | \(0.713044\pi\) | |||||||
\(62\) | −9.48792 | −1.20497 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.3370 | −1.41712 | ||||||||
\(65\) | 2.26162 | 0.280520 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.06916 | 0.985805 | 0.492903 | − | 0.870084i | \(-0.335936\pi\) | ||||
0.492903 | + | 0.870084i | \(0.335936\pi\) | |||||||
\(68\) | 7.75058 | 0.939896 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −10.2442 | −1.22442 | ||||||||
\(71\) | 5.00576 | 0.594075 | 0.297037 | − | 0.954866i | \(-0.404001\pi\) | ||||
0.297037 | + | 0.954866i | \(0.404001\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.18909 | −1.07550 | −0.537751 | − | 0.843104i | \(-0.680726\pi\) | ||||
−0.537751 | + | 0.843104i | \(0.680726\pi\) | |||||||
\(74\) | 17.4471 | 2.02818 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.8060 | −1.69836 | ||||||||
\(77\) | −10.7093 | −1.22044 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.78949 | −0.201333 | −0.100666 | − | 0.994920i | \(-0.532097\pi\) | ||||
−0.100666 | + | 0.994920i | \(0.532097\pi\) | |||||||
\(80\) | 2.77159 | 0.309873 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.589414 | −0.0650899 | ||||||||
\(83\) | −13.8879 | −1.52439 | −0.762197 | − | 0.647345i | \(-0.775879\pi\) | ||||
−0.762197 | + | 0.647345i | \(0.775879\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.10920 | −0.337240 | ||||||||
\(86\) | 0.373284 | 0.0402523 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.31451 | −0.246728 | ||||||||
\(89\) | −1.00000 | −0.106000 | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.9305 | 1.14583 | ||||||||
\(92\) | −14.4436 | −1.50585 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.06660 | 0.419438 | ||||||||
\(95\) | 5.93952 | 0.609382 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.52008 | −0.560479 | −0.280240 | − | 0.959930i | \(-0.590414\pi\) | ||||
−0.280240 | + | 0.959930i | \(0.590414\pi\) | |||||||
\(98\) | −34.6733 | −3.50253 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.49279 | 0.249279 | ||||||||
\(101\) | 12.8409 | 1.27772 | 0.638860 | − | 0.769323i | \(-0.279406\pi\) | ||||
0.638860 | + | 0.769323i | \(0.279406\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.7697 | −1.15970 | −0.579852 | − | 0.814722i | \(-0.696890\pi\) | ||||
−0.579852 | + | 0.814722i | \(0.696890\pi\) | |||||||
\(104\) | 2.36231 | 0.231644 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.3539 | 1.78269 | ||||||||
\(107\) | 15.4620 | 1.49477 | 0.747383 | − | 0.664393i | \(-0.231310\pi\) | ||||
0.747383 | + | 0.664393i | \(0.231310\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.88060 | −0.754824 | −0.377412 | − | 0.926045i | \(-0.623186\pi\) | ||||
−0.377412 | + | 0.926045i | \(0.623186\pi\) | |||||||
\(110\) | 4.69678 | 0.447820 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 13.3952 | 1.26573 | ||||||||
\(113\) | 2.01004 | 0.189088 | 0.0945442 | − | 0.995521i | \(-0.469861\pi\) | ||||
0.0945442 | + | 0.995521i | \(0.469861\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.79416 | 0.540308 | ||||||||
\(116\) | −5.80215 | −0.538716 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.4389 | 1.05303 | ||||||||
\(119\) | −15.0269 | −1.37751 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.08997 | −0.553634 | ||||||||
\(122\) | 20.5423 | 1.85981 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.1583 | 1.00205 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0158 | −1.06623 | −0.533113 | − | 0.846044i | \(-0.678978\pi\) | ||||
−0.533113 | + | 0.846044i | \(0.678978\pi\) | |||||||
\(128\) | 8.10252 | 0.716169 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.79378 | −0.420442 | ||||||||
\(131\) | 20.6066 | 1.80040 | 0.900202 | − | 0.435472i | \(-0.143419\pi\) | ||||
0.900202 | + | 0.435472i | \(0.143419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 28.7059 | 2.48912 | ||||||||
\(134\) | −17.1036 | −1.47752 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.24763 | −0.278482 | ||||||||
\(137\) | −10.9369 | −0.934400 | −0.467200 | − | 0.884152i | \(-0.654737\pi\) | ||||
−0.467200 | + | 0.884152i | \(0.654737\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.432073 | −0.0366479 | −0.0183240 | − | 0.999832i | \(-0.505833\pi\) | ||||
−0.0183240 | + | 0.999832i | \(0.505833\pi\) | |||||||
\(140\) | 12.0477 | 1.01822 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.6103 | −0.890397 | ||||||||
\(143\) | −5.01144 | −0.419077 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.32757 | 0.193294 | ||||||||
\(146\) | 19.4774 | 1.61196 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −20.5187 | −1.68663 | ||||||||
\(149\) | 13.6417 | 1.11757 | 0.558785 | − | 0.829313i | \(-0.311268\pi\) | ||||
0.558785 | + | 0.829313i | \(0.311268\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.3825 | 1.82146 | 0.910730 | − | 0.413002i | \(-0.135520\pi\) | ||||
0.910730 | + | 0.413002i | \(0.135520\pi\) | |||||||
\(152\) | 6.20396 | 0.503207 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 22.6997 | 1.82919 | ||||||||
\(155\) | −4.47624 | −0.359540 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.7366 | 0.936683 | 0.468342 | − | 0.883547i | \(-0.344852\pi\) | ||||
0.468342 | + | 0.883547i | \(0.344852\pi\) | |||||||
\(158\) | 3.79303 | 0.301757 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.96375 | −0.629590 | ||||||||
\(161\) | 28.0034 | 2.20698 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.49678 | 0.117237 | 0.0586184 | − | 0.998280i | \(-0.481330\pi\) | ||||
0.0586184 | + | 0.998280i | \(0.481330\pi\) | |||||||
\(164\) | 0.693183 | 0.0541285 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 29.4371 | 2.28476 | ||||||||
\(167\) | 0.555849 | 0.0430129 | 0.0215064 | − | 0.999769i | \(-0.493154\pi\) | ||||
0.0215064 | + | 0.999769i | \(0.493154\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.88506 | −0.606543 | ||||||||
\(170\) | 6.59033 | 0.505455 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.439002 | −0.0334736 | ||||||||
\(173\) | −14.0371 | −1.06722 | −0.533611 | − | 0.845730i | \(-0.679165\pi\) | ||||
−0.533611 | + | 0.845730i | \(0.679165\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.83304 | −0.365343 | ||||||||
\(176\) | −6.14144 | −0.462929 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.11962 | 0.158872 | ||||||||
\(179\) | −9.22570 | −0.689561 | −0.344780 | − | 0.938683i | \(-0.612047\pi\) | ||||
−0.344780 | + | 0.938683i | \(0.612047\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4704 | −0.778259 | −0.389129 | − | 0.921183i | \(-0.627224\pi\) | ||||
−0.389129 | + | 0.921183i | \(0.627224\pi\) | |||||||
\(182\) | −23.1685 | −1.71737 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.05213 | 0.446169 | ||||||||
\(185\) | 8.23124 | 0.605173 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.88955 | 0.503814 | ||||||||
\(188\) | −4.78255 | −0.348803 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.5895 | −0.913340 | ||||||||
\(191\) | 4.73905 | 0.342906 | 0.171453 | − | 0.985192i | \(-0.445154\pi\) | ||||
0.171453 | + | 0.985192i | \(0.445154\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.48587 | 0.106955 | 0.0534775 | − | 0.998569i | \(-0.482969\pi\) | ||||
0.0534775 | + | 0.998569i | \(0.482969\pi\) | |||||||
\(194\) | 11.7005 | 0.840045 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 40.7777 | 2.91269 | ||||||||
\(197\) | 4.51312 | 0.321547 | 0.160773 | − | 0.986991i | \(-0.448601\pi\) | ||||
0.160773 | + | 0.986991i | \(0.448601\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.28028 | 0.516085 | 0.258043 | − | 0.966134i | \(-0.416923\pi\) | ||||
0.258043 | + | 0.966134i | \(0.416923\pi\) | |||||||
\(200\) | −1.04452 | −0.0738588 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −27.2179 | −1.91504 | ||||||||
\(203\) | 11.2493 | 0.789543 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.278075 | −0.0194216 | ||||||||
\(206\) | 24.9473 | 1.73816 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.26828 | 0.434627 | ||||||||
\(209\) | −13.1611 | −0.910374 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0051 | 0.964154 | 0.482077 | − | 0.876129i | \(-0.339883\pi\) | ||||
0.482077 | + | 0.876129i | \(0.339883\pi\) | |||||||
\(212\) | −21.5852 | −1.48247 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −32.7735 | −2.24035 | ||||||||
\(215\) | 0.176109 | 0.0120105 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.6338 | −1.46860 | ||||||||
\(218\) | 16.7039 | 1.13133 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.52366 | −0.372405 | ||||||||
\(221\) | −7.03184 | −0.473013 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.76611 | −0.587022 | −0.293511 | − | 0.955956i | \(-0.594824\pi\) | ||||
−0.293511 | + | 0.955956i | \(0.594824\pi\) | |||||||
\(224\) | −38.4891 | −2.57166 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.26051 | −0.283405 | ||||||||
\(227\) | 21.8527 | 1.45042 | 0.725209 | − | 0.688529i | \(-0.241743\pi\) | ||||
0.725209 | + | 0.688529i | \(0.241743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.0211 | −1.32303 | −0.661514 | − | 0.749932i | \(-0.730086\pi\) | ||||
−0.661514 | + | 0.749932i | \(0.730086\pi\) | |||||||
\(230\) | −12.2814 | −0.809812 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.43120 | 0.159616 | ||||||||
\(233\) | −15.3296 | −1.00428 | −0.502139 | − | 0.864787i | \(-0.667453\pi\) | ||||
−0.502139 | + | 0.864787i | \(0.667453\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.91855 | 0.125153 | ||||||||
\(236\) | −13.4527 | −0.875697 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 31.8513 | 2.06461 | ||||||||
\(239\) | −7.27188 | −0.470379 | −0.235190 | − | 0.971950i | \(-0.575571\pi\) | ||||
−0.235190 | + | 0.971950i | \(0.575571\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.02887 | 0.259522 | 0.129761 | − | 0.991545i | \(-0.458579\pi\) | ||||
0.129761 | + | 0.991545i | \(0.458579\pi\) | |||||||
\(242\) | 12.9084 | 0.829785 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −24.1588 | −1.54661 | ||||||||
\(245\) | −16.3583 | −1.04509 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.4329 | 0.854718 | ||||||||
\(248\) | −4.67553 | −0.296896 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.11962 | 0.134057 | ||||||||
\(251\) | 6.99410 | 0.441464 | 0.220732 | − | 0.975335i | \(-0.429155\pi\) | ||||
0.220732 | + | 0.975335i | \(0.429155\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.8390 | −0.807183 | ||||||||
\(254\) | 25.4688 | 1.59806 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.49964 | 0.343727 | ||||||||
\(257\) | 19.3582 | 1.20753 | 0.603767 | − | 0.797161i | \(-0.293666\pi\) | ||||
0.603767 | + | 0.797161i | \(0.293666\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 39.7819 | 2.47193 | ||||||||
\(260\) | 5.63775 | 0.349638 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −43.6781 | −2.69844 | ||||||||
\(263\) | 5.73446 | 0.353602 | 0.176801 | − | 0.984247i | \(-0.443425\pi\) | ||||
0.176801 | + | 0.984247i | \(0.443425\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.65904 | 0.531921 | ||||||||
\(266\) | −60.8456 | −3.73068 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 20.1147 | 1.22870 | ||||||||
\(269\) | −5.07725 | −0.309565 | −0.154783 | − | 0.987949i | \(-0.549468\pi\) | ||||
−0.154783 | + | 0.987949i | \(0.549468\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.8909 | 0.904557 | 0.452278 | − | 0.891877i | \(-0.350611\pi\) | ||||
0.452278 | + | 0.891877i | \(0.350611\pi\) | |||||||
\(272\) | −8.61742 | −0.522508 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 23.1820 | 1.40048 | ||||||||
\(275\) | 2.21586 | 0.133621 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.6930 | −1.84417 | −0.922083 | − | 0.386993i | \(-0.873514\pi\) | ||||
−0.922083 | + | 0.386993i | \(0.873514\pi\) | |||||||
\(278\) | 0.915829 | 0.0549278 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.04821 | −0.301688 | ||||||||
\(281\) | −19.5982 | −1.16913 | −0.584564 | − | 0.811348i | \(-0.698734\pi\) | ||||
−0.584564 | + | 0.811348i | \(0.698734\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.1638 | 1.91194 | 0.955968 | − | 0.293469i | \(-0.0948099\pi\) | ||||
0.955968 | + | 0.293469i | \(0.0948099\pi\) | |||||||
\(284\) | 12.4783 | 0.740451 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.6223 | 0.628112 | ||||||||
\(287\) | −1.34395 | −0.0793308 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.33286 | −0.431345 | ||||||||
\(290\) | −4.93357 | −0.289709 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −22.9064 | −1.34050 | ||||||||
\(293\) | 22.7569 | 1.32947 | 0.664737 | − | 0.747077i | \(-0.268543\pi\) | ||||
0.664737 | + | 0.747077i | \(0.268543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.39666 | 0.314205 | ||||||||
\(296\) | 8.59771 | 0.499732 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −28.9152 | −1.67501 | ||||||||
\(299\) | 13.1042 | 0.757836 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.851142 | 0.0490590 | ||||||||
\(302\) | −47.4423 | −2.73000 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.4619 | 0.944154 | ||||||||
\(305\) | 9.69150 | 0.554933 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.883192 | 0.0504064 | 0.0252032 | − | 0.999682i | \(-0.491977\pi\) | ||||
0.0252032 | + | 0.999682i | \(0.491977\pi\) | |||||||
\(308\) | −26.6961 | −1.52115 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.48792 | 0.538878 | ||||||||
\(311\) | 2.98323 | 0.169163 | 0.0845816 | − | 0.996417i | \(-0.473045\pi\) | ||||
0.0845816 | + | 0.996417i | \(0.473045\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.07859 | 0.343582 | 0.171791 | − | 0.985133i | \(-0.445045\pi\) | ||||
0.171791 | + | 0.985133i | \(0.445045\pi\) | |||||||
\(314\) | −24.8771 | −1.40390 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.46081 | −0.250940 | ||||||||
\(317\) | −2.02998 | −0.114015 | −0.0570075 | − | 0.998374i | \(-0.518156\pi\) | ||||
−0.0570075 | + | 0.998374i | \(0.518156\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.15757 | −0.288769 | ||||||||
\(320\) | 11.3370 | 0.633755 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −59.3565 | −3.30781 | ||||||||
\(323\) | −18.4672 | −1.02754 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.26162 | −0.125452 | ||||||||
\(326\) | −3.17260 | −0.175714 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.290456 | −0.0160377 | ||||||||
\(329\) | 9.27244 | 0.511206 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.3999 | −0.681559 | −0.340779 | − | 0.940143i | \(-0.610691\pi\) | ||||
−0.340779 | + | 0.940143i | \(0.610691\pi\) | |||||||
\(332\) | −34.6196 | −1.90000 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.17819 | −0.0644676 | ||||||||
\(335\) | −8.06916 | −0.440866 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.1425 | 1.47855 | 0.739274 | − | 0.673405i | \(-0.235169\pi\) | ||||
0.739274 | + | 0.673405i | \(0.235169\pi\) | |||||||
\(338\) | 16.7133 | 0.909085 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.75058 | −0.420334 | ||||||||
\(341\) | 9.91871 | 0.537128 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −45.2288 | −2.44213 | ||||||||
\(344\) | 0.183950 | 0.00991790 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 29.7533 | 1.59955 | ||||||||
\(347\) | 17.0635 | 0.916019 | 0.458009 | − | 0.888947i | \(-0.348563\pi\) | ||||
0.458009 | + | 0.888947i | \(0.348563\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.3297 | 1.35587 | 0.677933 | − | 0.735124i | \(-0.262876\pi\) | ||||
0.677933 | + | 0.735124i | \(0.262876\pi\) | |||||||
\(350\) | 10.2442 | 0.547576 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 17.6465 | 0.940564 | ||||||||
\(353\) | −15.3713 | −0.818132 | −0.409066 | − | 0.912505i | \(-0.634146\pi\) | ||||
−0.409066 | + | 0.912505i | \(0.634146\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.00576 | −0.265678 | ||||||||
\(356\) | −2.49279 | −0.132117 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.5550 | 1.03351 | ||||||||
\(359\) | 4.81197 | 0.253966 | 0.126983 | − | 0.991905i | \(-0.459471\pi\) | ||||
0.126983 | + | 0.991905i | \(0.459471\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.2779 | 0.856730 | ||||||||
\(362\) | 22.1933 | 1.16645 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 27.2474 | 1.42815 | ||||||||
\(365\) | 9.18909 | 0.480979 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.4281 | 1.22294 | 0.611468 | − | 0.791269i | \(-0.290579\pi\) | ||||
0.611468 | + | 0.791269i | \(0.290579\pi\) | |||||||
\(368\) | 16.0590 | 0.837134 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −17.4471 | −0.907031 | ||||||||
\(371\) | 41.8495 | 2.17272 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.4886 | 0.543078 | 0.271539 | − | 0.962427i | \(-0.412467\pi\) | ||||
0.271539 | + | 0.962427i | \(0.412467\pi\) | |||||||
\(374\) | −14.6032 | −0.755115 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.00397 | 0.103347 | ||||||||
\(377\) | 5.26409 | 0.271115 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.6495 | −1.06069 | −0.530347 | − | 0.847781i | \(-0.677938\pi\) | ||||
−0.530347 | + | 0.847781i | \(0.677938\pi\) | |||||||
\(380\) | 14.8060 | 0.759529 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.0450 | −0.513946 | ||||||||
\(383\) | −11.8529 | −0.605654 | −0.302827 | − | 0.953046i | \(-0.597930\pi\) | ||||
−0.302827 | + | 0.953046i | \(0.597930\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.7093 | 0.545798 | ||||||||
\(386\) | −3.14947 | −0.160304 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.7604 | −0.698578 | ||||||||
\(389\) | 11.8172 | 0.599157 | 0.299578 | − | 0.954072i | \(-0.403154\pi\) | ||||
0.299578 | + | 0.954072i | \(0.403154\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0152 | −0.911068 | ||||||||
\(392\) | −17.0866 | −0.863001 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.56610 | −0.481933 | ||||||||
\(395\) | 1.78949 | 0.0900388 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.5070 | 1.83223 | 0.916116 | − | 0.400912i | \(-0.131307\pi\) | ||||
0.916116 | + | 0.400912i | \(0.131307\pi\) | |||||||
\(398\) | −15.4314 | −0.773507 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.77159 | −0.138579 | ||||||||
\(401\) | −1.45221 | −0.0725197 | −0.0362599 | − | 0.999342i | \(-0.511544\pi\) | ||||
−0.0362599 | + | 0.999342i | \(0.511544\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.1236 | −0.504291 | ||||||||
\(404\) | 32.0097 | 1.59254 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −23.8441 | −1.18336 | ||||||||
\(407\) | −18.2393 | −0.904086 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.3981 | 1.60198 | 0.800992 | − | 0.598674i | \(-0.204306\pi\) | ||||
0.800992 | + | 0.598674i | \(0.204306\pi\) | |||||||
\(410\) | 0.589414 | 0.0291091 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −29.3394 | −1.44545 | ||||||||
\(413\) | 26.0822 | 1.28342 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.8879 | 0.681730 | ||||||||
\(416\) | −18.0110 | −0.883062 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 27.8966 | 1.36447 | ||||||||
\(419\) | 10.4032 | 0.508227 | 0.254114 | − | 0.967174i | \(-0.418216\pi\) | ||||
0.254114 | + | 0.967174i | \(0.418216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.28300 | 0.0625297 | 0.0312648 | − | 0.999511i | \(-0.490046\pi\) | ||||
0.0312648 | + | 0.999511i | \(0.490046\pi\) | |||||||
\(422\) | −29.6856 | −1.44507 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.04456 | 0.439243 | ||||||||
\(425\) | 3.10920 | 0.150818 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 46.8394 | 2.26672 | ||||||||
\(428\) | 38.5434 | 1.86307 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.373284 | −0.0180014 | ||||||||
\(431\) | 2.37582 | 0.114439 | 0.0572195 | − | 0.998362i | \(-0.481777\pi\) | ||||
0.0572195 | + | 0.998362i | \(0.481777\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.3903 | 1.50852 | 0.754262 | − | 0.656574i | \(-0.227995\pi\) | ||||
0.754262 | + | 0.656574i | \(0.227995\pi\) | |||||||
\(434\) | 45.8555 | 2.20113 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.6447 | −0.940808 | ||||||||
\(437\) | 34.4145 | 1.64627 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.32745 | −0.397448 | −0.198724 | − | 0.980056i | \(-0.563680\pi\) | ||||
−0.198724 | + | 0.980056i | \(0.563680\pi\) | |||||||
\(440\) | 2.31451 | 0.110340 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.9048 | 0.708950 | ||||||||
\(443\) | 27.1908 | 1.29188 | 0.645938 | − | 0.763390i | \(-0.276466\pi\) | ||||
0.645938 | + | 0.763390i | \(0.276466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | 0.0474045 | ||||||||
\(446\) | 18.5808 | 0.879827 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 54.7919 | 2.58867 | ||||||||
\(449\) | 20.2755 | 0.956861 | 0.478430 | − | 0.878126i | \(-0.341206\pi\) | ||||
0.478430 | + | 0.878126i | \(0.341206\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.616176 | 0.0290146 | ||||||||
\(452\) | 5.01059 | 0.235679 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −46.3195 | −2.17388 | ||||||||
\(455\) | −10.9305 | −0.512430 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.8204 | −1.30138 | −0.650691 | − | 0.759343i | \(-0.725521\pi\) | ||||
−0.650691 | + | 0.759343i | \(0.725521\pi\) | |||||||
\(458\) | 42.4370 | 1.98295 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.4436 | 0.673437 | ||||||||
\(461\) | −3.25129 | −0.151428 | −0.0757138 | − | 0.997130i | \(-0.524124\pi\) | ||||
−0.0757138 | + | 0.997130i | \(0.524124\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8292 | −0.642699 | −0.321349 | − | 0.946961i | \(-0.604136\pi\) | ||||
−0.321349 | + | 0.946961i | \(0.604136\pi\) | |||||||
\(464\) | 6.45107 | 0.299483 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 32.4930 | 1.50521 | ||||||||
\(467\) | 19.5627 | 0.905253 | 0.452626 | − | 0.891700i | \(-0.350487\pi\) | ||||
0.452626 | + | 0.891700i | \(0.350487\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −38.9986 | −1.80079 | ||||||||
\(470\) | −4.06660 | −0.187578 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.63692 | 0.259461 | ||||||||
\(473\) | −0.390233 | −0.0179429 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.93952 | −0.272524 | ||||||||
\(476\) | −37.4588 | −1.71692 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.4136 | 0.705003 | ||||||||
\(479\) | −26.2070 | −1.19743 | −0.598714 | − | 0.800963i | \(-0.704321\pi\) | ||||
−0.598714 | + | 0.800963i | \(0.704321\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.6160 | 0.848815 | ||||||||
\(482\) | −8.53968 | −0.388972 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15.1810 | −0.690046 | ||||||||
\(485\) | 5.52008 | 0.250654 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.8600 | 1.30777 | 0.653887 | − | 0.756592i | \(-0.273137\pi\) | ||||
0.653887 | + | 0.756592i | \(0.273137\pi\) | |||||||
\(488\) | 10.1230 | 0.458246 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 34.6733 | 1.56638 | ||||||||
\(491\) | 27.5737 | 1.24438 | 0.622192 | − | 0.782865i | \(-0.286242\pi\) | ||||
0.622192 | + | 0.782865i | \(0.286242\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.23690 | −0.325933 | ||||||||
\(494\) | −28.4727 | −1.28105 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.4063 | −0.557058 | ||||||||
\(497\) | −24.1930 | −1.08521 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.9455 | 1.47484 | 0.737422 | − | 0.675432i | \(-0.236043\pi\) | ||||
0.737422 | + | 0.675432i | \(0.236043\pi\) | |||||||
\(500\) | −2.49279 | −0.111481 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.8248 | −0.661665 | ||||||||
\(503\) | 25.6894 | 1.14543 | 0.572717 | − | 0.819753i | \(-0.305890\pi\) | ||||
0.572717 | + | 0.819753i | \(0.305890\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.8409 | −0.571414 | ||||||||
\(506\) | 27.2139 | 1.20980 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −29.9527 | −1.32894 | ||||||||
\(509\) | −27.1811 | −1.20478 | −0.602390 | − | 0.798202i | \(-0.705785\pi\) | ||||
−0.602390 | + | 0.798202i | \(0.705785\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 44.4112 | 1.96464 | ||||||||
\(512\) | −27.8622 | −1.23135 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −41.0321 | −1.80985 | ||||||||
\(515\) | 11.7697 | 0.518635 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.25124 | −0.186969 | ||||||||
\(518\) | −84.3225 | −3.70492 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.36231 | −0.103594 | ||||||||
\(521\) | −0.901023 | −0.0394745 | −0.0197373 | − | 0.999805i | \(-0.506283\pi\) | ||||
−0.0197373 | + | 0.999805i | \(0.506283\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.0126235 | 0.000551986 0 | 0.000275993 | − | 1.00000i | \(-0.499912\pi\) | ||||
0.000275993 | 1.00000i | \(0.499912\pi\) | ||||||||
\(524\) | 51.3678 | 2.24401 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.1549 | −0.529978 | ||||||||
\(527\) | 13.9175 | 0.606257 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.5723 | 0.459665 | ||||||||
\(530\) | −18.3539 | −0.797242 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 71.5577 | 3.10242 | ||||||||
\(533\) | −0.628902 | −0.0272408 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.4620 | −0.668480 | ||||||||
\(536\) | −8.42842 | −0.364052 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.7618 | 0.463976 | ||||||||
\(539\) | 36.2476 | 1.56129 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.28499 | 0.399193 | 0.199596 | − | 0.979878i | \(-0.436037\pi\) | ||||
0.199596 | + | 0.979878i | \(0.436037\pi\) | |||||||
\(542\) | −31.5630 | −1.35575 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 24.7609 | 1.06162 | ||||||||
\(545\) | 7.88060 | 0.337568 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.6475 | −0.540770 | −0.270385 | − | 0.962752i | \(-0.587151\pi\) | ||||
−0.270385 | + | 0.962752i | \(0.587151\pi\) | |||||||
\(548\) | −27.2633 | −1.16463 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.69678 | −0.200271 | ||||||||
\(551\) | 13.8247 | 0.588951 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.64865 | 0.367778 | ||||||||
\(554\) | 65.0576 | 2.76403 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.07707 | −0.0456777 | ||||||||
\(557\) | 1.89455 | 0.0802747 | 0.0401374 | − | 0.999194i | \(-0.487220\pi\) | ||||
0.0401374 | + | 0.999194i | \(0.487220\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.398292 | 0.0168460 | ||||||||
\(560\) | −13.3952 | −0.566050 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 41.5406 | 1.75229 | ||||||||
\(563\) | 39.9171 | 1.68231 | 0.841153 | − | 0.540797i | \(-0.181877\pi\) | ||||
0.841153 | + | 0.540797i | \(0.181877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.01004 | −0.0845629 | ||||||||
\(566\) | −68.1749 | −2.86561 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.22863 | −0.219388 | ||||||||
\(569\) | 12.8214 | 0.537499 | 0.268750 | − | 0.963210i | \(-0.413390\pi\) | ||||
0.268750 | + | 0.963210i | \(0.413390\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.0157 | −1.00503 | −0.502513 | − | 0.864570i | \(-0.667591\pi\) | ||||
−0.502513 | + | 0.864570i | \(0.667591\pi\) | |||||||
\(572\) | −12.4924 | −0.522335 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.84866 | 0.118901 | ||||||||
\(575\) | −5.79416 | −0.241633 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.5046 | −1.18666 | −0.593331 | − | 0.804959i | \(-0.702187\pi\) | ||||
−0.593331 | + | 0.804959i | \(0.702187\pi\) | |||||||
\(578\) | 15.5429 | 0.646499 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.80215 | 0.240921 | ||||||||
\(581\) | 67.1207 | 2.78464 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.1872 | −0.794653 | ||||||||
\(584\) | 9.59820 | 0.397176 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −48.2361 | −1.99261 | ||||||||
\(587\) | 2.40697 | 0.0993462 | 0.0496731 | − | 0.998766i | \(-0.484182\pi\) | ||||
0.0496731 | + | 0.998766i | \(0.484182\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.5867 | −1.09549 | ||||||||
\(590\) | −11.4389 | −0.470930 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22.8136 | 0.937633 | ||||||||
\(593\) | −10.4715 | −0.430013 | −0.215006 | − | 0.976613i | \(-0.568977\pi\) | ||||
−0.215006 | + | 0.976613i | \(0.568977\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.0269 | 0.616042 | ||||||||
\(596\) | 34.0058 | 1.39293 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −27.7759 | −1.13584 | ||||||||
\(599\) | −9.28858 | −0.379521 | −0.189760 | − | 0.981830i | \(-0.560771\pi\) | ||||
−0.189760 | + | 0.981830i | \(0.560771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.0877 | −0.737814 | −0.368907 | − | 0.929466i | \(-0.620268\pi\) | ||||
−0.368907 | + | 0.929466i | \(0.620268\pi\) | |||||||
\(602\) | −1.80410 | −0.0735295 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 55.7948 | 2.27026 | ||||||||
\(605\) | 6.08997 | 0.247593 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.08445 | −0.165783 | −0.0828914 | − | 0.996559i | \(-0.526415\pi\) | ||||
−0.0828914 | + | 0.996559i | \(0.526415\pi\) | |||||||
\(608\) | −47.3008 | −1.91830 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.5423 | −0.831733 | ||||||||
\(611\) | 4.33904 | 0.175539 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.2800 | 0.819101 | 0.409551 | − | 0.912287i | \(-0.365685\pi\) | ||||
0.409551 | + | 0.912287i | \(0.365685\pi\) | |||||||
\(614\) | −1.87203 | −0.0755490 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.1861 | 0.450702 | ||||||||
\(617\) | −3.23902 | −0.130398 | −0.0651990 | − | 0.997872i | \(-0.520768\pi\) | ||||
−0.0651990 | + | 0.997872i | \(0.520768\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.62101 | 0.105347 | 0.0526737 | − | 0.998612i | \(-0.483226\pi\) | ||||
0.0526737 | + | 0.998612i | \(0.483226\pi\) | |||||||
\(620\) | −11.1583 | −0.448129 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.32330 | −0.253541 | ||||||||
\(623\) | 4.83304 | 0.193632 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −12.8843 | −0.514960 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 29.2569 | 1.16748 | ||||||||
\(629\) | −25.5926 | −1.02044 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.84085 | −0.192711 | −0.0963557 | − | 0.995347i | \(-0.530719\pi\) | ||||
−0.0963557 | + | 0.995347i | \(0.530719\pi\) | |||||||
\(632\) | 1.86916 | 0.0743511 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.30278 | 0.170885 | ||||||||
\(635\) | 12.0158 | 0.476831 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −36.9962 | −1.46584 | ||||||||
\(638\) | 10.9321 | 0.432806 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.10252 | −0.320280 | ||||||||
\(641\) | 41.4377 | 1.63669 | 0.818344 | − | 0.574728i | \(-0.194892\pi\) | ||||
0.818344 | + | 0.574728i | \(0.194892\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.2789 | −1.03634 | −0.518168 | − | 0.855279i | \(-0.673386\pi\) | ||||
−0.518168 | + | 0.855279i | \(0.673386\pi\) | |||||||
\(644\) | 69.8065 | 2.75076 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 39.1434 | 1.54007 | ||||||||
\(647\) | −32.8680 | −1.29218 | −0.646088 | − | 0.763263i | \(-0.723596\pi\) | ||||
−0.646088 | + | 0.763263i | \(0.723596\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.9582 | −0.469401 | ||||||||
\(650\) | 4.79378 | 0.188028 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.73115 | 0.146123 | ||||||||
\(653\) | −34.0840 | −1.33381 | −0.666904 | − | 0.745143i | \(-0.732381\pi\) | ||||
−0.666904 | + | 0.745143i | \(0.732381\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.6066 | −0.805165 | ||||||||
\(656\) | −0.770710 | −0.0300912 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −19.6540 | −0.766195 | ||||||||
\(659\) | 22.3303 | 0.869864 | 0.434932 | − | 0.900463i | \(-0.356772\pi\) | ||||
0.434932 | + | 0.900463i | \(0.356772\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.90059 | −0.190611 | −0.0953055 | − | 0.995448i | \(-0.530383\pi\) | ||||
−0.0953055 | + | 0.995448i | \(0.530383\pi\) | |||||||
\(662\) | 26.2830 | 1.02152 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.5062 | 0.562950 | ||||||||
\(665\) | −28.7059 | −1.11317 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.4863 | 0.522193 | ||||||||
\(668\) | 1.38561 | 0.0536110 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17.1036 | 0.660768 | ||||||||
\(671\) | −21.4750 | −0.829032 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.8142 | 0.686689 | 0.343344 | − | 0.939210i | \(-0.388440\pi\) | ||||
0.343344 | + | 0.939210i | \(0.388440\pi\) | |||||||
\(674\) | −57.5318 | −2.21604 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.6558 | −0.755992 | ||||||||
\(677\) | 2.59037 | 0.0995561 | 0.0497780 | − | 0.998760i | \(-0.484149\pi\) | ||||
0.0497780 | + | 0.998760i | \(0.484149\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.6788 | 1.02384 | ||||||||
\(680\) | 3.24763 | 0.124541 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −21.0239 | −0.805046 | ||||||||
\(683\) | −24.9388 | −0.954257 | −0.477128 | − | 0.878834i | \(-0.658322\pi\) | ||||
−0.477128 | + | 0.878834i | \(0.658322\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.9369 | 0.417876 | ||||||||
\(686\) | 95.8678 | 3.66025 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.488101 | 0.0186087 | ||||||||
\(689\) | 19.5835 | 0.746072 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.1377 | −1.10845 | −0.554226 | − | 0.832366i | \(-0.686986\pi\) | ||||
−0.554226 | + | 0.832366i | \(0.686986\pi\) | |||||||
\(692\) | −34.9915 | −1.33018 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36.1682 | −1.37293 | ||||||||
\(695\) | 0.432073 | 0.0163894 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.864593 | 0.0327488 | ||||||||
\(698\) | −53.6893 | −2.03217 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.0477 | −0.455362 | ||||||||
\(701\) | 37.5559 | 1.41847 | 0.709233 | − | 0.704974i | \(-0.249042\pi\) | ||||
0.709233 | + | 0.704974i | \(0.249042\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.8896 | 1.84391 | ||||||||
\(704\) | −25.1211 | −0.946786 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.5813 | 1.22621 | ||||||||
\(707\) | −62.0607 | −2.33403 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0916 | −0.604334 | −0.302167 | − | 0.953255i | \(-0.597710\pi\) | ||||
−0.302167 | + | 0.953255i | \(0.597710\pi\) | |||||||
\(710\) | 10.6103 | 0.398198 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.04452 | 0.0391451 | ||||||||
\(713\) | −25.9360 | −0.971312 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.01144 | 0.187417 | ||||||||
\(716\) | −22.9977 | −0.859464 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.1995 | −0.380644 | ||||||||
\(719\) | 3.86290 | 0.144062 | 0.0720310 | − | 0.997402i | \(-0.477052\pi\) | ||||
0.0720310 | + | 0.997402i | \(0.477052\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 56.8834 | 2.11845 | ||||||||
\(722\) | −34.5029 | −1.28406 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −26.1005 | −0.970017 | ||||||||
\(725\) | −2.32757 | −0.0864439 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.4042 | −0.385871 | −0.192935 | − | 0.981211i | \(-0.561801\pi\) | ||||
−0.192935 | + | 0.981211i | \(0.561801\pi\) | |||||||
\(728\) | −11.4172 | −0.423148 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.4774 | −0.720890 | ||||||||
\(731\) | −0.547558 | −0.0202522 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.9908 | −0.627569 | −0.313784 | − | 0.949494i | \(-0.601597\pi\) | ||||
−0.313784 | + | 0.949494i | \(0.601597\pi\) | |||||||
\(734\) | −49.6587 | −1.83293 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −46.1432 | −1.70086 | ||||||||
\(737\) | 17.8801 | 0.658623 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.1630 | 0.373854 | 0.186927 | − | 0.982374i | \(-0.440147\pi\) | ||||
0.186927 | + | 0.982374i | \(0.440147\pi\) | |||||||
\(740\) | 20.5187 | 0.754283 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −88.7050 | −3.25646 | ||||||||
\(743\) | 25.6666 | 0.941617 | 0.470809 | − | 0.882235i | \(-0.343962\pi\) | ||||
0.470809 | + | 0.882235i | \(0.343962\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.6417 | −0.499793 | ||||||||
\(746\) | −22.2318 | −0.813964 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.1742 | 0.627950 | ||||||||
\(749\) | −74.7284 | −2.73051 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.88134 | −0.0686510 | −0.0343255 | − | 0.999411i | \(-0.510928\pi\) | ||||
−0.0343255 | + | 0.999411i | \(0.510928\pi\) | |||||||
\(752\) | 5.31744 | 0.193907 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.1579 | −0.406346 | ||||||||
\(755\) | −22.3825 | −0.814582 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.6427 | 0.423161 | 0.211580 | − | 0.977361i | \(-0.432139\pi\) | ||||
0.211580 | + | 0.977361i | \(0.432139\pi\) | |||||||
\(758\) | 43.7691 | 1.58977 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.20396 | −0.225041 | ||||||||
\(761\) | −20.9113 | −0.758035 | −0.379017 | − | 0.925390i | \(-0.623738\pi\) | ||||
−0.379017 | + | 0.925390i | \(0.623738\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.0872 | 1.37885 | ||||||||
\(764\) | 11.8134 | 0.427395 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25.1236 | 0.907753 | ||||||||
\(767\) | 12.2052 | 0.440704 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.0699 | −0.759800 | −0.379900 | − | 0.925028i | \(-0.624042\pi\) | ||||
−0.379900 | + | 0.925028i | \(0.624042\pi\) | |||||||
\(770\) | −22.6997 | −0.818040 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.70395 | 0.133308 | ||||||||
\(773\) | −4.26541 | −0.153416 | −0.0767080 | − | 0.997054i | \(-0.524441\pi\) | ||||
−0.0767080 | + | 0.997054i | \(0.524441\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.47624 | 0.160791 | ||||||||
\(776\) | 5.76584 | 0.206982 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.0480 | −0.898015 | ||||||||
\(779\) | −1.65163 | −0.0591759 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.0921 | 0.396905 | ||||||||
\(782\) | 38.1854 | 1.36551 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −45.3383 | −1.61923 | ||||||||
\(785\) | −11.7366 | −0.418898 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.9571 | 1.67384 | 0.836920 | − | 0.547325i | \(-0.184354\pi\) | ||||
0.836920 | + | 0.547325i | \(0.184354\pi\) | |||||||
\(788\) | 11.2503 | 0.400774 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.79303 | −0.134950 | ||||||||
\(791\) | −9.71458 | −0.345411 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.9185 | 0.778349 | ||||||||
\(794\) | −77.3809 | −2.74615 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.1482 | 0.643245 | ||||||||
\(797\) | 36.9401 | 1.30849 | 0.654243 | − | 0.756284i | \(-0.272987\pi\) | ||||
0.654243 | + | 0.756284i | \(0.272987\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.96517 | −0.211033 | ||||||||
\(800\) | 7.96375 | 0.281561 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.07813 | 0.108692 | ||||||||
\(803\) | −20.3617 | −0.718549 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.0034 | −0.986990 | ||||||||
\(806\) | 21.4581 | 0.755829 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.4126 | −0.471855 | ||||||||
\(809\) | −17.3676 | −0.610613 | −0.305306 | − | 0.952254i | \(-0.598759\pi\) | ||||
−0.305306 | + | 0.952254i | \(0.598759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.5363 | −1.56388 | −0.781941 | − | 0.623352i | \(-0.785770\pi\) | ||||
−0.781941 | + | 0.623352i | \(0.785770\pi\) | |||||||
\(812\) | 28.0420 | 0.984081 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 38.6603 | 1.35504 | ||||||||
\(815\) | −1.49678 | −0.0524299 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.04600 | 0.0365950 | ||||||||
\(818\) | −68.6717 | −2.40105 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.693183 | −0.0242070 | ||||||||
\(821\) | 17.7581 | 0.619761 | 0.309880 | − | 0.950776i | \(-0.399711\pi\) | ||||
0.309880 | + | 0.950776i | \(0.399711\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.7787 | −0.968304 | −0.484152 | − | 0.874984i | \(-0.660872\pi\) | ||||
−0.484152 | + | 0.874984i | \(0.660872\pi\) | |||||||
\(824\) | 12.2937 | 0.428272 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −55.2844 | −1.92359 | ||||||||
\(827\) | 28.8725 | 1.00400 | 0.501998 | − | 0.864869i | \(-0.332599\pi\) | ||||
0.501998 | + | 0.864869i | \(0.332599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.4440 | 1.43941 | 0.719704 | − | 0.694281i | \(-0.244277\pi\) | ||||
0.719704 | + | 0.694281i | \(0.244277\pi\) | |||||||
\(830\) | −29.4371 | −1.02178 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 25.6399 | 0.888904 | ||||||||
\(833\) | 50.8611 | 1.76223 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.555849 | −0.0192360 | ||||||||
\(836\) | −32.8079 | −1.13468 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.0507 | −0.761730 | ||||||||
\(839\) | 15.0790 | 0.520583 | 0.260292 | − | 0.965530i | \(-0.416181\pi\) | ||||
0.260292 | + | 0.965530i | \(0.416181\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.5824 | −0.813186 | ||||||||
\(842\) | −2.71948 | −0.0937193 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 34.9118 | 1.20172 | ||||||||
\(845\) | 7.88506 | 0.271254 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.4331 | 1.01133 | ||||||||
\(848\) | 23.9993 | 0.824139 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.59033 | −0.226046 | ||||||||
\(851\) | 47.6931 | 1.63490 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.1724 | 1.23852 | 0.619260 | − | 0.785186i | \(-0.287433\pi\) | ||||
0.619260 | + | 0.785186i | \(0.287433\pi\) | |||||||
\(854\) | −99.2816 | −3.39735 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.1504 | −0.552009 | ||||||||
\(857\) | −14.1138 | −0.482117 | −0.241058 | − | 0.970511i | \(-0.577495\pi\) | ||||
−0.241058 | + | 0.970511i | \(0.577495\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.04904 | −0.104032 | −0.0520159 | − | 0.998646i | \(-0.516565\pi\) | ||||
−0.0520159 | + | 0.998646i | \(0.516565\pi\) | |||||||
\(860\) | 0.439002 | 0.0149699 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.03582 | −0.171521 | ||||||||
\(863\) | 44.3700 | 1.51037 | 0.755187 | − | 0.655510i | \(-0.227546\pi\) | ||||
0.755187 | + | 0.655510i | \(0.227546\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0371 | 0.477276 | ||||||||
\(866\) | −66.5356 | −2.26097 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −53.9285 | −1.83045 | ||||||||
\(869\) | −3.96525 | −0.134512 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.2494 | −0.618358 | ||||||||
\(872\) | 8.23146 | 0.278752 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −72.9457 | −2.46742 | ||||||||
\(875\) | 4.83304 | 0.163386 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.0474 | −1.31854 | −0.659268 | − | 0.751908i | \(-0.729134\pi\) | ||||
−0.659268 | + | 0.751908i | \(0.729134\pi\) | |||||||
\(878\) | 17.6510 | 0.595693 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.14144 | 0.207028 | ||||||||
\(881\) | −8.96712 | −0.302110 | −0.151055 | − | 0.988525i | \(-0.548267\pi\) | ||||
−0.151055 | + | 0.988525i | \(0.548267\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.30062 | 0.212033 | 0.106016 | − | 0.994364i | \(-0.466190\pi\) | ||||
0.106016 | + | 0.994364i | \(0.466190\pi\) | |||||||
\(884\) | −17.5289 | −0.589560 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −57.6343 | −1.93626 | ||||||||
\(887\) | −51.6559 | −1.73443 | −0.867217 | − | 0.497931i | \(-0.834093\pi\) | ||||
−0.867217 | + | 0.497931i | \(0.834093\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 58.0726 | 1.94769 | ||||||||
\(890\) | −2.11962 | −0.0710498 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21.8520 | −0.731660 | ||||||||
\(893\) | 11.3953 | 0.381329 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.22570 | 0.308381 | ||||||||
\(896\) | −39.1598 | −1.30824 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −42.9764 | −1.43414 | ||||||||
\(899\) | −10.4188 | −0.347486 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.9227 | −0.896926 | ||||||||
\(902\) | −1.30606 | −0.0434870 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.09953 | −0.0698292 | ||||||||
\(905\) | 10.4704 | 0.348048 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.5492 | −1.01437 | −0.507185 | − | 0.861837i | \(-0.669314\pi\) | ||||
−0.507185 | + | 0.861837i | \(0.669314\pi\) | |||||||
\(908\) | 54.4742 | 1.80779 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 23.1685 | 0.768029 | ||||||||
\(911\) | −13.9379 | −0.461784 | −0.230892 | − | 0.972979i | \(-0.574164\pi\) | ||||
−0.230892 | + | 0.972979i | \(0.574164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.7736 | −1.01846 | ||||||||
\(914\) | 58.9686 | 1.95051 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −49.9082 | −1.64901 | ||||||||
\(917\) | −99.5923 | −3.28883 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.5909 | 0.712217 | 0.356108 | − | 0.934445i | \(-0.384103\pi\) | ||||
0.356108 | + | 0.934445i | \(0.384103\pi\) | |||||||
\(920\) | −6.05213 | −0.199533 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.89150 | 0.226959 | ||||||||
\(923\) | −11.3211 | −0.372640 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.23124 | −0.270641 | ||||||||
\(926\) | 29.3127 | 0.963275 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −18.5362 | −0.608481 | ||||||||
\(929\) | 34.8126 | 1.14216 | 0.571082 | − | 0.820893i | \(-0.306524\pi\) | ||||
0.571082 | + | 0.820893i | \(0.306524\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −97.1601 | −3.18429 | ||||||||
\(932\) | −38.2135 | −1.25172 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −41.4654 | −1.35679 | ||||||||
\(935\) | −6.88955 | −0.225312 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.3529 | 0.958918 | 0.479459 | − | 0.877564i | \(-0.340833\pi\) | ||||
0.479459 | + | 0.877564i | \(0.340833\pi\) | |||||||
\(938\) | 82.6622 | 2.69901 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.78255 | 0.155989 | ||||||||
\(941\) | −39.9726 | −1.30307 | −0.651534 | − | 0.758619i | \(-0.725874\pi\) | ||||
−0.651534 | + | 0.758619i | \(0.725874\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.61121 | −0.0524683 | ||||||||
\(944\) | 14.9573 | 0.486819 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.827145 | 0.0268928 | ||||||||
\(947\) | −57.0642 | −1.85434 | −0.927168 | − | 0.374646i | \(-0.877764\pi\) | ||||
−0.927168 | + | 0.374646i | \(0.877764\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.7822 | 0.674620 | ||||||||
\(950\) | 12.5895 | 0.408458 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 15.6959 | 0.508707 | ||||||||
\(953\) | −47.9488 | −1.55321 | −0.776607 | − | 0.629985i | \(-0.783061\pi\) | ||||
−0.776607 | + | 0.629985i | \(0.783061\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.73905 | −0.153352 | ||||||||
\(956\) | −18.1273 | −0.586278 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 55.5488 | 1.79470 | ||||||||
\(959\) | 52.8583 | 1.70688 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.9633 | −0.353655 | ||||||||
\(962\) | −39.4587 | −1.27220 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.0431 | 0.323467 | ||||||||
\(965\) | −1.48587 | −0.0478317 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.9873 | −0.739222 | −0.369611 | − | 0.929187i | \(-0.620509\pi\) | ||||
−0.369611 | + | 0.929187i | \(0.620509\pi\) | |||||||
\(968\) | 6.36111 | 0.204454 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.7005 | −0.375679 | ||||||||
\(971\) | −4.86938 | −0.156266 | −0.0781330 | − | 0.996943i | \(-0.524896\pi\) | ||||
−0.0781330 | + | 0.996943i | \(0.524896\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.08822 | 0.0669454 | ||||||||
\(974\) | −61.1723 | −1.96009 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.8608 | 0.859794 | ||||||||
\(977\) | −5.28623 | −0.169121 | −0.0845607 | − | 0.996418i | \(-0.526949\pi\) | ||||
−0.0845607 | + | 0.996418i | \(0.526949\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.21586 | −0.0708191 | ||||||||
\(980\) | −40.7777 | −1.30259 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −58.4458 | −1.86508 | ||||||||
\(983\) | −21.4830 | −0.685202 | −0.342601 | − | 0.939481i | \(-0.611308\pi\) | ||||
−0.342601 | + | 0.939481i | \(0.611308\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.51312 | −0.143800 | ||||||||
\(986\) | 15.3395 | 0.488508 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 33.4855 | 1.06532 | ||||||||
\(989\) | 1.02040 | 0.0324470 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.9796 | −1.26999 | −0.634997 | − | 0.772514i | \(-0.718999\pi\) | ||||
−0.634997 | + | 0.772514i | \(0.718999\pi\) | |||||||
\(992\) | 35.6476 | 1.13181 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 51.2800 | 1.62650 | ||||||||
\(995\) | −7.28028 | −0.230800 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.8157 | −1.29265 | −0.646323 | − | 0.763064i | \(-0.723694\pi\) | ||||
−0.646323 | + | 0.763064i | \(0.723694\pi\) | |||||||
\(998\) | −69.8320 | −2.21049 | ||||||||
\(999\) | 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 | 4005.2.a.o.1.1 | 7 | ||
3.2 | odd | 2 | 445.2.a.f.1.7 | ✓ | 7 | ||
12.11 | even | 2 | 7120.2.a.bj.1.7 | 7 | |||
15.14 | odd | 2 | 2225.2.a.k.1.1 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
445.2.a.f.1.7 | ✓ | 7 | 3.2 | odd | 2 | ||
2225.2.a.k.1.1 | 7 | 15.14 | odd | 2 | |||
4005.2.a.o.1.1 | 7 | 1.1 | even | 1 | trivial | ||
7120.2.a.bj.1.7 | 7 | 12.11 | even | 2 |