Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 11 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.14896\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.14896 | −1.81805 | −0.909027 | − | 0.416738i | \(-0.863173\pi\) | ||||
−0.909027 | + | 0.416738i | \(0.863173\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 3.14896 | 1.28556 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.91596 | 2.30532 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −3.14896 | −0.909027 | ||||||||
\(13\) | 5.43886 | 1.50847 | 0.754235 | − | 0.656605i | \(-0.228008\pi\) | ||||
0.754235 | + | 0.656605i | \(0.228008\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −3.14896 | −0.813058 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.477092 | −0.115712 | −0.0578559 | − | 0.998325i | \(-0.518426\pi\) | ||||
−0.0578559 | + | 0.998325i | \(0.518426\pi\) | |||||||
\(18\) | −6.91596 | −1.63011 | ||||||||
\(19\) | −5.91596 | −1.35721 | −0.678607 | − | 0.734502i | \(-0.737416\pi\) | ||||
−0.678607 | + | 0.734502i | \(0.737416\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 3.14896 | 0.687160 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.65626 | −0.553869 | −0.276934 | − | 0.960889i | \(-0.589318\pi\) | ||||
−0.276934 | + | 0.960889i | \(0.589318\pi\) | |||||||
\(24\) | 3.14896 | 0.642779 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.43886 | −1.06665 | ||||||||
\(27\) | −12.3312 | −2.37314 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −6.56726 | −1.21951 | −0.609755 | − | 0.792590i | \(-0.708732\pi\) | ||||
−0.609755 | + | 0.792590i | \(0.708732\pi\) | |||||||
\(30\) | 3.14896 | 0.574919 | ||||||||
\(31\) | −9.68953 | −1.74029 | −0.870146 | − | 0.492794i | \(-0.835976\pi\) | ||||
−0.870146 | + | 0.492794i | \(0.835976\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.477092 | 0.0818206 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 6.91596 | 1.15266 | ||||||||
\(37\) | −4.56726 | −0.750853 | −0.375427 | − | 0.926852i | \(-0.622504\pi\) | ||||
−0.375427 | + | 0.926852i | \(0.622504\pi\) | |||||||
\(38\) | 5.91596 | 0.959695 | ||||||||
\(39\) | −17.1268 | −2.74248 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 2.52291 | 0.394012 | 0.197006 | − | 0.980402i | \(-0.436878\pi\) | ||||
0.197006 | + | 0.980402i | \(0.436878\pi\) | |||||||
\(42\) | −3.14896 | −0.485895 | ||||||||
\(43\) | 11.9003 | 1.81479 | 0.907393 | − | 0.420283i | \(-0.138069\pi\) | ||||
0.907393 | + | 0.420283i | \(0.138069\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.91596 | 1.03097 | ||||||||
\(46\) | 2.65626 | 0.391644 | ||||||||
\(47\) | 9.42632 | 1.37497 | 0.687485 | − | 0.726199i | \(-0.258715\pi\) | ||||
0.687485 | + | 0.726199i | \(0.258715\pi\) | |||||||
\(48\) | −3.14896 | −0.454513 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 1.50234 | 0.210370 | ||||||||
\(52\) | 5.43886 | 0.754235 | ||||||||
\(53\) | 6.15392 | 0.845306 | 0.422653 | − | 0.906292i | \(-0.361099\pi\) | ||||
0.422653 | + | 0.906292i | \(0.361099\pi\) | |||||||
\(54\) | 12.3312 | 1.67806 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 18.6291 | 2.46749 | ||||||||
\(58\) | 6.56726 | 0.862324 | ||||||||
\(59\) | −0.566092 | −0.0736989 | −0.0368495 | − | 0.999321i | \(-0.511732\pi\) | ||||
−0.0368495 | + | 0.999321i | \(0.511732\pi\) | |||||||
\(60\) | −3.14896 | −0.406529 | ||||||||
\(61\) | 2.04888 | 0.262332 | 0.131166 | − | 0.991360i | \(-0.458128\pi\) | ||||
0.131166 | + | 0.991360i | \(0.458128\pi\) | |||||||
\(62\) | 9.68953 | 1.23057 | ||||||||
\(63\) | −6.91596 | −0.871329 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.43886 | 0.674608 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.24102 | −0.151615 | −0.0758076 | − | 0.997122i | \(-0.524153\pi\) | ||||
−0.0758076 | + | 0.997122i | \(0.524153\pi\) | |||||||
\(68\) | −0.477092 | −0.0578559 | ||||||||
\(69\) | 8.36447 | 1.00696 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −3.62299 | −0.429970 | −0.214985 | − | 0.976617i | \(-0.568970\pi\) | ||||
−0.214985 | + | 0.976617i | \(0.568970\pi\) | |||||||
\(72\) | −6.91596 | −0.815053 | ||||||||
\(73\) | 15.6398 | 1.83050 | 0.915248 | − | 0.402891i | \(-0.131994\pi\) | ||||
0.915248 | + | 0.402891i | \(0.131994\pi\) | |||||||
\(74\) | 4.56726 | 0.530933 | ||||||||
\(75\) | −3.14896 | −0.363611 | ||||||||
\(76\) | −5.91596 | −0.678607 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 17.1268 | 1.93923 | ||||||||
\(79\) | −3.38007 | −0.380288 | −0.190144 | − | 0.981756i | \(-0.560895\pi\) | ||||
−0.190144 | + | 0.981756i | \(0.560895\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 18.0826 | 2.00918 | ||||||||
\(82\) | −2.52291 | −0.278609 | ||||||||
\(83\) | 1.73868 | 0.190845 | 0.0954224 | − | 0.995437i | \(-0.469580\pi\) | ||||
0.0954224 | + | 0.995437i | \(0.469580\pi\) | |||||||
\(84\) | 3.14896 | 0.343580 | ||||||||
\(85\) | −0.477092 | −0.0517479 | ||||||||
\(86\) | −11.9003 | −1.28325 | ||||||||
\(87\) | 20.6801 | 2.21713 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.54364 | −1.01162 | −0.505812 | − | 0.862644i | \(-0.668807\pi\) | ||||
−0.505812 | + | 0.862644i | \(0.668807\pi\) | |||||||
\(90\) | −6.91596 | −0.729006 | ||||||||
\(91\) | −5.43886 | −0.570148 | ||||||||
\(92\) | −2.65626 | −0.276934 | ||||||||
\(93\) | 30.5120 | 3.16394 | ||||||||
\(94\) | −9.42632 | −0.972251 | ||||||||
\(95\) | −5.91596 | −0.606964 | ||||||||
\(96\) | 3.14896 | 0.321390 | ||||||||
\(97\) | −3.93156 | −0.399190 | −0.199595 | − | 0.979879i | \(-0.563963\pi\) | ||||
−0.199595 | + | 0.979879i | \(0.563963\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −2.90794 | −0.289351 | −0.144675 | − | 0.989479i | \(-0.546214\pi\) | ||||
−0.144675 | + | 0.989479i | \(0.546214\pi\) | |||||||
\(102\) | −1.50234 | −0.148754 | ||||||||
\(103\) | −15.9287 | −1.56950 | −0.784749 | − | 0.619814i | \(-0.787208\pi\) | ||||
−0.784749 | + | 0.619814i | \(0.787208\pi\) | |||||||
\(104\) | −5.43886 | −0.533325 | ||||||||
\(105\) | 3.14896 | 0.307307 | ||||||||
\(106\) | −6.15392 | −0.597721 | ||||||||
\(107\) | −6.17232 | −0.596701 | −0.298350 | − | 0.954456i | \(-0.596436\pi\) | ||||
−0.298350 | + | 0.954456i | \(0.596436\pi\) | |||||||
\(108\) | −12.3312 | −1.18657 | ||||||||
\(109\) | −14.9240 | −1.42946 | −0.714729 | − | 0.699402i | \(-0.753450\pi\) | ||||
−0.714729 | + | 0.699402i | \(0.753450\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.3821 | 1.36509 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 19.0906 | 1.79589 | 0.897946 | − | 0.440105i | \(-0.145059\pi\) | ||||
0.897946 | + | 0.440105i | \(0.145059\pi\) | |||||||
\(114\) | −18.6291 | −1.74478 | ||||||||
\(115\) | −2.65626 | −0.247698 | ||||||||
\(116\) | −6.56726 | −0.609755 | ||||||||
\(117\) | 37.6149 | 3.47750 | ||||||||
\(118\) | 0.566092 | 0.0521130 | ||||||||
\(119\) | 0.477092 | 0.0437350 | ||||||||
\(120\) | 3.14896 | 0.287460 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.04888 | −0.185497 | ||||||||
\(123\) | −7.94454 | −0.716335 | ||||||||
\(124\) | −9.68953 | −0.870146 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 6.91596 | 0.616122 | ||||||||
\(127\) | 16.3815 | 1.45362 | 0.726812 | − | 0.686836i | \(-0.241001\pi\) | ||||
0.726812 | + | 0.686836i | \(0.241001\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −37.4737 | −3.29938 | ||||||||
\(130\) | −5.43886 | −0.477020 | ||||||||
\(131\) | 5.60812 | 0.489984 | 0.244992 | − | 0.969525i | \(-0.421215\pi\) | ||||
0.244992 | + | 0.969525i | \(0.421215\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.91596 | 0.512978 | ||||||||
\(134\) | 1.24102 | 0.107208 | ||||||||
\(135\) | −12.3312 | −1.06130 | ||||||||
\(136\) | 0.477092 | 0.0409103 | ||||||||
\(137\) | −2.50874 | −0.214336 | −0.107168 | − | 0.994241i | \(-0.534178\pi\) | ||||
−0.107168 | + | 0.994241i | \(0.534178\pi\) | |||||||
\(138\) | −8.36447 | −0.712031 | ||||||||
\(139\) | 3.30261 | 0.280124 | 0.140062 | − | 0.990143i | \(-0.455270\pi\) | ||||
0.140062 | + | 0.990143i | \(0.455270\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −29.6831 | −2.49977 | ||||||||
\(142\) | 3.62299 | 0.304035 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.91596 | 0.576330 | ||||||||
\(145\) | −6.56726 | −0.545381 | ||||||||
\(146\) | −15.6398 | −1.29436 | ||||||||
\(147\) | −3.14896 | −0.259722 | ||||||||
\(148\) | −4.56726 | −0.375427 | ||||||||
\(149\) | 6.83048 | 0.559574 | 0.279787 | − | 0.960062i | \(-0.409736\pi\) | ||||
0.279787 | + | 0.960062i | \(0.409736\pi\) | |||||||
\(150\) | 3.14896 | 0.257112 | ||||||||
\(151\) | −10.8189 | −0.880433 | −0.440216 | − | 0.897892i | \(-0.645098\pi\) | ||||
−0.440216 | + | 0.897892i | \(0.645098\pi\) | |||||||
\(152\) | 5.91596 | 0.479847 | ||||||||
\(153\) | −3.29955 | −0.266753 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.68953 | −0.778282 | ||||||||
\(156\) | −17.1268 | −1.37124 | ||||||||
\(157\) | 8.01766 | 0.639879 | 0.319940 | − | 0.947438i | \(-0.396337\pi\) | ||||
0.319940 | + | 0.947438i | \(0.396337\pi\) | |||||||
\(158\) | 3.38007 | 0.268904 | ||||||||
\(159\) | −19.3784 | −1.53681 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 2.65626 | 0.209343 | ||||||||
\(162\) | −18.0826 | −1.42070 | ||||||||
\(163\) | −18.2991 | −1.43330 | −0.716648 | − | 0.697435i | \(-0.754324\pi\) | ||||
−0.716648 | + | 0.697435i | \(0.754324\pi\) | |||||||
\(164\) | 2.52291 | 0.197006 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.73868 | −0.134948 | ||||||||
\(167\) | −17.9260 | −1.38716 | −0.693579 | − | 0.720381i | \(-0.743967\pi\) | ||||
−0.693579 | + | 0.720381i | \(0.743967\pi\) | |||||||
\(168\) | −3.14896 | −0.242948 | ||||||||
\(169\) | 16.5812 | 1.27548 | ||||||||
\(170\) | 0.477092 | 0.0365913 | ||||||||
\(171\) | −40.9145 | −3.12881 | ||||||||
\(172\) | 11.9003 | 0.907393 | ||||||||
\(173\) | −7.68791 | −0.584501 | −0.292250 | − | 0.956342i | \(-0.594404\pi\) | ||||
−0.292250 | + | 0.956342i | \(0.594404\pi\) | |||||||
\(174\) | −20.6801 | −1.56775 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.78260 | 0.133989 | ||||||||
\(178\) | 9.54364 | 0.715326 | ||||||||
\(179\) | 22.7197 | 1.69815 | 0.849076 | − | 0.528271i | \(-0.177160\pi\) | ||||
0.849076 | + | 0.528271i | \(0.177160\pi\) | |||||||
\(180\) | 6.91596 | 0.515485 | ||||||||
\(181\) | −13.6567 | −1.01509 | −0.507547 | − | 0.861624i | \(-0.669448\pi\) | ||||
−0.507547 | + | 0.861624i | \(0.669448\pi\) | |||||||
\(182\) | 5.43886 | 0.403155 | ||||||||
\(183\) | −6.45184 | −0.476934 | ||||||||
\(184\) | 2.65626 | 0.195822 | ||||||||
\(185\) | −4.56726 | −0.335792 | ||||||||
\(186\) | −30.5120 | −2.23725 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 9.42632 | 0.687485 | ||||||||
\(189\) | 12.3312 | 0.896962 | ||||||||
\(190\) | 5.91596 | 0.429189 | ||||||||
\(191\) | 9.42182 | 0.681739 | 0.340869 | − | 0.940111i | \(-0.389279\pi\) | ||||
0.340869 | + | 0.940111i | \(0.389279\pi\) | |||||||
\(192\) | −3.14896 | −0.227257 | ||||||||
\(193\) | −5.09919 | −0.367048 | −0.183524 | − | 0.983015i | \(-0.558751\pi\) | ||||
−0.183524 | + | 0.983015i | \(0.558751\pi\) | |||||||
\(194\) | 3.93156 | 0.282270 | ||||||||
\(195\) | −17.1268 | −1.22647 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 17.1284 | 1.22035 | 0.610174 | − | 0.792268i | \(-0.291100\pi\) | ||||
0.610174 | + | 0.792268i | \(0.291100\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.9225 | 0.845166 | 0.422583 | − | 0.906324i | \(-0.361123\pi\) | ||||
0.422583 | + | 0.906324i | \(0.361123\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 3.90794 | 0.275645 | ||||||||
\(202\) | 2.90794 | 0.204602 | ||||||||
\(203\) | 6.56726 | 0.460931 | ||||||||
\(204\) | 1.50234 | 0.105185 | ||||||||
\(205\) | 2.52291 | 0.176208 | ||||||||
\(206\) | 15.9287 | 1.10980 | ||||||||
\(207\) | −18.3706 | −1.27684 | ||||||||
\(208\) | 5.43886 | 0.377117 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.14896 | −0.217299 | ||||||||
\(211\) | 22.8331 | 1.57189 | 0.785947 | − | 0.618294i | \(-0.212176\pi\) | ||||
0.785947 | + | 0.618294i | \(0.212176\pi\) | |||||||
\(212\) | 6.15392 | 0.422653 | ||||||||
\(213\) | 11.4087 | 0.781708 | ||||||||
\(214\) | 6.17232 | 0.421931 | ||||||||
\(215\) | 11.9003 | 0.811597 | ||||||||
\(216\) | 12.3312 | 0.839031 | ||||||||
\(217\) | 9.68953 | 0.657768 | ||||||||
\(218\) | 14.9240 | 1.01078 | ||||||||
\(219\) | −49.2490 | −3.32794 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.59484 | −0.174548 | ||||||||
\(222\) | −14.3821 | −0.965265 | ||||||||
\(223\) | −15.8782 | −1.06328 | −0.531640 | − | 0.846970i | \(-0.678424\pi\) | ||||
−0.531640 | + | 0.846970i | \(0.678424\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 6.91596 | 0.461064 | ||||||||
\(226\) | −19.0906 | −1.26989 | ||||||||
\(227\) | −8.41830 | −0.558742 | −0.279371 | − | 0.960183i | \(-0.590126\pi\) | ||||
−0.279371 | + | 0.960183i | \(0.590126\pi\) | |||||||
\(228\) | 18.6291 | 1.23374 | ||||||||
\(229\) | 22.2844 | 1.47259 | 0.736296 | − | 0.676659i | \(-0.236573\pi\) | ||||
0.736296 | + | 0.676659i | \(0.236573\pi\) | |||||||
\(230\) | 2.65626 | 0.175149 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.56726 | 0.431162 | ||||||||
\(233\) | −12.4011 | −0.812421 | −0.406210 | − | 0.913780i | \(-0.633150\pi\) | ||||
−0.406210 | + | 0.913780i | \(0.633150\pi\) | |||||||
\(234\) | −37.6149 | −2.45897 | ||||||||
\(235\) | 9.42632 | 0.614905 | ||||||||
\(236\) | −0.566092 | −0.0368495 | ||||||||
\(237\) | 10.6437 | 0.691384 | ||||||||
\(238\) | −0.477092 | −0.0309253 | ||||||||
\(239\) | 19.3571 | 1.25211 | 0.626055 | − | 0.779779i | \(-0.284669\pi\) | ||||
0.626055 | + | 0.779779i | \(0.284669\pi\) | |||||||
\(240\) | −3.14896 | −0.203265 | ||||||||
\(241\) | −5.12445 | −0.330095 | −0.165047 | − | 0.986286i | \(-0.552778\pi\) | ||||
−0.165047 | + | 0.986286i | \(0.552778\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.9478 | −1.27965 | ||||||||
\(244\) | 2.04888 | 0.131166 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 7.94454 | 0.506525 | ||||||||
\(247\) | −32.1761 | −2.04732 | ||||||||
\(248\) | 9.68953 | 0.615286 | ||||||||
\(249\) | −5.47503 | −0.346966 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −8.99152 | −0.567540 | −0.283770 | − | 0.958892i | \(-0.591585\pi\) | ||||
−0.283770 | + | 0.958892i | \(0.591585\pi\) | |||||||
\(252\) | −6.91596 | −0.435664 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −16.3815 | −1.02787 | ||||||||
\(255\) | 1.50234 | 0.0940805 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.9476 | −1.11954 | −0.559770 | − | 0.828648i | \(-0.689111\pi\) | ||||
−0.559770 | + | 0.828648i | \(0.689111\pi\) | |||||||
\(258\) | 37.4737 | 2.33301 | ||||||||
\(259\) | 4.56726 | 0.283796 | ||||||||
\(260\) | 5.43886 | 0.337304 | ||||||||
\(261\) | −45.4189 | −2.81136 | ||||||||
\(262\) | −5.60812 | −0.346471 | ||||||||
\(263\) | 27.3312 | 1.68531 | 0.842657 | − | 0.538451i | \(-0.180990\pi\) | ||||
0.842657 | + | 0.538451i | \(0.180990\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.15392 | 0.378032 | ||||||||
\(266\) | −5.91596 | −0.362731 | ||||||||
\(267\) | 30.0525 | 1.83919 | ||||||||
\(268\) | −1.24102 | −0.0758076 | ||||||||
\(269\) | −12.0775 | −0.736376 | −0.368188 | − | 0.929751i | \(-0.620022\pi\) | ||||
−0.368188 | + | 0.929751i | \(0.620022\pi\) | |||||||
\(270\) | 12.3312 | 0.750453 | ||||||||
\(271\) | 25.8325 | 1.56921 | 0.784607 | − | 0.619993i | \(-0.212865\pi\) | ||||
0.784607 | + | 0.619993i | \(0.212865\pi\) | |||||||
\(272\) | −0.477092 | −0.0289280 | ||||||||
\(273\) | 17.1268 | 1.03656 | ||||||||
\(274\) | 2.50874 | 0.151558 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.36447 | 0.503482 | ||||||||
\(277\) | −18.2240 | −1.09497 | −0.547486 | − | 0.836815i | \(-0.684415\pi\) | ||||
−0.547486 | + | 0.836815i | \(0.684415\pi\) | |||||||
\(278\) | −3.30261 | −0.198077 | ||||||||
\(279\) | −67.0124 | −4.01193 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −4.05953 | −0.242171 | −0.121086 | − | 0.992642i | \(-0.538638\pi\) | ||||
−0.121086 | + | 0.992642i | \(0.538638\pi\) | |||||||
\(282\) | 29.6831 | 1.76760 | ||||||||
\(283\) | −3.16574 | −0.188184 | −0.0940918 | − | 0.995564i | \(-0.529995\pi\) | ||||
−0.0940918 | + | 0.995564i | \(0.529995\pi\) | |||||||
\(284\) | −3.62299 | −0.214985 | ||||||||
\(285\) | 18.6291 | 1.10349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.52291 | −0.148923 | ||||||||
\(288\) | −6.91596 | −0.407527 | ||||||||
\(289\) | −16.7724 | −0.986611 | ||||||||
\(290\) | 6.56726 | 0.385643 | ||||||||
\(291\) | 12.3803 | 0.725748 | ||||||||
\(292\) | 15.6398 | 0.915248 | ||||||||
\(293\) | 10.2517 | 0.598909 | 0.299455 | − | 0.954111i | \(-0.403195\pi\) | ||||
0.299455 | + | 0.954111i | \(0.403195\pi\) | |||||||
\(294\) | 3.14896 | 0.183651 | ||||||||
\(295\) | −0.566092 | −0.0329592 | ||||||||
\(296\) | 4.56726 | 0.265467 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.83048 | −0.395679 | ||||||||
\(299\) | −14.4470 | −0.835494 | ||||||||
\(300\) | −3.14896 | −0.181805 | ||||||||
\(301\) | −11.9003 | −0.685925 | ||||||||
\(302\) | 10.8189 | 0.622560 | ||||||||
\(303\) | 9.15698 | 0.526055 | ||||||||
\(304\) | −5.91596 | −0.339303 | ||||||||
\(305\) | 2.04888 | 0.117318 | ||||||||
\(306\) | 3.29955 | 0.188623 | ||||||||
\(307\) | −3.38972 | −0.193461 | −0.0967307 | − | 0.995311i | \(-0.530839\pi\) | ||||
−0.0967307 | + | 0.995311i | \(0.530839\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 50.1587 | 2.85343 | ||||||||
\(310\) | 9.68953 | 0.550329 | ||||||||
\(311\) | −29.4523 | −1.67009 | −0.835043 | − | 0.550185i | \(-0.814557\pi\) | ||||
−0.835043 | + | 0.550185i | \(0.814557\pi\) | |||||||
\(312\) | 17.1268 | 0.969613 | ||||||||
\(313\) | −22.0645 | −1.24716 | −0.623579 | − | 0.781761i | \(-0.714322\pi\) | ||||
−0.623579 | + | 0.781761i | \(0.714322\pi\) | |||||||
\(314\) | −8.01766 | −0.452463 | ||||||||
\(315\) | −6.91596 | −0.389670 | ||||||||
\(316\) | −3.38007 | −0.190144 | ||||||||
\(317\) | 21.1159 | 1.18598 | 0.592992 | − | 0.805208i | \(-0.297946\pi\) | ||||
0.592992 | + | 0.805208i | \(0.297946\pi\) | |||||||
\(318\) | 19.3784 | 1.08669 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 19.4364 | 1.08483 | ||||||||
\(322\) | −2.65626 | −0.148028 | ||||||||
\(323\) | 2.82246 | 0.157046 | ||||||||
\(324\) | 18.0826 | 1.00459 | ||||||||
\(325\) | 5.43886 | 0.301694 | ||||||||
\(326\) | 18.2991 | 1.01349 | ||||||||
\(327\) | 46.9950 | 2.59883 | ||||||||
\(328\) | −2.52291 | −0.139304 | ||||||||
\(329\) | −9.42632 | −0.519690 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.1409 | −1.71166 | −0.855830 | − | 0.517258i | \(-0.826953\pi\) | ||||
−0.855830 | + | 0.517258i | \(0.826953\pi\) | |||||||
\(332\) | 1.73868 | 0.0954224 | ||||||||
\(333\) | −31.5870 | −1.73096 | ||||||||
\(334\) | 17.9260 | 0.980869 | ||||||||
\(335\) | −1.24102 | −0.0678044 | ||||||||
\(336\) | 3.14896 | 0.171790 | ||||||||
\(337\) | −1.60099 | −0.0872115 | −0.0436057 | − | 0.999049i | \(-0.513885\pi\) | ||||
−0.0436057 | + | 0.999049i | \(0.513885\pi\) | |||||||
\(338\) | −16.5812 | −0.901901 | ||||||||
\(339\) | −60.1156 | −3.26503 | ||||||||
\(340\) | −0.477092 | −0.0258740 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 40.9145 | 2.21240 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −11.9003 | −0.641624 | ||||||||
\(345\) | 8.36447 | 0.450328 | ||||||||
\(346\) | 7.68791 | 0.413304 | ||||||||
\(347\) | 19.7193 | 1.05859 | 0.529293 | − | 0.848439i | \(-0.322457\pi\) | ||||
0.529293 | + | 0.848439i | \(0.322457\pi\) | |||||||
\(348\) | 20.6801 | 1.10857 | ||||||||
\(349\) | 15.3791 | 0.823223 | 0.411611 | − | 0.911359i | \(-0.364966\pi\) | ||||
0.411611 | + | 0.911359i | \(0.364966\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −67.0677 | −3.57981 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.3793 | −0.552436 | −0.276218 | − | 0.961095i | \(-0.589081\pi\) | ||||
−0.276218 | + | 0.961095i | \(0.589081\pi\) | |||||||
\(354\) | −1.78260 | −0.0947442 | ||||||||
\(355\) | −3.62299 | −0.192288 | ||||||||
\(356\) | −9.54364 | −0.505812 | ||||||||
\(357\) | −1.50234 | −0.0795125 | ||||||||
\(358\) | −22.7197 | −1.20077 | ||||||||
\(359\) | 23.8319 | 1.25780 | 0.628900 | − | 0.777486i | \(-0.283505\pi\) | ||||
0.628900 | + | 0.777486i | \(0.283505\pi\) | |||||||
\(360\) | −6.91596 | −0.364503 | ||||||||
\(361\) | 15.9985 | 0.842028 | ||||||||
\(362\) | 13.6567 | 0.717780 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.43886 | −0.285074 | ||||||||
\(365\) | 15.6398 | 0.818623 | ||||||||
\(366\) | 6.45184 | 0.337243 | ||||||||
\(367\) | −19.3945 | −1.01238 | −0.506192 | − | 0.862421i | \(-0.668947\pi\) | ||||
−0.506192 | + | 0.862421i | \(0.668947\pi\) | |||||||
\(368\) | −2.65626 | −0.138467 | ||||||||
\(369\) | 17.4483 | 0.908323 | ||||||||
\(370\) | 4.56726 | 0.237441 | ||||||||
\(371\) | −6.15392 | −0.319495 | ||||||||
\(372\) | 30.5120 | 1.58197 | ||||||||
\(373\) | 10.9015 | 0.564459 | 0.282230 | − | 0.959347i | \(-0.408926\pi\) | ||||
0.282230 | + | 0.959347i | \(0.408926\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.14896 | −0.162612 | ||||||||
\(376\) | −9.42632 | −0.486125 | ||||||||
\(377\) | −35.7184 | −1.83959 | ||||||||
\(378\) | −12.3312 | −0.634248 | ||||||||
\(379\) | 6.80767 | 0.349686 | 0.174843 | − | 0.984596i | \(-0.444058\pi\) | ||||
0.174843 | + | 0.984596i | \(0.444058\pi\) | |||||||
\(380\) | −5.91596 | −0.303482 | ||||||||
\(381\) | −51.5847 | −2.64277 | ||||||||
\(382\) | −9.42182 | −0.482062 | ||||||||
\(383\) | −24.2311 | −1.23815 | −0.619075 | − | 0.785332i | \(-0.712492\pi\) | ||||
−0.619075 | + | 0.785332i | \(0.712492\pi\) | |||||||
\(384\) | 3.14896 | 0.160695 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.09919 | 0.259542 | ||||||||
\(387\) | 82.3023 | 4.18366 | ||||||||
\(388\) | −3.93156 | −0.199595 | ||||||||
\(389\) | −18.2552 | −0.925574 | −0.462787 | − | 0.886470i | \(-0.653150\pi\) | ||||
−0.462787 | + | 0.886470i | \(0.653150\pi\) | |||||||
\(390\) | 17.1268 | 0.867248 | ||||||||
\(391\) | 1.26728 | 0.0640892 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −17.6598 | −0.890817 | ||||||||
\(394\) | −17.1284 | −0.862916 | ||||||||
\(395\) | −3.38007 | −0.170070 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.6742 | 0.887043 | 0.443522 | − | 0.896264i | \(-0.353729\pi\) | ||||
0.443522 | + | 0.896264i | \(0.353729\pi\) | |||||||
\(398\) | −11.9225 | −0.597623 | ||||||||
\(399\) | −18.6291 | −0.932622 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 30.4187 | 1.51904 | 0.759520 | − | 0.650485i | \(-0.225434\pi\) | ||||
0.759520 | + | 0.650485i | \(0.225434\pi\) | |||||||
\(402\) | −3.90794 | −0.194910 | ||||||||
\(403\) | −52.7001 | −2.62518 | ||||||||
\(404\) | −2.90794 | −0.144675 | ||||||||
\(405\) | 18.0826 | 0.898531 | ||||||||
\(406\) | −6.56726 | −0.325928 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.50234 | −0.0743771 | ||||||||
\(409\) | 15.4065 | 0.761802 | 0.380901 | − | 0.924616i | \(-0.375614\pi\) | ||||
0.380901 | + | 0.924616i | \(0.375614\pi\) | |||||||
\(410\) | −2.52291 | −0.124598 | ||||||||
\(411\) | 7.89992 | 0.389674 | ||||||||
\(412\) | −15.9287 | −0.784749 | ||||||||
\(413\) | 0.566092 | 0.0278556 | ||||||||
\(414\) | 18.3706 | 0.902865 | ||||||||
\(415\) | 1.73868 | 0.0853484 | ||||||||
\(416\) | −5.43886 | −0.266662 | ||||||||
\(417\) | −10.3998 | −0.509280 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.21914 | 0.157265 | 0.0786327 | − | 0.996904i | \(-0.474945\pi\) | ||||
0.0786327 | + | 0.996904i | \(0.474945\pi\) | |||||||
\(420\) | 3.14896 | 0.153654 | ||||||||
\(421\) | 13.1605 | 0.641402 | 0.320701 | − | 0.947180i | \(-0.396081\pi\) | ||||
0.320701 | + | 0.947180i | \(0.396081\pi\) | |||||||
\(422\) | −22.8331 | −1.11150 | ||||||||
\(423\) | 65.1920 | 3.16974 | ||||||||
\(424\) | −6.15392 | −0.298861 | ||||||||
\(425\) | −0.477092 | −0.0231424 | ||||||||
\(426\) | −11.4087 | −0.552751 | ||||||||
\(427\) | −2.04888 | −0.0991522 | ||||||||
\(428\) | −6.17232 | −0.298350 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.9003 | −0.573886 | ||||||||
\(431\) | 2.38429 | 0.114847 | 0.0574236 | − | 0.998350i | \(-0.481711\pi\) | ||||
0.0574236 | + | 0.998350i | \(0.481711\pi\) | |||||||
\(432\) | −12.3312 | −0.593285 | ||||||||
\(433\) | 9.02568 | 0.433747 | 0.216873 | − | 0.976200i | \(-0.430414\pi\) | ||||
0.216873 | + | 0.976200i | \(0.430414\pi\) | |||||||
\(434\) | −9.68953 | −0.465113 | ||||||||
\(435\) | 20.6801 | 0.991533 | ||||||||
\(436\) | −14.9240 | −0.714729 | ||||||||
\(437\) | 15.7143 | 0.751718 | ||||||||
\(438\) | 49.2490 | 2.35321 | ||||||||
\(439\) | 23.1241 | 1.10366 | 0.551828 | − | 0.833958i | \(-0.313931\pi\) | ||||
0.551828 | + | 0.833958i | \(0.313931\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.91596 | 0.329331 | ||||||||
\(442\) | 2.59484 | 0.123424 | ||||||||
\(443\) | −6.78799 | −0.322507 | −0.161254 | − | 0.986913i | \(-0.551554\pi\) | ||||
−0.161254 | + | 0.986913i | \(0.551554\pi\) | |||||||
\(444\) | 14.3821 | 0.682546 | ||||||||
\(445\) | −9.54364 | −0.452412 | ||||||||
\(446\) | 15.8782 | 0.751853 | ||||||||
\(447\) | −21.5089 | −1.01734 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 13.1114 | 0.618767 | 0.309383 | − | 0.950937i | \(-0.399877\pi\) | ||||
0.309383 | + | 0.950937i | \(0.399877\pi\) | |||||||
\(450\) | −6.91596 | −0.326021 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 19.0906 | 0.897946 | ||||||||
\(453\) | 34.0684 | 1.60067 | ||||||||
\(454\) | 8.41830 | 0.395090 | ||||||||
\(455\) | −5.43886 | −0.254978 | ||||||||
\(456\) | −18.6291 | −0.872388 | ||||||||
\(457\) | −19.0200 | −0.889718 | −0.444859 | − | 0.895601i | \(-0.646746\pi\) | ||||
−0.444859 | + | 0.895601i | \(0.646746\pi\) | |||||||
\(458\) | −22.2844 | −1.04128 | ||||||||
\(459\) | 5.88312 | 0.274600 | ||||||||
\(460\) | −2.65626 | −0.123849 | ||||||||
\(461\) | 18.8767 | 0.879177 | 0.439588 | − | 0.898199i | \(-0.355124\pi\) | ||||
0.439588 | + | 0.898199i | \(0.355124\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.6194 | 0.632945 | 0.316473 | − | 0.948602i | \(-0.397501\pi\) | ||||
0.316473 | + | 0.948602i | \(0.397501\pi\) | |||||||
\(464\) | −6.56726 | −0.304877 | ||||||||
\(465\) | 30.5120 | 1.41496 | ||||||||
\(466\) | 12.4011 | 0.574468 | ||||||||
\(467\) | −18.9801 | −0.878296 | −0.439148 | − | 0.898415i | \(-0.644720\pi\) | ||||
−0.439148 | + | 0.898415i | \(0.644720\pi\) | |||||||
\(468\) | 37.6149 | 1.73875 | ||||||||
\(469\) | 1.24102 | 0.0573052 | ||||||||
\(470\) | −9.42632 | −0.434804 | ||||||||
\(471\) | −25.2473 | −1.16333 | ||||||||
\(472\) | 0.566092 | 0.0260565 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −10.6437 | −0.488882 | ||||||||
\(475\) | −5.91596 | −0.271443 | ||||||||
\(476\) | 0.477092 | 0.0218675 | ||||||||
\(477\) | 42.5602 | 1.94870 | ||||||||
\(478\) | −19.3571 | −0.885375 | ||||||||
\(479\) | −5.51532 | −0.252001 | −0.126001 | − | 0.992030i | \(-0.540214\pi\) | ||||
−0.126001 | + | 0.992030i | \(0.540214\pi\) | |||||||
\(480\) | 3.14896 | 0.143730 | ||||||||
\(481\) | −24.8407 | −1.13264 | ||||||||
\(482\) | 5.12445 | 0.233412 | ||||||||
\(483\) | −8.36447 | −0.380596 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.93156 | −0.178523 | ||||||||
\(486\) | 19.9478 | 0.904849 | ||||||||
\(487\) | 28.0086 | 1.26919 | 0.634596 | − | 0.772844i | \(-0.281167\pi\) | ||||
0.634596 | + | 0.772844i | \(0.281167\pi\) | |||||||
\(488\) | −2.04888 | −0.0927484 | ||||||||
\(489\) | 57.6231 | 2.60581 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −12.9545 | −0.584626 | −0.292313 | − | 0.956323i | \(-0.594425\pi\) | ||||
−0.292313 | + | 0.956323i | \(0.594425\pi\) | |||||||
\(492\) | −7.94454 | −0.358167 | ||||||||
\(493\) | 3.13319 | 0.141112 | ||||||||
\(494\) | 32.1761 | 1.44767 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.68953 | −0.435073 | ||||||||
\(497\) | 3.62299 | 0.162513 | ||||||||
\(498\) | 5.47503 | 0.245342 | ||||||||
\(499\) | 3.93985 | 0.176372 | 0.0881859 | − | 0.996104i | \(-0.471893\pi\) | ||||
0.0881859 | + | 0.996104i | \(0.471893\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 56.4484 | 2.52193 | ||||||||
\(502\) | 8.99152 | 0.401311 | ||||||||
\(503\) | 28.7158 | 1.28037 | 0.640186 | − | 0.768220i | \(-0.278857\pi\) | ||||
0.640186 | + | 0.768220i | \(0.278857\pi\) | |||||||
\(504\) | 6.91596 | 0.308061 | ||||||||
\(505\) | −2.90794 | −0.129401 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −52.2137 | −2.31889 | ||||||||
\(508\) | 16.3815 | 0.726812 | ||||||||
\(509\) | 6.73822 | 0.298666 | 0.149333 | − | 0.988787i | \(-0.452287\pi\) | ||||
0.149333 | + | 0.988787i | \(0.452287\pi\) | |||||||
\(510\) | −1.50234 | −0.0665249 | ||||||||
\(511\) | −15.6398 | −0.691863 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 72.9508 | 3.22086 | ||||||||
\(514\) | 17.9476 | 0.791635 | ||||||||
\(515\) | −15.9287 | −0.701901 | ||||||||
\(516\) | −37.4737 | −1.64969 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.56726 | −0.200674 | ||||||||
\(519\) | 24.2089 | 1.06265 | ||||||||
\(520\) | −5.43886 | −0.238510 | ||||||||
\(521\) | 32.2003 | 1.41072 | 0.705361 | − | 0.708848i | \(-0.250785\pi\) | ||||
0.705361 | + | 0.708848i | \(0.250785\pi\) | |||||||
\(522\) | 45.4189 | 1.98793 | ||||||||
\(523\) | −28.4244 | −1.24291 | −0.621457 | − | 0.783449i | \(-0.713459\pi\) | ||||
−0.621457 | + | 0.783449i | \(0.713459\pi\) | |||||||
\(524\) | 5.60812 | 0.244992 | ||||||||
\(525\) | 3.14896 | 0.137432 | ||||||||
\(526\) | −27.3312 | −1.19170 | ||||||||
\(527\) | 4.62280 | 0.201372 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.9443 | −0.693229 | ||||||||
\(530\) | −6.15392 | −0.267309 | ||||||||
\(531\) | −3.91507 | −0.169899 | ||||||||
\(532\) | 5.91596 | 0.256489 | ||||||||
\(533\) | 13.7218 | 0.594355 | ||||||||
\(534\) | −30.0525 | −1.30050 | ||||||||
\(535\) | −6.17232 | −0.266853 | ||||||||
\(536\) | 1.24102 | 0.0536041 | ||||||||
\(537\) | −71.5435 | −3.08733 | ||||||||
\(538\) | 12.0775 | 0.520696 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −12.3312 | −0.530650 | ||||||||
\(541\) | 21.6078 | 0.928993 | 0.464496 | − | 0.885575i | \(-0.346235\pi\) | ||||
0.464496 | + | 0.885575i | \(0.346235\pi\) | |||||||
\(542\) | −25.8325 | −1.10960 | ||||||||
\(543\) | 43.0044 | 1.84550 | ||||||||
\(544\) | 0.477092 | 0.0204552 | ||||||||
\(545\) | −14.9240 | −0.639273 | ||||||||
\(546\) | −17.1268 | −0.732958 | ||||||||
\(547\) | 31.9393 | 1.36562 | 0.682812 | − | 0.730594i | \(-0.260757\pi\) | ||||
0.682812 | + | 0.730594i | \(0.260757\pi\) | |||||||
\(548\) | −2.50874 | −0.107168 | ||||||||
\(549\) | 14.1700 | 0.604759 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 38.8516 | 1.65514 | ||||||||
\(552\) | −8.36447 | −0.356015 | ||||||||
\(553\) | 3.38007 | 0.143735 | ||||||||
\(554\) | 18.2240 | 0.774262 | ||||||||
\(555\) | 14.3821 | 0.610487 | ||||||||
\(556\) | 3.30261 | 0.140062 | ||||||||
\(557\) | 18.6958 | 0.792169 | 0.396084 | − | 0.918214i | \(-0.370369\pi\) | ||||
0.396084 | + | 0.918214i | \(0.370369\pi\) | |||||||
\(558\) | 67.0124 | 2.83686 | ||||||||
\(559\) | 64.7244 | 2.73755 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.05953 | 0.171241 | ||||||||
\(563\) | 41.8680 | 1.76453 | 0.882263 | − | 0.470758i | \(-0.156019\pi\) | ||||
0.882263 | + | 0.470758i | \(0.156019\pi\) | |||||||
\(564\) | −29.6831 | −1.24988 | ||||||||
\(565\) | 19.0906 | 0.803148 | ||||||||
\(566\) | 3.16574 | 0.133066 | ||||||||
\(567\) | −18.0826 | −0.759397 | ||||||||
\(568\) | 3.62299 | 0.152017 | ||||||||
\(569\) | 14.7563 | 0.618618 | 0.309309 | − | 0.950962i | \(-0.399902\pi\) | ||||
0.309309 | + | 0.950962i | \(0.399902\pi\) | |||||||
\(570\) | −18.6291 | −0.780288 | ||||||||
\(571\) | −43.4272 | −1.81737 | −0.908686 | − | 0.417481i | \(-0.862913\pi\) | ||||
−0.908686 | + | 0.417481i | \(0.862913\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −29.6689 | −1.23944 | ||||||||
\(574\) | 2.52291 | 0.105304 | ||||||||
\(575\) | −2.65626 | −0.110774 | ||||||||
\(576\) | 6.91596 | 0.288165 | ||||||||
\(577\) | −19.1867 | −0.798754 | −0.399377 | − | 0.916787i | \(-0.630774\pi\) | ||||
−0.399377 | + | 0.916787i | \(0.630774\pi\) | |||||||
\(578\) | 16.7724 | 0.697639 | ||||||||
\(579\) | 16.0572 | 0.667313 | ||||||||
\(580\) | −6.56726 | −0.272691 | ||||||||
\(581\) | −1.73868 | −0.0721326 | ||||||||
\(582\) | −12.3803 | −0.513182 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −15.6398 | −0.647178 | ||||||||
\(585\) | 37.6149 | 1.55519 | ||||||||
\(586\) | −10.2517 | −0.423493 | ||||||||
\(587\) | 3.76583 | 0.155432 | 0.0777161 | − | 0.996976i | \(-0.475237\pi\) | ||||
0.0777161 | + | 0.996976i | \(0.475237\pi\) | |||||||
\(588\) | −3.14896 | −0.129861 | ||||||||
\(589\) | 57.3229 | 2.36195 | ||||||||
\(590\) | 0.566092 | 0.0233056 | ||||||||
\(591\) | −53.9367 | −2.21866 | ||||||||
\(592\) | −4.56726 | −0.187713 | ||||||||
\(593\) | 37.8401 | 1.55391 | 0.776954 | − | 0.629558i | \(-0.216764\pi\) | ||||
0.776954 | + | 0.629558i | \(0.216764\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.477092 | 0.0195589 | ||||||||
\(596\) | 6.83048 | 0.279787 | ||||||||
\(597\) | −37.5436 | −1.53656 | ||||||||
\(598\) | 14.4470 | 0.590784 | ||||||||
\(599\) | −32.2167 | −1.31634 | −0.658169 | − | 0.752870i | \(-0.728669\pi\) | ||||
−0.658169 | + | 0.752870i | \(0.728669\pi\) | |||||||
\(600\) | 3.14896 | 0.128556 | ||||||||
\(601\) | 3.26376 | 0.133132 | 0.0665658 | − | 0.997782i | \(-0.478796\pi\) | ||||
0.0665658 | + | 0.997782i | \(0.478796\pi\) | |||||||
\(602\) | 11.9003 | 0.485022 | ||||||||
\(603\) | −8.58287 | −0.349521 | ||||||||
\(604\) | −10.8189 | −0.440216 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.15698 | −0.371977 | ||||||||
\(607\) | 19.3916 | 0.787081 | 0.393541 | − | 0.919307i | \(-0.371250\pi\) | ||||
0.393541 | + | 0.919307i | \(0.371250\pi\) | |||||||
\(608\) | 5.91596 | 0.239924 | ||||||||
\(609\) | −20.6801 | −0.837998 | ||||||||
\(610\) | −2.04888 | −0.0829567 | ||||||||
\(611\) | 51.2685 | 2.07410 | ||||||||
\(612\) | −3.29955 | −0.133376 | ||||||||
\(613\) | 29.8111 | 1.20406 | 0.602029 | − | 0.798474i | \(-0.294359\pi\) | ||||
0.602029 | + | 0.798474i | \(0.294359\pi\) | |||||||
\(614\) | 3.38972 | 0.136798 | ||||||||
\(615\) | −7.94454 | −0.320355 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.60999 | −0.145333 | −0.0726664 | − | 0.997356i | \(-0.523151\pi\) | ||||
−0.0726664 | + | 0.997356i | \(0.523151\pi\) | |||||||
\(618\) | −50.1587 | −2.01768 | ||||||||
\(619\) | 26.7648 | 1.07577 | 0.537884 | − | 0.843019i | \(-0.319224\pi\) | ||||
0.537884 | + | 0.843019i | \(0.319224\pi\) | |||||||
\(620\) | −9.68953 | −0.389141 | ||||||||
\(621\) | 32.7549 | 1.31441 | ||||||||
\(622\) | 29.4523 | 1.18093 | ||||||||
\(623\) | 9.54364 | 0.382358 | ||||||||
\(624\) | −17.1268 | −0.685620 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 22.0645 | 0.881873 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.01766 | 0.319940 | ||||||||
\(629\) | 2.17900 | 0.0868826 | ||||||||
\(630\) | 6.91596 | 0.275538 | ||||||||
\(631\) | −42.4651 | −1.69051 | −0.845254 | − | 0.534364i | \(-0.820551\pi\) | ||||
−0.845254 | + | 0.534364i | \(0.820551\pi\) | |||||||
\(632\) | 3.38007 | 0.134452 | ||||||||
\(633\) | −71.9005 | −2.85779 | ||||||||
\(634\) | −21.1159 | −0.838618 | ||||||||
\(635\) | 16.3815 | 0.650080 | ||||||||
\(636\) | −19.3784 | −0.768405 | ||||||||
\(637\) | 5.43886 | 0.215496 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.0564 | −0.991218 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −12.7639 | −0.504144 | −0.252072 | − | 0.967708i | \(-0.581112\pi\) | ||||
−0.252072 | + | 0.967708i | \(0.581112\pi\) | |||||||
\(642\) | −19.4364 | −0.767093 | ||||||||
\(643\) | 1.15422 | 0.0455181 | 0.0227591 | − | 0.999741i | \(-0.492755\pi\) | ||||
0.0227591 | + | 0.999741i | \(0.492755\pi\) | |||||||
\(644\) | 2.65626 | 0.104671 | ||||||||
\(645\) | −37.4737 | −1.47553 | ||||||||
\(646\) | −2.82246 | −0.111048 | ||||||||
\(647\) | −11.1492 | −0.438321 | −0.219161 | − | 0.975689i | \(-0.570332\pi\) | ||||
−0.219161 | + | 0.975689i | \(0.570332\pi\) | |||||||
\(648\) | −18.0826 | −0.710351 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.43886 | −0.213330 | ||||||||
\(651\) | −30.5120 | −1.19586 | ||||||||
\(652\) | −18.2991 | −0.716648 | ||||||||
\(653\) | 16.0342 | 0.627468 | 0.313734 | − | 0.949511i | \(-0.398420\pi\) | ||||
0.313734 | + | 0.949511i | \(0.398420\pi\) | |||||||
\(654\) | −46.9950 | −1.83765 | ||||||||
\(655\) | 5.60812 | 0.219127 | ||||||||
\(656\) | 2.52291 | 0.0985030 | ||||||||
\(657\) | 108.164 | 4.21988 | ||||||||
\(658\) | 9.42632 | 0.367476 | ||||||||
\(659\) | 29.5362 | 1.15057 | 0.575283 | − | 0.817955i | \(-0.304892\pi\) | ||||
0.575283 | + | 0.817955i | \(0.304892\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.49650 | 0.369371 | 0.184686 | − | 0.982798i | \(-0.440873\pi\) | ||||
0.184686 | + | 0.982798i | \(0.440873\pi\) | |||||||
\(662\) | 31.1409 | 1.21033 | ||||||||
\(663\) | 8.17105 | 0.317337 | ||||||||
\(664\) | −1.73868 | −0.0674739 | ||||||||
\(665\) | 5.91596 | 0.229411 | ||||||||
\(666\) | 31.5870 | 1.22397 | ||||||||
\(667\) | 17.4444 | 0.675449 | ||||||||
\(668\) | −17.9260 | −0.693579 | ||||||||
\(669\) | 49.9997 | 1.93310 | ||||||||
\(670\) | 1.24102 | 0.0479449 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −3.14896 | −0.121474 | ||||||||
\(673\) | 11.5388 | 0.444788 | 0.222394 | − | 0.974957i | \(-0.428613\pi\) | ||||
0.222394 | + | 0.974957i | \(0.428613\pi\) | |||||||
\(674\) | 1.60099 | 0.0616678 | ||||||||
\(675\) | −12.3312 | −0.474628 | ||||||||
\(676\) | 16.5812 | 0.637740 | ||||||||
\(677\) | −48.8523 | −1.87755 | −0.938774 | − | 0.344533i | \(-0.888037\pi\) | ||||
−0.938774 | + | 0.344533i | \(0.888037\pi\) | |||||||
\(678\) | 60.1156 | 2.30872 | ||||||||
\(679\) | 3.93156 | 0.150880 | ||||||||
\(680\) | 0.477092 | 0.0182956 | ||||||||
\(681\) | 26.5089 | 1.01582 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.4736 | 1.35736 | 0.678679 | − | 0.734435i | \(-0.262553\pi\) | ||||
0.678679 | + | 0.734435i | \(0.262553\pi\) | |||||||
\(684\) | −40.9145 | −1.56440 | ||||||||
\(685\) | −2.50874 | −0.0958539 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −70.1726 | −2.67725 | ||||||||
\(688\) | 11.9003 | 0.453697 | ||||||||
\(689\) | 33.4703 | 1.27512 | ||||||||
\(690\) | −8.36447 | −0.318430 | ||||||||
\(691\) | −30.1855 | −1.14831 | −0.574156 | − | 0.818746i | \(-0.694670\pi\) | ||||
−0.574156 | + | 0.818746i | \(0.694670\pi\) | |||||||
\(692\) | −7.68791 | −0.292250 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.7193 | −0.748534 | ||||||||
\(695\) | 3.30261 | 0.125275 | ||||||||
\(696\) | −20.6801 | −0.783875 | ||||||||
\(697\) | −1.20366 | −0.0455919 | ||||||||
\(698\) | −15.3791 | −0.582106 | ||||||||
\(699\) | 39.0505 | 1.47702 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −11.2689 | −0.425621 | −0.212810 | − | 0.977094i | \(-0.568262\pi\) | ||||
−0.212810 | + | 0.977094i | \(0.568262\pi\) | |||||||
\(702\) | 67.0677 | 2.53131 | ||||||||
\(703\) | 27.0197 | 1.01907 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29.6831 | −1.11793 | ||||||||
\(706\) | 10.3793 | 0.390631 | ||||||||
\(707\) | 2.90794 | 0.109364 | ||||||||
\(708\) | 1.78260 | 0.0669943 | ||||||||
\(709\) | −43.0830 | −1.61802 | −0.809008 | − | 0.587797i | \(-0.799995\pi\) | ||||
−0.809008 | + | 0.587797i | \(0.799995\pi\) | |||||||
\(710\) | 3.62299 | 0.135968 | ||||||||
\(711\) | −23.3764 | −0.876685 | ||||||||
\(712\) | 9.54364 | 0.357663 | ||||||||
\(713\) | 25.7379 | 0.963893 | ||||||||
\(714\) | 1.50234 | 0.0562238 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.7197 | 0.849076 | ||||||||
\(717\) | −60.9549 | −2.27640 | ||||||||
\(718\) | −23.8319 | −0.889399 | ||||||||
\(719\) | 27.1078 | 1.01095 | 0.505475 | − | 0.862841i | \(-0.331317\pi\) | ||||
0.505475 | + | 0.862841i | \(0.331317\pi\) | |||||||
\(720\) | 6.91596 | 0.257742 | ||||||||
\(721\) | 15.9287 | 0.593214 | ||||||||
\(722\) | −15.9985 | −0.595404 | ||||||||
\(723\) | 16.1367 | 0.600130 | ||||||||
\(724\) | −13.6567 | −0.507547 | ||||||||
\(725\) | −6.56726 | −0.243902 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.5273 | 1.68851 | 0.844257 | − | 0.535939i | \(-0.180042\pi\) | ||||
0.844257 | + | 0.535939i | \(0.180042\pi\) | |||||||
\(728\) | 5.43886 | 0.201578 | ||||||||
\(729\) | 8.56700 | 0.317296 | ||||||||
\(730\) | −15.6398 | −0.578854 | ||||||||
\(731\) | −5.67756 | −0.209992 | ||||||||
\(732\) | −6.45184 | −0.238467 | ||||||||
\(733\) | −23.4004 | −0.864312 | −0.432156 | − | 0.901799i | \(-0.642247\pi\) | ||||
−0.432156 | + | 0.901799i | \(0.642247\pi\) | |||||||
\(734\) | 19.3945 | 0.715864 | ||||||||
\(735\) | −3.14896 | −0.116151 | ||||||||
\(736\) | 2.65626 | 0.0979111 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −17.4483 | −0.642282 | ||||||||
\(739\) | 41.0880 | 1.51145 | 0.755723 | − | 0.654892i | \(-0.227286\pi\) | ||||
0.755723 | + | 0.654892i | \(0.227286\pi\) | |||||||
\(740\) | −4.56726 | −0.167896 | ||||||||
\(741\) | 101.321 | 3.72213 | ||||||||
\(742\) | 6.15392 | 0.225917 | ||||||||
\(743\) | 16.0312 | 0.588128 | 0.294064 | − | 0.955786i | \(-0.404992\pi\) | ||||
0.294064 | + | 0.955786i | \(0.404992\pi\) | |||||||
\(744\) | −30.5120 | −1.11862 | ||||||||
\(745\) | 6.83048 | 0.250249 | ||||||||
\(746\) | −10.9015 | −0.399133 | ||||||||
\(747\) | 12.0246 | 0.439958 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.17232 | 0.225532 | ||||||||
\(750\) | 3.14896 | 0.114984 | ||||||||
\(751\) | 5.53050 | 0.201811 | 0.100905 | − | 0.994896i | \(-0.467826\pi\) | ||||
0.100905 | + | 0.994896i | \(0.467826\pi\) | |||||||
\(752\) | 9.42632 | 0.343743 | ||||||||
\(753\) | 28.3140 | 1.03182 | ||||||||
\(754\) | 35.7184 | 1.30079 | ||||||||
\(755\) | −10.8189 | −0.393741 | ||||||||
\(756\) | 12.3312 | 0.448481 | ||||||||
\(757\) | 25.0946 | 0.912077 | 0.456039 | − | 0.889960i | \(-0.349268\pi\) | ||||
0.456039 | + | 0.889960i | \(0.349268\pi\) | |||||||
\(758\) | −6.80767 | −0.247266 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.91596 | 0.214594 | ||||||||
\(761\) | 3.21785 | 0.116647 | 0.0583236 | − | 0.998298i | \(-0.481424\pi\) | ||||
0.0583236 | + | 0.998298i | \(0.481424\pi\) | |||||||
\(762\) | 51.5847 | 1.86872 | ||||||||
\(763\) | 14.9240 | 0.540284 | ||||||||
\(764\) | 9.42182 | 0.340869 | ||||||||
\(765\) | −3.29955 | −0.119295 | ||||||||
\(766\) | 24.2311 | 0.875505 | ||||||||
\(767\) | −3.07890 | −0.111173 | ||||||||
\(768\) | −3.14896 | −0.113628 | ||||||||
\(769\) | 9.89520 | 0.356830 | 0.178415 | − | 0.983955i | \(-0.442903\pi\) | ||||
0.178415 | + | 0.983955i | \(0.442903\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 56.5163 | 2.03538 | ||||||||
\(772\) | −5.09919 | −0.183524 | ||||||||
\(773\) | 18.3508 | 0.660033 | 0.330017 | − | 0.943975i | \(-0.392946\pi\) | ||||
0.330017 | + | 0.943975i | \(0.392946\pi\) | |||||||
\(774\) | −82.3023 | −2.95829 | ||||||||
\(775\) | −9.68953 | −0.348058 | ||||||||
\(776\) | 3.93156 | 0.141135 | ||||||||
\(777\) | −14.3821 | −0.515956 | ||||||||
\(778\) | 18.2552 | 0.654480 | ||||||||
\(779\) | −14.9254 | −0.534758 | ||||||||
\(780\) | −17.1268 | −0.613237 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.26728 | −0.0453179 | ||||||||
\(783\) | 80.9822 | 2.89407 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 8.01766 | 0.286163 | ||||||||
\(786\) | 17.6598 | 0.629903 | ||||||||
\(787\) | 6.04479 | 0.215473 | 0.107737 | − | 0.994179i | \(-0.465640\pi\) | ||||
0.107737 | + | 0.994179i | \(0.465640\pi\) | |||||||
\(788\) | 17.1284 | 0.610174 | ||||||||
\(789\) | −86.0649 | −3.06399 | ||||||||
\(790\) | 3.38007 | 0.120258 | ||||||||
\(791\) | −19.0906 | −0.678784 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.1436 | 0.395720 | ||||||||
\(794\) | −17.6742 | −0.627234 | ||||||||
\(795\) | −19.3784 | −0.687283 | ||||||||
\(796\) | 11.9225 | 0.422583 | ||||||||
\(797\) | −6.98324 | −0.247359 | −0.123679 | − | 0.992322i | \(-0.539469\pi\) | ||||
−0.123679 | + | 0.992322i | \(0.539469\pi\) | |||||||
\(798\) | 18.6291 | 0.659464 | ||||||||
\(799\) | −4.49722 | −0.159100 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −66.0034 | −2.33211 | ||||||||
\(802\) | −30.4187 | −1.07412 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 3.90794 | 0.137822 | ||||||||
\(805\) | 2.65626 | 0.0936209 | ||||||||
\(806\) | 52.7001 | 1.85628 | ||||||||
\(807\) | 38.0315 | 1.33877 | ||||||||
\(808\) | 2.90794 | 0.102301 | ||||||||
\(809\) | −12.1699 | −0.427870 | −0.213935 | − | 0.976848i | \(-0.568628\pi\) | ||||
−0.213935 | + | 0.976848i | \(0.568628\pi\) | |||||||
\(810\) | −18.0826 | −0.635357 | ||||||||
\(811\) | −45.0840 | −1.58311 | −0.791557 | − | 0.611096i | \(-0.790729\pi\) | ||||
−0.791557 | + | 0.611096i | \(0.790729\pi\) | |||||||
\(812\) | 6.56726 | 0.230466 | ||||||||
\(813\) | −81.3456 | −2.85292 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.2991 | −0.640989 | ||||||||
\(816\) | 1.50234 | 0.0525926 | ||||||||
\(817\) | −70.4019 | −2.46305 | ||||||||
\(818\) | −15.4065 | −0.538675 | ||||||||
\(819\) | −37.6149 | −1.31437 | ||||||||
\(820\) | 2.52291 | 0.0881038 | ||||||||
\(821\) | 3.79471 | 0.132436 | 0.0662182 | − | 0.997805i | \(-0.478907\pi\) | ||||
0.0662182 | + | 0.997805i | \(0.478907\pi\) | |||||||
\(822\) | −7.89992 | −0.275541 | ||||||||
\(823\) | −39.5469 | −1.37852 | −0.689259 | − | 0.724515i | \(-0.742064\pi\) | ||||
−0.689259 | + | 0.724515i | \(0.742064\pi\) | |||||||
\(824\) | 15.9287 | 0.554901 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.566092 | −0.0196969 | ||||||||
\(827\) | 21.2066 | 0.737424 | 0.368712 | − | 0.929544i | \(-0.379799\pi\) | ||||
0.368712 | + | 0.929544i | \(0.379799\pi\) | |||||||
\(828\) | −18.3706 | −0.638422 | ||||||||
\(829\) | −16.6338 | −0.577716 | −0.288858 | − | 0.957372i | \(-0.593276\pi\) | ||||
−0.288858 | + | 0.957372i | \(0.593276\pi\) | |||||||
\(830\) | −1.73868 | −0.0603504 | ||||||||
\(831\) | 57.3865 | 1.99072 | ||||||||
\(832\) | 5.43886 | 0.188559 | ||||||||
\(833\) | −0.477092 | −0.0165303 | ||||||||
\(834\) | 10.3998 | 0.360115 | ||||||||
\(835\) | −17.9260 | −0.620356 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 119.484 | 4.12995 | ||||||||
\(838\) | −3.21914 | −0.111203 | ||||||||
\(839\) | 44.0630 | 1.52122 | 0.760612 | − | 0.649207i | \(-0.224899\pi\) | ||||
0.760612 | + | 0.649207i | \(0.224899\pi\) | |||||||
\(840\) | −3.14896 | −0.108649 | ||||||||
\(841\) | 14.1289 | 0.487205 | ||||||||
\(842\) | −13.1605 | −0.453540 | ||||||||
\(843\) | 12.7833 | 0.440280 | ||||||||
\(844\) | 22.8331 | 0.785947 | ||||||||
\(845\) | 16.5812 | 0.570412 | ||||||||
\(846\) | −65.1920 | −2.24135 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.15392 | 0.211326 | ||||||||
\(849\) | 9.96879 | 0.342128 | ||||||||
\(850\) | 0.477092 | 0.0163641 | ||||||||
\(851\) | 12.1318 | 0.415874 | ||||||||
\(852\) | 11.4087 | 0.390854 | ||||||||
\(853\) | 8.75092 | 0.299626 | 0.149813 | − | 0.988714i | \(-0.452133\pi\) | ||||
0.149813 | + | 0.988714i | \(0.452133\pi\) | |||||||
\(854\) | 2.04888 | 0.0701112 | ||||||||
\(855\) | −40.9145 | −1.39925 | ||||||||
\(856\) | 6.17232 | 0.210966 | ||||||||
\(857\) | 0.827106 | 0.0282534 | 0.0141267 | − | 0.999900i | \(-0.495503\pi\) | ||||
0.0141267 | + | 0.999900i | \(0.495503\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.5033 | 0.392488 | 0.196244 | − | 0.980555i | \(-0.437125\pi\) | ||||
0.196244 | + | 0.980555i | \(0.437125\pi\) | |||||||
\(860\) | 11.9003 | 0.405799 | ||||||||
\(861\) | 7.94454 | 0.270749 | ||||||||
\(862\) | −2.38429 | −0.0812093 | ||||||||
\(863\) | 13.9927 | 0.476318 | 0.238159 | − | 0.971226i | \(-0.423456\pi\) | ||||
0.238159 | + | 0.971226i | \(0.423456\pi\) | |||||||
\(864\) | 12.3312 | 0.419516 | ||||||||
\(865\) | −7.68791 | −0.261397 | ||||||||
\(866\) | −9.02568 | −0.306705 | ||||||||
\(867\) | 52.8156 | 1.79371 | ||||||||
\(868\) | 9.68953 | 0.328884 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −20.6801 | −0.701119 | ||||||||
\(871\) | −6.74976 | −0.228707 | ||||||||
\(872\) | 14.9240 | 0.505390 | ||||||||
\(873\) | −27.1905 | −0.920260 | ||||||||
\(874\) | −15.7143 | −0.531545 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −49.2490 | −1.66397 | ||||||||
\(877\) | −6.87711 | −0.232223 | −0.116112 | − | 0.993236i | \(-0.537043\pi\) | ||||
−0.116112 | + | 0.993236i | \(0.537043\pi\) | |||||||
\(878\) | −23.1241 | −0.780402 | ||||||||
\(879\) | −32.2821 | −1.08885 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.9746 | −1.38047 | −0.690235 | − | 0.723585i | \(-0.742493\pi\) | ||||
−0.690235 | + | 0.723585i | \(0.742493\pi\) | |||||||
\(882\) | −6.91596 | −0.232872 | ||||||||
\(883\) | 22.6100 | 0.760887 | 0.380443 | − | 0.924804i | \(-0.375771\pi\) | ||||
0.380443 | + | 0.924804i | \(0.375771\pi\) | |||||||
\(884\) | −2.59484 | −0.0872739 | ||||||||
\(885\) | 1.78260 | 0.0599215 | ||||||||
\(886\) | 6.78799 | 0.228047 | ||||||||
\(887\) | 3.14606 | 0.105634 | 0.0528172 | − | 0.998604i | \(-0.483180\pi\) | ||||
0.0528172 | + | 0.998604i | \(0.483180\pi\) | |||||||
\(888\) | −14.3821 | −0.482633 | ||||||||
\(889\) | −16.3815 | −0.549418 | ||||||||
\(890\) | 9.54364 | 0.319903 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.8782 | −0.531640 | ||||||||
\(893\) | −55.7657 | −1.86613 | ||||||||
\(894\) | 21.5089 | 0.719365 | ||||||||
\(895\) | 22.7197 | 0.759436 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 45.4932 | 1.51897 | ||||||||
\(898\) | −13.1114 | −0.437534 | ||||||||
\(899\) | 63.6337 | 2.12230 | ||||||||
\(900\) | 6.91596 | 0.230532 | ||||||||
\(901\) | −2.93599 | −0.0978119 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 37.4737 | 1.24705 | ||||||||
\(904\) | −19.0906 | −0.634944 | ||||||||
\(905\) | −13.6567 | −0.453964 | ||||||||
\(906\) | −34.0684 | −1.13185 | ||||||||
\(907\) | 6.57950 | 0.218469 | 0.109234 | − | 0.994016i | \(-0.465160\pi\) | ||||
0.109234 | + | 0.994016i | \(0.465160\pi\) | |||||||
\(908\) | −8.41830 | −0.279371 | ||||||||
\(909\) | −20.1112 | −0.667045 | ||||||||
\(910\) | 5.43886 | 0.180297 | ||||||||
\(911\) | −10.0045 | −0.331464 | −0.165732 | − | 0.986171i | \(-0.552999\pi\) | ||||
−0.165732 | + | 0.986171i | \(0.552999\pi\) | |||||||
\(912\) | 18.6291 | 0.616872 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 19.0200 | 0.629125 | ||||||||
\(915\) | −6.45184 | −0.213291 | ||||||||
\(916\) | 22.2844 | 0.736296 | ||||||||
\(917\) | −5.60812 | −0.185196 | ||||||||
\(918\) | −5.88312 | −0.194172 | ||||||||
\(919\) | 5.27944 | 0.174153 | 0.0870764 | − | 0.996202i | \(-0.472248\pi\) | ||||
0.0870764 | + | 0.996202i | \(0.472248\pi\) | |||||||
\(920\) | 2.65626 | 0.0875744 | ||||||||
\(921\) | 10.6741 | 0.351723 | ||||||||
\(922\) | −18.8767 | −0.621672 | ||||||||
\(923\) | −19.7050 | −0.648596 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.56726 | −0.150171 | ||||||||
\(926\) | −13.6194 | −0.447560 | ||||||||
\(927\) | −110.162 | −3.61819 | ||||||||
\(928\) | 6.56726 | 0.215581 | ||||||||
\(929\) | −19.7726 | −0.648717 | −0.324359 | − | 0.945934i | \(-0.605148\pi\) | ||||
−0.324359 | + | 0.945934i | \(0.605148\pi\) | |||||||
\(930\) | −30.5120 | −1.00053 | ||||||||
\(931\) | −5.91596 | −0.193888 | ||||||||
\(932\) | −12.4011 | −0.406210 | ||||||||
\(933\) | 92.7441 | 3.03630 | ||||||||
\(934\) | 18.9801 | 0.621049 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −37.6149 | −1.22948 | ||||||||
\(937\) | −46.0026 | −1.50284 | −0.751419 | − | 0.659825i | \(-0.770630\pi\) | ||||
−0.751419 | + | 0.659825i | \(0.770630\pi\) | |||||||
\(938\) | −1.24102 | −0.0405209 | ||||||||
\(939\) | 69.4801 | 2.26740 | ||||||||
\(940\) | 9.42632 | 0.307453 | ||||||||
\(941\) | −37.3066 | −1.21616 | −0.608081 | − | 0.793875i | \(-0.708060\pi\) | ||||
−0.608081 | + | 0.793875i | \(0.708060\pi\) | |||||||
\(942\) | 25.2473 | 0.822602 | ||||||||
\(943\) | −6.70150 | −0.218231 | ||||||||
\(944\) | −0.566092 | −0.0184247 | ||||||||
\(945\) | 12.3312 | 0.401134 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49.7593 | 1.61696 | 0.808479 | − | 0.588524i | \(-0.200291\pi\) | ||||
0.808479 | + | 0.588524i | \(0.200291\pi\) | |||||||
\(948\) | 10.6437 | 0.345692 | ||||||||
\(949\) | 85.0626 | 2.76125 | ||||||||
\(950\) | 5.91596 | 0.191939 | ||||||||
\(951\) | −66.4930 | −2.15618 | ||||||||
\(952\) | −0.477092 | −0.0154626 | ||||||||
\(953\) | 20.5931 | 0.667076 | 0.333538 | − | 0.942737i | \(-0.391757\pi\) | ||||
0.333538 | + | 0.942737i | \(0.391757\pi\) | |||||||
\(954\) | −42.5602 | −1.37794 | ||||||||
\(955\) | 9.42182 | 0.304883 | ||||||||
\(956\) | 19.3571 | 0.626055 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.51532 | 0.178192 | ||||||||
\(959\) | 2.50874 | 0.0810114 | ||||||||
\(960\) | −3.14896 | −0.101632 | ||||||||
\(961\) | 62.8871 | 2.02862 | ||||||||
\(962\) | 24.8407 | 0.800897 | ||||||||
\(963\) | −42.6875 | −1.37559 | ||||||||
\(964\) | −5.12445 | −0.165047 | ||||||||
\(965\) | −5.09919 | −0.164149 | ||||||||
\(966\) | 8.36447 | 0.269122 | ||||||||
\(967\) | −36.0618 | −1.15967 | −0.579834 | − | 0.814735i | \(-0.696883\pi\) | ||||
−0.579834 | + | 0.814735i | \(0.696883\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.88781 | −0.285517 | ||||||||
\(970\) | 3.93156 | 0.126235 | ||||||||
\(971\) | 4.29180 | 0.137730 | 0.0688651 | − | 0.997626i | \(-0.478062\pi\) | ||||
0.0688651 | + | 0.997626i | \(0.478062\pi\) | |||||||
\(972\) | −19.9478 | −0.639825 | ||||||||
\(973\) | −3.30261 | −0.105877 | ||||||||
\(974\) | −28.0086 | −0.897454 | ||||||||
\(975\) | −17.1268 | −0.548496 | ||||||||
\(976\) | 2.04888 | 0.0655830 | ||||||||
\(977\) | 36.2757 | 1.16056 | 0.580281 | − | 0.814416i | \(-0.302943\pi\) | ||||
0.580281 | + | 0.814416i | \(0.302943\pi\) | |||||||
\(978\) | −57.6231 | −1.84258 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −103.214 | −3.29536 | ||||||||
\(982\) | 12.9545 | 0.413393 | ||||||||
\(983\) | 18.9549 | 0.604567 | 0.302284 | − | 0.953218i | \(-0.402251\pi\) | ||||
0.302284 | + | 0.953218i | \(0.402251\pi\) | |||||||
\(984\) | 7.94454 | 0.253263 | ||||||||
\(985\) | 17.1284 | 0.545756 | ||||||||
\(986\) | −3.13319 | −0.0997811 | ||||||||
\(987\) | 29.6831 | 0.944824 | ||||||||
\(988\) | −32.1761 | −1.02366 | ||||||||
\(989\) | −31.6104 | −1.00515 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.43374 | −0.236141 | −0.118070 | − | 0.993005i | \(-0.537671\pi\) | ||||
−0.118070 | + | 0.993005i | \(0.537671\pi\) | |||||||
\(992\) | 9.68953 | 0.307643 | ||||||||
\(993\) | 98.0615 | 3.11189 | ||||||||
\(994\) | −3.62299 | −0.114914 | ||||||||
\(995\) | 11.9225 | 0.377970 | ||||||||
\(996\) | −5.47503 | −0.173483 | ||||||||
\(997\) | 21.9062 | 0.693777 | 0.346888 | − | 0.937906i | \(-0.387238\pi\) | ||||
0.346888 | + | 0.937906i | \(0.387238\pi\) | |||||||
\(998\) | −3.93985 | −0.124714 | ||||||||
\(999\) | 56.3198 | 1.78188 |
(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 | 8470.2.a.co.1.1 | 4 | ||
11.3 | even | 5 | 770.2.n.f.141.2 | yes | 8 | ||
11.4 | even | 5 | 770.2.n.f.71.2 | ✓ | 8 | ||
11.10 | odd | 2 | 8470.2.a.cs.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.f.71.2 | ✓ | 8 | 11.4 | even | 5 | ||
770.2.n.f.141.2 | yes | 8 | 11.3 | even | 5 | ||
8470.2.a.co.1.1 | 4 | 1.1 | even | 1 | trivial | ||
8470.2.a.cs.1.1 | 4 | 11.10 | odd | 2 |