Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7605,2,Mod(1,7605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, 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("7605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7605.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: | \(60.7262307372\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13824.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 195) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.12603\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7605.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.12603 | 0.796225 | 0.398113 | − | 0.917337i | \(-0.369665\pi\) | ||||
0.398113 | + | 0.917337i | \(0.369665\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.732051 | −0.366025 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.85808 | 1.08025 | 0.540127 | − | 0.841584i | \(-0.318376\pi\) | ||||
0.540127 | + | 0.841584i | \(0.318376\pi\) | |||||||
\(8\) | −3.07638 | −1.08766 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.12603 | −0.356083 | ||||||||
\(11\) | −3.07638 | −0.927563 | −0.463781 | − | 0.885950i | \(-0.653508\pi\) | ||||
−0.463781 | + | 0.885950i | \(0.653508\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.21829 | 0.860125 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | −0.500000 | ||||||||
\(17\) | 1.95035 | 0.473028 | 0.236514 | − | 0.971628i | \(-0.423995\pi\) | ||||
0.236514 | + | 0.971628i | \(0.423995\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.42071 | −1.70243 | −0.851213 | − | 0.524820i | \(-0.824133\pi\) | ||||
−0.851213 | + | 0.524820i | \(0.824133\pi\) | |||||||
\(20\) | 0.732051 | 0.163692 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.46410 | −0.738549 | ||||||||
\(23\) | 8.79254 | 1.83337 | 0.916686 | − | 0.399608i | \(-0.130854\pi\) | ||||
0.916686 | + | 0.399608i | \(0.130854\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.09226 | −0.395400 | ||||||||
\(29\) | 6.68240 | 1.24089 | 0.620445 | − | 0.784250i | \(-0.286952\pi\) | ||||
0.620445 | + | 0.784250i | \(0.286952\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.15276 | 0.566252 | 0.283126 | − | 0.959083i | \(-0.408629\pi\) | ||||
0.283126 | + | 0.959083i | \(0.408629\pi\) | |||||||
\(32\) | 3.90069 | 0.689551 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.19615 | 0.376637 | ||||||||
\(35\) | −2.85808 | −0.483104 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.25207 | −1.35663 | −0.678316 | − | 0.734771i | \(-0.737290\pi\) | ||||
−0.678316 | + | 0.734771i | \(0.737290\pi\) | |||||||
\(38\) | −8.35596 | −1.35551 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.07638 | 0.486418 | ||||||||
\(41\) | −3.32218 | −0.518838 | −0.259419 | − | 0.965765i | \(-0.583531\pi\) | ||||
−0.259419 | + | 0.965765i | \(0.583531\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.54674 | 1.45586 | 0.727932 | − | 0.685649i | \(-0.240482\pi\) | ||||
0.727932 | + | 0.685649i | \(0.240482\pi\) | |||||||
\(44\) | 2.25207 | 0.339512 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.90069 | 1.45978 | ||||||||
\(47\) | 1.79759 | 0.262205 | 0.131103 | − | 0.991369i | \(-0.458148\pi\) | ||||
0.131103 | + | 0.991369i | \(0.458148\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.16864 | 0.166949 | ||||||||
\(50\) | 1.12603 | 0.159245 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.6569 | −1.46384 | −0.731918 | − | 0.681393i | \(-0.761375\pi\) | ||||
−0.731918 | + | 0.681393i | \(0.761375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.07638 | 0.414819 | ||||||||
\(56\) | −8.79254 | −1.17495 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.52460 | 0.988028 | ||||||||
\(59\) | −4.81805 | −0.627257 | −0.313629 | − | 0.949546i | \(-0.601545\pi\) | ||||
−0.313629 | + | 0.949546i | \(0.601545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.26795 | −0.802529 | −0.401264 | − | 0.915962i | \(-0.631429\pi\) | ||||
−0.401264 | + | 0.915962i | \(0.631429\pi\) | |||||||
\(62\) | 3.55011 | 0.450864 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.39230 | 1.04904 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.87855 | −0.718179 | −0.359090 | − | 0.933303i | \(-0.616913\pi\) | ||||
−0.359090 | + | 0.933303i | \(0.616913\pi\) | |||||||
\(68\) | −1.42775 | −0.173140 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.21829 | −0.384660 | ||||||||
\(71\) | 10.2993 | 1.22230 | 0.611148 | − | 0.791516i | \(-0.290708\pi\) | ||||
0.611148 | + | 0.791516i | \(0.290708\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.1101 | −1.30034 | −0.650172 | − | 0.759787i | \(-0.725303\pi\) | ||||
−0.650172 | + | 0.759787i | \(0.725303\pi\) | |||||||
\(74\) | −9.29209 | −1.08018 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.43233 | 0.623131 | ||||||||
\(77\) | −8.79254 | −1.00200 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.0968 | −1.24849 | −0.624246 | − | 0.781228i | \(-0.714594\pi\) | ||||
−0.624246 | + | 0.781228i | \(0.714594\pi\) | |||||||
\(80\) | 2.00000 | 0.223607 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.74089 | −0.413112 | ||||||||
\(83\) | 6.97707 | 0.765833 | 0.382916 | − | 0.923783i | \(-0.374920\pi\) | ||||
0.382916 | + | 0.923783i | \(0.374920\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.95035 | −0.211545 | ||||||||
\(86\) | 10.7499 | 1.15920 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.46410 | 1.00888 | ||||||||
\(89\) | 0.0930509 | 0.00986338 | 0.00493169 | − | 0.999988i | \(-0.498430\pi\) | ||||
0.00493169 | + | 0.999988i | \(0.498430\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.43659 | −0.671061 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.02414 | 0.208775 | ||||||||
\(95\) | 7.42071 | 0.761348 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.79759 | −0.487121 | −0.243561 | − | 0.969886i | \(-0.578316\pi\) | ||||
−0.243561 | + | 0.969886i | \(0.578316\pi\) | |||||||
\(98\) | 1.31593 | 0.132929 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.732051 | −0.0732051 | ||||||||
\(101\) | −2.79254 | −0.277869 | −0.138934 | − | 0.990302i | \(-0.544368\pi\) | ||||
−0.138934 | + | 0.990302i | \(0.544368\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.35395 | 0.823139 | 0.411570 | − | 0.911378i | \(-0.364981\pi\) | ||||
0.411570 | + | 0.911378i | \(0.364981\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | −6.35059 | −0.613934 | −0.306967 | − | 0.951720i | \(-0.599314\pi\) | ||||
−0.306967 | + | 0.951720i | \(0.599314\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.7996 | −1.13020 | −0.565098 | − | 0.825024i | \(-0.691162\pi\) | ||||
−0.565098 | + | 0.825024i | \(0.691162\pi\) | |||||||
\(110\) | 3.46410 | 0.330289 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.71617 | −0.540127 | ||||||||
\(113\) | −3.46410 | −0.325875 | −0.162938 | − | 0.986636i | \(-0.552097\pi\) | ||||
−0.162938 | + | 0.986636i | \(0.552097\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.79254 | −0.819909 | ||||||||
\(116\) | −4.89185 | −0.454197 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.42529 | −0.499438 | ||||||||
\(119\) | 5.57425 | 0.510991 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.53590 | −0.139627 | ||||||||
\(122\) | −7.05791 | −0.638994 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.30798 | −0.207263 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.9720 | −1.32855 | −0.664276 | − | 0.747487i | \(-0.731260\pi\) | ||||
−0.664276 | + | 0.747487i | \(0.731260\pi\) | |||||||
\(128\) | 1.64863 | 0.145719 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.5831 | 0.924649 | 0.462324 | − | 0.886711i | \(-0.347016\pi\) | ||||
0.462324 | + | 0.886711i | \(0.347016\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.2090 | −1.83905 | ||||||||
\(134\) | −6.61944 | −0.571832 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | −8.70654 | −0.743850 | −0.371925 | − | 0.928263i | \(-0.621302\pi\) | ||||
−0.371925 | + | 0.928263i | \(0.621302\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6569 | −0.988724 | −0.494362 | − | 0.869256i | \(-0.664598\pi\) | ||||
−0.494362 | + | 0.869256i | \(0.664598\pi\) | |||||||
\(140\) | 2.09226 | 0.176828 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.5973 | 0.973223 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.68240 | −0.554943 | ||||||||
\(146\) | −12.5104 | −1.03537 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.04093 | 0.496561 | ||||||||
\(149\) | 6.82431 | 0.559070 | 0.279535 | − | 0.960136i | \(-0.409820\pi\) | ||||
0.279535 | + | 0.960136i | \(0.409820\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.6810 | 1.03197 | 0.515984 | − | 0.856598i | \(-0.327426\pi\) | ||||
0.515984 | + | 0.856598i | \(0.327426\pi\) | |||||||
\(152\) | 22.8289 | 1.85167 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.90069 | −0.797820 | ||||||||
\(155\) | −3.15276 | −0.253235 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.98333 | 0.637139 | 0.318569 | − | 0.947900i | \(-0.396798\pi\) | ||||
0.318569 | + | 0.947900i | \(0.396798\pi\) | |||||||
\(158\) | −12.4954 | −0.994081 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.90069 | −0.308377 | ||||||||
\(161\) | 25.1298 | 1.98051 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.3222 | −0.965148 | −0.482574 | − | 0.875855i | \(-0.660298\pi\) | ||||
−0.482574 | + | 0.875855i | \(0.660298\pi\) | |||||||
\(164\) | 2.43201 | 0.189908 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.85641 | 0.609775 | ||||||||
\(167\) | −21.9416 | −1.69789 | −0.848947 | − | 0.528478i | \(-0.822763\pi\) | ||||
−0.848947 | + | 0.528478i | \(0.822763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.19615 | −0.168437 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.98870 | −0.532883 | ||||||||
\(173\) | −15.0506 | −1.14427 | −0.572136 | − | 0.820159i | \(-0.693885\pi\) | ||||
−0.572136 | + | 0.820159i | \(0.693885\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.85808 | 0.216051 | ||||||||
\(176\) | 6.15276 | 0.463781 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.104778 | 0.00785347 | ||||||||
\(179\) | 0.480775 | 0.0359348 | 0.0179674 | − | 0.999839i | \(-0.494280\pi\) | ||||
0.0179674 | + | 0.999839i | \(0.494280\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.85887 | 0.138169 | 0.0690844 | − | 0.997611i | \(-0.477992\pi\) | ||||
0.0690844 | + | 0.997611i | \(0.477992\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −27.0492 | −1.99409 | ||||||||
\(185\) | 8.25207 | 0.606704 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | −0.438763 | ||||||||
\(188\) | −1.31593 | −0.0959738 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.35596 | 0.606205 | ||||||||
\(191\) | −8.71875 | −0.630866 | −0.315433 | − | 0.948948i | \(-0.602150\pi\) | ||||
−0.315433 | + | 0.948948i | \(0.602150\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.45326 | −0.464516 | −0.232258 | − | 0.972654i | \(-0.574611\pi\) | ||||
−0.232258 | + | 0.972654i | \(0.574611\pi\) | |||||||
\(194\) | −5.40224 | −0.387858 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.855504 | −0.0611074 | ||||||||
\(197\) | −11.5930 | −0.825969 | −0.412984 | − | 0.910738i | \(-0.635514\pi\) | ||||
−0.412984 | + | 0.910738i | \(0.635514\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.801382 | 0.0568085 | 0.0284042 | − | 0.999597i | \(-0.490957\pi\) | ||||
0.0284042 | + | 0.999597i | \(0.490957\pi\) | |||||||
\(200\) | −3.07638 | −0.217533 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.14450 | −0.221246 | ||||||||
\(203\) | 19.0988 | 1.34048 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.32218 | 0.232031 | ||||||||
\(206\) | 9.40682 | 0.655404 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.8289 | 1.57911 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.29209 | −0.570851 | −0.285426 | − | 0.958401i | \(-0.592135\pi\) | ||||
−0.285426 | + | 0.958401i | \(0.592135\pi\) | |||||||
\(212\) | 7.80138 | 0.535801 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.15097 | −0.488830 | ||||||||
\(215\) | −9.54674 | −0.651082 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.01084 | 0.611696 | ||||||||
\(218\) | −13.2867 | −0.899890 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.25207 | −0.151834 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.7614 | 0.854563 | 0.427282 | − | 0.904119i | \(-0.359471\pi\) | ||||
0.427282 | + | 0.904119i | \(0.359471\pi\) | |||||||
\(224\) | 11.1485 | 0.744890 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.90069 | −0.259470 | ||||||||
\(227\) | −17.1114 | −1.13572 | −0.567860 | − | 0.823125i | \(-0.692229\pi\) | ||||
−0.567860 | + | 0.823125i | \(0.692229\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.39993 | 0.422919 | 0.211460 | − | 0.977387i | \(-0.432178\pi\) | ||||
0.211460 | + | 0.977387i | \(0.432178\pi\) | |||||||
\(230\) | −9.90069 | −0.652832 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −20.5576 | −1.34967 | ||||||||
\(233\) | −0.671557 | −0.0439952 | −0.0219976 | − | 0.999758i | \(-0.507003\pi\) | ||||
−0.0219976 | + | 0.999758i | \(0.507003\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.79759 | −0.117262 | ||||||||
\(236\) | 3.52706 | 0.229592 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.27679 | 0.406864 | ||||||||
\(239\) | 7.12983 | 0.461190 | 0.230595 | − | 0.973050i | \(-0.425933\pi\) | ||||
0.230595 | + | 0.973050i | \(0.425933\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.9383 | −1.73525 | −0.867623 | − | 0.497223i | \(-0.834353\pi\) | ||||
−0.867623 | + | 0.497223i | \(0.834353\pi\) | |||||||
\(242\) | −1.72947 | −0.111175 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.58846 | 0.293746 | ||||||||
\(245\) | −1.16864 | −0.0746617 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −9.69907 | −0.615892 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.12603 | −0.0712165 | ||||||||
\(251\) | 11.6480 | 0.735218 | 0.367609 | − | 0.929980i | \(-0.380176\pi\) | ||||
0.367609 | + | 0.929980i | \(0.380176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.0492 | −1.70057 | ||||||||
\(254\) | −16.8590 | −1.05783 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.9282 | −0.933013 | ||||||||
\(257\) | 7.27879 | 0.454038 | 0.227019 | − | 0.973890i | \(-0.427102\pi\) | ||||
0.227019 | + | 0.973890i | \(0.427102\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.5851 | −1.46551 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.9169 | 0.736229 | ||||||||
\(263\) | −23.9277 | −1.47545 | −0.737724 | − | 0.675103i | \(-0.764099\pi\) | ||||
−0.737724 | + | 0.675103i | \(0.764099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.6569 | 0.654647 | ||||||||
\(266\) | −23.8820 | −1.46430 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.30340 | 0.262872 | ||||||||
\(269\) | −4.38147 | −0.267143 | −0.133571 | − | 0.991039i | \(-0.542645\pi\) | ||||
−0.133571 | + | 0.991039i | \(0.542645\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.48825 | 0.151150 | 0.0755751 | − | 0.997140i | \(-0.475921\pi\) | ||||
0.0755751 | + | 0.997140i | \(0.475921\pi\) | |||||||
\(272\) | −3.90069 | −0.236514 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.80385 | −0.592272 | ||||||||
\(275\) | −3.07638 | −0.185513 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.7061 | −1.30419 | −0.652096 | − | 0.758137i | \(-0.726110\pi\) | ||||
−0.652096 | + | 0.758137i | \(0.726110\pi\) | |||||||
\(278\) | −13.1260 | −0.787247 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.79254 | 0.525455 | ||||||||
\(281\) | 29.7270 | 1.77336 | 0.886682 | − | 0.462379i | \(-0.153004\pi\) | ||||
0.886682 | + | 0.462379i | \(0.153004\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.9995 | 1.66440 | 0.832200 | − | 0.554476i | \(-0.187081\pi\) | ||||
0.832200 | + | 0.554476i | \(0.187081\pi\) | |||||||
\(284\) | −7.53958 | −0.447392 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.49508 | −0.560477 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.1962 | −0.776244 | ||||||||
\(290\) | −7.52460 | −0.441859 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.13319 | 0.475959 | ||||||||
\(293\) | 16.9586 | 0.990732 | 0.495366 | − | 0.868684i | \(-0.335034\pi\) | ||||
0.495366 | + | 0.868684i | \(0.335034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.81805 | 0.280518 | ||||||||
\(296\) | 25.3865 | 1.47556 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.68440 | 0.445145 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.2854 | 1.57270 | ||||||||
\(302\) | 14.2793 | 0.821679 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.8414 | 0.851213 | ||||||||
\(305\) | 6.26795 | 0.358902 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.6072 | −0.890752 | −0.445376 | − | 0.895344i | \(-0.646930\pi\) | ||||
−0.445376 | + | 0.895344i | \(0.646930\pi\) | |||||||
\(308\) | 6.43659 | 0.366759 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.55011 | −0.201632 | ||||||||
\(311\) | 24.9941 | 1.41728 | 0.708642 | − | 0.705568i | \(-0.249308\pi\) | ||||
0.708642 | + | 0.705568i | \(0.249308\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.16117 | 0.0656331 | 0.0328166 | − | 0.999461i | \(-0.489552\pi\) | ||||
0.0328166 | + | 0.999461i | \(0.489552\pi\) | |||||||
\(314\) | 8.98949 | 0.507306 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.12345 | 0.456980 | ||||||||
\(317\) | 8.62570 | 0.484467 | 0.242234 | − | 0.970218i | \(-0.422120\pi\) | ||||
0.242234 | + | 0.970218i | \(0.422120\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.5576 | −1.15100 | ||||||||
\(320\) | −8.39230 | −0.469144 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 28.2970 | 1.57693 | ||||||||
\(323\) | −14.4729 | −0.805296 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13.8752 | −0.768475 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.2203 | 0.564321 | ||||||||
\(329\) | 5.13766 | 0.283248 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.6227 | 1.40835 | 0.704174 | − | 0.710027i | \(-0.251317\pi\) | ||||
0.704174 | + | 0.710027i | \(0.251317\pi\) | |||||||
\(332\) | −5.10757 | −0.280314 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.7070 | −1.35191 | ||||||||
\(335\) | 5.87855 | 0.321179 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.1770 | 1.09911 | 0.549556 | − | 0.835457i | \(-0.314797\pi\) | ||||
0.549556 | + | 0.835457i | \(0.314797\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.42775 | 0.0774307 | ||||||||
\(341\) | −9.69907 | −0.525234 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.6665 | −0.899907 | ||||||||
\(344\) | −29.3694 | −1.58349 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.9474 | −0.911099 | ||||||||
\(347\) | −24.1937 | −1.29879 | −0.649393 | − | 0.760453i | \(-0.724977\pi\) | ||||
−0.649393 | + | 0.760453i | \(0.724977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.6761 | −1.37441 | −0.687206 | − | 0.726463i | \(-0.741163\pi\) | ||||
−0.687206 | + | 0.726463i | \(0.741163\pi\) | |||||||
\(350\) | 3.21829 | 0.172025 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.0000 | −0.639602 | ||||||||
\(353\) | 7.84509 | 0.417552 | 0.208776 | − | 0.977963i | \(-0.433052\pi\) | ||||
0.208776 | + | 0.977963i | \(0.433052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.2993 | −0.546628 | ||||||||
\(356\) | −0.0681180 | −0.00361025 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.541368 | 0.0286122 | ||||||||
\(359\) | −19.7145 | −1.04049 | −0.520245 | − | 0.854017i | \(-0.674160\pi\) | ||||
−0.520245 | + | 0.854017i | \(0.674160\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.0669 | 1.89826 | ||||||||
\(362\) | 2.09315 | 0.110014 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.1101 | 0.581532 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.1761 | −0.583388 | −0.291694 | − | 0.956512i | \(-0.594219\pi\) | ||||
−0.291694 | + | 0.956512i | \(0.594219\pi\) | |||||||
\(368\) | −17.5851 | −0.916686 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.29209 | 0.483073 | ||||||||
\(371\) | −30.4583 | −1.58131 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.75173 | −0.453147 | −0.226574 | − | 0.973994i | \(-0.572752\pi\) | ||||
−0.226574 | + | 0.973994i | \(0.572752\pi\) | |||||||
\(374\) | −6.75620 | −0.349355 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.53006 | −0.285191 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.7696 | −0.964130 | −0.482065 | − | 0.876135i | \(-0.660113\pi\) | ||||
−0.482065 | + | 0.876135i | \(0.660113\pi\) | |||||||
\(380\) | −5.43233 | −0.278673 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.81759 | −0.502312 | ||||||||
\(383\) | 6.07469 | 0.310402 | 0.155201 | − | 0.987883i | \(-0.450397\pi\) | ||||
0.155201 | + | 0.987883i | \(0.450397\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.79254 | 0.448110 | ||||||||
\(386\) | −7.26658 | −0.369859 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.51208 | 0.178299 | ||||||||
\(389\) | 9.66572 | 0.490072 | 0.245036 | − | 0.969514i | \(-0.421200\pi\) | ||||
0.245036 | + | 0.969514i | \(0.421200\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.1485 | 0.867237 | ||||||||
\(392\) | −3.59518 | −0.181584 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.0541 | −0.657657 | ||||||||
\(395\) | 11.0968 | 0.558343 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.3317 | 1.22117 | 0.610585 | − | 0.791950i | \(-0.290934\pi\) | ||||
0.610585 | + | 0.791950i | \(0.290934\pi\) | |||||||
\(398\) | 0.902382 | 0.0452323 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | −0.100000 | ||||||||
\(401\) | −8.89643 | −0.444267 | −0.222133 | − | 0.975016i | \(-0.571302\pi\) | ||||
−0.222133 | + | 0.975016i | \(0.571302\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.04428 | 0.101707 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.5059 | 1.06732 | ||||||||
\(407\) | 25.3865 | 1.25836 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.2887 | −1.39879 | −0.699394 | − | 0.714736i | \(-0.746547\pi\) | ||||
−0.699394 | + | 0.714736i | \(0.746547\pi\) | |||||||
\(410\) | 3.74089 | 0.184749 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.11552 | −0.301290 | ||||||||
\(413\) | −13.7704 | −0.677597 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.97707 | −0.342491 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25.7061 | 1.25733 | ||||||||
\(419\) | −28.8948 | −1.41160 | −0.705801 | − | 0.708411i | \(-0.749413\pi\) | ||||
−0.705801 | + | 0.708411i | \(0.749413\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0134 | −0.585498 | −0.292749 | − | 0.956189i | \(-0.594570\pi\) | ||||
−0.292749 | + | 0.956189i | \(0.594570\pi\) | |||||||
\(422\) | −9.33717 | −0.454526 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 32.7846 | 1.59216 | ||||||||
\(425\) | 1.95035 | 0.0946057 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.9143 | −0.866935 | ||||||||
\(428\) | 4.64895 | 0.224716 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.7499 | −0.518408 | ||||||||
\(431\) | −23.0229 | −1.10898 | −0.554488 | − | 0.832192i | \(-0.687086\pi\) | ||||
−0.554488 | + | 0.832192i | \(0.687086\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.8795 | −1.29174 | −0.645872 | − | 0.763446i | \(-0.723506\pi\) | ||||
−0.645872 | + | 0.763446i | \(0.723506\pi\) | |||||||
\(434\) | 10.1465 | 0.487047 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.63790 | 0.413680 | ||||||||
\(437\) | −65.2469 | −3.12118 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.6544 | −1.51078 | −0.755392 | − | 0.655274i | \(-0.772553\pi\) | ||||
−0.755392 | + | 0.655274i | \(0.772553\pi\) | |||||||
\(440\) | −9.46410 | −0.451183 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.89932 | 0.470331 | 0.235166 | − | 0.971955i | \(-0.424437\pi\) | ||||
0.235166 | + | 0.971955i | \(0.424437\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.0930509 | −0.00441104 | ||||||||
\(446\) | 14.3697 | 0.680425 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 23.9859 | 1.13323 | ||||||||
\(449\) | 15.0083 | 0.708284 | 0.354142 | − | 0.935192i | \(-0.384773\pi\) | ||||
0.354142 | + | 0.935192i | \(0.384773\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.2203 | 0.481255 | ||||||||
\(452\) | 2.53590 | 0.119279 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.2679 | −0.904290 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.0304 | −0.609537 | −0.304768 | − | 0.952427i | \(-0.598579\pi\) | ||||
−0.304768 | + | 0.952427i | \(0.598579\pi\) | |||||||
\(458\) | 7.20653 | 0.336739 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.43659 | 0.300108 | ||||||||
\(461\) | 28.7166 | 1.33746 | 0.668732 | − | 0.743503i | \(-0.266837\pi\) | ||||
0.668732 | + | 0.743503i | \(0.266837\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.460309 | −0.0213924 | −0.0106962 | − | 0.999943i | \(-0.503405\pi\) | ||||
−0.0106962 | + | 0.999943i | \(0.503405\pi\) | |||||||
\(464\) | −13.3648 | −0.620445 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.756195 | −0.0350301 | ||||||||
\(467\) | 34.0634 | 1.57627 | 0.788133 | − | 0.615505i | \(-0.211048\pi\) | ||||
0.788133 | + | 0.615505i | \(0.211048\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.8014 | −0.775816 | ||||||||
\(470\) | −2.02414 | −0.0933668 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14.8222 | 0.682245 | ||||||||
\(473\) | −29.3694 | −1.35041 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.42071 | −0.340485 | ||||||||
\(476\) | −4.08063 | −0.187036 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.02841 | 0.367211 | ||||||||
\(479\) | 30.9311 | 1.41328 | 0.706639 | − | 0.707574i | \(-0.250210\pi\) | ||||
0.706639 | + | 0.707574i | \(0.250210\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −30.3333 | −1.38165 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.12436 | 0.0511071 | ||||||||
\(485\) | 4.79759 | 0.217847 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.5380 | −0.749409 | −0.374704 | − | 0.927144i | \(-0.622256\pi\) | ||||
−0.374704 | + | 0.927144i | \(0.622256\pi\) | |||||||
\(488\) | 19.2826 | 0.872881 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.31593 | −0.0594475 | ||||||||
\(491\) | −18.6824 | −0.843125 | −0.421562 | − | 0.906799i | \(-0.638518\pi\) | ||||
−0.421562 | + | 0.906799i | \(0.638518\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.0330 | 0.586976 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.30551 | −0.283126 | ||||||||
\(497\) | 29.4361 | 1.32039 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.9966 | −0.492277 | −0.246138 | − | 0.969235i | \(-0.579162\pi\) | ||||
−0.246138 | + | 0.969235i | \(0.579162\pi\) | |||||||
\(500\) | 0.732051 | 0.0327383 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.1161 | 0.585399 | ||||||||
\(503\) | 15.9933 | 0.713104 | 0.356552 | − | 0.934275i | \(-0.383952\pi\) | ||||
0.356552 | + | 0.934275i | \(0.383952\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.79254 | 0.124267 | ||||||||
\(506\) | −30.4583 | −1.35404 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.9603 | 0.486284 | ||||||||
\(509\) | −1.42775 | −0.0632840 | −0.0316420 | − | 0.999499i | \(-0.510074\pi\) | ||||
−0.0316420 | + | 0.999499i | \(0.510074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.7537 | −1.40470 | ||||||||
\(512\) | −20.1069 | −0.888608 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.19615 | 0.361517 | ||||||||
\(515\) | −8.35395 | −0.368119 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.53006 | −0.243212 | ||||||||
\(518\) | −26.5576 | −1.16687 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.8172 | −0.517719 | −0.258859 | − | 0.965915i | \(-0.583347\pi\) | ||||
−0.258859 | + | 0.965915i | \(0.583347\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.6126 | 1.25114 | 0.625571 | − | 0.780167i | \(-0.284866\pi\) | ||||
0.625571 | + | 0.780167i | \(0.284866\pi\) | |||||||
\(524\) | −7.74736 | −0.338445 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.9434 | −1.17479 | ||||||||
\(527\) | 6.14896 | 0.267853 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.3088 | 2.36125 | ||||||||
\(530\) | 12.0000 | 0.521247 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.5261 | 0.673140 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.35059 | 0.274560 | ||||||||
\(536\) | 18.0846 | 0.781137 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.93367 | −0.212706 | ||||||||
\(539\) | −3.59518 | −0.154855 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.9315 | 1.45883 | 0.729415 | − | 0.684072i | \(-0.239792\pi\) | ||||
0.729415 | + | 0.684072i | \(0.239792\pi\) | |||||||
\(542\) | 2.80185 | 0.120350 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.60770 | 0.326177 | ||||||||
\(545\) | 11.7996 | 0.505439 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.0276116 | −0.00118059 | −0.000590294 | − | 1.00000i | \(-0.500188\pi\) | ||||
−0.000590294 | 1.00000i | \(0.500188\pi\) | ||||||||
\(548\) | 6.37363 | 0.272268 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.46410 | −0.147710 | ||||||||
\(551\) | −49.5881 | −2.11252 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.7157 | −1.34869 | ||||||||
\(554\) | −24.4417 | −1.03843 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.53343 | 0.361898 | ||||||||
\(557\) | −40.3651 | −1.71032 | −0.855162 | − | 0.518360i | \(-0.826543\pi\) | ||||
−0.855162 | + | 0.518360i | \(0.826543\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 5.71617 | 0.241552 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 33.4736 | 1.41200 | ||||||||
\(563\) | −14.1210 | −0.595129 | −0.297564 | − | 0.954702i | \(-0.596174\pi\) | ||||
−0.297564 | + | 0.954702i | \(0.596174\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.46410 | 0.145736 | ||||||||
\(566\) | 31.5284 | 1.32524 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −31.6844 | −1.32945 | ||||||||
\(569\) | 31.0316 | 1.30091 | 0.650456 | − | 0.759544i | \(-0.274578\pi\) | ||||
0.650456 | + | 0.759544i | \(0.274578\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.6336 | −1.24013 | −0.620065 | − | 0.784551i | \(-0.712894\pi\) | ||||
−0.620065 | + | 0.784551i | \(0.712894\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.6918 | −0.446266 | ||||||||
\(575\) | 8.79254 | 0.366674 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.7788 | 0.740140 | 0.370070 | − | 0.929004i | \(-0.379334\pi\) | ||||
0.370070 | + | 0.929004i | \(0.379334\pi\) | |||||||
\(578\) | −14.8593 | −0.618065 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.89185 | 0.203123 | ||||||||
\(581\) | 19.9410 | 0.827294 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.7846 | 1.35780 | ||||||||
\(584\) | 34.1790 | 1.41434 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.0959 | 0.788846 | ||||||||
\(587\) | −5.56204 | −0.229570 | −0.114785 | − | 0.993390i | \(-0.536618\pi\) | ||||
−0.114785 | + | 0.993390i | \(0.536618\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.3957 | −0.964002 | ||||||||
\(590\) | 5.42529 | 0.223356 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 16.5041 | 0.678316 | ||||||||
\(593\) | 33.4290 | 1.37276 | 0.686382 | − | 0.727241i | \(-0.259198\pi\) | ||||
0.686382 | + | 0.727241i | \(0.259198\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.57425 | −0.228522 | ||||||||
\(596\) | −4.99574 | −0.204634 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.14349 | 0.332734 | 0.166367 | − | 0.986064i | \(-0.446796\pi\) | ||||
0.166367 | + | 0.986064i | \(0.446796\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.1176 | 0.942987 | 0.471494 | − | 0.881869i | \(-0.343715\pi\) | ||||
0.471494 | + | 0.881869i | \(0.343715\pi\) | |||||||
\(602\) | 30.7242 | 1.25223 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.28316 | −0.377726 | ||||||||
\(605\) | 1.53590 | 0.0624431 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.96702 | 0.282783 | 0.141391 | − | 0.989954i | \(-0.454842\pi\) | ||||
0.141391 | + | 0.989954i | \(0.454842\pi\) | |||||||
\(608\) | −28.9459 | −1.17391 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.05791 | 0.285767 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.3851 | −1.38880 | −0.694401 | − | 0.719589i | \(-0.744330\pi\) | ||||
−0.694401 | + | 0.719589i | \(0.744330\pi\) | |||||||
\(614\) | −17.5742 | −0.709239 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 27.0492 | 1.08984 | ||||||||
\(617\) | 15.6089 | 0.628392 | 0.314196 | − | 0.949358i | \(-0.398265\pi\) | ||||
0.314196 | + | 0.949358i | \(0.398265\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.0626 | −0.645610 | −0.322805 | − | 0.946465i | \(-0.604626\pi\) | ||||
−0.322805 | + | 0.946465i | \(0.604626\pi\) | |||||||
\(620\) | 2.30798 | 0.0926906 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 28.1441 | 1.12848 | ||||||||
\(623\) | 0.265947 | 0.0106550 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.30751 | 0.0522588 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.84420 | −0.233209 | ||||||||
\(629\) | −16.0944 | −0.641725 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.6719 | −1.45988 | −0.729942 | − | 0.683509i | \(-0.760453\pi\) | ||||
−0.729942 | + | 0.683509i | \(0.760453\pi\) | |||||||
\(632\) | 34.1381 | 1.35794 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.71281 | 0.385745 | ||||||||
\(635\) | 14.9720 | 0.594147 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −23.1485 | −0.916458 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.64863 | −0.0651677 | ||||||||
\(641\) | −26.6422 | −1.05230 | −0.526152 | − | 0.850390i | \(-0.676366\pi\) | ||||
−0.526152 | + | 0.850390i | \(0.676366\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.06096 | 0.0812762 | 0.0406381 | − | 0.999174i | \(-0.487061\pi\) | ||||
0.0406381 | + | 0.999174i | \(0.487061\pi\) | |||||||
\(644\) | −18.3963 | −0.724916 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.2970 | −0.641197 | ||||||||
\(647\) | 15.5271 | 0.610432 | 0.305216 | − | 0.952283i | \(-0.401271\pi\) | ||||
0.305216 | + | 0.952283i | \(0.401271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.8222 | 0.581821 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.02047 | 0.353269 | ||||||||
\(653\) | −40.8736 | −1.59951 | −0.799754 | − | 0.600328i | \(-0.795037\pi\) | ||||
−0.799754 | + | 0.600328i | \(0.795037\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.5831 | −0.413515 | ||||||||
\(656\) | 6.64437 | 0.259419 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.78517 | 0.225530 | ||||||||
\(659\) | −1.83473 | −0.0714708 | −0.0357354 | − | 0.999361i | \(-0.511377\pi\) | ||||
−0.0357354 | + | 0.999361i | \(0.511377\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.3682 | −0.675543 | −0.337772 | − | 0.941228i | \(-0.609673\pi\) | ||||
−0.337772 | + | 0.941228i | \(0.609673\pi\) | |||||||
\(662\) | 28.8519 | 1.12136 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.4641 | −0.832969 | ||||||||
\(665\) | 21.2090 | 0.822449 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 58.7553 | 2.27501 | ||||||||
\(668\) | 16.0624 | 0.621472 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.61944 | 0.255731 | ||||||||
\(671\) | 19.2826 | 0.744396 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.50792 | −0.366503 | −0.183252 | − | 0.983066i | \(-0.558662\pi\) | ||||
−0.183252 | + | 0.983066i | \(0.558662\pi\) | |||||||
\(674\) | 22.7200 | 0.875141 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.7375 | −0.797008 | −0.398504 | − | 0.917167i | \(-0.630470\pi\) | ||||
−0.398504 | + | 0.917167i | \(0.630470\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.7119 | −0.526215 | ||||||||
\(680\) | 6.00000 | 0.230089 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.9215 | −0.418205 | ||||||||
\(683\) | −16.6879 | −0.638543 | −0.319272 | − | 0.947663i | \(-0.603438\pi\) | ||||
−0.319272 | + | 0.947663i | \(0.603438\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.70654 | 0.332660 | ||||||||
\(686\) | −18.7670 | −0.716529 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −19.0935 | −0.727932 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.6459 | 0.861490 | 0.430745 | − | 0.902474i | \(-0.358251\pi\) | ||||
0.430745 | + | 0.902474i | \(0.358251\pi\) | |||||||
\(692\) | 11.0178 | 0.418833 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.2429 | −1.03413 | ||||||||
\(695\) | 11.6569 | 0.442171 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.47941 | −0.245425 | ||||||||
\(698\) | −28.9122 | −1.09434 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.09226 | −0.0790801 | ||||||||
\(701\) | −9.33818 | −0.352698 | −0.176349 | − | 0.984328i | \(-0.556429\pi\) | ||||
−0.176349 | + | 0.984328i | \(0.556429\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 61.2361 | 2.30956 | ||||||||
\(704\) | −25.8179 | −0.973049 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.83383 | 0.332465 | ||||||||
\(707\) | −7.98133 | −0.300169 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.4424 | 1.06818 | 0.534088 | − | 0.845429i | \(-0.320655\pi\) | ||||
0.534088 | + | 0.845429i | \(0.320655\pi\) | |||||||
\(710\) | −11.5973 | −0.435239 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.286260 | −0.0107280 | ||||||||
\(713\) | 27.7207 | 1.03815 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.351951 | −0.0131530 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.1992 | −0.828465 | ||||||||
\(719\) | −31.8969 | −1.18955 | −0.594776 | − | 0.803891i | \(-0.702759\pi\) | ||||
−0.594776 | + | 0.803891i | \(0.702759\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.8763 | 0.889200 | ||||||||
\(722\) | 40.6125 | 1.51144 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.36079 | −0.0505733 | ||||||||
\(725\) | 6.68240 | 0.248178 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.68029 | −0.173583 | −0.0867913 | − | 0.996227i | \(-0.527661\pi\) | ||||
−0.0867913 | + | 0.996227i | \(0.527661\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.5104 | 0.463030 | ||||||||
\(731\) | 18.6194 | 0.688665 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.1306 | −0.521926 | −0.260963 | − | 0.965349i | \(-0.584040\pi\) | ||||
−0.260963 | + | 0.965349i | \(0.584040\pi\) | |||||||
\(734\) | −12.5847 | −0.464508 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34.2970 | 1.26420 | ||||||||
\(737\) | 18.0846 | 0.666156 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.8882 | 0.437314 | 0.218657 | − | 0.975802i | \(-0.429832\pi\) | ||||
0.218657 | + | 0.975802i | \(0.429832\pi\) | |||||||
\(740\) | −6.04093 | −0.222069 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −34.2970 | −1.25908 | ||||||||
\(743\) | −24.0100 | −0.880840 | −0.440420 | − | 0.897792i | \(-0.645170\pi\) | ||||
−0.440420 | + | 0.897792i | \(0.645170\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.82431 | −0.250023 | ||||||||
\(746\) | −9.85473 | −0.360807 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.39230 | 0.160599 | ||||||||
\(749\) | −18.1505 | −0.663205 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.8698 | 0.579098 | 0.289549 | − | 0.957163i | \(-0.406495\pi\) | ||||
0.289549 | + | 0.957163i | \(0.406495\pi\) | |||||||
\(752\) | −3.59518 | −0.131103 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.6810 | −0.461510 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.1638 | 1.31440 | 0.657198 | − | 0.753718i | \(-0.271742\pi\) | ||||
0.657198 | + | 0.753718i | \(0.271742\pi\) | |||||||
\(758\) | −21.1352 | −0.767665 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −22.8289 | −0.828091 | ||||||||
\(761\) | 14.6181 | 0.529906 | 0.264953 | − | 0.964261i | \(-0.414644\pi\) | ||||
0.264953 | + | 0.964261i | \(0.414644\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.7242 | −1.22090 | ||||||||
\(764\) | 6.38256 | 0.230913 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.84029 | 0.247150 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.3590 | −0.662042 | −0.331021 | − | 0.943623i | \(-0.607393\pi\) | ||||
−0.331021 | + | 0.943623i | \(0.607393\pi\) | |||||||
\(770\) | 9.90069 | 0.356796 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.72412 | 0.170025 | ||||||||
\(773\) | −8.53039 | −0.306817 | −0.153408 | − | 0.988163i | \(-0.549025\pi\) | ||||
−0.153408 | + | 0.988163i | \(0.549025\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.15276 | 0.113250 | ||||||||
\(776\) | 14.7592 | 0.529824 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.8839 | 0.390207 | ||||||||
\(779\) | 24.6530 | 0.883284 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.6844 | −1.13376 | ||||||||
\(782\) | 19.3098 | 0.690516 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.33728 | −0.0834743 | ||||||||
\(785\) | −7.98333 | −0.284937 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.42575 | −0.122115 | −0.0610574 | − | 0.998134i | \(-0.519447\pi\) | ||||
−0.0610574 | + | 0.998134i | \(0.519447\pi\) | |||||||
\(788\) | 8.48668 | 0.302326 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.4954 | 0.444567 | ||||||||
\(791\) | −9.90069 | −0.352028 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 27.3982 | 0.972327 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.586652 | −0.0207933 | ||||||||
\(797\) | −28.1009 | −0.995387 | −0.497693 | − | 0.867353i | \(-0.665819\pi\) | ||||
−0.497693 | + | 0.867353i | \(0.665819\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.50592 | 0.124031 | ||||||||
\(800\) | 3.90069 | 0.137910 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.0177 | −0.353736 | ||||||||
\(803\) | 34.1790 | 1.20615 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.1298 | −0.885710 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.59092 | 0.302228 | ||||||||
\(809\) | −36.1693 | −1.27164 | −0.635822 | − | 0.771836i | \(-0.719339\pi\) | ||||
−0.635822 | + | 0.771836i | \(0.719339\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.9825 | 0.490993 | 0.245497 | − | 0.969397i | \(-0.421049\pi\) | ||||
0.245497 | + | 0.969397i | \(0.421049\pi\) | |||||||
\(812\) | −13.9813 | −0.490648 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 28.5860 | 1.00194 | ||||||||
\(815\) | 12.3222 | 0.431627 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −70.8435 | −2.47850 | ||||||||
\(818\) | −31.8540 | −1.11375 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.43201 | −0.0849294 | ||||||||
\(821\) | −4.23955 | −0.147961 | −0.0739806 | − | 0.997260i | \(-0.523570\pi\) | ||||
−0.0739806 | + | 0.997260i | \(0.523570\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.6401 | 1.17262 | 0.586310 | − | 0.810087i | \(-0.300580\pi\) | ||||
0.586310 | + | 0.810087i | \(0.300580\pi\) | |||||||
\(824\) | −25.6999 | −0.895299 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.5059 | −0.539520 | ||||||||
\(827\) | 6.94609 | 0.241539 | 0.120770 | − | 0.992681i | \(-0.461464\pi\) | ||||
0.120770 | + | 0.992681i | \(0.461464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.3654 | 0.464201 | 0.232100 | − | 0.972692i | \(-0.425440\pi\) | ||||
0.232100 | + | 0.972692i | \(0.425440\pi\) | |||||||
\(830\) | −7.85641 | −0.272700 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.27925 | 0.0789714 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.9416 | 0.759321 | ||||||||
\(836\) | −16.7119 | −0.577994 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −32.5364 | −1.12395 | ||||||||
\(839\) | −20.0721 | −0.692967 | −0.346483 | − | 0.938056i | \(-0.612624\pi\) | ||||
−0.346483 | + | 0.938056i | \(0.612624\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6544 | 0.539808 | ||||||||
\(842\) | −13.5275 | −0.466188 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.07023 | 0.208946 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.38973 | −0.150833 | ||||||||
\(848\) | 21.3138 | 0.731918 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.19615 | 0.0753274 | ||||||||
\(851\) | −72.5566 | −2.48721 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −54.6353 | −1.87068 | −0.935338 | − | 0.353755i | \(-0.884905\pi\) | ||||
−0.935338 | + | 0.353755i | \(0.884905\pi\) | |||||||
\(854\) | −20.1721 | −0.690275 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.5368 | 0.667754 | ||||||||
\(857\) | 3.66436 | 0.125172 | 0.0625860 | − | 0.998040i | \(-0.480065\pi\) | ||||
0.0625860 | + | 0.998040i | \(0.480065\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.1460 | 0.960330 | 0.480165 | − | 0.877178i | \(-0.340577\pi\) | ||||
0.480165 | + | 0.877178i | \(0.340577\pi\) | |||||||
\(860\) | 6.98870 | 0.238313 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25.9246 | −0.882994 | ||||||||
\(863\) | −50.4623 | −1.71776 | −0.858878 | − | 0.512180i | \(-0.828838\pi\) | ||||
−0.858878 | + | 0.512180i | \(0.828838\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.0506 | 0.511734 | ||||||||
\(866\) | −30.2671 | −1.02852 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.59639 | −0.223896 | ||||||||
\(869\) | 34.1381 | 1.15806 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 36.3000 | 1.22927 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −73.4701 | −2.48516 | ||||||||
\(875\) | −2.85808 | −0.0966209 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.2087 | 0.783702 | 0.391851 | − | 0.920029i | \(-0.371835\pi\) | ||||
0.391851 | + | 0.920029i | \(0.371835\pi\) | |||||||
\(878\) | −35.6439 | −1.20292 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.15276 | −0.207409 | ||||||||
\(881\) | 17.1152 | 0.576624 | 0.288312 | − | 0.957536i | \(-0.406906\pi\) | ||||
0.288312 | + | 0.957536i | \(0.406906\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.3589 | −0.718783 | −0.359391 | − | 0.933187i | \(-0.617016\pi\) | ||||
−0.359391 | + | 0.933187i | \(0.617016\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.1470 | 0.374489 | ||||||||
\(887\) | −34.3200 | −1.15235 | −0.576177 | − | 0.817325i | \(-0.695456\pi\) | ||||
−0.576177 | + | 0.817325i | \(0.695456\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −42.7913 | −1.43517 | ||||||||
\(890\) | −0.104778 | −0.00351218 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.34196 | −0.312792 | ||||||||
\(893\) | −13.3394 | −0.446385 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.480775 | −0.0160705 | ||||||||
\(896\) | 4.71191 | 0.157414 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.8998 | 0.563953 | ||||||||
\(899\) | 21.0680 | 0.702656 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.7846 | −0.692436 | ||||||||
\(902\) | 11.5084 | 0.383187 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.6569 | 0.354443 | ||||||||
\(905\) | −1.85887 | −0.0617910 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 58.9083 | 1.95602 | 0.978010 | − | 0.208560i | \(-0.0668777\pi\) | ||||
0.978010 | + | 0.208560i | \(0.0668777\pi\) | |||||||
\(908\) | 12.5264 | 0.415703 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.5007 | 1.83882 | 0.919410 | − | 0.393299i | \(-0.128666\pi\) | ||||
0.919410 | + | 0.393299i | \(0.128666\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.4641 | −0.710358 | ||||||||
\(914\) | −14.6727 | −0.485328 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.68507 | −0.154799 | ||||||||
\(917\) | 30.2473 | 0.998855 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.7311 | 1.80541 | 0.902707 | − | 0.430257i | \(-0.141577\pi\) | ||||
0.902707 | + | 0.430257i | \(0.141577\pi\) | |||||||
\(920\) | 27.0492 | 0.891785 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.3358 | 1.06492 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.25207 | −0.271326 | ||||||||
\(926\) | −0.518323 | −0.0170332 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 26.0660 | 0.855657 | ||||||||
\(929\) | 17.1818 | 0.563718 | 0.281859 | − | 0.959456i | \(-0.409049\pi\) | ||||
0.281859 | + | 0.959456i | \(0.409049\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.67213 | −0.284218 | ||||||||
\(932\) | 0.491614 | 0.0161033 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 38.3565 | 1.25506 | ||||||||
\(935\) | 6.00000 | 0.196221 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.6401 | 1.29499 | 0.647493 | − | 0.762071i | \(-0.275817\pi\) | ||||
0.647493 | + | 0.762071i | \(0.275817\pi\) | |||||||
\(938\) | −18.9189 | −0.617724 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.31593 | 0.0429208 | ||||||||
\(941\) | 33.3796 | 1.08815 | 0.544073 | − | 0.839038i | \(-0.316882\pi\) | ||||
0.544073 | + | 0.839038i | \(0.316882\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.2105 | −0.951223 | ||||||||
\(944\) | 9.63611 | 0.313629 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.0709 | −1.07523 | ||||||||
\(947\) | −20.5599 | −0.668108 | −0.334054 | − | 0.942554i | \(-0.608417\pi\) | ||||
−0.334054 | + | 0.942554i | \(0.608417\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −8.35596 | −0.271103 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.1485 | −0.555786 | ||||||||
\(953\) | 54.8753 | 1.77758 | 0.888792 | − | 0.458311i | \(-0.151545\pi\) | ||||
0.888792 | + | 0.458311i | \(0.151545\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.71875 | 0.282132 | ||||||||
\(956\) | −5.21939 | −0.168807 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 34.8294 | 1.12529 | ||||||||
\(959\) | −24.8840 | −0.803547 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.0601 | −0.679359 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.7202 | 0.635144 | ||||||||
\(965\) | 6.45326 | 0.207738 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.9215 | −0.351211 | −0.175605 | − | 0.984461i | \(-0.556188\pi\) | ||||
−0.175605 | + | 0.984461i | \(0.556188\pi\) | |||||||
\(968\) | 4.72500 | 0.151867 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.40224 | 0.173456 | ||||||||
\(971\) | −31.4711 | −1.00996 | −0.504978 | − | 0.863132i | \(-0.668499\pi\) | ||||
−0.504978 | + | 0.863132i | \(0.668499\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.3164 | −1.06807 | ||||||||
\(974\) | −18.6223 | −0.596698 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.5359 | 0.401264 | ||||||||
\(977\) | 31.5533 | 1.00948 | 0.504740 | − | 0.863271i | \(-0.331588\pi\) | ||||
0.504740 | + | 0.863271i | \(0.331588\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.286260 | −0.00914890 | ||||||||
\(980\) | 0.855504 | 0.0273281 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.0370 | −0.671317 | ||||||||
\(983\) | 43.6214 | 1.39131 | 0.695654 | − | 0.718377i | \(-0.255115\pi\) | ||||
0.695654 | + | 0.718377i | \(0.255115\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5930 | 0.369384 | ||||||||
\(986\) | 14.6756 | 0.467365 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 83.9401 | 2.66914 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.9948 | 0.571624 | 0.285812 | − | 0.958286i | \(-0.407737\pi\) | ||||
0.285812 | + | 0.958286i | \(0.407737\pi\) | |||||||
\(992\) | 12.2979 | 0.390460 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 33.1460 | 1.05133 | ||||||||
\(995\) | −0.801382 | −0.0254055 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.2091 | −0.766710 | −0.383355 | − | 0.923601i | \(-0.625231\pi\) | ||||
−0.383355 | + | 0.923601i | \(0.625231\pi\) | |||||||
\(998\) | −12.3826 | −0.391963 | ||||||||
\(999\) | 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 | 7605.2.a.ch.1.3 | 4 | ||
3.2 | odd | 2 | 2535.2.a.bk.1.2 | 4 | |||
13.2 | odd | 12 | 585.2.bu.d.316.3 | 8 | |||
13.7 | odd | 12 | 585.2.bu.d.361.3 | 8 | |||
13.12 | even | 2 | 7605.2.a.ci.1.2 | 4 | |||
39.2 | even | 12 | 195.2.bb.b.121.2 | ✓ | 8 | ||
39.20 | even | 12 | 195.2.bb.b.166.2 | yes | 8 | ||
39.38 | odd | 2 | 2535.2.a.bj.1.3 | 4 | |||
195.2 | odd | 12 | 975.2.w.i.199.3 | 8 | |||
195.59 | even | 12 | 975.2.bc.j.751.3 | 8 | |||
195.98 | odd | 12 | 975.2.w.i.49.3 | 8 | |||
195.119 | even | 12 | 975.2.bc.j.901.3 | 8 | |||
195.137 | odd | 12 | 975.2.w.h.49.2 | 8 | |||
195.158 | odd | 12 | 975.2.w.h.199.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.bb.b.121.2 | ✓ | 8 | 39.2 | even | 12 | ||
195.2.bb.b.166.2 | yes | 8 | 39.20 | even | 12 | ||
585.2.bu.d.316.3 | 8 | 13.2 | odd | 12 | |||
585.2.bu.d.361.3 | 8 | 13.7 | odd | 12 | |||
975.2.w.h.49.2 | 8 | 195.137 | odd | 12 | |||
975.2.w.h.199.2 | 8 | 195.158 | odd | 12 | |||
975.2.w.i.49.3 | 8 | 195.98 | odd | 12 | |||
975.2.w.i.199.3 | 8 | 195.2 | odd | 12 | |||
975.2.bc.j.751.3 | 8 | 195.59 | even | 12 | |||
975.2.bc.j.901.3 | 8 | 195.119 | even | 12 | |||
2535.2.a.bj.1.3 | 4 | 39.38 | odd | 2 | |||
2535.2.a.bk.1.2 | 4 | 3.2 | odd | 2 | |||
7605.2.a.ch.1.3 | 4 | 1.1 | even | 1 | trivial | ||
7605.2.a.ci.1.2 | 4 | 13.12 | even | 2 |