Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 35 x^{13} + 32 x^{12} + 477 x^{11} - 392 x^{10} - 3236 x^{9} + 2330 x^{8} + 11690 x^{7} - 7119 x^{6} - 22246 x^{5} + 11137 x^{4} + 20034 x^{3} - 8392 x^{2} + \cdots + 2560 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.804723\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.804723 | 0.464607 | 0.232303 | − | 0.972643i | \(-0.425374\pi\) | ||||
0.232303 | + | 0.972643i | \(0.425374\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.337817 | −0.151076 | −0.0755382 | − | 0.997143i | \(-0.524067\pi\) | ||||
−0.0755382 | + | 0.997143i | \(0.524067\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.35242 | −0.784141 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.271849 | −0.0701912 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.72499 | −0.418372 | −0.209186 | − | 0.977876i | \(-0.567081\pi\) | ||||
−0.209186 | + | 0.977876i | \(0.567081\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.84801 | 0.882794 | 0.441397 | − | 0.897312i | \(-0.354483\pi\) | ||||
0.441397 | + | 0.897312i | \(0.354483\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.804723 | −0.175605 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.18228 | −0.246522 | −0.123261 | − | 0.992374i | \(-0.539335\pi\) | ||||
−0.123261 | + | 0.992374i | \(0.539335\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88588 | −0.977176 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.30721 | −0.828924 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.19613 | 1.52198 | 0.760991 | − | 0.648762i | \(-0.224713\pi\) | ||||
0.760991 | + | 0.648762i | \(0.224713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.39204 | 0.788834 | 0.394417 | − | 0.918932i | \(-0.370947\pi\) | ||||
0.394417 | + | 0.918932i | \(0.370947\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.804723 | −0.140084 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.337817 | 0.0571015 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.55083 | −1.40575 | −0.702874 | − | 0.711315i | \(-0.748100\pi\) | ||||
−0.702874 | + | 0.711315i | \(0.748100\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.804723 | 0.128859 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.35008 | 0.523195 | 0.261598 | − | 0.965177i | \(-0.415751\pi\) | ||||
0.261598 | + | 0.965177i | \(0.415751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.49568 | 1.14308 | 0.571541 | − | 0.820574i | \(-0.306346\pi\) | ||||
0.571541 | + | 0.820574i | \(0.306346\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.794689 | 0.118465 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.05444 | −0.591401 | −0.295701 | − | 0.955281i | \(-0.595553\pi\) | ||||
−0.295701 | + | 0.955281i | \(0.595553\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.38814 | −0.194378 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.73577 | −1.19995 | −0.599975 | − | 0.800019i | \(-0.704823\pi\) | ||||
−0.599975 | + | 0.800019i | \(0.704823\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.337817 | 0.0455513 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.09658 | 0.410152 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.60840 | 0.469774 | 0.234887 | − | 0.972023i | \(-0.424528\pi\) | ||||
0.234887 | + | 0.972023i | \(0.424528\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.64244 | 0.466367 | 0.233183 | − | 0.972433i | \(-0.425086\pi\) | ||||
0.233183 | + | 0.972433i | \(0.425086\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.35242 | 0.296377 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.337817 | −0.0419011 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.01726 | −0.612956 | −0.306478 | − | 0.951878i | \(-0.599151\pi\) | ||||
−0.306478 | + | 0.951878i | \(0.599151\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.951407 | −0.114536 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.791482 | −0.0939316 | −0.0469658 | − | 0.998896i | \(-0.514955\pi\) | ||||
−0.0469658 | + | 0.998896i | \(0.514955\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.54964 | 1.00066 | 0.500330 | − | 0.865835i | \(-0.333212\pi\) | ||||
0.500330 | + | 0.865835i | \(0.333212\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.93178 | −0.454003 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.5648 | −1.75118 | −0.875589 | − | 0.483057i | \(-0.839526\pi\) | ||||
−0.875589 | + | 0.483057i | \(0.839526\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.59115 | 0.399017 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.6191 | 1.27536 | 0.637680 | − | 0.770301i | \(-0.279894\pi\) | ||||
0.637680 | + | 0.770301i | \(0.279894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.582732 | 0.0632061 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.59561 | 0.707124 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.70415 | −0.498639 | −0.249319 | − | 0.968421i | \(-0.580207\pi\) | ||||
−0.249319 | + | 0.968421i | \(0.580207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.53438 | 0.366498 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.29992 | −0.133369 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.95235 | −1.01051 | −0.505254 | − | 0.862971i | \(-0.668601\pi\) | ||||
−0.505254 | + | 0.862971i | \(0.668601\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.35242 | 0.236427 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.2805 | 1.81898 | 0.909488 | − | 0.415730i | \(-0.136474\pi\) | ||||
0.909488 | + | 0.415730i | \(0.136474\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.6336 | 1.24483 | 0.622413 | − | 0.782689i | \(-0.286153\pi\) | ||||
0.622413 | + | 0.782689i | \(0.286153\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.271849 | 0.0265298 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.18691 | 0.114743 | 0.0573715 | − | 0.998353i | \(-0.481728\pi\) | ||||
0.0573715 | + | 0.998353i | \(0.481728\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4650 | 1.38550 | 0.692749 | − | 0.721178i | \(-0.256399\pi\) | ||||
0.692749 | + | 0.721178i | \(0.256399\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.88105 | −0.653120 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.5775 | −1.08912 | −0.544558 | − | 0.838723i | \(-0.683303\pi\) | ||||
−0.544558 | + | 0.838723i | \(0.683303\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.399394 | 0.0372437 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.35242 | −0.217481 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.72499 | 0.158130 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.69589 | 0.243080 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.33962 | 0.298705 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.9915 | 1.77396 | 0.886981 | − | 0.461806i | \(-0.152798\pi\) | ||||
0.886981 | + | 0.461806i | \(0.152798\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.03195 | 0.531083 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.62283 | −0.403898 | −0.201949 | − | 0.979396i | \(-0.564728\pi\) | ||||
−0.201949 | + | 0.979396i | \(0.564728\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.84801 | −0.333665 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.45505 | 0.125231 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.8908 | 1.52852 | 0.764258 | − | 0.644911i | \(-0.223106\pi\) | ||||
0.764258 | + | 0.644911i | \(0.223106\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.09613 | −0.686705 | −0.343352 | − | 0.939207i | \(-0.611562\pi\) | ||||
−0.343352 | + | 0.939207i | \(0.611562\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.26270 | −0.274769 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.76879 | −0.229936 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.804723 | 0.0663724 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.23448 | 0.264979 | 0.132489 | − | 0.991184i | \(-0.457703\pi\) | ||||
0.132489 | + | 0.991184i | \(0.457703\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.5150 | −1.75087 | −0.875433 | − | 0.483339i | \(-0.839424\pi\) | ||||
−0.875433 | + | 0.483339i | \(0.839424\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.05791 | 0.328062 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.48371 | −0.119174 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.1699 | 1.21069 | 0.605344 | − | 0.795964i | \(-0.293036\pi\) | ||||
0.605344 | + | 0.795964i | \(0.293036\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.02987 | −0.557505 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.18228 | 0.0931767 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.7280 | 1.31024 | 0.655120 | − | 0.755525i | \(-0.272618\pi\) | ||||
0.655120 | + | 0.755525i | \(0.272618\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.271849 | 0.0211634 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.6673 | 1.44452 | 0.722259 | − | 0.691622i | \(-0.243104\pi\) | ||||
0.722259 | + | 0.691622i | \(0.243104\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.05214 | −0.692234 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.84617 | 0.216391 | 0.108195 | − | 0.994130i | \(-0.465493\pi\) | ||||
0.108195 | + | 0.994130i | \(0.465493\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.88588 | 0.369338 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.90376 | 0.218260 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.8283 | 1.10832 | 0.554160 | − | 0.832410i | \(-0.313039\pi\) | ||||
0.554160 | + | 0.832410i | \(0.313039\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.2463 | −1.43056 | −0.715281 | − | 0.698837i | \(-0.753701\pi\) | ||||
−0.715281 | + | 0.698837i | \(0.753701\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.93115 | 0.216677 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.88862 | 0.212375 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.72499 | 0.126144 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.30721 | 0.313304 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.53657 | 0.328254 | 0.164127 | − | 0.986439i | \(-0.447519\pi\) | ||||
0.164127 | + | 0.986439i | \(0.447519\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.96448 | 0.501314 | 0.250657 | − | 0.968076i | \(-0.419353\pi\) | ||||
0.250657 | + | 0.968076i | \(0.419353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.271849 | −0.0194675 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.05837 | 0.217900 | 0.108950 | − | 0.994047i | \(-0.465251\pi\) | ||||
0.108950 | + | 0.994047i | \(0.465251\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.1399 | −0.789688 | −0.394844 | − | 0.918748i | \(-0.629201\pi\) | ||||
−0.394844 | + | 0.918748i | \(0.629201\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.03750 | −0.284783 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.19613 | −0.575255 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.13172 | −0.0790425 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.78122 | 0.193308 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.84801 | −0.266172 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.6682 | 1.00980 | 0.504900 | − | 0.863178i | \(-0.331529\pi\) | ||||
0.504900 | + | 0.863178i | \(0.331529\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.636924 | −0.0436413 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.53217 | −0.172693 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.39204 | −0.298151 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.88009 | 0.464913 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.72499 | −0.116035 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.4786 | 1.37135 | 0.685674 | − | 0.727909i | \(-0.259507\pi\) | ||||
0.685674 | + | 0.727909i | \(0.259507\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.4936 | 0.766243 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.36703 | −0.621712 | −0.310856 | − | 0.950457i | \(-0.600616\pi\) | ||||
−0.310856 | + | 0.950457i | \(0.600616\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.0926 | 1.65816 | 0.829081 | − | 0.559128i | \(-0.188864\pi\) | ||||
0.829081 | + | 0.559128i | \(0.188864\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.804723 | 0.0529469 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.9120 | 1.56653 | 0.783263 | − | 0.621691i | \(-0.213554\pi\) | ||||
0.783263 | + | 0.621691i | \(0.213554\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.36966 | 0.0893468 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.5254 | −0.813609 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.6714 | −1.01370 | −0.506850 | − | 0.862034i | \(-0.669190\pi\) | ||||
−0.506850 | + | 0.862034i | \(0.669190\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8205 | −0.697008 | −0.348504 | − | 0.937307i | \(-0.613310\pi\) | ||||
−0.348504 | + | 0.937307i | \(0.613310\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.8115 | 1.01431 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.337817 | −0.0215824 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.84801 | 0.244843 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.35014 | 0.592541 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.5868 | 1.61503 | 0.807513 | − | 0.589850i | \(-0.200813\pi\) | ||||
0.807513 | + | 0.589850i | \(0.200813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.18228 | 0.0743293 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.468937 | 0.0293660 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.0997874 | −0.00622457 | −0.00311228 | − | 0.999995i | \(-0.500991\pi\) | ||||
−0.00311228 | + | 0.999995i | \(0.500991\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.55083 | 0.531323 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.2808 | −1.19345 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.4546 | −1.38461 | −0.692305 | − | 0.721605i | \(-0.743405\pi\) | ||||
−0.692305 | + | 0.721605i | \(0.743405\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.95109 | 0.181284 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.78554 | −0.231671 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.5223 | 1.92195 | 0.960973 | − | 0.276642i | \(-0.0892217\pi\) | ||||
0.960973 | + | 0.276642i | \(0.0892217\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.29902 | −0.200401 | −0.100201 | − | 0.994967i | \(-0.531948\pi\) | ||||
−0.100201 | + | 0.994967i | \(0.531948\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.804723 | −0.0487040 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.88588 | 0.294630 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.3345 | −0.861279 | −0.430640 | − | 0.902524i | \(-0.641712\pi\) | ||||
−0.430640 | + | 0.902524i | \(0.641712\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.3319 | −0.618557 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.75341 | 0.283565 | 0.141782 | − | 0.989898i | \(-0.454717\pi\) | ||||
0.141782 | + | 0.989898i | \(0.454717\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.7122 | 0.993437 | 0.496719 | − | 0.867912i | \(-0.334538\pi\) | ||||
0.496719 | + | 0.867912i | \(0.334538\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.04608 | −0.0619643 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.35008 | −0.197749 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0244 | −0.824965 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.00888 | −0.469489 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.9887 | 1.34301 | 0.671507 | − | 0.740998i | \(-0.265647\pi\) | ||||
0.671507 | + | 0.740998i | \(0.265647\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.21898 | −0.0709718 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.30721 | 0.249930 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.18228 | −0.0683730 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.49568 | −0.432044 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.7107 | 0.845109 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.23048 | −0.0704570 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.25287 | 0.128578 | 0.0642890 | − | 0.997931i | \(-0.479522\pi\) | ||||
0.0642890 | + | 0.997931i | \(0.479522\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.1665 | 0.578354 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.2444 | −1.09125 | −0.545625 | − | 0.838029i | \(-0.683708\pi\) | ||||
−0.545625 | + | 0.838029i | \(0.683708\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.1366 | 1.36428 | 0.682140 | − | 0.731222i | \(-0.261050\pi\) | ||||
0.682140 | + | 0.731222i | \(0.261050\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.794689 | −0.0447756 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.52023 | 0.310047 | 0.155024 | − | 0.987911i | \(-0.450455\pi\) | ||||
0.155024 | + | 0.987911i | \(0.450455\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.19613 | −0.458895 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.955135 | 0.0533104 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.63778 | −0.369336 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.88588 | −0.271020 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.6403 | 0.643712 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.05444 | 0.223529 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.60003 | −0.417735 | −0.208868 | − | 0.977944i | \(-0.566978\pi\) | ||||
−0.208868 | + | 0.977944i | \(0.566978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.1152 | 1.10230 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.69492 | 0.0926032 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.11912 | −0.224383 | −0.112191 | − | 0.993687i | \(-0.535787\pi\) | ||||
−0.112191 | + | 0.993687i | \(0.535787\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.31665 | −0.506011 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.39204 | −0.237842 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.321402 | 0.0173037 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.22235 | 0.280350 | 0.140175 | − | 0.990127i | \(-0.455233\pi\) | ||||
0.140175 | + | 0.990127i | \(0.455233\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.9918 | 0.909549 | 0.454774 | − | 0.890607i | \(-0.349720\pi\) | ||||
0.454774 | + | 0.890607i | \(0.349720\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.30721 | −0.229902 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.5693 | 1.09480 | 0.547398 | − | 0.836872i | \(-0.315618\pi\) | ||||
0.547398 | + | 0.836872i | \(0.315618\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.267376 | 0.0141909 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.38814 | 0.0734681 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.77260 | −0.0935541 | −0.0467771 | − | 0.998905i | \(-0.514895\pi\) | ||||
−0.0467771 | + | 0.998905i | \(0.514895\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.19282 | −0.220675 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.804723 | 0.0422370 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.88821 | −0.151176 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.53966 | −0.497966 | −0.248983 | − | 0.968508i | \(-0.580096\pi\) | ||||
−0.248983 | + | 0.968508i | \(0.580096\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.88081 | −0.410259 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.73577 | 0.453539 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.8531 | 1.49396 | 0.746978 | − | 0.664849i | \(-0.231504\pi\) | ||||
0.746978 | + | 0.664849i | \(0.231504\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.68747 | 0.138780 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.19613 | 0.422122 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.74582 | 0.346509 | 0.173255 | − | 0.984877i | \(-0.444572\pi\) | ||||
0.173255 | + | 0.984877i | \(0.444572\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.0876 | 0.824195 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.38307 | 0.428355 | 0.214177 | − | 0.976795i | \(-0.431293\pi\) | ||||
0.214177 | + | 0.976795i | \(0.431293\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.337817 | −0.0172168 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.6330 | −0.896336 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.44907 | 0.377683 | 0.188841 | − | 0.982008i | \(-0.439527\pi\) | ||||
0.188841 | + | 0.982008i | \(0.439527\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.03942 | 0.103138 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.72009 | −0.187654 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.25806 | 0.264562 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.2952 | −1.62085 | −0.810425 | − | 0.585843i | \(-0.800763\pi\) | ||||
−0.810425 | + | 0.585843i | \(0.800763\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.09658 | −0.155023 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.8338 | −0.990454 | −0.495227 | − | 0.868764i | \(-0.664915\pi\) | ||||
−0.495227 | + | 0.868764i | \(0.664915\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.39204 | 0.218783 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.21315 | −0.0602820 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.55083 | 0.423849 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.3553 | −0.858163 | −0.429082 | − | 0.903266i | \(-0.641163\pi\) | ||||
−0.429082 | + | 0.903266i | \(0.641163\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.3971 | 0.710159 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.60840 | −0.177558 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.92513 | −0.192677 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.51514 | −0.319048 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.5545 | −1.39498 | −0.697490 | − | 0.716595i | \(-0.745700\pi\) | ||||
−0.697490 | + | 0.716595i | \(0.745700\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.37781 | 0.359572 | 0.179786 | − | 0.983706i | \(-0.442459\pi\) | ||||
0.179786 | + | 0.983706i | \(0.442459\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.53776 | 0.463742 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.42810 | 0.408823 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.64244 | −0.176270 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.804723 | −0.0388524 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.08144 | −0.389269 | −0.194635 | − | 0.980876i | \(-0.562352\pi\) | ||||
−0.194635 | + | 0.980876i | \(0.562352\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.91199 | 0.236055 | 0.118028 | − | 0.993010i | \(-0.462343\pi\) | ||||
0.118028 | + | 0.993010i | \(0.462343\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.22811 | −0.106830 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.54942 | −0.217628 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.96827 | −0.475760 | −0.237880 | − | 0.971295i | \(-0.576452\pi\) | ||||
−0.237880 | + | 0.971295i | \(0.576452\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.35242 | −0.112020 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.86795 | 0.468841 | 0.234420 | − | 0.972135i | \(-0.424681\pi\) | ||||
0.234420 | + | 0.972135i | \(0.424681\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.58914 | 0.0753326 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.60286 | 0.123111 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.5207 | −0.685276 | −0.342638 | − | 0.939467i | \(-0.611320\pi\) | ||||
−0.342638 | + | 0.939467i | \(0.611320\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.35008 | −0.157749 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.3136 | −0.813465 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.337817 | 0.0158371 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.82950 | −0.319471 | −0.159735 | − | 0.987160i | \(-0.551064\pi\) | ||||
−0.159735 | + | 0.987160i | \(0.551064\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.42991 | 0.346798 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.0736 | 0.748623 | 0.374312 | − | 0.927303i | \(-0.377879\pi\) | ||||
0.374312 | + | 0.927303i | \(0.377879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.5734 | 0.863177 | 0.431589 | − | 0.902071i | \(-0.357953\pi\) | ||||
0.431589 | + | 0.902071i | \(0.357953\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.19397 | −0.0553692 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.2575 | 0.706034 | 0.353017 | − | 0.935617i | \(-0.385156\pi\) | ||||
0.353017 | + | 0.935617i | \(0.385156\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.01726 | 0.231676 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.2075 | 0.562494 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.49568 | −0.344652 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.8009 | −0.862645 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.5502 | 0.940930 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.8332 | −0.906200 | −0.453100 | − | 0.891460i | \(-0.649682\pi\) | ||||
−0.453100 | + | 0.891460i | \(0.649682\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.55083 | −0.389884 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.951407 | 0.0432905 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.36207 | 0.152664 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.1839 | 1.45839 | 0.729196 | − | 0.684305i | \(-0.239894\pi\) | ||||
0.729196 | + | 0.684305i | \(0.239894\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.4614 | 0.608746 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.29478 | −0.329209 | −0.164604 | − | 0.986360i | \(-0.552635\pi\) | ||||
−0.164604 | + | 0.986360i | \(0.552635\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.1383 | −0.636755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.794689 | −0.0357186 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.791482 | 0.0355028 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.7508 | −1.68996 | −0.844979 | − | 0.534799i | \(-0.820387\pi\) | ||||
−0.844979 | + | 0.534799i | \(0.820387\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.0220 | 0.671133 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.7322 | 0.835228 | 0.417614 | − | 0.908625i | \(-0.362866\pi\) | ||||
0.417614 | + | 0.908625i | \(0.362866\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.17546 | −0.274804 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.804723 | 0.0357390 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.5377 | −0.644370 | −0.322185 | − | 0.946677i | \(-0.604417\pi\) | ||||
−0.322185 | + | 0.946677i | \(0.604417\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.54964 | −0.378214 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.5742 | −0.731769 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.26785 | −0.188064 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.05444 | 0.178314 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.29038 | 0.100537 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.4815 | 0.897312 | 0.448656 | − | 0.893705i | \(-0.351903\pi\) | ||||
0.448656 | + | 0.893705i | \(0.351903\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.0237 | −1.35657 | −0.678285 | − | 0.734799i | \(-0.737277\pi\) | ||||
−0.678285 | + | 0.734799i | \(0.737277\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.93178 | 0.171597 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.57623 | −0.330026 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6022 | −0.939227 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.48848 | −0.368369 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.35008 | 0.145108 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.400959 | −0.0173350 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.9327 | 0.514933 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.2602 | −0.785066 | −0.392533 | − | 0.919738i | \(-0.628401\pi\) | ||||
−0.392533 | + | 0.919738i | \(0.628401\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.4879 | −0.664649 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.88654 | −0.209316 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.3950 | −1.00030 | −0.500149 | − | 0.865940i | \(-0.666721\pi\) | ||||
−0.500149 | + | 0.865940i | \(0.666721\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.56856 | −0.365697 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.5388 | 1.34360 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.5648 | 0.661883 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.32454 | 0.0986710 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.2014 | 0.813589 | 0.406794 | − | 0.913520i | \(-0.366647\pi\) | ||||
0.406794 | + | 0.913520i | \(0.366647\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.49568 | 0.317034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.38814 | 0.0586073 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.0333 | −0.802158 | −0.401079 | − | 0.916043i | \(-0.631365\pi\) | ||||
−0.401079 | + | 0.916043i | \(0.631365\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.91107 | 0.164540 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.59115 | −0.150814 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.6935 | −1.16097 | −0.580487 | − | 0.814270i | \(-0.697138\pi\) | ||||
−0.580487 | + | 0.814270i | \(0.697138\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.55319 | −0.316091 | −0.158046 | − | 0.987432i | \(-0.550519\pi\) | ||||
−0.158046 | + | 0.987432i | \(0.550519\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.65068 | 0.152509 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.77648 | 0.240896 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.1096 | 0.545762 | 0.272881 | − | 0.962048i | \(-0.412024\pi\) | ||||
0.272881 | + | 0.962048i | \(0.412024\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.60447 | 0.232914 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.6191 | −0.482041 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.73577 | 0.361799 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.794689 | 0.0328563 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.7363 | −1.59882 | −0.799409 | − | 0.600787i | \(-0.794854\pi\) | ||||
−0.799409 | + | 0.600787i | \(0.794854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.9006 | 0.696378 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.46114 | 0.101238 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.05735 | −0.330876 | −0.165438 | − | 0.986220i | \(-0.552904\pi\) | ||||
−0.165438 | + | 0.986220i | \(0.552904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.582732 | −0.0238897 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.96454 | −0.366894 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.2329 | 1.68473 | 0.842366 | − | 0.538906i | \(-0.181162\pi\) | ||||
0.842366 | + | 0.538906i | \(0.181162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.8925 | 0.974595 | 0.487297 | − | 0.873236i | \(-0.337983\pi\) | ||||
0.487297 | + | 0.873236i | \(0.337983\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.8027 | 0.480643 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.337817 | −0.0137342 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.3096 | −0.661986 | −0.330993 | − | 0.943633i | \(-0.607384\pi\) | ||||
−0.330993 | + | 0.943633i | \(0.607384\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.59561 | −0.267268 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.05444 | −0.164025 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.34724 | −0.215973 | −0.107986 | − | 0.994152i | \(-0.534440\pi\) | ||||
−0.107986 | + | 0.994152i | \(0.534440\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.910718 | −0.0367237 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.1242 | 1.01146 | 0.505731 | − | 0.862691i | \(-0.331223\pi\) | ||||
0.505731 | + | 0.862691i | \(0.331223\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.58680 | −0.224553 | −0.112276 | − | 0.993677i | \(-0.535814\pi\) | ||||
−0.112276 | + | 0.993677i | \(0.535814\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.09233 | 0.204348 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.70415 | 0.188468 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.3012 | 0.932049 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.09658 | −0.123666 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.7501 | 0.588125 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.4265 | 1.01221 | 0.506106 | − | 0.862471i | \(-0.331085\pi\) | ||||
0.506106 | + | 0.862471i | \(0.331085\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.8038 | 0.469160 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.75348 | −0.268004 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.86190 | 0.0736556 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.11538 | −0.281041 | −0.140520 | − | 0.990078i | \(-0.544878\pi\) | ||||
−0.140520 | + | 0.990078i | \(0.544878\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.4604 | −0.491390 | −0.245695 | − | 0.969347i | \(-0.579016\pi\) | ||||
−0.245695 | + | 0.969347i | \(0.579016\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.03770 | −0.0802342 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.36127 | 0.0928313 | 0.0464156 | − | 0.998922i | \(-0.485220\pi\) | ||||
0.0464156 | + | 0.998922i | \(0.485220\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.60840 | −0.141642 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.53438 | −0.138523 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.8552 | −1.09006 | −0.545029 | − | 0.838417i | \(-0.683481\pi\) | ||||
−0.545029 | + | 0.838417i | \(0.683481\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.56167 | 0.0610195 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.1123 | −0.784657 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.4355 | 0.951874 | 0.475937 | − | 0.879479i | \(-0.342109\pi\) | ||||
0.475937 | + | 0.879479i | \(0.342109\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.8633 | 0.461429 | 0.230715 | − | 0.973021i | \(-0.425894\pi\) | ||||
0.230715 | + | 0.973021i | \(0.425894\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.38814 | −0.0539109 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.29992 | 0.0504089 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.69012 | −0.375203 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.4796 | 0.637138 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.64244 | −0.140615 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.56662 | 0.330219 | 0.165109 | − | 0.986275i | \(-0.447202\pi\) | ||||
0.165109 | + | 0.986275i | \(0.447202\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21.0445 | 0.810004 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.4161 | 1.70705 | 0.853524 | − | 0.521054i | \(-0.174461\pi\) | ||||
0.853524 | + | 0.521054i | \(0.174461\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.95235 | 0.381936 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.53786 | −0.288851 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.8614 | −1.21914 | −0.609572 | − | 0.792731i | \(-0.708659\pi\) | ||||
−0.609572 | + | 0.792731i | \(0.708659\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.04382 | −0.230923 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.1925 | 0.770394 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.73577 | −0.332806 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.1899 | −1.37673 | −0.688365 | − | 0.725365i | \(-0.741671\pi\) | ||||
−0.688365 | + | 0.725365i | \(0.741671\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.35242 | −0.0893611 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.73501 | 0.103745 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.77887 | −0.218890 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.2425 | 0.727818 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.7478 | 1.04802 | 0.524010 | − | 0.851712i | \(-0.324436\pi\) | ||||
0.524010 | + | 0.851712i | \(0.324436\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.9037 | −1.24099 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.10220 | 0.0415111 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.2805 | −0.687508 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.7540 | 0.929656 | 0.464828 | − | 0.885401i | \(-0.346116\pi\) | ||||
0.464828 | + | 0.885401i | \(0.346116\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.6150 | 1.37317 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.19262 | −0.194465 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.337817 | 0.0126336 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.6112 | −0.470972 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.3846 | −0.499160 | −0.249580 | − | 0.968354i | \(-0.580292\pi\) | ||||
−0.249580 | + | 0.968354i | \(0.580292\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.6336 | −0.470500 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.70748 | −0.323835 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −40.0453 | −1.48725 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.06117 | 0.0393565 | 0.0196783 | − | 0.999806i | \(-0.493736\pi\) | ||||
0.0196783 | + | 0.999806i | \(0.493736\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.95044 | 0.0722384 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.9300 | −0.478233 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.7890 | 0.878665 | 0.439333 | − | 0.898324i | \(-0.355215\pi\) | ||||
0.439333 | + | 0.898324i | \(0.355215\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.271849 | −0.0100273 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.01726 | 0.184813 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.7619 | −0.653383 | −0.326691 | − | 0.945131i | \(-0.605934\pi\) | ||||
−0.326691 | + | 0.945131i | \(0.605934\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.09658 | 0.113756 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.9218 | −0.767548 | −0.383774 | − | 0.923427i | \(-0.625376\pi\) | ||||
−0.383774 | + | 0.923427i | \(0.625376\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.09266 | −0.0400321 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −27.3330 | −1.00006 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.18691 | −0.0433688 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.8653 | 0.761386 | 0.380693 | − | 0.924701i | \(-0.375685\pi\) | ||||
0.380693 | + | 0.924701i | \(0.375685\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.5903 | 0.750352 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.26814 | 0.264515 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.0153 | 0.981887 | 0.490944 | − | 0.871191i | \(-0.336652\pi\) | ||||
0.490944 | + | 0.871191i | \(0.336652\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.951407 | 0.0345339 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.7456 | 0.715776 | 0.357888 | − | 0.933765i | \(-0.383497\pi\) | ||||
0.357888 | + | 0.933765i | \(0.383497\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.4650 | −0.523669 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.37083 | −0.0495625 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.60840 | 0.130292 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.3583 | −0.589895 | −0.294947 | − | 0.955514i | \(-0.595302\pi\) | ||||
−0.294947 | + | 0.955514i | \(0.595302\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.0803012 | −0.00289198 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.7453 | 0.458417 | 0.229208 | − | 0.973377i | \(-0.426386\pi\) | ||||
0.229208 | + | 0.973377i | \(0.426386\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.4590 | −0.770830 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.88105 | 0.246856 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.8912 | 0.461874 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.791482 | 0.0283215 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −35.3025 | −1.26161 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.12464 | −0.182906 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.8399 | 0.600279 | 0.300139 | − | 0.953895i | \(-0.402967\pi\) | ||||
0.300139 | + | 0.953895i | \(0.402967\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.0697 | −0.643299 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.5775 | 0.411647 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.64244 | 0.129347 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.37481 | 0.0842259 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.1295 | 0.358804 | 0.179402 | − | 0.983776i | \(-0.442584\pi\) | ||||
0.179402 | + | 0.983776i | \(0.442584\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.99388 | 0.247426 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.0661 | 0.391003 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.54964 | −0.301710 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.399394 | −0.0140768 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.3667 | 0.892949 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.6959 | 0.411204 | 0.205602 | − | 0.978636i | \(-0.434085\pi\) | ||||
0.205602 | + | 0.978636i | \(0.434085\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.4726 | −1.45630 | −0.728150 | − | 0.685417i | \(-0.759620\pi\) | ||||
−0.728150 | + | 0.685417i | \(0.759620\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.65480 | −0.0931077 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.65101 | −0.197946 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.8435 | 1.00911 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.35242 | 0.0822003 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.6978 | 0.931759 | 0.465880 | − | 0.884848i | \(-0.345738\pi\) | ||||
0.465880 | + | 0.884848i | \(0.345738\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.3736 | −0.919327 | −0.459664 | − | 0.888093i | \(-0.652030\pi\) | ||||
−0.459664 | + | 0.888093i | \(0.652030\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.93178 | 0.136887 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.0398 | 0.766399 | 0.383200 | − | 0.923666i | \(-0.374822\pi\) | ||||
0.383200 | + | 0.923666i | \(0.374822\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.08626 | −0.280848 | −0.140424 | − | 0.990091i | \(-0.544846\pi\) | ||||
−0.140424 | + | 0.990091i | \(0.544846\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.5353 | −0.400156 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.72499 | −0.0597674 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.30613 | −0.218233 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.9175 | −0.653883 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.2263 | 1.52686 | 0.763431 | − | 0.645889i | \(-0.223513\pi\) | ||||
0.763431 | + | 0.645889i | \(0.223513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.1765 | 1.31643 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.82518 | 0.131746 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.337817 | −0.0116213 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.4487 | 0.461558 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.1095 | 0.346548 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.0636 | 1.02936 | 0.514679 | − | 0.857383i | \(-0.327911\pi\) | ||||
0.514679 | + | 0.857383i | \(0.327911\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.05797 | 0.104580 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.85196 | −0.268218 | −0.134109 | − | 0.990967i | \(-0.542817\pi\) | ||||
−0.134109 | + | 0.990967i | \(0.542817\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.7699 | −1.45929 | −0.729645 | − | 0.683826i | \(-0.760315\pi\) | ||||
−0.729645 | + | 0.683826i | \(0.760315\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.69589 | −0.0918756 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.33604 | −0.0454793 | −0.0227396 | − | 0.999741i | \(-0.507239\pi\) | ||||
−0.0227396 | + | 0.999741i | \(0.507239\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.961487 | −0.0326915 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.2858 | −0.383284 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.5648 | 0.528000 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.01726 | −0.170003 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.4121 | 0.792380 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.33962 | −0.112900 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.0933 | −1.01618 | −0.508089 | − | 0.861305i | \(-0.669648\pi\) | ||||
−0.508089 | + | 0.861305i | \(0.669648\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.4995 | 0.623974 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.2296 | 0.445717 | 0.222858 | − | 0.974851i | \(-0.428461\pi\) | ||||
0.222858 | + | 0.974851i | \(0.428461\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.3466 | 0.953940 | 0.476970 | − | 0.878920i | \(-0.341735\pi\) | ||||
0.476970 | + | 0.878920i | \(0.341735\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.980941 | −0.0329740 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.2119 | −0.410035 | −0.205017 | − | 0.978758i | \(-0.565725\pi\) | ||||
−0.205017 | + | 0.978758i | \(0.565725\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.9915 | −0.670495 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.59115 | −0.120308 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.6015 | −0.522085 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.00926 | −0.167441 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.951407 | −0.0317666 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.9977 | 1.20059 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.0691 | 0.502025 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.03195 | −0.200731 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.50172 | 0.216124 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.23015 | −0.206869 | −0.103434 | − | 0.994636i | \(-0.532983\pi\) | ||||
−0.103434 | + | 0.994636i | \(0.532983\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −43.0034 | −1.42633 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.1522 | 0.932725 | 0.466362 | − | 0.884594i | \(-0.345564\pi\) | ||||
0.466362 | + | 0.884594i | \(0.345564\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.6191 | −0.384535 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.990195 | −0.0327348 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.62283 | 0.152659 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.87149 | −0.325631 | −0.162815 | − | 0.986657i | \(-0.552057\pi\) | ||||
−0.162815 | + | 0.986657i | \(0.552057\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.81293 | 0.0597382 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.791482 | −0.0260519 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 41.7783 | 1.37366 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.7195 | −0.976118 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.9140 | −0.915827 | −0.457914 | − | 0.888997i | \(-0.651403\pi\) | ||||
−0.457914 | + | 0.888997i | \(0.651403\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.84801 | 0.126113 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.4864 | −0.507002 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.582732 | −0.0190574 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.9572 | −0.390624 | −0.195312 | − | 0.980741i | \(-0.562572\pi\) | ||||
−0.195312 | + | 0.980741i | \(0.562572\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.4232 | 0.633853 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.77722 | −0.123134 | −0.0615669 | − | 0.998103i | \(-0.519610\pi\) | ||||
−0.0615669 | + | 0.998103i | \(0.519610\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.96074 | −0.128979 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.45505 | −0.0473328 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.1233 | −1.43382 | −0.716908 | − | 0.697168i | \(-0.754443\pi\) | ||||
−0.716908 | + | 0.697168i | \(0.754443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.54964 | 0.277533 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.44226 | 0.144050 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.94441 | 0.192558 | 0.0962791 | − | 0.995354i | \(-0.469306\pi\) | ||||
0.0962791 | + | 0.995354i | \(0.469306\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.53253 | −0.0495915 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.59561 | −0.213206 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.8908 | −0.577724 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.7100 | −0.377741 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.79212 | −0.0899747 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.35272 | −0.0757368 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.4748 | −1.52669 | −0.763343 | − | 0.645993i | \(-0.776444\pi\) | ||||
−0.763343 | + | 0.645993i | \(0.776444\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.34157 | −0.171596 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.7191 | 1.85230 | 0.926148 | − | 0.377161i | \(-0.123100\pi\) | ||||
0.926148 | + | 0.377161i | \(0.123100\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.09613 | 0.259550 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.93178 | −0.125918 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.9982 | 0.735776 | 0.367888 | − | 0.929870i | \(-0.380081\pi\) | ||||
0.367888 | + | 0.929870i | \(0.380081\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.70415 | 0.150345 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.0279 | −1.08643 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.3095 | 0.520194 | 0.260097 | − | 0.965583i | \(-0.416246\pi\) | ||||
0.260097 | + | 0.965583i | \(0.416246\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.03317 | −0.0329196 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.26270 | 0.103853 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.86200 | −0.281795 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.1657 | −1.18061 | −0.590304 | − | 0.807181i | \(-0.700992\pi\) | ||||
−0.590304 | + | 0.807181i | \(0.700992\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.11591 | −0.194083 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.76326 | 0.119303 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.2441 | 0.957840 | 0.478920 | − | 0.877859i | \(-0.341028\pi\) | ||||
0.478920 | + | 0.877859i | \(0.341028\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36.8303 | 1.16526 |
(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 | 8008.2.a.z.1.9 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.z.1.9 | ✓ | 15 | 1.1 | even | 1 | trivial |