Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.6988960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 22x^{4} - 11x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 693) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.25947\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.25947 | −1.59769 | −0.798844 | − | 0.601538i | \(-0.794555\pi\) | ||||
−0.798844 | + | 0.601538i | \(0.794555\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.10522 | 1.55261 | ||||||||
\(5\) | −1.54336 | −0.690212 | −0.345106 | − | 0.938564i | \(-0.612157\pi\) | ||||
−0.345106 | + | 0.938564i | \(0.612157\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.49721 | −0.882898 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.48718 | 1.10274 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.53716 | 0.703683 | 0.351841 | − | 0.936060i | \(-0.385556\pi\) | ||||
0.351841 | + | 0.936060i | \(0.385556\pi\) | |||||||
\(14\) | 2.25947 | 0.603870 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.568054 | −0.142014 | ||||||||
\(17\) | 6.59570 | 1.59969 | 0.799846 | − | 0.600206i | \(-0.204915\pi\) | ||||
0.799846 | + | 0.600206i | \(0.204915\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.56151 | −1.73473 | −0.867365 | − | 0.497672i | \(-0.834188\pi\) | ||||
−0.867365 | + | 0.497672i | \(0.834188\pi\) | |||||||
\(20\) | −4.79248 | −1.07163 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.61973 | 1.17179 | 0.585897 | − | 0.810385i | \(-0.300742\pi\) | ||||
0.585897 | + | 0.810385i | \(0.300742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.61803 | −0.523607 | ||||||||
\(26\) | −5.73266 | −1.12427 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.10522 | −0.586831 | ||||||||
\(29\) | 5.45068 | 1.01217 | 0.506083 | − | 0.862485i | \(-0.331093\pi\) | ||||
0.506083 | + | 0.862485i | \(0.331093\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.32545 | −0.956478 | −0.478239 | − | 0.878230i | \(-0.658725\pi\) | ||||
−0.478239 | + | 0.878230i | \(0.658725\pi\) | |||||||
\(32\) | 6.27793 | 1.10979 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −14.9028 | −2.55581 | ||||||||
\(35\) | 1.54336 | 0.260876 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.18609 | −1.01699 | −0.508493 | − | 0.861066i | \(-0.669797\pi\) | ||||
−0.508493 | + | 0.861066i | \(0.669797\pi\) | |||||||
\(38\) | 17.0850 | 2.77156 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.85410 | 0.609387 | ||||||||
\(41\) | −9.78690 | −1.52846 | −0.764229 | − | 0.644946i | \(-0.776880\pi\) | ||||
−0.764229 | + | 0.644946i | \(0.776880\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.61149 | 1.46574 | 0.732870 | − | 0.680369i | \(-0.238181\pi\) | ||||
0.732870 | + | 0.680369i | \(0.238181\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.6976 | −1.87216 | ||||||||
\(47\) | 3.84418 | 0.560731 | 0.280366 | − | 0.959893i | \(-0.409544\pi\) | ||||
0.280366 | + | 0.959893i | \(0.409544\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.91538 | 0.836561 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.87845 | 1.09254 | ||||||||
\(53\) | 0.531600 | 0.0730209 | 0.0365105 | − | 0.999333i | \(-0.488376\pi\) | ||||
0.0365105 | + | 0.999333i | \(0.488376\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.49721 | 0.333704 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12.3157 | −1.61712 | ||||||||
\(59\) | −1.76077 | −0.229233 | −0.114616 | − | 0.993410i | \(-0.536564\pi\) | ||||
−0.114616 | + | 0.993410i | \(0.536564\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.74760 | −0.607868 | −0.303934 | − | 0.952693i | \(-0.598300\pi\) | ||||
−0.303934 | + | 0.952693i | \(0.598300\pi\) | |||||||
\(62\) | 12.0327 | 1.52815 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0487 | −1.63109 | ||||||||
\(65\) | −3.91576 | −0.485691 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.60824 | −1.17383 | −0.586917 | − | 0.809647i | \(-0.699658\pi\) | ||||
−0.586917 | + | 0.809647i | \(0.699658\pi\) | |||||||
\(68\) | 20.4811 | 2.48370 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.48718 | −0.416798 | ||||||||
\(71\) | −9.94228 | −1.17993 | −0.589966 | − | 0.807428i | \(-0.700859\pi\) | ||||
−0.589966 | + | 0.807428i | \(0.700859\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.71346 | 1.13687 | 0.568437 | − | 0.822727i | \(-0.307548\pi\) | ||||
0.568437 | + | 0.822727i | \(0.307548\pi\) | |||||||
\(74\) | 13.9773 | 1.62483 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −23.4802 | −2.69336 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.07029 | 0.232926 | 0.116463 | − | 0.993195i | \(-0.462844\pi\) | ||||
0.116463 | + | 0.993195i | \(0.462844\pi\) | |||||||
\(80\) | 0.876713 | 0.0980195 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 22.1132 | 2.44200 | ||||||||
\(83\) | −0.0442404 | −0.00485601 | −0.00242801 | − | 0.999997i | \(-0.500773\pi\) | ||||
−0.00242801 | + | 0.999997i | \(0.500773\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.1795 | −1.10413 | ||||||||
\(86\) | −21.7169 | −2.34179 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.38297 | 0.676594 | 0.338297 | − | 0.941039i | \(-0.390149\pi\) | ||||
0.338297 | + | 0.941039i | \(0.390149\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.53716 | −0.265967 | ||||||||
\(92\) | 17.4505 | 1.81934 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.68582 | −0.895874 | ||||||||
\(95\) | 11.6702 | 1.19733 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2498 | −1.34532 | −0.672658 | − | 0.739953i | \(-0.734848\pi\) | ||||
−0.672658 | + | 0.739953i | \(0.734848\pi\) | |||||||
\(98\) | −2.25947 | −0.228241 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.12957 | −0.812957 | ||||||||
\(101\) | 5.53071 | 0.550326 | 0.275163 | − | 0.961398i | \(-0.411268\pi\) | ||||
0.275163 | + | 0.961398i | \(0.411268\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.70087 | 0.660257 | 0.330128 | − | 0.943936i | \(-0.392908\pi\) | ||||
0.330128 | + | 0.943936i | \(0.392908\pi\) | |||||||
\(104\) | −6.33584 | −0.621280 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.20114 | −0.116665 | ||||||||
\(107\) | −5.75478 | −0.556335 | −0.278168 | − | 0.960533i | \(-0.589727\pi\) | ||||
−0.278168 | + | 0.960533i | \(0.589727\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.7061 | 1.31281 | 0.656405 | − | 0.754409i | \(-0.272076\pi\) | ||||
0.656405 | + | 0.754409i | \(0.272076\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.568054 | 0.0536761 | ||||||||
\(113\) | −14.6044 | −1.37387 | −0.686933 | − | 0.726721i | \(-0.741043\pi\) | ||||
−0.686933 | + | 0.726721i | \(0.741043\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.67327 | −0.808787 | ||||||||
\(116\) | 16.9255 | 1.57150 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.97841 | 0.366242 | ||||||||
\(119\) | −6.59570 | −0.604627 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 10.7271 | 0.971184 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −16.5367 | −1.48504 | ||||||||
\(125\) | 11.7574 | 1.05161 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.5063 | 1.19849 | 0.599244 | − | 0.800566i | \(-0.295468\pi\) | ||||
0.599244 | + | 0.800566i | \(0.295468\pi\) | |||||||
\(128\) | 16.9273 | 1.49618 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.84756 | 0.775983 | ||||||||
\(131\) | −4.30276 | −0.375934 | −0.187967 | − | 0.982175i | \(-0.560190\pi\) | ||||
−0.187967 | + | 0.982175i | \(0.560190\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.56151 | 0.655666 | ||||||||
\(134\) | 21.7096 | 1.87542 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.4709 | −1.41236 | ||||||||
\(137\) | 12.5285 | 1.07038 | 0.535191 | − | 0.844731i | \(-0.320239\pi\) | ||||
0.535191 | + | 0.844731i | \(0.320239\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.2263 | 0.952200 | 0.476100 | − | 0.879391i | \(-0.342050\pi\) | ||||
0.476100 | + | 0.879391i | \(0.342050\pi\) | |||||||
\(140\) | 4.79248 | 0.405038 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 22.4643 | 1.88516 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.41237 | −0.698609 | ||||||||
\(146\) | −21.9473 | −1.81637 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −19.2092 | −1.57898 | ||||||||
\(149\) | −12.1151 | −0.992505 | −0.496252 | − | 0.868178i | \(-0.665291\pi\) | ||||
−0.496252 | + | 0.868178i | \(0.665291\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7878 | 0.877898 | 0.438949 | − | 0.898512i | \(-0.355351\pi\) | ||||
0.438949 | + | 0.898512i | \(0.355351\pi\) | |||||||
\(152\) | 18.8827 | 1.53159 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.21909 | 0.660173 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.70295 | −0.295527 | −0.147764 | − | 0.989023i | \(-0.547207\pi\) | ||||
−0.147764 | + | 0.989023i | \(0.547207\pi\) | |||||||
\(158\) | −4.67776 | −0.372143 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.68911 | −0.765992 | ||||||||
\(161\) | −5.61973 | −0.442897 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.5447 | 1.76584 | 0.882918 | − | 0.469526i | \(-0.155575\pi\) | ||||
0.882918 | + | 0.469526i | \(0.155575\pi\) | |||||||
\(164\) | −30.3905 | −2.37310 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0999599 | 0.00775839 | ||||||||
\(167\) | −14.2177 | −1.10020 | −0.550099 | − | 0.835099i | \(-0.685410\pi\) | ||||
−0.550099 | + | 0.835099i | \(0.685410\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.56280 | −0.504830 | ||||||||
\(170\) | 23.0004 | 1.76405 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 29.8458 | 2.27572 | ||||||||
\(173\) | −18.8789 | −1.43534 | −0.717670 | − | 0.696384i | \(-0.754791\pi\) | ||||
−0.717670 | + | 0.696384i | \(0.754791\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.61803 | 0.197905 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.4222 | −1.08099 | ||||||||
\(179\) | 4.39825 | 0.328741 | 0.164370 | − | 0.986399i | \(-0.447441\pi\) | ||||
0.164370 | + | 0.986399i | \(0.447441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.87924 | 0.362671 | 0.181336 | − | 0.983421i | \(-0.441958\pi\) | ||||
0.181336 | + | 0.983421i | \(0.441958\pi\) | |||||||
\(182\) | 5.73266 | 0.424933 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.0337 | −1.03457 | ||||||||
\(185\) | 9.54737 | 0.701937 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 11.9370 | 0.870597 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −26.3684 | −1.91296 | ||||||||
\(191\) | −15.8326 | −1.14561 | −0.572805 | − | 0.819692i | \(-0.694145\pi\) | ||||
−0.572805 | + | 0.819692i | \(0.694145\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.33475 | −0.599948 | −0.299974 | − | 0.953947i | \(-0.596978\pi\) | ||||
−0.299974 | + | 0.953947i | \(0.596978\pi\) | |||||||
\(194\) | 29.9376 | 2.14940 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.10522 | 0.221801 | ||||||||
\(197\) | 3.63957 | 0.259309 | 0.129654 | − | 0.991559i | \(-0.458613\pi\) | ||||
0.129654 | + | 0.991559i | \(0.458613\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.58189 | −0.324801 | −0.162401 | − | 0.986725i | \(-0.551924\pi\) | ||||
−0.162401 | + | 0.986725i | \(0.551924\pi\) | |||||||
\(200\) | 6.53779 | 0.462291 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.4965 | −0.879250 | ||||||||
\(203\) | −5.45068 | −0.382562 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.1047 | 1.05496 | ||||||||
\(206\) | −15.1404 | −1.05488 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.44125 | −0.0999325 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.16946 | 0.0805087 | 0.0402543 | − | 0.999189i | \(-0.487183\pi\) | ||||
0.0402543 | + | 0.999189i | \(0.487183\pi\) | |||||||
\(212\) | 1.65074 | 0.113373 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.0028 | 0.888850 | ||||||||
\(215\) | −14.8340 | −1.01167 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.32545 | 0.361515 | ||||||||
\(218\) | −30.9686 | −2.09746 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.7344 | 1.12568 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.93300 | −0.263373 | −0.131687 | − | 0.991291i | \(-0.542039\pi\) | ||||
−0.131687 | + | 0.991291i | \(0.542039\pi\) | |||||||
\(224\) | −6.27793 | −0.419462 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 32.9982 | 2.19501 | ||||||||
\(227\) | 24.3591 | 1.61677 | 0.808384 | − | 0.588655i | \(-0.200342\pi\) | ||||
0.808384 | + | 0.588655i | \(0.200342\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.2275 | −1.60100 | −0.800498 | − | 0.599336i | \(-0.795431\pi\) | ||||
−0.800498 | + | 0.599336i | \(0.795431\pi\) | |||||||
\(230\) | 19.5970 | 1.29219 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.6115 | −0.893638 | ||||||||
\(233\) | 28.1961 | 1.84719 | 0.923594 | − | 0.383372i | \(-0.125237\pi\) | ||||
0.923594 | + | 0.383372i | \(0.125237\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.93296 | −0.387024 | ||||||||
\(236\) | −5.46757 | −0.355909 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14.9028 | 0.966005 | ||||||||
\(239\) | 18.6392 | 1.20567 | 0.602834 | − | 0.797867i | \(-0.294038\pi\) | ||||
0.602834 | + | 0.797867i | \(0.294038\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.4814 | −1.12608 | −0.563039 | − | 0.826430i | \(-0.690368\pi\) | ||||
−0.563039 | + | 0.826430i | \(0.690368\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.7423 | −0.943782 | ||||||||
\(245\) | −1.54336 | −0.0986018 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.1848 | −1.22070 | ||||||||
\(248\) | 13.2988 | 0.844473 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −26.5655 | −1.68015 | ||||||||
\(251\) | −4.04114 | −0.255075 | −0.127537 | − | 0.991834i | \(-0.540707\pi\) | ||||
−0.127537 | + | 0.991834i | \(0.540707\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −30.5171 | −1.91481 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.1495 | −0.759341 | ||||||||
\(257\) | 9.68475 | 0.604118 | 0.302059 | − | 0.953289i | \(-0.402326\pi\) | ||||
0.302059 | + | 0.953289i | \(0.402326\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.18609 | 0.384385 | ||||||||
\(260\) | −12.1593 | −0.754088 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.72197 | 0.600625 | ||||||||
\(263\) | 5.08831 | 0.313759 | 0.156879 | − | 0.987618i | \(-0.449857\pi\) | ||||
0.156879 | + | 0.987618i | \(0.449857\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.820452 | −0.0504000 | ||||||||
\(266\) | −17.0850 | −1.04755 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −29.8357 | −1.82251 | ||||||||
\(269\) | −0.224607 | −0.0136945 | −0.00684725 | − | 0.999977i | \(-0.502180\pi\) | ||||
−0.00684725 | + | 0.999977i | \(0.502180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.3590 | −1.47971 | −0.739853 | − | 0.672769i | \(-0.765105\pi\) | ||||
−0.739853 | + | 0.672769i | \(0.765105\pi\) | |||||||
\(272\) | −3.74671 | −0.227178 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −28.3078 | −1.71014 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.4997 | −1.05146 | −0.525729 | − | 0.850652i | \(-0.676207\pi\) | ||||
−0.525729 | + | 0.850652i | \(0.676207\pi\) | |||||||
\(278\) | −25.3655 | −1.52132 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.85410 | −0.230327 | ||||||||
\(281\) | −14.3550 | −0.856345 | −0.428173 | − | 0.903697i | \(-0.640842\pi\) | ||||
−0.428173 | + | 0.903697i | \(0.640842\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.0055 | 1.66475 | 0.832376 | − | 0.554212i | \(-0.186980\pi\) | ||||
0.832376 | + | 0.554212i | \(0.186980\pi\) | |||||||
\(284\) | −30.8730 | −1.83197 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.78690 | 0.577702 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.5032 | 1.55901 | ||||||||
\(290\) | 19.0075 | 1.11616 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 30.1624 | 1.76512 | ||||||||
\(293\) | −13.3587 | −0.780421 | −0.390211 | − | 0.920726i | \(-0.627598\pi\) | ||||
−0.390211 | + | 0.920726i | \(0.627598\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.71750 | 0.158219 | ||||||||
\(296\) | 15.4480 | 0.897895 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.3737 | 1.58571 | ||||||||
\(299\) | 14.2582 | 0.824571 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.61149 | −0.553997 | ||||||||
\(302\) | −24.3747 | −1.40261 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.29535 | 0.246355 | ||||||||
\(305\) | 7.32727 | 0.419558 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.14669 | −0.179591 | −0.0897955 | − | 0.995960i | \(-0.528621\pi\) | ||||
−0.0897955 | + | 0.995960i | \(0.528621\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −18.5708 | −1.05475 | ||||||||
\(311\) | 24.5598 | 1.39266 | 0.696329 | − | 0.717722i | \(-0.254815\pi\) | ||||
0.696329 | + | 0.717722i | \(0.254815\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.5445 | −1.21776 | −0.608882 | − | 0.793261i | \(-0.708382\pi\) | ||||
−0.608882 | + | 0.793261i | \(0.708382\pi\) | |||||||
\(314\) | 8.36670 | 0.472160 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.42870 | 0.361642 | ||||||||
\(317\) | −7.38572 | −0.414823 | −0.207412 | − | 0.978254i | \(-0.566504\pi\) | ||||
−0.207412 | + | 0.978254i | \(0.566504\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 20.1389 | 1.12580 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.6976 | 0.707611 | ||||||||
\(323\) | −49.8735 | −2.77503 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.64238 | −0.368453 | ||||||||
\(326\) | −50.9391 | −2.82126 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 24.4400 | 1.34947 | ||||||||
\(329\) | −3.84418 | −0.211937 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.0897 | −1.15919 | −0.579597 | − | 0.814903i | \(-0.696790\pi\) | ||||
−0.579597 | + | 0.814903i | \(0.696790\pi\) | |||||||
\(332\) | −0.137376 | −0.00753949 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 32.1245 | 1.75777 | ||||||||
\(335\) | 14.8290 | 0.810195 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.2973 | −1.10566 | −0.552831 | − | 0.833293i | \(-0.686452\pi\) | ||||
−0.552831 | + | 0.833293i | \(0.686452\pi\) | |||||||
\(338\) | 14.8285 | 0.806562 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −31.6097 | −1.71428 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −24.0019 | −1.29410 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 42.6565 | 2.29323 | ||||||||
\(347\) | 16.4180 | 0.881366 | 0.440683 | − | 0.897663i | \(-0.354736\pi\) | ||||
0.440683 | + | 0.897663i | \(0.354736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.3977 | −1.52009 | −0.760047 | − | 0.649868i | \(-0.774824\pi\) | ||||
−0.760047 | + | 0.649868i | \(0.774824\pi\) | |||||||
\(350\) | −5.91538 | −0.316190 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.54122 | 0.348154 | 0.174077 | − | 0.984732i | \(-0.444306\pi\) | ||||
0.174077 | + | 0.984732i | \(0.444306\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.3445 | 0.814403 | ||||||||
\(356\) | 19.8205 | 1.05049 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.93773 | −0.525225 | ||||||||
\(359\) | 3.56688 | 0.188253 | 0.0941265 | − | 0.995560i | \(-0.469994\pi\) | ||||
0.0941265 | + | 0.995560i | \(0.469994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.1765 | 2.00929 | ||||||||
\(362\) | −11.0245 | −0.579436 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.87845 | −0.412943 | ||||||||
\(365\) | −14.9914 | −0.784685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.38020 | 0.333044 | 0.166522 | − | 0.986038i | \(-0.446746\pi\) | ||||
0.166522 | + | 0.986038i | \(0.446746\pi\) | |||||||
\(368\) | −3.19231 | −0.166411 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −21.5720 | −1.12148 | ||||||||
\(371\) | −0.531600 | −0.0275993 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.6135 | −1.27444 | −0.637218 | − | 0.770683i | \(-0.719915\pi\) | ||||
−0.637218 | + | 0.770683i | \(0.719915\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.59974 | −0.495069 | ||||||||
\(377\) | 13.8293 | 0.712243 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.5946 | 1.62291 | 0.811453 | − | 0.584418i | \(-0.198677\pi\) | ||||
0.811453 | + | 0.584418i | \(0.198677\pi\) | |||||||
\(380\) | 36.2384 | 1.85899 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 35.7734 | 1.83033 | ||||||||
\(383\) | −17.0187 | −0.869614 | −0.434807 | − | 0.900524i | \(-0.643183\pi\) | ||||
−0.434807 | + | 0.900524i | \(0.643183\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.8321 | 0.958531 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −41.1436 | −2.08875 | ||||||||
\(389\) | 2.70796 | 0.137299 | 0.0686495 | − | 0.997641i | \(-0.478131\pi\) | ||||
0.0686495 | + | 0.997641i | \(0.478131\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.0660 | 1.87451 | ||||||||
\(392\) | −2.49721 | −0.126128 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.22352 | −0.414295 | ||||||||
\(395\) | −3.19520 | −0.160768 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.9423 | −1.05106 | −0.525531 | − | 0.850774i | \(-0.676133\pi\) | ||||
−0.525531 | + | 0.850774i | \(0.676133\pi\) | |||||||
\(398\) | 10.3526 | 0.518931 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.48718 | 0.0743592 | ||||||||
\(401\) | 12.7290 | 0.635658 | 0.317829 | − | 0.948148i | \(-0.397046\pi\) | ||||
0.317829 | + | 0.948148i | \(0.397046\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.5115 | −0.673057 | ||||||||
\(404\) | 17.1741 | 0.854441 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.3157 | 0.611216 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.25063 | 0.407967 | 0.203984 | − | 0.978974i | \(-0.434611\pi\) | ||||
0.203984 | + | 0.978974i | \(0.434611\pi\) | |||||||
\(410\) | −34.1287 | −1.68550 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 20.8077 | 1.02512 | ||||||||
\(413\) | 1.76077 | 0.0866418 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0682789 | 0.00335168 | ||||||||
\(416\) | 15.9281 | 0.780941 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.81767 | 0.284212 | 0.142106 | − | 0.989851i | \(-0.454613\pi\) | ||||
0.142106 | + | 0.989851i | \(0.454613\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.60495 | 0.370643 | 0.185321 | − | 0.982678i | \(-0.440667\pi\) | ||||
0.185321 | + | 0.982678i | \(0.440667\pi\) | |||||||
\(422\) | −2.64235 | −0.128628 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.32752 | −0.0644700 | ||||||||
\(425\) | −17.2678 | −0.837609 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.74760 | 0.229753 | ||||||||
\(428\) | −17.8698 | −0.863771 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33.5171 | 1.61634 | ||||||||
\(431\) | −23.3450 | −1.12449 | −0.562244 | − | 0.826971i | \(-0.690062\pi\) | ||||
−0.562244 | + | 0.826971i | \(0.690062\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.5912 | −0.653153 | −0.326576 | − | 0.945171i | \(-0.605895\pi\) | ||||
−0.326576 | + | 0.945171i | \(0.605895\pi\) | |||||||
\(434\) | −12.0327 | −0.577588 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 42.5605 | 2.03828 | ||||||||
\(437\) | −42.4936 | −2.03275 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.4203 | −1.78597 | −0.892986 | − | 0.450084i | \(-0.851394\pi\) | ||||
−0.892986 | + | 0.450084i | \(0.851394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −37.8109 | −1.79848 | ||||||||
\(443\) | 29.2812 | 1.39119 | 0.695597 | − | 0.718432i | \(-0.255140\pi\) | ||||
0.695597 | + | 0.718432i | \(0.255140\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.85124 | −0.466993 | ||||||||
\(446\) | 8.88651 | 0.420789 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.0487 | 0.616493 | ||||||||
\(449\) | 4.90362 | 0.231416 | 0.115708 | − | 0.993283i | \(-0.463086\pi\) | ||||
0.115708 | + | 0.993283i | \(0.463086\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −45.3498 | −2.13308 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −55.0387 | −2.58309 | ||||||||
\(455\) | 3.91576 | 0.183574 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.55754 | 0.0728585 | 0.0364292 | − | 0.999336i | \(-0.488402\pi\) | ||||
0.0364292 | + | 0.999336i | \(0.488402\pi\) | |||||||
\(458\) | 54.7413 | 2.55789 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −26.9324 | −1.25573 | ||||||||
\(461\) | 17.6580 | 0.822414 | 0.411207 | − | 0.911542i | \(-0.365107\pi\) | ||||
0.411207 | + | 0.911542i | \(0.365107\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.54726 | −0.211329 | −0.105664 | − | 0.994402i | \(-0.533697\pi\) | ||||
−0.105664 | + | 0.994402i | \(0.533697\pi\) | |||||||
\(464\) | −3.09628 | −0.143741 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −63.7083 | −2.95123 | ||||||||
\(467\) | 2.04275 | 0.0945271 | 0.0472636 | − | 0.998882i | \(-0.484950\pi\) | ||||
0.0472636 | + | 0.998882i | \(0.484950\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.60824 | 0.443667 | ||||||||
\(470\) | 13.4054 | 0.618344 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.39701 | 0.202389 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.7963 | 0.908317 | ||||||||
\(476\) | −20.4811 | −0.938749 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −42.1147 | −1.92628 | ||||||||
\(479\) | 8.13148 | 0.371537 | 0.185768 | − | 0.982594i | \(-0.440523\pi\) | ||||
0.185768 | + | 0.982594i | \(0.440523\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.6951 | −0.715636 | ||||||||
\(482\) | 39.4988 | 1.79912 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.4493 | 0.928555 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.7773 | −1.30402 | −0.652011 | − | 0.758209i | \(-0.726075\pi\) | ||||
−0.652011 | + | 0.758209i | \(0.726075\pi\) | |||||||
\(488\) | 11.8558 | 0.536685 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.48718 | 0.157535 | ||||||||
\(491\) | 5.29273 | 0.238858 | 0.119429 | − | 0.992843i | \(-0.461894\pi\) | ||||
0.119429 | + | 0.992843i | \(0.461894\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 35.9510 | 1.61915 | ||||||||
\(494\) | 43.3476 | 1.95030 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.02514 | 0.135833 | ||||||||
\(497\) | 9.94228 | 0.445972 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.4668 | −1.14005 | −0.570025 | − | 0.821628i | \(-0.693066\pi\) | ||||
−0.570025 | + | 0.821628i | \(0.693066\pi\) | |||||||
\(500\) | 36.5092 | 1.63274 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.13085 | 0.407530 | ||||||||
\(503\) | 42.0133 | 1.87328 | 0.936640 | − | 0.350293i | \(-0.113918\pi\) | ||||
0.936640 | + | 0.350293i | \(0.113918\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.53588 | −0.379842 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 41.9399 | 1.86078 | ||||||||
\(509\) | 31.9838 | 1.41766 | 0.708829 | − | 0.705380i | \(-0.249224\pi\) | ||||
0.708829 | + | 0.705380i | \(0.249224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.71346 | −0.429698 | ||||||||
\(512\) | −6.40330 | −0.282989 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.8824 | −0.965193 | ||||||||
\(515\) | −10.3419 | −0.455717 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.9773 | −0.614127 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.77849 | 0.428815 | ||||||||
\(521\) | −33.9429 | −1.48707 | −0.743533 | − | 0.668699i | \(-0.766852\pi\) | ||||
−0.743533 | + | 0.668699i | \(0.766852\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.1926 | 0.751779 | 0.375890 | − | 0.926664i | \(-0.377337\pi\) | ||||
0.375890 | + | 0.926664i | \(0.377337\pi\) | |||||||
\(524\) | −13.3610 | −0.583679 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.4969 | −0.501289 | ||||||||
\(527\) | −35.1250 | −1.53007 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.58133 | 0.373101 | ||||||||
\(530\) | 1.85379 | 0.0805234 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 23.4802 | 1.01799 | ||||||||
\(533\) | −24.8310 | −1.07555 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.88170 | 0.383989 | ||||||||
\(536\) | 23.9938 | 1.03638 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.507492 | 0.0218796 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.65418 | 0.329079 | 0.164539 | − | 0.986370i | \(-0.447386\pi\) | ||||
0.164539 | + | 0.986370i | \(0.447386\pi\) | |||||||
\(542\) | 55.0386 | 2.36411 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 41.4073 | 1.77532 | ||||||||
\(545\) | −21.1535 | −0.906117 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.9128 | −1.70655 | −0.853275 | − | 0.521462i | \(-0.825387\pi\) | ||||
−0.853275 | + | 0.521462i | \(0.825387\pi\) | |||||||
\(548\) | 38.9038 | 1.66189 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −41.2154 | −1.75583 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.07029 | −0.0880376 | ||||||||
\(554\) | 39.5402 | 1.67990 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 34.8600 | 1.47840 | ||||||||
\(557\) | −17.3280 | −0.734211 | −0.367105 | − | 0.930179i | \(-0.619651\pi\) | ||||
−0.367105 | + | 0.930179i | \(0.619651\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.3859 | 1.03142 | ||||||||
\(560\) | −0.876713 | −0.0370479 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 32.4346 | 1.36817 | ||||||||
\(563\) | −36.7312 | −1.54803 | −0.774017 | − | 0.633164i | \(-0.781756\pi\) | ||||
−0.774017 | + | 0.633164i | \(0.781756\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.5399 | 0.948259 | ||||||||
\(566\) | −63.2776 | −2.65976 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24.8280 | 1.04176 | ||||||||
\(569\) | −30.9746 | −1.29852 | −0.649261 | − | 0.760566i | \(-0.724922\pi\) | ||||
−0.649261 | + | 0.760566i | \(0.724922\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.7450 | 1.11925 | 0.559623 | − | 0.828748i | \(-0.310946\pi\) | ||||
0.559623 | + | 0.828748i | \(0.310946\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −22.1132 | −0.922989 | ||||||||
\(575\) | −14.7126 | −0.613559 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.6529 | −1.27610 | −0.638048 | − | 0.769996i | \(-0.720258\pi\) | ||||
−0.638048 | + | 0.769996i | \(0.720258\pi\) | |||||||
\(578\) | −59.8833 | −2.49082 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −26.1222 | −1.08467 | ||||||||
\(581\) | 0.0442404 | 0.00183540 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −24.2566 | −1.00374 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.1835 | 1.24687 | ||||||||
\(587\) | 16.6367 | 0.686670 | 0.343335 | − | 0.939213i | \(-0.388443\pi\) | ||||
0.343335 | + | 0.939213i | \(0.388443\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 40.2684 | 1.65923 | ||||||||
\(590\) | −6.14013 | −0.252785 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.51403 | 0.144426 | ||||||||
\(593\) | 37.7740 | 1.55119 | 0.775596 | − | 0.631230i | \(-0.217450\pi\) | ||||
0.775596 | + | 0.631230i | \(0.217450\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.1795 | 0.417321 | ||||||||
\(596\) | −37.6199 | −1.54097 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −32.2160 | −1.31741 | ||||||||
\(599\) | −25.0536 | −1.02366 | −0.511832 | − | 0.859086i | \(-0.671033\pi\) | ||||
−0.511832 | + | 0.859086i | \(0.671033\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.9247 | −1.75093 | −0.875467 | − | 0.483277i | \(-0.839446\pi\) | ||||
−0.875467 | + | 0.483277i | \(0.839446\pi\) | |||||||
\(602\) | 21.7169 | 0.885115 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 33.4985 | 1.36303 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.72896 | 0.354298 | 0.177149 | − | 0.984184i | \(-0.443313\pi\) | ||||
0.177149 | + | 0.984184i | \(0.443313\pi\) | |||||||
\(608\) | −47.4706 | −1.92519 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.5558 | −0.670323 | ||||||||
\(611\) | 9.75332 | 0.394577 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.79301 | 0.355146 | 0.177573 | − | 0.984108i | \(-0.443175\pi\) | ||||
0.177573 | + | 0.984108i | \(0.443175\pi\) | |||||||
\(614\) | 7.10986 | 0.286931 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.31423 | −0.334718 | −0.167359 | − | 0.985896i | \(-0.553524\pi\) | ||||
−0.167359 | + | 0.985896i | \(0.553524\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.35834 | 0.0947899 | 0.0473949 | − | 0.998876i | \(-0.484908\pi\) | ||||
0.0473949 | + | 0.998876i | \(0.484908\pi\) | |||||||
\(620\) | 25.5221 | 1.02499 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −55.4922 | −2.22504 | ||||||||
\(623\) | −6.38297 | −0.255728 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.05573 | −0.202229 | ||||||||
\(626\) | 48.6791 | 1.94561 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.4985 | −0.458838 | ||||||||
\(629\) | −40.8016 | −1.62686 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.3297 | 1.60550 | 0.802750 | − | 0.596316i | \(-0.203369\pi\) | ||||
0.802750 | + | 0.596316i | \(0.203369\pi\) | |||||||
\(632\) | −5.16995 | −0.205649 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.6878 | 0.662758 | ||||||||
\(635\) | −20.8451 | −0.827211 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.53716 | 0.100526 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −26.1250 | −1.03268 | ||||||||
\(641\) | 12.6982 | 0.501551 | 0.250775 | − | 0.968045i | \(-0.419314\pi\) | ||||
0.250775 | + | 0.968045i | \(0.419314\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.7309 | 0.580929 | 0.290465 | − | 0.956886i | \(-0.406190\pi\) | ||||
0.290465 | + | 0.956886i | \(0.406190\pi\) | |||||||
\(644\) | −17.4505 | −0.687645 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 112.688 | 4.43364 | ||||||||
\(647\) | −4.64105 | −0.182459 | −0.0912293 | − | 0.995830i | \(-0.529080\pi\) | ||||
−0.0912293 | + | 0.995830i | \(0.529080\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 15.0083 | 0.588673 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 70.0062 | 2.74165 | ||||||||
\(653\) | −22.8707 | −0.895001 | −0.447500 | − | 0.894284i | \(-0.647686\pi\) | ||||
−0.447500 | + | 0.894284i | \(0.647686\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.64072 | 0.259474 | ||||||||
\(656\) | 5.55949 | 0.217062 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.68582 | 0.338609 | ||||||||
\(659\) | 17.8597 | 0.695717 | 0.347858 | − | 0.937547i | \(-0.386909\pi\) | ||||
0.347858 | + | 0.937547i | \(0.386909\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.7110 | −0.727774 | −0.363887 | − | 0.931443i | \(-0.618551\pi\) | ||||
−0.363887 | + | 0.931443i | \(0.618551\pi\) | |||||||
\(662\) | 47.6516 | 1.85203 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.110478 | 0.00428736 | ||||||||
\(665\) | −11.6702 | −0.452549 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.6313 | 1.18605 | ||||||||
\(668\) | −44.1491 | −1.70818 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −33.5057 | −1.29444 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.15894 | 0.275957 | 0.137978 | − | 0.990435i | \(-0.455940\pi\) | ||||
0.137978 | + | 0.990435i | \(0.455940\pi\) | |||||||
\(674\) | 45.8611 | 1.76650 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.3789 | −0.783804 | ||||||||
\(677\) | −23.0053 | −0.884166 | −0.442083 | − | 0.896974i | \(-0.645760\pi\) | ||||
−0.442083 | + | 0.896974i | \(0.645760\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.2498 | 0.508482 | ||||||||
\(680\) | 25.4205 | 0.974831 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.0889 | −0.692152 | −0.346076 | − | 0.938206i | \(-0.612486\pi\) | ||||
−0.346076 | + | 0.938206i | \(0.612486\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.3360 | −0.738792 | ||||||||
\(686\) | 2.25947 | 0.0862671 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.45985 | −0.208155 | ||||||||
\(689\) | 1.34876 | 0.0513836 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.6850 | −1.01514 | −0.507572 | − | 0.861609i | \(-0.669457\pi\) | ||||
−0.507572 | + | 0.861609i | \(0.669457\pi\) | |||||||
\(692\) | −58.6232 | −2.22852 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −37.0961 | −1.40815 | ||||||||
\(695\) | −17.3262 | −0.657221 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −64.5514 | −2.44506 | ||||||||
\(698\) | 64.1638 | 2.42864 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.12957 | 0.307269 | ||||||||
\(701\) | −14.2569 | −0.538477 | −0.269238 | − | 0.963074i | \(-0.586772\pi\) | ||||
−0.269238 | + | 0.963074i | \(0.586772\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46.7762 | 1.76420 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.7797 | −0.556242 | ||||||||
\(707\) | −5.53071 | −0.208004 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.0584 | 0.603085 | 0.301543 | − | 0.953453i | \(-0.402498\pi\) | ||||
0.301543 | + | 0.953453i | \(0.402498\pi\) | |||||||
\(710\) | −34.6706 | −1.30116 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.9396 | −0.597363 | ||||||||
\(713\) | −29.9276 | −1.12080 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.6575 | 0.510406 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.05928 | −0.300770 | ||||||||
\(719\) | −37.0621 | −1.38218 | −0.691091 | − | 0.722768i | \(-0.742869\pi\) | ||||
−0.691091 | + | 0.722768i | \(0.742869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.70087 | −0.249554 | ||||||||
\(722\) | −86.2588 | −3.21022 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.1511 | 0.563087 | ||||||||
\(725\) | −14.2701 | −0.529977 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.6597 | 0.543698 | 0.271849 | − | 0.962340i | \(-0.412365\pi\) | ||||
0.271849 | + | 0.962340i | \(0.412365\pi\) | |||||||
\(728\) | 6.33584 | 0.234822 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 33.8726 | 1.25368 | ||||||||
\(731\) | 63.3945 | 2.34473 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.9555 | −1.06949 | −0.534747 | − | 0.845012i | \(-0.679593\pi\) | ||||
−0.534747 | + | 0.845012i | \(0.679593\pi\) | |||||||
\(734\) | −14.4159 | −0.532100 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 35.2802 | 1.30045 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.43921 | 0.310441 | 0.155221 | − | 0.987880i | \(-0.450391\pi\) | ||||
0.155221 | + | 0.987880i | \(0.450391\pi\) | |||||||
\(740\) | 29.6467 | 1.08983 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.20114 | 0.0440951 | ||||||||
\(743\) | −47.7420 | −1.75149 | −0.875743 | − | 0.482778i | \(-0.839628\pi\) | ||||
−0.875743 | + | 0.482778i | \(0.839628\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.6979 | 0.685039 | ||||||||
\(746\) | 55.6135 | 2.03615 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.75478 | 0.210275 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.931618 | −0.0339952 | −0.0169976 | − | 0.999856i | \(-0.505411\pi\) | ||||
−0.0169976 | + | 0.999856i | \(0.505411\pi\) | |||||||
\(752\) | −2.18370 | −0.0796314 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −31.2468 | −1.13794 | ||||||||
\(755\) | −16.6495 | −0.605936 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.9127 | −0.578355 | −0.289178 | − | 0.957275i | \(-0.593382\pi\) | ||||
−0.289178 | + | 0.957275i | \(0.593382\pi\) | |||||||
\(758\) | −71.3872 | −2.59290 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −29.1428 | −1.05712 | ||||||||
\(761\) | −0.221975 | −0.00804657 | −0.00402328 | − | 0.999992i | \(-0.501281\pi\) | ||||
−0.00402328 | + | 0.999992i | \(0.501281\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.7061 | −0.496195 | ||||||||
\(764\) | −49.1638 | −1.77868 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 38.4532 | 1.38937 | ||||||||
\(767\) | −4.46736 | −0.161307 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.0307 | −1.58779 | −0.793894 | − | 0.608056i | \(-0.791949\pi\) | ||||
−0.793894 | + | 0.608056i | \(0.791949\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −25.8812 | −0.931485 | ||||||||
\(773\) | 44.3759 | 1.59609 | 0.798045 | − | 0.602598i | \(-0.205868\pi\) | ||||
0.798045 | + | 0.602598i | \(0.205868\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.9422 | 0.500819 | ||||||||
\(776\) | 33.0876 | 1.18778 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.11856 | −0.219361 | ||||||||
\(779\) | 74.0038 | 2.65146 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −83.7497 | −2.99488 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.568054 | −0.0202876 | ||||||||
\(785\) | 5.71498 | 0.203977 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.2307 | −0.614210 | −0.307105 | − | 0.951676i | \(-0.599360\pi\) | ||||
−0.307105 | + | 0.951676i | \(0.599360\pi\) | |||||||
\(788\) | 11.3017 | 0.402605 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.21948 | 0.256857 | ||||||||
\(791\) | 14.6044 | 0.519272 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.0454 | −0.427746 | ||||||||
\(794\) | 47.3185 | 1.67927 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.2278 | −0.504290 | ||||||||
\(797\) | −32.7314 | −1.15941 | −0.579703 | − | 0.814828i | \(-0.696832\pi\) | ||||
−0.579703 | + | 0.814828i | \(0.696832\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.3551 | 0.896997 | ||||||||
\(800\) | −16.4358 | −0.581094 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.7609 | −1.01558 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.67327 | 0.305693 | ||||||||
\(806\) | 30.5289 | 1.07534 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.8113 | −0.485882 | ||||||||
\(809\) | −36.9725 | −1.29988 | −0.649942 | − | 0.759984i | \(-0.725207\pi\) | ||||
−0.649942 | + | 0.759984i | \(0.725207\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.4600 | −0.577990 | −0.288995 | − | 0.957331i | \(-0.593321\pi\) | ||||
−0.288995 | + | 0.957331i | \(0.593321\pi\) | |||||||
\(812\) | −16.9255 | −0.593970 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34.7946 | −1.21880 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −72.6774 | −2.54266 | ||||||||
\(818\) | −18.6421 | −0.651805 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 46.9035 | 1.63794 | ||||||||
\(821\) | 7.48406 | 0.261195 | 0.130598 | − | 0.991435i | \(-0.458310\pi\) | ||||
0.130598 | + | 0.991435i | \(0.458310\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.6217 | −1.65999 | −0.829994 | − | 0.557772i | \(-0.811656\pi\) | ||||
−0.829994 | + | 0.557772i | \(0.811656\pi\) | |||||||
\(824\) | −16.7335 | −0.582939 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.97841 | −0.138427 | ||||||||
\(827\) | −37.8258 | −1.31533 | −0.657666 | − | 0.753310i | \(-0.728456\pi\) | ||||
−0.657666 | + | 0.753310i | \(0.728456\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.27021 | −0.217773 | −0.108887 | − | 0.994054i | \(-0.534729\pi\) | ||||
−0.108887 | + | 0.994054i | \(0.534729\pi\) | |||||||
\(830\) | −0.154274 | −0.00535494 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −33.1067 | −1.14777 | ||||||||
\(833\) | 6.59570 | 0.228527 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.9431 | 0.759371 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.1449 | −0.454082 | ||||||||
\(839\) | 13.8793 | 0.479166 | 0.239583 | − | 0.970876i | \(-0.422989\pi\) | ||||
0.239583 | + | 0.970876i | \(0.422989\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.709871 | 0.0244783 | ||||||||
\(842\) | −17.1832 | −0.592172 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.63142 | 0.124998 | ||||||||
\(845\) | 10.1288 | 0.348440 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.301978 | −0.0103700 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 39.0160 | 1.33824 | ||||||||
\(851\) | −34.7641 | −1.19170 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.4608 | −0.871762 | −0.435881 | − | 0.900004i | \(-0.643563\pi\) | ||||
−0.435881 | + | 0.900004i | \(0.643563\pi\) | |||||||
\(854\) | −10.7271 | −0.367073 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.3709 | 0.491187 | ||||||||
\(857\) | −50.8757 | −1.73788 | −0.868941 | − | 0.494916i | \(-0.835199\pi\) | ||||
−0.868941 | + | 0.494916i | \(0.835199\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.2976 | −1.27258 | −0.636288 | − | 0.771452i | \(-0.719531\pi\) | ||||
−0.636288 | + | 0.771452i | \(0.719531\pi\) | |||||||
\(860\) | −46.0629 | −1.57073 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 52.7474 | 1.79658 | ||||||||
\(863\) | −12.8773 | −0.438348 | −0.219174 | − | 0.975686i | \(-0.570336\pi\) | ||||
−0.219174 | + | 0.975686i | \(0.570336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.1370 | 0.990689 | ||||||||
\(866\) | 30.7090 | 1.04353 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.5367 | 0.561291 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.3777 | −0.826007 | ||||||||
\(872\) | −34.2271 | −1.15908 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 96.0133 | 3.24770 | ||||||||
\(875\) | −11.7574 | −0.397472 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.8105 | −0.365046 | −0.182523 | − | 0.983202i | \(-0.558426\pi\) | ||||
−0.182523 | + | 0.983202i | \(0.558426\pi\) | |||||||
\(878\) | 84.5501 | 2.85343 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.9303 | −0.671467 | −0.335734 | − | 0.941957i | \(-0.608984\pi\) | ||||
−0.335734 | + | 0.941957i | \(0.608984\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.1591 | −0.913976 | −0.456988 | − | 0.889473i | \(-0.651072\pi\) | ||||
−0.456988 | + | 0.889473i | \(0.651072\pi\) | |||||||
\(884\) | 51.9639 | 1.74773 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −66.1602 | −2.22269 | ||||||||
\(887\) | −6.37071 | −0.213908 | −0.106954 | − | 0.994264i | \(-0.534110\pi\) | ||||
−0.106954 | + | 0.994264i | \(0.534110\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.5063 | −0.452986 | ||||||||
\(890\) | 22.2586 | 0.746110 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.2128 | −0.408916 | ||||||||
\(893\) | −29.0678 | −0.972718 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.78809 | −0.226901 | ||||||||
\(896\) | −16.9273 | −0.565502 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.0796 | −0.369731 | ||||||||
\(899\) | −29.0273 | −0.968114 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.50628 | 0.116811 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 36.4703 | 1.21298 | ||||||||
\(905\) | −7.53044 | −0.250320 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.2413 | −0.373262 | −0.186631 | − | 0.982430i | \(-0.559757\pi\) | ||||
−0.186631 | + | 0.982430i | \(0.559757\pi\) | |||||||
\(908\) | 75.6403 | 2.51021 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.84756 | −0.293294 | ||||||||
\(911\) | −32.3301 | −1.07114 | −0.535572 | − | 0.844490i | \(-0.679904\pi\) | ||||
−0.535572 | + | 0.844490i | \(0.679904\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −3.51921 | −0.116405 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −75.2315 | −2.48572 | ||||||||
\(917\) | 4.30276 | 0.142090 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.9783 | −0.560063 | −0.280031 | − | 0.959991i | \(-0.590345\pi\) | ||||
−0.280031 | + | 0.959991i | \(0.590345\pi\) | |||||||
\(920\) | 21.6590 | 0.714076 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −39.8977 | −1.31396 | ||||||||
\(923\) | −25.2252 | −0.830298 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.1954 | 0.532501 | ||||||||
\(926\) | 10.2744 | 0.337638 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 34.2189 | 1.12329 | ||||||||
\(929\) | 7.11309 | 0.233373 | 0.116686 | − | 0.993169i | \(-0.462773\pi\) | ||||
0.116686 | + | 0.993169i | \(0.462773\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.56151 | −0.247819 | ||||||||
\(932\) | 87.5551 | 2.86796 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.61554 | −0.151025 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.6317 | 0.510665 | 0.255332 | − | 0.966853i | \(-0.417815\pi\) | ||||
0.255332 | + | 0.966853i | \(0.417815\pi\) | |||||||
\(938\) | −21.7096 | −0.708843 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.4231 | −0.600897 | ||||||||
\(941\) | −5.05065 | −0.164646 | −0.0823232 | − | 0.996606i | \(-0.526234\pi\) | ||||
−0.0823232 | + | 0.996606i | \(0.526234\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −54.9997 | −1.79104 | ||||||||
\(944\) | 1.00021 | 0.0325541 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.3081 | 0.659925 | 0.329963 | − | 0.943994i | \(-0.392964\pi\) | ||||
0.329963 | + | 0.943994i | \(0.392964\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.6447 | 0.799999 | ||||||||
\(950\) | −44.7292 | −1.45121 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16.4709 | 0.533823 | ||||||||
\(953\) | −29.3431 | −0.950515 | −0.475257 | − | 0.879847i | \(-0.657645\pi\) | ||||
−0.475257 | + | 0.879847i | \(0.657645\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.4355 | 0.790714 | ||||||||
\(956\) | 57.8787 | 1.87193 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.3729 | −0.593600 | ||||||||
\(959\) | −12.5285 | −0.404567 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.63962 | −0.0851491 | ||||||||
\(962\) | 35.4627 | 1.14336 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −54.2837 | −1.74836 | ||||||||
\(965\) | 12.8635 | 0.414092 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.2155 | 1.13245 | 0.566227 | − | 0.824249i | \(-0.308402\pi\) | ||||
0.566227 | + | 0.824249i | \(0.308402\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −46.2046 | −1.48354 | ||||||||
\(971\) | −4.93270 | −0.158298 | −0.0791490 | − | 0.996863i | \(-0.525220\pi\) | ||||
−0.0791490 | + | 0.996863i | \(0.525220\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.2263 | −0.359898 | ||||||||
\(974\) | 65.0215 | 2.08342 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.69689 | 0.0863255 | ||||||||
\(977\) | −30.3307 | −0.970366 | −0.485183 | − | 0.874413i | \(-0.661247\pi\) | ||||
−0.485183 | + | 0.874413i | \(0.661247\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −4.79248 | −0.153090 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11.9588 | −0.381620 | ||||||||
\(983\) | 40.7718 | 1.30042 | 0.650209 | − | 0.759756i | \(-0.274681\pi\) | ||||
0.650209 | + | 0.759756i | \(0.274681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.61718 | −0.178978 | ||||||||
\(986\) | −81.2303 | −2.58690 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −59.5730 | −1.89527 | ||||||||
\(989\) | 54.0140 | 1.71754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.0927 | 0.352370 | 0.176185 | − | 0.984357i | \(-0.443624\pi\) | ||||
0.176185 | + | 0.984357i | \(0.443624\pi\) | |||||||
\(992\) | −33.4328 | −1.06149 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22.4643 | −0.712525 | ||||||||
\(995\) | 7.07151 | 0.224182 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.3185 | −0.833515 | −0.416757 | − | 0.909018i | \(-0.636834\pi\) | ||||
−0.416757 | + | 0.909018i | \(0.636834\pi\) | |||||||
\(998\) | 57.5415 | 1.82144 | ||||||||
\(999\) | 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 | 7623.2.a.cu.1.1 | 8 | ||
3.2 | odd | 2 | inner | 7623.2.a.cu.1.8 | 8 | ||
11.3 | even | 5 | 693.2.m.h.64.1 | ✓ | 16 | ||
11.4 | even | 5 | 693.2.m.h.379.1 | yes | 16 | ||
11.10 | odd | 2 | 7623.2.a.cv.1.8 | 8 | |||
33.14 | odd | 10 | 693.2.m.h.64.4 | yes | 16 | ||
33.26 | odd | 10 | 693.2.m.h.379.4 | yes | 16 | ||
33.32 | even | 2 | 7623.2.a.cv.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
693.2.m.h.64.1 | ✓ | 16 | 11.3 | even | 5 | ||
693.2.m.h.64.4 | yes | 16 | 33.14 | odd | 10 | ||
693.2.m.h.379.1 | yes | 16 | 11.4 | even | 5 | ||
693.2.m.h.379.4 | yes | 16 | 33.26 | odd | 10 | ||
7623.2.a.cu.1.1 | 8 | 1.1 | even | 1 | trivial | ||
7623.2.a.cu.1.8 | 8 | 3.2 | odd | 2 | inner | ||
7623.2.a.cv.1.1 | 8 | 33.32 | even | 2 | |||
7623.2.a.cv.1.8 | 8 | 11.10 | odd | 2 |